EXPERIMENTAL AND NUMERICAL STUDY OF LOCAL SCOUR AROUND SIDEBY-SIDE BRIDGE PIERS UNDER ICE-COVERED CONDITIONS

By

Mohammad Reza Namaee

B.Sc., Islamic Azad University of Karaj, Iran, 2008
M.Sc., Khajeh Nasir Toosi University of Technology, Tehran, Iran, 2011

DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN
NATURAL RESOURCES AND ENVIRONMENTAL STUIDES

UNIVERSITY OF NORTHERN BRITISH COLUMBIA

April 2019
© MOHAMMAD REZA NAMAEE
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ABSTRACT
Local scour around piers and abutments is one of the main causes of the collapse of many bridges
constructed inside rivers. Many researchers have conducted various studies to predict the
maximum depth of a scour hole around bridge piers and abutments. However, most of them have
been done in small-scale laboratory flumes and specifically for the open channel condition.
Besides, most of the existing research on bridge piers uses uniform sediment which is not an
appropriate representative of natural river systems. This can result in excessively conservative
design values for scour in low risk or non-critical hydrologic conditions. The most severe cases of
bridge pier scouring occur in cold regions when the surface of water turns into ice in which, an
additional boundary layer is being added to the water surface, which leads to significant changes
in the flow field and scour pattern around bridge piers. Ice cover also causes the maximum flow
velocity to move closer to the channel bed. A precise prediction of maximum scour depth at piers
under ice cover flow conditions is crucial for the safe design of the bridge foundation, because
underestimation may result in bridge failure and over-estimation will lead to unnecessary
construction cost. However, there is a dire paucity of information regarding local scour prediction
under ice-covered flow conditions compared to the open channel condition. In the current study, a
set of flume experiments was completed investigating local scour around four pairs of circular
bridge piers with 60 mm, 90 mm, 110 mm and 170 mm in diameter with non-uniform bed under
open channel, smooth and rough ice cover conditions. In order to simulate the ice cover condition,
artificial smooth and rough ice covers were created to investigate the impacts of ice cover
roughness on the scour geometry around the circular bridge piers. To represent non-uniform
sediment condition, three different bed materials with average particle size (D 50) of 0.47 mm, 0.50
mm, 0.58 mm were used. In this study, regardless of flume cover and sediment grain size, the

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maximum scour depths were observed to be at the upstream face of the pier nearly perpendicular
to the approach flow and was maximized for the finest grain size under rough ice-cover condition.
Further, the smaller the pier size and the greater the spacing distance between the bridge piers, the
weaker the horseshoe vortices around the bridge piers and, thus, the shallower the scour holes
around them. Results showed that, regardless of flow cover, the maximum scour depth decreases
with an increase in the grain size of armor layer. Under the same flow condition, both scour volume
and scour areas of a scour hole in the fine sand bed are larger comparing to those in the channel
bed with coarser sands. The vertical velocity distribution which is a representative of the strength
of downfall velocity was the greatest under rough ice cover. Under nearly the same flow
conditions, the maximum value of turbulence kinetic energy and turbulent intensity occurred at
the largest diameter pier. Several empirical equations were developed to estimate the maximum
scour depth around side-by-side bridge piers under both open channel and ice-covered flow
conditions. In addition to the experimental study, the numerical study was also done for the finest
and the coarsest sediment types. The numerical study was in good agreement with the experimental
study. The simulated result of local scour around the bridge piers represents information regarding
the scour depth, morphological changes, and deposition patterns in the vicinity of the bridge piers.

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TABLE OF CONTENTS

ABSTRACT ............................................................................................................................... i
TABLE OF CONTENTS .......................................................................................................... iii
CO-AUTHORSHIP .................................................................................................................. vi
List of Tables .......................................................................................................................... viii
List of Figures ........................................................................................................................... ix
ACKNOWLEDGEMENT ........................................................................................................xiv
1. INTRODUCTION...................................................................................................................1
1.1 Definition of scour and different types of scour ....................................................................4
1.2 Local scour characteristics around bridge piers in open channels..........................................7
1.3 Clear-water and live-bed scour .............................................................................................8
1.4 Sediment transport in a river Channel ................................................................................ 10
1.5 Importance of bed shear stress and methods to predict it .................................................... 11
1.6 Shields Parameter and importance of critical shear stress ................................................... 12
1.7 The Shields diagram .......................................................................................................... 14
1.8 The modified shields diagram ............................................................................................ 16
1.9. Bridge scour prediction ..................................................................................................... 17
1.10 Predicting bridge scour using empirical equations ............................................................ 18
1.10.1 Colorado State University equation ......................................................................... 18
1.10.2 Neil (1964) equation ................................................................................................ 19
1.10.3 Jain and Fisher equation (1979) ............................................................................... 19
1.10.4 Froehlich equation (Froehlich 1989) ........................................................................ 20
1.10.5 Melville and Sutherland equation (1988): ................................................................ 20
1.11 Bridge scour modeling ..................................................................................................... 20
1.11.1 Laboratory models ................................................................................................... 20
1.11.2 Numerical models.................................................................................................... 22
1.11.3 Hydrodynamic model .............................................................................................. 23
1.11.4 Turbulence models .................................................................................................. 25
1.11.5. Free surface Tracking (VOF Method) ..................................................................... 28
1.12 Scour around multiple pile bridge piers ............................................................................ 29
1.13 Impact of ice on the bridge pier scouring .......................................................................... 31
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1.14 Hydraulic characteristics of ice scour ............................................................................... 35
1.15 Sediment transport under ice-covered flow....................................................................... 36
1.16 Transverse flow distributions under ice-covered flow ....................................................... 38
1.17 Research objectives .......................................................................................................... 39
1.17.1 Objective one .......................................................................................................... 40
1.17.2 Objective two .......................................................................................................... 40
1.17.3 Objective three ........................................................................................................ 41
1.17.4 Objective four ......................................................................................................... 42
1.17.5 Objective five .......................................................................................................... 42
1.17.6 Objective six ........................................................................................................... 43
1.17.7 Objective seven ....................................................................................................... 44
1.18 The innovations of the research ........................................................................................ 45
2. EXPERIMENTAL SETUP ................................................................................................... 46
2.1 Measurement apparatus...................................................................................................... 52
2.2 Reference ........................................................................................................................... 54
3 RESULTS AND DISCUSSION ............................................................................................. 63
3.1 Local scour around two side-by-side cylindrical bridge piers under ice-covered conditions 64
3.1.1. Methodology ............................................................................................................ 66
3.1.2. Results and discussion .............................................................................................. 71
3.1.3. Conclusions .............................................................................................................. 92
3.1.4. Reference ................................................................................................................. 96
3.2. Impact of armour layer on the depth of scour hole around side-by-side bridge piers under
ice-covered and open channel conditions ................................................................................. 99
3.2.1. Experiment setup .................................................................................................... 102
3.2.2 Results and discussion ............................................................................................. 105
3.2.3. Conclusions ............................................................................................................ 124
3.2.4. Reference ............................................................................................................... 126
3.3. Effects of ice cover on the incipient motion of bed material and shear stress around side-byside bridge piers ..................................................................................................................... 129
3.3.1. Experimental setup ................................................................................................. 137
3.3.2. Results and discussions .......................................................................................... 142
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3.3.3. Conclusion ............................................................................................................. 142
3.3.4. References: ............................................................................................................. 164
3.4. Scour patterns and velocity profiles around side-by-side bridge piers under ice-covered
flow ..................................................................................................................................... 169
3.4.1. Methodology .......................................................................................................... 173
3.4.2. Results and discussions .......................................................................................... 178
3.4.3. Conclusions ............................................................................................................ 195
3.4.4. References .............................................................................................................. 198
3.5. Three-dimensional numerical modeling of local scour around bridge piers under ice-covered
flow condition ......................................................................................................................... 202
3.5.1 Experiment setup..................................................................................................... 205
3.5.2 Numerical model ..................................................................................................... 207
3.5.3. Principal results and discussion .............................................................................. 216
3.5.4. Conclusions ............................................................................................................ 226
3.5.5. Reference ............................................................................................................... 228
4. GENERAL CONCLUSIONS .............................................................................................. 230
APPENDIX I .......................................................................................................................... 239
A.I.1. Effects of ice cover on local scour around bridge piers in non-uniform sand bed .......... 240
Methodologies and experimental Setup ............................................................................ 243
Results and discussions .................................................................................................... 246
Conclusions ..................................................................................................................... 254
References ....................................................................................................................... 256
A.I.2. Comparison of three commonly used Equations for calculating local scour depth around
bridge pier under ice covered flow condition ......................................................................... 258
Materials and Methods ..................................................................................................... 260
Experiment setup ............................................................................................................. 264
Results and discussion...................................................................................................... 267
Summary and conclusions ................................................................................................ 272
References ....................................................................................................................... 273
APPENDIX II ......................................................................................................................... 275

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CO-AUTHORSHIP
Regarding all the chapters in this dissertation, I was the primary investigator whose responsibility
was to design the experimental plan, collect, process and to interpret the data. In terms of the
formation of the manuscripts, my duty was to write them and to implement reviewers’ comments
and their feedback into the final versions of the dissertation. However, it would be surely
impossible to do this amount of work alone. Therefore, I would like to acknowledge Dr. Sui who
truly contributed to the finalization of the manuscripts, supervision of the experimental design,
data analysis of the current research and, whereby, he is included in authorship of all the
corresponding publications. Further, Yuquan Li, who assisted me in doing the experiments
throughout the field work, is included in a publication to acknowledge his contribution.
Additionally, Dr. Todd Whitcombe and Dr. Ramaswami Balachandar truly contributed to this
work by making some rich comments to some of the manuscripts are also included in some of the
publications.
Publications and authorships stemming from this dissertation (submitted, accepted or published)
1) Namaee, M. R., & Sui, J. (2018). Local scour around two side-by-side cylindrical bridge piers
under ice-covered conditions. International Journal of Sediment Research. (Published online)
(Chapter 3.1) [https://doi.org/10.1016/j.ijsrc.2018.11.007]
2) Namaee, M. R., & Sui, J. (2018). Impact of armor layer on the depth of scour hole around sideby-side bridge piers – an experimental study using non-uniform sands. Journal of Hydrology and
Hydromechanics. (Accepted) (Chapter 3.2)
3) Namaee, M. R., & Sui, J. (2018). Effects of ice cover on the incipient motion of bed material
and shear stress around side-by-side bridge piers. Cold Region Science and Technology. (Under
revision) (Chapter 3.3)
4) Namaee, M. R., Sui, J. & Whitcombe, T., (2018). Scour patterns and velocity profiles around
bridge piers under ice-covered flow. ASCE Journal of Hydraulic Engineering, (Submitted).
(Chapter 3.4)

vi

5) Namaee, M. R., & Sui, J. (2019). Three-dimensional numerical modeling of local scour around
bridge piers under open channel and ice-covered flow condition, (Submitted). (Chapter 3.5)
6) Namaee, M. R., Li, Y., & Sui, J. (2018). Effects of ice cover on local scour around bridge piers
in non-uniform sand bed. Proceedings of the 6th International Conference on Estuaries and Coasts
(ICEC-2018), University of Caen Basse-Normandie, France, August 20-23, 2018 (Chapter AI-1)
7) Namaee, M. R., Li, Y., Sui, J., & Whitcombe, T. (2018). Comparison of three commonly used
equations for calculating local scour depth around bridge pier under ice-covered flow condition.
World Journal of Engineering and Technology, 6 (02), 50. (Chapter AI-2)

vii

List of Tables
Table 1-1 Empirical Constants for the standard k−ε………………………………………………………26
Table 1-2: Empirical Constants for the RNG k-ε model…………………………………………………..27
Table 1-3: Empirical Constants for Realizable k-ε model……………….………………………………..27
Table 3-1: The values of the intercept, R2, P-value, α, MAE, and RMSE of the dimensionless parameters
with respect to Eq. 3-1-3 ........................................................................................................................ 85
Table 3-2: Grain size characteristics of samples of armour layer in scour hole around the 11-cm-pier
under rough covered flow condition compared to those of associated deposition ridge ......................... 116
Table 3-3: Different combinations of dimensionless variables .............................................................. 124
Table 3-4: Location of maximum velocity based on (z/y0) values according to flow cover ................... 185
Table AI-1: Comparison of calculated pier scour to measured pier scour from three equations under
smooth and rough ice-covered flow condition ............................................................................. 270
Table AI-2: Error Values of the three equations with respect to measured data under open, smooth and
rough flow ........................................................................................................................................... 271

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List of Figures
Figure 1–1: Main causes of bridge failure (Adopted by Imhof, 2004) ....................................................... 1
Figure 1–2: Different natural hazards causing bridge collapse (Adopted by Imhof, 2004)......................... 2
Figure 1–3: General scouring of river bed at Sg. Jeniang, Kedah .............................................................. 5
Figure 1–4: Sketch of the type of scour that can occur at a bridge crossing (Adapted from Brandimarte et
al. 2012) .................................................................................................................................................. 6
Figure 1–5: Illustration of the flow and scour pattern at a circular pier (Masjedi et al, 2010).................... 8
Figure 1–6: Pier scour depth in a sand-bed stream as a function of time (Richardson and Davis, 2001)..... 9
Figure 1–7: Forces acting on a sediment particle include gravity (F G), lift (FL), drag (FD), and resistance or
friction (Fr) (van Rijn, 1984) ................................................................................................................. 14
Figure 1–8: Types of sediment loads in rivers (Louck, 2005) ................................................................. 14
Figure 1–9: The Shield's Diagram (Cao, 2006)....................................................................................... 16
Figure 1–10: Indicates the relation between the critical Shields parameter (Ɵc) and sediment-fluid
parameter (S*) (Madsen & Grant, 1977) ................................................................................................ 17
Figure 1–11: Velocity profile for open water and floating smooth and rough covers from experiments
(Zabilansky et al., 2006) ........................................................................................................................ 36
Figure 1–12: Comparison of velocity and suspended sediment concentration distributions between
covered flow and free surface flow (Lau & Krishnappan) ...................................................................... 39
Figure 2–1:Two pumps in action ........................................................................................................... 46
Figure 2–2:Measuring points around the bridge piers ............................................................................. 47
Figure 2–3: Downstream view of the bridge piers with rough ice cover on ............................................. 48
Figure 2–4: Downstream view of the bridge piers with rough ice cover on and larger tail gate in action . 48
Figure 2–5: The SonTek-IQ used to collect flow (area-velocity) and volume data .................................. 49
Figure 2–6: 10-Mhz Acoustic Droppler Velocimeter (ADV) in practice used to measure velocity field
around bridge piers ................................................................................................................................ 49
Figure 2–7: Experimental setup ............................................................................................................ 51
Figure 2–8: 3D-down looking ADV probe ............................................................................................. 53
Figure 3–1: Plan view and side-view of the experimental flume. ............................................................ 67
Figure 3–2: The spacing ratio and measuring points around the circular bridge piers .............................. 68
Figure 3–3: Variation of scour depth around the 9-cm-piers for D50= 0.50 mm type under open, smooth,
and rough covered flow conditions ........................................................................................................ 73
Figure 3–4: (a) Contours of scour holes and deposition mounds around the 9-cm-piers under open channel
flow conditions (D50 = 0.50 mm) and (b) Contours of scour holes and deposition mounds around the 9cm-piers under rough covered condition (D50 = 0.50 mm). ..................................................................... 74
Figure 3–5: Relative MSD (ymax/y0) against pier spacing (G/D) under open channel, smooth, and rough
covered flow conditions (D50 = 0.50 mm). ............................................................................................. 76
Figure 3–6: Variation of pier spacing (G/D) with respect to pier Reynolds number (Re b)........................ 76
Figure 3–7: Variation of the relative MSD (ymax/y0) against flow Froude number (Fr) under open channel
flow conditions (D50 = 0.50 mm); .......................................................................................................... 78
Figure 3–8: The impact of sediment size on local scour around the 11-cm-pier under open channel flow
conditions;............................................................................................................................................. 80
Figure 3–9: Dependence of the relative MSD (ymax/y0) on flow Froude number (Fr) under covered
conditions compared to that under open channel flow conditions (D50 = 0.47 mm) ................................. 86
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Figure 3–10: Dependence of the relative MSD (ymax/y0) on flow Froude number (Fr) and grain size of
sediment (D50) under smooth covered flow conditions …………………………………………………...87
Figure 3–11: Comparison of calculated relative MSD (ymax/y0) to those observed under open channel flow
conditions. ............................................................................................................................................. 90
Figure 3–12: Comparison of calculated maximum scour depth (ymax/y0) to those observed under covered
flow conditions. ..................................................................................................................................... 91
Figure 3–13: Sensitivity analysis of dimensionless parameters of Eq. 3-1-11.......................................... 92
Figure 3–14a: Plan view and vertical view of experiment flume ........................................................... 104
Figure 3-14b: The spacing ratio and measuring around the circular bridge piers ................................... 104
Figure 3-15: Rough model ice cover on water surface .......................................................................... 105
Figure 3-16: Armour layer developed around the 17-cm-pier ............................................................... 105
Figure 3–17a: Scour morphology and the deposition ridge around the 11-cm-pier under smooth icecovered condition for D50=0.47 mm ..................................................................................................... 107
Figure 3–17b: Scour morphology and the deposition ridge around the 11-cm-pier under smooth icecovered condition for D50=0.58 mm ..................................................................................................... 107
Figure 3–18: Scour profiles around the 9-cm-pier under ice-covered and open channel flow condition for
D50=0.47 mm ....................................................................................................................................... 108
Figure 3–19a: A view of the scour pattern and deposition ridge around the 11-cm pier under rough icecovered condition (D50=0.58 mm) ........................................................................................................ 110
Figure 3–19b: Cross sections of scour and deposition ridge around the 9-cm-piers under open channel,
smooth and rough covered flow conditions (D 50=0.47 mm) .................................................................. 110
Figure 3–20: Relationship between scour volume and scour area ......................................................... 112
Figure 3–21: Grain size distribution curves of three non-uniform sands used in this study .................... 113
Figure 3–22: Grain size distribution curves of the armour layer in scour hole around the 11-cm-pier,
original sand and deposition ridge for sand bed of D50=0.50 mm under rough covered condition .......... 114
Figure 3–23a: Grain size distributions of armour layer samples in scour hole generated from three sands
around the 11-cm-pier ......................................................................................................................... 115
Figure 3–23b: Grain size distributions of samples of deposition ridge generated from three sands
downstream of around the 11-cm-pier .................................................................................................. 115
Figure 3–24: Relation between the relative MSD (ymax/D50A) with densimetric Froude number (Fr 0) .... 118
Figure 3–25a: Variation of relative MSD (ymax/D50A) with (D50A/D50B) distinguished by pier size.......... 119
Figure 3–25b: Variation of relative MSD (ymax/D50A) with (D50A/D50B) distinguished by different covered
conditions ............................................................................................................................................ 120
Figure 3–26: Variation of relative MSD (ymax/D50A) with the ratio of pier spacing (D50A/D) distinguished
by different covered conditions ............................................................................................................ 121
Figure 3–27: Comparison of calculated relative MSD (ymax/D50A) to those observed under open flow
condition ............................................................................................................................................. 123
Figure 3–28: Comparison of calculated relative MSD (ymax/D50A) to those observed under ice-covered
flow condition ..................................................................................................................................... 123
Figure 3-29a: Plan view and vertical view of experiment flume ........................................................... 140
Figure 3-29b: The spacing ratio and measuring points around the circular bridge piers ......................... 141
Figure 3-30a: Downstream view of the entire experimental model with the ice cover ........................... 141
Figure 3-30b: The ADV measurement around the bridge piers under rough ice-covered condition ....... 142

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Figure 3-31a: Relative MSD (ymax/y0) against pier spacing (G/D) under open channel, smooth, and rough
covered flow conditions (D50 = 0.50 mm). ........................................................................................... 144
Figure 3-31b: Variation of pier spacing (G/D) with respect to pier Reynolds number (Reb)……………144
Figure 3-32: Dimensionless shear stress (τ*) vs S*(U/U*) ................................................................... 145
Figure 3-33: Dimensionless shear stress (τ*) vs. shear Reynolds number (Re*) for the incipient motion of
the finest sediment (D50=0.47 mm) and the coarsest sediment (D50=0.58 mm) under open and rough icecovered flow conditions ....................................................................................................................... 147
Figure 3-34a: Variation of the dimensionless shear stress against the densimetric Froude number
classified by the sediment size ............................................................................................................. 149
Figure 3-34b: Variation of the dimensionless shear stress against the densimetric Froude number
classified by cover conditions for flow ................................................................................................. 149
Figure 3-35: Variation of the densimetric Froude number against the dimensionless shear Reynolds
number classified by particle grain size ................................................................................................ 150
Figure 3-36: Variation of the dimensionless shear stress against the dimensionless transport-stage
parameter classified by particle grain size ............................................................................................ 152
Figure 3-37: Ux velocity component profile in the scour hole under both ice-covered and open channel
flow conditions at the upstream face of the 6-cm pier for D50=0.47mm ................................................ 154
Figure 3-38a: Variation of the relative MSD with U*/U*c classified by particle grain size for open flow
condition ............................................................................................................................................. 156
Figure 3-38b: Variation of the relative MSD with U*/U*c classified by particle grain size for smooth
covered flow condition ........................................................................................................................ 156
Figure 3-38c: Variation of the relative MSD with U*/U*c classified by particle grain size for rough
covered flow condition ........................................................................................................................ 157
Figure 3-38d: Variation of the relative MSD with U*/U*c classified by flow cover conditions for
sediment of D50=0.50 mm .................................................................................................................... 157
Figure 3-38e: Variation of the relative MSD with U*/U*c classified by flow cover conditions for
sediment of D50=0.47 mm .................................................................................................................... 158
Figure 3-38f: Variation of the relative MSD with U*/U*c classified by flow cover conditions for sediment
of D50=0.58 mm .................................................................................................................................. 158
Figure 3-39: Variation of the relative measured MSD against calculated MSD ..................................... 159
Figure 3-40: Plan view and vertical view of experiment flume (Dimensions in m) ............................... 177
Figure 3-41: The spacing ratio and measuring points around the circular bridge piers........................... 177
Fig. 3-42a: Scour depth around the 110-mm bridge pier for D50= 0.47 mm type sediment under a) open
flow and b) rough-covered flow conditions using the highest flow discharge........................................ 180
Figure 3-42b: Cross-section of scour and depositional pattern at the upstream and downstream of the 110mm bridge pier under a) open flow condition and b) rough covered flow conditions for D 50=0.47 mm . 180
Figure 3-43: a) Scour pattern around the 110-mm bridge pier for D50=0.47 mm type under open for the
highest flow discharge; b) Scour pattern around the 110-mm bridge pier for D50= 0.47 mm type under
smooth for the highest flow discharge; c) scour patterns around the 110-mm bridge pier for D50= 0.47 mm
type under rough for the highest flow discharge ................................................................................... 181
Figure 3-44: Scour hole velocity profiles for the streamwise (Ux) and vertical (Uz) velocity components
under open, smooth and rough ice-cover distinguished by the pier size and under D50= 0.47 mm for the
lowest discharge .................................................................................................................................. 186

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Figure 3-45: Scour hole velocity profiles for the streamwise (Ux) and vertical (Uz) velocity components
distinguished by flow cover for all the pier size and under D50= 0.47 mm for the lowest discharge ....... 187
Figure 3-46: The vertical velocity distribution for the lowest discharge for the 90-mm bridge pier under
rough ice-covered condition for the three values of D50. ....................................................................... 188
Figure 3-47: a) Vertical velocity component (Uz) of the 60- and 170-mm bridge piers from the scour hole
up to the maximum velocity locale under open, smooth and rough-covered flow covers; b) Vertical
velocity component (Uz) of the 90- and 110-mm bridge piers from the scour hole up to the maximum
velocity locale under open, smooth and rough-covered flow covers; c) Vertical velocity component (Uz)
of all the bridge piers from the maximum velocity locale toward the free surface under open, smooth and
rough-covered flow covers .................................................................................................................. 188
Figure 3-48: Scour hole velocity profiles for the resultant of the three average velocity components under
open, smooth and rough ice cover for D50= 0.47 mm for the lowest discharge. ..................................... 189
Figure 3-49: Distribution of the turbulent intensity values at the upstream of the piers nondimensionalized by the shear velocity for the streamwise (x) flow velocity component ........................ 192
Figure 3-50: Distribution of the turbulent intensity values at the upstream of the piers nondimensionalized by the shear velocity for the vertical (z) flow velocity component .............................. 192
Figure 3-51: Distributions of the turbulent kinetic energy at the upstream of the piers .......................... 193
Figure 3-52: Percentage of velocity fluctuation components (u' and w') from each quadrant (i = 1, 2, 3 and
4) at the upstream of 60 mm pier for D50= 0.47 mm ............................................................................. 194
Figure 3-53: Plan view and side-view of experiment flume ................................................................. 206
Figure 3-54: The spacing ratio and measuring points around the circular bridge piers........................... 207
Figure 3-55: The calculation model and boundary conditions for rough ice-covered flow condition ..... 215
Figure 3-56: (a) Simulated bed elevation contours around the 110-mm bridge piers in channel bed with
fine sediment at t=450 s under open channel condition; (b) Laboratory measured bed elevation contours
around 110-mm bridge piers in channel bed with fine sediment under open channel condition………...217
Figure 3-57: Simulated scour depths compared to those of experiments around the 110-mm bridge piers in
channel bed under open channel flow condition .................................................................................. 218
Figure 3-58: (a): Flow field at the plane z= 0.326 m at the end of simulation time, and (b): The distribution
of turbulent energy at the cross section of the bridge pier under open channel flow condition ............... 218
Figure 3-59: (a) Flow streamlines around the 110-mm bridge pier: (a) at initial stage (t= 22.25 s) and (b)
at the last second of simulation (t= 445 s) ............................................................................................ 219
Figure 3-60: (a) Simulated bed elevation contours around 110-mm bridge piers in channel bed with fine
sediment at t=450 s under smooth-ice-covered condition; (b) Laboratory measured bed elevation contours
around 110-mm bridge piers in channel bed with fine sediment under smooth-ice-covered condition ... 221
Figure 3-61:Simulated scour depths compared to those of experiments around the 110-mm bridge piers in
channel bed under smooth ice-covered condition ................................................................................. 222
Figure 3-62: (a): Flow field at the plane z= 0.326 m at the end of simulation time, and (b): The distribution
of turbulent energy at the cross section of the bridge pier under the smooth-covered flow condition ..... 222
Figure 3-63: (a) Simulated bed elevation contours around 110-mm bridge piers in channel bed with fine
sediment under rough-ice-covered condition; (b) Laboratory measured bed elevation contours around 110mm bridge piers in channel bed with fine sediment under rough-ice-covered condition ........................ 224
Figure 3-64: Simulated scour depths compared to those of experiments around the 110-mm bridge piers in
channel bed under rough ice-covered condition ................................................................................... 225

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Figure 3-65: (a) Flow field at the plane z= 0.326 m at the end of simulation time, and (b): The distribution
of turbulent energy at the cross section of the bridge pier for the rough-covered flow condition ........... 225
Figure 3-66: Comparison of the simulated maximum scour depths (MSD) to those of laboratory
experiments ......................................................................................................................................... 226

xiii

ACKNOWLEDGEMENT
Firstly, I would like to express my sincere gratitude to my supervisor Dr. Jueyi Sui for his
continuous support of my Ph.D. study and related research, for his patience, motivation, and
immense knowledge. His guidance helped me in all the time of research and writing of this
dissertation. I could not have imagined having better advisor and mentor for my Ph.D. study.
Besides my supervisor, I would like to thank the rest of my dissertation committee member: Dr.
Jianbing Li, Dr. Liang Chen, Dr. Samuel Li and my co-supervisor Dr. Youmin Tang for their
insightful comments and encouragement. I am also grateful to Dr. Peng Wu for his in-depth
knowledge which encouraged me to look at my research from a more in-depth perspective.
My sincere thanks also go to Dr. Phil Owens and Dr. Ellen Petticrew who provided me an
opportunity to stay and do my research at The Dr. Max Blouw Quesnel River Research Center
(QRRC), and who gave me access to the laboratory and research facilities. Huge thanks are
extended to QQRC staff (Lazlo Enyedy and Michael Allchin) and my friends (Todd French and
Yuquan Li) without whom it would be impossible to conduct this research.
I am also grateful to Dr. George Jones and Dr. Alia Hamieh who provided me with teaching
contracts throughout my Ph.D. which helped me financially. I would also like to thank the staff
and all the wonderful friends I met at The University of Northern British Columbia and Prince
George who were really welcoming and supportive of foreign students.
I would like to express my gratitude to Dr. Bill McGill, Dr. David Connell, Dr. Peter Jackson and
Dr. Todd Whitcombe as my course supervisors in my first year of Ph.D., who widened my
scientific perspective and assisted me to understand the interaction between natural science and
social science. My appreciation also goes to my classmates who presented different subjects which
made me keener on different aspects of science.
Last but not the least, I would like to thank my beloved family: my parents, my sisters and my
brother-in-law and my newly-born niece (Artemis) for supporting me spiritually and financially
throughout writing this dissertation and especially in my life.

xiv

1. INTRODUCTION
Local scour is the abrupt decrease in bed elevation near a pier due to erosion of bed material in the
vicinity of the local flow structure induced by the pier (Shen et al., 1969). Overlooking the local
scour phenomenon in the bridge pier design might possibly result in huge financial cost or even
high casualty rate. According to a broad collection of bridge failure data worldwide assembled by
Imhof (2004), natural hazard is the principal cause of bridge failure as it amounts to approximately
30% of all collected bridge collapse cases (Figure 1-1). Among the natural hazard causes listed,
flooding or scour is responsible worldwide for about 60% of the failure cases (Figure 1-2). Due to
the local scour, the insertion depth of the pile reduces as the scour depth around the pile grows,
which is directly associated with the stability of the pier. The deeper the depth of local scour around
the pier, the more vulnerable it becomes which leads to bridge collapse in the most extreme case
(Zhang et al, 2005).

Figure 1–1: Main causes of bridge failure (Adopted by Imhof, 2004)

1

Figure 1–2: Different natural hazards causing bridge collapse (Adopted by Imhof, 2004)

The Federal Highway Administration (FHWA) has estimated that 60% of bridge failure cases in
the USA are due to scour (FHWA, 1988; Parola et al, 1997) and on average, approximately 50 to
60 bridges collapse in the USA annually. Wardhana & Hadipriono (2003) studied 500 failures of
bridge structures in the United States between 1989 and 2000 and reported that the most frequent
causes of bridge failures were due to floods and scour. On average, the age of the 500 failed bridges
was 52.5 years and its range was from 1 to 157 years (Brandimarte et al, 2012). Bridge damage
and failure have huge negative social and economic impacts in terms of reconstruction costs,
maintenance and monitoring of existing structures, the disruptions of traffic flow and, in some lifethreatening cases, the cost of human lives (Brandimarte et al 2012). In a broad research on bridge
scour, the Federal Highway Administration (Brice and Blodgett, 1978) reported that damages to
bridges and highways from major regional floods in 1964 and 1972 is equivalent to approximately
100 million US dollars per event. A report of road administration declared that scour caused by
rivers results in hefty expenses of 36 New Zealand million dollars per year in New Zealand
(Macky, 1990). Hereby, it is necessary to consider scour as one of the most important causes of
2

bridge failure when designing the bridge foundation (Briaud et al, 2006). Moreover, a precise
prediction of scour depth will not only prevent those bridge failures which are the consequence of
underestimation of scour depth, but also will efficiently reduce unnecessary construction cost of
those bridge piers in which scour depths are overestimated. Many hydraulic researchers have done
experiments to investigate the local scour around bridge piers and develop empirical equations to
estimate the maximum scour depth (Ettema et al., 2011; Melville, 1997; Melville & Sutherland,
1988; Richardson et al., 2001; Sheppard et al., 2013).
A great number of bridges are constructed in extreme cold regions whose piers are exposed to the
impact of ice in addition to the local scour around the piers. These types of bridge piers have not
been thoroughly examined in terms of flow field and prediction of maximum scour depth around
them. It has been proved that the formation of a stable ice cover effectively doubles the wetted
perimeter compared to open channel conditions, alters the hydraulics of an open channel by
imposing an extra boundary to the flow, causing the velocity profile to be shifted towards the
smoother boundary (channel bed) and adding up to the flow resistance (Sui et al., 2010; Wang et
al., 2008). Besides, the influence of an ice cover on a channel involves complex interactions among
the ice cover, ice roughness, fluid flow sediment, bed geometry, water depth, and channel
geometry and this complex interaction can have a dramatic effect on the sediment transport process
(Hains, 2004). The investigation into scour under the ice was prompted by the collapse of a bridge
over the White River in White River Junction, Vermont in 1990. It is interesting to know that the
bridge had survived more dramatic ice and flood events during its service life than the one that led
to the failure of the bridge piers. The failure of the bridge piers was the result of multiple bridge
pier scour cycles which had already undermined the foundation of the piers (Zabilansky, 1996). In
order to get a better understanding of the flow field and scouring process around bridge piers under
3

ice-covered condition, my PhD dissertation conducted a comprehensive experimental study on the
local scour around bridge pier, by carrying out three sets of flume experiments in a non-uniform
bed by incorporating four different sets of circular bridge piers with a fixed distance in-between
under open, rough and smooth ice-covered flow condition.
1.1 Definition of scour and different types of scour
Scouring can be defined as a process due to which the sediment particles around the surroundings
of the abutment or pier of the bridge, gets eroded and removed over a certain depth which is called
scour depth (Chang, 1992). Bed scour may be a natural occurrence or due to man-made changes
to a river (Maddison, 2012). Brandimarte et al. (2012) state that scour at bridge foundation is
typically as the result of the joint impacts of three different scour processes (general scour,
contraction scour and local scour I the vicinity of the piers) that may arise either independently or
concurrently. General scour (degradation) is defined as the general dropping in the sediment bed
by the kinetic energy of the oncoming flow which can occur more rapidly during the flood and can
affect the reach of the river on which the bridge is located, while aggradation involves the
deposition of material eroded from the channel or watershed upstream of the bridge (Richardson
et al, 1993). Figure 1-3 illustrates a bridge damage case in Malaysia due to flooding and scouring
at the pier. Rivers that transport significant amounts of bed material are most susceptible to scour
and channel instability which includes sand-bed rivers and upland gravel bed rivers (Maddison,
2012). The main causes of general scour that induce aggradation or degradation of the bed channel
are either due to human activities, such as land-use changes (urbanization, deforestation); dam
construction, reservoir construction, channel alterations, river bed material mining or due to natural
phenomena, such as channel straightening, climate changes and land activities such as landslides,
mudflows (Brandimarte, et al. 2012).
4

Figure 1–3: General scouring of river bed at Sg. Jeniang, Kedah

Contraction scour occurs when the cross-section area of flow of a stream at flood stage is reduced,
either by a natural contraction or bridge. From continuity principle, a decrease in flow area leads
to an increase in average velocity and bed shear stress through the contraction. Therefore, there is
an increase in erosive forces in the contraction. Because of that, more bed material is removed
from the contracted reach than is transported into the reach. This increase in transport of bed
material from the reach lowers the natural bed elevation (Richardson et al, 1993). This lowering
may be uniform or non-uniform across the bed. Non-uniform contraction scour means that the
depth of scour may be deeper in some parts of the cross section. As the bed elevation is lowered,
the flow area increases and, in the riverine situation, the velocity and shear stress decreases until
relative equilibrium is reached; i.e., the quantity of bed material that is transported into the reach
is equal to that removed from the reach, or the bed shear stress decreases to a value such that no
sediment is transported out of the reach. The natural process of scouring can also be impacted by
the placement of the artificial obstruction in the way of river flow, such as weirs and piers
(Richardson et al, 1993) which triggers local scour around bridge piers and is the main interest in
5

this dissertation. The local scour around bridge foundations usually results from the joint effect of
contraction scour, due to the flow velocity increase, which is the result of the reduction of the
channel section, and the pier and abutment scour which is the result of the (local) alteration of the
flow field induced by piers and abutments (Graf, 1998). Figure 1-4 illustrates the contraction scour
due to narrowing of the flow cross section and local scour around bridge piers and abutments.
Total scour is the addition of long-term degradation of the river bed (general scour), contraction
scour at the bridge and local scour at the piers or abutments. In the process of local scour, the
material from around piers, abutments, embankments would be removed because of the flow
alteration induced by the obstruction of the flow (Richardson & Davis, 2001). Compared to general
scour and constriction scour, local scour can cause serious damage to the bridge because it
specifically occurs around the bridge piers.

Figure 1–4: Sketch of the type of scour that can occur at a bridge crossing (Adapted from Brandimarte et
al. 2012)

6

1.2 Local scour characteristics around bridge piers in open channels
The main feature of the flow around a pier is the system of vortices which develop about the pier.
These vortex systems are the basic mechanism of local scour, which has long been described by
investigators (Tison, 1961; Breusers et. al., 1977; Chabert & Engeldinger, 1956; Laursen and Toch,
1956; Shen et. al.,1969; Melville, 1975; Hjorth, 1975; Melville and Raudkivi 1977; Ettema, 1980;
Baker, 1981; Jain, 1980; Raudkivi and Ettema, 1983; Melville and Sutherland, 1988; Kothyari,
1998; Dargahi, 1990; Yanmaz and Altimbilek, 1991; HEC-18, 1991; Dey, 1997; Ahmed and
Rajaratnam, 1998; Graf and Istiarto, 2002). It has been described that, depending on the type of
pier and freestream conditions, these vortex systems can be characterized by three basic systems:
downflow, horseshoe vortices, and wakes (Laird, 1971; Dargahi, 1989,1990; Ahmed and
Rajaratnam, 1998; Ansari et al, 2002; Graf and Istiarto 2002). Figure 1-5 illustrates the flow and
scour pattern around a circular pier. As it is depicted in Figure 1-5, the strong vortex motion caused
by the existence of the pier entrains bed sediments from around the pier base (Lauchlan & Melville,
2001). The downflow rolls up while it continues to dig a hole through interaction with the
oncoming flow. Near the water surface, the water depth is increased, and a vertical pressure
gradient is developed due to the stagnation of the approaching flow. The vortex then extends
downstream along the sides of the pier. This vortex is often referred to as a horseshoe vortex
because of its great similarity to a horseshoe (Breusers et al., 1977). The primary vortex then
extends to the downstream of the piers and loses its identity after some distances. In the corner of
downstream piers, the flow accelerates and leads to the development of concentrated vortices,
which are termed as wake vortices. Wake vortices are created due to the separation of the flow
upstream and downstream of the pier corners (Zhang, 2005; Kwan & Melville, 1994).

7

Figure 1-5: Illustration of the flow and scour pattern at a circular pier (Masjedi et al, 2010)

1.3. Clear-water and live-bed scour
There are two main classifications of local scour at piers based on the mode of sediment transport
by the approaching stream, namely clear-water scour and live-bed scour. These classifications
depend on the ability of the flow approaching the bridge to transport bed material. Distinguishing
between these two types of scour is important because both the development of the scour hole with
time and the relationship between scour depth and approach flow velocity depends on the type of
scour (Raudkivi & Ettema, 1983). Laursen (1960) was the first to distinguish between live-bed
and clear-water scour for both contraction and local scour (Richardson, 1996). Two conditions
might occur for contraction and local scour which are clear-water and live-bed scour. Clear-water
scour occurs when there is no movement of the bed material in the flow upstream of the crossing
or if there is any movement of the bed materiel, it would be in suspension through the scour hole
at the pier at less than the capacity of the flow. This happens when the shear stress exerted on the
sediment by the flow is less than the critical shear stress of the sediment. Under clear-water scour,
the maximum scour depth is reached more gradually and once it is developed, the flow can no
longer remove sediment from the scour hole. Clear-water scour reaches its maximum over a longer
8

period than live-bed scour (Chee, 1982; Melville, 1984; Richardson & Davis, 2001). Chabert and
Engeldinger (1956) observed that the equilibrium clear-water scour depth is 10% greater than live
bed scour depth (Figure 1-6). This is because clear-water scour occurs mainly in coarse-bed
material streams. On the other hand, live-bed scour occurs when there is transport of bed material
from the upstream reach into the crossing (Raudkivi & Ettema, 1983). This happens when the
shear stress exerted on the sediment by the flow is greater than the critical shear stress of the
sediment. Under live-bed conditions, the depth of local scour develops more rapidly compared to
clear-water scour, then it oscillates about the equilibrium scour depth due to spreading bed-form.

Figure 1-6: Pier scour depth in a sand-bed stream as a function of time (Richardson and Davis, 2001)

Critical shear velocity is used to determine the velocity associated with the initiation of motion.
They are used as an indicator for clear-water or live-bed scour conditions. If the mean velocity (V)
in the upstream reach is equal to or less than the critical shear velocity (Vc) of the median diameter
(D50) of the bed material, then contraction and local scour will be clear-water scour. On the other
hand, if the mean velocity is greater than the critical shear velocity of the median bed material size,
live-bed scour will occur. This method can be applied to any unvegetated channel or overbank area
9

to determine whether scour is clear-water or live-bed. (Richardson et al, 1993). Sheppard, et. al.
(2013) stated that the sediment critical velocity (Vc) can be estimated from Shields’ diagram, using
Equations (1-1) to (1-4). It should be mentioned that shields diagram will be explained in the
upcoming section:

u * = [16.2 D50 (

Re =

1

9.09  10−6
− D50 (38.76 + 9.6 ln( D50 )) − 0.005)]2
D50

u * D50
2.32  10−7

(1-1)
(1-2)

For 5<Re<70
Vc = 2.5u * ln[

73.5 y1

111
D50 (Re(2.85 − 0.58ln(Re) + 0.002Re) +
− 6)
Re

(1-3)

For Re>70
Vc = 2.5u * ln(

2.21y1
)
D50

In which u* is friction (shear) velocity (

(1-4)

0
) [L/T]; D50 is median grain size; y1 is average flow


depth in the upstream main channel [L] and τ0 is bed shear stress [F/L2].
1.4 Sediment transport in a river Channel
In terms of mode of sediment particle motion, there are three modes of particle motion: (a) rolling
and sliding (traction), saltation (hopping) and suspended motion. That portion of the sediment load
that is transported along the bed by sliding, rolling or hopping is bedload. Bedload initiates when
bed shear stress exceeds the critical value for the incipient motion of particles. With increasing
bed shear stress or shear velocity, the particles acted on turbulent flow will regularly jump or saltate
(Van Rijn, 1984). Suspended load is the type of sediment that is carried in the body of the flow
10

and moves at the same velocity as the flow. It particularly occurs for a small particle (e.g. Clay
and fine silt) because these types of particles with a large relative surface area are held in
suspension more easily due to the electrostatic attraction between the unsatisfied charges on the
grain's surface and the water molecules. This force, tending to keep the particle in the flow, is large
compared to the weight of the particle (Van Rijn, 1984). The total load is the sum of bed load and
suspended load. In most natural rivers, sediments are mainly transported as suspended load, while
the bed load transport rate is about 5-25% of that in suspension (Yang, 2003).
1.5 Importance of bed shear stress and methods to predict it
Bed shear stress provides an index of fluid force per unit area on the stream bed, which has been
related to sediment mobilization and transport in many theoretical and empirical treatments of
sediment transport. Bed shear stress and shear velocity are fundamental variables in river studies
to calculate the transport field and the scour, deposition and channel change (Wilcock, 1996). The
difficulty of estimating these variables accurately, particularly in complex flow fields when flow
is highly three-dimensional, has long been recognized (Biron et al, 2004). One of the most popular
methods to calculate bed shear stress is to use the reach-average bed shear stress in which

 0 = gRS f where τ0 is bed shear stress, ρ is water density, g is acceleration due to gravity, R is
hydraulic radius and Sf is the energy slope. However, this method is not appropriate for local smallscale estimates of the variation in shear stress and it lacks accuracy (Babaeyan-Koopaei et al.,
2002). There are totally four different methods to predict local bed shear stress, which are log
profile, drag, Reynolds and turbulent kinetic energy (TKE) with more accuracy. Until recently,
Reynolds stress and the turbulent kinetic energy method were not used broadly because of the
difficulty in obtaining detailed turbulence measurements close to the bed in natural rivers (Dietrich
and Whiting, 1989; Wilcock, 1996). Fortunately, the development of measuring devices such as
11

the Acoustic Doppler Velocimeter (ADV) has allowed comprehensive field measurements of
turbulent velocity fluctuations in the three components of velocity at high frequencies with small
errors in the Reynolds shear stress (McLelland & Nicholas, 2000). Biron, et. al., 2004 compared
shear stress estimated from the log profile, drag, Reynolds and turbulent kinetic energy (TKE)
approaches in a laboratory flume in a simple boundary layer, over Plexiglas, sand and in a complex
flow field around deflectors. They concluded that in a complex flow field around deflectors, the
TKE method provided the best estimate of shear stress as it is not affected by local streamline
variations and it considers the increased streamwise turbulent fluctuations close to the deflectors.
The turbulent kinetic energy (TKE) is 𝜏 = 𝐶1 [0.5𝜌(𝑢′2 + 𝑣′2 + 𝑤′2 )]. In which, ρ is the flow
density, C1=0.19 is a proportionality constant and u′, v′, w′ are turbulence fluctuations in the
longitudinal, transverse and vertical directions, respectively. For the local scour in open channel,
a flow resistance calculation leads directly to the estimation of the shear velocity associated with
the bed surface drag. To estimate sediment transport rate under ice cover, it is first necessary to
estimate flow resistance (or a relationship between flow depth and mean velocity of the flow), and
then the flow drag on the bed. As it was mentioned earlier, ice cover presence alters mean flow
distribution and flow turbulence characteristics. The flow velocity profile under ice cover can be
categorized as upper portion and lower portion, which are divided by the locus of the point of the
maximum velocity. The upper portion of the flow is mainly affected by the ice cover and the lower
portion of the flow is mainly affected by river bed (Sui et al, 2010).
1.6 Shields Parameter and importance of critical shear stress
As it was mentioned earlier, for a particle to become entrained, the bed or boundary shear stress
caused by the water flowing parallel to the stream bed must exceed a critical shear stress. In other
words, the moment where the directive forces (shear forces) overcome preventive forces (inertia,

12

friction) is known as the moment of incipient motion and is the threshold of particle entrainment.
The shear stress at this threshold is known as the critical shear stress (Wiberg & Smith 1987).
Figure 1-7 illustrates these forces. This critical shear stress is a function of both the bed sediment
and the condition of the sediments (Beltaos et al., 2011). The threshold when the two forces are
equivalent is the critical condition at which the directive forces are just balancing the resisting
forces (Wiberg & Smith 1987). Totally, of the total sediment load, there are two kinds of distinctive
sediment types, the bed load and the suspended load. Mathematically, if the shear stress is higher
than the critical shear stress, and less than the critical shear stress for initiation of suspended
particle, the sediments will start to move which is called bedload transport and the bed load
transport is in shape of Traction (rolling & sliding) or saltation (hopping). However, if the shear
stress is higher than the critical shear stress for initiation of suspended particle, the sediment starts
to move in suspension (Hasanzadeh, 2012). Dissolved load is material, especially ions, that are
carried in solution by a stream which is not within the scope of this research and it should be noted
that if the bed shear stress is less than critical shear stress there would be no motion (Figure 1-8).

   cr

no motion

(1-5)

 cr     cr

bed load transport

(1-6)

   cr

bed & suspended loads transport

(1-7)

Where τ is bed shear stress,  cr is critical shear stress or shear stress of exact moment at which
sediment particle initiates,  cr is critical shear stress for initiation of suspended particle.

13

Figure 1-7: Forces acting on a sediment particle include gravity (F G), lift (FL), drag (FD), and resistance or
friction (Fr) (van Rijn, 1984)

Figure 1-8: Types of sediment loads in rivers (Louck, 2005)

1.7 The Shields diagram
Several studies (Brownlie, 1983; Liu, 1999; Van-Rijn, 1993; Hasanzadeh, 2012) stated that the
Shields diagram is properly defined to describe sediment movement and used the critical shear
stress parameter to describe the flow conditions affecting on the movement of sediment particles.
It should be mentioned that shield diagram represents the relationship between critical Shields
parameter and the hydraulic conditions of the flow at the bottom of the channel which is expressed

14

in term of particle Reynolds number. The amount of particle Reynolds number depends on the
determination of the diameter of a particle which is usually taken as the average grain size (D50)
and the shear velocity values.

cr =

Re* =

=

U *2cr

( s − 1)  g  D50

=

 cr
( s − 1)    g  D50

(1-8)

U *cr  D50


(1-9)

U*2

=
,U * =
( s − 1)  g  D50 ( s − 1)    g  D50

gRS

(1-10)

Where Ɵ is dimensionless mobility Shields parameter, Ɵcr is dimensionless critical mobility
Shields parameter, Re* is dimensionless Reynolds particle number, U* is shear velocity (m/s),
Ucr* is critical shear velocity (m/s), τ is shear stress (N/m2), τcr critical shear stress (N/m2), υ is
kinematics viscosity (m2/s), D50 is median diameter of particle (m); S is relative density (ρs/ρ).
Therefore, above equations are considered a mathematical formula to describe the initiation of
sediment movement. Sediment particle starts moving when the mobility Shields parameter value
becomes greater than a critical Shields parameter which is shown in the following equations.
Figure 1-9 illustrates Shields diagram, which represents the relationship between a critical mobility
Shields parameter and a Reynolds number of sediments.
U *  U *cr

(1-11)

 b   bcr with  bcr =   U *cr

(1-12)

U*2cr
( S − 1)  g  D50

(1-13)

   cr with cr =

15

Figure 1-9: The Shield's Diagram (Cao, 2006)

1.8 The modified shields diagram
Madsen & Grant (1977) pointed out the difficulty of applying the shields diagram due to the
presence of U*cr in both axes of the diagram. Therefore, they worked to use a new variable instead
of Reynolds number on the horizontal axis of diagram as it is shown in Figure 1-10. This figure
indicates the relation between the critical Shields parameter in the Y-axis and new variable which
is sediment-fluid parameter (S*) in the X-axis. S* Value is calculated from the following equation:

S* =

Re*
D50
( s − 1) gD50 =
4
4 c

(1-14)

16

Figure 1-10: Indicates the relation between the critical Shields Parameter (Ɵc) and Sediment-Fluid
Parameter (S*) (Madsen & Grant, 1977)

1.9. Bridge scour prediction
It has been found that bridge scour is related to many factors such as the geometry of the channel,
dynamic properties of the flow and geometry of the bridge piers and abutments (Deng and Cai,
2009). Predicting bridge scour using the available information of these factors prior to or during
flood events is highly crucial in preventing disastrous failures of bridges and possible loss of life.
Scour prediction practice can be generally categorized into two groups which are prediction of
bridge scour using empirical equations and prediction of bridge scour using other methods, such
as neural networks and numerical modelling (Deng and Cai, 2009). By incorporating these two
methods, the final scour depth and real-time scour depth can be predicted.

17

1.10 Predicting bridge scour using empirical equations
In the past few decades, many researches have been done to estimate the maximum scour depth,
which is the main reason of bridge failure, around bridge piers. (Laursen and Toch, 1956; Liu et
al. 1961; Tison, 1961; Shen et al., 1969; Breusers, et al., 1977; Jain and Fischer, 1980; Raudkivi
1986; Melville and Sutherland, 1988; Froehlich, 1989; Melville, 1992; Abed and Gasser, 1993;
Richardson and Richardson, 1994; Melville, 1997; Coleman et. al., 2003; Dey & Barbhuiya, 2005;
Dey & Raikar, 2005; Heza et al., 2007; Sheppard et al., 2013). However, due to the difference
between site and laboratory conditions and the limitation of collected data specifically those of
small-scale laboratory flumes, the development of these formulae has a great deal of uncertainty
and limitations with respect to the factors considered in constructing the scour model, parameters
used in the equation, laboratory or site conditions, etc. It is noteworthy to mention that it is
generally believed that most existing equations might overestimate the scour depth and are
generally conservative deductions from comparative studies by different researchers based on the
conducted laboratory experiments and field tests (Johnson and Ayyub 1996; Melville 1997; AtaieAshtiani & Beheshti, 2006; Lu et al. 2008). In this section, a brief review of some of the most
common equations is presented.
1.10.1 Colorado State University equation
Among all the equations, one of the most commonly used pier scour equations in the United States
is the Colorado State University equation (Deng and Cai, 2009) recommended by the U.S.
Department of Transportation’s Hydraulic Engineering Circular No. 18 (HEC-18) (Federal
Highway Administration 1993), which is expressed as follows:

d s = 2.0 yK1 K 2 K3 (b / y) 0.65 Fr 0.43

(1-15)

18

Where ds=scour depth; y=flow depth at the upstream of the pier; K1, K2, and K3=correction factors
for the pier nose shape, angle of attack flow, and bed condition, respectively; b=pier width; and
Fr=Froude number. It is recommended in the HEC-18 that the limiting value of d s/y is 2.4 for
Fr<0.8 and 3.0 for Fr>0.8. Eq. (1-15) was developed from laboratory data and was recommended
for both live-bed and clear-water conditions. A few other commonly used equations are also listed
in the following section. For the purpose of simplification, repeated terms in the following
equations will not be explained again.
1.10.2 Neil (1964) equation
Equation presented by Neil (1964), which was developed from the design curves by Laursen and
Toch (1956).

d s = 1.35b0.7 y 0.3

(1-16)

Shen’s equation (Shen et al. 1969)
 Vb 
d s = 0.00022 
 

0.3

(1-17)

Where V=average velocity of approach flow and ν=1×10-6 m2/s.
1.10.3 Jain and Fisher equation (1979)
y

d s = 2.0b( Fr − Frc ) 0.25 ( ) 0.5 for( Fr − Frc )  0.2


b

y
d = 1.85b( Fr ) 0.25 ( ) 0.5 for0  ( Fr − Fr )
c
c
 s
b


(1-18)

Where Frc=critical Froude number. For 0<(Fr-Frc) <0.2, the larger of the two scour depths
computed using the two equations is used.
19

1.10.4 Froehlich equation (Froehlich 1989)

b
y
b 0.082
d s = 0.32bF 0.2 ( e ) 0.62 ( ) 0.46 (
)
b
b
D50

(1-19)

Where ɸ=coefficient based on the shape of the pier nose; be=width of the bridge pier projected
normal to the approach flow; and D50=median grain size of bed material.
1.10.5 Melville and Sutherland equation (1988):

d s = K1K d K y K a K s b

(1-20)

Where Kl=flow intensity factor; Kd=sediment size factor; Ky =flow depth factor; Ka=pier
alignment factor; and Ks=pier shape factor.
1.11 Bridge scour modeling
As discussed earlier, bridge scour is a very complicated hydraulic process which involves the
interaction between the flow around a bridge pier or abutment and the erodible bed surrounding it
and it is dependent on many hydraulic factors such as geometry of the channel, dynamic hydraulic
properties of the flow, geometry of the bridge piers and abutments (Deng & Cai, 2009). To study
the complicated bridge scour process, different numerical models as well as laboratory models
have been developed in the past few decades. In this section, these types of hydraulic modelling
would be discussed more in details.
1.11.1 Laboratory models
Laboratory models are very common and trustworthy in the design of different hydraulic problems.
One of the most important advantages of laboratory studies of bridge scour is that they can be very
helpful in terms of getting a better and clearer understanding of the effect of different variables
and parameters associated with scour and therefore improve the scour prediction equations.
20

Besides, they can be useful to develop alternative or improved scour countermeasures which is
primarily important during floods (Deng & Cai, 2009). As it was mentioned before, a numerous
laboratory researches have been done to investigate bridge pier scours. For instance, a large
circular pier at the Imbaba Bridge with a scale of 1:60 was constructed at the Hydraulics and
Sediment Research Institute to study the deep scour hole downstream of one of the major bridges
across the Nile River (Abed & Gasser, 1993). In order to do so, a series of clear-water scour tests
were performed to investigate the causes of the local scour downstream the circular pier. It was
found that the large scour hole downstream the circular pier was formed by the turbulent velocity
fields at the intersection of the wake vortex streams from adjacent piers which was enlarged by the
confluence flow. Based upon the results of this investigation, an empirical formula was developed
to predict the wake and confluence maximum local scour depth downstream of a circular pier for
a clear-water condition. Umbrell et al. (1998) put a tilting fume with the dimension of 21.3 m long,
1.8 m wide, and 0.6 m deep in practice to investigate clear-water bridge contraction scour caused
by pressure flow beneath a bridge without the localized effect of piers or abutments. In their
laboratorial experiment, different factors such as approach velocity, pressure-flow velocity under
the bridge deck, and sediment size were studied. Sheppard & William (2006) studied the local
clear-water and live-bed scour using laboratory tests for a range of water depths and flow velocities
with two different uniform cohesionless sediment diameters (0.27 and 0.84 mm) and a circular pile
with a diameter of 0.15 m. The tests were done in a tilting flume located in the Hydraulics
Laboratory at the University of Auckland in Auckland, New Zealand. In their experiments, large
bed forms were observed to travel through the scour hole during a number of the live-bed scour
tests and they concluded that Sheppard’s equations appeared to perform well for the range of
conditions covered by the experiments.

21

1.11.2 Numerical models
Since experiments are sometimes very costly and time-consuming, application of Computational
fluid dynamics (CFD) models has become greatly popular among many hydraulic researchers.
Computational fluid dynamics (CFD) can be defined as a branch of fluid mechanics that uses
numerical methods and algorithms to solve and investigate problems involving fluid flows. The
term “CFD model” is commonly used to refer to a high-order numerical model capable of solving
complex flow situations with relatively few simplifications such as three-dimensional, multi-fluid,
compressible. (Toombes & Chanson, 2011). Not only CFD models can save time and money but
also, they are free of scaling effect and can be used for various types of geometry and hydraulic
conditions of a specific hydraulic problem, in this case, it is unnecessary to set up an entirely new
experimental setup. Besides, usage of modern laboratorial equipment is very costly and there
would be always experimental errors in the system which sometime cannot be simply neglected.
That’s why most CFD numerical models have been developed along with laboratory models and
their results have been compared with each other in order to verify the validity, reliability and
accuracy of them. In the case of numerical modelling of scour around bridge pier, most CFD
numerical models have not been very accurate and precise due to extremely complex 3D flow field
around bridge piers as well as lack of an accurate sediment transport equations in them. It should
be mentioned that the application of the sediment transport equation is to predict the complex
process of scouring around bridge piers. That is why many hydraulic researchers have devoted
their investigations to develop sediment transport equation (e.g. Wu et al., 2000a; Olsen, 1998;
Feurich & Olsen, 2011; Zhu et al, 2012). Regardless of deficiency of numerical model in an
accurate prediction of scour pattern around bridge piers, in this section, some of the most
significant studies on scour around bridge pier will be presented. Fukuoka et al. (1994) developed

22

a three-dimensional (3D) numerical simulation model for the local scour around a bridge pier.
Their study demonstrated that the developed numerical model can accurately obtain solutions that
are in good agreement with the experimental results of the local scour from the large-scale
hydraulic model. Richardson & Panchang (1998) used a fully 3D hydrodynamic model to simulate
the flow occurring at the base of a cylindrical bridge pier within a scour hole. The results of the
numerical simulation were also compared with laboratory observations by Melville and Raudkivi
(1977). Relatively good agreements were attained between these studies quantitatively and
qualitatively. It was concluded that the discrepancies between the results of the two studies might
be due to the parameters chosen in the numerical model. Besides, numerical results for bridge
scour were also compared to empirical equations. Young et al. (1998) developed a numerical
model for clear-water abutment scour depth along with an independent 3D finite element model.
In their study, the predicted scour depths were in good agreement with the predicted results from
the finite element model. They also concluded, from a comparative study, that the HEC-18
(Federal Highway Administration (1993) prediction overestimates measurement by 22%.
Salaheldin et al. (2004) inspected the performance of several turbulence models (the standard, the
RNG, the realizable k-ε model and RSM model) in simulating three-dimensional flow around
bridge piers by using FLUENT. The results specified that despite the overestimation of near bed
velocity field, standard k-ε and RNG k-ε models are able to simulate 3D-flow around the bridge
piers accurately.
1.11.3 Hydrodynamic model
Numerical model of turbulent flow is one of the most complicated fields in hydraulic engineering.
To simulate a wide variety of hydrodynamic problems, several commercially CFD models are
most common and available for the numerical simulation, such as FLUENT and FLOW-3D. The
23

commercially available CFD package FLOW-3D is one of the most recent practical CFD model
for simulation of hydraulic models and is my first choice to be used to simulate this hydraulic
problem. FLOW-3D uses a finite-volume approach to solve the RANS equations by implementing
of the Fractional Area/Volume Obstacle Representation (FAVOR) method to define an obstacle
(FLOW-3D User’s Manual, 2000). The general governing RANS and continuity equations for an
incompressible flow, including the FAVOR variables, are given by:

(1-21)

(1-22)
where ui represents the velocities in the xi directions which are x, y, z-directions; t is time; Ai is
the fractional area open to flow in the subscript directions; VF is the volume fraction of fluid in
each cell; ρ is fluid density; p is hydrostatic pressure; gi is gravitational acceleration in the subscript
directions; and fi represents the Reynolds stresses for which a turbulence closure model is required
(Kim, D. G., 2007). To numerically solve the free surface profile over the side weir, it is important
that the free surface is accurately tracked. In FLOW-3D, the free surface is defined in terms of the
volume of fluid (VOF) function, F, which represents the volume of fraction occupied by the fluid
(FLOW-3D User’s Manual, 2000). A two-equation renormalized group theory model (RNG
model), as outlined by Yakhot & Orszag (1986) was used for turbulence closure. The RNG model
is known for an accurate description of low intensity turbulence flows and flows having strong
shear regions (Dargahi, 2010). For each cell, values of the state variables are solved at discrete
times using a staggered grid technique. The staggered grid places all dependent variables at the
center of each cell except for the velocities and the fractional areas (FLOW-3D User’s Manual,
24

2000). Velocities and fractional areas are in the center of the cell faces normal to their associated
direction. Pressures and velocities are coupled by using SOR (Successive over Relaxation) method
which is a semi- implicit method. This semi-implicit formulation of the finite difference equations
allows for an efficient solution of low speed and incompressible flow problems (Dargahi, 2010).
Over the years, many numerical investigations of the sediment transport have been published (e.g.
Wu, et al., (2000b); Olsen, (2009); Olsen & Kjellesvig, (1998); Zhu & Liu, (2012). Wu et al.
(2000b) obtained a formula for the fractional bed load transport by regression analysis in which
the effects of different sediment sizes is included. Compared to the turbulent flow, sediment
transport around bridge piers under ice cover involves much more complexity. In the local scour
hole, the bed slope is relatively steep, and this will greatly affect the bed load transport rate.
1.11.4 Turbulence models
FLOW-3D gives the user the choice of three turbulent k-ε models: The standard model as
introduced by Launder & Spalding, (1983). The Renormalization Group (RNG) model designed
by Yakhot & Orszag (1986) and the realizable model designed by Shih et al, (1995).
o

The standard k−ε: The standard k−ε model has been the most widely used two equation

models since it was introduced by Launder & Spalding, (1983). As a result, its strengths and
weaknesses are well known. According to Wilcox (1998), it is generally inaccurate for flows with
adverse pressure gradient (and therefore also for separated flows). The standard k-ε model is a
semi-empirical model based on model transport equations for the turbulence kinetic energy (k) and
its dissipation rate (ε). The model transport equation for k is derived from the exact equation, while
the model transport equation for ε is obtained using physical reasoning and bears little resemblance
to its mathematically exact counterpart. The mathematical surgery involved in closing the εequation is more far-reaching than the k equation. As a result, many of the shortcomings of the
25

standard k – ε model are due to the inaccuracy of the ε equation. The closure coefficients are found
through calibration with experimental data for fundamental turbulent shear flows such as
incompressible equilibrium flow past a flat plate. Naturally, the closures are less reliable for
complex turbulent flows and care must be taken when interpreting results. Motion equation of
viscous incompressible fluid (Navior-Stokes equation) can be written as:
u i
u
 2ui
1 p
+ u j i = fi −
+
t
x j
  xi
 x j x j

u = u i + u i

Substituting i

,

(1-23)

p = p + p  into equation (1-23), and taking time-averaging, The

Reynolds equation can be obtained as follows:


u i
u
1  p 1   u i
+ u j i = fi −
+

−  u iu j 

  xi   x j   x j
t
x j


Where

−  u iu j

(1-24)

is Reynolds stress. Standard k−ε models are employed as follows:

 u
u  u
 k 
k
k
 
 + t
 +  t  i + j  i − 
+ ui
=
 x

t
 xi  xi 
 k  xi 
 j  xi   x j

(1-25)

 t   


 
  u i u l  u i
2


+ ul
=
+
− C 2
 +
 − C 1  t 
t
 xl  xl 
    xl 
k   xl  xi   xl
k

(1-26)

 t = C

k2



(1-27)

The empirical constants of standard k−ε models can be taken according to Table 1-1.

26

Table 1-1 Empirical Constants for the standard k−ε

C

C1

C 2

k



0.09

1.44

1.92

1.0

1.3

o The RNG k-ε model: A more recent version of the k−ε model has been developed by Yakhot
& Orszag (1986). Using techniques from renormalization group theory, they developed a new
k−ε model which is known as the RNG model. The main difference between the RNG and the
standard k−ε models is in the expression for Cε2, which alters the form of the dissipation term.
The RNG model decreases dissipation in regions of high mean strain rates. This should make
the RNG more suitable for non-equilibrium flows, such as flows with adverse pressure gradients.
The empirical constants of the RNG k-ε models can be taken according to Table 1-2.
Table 1-2: Empirical Constants for the RNG k-ε model
𝐶1𝜀
𝐶2𝜀


1.42

o



1.68

0.72

k

0.72

Realizable k-ε model: The realizable k−ε model was developed by Shih, et al (1995). In

the standard k−ε model, the normal Reynolds stress u2 becomes negative (non-realizable) when
the strain rate is large. Large strain rates can also cause the Schwartz inequality for shear stresses
to be violated. To overcome these problems, the realizable k−ε model makes the eddy-viscosity
coefficient, Cν, dependent on the mean flow and turbulence parameters. The notion of variable
Cν has been suggested by many authors and is well substantiated by experimental evidence. For
example, Cν is found to be around 0.09 in the defect layer of an equilibrium boundary layer, but
only 0.05 in a strong shear flow. Of note, in the realizable model, Cν can be shown to recover
this standard value of 0.09 for simple equilibrium flows. The empirical constants of The
Realizable k-ε model can be taken according to Table 1-3.
27

Table 1-3: Empirical Constants for Realizable k-ε model
𝐶1𝜀
𝐶2


1.44



1.9

1.2

k

1.0

1.11.5. Free surface Tracking (VOF Method)
Several methods have been used to approximate free surface. A simple, but powerful method is
VOF (Hirt & Nichols, 1981). This method is proved to be more flexible and effective than other
methods for simulating complex free surface problems. Volume of Fluid (VOF) model is designed
for two or more immiscible fluids, where the position of the interface between the fluids is of
interest. In each cell of a mesh, it is usual to use only one value for each dependent variable defining
the fluid state. Therefore, using several points in a cell to define the region filled by a certain fluid
seems unnecessary. Supposing that a function F is defined in such a way whose value is unity at
any point occupied by a certain fluid and is zero otherwise. The average value of F in a cell would
then represent the fractional volume of the cell occupied by a certain fluid. Particularly, a unit
value of F would correspond to a cell full of a certain fluid, while a zero value would indicate that
the cell contained no this fluid. Cells with F values within the range of zero and one must then
contain a free surface. For air-water flow field, a single set of momentum equation is shared by air
and water, and the volume fraction of each of the fluids in each computational cell is tracked
throughout the domain. In each cell, the summation of the volume fractions of air and water is
unity. Therefore, an extra variable, the volume fraction of air or water is presented. If FW denotes
the volume fraction of water, then the volume fraction of air (Fa) can be expressed as:

Fa = 1 − Fw

(1-28)

Once the volume fraction of air and water is known at each location, the fields for all variables and
properties are shared by air and water and represent volume-averaged values. Thus, the variables
and properties in any given cell are either purely representative of water or air, or representative
28

of a mixture of them, depending upon the volume fraction values. The tracking of the interface
between air and water is accomplished by the solution of the continuity equation with the following
form:

 Fa
 Fa
+ ui
=0
t
 xi

(1-29)

The value of Fa in a cell represents the fractional volume of the cell occupied by air. In particular,
Fa=1 will correspond to a cell full of air, while Fa=0 will indicate that the cell is full of water.
Therefore, the interface information can be known according to the value of Fa. In summary, the
VOF technique can locate free surface as well as a distribution of air concentration because it
follows regions rather than surfaces.
1.12 Scour around multiple pile bridge piers
Nowadays, multiple pile bridge piers have become tremendously common in bridge design for
geotechnical and economic reasons. These types of pier not only can significantly reduce
construction costs but also are more practical and efficient (Ataie-Ashtiani & Beheshti 2006). In
this section, some of the most fundamental studies of scour around multiple pile bridge piers is
presented. Chow and Herbich’s study in 1978 did the first study introducing wave scour at pile
groups. They studied the wave scour around 3-legged pile structures, 4-legged pile structures and
6-legged pile structures. Hannah (1978) studied 2-pile tandem, 2-pile side by side, 2-pile staggered,
3-pile tandem, 4-pile square and 6-pile rectangular arrangements in steady current. It was
concluded that due to progressive protrusion of a pile cap into the flow, scour depths increase and
the pile cap very quickly becomes the dominant feature causing local scour. Salim & Jones (1996)
studied the scour around submerged and unsubmerged pile groups and presented equations for the
effect of pile spacing and angle of attack at pile groups. They observed that the scour depth
decreases as the spacing between the piles increases. Zhao and Sheppard (1998) investigated the
29

effect of flow skew angle on local scour at pile groups. Sumer and Fredsøe (1998) studied wave
scour around groups of piles with different configurations (2-pile, 3-pile including the triangular
group, and 4×4 arrangements). Ataie-Ashtiani and Beheshti 2006, did 112 experiments including
a variety of conditions including different pile group arrangements, spacing, flow rates, and
sediment grain sizes under steady clear-water scour conditions. It was concluded that the scour at
a pile group is different from that around a single pile, depending on the pile spacing and for very
small pile spacing, the pile group behaves as a single body. Besides, for the two-pile side-by-side
arrangement, the scour depth increases by as much as a factor of 1.5, while this value for the
tandem arrangement is about 1.2. Sheppard and Jones (1998) conducted experiments on complex
pier components (pile group, pile cap, and columns) and presented a superposition procedure that
combines scour depth predictions for the individual components to obtain a prediction for scour at
the composite structure. Sumer et al. (2005) described the scour geometry for pile groups with
varying pile spacing. According to them, scour around pile groups is caused by two mechanisms.
Those causing local scour at individual piles, and those causing a global scour (the general
lowering of the bed) over the entire area of the pile group. As pile spacing decreases, the scour
holes at individual piles overlap and, at the limit, merge into one large scour-hole. Mostafa (2011)
did an experimental study of scour around single pile and different configurations of pile groups
exposed to waves and currents. Four different sets of experiments were used in this study: single
pile, group of two piles with side-by-side arrangement, group of two piles with tandem
arrangement and group of three piles. It was concluded that the case of side-by-side pile
arrangement induced more scour compared to the case of tandem pile arrangement and the case of
three piles with triangular arrangement. Although a great number of studies have been done about
scour around single piers over the past decade or so, less studies have been done about scour at

30

pile groups and to the authors’ knowledge, no study is yet available investigating scour under ice
cover for pile groups.
1.13 Impact of ice on the bridge pier scouring
Many rivers become ice-covered during the winter months. Engineers and resource managers often
overlook the winter season even though most rivers in Canada and northern parts of the United
States, Europe, and Asia are annually affected by ice. The reason why the winter season is
overlooked is that all the design criteria are often centered on large open channel flow event;
however, this is a dangerous assumption because there are some ice-affected sediment processes
that are essential to consider for safe civil engineering designs (Turcotte et al., 2011). Ice-cover
presence can cause significant damage on the foundation of bridges that requires expensive repairs.
One very recent example has happened at the upstream of Melvin Price Lock and Dam where iceinduced scour was repaired at a cost more than $1,000,000 and the scour hole re-appeared within
a year of the repair (Carr & Dahl, 2017). Ice-cover presence imposes a floating solid boundary on
the upper surface of the flow which will lead to increase in channel flow resistance and causes
redistribution of velocity gradient over its depth (Ashton, 1986; Smith & Ettema, 1995; Sui et al.,
2010). Besides, ice-cover causes changes in the hydraulic characteristics of flow such as bed shear
stress distribution and sediment transport rate (Lau and Krishnappan, 1985). Although the problem
of scour around bridge pier has been broadly studied and documented by several investigators
(Chabert & Engeldinger, 1956; Laursen and Toch 1956; Shen et. al., 1969; Melville, 1975; Hjorth
1975; Melville & Raudkivi, 1977; Ettema, 1980; Baker, 1981; Jain, 1981; Raudkivi & Ettema,
1983; Melville & Sutherland, 1988; Kothyari, 1989; Dargahi, 1990; Yanmaz & Altimbilek, 1991;
HEC-18 (1991), Dey, 1997; Ahmed and Rajaratnam 1998; Graf & Istiarto, 2002), this issue has
not been properly scrutinized under ice-covered flow condition. The lesser number of studies on
31

the scour around bridge pier under ice-covered flow condition is due to the inherent difficulty in
collecting field data while ice is present and complications in lab measurements representing
differing scales and temperature effects (Moore & Landrigan, 1999). Some of the most significant
studies on scour under ice cover will be presented in the following section. Krishnappan (1984)
did experiments to test the validity of a turbulent flow model (k-ε model), first introduced by Lau
& Krishnappan, (1981). Thirty-two flows were tested all together. Seventeen of them were freesurface flows, and the remaining fifteen were flows with top cover. For flows with top cover, three
types of covers were tested which were natural ice cover, plywood cover and plywood covered
with "Mactac." The natural ice cover was formed by reducing the temperature in the cold room to
-10° C and maintaining it at that value overnight. Their method uses the k-ε turbulence model to
numerically determine velocity distribution and suspended-sediment concentration. The study
indicates that this model can predict the average flow properties in such flows with reasonable
accuracy and it is recommended that this turbulent model can be used for practical applications
when predicting time-averaged flow properties in flows with and without top cover. It is based on
the assumptions that bed-load transport can be estimated by treating an ice-covered flow as a twolayer flow divided at the elevation of the velocity maximum. However, their findings showed a
great deal of limitation for dune regime. Hereby, flume experiments done by Smith and Ettema
(1997) revealed that the two-layer assumption is especially insufficient for characterizing flow
resistance and sediment transport in the dune regime, because bedform geometry and the
macroscale turbulence structures within an ice-covered flow increase with the full depth of flow.
This finding was not considered in Krishnappan, (1984) because their flume experiments were
done with a bed in the ripple regime. It should be mentioned that ripple geometry principally
increases with bed sediment size rather than flow depth and is insensitive to ice-cover presence.

32

Lau & Krishnappan (1985) developed a method to calculate sediment transport in ice-covered
flows. This study revealed very important characteristics of flow under ice-cover conditions. It
was concluded that the presence of ice is greatly influential on the dynamics of flow and sediment
transport in a river. The ice cover almost doubles the wetted perimeter leading to increase in the
total boundary shear and flow depth and a decrease in the average velocity. However, the bed shear
stress and the eddy viscosity are both smaller than the corresponding free-surface flow values. It
was also concluded that the reduction in the bed shear stress results in significant changes on
sediment transport and lessens the ability of the flow to entrain and suspend sediment. Since, the
sediment transport rate is very sensitive to changes in bed shear stress, decrease in sediment
concentration and flow velocity noticeably reduces the suspended sediment transport. Another
remarkable study on local scour around bridge piers was done by Zabilansky (1996). In his
research, he developed an instrumentation package for measuring and monitoring ice forces on a
bridge pier and for monitoring the development of bed scour due to ice and open-water floods. It
was concluded that the faster velocity resulted in more aggressive bed scour and the bulk of the
scour occurred in the initial stages of breakup while the ice sheet was still intact. Once the ice sheet
broke up and the ice was free floating, the scour activity died down. Zabilansky & White (2005)
investigated the impact of ice cover on scour in narrow rivers. It was concluded that when
discharge increases above the freeze-up datum, the pressurized flow condition, combined with the
rough underside of the ice, will cause the maximum velocity in the flow to both increase and shift
closer to the bed. The result will be increased shear stresses on the bed which results in live-bed
scour. Moreover, the increase in shear stress on the bed due to the ice-cover accelerates the scour
around bridge piers. Ackermann et al. (2002) performed a laboratory investigation on the effect of
ice cover on local scour around circular bridge under rough, smooth and open channel condition

33

for a uniform sand type with D50= 31.8 mm. It was found that covered flows gave larger scour
depths for all flow velocities, although the scour development followed a similar pattern for both
covered and free surface flow conditions. Hains & Zabilansky (2004) carried out twenty test using
mean flow velocity in the clear water scour range under open water, floating and fixed ice-cover.
Styrofoam was used to simulate both smooth and rough surface. It was found that under clearwater scour, the equilibrium scour depths for the fixed and floating covers were similar, but up to
21% higher than those found for open water. Ettema et al. (2000) proposed a method for estimating
rates of sediment transport in ice-covered alluvial channels. The method extends existing, openwater procedures for estimating rates of sediment transport to conditions of ice-covered flow. This
study uses laboratory flume data to enable sediment transport in covered flow to be estimated using
procedures for estimating rates of sediment transport in open-water flow. In other words, the
proposed method smooths the extension of suitable open-water procedures to ice-covered flow
conditions. Based on a series of experiments under both ice-covered and free surface conditions,
Wang et al. (2008) discusses the impact of flow velocity and critical shear Reynolds number on
incipient motion of bed material. It was found that the deeper the flow depth under ice cover, the
higher the flow velocity needed for the incipient motion of bed material. Besides, the location of
the maximum velocity moves to the bed with increase in the ratio of undercover resistance
coefficient to the resistant coefficient of channel bed (ni/nb). Therefore, since near-bed velocity is
higher under ice-covered conditions, a higher shear stress is exerted on the river bed. A series of
experiments for the incipient motion of frazil particles under ice cover have been carried out by
Sui et al. (2010) in laboratory under different flow and boundary conditions. To investigate the
impacts of ice cover on the incipient motion of frazil particles, foam panels were used to simulate
smooth ice cover. To study the impact of rough ice cover on the incipient motion of frazil particles,

34

the foam panels were modified by adding small wood pieces to create rough underside surface.
Measurements on flow velocities across the measuring cross-section at different water depths have
been conducted to compare the velocity profile under different flow and boundary conditions. It
was found that less critical dimensionless shear stress for incipient motion was needed if the
sediment size is smaller. Moreover, the velocity profile under ice cover is entirely different
compare to the velocity profile in open channels because the presence of an ice cover causes the
velocity profile to be shifted towards the smoother boundary (channel bed) and adding up to the
flow resistance. The most recent study on scour around bridge piers was done by Hirshfield (2015).
In her dissertation, 54 flume experiments were completed investigating scour around a single pier
under open, smooth and rough ice cover conditions. She used two different circular piers with
diameters of 11 cm and 22 cm in non-uniform sediments under rough, smooth and open channel
conditions. It was concluded that scour depth is greater under rough ice cover compared to open
channel conditions for 60 percent of experiments and it is greater under smooth ice cover compared
to open channel conditions for 53 percent of experiments and the smallest grain size yielded the
larger pier depth under all channel cover and vice versa.
1.14 Hydraulic characteristics of ice scour
The impact of ice cover on the annual sediment transport budget in cold regions can be significant
(Lawson et al., 1986). As it was mentioned earlier, due presence of ice on the water surface and
limitation in its measurement, the impact of ice cover on the annual sediment transport is often
neglected in sediment budgets (Knack & Shen, 2015). The presence of ice has been found to
increase local clear-water scour depth at bridge piers by 10%–35% (Hains & Zabilansky, 2004;
Ackermann et al., 2002). For bridge abutments, flume experiments revealed that with larger ice
cover roughness, scour increased (Wu et al., 2014). For example, a bridge at White River Junction
35

whose foundation collapsed was found to have weakened because of recurring scour and
redeposition of non-structural fill (Zabilansky & White, 2005). The velocity profile under icecovered condition, is totally different compared to open channel flow. An ice cover changes the
velocity profile in a river, with the ice acting as a flow boundary on the water (Sui et al., 2010).
Under ice-covered condition, the maximum velocity occurs between the bed and the bottom of the
ice cover and is dependent on the relative roughness of the two boundaries. The velocity drops to
zero at each boundary due to the no-slip boundary condition, resulting in a parabola-shaped profile
(Muste et al. 2000; Zabilansky et al., 2006). Figure 1-11 shows Velocity profile for open water
and floating smooth and rough covers from experiments.

Figure 1-11: Velocity profile for open water and floating smooth and rough covers from experiments
(Zabilansky et al., 2006)

1.15 Sediment transport under ice-covered flow
The ratio between suspended load and bed load, vertical distribution of suspended sediment and
vertical diffusivity is affected by the presence of ice for flows under ice-covered condition
(Prowse, 1993). It should be noted that the impact of ice on sediment transport in a stream is
typically most significant during ice formation and breakup (Ettema & Kempema 2012). For

36

example, during breakup on the Liard, Saint John, and Lower Nelson Rivers in Canada, it was
observed that suspended sediment loads around 10 times that of open-water or ice-covered
conditions (Prowse 1993). The magnitude of any sediment transport will depend on the impact of
ice on the shear stress, especially if it exceeds the critical shear stress of incipient motion of
sediment. Furthermore, under conditions where erosion occurs, the magnitude of erosion is a
function of water depth, ice thickness, and ice roughness (Ettema & Kempema, 2012). Besides,
Variation in thickness through an ice jam can lead to variations in sediment transport capacity and
can affect general scour and deposition (Beltaos et al., 2007). Ice cover can either increase or
decrease bed load and suspended sediment transport depending on the type of ice cover acting on
water surface (Prowse 2001; Ettema & Kempema 2012). If an ice cover is floating or a jam is
restricting flow, the drop-in flow can reduce the transport of both suspended and bed-load sediment
which leads to deposition (Ettema &Kempema 2012). However, if an ice is attached and is not
floating type, the restraint on the cross-sectional area causes increased velocity and sediment
transport capacity (Zabilansky, 1996; Hirshfield & Sui 2011). The rate of sediment transport for
these two cases will be discussed more thoroughly in this section. In the case of smooth floating
ice, the wetted perimeter increases causing a decrease in velocity and lower bed shear stress that,
in turn, result in a loss in sediment transport capacity (Ettema, 2002; Turcotte et al., 2011).
However, the magnitude of the loss in sediment transport capacity and the possibility of general
or local scour depends on the roughness of ice, change in resistance near melt times, irregularity
in thickness, depth of flow beneath ice that is jammed, whether the cover is attached to the shore,
and the presence of structures (Wang et al. 2008). Muste et al. (2000) concluded that the presence
of a rough cover in a flume reduced overall rates of sediment transport but amplified the proportion
of sediment moving in suspension. In the case of an attached cover, the restraint on the cross-

37

sectional area causes increased velocity and sediment transport capacity (Zabilansky 1996;
Hirshfield and Sui 2011). As it was mentioned earlier, the presence of ice cover also tends to shift
the velocity maximum closer to the bed, increasing erosion (Zabilansky et al. 2006). Rougher ice
can push the maximum velocity even further towards the bed to reduce and loose energy, causing
scour (Hains & Zabilansky, 2004). Therefore, a lower average velocity threshold is needed in an
ice-covered flow to reach critical shear stress for bed deformation compared to an open-water flow
(Beltaos et al., 2007). Increased turbulence near the bed caused by an ice cover as well as increase
in velocity profiles magnifies around bridge piers, abutments, and other hydraulic structures
causing a more intensified localized scour (Beltaos et al. 2007). An increase in velocity, and thus
erosion, is more intense at thickened parts of ice covers (Mercer & Cooper, 1977). However,
increased depth can lower the probability of erosion, as the maximum velocity will be farther away
from the bed (Hirshfield & Sui, 2011). Larger ice roughness also tends to push the maximum
velocity further to the bed, increasing the gradient between the maximum and minimum velocities
and increasing scour (Hirshfield & Sui, 2011). Increased ice roughness can occur due to dynamic
growth in steep, narrow rivers or due to waves that can occur as ice covers remain in place through
the winter season (Zabilansky et al., 2006).
1.16 Transverse flow distributions under ice-covered flow
In terms of transverse flow distributions and velocities of secondary currents, ice cover can impact
flows in an existing thalweg, altering the position of the thalweg and changing the morphology of
the stream which in an extreme case will lead to bank and bed erosion (Beltaos et al., 2007). Ettema
& Daly (2004) stated that thalweg shifts can accelerate localized erosion and develop scour holes
which is possible to make permanent bed deformations. For example, on the Missouri River in
Culbertson, Montana, a thalweg shift from a primary flow channel to a secondary channel with
38

different roughness resulted in erosion of the bed and banks of the secondary channel (Zabilansky
et al. 2006). Shifting in the position of thalweg may also reduce velocities and provide locations
for frazil deposition (Ettema, 2002). Sui et al., (2006) stated that this frazil deposition decreases
the cross-sectional area and increases velocity and subsequent scour. Figure 1-12 compares
velocity and suspended sediment concentration distributions between covered flow and free
surface flow (Lau et al, 1985)

Figure 1-12: Comparison of velocity and suspended sediment concentration distributions between
covered flow and free surface flow (Lau & Krishnappan)

1.17 Research objectives
As it was mentioned earlier, scour around bridge pier under ice cover conditions needs to be
scrutinized more in details. My study aims at contributing to the understanding of local scour under
39

open and ice-covered flow conditions around two side-by-side bridge piers by incorporating four
different sets of circular bridge piers with a fixed distance from each other. Besides, in order to
consider the non-uniformity of sediment, three different types of bed materials are used. The main
objectives of this study are listed as follows.
1.17.1 Objective one
The hydraulic characteristics of velocity distribution around bridge piers under ice cover
The velocity distribution under ice cover is totally different to that of an open channel. Under icecovered flow condition, a new boundary is added to the surface of water which causes the velocity
to drop to zero at ice cover and the channel bed due to the no-slip boundary condition, resulting in
a parabola-shaped profile (Muste et al. 2000; Prowse 2001; Ettema and Daly 2004; Zabilansky et
al. 2006). Besides, under ice-covered condition, the maximum velocity occurs between the bed
and the bottom of the ice cover and is dependent on the relative roughness of ice cover roughness
and the channel bed roughness. In this study, the velocity distribution of flow under ice-covered
and open channel flow conditions will be measured by means of SonTek 16 MHz Acoustic
Doppler Velocimeter (ADV). The main objective is to analyze the velocity profile distribution
between open channel and ice-covered flow condition
1.17.2 Objective two
The impact of flow depth and approaching velocity on scour around bridge piers under icecovered and open-channel flow condition
The well-known dimensionless number which includes approach velocity and flow depth and is
one of the most influential dimensionless parameters in prediction of scour depth is Froude number
(Froehlich, 1989). Froude number, Fr, is a dimensionless value that describes different flow
40

regimes of open channel flow. It can be interpreted as the ratio of water velocity to wave velocity.
At critical flow (Fr=1) water velocity equals wave velocity so any disturbance to the surface will
remain stationary. In subcritical flow (Fr<1) the flow is controlled from a downstream point and
information is transmitted upstream. This condition leads to backwater effects. Supercritical flow
(Fr>1) is controlled upstream and disturbances are transmitted downstream (Douglas et al 1995).
Another important dimensionless parameter which considers both the mean particle size of the
sediments (D50) and inertia force is densimetric Froude number (Khwairakpam et al, 2012). In the
proposed experimental study, different combinations of flow velocity and flow depth are
incorporated to make a wide range of Froude number and densimetric Froude number in subcritical
flow regime. The ultimate purpose of this objective is to measure the real-time and maximum scour
depth under different flow conditions in terms of velocity and water depth for ice-covered and
open channel flow and interpret their possible difference which can lead to derivation of useful
scour predictive formula.
1.17.3 Objective three
The impact of non-uniformity of sediment on local scour around bridge piers under icecovered and open-channel flow condition
Most of the existing researches on bridge piers use uniform sediment which is not an appropriate
representative of natural river system and can result in excessively conservative design values for
scour in low risk or non-critical hydrologic conditions. In the present study, flume experiments are
completely investigating local scour around two adjacent circular bridge piers with non-uniform
bed. To represent non-uniform sediment condition, three different bed materials with average
particle size (D50) of 0.47 mm, 0.50 mm, 0.58 mm are used. The purpose of using non-uniform

41

sediment bed is to represent a more actual prototype of a natural river as well as analyzing the
scour depths between these three different sediments.
1.17.4 Objective four
Difference between scour patterns of two side-by-side bridge piers with a single bridge pier
As it was discussed earlier, multiple pile bridge piers have become greatly common in bridge
design for geotechnical and economic reasons. Scour around pile groups is caused by 2
mechanisms: Those causing local scour at individual piles, and those causing a global scour (the
general lowering of the bed) over the entire area of the pile group (Sumer et al, 2005). To the
author’s knowledge, there has not been a comprehensive study on scour for two side-by-side bridge
piers under ice-covered flow condition and most of the studies have been done for single bridge.
The main objective of this proposal is performing a more comprehensive study on scour around
two side-by-side bridge piers by incorporating four different sets of circular bridge piers with a
fixed distance from each other under open, rough and smooth ice-covered flow condition. Totally,
3 sets of flume experiments will be carried out in a non-uniform bed and suitable mathematical
models regarding scour estimation of bridge piers for open and ice-covered flow condition will be
developed.
1.17.5 Objective five
Impacts of two different types of ice cover on local scour under ice cover
As it was mentioned earlier, the presence of ice cover causes fundamental changes in the properties
of flow. Since ice cover is the most important parameter in this study, it has been decided to use
two different types of ice cover to represent impact of ice-roughness on local scour around bridge
piers which are rough and smooth ice covers. In order to simulate ice cover, 13 panels of Styrofoam
42

with dimensions of 1.2 m × 2.4 m (4×8 foot) will be used to cover nearly the entire surface of
flume. Styrofoam density is 0.026 gr/cm3 and it will get floatable during the experiments when the
water flows beneath it. The smooth ice cover is the even surface of the original Styrofoam panels
while the rough ice cover is made by attaching small Styrofoam cubes to the bottom of the smooth
cover. The dimensions of Styrofoam cubes are 25 mm×25 mm× 25 mm and are spaced 35 mm
apart. The main objective of using two different types of ice cover is to more realistically examine
the impact of them on local scour depth around bridge piers as well as proposing a more general
scour predictive formula which will have a wider application in bridge engineering design.
1.17.6 Objective six
Dimensional analysis of variables impacting the local scour around bridge piers
Scour at piers is influenced by various parameters including duration of scour hole equilibrium
time; pier characteristics such as pier size, pier shape and angle of attack; sediment characteristics
such as sediments density and sediment cohesion, approaching flow characteristics such as flow
depth and flow velocity, properties of fluid such as fluid density and fluid viscosity, flume
characteristics such as flume width, flume slope and flume roughness. The relationship showing
the influence of various parameters on the maximum scour depths at piers can be given in
functional form as follows:
ymax = f (Ks, Kɵ C, y0, U, W, D, ρw, ρS, g, µ, D50, S0, ni, nb, T0, G)

(1-30)

In which ymax is maximum scour depth; f is function symbol; Ks is simplified pier shape coefficient
which is one for circular bridge piers (Melville and Sutherland 1998); Kɵ is factor for angles
between approach flow and pier axial; C is cohesion of the sediment particles; y0 is approaching
flow depth; U is approaching velocity; W is channel width; D is pier diameter; ρ w is water density;
43

ρs is sand density; g is acceleration due to gravity; µ is dynamic viscosity of fluid; D 50 is particle
mean diameter; S0 is the longitudinal channel slope; ni and nb are the roughness of the ice cover
and the channel bed and T0 is time needed for the scour depth to reach to the equilibrium condition.
Hereby, the following dimensionless parameters are effective in scour under the present
experimental conditions:
ymax/y0= f(U/(σgD50)0.5, U/(gy0) 0.5, ni/nb, D50/W, D50/y0, y0/D, y0/W, D/D50, W/D, ρs/ρw, G/D)

(1-31)

In order to simplify the above equation and select the most dominant parameters to develop an
equation for prediction of scour under open channel and ice-covered flow condition, linear
regression and sensitivity analysis for each of the dimensionless parameters will be developed and
corresponding statistical analysis will be done
1.17.7 Objective seven
CFD simulation of local scour around bridge piers under ice cover
Due to the uncertainties involved in the physical study, such as idealized flow condition, uniform
sediments, simplified geometries, formulae derived from this approach are appeared to
overestimate the scour depth obtained from field measurements. Physical experiments can
overcome some of the shortcomings, but they are usually time-consuming and highly cost in model
construction and experimentation. In viewing these aspects, recently, the computer-based
numerical simulation becomes an alternative and promising way to deal with local scour.
Computational Fluid Dynamics (CFD) has emerged as a powerful hydraulic engineering design
and analysis tool along with experimental study. Due to the complex 3D flow field and limitations
of computer capabilities, numerical studies about the local scour around bridge piers or piers are
not well addressed as experimental studies. In the present research, hydraulic model will be
44

employed to simulate the flow field around a bridge pier under ice cover and sediment model will
be used to calculate the variation of channel bed elevation. Numerical results will also be compared
with original experimental data.
1.18 The innovations of the research
This research is associated with local scour around four different set of side-by-side bridge piers
under different flow conditions in term of approaching velocity and flow depths. As the proposed
experimental focuses on the local scour around bridge piers under ice cover conditions. The study
has the following innovations.
1. The entire process of local scour around bridge piers under ice covered conditions will be carried
out by a series of large-scale flume experiments;
2. The local scour process under different flow conditions, namely, open channel, smooth, rough
cover will be compared;
3. The local scour process will be performed under three different bed materials with average
particle size (D50) of 0.47 mm, 0.50 mm, 0.58 mm are used.
4. Through Dimensional Analysis, empirical formulae to estimate the scour depth under ice covers
will be derived;
5. Simulation of flow around bridge pier under ice-covered condition

45

2. EXPERIMENTAL SETUP
Experiments are carried out at the Quesnel River Research Centre, Likely, BC, Canada in a largescale flume. The flume is 40 m long, 2 m wide and 1.3m deep. The longitudinal slope of the flume
bottom is 0.2 percent. Three supply valves and two different tailgates with the height of 100 mm
and 200 mm are used to make different range of flow conditions in term of velocity and flow depth.
Inlet discharge is supplied by means of three pumps under two tailgates and one tailgate
configuration. The highest discharge is when all the pumps are simultaneously in action and it is
exclusively for two-tailgate configuration in order to avoid live-bed scour. Figure 2-1 shows two
pumps in action.

Figure 2-1: Two pumps in action

A holding tank with a volume of nearly 90 m3 is located at the upstream of the flume to keep a
constant head in the experimental zone. It should be noted that the holding tank is 40 m in length,
2 m in width and 1.3 m in depth. At the end of the holding tank, water overflows from a rectangular
weir to the flume. In order to protect the flume from weather elements and keep running
experiments safe, the whole length of the flume (40 m) is covered with plastic cover. Two sand
boxes with the depth of 0.30 m are filled with non-uniform sediment with average particle size
46

(D50) of 0.47 mm, 0.50 mm, 0.58 mm. The first sand box is 5.6 m in length and the second sand
box is 5.8 m in length. The distance between the sand boxes is 10.2 m. Four different pairs of
bridge piers with diameter of 60 mm, 90 mm, 110 mm and 170 mm are used. Bridge piers are
constructed from PVC plumbing pipe and are circular in shape. Figure 2-2 shows measuring points
around the bridge piers.

Figure 2–2: Measuring points around the bridge piers

A transparent viewing window is constructed inside each of the sand boxes which makes it possible
to observe the process of scouring around bridge piers through it. A rectangular weir is used in the
middle of the flume at 40 m in order to create a constant head. Since the flow of water is turbulent
while entering the flume, a flow diffuser is placed at the downstream of the rectangular to dissipate
the turbulence in the flow of water. A pair of bridge piers are placed inside both sand boxes with
the constant distance of 0.50 m from each other and are fixed to the bottom of the flume. Since
there is one pair of bridge piers in each of the sand boxes, two experiments are being done
47

simultaneously in each experimental run. The left bride piers are placed at 0.25 m and the right
bridge piers are placed at 0.25 m from the center line of the flume in each of the sand boxes. Figure
2-3 and Figure 2-4 show the downstream view of the bridge piers in both sand boxes while the
experiment is running.

Figure 2-3: Downstream view of the bridge piers
with rough ice cover on

Figure 2-4: Downstream view of the bridge piers
with rough ice cover on and larger tail gate in action

The first configuration consisted of 60 mm bridge pier in the first sand box and 90 mm bridge pier
in the second sand box and the second configuration consisted of 110 mm bridge pier in the first
sand box and 170 mm bridge pier in the second sand box. The water depth in the flume is adjusted
by the position of the tailgates. Since the sediment needs to be restored, after each sand box, a
sediment trap will be installed to collect sediment during and after experiments. In front of the first
sand box, a 2D flow meter by Sontek Incorporated was installed to measure the approaching flow
velocity, water depth and mainly the inflow discharge during the experiment (Figure 2-5).

48

Figure 2-5: The SonTek-IQ used to collect flow (area-velocity) and volume data

A staff gauge is also installed in the middle of each sand box to manually verify water depth. The
scour hole velocity field is measured by using a 10-Mhz Acoustic Droppler Velocimeter (ADV)
(Figure 2-6).

Figure 2-6: 10-Mhz Acoustic Droppler Velocimeter (ADV) in practice used to measure velocity field
around bridge piers

108 Experiments (36 experiment for each type of the sand) will be conducted under open channel,
smooth ice and rough ice conditions. In order to simulate ice cover, 13 panels of Styrofoam with
dimensions of 1.2 m × 2.4 m (4×8 foot) are used to cover nearly the entire surface of flume.
Styrofoam density was 0.026 gr/cm3 and it will get floatable during the experiments when the
49

water flows beneath it. In the present study, two types of ice cover are used, namely smooth cover
and rough cover. The smooth ice cover is the even surface of the original Styrofoam panels while
the rough ice cover is made by attaching small Styrofoam cubes to the bottom of the smooth cover.
The dimensions of Styrofoam cubes are 25 mm×25 mm× 25 mm and are spaced 35 mm. In order
to avoid the turbulence effect of incoming flow on the Styrofoam especially at high discharges,
the position of first Styrofoam is decided to start from the middle of the flow diffuser section. In
this case, the flow will get less turbulent while reaching the first Styrofoam. It should be mentioned
that at the beginning of each experiment, the flume is slowly filled to avoid initial scouring. The
durations of the experimental runs until scour hole reaches to equilibrium condition is chosen 24
h which is based on the previous experiment on single bridge pier (Hirshfield, 2015) and
experiment on scour around bridge abutment (Wu et al, 2015) and my own observation. In
addition, it was observed that after a period of 6 hours, the material which was transported into the
scour hole was nearly at the same rate at which it was transported out and there was not any
significant difference (less than 1.5 mm) in scour depth. Therefore, the maximum scour depths
obtained after 24 h are adopted as the equilibrium scour depths. After 24h, the flume is gradually
drained. The scour depth is manually measured along the outside lines of the circular bride piers.
Figure 2-7 shows the experimental setup.

50

Figure 2-7: Experimental setup

51

2.1 Measurement apparatus
As it was mentioned before, measurement of components of velocity in x, y and z directions can be
very useful in determination of shear velocity, turbulent kinetic energy and flow field characteristics
around bridge piers. Recently, Acoustic Doppler Velocimeter (ADV) has been widely used to
determine the flow field around in turbulent flow (Zhang et al. 2005). (ADV) is designed to record
instantaneous velocity components at a single-point with such a relatively high frequency which can
be consequently used to determine the turbulent properties and the bed shear stress (Chanson, 2008).
In this study, to measure the flow field in the scour hole around the bridge piers under ice cover, a
SonTek 10MHz Acoustic Doppler Velocimeter (ADV) which is known for its accuracy, portability,
reliability and ease of operation is used. The ADV is a high-precision instrument used to measure 3D
water velocity in a wide range of environments including laboratories, rivers, estuaries, and the ocean
that can be used to compute the mean velocity, Reynolds stresses, shear stresses, turbulent kinetic
energy and other hydraulic parameters (Cea & Pena, 2007). The ADV measures the velocity in the
sampling volume located at the intersection of the transmitted and received acoustic beam as shown
in Figure 2-8. As it is clear in the figure, the probe head includes one transmitter and three receivers.
The 3D down-looking ADV receiver used in this study is focused in a sampling volume located 0. 10
m below the transmitter. An ADV system records simultaneously nine values with each sample: three
velocity components, three signal strength values and three correlation values. Signal strengths and
correlations are used primarily to determine the quality and accuracy of the velocity data. One of the
most important issues regarding the ADV measurement is noise from ADV. The existence of Doppler
noise from the ADV always can occur when measuring the velocity. Noise also occurs when a high
level of turbulence exists at the measuring location. Hence, the examination and filtering of the signal
is needed before analyzing the mean point velocity and turbulent kinetic energy (Nikora & Goring,

52

1998). In other words, "raw" ADV velocity data are not "true" turbulent velocities and they should
never be used without adequate post-processing (Nikora & Goring, 1998). One method of dealing
with this noise is to filter the data according to the value of a correlation coefficient that is a measure
of the coherence of the return signals from two successive acoustic pulses (Goring & Nikora, 2002).
In this research, scour hole velocity and approach velocity will be analyzed and filtered using the
WinADV software supplied by Sontek. Velocity data will be filtered for correlations values above
70 (SonTek, 1997).

Figure 2-8: 3D-down looking ADV probe

(http://www.sontek.com/productsdetail.php?Argonaut-ADV-6)

53

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Chapter 3

RESULTS AND DISCUSSION

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3.1 Local scour around two side-by-side cylindrical bridge piers under ice-covered conditions
Scour is the local lowering of the stream bed elevation which occurs around a structure constructed
in flowing water, such as bridge piers, abutments, spur dikes, jetties, and breakwaters (Melville &
Coleman, 2000). As noted by Briaud et al. (2006), 1502 bridges collapsed due to bridge scour between
1966 and 2005. Wardhana and Hadipriono (2003) studied 500 cases of bridge structure failures in the
United States between 1989 and 2000 and stated that the most common causes of bridge failures were
floods and scour. The scour around bridge infrastructure is extremely difficult to track due to the
complexity of the flow structure around this infrastructure. An accurate prediction of scour depth
around bridge infrastructure will not only prevent bridge failures, which are the consequence of
underestimation of scour depth, but also will efficiently reduce unnecessary, over-estimated
construction cost. Many hydraulic researchers have done experiments to investigate the local scour
around bridge piers and develop empirical equations to estimate the maximum scour depth (Ettema
et al., 2011; Melville, 1997; Melville & Sutherland, 1988; Richardson et al., 2001; Sheppard et al.,
2013; Williams et al., 2013). However, due to different laboratory conditions and limitations on data
collection, specifically in small-scale laboratory flumes, most of the empirical equations for
determining scour depth have a great deal of uncertainty and substantial limitations. Moreover,
bridges constructed in rivers in cold regions are exposed to the impact of ice in addition to the local
scour around bridge piers. The influence of ice cover on a channel involves in complex interactions
among the ice cover, fluid flow, and channel geometry. This complex interaction can have a dramatic
effect on the sediment transport process (Hains et al., 2004). The formation of a stable ice cover in
natural rivers effectively doubles the wetted perimeter compared to open channel conditions and
causes the maximum velocity to be lowered towards the channel bed (Sui et al., 2010; Wang et al.,
2008). Zabilansky and White (2005) investigated the impact of ice cover on scour in narrow rivers.

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It was found that when discharge increases above the freeze-up datum, the pressurized flow condition,
combined with the rough underside of the ice, will cause the maximum velocity in the flow to increase
and shift closer to the bed. Using uniform sand as the bed material, Ackermann et al. (2002) reported
that covered flow results in larger scour depths compared to open channel flow, although the scour
development follows a similar pattern for both covered and open channel flow conditions. Sui et al.
(2008, 2009) studied the impacts of ice cover on local scour caused by square jets compared to those
under open channel flow conditions. Wu et al. (2015a) studied the effect of relative bed coarseness,
flow shallowness, and pier Froude number on local scour around a bridge pier and reported that the
scour depth under covered conditions is larger compared to that under open channel flow conditions.
Wu et al. (2014b) investigated scour morphology around a bridge abutment under ice cover. It was
found that, at different locations around the abutment, the sediment sorting process under ice cover
was more obvious. Wu et al. (2015b) studied the impact of ice cover on local scour around bridge
abutments. Hirshfield (2015) did 54 flume experiments to investigate local scour around a single pier
under open channel, smooth covered and rough covered flow conditions. It was concluded that the
scour depth under rough cover is 60% greater compared to that under open channel conditions for 60
percent of the experiments; and the scour depth under smooth cover is 53% greater than that under
open channel conditions. Multiple pile bridge piers have become more common in recent years in
bridge design for geotechnical and economic reasons. These types of pier not only can significantly
reduce construction costs but also are more practical and efficient (Ataie-Ashtiani & Beheshti, 2006).
However, the mechanisms of the scouring process around pile groups are much more complex.
According to Hannah (1978), if the pier spacing ratio is 0.25, the maximum scour depth around sideby-side piers is about 50% more than that around a single pier and for G/D < 0.25, the two side-byside piers can be assumed to act as a single bridge pier (where G represents the bridge spacing distance

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and D represents the diameter of the bridge pier). Ataie-Ashtiani and Beheshti (2006) investigated
local scour for different pier arrangements and with different bridge pier spacings. It was found that
with an increase in the space between the two piers, scour depth is reduced. To the authors’
knowledge, all reported research regarding local scour around pile groups has been done under open
channel flow conditions (Ataie-Ashtiani & Beheshti, 2013; Hannah, 1978; Melville & Coleman,
2000). As pointed out by Ettema et al. (2011), the impact of ice cover on bridge pier scour is still
unknown and needs further investigation. In this regard, a more in-depth study has been done here to
investigate the impact of ice cover on local scour around four pairs of side-by-side bridge piers under
different sediment compositions and flow conditions.
3.1.1. Methodology
Experiments were done in a large-scale flume at the Quesnel River Research Centre of the University
of Northern British Columbia. The flume was 38.2 m long, 2 m wide and 1.3 m deep. Since the
experimental flume was long, in order to generate a higher velocity as well as to avoid large amount
of energy dissipation for the second sand box which would ultimately lead to smaller scour depth, the
relatively steep slope of 0.2% was used. Figure 3.1 shows a plan view and a side view of the
experimental flume. A holding tank with a volume of 90 m3 was located at the upstream end of the
flume to maintain a constant discharge during the experimental runs. To create different velocities,
three input valves were connected to control the inlet volumetric discharge. At the end of the holding
tank and upstream of the main flume, water overflowed from a rectangular weir into the flume. Two
sand boxes were constructed in the flume. Both had a depth of 0.30 m and were 10.2 m apart. The
lengths of the sand boxes were 5.6 m and 5.8 m. In each sand box, a pair of bridge piers was placed.
Three natural non-uniform sediment compositions with median grain sizes of 0.50, 0.47, and 0.58
mm were used. It should be noted that the selection of these three sands was based on their availability
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in the research center. This selection also was based upon the fact that the masonry (D50 = 0.47 mm),
concrete (D50 = 0.58 mm) and bedding sand (D50 = 0.50 mm) were the three most common sands
already excavated from the surrounding mines (Hirshfield, 2015). Four pairs of cylindrical bridge
piers with diameters of 60, 90, 110, and 170 mm were used, and each pier was offset from the centre
line by 0.25 m, as illustrated in Figure 3-2. The bridge pier spacing ranges from 1.94 to 7.33 relative
to D as illustrated in Figure 3.2. The water level in the flume was controlled by the downstream
tailgate.

Figure 3–1: Plan view and side view of the experimental flume.

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Figure 3–2: The spacing ratio and measuring points around the circular bridge piers

In front of the first sand box, a SonTek two-dimensional (2D) Flow Meter was installed to measure
flow velocities and water depth. A staff gauge was also installed in the middle of each sand box to
manually verify the water depth. The velocity fields in the scour holes were measured using a 10MHz Acoustic Doppler Velocimeter (ADV). The ADV is a high-precision instrument that can be used
to measure three-dimensional (3D) flow velocity in a wide range of environments including
laboratories, rivers, estuaries, and the ocean (Cea et al., 2007). Styrofoam panels were used to
represent ice cover and covered the entire surface of the flume. Two types of model ice cover were
used, namely smooth cover and rough cover. The smooth cover was the smooth surface of the original
Styrofoam panels while the rough cover was made by attaching small Styrofoam cubes to the bottom
of the smooth cover. The dimensions of Styrofoam cubes were 25 mm × 25 mm × 25 mm and they

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were spaced 35 mm apart. Although ice accumulation in natural rivers is assumed to be floating,
Hains et al., (2004) claimed that fixed rough ice covers cause the deepest local scour around bridge
piers compared to those of floating covers and smoother ice, because the rigid ice cover causes the
maximum velocity to be closer to the bed. 108 Experiments (36 experiments for each sediment type)
were done under open channel, smooth covered, and rough covered conditions. In terms of different
boundary conditions (open channel, smooth, and rough covered flows), for each sediment type and
each boundary condition, 12 experiments were done. Throughout the calibration stage of the
experiments, local scour around bridge piers was carefully watched hourly for any changes in the
scour depths. It was observed that after approximately a period of 6 hr, no significant change in scour
depth was observed and scour hole equilibrium depth was achieved. The experiment was continued
for 24 hr and again no obvious change in scour depth was observed. A limited number of experiments
were also extended to 38 hr and there was not any change in scour depth between 24-hr and 38-hr
experiments. Further, according to Wu et al. (2014a), who did a lot of experiments regarding local
scour around a semi-circular bridge abutment, the time for development of equilibrium scour depth
was 24 hr. Based on the current experimental results and the results of Wu et al. (2014a), the
experimental run time of 24 hr was chosen. After 24 hr, the flume was gradually drained, and the
scour and deposition pattern around the piers was measured. To accurately read the scour depth at
different locations and to draw scour hole contours, the outside perimeter of each bridge pier was
equally divided and labeled. The measurement of the scour hole was subject to an error of +/-0.3 mm.
Of note, there are three types of similitude: geometric, kinematic, and dynamic. Geometric similarity
is similarity of shape and dimensions. According to geometric similarity, the model and its prototype
are identical in shape but differ only in size. Kinematic similarity is similarity of motion. According
to kinematic similarity, the ratios of the velocities at all corresponding points in the flows are the

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same. Dynamic similarity is similarity of forces. According to dynamic similarity, the forces that act
on a system in the model and prototype must be in the same ratio throughout the entire flow field
(Yang, 2005). In fact, it is not practical for a physical model of local scour around a bridge pier to
satisfy all these similarities because of extremely complicated flow conditions. In scour modelling,
inertial, gravitational, and viscous forces are very significant for defining similarity (Heller, 2011).
In terms of kinematic and dynamic similarity, the pier Reynolds number (Reb) which is a measure of
the ratio of the inertia force on an element of fluid to the viscous force on the element is usually high
and scale effects related to Reb are negligible (Heller, 2011). Therefore, the Froude number (Fr) which
is a measure of the ratio of the inertia force to gravity force is considered as the most applicable and
experimental design follows to this form of similitude (Heller, 2011). In the current study, flows of
all experimental runs in the flume were turbulent (Reb > 4,000) and subcritical (Fr < 1) which occurs
in most rivers where inertial forces are dominant. Of note, the flow Reynolds number was in the
domain of turbulent flow (It ranged from 4802 to 39030). Of note, in open channel, it is common to
use flow Froude number rather than flow Reynolds number in order to do kinematic and dynamic
similarity. One of the issues raised by placement of a bridge pier is the blockage of the flow cross
section. The blockage or wall interference refers to the influence of the side walls of a test section on
the local scour depth. Chiew (1984) suggested that if the ratio of pier size to channel width is less
than 10 percent (D/W < 10%), the sidewalls will have no significant impact on flow characteristics
and the scour profile. Significant sidewall effects in terms of scour occurring very close to the
sidewall are present in the study done by Sheppard et al. (2004) in which the blockage ratio is 15%.
In the current study, the ratio of D/W ranges from 6 to 17%. Therefore, in order to minimize the
impact of the blockage ratio, the 170-mm pier whose blockage ratio exceed 15% was located in the
second sand box. Further, as suggested by Ettema (1980), when D/D50 < 25, individual grains are

70

relatively large compared to the scour hole and entrainment of sediment particles is hindered because
the porous bed dissipates some of the energy of the down flow. Considering the work of Ettema
(1980), Breusers and Raudkivi (1991) confirmed that relative scour depth is not affected by particle
size when D/D50 > 25. Yanmaz (2002) observed that relative scour depth is not affected by the particle
size when D/D50 > 50. In the current study, the ratio of D/D50 ranges from 206.9 to 723.4 in order to
avoid the impact of D/D50 (the relative pier size) on scour depth.
3.1.2. Results and discussion
• Scour patterns and deposition patterns
Figure 3-3a shows scour depths around the 9-cm-piers and Figure 3-3b shows the scour and
deposition patterns at the pier face for the 9-cm-piers under different boundary conditions for D50 =
0.50 mm. The results indicate that, regardless of the roughness of ice cover and the grain size of
sediment, the maximum scour depths always occurred at the upstream, front face of the bridge piers.
The downflow generated by the flow hitting the upstream face of the pier, acts like a vertical jet which
erodes a groove in front of the pier. Under covered conditions, the strength of this downflow jet is
intensified. The eroded sand particles are carried around the pier by the combined action of
accelerating flow and the spiral motion of the horseshoe vortex (Hafez, 2016). Melville and Coleman
(2000) declared that the wake-vortex system acts like a vacuum cleaner sucking up stream bed
material and carrying the sediment moved by the horseshoe vortex system and by the downward flow
to the downstream side of the pier. However, wake vortices are not as strong as the horseshoe vortices,
and, therefore, are not able to carry the same amount of sediment load as that carried by the horseshoe
vortex. Hereby, sediment deposition occurs downstream of bridge piers in the form of a deposition
mound, as clearly shown in Figure 3-3b. Figure 3-4(a-b) shows the scour depth contours around the
9-cm-piers for sediment of D50 = 0.50 mm under rough covered and open channel flows. These scour
71

depth contours are mapped using Surfer 13 Plotting Software (Golden Software Incorporated, U.S).
The deepest point of the scour hole is clearly at the front face of the bridge piers and the deposition
mound is located downstream of the bridge piers. Under the rough covered flow, both the maximum
scour depth and maximum deposition height are clearly greater than that of the open channel flow.
By plotting the scour depth contours, the horseshoe vortex which is the primary reason for the local
scour phenomenon, must have occurred closer to the channel bed which led to a greater scour depth
under the rough covered flow conditions. The results also indicate that under the rough covered flow
conditions, more sediment deposition develops at the downstream side of bridge piers and the
deposition mound is wider than those under open channel flow and smooth covered flow conditions.
Moreover, a more intense irregular deposition mound was observed downstream of the piers, as
shown in Figure 3-4b. The reason for this deposition might be due to the velocity distribution changes
and greater strength of the horseshoe vortex near the bed surface under ice covered conditions. Similar
scour/deposition patterns have been observed for other bridge piers regardless of sediment type and
pier size. The height of the deposition mound downstream of the bridge piers depends on the depth
of the scour hole upstream of the bridge pier as well as on the interaction between horseshoe vortices
and wake vortices. The results indicate that, the higher the velocity of approaching flow under rough
covered flow conditions, the larger the deposition mound downstream of the bridge pier.

72

Figure 3–3a: Variation of scour depth around the 9cm-piers for D50= 0.50 mm type under open, smooth,
and rough covered flow conditions

Figure 3–3b: Scour and deposition patterns at the
pier face of the 9-cm-piers under open channel,
smooth, and rough covered flow conditions (D50 =
0.50 mm).

73

Figure 3–4: (a) Contours of scour holes and deposition mounds around the 9-cm-piers under open channel
flow conditions (D50 = 0.50 mm) and (b) Contours of scour holes and deposition mounds around the 9-cmpiers under rough covered condition (D 50 = 0.50 mm).

74

• Effect of pier spacing distance on the scour patterns
Figure 3-5 shows the ratio of the maximum scour depth to the depth of approaching flow (ymax/y0,
termed as relative MSD) against the ratio of pier spacing distance to pier diameter (G/D, termed as
bridge pier spacing ratio) for D50 = 0.50 mm. In Figure 3-5, the Froude number ranges from 0.072 to
0.270 and G/D ranges from 3.54 to 7.33. In the current study, the Froude number in the first sand box
was higher than that in the second sand box because of the longitudinal slope of the bed channel and
the dissipation of momentum of the flow due to friction. In the first sand box, either the 9-cmdiameter piers or the 11-cm-diameter piers were placed; and in the second sand box, either the 6-cmdiameter piers or the 17-cm-diameter piers were placed. More experiments should have been done to
place either the 17-cm piers or the 6-cm piers in the first sand box (under the same flow condition);
and either the 9-cm-piers or the 11-cm piers in the first sand box (under the same flow condition).
However, due to budget limitations and time constraints, those experimental runs have not been done.
According to Figure 3-5, the relative MSD decreases with the increase in G/D. Also, for the same
bridge pier spacing ratio (G/D) and for the same sediment, the relative MSD under open channel flow
conditions is the lowest, and the relative MSD under the rough covered flow reaches the highest.
Figure 3-6 shows the changes of the pier Reynold number (Reb) with the pier spacing ratio (G/D) for
D50 = 0.50 mm. The pier Reynolds number is defined as:
Reb = UD


(3-1-1)

Where U is the average velocity of the approaching flow; D is the diameter of the bridge pier, and ν
is the kinematic viscosity. As shown in Figure 3-6, the pier Reynold number (Reb) decreases with
increases in G/D. Hopkins et al. (1980) stated that the strength of the horseshoe vortex system is a
function of the pier Reynolds number (Reb). Therefore, it can be concluded that the strength of
75

horseshoe vortices, which is a function of Reb, decreases with the increase in the pier spacing ratio.
Therefore, the smaller the pier size (D) and the larger the pier spacing (G), the weaker the horseshoe
vortices around bridge piers, which will result in shallower scour depths around the bridge piers.
According to Figure 3-6, under the same flow condition (velocity and flow depth), the lowest pier
Reynolds number (Reb) occurred under the open channel flow conditions, and the maximum pier
Reynolds number (Reb) occurred under rough covered flow condition. However, with an increase in
the pier spacing ratio, the pier Reynolds number under rough covered flow conditions, gets closer to
those of the smooth covered and open channel flow conditions, implying that the influence of ice
cover on pier Reynolds number diminishes as the pier spacing distance increases.

Figure 3–5: Relative MSD (ymax/y0) against pier
spacing (G/D) under open channel, smooth, and
rough covered flow conditions (D 50 = 0.50 mm).

Figure 3–6: Variation of pier spacing (G/D) with
respect to pier Reynolds number (Reb).

• Effects of flow Froude Number on scour depth
Figure 3-7(a-c) shows the impacts of flow Froude number (Fr) on the relative MSD for D50 = 0.50
mm under open channel, smooth covered, and rough covered flow conditions, respectively. Overall,
regardless of flow cover, the larger the flow Froude number, the greater the relative MSD. Under
open channel flow conditions, both the 11-cm-piers and 9-cm-piers which are exposed to flows with
higher Froude numbers have deeper scour holes (Figure 3-7a). For flow with lower Froude numbers,
76

the average depths of scour holes around the 17-cm-piers and 6-cm-piers are 0.14 and 0.09 cm,
respectively. While for flow with higher Froude number, the average depths of scour holes around
the 11-cm-piers and 9-cm-piers are 0.27 and 0.21 cm, respectively. Regarding the flow under smooth
and rough covered conditions, similar trends as for open channel flow condition is seen between MSD
and Froude number (Figure 3-7b, c). Regardless of the pier size, a deeper scour hole results under
both smooth and rough covered flow conditions compared to that under open channel flow conditions
which signifies the impact of flow cover on the scour pattern as well as on the characteristics of the
flow field around the piers. Under nearly the same Froude number and bed sediment type, the largest
scour depth occurs under rough covered flow conditions which indicates that the cover roughness
plays an important role in the local scour around the bridge pier. Also, the impact of Froude number
on each individual bridge pier under different cover conditions has been examined, as shown in Figure
3-7d. According to Figure 3-7d, the relative MSD for the 6-cm pier under rough covered flow
conditions is greater than those under both smooth covered and open channel flow conditions.
Besides, for flow with larger Froude numbers, the difference between the relative MSD under the
rough covered flow conditions and those under both smooth covered and open channel flow
conditions becomes more distinct, implying that the effect of the larger Froude number is more
dominant under rough covered flow conditions. According to Figure 3-7e, the relative MSD around
the 17-cm pier in the channel bed with the finest sediment is obviously larger than that with the
coarsest sediment. Similarly, the impact of Froude number on relative MSD becomes more distinct
for higher values of Froude number. Similar trends have been observed for local scour around other
piers. According to Wu et al. (2014a), the dimensionless shear stress increases with the increase in
Froude number. Therefore, for the same Froude number, the finer the sediment in the channel bed,

77

the lower the dimensionless shear stress is needed to initiate motion of the sediment. This is the reason
that larger scour depths occur for flow with higher Froude numbers.

Figure 3–7a: Variation of the relative MSD (ymax/y0)
against flow Froude number (Fr) under open channel
flow conditions (D50 = 0.50 mm);

Figure 3–7c: Variation of the relative MSD (ymax/y0)
against Froude number (Fr) under rough covered flow
conditions (D50 = 0.50 mm)

Figure 3–7b: Variation of the relative MSD (ymax/y0)
against flow Froude number (Fr) under smooth
covered flow conditions (D50 = 0.50 mm);

Figure 3–7d: Variation of the relative MSD (ymax/y0)
against Froude number (Fr) for the 6 cm-pier under
different flow conditions;

78

Figure 3–7e: Variation of the relative MSD (ymax/y0) against Froude number (Fr) for the 17 cm-pier under
different flow conditions for three D 50 values

• Effects of grain size of sediment on scour depth
The grain size of bed material is another important variable affecting the depth of the scour hole.
Figure 3-8(a-c) shows the impact of grain size of sediment on local scour depth around the 11-cmpier under open channel, smooth covered, and rough covered flow conditions, respectively.
According to Figure 3-8, under nearly the same flow condition (same flow Froude number), as the
grain size of the bed material gets larger, the depth of the scour hole around the bridge piers gets
smaller. Regardless of flow cover, the difference between depths of scour holes is obvious between
the finest bed material (D50 = 0.47 mm) and the other coarser types of sediment. Experimental results
showed that, for other piers with different diameters, similar relation between scour depth and grain
size of bed material exists. A sediment particle starts to move when the shear stress acting on it is
greater than the resistance force. The magnitude of shear stress required to move a particle is known
as the critical shear stress (τcr). The greater the dimensionless shear stress, the greater the capacity for
sediment transport (Wiberg & Smith, 1987). As the median grain size and density of the sediment
79

particles increase, the value of the dimensionless shear stress decreases. Therefore, the larger the
median grain size, the lower the dimensionless shear stress for initiating motion for the sediment
particles. Results of the current study showed that, for these three sands, the relative MSD increases
with the increase in Froude number. Also, the increasing rate of the relative MSD is highest around
bridge piers for a channel bed with the finest sediment particles. Thus, it can be concluded that, since
dimensionless shear stress increases with Froude number, the relative MSD increases with
dimensionless shear stress. Therefore, for the channel bed with the finest sediment, the dimensionless
shear stress which represents the capacity for sediment transport is highest compared to those of other
types of sediment.

Figure 3–8a: The impact of sediment size on local scour around the 11-cm-pier under open channel flow
conditions;

80

Figure 3–8b: The impact of sediment size on local scour around the 11-cm-pier under smooth covered flow
conditions;

Figure 3–8c: The impact of sediment size on local scour around the 11-cm-pier under rough covered flow
conditions.

81

• F o r m ul a f o r d et e r mi ni n g t h e m a xi m u m d e pt h of t h e s c o u r h ol e
O v er all, t h e d e pt h of s c o ur h ol es ar o u n d bri d g e pi ers u n d er c o v er e d c o n diti o ns d e p e n ds o n fl o w
i nt e nsit y, pi er si z e, gr ai n si z e of t h e b e d m at eri al, s p a ci n g dist a n c e b et w e e n si d e-b y -si d e pi ers, a n d
r o u g h n ess of t h e c h a n n el b e d a n d i c e c o v er. T h e s c o ur d e pt h c a n b e d es cri b e d b y t h e f oll o wi n g
r elati o n,
y m a x = f ( G , y 0, U , g ,  w ,  s , D , D 5 0, n b, ni )

W h er e,

(3 -1 -2)

y m a x is t h e m a xi m u m d e pt h of s c o ur h ol e; y 0 is t h e d e pt h of a p pr o a c hi n g fl o w; g is t h e

gr a vit ati o n al a c c el er ati o n; ρ

s is t h e d e nsit y of t h e s e di m e nt; ρ

w

is t h e d e nsit y of w at er a n d n i a n d n b

ar e t h e r o u g h n e ss c o effi ci e nt s of t h e m o d el i c e c o v er a n d t h e c h a n n el b e d, r es p e cti v el y . Usi n g
di m e nsi o n al a n al ysis, t h e r el ati v e M S D c a n b e d es cri b e d as f oll o w s,


y ma x
n D
= f( U , i , 5 0 , s , G )
y0
gy 0 nb y 0  w D

(3 -1 -3)

T h e first di m e nsi o nl ess v ari a bl e is t h e Fr o u d e n u m b er of t h e a p pr o a c hi n g fl o w. I n t h e c urr e nt st u d y,
t h e Fr o u d e n u m b er of t h e a p pr o a c hi n g fl o w is l ess t h a n 1, i m pl yi n g t h e fl o w i n t h e fl u m e is s u b criti c al
fl o w. C o nsi d eri n g t h e d o min a nt p ar a m et ers aff e cti n g t h e s c o uri n g pr o c ess u n d er b ot h o p e n c h a n n el
a n d c o v er e d fl o w c o n diti o ns, r e gr essi o n a n al ysis of t h e r el ati v e M S D a g ai nst e a c h of t h e ot h er
di m e nsi o nl e ss v ari a bl e s h as b e e n d o n e, a n d t h e c orr es p o n di n g st atisti c al a n al ysis h as b e e n d o n e. T h e
g e n er al f or m o f r e gr essi o n a n al ysis is as f oll o w s,
y ma x

y0

= A Y + B

(3 -1 -4)

82

Where,  is the dimensionless variables from Eq. 3-1-3, and A and B are constants. The statistical
analysis for each of the dimensionless variables includes calculations of the associated coefficient of
determination (R2), P-value, Theil’s coefficient (α), the Mean Absolute Error (MAE), and the Root
Mean Square Error (RMSE). The Theil’s coefficient (α), Mean Absolute Error (MAE) and Root
Mean Square Error (RMSE) are computed using the following equations, respectively:

(3-1-5)
n

MAE = 1  ei
n i =1

RMSE =

n

(3-1-6)
ei2

n
i =1

(3-1-7)

where  is Theil’s coefficient ( = 0 for a model yielding a perfect forecast and  = 1 for an
unsuccessful model); (ymax)0 is the maximum depth of the scour hole obtained from experimental
runs, and (ymax)C is the predicted maximum depth of the scour hole obtained using the developed
formula; ei is the error in predicting the maximum depth of scour hole for event i of the record using
the developed formula; and n is number of datasets. Hereby, the values of , MAE and RMSE obtained
from Eqs. 3-1-5 to 3-1-7 are smaller, implying a more successful prediction of the maximum depth
of the scour hole using the developed formulae. The P-value, which is a number between 0 and 1,
gives the evidence against a null hypothesis. The smaller the P-value (typically ≤ 0.05), the stronger
the evidence that the null hypothesis is not true (Storey & Tibshirani, 2003). Table 3-1 lists the results
of the regression analysis between the relative MSD and other parameters as given in Eq. 3-1-3 under
83

open channel, smooth covered, and rough covered flow conditions. The second column of Table 3-1
gives values of slope of the regression line, which represent the rate of change in the relative MSD as
the dimensionless variables change (such as Fr). A negative value of the regression slope indicates
that the relative MSD decreases with respect to the associated variable (such as the pier spacing ratio,
G/D), whilst a positive value indicates that the relative MSD increases with respect to the associated
variable. The results show that the relative MSD increases with the Froude Number (Fr) which
implies that the higher the Froude number (higher velocity and/or shallower water depth), the deeper
the scour hole will be. The relative MSD against the roughness ratio (ni/nb) has a positive slope,
indicating that as the model ice cover gets rougher, the depth of scour hole increases. The linear
regression between the relative MSD and D50 or y0 (Table 3-1) shows that as D50 or y0 decreases, the
relative MSD increases which means that as the sediment gets coarser of the flow gets deeper, the
relative MSD decreases. However, according to Table 3-1 the relative MSD increases with increases
in the ratio of D50/y0. The regression coefficient between the relative MSD and the specific gravity of
sediment (s/w) indicates that sediment having a higher density (D50 = 0.47 mm) is expected to have
a deeper scour hole. In terms of the bridge pier spacing distance, since it was not possible to examine
a variety of pier spacings, the pier spacing ratio is not as influential as might be was expected.
However, the negative regression coefficient between the relative MSD and the pier spacing (G/D)
indicates that the relative MSD increases as G/D decreases. In other words, as the piers get closer to
each other and the pier diameter gets larger, the relative MSD increases correspondingly. Finally, by
considering the (R2), P-value, MAE, and RMSE of the regression equations using the various
dimensionless variables as listed in Table 3-1, the dimensionless groups which have a strong relation
with the relative MSD are chosen for further analysis, and can be expressed as follows:

84

y max

y0

æ

ö
u , ni , D50 , G ÷
ç gy n
y0 D ÷
b
ø
è
0

= fç

(3-1-8)

Eq. 3-1-8 implies that the relative MSD of scour holes around the side-by-side bridge piers primarily
depends on the Froude number of the approaching flow, the grain size of sediment, the spacing
distance between piers, the bridge pier diameter and the roughness coefficient of the channel bed and
the model ice cover. As shown in Figure 3-9, although the data points are scattered, under the
condition of nearly the same flow Froude number and same bed material (i.e., D50 = 0.47 mm), the
relative MSD around a bridge pier under rough covered flow conditions is maximum compared to
those under both smooth covered and open channel flow conditions.
Table 3-1: The values of the intercept, R2, P-value, α, MAE, and RMSE of the dimensionless parameters
with respect to Eq. 3-1-3
Coefficients Intercept
R Square
P-value
α
MAE
RMSE
Fr

3.201

-0.141

0.651

5.3E-26

0.167 0.077

0.103

ni/nb

0.118

0.201

0.45

0.0061

0.311 0.139

0.182

D50/y0

99.259

-0.061

0.416

2.9E-14

0.236 0.108

0.143

s/w

0.421

-0.415

0.074

0.004

0.309 0.136

0.181

G/D

-0.011

0.314

0.017

0.0184

0.324 0.141

0.187

D50

-1198.98

0.878672

0.08772

0.001856

0.295 0.135

0.180

y0

-0.194

0.23

0.37

1.63E-12

0.229 0.107

0.139

The experiments showed that, similar results were obtained for other sediment grain sizes. Figure 310 (a-c) shows the dependence of the relative MSD on flow Froude number (Fr) and grain size of
sediment (D50) under different boundary conditions (open channel, smooth covered, and rough
covered flow conditions). According to Figure 3-10, under nearly the same Froude number (Fr),
regardless of flow cover, the relative MSD is deepest around piers in the finest sand bed (D50 = 0.47
85

mm). According to Figure 3-9 and Figure 3-10, the deepest scour hole around a bridge pier occurs in
the finest sand bed under rough covered flow conditions. One can observe that results for sediment
sizes 0.47 and 0.50 mm seem close. Since the median grain size of sediment of 0.47 mm is very close
to that of 0.50 mm, this small difference resulted in a very close critical shear stress which defines
the threshold for sediment transport.

Figure 3–9: Dependence of the relative MSD (ymax/y0) on flow Froude number (Fr) under covered conditions
compared to that under open channel flow conditions (D50 = 0.47 mm)

86

Figure 3–10a: Dependence of the relative MSD (ymax/y0) on flow Froude number (Fr) and grain size of
sediment (D50) under open channel flow condition

Figure 3–10b: Dependence of the relative MSD (ymax/y0) on flow Froude number (Fr) and grain size of
sediment (D50) under smooth covered flow conditions
87

Fi g ur e 3 – 1 0 c : D e p e n d e n c e of t h e r el ati v e M S D ( ym a x /y 0 ) o n fl o w Fr o u d e n u m b er ( Fr) a n d gr ai n si z e of
s e di m e nt ( D 5 0 ) u n d er r o u g h c o v er e d fl o w c o n diti o ns

T o d e v el o p s uit a bl e e q u ati o ns f or d et er mi ni n g t h e r el ati v e M S D ar o u n d t h e s i d e-b y -si de pi ers u n d er
c o v er e d fl o ws, t h e i m p a ct of t h e r o u g h n ess of t h e m o d el i c e c o v er m ust b e e x a mi n e d. As m e nti o n e d
e arli er, t h e pr es e n c e of i c e c o v er c h a n g es t h e v el o cit y fi el d a n d t ur b ul e n c e c h ar a ct eristi c s. F or
c o n cr et e wit h tr o w el fi nis h, t h e r o u gh n e ss c o ef fi ci e nt is s u g g est e d b y M a ys ( 1 9 9 9) t o b e 0. 0 1 3.
T h er ef or e, d u e t o a r el ati v el y s m o ot h c o n cr et e -li k e s urf a c e of t h e St yr of o a m p a n el, t h e r o u g h n ess of
t h e m o d el e d s m o ot h i c e-c o v er is s u g g est e d t o b e 0. 0 1 3. I n t er ms of t h e r o u g h i c e -c o v er e d fl o w
c o n diti o n, L i ( 2 0 1 2) r e vi e w e d s e v er al m et h o ds f or c al c ul ati n g t h e M a n ni n g’s c o effi ci e nt f or i c e c o v er,
t h e f oll o wi n g e q u ati o n c a n b e us e d d e p e n di n g o n t h e si z e of t h e s m all c u b es:

ni

k S1 6

(8 g ) ( R K )
=
0. 8 6 7 l n (1 2 R K )
-1 2

1 6

S

S

(3 -1 -9)

W h er e , K s is t h e a v er a g e r o u g h n ess h ei ght of t h e i c e c o v er u n d ersi d e a n d R is t h e h y dr a uli c r a di us.
B y usi n g E q. 3 -1 -9, a M a n ni n g’s c o effi ci e nt of 0. 0 2 1 w as esti m at e d as t h e r o u g h i c e c o v er r o u g h n e ss
88

c o effi ci e nt. T his v al u e als o a gr e es wit h fi n di n g s of C ar e y ( 1 9 6 6) , H ai ns et al. Z a bil a ns k y ( 2 0 04), a n d
W u et al. ( 2 0 1 4 b) . Si n c e t h e D 5 0 v al u es of t h e t hr e e s a n ds us e d i n t his st u d y ar e k n o w n, t h e si m pl e
e q u ati o n pr o p o s e d b y H a g er ( 1 9 9 9) is us e d f or d et er mi ni n g t h e r o u g h n ess c o effi ci e nt of t h e c h a n n el
b e d:

n b = 0. 0 3 9 D 51/0 6

(3 -1 -1 0)

T h e H a g er ( 1 9 9 9) e q u ati o n is t h e r e vis e d f or m of t h e Stri c kl er ( 1 9 2 3) e q u ati o n f or c al c ul ati n g
M a n ni n g’s r o u g h n ess c o effi ci e nt f or str e a m b e ds c o m p o s e d of c o b bl es a n d

s m all b o ul d ers:

n = 0. 0 3 9 D 5 0 1/ 6 . T h er ef or e, t h e r o u g h n ess c o effi ci e nt of s a n d b e d, n b , is esti m at e d as 0. 0 1 0 9 f or D 5 0 =
0. 4 7 m m, 0. 0 1 1 0 f or D 5 0 = 0. 0 5 0 m m, a n d 0. 0 1 1 3 f or D 5 0 = 0. 5 8 m m. E v e nt u all y, E qs. 3 -1 -1 1 a n d 3 1 -1 2 ar e pr o p o s e d f or c al c ul ati n g t h e r el ati v e M S D u n d er c o v er e d fl o w a n d o p e n c h a n n el fl o w
c o n diti o ns, r es p e cti v el y:

y ma x

y0

æD ö
= 5. 9 6 çç 5 0 ÷÷
è y0 ø

- 0. 0 7 0

æG ö
ç ÷
èD ø

- 0. 2 5 6

æn ö
çç i ÷÷
ènb ø

0. 5 4 6

( Fr )

1. 6 7 7

wit h R 2 = 0. 9 0

(3 -1 -1 1)

wit h R 2 = 0. 9 2

(3 -1 -1 2)

Fi g ur es 3 -1 1 a n d 3 -1 2 s h o w c o m p aris o ns of t h e c al c ul at e d r el ati v e M S D t o t h o s e of o bs er v e d u n d er
o p e n c h a n n el fl o w a n d c o v er e d fl o w c o n diti o ns , r es p e cti v el y. Of n ot e, E q. 3 -1 -1 1 a n d Fi g ur e 3 -1 2
ar e r es ult s f or b ot h s m o ot h c o v er e d a n d r o u g h c o v er e d fl o w c o n diti o ns. Fr o m E qs. 3 -1 -1 1 a n d 3 -1 1 2, it is o b vi o u s t h at t h e Fr o u d e n u m b er of t h e a p pr o a c hi n g fl o w is t h e m o st i nfl u e nti al f a ct or si n c e
it s i n d e x is m u c h hi g h er t h a n t h o s e f or t h e ot h er v ari a bl es. T his m e a ns t h at as t h e Fr o u d e n u m b er
i n cr e a s es, t h e r el ati v e M S D ar o u n d bri d g e pi ers i n cr e as es a c c or di n gl y. I n ot h er w or ds, r e g ar dl ess of
89

the flow cover and the size of sediment, the higher the flow velocity and the shallower the flow depth,
the greater the relative MSD will be. As Sui et al. (2010) indicated, the formation of a stable ice cover
effectively doubles the wetted perimeter compared to open channel conditions, thus, altering the
hydraulics of an open channel by imposing an extra boundary to the flow, causing the velocity profile
to shift towards the smoother boundary (channel bed) and adding to the flow resistance. This
significant change in the velocity profile, increases the effect of the Froude number under ice-covered
flow conditions compared to that for open channel flow conditions. Therefore, under nearly the same
Froude number, the maximum scour depth under the rough covered flow condition is greater than
that under the smooth covered condition. The turbulent horseshoe vortex and roughness of flow cover
are related to each other. Therefore, the positive index of the roughness ratio implies that as the model
ice cover gets rougher, the turbulent horseshoe vortex around the bridge piers gets stronger which
will eventually lead to a larger scour depth. The negative index for G/D implies that as the space
between the piers decreases, the maximum scour depth increases which is in good agreement with
results of Hannah (1978) and Ataie-Ashtiani and Beheshti (2006).

Figure 3–11: Comparison of calculated relative MSD (ymax/y0) to those observed under open channel flow
conditions.
90

Figure 3–12: Comparison of calculated maximum scour depth (ymax/y0) to those observed under covered flow
conditions.

• Sensitivity analysis:
In order to see the rate of change of relative MSD to each of the parameters in Eq. 3-1-11, sensitivity
analysis has been done. In this regard, the following graph has been obtained by keeping a particular
parameter changing from -20% to +20% and keeping the other parameters constant. According to
Fig. 3-13, the relative MSD is the most sensible to Fr number as it shows the highest Mean value of
Error. According to Fig. 3-13, if Froude number decreases up to 20 percent while the other parameters
are kept constant, the relative MSD would decrease up to -31 percent which is very significant. The
next parameter which relative MSD is most sensible to is the roughness coefficient. For instance, if
20 percent is added to the roughness of the ice surface the relative MSD would increase up to 10.75
percent. This result states the importance of ice cover roughness coefficient on the rate of change
relative MSD. The bridge pier spacing (G/D) is the next sensible parameter. For the present study, if
bridge pier spacing increases up to 20 percent, the relative MSD decreases up to 4.3 percent. The

91

ratio of D50/yo shows the least amount of sensitivity to the relative MSD. According to Fig. 3-13, if
D50/yo increases up to 20 percent, the relative MSD decrease just up to 1 percent.

Figure 3–13: Sensitivity analysis of dimensionless parameters of Eq. 3-1-11

3.1.3. Conclusions
In the current study, 108 experiments were done in a large-scale flume with non-uniform sediment to
investigate the local scour process around four pairs of side-by-side cylindrical bridge piers under
open channel, smooth covered, and rough covered flow conditions. The following conclusions can
be drawn from the current study.
1) The pier Reynolds number (Reb) decreases with the increase in the pier spacing ratio (G/D), which
implies that the strength of the horseshoe vortices decreases as the spacing distance between the sideby-side piers increases. The results showed that, under the same flow condition (velocity and flow
depth), the lowest pier Reynolds Number (Reb) occurred under open channel flow conditions, and the
highest pier Reynolds Number (Reb) occurred under rough covered flow conditions. Further, it was
observed that the influence of ice cover on pier Reynolds Number fades away as the pier spacing
distance increases regardless of flow cover. Also, for the same bridge pier spacing ratio (G/D) and
92

for the same sediment, the relative MSD under open channel flow conditions is the lowest and reaches
the maximum under the rough covered flow conditions. This implies that the impact of the pier
spacing ratio under the rough ice-covered flow condition is clearly intensified compared to those
under both open channel and smooth covered flow conditions. In other words, the smaller the pier
size (D) and the larger the pier spacing (G), the weaker the horseshoe vortices around the side-byside bridge piers.
2) Under the same flow conditions, the effect of flow Froude number on the scour process is stronger
than that of pier size. Regardless of ice cover and pier size, the maximum scour depth increases with
flow Froude number, especially for finer sand beds. In other words, the local scour depth around
bridge piers for a coarse sand bed is less than that for a finer sand bed. The results of this experimental
study allow the impacts of ice cover, flow Froude number, and pier spacing distance on local scour
around bridge piers to be prioritized. Overall, one can say that the deepest scour hole occurs around
closely spaced large side-by-side piers under rough covered flow conditions which have higher
Froude numbers. The results also indicate that, regardless of the roughness of the model ice cover
and the grain size of sediment, the maximum scour depths always occurred at the upstream front face
of the bridge piers. Also, the amount of sediment transported to the downstream side of the bridge
pier to form the deposition mound is greatest under rough covered flow conditions. The results
indicate that the impact of pier spacing on scour depth under covered flow conditions is similar to
that under open channel conditions, however, the scouring process under covered flow conditions is
more intense. It was found that the most extreme scour depth around side-by-side bridge piers occurs
under rough covered flow conditions with the higher Froude number and smaller bridge pier spacing.
3) Using data collected from the current experiments, empirical equations for predicting the relative
MSD (ymax/y0) under both channel flow and covered flow conditions have been developed. Among
93

all the dimensionless parameters, flow Froude number was the most influential factor which had a
positive relation with the relative MSD (ymax/y0). The impact of the Froude number is most distinct
under rough covered flow conditions with smaller pier spacing ratios. Namely, for nearly the same
Froude number, the largest scour depth occurs under rough covered flow conditions with smaller pier
spacing. This means that under rough covered flow conditions, the maximum velocity is located
closer to channel bed. Thus, the shear stress increases, and the horseshoe vortexes are intensified due
to the smaller pier spacing ratio. Both the roughness of the ice cover and the pier spacing ratio are
two major factors leading to the most critical local scour pattern.
4) Sensitivity analysis was done for Eq. 3-1-11 and it was concluded that the relative MSD is most
sensible to Fr, ni/nb, G/D and D50/y0, respectively.

94

• Notation:
A: Constant of the linear regression equation
B: Constant of the linear regression equation
D: Pier width (m)
D50: Median particle diameter (mm)
Fr: Flow Froude number
g: Acceleration due to gravity (m/s2)
G: Bridge spacing (m)
Ks: Average roughness height (m)
MSD: Relative maximum scour depth defined as ymax/y0
MAE: Mean Absolute Error
n: and the number of datasets
ni: Ice cover roughness
nb: Channel bed roughness
R: Hydraulic radius (m)
R2: Coefficient of determination
Reb: Pier Reynold number
RMSE: Root Mean Square Error
U: Average approach velocity (m/s)
Uc= Critical velocity for incipient motion of the particle size D 50
W: channel width (m)
ymax: Maximum scour depth (m)
y0: Approach flow depth (m)
α: Theil’s coefficient

s: Density of the sediment (kg/m3)
w: Density of water (kg/m3)
ψ: Dimensionless variable
ei: Error in the predicted scour depth
ν: The kinematic viscosity (m2/s)
τcr: Critical shear stress (Pa)
θ: Temperature (degrees)
95

3.1.4. Reference
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ice covers”. Proceedings, International Conference. 16th IAHR International Symposium on
Ice, IAHR, Dunedin, New Zealand.
Ataie-Ashtiani, B., & Beheshti, A. A. (2006). Experimental investigation of clear-water local
scour at pile groups. Journal of Hydraulic Engineering, 132(10), 1100-1104.
Breusers, H.N.C., & Raudkivi, A.J. (1991). Scouring, Hydraulic Structures Design Manual,
No. 2, I.A.H.R., Balkema, 143pp.
Briaud, J. L., Gardoni, P., & Yao, C. (2006). Bridge scour. Geotechnical News, 24(3),
September, BiTech Publishers Ltd.
Carey, K. (1966). Observed configuration and computed roughness of the underside of river
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Cea, L., Puertas, J., & Pena, L. (2007). Velocity measurements on highly turbulent free
surface flow using ADV. Experiments in fluids, 42(3), 333-348.
Chiew, Y. M. (1984). Local scour at bridge piers (Ph.D. dissertation), Department of Civil
Engineering, University of Auckland, New Zealand.
Ettema, R. (1980). Scour at bridge piers, Report No. 216, Department of Civil Engineering,
University of Auckland, New Zealand.
Ettema, R., Melville, B. W., & Constantinescu, G. (2011). Evaluation of bridge scour
research: Pier scour processes and predictions. Washington, DC: Transportation Research
Board of the National Academies.
Hafez, Y. I. (2016). Mathematical modeling of local scour at slender and wide bridge piers.
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Hager, W. (1999). Wastewater Hydraulics: Theory and Practice. Springer: Berlin, New
York.
Hains, D., Zabilansky, L.J., & Weisman, R.N. (2004). An experimental study of ice effects
on scour at bridge piers. Cold Regions Engineering and Construction Conference and Expo,
16–19 May 2004, Edmonton, Alberta, Canada.
Hannah, C. R. (1978). Scour at pile groups. Research Report No. 28-3, Civil Engineering
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Heller, V. (2011). Scale effects in physical hydraulic engineering models.” Journal of
Hydraulic Research, 49(3), 293-306.
Hirshfield, F. (2015). The impact of ice conditions on local scour around bridge piers, Ph.D.
dissertation, Environmental Engineering Program, University of Northern British Colombia,
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Hopkins, G. R., Vance, R. W., & Kasraie, B. (1980). Scour around bridge piers, FHWARD-79-103 U.S. Department of Transportation, Federal Highway Administration, Offices of
Research and Development, Environmental Division.
Li, S. S. (2012). Estimates of the Manning's coefficient for ice-covered rivers. Proceedings
of the Institution of Civil Engineers-Water Management, 165(9), 495-505.
Mays, L. W. (Ed.). (1999). Hydraulic design handbook. New York: McGraw-Hill
Professional Publishing.
Melville, B. W. (1997). Pier and abutment scour: Integrated approach. Journal of Hydraulic
Engineering, 123(2), 125-136.
Melville, B. W. & Sutherland, A. J. (1988). Design method for local scour at bridge piers.
Journal of Hydraulic Engineering, 114(10), 1210-1226.
Melville, B. W. & Coleman, S. E. (2000). Bridge scour. Highlands Ranch, Colo, U.S.: Water
Resources Publications.
Richardson, E. V., Simons, D. B. & Lagasse, P. F. (2001). River engineering for highway
encroachments-Highways in the river environment. Federal Highway Administration,
Hydraulic Series No. 6, Washington, DC.
Sheppard, D. M., Odeh, M., & Glasser, T. (2004). Large scale clear-water local pier scour
experiments. Journal of Hydraulic Engineering, 130(10), 957-963.
Sheppard, D. M., Melville, B. & Demir, H. (2013). Evaluation of existing equations for local
scour at bridge piers. Journal of Hydraulic Engineering, 140(1), 14-23.
Storey, J. D. & Tibshirani, R. (2003). Statistical significance for genomewide studies.
Proceedings of the National Academy of Sciences, 100(16), 9440-9445.
Strickler, A. (1923). Beiträge zur Frage der Geschwindigkeitsformel und der
Rauhigkeitszahlen für Ströme, Kanäle und geschlossene Leitungen: mit... Tab. Im
Selbstverlag.
Sui, J., Faruque, M.A.A., & Balachandar, R. (2008). Influence of channel width and tailwater
depth on local scour caused by square jets. Journal of Hydro-Environment Research, 2, 39 45.
Sui, J., Faruque, M.A.A. & Balachandar, R. (2009). Local scour caused by submerged square
jets under ice cover. Journal of Hydraulic Engineering, 135 (4), 316-319.
Sui, J., Wang, J., He, Y. & Krol, F. (2010). Velocity profiles and incipient motion of frazil
particles under ice cover. International Journal of Sediment Research, 25(1), 39-51.
Yanmaz, A. M. (2002). Dynamic reliability in bridge pier scouring. Turkish Journal of
Engineering and Environmental Sciences, 26(4), 367-376.

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Yang, Q. (2005). Numerical investigations of scale effects on local scour around a bridge
pier. (Ph.D. dissertation), Department of Civil and Environmental Engineering, Florida State
University, Tallahassee, FL, U.S.
Wang, J., Sui, J. & Karney, B. (2008). Incipient motion of non-cohesive sediment under ice
cover–an experimental study”. Journal of Hydrodynamics, 20(1), 117-124.
Wardhana, K., & Hadipriono, F. C. (2003). Analysis of recent bridge failures in the United
States. Journal of performance of constructed facilities, 17(3), 144-150.
Wiberg, P. L., & Smith, J. D. (1987). Calculations of the critical shear stress for motion of
uniform and heterogeneous sediments. Water Resources Research, 23(8), 1471-1480
Williams, P., Balachandar, R., & Bolisetti, T. (2013). Evaluation of local bridge pier scour
depth estimation methods. Proceedings., 24th Canadian Congress of Applied Mechanics
(CANCAM), University of Saskatchewan, Saskatoon, Canada.
Wu, P., Balachandar, R. & Sui, J. (2015a). Local scour around bridge piers under ice-covered
conditions. Journal of Hydraulic Engineering, 142(1), 04015038.
Wu, P., Hirshfield, F., & Sui, J. Y. (2015b). Local scour around bridge abutments under ice
covered condition–an experimental study. International Journal of Sediment Research,
30(1), 39-47.
Wu, P., Hirshfield, F. & Sui, J. (2014a). Armor layer analysis of local scour around bridge
abutment under ice covered condition, River Research and Applications, 31(6), 736-746.
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scour around semi-circular bridge abutment. Journal of Hydrodynamics, 26(1), 10-18.
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3.2. Impact of armour layer on the depth of scour hole around side-by-side bridge
piers under ice-covered and open channel conditions
Bed scour may be a natural occurrence or due to manmade changes to a river. Depending on
the intensity of approaching flow for sediment transport, local scour process around bridge
piers is classified as either clear-water scour or live bed scour. Clear-water scour occurs when
there is no movement of the bed material in the upstream flow while live-bed scour occurs
when the scour hole is consistently supplied with sediments by the upstream flow
(Richardson and Davis, 2001). Local scour around bridge pier is a process of scouring as the
result of installation of artificial obstacles such as weirs, abutments and piers in rivers
(Richardson et al, 1993). More specifically, flow contraction in rivers caused by installation
of hydraulic constructions such as bridge piers and abutments can lead to substantial local
alteration of the flow patterns and significant increase of shear stress. As the result of
increased shear stress around the hydraulic structures which is itself direct consequence of
increased turbulence, flow velocities and the complex flow structures (downwelling,
upwelling, horseshoe vortices) causes increased sediment entrainment at the river bed which
eventually results in development of local scour holes (Török et al, 2014). The main feature
of the flow around a pier is the system of vortices which develop around the pier. These
vortex systems have been discussed by many researchers (Melville and Raudkivi, 1977;
Raudkivi and Ettema, 1983; Melville and Sutherland, 1988; Kothyari, 1992, to mention only
a few). One of the phenomena associated with characteristics of flow in the vicinity of bridge
piers is the development of armour layer. Bed armouring process typically occurs in streams
with non-uniform bed materials. This phenomenon occurs mainly due to selective erosion
process in which the bed shear stress of finer sediment particles exceeds the associated

99

critical shear stress for movement. As a consequence, finer sediment particles are transported
and leave coarser grains behind. Through this process, the coarser grains get more exposed
to the flow while the remaining finer grains get hidden among larger ones (Mao et al, 2011).
Armour layer is also partially due to the reduced exposure of the flow with those sediments
inside the scour hole zone (Sui et al., 2010). For the same bed sediments, Dey and Raika
(2007) found that the scour depth around bridge piers with an armour layer is less than that
without armour layer. Froehlich (1995) stated that the thickness of the natural armour layer
is up to one to three times the particle grain size of armour layer. Raudkivil and Ettema,
(1985) found that due to the local flow structure around a pier, local scour may either develop
through the armour layer and into the finer, more erodible sediment, or it may trigger a more
extensive localized type of scour caused by the erosion of the armour layer itself. Sui et al
(2010) studied clear-water scour around semi-elliptical abutments with armoured beds. The
results showed that for any bed material having the same grain size, with the increase in the
particle size of armour-layer, scour depth will decrease. Török and Baranya (2014)
investigated armour layer development in a scour hole around a single groin in laboratory.
The main goal of their research was to study bed morphology, sediment transport, bed
composition and hydrodynamics under conditions when bed armour development is
expected. Guo (2012) studied the relevant scour mechanism of clear water scour around piers
and proposed a scour depth equation. Zhang et al. (2012) studied bed morphology and grain
size characteristics around a spur dyke. It was found that the mean grain size and the
geometric standard deviation of the bed sediment are two important parameters in
characterizing the changes of the bed morphologies and the bed compositions around the
spur dyke. Kothyari et al. (1992) concluded that an increase in the geometric standard

100

deviation of sediment gradation (σg) would lead to a decrease in scour depth because of the
armouring effect on the bed. The presence of ice cover imposes a solid boundary to flow.
The velocity profile under ice-covered condition, is totally different compared to open
channel flow. Under ice-covered condition, the maximum velocity occurs between channel
bed and the bottom of the ice cover and is dependent on the relative roughness of these two
boundaries (Sui et al., 2010). The velocity drops to zero at each boundary due to the no-slip
boundary condition, resulting in a parabola-shaped profile (Zabilansky et al., 2006). The
presence of ice cover has been found to increase local scour depth around bridge piers by
10%~35% (Hains and Zabilansky, 2004). Based on experiments in laboratory, Wu et al.
(2014) claimed that with increase in ice cover roughness, scour depth around bridge
abutments increased, correspondingly. The impact of ice on sediment transport in a stream
is typically most significant during ice formation and breakup (Ettema and Kempema 2012;
Sui et al, 2000). Ice cover can either increase or decrease bed load and suspended sediment
transport depending on the type of ice cover (Ettema and Kempema 2012; Sui et al, 2000).
Ettema et al. (2000) proposed a method for estimating sediment transport rate in ice-covered
alluvial channels. Wu et al (2014) investigated the impact of ice cover on local scour around
bridge abutment. Results show that with increase in densimetric Froude number, there is a
corresponding increase in the scour depth. Results also showed that with increase in grain
size of the armour layer, the maximum scour depth decreases and with increase in ice cover
roughness, the maximum scour depth increases correspondingly (Wu et al, 2014). Up to date,
research work regarding the impact of ice cover on local scour in the vicinity of bridge piers
is limited. In present study, three non-uniform sediments and two types of ice cover are used
to study the development of armour layer in the scour hole around four pairs of bridge piers

101

as well as to investigate the impact of ice cover and armour layer on the maximum scour
depth under ice covered conditions.
3.2.1. Experiment setup
Experiments were carried out in a large-scale flume at the Quesnel River Research Centre of
the University of Northern British Columbia. The flume is 38.2 m long, 2 m wide and 1.3 m
deep, as showed in Figure 3-14a. The longitudinal slope of the channel bed was 0.2 percent.
A holding tank with a volume of 90 m3 was located at the upstream of the flume to keep a
constant discharge during each experimental run. To create different velocities, three valves
were connected to adjust the amount of water into the flume. Two sand boxes were filled
with natural non-uniform sediment. Theses sand boxes were spaced 10.2 m away from each
other and were 0.30 m deep and 5.6 m and 5.8 m in length, respectively. Three types of nonuniform sediments with different gain sizes were used in this experimental study. The natural
non-uniform sediments had median grain sizes of 0.50 mm, 0.47 mm and 0.58 mm and the
geometric standard deviation (σg) of 2.61, 2.53 and 1.89, respectively. According to Dey and
Barbhuiya, (2004), sediments used in this study can be treated as non-uniform since σg is
larger than 1.84. Four pairs of bridge piers with different diameters of 60 mm, 90 mm, 110
mm and 170 mm were used. Inside each sand box, a pair of bridge piers was placed
symmetrically to the center line of flume. The distance from the centre line of each pier to
the flume center is 0.25 m, as illustrated in Figure 3-14b. Water level in the flume was
controlled by adjusting the tailgate. In front of the first sand box, a SonTek incorporated 2D
Flow Meter was installed to measure flow velocities and water depth during experiment runs.
A staff gauge was also installed in the middle of each sand box to manually verify water
depth. Velocity fields in scour holes were measured using a 10-MHZ Acoustic Doppler

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Velocimeter (ADV). The ADV is a high-precision instrument that can be used to measure
3D flow velocity in a wide range of environments including laboratories, rivers, estuaries,
and the ocean (Cea and Pena, 2007). Styrofoam panels which were used to model ice cover,
had covered the entire surface of flume. In present study, two types of model ice cover were
used, namely smooth cover and rough cover. As showed in Figure 3-15, the smooth cover
was the surface of the original Styrofoam panels while the rough cover was made by
attaching small Styrofoam cubes to the bottom of the smooth cover. The dimensions of
Styrofoam cubes were 25 mm × 25 mm × 25 mm and were spaced 35 mm apart. A total of
108 flume experiments were completed under both open channel and ice-covered flow
conditions. In terms of different boundary conditions (open channel, smooth covered and
rough covered flow conditions), for each sediment type and each boundary condition, 12
experiments were done. Experimental runs were taken under clear-water scour conditions.
After 24 hours, the flume was gradually drained, and the scour and deposition pattern around
the piers was measured. To accurately read the scour depth at different locations and to draw
scour hole contours, the outside perimeter of each bridge pier was equally divided and
labeled as the reference points. The measurement of scour hole was subject to an error of +/0.3 mm. After each experiment, sand samples within the scour hole which represent armour
layer were collected. The samples were taken from the top layer of 5 mm of the armour layer
in each scour hole. The sampling process is based on the sampling methodology for
collecting armour samples proposed by Bunte and Abt (2001). The collected sand samples
were eventually sieved and the mediums grain size of armour layer (D 50) were calculated.
The scour contours were also plotted by using Surfer 13, Golden Software. In present study,
108 Experiments (36 experiments for each sediment type) were conducted under open

103

channel, smooth covered and rough covered conditions. For each sediment type, 12
experiments were done for open flow condition, 12 experiments for smooth ice-covered flow
condition and 12 experiments for rough ice-covered flow condition, respectively. Flow depth
in the flume were controlled by adjusting downstream tailgate. The flow depth ranges from
90 mm to 280 mm. The flow velocity ranges between 0.7 m/s and 2.709 m/s.

Figure 3–14a: Plan view and vertical view of experiment flume

Figure 3-14b: The spacing ratio and measuring points around the circular bridge piers

104

Figure 3-15: Rough model ice cover on water surface

3.2.2 Results and discussion
• Scour patterns and bed morphology
Figure 3-16 shows the scour morphology and developed armour layer around the 17-cm-pier.
Results indicate that the geometry of the scour holes under open flow condition is
approximately similar to that under ice-covered flow condition. As shown in Figure 3-16,
the armour layer covers the scour holes around bridge pier. At the downstream of bridge pier,
a deposition ridge was developed.

Figure 3-16: Armour layer developed around the 17-cm-pier
105

Figure 3-17 shows the scour contours and bed morphology around the 11-cm-pier under
smooth covered flow condition for the finest and the coarsest sediments. Under the same
flow condition and ice-covered condition, the maximum scour depth occurs in channel bed
with the finest sediment (D50=0.47 mm). Due to the horseshoe vortex system, the maximum
depth of sour hole is located at the upstream face of the piers, and the scour hole extends
along the sides of the piers towards the downstream face of the pier where the wake vortex
exists. This scouring process around bridge piers is substantially due to the merging of the
locally enhanced flow at the sides of the pier with the turbulent horseshoe vortices in front
of the piers. Besides, sediment deposition ridge, which is developed at the downstream of
the piers, travels further downstream as vortex shedding occurs. Under the same flow
condition and ice-covered condition, as the sediment gets coarser, the turbulence of flow
between the piers slightly decreases. Thus, with respect to Figure 3-17, a slight deposition
which is caused by the jet-like flow has developed between piers, especially for channel bed
with sediment of D50=0.47 mm.

106

Figure 3–17a: Scour morphology and the deposition ridge around the 11-cm-pier under smooth icecovered condition for D50=0.47 mm

Figure 3–17b: Scour morphology and the deposition ridge around the 11-cm-pier under smooth icecovered condition for D50=0.58 mm

Figure 3-18 shows the variation in scour depth elevation for sediment of D50=0.58 mm under
conditions of open channel, smooth ice-covered and rough ice-covered flows. The following
results are obtained from the Figure 3-18:

107

Figure 3–18: Scour profiles around the 9-cm-pier under ice-covered and open channel flow
condition for D50=0.47 mm

Under the same boundary condition (either covered flow or open flow), the maximum scour
depth is located at the upstream nose of the pier (at point 9 of the 11-cm-pier as showed in
Figure 3-14b). The primary horseshoe vortex which is stronger at the front face of pier is
responsible for this. As confirmed by Muzzammil and Gangadhariah (2003), the primary
horseshoe vortex which generates in front of a pier is the main reason for scour over the
entire scouring process. Results showed that the interaction between the primary horseshoe
vortex and the finer sediment is more intense than that of coarser sediment. Also, the lowest
scour hole is located at point 4 which is behind the pier as showed in Figure 3-18a. Figure 318b shows that, for the same sediment (such as D50=0.47 mm), the deepest scour hole has
occurred under rough ice-covered flow condition. Besides, regardless of flow cover, the
maximum scour depth is located at the upstream face, namely, location point 7 for the 9-cmpier, similar to that of the 11-cm-pier. According to Sui et al. (2010), the existence of an ice
cover on water surface doubles the wetted perimeter compared to that under open flow
condition and alters the hydraulics of an open channel by imposing an extra boundary to the
108

flow. As a consequence, the maximum flow velocity is shifted towards the channel bed. The
velocity profile is significant changed (comparing to that under open flow condition). Thus,
the strength of primary horseshoe vortexes under ice-covered flow condition is amplified,
this leads to more intense scour depths. Under covered flow condition, the roughness of ice
cover has significant impacts on velocity field and flow characteristics, namely, the rougher
the ice cover, the more effects on velocity field and flow characteristics. For channel bed
with the same sediment, the rough ice cover will lead to a deeper scour hole comparing to
that of smooth ice-cover.
Figure 3-19a shows the pattern of scour hole and deposition ridge around the 11-cm pier
under rough covered flow condition (D50=0.58 mm), while Figure 3-19b shows scour depths
around the 9-cm-pier under different boundary conditions for D50=0.47 mm. Results indicate
that, regardless of the roughness of ice cover and grain size of sediment, the maximum scour
depths always occur at the upstream front face of bridge piers. It has been observed from
experiments that the horseshoe vortex shifts the maximum downflow velocity closer to the
pier in the scour hole. Besides, under covered condition, the strength of this downflow jet is
intensified. The eroded sand particles are carried around the pier by the combined action of
accelerating flow and the spiral motion of the horseshoe vortex. As clearly showed in Figure
3-19a, the deposition ridge has been formed downstream of the pier. Melville and Coleman
(2000) stated that the wake-vortex system acts like a vacuum cleaner sucking up stream bed
material and carrying the sediment moved by the horseshoe vortex system and by the
downward flow to the downstream of the pier. However, wake vortices are normally not as
strong as the horseshoe vortices and therefore, they are not able to carry the same amount of

109

sediment load as that carried by the horseshoe vortex. Hereby, sediment deposition occurs
downstream of bridge piers in the form of deposition mound as shown in Figure 3-19a.

Figure 3–19a: A view of the scour pattern and
deposition ridge around the 11-cm pier under Figure 3–19b: Cross sections of scour and
rough ice-covered condition (D50=0.58 mm)
deposition ridge around the 9-cm-piers under
open channel, smooth and rough covered flow
conditions (D50=0.47 mm)

• Scour area and Scour Volume

Accurate determination of scour volume and scour area is important in practical decisionmaking for the control of local scour and safe design of countermeasures. However, there is
very limited research work for examining the scour volume and scour area under ice-covered
flow condition. Wu et al (2014) found that there was a linear correlation between scour depth
and volume of scour hole around bridge abutments under ice covered condition.
Khwairakpam et al. (2012) developed two formulae to estimate scour volume and scour area
around a vertical pier under clear water condition in terms of approach flow depth and pier
diameter. Figure 3-20 gives the relationship between scour volume (V) and scour area (A) in
terms of grain size of sediment. These relationships can be described as follows:
Under open flow condition:
110

V = 0.229 A1.256

(3-2-1)

Under ice-covered flow condition:

V = 0.465 A1.158

(3-2-2)

In which V is volume of scour hole (cm3) and A is surface area of scour hole. The following
results are obtained from the scour volume and scour area analysis.
(a) In terms of grain size of sediment, under the same flow condition, the finest sediment
(D50 = 0.47 mm) yielded the largest scour volume and scour area and the impact of ice cover
on scour volume and scour area is more significant for finer sediment type. On the other
hand, under the same flow conditions, the coarsest sediment (namely, D 50 = 0.58 mm) yielded
the smallest scour volume and scour area.
(b) In terms of flow cover, results indicated that the flow under ice-covered condition led to
larger amount of scour volume and scour area. It was found that, the maximum amount of
scour volume and scour area occurred under rough covered flow condition. Also, under the
same flow condition, intense scouring process around bridge piers with smaller pier spacing
has been observed, especially in channel bed with the finest sediment.

111

Figure 3–20: Relationship between scour volume and scour area

• Grain size analysis of armour layer
Sieve analyses (ASTM D422-63) were performed to obtain the grain size distribution of the
three non-uniform sediments. The grain size distribution curves for these three non-uniform
sediments used in this experimental study are displayed in Figure 3-21. Sieve analyses
revealed that the material collected was almost exclusively coarser than 0.075 mm (#200
sieve). The sediments were classified according to the unified soil classification system
(ASTM D2487-11). All three sediments were classed as poorly-graded sands (SP).

112

Figure 3–21: Grain size distribution curves of three non-uniform sands used in this study

As the experiments initiated, the armour layer evolution gradually started to develop inside
the scour hole. The first sign of armour layer development was inside the scour hole at the
upstream face of the pier where the downflow and horseshoe vortex exists and in which the
armour layer was denser. The armour layer then extended to the sides and downstream of the
pier where the armour layer particles were more separated from each other and it eventually
disintegrates at the end of the deposition ridge. Results showed that the armour layer which
was formed on the deposition ridges was composed of finer sediment particles compared to
those of armour layer formed inside the scour holes. The maximum depth of scour hole
remained quite constant once the armour layer was formed which is due to the slope stability
caused by formation of the armour layer. The samples of armour layer developed within the
scour hole were collected for each experimental run and the D50 of the armour layers were
extracted from armour layer grain size distribution graphs (described as D 50A). Figure 3-22
displays the distribution curves of grain sizes of armour layer in scour hole around the 11cm-pier for D50=0.50 mm compared to those of the original sands and deposition ridge under
rough covered flow condition.

113

Figure 3–22: Grain size distribution curves of the armour layer in scour hole around the 11-cm-pier,
original sand and deposition ridge for sand bed of D50=0.50 mm under rough covered condition

Table 3-2 shows the grain size characteristics of samples of armour layers in scour holes
around the 11-cm-pier compared to those of correspondingly deposition ridges for three
sands under rough covered flow condition. One can see from Table 3-2, the armour layer
generated in sand bed of D50=0.58 mm is coarser than that in sand beds of D50=0.47 mm and
D50=0.50 mm. To better distinguish the difference in grain size distributions between the
samples of armour layers in scour holes and the samples of the associate deposition ridges,
the grain size distributions are separately displayed in Figures 3-23(a-b). Results indicate that
the armour layer generated in sand bed of D50=0.58 mm is the coarsest comparing to those
of D50=0.47 mm and D50=0.50 mm. Regarding the deposition ridge in sand bed of D50=0.58
mm, the deposition ridge is covered by coarsest sand particles comparing to those of
D50=0.47 mm and D50=0.50 mm. With decrease in D50 of the original sand, the grain size of
the armour layer decreases correspondingly. These results are in good agreement with
findings of Wu et al (2015) who investigated the armour layer in scour holes around square
and semi-circular abutments.

114

Figure 3–23a: Grain size distributions of armour layer samples in scour hole generated from three
sands around the 11-cm-pier

Figure 3–23b: Grain size distributions of samples of deposition ridge generated from three sands
downstream of around the 11-cm-pier

115

Table 3-2: Grain size characteristics of samples of armour layer in scour hole around the 11-cm-pier
under rough covered flow condition compared to those of associated deposition ridge
Geometric
Uniformity
D10
D16
D30
D50
D60
D84
D90
standard
Coefficient of
coefficient
(mm)
(mm)
(mm) (mm) (mm) (mm) (mm)
deviation
curvature (Cc)
(CU)
(σg)
Composition of armour layer (DXA)
Sample 1, for
0.22
0.28
0.40 0.70 1.10 3.30 3.80
3.43
5.00
0.66
D50=0.50mm
Sample 2, for
0.21
0.26
0.38 0.55 0.62 1.40 2.10
2.32
2.95
1.11
D50=0.47mm
Sample 3, for
0.23
0.28
0.39 1.40 2.10 3.80 4.00
3.68
9.13
0.31
D50=0.58mm
Composition of deposition ridge (DXR)
Sample 1, for
0.18
0.21
0.27 0.40 0.48 0.75 0.88
1.89
2.67
0.84
D50=0.50mm
Sample 2, for
0.17
0.19
0.24 0.34 0.40 0.63 0.72
1.82
2.35
0.85
D50=0.47mm
Sample 3, for
0.18
0.21
0.30 0.47 0.53 0.90 1.30
2.07
2.94
0.94
D50=0.58mm

• Determination of scour depth with influence of armour layer:
Considering a bridge pier in a river whose flow is assumed to be steady and uniform, Breusers
et al (1977) pointed out that following parameters may influence the scouring phenomenon
as follows: 1) variables characterizing the fluid such as acceleration due to gravity (g) and
density of fluid (ρw); 2) variables characterizing the bed material such as sediment density
(ρs), median grain size of the bed material (D50B) and median grain size of sediment particles
of the armor layer; 3) variables characterizing the flow such as depth of approaching flow
(y0) and the mean velocity of approaching flow (U); 4) variables characterizing the bridge
pier and channel geometry such as pier shape and size and channel width. In addition to
above-mentioned parameters, in the present study, the effect of ice cover roughness is an
important parameter which must be considered. Therefore, conceptually at least, with
influence of armour layer in scour hole around bridge pier, the maximum scour depth of
scour hole may be evaluated by means of a general formula for computation:
116

(

y m a x = f U,g ,D 5 0 A ,D 5 0 B ,n b ,n i ,D ,B , y 0 , r w , r s

)

(3 -2 -3)

I n w hi c h, ym a x is t h e m a xi mu m d e pt h of s c o ur h ol e ar o u n d bri d g e pi er; D 5 0 A is t h e m e di a n
gr ai n si z e of ar m o ur l a y er; n b is t h e M a n ni n g r o u g h n e ss c o effi ci e nt of c h a n n el b e d; n i is
M a n ni n g r o u g h n e ss c o effi ci e nt of i c e c o v er;

D

is t h e di a m et er of bri d g e pi er; B

is t h e

c h a n n el wi dt h; ρ w a n d ρ s ar e t h e d e nsit y of w at er a n d s e di m e nt, r es p e cti v el y, wit h  ρ = ρ s ρ w . T hr o u g h di m e nsi o n al a n al ysis b y m e a ns of B u c ki n g h a m  t h e ori es, t h e m a xi m u m d e pt h
of s c o ur h ol e c a n b e e x pr e ss e d as f oll o w s
æ
y ma x
= fç
ç
D 50A
è

(

U
D r rW

)

ö
D 50A n i D 50A D 50A D 50A ÷
,
, ,
,
,
B
D ÷
g D50A D 50B n b y0
ø

U

T h e t er m Fr 0 =

(D r r ) g D
W

(3 -2 -4)

is c all e d d e nsi m etri c Fr o u d e n u m b er a n d is a crit eri o n of
50A

h y dr a uli c c o n diti o ns f or ass ess m e nt of t h e i n ci pi e nt m oti o n of b e d m at eri al ( A g uirr e -P e,
2 0 0 3). It is a t er m t h at d es cri b es t h e i n ci pi e nt m oti o n of t h e s e di m e nt arti cl e s. T h e l ar g er t h e
d e nsi o m etri c Fr o u d e n u m b er, t h e l ar g er s h e ar str ess is n e e d e d t o tr a ns p ort t h e s e di m e nt
p arti cl es. E q. 3 -2 -4 c a n b e als o e x pr ess e d as f oll o ws:
b

c

d

e
f
ö æn ö æD
ö æD
ö æD
ö
aæ D
y ma x
5
0
A
i
5
0
A
5
0
A
5
0
A
= A Fr 0 çç
÷÷ çç ÷÷ çç
÷÷ ç
÷ ç
÷
D 50A
è D 50B ø è n b ø è y0 ø è B ø è D ø

( )

(3 -2 -5)

Si n c e t h e v al u e s of D 5 0 A / B is tr ul y ti n y, t h e t er m D5 0 A / B c a n b e n e gl e ct e d fr o m E q. 3 -2 -5.
B esi d e s, t h e t er m ( D 5 0 A / y0 ) c a n b e als o i g n or e d fr o m E q. 3 -2 -5 d u e t o it s w e a k c orr el ati o n
wit h ( y m a x / D5 0 A ). T h er ef or e, t h e f oll o wi n g p ar a m et ers h a v e b e e n us e d t o ass ess t h e r el ati v e
m a xi m u m s c o ur d e pt h ( M S D) of s c o ur h ol e (y m a x / D5 0 A ) ar o un d bri d g e pi er.
a

c

æ D ö æ D öb æ n ö
d
y ma x
= A çç 5 0 A ÷÷ ç 5 0 A ÷ çç i ÷÷ Fr 0
D 50A
è D 50B ø è D ø è n b ø

( )

(3 -2 -6)

117

In the case of open channel flow condition, the ratio of roughness coefficient of ice cover to
roughness coefficient of channel bed would be omitted from Eq. 3-2-6. Each of the
independent dimensionless variables of Eq. 3-2-6 were assessed separately to study their
impact on the local scour around bridge piers.
• Variation of relative MSD (ymax/D50A) with densimetric Froude number (Fr0):
Figure 3-24 illustrates the variation of relative MSD with densimetric Froude number (Fr0).
With increase in Fr0, the relative MSD increases correspondingly. Besides, under the same
Fr0, the values of the relative MSD under ice-covered conditions are larger than those under
open flow condition. On the other hand, with the same values of relative MSD, the larger
value of densimetric Froude number is needed to initiate sediment transportation for the open
channel flow condition which means that a lower values of shear stress is needed to initiate
motion for sediment transportation under ice-covered flow conditions.

Figure 3–24: Relation between the relative MSD (ymax/D50A) with densimetric Froude number (Fr 0)

118

• Variation of relative MSD (ymax/D50A) with the grain size of armour layer (D50A/D50B):
Figure 3-25a illustrates the variation of relative MSD (ymax/D50A) against ratio of grain size
of armour layer (D50A/D50B) distinguished by different pier sizes. Regardless of size of bridge
pier, as the grain size of armour layer (D50A/D50B) increases, the relative MSD of scour hole
decreases and vice versa. From Figure 3-25b, one can see that the variation of relative MSD
(ymax/D50A) against ratio of (D50A/D50B) distinguished by different covered conditions.
Regardless of flow cover, the relative MSD (ymax/D50A) decreases as the grain size of armour
layer (D50A/D50B) increases. Under rough covered condition, the relative MSD (ymax/D50A)
showed a sharper descending trend with the grain size of armour layer (D50A/D50B) compared
to those of under both smooth covered and open flow conditions. Also, under smooth covered
flow condition, the relative MSD (ymax/D50A) showed a sharper descending trend with the
grain size of armour layer (D50A/D50B) compared to those of under open flow condition. The
reason for this is due to strong turbulent flows and different velocity fields close to channel
bed which are caused by ice cover, and it get more intensified under rough covered flow
condition. Similar results were also reported by Dey and Raikar (2007).

Figure 3–25a: Variation of relative MSD (ymax/D50A) with (D50A/D50B) distinguished by pier size
119

Figure 3–25b: Variation of relative MSD (ymax/D50A) with (D50A/D50B) distinguished by different
covered conditions

• Variation of relative MSD (ymax/D50A) with the pier spacing (D50A/D):
Figure 3-26 illustrates the variation of relative MSD (ymax/D50A) with ratio of the pier spacing
(D50A/D) distinguished by different covered conditions. Regardless of flow cover, the relative
MSD (ymax/D50A) decreases with increase in ratio of the pier spacing (D50A/D). Under rough
covered condition, the relative MSD (ymax/D50A) showed a sharper descending trend with the
pier spacing (D50A/D) compared to those of under both smooth covered and open flow
conditions. Besides, under the same values of (D50A/D), the rough ice-covered flow has
resulted in largest relative MSD.

120

Fi g ur e 3 – 2 6: V ari ati o n of r el ati v e M S D ( y m a x /D 5 0 A ) wit h t h e r ati o of pi er s p a ci n g ( D 5 0 A /D)
disti n g uis h e d b y diff er e nt c o v er e d c o n diti o ns

• V a ri ati o n of r el ati v e M S D ( y m a x / D5 0 A ) wit h r o u g h n ess of i c e c o v e r ( n i/ nb ):
As p oi nt e d o ut b y M a ys ( 1 9 9 9), d u e t o a r el ati v el y s m o ot h c o n cr et e -li k e s urf a c e of t h e
St yr of o a m p a n el, t h e r o u g h n ess of t h e m o d el s m o ot h i c e -c o v er w as ass u m e d t o b e 0. 0 1 3. I n
t er ms of m o d el r o u g h i c e-c o v er, Li ( 2 0 1 2) r e vi e w e d s e v er al m et h o ds f or c al c ul ati n g t h e
M a n ni n g’s c o effi ci e nt f or i c e c o v er, t h e f oll o wi n g e q u ati o n c a n b e us e d d e p e n di n g o n t h e
si z e of t h e s m all c u b e s:
ni

k S1 6

(8 g ) ( R K )
=
0. 8 6 7 l n (1 2 R K )
-1 2

1 6

S

(3 -2 -7)

S

I n w hi c h, Ks is t h e a v er a g e r o u g h n ess h ei g ht of t h e i c e c o v er u n d ersi d e a n d R is t h e h y dr a uli c
r a di us. B y usi n g E q. 3 -2 -7, a M a n n i n g’s c o effi ci e nt of 0. 0 2 1 w as d et er mi n e d as t h e r o u g h n es s
c o effi ci e nt of m o d el r o u g h i c e c o v er. T his v al u e als o a gr e es wit h r es ult of H ai ns a n d
Z a bil a ns k y ( 2 0 0 4) . T o c al c ul at e c h a n n el b e d r o u g h n e ss c o effi ci e nt f or n o n -u nif or m s a n d b e d,
t h e f oll o wi n g e q u ati o n pr o p o s e d b y H a g er ( 1 9 9 9) w as us e d:
n b = 0. 0 3 9 D 51/0 6

(3 -2 -8)

121

T h er ef or e, t h e r o u g h n e ss c o effi ci e nt of s a n d b e d n b is d et er mi n e d as 0. 0 1 0 9 f or s a n d b e d of
D 5 0 = 0. 4 7 m m, 0. 0 1 1 0 f or s a n d b e d of D 5 0 = 0. 0 5 0 m m, a n d 0. 0 1 1 3 f or s a n d b e d of D 5 0 = 0. 5 8
m m, r es p e cti v el y. R es ult s i n di c at e t h at wit h i n cr e as e i n n i/ nb , t h e r el ati v e M S D (y m a x / D5 0 A )
i n cr e a s es c orr es p o n di n gl y. F oll o wi n g E q. 3 -2 -9 a n d 3 -2 -1 0 ar e d e v el o p e d t o pr e di ct t h e
r el ati v e M S D (y m a x / D5 0 A ) u n d er i c e -c o v er e d c o n diti o n a n d o p e n fl o w c o n diti o n, r es p e cti v el y.
O p e n fl o w c o n diti o n:

ö
1. 2 8 9 æ D
y ma x
= 1. 4 3 3 Fr 0
çç 5 0 A ÷÷
D 50A
è D 50B ø

( )

- 0. 1 9 0

æD ö
ç 50A ÷
è D ø

- 0. 4 8 8

R 2 = 0. 8 5

(3 -2 -9)

R 2 = 0. 8 8

(3 -2 -1 0)

I c e-c o v er e d fl o w c o n diti o n:

ö
0. 8 9 2 æ D
y ma x
= 4 7. 1 9 0 Fr 0
çç 5 0 A ÷÷
D 50A
è D 50B ø

( )

- 0. 6 5 2

æD ö
ç 50A ÷
è D ø

- 0. 3 6 7

æn ö
çç i ÷÷
ènb ø

0. 4 8 4

A c c or di n g t o E q. 3 -2 -9 a n d E q. 3 -2 -1 0, t h e m o st si g nifi c a nt v ari a bl e is t h e d e nsi m etri c
Fr o u d e n u m b er si n c e t his v ari a bl e h a s t h e l ar g est p o w er c o m p ari n g t o all ot h er v ari a bl e s.
Fi g ur e 3 -2 7 s h o w e d t h e c o m p aris o n of c al c ul at e d r el ati v e M S D ( y m a x / D5 0 A ) t o t h o s e o bs er v e d
u n d er o p e n fl o w c o n diti o n, a n d Fi g ur e 3 -2 8 s h o w t h e c o m p aris o n of c al c ul at e d r el ati v e M S D
( ym a x / D5 0 A ) t o t h o s e o bs er v e d u n d er i c e-c o v er e d fl o w c o n diti o n. As s h o w e d i n Fi g ur es 3 -2 7
a n d 3 -2 8 , t h e c al c ul at e d r el ati v e M S D ( ym a x / D5 0 A ) a gr e e d w ell wit h t h o s e o bs er v e d u n d er
b ot h o p e n fl o w c o n diti o n a n d i c e -c o v er e d c o n diti o n. T o b ett er s p e cif y t h e c o rr el ati o n of
diff er e nt di m e nsi o nl e ss v ari a bl e s of E q u ati o n 1 0 wit h e a c h ot h er a n d t h eir i m p a ct o n t h e
r el ati v e

M S D ( y m a x / D5 0 A ), diff er e nt c o m bi n ati o n of t h o s e di m e nsi o nl ess v ari a bl e s ar e

g e n er at e d i n T a bl e 3 -3 . As o n e c a n s e e fr o m T a bl e 3 -3 t h e d e nsi m etri c Fr o u d e n u m b er is t h e
m o st d o mi n a nt p ar a m et er si n c e it s i n di vi d u al R 2 c o effi ci e nt is 0. 7 8 4. T h e n e xt d o mi n a nt t er m
is r ati o of gr ai n si z e of ar m o ur l a y er (D 5 0 A / D5 0 B ) wit h R 2 c o effi ci e nt of 0. 6 9 4. Wit h r es p e ct
122

to combination of two terms, the combination of (D50A/D50B) and (Fr0) is the most accurate
one with R2 equal to 0.787. With respect to combination of three terms, the combination of
(ni/nb); (D50A/D); (Fr0) is the most accurate with R2 equal to 0.857.

Figure 3–27: Comparison of calculated relative MSD (ymax/D50A) to those observed under open flow
condition

Figure 3–28: Comparison of calculated relative MSD (ymax/D50A) to those observed under icecovered flow condition

123

Table 3-3: Different combinations of dimensionless variables
ymax/D50A= f ()
R2
Equation
(D50A/D50B); (ni/nb); (D50A/D); (Fr0)

0.890

47.190(D50A/D50B)-0.652(ni/nb)0.484(D50A/D)-0.367(Fr0)0.892

(ni/nb); (D50A/D); (Fr0)

0.857

21.573(ni/nb)0.613(D50A/D)-0.555(Fr0)1.13

(D50A/D50B); (D50A/D); (Fr0)

0.856

7.948(D50A/D50B)-0.772(D50A/D)-0.32(Fr0)0.889

(D50A/D50B); (ni/nb); (Fr0)

0.806

47.215(D50A/D50B)-1.132(ni/nb)0.008(Fr0)0.859

(D50A/D50B); (Fr0)

0.787

45.658(D50A/D50B)-1.132(Fr0)0.859

(D50A/D50B); (ni/nb); (D50A/D)

0.756

7.948(D50A/D50B)-1.329(ni/nb)0.313(D50A/D)-0.370

(D50A/D50B); (D50/D)

0.748

26.245(D50A/D50B)-1.577(D50A/D)-0.252

(D50A/D50B); (ni/nb)

0.742

841.012(D50A/D50B)-1.776(ni/nb)0.533

(Fr0)

0.784

19.345(Fr0)1.6851

(D50A/D50B)

0.694

110.9(D50A/D50B)-1.83

(D50/D)

0.568

0.4123(D50A/D)-0.992

(ni/nb)

0.137

5617.1(ni/nb)1.1492

3.2.3. Conclusions
In present study, to investigate the impact of armour layer and ice cover on scour depth
around bridge piers, three non-uniform sediments and four pairs of model piers were used to
conduct 108 experiments in a large-scale flume under both open flow condition and icecovered flow condition. Following conclusions can be drawn from the present study.
1) Although the scour depth under ice-covered flow condition was larger comparing to that
under open flow condition, the geometry of the scour holes under open flow condition is
similar to that under ice-covered flow condition. Results showed that, regardless of flow
cover, the maximum scour depth decreases with increase in the grain size of armour layer.
Also, although the maximum depth of scour hole around largest pier was deepest, the grain
size distribution of armor layer in scour hole around larger piers did not show a significant
difference from those around smaller piers.

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2) Under the same flow condition and same covered condition, the maximum scour depth
occurs in channel bed with the finest sediment. Due to the horseshoe vortex system,
maximum scour depth is located at the upstream face of the piers and extends along the sides
of the piers towards the rear side of the pier where wake vortex exists. Due to effect of ice
cover, the horseshoe vortex shifts the maximum downflow velocity closer to the pier in the
scour hole. Thus, the strength of downflow gets more intensified which leads to a larger and
wider deposition ridge downstream of the pier.
3) Under the same flow condition, both scour volume and scour area of scour hole in the
finest sand bed are largest comparing to those in channel bed with coarser sands. With respect
to the impact of ice cover, it was found that both scour volume and scour area of scour hole
under rough covered flow condition are largest comparing to those under both smooth
covered condition and open flow condition.
4) Based on data collected in laboratory, two formulae have been developed to predict the
relative MSD (ymax/D50A) under both open flow condition and ice-covered condition.
Following dimensionless variables are considered in the proposed formulae for determining
the relative MSD (ymax/D50A): densimetric Froude number (Fr0), grain size of armour layer
(D50A/D50B), pier spacing (D50A/D), and roughness of ice cover (ni/nb). Results showed that
the calculated relative MSD (ymax/D50A) agreed well with those observed under both open
flow condition and ice-covered condition.
5) Results showed with increase in densimetric Froude number (Fr0), the relative MSD
increases correspondingly. Besides, under the same Fr 0, the values of the relative MSD under
ice-covered conditions are larger than those under open flow condition. Results also indicate
that, under ice-covered flow condition, a smaller value of densimetric Froude number is

125

needed to initiate movement of sediment comparing to that under open flow condition which
can be justified by the higher flow velocity near channel bed under ice-covered flow
conditions and its impact on the threshold of sediment motion.

3.2.4. Reference
Aguirre-Pe J., Olivero M. L., and Moncada A. T. (2003), Particle densimetric Froude number
for estimating sediment transport. Journal Hydraul. Eng., Vol. 129, No. 6, pp. 428–437
Bunte, K., and Abt, S. R. (2001). Sampling surface and subsurface particle-size distributions
in wadable gravel-and cobble-bed streams for analyses in sediment transport, hydraulics, and
streambed monitoring. Gen. Tech. Rep. RMRS-GTR-74. Fort Collins, CO: US Department
of Agriculture, Forest Service, Rocky Mountain Research Station. 428 p., 74.
Breusers, H. N. C., Nicollet, G., and Shen, H. W. (1977). Local scour around cylindrical
piers. Journal of Hydraulic Research, 15(3), 211-252.
Cea, L., Puertas, J., and Pena, L. (2007). Velocity measurements on highly turbulent free
surface flow using ADV. Experiments in fluids, 42(3), 333-348.
Dey, S., and Raikar, R. (2007). Clear-water scour at piers in sand beds with an armor layer
of gravels. Journal of Hydraulic Engineering, 133, 703-711.
Dey, S., and Barbhuiya, A. K. (2004). Clear-water scour at abutments in thinly armored beds.
Journal of hydraulic engineering, 130(7), 622-634.
Ettema, R., Braileanu, F., and Muste, M. (2000). Method for estimating sediment transport
in ice-covered channels. Journal of Cold Regions Engineering, 14(3), 130-144.
Ettema, R., and Kempema, E. W. (2012). River Ice Effects on Gravel Bed Channels. GravelBed Rivers: Processes, Tools, Environments, 523-540.
Froehlich, D.C. (1995). Armor limited clear water construction scour at bridge, Journal of
Hydraulic Engineering, ASCE 121: 490–493.
Guo, J. (2012). Pier scour in clear water for sediment mixtures. Journal of Hydraulic
Research 50(1): 18–27.
Hager, W. (1999). “Wastewater Hydraulics: Theory and Practice.” Springer: Berlin, New
York.
Hains, D., Zabilansky, L.J. and Weisman, R.N. (2004) An experimental study of ice effects
on scour at bridge piers. Cold Regions Engineering and Construction Conference and Expo,
(16–19 May 2004, Edmonton, Alberta).
Kothyari, U. C., Garde, R. C. J., and Ranga Raju, K. G. (1992). Temporal variation of scour
around circular bridge piers. Journal of Hydraulic Engineering, 118(8), 1091-1106.
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Khwairakpam, P., Ray, S. S., Das, S., Das, R., and Mazumdar, A. (2012). “Scour hole
characteristics around a vertical pier under clear water scour conditions”. ARPN J. Eng.
Appl. Sci, 7(6), 649-654.
Li, S. S. (2012). Estimates of the Manning's coefficient for ice-covered rivers. In Proceedings
of the Institution of Civil Engineers-Water Management (Vol. 165, No. 9, pp. 495-505).
Thomas Telford Ltd.
Mays, L. W. (Ed.). (1999). Hydraulic design handbook. McGraw-Hill Professional
Publishing
Melville, B. W., and Raudkivi, A. J. (1977). Flow characteristics in local scour at bridge
piers. Journal of Hydraulic Research, 15(4), 373-380.
Melville, B. W., and Sutherland, A. J. (1988). Design method for local scour at bridge piers.
Journal of Hydraulic Engineering, 114(10), 1210-1226.
Mao L., Cooper, J. and Frostick, L. (2011). Grain size and topographical differences between
static and mobile armour layers. Earth surface Processes and Landforms, 36(10), 1321-1334.
Melville, B. W. and Coleman, S. E. (2000). Bridge scour. Water Resources Publication.
Muzzammil, M., and Gangadhariah, T. (2003). The mean characteristics of horseshoe vortex
at a cylindrical pier. Journal of Hydraulic Research, 41(3), 285-297.
Richardson, E., and Davis, S. (2001). Evaluating scour at bridges, 4th edition. Publication
No. FHWA NHI 01-001. p380.
Richardson, E. V., Harrison, L. J., Richardson, J. R., and Davis, S. R. (1993). Evaluating
scour at bridges (No. HEC 18 (2nd edition)).
Raudkivi, A. J., and Ettema, R. (1983). Clear-water scour at cylindrical piers. Journal of
Hydraulic Engineering, 109(3), 338-350.
Sui, J., Wang, D., and Karney, B. (2000). Sediment concentration and deformation of
riverbed in a frazil jammed river reach, Canadian Journal of Civil Engineering, 27(6): 11201129.
Sui, J., Wang, J., Yun, H. E., and Krol, F. (2010). Velocity profiles and incipient motion of
frazil particles under ice cover. International Journal of Sediment Research, 25(1), 39-51.
Török, G. T., Baranya, S., Rüther, N., and Spiller, S. (2014). Laboratory analysis of armor
layer development in a local scour around a groin. In Proceedings of the International
Conference on Fluvial Hydraulics River Flow, Lausanne EPFL, Lausanne, Switzerland (pp.
3-5).
Wu, P., Hirshfield, F., Sui, J., Wang, J., and Chen, P. P. (2014). “Impacts of ice cover on
local scour around semi-circular bridge abutment. Journal of Hydrodynamics”, 26(1), 10-18.
Wu, P., Hirshfield, F., and Sui, J. (2015). Armour layer analysis of local scour around bridge
abutments under ice cover. River research and applications, 31(6), 736-746.
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Zhang, H., Nakagawa, H., and Mizutani, H. (2012). Bed morphology and grain size
characteristics around a spur dyke. International Journal of Sediment Research, 27(2), 141157.
Zabilansky, L. J., Hains, D. B., and Remus, J. I. (2006). Increased bed erosion due to ice. In
Current Practices in Cold Regions Engineering (pp. 1-12).

128

3.3. Effects of ice cover on the incipient motion of bed material and shear stress
around side-by-side bridge piers
An alluvial river bed is likely to experience continuous changes over time. In one case,
flowing water erodes, moves and gradually collects sediment in the river, modifying its bed
elevation and slightly changing its boundaries. Changes in bed elevation could be resulted
from either natural processes or human activities which lead to alteration of the river bed or
river geometry (Chiew, 1987). Placement of bridge piers inside the river is one of the most
common engineering practices in which the bridge pier is in direct contact with the flowing
water. The main issue associated with the interaction of flowing water and the bridge pier is
the scouring process which occurs around the bridge piers and is known as local scour.
According to Shen et al (1969), local scour is the abrupt decrease in bed elevation near a pier
due to erosion of bed material by the local flow structure caused by the pier. Overlooking the
local scour phenomenon in the bridge pier design might possibly result in either a huge
financial cost or a high casualty rate. According to Briaud et al (2006), 1502 bridges
collapsed due to bridge scour between 1966 and 2005 in the United States, with an average
rate of one bridge collapse every 10 days. Wardhana and Hadipriono (2003) studied 500
cases of bridge structure failures between 1989 and 2000 in the United States and stated that
the most common causes of bridge failures were due to floods and scouring process. Due to
its inherent importance, local scour has been studied extensively by many researchers (such
as: Ettema, et al, 2011; Graf and Istiarto, 2002; Kothyari, 1992; Melville and Raudkivi, 1977;
Melville and Sutherland, 1988; Raudkivi and Ettema, 1983; Yanmaz and Altimbilek, 1991).
Melville and Raudkivi (1977) investigated the flow patterns, distributed turbulence intensity
and boundary shear stresses in the scour zone. The main results concerned the flow patterns
in vertical and horizontal planes, the turbulence intensity and the bed shear stress distribution.

129

A significant limitation of Melville and Raudkivi’s work was that the bed sediments had a
uniform grain size which is not an appropriate representative of bed material in natural rivers;
this is also the case in most of the experimental studies. Also, most of the reported studies
regarding the maximum scour depth around bridge piers have been done in small-scale
laboratory flumes under open flow condition. This can result in tremendous conservative
results. Up to date, research work regarding local scour around bridge pier under ice-covered
flow condition is very limited, primarily due to the difficulties in obtaining field data from
ice-covered rivers. Ice cover presence adds a level of complexity to hydraulic processes in
rivers, and sometimes extremely influences river characteristics such as hydrodynamics and
morphology (Ettema and Zabilansky, 2004). When ice floes move discretely and freely (for
example, in the case of low surface concentrations of ice pans during freeze-up), the
resistance effect caused by flowing ice is slight and water levels do not modify greatly
(Wang, et al, 2008). In practice, ice cover appears quite often in rivers in the cold regions
during the winter. From the hydraulics point of view, the presence of an ice cover increases
the wetted perimeter by adding an additional boundary to the water surface.
Under ice-covered flow conditions, the flow is highly sensitive to the friction parameter
(Hoque, 2009). Ackermann et al (2002) did a laboratory investigation on the effect of ice
cover on local scour around circular bridge piers. Their results showed that for equivalent
averaged flow velocities, the existence of an ice cover could increase the local scour depth
scour by 25% to 35 % from the free surface condition. Bacuta and Dargahi (1986) carried
out laboratory tests in a flume with a simulated ice cover for clear-water conditions. They
found the extent of scour is larger for ice-covered flows. Besides, the appearance of an ice
cover in river changes the velocity profile (Sui et al., 2010a). Under ice-covered flow

130

condition, the upper portion of the flow is mainly affected by the ice cover resistance while
the lower portion of flow is primarily influenced by the channel bed resistance (Sui et al.,
2010a). The maximum flow velocity under ice cover is located somewhere between the
channel bed and ice cover depending on the ratio of the ice resistance coefficient to the bed
resistance coefficient (Crance and Frothingham, 2008). According to Wang et al. (2008), it
is expected that as the ice resistance increases, the maximum flow velocity will move closer
to the channel bed. Since ice cover imposes an additional solid boundary on the flow, the
incipient motion of sediment under ice-covered flow condition is different from that under
open channel flow condition. Wang et al. (2008) also studied the impacts of flow velocity
and water depth on the incipient motion of bed material under ice-covered condition. It was
found that the deeper the flow depth under ice cover, the higher the flow velocity needed for
the incipient motion of bed material. One of the main objectives of the studies on local scour
process is to help river engineers to predict the incipient motion of bed material. On the other
side, the development of an armour layer in the scour hole around bridge piers is associated
with incipient motion of sediment particles. Bed armouring process typically occurs in
streams with non-uniform bed materials. This phenomenon occurs mainly due to selective
erosion process in which the bed shear stress of finer sediment particles exceeds the
associated critical shear stress for movement. Consequently, finer sediment particles are
transported and leave coarser grains behind. Through this process, the coarser grains get
more exposed to the flow while the remaining finer grains get hidden among larger ones
(Mao et al, 2011). Armour layer is also partially due to the reduced exposure of the flow with
those sediments inside the scour hole zone (Sui et al., 2010b). For the same bed sediments,
Dey and Raika (2007) found that the scour depth around bridge piers with an armour layer

131

is less than that without armour layer. Froehlich (1995) stated that the thickness of the natural
armour-layer is up to one to three times the particle grain size of armour-layer. Raudkivil and
Ettema, (1983) found that due to the local flow structure around a pier, local scour may either
develop through the armour layer and into the finer, more erodible sediment, or it may trigger
a more extensive localized type of scour caused by the erosion of the armour layer itself. Sui
et al (2010b) studied clear-water scour around semi-elliptical abutments with armoured beds.
The results showed that for any bed material having the same grain size, with increase in the
particle size of armour-layer, scour depth will decrease. In terms of hydraulic engineering
design, determination of the critical condition for incipient motion of sediment and the
sediment transport rate is highly crucial. To study the incipient motion of sediment particle,
the Shields diagram (Shields 1936) is widely accepted. It is a graph of boundary shear stress
non-dimensionalized by the submerged specific weight and the mean size of the sediment
particle which is called the Shields parameter, Shields criterion, Shields number or
dimensionless shear stress (τc*) against the boundary Reynolds number (Re*) (Miller, et al.,
1977). According to Shields (1936), the critical conditions in which sediment is on the verge
of becoming entrained can be determined by relating the critical Shields value (τc*) and the
shear Reynolds number (Re*). The boundary shear Reynolds number is defined as follows:

Re* =

U *Di



(3-3-1)

Where, Di is the grain size diameter, ν is the kinetic viscosity of fluid, and U* is shear
velocity. In this study, since the applied bed materials are composed of non-uniform natural
sediment, the particle grain size is not constant. Therefore, the median grain size of nonuniform sand (D50) is used to represent the particle size for calculating the critical shear
Reynolds number. The shear velocity (U*) in Eq. 3-3-1 can be determined as follows:
132

U *=

g RS

(3 -3 -2)

W h e r e, S is t h e c h a n n el sl o p e, R is t h e h y dr a uli c r a di us a n d g is t h e gr a vit ati o n al a c c el er ati o n.
T h e di m e nsi o nl ess s h e ar str ess is us e d t o c al c ul at e t h e i niti ati o n of s e di m e nt m oti o n i n a fl ui d
fl o w ( M a ds e n, 1 9 9 1). T h e criti c al di m e nsi o nl e ss s h e ar str ess ( τ c * ) is d efi n e d as f oll o w s:

t c* =

r U c* 2
t
=
(r s - r ) g D 50 (r s - r ) g D 50

(3 -3 -3)

I n w hi c h, ρ s a n d ρ ar e t h e m a ss d e nsit y of s e di m e nt a n d w at er, r es p e cti v el y, a n d U * c is t h e
criti c al s h e ar v el o cit y t h at i niti ali z es t h e m oti o n of t h e p arti cl es . I n g e n er al, t h e t h e or eti c al

pr e di cti o n of t h e cr iti c al c o n diti o n f or i n ci pi e nt m oti o n is b a s e d o n a f or c e or m o m e nt u m
b al a n c e b et w e e n t h e d est a bili zi n g h y dr o d y n a mi c dr a g ( F D ) a n d lift f or c es (F L ) a g ai nst t h e
r esisti n g gr a vit ati o n al (W ) a n d fri cti o n al f or c es (F R ). S e di m e nt p arti cl e will b e m o v e d if t h e
a p pli e d f or c es o v er c o m e t h e r esist a n c e f or c e. At t h e t hr es h ol d of m o v e m e nt, t h e a p pli e d
f or c es ar e j u st i n b al a n c e wit h t h e r esisti n g f or c e ( C h a n g, 1 9 8 8). I n ot h er w or ds, a s e di m e nt
p arti cl e is at a st at e of i n ci pi e nt m oti o n w h e n t h e f oll o wi n g c o n diti o ns h a v e b e e n s atisfi e d:

F D = F R si n 

W = F L + F R c os 

(3 -3 -4)

T h e s u b m er g e d w ei g ht of t h e p arti cl e c a n b e gi v e n b y:

W =  d (  s −  g)
6
3

(3 -3 -5)

W h er e d is s e di m e nt si z e i n t h e ar m or l a y er. A p art fr o m g e o m etri c d et ails s u c h a s b e d sl o p e,
p arti cl e e x p o s ur e a n d p o c k et g e o m etr y, a c c ur at e pr e d i cti o n of i n ci pi e nt moti o n r e q uir e s
pr e cis e k n o wl e d g e of t h e h y dr o d y n a mi c dr a g ( F D ) a n d lift f or c es ( F L ) a cti n g o n t h e p arti cl e.
B y usi n g Y a n g’s crit eri a ( 2 0 0 3) f or i n ci pi e nt m oti o n, t h e dr a g f or c e c a n b e e x pr ess e d as:

133



FD = CD  d
Vs2
4 2
2

(3-3-6)

where, CD is the drag coefficient at velocity Vs, and Vs is the local velocity at a distance of
“s” above the bed. The lift force acting on the particle can be obtained as:


FL = CL  d
Vs2
4 2
2

(3-3-7)

Where CL is the lift coefficient at velocity Vs. Meyer-Peter and Mueller (1948) proposed the
following equation to calculate the sediment size in the armor layer.

d=

SH
1/6 3/2
K1(n / D90
)

(3-3-8)

where, d is the grain size in the armor layer; S is the channel slope; H is the mean flow depth;
K1 is the constant number equal to 0.058 when H is in meters; n is the channel bottom
roughness or Manning’s roughness, and D90 is the bed material size where 90% of the
material is finer. To calculate the critical bed shear velocity in Eq. 3-3-3, Eq. 3-3-9 which is
developed based on the “Law of wall method” can be used. The Law of wall method was
originally proposed by von Kármán (von Kármán 1930) and supposed that the velocity
profile in the lower portion of an open channel flow has a logarithmic distribution (Barenblatt
and Chorin, 1997).

U c* =

uk
Ln z z0

(

)

(3-3-9)

In which, u is the average cross-section flow velocity, k is the Von Karman’s constant
which is supposed to be 0.4, z represents the distance from channel bed which is supposed
to be depth of water, and z0 is the roughness height which is supposed to be D50 of the
sediment particles. Due to the presence of U c* in both axes of the Shields diagram, Madsen

134

a n d Gr a nt ( 1 9 7 7) i ntr o d u c e d a n e w v ari a bl e r at h er t h a n t h e s h e ar R e y n ol ds n u m b er i n t h e
h ori z o nt al a xis of t h e S hi el d s di a gr a m w hi c h is c all e d t h e s e di m e nt -fl uid p ar a m et er ( S * ). T h e
s e di m e nt -fl ui d p ar a m et er (S * ) c a n b e c al c ul at e d fr o m t h e f oll o wi n g e q u ati o n:
S*=

D 50
4u

(S G - 1) g D

50

(3 -3 -1 0)

I n w hi c h, S G r e pr es e nt s t h e s p e cifi c w ei g ht of s e di m e nt.
Of n ot e, si n c e a n a d diti o n al b o u n d ar y is a d d e d t o t h e w at er s urf a c e f or t h e c as e of i c e -c o v er e d
fl o w c o n diti o n, h y dr a uli c r a di us (R ) is diff er e nt fr o m t h at of t h e o p e n c h a n n el c o n diti o n.
T h er ef or e, a n e m piri c al e q u ati o n i ntr o d u c e d b y ( T a n g a n d D a v ar 1 9 8 5) w hi c h is f or h y dr a uli c
r a di us e sti m ati o n, h as b e e n a d o pt e d f or v ari o us c o v er e d c o n diti o ns i n cl u di n g o p e n w at er t o
c o m pl et el y c o v er e d fl o w r e gi m es. T h e e q u ati o n c a n b e st at e d as f oll o w s f or r e ct a n g ul ar
c h a n n els:

R =

y0 w
2 y0 + w 1 + a 1 0 0

(

)

(3 -3 -1 1)

W h er e , y 0 is t h e fl o w d e pt h, w is t h e c h a n n el wi dt h, a n d a is t h e p er c e nt a g e of t h e c o v er. I n
a n i c e -c o v er e d c h a n n el, t h e str e a m fl o w cr o ss s e cti o n c a n b e s plit i nt o t w o p art s: t h e l o w er
p art d o mi n at e d b y t h e b e d a n d t h e u p p er p art d o mi n at e d b y t h e i c e c o v er ( L ars e n, 1 9 6 9 ).
As ht o n ( 1 9 8 6) st at e d t h at i c e c o v er pr es e n c e i n cr e a s es t h e t ot al c h a n n el h y dr a uli c r esis t a n c e
d u e t o t h e e xtr a r esist a n c e of t h e u p p er b o u n d ar y l a y er i n d u c e d b y t h e i c e c o v er. T h e l o c ati o n
of m a xi m u m v el o cit y d efi n e s t h e i nt erf a c e b et w e e n t h e u p p er i c e z o n e a n d l o w er b e d z o n e.
I n t h e c urr e nt st u d y, si n c e t h e c h a n n el-b e d a n d si d e w alls h a v e i n h o m o g e n e o us r o u g h n e ss,
t h e c h a n n el b e c o m e s a c o m p o sit e c h a n n el. Pr es e n c e of a n i c e c o v er c o m pli c at es t h e e x a ct
esti m ati o n of t h e r esist a n c e t o fl o w as it c a u s es t h e f l o w r e gi m e t o c h a n g e fr o m o p e n w at er
fl o w t o p arti all y c o v er e d a n d fi n all y t o t h e f ull y c o v er e d fl o w. S e v er al r es e ar c h er s h a v e tri e d
135

t o esti m at e fl o w r esist a n c e dir e ctl y usi n g fi el d o bs er v ati o ns. S o m e r es e ar c h ers h a v e pr o vi d e d
e m piri c al or s e mi -e m piri c al m et h o ds i n c o m p o sit e r esist a n c e esti m ati o ns ( S h e n a n d Y a p a,
1 9 8 6 ; S mit h a n d Ett e m a, 1 9 9 7 ; D a v ar et al., 1 9 9 8 ; B elt a o s, 2 0 0 9 ). I n t his p a p er t h e m et h o d
pr es e nt e d b y L ars e n ( 1 9 6 9) is e m pl o y e d. T h e L ars e n m et h o d c a n b e writt e n as f oll o w s:

(
)
n =
(n n ) ( y y ) + 1
c

0. 6 3 n b y i y b + 1

5 3

(3 -3 -1 2)

5 3

b

i

i

b

W h er e , y i a n d y b ar e t h e t ot al d e pt hs of t h e i c e a n d b e d z o n es, r es p e cti v el y; n c , nb a n d n i ar e
t h e M a n ni n g r o u g h n ess c o effi ci e nt s f or t ot al cr o ss s e cti o n, u p p er i c e-c o v er ( i) a n d l o w er b e d
(b ) b o u n d ar y l a y ers, r es p e cti v el y. I n t er ms of n i of s m o ot h i c e -c o v er e d fl o w, as p oi nt e d o ut
b y M a ys ( 1 9 9 9), d u e t o a r el ati v el y s m o ot h c o n cr et e -li k e s urf a c e of t h e St yr of o a m p a n el, t h e
r o u g h n ess of t h e m o d el s m o ot h i c e-c o v er w as a ss u m e d t o b e 0. 0 1 3. I n t er ms of n i of r o u g h
i c e-c o v er, Li ( 2 0 1 2) pr o p o s e d t h e f oll o wi n g e q u ati o n w hi c h c a n b e us e d d e p e n di n g o n t h e
si z e of t h e s m all c u b e s:
ni

K S1 6

(8 g ) ( R K )
=
0. 8 6 7 l n (1 2 R K )
-1 2

1 6

S

(3 -3 -1 3)

S

I n w hi c h, Ks is t h e a v er a g e r o u g h n ess h ei g ht of t h e i c e c o v er u n d ersi d e a n d R is t h e h y dr a uli c
r a di us.
T h e tr a ns p ort ati o n pr o c ess of u nif or m s e di m e nt h as b e e n br o a dl y st u di e d a n d t h e m e c h a nis m
of s e di m e nt tr a ns p ort h as b e e n w ell dis c uss e d ( A g uirr e -P e et al, 2 0 0 3; M o nt g o m er y a n d
B uffi n gt o n, 1 9 9 7; S c h vi d c h e n k o a n d P e n d er, 2 0 0 0; Y ali n a n d K ar a h a n, 1 9 7 9). H o w e v er, t h e
k n o wl e d g e f or esti m ati n g t h e n o n -u nif or m s e di m e nt tr a ns p ort is still li m it e d.

M or e o v er,

r es ult s of l a b or at or y e x p eri m e nt s usi n g u nif or m s e di m e nt is n ot a n a p pr o pri at e r e pr es e nt ati v e
of n at ur al ri v er s yst e ms si n c e b e d m at eri als i n n at ur al ri v er b e ds ar e n o n - u nif or m a n d
136

composed of sediment particles with different grain-size. During the movement process of
non-uniform sediment, the coarse grains are easier to be entrained than the same particle size
of uniform sediment, because they have higher probabilities to be exposed to the flow. On
the other hand, the finer grain tends to be hidden beneath the coarse grains (Huang et al,
2015). One of the earliest researches regarding the calculation of the bed load transport rate
in a non-uniform riverbed was done by Einstein (1950). In his proposed bed-load function,
he used a comprehensive hiding factor to represent the interaction effects between the coarse
particles and the fine particles. Ever since, several researchers have developed formulae to
determine the incipient motion of non-uniform sediment mixtures (Andrews, 1983; Dey and
Debnath, 2000; Egiazaroff, 1965; Kuhnle, 1993; Nakagawa et al, 1982; Patel and Ranga
Raju, 1999; Xu et al., 2008). For instance, Xu et al (2008) studied the incipient velocity of
non-uniform sediment. As pointed out by Xu et al (2008), the incipient velocity for the coarse
particles of the non-uniform sediment is less than that for same particle size of uniform
sediment, and the incipient velocity for the finer particles of the non-uniform sediment is
greater than that for the same particle size of uniform sediment.
The primary objective of this study is to investigate the features of the incipient motion of
three non-uniform sediments under ice-covered conditions by comparing to those of under
open channel flow conditions, and to identify the effects of flow roughness caused by ice
cover on the incipient motion of non-uniform sediment
3.3.1. Experimental setup
Experiments were carried out in a large-scale flume at the Quesnel River Research Centre of
the University of Northern British Columbia. The flume is 38.2 m long, 2 m wide and 1.3 m
deep, as shown in Figure 3-29a. The longitudinal slope of the channel bed is 0.2 percent. A

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holding tank with a volume of 90 m3 is located at the upstream of the flume to keep a constant
discharge during each experimental run. To create different velocities, three valves are
connected to adjust the amount of water into the flume. Two sand boxes are filled with natural
non-uniform sediment. Theses sand boxes are spaced 10.2 m away from each other and are
0.30 m deep and 5.6 m and 5.8 m in length, respectively. Three types of non-uniform
sediments with different gain sizes are used in this experimental study. The median grain
sizes of three natural non-uniform sediments are 0.50 mm, 0.47 mm and 0.58 mm with the
geometric standard deviation (σg) of 2.61, 2.53 and 1.89, respectively. According to Dey and
Barbhuiya (2004), sediments used in this study can be treated as non-uniform since σg is
larger than 1.84. Most of the studies on local scour have been limited to only single piers
under open flow condition and provide detailed information around single piers. However,
practically, due to geotechnical and economic reasons, bridge designs are often constructed
in complex piers or pier group arrangements in which the direct application of the results
derived from local scour around single piers may be problematic and not applicable. In this
study, four pairs of bridge piers with different diameters of 60 mm, 90 mm, 110 mm and 170
mm have been used. Of note, that the piers are vertical, non-sloping. Inside each sand box, a
pair of bridge piers was placed symmetrically to the center line of the flume. The distance
from the center line of each pier to the flume center is 0.25 m, as illustrated in Figure 3-29b.
In order to avoid the bed material from initial erosion, the water depths were increased
gradually and when the water overflowed from the top of the tailgate, the volumetric
discharge was increased to the desired amount. Flow velocity ranges from 0.07 m/s to 0.27
m/s. In front of the first sand box, a SonTek incorporated 2D Flow Meter was installed to
measure flow velocities, flow discharge and water depth during each experiment run. A staff

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gauge was also installed in the middle of each sand box to manually verify water depth.
Velocity fields in scour holes were measured using a 10-MHZ Acoustic Doppler Velocimeter
(ADV). The ADV is a high-precision instrument that can be used to measure 3D flow
velocity in a wide range of environments including laboratories, rivers, estuaries, and the
ocean (Cea et al., 2007). The Styrofoam panels which were used to model ice cover, had
covered the entire surface of flume. Figure 3-30a shows the entire experimental model with
the ice cover and Figure 3-30b shows the ADV measurement around the scour hole. In the
current study, two types of model ice cover were used, namely smooth cover and rough
cover. The smooth cover was the surface of the original Styrofoam panels while the rough
cover was made by attaching small Styrofoam cubes to the bottom of the smooth cover. The
dimensions of Styrofoam cubes were 25 mm × 25 mm × 25 mm and spaced 35 mm apart.
Since the flow in the rivers is normally subcritical flow, especially when the water surface is
covered by ice, it does not have a very high velocity value in which live-bed scour occurs.
Therefore, it was decided to do the experiments under clear water conditions. Each
experiment run lasted 24 hours. Afterward, the flume was gradually drained, and the scour
and deposition pattern around the piers was measured using manual calipers. To accurately
read the scour depths at different locations and to draw the scour hole contours, the outside
perimeter of each bridge pier was equally divided and labeled as the reference points. The
scour contours were plotted by using Surfer 13 (Golden Software). The measurement of the
scour hole was subject to an error of +/-0.3 mm. After each experiment, sand samples within
the scour hole which represent the composition of the armour layer were collected. The
samples were taken from the top layer of 5 mm of the armour layer in each scour hole. The
sampling process is followed the sampling methodology for collecting armour samples

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proposed by Bunte and Abt (2001). The collected sand samples were eventually sieved and
the mediums grain size of the armour layer (D50) were determined. In total, 108 experiments
were done, namely, 36 experiments for each sediment type. For each sediment type, 12
experiments were done under open flow condition, 12 experiments under smooth ice-covered
flow condition and 12 experiments under rough ice-covered flow condition, respectively.
Table 3-3 shows the experimental values obtained regarding incipient motion of sediment
particles for D50=0.50 mm. Of note, in the current study, the motion of the sediment was
observed through the transparent window of the flume. The layers of sediment could easily
be moved when the critical value was reached. It was observed from the transparent window
that the sediment particles were moved by saltation (bouncing) and by traction (being pushed
along by the force of the flow).

Figure 3-29a: Plan view and vertical view of experiment flume

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Figure 3-29b: The spacing ratio and measuring points around the circular bridge piers

Figure 3-30a: Downstream view of the entire experimental model with the ice cover

141

Figure 3-30b: The ADV measurement around the bridge piers under rough ice-covered condition

3.3.2. Results and discussions
• Effect of pier spacing distance on the scour patterns
Multiple bridge piers have become more common in recent years in bridge design for
geotechnical and economic reasons. These types of pier not only can significantly reduce
construction costs but also are more practical and efficient (Ataie-Ashtiani & Beheshti,
2006). However, the mechanisms of the scouring process around pier groups are much more
complex. According to Hannah (1978), if the pier spacing ratio is 0.25, the maximum scour
depth around side-by-side piers is about 50% more than that around a single pier and for G/D
< 0.25, the two side-by-side piers can be assumed to act as a single bridge pier (where G
represents the bridge spacing distance and D represents the pier diameter). Ataie-Ashtiani
and Beheshti (2006) investigated local scour for different pier arrangements and with
different bridge pier spacings. It was found that with an increase in the pier spacing distance
between two piers, scour depth is reduced. To the authors’ knowledge, all reported research
regarding local scour around pier groups has been done under open channel flow conditions
(Ataie-Ashtiani & Beheshti, 2013; Hannah, 1978; Melville & Coleman, 2000). As pointed
out by Ettema et al. (2011), the impact of ice cover on bridge pier scour is still unknown and
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needs further investigation. In this regard, a more in-depth study has been done here to
investigate the impact of ice cover on local scour around four pairs of side-by-side bridge
piers under different sediment compositions and flow conditions. Figure 3-31a shows the
ratio of the maximum scour depth to the depth of approaching flow (ymax/y0, termed as
relative MSD) against the ratio of pier spacing distance to pier diameter (G/D, termed as
bridge pier spacing ratio) for D50 = 0.50 mm. Of note, the maximum scour depth between
left hand side and the right-hand side bridge piers were more or less identical. In Fig. 3-31a,
the Froude number ranges from 0.072 to 0.270 and G/D ranges from 3.54 to 7.33. As
indicates in Figure 3-31a, the relative MSD decreases with the increase in G/D. Also, for the
same bridge pier spacing ratio (G/D) and for the same sediment, the relative MSD under
open channel flow conditions is the lowest, and the relative MSD under the rough covered
flow reaches the highest. Figure 3-31b shows the changes of the pier Reynold number (Reb)
with the pier spacing ratio (G/D) for D50 = 0.50 mm. The pier Reynolds number is defined
as:

Reb = UD



(3-3-14)

Where, U is the average velocity of the approaching flow and ν is the kinematic viscosity.
As shown in Figure 3-31b, the pier Reynold number (Reb) decreases with the increases in
G/D. Hopkins et al. (1980) stated that the strength of the horseshoe vortex system is a
function of the pier Reynolds number (Reb). Therefore, it can be concluded that the strength
of horseshoe vortices, which is a function of Reb, decreases with the increase in the pier
spacing ratio. Namely, the smaller the pier size (D) and the larger the pier spacing (G), the
weaker the horseshoe vortices around bridge piers, which will result in shallower scour
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depths around the pier group. According to Figure 3-31b, under the same flow condition
(velocity and flow depth), the lowest pier Reynolds number (Reb) occurred under the open
channel flow conditions, and the highest pier Reynolds number (Reb) occurred under rough
covered flow condition. However, with an increase in the pier spacing ratio, the pier
Reynolds number under rough covered flow conditions, gets closer to those of the smooth
covered and open channel flow conditions, implying that the influence of ice cover on pier
Reynolds number diminishes as the pier spacing distance increases.

Figure 3–31a: Relative MSD (ymax/y0) against
pier spacing (G/D) under open channel,
smooth, and rough covered flow conditions
(D50 = 0.50 mm).

Figure 3–31b: Variation of pier spacing (G/D)
with respect to pier Reynolds number (Reb).

• Shear stress vs. sediment-fluid parameter for the incipient motion of sediment
To the authors’ knowledge, shear stress against sediment-fluid parameter for the incipient
motion of sediment under ice-covered flow conditions have not been studied. This
information will give a better insight to the hydraulic engineers in terms of sediment incipient
motion under ice-covered condition. In Figure 3-32, the relationship between [S*(U/U*)] and
the dimensionless shear stress (τ*) is given for channel bed for those three non-uniform
sediments. Of note, U is the mean velocity of approaching flow (m/s); U* is the shear velocity
144

(m/s) and S* is the sediment-fluid parameter. For each type of the sediment, the sedimentfluid parameter (S*) is unique and the dimensionless shear stress increases with the increase
in [S*(U/U*)] correspondingly. Also, for all three sands, the larger the [S*(U/U*)], the
greater the dimensionless shear stress for the incipient motion of bed material. For the same
[S*(U/U*)], the finer the sediment, the higher the dimensionless shear stress. Of note, Eq. 33-3 in conjunction with Eq. 3-3-9 are used to calculate the dimensionless shear stress.

Figure 3-32: Dimensionless shear stress (τ*) vs S*(U/U*)

•

Dimensionless shear stress (τ*) vs. shear Reynolds number (Re*) for the incipient
motion of sediment

The relationship between the dimensionless shear Reynolds number and the dimensionless
shear stress for the incipient motion of the coarsest sediment (D50=0.58 mm) and that of the
finest sediment (D50=0.47 mm) under both open flow and rough ice-covered flow conditions
have been shown in Figure 3-33. From Figure 3-33, the following results can be drawn:
1) With the increase in the dimensionless shear Reynolds number, the dimensionless shear
stress increases correspondingly. For all three sands, the larger the dimensionless shear
Reynolds number, the greater the dimensionless shear stress for the incipient motion of bed
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material. However, for the same dimensionless shear stress, the dimensionless shear
Reynolds number for the finer sediment is lower for the incipient motion of sediment
particles.
2) In terms of the impacts of ice cover on the incipient motion of bed material, for the same
grain size of sediment, the dimensionless shear stress is lower under rough ice- covered flow
condition, implying that the threshold of the dimensionless shear stress for the incipient
motion of bed material under rough ice-covered flow condition is lower than that under open
flow conditions.
Of note, Wang et al (2008) also studied dimensionless shear stress (τ*) against shear
Reynolds number (Re*) for the incipient motion of sediment under ice-covered condition.
Their result showed that for bed material of same grain size, the larger the shear Reynolds
number, the greater the dimensionless shear stress for the incipient motion of bed material.
For the same dimensionless shear stress, the finer the particle, the lower the shear Reynolds
number for the incipient motion of sediment.

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Fi g ur e 3 -3 3: Di m e nsi o nl ess s h e ar str ess (τ *) vs. s h e ar R e y n ol ds n u m b er ( R e *) f or t h e i n ci pi e nt
m oti o n of t h e fi n est s e di m e nt ( D 5 0 = 0. 4 7 m m) a n d t h e c o ar s est s e di m e nt ( D 5 0 = 0. 5 8 m m) u n d er o p e n
a n d r o u g h i c e -c o v er e d fl o w c o n diti o ns

• S h e a r st r ess vs. d e nsi m et ri c F r o u d e n u m b e r f o r i n ci pi e nt m oti o n of b e d m at e ri al
Asi d e fr o m t h e S hi el d s p ar a m et er w hi c h is us e d t o d es cri b e t h e i n ci pi e nt m oti o n of t h e
s e di m e nt p arti cl e s, t h e d e nsi m etri c Fr o u d e n u m b er is a n ot h er i m p ort a nt v ari a bl e u s e d t o
d es cri b e h y dr a uli c c o n diti o n of b e d m at eri al ( A g uirr e -P e et al., 2 0 0 3). T h e d e nsi m etri c fl o w
Fr o u d e n u m b er is d efi n e d as f oll o w s:
Fr 0 =

(

U

g D50 r s - r

) r

(3 -3 -1 5)

I n w hi c h, U r e pr es e nt s t h e m e a n v el o cit y of t h e a p pr o a c hi n g fl o w. Si n c e t h e distri b uti o n of
fl o w vel o cit y u n d er i c e c o v er e d c o n diti o n is diff er e nt fr o m t h at of u n d er o p e n c h a n n el
c o n diti o n, t h e b o u n d ar y c o n diti o ns of fl o w si g nifi c a ntl y aff e ct t h e i n ci pi e nt m oti o n of b e d
m at eri al. T h e r el ati o ns hi p b et w e e n t h e d e nsi m etri c Fr o u d e n u m b er a n d t h e di m e nsi o nl es s
s h e ar str ess is s h o w n i n Fi g ur e 3 -3 4 a a n d Fi g ur e 3 -3 4 b. T h e m ai n r e a s o n f or pr es e nti n g
Fi g ur e 3 -3 4 is t o s h o w h o w t h e di m e nsi o nl e ss s h e ar str ess a n d t h e d e nsi m etri c Fr o u d e
147

number correlate to each other under different cover conditions (open flow or free cover,
smooth covered and rough covered conditions) and different grain size of bed materials.
Following results can be observed from Figure 3-34
1) The dimensionless shear stress increases with the increase in the densimetric Froude
number. As showed in Figure 3-34a, for the same densimetric Froude number, a lower
dimensionless shear stress can initiate motion of the finest sediment type (D50=0.47 mm).
Besides, under the same dimensionless shear stress, the densimetric Froude number for the
coarser sediment (D50=0.58 mm) is lower. In other words, a larger particle requires more
kinetic energy to be moved. Namely, the larger the particle, the more densimetric Froude
number is needed for the incipient motion of bed material. This result is in good agreement
with the study of Wang et al (2008).
3) With the same dimensionless shear stress for the incipient motion of bed material, the
values of the densimetric Froude number under open flow condition are slightly smaller than
that under ice-covered flow condition which is more distinct for higher values. The reason
for this is that under ice-covered condition, both the bed roughness and ice cover roughness
affect both the flow velocity distribution and the densnimetric Froude number. Wang et al
(2008) also stated that for the same bed material, the more the roughness coefficient of ice
cover, the less the densimetric Froude number for incipient motion of bed material, since a
larger roughness coefficient of ice cover leads to an increased near-bed velocity. And thus,
it can move larger particles.

148

Figure 3-34a: Variation of the dimensionless shear stress against the densimetric Froude number
classified by particle grain size

Figure 3-34b: Variation of the dimensionless shear stress against the densimetric Froude number
classified by cover conditions for flow

• Shear Reynolds number vs. densimetric Froude number for the incipient motion of
bed material
To the authors’ knowledge, shear Reynolds number against the densimetric Froude number
for the incipient motion of sediment under ice-covered flow conditions have not been studied.
Results of present study will give a better insight to the hydraulic engineers in terms of
149

understanding the incipient motion of sediment under ice-covered condition. The variation
of the densimetric Froude number against the shear Reynolds number is shown in Figure 335. Results indicate that the dimensionless shear Reynolds number increases with the
increase in the densimetric Froude number, correspondingly. For the same densimetric
Froude number, the dimensionless shear Reynolds number for the coarser sand
(D50=0.58mm) is higher. In other words, the larger the grain size of sediment, the higher the
dimensionless shear Reynolds number for the incipient motion of bed material.

Figure 3-35: Variation of the densimetric Froude number against the dimensionless shear Reynolds
number classified by particle grain size

• Shear stress vs. dimensionless transport-stage parameter for the incipient motion of
bed material
To the authors’ knowledge, the shear stress against the dimensionless transport-stage
parameter for the incipient motion of sediment under ice-covered flow conditions have not
been investigated. Van Rijn (1984) found that the movement of bed load material is a
function of the dimensionless transport-stage parameter which is defined as follows:

150

(U * ) - (U )
T =
2

(U )
*
c

*
c

2

(3 -3 -1 6)

2

Fi g ur e 3 -3 6 s h o ws t h e r el ati o ns hi p b et w e e n t h e di m e nsi o nl e ss s h e ar str ess (  * ) a n d t h e
di m e nsi o nl e ss tr a ns p ort -st a g e p ar a m et er ( T ). T h e f oll o wi n g res ult s h a v e b e e n dr a w n:
1 ) Wit h t h e i n cr e as e i n t h e

di m e nsi o nl e ss s h e ar str ess , t h e di m e nsi o nl e ss tr a ns p ort -st a g e

p ar a m et er ( T ) d e cr e as es. T h e d e cr e asi n g tr e n d of T -v al u e is v er y s h ar p w h e n  * > 0. 0 1. F or

 * < 0. 0 1, T -v al u e gr a d u all y d e cr e a s es, a n d n e arl y a p pr o a c h es a c o nst a nt w h e n t h e s c o ur h ol e
r e a c h e s t h e e q uili bri u m c o n diti o n at w hi c h t h e ar m o ur l a y er is c o m pl et el y f or m e d a n d
pr e v e nt s t h e s c o ur h ol e fr o m f urt h er s c o uri n g. I n ot h er w or d, t h e r at e of s e di m e nt er o si o n is
f ast er at t h e b e gi n ni n g. D uri n g t h e s c o uri n g pr o c ess, a n ar m o ur l a y er is gr a d u all y d e v el o p e d.
T his r es ult s i n t h e d e cr e as e i n t h e r at e of s e di m e nt er o si o n u ntil t h e s c o ur h ol e r e a c h e s
e q uili bri u m c o n diti o n.
2) Wit h t h e s a m e di m e nsi o nl e ss tr a ns p ort -st a g e p ar a m et er, t h e di m e nsi o nl ess s h e ar str ess f or
t h e fi n er t h e s a n d is l ar g er. As dis c u ss e d e arli er, s e di m e nt p arti cl e will g et m o v e d w h e n t h e
s h e ar str ess a cti n g o n it is gr e at er t h a n t h e r esist a n c e of t h e p arti cl e t o m o v e m e nt. T h e gr e at er
di m e nsi o nl e ss s h e ar st r ess, t h e gr e at er t h e c a p a cit y f or s e di m e nt tr a ns p ort. T h e r e sist a n c e of
t h e p arti cl e a g ai nst m o v e m e nt a n d e ntr ai n m e nt is hi g hl y d e p e n d e nt o n t h e p arti cl e si z e.
T h er ef or e, f or fi n er p arti cl es i n n o n -u nif or m s e di m e nt, hi g h di m e nsi o nl ess s h e ar str ess v al u e s
l e a d t o gr e at er s e di m e nt tr a ns p ort. O n t h e ot h er h a n d, f or t he c o ars er s e di m e nt wit h t h e s a m e
tr a ns p ort-st a g e p ar a m et er as of t h e fi n er s e di m e nt, t h e di m e nsi o nl e ss s h e ar str ess is s m all er,
i m pl yi n g t h at t h e s e di m e nt tr a ns p ort c a p a cit y f or t h e c o ars e s e di m ent is l o w er. Of n ot e, t h e
diff er e n c e b et w e e n r es ult s f or fi n e r s a n d a n d t h o s e f or c o ars er s a n d is n ot s o o b vi o us, si n c e
t h e gr ai n si z es of t h es e 3 s a n ds ar e n ot s o diff er e nt.
151

Figure 3-36: Variation of the dimensionless shear stress against the dimensionless transport-stage
parameter classified by particle grain size

• Scour hole velocity profile
Scour hole velocity profiles were measured for approaching flow depths range from 0.18 m
to 0.28 m. For shallow flow depths (less than 0.10 m), scour hole velocity measurements
were unable to be conducted due to limitations of the ADV in shallow water. Since the ADV
must be located 10 cm from the probe head, the velocity profile does not fully cover up to
the water surface. In order to gain an entire velocity profile, it is recommended to use the
Sontek’s 16 MHz micro ADV that can be used to measure flow velocity 0.05 m from the
probe head. Of note, since the ADV functions on the principal of a Doppler shift, the velocity
values close to the bed are representative of both sediment and water mixture velocity. Even
though clear water scour was achieved, it is impossible to achieve water velocity
measurements within 10 mmm of the bed. This was also noted by Muste et al. (2000).
Velocity measurements were performed one hour before the end of the experimental run, at
which the scour hole was fully developed and stabilized based on the visual observation. Of
note, the rate of change of scouring around the bridge pier was too small as it gets closer to
the equilibrium scour depth (24 hours). The ADV measures velocity in x, y and z directions.
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Therefore, the streamwise velocity component (Ux) is the component of scour hole velocity
in the direction of the flow, the span-wise velocity component (Uy) is the component of scour
hole velocity in the lateral direction and the velocity component (Uz) is the component of
scour hole velocity in the vertical direction. Figure 3-37 shows just Ux scour hole velocity
component profile at the upstream face of the 60-mm pier for the finest sand of D50=0.47
mm under both ice-covered and open channel flow conditions. Since the location of
maximum flow velocity was important, only Ux is shown in Figure 3-37. In order to be able
to generalize the velocity profiles and to compare different velocity profiles under different
flow conditions, the depth of flow on the vertical axis has been non-dimensionalized by ratio
of vertical distance of the location of ADV measurement from bed (z) to the approaching
flow depth (y0). The streamwise scour hole velocity component (Ux) is also nondimensionalized divided by the approaching flow velocity (U). Of note, a SonTek
incorporated 2D Flow Meter was installed at the upstream of the first sand box to measure
flow velocities and water depth. Results showed that, the streamwise velocity distribution
follows a reverse C-shaped profile which begins from the scour hole up to the water surface.
The same pattern was also reported by Kumar and Kothyari (2011). In terms of velocity
magnitude, the streamwise velocity in the scour hole under rough covered condition is
generally greater than those under both smooth covered and open flow conditions.
Regardless of the cover conditions of flow, the magnitude of velocity is the least in the scour
hole. Also, the values of the velocity component are mostly negative within the scour hole
which is an indication of the reversal flow happening due to the presence of the horseshoe
vortex which is strongest at the pier face. On the other hand, the location of the maximum

153

velocity is closer to the bed under rough covered flow condition than that under smooth
covered flow condition.

Figure 3-37: Ux velocity component profile in the scour hole under both ice-covered and open
channel flow conditions at the upstream face of the 6-cm pier for D50=0.47mm

• Variation of the relative maximum scour depth with the near-bed velocity
distribution
To better illustrate the impacts of the near-bed velocity on the relative maximum scour depth
(MSD) under ice-covered condition, the variation of the relative MSD (ymax/y0) with U*/U*c
under different conditions is given in Figure 3-38. Of note, by near-bed we refer to the ratio
of shear velocity (U*) over critical shear velocity (Uc*) that initializes the motion of the
particles. Shear velocity is usually applied to motion near the bed where the shearing stress
is often assumed to be independent of height and approximately proportional to the square
of the mean velocity. As outlined by Melville and Coleman (2000), the maximum scour depth
occurs when U*/U*c = 1. Of note, results for sand of D50=0.50 mm are not included in Figure
3-38 since they are not obviously different from those of the finest sand.
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1) For the same sediment, with increase in U*/U*c, the relative MSD (ymax/y0) decreases. For
ymax/y0<0.20, the trend of decrease in U*/U*C is very sharp, indicating the early state of
scouring. For ymax/y0>0.20, the scouring process gradually decreases during the experiment
run, indicating the weaker horseshoe vortex and wake vortex and, consequently, a decrease
in the bed shear stress. When the bed shear stress becomes less than the critical shear stress,
the scour depth will reach to the equilibrium state at which the sediment particles may not be
transported or moved into suspension. The reason is due to the decrease in scour rate when
the scour hole reaches the equilibrium condition at which the armour layer is completely
formed and prevents the scour hole from further scouring.
2) Regardless of the flow cover conditions, with the same U*/U*c -values, the finer the
sediment, the larger the relative MSD (ymax/y0) of the scour hole. In other words, due to a
lower threshold of sediment motion for the finest sediment type, under the same U*/U*c, a
scour hole with a larger MSD has developed.
3) Regarding the impact of ice cover on the (ymax/y0) ~ (U*/U*c) relationship, with the same
U*/U*c values, the relative MSD (ymax/y0) is greater under rough covered flow condition. On
the other side, for the same relative MSD, under the rough ice-covered flow condition, the
U*/U*c -value is greater than that of under smooth covered condition, implying that the nearbed velocity is higher under rough ice-covered flow condition.

155

Figure 3-38a: Variation of the relative MSD with U*/U*c classified by particle grain size for open
flow condition

Figure 3-38b: Variation of the relative MSD with U*/U*c classified by particle grain size for
smooth covered flow condition

156

Figure 3-38c: Variation of the relative MSD with U*/U*c classified by particle grain size for rough
covered flow condition

Figure 3-38d: Variation of the relative MSD with U*/U*c classified by flow cover conditions for
sediment of D50=0.50 mm

157

Figure 3-38e: Variation of the relative MSD with U*/U*c classified by flow cover conditions for
sediment of D50=0.47 mm

Figure 3-38f: Variation of the relative MSD with U*/U*c classified by flow cover conditions for
sediment of D50=0.58 mm

A relationship between (ymax/y0), (U*/U*c) and (D50/y0) has been established, as shown in
Figure 3-39:

158

æ
ö
y ma x
= 2. 5 1 4 çç U * ÷÷
y0
èU c ø

- 1. 9 5 5

æD ö
çç 5 0 ÷÷
è y0 ø

- 0. 5 7 7

(3 -3 -1 7)

A c c or di n g t o E q. 3 -3 -1 7, f or t h e s a m e D 5 0 / y0 – v al u e, t h e hi g h er t h e U */ U * c – v al u e, t h e l o w er
t h e r el ati v e M S D. Si mil arl y, f or t h e s a m e t h e U */ U * c – v al u e, t h e m or e t h e D 5 0 / y0 – v al u e, t h e
l e ss t h e r el ati v e M S D, i n di c ati n g t h at t h e r el ati v e M S D d e cr e as es as t h e gr ai n si z e of b e d
m at eri al g et s c o ars er.

Fi g ur e 3 -3 9: V ari ati o n of t h e r el ati v e m e as ur e d M S D a g ai nst c al c ul at e d M S D

3. 3. 3 . C o n cl usi o ns
T h er e is a p a u cit y of i nf or m ati o n i n t er ms of m a xi m u m s c o ur d e pt h c h ar a ct eristi cs a n d
i n ci pi e nt m oti o n of s e di m e nt p arti cl es ar o u n d bri d g e pi ers u n d er i c e -c o v er e d fl o w c o n diti o ns
d u e t o m e as ur e m e nt r estr ai nt. I n t h e pr es e nt st u d y, a s eri es of l ar g e s c al e -fl u m e e x p eri m e nt s
h a v e b e e n c o n d u ct e d b y usi n g t hr e e n o n -u nif or m s e di m e nt s a n d f o ur p airs of si d e -b y -si d e
b ri d g e pi ers of diff er e nt di a m et ers u n d er diff er e nt i c e-c o v er e d c o n diti o ns t o i n v e sti g at e t h e
eff e ct s of i c e c o v er o n t h e i n ci pi e nt m oti o n of b e d m at eri al a n d s h e ar str ess ar o u n d bri d g e
pi ers. T h e o bt ai n e d r es ult s c a n c o ntri b ut e t o d esi g n of bri d g e pi ers i n c ol d r e gi o ns b y
c o nsi d eri n g t h e i m p a ct of i c e. F oll o wi n g c o n c l usi o ns h a v e b e e n dr a w n:
159

1) It is found the presence of ice cover can result in a deeper maximum scour depth compared
to that under open flow condition, and consequently, the required flow velocity for incipient
motion of sediment particles under ice-covered conditions decreases with the increase in the
relative roughness coefficient of ice cover.
2) The pier Reynolds number (Reb) decreases with the increase in the pier spacing ratio
(G/D), implying that the strength of the horseshoe vortices decreases as the spacing distance
increases. Results showed that, under the same flow condition (velocity and flow depth), the
least pier Reynolds Number (Reb) occurred under open channel flow conditions, and the
highest pier Reynolds Number (Reb) occurred under rough covered flow conditions. Further,
it was observed that the influence of ice cover on pier Reynolds Number fades away as the
pier spacing distance increases regardless of flow cover. Also, for the same bridge pier
spacing ratio (G/D) and the same sediment, the relative MSD under open channel flow
conditions is the lowest and the maximum under the rough covered flow conditions,
respectively. This implies that the impact of the pier spacing ratio under the rough icecovered flow condition is clearly intensified compared to those under both open channel and
smooth covered flow conditions. In other words, the smaller the pier size (D) and the larger
the pier spacing (G), the weaker the horseshoe vortices around the side-by-side bridge piers.
3) The larger the sediment-fluid parameter, the greater the dimensionless shear stress for
incipient motion of bed material. In other word, with the increase in the sediment-fluid
parameter, the dimensionless shear stress increases correspondingly. However, for the same
sediment-fluid parameter, a higher dimensionless shear stress is resulted in channel bed with
finer sediment. Meanwhile, for the same dimensionless shear stress, the finer sediment has a

160

lower sediment-fluid value while the coarser sediment has a greater sediment-fluid parameter
value for the incipient motion of bed material.
4) The dimensionless shear stress increases with the increase in the densimetric Froude
number. For the same densimetric Froude number, the dimensionless shear stress is for the
finest sediment type (D50=0.47 mm) is the least. It is also found that the dimensionless shear
Reynolds number increases with the increase in densimetric Froude number. With the same
densimetric Froude number, the dimensionless shear Reynolds number for the coarser sand
(D50=0.58 mm) is higher.
5) For the same relative MSD, the U*/Uc –value under the rough ice-covered flow condition
is more than that under smooth covered condition, implying that the near-bed velocity is
higher under rough ice-covered flow condition than that under smooth covered condition.
6) For the streamwise velocity component (Ux), it can be described as a reverse C-shaped
profile shape which begins from the scour hole up to the water surface. In terms of velocity
magnitude, the streamwise velocity in the scour hole under rough covered condition is
generally greater than those under both smooth covered and open flow conditions.
Regardless of the cover conditions of flow, the magnitude of velocity is the least in the scour
hole. Moreover, the location of the maximum velocity is closer to the bed under rough
covered flow condition than that under smooth covered flow condition.
7) In terms of the effects of rough ice cover vs those of smooth ice cover, the MSD under
rough ice-covered flow condition was deeper. The location of the maximum velocity was
closer to the bed under rough covered flow condition than that under smooth covered flow
condition. For the same bed material, the dimensionless shear stress for incipient motion of
sediment increases with the shear Reynolds number as the ice cover becomes rougher. The

161

results are in good agreement with the result of Ackermann et al., (2002) in which they stated
that the rough cover gave slightly larger scour depths than the smooth cover.
Notation:
a
Percentage of the cover
D50
50th percentile particle diameter (m)
D90
The bed material size where 90% of the material is finer.
Di
Grain size diameter (m)
D
The diameter of the bridge pier (m)
d
Sediment size in the armor layer (m)
Fr0
Densimetric Froude number
g
Gravitational acceleration (m/s2)
k
Von Karman’s constant
Ks
The average roughness height (m)
Re*
The boundary shear Reynolds number
R
Hydraulic radius (m)
S
Channel slope
*
S
The sediment-fluid parameter
S. G Specific weight of the sediment
T
Dimensionless transport-stage parameter
U
Mean approach flow velocity (m/s)
U*
Shear velocity (m/s)
U*c Critical shear velocity (m/s)
Ux
Scour hole velocity component in x-direction (m/s)
Uy
Scour hole velocity component in y-direction (m/s)
Uz
Scour hole velocity component in z-direction (m/s)

u
ymax
y0
w
z
z0
ρs
ρ
ν
τ
τc*
Re*
Reb

Average cross-sectional velocity (m/s)
Relative maximum scour depth (MSD) (m)
The depth of approaching flow (m)
Cross-section width (m)
Distance from channel bed (m)
Roughness height (m)
Mass density of sediment (kg/m3)
Mass density of water (kg/m3)
Kinetic viscosity of fluid (m2/s)
Shear stress (Pa)
Dimensionless shear stress, critical Shields value
Shear Reynolds number
The pier Reynolds number
162

MSD
yi
yb
n
nc
nb
ni
W
FR
FL
α
CD
CL
Vs
H
K1
s

Relative maximum scour depth
The total depths of the ice (m)
The total depths of the bed zone (m)
The channel bottom roughness or Manning’s roughness
Manning roughness coefficients for total cross section
Manning roughness coefficients for upper ice‐cover
Manning roughness coefficients for the lower bed boundary layers
Resisting gravitational (N)
Frictional forces (N)
Lift force (N)
Scour angle
Drag coefficient at velocity Vs
Lift coefficient at velocity Vs
The local velocity at a distance s above the bed.
The mean flow depth (m)
The constant number equal to 0.058
Distance above the bed associated with Vs (m)

163

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ice covers. Proc. Int. Conf. 16th IAHR International Symposium on Ice, IAHR, Dunedin,
New Zealand
Aguirre-Pe, J., Olivero, M. I. A. L., Moncada, A. T. (2003). Particle densimetric Froude
number for estimating sediment transport. Journal of Hydraulic Engineering, 129(6): 428437.
Andrews, E. D. (1983). Entrapment of gravel from naturally sorted riverbed material. Geol.
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Ashton, G. D. (1986). River and lake ice engineering. Water Resources Publication.
Ataie-Ashtiani, B., & Beheshti, A. A. (2006). Experimental investigation of clear-water
local scour at pile groups. Journal of Hydraulic Engineering, 132(10), 1100-1104.
Batuca, D. and Dargahi, B. Some experimental results on local scour around cylindrical piers
for open and covered flow. In Third International Symposium on River Sedimentation,
University of Mississippi (1986).
Barenblatt, G. I., Chorin, A. J. (1997). Scaling laws and zero viscosity limits for wallbounded shear flows and for local structure in developed turbulence. Commun. Pure Appl.
Math, 50(4).
Beheshti, A. A., Ataie-Ashtiani, B., & Khanjani, M. J. (2013). Discussion of “Clear-Water
Local Scour around Pile Groups in Shallow-Water Flow” by Ata Amini, Bruce W.
Melville, Thamer M. Ali, and Abdul H. Ghazali. Journal of Hydraulic Engineering, 139(6),
679-680.
Beltaos, S. (2009), River flow abstraction due to hydraulic storage at freezeup, Can. J. Civ.
Eng., 36(3), 519–523.
Briaud, J. L., Gardoni, P., Yao, C. (2006). “Bridge Scour”. Geotechnical News, Vol. 24,
No.3, September, BiTech Publishers Ltd.
Bunte, K., Abt, S. R. (2001). Sampling surface and subsurface particle-size distributions in
wadable gravel-and cobble-bed streams for analyses in sediment transport, hydraulics, and
streambed monitoring. Gen. Tech. Rep. RMRS-GTR-74. Fort Collins, CO: US Department
of Agriculture, Forest Service, Rocky Mountain Research Station. 428 p., 74.
Cea, L., Puertas, J., & Pena, L. (2007). Velocity measurements on highly turbulent free
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Chiew, Y. M., Melville, B. W. (1987). Local scour around bridge piers. Journal of Hydraulic
Research, 25(1): 15-26.
Chang, H.H. (1988). Fluvial processes in river engineering. Krieger Publishing, Malabar,
Florida, 432 pp
Crance, M. J., & Frothingham, K. M. (2008). The impact of ice cover roughness on stream
hydrology. In 65 th Eastern snow conference, Fairlee (Lake Morey), Vermont (p. 149).
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Canadian Committee on River Ice Processes and Environment
Dey, S., Barbhuiya, A. K. (2004). Clear-water scour at abutments in thinly armored beds.
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Dey S, Debnath K 2000 Influence of stream-wise bed slope on sediment threshold under
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National Academies, Washington, DC.
Ettema, R., & Zabilansky, L. (2004). Ice influences on channel stability: Insights from
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Kothyari, U. C., Garde, R. C. J., Ranga Raju, K. G. (1992). Temporal variation of scour
around circular bridge piers. Journal of Hydraulic Engineering, 118(8): 1091-1106.
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Kumar, A., & Kothyari, U. C. (2011). Three-dimensional flow characteristics within the
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3.4. Scour patterns and velocity profiles around side-by-side bridge piers under icecovered flow
Bridges constructed with elements within the boundaries of rivers are potentially exposed to
scour around their foundations. If the depth of scour exceeds a critical value, instability and
vulnerability caused by the scour will threaten the bridge foundation, which might possibly
lead to critical issues such as bridge collapse, significant transport disruption and in an
extreme case, human casualty. Melville & Coleman (2000) studied 31 cases of bridge failures
due to scour in New Zealand and concluded that on average one major bridge failure each
year can be attributed to scour occurring around the bridge foundations. Wardhana &
Hadipriono (2003) studied 500 cases of bridge structure failures in the United States between
1989 and 2000 and stated that the most common cause of bridge failure was due to either
floods or scour. Sutherland (1986), in conjunction with National Roads Board of New
Zealand, determined that of the 108 bridge failures recorded between 1960 and 1984, 29
could be attributed to abutment scour. Local scour around bridge foundations has been the
focal point of many studies (Melville & Sutherland, 1988; Ahmed & Rajaratnam, 1998;
Melville & Chiew, 1999; Graf & Istiarto, 2002; Dey & Raikar, 2007; Ettema et al, 2011;
Sheppard et al. 2013; Wu & Balachandar, 2018; Williams et al., 2018; Williams et al., 2017;
Wu & Balachandar, 2016; Wu et al., 2015a, 2015b, 2014a, 2014b). Important to
understanding bridge pier scour is to better comprehend the the velocity distribution in the
vicinity of bridge piers. The flow field at piers has been documented in literature (Dey et al.,
1995; Graf & Istiarto, 2002; Unger and Hager, 2007; Beheshti & Ataie-Ashtiani; 2009 and
Kumar and Kothyari; 2012).

169

Graf and Istiarto (2002) performed an experimental study of the flow pattern in the upstream
and downstream plane of a cylinder positioned vertically in a scour hole. Detailed
measurements were obtained by using an acoustic-Doppler velocity profiler (ADVP) in and
around the scour hole. The results indicated that in the upstream reach of the cylinder, a
vortex system was detected which was a rather strong one (horseshoe vortex) and was
positioned at the foot of the cylinder. Another but weaker vortex (not so visible) was probably
due to the change in the slope of the bottom leading into the scour hole. Besides, in the
downstream reach of the cylinder, there existed a flow reversal towards the water surface. In
their study, the results indicated that the turbulent kinetic energy was very strong at the foot
of the cylinder on the upstream side and in the wake behind the cylinder. Unger and Hager
(2007) investigated the temporal evolution of the vertical deflected flow at the pier front and
the horseshoe vortex inside the scour hole as it formed. Their work provided novel insight
into the complex two-phase flow around circular bridge piers placed in loose sediment. A
three-dimensional turbulent flow field around a complex bridge pier placed on a rough fixed
bed was experimentally investigated by Beheshti & Ataie-Ashtiani, (2009). Comparison of
flow patterns with the observed scour map revealed that the scour patterns at the upstream
and sides of the pier correlate well with the contracted flow below the pile cap. A flow field
analysis around side-by-side piers with and without a scour hole was carried out by AtaieAshtiani and Aslani-Kordkandi, (2012). They found that the streamwise velocity increased
between the two piers. As a result, the maximum depth of scour hole was approximately 15%
greater than in the single-pier case. Kumar and Kothyari (2012) performed their study on
flow patterns and turbulence characteristics within a developing (transient stage) scour hole
around circular uniform and compound piers with measurements obtained using an acoustic

170

Doppler velocimeter (ADV). According to their study, the measurements of velocity,
turbulence intensities, and Reynolds shear stress made around each of the pier at different
vertical planes exhibited almost similar profiles along the flow depth. However, at certain
locations close to the pier, a significant change occurred in the vertical profile of the flow
parameters. Besides, the observations made in the upstream planes revealed that within the
scoured region, the bed shear stress was much smaller compared with the bed shear stress of
the approach flow.
Due to the difficulty of making velocity measurements under ice-covered conditions, nearly
all the studies regarding velocity distribution around bridge piers have been carried out using
open channel flow conditions. The number of studies on the flow field around both bridge
abutments and bridge pier under ice-covered condition is limited. Wu et al. (2015a, 2015b,
2014a, 2014b) studied the effect of relative bed coarseness, flow shallowness, and pier
Froude number on local scour around a bridge pier and reported that the scour depth under
covered conditions is larger compared to that under open channel flow conditions. It has been
found the presence of an ice cover alters the hydraulics of the channel by imposing an extra
boundary to the water surface (Sui et al., 2010). Under ice-covered flow conditions, the
velocity drops to zero at each boundary (ice-covered water surface and the bed) due to the
no-slip boundary condition, resulting in a parabolic-shaped profile (Ettema, et al. 2000;
Zabilansky et al., 2006). In addition, the maximum velocity occurs between the bed and the
bottom of the ice cover and is dependent on the relative roughness of the two boundaries
(Wang et al., 2008). Sui et al., 2010 showed that the upper flow is mainly influenced by the
ice cover resistance while the lower flow is primarily impacted by the channel bed resistance.
Wang et al. (2008) stated that the location of maximum velocity depends on the relative

171

magnitudes of the ice and bed resistance coefficients. According to Wang et al. (2008), it is
expected that as the ice resistance increases, the maximum flow velocity will move closer to
the channel bed. In terms of local scour depth, the severity of the local scour in the vicinity
of a bridge’s foundation gets more intense during the freezing period at which the water
surface is covered by ice. The presence of ice has been found to increase local clear-water
scour depth at bridge piers by 10%–35% (Hains & Zabilansky, 2004). In terms of transverse
flow distributions and velocities of secondary currents, ice cover can impact flows in an
existing thalweg, altering the position of the thalweg and changing the morphology of the
stream which in an extreme case will lead to bank and bed erosion (Beltaos et al., 2007).
Zabilansky et al. (2006) performed a series of flume experiments under smooth and rough
ice cover conditions and found that the maximum velocity for rough ice cover was 20 percent
greater than for smooth ice cover. This statement was confirmed by Muste et al. (2000) who
found that the measured maximum velocity under smooth cover is located roughly at 0.8y0,
while maximum velocity under rough cover is approximately located at 0.6y0, where y0
represents the approaching flow depth.
In the current study, a series of large-scale flume experiments were conducted to examine
scour hole patterns along with scour hole velocity profile measurements around four sideby-side bridge piers under ice-covered and open channel flow conditions. The main objective
of this study is to gain a better understanding of the flow field and velocity distribution
around bridge piers under different flow cover and to focus on their associated distinctive
flow field characteristics.

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3.4.1. Methodology
Experiments were carried out in a large-scale flume at the Quesnel River Research Centre of
the University of Northern British Columbia, Canada. The flume was 38.2 m long, 2 m wide
and 1.3 m deep. Figure 3-40 shows a plan view and a side view of the experiment flume. The
longitudinal slope of the flume was 0.2 percent. A holding tank with a volume of 90 m3 was
located at the upstream end of the flume to maintain a constant discharge during the
experimental runs. To create different velocities, three input valves were connected to control
the inlet volume discharge. Water level in the flume was controlled by the downstream
tailgate. Two types of tailgate configurations (one-tailgate and two-tailgate configurations)
were incorporated to produce a wide range of main channel approaching velocities. The
range of flow depth was from 0.09 m to 0.137 m for one-tailgate configuration and from
0.165 m to 0.28 m for two-tailgate configuration. For the case of two-tailgate configuration,
two pumps were employed for the lowest flow discharge while three pumps were employed
to create the highest flow discharge. At the end of the holding tank and upstream of the main
flume, water overflowed from a rectangular weir into the flume. Two sand boxes were
constructed in the flume. Both had a depth of 0.3 m and were 10.2 m apart. The length of the
sand boxes were 5.6 m and 5.8 m, respectively. Three natural, non-uniform sediments with
median grain sizes of 0.47 mm, 0.50 mm and 0.58 mm were used. Side-by-side cylindrical
bridge piers with diameters of 60 mm, 90 mm, 110 mm and 170 mm were used. The distance
between the center of left pier and the center of the right pier was 0.50 m. Figure 3-41 shows
the piers and the space ratio (G/D) in which G is the distance from the outside to outside of
the piers and D is the pier diameter. The geometric channel aspect ratio (channel width/flow
depth) of the current experiments ranged from 7.14 to 22.2. Of note, Roussinova et al. (2006)

173

declared that velocity dip would not be significant when the geometric channel aspect ratio
(channel width/ flow depth) is greater than five as secondary flow effects are minimal. The
bridge pier spacing ratio G/D ranged from 1.94 to 7.33 (Figure 3-41). In front of the first
sand box, a 2D Flow Meter (SonTek Inc.) was installed to measure flow velocities and water
depth. A staff gauge was also installed in the middle of each sand box to manually verify
water depth. Styrofoam panels were used as ice cover across the entire surface of flume. Both
smooth and rough ice cover were simulated. The smooth cover was the smooth surface of
the original Styrofoam panels while the rough cover was made by attaching small Styrofoam
cubes to the bottom of the smooth cover. The dimensions of Styrofoam cubes were 25 mm
× 25 mm × 25 mm and they were spaced 35 mm apart. The velocity field in the scour holes
were measured using a 10-MHZ acoustic Doppler velocimeter (ADV). The sampling volume
of the 10-MHz ADV is 100 mm from the sensor head. In a standard configuration, the
sampling volume is approximately a cylinder of water with a diameter of 6 mm and a height
of 9 mm. In the current study, the ADV measured the scour hole velocity profiles at
approaching flow depths within 0.18-0.28 m range for four sets of bridge piers (60 mm, 90
mm 110 mm and 170 mm) under the two-tailgate flume configurations for the highest and
lowest levels of discharge. Scour hole velocity measurements for shallow flow depths (onetailgate flume configuration) were inaccessible due to the limitations of the ADV in
measuring shallow flow depths. Velocity measurements were performed at one hour before
the end of the experimental run (total test time = 24 hours) at which point the scour hole was
fully developed and stabilized. For the purposes of these experiments, the streamwise
velocity component, Ux, is the component in the direction of the flow, the span-wise velocity
component is denoted as Uy, and the velocity component, Uz, is the component in the vertical

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direction. Of note, a negative value of Uz means the velocity vector is directed downwards.
To develop the three-dimensional velocity profiles, measurements were obtained at each
point for 120 seconds. Of note, for velocity values very close to the channel bed, the presence
of sediment affected the ADV velocity measurement, therefore, the velocity values are
representative of sediment and water velocity as previous noted by Muste et al. (2000). The
scour hole flow field was measured at 20 mm increments from the bottom of scour hole in
front of the bridge pier up to free surface for each experimental run. In the ice-covered
experiments, a part of the Styrofoam was cut to allow for the ADV to be positioned inside
the flow for flow field measurements. Further, since the ADV measuring volume is located
100 mm from the probe head, the velocity profile for each channel condition is not up to the
water surface. After the experiments were completed, collected data were analyzed to filter
out for velocity spikes. Signal strengths and correlations are used principally to judge the
quality and accuracy of the velocity data (Fugate & Friedrichs, 2002). In the current study,
data quality was defined based on signal-to-noise ratio amplitudes (SNR 15) and correlation
coefficient scores ( 70). In terms of uncertainty in velocity measurements, at a sampling
rate of 25Hz and an SNR above 15, uncertainty due to Doppler noise can be estimated as 1%
of the maximum velocity range (Sontek, 1997). In total, 108 experiments (36 experiments
for each sediment type) were conducted under open channel, smooth covered, and rough
covered conditions. In terms of different boundary conditions (open channel, smooth, and
rough covered flows), for each sediment type and each boundary condition, 12 experiments
were carried out. In the preliminary stage of the experiments, local scour around bridge piers
was carefully observed for any changes in the scour depths. It was observed that after
approximately a period of 6 hours, no significant change in scour depth was observed and

175

scour hole equilibrium depth was achieved. The experiment was continued for 24 hours and
again no obvious change in scour depth was observed. For the 110-mm bridge pier under
open channel and ice-covered flow condition for the highest discharge, the experimental time
was extended to 38 hours and there was not any significant change in scour depth between
24 hr. and 38 hr. experiments. Further, according to Wu et al. (2014a), who did a series of
experiments regarding local scour around a semi-circular bridge abutment, the time for
development of equilibrium scour depth was 24 hr. Based on the current experimental results
and the results of Wu et al. (2014a), the experimental run time of 24 hr. was chosen. After
24 hours, the flume was gradually drained, and the scour and deposition pattern around the
piers was measured. To accurately read the scour depth at different locations and to draw
scour hole contours, the outside perimeter of each bridge pier was divided between 6 and 12
labeled segments based on the diameter of the cylinder (Figure 3-41).The measurement of
scour hole was subject to an error of +/-0.3 mm. Of note, the maximum scour depth between
left hand side and the right-hand side bridge piers were more or less identical. Of note, since
an additional boundary is added to the flow for the case of ice-covered flow condition,
hydraulic radius (R) is calculated from the following equation:
Wy0
y0
R= A=
=
P 2(y0 + W) (y0 + 2)

(3-4-1)

Where W is the width of the channel.

176

Figure 3-40: Plan view and vertical view of experiment flume (Dimensions in m)

Figure 3-41: The spacing ratio and measuring points around the circular bridge piers

177

3.4.2. Results and discussions
• Local Scour pattern around bridge piers
Figure 3-42a shows scour depth around the 110 mm bridge pier and Figure 3-42b compares
the scour and depositional pattern upstream and downstream of the pier for D 50 = 0.47 mm
under open and rough flow conditions for the highest flow discharge, respectively. Figure 342 (a-b) also compares the scour depth with that of Hirshfield (2015) in which local scour
around 110-mm single bridge pier under open and rough ice cover conditions for D50=0.47
mm is reported. According to Figure 3-42a, regardless of flow cover and number of piers,
the maximum scour depth occurred at point 8 which is at the pier face where the horseshoe
vortex and down-flow velocity coexist and are the strongest. The least amount of scour
occurred near point 3 which is diametrically opposed to point 8 behind the pier. Further,
regardless of flow cover, it is obvious that the scour depth is deeper for the side-by-side pier
compared to the single bridge pier in the study of Hirshfield (2015). Besides, according to
Figure 3-42b, sediment ridges have been developed downstream of the side-by-side bridge
pier under all the flow cover conditions. Sediment ridges downstream of the pier, as noted in
the present study, were not reported by Hirshfield (2015) for the single bridge pier. The
reason is due to confining effects of the side-by-side bridge pier compared to the singular
bridge pier which has resulted in greater scour depth and developed sediment ridge at the
downstream side of the bridge pier. According to Hodi (2009), as blockage ratio increases,
larger amount of discrepancies will be developed in both scour depth and bed geometry. In
the present study, regardless of flume cover and sediment grain size, the maximum scour
depths were always located at the upstream face of the pier. According to Williams (2018),
the scour commences in the region of the highest velocity in the vicinity of the separating

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streamline. The horseshoe vortex which forms at the pier face shifts the maximum downflow
velocity closer to the pier in the scour hole. The downflow acts as a vertical jet to erode a
groove in front of the pier. The eroded sand particles are carried around the pier by the
combined action of accelerating flow and the spiral motion of the horseshoe vortex (Hafez,
2016). Melville and Coleman (2000) report a wake-vortex system which occurs behind the
pier, acts like a vacuum cleaner sucking up bed material and carrying the sediment moved
by the horseshoe vortex system and by the downward flow to downstream of the pier.
However, wake-vortices are not normally as strong as the horseshoe vortex and therefore,
are not able to carry the same sediment load as the horseshoe vortex does. Therefore,
sediment deposition is likely to occur downstream of the pier in the form of sediment ridge
which is clearly shown in Figure 3-42b. The scour pattern around the 110-mm bridge pier
under highest flow discharge viewed from the top for D50= 0.47 mm was mapped into Surfer
13 plotting software (Golden Software, 1999) as shown in Figure 3-43 (a-c) for open,
smooth, and rough flow cover, respectively. According to Figure 3-43, the deepest location
of scour depth around the pier is clearly at the face of bridge pier and the location of
deposition ridge is downstream of the pier which is densest and most widely spread for the
rough ice-covered flow condition. The same pattern was observed for the other bridge piers
regardless of sediment type and bridge pier diameter. It was experimentally noted by Qadar
(1981) that the maximum value of scour depth should certainly be a function of the initial
vortex strength. Therefore, the deepest scour depth, which is the result of a stronger vortex,
should occur under the highest approach velocity and rougher ice cover type as observed in
these experiments.

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Fig. 3-42a: Scour depth around the 110-mm bridge pier for D50= 0.47 mm type sediment under a)
open flow and b) rough covered flow conditions using the highest flow discharge

Figure 3-42b: Cross-section of scour and depositional pattern at the upstream and downstream of
the 110-mm bridge pier under a) open flow condition and b) rough covered flow conditions for
D50=0.47 mm

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Figure 3-43: a) Scour pattern around the 110-mm bridge pier for D50=0.47 mm type under open for
the highest flow discharge; b) Scour pattern around the 110-mm bridge pier for D50= 0.47 mm type
under smooth for the highest flow discharge; c) scour patterns around the 110-mm bridge pier for
D50= 0.47 mm type under rough for the highest flow discharge

• Flow velocity profiles
Scour hole velocity profiles for the streamwise (Ux) vertical (Uz) velocity components under
open, smooth and rough ice cover for all the pier size separately and under D50=0.47 mm for
the lowest discharge is presented in Figure 3-44. Figure 3-45 shows scour hole velocity
profiles for the streamwise (Ux) and vertical (Uz) velocity components distinguished by flow
cover for all the pier size under D50= 0.47 mm for the lowest discharge. Figure 3-46 shows
the vertical velocity distribution for the lowest discharge for the 90-mm bridge pier under
rough ice-covered condition for the three D50s. Of note, regardless of pier size, since the
lateral (y) velocity profiles, does not exhibit any meaningful pattern in the flow and
constantly changes between positive and negative values along the entire profile, they are
not presented. In order to be able to generalize the velocity profiles and to compare different
velocity profiles under different flow cover, the depth of flow on the vertical axis has been
non-dimensionalized by taking the ratio of vertical distance from bed (z) to approach flow
depth (y0). The streamwise scour hole velocity component (Ux) and the vertical scour hole
velocity component (Uz) are also non-dimensionalized by the approaching flow velocity (U).
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Of note, the ADV location for the velocity measurement of all the experiments was set at 10
mm upstream of the pier face where the maximum scour depth occurred. The following
outcome can be concluded from Figure 3-44 to Figure 3-46:
1)

For the streamwise velocity distribution is a reverse C-shaped profile which begins

from the scour hole up to the water surface. The same pattern was also reported by Hirshfield
(2015) and Kumar and Kothyari (2011). In terms of velocity magnitude, the streamwise
velocity for rough cover is generally greater than the scour hole velocity for smooth and open
channel conditions. As expected, the magnitude of velocity is smallest in the scour hole and
is the highest at the water surface. Furthermore, regardless of flow cover, pier size and
sediment type, the values of the velocity component are mostly negative within the scour
hole which is an indication of reversal flow happening due to the presence of horseshoe
vortex which is strongest at the pier face. Moreover, for the 90-mm and 110-mm bridge piers,
which were placed in the first sand box and were exposed to nearly the same flow depth and
approaching flow velocity, the average value of U x is higher for the 110-mm pier under all
flow cover conditions. Similarly, for the 60 mm and 170 mm bridge piers which were placed
in the second sand box and were exposed to nearly the same flow depth and approaching
flow velocity, the average value of Ux is higher for the 170-mm pier under all flow cover
conditions. In other words, the results indicate the strength and intensity of the horseshoe
vortex increased with pier size.
2)

Within the scour hole upstream of the pier, the most significant feature is the

appearance of down-flow velocities in the vertical direction due to obstruction of the flow
by the pier and is represented by negative values of U z. Therefore, the vertical velocity
distribution (Uz) is highly significant in terms of scour hole development. In terms of flow

182

cover, it is obvious that the value of U z is the largest under rough ice cover. According to
Tison (1961), the downward velocity originates from the horizontal curvature of the
streamline in front of the pier and the reduction of velocity near the bed by friction.
Downward velocity intensifies the horseshoe vortex at the pier face and can effectively speed
up the process of scour hole development, which in an extreme case, leads to bridge failure.
Generally, considering the absolute value of Uz, the value of Uz diminishes from the channel
bed toward the scour hole. From the channel bed toward the free surface, U z values tend to
move toward zero and the positive direction which implies that downflow velocity vectors
are changing their direction and diminishing as they get closer to free surface which causes
the velocity profile to have a parabolic shaped profile.
3) Under the same flow cover and flow condition, the larger pier yielded the larger values of
the streamwise and vertical (U x, Uz) velocity. However, these values are larger under rough
ice-covered flow conditions. The larger scour hole velocity under rough ice cover justifies
the findings of greater pier scour depth
4) The vertical velocity distribution exhibits the same pattern for the three sands as seen in
Figure 3-46. According to the figure, the finest sediment (D50= 0.47 mm), has a greater
velocity magnitude and, consequently, a deeper scour depth. Besides, the location of
maximum velocity under the finest sediment is closer to the bed which has resulted in
stronger horseshoes vortices.
Table 3-4 represents the location of maximum velocity based on z/y0 for different flow cover.
Of note, the velocity profiles were measured before the cylinder inside the scour hole in the
upstream region. According to Table 3-4, the location of maximum velocity is closer to the
bed which is in good agreement with the findings of Zabilansky et al. (2006) and Muste et

183

al. (2000). Figure 3-47a shows vertical velocity component (Uz) for the 60- and 170-mm
bridge piers (bridges in the second sand box) from the scour hole up to the maximum velocity
point under open, smooth and rough-covered flow covers, while Figure 3-47b shows Uz of
the 90- and 110-mm bridge piers (bridges in the first sand box) from the scour hole up to the
maximum velocity point under open, smooth and rough-covered flow covers. As mentioned
before, the location of maximum velocity is expected to depend on the relative magnitudes
of the ice and bed resistance coefficients and the rougher the ice cover, the closer the location
of the maximum velocity to the channel bed. Therefore, the magnitude of vertical velocity is
generally higher near the channel bed under rough flow cover compared to open channel
flow cover. According to Figures 3-47(a-b), location of the maximum velocity is closer to
the bed under ice-covered condition which is in good agreement with the previous findings.
Since there was not any significant change from the maximum location of the vertical
component of velocity (Uz) up to the free surface, a general linear relationship is developed
for all the bridge piers under open channel and ice-covered flow conditions in Figure 3-47c
which reads as follows:

z / y0 = 0.5816(Uz / U) + 0.5503

(3-4-2)

Of note, due to the limitations of ADV in measuring the full vertical velocity profile, there
is no data in the upper portions of the depth. Resultant of the three average velocity
components is calculated for the lowest discharge of D50= 0.47 mm from the Eq. 3 and are
presented in Figure 3-48. The results indicate regardless of flow discharge and pier size, the
resultant velocity is highest for rough cover. For the 90-mm pier and 110-mm pier which
were placed in the first sand box and were under nearly the same flow condition, the larger
pier has resulted in larger values of resultant velocity component which implies that the

184

str e n gt h a n d i nt e nsit y of h ors es h o e v ort e x i n cr e a s es wit h pi er si z e. T h e s a m e tr e n d c a n b e
s e e n f or t h e 6 0 -m m pi ers a n d 1 7 0 -m m pi ers w hi c h w e r e pl a c e d i n t h e s e c o n d s a n d b o x.

U R =

(u ) + (v ) + (w )
2

2

2

(3 -4 -3)

i n w hi c h u , v a n d w ar e a v er a g e v el o cit y c o m p o n e nt s i n X Y Z c o or di n at es a n d U R is t h e
t ot al v el o cit y or t h e r es ult a nt of t h e t hr e e a v er a g e v el o cit y c o m p o n e nt s. Of n ot e, u , v a n d
w ar e ti m e -a v er a g e d v el o citi es c al c ul at e d b y t a ki n g t h eir a v er a g e s fr o m i nst a nt a n e o u s

v el o cit y v al u es i n t h eir ass o ci at e d dir e cti o n as f oll o ws:

(3 -4 -4)

u¢= u - u ;

v¢ = v - v ;

w ¢= w - w

(3 -4 -5)

i n w hi c h, n is t h e n u m b er of ti m e s eri e s d at a, u i, vi a n d w i ar e i nst a nt a n e o us fl o w v el o citi e s
i n X Y Z c o or di n at e s yst e m a n d u', v', w' ar e v el o cit y fl u ct u ati o ns i n X Y Z c o or di n at e s yst e m,
r es p e cti v el y.
T a bl e 3 -4 : L o c ati o n of m a xi m u m v el o cit y b as e d o n ( z/ y 0 ) v al u es a c c or di n g t o fl o w c o v er
Fl o w c o v er
St a g e of m a xi m u m v el o cit y ( z/ y 0 )
O p e n c h a n n el
0. 2 5
S m o ot h c o v er
0. 1 5
R o u g h c o v er
0. 1 0

185

Figure 3-44: Scour hole velocity profiles for the streamwise (Ux) and vertical (Uz) velocity
components under open, smooth and rough ice-cover distinguished by the pier size and under D50=
0.47 mm for the lowest discharge

186

Figure 3-45: Scour hole velocity profiles for the streamwise (Ux) and vertical (Uz) velocity
components distinguished by flow cover for all the pier size and under D50= 0.47mm for the lowest
discharge

187

Figure 3-46: The vertical velocity distribution for the lowest discharge for the 90-mm bridge pier
under rough ice-covered condition for the three values of D50

Figure 3-47: a) Vertical velocity component (Uz) of the 60- and 170-mm bridge piers from the
scour hole up to the maximum velocity locale under open, smooth and rough-covered flow covers;
b) Vertical velocity component (Uz) of the 90- and 110-mm bridge piers from the scour hole up to
the maximum velocity locale under open, smooth and rough-covered flow covers; c) Vertical
velocity component (Uz) of all the bridge piers from the maximum velocity locale toward the free
surface under open, smooth and rough-covered flow covers

188

Figure 3-48: Scour hole velocity profiles for the resultant of the three average velocity components
under open, smooth and rough ice cover for D50= 0.47 mm for the lowest discharge.

•

Turbulence intensities and turbulent kinetic energy (TKE)

In terms of ice-covered flow condition, the formation of a stable ice cover almost doubles
the wetted perimeter compared to open channel conditions, alters the hydraulics of an open
channel by imposing an extra boundary to the flow, causing velocity profile to be shifted
towards the smoother boundary (channel bed) and adding up to the flow resistance. Since
near-bed velocity is higher under ice-covered conditions, a higher shear stress is exerted on
the river bed (Sui et al., 2010; Wang et al., 2008). As the near bed velocity increases, the
kinetic energy exerted on the bed increases correspondingly. An increase in kinetic energy
affects the capacity of flow in terms of sediment transport rate. To determine turbulence
intensities along with turbulent kinetic energy, the root-mean-square of the turbulent velocity
fluctuations about the mean velocity are calculated as shown in Eqs. (6) to (8). The RMS
values are equal to the standard deviation of the individual velocity measurements in x, y and
z directions, respectively. RMSs are considered as a measure of the violence of turbulent
fluctuations yielding the spread of velocities around the mean velocity and they are
calculated as follows (Wilcox and Wohl, 2007).

189

Where, RMS [u'] is the Root-mean-square of the velocity fluctuations in streamwise
direction; RMS [v'] is the Root-mean-square of the velocity fluctuations in lateral direction
and RMS [w'] is the Root-mean-square of the velocity fluctuations in vertical direction. The
root mean squares of the streamwise, cross-stream, and vertical velocities (RMSu ', RMSv',
RMSw') for each time series were used to estimate TKE. RMS [u'], RMS [v'], RMS [w'] are
also called turbulent intensities for the streamwise (x), lateral (y) and vertical (z) directions,
respectively. Figure 3-49 and Figure 3-50 show the turbulent intensity values nondimensionalized by the shear velocity for the streamwise (x) and vertical (z) flow velocity
components. Of note, turbulent energy is the mean kinetic energy per unit mass and has the
unit of J/kg in SI unit. Since fluctuations for the lateral direction measurements did not
display any meaningful patterns, the lateral turbulent component (y) is not presented. The
same unstructured turbulent intensities pattern was also observed by other studies such as
Muste et al., (2000) and Robert and Tran, (2012). Turbulent kinetic energy (TKE) which is
defined as the mean energy per unit mass of turbulent eddies is calculated as follows (Clifford
and French, 1993):
TKE = 1 (RMSu2' + RMSv2' + RMSw2 ')
2

(3-4-9)

190

Figure 3-51 shows TKE values for all the piers for D50=47 mm for the lowest discharge.
Analysis of TKE values shows a pattern similar to the turbulent intensity. The following
observations can be obtained from Figure 3-49 to Figure 3-51:
1) Regardless of flow cover, the streamwise and vertical turbulent intensities are highest just
over the channel bed and diminishes towards the flow surface. According to Muste et al.
(2000), observing the highest value of turbulent intensity near the bed is due to the highest
rate of sediment movement near the bed. Muste et al. (2000) also concluded the turbulent
intensities are relevant to sediment transport as the strength of the turbulence will affect
sediment suspension.
2) The streamwise turbulent intensity and the vertical turbulent intensity for the rough flow
conditions are greater than those for open channel and smooth ice-covered flow conditions.
As the turbulent intensity in both the streamwise and vertical direction are higher under the
rough ice-covered flow conditions, there is more potential for sediment transport due to the
higher kinetic energy than in the open channel and smooth ice-covered flow conditions.
3) Regardless of pier size, the vertical turbulent intensities are less than the streamwise
turbulent intensities which indicates the turbulence is primarily related to fluctuations in the
streamwise velocity. The same argument was also presented by Muste et al., (2000).
4) Similar to the observations made for the velocity profile, for the 90 mm and 110 mm
bridge piers in the first sand box, exposed to nearly the same flow depth and approaching
flow velocity, the streamwise and vertical turbulent intensities are higher for 110 mm than
90 mm pier under all forms of flow cover. Similar results were obtained for the 60 mm and
170 mm bridge piers in the second sand box with the 170 mm pier having higher values than
the 60 mm pier under all flow cover conditions. The results show the turbulent intensity
191

increases with pier size. The above statement can also be generalized for TKE. Therefore, it
can also be concluded that, under nearly the same flow condition, the maximum value of
turbulence kinetic energy occurs at a larger diameter pier.

Figure 3-49: Distribution of the turbulent intensity values at the upstream of the piers nondimensionalized by the shear velocity for the streamwise (x) flow velocity component

Figure 3-50: Distribution of the turbulent intensity values at the upstream of the piers nondimensionalized by the shear velocity for the vertical (z) flow velocity component

192

Fi g ur e 3 -5 1: Distri b uti o ns of t h e t ur b ul e nt ki n eti c e n er g y at t h e u pstr e a m of t h e pi er s

3. 4 Q u a d r a nt a n al ysis a n d R e y n ol ds st r ess es
T h e R e y n ol ds s h e ar str ess is ass o ci at e d wit h t h e b al a n c e of m e a n li n e ar m o m e nt u m a n d is
i m p ort a nt i n e x a mi ni n g t ur b ul e nt fl o ws a n d s e di m e nt tr a ns p ort. Th e c o m p o n e nt of R e y n ol d s
str ess f or c o nst a nt d e nsit y i n x -z pl a n e, w hi c h h a s t h e di m e nsi o ns of v el o cit y s q u ar e d, is
d e fi n e d as:

t xz = u ¢w ¢

(3 -4 -1 0)

W h er e τ x z is t h e s h e ar str ess i n x-z pl a n e, u' r e pr es e nt s fl u ct u ati o n (t ur b ul e n c e) of v el o cit y i n
x dir e cti o n a n d w' r e pr es e nt s fl u ct u ati o n (t ur b ul e n c e) of v el o cit y i n z dir e cti o n. Q u a dr a nt
a n al ysis, first i ntr o d u c e d b y L u a n d Will m art h ( 1 9 7 3), is us e d t o i n v e s ti g at e t h e str u ct ur e of
t h e R e y n ol ds s h e ar str ess i n a t ur b ul e nt b o u n d ar y l a y er. I n t h e c urr e nt st u d y, t his a n al ysis is
a p pli e d t o t h e 6 0 -m m pi er t o e x a mi n e t h e c o ntri b uti o n of e a c h q u a dr a nt t o t h e R e y n ol d s s h e ar
str ess. I n q u a dr a nt a n al ysis, t h er e ar e f o u r q ua dr a nt s (i = 1 t o 4) i n t h e u ' – w ' pl a n e: (i) i = 1
r e pr es e nt s t h e o ut w ar d m oti o n ( u'> 0 a n d w '> 0); (ii) i = 2 r e pr es e nt s ej e cti o n ( u '< 0 a n d w '> 0);
(iii) i = 3 r e pr es e nt s t h e i n w ar d m oti o n ( u'< 0 a n d w '< 0); a n d (i v) i = 4 r e pr es e nt s s w e e p ( u '> 0
a n d w '< 0) ( Afz ali m e hr et al., 2 0 1 6). B e c a us e of li mit e d s p a c e, Fi g ur e 3 -5 2 o nl y s h o ws t h e
193

percentage of velocity fluctuation components (u' and w') from each quadrant (i = 1, 2, 3 and
4) at the upstream face of 0.06 m bridge pier. Of note, the percentage is defined as (u'w'/U*2)
*100 in which U* is shear velocity. Similar trends were observed for the other bridge piers
sizes. In general, only outward motion and ejection have been observed and sweeps and
inward motion do not contribute to the Reynolds stress distribution. Between the outward
motion and ejection, outward motion is the most frequently occurring event while ejection
has occurred at the upper portion of the flow near the free surface and inside the upper portion
of the scour hole. In terms of the maximum point of Reynolds shear stress values for the icecovered flow conditions, the values reached to their maximum closer to the channel bed in
compared to open channel flow conditions. Regardless of flow cover, values of Reynolds
shear stress gradually become smaller towards the free surface of the flow. Regardless of
sediment type, the values of Reynolds shear stress follow the same pattern for open channel,
smooth and rough covered flow conditions.

Figure 3-52: Percentage of velocity fluctuation components (u' and w') from each quadrant (i = 1, 2,
3 and 4) at the upstream of 60 mm pier for D50= 0.47 mm

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3.4.3. Conclusions
In this paper, the three-dimensional velocity measurements along with scour hole
development patterns around paired bridge piers were investigated under open channel,
smooth, and rough ice-covered flow conditions with a non-uniform bed. A total of 108
experiments incorporating four side-by-side bridge piers with 60 mm, 90 mm, 110 mm and
17 mm diameter, respectively, were performed. The following is the summary of the
milestones from this study:
1) In terms of scour hole pattern, regardless of sediment type and flow cover, the deepest
point in each scour hole is clearly at the front face of bridge piers and the deposition mound
is located downstream of bridge piers. Under the rough covered flow conditions, both the
maximum scour depth and maximum deposition height are clearly greater than for open
channel flow. The results indicate under the rough covered flow condition more sediment
deposition develops at the downstream side of bridge piers and the deposition mound is wider
spread than those under open flow.
2) For the streamwise velocity component (Ux), there is a logarithmic pattern which begins
from the scour hole up to the water surface (or simulated ice-cover). In terms of velocity
magnitude, the streamwise velocity for rough cover is generally greater than the scour hole
velocity for smooth and open channel conditions. Regardless of sediment type, the rough ice
cover resulted in a larger maximum velocity compared to the smooth ice cover.
3) The vertical velocity distribution (U z), which is a representative of the strength of downfall
velocity, is the greatest under rough ice cover. Generally, considering the absolute value of
Uz, the values of Uz diminish from the channel bed toward the scour hole and from the
channel bed toward the free surface. They tend to move toward right which implies

195

downflow velocity vectors are diminishing as they get closer to free surface which results in
the velocity profile having a parabola-shaped profile pattern.
4) There is no significant difference in velocity field for the different sediment types and
different types of sediment. Different types of armor layer and sediment ridge development
were observed which are the result of differences in critical shear stress in the sediment
particles.
5) Regardless of flow cover, the streamwise turbulent intensity along with the vertical
turbulent intensity are highest just over the channel bed and diminishes towards the flow
surface. The streamwise turbulent intensity, the vertical turbulent intensity and turbulence
kinetic energy for the rough flow conditions are greater than those for open channel and
smooth ice-covered flow conditions.
6) Under nearly the same flow conditions, the maximum value of turbulence kinetic energy
and turbulent intensity occurs at the largest diameter pier.
7) Quadrant analysis revealed only outward motion and ejection have been observed at the
upstream face of the pier while sweeps and inward motion do not contribute to the Reynolds
stress distribution. Among outward motion and ejection, outward motion is the most
frequently occurring event while ejection has only occurred at the upper portion of the flow
near the free surface and within the upper reaches of the scour hole.

196

Notations:
D50: 50th percentile particle diameter (mm)
Uz: Vertical velocity component (m/s)
G: Bridge spacing (m)
D: Pier width (mm)
Ux: The streamwise velocity component (m/s)
Uy: The span-wise velocity component (m/s)
ymax: Maximum scour depth (mm)
y0: Approach flow depth (mm)
U: Average approach velocity (m/s)
U*= Shear velocity (m/s)
ɵ: Flow temperature (degree)
S: longitudinal slope of the channel
R: Hydraulic radius (m)
W: width of the channel (m)
Q: Volumetric flow discharge (m3/s)
z: The vertical distance from bed (m)
TKE: turbulent kinetic energy (J/kg)
UR: The resultant of the three average velocity components (m/s)
u : Average velocity components (Time-averaged velocities) in x-direction (m/s)
v : Average velocity components (Time-averaged velocities) in y-direction (m/s)
w : Average velocity components (Time-averaged velocities) z-direction (m/s)
ui: Instantaneous flow velocity in in x-direction (m/s)
vi: Instantaneous flow velocity in y-direction (m/s)
wi: Instantaneous flow velocity z-direction (m/s)
u': Velocity fluctuations in x-direction (m/s)
v': Velocity fluctuations in y-direction (m/s)
w': Velocity fluctuations in z-direction (m/s)
RMS [u']: Root-mean-square of the velocity fluctuations in streamwise direction (m/s)
RMS [v']: Root-mean-square of the velocity fluctuations in lateral direction (m/s)
RMS [w']: Root-mean-square of the velocity fluctuations in vertical direction (m/s)
τxz: Shear stress in x-z plane (m2/s2)
n: Number of time series data
i: Number of quadrants

197

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Beheshti, A. A., & Ataie-Ashtiani, B. (2009). Experimental study of three-dimensional flow
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Sheppard, D. M., Melville, B., & Demir, H. (2013). Evaluation of existing equations for local
scour at bridge piers. Journal of Hydraulic Engineering, 140(1), 14-23.
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3.5. Three-dimensional numerical modeling of local scour around bridge piers under
ice-covered flow condition
Piers which are constructed inside the rivers are one of the most frequently used foundation
in offshore platforms, bridges, etc. Due to local scour process, the flow pattern around these
foundations will be changed and the turbulence will be enhanced, which ultimately leads to
the creation of horseshoe vortex in front of the pier, the wake vortex behind the pier, and the
contraction of streamlines at the side of the pier (Zhang et al, 2017). The horseshoe vortex is
created by the flow of water separating at the upstream face of the bridge pier where the
initial scour hole has developed. Wake vortices develop behind a bridge pier and disturb the
downstream flow pattern. These vortices are the main causes of local scour creation and they
lead to intensified local sediment transport capacity, and the expansion of local scour around
the piers. Due to the local scour, the insertion depth of the pier reduces as the scour depth
around the pier grows, which is directly associated with the stability of pier foundation. The
deeper the depth of local scour around the pier, the more vulnerable pier foundation becomes
which leads to bridge collapse in the many case (Zhang et al, 2017). Therefore, it is
commonly accepted that the local scour is one of the main causes of pier foundation failure
in river and marine environments. Thus, the estimation of riverbed deformation in the
vicinity of bridge piers is crucial for the safe design of bridge piers. The development of
scour hole around bridge piers is affected by the characteristics of flow pattern near the bed
and around the pier. The characteristics of flow pattern around the piers are clearly fully
three-dimensional and complex. The tremendous complexity of three-dimensional flow field
around a pier is attributed to separation and generation of multiple vortices. It is even more
aggravated because of the dynamic interaction between the flow and the moveable bed

202

throughout the development of a scour hole (Esmaeili, 2009). Therefore, precise prediction
of scour patterns around bridge piers mainly depend on the flow field and mechanism of
sediment transport in and out of the scour hole. Up to date, many researchers have done
experiments to investigate the local scour around bridge piers and develop empirical
equations to estimate the maximum scour depth under open channel flow condition (Ettema
et al., 2011; Sheppard et al., 2013). In winter, ice cover appears in many rivers in the northern
region. The influence of ice cover on a channel involves in complex interactions among the
ice cover, fluid flow, and channel geometry. This complex interaction can have a dramatic
effect on the sediment transport process (Hains et al., 2004). The formation of a stable ice
cover in natural rivers effectively doubles the wetted perimeter compared to open channel
conditions and causes the maximum velocity to be lowered towards the channel bed (Sui et
al., 2010). The most extreme case of local scour around bridge piers occurs in cold regions
where the surface of flow is covered with ice. Zabilansky and White (2005) investigated the
impact of ice cover on scour in narrow rivers. It was found that when discharge increases
above the freeze-up datum, the pressurized flow condition, combined with the rough
underside of the ice, will cause the maximum velocity in the flow to increase and shift closer
to the bed. Wu et al (2015) studied the effect of relative bed coarseness, flow shallowness,
and pier Froude number on local scour around a bridge pier and reported that the scour depth
under covered conditions is larger compared to that under open channel flow conditions. Wu
et al (2014) investigated scour morphology around a bridge abutment under ice cover. It was
found that, at different locations around the abutment, the sediment sorting process under ice
cover was more obvious. Wu et al (2015) studied the impact of ice cover on local scour
around bridge abutments.

203

In recent years, by means of computer science, the numerical method has been widely applied
in many fields of science such as hydromechanics. Not only CFD models are timely and
monetary efficient and are highly precise, but also, they are free of scaling effect and can be
employed for various types of geometry and hydraulic conditions of a specific hydraulic
problem (Toombes & Chanson, 2011). Regarding the numerical modelling of local scour
around bridge pier, Richardson and Panchang (1998) used a fully 3D hydrodynamic model
to simulate the flow pattern at the base of a cylindrical bridge pier within a scour hole.
Vasquez and Walsh (2009) applied FLOW-3D to simulate the initial stages of scour
development in a complex pier made of a large pile cap and 10 cylindrical piles. Kim et al
(2014) studied the local scour around two adjacent cylinders, in which the Large-eddy
simulation (LES) was employed to simulate the instantaneous turbulent flow around the
cylinders. In their research, the effects of both the longitudinal and transverse spacing
distance between cylinders on the flow structure, scour evolution, bed topography, and
maximum scour depth were examined in detail. To the authors’ knowledge, only few studies
have been carried out to compare results of numerical simulation of local scour to those of
laboratory experiments, and none of those studies was devoted to investigating this
phenomenon under ice-covered condition. In present study, to understand the mechanisms
of local scour around side-by-side bridge piers, the velocity vectors, streamline around bridge
piers, morphological changes of scour hole and deposition patterns under both open channel
flow and ice-covered (smooth-covered and rough-covered) flows conditions have been
studied. Further, based on the experimental results, it has been assessed whether it is feasible
to use the FLOW-3D numerical model to simulate the flow field and local scour depth pattern
around bridge piers. A comparison between the results of numerical simulation of local scour

204

under different flow covers (open channel flow and the ice-covered flow) and those of
laboratory experiments has been presented. The impacts of ice cover on the local scour
process around bridge piers have been investigated.
3.5.1 Experiment setup
Experiments were done in a large-scale flume at the Quesnel River Research Centre of the
University of Northern British Columbia, Canada. The flume is 38.2 m long, 2 m wide and
1.3 m deep. Figure 3-53 shows a plan and side view of the experimental flume. A holding
tank with a volume of 90 m3 was located at the upstream end of the flume to maintain a
constant discharge during the experimental runs. To create different velocities, three input
valves are connected to control the inlet volumetric discharge. At the end of the holding tank
and upstream of the main flume, water overflows from a rectangular weir into the flume.
Two sand boxes were constructed in the flume. Both have a depth of 0.30 m and are 10.2 m
spaced apart. The lengths of the sand boxes are 5.6 m and 5.8 m, respectively. In each sand
box, a pair of bridge piers was placed. Three natural non-uniform sediment compositions
with median grain sizes of 0.50 mm, 0.47 mm, and 0.58 mm were used. Four pairs of
cylindrical bridge piers with diameters of 60 mm, 90 mm, 110 mm, and 170 mm were used.
Each pier was offset from the centre line by 25 cm, as illustrated in Figure 3-54. The water
level in the flume was controlled by the downstream tailgate. In front of the first sand box, a
SonTek two-dimensional Flow Meter was installed to measure flow velocities and water
depth. A staff gauge was also installed in the middle of each sand box to manually verify the
water depth. The velocity fields in the scour holes were measured using a 10-MHz Acoustic
Doppler Velocimeter (ADV). Styrofoam panels were used to represent ice cover and covered
the entire surface of the flume. Two types of model ice cover were used, namely smooth

205

cover and rough cover. The smooth cover was the smooth surface of the original Styrofoam
panels while the rough cover was made by attaching small Styrofoam cubes to the bottom of
the smooth cover. The dimensions of Styrofoam cubes were 25 mm × 25 mm × 25 mm and
they were spaced 35 mm apart. 108 Experiments (36 experiments for each sediment type)
were done under open channel, smooth covered, and rough covered flow conditions. In terms
of different boundary conditions (open channel, smooth, and rough covered flows), for each
sediment type and each boundary condition, 12 experiments were done. Throughout the
calibration stage of the experiments, local scour around bridge piers was carefully watched
hourly for any changes in the scour depths. It was observed that after approximately a period
of 24 hours, no obvious change in scour depth was observed and scour hole equilibrium depth
was achieved. After 24 hours, the flume was gradually drained, and the scour and deposition
pattern around the piers was measured.

Figure 3-53: Plan view and side view of experiment flume

206

Figure 3-54: The spacing ratio and measuring points around the circular bridge piers

3.5.2 Numerical model
In present study, FLOW-3D which is a widely used computational fluid dynamics (CFD)
model has been evaluated. FLOW-3D adopts the volume of fluid (VOF) method (Hirt and
Nichols, 1981) to track the free water surface. The Fractional Area/Volume Obstacle
Representation (FAVOR) method (Hirt and Sicilian, 1985) is also employed to model
complex geometric regions (such as the packed sediment) in fixed rectangular meshes using
area fractions (Ai) and volume fractions (VF) in FLOW-3D. The area fractions (Ai) are
defined at each of the six faces as ratios of the particular open area to the total area in each
mesh cell and VF is defined as the ratio of the volume open to fluid to the total cell volume.
Ai and VF associated with the packed sediments are updated at each time step to describe the
modifications of the geometry of the packed sediment. The FAVOR method is able to
precisely define the geometry by using a smaller number of mesh cells than the finite

207

diff er e n c e m et h o d ( F D M) w hi c h c a n r e d u c e t h e c o m p ut ati o n ti m e t o a gr e at e xt e n d ( Fl o w
S ci e n c e I n c. , 2 0 1 5).
• G o v e r ni n g e q u ati o ns
F L O W -3 D i n c or p or ates v ari o us t ur b ul e n c e m o d els, a s e di m e nt tr a ns p ort m o d el a n d a n
e m piri c al b e d er o si o n m o d el t o g et h er wit h V O F ( V ol u m e of Fr a cti o n) m et h o d f or c al c ul ati n g
t h e fr e e s urf a c e of t h e fl ui d wit h o ut s ol vi n g t h e air c o m p o n e nt ( Hirt & Ni c h ols, 1 9 8 1). T h e
R A N S ( R A N: R e -N or m alis ati o n G r o u p) e q u ati o ns cl o s e d wit h R N G k −ε t ur b ul e n c e m o d el
ar e a d o pt e d as t h e g o v er ni n g e q u ati o ns f or t h e i n c o m pr essi bl e vis c o us fl ui d m oti o n ar o u n d
t h e bri d g e pi ers. T h e g e n er al g o v er ni n g R A N S a n d c o nti n uit y e q u ati o ns f or N e wt o ni a n,
i n c o m pr essi bl e fl ui d fl o w, i n cl u di n g t h e F A V O R v ari a bl es, are gi v e n a s f oll o ws. N ot e t h at
ar e a fr a cti o ns ( A i) a n d v ol u m e fr a cti o ns (V F ) a p p e ar i n e q u ati o ns.

W h er e :
ét
ù
fi = 1 ê b ,i - ¶ A j S ij ú
V F êë r
¶x j
úû

)

(3 -5 -3)

æ¶u
¶u jö
÷
S ij = n + n T çç i +
÷
è ¶ x j ¶ xi ø

(3 -5 -4 )

(

(

)

W h er e u i = v el o cit y c o m p o n e nt i n s u bs cri pt dir e cti o n, V F = v ol u m e fr a cti o n of fl ui d i n e a c h
c ell, A i = fr a cti o n al ar e a o p e n t o fl o w i n s u bs cri pt dir e cti o n, p = pr ess ur e, ρ = m ass d e nsit y
of fl ui d, t = ti m e, g i = gr a vit ati o n al f or c e i n s u bs cri pt dir e cti o n a n d fi = diff usi o n tr a ns p ort
t er m. V F a n d A j ( c ell f a c e ar e as) = 1, t h er e b y r e d u ci n g t h e e q u ati o ns t o t h e b a si c
208

incompressible RANS equations. Sij= strain rate tensor, τb,i = wall shear stress and ν =
kinematic viscosity, νT= kinematic eddy viscosity.
• Sediment scour model
The sediment scour model in FLOW-3D is fully coupled with the fluid flow (Flow Science
Inc, 2015). It simulates all the sediment transport processes of non-cohesive soil including
bedload transport, suspended load transport, entrainment and deposition. It allows multiple
non-cohesive sediment species with different properties such as grain size, mass density,
critical shear stress, angle of repose, and parameters for entrainment and transport. It
approximates the motion of the sediment particles by predicting the erosion, advection, and
deposition of them. The sediment scour model incorporates four sediment transport
mechanisms, which could define the sediment transport processes. The first mechanism of
the sediment transport is entrainment and it occurs when the bed shear stress exceeds the
critical shear stress, as the result, the sediment particles that are set at the top of the packed
bed may be lifted and move into suspension. The second mechanism is suspended load
transport in which the sediment particles are carried by the flow current within a certain
height above the packed bed. The third mechanism is deposition, which occurs when the
ability of flow to carry the suspended sediments decreases because of impact of gravity,
buoyancy, and friction and as the result the suspend sediments are deposited where the
slowing flow can no longer move them. The last mechanism of the sediment transport is bedload transport, which includes grains that roll, slide or bounce along the bed in response of
the shear stress applied by fluid flow (Zhang, 2017). Therefore, sediment scour model can
be used to compute the suspended sediment transport, settling of sediment due to gravity, the
entrainment of the sediment due to bed shearing and flow perturbations, bed-load transport,

209

w h er e b y s e di m e nt gr ai ns r oll, h o p or sli d e al o n g t h e p a c k e d s e di m e nt b e d ( Fl o w S ci e n c e s
I n c 2 0 1 5).
• D e p ositi o n a n d e nt r ai n m e nt
D e p o siti o n is t h e pr o c ess t h at t h e s e di m e nt gr ai ns eit h er s ettl e o ut of s us p e nsi o n o nt o p a c k e d
b e d d u e t o t h eir w ei g ht or c o m e t o r est i n b e d -l o a d tr a ns p ort. S ettli ng a n d e ntr ai n m e nt of
gr ai ns ar e o p p o sit e pr o c ess es a n d oft e n o c c ur at t h e s a m e ti m e ( Fl o w S ci e n c es I n c 2 0 1 5).
A c c or di n g t o M ast b er g e n a n d V a n D e n B er g ( 2 0 0 3 ), t h e e ntr ai n m e nt lift v el o cit y of s e di m e nt
is c o m p ut e d as:

(

U lift,i = a i n s d *0. 3 q i - q cr' ,i

)

1. 5

(

g di r i- r f

rf

)

(3 -5 -5 )

W h er e , α i is t h e e ntr ai n m e nt p ar a m et er, w h o s e r e c o m m e n d e d v al u e is 0. 0 1 8 (M ast b er g e n a n d
V a n D e n B er g, 2 0 0 3) a n d n s is t h e o ut w ar d p oi nti n g n or m al t o t h e p a c k e d b e d i nt erf a c e. U lift,i
is u s e d t o c o m p ut e t h e a m o u nt of p a c k e d s e di m e nt t h at is c o n v ert e d i nt o s us p e nsi o n,
eff e cti v el y a cti n g as a m a ss s o ur c e of s us p e n d e d s e di m e nt at t h e p a c k e d b e d i nt erf a c e. θ i is
t h e l o c al S hi el ds p ar a m et er w hi c h is c al c ul at e d b as e d o n t h e l o c al b e d s h e ar str ess, θ cr,i is t h e
criti c al S hi el ds p ar a m et er, ǁg ǁ is t h e m a g nit u d e of t h e a c c el er ati o n of gr a vit y, d i is t h e
di a m et er, ρ i is t h e d e nsit y of t h e s e di m e nt s p e ci e s i, ρ f is t he fl ui d d e nsit y a n d d * is
di m e nsi o nl e ss di a m et er of t h e s e di m e nt, w hi c h c a n b e c o m p ut e d b y:

(

)

ér r - r
g ù
ú
d *, i = d i ê f i 2 f
m f
êë
úû

1 3

(3 -5 -6 )

I n w hi c h,  f is t h e d y n a mi c visc o sit y of fl ui d. T h e l o c al S hi el ds p ar a m et er is c o m p ut e d b as e d
o n t h e l o c al b e d s h e ar str ess, τ:

qi=

t
g d i(r i - r f )

(3 -5 -7 )
210

w h er e, τ is c al c ul at e d usi n g t h e l a w of t h e w all a n d t h e q u a dr ati c l a w of b ott o m s h e ar str ess
f or 3 D t ur b ul e nt fl o w a n d s h all o w w at er t ur b ul e nt fl o w, r es p e cti v el y, wit h c o nsi d er ati o n of
b e d s urf a c e r o u g h n e ss ( Fl o w S ci e n c es I n c 2 0 1 5). T h e di m e nsi o nl ess crit i c al S hi el d s
p ar a m et er is c o m p ut e d usi n g t h e S o uls b y -W hit e h o us e e q u ati o n

(S o uls b y &

W hit e h o us e,

1 9 9 7):

q cr ,i =

(

)

0. 3 + 0. 0 5 5 é1 - e x p - 0. 0 2 d * ù
i û
ë
1 + 1. 2 d i*

(3 -5 -8 )

D e p o siti o n is t h e pr o c ess t h at s e di m e nt gr ai ns eit h er s ettl e o ut of s us p e nsi o n o n t h e p a c k e d
b e d d u e t o t h e w ei g ht or c o m e t o r est i n b e dl o a d tr a ns p ort ( Fl o w S ci e n c es I n c 2 0 1 5) . T h e
s etti n g v el o cit y of t h e s e di m e nt is c o m p ut e d as f oll o w ( S o uls b y, 1 9 9 7):

u s ettli n g,i =

0. 5
vfé
ù
2
3
1
0.
3
6
+
1.
0
4
9
d
- 1 0. 3 6 ú
ê
*
û
dië

(

)

(3 -5 -9 )

W h er e , v f is t h e ki n e m ati c vis c o sit y of fl ui d.
• S us p e n d e d s e di m e nt
S us p e n d e d s e di m e nt is tr a ns p ort e d b y a d v e cti o n al o n g wit h t h e fl ui d. F L O W -3 D ass u m e s
t h er e ar e t ot all y i s e di m e nt s p e ci e s. T h e tr a ns p ort e q u ati o n f or e a c h s e di m e nt s p e ci e s i is:

(3 -5 -1 0 )
W h er e, C s,i is t h e c o n c e ntr ati o n of t h e s us p e n d e d s e di m e nt, i n u nit s of m ass p er u nit v ol u m e
of s p e ci e s i, D f is t h e diff u si vit y; u s,i is t h e s us p e n d e d s e di m e nt v el o cit y. Of n ote, e a c h
s e di m e nt s p e ci es i n s us p e nsi o n m o v es at it s o w n v el o cit y t h at is diff er e nt fr o m t h o s e of fl ui d
a n d ot h er s p e ci es. T his is d u e t o diff er e n c e i n i n erti a a n d dr a g f or c e b et w e e n gr ai ns wit h
diff er e nt m ass d e nsit y. S u p p o si n g t h at t h er e ar e n ot str o n g i n t er a cti o ns b et w e e n e a c h gr ai n,
a n d t h at t h e v el o cit y diff er e n c e b et w e e n t h e s us p e n d e d gr ai ns a n d t h e fl ui d -s e di m e nt mi xt ur e
211

is pri m aril y t h e s etti n g v el o cit y of t h e gr ai ns, t h e s e di m e nt v el o cit y of s p e ci es i c a n b e
c al c ul at e d as:

u s,i = u + u s ettli n g,i c s,i

(3 -5 -1 1 )

W h er e , u r e pr es e nt s t h e v el o cit y of t h e fl ui d-s e di m e nt mi xt ur e, a n d c s,i is t h e v ol u m e of
s us p e n d e d s e di m e nt s p e ci es i p er v ol u m e of t h e fl ui d -s e di m e nt mi xt ur e a n d is c o m p ut e d as
f oll o w:
c s ,i =

C s ,i

(3 -5 -1 2 )

i

S e di m e nt is e ntr ai n e d b y t h e pi c ki n g u p a n d r e -s us p e nsi o n of p a c k e d s e di m e nt d u e t o
s h e ari n g a n d s m all e d di e s at t h e p a c k e d s e di m e nt i nt erf a c e. T h e e m piri c al m o d el us e d i n
F L O W -3 D is b a s e d o n m et h o d pr o p o s e d b y M ast b er g e n a n d V o n d e n B er g ( 2 0 0 3) . T h e fir st
st e p t o c o m p ut e t h e criti c al S hi el d s n u m b er is t h e c al c ul ati o n of t h e di m e nsi o nl ess p ar a m et er
d * fr o m E q. 1 1. A c c or di n g t o E q. 1 1, t h e di m e nsi o nl ess criti c al S hi el ds p ar a m et er is
c o m p ut e d usi n g t h e S o uls b y -W hit e h o us e e q u ati o n (S o uls b y & W hit e h o us e, 1 9 9 7):
q cr ,i =

(

)

0. 3
+ 0. 0 5 5 éë1 - e x p - 0. 0 2 d i* ùû
1 + 1. 2 d i*

(3 -5 -1 3 )

• B e d -l o a d t r a ns p o rt
B e d -l o a d tr a ns p ort is t h e s e di m e nt tr a ns p ort d u e t o r olli n g or b o u n ci n g o v er t h e s urf a c e of
t h e p a c k e d b e d of s e di m e nt. F L O W-3 D c o nsi d ers t hr e e e q u ati o ns f or v ol u m etri c tr a ns p ort
r at e of se di m e nt p er wi dt h of b e d, n a m el y, m o d els pr o p o s e d b y M e y er -P et er &

M ull er

( 1 9 4 8); Ni els e n ( 1 9 9 2) a n d V a n Rij n ( 1 9 8 4). I n t h e c urr e nt st u d y, M e y er -P et er & M ull er
( 1 9 4 8) e q u ati o n w a s us e d. T his m o d el pr e di ct s t h e v ol u m etri c fl o w of s e di m e nt p er u nit
wi dt h o v er t h e s urf a c e of t h e p a c k e d b e d:

212

(

f i = b i q i - q 'cr ,i

)

1. 5

(3 -5 -1 4 )

W h er e , t h e t y pi c al v al u e of β i = 8 ( 5 a n d 1 3 f or l o w a n d hi g h s e di m e nt tr a ns p ort, r es p e cti v el y)
( V a n Rij n, 1 9 8 4), ϕ i is t h e di m e nsi o nl e ss b e d-l o a d tr a ns p ort r at e a n d is r el at e d t o t he
v ol u m etri c b e d -l o a d tr a ns p ort r at e (q b,i ) b y:
1

é æ r - r ö ù2
f ÷ 3ú
q b ,i = f i ê g çç i
d
êë è r f ÷ø i úû

(3 -5 -1 5 )

T h e b e dl o a d tr a ns p ort v el o cit y is pr o p o s e d b y ( v a n Rij n, 1 9 8 4):

u b e dl o a d ,i =

q b ,i
d i c b ,i fb

(3 -5 -1 6 )

w h er e, fb is t h e criti c al p a c ki n g fr a cti o n of t h e s e di m e nt, c b ,i is t h e v ol u m e fr a cti o n of s p e ci e s
i i n t h e b e d m at eri al w hi c h is us e d t o a c c o u nt f or t h e eff e ct of m ulti pl e s p e ci e s, q b ,i is t h e
v ol u m etri c b e d -l o a d tr a ns p ort r at e, a n d δ i is t h e b e d-l o a d t hi c k n e ss w hic h is c al c ul at e d b y:
di

di

= 0. 3 d

0. 7
*

æ q
ö
ç 'i - 1 ÷
çq
÷
è cr ,i ø

0. 5

(3 -5 -1 7 )

• M o d el s et u p
T h e n u m eri c al si m ul ati o ns of l o c al s c o ur ar o u n d bri d g e pi ers i n c h a n n el wit h t h e fi n e st
s e di m e nt ( D 5 0 = 0. 4 7 0 m m) a n d t h e c o ars est s e di m e nt ( D 5 0 = 0. 5 8 0 m m ) h a v e b e e n c arri e d o ut.
I n t ot al, 7 2 n u m eri c al m o d els h a v e b e e n est a blis h e d t o si m ul at e l o c al s c o ur pr o c ess ar o u n d
f o ur p airs of si d e-b y -si d e bri d g e pi ers u n d er o p e n c h a n n el, s m o ot h i c e -c o v er e d a n d r o u g h
i c e-c o v er e d fl o w c o n diti o ns. Fi g ur e 3 -5 4 sh o ws t h e bri d g e pi er di a m et ers a n d t h eir ass o ci at e d
bri d g e pi er s p a ci n g G/ D. T h e s c al e of t h e n u m eri c al m o d els is s et t o b e 5 m × 2 m × 1 m f or
all t h e m o d els a n d a p air of bri d g e pi ers is l o c at e d at t h e c e nt er of t h e c h a n n el. T h e
c o m p ut ati o n al d o m ai n is l o n g e n o u g h a n d pr o vi d e s a d e q u at e dist a n c e d o w nstr e a m of pi er s
213

to ensure there is not any interference between the turbulent flow and the downstream
boundary. The thickness of the packed bed equals to 0.30 m. The packed bed is composed
of the finest sand and the coarsest sand with D50 of 0.470 mm and 0.580 mm respectively, as
of the experimental study. The entrainment coefficient, which can be used to scale the scour
rate, uses a default value of 0.018 from the data of (Mastbergen and Van Den Berg, 2003).
The critical Shields number was calculated using the Soulsby-Whitehouse equation. The bed
load coefficient is used to control the rate at which bed load transport occurs at a given shear
stress, which is higher than the critical shear stress with a default value of 8.0 (suggested
vales ranging from 5.0 for low transport to 13.0 for very high sand transport) (Soulsby, 1997).
The angle of repose, which describes the maximum resting angle of the bed, equals to default
value of 32 degrees. The other corresponding parameters are the same with the experiment
in order to verify the applicability, validity and accuracy of the current numerical models
leading to a significant improvement in the case of numerical simulation of sediment
transport around bridge piers especially under ice-covered conditions.
• Meshing
The computational domain is subdivided into a mesh of fixed rectangular cells using
Cartesian coordinates. A multi-block mesh based on hexahedral elements is considered by
using three mesh blocks. Fine cells with grid size of 20×20 mm is used for the second mesh
block in which bridge piers are present and is from 0.5 m to 4.5 m from the origin. Whereas,
to optimize the computational time, 30 mm×30 mm cells are adopted from 0 to 1.5 m and
from 4.5 to 5.6 m from the origin for the first and third mesh blocks, respectively. The
sensitivity analysis showed that no significant changes were observed in bed scour with using
smaller grid although the simulation time with the finer mesh increased in 2.2 times. Total

214

number of real cells are 1,072,963 in which 35,376 cells are for the first mesh block,
1,000,000 cells are for the second mesh block and 37,587 cells are allocated to the third mesh
block.
• Boundary Conditions
To simulate flow fields and scour process around bridge piers, it is important that the
boundary conditions are preciously given. Figure 3-55 illustrates the boundary conditions for
the numerical models under rough ice-covered flow conditions. Because the flow domain is
defined as a hexahedral in cartesian coordinates, there are totally six different boundaries on
the mesh to be fixed, in addition to the boundary conditions for the pier surface and the ice
cover bottom surface. The boundaries of the mesh and their coordinate directions were set as
follows: sidewalls y—no slip/wall; top z—symmetry; bottom z—no slip/wall; left x—
specific velocity; and right x—outflow. The bridge pier was modeled as a smooth surface
with no slip. For the case of smooth ice-covered flow condition, smooth non-floatable ice
cover was applied at the same water depth of physical model. However, for the case of rough
ice-covered flow condition, in addition to the simulated smooth ice cover, ice cubes which
had the dimension of 35 mm × 35 mm × 35 mm were simulated. With this configuration, the
flow moves from left to right, parallels with the slip walls, and locates between the no-slip
floor and on the sediment bed until it reaches to the outflow boundary.

215

Figure 3-55: The calculation model and boundary conditions for rough ice-covered flow condition

3.5.3. Principal results and discussion
In this section, based on experimental results under different flow and cover conditions (open
channel, smooth ice-covered and rough ice-covered flow), the mechanisms of local scour
around the side-by-side bridge piers in channel bed with different bed material will be
examined. To avoid repetition, simulation results of the maximum depth of scour hole around
the 110-mm side-by-side piers have been presented for channel bed with the fine sand.
o Local scour under open flow condition
Simulation results of local scour around the 110-mm side-by-side piers under open flow
condition show the scour profile, morphological changes, and deposition patterns in the
vicinity of the bridge piers. Figure 3-56a illustrates the simulation results around the 110mm side-by-side piers in channel bed with sand of 0.470 mm after 450 s, compared to those
of laboratory experiment (with average approaching velocity of 0.20 m/s and flow depth of
0.253 m) as showed in Figure 3-56b. As shown in Figure 3-56, the maximum scour depth of
numerical simulation which occurs at the pier face agrees well with the experimental result.
For both numerical simulation and laboratory experiment, the maximum scour depth of 75
216

mm appears in front of the bridge piers, which is due to the acceleration of the flow at these
areas. Of note, the upstream face of the bridge pier is the location where the horseshoe vortex
is formed, which is mainly caused by the down flow in front of the pier. The horseshoe vortex
along with the acceleration of the flow at the sides of the pier increase the bed shear stress,
which will ultimately lead to development of local scour around the bridge piers. As
illustrated in Figure 3-57, the simulated scour depths around the bridge pier are compared to
those of experiment for channel bed with both coarse and fine sand. Of note, point “8” in
Figure 3-57 is the apex of the pier face facing upstream. Figure 3-58a shows two-dimensional
velocity field at the x-y plan at the water depth of z= 0.326 m at the last second of simulation
time, and Figure 3-58b shows the distribution of turbulent energy (mean kinetic energy per
unit mass) at the cross section of the bridge piers under open channel flow condition. One
can see from Figure 3-58b, the turbulent energy which is associated with eddies of flow
increases from the channel bed toward water surface and reaches the maximum around the
sides of bridge piers. Due to the flow being impeded in front of bridge pier, flow velocity
decrease at this location which is clearly seen in Figure 3-58a. Figure 3-59 illustrates flow
streamlines around the right-hand side bridge pier at the initial stage of the development of
the scour hole (t=22.25 s) and at the final stage (t=445 s). The streamlines in Figure 3-59
clearly show how the obstruction caused by bridge pier leads flow velocity to separate at the
pier face. Besides, the acceleration of the flow at the sides of bridge pier, and the existence
of the wake vortex at the back of bridge pier can been clearly seen in Figure 3-59. By
comparing Figure 3-59a to Figure 3-59b, one can see that the scouring process gradually
declines over the course of time which will cause the horseshoe vortex and the wake vortex
to become weaker and, consequently, the bed shear stress decrease. When the bed shear stress

217

becomes less than the critical shear stress, the scour depth will reach to the equilibrium state
at which the sediment particles may not be transported or moved into suspension any more.

Figure 3-56: (a) Simulated bed elevation contours around the 110-mm bridge piers in channel bed
with fine sediment at t=450 s under open channel condition; (b) Laboratory measured bed elevation
contours around 110-mm bridge piers in channel bed with fine sediment under open channel
condition

218

Figure 3-57: Simulated scour depths compared to those of experiments around the 110-mm bridge
piers in channel bed under open channel flow condition

Figure 3-58: (a): Flow field at the plane z= 0.326 m at the end of simulation time, and (b): The
distribution of turbulent energy at the cross section of the bridge pier under open channel flow
condition

Figure 3-59: (a) Flow streamlines around the 110-mm bridge pier: (a) at initial stage (t= 22.25 s) and
(b) at the last second of simulation (t= 445 s)

o Local scour under ice-covered flow conditions
The appearance of an ice cover in a river changes the velocity profile, with the ice cover
acting as a flow boundary that increases the wetted perimeter and the composite roughness.
The presence of ice cover tends to shift the velocity maximum closer to the bed, and lead to
219

more erosion (Sui et al., 2010). The maximum velocity occurs between the bed and the
bottom of the ice cover in a region depends on the relative roughness of the two boundaries.
The velocity drops to zero at each boundary due to the no-slip boundary condition, leading
to a parabola-shaped profile. The rougher the ice cover, the further the maximum velocity
shifts towards the bed in order to reduce energy, causing more scour (Sui et al., 2010).
Therefore, a lower average velocity threshold is needed to reach to the critical shear stress
for bed deformation in an ice-covered flow as compared to an open-water flow (Beltaos,
2011). As pointed out by Hains and Zabilansky (2004), the presence of ice has resulted in
increase in local scour depth at bridge piers by 10%–35%. In this section, results of numerical
simulation of flow under ice-covered condition will be presented with comparison to those
of experiments in laboratory. In present study, since the local scour patterns around the sideby-side bridge piers in channel bed with the coarse sediment are similar to those of in channel
bed with the fine sediment, to avoid repetition, only the results for channel bed with fine sand
is presented in this paper.
o Local scour under smooth ice-covered flow condition
Simulated results of local scour patterns around the 110-mm side-by-side bridge piers under
smooth-covered flow condition will be described by the scour depth, morphological changes,
and deposition patterns. Figure 3-60a illustrates simulated bed elevation contours around the
110-mm bridge piers in channel bed with fine sediment and Figure 3-60b illustrates those of
laboratory experiment (with an average approaching velocity of 0.20 m/s corresponding to a
water depth of 0.255 m). One can see from Figures 3-60 (a-b), results of the numerical
simulation agree well with those of experimental study. The maximum scour depth appears
at the upstream pier face (point “8”) with a scour depth of 85 mm. However, results of

220

simulated scour depth show more irregular distributed comparing to those of experiments.
The difference between the simulated scour pattern and that of experiments is due to the fact
whether the ice cover floats freely. In laboratory experiments, model ice cover floated freely
on water surface. However, in the numerical simulation, ice cover had to be considered as
rigid due to the restriction in numerical model for simulating the ice-covered flow. In the
case of a non-moving ice cover, the restraint on the cross-sectional area causes increased
velocity and sediment transport capacity with any increase in scour (Zabilansky, 1996). If an
ice cover floats freely, the drop-in flow can reduce the transport of both suspended and bedload sediment compared to non-moving ice cover (Ettema and Kempema, 2012). Figure 361 shows the comparison between the simulated scour depths and those of experiments
around the bridge pier in channel bed with both coarse and fine sands. As results showed in
Figure 3-61, for both numerical simulation and laboratory experiment, the maximum scour
depth occurred at the upstream apex of the pier face (point 8). However, the simulated scour
depth is slightly deeper than that of laboratory experiment. Figure 3-62a shows the simulated
two-dimensional velocity field at the x-y plan at the water depth of z= 0.326 m at the last
second of numerical simulation under smooth covered condition. Since the flow in front of
the bridge pier is impeded, flow velocity decreases clearly in front of bridge piers, as showed
in Figure 3-62. Figure 3-62b shows the distribution of turbulent energy at the cross section
where the bridge piers are located under smooth covered condition. Obviously, the turbulent
energy is higher near the bridge piers.

221

Figure 3-60: (a) Simulated bed elevation contours around 110-mm bridge piers in channel bed with
fine sediment at t=450 s under smooth-ice-covered condition; (b) Laboratory measured bed elevation
contours around 110-mm bridge piers in channel bed with fine sediment under smooth-ice-covered
condition

Figure 3-61: Simulated scour depths compared to those of experiments around the 110-mm bridge
piers in channel bed under smooth ice-covered condition

222

Figure 3-62: (a): Flow field at the plane z= 0.326 m at the end of simulation time, and (b): The
distribution of turbulent energy at the cross section of the bridge pier under the smooth-covered flow
condition

o Local scour under rough ice-covered flow condition
Figure 3-63a illustrates simulated bed elevation contours around the 110-mm bridge piers in
channel bed with fine sediment compared to those of laboratory experiment as showed in
Figure 3-63b (with an average approaching flow velocity of 0.19 m/s corresponding to a
water depth of 0.220 m). For both laboratory experiments and numerical simulation, the
maximum scour depth around the bridge piers reaches a value of 95 mm. However, with
respect to the numerical simulation, the simulated scour field around bridge piers is more
widely spread. The difference between the simulated scour patterns and those of experiments
based on whether the ice cover floats freely. In laboratory experiments, model ice cover
floated freely on water surface. However, in the numerical simulation, ice cover had to be
considered as rigid due to the restriction of the numerical model in simulating the ice-covered
flow. Besides, the local scour process in the vicinity of the bridge piers is an extremely
complex phenomenon and is related to many factors such as the flow velocity, water depth,
grain size distribution of sediment, critical shield stress for each type of sediment. Under
rough ice-covered flow condition, the zone of maximum flow velocity is closer to channel
bed comparing to that under the smooth covered condition (Sui, et al., 2010). In addition to

223

forcing the maximum of the velocity profile closer to the bed, erosion may even act as a
relief, and the erosion provides a balance between the increased shear stress and the depth of
the bed (Hains, 2004). This leads to the difference between the scour depths under smooth
covered condition and those under rough ice-covered condition. This is also the reason for
more irregular distribution in the scour-deposition patterns of channel bed under rough
covered condition comparing to that under both smooth ice-covered and open channel flow
conditions. Similarly, flow under smooth ice-covered flow condition also resulted in more
irregular distribution in scour pattern around bridge piers comparing to that under open
channel flow condition. Figure 3-64 shows the difference between the simulated scour depths
around the bridge pier and those of laboratory experiments. As shown in Figure 3-64, similar
to the results under both open channel and smooth ice-covered flow conditions, the deepest
scour depth under rough covered flow condition also occurs at point “8” - the apex of the
pier face facing upstream. Figure 3-65a shows the simulated two-dimensional velocity field
at the x-y plan for z= 0.326 m at the last second of numerical simulation under rough covered
flow condition. Since the flow in front of the bridge pier is impeded, flow velocity decreases
clearly in front of bridge piers, as showed in Figure 3-65. Figure 3-65b shows the distribution
of turbulent energy at the cross section where the bridge piers are located under rough
covered condition. Clearly, the turbulent energy is higher near the bridge piers. The
comparison between the simulated scour depths around bridge piers and those of measured
in laboratory experiments are presented in Figure 3-66. As indicated in Figure 3-66, the
simulated maximum scour depths around bridge piers agree well with those of laboratory
experiments.

Based on both simulated and measured results in laboratory, following

224

relationship have been derived between the simulated maximum scour depth (MSD) and
those of laboratory experiments:
a) channel bed with coarse sand: MSDNum = 0.9786MSDExp + 5.4573

(3-5-18)

b) channel bed with fine sand: MSDNum = 0.9885MSDExp + 5.286

(3-5-19)

Figure 3-63: (a) Simulated bed elevation contours around 110-mm bridge piers in channel bed with
fine sediment under rough-ice-covered condition; (b) Laboratory measured bed elevation contours
around 110-mm bridge piers in channel bed with fine sediment under rough-ice-covered condition

Figure 3-64: Simulated scour depths compared to those of experiments around the 110-mm bridge
piers in channel bed under rough ice-covered condition

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Figure 3-65: (a) Flow field at the plane z= 0.326 m at the end of simulation time, and (b): The
distribution of turbulent energy at the cross section of the bridge pier for the rough-covered flow
condition

Figure 3-66: Comparison of the simulated maximum scour depths (MSD) to those of laboratory
experiments

3.5.4. Conclusions
In this study, three-dimensional numerical models have been established to simulate the local
scour around the side-by-side bride piers under both smooth and rough ice-covered flow
conditions by comparing to those under open channel flow condition. Following conclusions
have been obtained:

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1) The RNG k-ε turbulence model and the sediment scour model adopted in this research
were successful to simulate flow fields and the local scour process around bridge piers
under both open ice-covered conditions.
2) On the upstream side of the bridge piers, the horseshoe vortex together with the
acceleration of the flow around the bridge piers resulted in a high bed shear stress, which
is the main factor that induces local scour around bridge piers. On the downstream side
of the bridge pier, the wake vortex together with the gravity force and bed friction,
resulted in the sediment deposition downstream of the bridge piers.
3) Results of both numerical simulations and experimental studies showed that the
maximum scour depth and turbulent energy around bridge piers under rough ice cover
condition were highest, comparing to those under both open channel and smooth covered
flow conditions. The reason for this difference is that, under rough ice-covered flow
condition, the zone of maximum flow velocity is closer to channel bed comparing to that
under the smooth covered condition. In addition to forcing the maximum of the velocity
profile closer to the bed, erosion may even act as a relief, and the erosion provides a
balance between the increased shear stress and the depth of the bed.
4) The simulated scour range under ice-covered flow conditions were more widely spread
and more irregular distributed. The main reason for the difference between the simulated
scour depths and those of measured in laboratory experiment is due to the fact whether
or not the ice cover floats freely. In laboratory experiments, model ice cover floats freely
on water surface. However, in the numerical simulation, ice cover had to be considered
as rigid due to the restriction of the numerical model in simulating the floating ice.

227

3.5.5. Reference
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in the Mackenzie Delta. Canadian Journal of Civil Engineering 386:638–649.
Ettema, R., and E. W. Kempema. (2012). River‐Ice Effects on Gravel‐Bed Channels. In
Gravel-Bed Rivers: Processes, Tools, Environments, ed. M. Church, P. Biron, and A. Roy,
523–540. Chichester, UK: Wiley-Blackwell
Ettema, R., Melville, B. W., & Constantinescu, G. (2011). Evaluation of bridge scour
research: Pier scour processes and predictions. Washington, DC: Transportation Research
Board of the National Academies.
Flow Sciences Inc. (2015). FLOW-3D User’s Manual Version 11.1. Santa Fe, New Mexico.
Hains, D., and L. Zabilansky. (2004). Laboratory Test of Scour under Ice: Data and
Preliminary Results. ERDC/CRREL TR-04-9. Hanover, NH: U.S. Army Engineer Research
and Development Center.
Hains, D., Zabilansky, L.J., & Weisman, R.N. (2004). An experimental study of ice effects
on scour at bridge piers. Cold Regions Engineering and Construction Conference and Expo,
16–19 May 2004, Edmonton, Alberta, Canada
Hirt, C.W., Nichols, B.D., (1981). Volume of fluid (VOF) method for the dynamics of free
boundaries. J. Comput. Phys. 39, 201–225.
Hirt, C.W., Sicilian, J.M., (1985). A porosity technique for the definition of obstacles in
rectangular cell meshes, In: Proceedings of the International Conference on Numerical Ship
Hydrodynamics, 4th. Washington,D.C., pp. 1–19.
Kim, H.S., Nabi, M., Kimura, I., Shimizu, Y. (2014). Numerical investigation of local scour
at two adjacent cylinders. Adv. Water Resour. 70, 131–147. http://dx.doi.org/
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Launder, B. E., and Spalding, D. B., (1974). The Numerical Computation of Turbulent
Flows, Computer Methods in Applied Mechanics and Engineering, Vol. 3, pp. 269-289
Mastbergen, D.R., Von den Berg, J.H., (2003). Breaching in fine sands and the generation
of sustained turbidity currents in submarine canyons. Sedimentology 50, 625–637.
Richardson, J. E., & Panchang, V. G. Three-dimensional simulation of scour-inducing flow
at bridge piers. Journal of Hydraulic Engineering, 1998, 124(5): 530-540.
Soulsby, R. L., & Whitehouse, R. J. S. (1997). Threshold of sediment motion in coastal
environments. In Pacific Coasts and Ports' 97: Proceedings of the 13th Australasian Coastal
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Volume 1 (p. 145). Centre for Advanced Engineering, University of Canterbury.
Soulsby, R., (1997). Dynamics of Marine Sands. Thomas Telford Publishing.
http://dx.doi.org/10.1680/doms.25844.
Sui, J., Wang, J., He, Y. & Krol, F. (2010). Velocity profiles and incipient motion of frazil
particles under ice cover. International Journal of Sediment Research, 25(1), 39-51.
Sheppard, D. M., Melville, B. & Demir, H. (2013). Evaluation of existing equations for local
scour at bridge piers. Journal of Hydraulic Engineering, 140(1), 14-23.
Toombes, L., & Chanson, H. (2011, January). Numerical limitations of hydraulic models. In
34th IAHR World Congress, 33rd Hydrology and Water Resources Symposium and 10th
Conference on Hydraulics in Water Engineering (pp. 2322-2329). Engineers Australia.
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1431–1456.
Vasquez, J. A., & Walsh, B. W. (2009, August). CFD simulation of local scour in complex
piers under tidal flow. In 33rd IAHR Congress: Water Engineering for a Sustainable
Environment.
Wu, P., Hirshfield, F., Sui, J. Y. Local scour around bridge abutments under ice covered
condition–an experimental study. International Journal of Sediment Research, 2015, 30(1):
39-47.
Wu, P., Balachandar, R., Sui, J. Local scour around bridge piers under ice-covered
conditions. Journal of Hydraulic Engineering, 2015, 142(1).
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theory. J. Sci. Comput. 1, 3–51. http://dx.doi.org/10.1007/BF01061452
Zabilansky, L. J., & K. D. White, (2005). Ice cover effects on scour in narrow rivers. Ice
Engineering, U.S. Army Cold Regions Research and Engineering Laboratory (CRREL), TN05-3.
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229

4. GENERAL CONCLUSIONS

Experiments have been done in a large-scale flume to study the effect of ice cover roughness
and non-uniform sediments on the local scour around four pairs of side-by-side bridge piers.
It was found that existence of ice cover on the water surface affects bed morphology,
maximum scour depth, armor layer, vertical velocity distribution, scour volume and scour
area. The general conclusions are as follows:
1) The pier Reynolds number (Reb) decreases with the increase in the pier spacing ratio
(G/D), which implies that the strength of the horseshoe vortices decreases as the spacing
distance between the side-by-side piers increases. The results showed that, under the same
flow condition (velocity and flow depth), the lowest pier Reynolds Number (Reb) occurred
under open channel flow conditions, and the highest pier Reynolds Number (Reb) occurred
under rough covered flow conditions. Further, it was observed that the influence of ice cover
on pier Reynolds Number fades away as the pier spacing distance increases regardless of
flow cover. Also, for the same bridge pier spacing ratio (G/D) and for the same sediment, the
relative MSD under open channel flow conditions is the lowest and reaches the maximum
under the rough covered flow conditions. This implies that the impact of the pier spacing
ratio under the rough ice-covered flow condition is clearly intensified compared to those
under both open channel and smooth covered flow conditions. In other words, the smaller
the pier size (D) and the larger the pier spacing (G), the weaker the horseshoe vortices around
the side-by-side bridge piers.
2) Under the same flow conditions, the effect of flow Froude number on the scour process is
stronger than that of pier size. Regardless of ice cover and pier size, the maximum scour
depth increases with flow Froude number, especially for finer sand beds. In other words, the
local scour depth around bridge piers for a coarse sand bed is less than that for a finer sand
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bed. The results of this experimental study allow the impacts of ice cover, flow Froude
number, and pier spacing distance on local scour around bridge piers to be prioritized.
Overall, one can say that the deepest scour hole occurs around closely spaced large side-byside piers under rough covered flow conditions which have higher Froude numbers. The
results also indicate that, regardless of the roughness of the model ice cover and the grain
size of sediment, the maximum scour depths always occurred at the upstream front face of
the bridge piers. Also, the amount of sediment transported to the downstream side of the
bridge pier to form the deposition mound is greatest under rough covered flow conditions.
The results indicate that the impact of pier spacing on scour depth under covered flow
conditions is similar to that under open channel conditions, however, the scouring process
under covered flow conditions is more intense. It was found that the most extreme scour
depth around side-by-side bridge piers occurs under rough covered flow conditions with the
higher Froude number and smaller bridge pier spacing.
3) Using data collected from the current experiments, empirical equations for predicting the
relative MSD (ymax/y0) under both channel flow and covered flow conditions have been
developed. Among all the dimensionless parameters, flow Froude number was the most
influential factor which had a positive relation with the relative MSD (ymax/y0). The impact
of the Froude number is most distinct under rough covered flow conditions with smaller pier
spacing ratios. Namely, for nearly the same Froude number, the largest scour depth occurs
under rough covered flow conditions with smaller pier spacing. This means that under rough
covered flow conditions, the maximum velocity is located closer to channel bed. Thus, the
shear stress increases, and the horseshoe vortexes are intensified due to the smaller pier

231

spacing ratio. Both the roughness of the ice cover and the pier spacing ratio are two major
factors leading to the most critical local scour pattern.
4) Sensitivity analysis was done, and it was concluded that the relative MSD is most sensible
to Fr, ni/nb, G/D and D50/y0, respectively.
5) Although the scour depth under ice-covered flow condition was larger comparing to that
under open flow condition, the geometry of the scour holes under open flow condition is
similar to that under ice-covered flow condition. Results showed that, regardless of flow
cover, the maximum scour depth decreases with increase in the grain size of armour layer.
Also, although the maximum depth of scour hole around largest pier was deepest, the grain
size distribution of armor layer in scour hole around larger piers did not show a significant
difference from those around smaller piers.
6) Under the same flow condition and same covered condition, the maximum scour depth
occurs in channel bed with the finest sediment. Due to the horseshoe vortex system,
maximum scour depth is located at the upstream face of the piers and extends along the
sides of the piers towards the rear side of the pier where wake vortex exists. Due to effect
of ice cover, the horseshoe vortex shifts the maximum downflow velocity closer to the pier
in the scour hole. Thus, the strength of downflow gets more intensified which leads to a
larger and wider deposition ridge downstream of the pier.
7) Under the same flow condition, both scour volume and scour area of scour hole in the
finest sand bed are largest comparing to those in channel bed with coarser sands. With
respect to the impact of ice cover, it was found that both scour volume and scour area of
scour hole under rough covered flow condition are largest comparing to those under both
smooth covered condition and open flow condition.
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8) Based on data collected in laboratory, two formulae have been developed to predict the
relative MSD (ymax/D50A) under both open flow condition and ice-covered condition.
Following dimensionless variables are considered in the proposed formulae for
determining the relative MSD (ymax/D50A): densimetric Froude number (Fr0), grain size of
armour layer (D50A/D50B), pier spacing (D50A/D), and roughness of ice cover (ni/nb). Results

showed that the calculated relative MSD (ymax/D50A) agreed well with those observed under
both open flow condition and ice-covered condition.
9) Results showed with increase in densimetric Froude number (Fr0), the relative MSD
increases correspondingly. Besides, under the same Fr0, the values of the relative MSD
under ice-covered conditions are larger than those under open flow condition. Results also
indicate that, under ice-covered flow condition, a smaller value of densimetric Froude
number is needed to initiate movement of sediment comparing to that under open flow
condition which can be justified by the higher flow velocity near channel bed under icecovered flow conditions and its impact on the threshold of sediment motion.
10) It is found the presence of ice cover can result in a deeper maximum scour depth
compared to that under open flow condition, and consequently, the required flow velocity
for incipient motion of sediment particles under ice-covered conditions decreases with the
increase in the relative roughness coefficient of ice cover.
11) The larger the sediment-fluid parameter, the greater the dimensionless shear stress for
incipient motion of bed material. In other word, with the increase in the sediment-fluid
parameter, the dimensionless shear stress increases correspondingly. However, for the same
sediment-fluid parameter, a higher dimensionless shear stress is resulted in channel bed with
finer sediment. Meanwhile, for the same dimensionless shear stress, the finer sediment has a
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lower sediment-fluid value while the coarser sediment has a greater sediment-fluid parameter
value for the incipient motion of bed material.
12) The dimensionless shear stress increases with the increase in the densimetric Froude
number. For the same densimetric Froude number, the dimensionless shear stress is for the
finest sediment type (D50=0.47 mm) is the least. It is also found that the dimensionless shear
Reynolds number increases with the increase in densimetric Froude number. With the same
densimetric Froude number, the dimensionless shear Reynolds number for the coarser sand
(D50=0.58 mm) is higher.
13) For the same relative MSD, the U*/Uc –value under the rough ice-covered flow condition
is more than that under smooth covered condition, implying that the near-bed velocity is
higher under rough ice-covered flow condition than that under smooth covered condition.
14) For the streamwise velocity component (Ux), it can be described as a reverse C-shaped
profile shape which begins from the scour hole up to the water surface. In terms of velocity
magnitude, the streamwise velocity in the scour hole under rough covered condition is
generally greater than those under both smooth covered and open flow conditions.
Regardless of the cover conditions of flow, the magnitude of velocity is the least in the scour
hole. Moreover, the location of the maximum velocity is closer to the bed under rough
covered flow condition than that under smooth covered flow condition.
15) In terms of the effects of rough ice cover vs those of smooth ice cover, the MSD under
rough ice-covered flow condition was deeper. The location of the maximum velocity was
closer to the bed under rough covered flow condition than that under smooth covered flow
condition. For the same bed material, the dimensionless shear stress for incipient motion of
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sediment increases with the shear Reynolds number as the ice cover becomes rougher. The
results are in good agreement with the result of Ackermann et al (2002). in which they stated
that the rough cover gave slightly larger scour depths than the smooth cover.
16) In terms of scour hole pattern, regardless of sediment type and flow cover, the deepest
point in each scour hole is clearly at the front face of bridge piers and the deposition mound
is located downstream of bridge piers. Under the rough covered flow conditions, both the
maximum scour depth and maximum deposition height are clearly greater than for open
channel flow. The results indicate under the rough covered flow condition more sediment
deposition develops at the downstream side of bridge piers and the deposition mound is wider
spread than those under open flow.
17) For the streamwise velocity component (Ux), there is a logarithmic pattern which begins
from the scour hole up to the water surface (or simulated ice-cover). In terms of velocity
magnitude, the streamwise velocity for rough cover is generally greater than the scour hole
velocity for smooth and open channel conditions. Regardless of sediment type, the rough ice
cover resulted in a larger maximum velocity compared to the smooth ice cover.
18) The vertical velocity distribution (Uz), which is a representative of the strength of
downfall velocity, is the greatest under rough ice cover. Generally, considering the absolute
value of Uz, the values of Uz diminish from the channel bed toward the scour hole and from
the channel bed toward the free surface. They tend to move toward right which implies
downflow velocity vectors are diminishing as they get closer to free surface which results in
the velocity profile having a parabola-shaped profile pattern.

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19) There is no significant difference in velocity field for the different sediment types and
different types of sediment. Different types of armor layer and sediment ridge development
were observed which are the result of differences in critical shear stress for the sediment
particles.
20) Regardless of flow cover, the streamwise turbulent intensity along with the vertical
turbulent intensity are highest just over the channel bed and diminishes towards the flow
surface. The streamwise turbulent intensity, the vertical turbulent intensity and turbulence
kinetic energy for the rough flow conditions are greater than those for open channel and
smooth ice-covered flow conditions.
21) Under nearly the same flow conditions, the maximum value of turbulence kinetic energy
and turbulent intensity occurs at the largest diameter pier.
22) In terms of grain size of sediment, under the same flow condition, the finest sediment
size of D50 = 0.47 mm yielded the largest scour volume and scour area. The impact of ice
cover on local scour volume and area is more significant for finer sediment type. On the other
hand, under the same flow conditions, the coarsest sediment of D50 = 0.58 mm yielded the
smallest scour volume and scour area.
23) In terms of flow cover, it was found that the rough ice-covered flow has led to the
maximum amount of scour volume and scour area. Besides, under the same flow condition,
the flow turbulence caused by high velocities and lower flow depths occurring around bridge
piers with smaller pier spacing is more significant for finer sediment. It was also found that,
regardless of whether or not the flow is covered, the scour volume decreases with the increase
in bed sediment size.
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24) The RNG k−ε turbulence model and the sediment scour model adopted in this research
were quite successful to simulate flow field and the local scour around bridge piers.
25) On the upstream side of the pier, the horseshoe vortex along with the acceleration of the
flow around the bridge piers resulted in high bed shear stress, which is the main factor that
induces local scour around bridge piers. On the downstream side of the pier, the wake vortex,
along with the gravity force and bed friction, resulted in the sediment deposition downstream
of the piers.
26) In both the numerical and experimental studies, the maximum scour depth and turbulent
energy which were achieved under rough ice cover condition were highest. The reason is due
to more pressurized flow under rough ice-covered flow condition. Pressurized flow causes
more restriction in flow area which causes more increase in velocity and shift the maximum
velocity more closely to the bed. In addition to forcing the maximum of the velocity profile
closer to the bed, erosion may even act as a relief of pressurized flow; if discharge rises above
freeze-up levels, erosion provides a balance between the increased shear stress and the depth
of the bed.
27) The values of maximum scour depth obtained by numerical model under ice-covered
flow conditions were more widespread. The main reason for the difference between the
numerical and experimental maximum scour depth is due to the fact the type of the ice cover
in the experiment was floating ice, however, in the numerical simulation, the type of ice
cover is assumed to be rigid due to the restriction of the numerical model in simulating the
floating ice.

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28) The values of maximum scour depth obtained by numerical model under open channel
flow conditions were in good agreement with the experimental value which confirms that the
model is accurate enough to predict hydraulic of flow under open channel flow conditions.
The present study would be helpful to engineers and scientists for safe design of the bridge
pier structures in cold regions. This investigation on the hydraulics over scoured bed around
the bridge piers under ice-covered flow conditions contributes to the field of fluid dynamics
and river engineering. It is highly recommended to do more experiments under different pile
group arrangements, pier spacing, flow rates, and sediment grain sizes to have a more
through perception of local scour phenomenon under ice-covered flow conditions.

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APPENDIX I

239

A.I.1. Effects of ice cover on local scour around bridge piers in non-uniform sand bed
Local scour is considered as one of the major reasons for failure of hydraulic structures
especially bridge foundation. Bridge failure may result in the loss of lives and financial costs
for reconstruction and restoration. Difficulties in perceiving the clear interaction between the
geometries of bridge piers with scouring mechanisms make the prediction of local scour
depth around bridge piers difficult. The foremost feature of the flow around bridge
foundations is the large-scale eddy structure, or system of vortices (Breusers et al. 1977).
The vortex system around bridge piers and abutments removes the erodible bed materials
and may result in the failure of bridge foundation. Numerous studies have been conducted
with the purpose of predicting scour depth of scour holes, and various equations have been
developed (Laursen and Toch, 1956; Liu et al., 1961; Shen et al., 1969; Jain and Fischer,
1980; Raudkivi and Ettema, 1983; Melville and Sutherland, 1988; Froehlich, 1989; Melville,
1992; Abed and Gasser, 1993; Richardson and Richardson, 1994 and Heza et al., 2007, to
mention only several). Most of these empirical equations were developed based either on
laboratory results or field data. These empirical equations were different from each other in
terms of the factors considered in the scour model, parameters used in the equation,
laboratory or site conditions, flow condition, grain sizes of bed material, etc. For instance,
Raudkivi and Ettema (1983) studied relationship between local scour depth and particle size
distribution of bed sediment and developed an equation to estimate the maximum depth of
local scour hole. Although numerous studies have been conducted to investigate local scour
around bridge foundation, this challenging phenomenon has been remained as one of the
main issues in terms of bridge pier design. Local scour process around bridge pier gets more
complicated when the water surface is covered ice. In this situation, the presence of ice cover

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leads to a different set of geomorphological conditions comparing to those under open flow
conditions (Hicks, 2009). The characteristics of flow under ice cover affects the process of
sediment transport, traverse and vertical mixing and mean flow velocity (Andre and Thang,
2012). It has been proved that the formation of a stable ice cover effectively doubles the
wetted perimeter compared to that under open channel condition, alters the hydraulics of an
open channel by imposing an extra boundary to the flow, causing velocity profile to be
shifted towards the smoother boundary (channel bed) and adding up to the flow resistance
(Sui et al., 2010; Wang et al., 2008). However, up to date, there is still very limited research
work regarding local scour around bridge infrastructures under ice covered condition, and
this issue is one of the major concerns in bridge foundation design field. Using non-uniform
sediments, Wu et al (2013) carried out experiments to investigate scour morphology around
bridge abutment under ice cover. It was found that that under ice cover, at different locations
of the abutment, the sediment sorting process were observed. Wu et al (2014) assessed the
impacts of ice cover on local scour around a semi-circular bridge abutment. It was found that
the average scour depth under ice-covered condition was always greater compared to that in
open flow condition. The average scour depth under rough ice cover was 35% greater than
that under smooth ice cover. Wu et al (2014) studied the incipient motion of bed material
and shear stress distribution around bridge abutments under ice-covered condition. They
claimed that the average scour angle around a semi-circular abutment is around 10 degrees
larger than that around the square abutment. Wu et al (2015) compared the scour profile
under an ice-covered condition with previous studies by considering the role of relative bed
coarseness, flow shallowness, and pier Froude number. It is found that the scour depth under
ice-covered condition is larger compared to that under open flow condition. Besides, the

241

presence of an ice cover results in a greater scour depth in flow with a shallower flow depth,
and with the increase in flow depth, the impact of ice cover decreases. In terms of protection
against possible undermining caused by local scour process around bridge infrastructure,
riprap is the most commonly employed countermeasure (Lauchlan and Melville, 2001). The
most suitable countermeasure for avoiding local scour process around hydraulic structure
depends on the relative effectiveness, cost, maintenance, and ability to detect failures (Deng
and Cai, 2009). Having an accurate and precise estimation of scour area and scour volume is
crucial for the safe design of bridge piers and abutments. Very few studies have thoroughly
investigated scour volume and scour area around bridge piers, especially under condition of
ice-covered flow. In this case, Wu et al (2014) found that there was a linear correlation
between scour depth and volume of scour hole around bridge abutments under ice covered
condition. Khwairakpam et al. (2012) developed two equations to estimate scour volume and
scour area around a vertical pier under clear water condition in terms of approach flow depth
and pier diameter. Hirshfield (2015) found that scour area and volume increase with pier
size. The aim of this study is to thoroughly investigate scour volumes and scour areas based
on a series of large-scaled flume experiments using non-uniform natural sediment under
conditions of open channel and ice-covered flow around four pairs of side-by-side cylindrical
bridge piers and to investigate how different scour volume and scour area are under icecovered flow compared to those of under open flow condition.

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Methodologies and experimental Setup
Experiments have been carried out in a large-scale flume at the Quesnel River Research
University of Northern British Columbia. The flume is 40-m long, 2-m wide and 1.3-m deep.
The longitudinal slope of the flume bottom was 0.2 percent. A holding tank with a volume
of nearly 90 m3 was located at the upstream end of the flume and provides a constant head
in the experimental zone. At the end of the holding tank, water overflowed from a rectangular
weir into the flume section for experiments. A flow diffuser was placed downstream of the
rectangular weir to maintain the flow to be uniform. Two sand boxes with the depth of 0.30
m were spaced 10.2 m. Figure AI-1 shows the experimental setup. Three natural non-uniform
sediments were used in this experimental study. The median grain sizes of these sands (D50)
were 0.58 mm, 0.50 mm and 0.47 mm, and the geometric standard deviation (σ g) is 2.61,
2.53 and 1.89, respectively. For all the three sediments, the geometric standard deviation (σ g)
is larger than 1.4 which can be treated as non-uniform sediments (Dey and Barbhuiya, 2004).
The first sand box was 5.6-m long and the second sand box was 5.8-m in long. Four pairs of
bridge piers with diameter of 60 mmm, 90 mm, 110 mm and 170 mm were used in this
experimental study. Bridge piers were made of PVC circular plumbing pipe. A pair of sideby-side bridge piers were placed inside each sand box. The distance between the central lines
of these side-by-side bridge piers was 0.50 m, namely, each pier was offset from the centre
line by 0.25 m, as illustrated in Figure AI-2. Water depth in the flume was adjusted by
adjusting the tailgate. In front of the first sand box, a SonTek Incorporated 2D flow meter
was installed to measure the approaching flow velocity and water depth during the
experiment. A staff gauge was also installed in the middle of each sand box to manually
verify water depth. The scour hole velocity field was measured using a 10-Mhz Acoustic

243

Droppler Velocimeter (ADV) by SonTek. The ADV is a high-precision instrument used to
measure 3D water velocity in a wide range of environments including laboratories, rivers,
estuaries, and the ocean (Cea et al, 2007). The Styrofoam panels were used to simulate ice
cover. Styrofoam density was 0.026 gr/cm3 and was floated on water surface during the
experimental runs. In the present study, two types of model ice cover were used, namely
smooth cover and rough cover. The smooth ice cover was the surface of the original
Styrofoam panels while the rough ice cover was made by attaching small Styrofoam cubes
to the bottom of the smooth cover. The dimensions of Styrofoam cubes were 25 mm×25
mm× 25 mm and were 35 mm spaced apart. Figure AI-3a shows the local scour around a
bridge pier under condition of rough ice-covered flow and Figure AI-3b shows the top view
of local scour around the 9-cm-bridge pier in sand bed of for D50=0.50 mm under rough icecovered condition. Each experimental run lasted 24 hours, and this allowed the local scour
process to reach an equilibrium condition. After 24 hours, the flume was gradually drained.
The scour depth was manually measured along the outside lines of the circular bridge piers.
In terms of scour depth measurement, the outside perimeter of each bridge pier was equally
divided into numbered measuring point in order to accurately read the scour depth at different
locations to draw scour hole contours, as shown in Figure AI-2. The scour hole around bridge
piers were measured at proper increments from numbered measuring point along each bridge
pier. In total, 108 Experiments were conducted to investigate scour area and scour volume.
For each sediment type, 36 experiments have been carried out under different flow
conditions, namely, open channel, smooth ice-covered and rough ice-covered. It should be
mentioned that the range of Froude number in the first sand box was higher than the second
sand box. This is because of the longitudinal slope of the channel and dissipation of

244

momentum of flow due to friction. The flow Froude number in the first sand box ranges from
0.072 to 0.240, and in the second sand box ranges from 0.054 to 0.177.

Figure AI-1: Plan view and vertical view of experiment flume

Figure AI-2: Measuring points around the circular bridge pier

245

Figure AI-3a: Side view of scour hole around the 11-cm-bridge pier under rough ice-covered
condition

Figure AI-3b: Top view of the local scour pattern around the 9-cm-bridge pier under rough icecovered condition (D50=0.50 mm)

Results and discussions
To compute scour hole volume and area for each experimental run, all measured data for
scour hole were input into the Surfer 12 which is a surface and contour mapping program.
The planar area defined in the Surfer 12 is computed by projecting the cut and fill portions
of the surface onto a plane and calculating the area of the projection where positive planar
area represents the projection of the cut (map areas where the upper surface is above the
lower surface) onto a horizontal plane and negative planar area represents the projection of
the fill (map areas where the upper surface is below the lower surface) onto a horizontal
plane. In terms of scour volume, the cut and fill volumes section of the grid volume report

246

display the positive volume (cut) and the negative volume (fill). The cut portion is the volume
between the upper and lower surface when the upper surface is above the lower surface while
the fill portion is the volume between the upper and lower surfaces when the upper surface
is below the lower surface (Yang et al, 2004). For instance, Figure AI-4a and Figure AI-4b
display the scour volume and scour area associated with the 17-cm-bridge pier under smooth
and rough ice-covered condition for sediment of D50= 0.47 mm, respectively. As Figure AI4b shows the blue regions are the planar areas which are needed to be filled while the red
regions are the planar areas needed to be cut off. Planar area is independent of the depth of
scour hole. It should be mentioned that among a pair of piers, the one which shows the highest
scour volume and scour area was selected in order to investigate the most critical case in
terms of bridge pier design.

Figure AI-4a: 3-D scour volume view for the 17-cm-bridge pier under rough ice-covered flow
condition for sediment of D50=0.47 mm

247

Figure AI-4b: Top view of cut and fill scour area for the 17-cm-bridge pier under smooth icecovered flow condition for sediment of D 50=0.47 mm

Figure AI-5 shows the changes in scour volume with respect to pier size and grain size of
sediment under different flow conditions (open channel, smooth ice-covered and rough icecovered flows). In Figure AI-5, for each type of sediment, the first three experiments, the
second three experiments, the third three experiments and the last three experiments are
associated with different pier diameters of 6 cm, 9 cm, 11 cm and 17 cm, respectively. One
can see from Figure AI-5 that for sediment of D50=0.50 mm, the volumes of scour hole under
rough ice-covered condition are the highest and the volumes of scour hole under open flow
condition are the lowest. The mean scour volume under open flow, smooth ice-covered and
rough ice-covered flow conditions is 459.96 cm3, 661.81 cm3 and 1069.24 cm3, respectively.
The difference between the mean scour volume under rough ice-covered flow condition and
that under open flow condition is 56.98%, and the difference between the mean scour volume
under smooth ice-covered flow condition and that under open flow condition is 35.10 %.
These differences indicate that, under nearly the same flow condition with the same bed

248

material, the presence of rough ice cover and smooth ice cover resulted in an increase in
scour volume of 56.98% and 35.10 % compared to those under the open channel flow
condition, respectively. The reason for an increase in the scour volume under ice-covered
condition compared to that under open flow condition is the modification of flow velocity
distribution caused by ice cover. Ice cover imposes an extra solid boundary on water surface,
and thus changes velocity distribution and increases turbulent intensity. The maximum flow
velocity under ice-covered flow condition is located between channel bed and ice cover,
depending on the roughness of ice cover and channel bed. The near bed flow velocity under
ice-covered conditions is higher than that under open flow conditions. As the near bed
velocity increases, the kinetic energy exerted on the bed material also increases, implying
more sediment transport (Sui et al, 2010). In terms of scour volume for sediment of D 50=0.47
mm, similar to results for sediment of D50=0.50 mm, the volume of scour hole under rough
ice-covered flow condition is the highest and the volume of scour hole under open flow
condition is the lowest. Besides, under ice-covered condition, the volume of scour hole for
sediment of D50=0.47 mm is significantly increased compared to that for sediment of
D50=0.50 mm. This reveals the fact that under the same flow condition, the impact of ice
cover on local scour process is significant for finer sediment type. The mean scour volume
under open flow, smooth ice-covered and rough ice-covered conditions is 1059.66 cm3;
1187.77 cm3 and 1529.95 cm3, respectively. Namely, under the same flow condition and with
the same sand bed, compared to the scour volumes under the open channel flow and smoothice-covered flow conditions, the presence of rough ice cover resulted in the increase in the
scour volume of 30.72 % and 22.35%, respectively.

249

In terms of scour volume for sediment of D50=0.58 mm, similar to those of D50=0.50 mm
and D50=0.47 mm, the volume of scour hole under rough ice-covered condition is the highest
and the volume of scour hole under open channel condition is the lowest. However, the
difference between volume of scour hole around same bridge pier in bed sand of D 50=0.58
mm and that in bed sand of D50=0.47 mm has relatively decreased. This result shows that,
regardless of whether or not the flow is covered, as the grain size of bed sediment increase,
the volume of scour hole decrease. For sediment of D50=0.58 mm, the mean scour volume
under open flow, smooth ice-covered and rough ice-covered conditions is 392.58 cm3;
610.72 cm3 and 965.76 cm3, respectively. Namely, under the same flow condition and with
the same sand bed, compared to the scour volumes under the open channel flow and smoothice-covered flow conditions, the presence of rough ice cover resulted in the increase in the
scour volume of 36.82 % and 58.1%, respectively. The grain size of sediment plays a key
role on the volume of scour hole. For instance, regardless of whether or not the flow is
covered, for sediment of D50= 0.47 mm, the mean scour volume around the 11-cm-bridge
pier is 2684.5 cm3 with the highest scour volume of 3366.72 cm3. However, for sediment of
D50= 0.50 mm, the average volume of scour hole around the 11-cm-pier is 1275.5cm3. It is
worth mentioning that there is a tremendous difference of 52.49% between the mean volume
of scour hole around the 11-cm-bridge pier for bed sand of D50= 0.47 mm and that for bed
sand of D50= 0.50 mm. Results also showed that it takes slightly shorter time for the scour
hole to reach the equilibrium state for the finer sediment. In contrast, for the coarser sediment,
it takes longer time for the scour hole to reach an equilibrium state.

250

Figure AI-5: Variation of scour volume around bridge pier

Figure AI-6 shows the scour area with respect to sediment types under different flow
conditions (open channel, smooth ice-covered and rough ice-covered flows). Similar to
Figure AI-6, for each type of sediment, the first three experiments, the second three
experiments, the third three experiments and the last three experiments are associated with
different pier diameters of 6 cm, 9 cm, 11 cm and 17 cm, respectively. Unlike the volume of
scour hole, the scour area is not dominantly highest for flow under rough ice-covered
condition comparing to those under smooth ice-covered and open channel flow conditions.
In terms of scour area for sediment of D50= 0.47 mm, in most cases, the scour area under
rough ice-covered condition is the highest and the scour area under open channel condition
is the lowest. However, under the same flow condition and with the same sand bed, compared
to the scour area under the smooth-ice-covered flow condition, the presence of rough ice
cover didn’t result in clearly increase in the scour area. This means that the impact of smooth
ice-covered flow on scour area is nearly the same as that of rough ice-covered flow. For
251

sediment of D50= 0.47 mm, the mean scour areas under open flow, smooth ice-covered and
rough ice-covered conditions are 546.09 cm2 ; 618.40 cm2 and 796.77 cm2, respectively.
Namely, under the same flow condition and with the same sand bed, compared to the scour
area under the open channel flow and smooth-ice-covered flow conditions, the presence of
rough ice cover resulted in the increase in the mean scour area of 31.46 % and 22.39%,
respectively. In terms of scour area for sediment of D 50= 0.50 mm, the mean scour areas
under open flow, smooth ice-covered and rough ice-covered conditions are 443.54 cm2;
585.44 cm2 and 714.85 cm2, respectively. Namely, under the same flow condition and with
the same sand bed, compared to the scour area under the open channel flow and smooth-icecovered flow conditions, the presence of rough ice cover resulted in the increase in the mean
scour area of 37.95 % and 18.10 %, respectively. In terms of scour area for sediment of D50=
0.58 mm, in most cases, the scour area under rough ice-covered condition is the highest and
the scour area under open channel condition is the lowest. For sediment of D 50= 0.58 mm,
the mean scour areas under open flow, smooth ice-covered and rough ice-covered conditions
are 426.10 cm2, 607.19 cm2 and 700.78 cm2, respectively. Namely, under the same flow
condition and with the same sand bed, compared to the scour area under the open channel
flow and smooth-ice-covered flow conditions, the presence of rough ice cover resulted in the
increase in the mean scour area of 13.40 % and 15.39%, respectively. The grain size of
sediment plays a key role on the scour area. For instance, regardless of whether or not the
flow is covered, for sediment of D50=0.47 mm, the mean scour area around the 11-cm-bridge
pier is 1151.70 cm2 with the highest scour area of 1524.94 cm2. However, for sediment of
D50=0.50 mm, the average scour area around the 11-cm-pier is 881.47 cm2 with the highest
scour area of 1216.82 cm2. It is worth mentioning that there is a tremendous difference of

252

52.49% between the mean scour area around the 11-cm-bridge pier for bed sand of D50=0.47
mm and that for bed sand of D50=0.50 mm.

Figure AI-6: Variation of scour area around bridge pier

Figure AI-7: Scour volume (V) vs. scour area (A)

Figure AI-7 shows the relationships between scour volume (V) and scour area (A) under
condition of both ice-covered flows and open channel flows. These relationships can be
described as follows:
Under condition of open channel flow:
253

1.2557

V = 0.2288(A)

(AI-1)

Under condition of ice-covered flow
1.158

V = 0.4649(A)

(AI-2)

According to Eq. AI-1 and Eq. AI-2, the coefficient factor of regression equation under icecovered flow is larger than that under open channel flow, implying that the flow under icecovered condition has led to higher amount of scour volume and scour area. Figure AI-8
gives the relationship between scour volume and scour area in terms of grain size of
sediment. One can see from Figure AI-8 that the largest amount of scour volume and scour
area occurs in the finest sand of D50= 0.47 mm.

Figure AI-8: Relationship between scour volume and scour area in terms sediment type

Conclusions
In the present study, the main objective was to thoroughly investigate the correlation between
scour volume and scour area under conditions of ice-covered and open channel flow in flume
with non-uniform sediment. In this study, three natural non-uniform sediment mixtures with
254

median grain size of 0.58 mm, 0.50 mm and 0.47 mm were used. Besides, two types of
artificial ice cover namely rough and smooth ice cover were used to simulate ice-covered
flow conditions. Totally, 108 Experiments have been conducted in a large-scaled flume to
study scour area, scour volume around four pairs of side-by-side cylindrical bridge piers. The
following are the major conclusions of this study:
1) In terms of grain size of sediment, under the same flow condition, the finest sediment size
of D50 = 0.47 mm yielded the largest scour volume and scour area. The impact of ice cover
on local scour volume and area is more significant for finer sediment type. On the other hand,
under the same flow conditions, the coarsest sediment of D50 = 0.58 mm yielded the smallest
scour volume and scour area.
2) In terms of flow cover, it was found that the rough ice-covered flow has led to the
maximum amount of scour volume and scour area. Besides, under the same flow condition,
the flow turbulence caused by high velocities and lower flow depths occurring around bridge
piers with smaller pier spacing is more significant for finer sediment. It was also found that,
regardless of whether or not the flow is covered, the scour volume decreases with the increase
in bed sediment size.
3) Finally, two empirical equations were developed to predict scour volume and scour area
under conditions ice-covered flow and open channel flow.

255

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Hydraulic Engineering (pp. 1738-1743). ASCE.
Andre, R., Thang, T. (2012). Mean and turbulent flow fields in a simulated ice-cover channel
with a gravel bed: Some laboratory observations. Journal of Earth Surface Processes and
Landforms, 37(9): 951-956.
Barbhuiya, A. K., and Dey, S. (2004). Local scour at abutments: A review. Sadhana, 29(5),
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Cea, L., Puertas, J., and Pena, L. (2007). Velocity measurements on highly turbulent free
surface flow using ADV. Experiments in fluids, 42(3), 333-348.
Deng, L., and Cai, C. S. (2009). Bridge scour: Prediction, modeling, monitoring, and
countermeasures. Practice periodical on structural design and construction, 15(2), 125-134.
Froehlich, D. C. (1989). Local scour at bridge abutments. In Proceedings of the 1989
National Conference on Hydraulic Engineering (pp. 13-18).
Heza, Y. B. M., Soliman, A. M., and Saleh, S. A. (2007). Prediction of the scour hole
geometry around exposed bridge circular-pile foundation. Journal of Engineering and
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Hicks, F. (2009). An overview of river ice problems. Journal of Cold Regions Science and
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Hirshfield, F. (2015). The impact of ice conditions on local scour around bridge piers
(Doctoral dissertation, University of Northern British Colombia
Jain, S. C., and Fischer, E. E. (1980). Scour around bridge piers at high flow velocities.
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Khwairakpam, P., Ray, S. S., Das, S., Das, R., and Mazumdar, A. (2012). Scour hole
characteristics around a vertical pier under clear water scour conditions. ARPN J. Eng. Appl.
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Yang, C. S., Kao, S. P., Lee, F. B., & Hung, P. S. (2004, July). Twelve different interpolation
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Lauchlan, C. S., and Melville, B. W. (2001). Riprap protection at bridge piers. Journal of
Hydraulic Engineering, 127(5), 412-418.
Laursen, E. M., and Toch, A. (1956). Scour around bridge piers and abutments (Vol. 4).
Ames, IA: Iowa Highway Research Board
Liu, H. K., Chang, F. F., and Skinner, M. M. (1961). Effect of bridge constriction on scour
and backwater. Civil Engineering Section, Colorado State University
Melville, B. W. (1992). Local scour at bridge abutments. Journal of Hydraulic Engineering,
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Hydraulic Engineering, 109(3), 338-350.
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Fort Collins, Colorado.
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Wang, J., Sui, J., and Karney, B. (2008). Incipient motion of non-cohesive sediment under
ice cover – an experimental study. Journal of Hydrodynamics, 20(1), 117-124.
Wu, P., Hirshfield, F., and Sui, J. (2013). Scour morphology around bridge abutment with
non-uniform sediments under ice cover, Proceedings of 2013 IAHR Congress, Tsinghua
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Wu, P., Hirshfield, F., Sui, J., Wang, J., and Chen, P. P. (2014). Impacts of ice cover on local
scour around semi-circular bridge abutment. Journal of Hydrodynamics, 26(1): 10-18.
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257

A.I.2. Comparison of three commonly used Equations for calculating local scour depth
around bridge pier under ice covered flow condition

Scouring can be defined as the process by which the particles of soil or rock around an
abutment or pier of a bridge get eroded and removed to a certain depth which is called the
scour depth (Warren, 2011). The U.S. Federal Highway Administration (FHWA) has
estimated 60% of bridge failure cases in the USA are due to scour and on average,
approximately 50 to 60 bridges collapse annually in the USA (FHWA, 1988). Wardhana &
Hadipriono (2003) studied 500 failures of bridge structures in the United States between 1989
and 2000 and reported that the most frequent causes of bridge failures were due to floods,
scour, and their cumulative impact. The average age of the 500 failed bridges was 52.5 years
but ranged from 1 to 157 years old (Brandimarte et al. 2012). Brice & Blodgett (1978) reported
that damages to bridges and highways from major regional floods in 1964 and 1972 were
equivalent to approximately 100 million US dollars per event. Bridge foundations should be
designed to withstand the effects of scour. Bridge damage and failure have huge negative
social and economic impacts in terms of reconstruction costs, maintenance and monitoring of
existing structures, the disruptions of traffic flow, and in some life-threatening cases, the cost
of human lives (Brandimarte et al. 2012). Moreover, a precise prediction of scour depth will
not only help to prevent those bridge failures which are the consequence of under-estimation
of scour depth but also will efficiently reduce unnecessary construction cost of those bridge
piers in which scour depths are over-estimated. To safely design bridges located on waterways
under severe flooding conditions, many researchers have developed several laboratoryderived equations for predicting bridge pier scour depth (Liu et al. 1961; Shen et al. 1969;

258

Jain and Fischer 1980; Melville and Sutherland 1988; Froehlich 1989; Melville 1992; Heza
et al. 2007). These equations are mostly empirical formulae which are usually based on
regressional analysis of laboratory and/or field scour data. However, they differ from each
other in terms of the factors considered in constructing the scour model, parameters used in
the equation, laboratory and/or site conditions. Since the number of these equations is
relatively large, selection of the best performing equations for a special case is a difficult task.
Comparison studies of scour formulae especially for different flow conditions might be
helpful to select the one with the best performance. Additionally, many rivers become icecovered during the winter months. However, the winter season is often overlooked even
though most rivers in Canada and northern parts of the United States, Europe, and Asia are
annually affected by ice. The relatively smaller number of studies on the scour around bridge
pier under ice-covered flow condition is due to the inherent difficulty in collecting field data
while ice is present and complications in lab-based measurements as a result of different scales
and of temperature effects (Moore and Landrigan, 1999). Ice cover can significantly change
the flow field and impact sediment transport in natural rivers. The formation of a stable ice
cover effectively doubles the wetted perimeter compared to open channel conditions. This
alters the hydraulics of the channel by imposing an extra boundary to the flow, causing the
velocity profile to be shifted towards a smoother boundary (channel bed) and adding to the
flow resistance (Sui et al. 2010). Furthermore, ice cover can lead to issues such as ice
jamming, flooding, restricting the generation of hydro-power, blocking river navigation, and
affecting the overall ecosystem balance (Hicks, 2009). One of the latest studies on bridge pier
scour under ice-covered flow condition was conducted by Hirshfield (2015). These
experiments were conducted in a large-scale flume to study the impact of ice cover roughness

259

and non-uniformity of sediment on the local scour around a single circular bridge pier under
open channel, smooth ice and rough ice-covered conditions. It was concluded turbulence
intensity was greater under ice covered than open channel conditions. In addition, it was
observed that local pier scour under rough and smooth ice cover was on average 37 and 20
percent greater than open channel scour depth, respectively. Another significant study on local
Scour around bridge piers under ice-covered conditions was carried out by Wu et al. (2015).
In this study, the scour profile under an ice cover is compared with previous studies by
examining the role of relative bed coarseness, flow shallowness, and pier Froude number. It
was concluded the scour depth under an ice-covered condition is larger than under open
channel flow conditions. Further, the presence of the ice cover becomes more significant with
respect to scour at shallower flow depths.
Materials and Methods
Most of the equations for the prediction of bridge pier scouring express the final scour depth
as a function of the flow characteristics (mean flow velocity at the approach section, water
depth), flow properties (density and viscosity of the fluid), stream bed material properties
(mean particle diameter, density) and bridge geometry (shape and dimension of the pier,
angle of attack of the flow). In this paper, scour around circular bridge piers will be
experimentally examined and subsequently the validity and reliability of three of the more
commonly used and cited scour equations developed specifically for open channel flow
condition will be investigated to see how accurately they predict scouring around bridge piers
under ice-covered flow conditions.

260

• HEC-18/Jones Equation
The most commonly used pier scour equation in the United States is the Colorado State
University (CSU) equation proposed by Richardson and Davis (1995) and is recommended
by the U.S. Department of Transportation’s Hydraulic Engineering (HEC-I8) (1993). It was
developed from laboratory data and is recommended for both live-bed and clear-water
conditions. The HEC-18/Jones equation is based on the Colorado State University (CSU)
equation:

ys y0 = 2K1K2K3K4(b y0)0.65Fr 0.43

(AI-2-1)

where ys = scour depth; y0= the approach flow depth; ys/y0 is a dimensionless expression of
the relative scour depth with respect to flow depth; K1 = correction factor for pier nose shape
which is unity for circular cylinder; K2 = correction factor for angle of attack flow which is
unity for 900; K3 = correction factor for bed condition which is 1.1 for clear water scour; b =
nominal pier width; and Fr = approach flow Froude number. K4 is a correction factor to
account for armoring of the scour hole:

2 0.5

K 4 = [1 − 0.89(1 − VR) ]

(AI-2-2)

Where VR is the velocity ratio and is dimensionless:

V −V
VR = [ 0 i50 ]
Vc90 − Vi50

(AI-2-2a)

Where Vo is the approach velocity directly upstream from the pier and V i50 is the approach
velocity, in feet per second, required to initiate scour at the pier for the particle size D 50. Vi50
261

is calculated as follows:
Vi50 = 0.645[

D50 0.053
] Vc50
b

(AI-2-2b)

Where D50 is the particle size for which 50 percent of the bed material is finer, in units of
feet and Vc50 is the critical velocity, in feet per second, for incipient motion of the particle
size D50. Vc50 is defined as follows:
1/ 3
Vc50 = 11.21y01/ 6 D50

(AI-2-2c)

While D90 is the particle size for which 90 percent of the bed material is finer, in units of
feet, and Vc90 is the critical velocity, in feet per second, for the incipient motion of the particle
size as given by:
1/ 6

1/3

Vc90 = 11.21y0 D90
•

(AI-2-2d)

Gao’s simplified Equation

Gao’s simplified pier scour equation is based on laboratory and field data from China (Gao
et al. 1993). This equation has different forms depending upon whether the scour condition
is live-bed scour (bed material upstream from bridge is in motion) or clear-water scour (bed
material upstream from bridge is not in motion) as discussed in Landers & Mueller (1996).
The Gao’s simplified equation for clear-water pier scour is defined as [19]:
V − Vic
y s = 1.141K s b 0.6 y 00.15 Dm−0.07 ( 0
)
Vc − Vic

(AI-2-3)

where ys is the depth of pier scour below the ambient bed, in feet; Ks is the simplified pier
shape coefficient which is 1.0 for cylinders; b is the width of bridge pier, in feet; y0 is the
262

depth of flow directly upstream from the pier, in feet; Dm is the mean particle size of the bed
material, in feet (for this study D50 was used as Dm); Vo is the approach velocity directly
upstream from the pier, in feet per second; and Vc is the critical (incipient motion) velocity,
in feet per second, for the Dm-sized particle. Vic is the approach velocity, in feet per second,
corresponding to critical velocity at the pier. Vic can be calculated using the following
equation:
Vic = 0.645(

Dm 0.053
) Vc
b

(AI-2-4)

If the density of water is assumed to be 62.4 pounds per cubic foot and the bed material is
assumed to have a specific gravity of 2.65, the equation for V c can be expressed as:

 10 + 0.3048y 0  
y

Vc = 3.28( 0 ) 0.14  8.85Dm + 6.05E −7 
0.72  

Dm
D
(
0
.
3048
)
m





•

0.5

(AI-2-5)

Froehlich Design Equation

The Froehlich design equation is included as a pier-scour calculation option within the
computer model HEC-RAS, Version 3.1 (Brunner, 2002). The Froehlich’s (1988) design
equation is defined as:
b
y
b 0.08
y s = 0.32bFr10.2 ( e ) 0.62 ( 0 ) 0.46 (
)
+b
b
b
D50

(AI-2-6)

where ϕ is a dimensionless coefficient based on the shape of the pier nose, and is 1.0 for
round-nosed piers; Fr1 is the Froude Number directly upstream from the pier; b e is the width
of the bridge pier projected normal to the approach flow, in feet; b is the width of the bridge
pier, in feet; D50 is the particle size for which 50 percent of the bed material is finer, in feet
263

and y0 is the depth of flow directly upstream from the pier, in feet.
Experiment setup
Experiments were carried out at the Quesnel River Research Centre, Likely, BC, Canada in
a large-scale flume. The flume measures 40 m long, 2 m wide and 1.3 m deep. The
longitudinal slope of the flume bottom was 0.2 percent. A holding tank with a volume of
nearly 90 m3 was located at the upstream end of the flume and provided a constant head in
the experimental zone. Two valves were connected to the holding tank to allow for control
of the flow velocity. At the end of the holding tank and upstream of the main flume, water
overflowed from a rectangular weir into the flume. Since the flow of water was turbulent
while entering the flume, a flow diffuser was placed downstream of the rectangular weir to
dissipate the turbulence in the flow of water. Figure AI-9a shows the experimental setup.
Two sand boxes with the depth of 0.30 m were filled with a uniform sediment having a
median particle size (D50) of 0.47 mm. The first sand box was 5.6 m in length and the second
sand box was 5.8 m in length. The distance between the sand boxes was 10.2 m. Four
different pairs of bridge piers with diameter of 60 mm, 90 mm, 110 mm and 170 mm were
used (Figure AI-9b). Bridge piers were constructed from PVC plumbing pipe and were
circular in shape. One pair of bridge piers were in each sand box so two experiments were
carried out simultaneously in each experimental run. Each pier was offset from the centre
line by 0.25 m, as illustrated in Figure AI-9b. The water depth in the flume was adjusted by
the position of the tailgates. In front of the first sand box, a SonTek Incorporated 2D flow
meter was installed to measure the approaching flow velocity, water depth, and inflow
discharge during the experiment. A staff gauge was also installed in the middle of each sand
box to manually verify water depth. The scour hole velocity field was measured using a 10264

Mhz Acoustic Droppler Velocimeter (ADV) by SonTek. In order to simulate ice cover, 13
panels of Styrofoam with dimensions of 1.2 m × 2.4 m (4×8 foot) were used to cover nearly
the entire surface of flume. Styrofoam density was 0.026 gr/cm3 and the Styrofoam was
floated on the surface in the flume during the experimental runs. In the present study, two
types of model ice cover were used, namely smooth cover and rough cover. The smooth ice
cover was the surface of the original Styrofoam panels while the rough ice cover was made
by attaching small Styrofoam cubes to the bottom of the smooth cover. The dimensions of
Styrofoam cubes were 25 mm×25 mm× 25 mm and were spaced 35 mm apart for the
Styrofoam covering panels. 36 experiments were conducted under open channel, smooth and
rough ice conditions. Figure AI-10 shows the rough ice-covered flow around a bridge pier in
experiment as well as ADV measurement around scour depth. The experimental runs were
24 hours long which allowed the scour hole to reach an equilibrium depth as noted in
previous experiments conducted by Hirshfield (2015). After 24 hours, the flume was
gradually drained. The scour depth was manually measured along the outside lines of the
circular bridge piers

265

Figure AI-9a: Measuring points around the circular bridge piers

Figure AI-9b: Experimental setup –plan and side views, respectively

Figure AI-10: 10-Mhz Acoustic Droppler Velocimeter in use to measure the velocity field around
bridge piers under rough ice-covered flow conditions
266

Results and discussion
Maximum scour depths calculated by the above three pier-scour equations were
compared to 36 sets of experimental data. In this section, comparisons between the results
from each equation and the experimental results are discussed along with an Error
analysis including RMSE (Root Mean Squared Error), Index of Agreement (Ia) and MAE
(Mean Absolute Error). The Absolute Error (MAE); Root Mean Square Error (RMSE)
and Index of Agreement (Ia) are mathematically described by the following equations:
n

e

MAE = i =1
n

i

(AI-2-7)
n

RMSE =

(y − x )
i =1

i

i

n

(AI-2-8)

n

Ia = 1−

2

(y − x )
i =1

i

i

2

(x − x + y − x )
n

i =1

2

i

i

(AI-2-9)

Where xi is scour depth obtained from experiments and yi is the corresponding predicted
scour depths; x is the mean experimental scour depth and n is number of records. Smaller
values of MAE and RMSE indicate a more successful prediction. The Index of Agreement
(Ia) is a standardized measure of the degree of model prediction error and varies between
0 and 1. A value of 1 indicates a perfect match, while 0 indicates no agreement (Willmot,
1981). Table AI-1 demonstrates the performance of the Gao’s simplified equation (SCE),
the HEC-18/Jones equation (HJE) and Froehlich Design Equation (FDE) under smooth
and rough flow conditions. The measured scour in Table AI-1 stands for the maximum

267

scour depth between left and right bridge pier. Table AI-2 provides a comparison of the
predicted maximum scour depth from the three equations to maximum measured scour
depth under smooth and rough ice-covered flow condition. It should be mentioned the
residual values are defined as predicted scour depth minus measured scour depth. A
negative residual value indicates over-estimated scour depth. From the data provided, it is
possible to determine which equation is most useful under various conditions. Evaluation
of these equations are important to bridge design especially for the case of flow under icecovered condition. The scatterplots in Figure AI-11(a-c) compare predicted pier scour
depth for each of the three equations to the measured scour depths obtained experimentally
under the different flow conditions. Pier-scour depths calculated using the Froehlich
design equation exceeded measured scour depths for every measurement of both open
channel and ice-covered flows (Figure AI-11a, Table AI-1). Likewise, Pier-scour depths
calculated using the HEC-18/Jones equation similarly exceeded measured pier scour for
all 36 observations (Figure AI-11b and Table AI-1). However, overestimations were larger
for the Froehlich design than for the HEC-18/Jones equation. Overall, the most reliable
and accurate equation which has predicted the pier scour depths under open channel and
ice-covered flow to a very good extent was Gao’s simplified equation. Pier-scour depths
calculated using the Gao’s simplified equation were smaller than measured scour depths
for 6 of the 12 measurements for open channel flow and for 9 of the 12 measurements for
smooth ice cover. However, it completely underestimated Pier-scour depths for the rough
ice cover flow (Figure AI-11c and Table AI-1). Statistics for calculated and measured pier
scour are summarized in Table AI-2. The averages of pier-scour depths for open channel
flow calculated from Froehlich equation was 0.46 ft, from the HEC-18/Jones was 0.38 ft,

268

and from the Gao’s simplified equation was 0.15 ft. The average of the measured pierscour depths was 0.15 ft. This result indicates Gao’s simplified equation was entirely
successful in predicting the scour depth under open channel conditions. Both the Froehlich
and HEC-18/Jones equations resulted in significant over-estimation of the average scour
depth. Furthermore, from Table AI-2, the highest index of agreement value (I a) and the
lowest RMSE and MAE values are for the Gao’s simplified equation for the case of open
channel flow. In terms of smooth ice-covered flow, the averages of pier-scour depths for
open channel flow calculated from Froehlich equation was 0.46 ft, from the HEC-18/Jones
was 0.37 ft, and from the Gao’s simplified equation was 0.13 ft. The actual average
measured pier-scour depth was 0.16 ft again indicating Gao’s simplified equation
provided the best agreement with the measured value and was more successful in
predicting the scour depth. Both the Froehlich and HEC-18/Jones equations resulted in
the significant over-estimation of the scour depth on average. The highest index of
agreement value (0.84) and the lowest RMSE and MAE values were obtained with Gao’s
simplified equation under the smooth ice-covered flow condition. In terms of rough icecovered flow, the averages of pier-scour depths for open channel flow calculated from
Froehlich equation was 0.46 ft, from the HEC-18/Jones was 0.37 ft, and from the Gao’s
simplified equation was 0.14 ft. In this case, the rough ice surface increased the average
measured pier-scour depths to 0.22 ft which is higher than the average scour depth
calculated using Gao’s simplified equation. However, the results from Gao’s equation
were closer to the experimental results than either the Froehlich or the HEC-18/Jones
equation might suggest it was more successful in calculating scour depth. Further, the
highest index of agreement value (0.78) and the lowest RMSE and MAE values are for

269

the Gao’s simplified equation under rough ice-covered flow condition. Mathematically,
Gao’s simplified equation is the most successful of the three equations at calculating scour
depth, but it does underestimate the extent of scour. In practical terms, this could lead to
a false sense of security in practical situations as increased scour depth could lead to
premature failure of a pier.
Table AI-1: Comparison of calculated pier scour to measured pier scour from three equations under
smooth and rough ice-covered flow condition
Equations

Cover

Pier
Size
(ft.)

Pier
Identification

Measured
Scour (ft.)

Smooth
Smooth
Smooth
Smooth

0.197
0.197
0.197
0.295

Right
Left
Right
Left

0.10
0.11
0.14
0.10

Smooth
Smooth

0.295
0.295

Right
Left

0.22
0.21

0.19
0.16

-0.03
-0.05

0.38
0.41

0.15
0.2

0.36
0.39

0.14
0.18

Smooth
Smooth

0.361
0.361

Left
Right

0.14
0.26

0.08
0.19

-0.06
-0.07

0.47
0.45

0.33
0.18

0.33
0.39

0.2
0.13

Smooth
Smooth

0.361
0.558

Left
Left

0.26
0.10

0.18
0.08

-0.08
-0.02

0.49
0.71

0.23
0.61

0.43
0.42

0.17
0.33

Smooth
Smooth
Rough
Rough
Rough
Rough
Rough
Rough
Rough
Rough
Rough
Rough
Rough
Rough

0.558
0.558
0.197
0.197
0.197
0.295
0.295
0.295
0.361
0.361
0.361
0.558
0.558
0.558

Left
Left
Left
Right
Left
Right
Right
Left
Left
Right
Right
Left
Left
Right

0.16
0.16
0.15
0.19
0.18
0.31
0.31
0.24
0.22
0.26
0.28
0.16
0.19
0.20

0.17
0.20
0.09
0.10
0.14
0.10
0.13
0.15
0.11
0.19
0.17
0.12
0.18
0.18

0.01
0.04
-0.06
-0.09
-0.04
-0.21
-0.18
-0.09
-0.11
-0.08
-0.11
-0.05
-0.01
-0.02

0.67
0.72
0.28
0.26
0.3
0.4
0.37
0.41
0.47
0.45
0.49
0.7
0.67
0.73

0.51
0.56
0.13
0.07
0.11
0.1
0.07
0.17
0.25
0.18
0.21
0.54
0.48
0.53

0.46
0.55
0.27
0.25
0.31
0.32
0.32
0.38
0.36
0.38
0.42
0.46
0.47
0.55

0.3
0.39
0.11
0.06
0.13
0.02
0.01
0.14
0.14
0.12
0.15
0.3
0.28
0.35

Gao’s simplified
Calculated Residual
scour (ft.)
(ft.)
0.06
-0.03
0.10
-0.01
0.10
-0.04
0.11
0.01

Froehlich Design
Calculated
Residual (ft.)
scour (ft.)
0.28
0.19
0.26
0.15
0.29
0.15
0.4
0.3

Hec-18/Jones
Calculated
Residual (ft.)
scour (ft.)
0.24
0.15
0.25
0.13
0.28
0.14
0.33
0.23

270

Table AI-2: Error Values of the three equations with respect to measured data under open, smooth
and rough flow
Cover

RMSE (%)

Ia

MAE (%)

SCE

HJE

FDE

SCE

HJE

FDE

SCE

HJE

FDE

Open

3.58

24.88

35.5

0.9

0.48

0.34

6.8

23

38

Smooth

4.38

22.33

33.91

0.84

0.56

0.41

14.1

26

25

Rough

10.33

18.21

29.19

0.46

0.78

0.64

15.7

45

39

Figure AI-11a: Comparison of calculated to measured pier scour for Froehlich equation under open,
smooth and rough flow condition.

Figure AI-11b: Comparison of calculated to measured pier scour for HEC-18/Jones equation under
open, smooth and rough flow condition.

271

Figure AI-11c: Comparison of calculated scour depths to the measured scour depth for Gao’s
simplified equation under open, smooth and rough flow condition

Summary and conclusions
Three pier-scour equations, namely the Froehlich design equation, the HEC-18/Jones
equation and Gao’s simplified equation, were evaluated against the data from 36 flume
experimental runs obtained for open channel, rough and smooth ice-covered flow under
uniform bed sediment type. The most important result that can be obtained from the
comparison of these three equations is that under nearly the same flow depth and approach
flow velocity but different flow cover, the average calculated values from the three equations
stayed nearly constant. On the other hand, in terms of ice cover, the rougher the ice surface,
the more turbulent the flow and the deeper the scour depth generated. Although Gao’s
simplified equation was reasonably successful in prediction of pier scour depth for both the
open-channel and smooth-ice conditions, it underestimated the pier-scour depth under rough
ice-covered flow conditions. Therefore, it can be concluded that none of the equations
adequately model scour depth under rough ice conditions and the equations are in need of
another term to make them more suitable to be used for the ice-covered flow conditions.

272

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Army Corps of Engineers Report CPD-69, 350 p.
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534-539.
Gao, D., Posada, G., & Nordin, C. F. (1993). Pier scour equations used in China. In Hydraulic
Engineering (pp. 1031-1036). ASCE
Heza, Y. B. M., Soliman, A. M. and Saleh, S. A. (2007). Prediction of the scour hole
geometry around exposed bridge circular-pile foundation. Journal of Engineering and
Applied Science, 54(4), 375.
Hirshfield, F. (2015). The Impact of Ice Conditions on Local Scour Around Bridge Piers
(Doctoral dissertation, University of Northern British Columbia).
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Jain, S. C. and Fischer, E. E. (1980). Scour around bridge piers at high flow velocities.
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Landers, M.N. and Mueller, D.S. (1996). Channel scour at bridges in the United States: U.S.
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Publication FHWA-IP-90-017, 204 p.
Shen, H., Schneider, V. R. and Karaki, S. (1969). Local scour around bridge piers Journal of
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274

APPENDIX II

275

Run #
1A
2A
3A
4A
5A
6A
7A
8A
9A
10A
11A
12A
13A
14A
15A
16A
17A
18A
19A
20A
21A
22A
23A
24A
25A
26A
27A
28A
29A
30A
31A
32A
33A
34A
35A
36A

Table AII-1: Experimental data collected for D50= 0.50 mm
D
D50
ɵ
y0
ymax
Cover
(mm)
(mm) (degrees) (mm)
(mm)
Open flow
60
0.50
10.61
200
12
Open flow
60
0.50
10.33
130
16
Open flow
60
0.50
11.02
230
20
Open flow
90
0.50
10.61
180
19
Open flow
90
0.50
10.33
90
25
Open flow
90
0.50
11.02
210
29
Open flow
110
0.50
11.37
195
25
Open flow
110
0.50
10.78
90
30
Open flow
110
0.50
10.85
230
35
Open flow
170
0.50
11.37
220
15
Open flow
170
0.50
10.78
110
27
Open flow
170
0.50
10.85
260
55
Smooth
60
0.50
10.91
240
20
Smooth
60
0.50
10.97
120
25
Smooth
60
0.50
11.10
260
30
Smooth
90
0.50
10.91
190
26
Smooth
90
0.50
10.97
100
35
Smooth
90
0.50
11.10
220
36
Smooth
110
0.50
10.85
120
30
Smooth
110
0.50
11.13
100
42
Smooth
110
0.50
10.89
260
52
Smooth
170
0.50
10.85
180
26
Smooth
170
0.50
11.13
120
47
Smooth
170
0.50
10.89
280
45
Rough
60
0.50
11.17
220
21
Rough
60
0.50
11.24
110
35
Rough
60
0.50
11.30
240
41
Rough
90
0.50
11.17
195
41
Rough
90
0.50
11.24
137
53
Rough
90
0.50
11.30
229
59
Rough
110
0.50
11.13
210
42.5
Rough
110
0.50
10.89
120
45
Rough
110
0.50
11.37
230
61
Rough
170
0.50
11.13
220
21
Rough
170
0.50
10.89
120
35
Rough
170
0.50
11.37
240
41

U

Q

(m/s)
0.11
0.16
0.15
0.13
0.21
0.18
0.13
0.23
0.18
0.11
0.16
0.14
0.10
0.16
0.16
0.13
0.21
0.18
0.13
0.17
0.12
0.07
0.13
0.15
0.15
0.18
0.19
0.13
0.13
0.16
0.13
0.19
0.19
0.12
0.16
0.17

(m3/s)
0.044
0.042
0.069
0.045
0.037
0.075
0.051
0.041
0.084
0.048
0.035
0.075
0.048
0.038
0.083
0.049
0.042
0.077
0.032
0.035
0.060
0.026
0.030
0.087
0.068
0.040
0.091
0.050
0.037
0.076
0.054
0.047
0.087
0.053
0.039
0.082

276

Run #
1B
2B
3B
4B
5B
6B
7B
8B
9B
10B
11B
12B
13B
14B
15B
16B
17B
18B
19B
20B
21B
22B
23B
24B
25B
26B
27B
28B
29B
30B
31B
32B
33B
34B
35B
36B

Table AII-2: Experimental data collected for D50=0.47 mm
D
D50
ɵ
y0
ymax
U
Cover
(mm)
(mm) (degrees) (mm)
(mm)
(m/s)
Open flow
60
0.47
11.83
250
22
0.11
Open flow
60
0.47
11.62
110
35
0.18
Open flow
60
0.47
11.45
280
25
0.17
Open flow
90
0.47
11.83
200
35
0.13
Open flow
90
0.47
11.62
90
60
0.25
Open flow
90
0.47
11.45
230
68
0.20
Open flow
110
0.47
11.50
242
25
0.12
Open flow
110
0.47
11.83
100
71
0.28
Open flow
110
0.47
11.72
253
75
0.20
Open flow
170
0.47
11.50
250
24
0.12
Open flow
170
0.47
11.83
100
45
0.18
Open flow
170
0.47
11.72
270
48
0.16
Smooth
60
0.47
11.62
250
29
0.12
Smooth
60
0.47
11.59
110
35
0.17
Smooth
60
0.47
11.55
260
42
0.17
Smooth
90
0.47
11.62
200
31.2
0.15
Smooth
90
0.47
11.59
100
64
0.23
Smooth
90
0.47
11.55
240
68
0.20
Smooth
110
0.47
11.59
243
42
0.10
Smooth
110
0.47
11.10
90
78
0.21
Smooth
110
0.47
11.57
255
85
0.20
Smooth
170
0.47
11.59
260
29
0.09
Smooth
170
0.47
11.10
105
48
0.15
Smooth
170
0.47
11.54
250
46
0.18
Rough
60
0.47
11.48
220
47
0.16
Rough
60
0.47
11.45
100
55
0.17
Rough
60
0.47
11.59
250
57
0.22
Rough
90
0.47
11.48
220
67
0.14
Rough
90
0.47
11.45
100
73
0.23
Rough
90
0.47
11.59
230
85
0.20
Rough
110
0.47
11.58
240
80
0.12
Rough
110
0.47
11.61
90
92
0.20
Rough
110
0.47
11.62
220
95
0.19
Rough
170
0.47
11.58
220
49
0.12
Rough
170
0.47
11.61
110
58
0.16
Rough
170
0.47
11.62
280
61
0.17

Q
(m3/s)
0.056
0.040
0.094
0.054
0.045
0.093
0.058
0.056
0.101
0.059
0.036
0.084
0.061
0.037
0.090
0.060
0.046
0.096
0.048
0.038
0.102
0.049
0.032
0.089
0.072
0.034
0.109
0.061
0.046
0.090
0.058
0.037
0.085
0.053
0.036
0.093

277

Run#
1C
2C
3C
4C
5C
6C
7C
8C
9C
10C
11C
12C
13C
14C
15C
16C
17C
18C
19C
20C
21C
22C
23C
24C
25C
26C
27C
28C
29C
30C
31C
32C
33C
34C
35C
36C

Table AII-3: Experimental data collected for D50=0.58 mm
D
D50
ɵ
y0
ymax
Cover
(mm)
(mm) (degrees) (mm)
(mm)
Open flow
60
0.58
11.35
210
12
Open flow
60
0.58
11.25
130
12
Open flow
60
0.58
11.12
240
15
Open flow
90
0.58
11.35
170
18
Open flow
90
0.58
11.25
90
25
Open flow
90
0.58
11.12
230
38
Open flow
110
0.58
11.6
200
20
Open flow
110
0.58
11.69
100
24
Open flow
110
0.58
11.64
220
36
Open flow
170
0.58
11.6
250
17
Open flow
170
0.58
11.69
100
27
Open flow
170
0.58
11.64
270
27
60
0.58
11.06
200
15
Smooth
60
0.58
11.07
120
19
Smooth
60
0.58
11.12
220
18
Smooth
90
0.58
11.06
170
20
Smooth
90
0.58
11.07
100
34
Smooth
90
0.58
11.12
240
43
Smooth
110
0.58
11.06
210
27
Smooth
110
0.58
10.74
90
32
Smooth
110
0.58
10.08
230
50
Smooth
170
0.58
11.06
260
18
Smooth
170
0.58
10.74
105
32
Smooth
170
0.58
10.08
250
37
Smooth
Rough
60
0.58
8.28
220
32
Rough
60
0.58
8.65
100
41
Rough
60
0.58
8.79
250
45
Rough
90
0.58
8.28
220
38
Rough
90
0.58
8.65
100
43
Rough
90
0.58
8.79
230
49
Rough
110
0.58
10.43
195
31
Rough
110
0.58
8.39
90
33
Rough
110
0.58
8.34
190
60
Rough
170
0.58
10.43
200
39
Rough
170
0.58
8.39
140
36
Rough
170
0.58
8.34
220
37

U

Q

(m/s)
0.09
0.16
0.15
0.11
0.25
0.20
0.15
0.28
0.20
0.12
0.18
0.16
0.11
0.15
0.15
0.13
0.23
0.20
0.11
0.21
0.20
0.09
0.15
0.18
0.16
0.17
0.22
0.14
0.23
0.20
0.14
0.20
0.15
0.11
0.15
0.13

(m3/s)
0.038
0.042
0.072
0.037
0.045
0.093
0.059
0.056
0.087
0.059
0.036
0.084
0.044
0.036
0.066
0.044
0.046
0.096
0.047
0.038
0.094
0.049
0.032
0.089
0.072
0.034
0.109
0.061
0.046
0.090
0.054
0.037
0.057
0.044
0.042
0.057

278

Figure AII-1: Scour hole velocity profiles for the lateral (Uy) component under open, smooth and
rough ice-cover distinguished by the pier size and under D50= 0.47 mm for the lowest discharge

Figure AII-2: Scour hole velocity profiles for the lateral (Uy) velocity component distinguished by
flow cover for all the pier size and under D50= 0.47 mm for the lowest discharge
279