BEDLOAD TRANSPORT OF SMALL RIVERS IN MALAYSIA
by
ZAHRA ZANGENEH SIRDARI
Thesis submitted in fulfilment of the requirements
for degree of
Doctor of Philosophy
May 2013
1
ACKNOWLEDGEMENTS
I would like to thank all the individuals and organizations who have helped or
provided the guidance during the study. Among the organisations, firstly I would like
to thanks the Universiti Sains Malaysia who provided the opportunity to study in this
university under fellowship scheme. I am also thankful to USM for all efforts from
granting the study leave to providing all reports and drawings required for this thesis
work.
First and foremost I would like to express my genuine gratitude to my
supervisor, Prof. Dr. Hj Aminuddin Ab. Ghani for his supervision, advice and
guidance. I really was honoured to have the opportunity to work under his
supervision. Also I would like to special thanks to my second Supervisor Mr.
Zorkeflee Abu Hasan for his guidance and technical support.
I would also like to thank River Engineering and Urban Drainage Research
Centre (REDAC) and its staffs especially Mrs. Nor Mawati Mohamad, Mr. Mohd
Sufian Osman, Mr. Rahim Ghazali and Mr. Khairul Nizam Abu for helping me in
field measurements and data collection.
I don’t have words to express my thanks to Dr. Farshid Bateni, in fact no words
can express his generosity. All through this work he has provided his guidance and
help in modelling and programming in MATLAB. I am also thankful to all officers,
seniors, colleges and friends who helped one or another way to make possible this
study.
Last but not least I would extend my word of thanks to my family specially my
lovely sister Nasim who helped me during all this duration of my study.
ii
2
TABLE OF CONTENTS
1
ACKNOWLEDGEMENTS ................................................................................................ ii
2
TABLE OF CONTENTS................................................................................................... iii
3
LIST OF TABLES ............................................................................................................ vii
4
LIST OF FIGURES ............................................................................................................ x
5
LIST OF ABREVIATIONS ............................................................................................. xx
6
LIST OF SYMBOLS ....................................................................................................... xxi
7
ABSTRAK ..................................................................................................................... xxiv
8
ABSTRACT .................................................................................................................. xxvi
1
CHAPTER 1- INTRODUCTION ....................................................................................... 1
2
1.1
Background............................................................................................................... 1
1.2
Problem Statement.................................................................................................... 3
1.3
Objective of the Investigation................................................................................... 5
1.4
Scope of Work .......................................................................................................... 5
1.5
Structure of Thesis .................................................................................................... 6
CHAPTER 2 - LITERATURE REVIEW .......................................................................... 8
2.1
Introduction .............................................................................................................. 8
2.2
Bedload Transport .................................................................................................... 8
2.3
Bedload Transport Analysis ..................................................................................... 9
2.4
Bed Load Transport Equations ............................................................................... 12
2.4.1
2.5
2.6
Performance of Bedload Transport Equations ........................................ 19
Regression Analysis ............................................................................................... 21
2.5.1
Linear Regression ................................................................................... 21
2.5.2
Multiple Linear Regression ..................................................................... 22
2.5.3
Least- Square Method ............................................................................. 23
2.5.4
Polynomial Regression............................................................................ 24
2.5.5
Nonlinear Regression .............................................................................. 24
Soft Computing Modelling ..................................................................................... 25
iii
2.6.1
Genetic Programming (GP)..................................................................... 26
2.6.2
Artificial Neural Network (ANN) ........................................................... 28
2.7
Application of Soft Computing Modelling in Prediction of Bedload Transport .... 30
2.8
River Channel Confluence...................................................................................... 36
2.9
Sediment Transport Modelling ............................................................................... 41
2.9.1
SSIIM ...................................................................................................... 48
2.9.1.1
SIMPLE Algorithm ................................................................. 49
2.9.1.2
Control Volume Scheme.......................................................... 49
2.9.1.3
SSIIM Application ................................................................... 50
2.10 Summary................................................................................................................. 55
3
CHAPTER 3 METHODOLOGY .................................................................................... 58
3.1
Introduction ............................................................................................................ 58
3.2
Study Area .............................................................................................................. 59
3.3
River Hydrology and Hydraulic ............................................................................. 61
3.4
3.5
4
3.3.1
Stream Flow Data.................................................................................... 61
3.3.2
Water Level Record ................................................................................ 61
3.3.3
Stage Discharge Data .............................................................................. 62
3.3.4
Flood Frequency Analysis....................................................................... 63
Field Data Measurement......................................................................................... 67
3.4.1
Flow Measurement .................................................................................. 68
3.4.2
Geometry Data ........................................................................................ 70
3.4.3
Sediment Data ......................................................................................... 72
3.4.3.1
Bed Material ............................................................................ 72
3.4.3.2
Bedload .................................................................................... 73
Techniques for Bedload Prediction ........................................................................ 75
3.5.1
Performance of Bedload Transport Equation .......................................... 76
3.5.2
Dimensional Analysis ............................................................................. 77
3.5.3
Nonlinear Regression Method (NLR) ..................................................... 78
3.5.4
Artificial Neural Network (ANN) ........................................................... 79
3.5.5
Genetic Programming Method (GP) ....................................................... 80
CHAPTER 4 BEDLOAD TRANSPORT CHARACTERISTICS ................................... 82
4.1
Introduction ............................................................................................................ 82
4.2
River Characteristics .............................................................................................. 83
4.2.1
Summary of River Data Collection ......................................................... 83
4.2.2
Typical Cross-Sections for the River Study Site ..................................... 87
iv
4.2.3
Parameter Affecting Bedload Transport ................................................. 90
4.3
Particle Size Distribution ........................................................................................ 93
4.4
Evaluation of Bedload Size Distribution with Increasing Shear Stress .................. 97
4.5
Fractional Transport Rate ..................................................................................... 102
4.6
Performance of Bedload Transport Equation ....................................................... 107
4.6.1
Assessment of Existing Equation for Kurau River ............................... 107
4.6.2
Prediction of Bedload Transport in Kurau River with Nonlinear
Regression Method ............................................................................... 109
4.6.3
Prediction of Bedload Transport in Kurau River by Genetic Programming
............................................................................................................... 112
4.7
4.6.4
Combination of ANN and GP ............................................................... 117
4.6.5
Comparison of Bedload Equations for Kurau River ............................. 122
Development of Bedload Equation for Small Rivers (Kurau, Lui, Semenyih) .... 126
4.7.1
Assessment of Existing Equations for Small Rivers (Kurau, Luie and
Semenyih) ............................................................................................. 127
4.7.2
Nonlinear Regression Result for Small Rivers (Kurau, Lui and Semenyih)
............................................................................................................... 129
4.7.3
4.8
Sensitivity Analysis .............................................................................................. 134
4.9
Genetic Programming Result................................................................................ 136
4.9.1
5
Artificial Neural Network Results ........................................................ 131
Comparison of Bedload Equations for Small Streams .......................... 139
CHAPTER 5 RIVER CONFLUENCE SEDIMENT TRANSPORT MODELLING .... 142
5.1
Introduction .......................................................................................................... 142
5.2
SSIIM ................................................................................................................... 143
5.3
SSIIM versions ..................................................................................................... 144
5.4
Theoretical Basis .................................................................................................. 145
5.4.1
5.4.2
Water Flow Calculation ........................................................................ 146
5.4.1.1
The k-ε turbulence model ...................................................... 146
5.4.1.2
Wall laws ............................................................................... 147
Sediment Flow Calculation ................................................................... 148
5.5
Graphical Interface ............................................................................................... 149
5.6
Input Files ............................................................................................................. 150
5.7
Output Files .......................................................................................................... 151
5.8
Making a Grid in SSIIM ....................................................................................... 153
5.8.1
Grid Editor ............................................................................................ 156
5.8.2
Multiblock and One Block Grid ............................................................ 156
v
5.9
Sediment Flow Simulation in Confluence of Kurau and Ara River ..................... 160
5.9.1
Characteristics of Kurau -Ara Confluence ............................................ 161
5.9.2
Input Data .............................................................................................. 163
5.9.3
Input Files ............................................................................................. 165
5.9.3.1
Control File ............................................................................ 165
5.9.3.2
Timei File .............................................................................. 166
5.9.4
Numerical Algorithms ........................................................................... 169
5.9.5
Sensitivity Analysis............................................................................... 170
5.9.6
Calibration and Validation .................................................................... 171
5.9.7
5.9.6.1
Model Calibration .................................................................. 171
5.9.6.2
Model Validation ................................................................... 183
Short Term Changes in Bedload Transport, Bed Morphology and Bed
Material Characteristics ........................................................................ 186
5.9.8
6
5.9.7.1
Morphological Changes ......................................................... 188
5.9.7.2
Lateral bar .............................................................................. 209
5.9.7.3
Bedload Transport Rates........................................................ 211
5.9.7.4
Sediment Pattern .................................................................... 220
High Flow Modelling ............................................................................ 229
CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS ................................... 236
6.1
6.2
Conclusion ............................................................................................................ 236
6.1.1
Bedload Transport Characteristics ........................................................ 236
6.1.2
Estimating Bedload Transport............................................................... 237
6.1.3
Sediment Transport in River Channel Confluence ............................... 238
Recommendations ................................................................................................ 240
7
REFERENCES ............................................................................................................... 241
8
APPENDIX A
9
APPENDIX B
10
APPENDIX C
vi
3
TABLES
LIST OF TABLES
TITLE
PAGES
Table 2.1
Bedload transport equations, Deterministic Shear stress method
13
Table 2.2
Bedload transport equations, Deterministic Stream power method
14
Table 2.3
Bedload transport equations, Deterministic Energy slope method
14
Table 2.4
Bedload transport equations, Deterministic Regression method
15
Table 2.5
Bedload transport equations, Deterministic Discharge and velocity 17
method
Table 2.6
Bedload transport equations, Deterministic Equal mobility method
17
Table 2.7
Bedload transport equations, Deterministic Probabilistic method
19
Table 2.8
Comparison of bedload equations and the ANN model (Sasal et 32
al., 2009)
Table 2.9
Summary of the major foregoing studies considering the 38
morphodynamics of channel confluences (Leite Ribeiro et al.,
2012)
Table 2.10
Summary of Some 3D hydrodynamic/sediment transport Models 44
(Papanicolaou et al, 2008)
Table 2.11
Applications for selected 3D models (Papanicolaou et al, 2008)
46
Table 3.1
Flood ranking for Kurau River at Pondok Tanjung
64
Table 3.2
Summary of flood frequency analysis for Kurau River at Pondok 65
Tanjung
Table 3.3
Goodness of fit test with chi-squared statistic value
65
Table 3.4
Typical cross sections along Kurau River (19 June 2010)
70
Table 3.5
The common bedload transport equations
77
Table 3.6
Multigene GP range of initially defined parameters
81
vii
Table 4.1
Range of field data
85
Table 4.2
Summary of large and medium rivers (Monalis and Wu, 2001)
86
Table 4.3
The classification of sediments by particle size according to the
Wentworth scale
98
Table 4.4
Summary of bedload transport equations assessment
108
Table 4.5
Parameter estimates of experimental data based on equation (3-14)
110
Table 4.6
Statistical analysis of experimental data based on equation (3-14
110
Table 4.7
Parameter estimates of experimental data base on equation (4-1)
111
Statistical analysis of experimental data base on equation (4-1)
111
Table 4.9
Assessment of NLR equation
112
Table 4.10
Summary of results of ANN
119
Table 4.11
Comparison of bedload transport equations
124
Table 4.12
Summary of bedload transport equations assessment
127
Table 4.13
Parameter estimates of experimental data based on equation (4-7)
129
Table 4.14
Parameter estimates of experimental data based on equation (4-8)
130
Table 4.15
Statistical analysis of experimental data base on equation (4-7)
130
Table 4.16
Sensitivity analysis results for parameters
135
Table 4.17
Bedload equations assessment
140
Table 5.1
Comparison of Cont value for one and two block grid
159
Table 5.2
Sediment characteristics
165
Table 5.3
Comparison of Bedload transport rate
173
Table 4.8
viii
Table 5.4
Parameter calibrated in SSIIM
174
Table 5.5
Comparisons of water and bed level for Q=15 m3/s (19 July 2012)
183
Table 5.6
Comparisons of water and bed level for Q=43 m3/s (27 Sept 2012)
183
Table 5.7
Comparisons of water and bed level for Q=11 m3/s (8 Oct 2012)
185
Table 5.8
Hydraulic condition during an event at Kurau _Ara confluence
187
ix
4
FIGURES
LIST OF FIGURES
TITLE
PAGES
Figure 2.1
Schematic representation of sediment transport in a stream
(Singh, 2005)
9
Figure 2.2
Comparison of the performance of the ANN with simple 31
regression and analytical approximation equations (Caamano et
al., 2006)
Figure 2.3
The ANFIS model for bed load sediment (Azamathulla et al., 33
2009)
Figure 2.4
Predicted bed load against measured bed load using ANFIS 33
(Azamathulla et al., 2009)
Figure 2.5
Observed versus predicted sediment load by SVM for 34
Langat, Kurau and Muda rivers (Azamathulla et al., 2010b)
Figure 2.6
Observed versus predicted sediment load by FFNN for 35
Langat, Kurau and Muda rivers (Ab. Ghani et al., 2011)
Figure 2.7
Observed versus predicted sediment load by GEP for Langat, 35
Kurau and Muda rivers (Ab. Ghani and Azamathulla, 2012;
Azamathulla et al., 2010a; Chang et al., 2012; Zakaria et al.,
2010)
Figure 2.8
(a) Measured bed levels after the flushing (b) Simulated bed 52
levels after the flushing (Haun and Olsen, 2012)
Figure 2.9
Comparison of bed level changes: (a) measurements; (b) 53
numerical simulation with uniform sediment; and (c) nonuniform
sediment (Feurich and Olsen, 2011)
Figure 2.10
Comparison between measured values and simulation results at: 53
(a) cross section 80; (b) cross section 60; and (c) cross section 20
Figure 2.11
Measured water depths before (a) and after (b) the flood, 54
together with measured (c) and computed (d) bed elevation
changes (Fischer-Antze et al., 2008).
Figure 3.1
Research framework for present study
58
Figure 3.2
Kurau River sub-basin and data collection sites
60
x
Figure 3.3
Ara -Kurau river
60
Figure 3.4
Pondok Tanjung stream flow station (5007421)
61
Figure 3.5
Discharge hydrograph for Kurau River at Pondok Tanjung
62
Figure 3.6
Water level chart for Kurau River at Pondok Tanjung
62
Figure 3.7
Stage-discharge relationship at Pondok Tanjung for 1996-2007
63
Figure 3.8
Flood frequency analysis using difference types of distribution
66
Figure 3.9
Langat River basin and data collection sites by Ariffin (2004)
67
Figure 3.10
Electromagnetic current meter
68
Figure 3.11
SonTek River Surveyor Hydroboard with optional GPS
69
Figure 3.12
River surveying at Ara River with river surveyor (ADP)
72
Figure 3.13
Van Veen grab for bed material sampling
73
Figure 3.14
Hand held Helley-Smith sampler for bed load sampling
75
Figure 3.15
Feed-forward multilayer network
80
Figure 4.1
Cross section KRU1 along Kurau River
87
Figure 4.2
Cross section KRU2 along Kurau River
87
Figure 4.3
Cross section KRU3 along Kurau River
88
Figure 4.4
Cross section KRU4 along Kurau River
88
Figure 4.5
Cross section KRU5 along Kurau River
89
Figure 4.6
Cross section A1 along Ara River
89
Figure 4.7
Scatter plot of bedload transport rate against discharge
90
Figure 4.8
Scatter plot of bedload transport rate against velocity
90
Figure 4.9
Scatter plot of bedload transport rate against width
91
xi
Figure 4.10
Scatter plot of bedload transport rate against water depth
91
Figure 4.11
Scatter plot of bedload transport rate against B/Y ratio
91
Figure 4.12
Scatter plot of bedload transport rate against hydraulic radius
92
Figure 4.13
Scatter plot of bedload transport rate against area
92
Figure 4.14
Scatter plot of bedload transport rate against slope
92
Figure 4.15
Scatter plot of bedload transport rate
93
Figure 4.16
Bedload frequency distribution size of upstream (KRU5) and 95
downstream (KRU1) of Kurau River
Figure 4.17
Particle size distributions of bedload and bed material samples 96
for Kurau River.
Figure 4.18
Comparison of particle size distributions of bedload samples for 97
upstream and downstream of Kurau River in same discharge.
Figure 4.19
Mean bed load grain size distributions for shear stress bands 98
arranged in order of increasing shear stress (upstream of Kurau
River KRU5).
Figure 4.20
Mean bed load grain size distributions for shear stress bands 100
arranged in order of increasing shear stress (downstream of
Kurau River KRU1).
Figure 4.21
Variation in grain size at the10th, 16th, 30th, 50th, 84th and 90th 101
percentiles of the bedload size distribution with increasing shear
stress.
Figure 4.22
Transport ratio as a function of grain size at upstream (a) the 103
transport ratio Pi/fi where pi is the proportion of each size
fraction i present in transported material and fi is the proportion
of each size fraction in the bed material (b) the scaled fractional
transport rate computed as qbpi/fi, where qb is the sediment
transport rate.
Figure 4.23
Transport ratio as a function of grain size at downstream (a) the 104
transport ratio Pi/fi (b) the scaled fractional transport rate qbpi/fi.
Figure 4.24
Comparison of predicted and measured bedload rates for Kurau
River
xii
108
Figure 4.25
Bedload rating curve along Kurau River
109
Figure 4.26
Validation of NLR equation in Kurau River
112
Figure 4.27
Expression genes for GP formulation
114
Figure 4.28
Measured versus predicted values of Tb for the training data set.
115
Figure 4.29
Measured versus predicted values of Tbfor testing data set.
116
Figure 4.30
Measured versus predicted values of Tb for validation data set.
116
Figure 4.31
Measured versus predicted values of Tb for all data set.
117
Figure 4.32
Measured versus predicted values of Tb by GP-ANN
118
Figure 4.33
Measured versus predicted values of Tb by ANN for training data 119
set
Figure 4.34
Measured versus predicted values of Tb by ANN for testing data 120
set
Figure 4.35
Measured versus predicted values of Tb by ANN for validation 121
data set
Figure 4.36
Measured versus predicted values of Tb by ANN for total data set
121
Figure 4.37
Measured versus predicted values of Tb by ANN-GP
122
Figure 4.38
Comparison of bedload rating curve for Kurau River
125
Figure 4.39
Comparisons of predicted and measured bedload rates for Kurau 125
River
Figure 4.40
Bedload rating curve for three rivers
Figure 4.41
Performance of existing bedload transport formula in Kurau, Lui 128
and Semenyih rivers.
Figure 4.42
Measured versus predicted values of Tb for total data set
modelled by NLR
Figure 4.43
Measured versus predicted values of Tb by ANN for the training 133
data set
Figure 4.44
Measured versus predicted values of Tb by ANN for testing data 133
xiii
126
131
set
Figure 4.45
Measured versus predicted values of Tb by ANN for validation 134
data set
Figure 4.46
Measured versus predicted values of Tb by ANN with for total 134
data set.
Figure 4.47
Measured versus predicted values of Tb for the training data set.
137
Figure 4.48
Measured versus predicted values of Tb for testing data set
138
Figure 4.49
Measured versus predicted values of Tb for total dataset
138
Figure 4.50
Measured versus predicted values of Tb for validation dataset
139
Figure 4.51
Comparison of bedload rating curve for small streams
141
Figure 4.52
Comparisons of predicted and measured bedload rates for small 141
streams by different models
Figure 5.1
Structured grid
144
Figure 5.2
Unstructured grid
145
Figure 5.3
SSIIM graphical interface
150
Figure 5.4
SSIIM flowchart (Olsen, 2011)
153
Figure 5.5
Koordina file
154
Figure 5.6
3D grid generation
155
Figure 5.7
Koosurf file
155
Figure 5.8
Two block grid
157
Figure 5.9
One block grid
158
Figure 5.10
View of the confluence of the Kurau and Ara rivers
162
Figure 5.11
Contour bed level of the Kurau-Ara confluence
162
Figure 5.12
Sediment distribution size of bedload in Kurau River branch
163
xiv
Figure 5.13
Sediment distribution size of bedload in Ara River
164
Figure 5.14
Sediment distribution size of bedload in main Kurau River
164
Figure 5.15
Control file used in SSIIM modelling
167
Figure 5.16
Time File
168
Figure 5.17
Comparison of Bedload transport rate
172
Figure 5.18
Measured and simulated average velocity in Ara mouth
175
Figure 5.19
Measured and simulated average velocity in Kurau mouth
175
Figure 5.20
Comparison cross-sectional bed level and average velocity a) 176
simulated b) Measured, April 2012 at Ara River
Figure 5.21
Comparison cross-sectional bed level and average velocity a) 177
simulated b) Measured, April 2012 at Kurau River
Figure 5.22
Measured bed level (April 2012)
178
Figure 5.23
Simulated contour bed level
178
Figure 5.24
Comparison cross sectional bed level in different condition of 179
Ara and Kurau confluence (Measured BL, April 2012)
Figure 5.25
Comparison of measured and simulated Longitudinal bed level 180
at downstream of confluence (AA') (Measured BL, April 2012)
Figure 5.26
Scatter plot of measured bed level against simulated bed level 180
(April 2012)
Figure 5.27
Comparison of measured and simulated water level at 181
downstream of confluence (AA') (April 2012)
Figure 5.28
Scatter plot of measured water level against simulated water 181
level (April 2012)
Figure 5.29
Measured water level (April 2012)
182
Figure 5.30
Simulated water level
182
Figure 5.31
Comparisons of water and bed level (AA') for Q=15 m3/s (19 184
July 2012)
xv
Figure 5.32
Comparisons of water and bed level (AA') for Q=15 m3/s (20 184
July 2012)
Figure 5.33
Comparisons of water and bed level (AA') for Q=11 m3/s (8 Oct 185
2012)
Figure 5.34
Morphology of Kuaru -Ara confluence
Figure 5.35
Longitudinal bed change profile of Ara and downstream of 189
confluence after Q=15m3/s
Figure 5.36
Longitudinal bed change profile of Kurau and downstream of 189
confluence after Q=15m3/s
Figure 5.37
Bed morphology after Q=15 m3/s
Figure 5.38
Change in bed morphology after Q=15m3/s. Zone of erosion and 190
deposition during each period are illustrated with colour change
from white as deposition to black as erosion.
Figure 5.39
Channel cross section profiles, Q=15m3/s (Measured bed level 191
April 2012)
Figure 5.40
Bed morphology after Q=31 m3/s
192
Figure 5.41
Channel cross section profiles, Q=31m3/s
193
Figure 5.42
Longitudinal bed change profile of Ara and downstream of 194
confluence between Q=15m3/s and Q=31m3/s (Measured bed
level April 2012)
Figure 5.43
Longitudinal bed change profile of Kurau and downstream of 194
confluence between Q=15m3/s and Q=31m3/s (Measured bed
level April 2012)
Figure 5.44
Change in bed morphology between Q=15m3/s and Q=31m3/s. 195
Zone of erosion and deposition during each period are illustrated
with colour change from white as deposition to black as erosion.
Figure 5.45
Flow separation Mr>1
196
Figure 5.46
Flow separation at Ara- Kurau confluence (Mr>1)
196
Figure 5.47
Bed morphology after Q=43m3/s
197
Figure 5.48
Channel cross section profiles, Q=43m3/s
199
xvi
187
190
Figure 5.49
Longitudinal bed change profile of Ara and downstream of 200
confluence between Q=31m3/s and Q=43m3/s (Measured bed
level April 2012)
Figure 5.50
Longitudinal bed change profile of Kurau and downstream of 200
confluence between Q=31m3/s and Q=43m3/s (Measured bed
level April 2012)
Figure 5.51
Change in bed morphology between Q=31m3/s and Q=43m3/s. 201
Zone of erosion and deposition during each period are illustrated
with colour change from white as deposition to black as erosion.
Figure 5.52
Longitudinal bed change profile of Ara and downstream of 202
confluence between Q=43m3/s and Q=35m3/s (Measured bed
level April2012)
Figure 5.53
Longitudinal bed change profile of Kurau and downstream of 202
confluence between Q=43m3/s and Q=35m3/s (Measured bed
level April2012)
Figure 5.54
Bed mophology after Q=35m3/s
Figure 5.55
Change in bed morphology between Q=43m3/s and Q=35m3/s. 203
Zone of erosion and deposition during each period are illustrated
with colour change from white as deposition to black as erosion.
Figure 5.56
Channel cross section profiles, Q=35m3/s
204
Figure 5.57
Bed morphology after Q=13 m3/s
205
Figure 5.58
Flow separation Mr<1
206
Figure 5.59
Longitudinal bed change profile of Ara and downstream of 206
confluence between Q=35m3/s and Q=13m3/s (Measured bed
level April 2012)
Figure 5.60
Longitudinal bed change profile of Kurau and downstream of 207
confluence between Q=35m3/s and Q=13m3/s (Measured bed
level April 2012)
Figure 5.61
Change in bed morphology between Q=35m3/s and Q=13m3/s. 207
Zone of erosion and deposition during each period are illustrated
with colour change from white as deposition to black as erosion.
Figure 5.62
Channel cross section profiles, Q=13 m3/s
Figure 5.63
longitudinal profile of lateral change in different flow 210
momentum
xvii
203
208
Figure 5.64
Cross sectional lateral change in different flow momentum
210
Figure 5.65
Bed load transport rating curve in Ara and Kurau River branch
211
Figure 5.66
Bed load transport rate value by SSIIM against the calculated 212
bedload transport rate with Eq. 4.11
Figure 5.67
Bed morphology and spatial distribution of bedload transport 213
rate Mr=0.9.
Figure 5.68
Bed morphology and spatial distribution of bedload transport 214
rate Mr=1.3.
Figure 5.69
: Bed morphology and spatial distribution of bedload transport 215
rate Mr=2.6.
Figure 5.70
Bed morphology and spatial distribution of bedload transport 216
rate Mr=0.7.
Figure 5.71
Shear layer and distinct vortices about vertical axes at RSK1
218
Figure 5.72
Shear layer in the confluence of Ara and Kurau
218
Figure 5.73
Bedload rate in cross sections at downstream of confluence
219
Figure 5.74
Distribution of bed median size, D50 Q=15 m3/s, Mr<1
222
Figure 5.75
Bed shear stress in confluence Q=15m3/s
223
Figure 5.76
Distribution of bed median size at high flow, D50 Q=43 m3/s, 224
Mr>1
Figure 5.77
Bed shear stress in confluence Q=43m3/s
Figure 5.78
Distribution of bed median size at low flow, D50 Q=13 m3/s, 226
Mr<1
Figure 5.79
Bed shear stress at low flow Q=13m3/s
228
Figure 5.80
Hydrograph of the October 2007 flood
229
Figure 5.81
The morphology of Kurau-Ara confluence before flood
230
Figure 5.82
Bed morphology of Kurau-Ara confluence after flood
231
xviii
225
Figure 5.83
Change in bed morphology after Q=191.32m3/s. Zone of erosion 232
and deposition during each period are illustrated with colour
change from white as deposition to black as erosion.
Figure 5.84
Longitudinal bed change profile of downstream of confluence
232
Figure 5.85
Modelled cross section changes before and after flood 2007
234
Figure 5.86
Bed morphology and spatial distribution of bedload transport 235
rate (Q=191.32m3/s)
xix
5
LIST OF ABREVIATIONS
Abbreviation
Description
ANN
Artificial Neural Network
ADP
Acoustic Doppler Profiler
ASCE
American Society of Civil Engineers
ARI
Average Recurrence Interval
BL
Bed Level
CFD
Computational Fluid Dynamics
CHZ
Confluence Hydrodynamic Zone
DID
Department of Irrigation and Drainage
DR
Discrepancy Ratio
EDM
Electronic Distance Meter
GA
Genetic Algorithm
GP
Genetic Programming
GPS
Global Positioning System
MAE
Mean Absolute Error
Mr
Momentum ratio
NLR
Non Linear Regression
RMSE
Root Mean Square Error
SSIIM
Sediment Simulation In Intakes with Multiblock option
SVM
Support Vector Machines
WL
Water Level
WS
Water Surface
xx
6
Symbol
LIST OF SYMBOLS
Description
Flow area (
)
Section width of the channel (m)
River channel width (m)
Cs =(B/y0)
Conveyance shape
Cz
Chezy resistance coefficient
d1=θ-θcr
The Shield's parameter difference
d3= dsʋav
The average flow velocity with sediment particle
diameter(m2/s2)
Sediment diameter where 50% of bed material is finer
, ,
d50sub
Size of particle intermediate axis for which i% of sample of
bed material is finer
Submerged median particle size
ds
Sediment particle diameter
Dgr
Dimensionless particle parameter
E
East
f
Friction factor
fs
Wilcock’s friction coefficient
fi
Proportion of each size fraction present in bed material
Fr
Froude number
g
Acceleration due to gravity
Sectional bed load transport rate
Gs
Sediment specific gravity = 2.65
Gradation coefficient
xxi
Width of Helley-Smith sampler nozzle
n
Manning’s roughness coefficient
N
North
P
Wetted perimeter of cross section of flow (m)
Q
Flow discharge (m3/s)
Bed material discharge for all size fractions (m3/s)
q
Water discharge per unit width
qb
Bedload discharge per unit width
qbpi/fi
Scale fractional transport rate
Pi
R
Proportion of each size fraction present in transported
material
Hydraulic Radius
R2
Coefficient of determination
Re
Reynolds number
R/d50
Standardization with hydraulic radius
Sf
Channel slope
Water surface slope
Bed load transport rate (kg/s)
Total bed load transport rate (kg/s)
Suspended load transport rate (kg/s)
Suspended load discharge (m3/s)
Time the bed load sampler on the bed
u* and u*cr
Shear and critical shear velocity
U
Inequality coefficient
Average flow velocity
xxii
Mean weighted bed load sample of vertical for n section
w
weights on the network connections
,
Flow depth
y/B
width scale ratio
Z
Vertical coordinate (elevation)
αs
Wiberg and Smith's coefficient
Standardized coefficient
and
s
Specific weight of water and sediment
Γ
Diffusion coefficient
θ and θcr
κ
Shields’ and critical Shields’ parameters for initiation of
motion
von Karman constant =0.4
μ
Dynamic viscosity of water
П
Shear stress due to relative density
ρ and ρs
Density of water and sediment
and
cr
Shear and critical shear stress at the bed
v
kinematic viscosity
Φb
Dimensionless intensity of the bedload rate
ωs
Fall velocity of sediment particles (d50)
ωs*
Standardized fall velocity due to sediment particle
xxiii
PENGANGKUTAN BEBAN ENDAPAN DASAR UNTUK SUNGAI KECIL
DI MALAYSIA
7
ABSTRAK
Pengangkutan beban endapan dasar merupakan komponen penting proses
dinamik sungai dan pengganggaran kadar pengangkutan beban endapan dasar adalah
penting untuk pengiraan variasi morfologi sungai untuk tujuan keselamatan umum,
pengurusan sumber air dan alam sekitar yang mampan. Pelbagai persamaan beban
endapan yang terkenal adalah terhad kepada kajian eksperimen saluran dalam
makmal atau kajian tapak. Persamaan ini yang dipengaruhi oleh kebolehpercayaan
dan perwakilan data yang digunakan dalam menentukan pembolehubah dan pemalar
memerlukan parameter yang kompleks dalam pengganggaran pengangkutan beban
endapan. Oleh itu, satu persamaan baru yang mudah dan tepat adalah perlu untuk
kegunaan di sungai-sungai kecil. Dalam kajian ini, data yang mudah diperolehi
seperti kadar alir, kedalaman sungai, kecerunan sungai dan saiz diameter zarah
endapan permukaan d50 daripada tiga sungai kecil di Malaysia digunakan untuk
meramal pengangkutan endapan dasar. Model genetic programming (GP) dan
artificial neural network (ANN) adalah berguna dalam menafsir data tanpa sebarang
had untuk pangkalan data yang luas digunakan sebagai alat untuk pemodelan
pengangkutan beban endapan untuk sungai-sungai kecil. Keupayaan GP dan ANN
untuk meramal data hujan adalah memuaskan. Model yang diperolehi menunjukkan
kejituan yang tinggi dengan ketepatan keseluruhan sebanyak 97% untuk ANN dan
93% untuk GP berbanding dengan kaedah konvensional dan persamaan empirical.
Satu model numerikal tiga dimensi telah digunakan untuk mengkaji morfologi
dasar dan pengangkutan beban endapan dasar sungai di pertemuan Sungai Ara dan
xxiv
Kurau untuk jangka masa pendek dengan kadar alir tinggi pada 100 ARI. Model tiga
dimensi SSIIM2 dengan k-epsilon aliran gelora yang merupakan model pengiraan
bendalir dinamik dengan grid adaptif, bukan ortogon dan tidak berstruktur telah
digunakan untuk pemodelan hidrodinamik pertemuan sungai. Model numerikal ini
telah diuji dengan data dari kajian tapak di pertemuan Ara-Kurau. Ketepatan yang
memuaskan telah didapati di antara data endapan dasar dan aras dasar yang dianggar
dengan yang dicerap di tapak. Kajian menunjukkan bahawa model numerikal
merupakan alat yang berguna dalam meramal kadar pengangkutan beban dasar di
kawasan yang bersekitaran dinamik kompleks. Keputusan menunjukkan bahawa
perubahan hidrologi jangka pendek boleh mempengaruhi morfo-dinamik pertemuan
Ara-Kurau. Untuk keadaan aliran yang berbeza, pengangkutan endapan dasar
berhampiran pinggir lapisan ricih dan juga lapisan ricih yang menyebabkan aliran
gelora menunjukkan peningkatan aliran gelora menyumbang kepada peningkatan
kapasiti
pengangkutan
endapan
beban
dasar
sungai.
Keputusan
simulasi
menunjukkan taburan saiz zarah beting pasir di tepi hilir pertemuan sungai adalah
tidak berubah dimana saiz median tidak berubah sepanjang tempoh kajian manakala
saiz zarah di hulu beting pasir adalah lebih dipengaruhi oleh keadaan aliran.
xxv
BEDLOAD TRANSPORT OF SMALL RIVERS IN MALAYSIA
8
ABSTRACT
Bedload transport is an essential component of river dynamics and estimation
of bedload transport rate is important for practical computations of river
morphological variations because the transport of sediment through river channels
has major effects on public safety, water resources management and environmental
sustainability. Numerous well-known bedload equations are derived from limited
flume experiments or field conditions. These time-consuming equations, based on
the relationship between the reliability and representativeness of the data utilized in
defining variables and constants, require complex parameters to estimate bedload
transport. Thus, a new simple equation based on a balance between simplicity and
accuracy is necessary for using in small rivers. In this study the easily accessible data
including flow discharge, water depth, slope, and surface grain diameter d50 from the
three small rivers in Malaysia used to predict bedload transport. Genetic
programming (GP) and artificial neural network (ANN) models that are particularly
useful in data interpretation without any restriction to an extensive database are
presented as complementary tools for modelling bed load transport in small streams.
The ability of GP and ANN as precipitation predictive tools showed to be acceptable.
The developed models demonstrate higher performance with an overall accuracy of
97% for ANN and 93% for GP compared with other traditional methods and
empirical equations.
A three-dimensional numerical model was applied to study the bed
morphology and bedload transport of the junction of Ara and Kurau rivers for short
term event and for high flow with 100 ARI. SSIIM2 a 3D, k-epsilon turbulence
xxvi
computational fluid dynamics model with an adaptive, non-orthogonal and
unstructured grid has been used for modelling the hydrodynamic of confluence. The
numerical model was tested against field data from Ara-Kurau confluence.
Satisfactory agreement was found between computed and measured bedload and bed
elevation in the field. The study indicates that numerical models became a useful
tool for predicting the bedload transport rate in such complex dynamic environment.
The results have demonstrated that the short term hydrologic variability can
considerably influence the morphodynamics of Ara-Kurau channel confluence and
for the different flow conditions the bedload transported near to edge of shear layer.
The coincidence of the shear layer that was generated the considerable turbulence
indicated that the increasing turbulence levels contribute substantially to the required
increase in bedload transport capacity. The simulation results showed the grain size
distribution on the bar at the downstream junction corner is remarkably constant and
the particle size in the upstream part of the bar is more affected by the changes in
flow conditions than the downstream end where the median diameters not varied
during the period.
xxvii
1
CHAPTER 1INTRODUCTION
1.1
Background
Bedload transport is an essential component of river dynamics that depends on
water flow, river morphology and response of sediment particles to applied stress and
their mutual interactions. Estimation of bedload transport rate is important for
practical computations of river morphological variations because the transport of
sediment through river channels has major effects on public safety, water resources
management and environmental sustainability (Yeganeh-Bakhtiary et al. 2009; Frey
and Church 2011).
The relationship between bedload transport rates and hydraulic variables is
extremely complex because of various characteristics of alluvial rivers such as
sediment transport, the interaction between sediment supply and bed surface
adjustment, and the hydrodynamics of bedform progress. The difficulties associated
with bedload field measurement causes a long history of interest in developing
equations for the prediction of bedload transport. Numerous well-known bed load
equations were derived from limited flume experiments or field conditions (Bagnold,
1980; Camenen and Larson, 2005; Yang, 1996). Although morphologist and
engineers have gained profound insight into the mechanics of bedload transport ever
since the development of the duBoys equation (du Boys, 1879) (the first physically
based bedload transport equation) a simple question still cannot be answered: for
given sedimentary and hydraulic characteristics, what is the rate of bedload transport
in an alluvial channel? In other words, there is no single bedload equation that can be
applied universally to all rivers and no completely objectively or universally
1
applicable guidelines exist to facilitate the selection of an appropriate formula as the
bedload transport function (Almedeij and Diplas, 2003; Gomez and Church, 1989;
Simons and Şentürk, 1992; Yang and Huang, 2001). To overcome the difficulties of
developing the equations based on a balance between simplicity and accuracy, new
mathematical modelling methods can be used to improve the sensitivity and
performance of the prediction equations; the simple formula can be adopted to
estimate the bedload transport of small streams.
River flow, sediment transport and morphological processes are among the
most complex and least understood processes or phenomena in nature. A river
confluence has always been a challenging subject for river hydrodynamics and
morphodynamics considerations due to complex flow phenomena and processes
occurring in both the confluence and the downstream of confluence channel. The
complexity of the phenomena and processes arises from the strong three dimensional
flow effects resulting from several principal factors, including a) the discharge or
momentum ratio between tributary and main stream b) the planform shape of
upstream and post confluence channel and angle of the confluence c) the difference
between the levels of tributary and main stream (Best, 1986; Leite Ribeiro et al.,
2012; Rhoads, 1996).
In the last decade, the development of hydrodynamic existing methods and new
methods and tools for investigation of complex flows especially in three dimensions
has greatly improved the understanding of the dynamics of confluences (Biron et al.,
2004; Bradbrook et al., 2000; Weerakoon and Tamai, 1989) Therefore, laboratory
studies combined with field observations are needed to link a global quantitative
2
model of channel confluences for better understanding of complex hydrodynamic
and morphodynamics of river channel confluences .
1.2
Problem Statement
River sedimentation problems are assuming increasing importance in many
Malaysian rivers and can represent a key impediment to sustainable development.
Despite more than six decades of research, sedimentation is still probably the most
serious technical problem faces by water resource manager and engineers. Such
problems include accelerated soil erosion, reservoir sedimentation and the wider
impact of sediment on aquatic ecology, river morphology and water resource
exploitation.
Sediment transport in small streams is diverse and highly variable due to the
various characteristics of channel morphology. Numerous well-known bed load
equations were derived from limited flume experiments or field conditions (Bagnold,
1980; Camenen and Larson, 2005; Yang, 1996). In such conditions, equations based
on the relationship between the reliability and representativeness of the data utilized
in defining reference values, constants, and relevant coefficients are time consuming
and required complex parameter to estimate bed load transport. Although a known
equation may produce reasonable predictions of bedload transport rates in a
particular stream reach at a particular time, the same equation usually overpredict or
underpredict the observed bed load transport by a different order of magnitude when
applied to a different river or even to the same river at a different time. Therefore,
there is a real need to consider and derive a simple equation to predict bedload
transport with easy accessible data for specific conditions.
3
Kurau River is selected as the case study due to its importance as a main
domestic water supply and Kerian irrigation scheme areas in the state of Perak. Bukit
Merah reservoir and the dam that was constructed approximately at the mid section
of the Kurau River system requires the river management such as controlling the
sediment transport and consideration changes in river morphology.
Human activity includes the recently railway construction, changes in land use
from 2004 to 2015 according to the Taiping Town Council on Larut Matang Local
Plan 2015 (Hamidun, 2010), and increasing river sand mining makes change to river
hydrology and increase in sediment load along the river. The loss of river capacity
due to sedimentation can have a serious impact on water resources development by
reducing the supply of irrigation water, water supply, and the effectiveness of flood
control schemes. Kurau River sedimentation becomes the main cause of frequent
flooding in urban areas(Hamidun, 2010). The blockage of hydraulic structure of
higher sediment yield and overflowing water cause serious damages to the
environment, infrastructures and also has an effect on the social activity. Therefore,
integrated sediment management in Kurau River is one of the highest concerns of
governments and engineers.
Upstream of Kurau River as a selected case study consisting of two main river
tributaries namely Kurau River and Ara River. The river condition and morphology
can be different in each section of river. One of the complex and effective place of
the river due to sediment transport behaviour is the confluence of two river channels.
The sediment transport in the confluences changes periodically in different flow
4
condition. Evaluation of the bedload transport in confluence requires the use of
numerical modelling techniques as the simple empirical equation individually cannot
evaluate such complex condition.
1.3
Objective of the Investigation
To establish bedload particle sizes characteristic and its effect on bedload
transport
To estimate the bedload transport rate in small streams by statistical analysis,
artificial neural network and genetic programming and evaluate the prediction
methods.
To evaluate the changes in bed load sediment transport, bed morphology and
spatial pattern of bed material in response to flow discharge variability in river
channel confluence with a 3D numerical model.
1.4
Scope of Work
This study was carried out on Kurau River, a natural stream in Perak, Malaysia.
Herein, the genetic programming, artificial neural network and nonlinear regression
models which are particularly useful in modelling processes with data interpretation
without any restriction to an extensive database, are employed as a complimentary
tool for modelling bed load transport in small streams.
Hydraulic and sediment data were taken at six locations along Kurau River
and combine with the Lui and Semenyih Rivers data (Ariffin, 2004) for development
of bedload transport equation.
5
The performance of the genetic programming, artificial neural network and
statistical (nonlinear regression) models were evaluated and compared with six
bedload transport equations such as Meyer-Peter and Müller (1948), based on energy
slope method and Rottner (Yang, 1996), Chang (Cheng, 2002), Julien (2002) and
vanRijn (1993) based on regression method and Wong and Parker (2006) based on
the shear stress method.
SSIIM, a three dimensional computational fluid dynamic program was used in
this study for modelling the Ara-Kurau confluence. It solves the Navier-Stokes
equations in a three-dimensional non-orthogonal grid for flow and the convectiondiffusion equation for sediments. SSIIM uses the "k-epsilon" model for turbulence,
the control volume method with the SIMPLE algorithm.
The field site for the modelling is the junction of the Kurau and Ara rivers in
Pondok Tanjung at the upstream of the Bukit Merah reservoir in Perak. The study
was carried at confluence limited in areas with approximately 141.5 m in length and
111.5 m in width.
1.5
Structure of Thesis
The thesis consists of six chapters, organised as follows:
Chapter 1 gives a brief introduction on the bedload transport and objective of
study, scope of work and sedimentation problem.
Chapter 2 has a brief review about the headworks and different types of
traditional and innovative methods to estimate bedload transport rate. Selection of
6
the models and summary of model application relevant to this study was briefed in
this section.
Chapter 3 states some facts about the study for which this study has been done.
Data collection, data analysis and some soft computing method for predicting
bedload transport were also explained in this chapter.
Chapter 4 describes bedload characteristics and results of prediction method of
bedload transport.
Chapter 5 illustrates the theory behind the SSIIM. It is not possible to go into
further detail due to dearth of space and time. Maximum reference has been made to
user manual for SSIIM. Manual in itself is quite explanatory. It is readily available
over the net. One of the nicety of this program or the liberality of the developer is
that this program is freely available over net with manual. This chapter also provides
the information the way the program is used herby. It includes the bedload transport
characteristic in confluence zone, which is the main theme of this work.
Chapter 6 summarized the conclusions of study and recommendations for
future study. Bibliography and appendices are enclosed at the end of this thesis.
7
2
CHAPTER 2 -
LITERATURE REVIEW
2.1
Introduction
Bedload transport is an important physical process in defining the
morphological development of alluvial rivers (Barry et al., 2008). Bedload transport
rate estimation is needed for the realistic computations of river morphological
variations because the transport of sediment through river channels has a major
disbursement for public safety, water resources management, and environmental
sustainability (Frey and Church, 2011; Yeganeh-Bakhtiary et al., 2009).
Sediment transport in small streams is greatly variable and different due to the
various characteristics of channel morphology. The hydraulic geometry of channels
in small streams is affected by various parameters. Each channel section is in many
ways unique because it is influenced by its own particular history of flow conditions,
sediment transport, and distribution of channel roughness elements, and management
activities, all of which should be considered in bedload transport estimation (Beschta
and Platts, 1986).
2.2
Bedload Transport
Streams typically carry large amount of sediment to lower elevation. This
material is called the stream load, and it is divided into bedload, suspended load, and
dissolved load (Figure 2.1). Bedload transport refers to the movement of bed
sediments along the stream bed by rolling, sliding, or jumping (Wang et al., 2011),
and is absolutely dependent on the river’s morphological characteristics.
8
Bedload transpoort as a funndamental physical
p
process in alluuvial rivers provides
p
the majorr process relation
r
bettween the hydraulic and
a
sedimeent conditio
ons that
manage riiver channeel morpholoogy. To claarify the caauses and effect of chaanges in
channel morphology
m
and also too make info
ormed manaagement deccisions thatt affect a
river’s funnction, it will
w requiree a good kn
nowledge regarding
r
thhe role of bedload
movementt in formingg and mainntaining chaannel geometry (Gomeez, 2006; Goodwin,
G
2004).
Figure 2.1: Schemaatic represenntation of sed
diment transpport in a streaam (Singh, 2005)
2
2.3
dload Transsport Analyysis
Bed
Oveer the yearss sediment transport such
s
as sannd or gravvel under hydraulic
h
conditionss is objectiive by geoologists and
d engineers to understtand the grrain-size
distributioons found in
i sedimenttary deposits and to study
s
the size sorting process
(Niekerk et
e al., 1992)).
9
Sediment size moves as bedload in rivers is important in sediment load
calculations and stability analyses. Moreover, knowledge of sediment sorting
patterns and processes is important because it is essential in understanding modern
and older fluvial systems, boundary roughness and heavy mineral advancement
(Carling and Dawson, 1996; Force et al., 1991; Robert, 1990) .
Bedload size distribution and bed material particle size specifications are
required to determine the sediment transport process (Ghoshal et al., 2010). The
extracted parameter from affective factors on sediment transport can be used as a
basis for the prediction of sediment transport rates. Bedload size and bed material
demonstrate the size of material transported downstream and the size of material
accumulating upstream. The characteristics of bed material are indicators of the
resistance of the armoring layer and the ability of the stream to move surface
particles (Wilcock and Kenworthy, 2002).
Bedload transport in rivers is basically the process of movement of individual
particles. The individual sediment size and the characteristic of the bed sediment
influence sediment transport. However, the arrangement of different grain sizes
(Buffington and Montgomery, 1997; Church, 2006) and patterns, such as sheltering,
imbrications, armoring, and variations in sorting, can also affect the stabilities and in
turn the critical shear stress required to carry the sediment (Charlton, 2007; Clayton,
2010).
The characteristics of particle movement courses are essential to sediment
transport theory, the development of channel morphology, and are the basis for a
10
method of measuring the bed load transport rate (Pyrce and Ashmore, 2003).
Measurement on the variations in transport rates between particles of different sizes
is required when riverbed have different particle sizes, particularly in gravel bed
rivers due to the wide range of particle size. The movement of individual particles
depend on their relative as well as absolute size was shown by many researches that
using the field and laboratory sediment transport data. The overall transport rate of
mixed-sized sediments and the effects of changing sands and gravel contents were
studied in a laboratory flume (Curran and Wilcock, 2005; Wilcock and Crowe, 2003;
Wilcock et al., 2001). In an attempt to assess the evolution of bedload grain size,
Kuhnle (1989) worked on a stream with sand and gravel mixture. He discovered that
sediment size had a bimodal distribution and that sand fraction was entrained at
lower velocities rather than gravel fraction.
Fractional bedload transport has been studied in the field (Bond, 2004; Diplas,
1992; Kuhnle, 1989; Kuhnle, 1992; Powell et al., 2001; Wathen et al., 1995) and in
the laboratory (Wilcock and McArdell, 1993; Wilcock and Southard, 1989). A
supplementary study was performed on sand, gravel, and sand–gravel mixture to
determine the critical shear stress of each size fraction from five different sediment
beds (Kuhnle, 1993). All grain sizes of sand and gravel beds start to move at a nearly
identical shear stress. However, a constant relationship between critical shear stress
and grain sizes was observed in sand size sediments for the beds composed of sand–
gravel mixture, but for the gravel fraction, the critical shear stress increased with the
increase in size. Further studies show that most sand sizes may have nearly equal
entrainment mobility in both laboratory and field studies (Church et al., 1991; Parker
et al., 1982; Wilcock and Southard, 1989). The experiments were conducted in a
11
flume with mixed-sized sediments (Lanzoni and Tubino, 1999). Results show that
the capacity of the sediment transport be modified by the different mobility of the
diverse grain-size fractions in the mixture and induce a longitudinal and transverse
pattern in sorting.
Powell et al. (2001) classified a second major threshold of approximately 4.5c
in the Nahal Eshtemo River. Below this threshold, size selective occurs and above it,
a condition approaching equal mobility occurs. This range of threshold is about twice
as that as in sediment mixtures with comparable sorting coefficients in flume studies
(Wilcock and McArdell, 1993).
2.4
Bed Load Transport Equations
Bedload transport equations are usually developed based on hydraulic
principles and attempts to relate the level of bedload transport to several parameters
such as water discharge, shear stress or stream power (Martin, 2003; Yang, 1972).
One of the main problems in measuring bed material transport is that, under
natural conditions, bedload discharge is not a steady process and variations up to
more than 50 percent may be expected (Dietrich and Gallinati, 1991). Because of
difficulties in field measurements of bedload discharge, a large number of transport
formulae have been developed for a wide range of sediment sizes and hydraulic
conditions (Bagnold, 1980; Schoklitsch, 1934). Because of the relationship between
the reliability and representativeness of the data utilized in defining reference values,
constants, and other relevant coefficients and the performance of a particular
equation, most sediment transport equations do not represent a fundamental or
12
complete correlation. Therefore it is really difficult, if not possible, to recommend a
global equation for engineers to use in the field under all conditions (Camenen and
Larson, 2005; Khorram and Ergil, 2010; Wu et al., 2000).
Numerous bed load transport equations have been formulated under limited
laboratory or field conditions that are available in the literature (Habersack and
Laronne, 2002). Table 2.1 to Table 2.7 are summary of bedload equations based on
derivation approach with their name and years and cited references.
Table 2.1: Bedload transport equations, Deterministic Shear stress method
Range of
applicability
No
Name
Equation
1
Du Boys
(1879)
0.125≤ d50≤
0.173
0.0125
0.019
qb 0
d
4.0 (mm)
50
d 34 0
50
Sf > 0.00005
2
Kalinske
(1947)
3
Grand and
Albertson
(1961)
Sato,
Kikkawa
and
Ashida
(1958)
4
qb
f cr
u* s d50
0
qb
f 0 c r
u* s d 50
qb Gs gd50
u 2
F *2
u*c
3
0.088≤ d35 ≤
45.3(mm)
Sf > 0.00005
0.088≤ d50≤
45.3(mm)
u*3 u*2
F
f ( n)
Gs g u*c 2
Shields
(1936)
u 2
1 8 *c
u * 2
n 0 .0 2 5 : f ( n ) 0 .6 2 3
6
Ribberink
(1998)
7
Wilson
(1996)
qb
10qs f ( 0 cr )
(Gs 1) d50
b 11( c r )1.65
b 12( cr )
(Yang,
1996)
(Yang,
1996)
(Yang,
1996)
20 ≤ Re ≤1000 (Garde
and Raju,
0.088 ≤ d50 ≤
2000)
5.66(mm)
1
4
n 0 .0 2 5 : f ( n ) 0 .6 2 3 ( 4 0 n ) 3 .5
5
Cited
references
3
2
13
1.56 ≤ d50 ≤
2.47(mm)
1.06 < Gs<
4.20
0.088 ≤ d50 ≤
2.83(mm)
(Ribberink
, 1998)
0.088 ≤ d50 ≤
2.83(mm)
(Wilson,
1966)
(Yang,
1996)
Table 2.1: Continue
No
Name
Equation
8
Wong and
Parker
(2006)
4.93( 0.047)1.6
b
3
3.97( 0.0495) 2
9
Graf and
Suszka
(1987)
10
Wiberg
and Smith
(1989)
11
Paintal
(1971)
12
Low
(1989)
13
Femandez
-Luque
and Van
Beek
(1976)
Range of
applicability
Cited
references
0.088 ≤ d50 ≤
4(mm)
(Wong and
Parker,
2006)
2.5
0.088 ≤ d50 ≤ 4
0.045
1.5
b 12 1
0.068 (mm)
2.5
0.068
10.5
b s ( c r )
3
s 9.64( 0.166 )
2
16.56 1018 16
qb
6.42
( cr )d50 vav s f 0.5
0.5
(Gs 1)
b 5.7( cr )
3
2
(Graf,
1998)
0.088≤ d35 ≤
5.66
(mm)
(Wiberg
and Smith,
1989)
1≤ d50 ≤ 25(mm)
0.007 < θ < 0.06
(Paintal,
1971)
0.088≤ d50 ≤
5.66 (mm)
θcr=0.06
(Low,
1989)
0.9 ≤ d50 ≤ 3.3
(mm)
0.05 < θcr <
0.058
(Fernandez
Luque and
Van Beek,
1976)
Table 2.2: Bedload transport equations, Deterministic Stream power method
No
Name
1
Chang,
Simons and
Richardson
(1967)
2
Dou (1964)
3
Bagnold
(1966)
Equation
qb K t va v ( 0 c r )
Range of
applicability
Cited
0.1 ≤ Kt ≤ 4(mm)
0.19≤ d50 ≤ 0.93
(mm)
0.001≤ Sf ≤0.0005
(Yang,
1996)
references
v 0.088≤ d50 ≤ 45.3
qb 0.01 s 0 (vav vcr ) av (mm)
s
gGs
(Wu,
2007)
qb s
(Bagnold
, 1977)
tan 0 vav eb
0.088≤ d50 ≤ 1.41
(mm)
Table 2.3: Bedload transport equations, Deterministic Energy slope method
14
No
Name
1
Meyer Peter
(1934)
2
Meyer Peter and
Muller
(1948)
Smart and
Jaeggi
(1983)
3
4
Pica
(1972)
Equation
qb (250q2 3s f 42.5d50 )3 2
8( cr ) 3 2
0
cr
cr
b
d90 0.06 vav 0.5
s f ( cr )
u*
d30
b 4
qb 10.217d500.594 s f 1.681q0.237
Range of
applicability
Cited
references
3≤ d50 ≤ 29(mm)
Gs =2.65
Rh< 20
(Yang,
1996)
0.4≤ d50 ≤ 30(mm)
0.25≤ Gs ≤3.2
1≤ Rh ≤<120 (cm)
0.0004≤ Sf ≤0.02
0.088≤ d50 ≤ 2.83
(mm)
0.03≤ Sf ≤ 0.2
(van Rijn,
1993)
0.088≤ d50 ≤ 45.3
(mm)
(Smart
and
Jaeggi,
1983)
(Pica,
1972)
Table 2.4: Bedload transport equations, Deterministic Regression method
No
Name
Equation
1
Abrahams
and Gao
(2006)
v
b 1.5 (1 c r )3.4 ( a v )
u*
2
Nielsen
(1992)
3
Brown
(1950)
4
Rottner
(1959)
5
England
and
Fredsoe
(1976)
Range of
applicability
Cited
references
0.088≤ d50 ≤
5.66 (mm)
(Abraham
s and Gao,
2006)
0.69≤ d50 ≤ 28.7
(mm)
b 12 ( c r )
1.25≤ Gs ≤4.22
0.001≤ Sf ≤ 0.01
0.391
0.088≤
d50 ≤
2.15e
0.068
45.3
(mm)
0.18 0.52
b 40 3
15 1.5
0.52
12
2 3
d
0.667 50 0.14
Rh
qb s Rh va v
2 3
d 50
0.778
Rh
b 18.74( cr )
12
3
0.088≤ d50 ≤
45.3 (mm)
0.3 ≤ d50 ≤ 7
0.7(cr ) (mm)
θcr= 0.05
15
12
(Nielsen,
1992)
(Julien,
2002)
(Yang,
1996)
(Engelund
and
Fredsoe,
1982)
Table 2.4: Continue
No
6
7
8
9
10
11
Name
van Rijn
(1984,19
87,1993)
England
and
Hansen
(1967)
Fredsoe
and
Deigaard
(1992)
Ashida
and
Michiue
(1972)
Julien
(2002)
Lefort
Sogreah
(1991)
Range of
applicability
Equation
b
0.053 1.5 cr
( 1) 2.1
0.3
D*
v
b 0.05 av 5 2
u*
2
qb
30
( cr ) 1 2 (cr )1 2
qb 17( c r ) 1 2 ( c r )1 2
b
Madsen
(1991)
13
Smart
(1983)
14
Nino and
Garcia
(1998)
0.088≤ d50 ≤
45.3(mm)
0.088≤ d50 ≤ 45.3
(mm)
θcr= 0.05
18 g d50 2
d 1.5 Qlc
Qs
4.45 90
s f 1
Q
Q
d30 s
0.375
Qlc 0.295s f 13 6 1 1.2s f
b
d
12
3
gd 50
(Engelun
d and
Hansen,
1967)
(Fredsøe
and
Deigaard,
1992)
(Ashida,
1972)
0.088 ≤ d50 ≤ 1.41
(mm)
(Lefort,
1991)
gd505
b ( c r ) 0.5 0.7 cr 0.5
qb 4 s
d 0.2
v
50 s f 0.6 av
u*
d 90
(van
Rijn,
1993)
(Julien,
2002)
g (Gs 1)d503
0.2
references
0.088≤ d50 ≤ 2.83
(mm)
Sf > 0.0001
0.1<Θ< 1.0
32
83
12
0.2 ≤ d50 ≤ 2
(mm)
Fr <0.9
0.31<vav <1.29
m/s
0.001≤ Sf ≤ 0.01
0.1≤ Rh ≤1 (m)
0.088≤ d50≤ 45.3
(mm)
Cited
(Madsen,
1991)
d50 < 29 (mm)
sf <0.2
(van
Rijn,
1993)
0.088 ≤ d50 ≤ 5.66
(mm)
(Nino
and
Garcia,
1998)
( c r )
( cr ) 0.5 0.7cr 0.5
16
0.088 ≤ d50 ≤ 5.66
(mm)
d =0.23
Table 2.4: Continue
Range of
applicability
Cited
references
No
Name
Equation
15
Rickenman
(1990)
0.2
0.088≤ d50 ≤ 5.66
3.1 d90 0.5
1.1
b
( cr )Fr (mm)
(Gs 1)0.5 d30
0.03≤ Sf ≤ 0.2
(Rickenm
ann, 1991)
b 13 1.5 exp
(Cheng,
2002)
16
Chang
(2002)
17
Camenen
and Larson
(2005)
18
Bhattachar
ya, Price
and
Solomatine
(2007)
θcr= 0.05
0.088≤ d50 ≤ 5.66
(mm)
0.05
1.5
b 12 0.5 exp 4.5
T*0.898
0.072078 0.353
D*
T0.13
b 0.000182 *0.0673
D*
T0.13
0.0000124 *0.673
D*
c r
0.088≤ d50 ≤ 5.66
(mm)
0.088 ≤ d50 ≤ 5.66
(mm)
T* 0.04 and D* 181.3
T* 0.04 and D* 181.3
T* 0.04
(Camenen
and
Larson,
2005)
(Bhattacha
rya et al.,
2007)
Table 2.5: Bedload transport equations, Deterministic Discharge and velocity method
No
Name
1
Casey
(1935)
2
Sckoklitsch
(1934)
Equation
q b 0.367 S f 9 8 ( q q c r )
d 1.8
q c r 6.5 10 6 500.5
sf
qb
s
2 .5
S
3 2
f
(q qcr )
q c r 0 .2 6 G s 1
3
Barekyan
(1962)
5 3
1 0 6
d 1 .5
5 07 6
sf
Range of
applicability
Cited
references
0.0625≤ d50 ≤ 2
(mm)
(Casey,
1935)
0.305≤ d50 ≤ 7.02
(mm)
(Yang,
1996)
0.24< vav≤ 0.0876
Sf >0.003
v v
qb 0.187qS f s av cr (mm)
s vcr
0.088≤ d50 ≤ 45.3
17
(Barekyan,
1962)
Table 2.6: Bedload transport equations, Deterministic Equal mobility method
No
Name
1
Pitlick et
al.,
(1990a,b)
Equation
qb
=
w*u*3s
, 50 ,
cr
(Gs 1) g
u*2
(Gs 1) gd50sub
4.5
0.853
11.9 1
50 1.59
50
W * 0.00218exp 14.2 50 1 9.2850* 12
1.0 50 1.59
14.2
50 1.0
0.002550
2
Parker and
Klingeman
and Mclem
(1982)
qb
=
w * u*3 s
, 50
,
(Gs 1) g
cr
u*2
(Gs 1) gd50 sub
4.5
0.853
11.2 1
50 1.65
50
*
W 0.0025exp 14.2 50 1 50 12
0.95 50 1.65
14.2
50 0.95
0.002550
3
Parker and
Klingeman
(1982)
4
Wilcock
(2001)
Wilcock
and Crowe
(2003)
0.0747 d 0.018
w * u*3 s
i
= 11.2 1
qb
d50
u*3
2
u*
50 , =
cr
(Gs 1) gd50 sub
qb
W
*
4.5
w * u *3 s
( G s 1) g
qb
=
4 .5
1 1 .2 1 0 .8 4 6 c r
0
W g*
0
0 .0 0 2 5
cr
u*2
=
, 50
cr
( G s 1) g d 5 0 s u b
5
2.0≤ d50≤ 45.3
(mm)
0.79≤vav ≤ 1.13
(m/s)
2.9×10-4≤ Sf ≤
3.3×10-3
(Pitlick et
al., 2009)
2≤ d50 ≤ 45.3
(mm)
Sf >0.003
θcr=0.0876
(Pitlick et
al., 2009)
2≤ d50 ≤ 45.3
(mm)
Sf >0.003
θcr=0.0876
(Pitlick et
al., 2009)
2.0≤ d50 ≤ 45.3
(mm)
(Pitlick et
al., 2009)
2.0≤ d50 ≤ 45.3
(mm)
(Pitlick et
al., 2009)
0 cr
u*2
( G s 1) g d 5 0 s u b
18
Cited
references
0 cr
w * u *3 s
, 50
,
( G s 1) g
cr
4 .5
0 .8 5 3
1 4 1
5 0 0 .5
7 .5
0 .0 0 2
Range of
applicability
5 0 1 .3 5
5 0 1 .3 5
Table 2.7: Bedload transport equations, Deterministic Probabilistic method
No
Name
1
Einstein
(1942
and
1950)
Equation
b
s
qb
s
1
gd503
Range of
applicability
Cited
references
0.315≤ d50 ≤ 28.6
(mm)
1.25≤ Gs ≤ 4.25
(van Rijn,
1993)
2
EinsteinBrown
(1950)
k exp( 391 / )
0.088≤ d50 ≤ 5.66
0.182 (mm)
b
0.465
40k 3
0.182
(Yang,
1996)
3
Gill
(1972)
b 40 cr 1
0
0.088≤ d50 ≤ 2.83
(mm)
(Gill,
1972)
4
Parker
(1979)
2.83≤ d50 ≤ 5.66
(mm)
0.00035≤Sf ≤
0.0108
(Pitlick et
al., 2009)
5
Yalin
(1963)
4.5
0.03 cr
b 11.20
3
0.315≤ d50 ≤ 28.65
b 0.635r 1 ln(1 r ) (mm)
r
r
2.4.1
3
1
cr
1, =2.45
( s )0.4
cr
(van Rijn,
1993)
Performance of Bedload Transport Equations
Gomez and Church (1989) used 88 bedload transport observations from 4
natural gravel bed rivers and 45 bedload transport observation from 3 flumes to
analyse some bedload transport equations. The authors conclude that there is no
equation to be tested performed consistently well, due to limited data used and the
complexity of transport occurrence. They found the best prediction of bedload
transport under limited hydraulic information is achieved by using equations based
on the power flow concept.
19
The performance of 13 sediment transport formula in terms of their ability to
describe sediment transport was tested by Yang and Huang (2001) . They achieved
that the sediment transportation formulae based on the level of energy dissipation or
the concept of power flow, more accurately describe transported observed data. Also
the rate formulae complexity does not always translate into increased model
accuracy.
Prior to the extensive work of Yang and Huang (2001), Barry et al. (2004)
performed simple regressions to complex multi-parameter formulation for 24 gravel
bed rivers with 2104 bedload transport observation in Idaho to evaluate the fitness of
eight different formulations of four bedload transport equations. The authors
concluded that there was no reliable relationship between formulae performance and
degree of calibration or complication. They found that transport data were best
described by a simple power function of discharge. They proposed a new bedload
transport equation and identify the channel and watershed characteristics effect on
the proposed power function by controlling the exponent and coefficient.
The ability of the deterministic empirical equations of van Rijn (1984, 1993)
and Meyer-Peter and Muller (1948) was assessed by Claude et al. (2012) for a large
sand–gravel bed river to determine the unit and total bedload transport rates by
comparing bedload discharges obtained from bedload measurements with
predictions. The authors concluded that the tested equations were unable to predict
the daily temporal variations of the total bedload transport at low and medium flow
conditions. The formulas described the bedload hysteresis but underestimated its
magnitude. For high flow conditions, the best agreement was observed for the total
20
bedload discharges computed by the van Rijn equation. The obtained results
indicated that the empirical equations only able to predict the temporal variations of
bedload transport if the flow velocities followed a similar trend.
The equations of Meyer-Peter and Mueller (1948), Einstein-Brown (1950),
Schoklitsch (1950), Frijlink (1952), Yalin (1963), Bagnold (1980), Engelund and
Hansen (1967), Bijker (1971), Ackers and White (1973), Parker et al. (1982), van
Rijn (1984, 1987) and Cheng were evaluated with measured bedload by a HelleySmith sampler in the Node River, a gravel bed river in the northeast part of Iran
(Haddadchi et al., 2012). The results indicated that the statistic equation such as van
Rijn- Stochastic, Einstein and Bijker were not able to predict bed load in that gravel
bed river. Van Rijn, Frijlink and Myer-Peter and Mueller equations based on shear
stress achieved good results while some of them like Yalin and Cheng’s gave very
poor results. Equations based on the energy concept including Bagnold and Engelund
and Hansen equations tended to overestimate the real state in that river. Generally the
equations presented by van Rijn, Meyer-Peter and Mueller, and Ackers and White
might tolerably predict bedload transport in the range of field data of Node River.
2.5
2.5.1
Regression Analysis
Linear Regression
Regression is a highly useful statistical method to determine a quantitative
relation between one or more independent variables and a dependent variable.
Throughout engineering, regression may be applied to correlating data in a wide
variety of problems ranging from simple to complex physical and industrial systems.
If nothing is known a function may be assumed and fitted to experimental data on the
21
system. In other cases where the result of linear regression is unacceptable other
method such as nonlinear regression may give better results.
Simple linear regression is a relationship between a response variable Y and a
single explanatory variable X. In the simplest case the proposed functional relation
is:
Y 0 1 X
(2-1)
In this model ε is a random error (or residual) which is the amount of variation
in Y not accounted by linear regression. The parameters 0 and 1 , called the
regression coefficients, are unknown and to be estimated. It will be assumed that the
error ε is independent and have a normal distribution with mean zero and variance σ2,
regardless of what fixed value of X is being considered. Then the value of 0 and 1
can be estimated by the method of the last squares (Bethea et al., 1995).
2.5.2
Multiple Linear Regression
The multiple linear regression is similar to simple linear regression except that
a number of independent variables, X1,X2, …Xp, have relationship to a single
dependent variable Y (Bethea et al., 1995). The general form of the multiple
regression method is given by:
Y 0 1 X 1 2 X 2 ... p X p
(2-2)
where the ε is random error (or residual). The general form of multiple linear
regressions is shown below using logarithmic transformation
LnY Ln 0 1 Ln ( X 1 ) 2 Ln ( X 2 ) ... p Ln ( X p ) 1
or
22
(2-3)
Y 0 ( X 1 ) 1 ( X 2 ) 2 ...( X p )
p
(2-4)
The regression coefficients ( i ) are same to simple regression and can be obtained
from last square technique.
2.5.3
Least- Square Method
The least-square method is probably the most popular technique in statistics.
The method has been adopted to find the best-fit line or curve from a given set of
data. In the standard formulation, a set of N pairs of observations {Yi , Xi} is used to
find a function relating the value of the dependent variable Y to the values of an
independent variable X . Assume that the set of data points are (x1,y1), (x2,y2), …,
(xp,yp) where x is the independent variable and y is dependent variable. The fitting
curve f(x) has the deviation (error) of ε from each data point, i.e., ε1=y1-f(x1), ε2=y2f(x2),..., εp=yp-f(xp). According to the method of least squares, the best fitting curve
has the property that:
SS E 12 22 ... p2 i2 yi f ( x) minimum
p
p
i 1
i 1
2
(2-5)
If suppose the f(x) is a simple linear function then
SS E yi 0 1 X i minimum
p
2
i 1
(2-6)
To determine the minimum sum of square due to error (SSE), the partial
derivative of SSE which respect to each constant ( 0 , 1 ) is set equal to zero to yield:
( SS E )
p
yi 0 1 X i 2 0
0
0 i 1
23
(2-7)
( SS E )
p
yi 0 1 X i 2 0
1
1 i 1
(2-8)
The solutions of these equations are
0 Y 1 X
1
(2-9)
( X X )(Y Y )
(X X )
i
i
i
(2-10)
2
i
i
This solution for estimation of 0 , 1 is called least-square solution. For multi
linear regression this method can be used to determine the regression coefficients of
i .
2.5.4
Polynomial Regression
In the case of polynomial or curvilinear regression, as given by the model:
Y 0 1 X 2 X 2 ... p X p
(2-11)
there is only one independent variable (X). Therefore the power of X can be
considered as W1=X, W2=X2,…, Wp=Xp and the model is reduced to multiple
regression as given by Equation (2.2).
2.5.5
Nonlinear Regression
Nonlinear regression is a method of finding a nonlinear model of the
relationship between the dependent variable and a set of independent variables. The
nonlinear regression is utilized when no linearizing transformation can be found
(Bethea et al., 1995). This procedure estimates the parameter value that minimizes
24
the error sum of squares in a nonlinear least-squares routine. Because the model is
nonlinear, the result of least-squares procedure is a set of nonlinear equations that
must be solved simultaneously using other methods, such as Gauss-Newton,
Marquardt , steepest-descent, or multi variant secant.
Unlike traditional linear regression, which is restricted to estimate linear
models, nonlinear regression can estimate models with arbitrary relationships
between independent and dependent variables. For example Equation (2.12) is a nonlinear formula which can be found by nonlinear regression
Y 1 Ln1 2 exp 3 X
2.6
(2-12)
Soft Computing Modelling
The river flow condition and river environment have most effect on the
bedload transport rate in different river, and the computed results from various
equations often differ from each other and even from the measured data set.
Consequently the recent proposed equations need to be adopted for the new
conditions (Khorram and Ergil, 2010).
Various kinds of soft computing techniques have been introduced and applied
in water engineering problems since the last two decades (Nagy et al., 2002). Soft
computing technique such as artificial neural networks (ANNs) and genetic
programming have been successfully applied. The regression method also has been
widely used to analyse and develop relationship between variables specifically in
water sciences. Many researchers modelled sediment transport by using the
25
regression technique such as Yang (1996), Ariffin (2004) , Karim and Kennedy
(1990), and Sinnakaudan et al. (2006).
2.6.1
Genetic Programming (GP)
Genetic programming the extent of genetic algorithms (GA) (Koza, 1992) is a
well-known method in artificial intelligence that plays an important role in modelling
and simulating numerous non-convex and complex phenomena to explain the
nonlinear relationships between parameters (Liu et al., 2003; Nasseri et al., 2011;
Tabesh and Dini, 2009)
The basic difference between a GP and GA is in the nature of individuals. In
GA, individuals are linear strings of fixed length (as chromosomes), whereas in GP,
individuals are nonlinear entities of different sizes and shapes (as parse trees). The
major advantages of GP are used in works where (i) the interrelationships among the
relevant variables are poorly understood (or where it is suspected that the current
understanding may well be less than satisfactory), (ii) finding the ultimate solution is
difficult, (iii) small improvements in the performance are routinely measured (or
easily measurable), (v) an approximate solution is acceptable (or is the only result
that is ever likely to be obtained), and (vi) conventional mathematical analysis does
not, or cannot, provide analytical solutions (Banzhaf et al., 1998). Comprehensive
presentations of GP can be found in Babovic and Abbott (1997) and Babovic and
Keijzer (2000).
Prior to its natural optimized behaviour and acceptable resulted equations, GP
has been applied to a wide range of problems in engineering and science
26
applications, artificial intelligence, industrial, and mechanical models such as water
resources ,hydraulic processes and electricity demand, etc (Ashour et al., 2003;
Azamathulla et al., 2011; Babovic and Bojkov, 2001; Harris et al., 2003; Khu et al.,
2001; Muttil and Lee, 2005; Sivapragasam et al., 2006; Sreekanth and Datta, 2011;
Zhang et al., 2005).
Reported GP applications include sediment transport modelling (Babovic and
Abbott, 1997), effect of flexible vegetation on flow in wetlands (Babovic and
Keijzer, 2003), sedimentary particle settling velocity equations (Babovic and Bojkov,
2001), emulating the rainfall runoff process (Liong et al., 2007; Whigham and
Crapper, 2001), evolutionary computation approach to sediment transport modelling
(Kizhisseri et al., 2005), modelling the bed material load for rivers (Zakaria et al.,
2010), and Suspended sediment modelling (Kisi et al., 2012).
Multigene GP is an approach developed by Hinchliffe et al. (1996) and Hiden
(1998) to enhance the GP accuracy. The amount of trees that can be employed is the
main difference between multigene GP and traditional GP. Several trees may
describe the model in multigene GP, whereas a single tree expresses the model in
traditional GP. All of the genes have specific optimal weights, and a summation of
weighted genes plus a bias term forms the final formula as the best obtained
numerical model. Multigene GP can be written as
Y = d0 +d1*gene1 +d2*gene2 + ….+dn*genen
(2-13)
where d0 is the bias term and di is the weight of the ith gene. Multigene GP is actually
a linear combination of nonlinear terms, a characteristic that may precisely identify
the pattern of engineering problems (Hinchliffe et al., 1996).
27
GPTIPS was employed in this study to perform a multigene GP for accurate
estimation of bedload transport. It is a new “Genetic Programming & Symbolic
Regression” code based on multigene GP for use with MATLAB (Searson, 2009b).
2.6.2
Artificial Neural Network (ANN)
As of this writing, ANNs have proved to be better alternatives for modelling
complex and nonlinear processes (Kumar, 2003). An important advantage of ANN is
that variables do not need to be stationary and normally distributed for analysing
compare to classical stochastic model. ANN's structure can control the non stationary
effects present in global phenomena, in morphological changes in rivers and others
effort (Ariffin, 2004). The application of ANN models is the topic of a large number
of literatures (Lingireddy and Brion, 2005).
ANN is an algorithm designed after the function of the human brain, which
obtains knowledge through a learning process that involves finding an optimal set of
weights for the connections and threshold values for the nodes. A neural network
consists of a number of simple processing elements or units called neurons or nodes.
Each neuron multiplies every input by its interconnection weight, which is usually
determined through training the system, sums the product, and then transmits the
sum through an activation (or transfer) function to reach its result. This type of
network in which data flow in one direction (forward) is known as a feed-forward
network.
28
The network solves the problem by using the information giving from weights.
The net usually has two or more layers of processing units, where each unit in each
layer is connected to all of the processing units in the side layers. The desired output
is achieved by adjusting the weights on the links between the neurons, calculating the
value of error function for a particular input, and then back-propagating the error
from one layer to the previous one (Rumelhart et al., 1985).
The neural networks have been used for many branches of science. It is
becoming a strong tool for providing hydraulic and environmental engineers with
sufficient details for design purposes and management practices. The technique has a
growing body of applications for river engineering and water resources such as
Maier and Dandy (2000) and Raghuwanshi et al. (2006).
The ASCE Task Committee (2000a, b) on the application of ANNs in water
resources concluded that the advantage of ANNs is their ability to extract the
relationship between the inputs and outputs of a process without explicitly providing
the physics to the user and have them reveal it back after training.
Widespread reviews on the ANN application in the area of river engineering
show that the model is capable of describing flow and sediment transport processes
in a river system. In addition, the ANN can be successfully applied for sediment
transport when other approaches cannot succeed due to the uncertainty and the
stochastic nature of the sediment movement (Chang et al., 2012; Kumar, 2012; Nagy
et al., 2002; Yitian and Gu, 2003).
29
Among the numerous ANN structures, the multilayer, feed-forward network is
the most widely used in the area of sediment transport (Rumelhart et al., 1985). The
Levenberg-Marquardt (LM) algorithm, a standard second-order nonlinear leastsquares technique based on the backpropagation process was used in this study to
train the ANN models.
2.7
Application of Soft Computing Modelling in Prediction of Bedload
Transport
Caamano et al. (2006) applied ANN techniques with a set of 82 field
measurements of the Boise River to derive the bed load sediment transport formula.
They used four inputs to give the best balance between input variables and prediction
of sediment transport, namely: the grain Froude number (Fg), the grain Reynolds
number (Rg), the characteristics of the particle size distribution of the transported
sediment as the grain size standard deviation-mean sediment diameter ratio ( g/d50)
and the relative roughness (h/d50). For the application of sediment transport a 2 layer
feedforward network (Marquandt (LM) algorithm) formed by 4 inputs, 3 neurons and
1 output. They derived a pure advection equation by the linear ANN that able to
imitate the exact physical response for a phenomenon mathematically.
34
4
C 3.1
h
5.62(6.61Rg Fg )
2.52(7.38Rg )
1 31570e
d50
*
1 3.11e
(2-14)
For the purposes of comparison a simple regression equation also developed to
predict sediment transport rates from field observations For the Boise River.
C 0.219108 Q1.808
(2-15)
30
The performancce of approoaching ANN
N results coompared wiith 2 otherss derived
y concludedd the artificcial neural networks
n
formula foor Boise River (Figuree 2.2). They
can be appplied on a stream
s
reach to provid
de predictionns of sedim
ment transpo
ort better
than geneeral sedimeent transpoort formulaae or simple sedimennt discharge rating
equations..
Figure 2.22: Comparisoon of the performance
p
e of the AN
NN with sim
mple regression and
analytical approximatio
a
on equations (Caamano et
e al., 2006)
Sasaal et al. (2009) emplooyed the feeedforward––backpropaagated (Lev
venberg–
Marquardtt algorithm
m) Artificial Neural Neetwork (AN
NN) architeccture from bedload
measurem
ments in 16 different
d
rivvers. The AN
NN with thee two inputss, two hiddeen layers
with four neurons, annd one outpuut case (AN
NN, 2, 4, 4, 1) was seleected and co
ompared
with the other methhods.
Theey conclud
ded that thhe ANN m
model was able to
successfullly predict bedload
b
traansport in both
b
sand-bbed and graavel-bed riv
vers. The
ANN moddel significantly outpeerformed traaditional beedload moddels and sho
owed its
superior performance
p
e for all staatistical parrameters exxcept for thhe discrepan
ncy ratio
31
1
(Table 2.8). The authors suggested that bedload transport in a variety of sediment
types could be described as a nonlinear function of excess dimensionless shear stress
and dimensionless median particle size.
Table 2.8: Comparison of bedload equations and the ANN model (Sasal et al., 2009)
Error
Discrepancy ratio (%)
Tb
R2
MAE
RMSE
0.75 < r < 1.25
0.50 < r < 1.50
0.25 < r < 1.75
Parker et al.
1.57
0.140
1.44
8.275
0.027
0.074
0.115
Van Rijn
10.5
0.242
10.4
80.09
0.034
0.115
0.263
Bagnold
0.17
0.581
0.10
0.368
0.169
0.392
0.520
ANN
0.14
0.947
0.05
0.082
0.243
0.358
0.513
Measured
0.14
Method
Azamathulla et al. (2009) used ANFIS technique as an option for better
predicting bed material load transport, based on measured field data of several
Malaysian rivers. Figure 2.3 shows the scenarios of building the ANFIS model with
the inputs and output in the network. From the 346 collected data sets, around 80%
of these patterns were used for training (chosen randomly until the best training
performance was obtained), while the remaining patterns (20%) were used for testing
or validation. From the analysis, the ANFIS model obtained an accuracy of 90.4% in
predicting bed-load transport for all the measured data with an average discrepancy
ratio of 1.18 (Figure 2.4).
32
Input
Inputmf
Rule
Outputmf
Output
Ψ
R
Cv
d50
V
Ss
Figure 2.3: The ANFIS model for bed load sediment (Azamathulla et al., 2009)
Figure 2.4: Predicted bed load against measured bed load using ANFIS (Azamathulla et al.,
2009)
The performance of three soft computing techniques, namely Gene-Expression
Programming (GEP) (Ab. Ghani and Azamathulla, 2012; Azamathulla et al., 2010;
33
Chang et al., 2012; Zakaria et al., 2010), Feed Forward Neural Networks (FFNN)
(Ab. Ghani et al., 2011), and Support Vector Machine (SVM) (Azamathulla et al.,
2010b) were evaluated in the prediction of total bed material load for three
Malaysian rivers namely Kurau, Langat and Muda. The results of evaluation
comparisons with traditional method were very good: FFNN (R2 = 0.958, RMSE =
0.0698), SVM (R2 = 0.958, RMSE = 0.0698), GEP (R2 = 0.97, RMSE = 0.057),
Yang (1972) (R2=0.722, RMSE=12.735) and Engelund-Hansen (1967) (R2=0. 648,
RMSE= 6.654), which supported the use of the soft computing techniques in the
prediction of sediment loads in Malaysian rivers. Figure 2.5 to Figure 2.7
demonstrate the predicted total bed material load against the measured total bed
material load for three GEP, FFNN and SVM performances.
Figure 2.5: Observed versus predicted sediment load by SVM for Langat, Kurau and
Muda rivers (Azamathulla et al., 2010b)
34
Figure 2.6: Observed versus predicted sediment load by FFNN for Langat, Kurau and
Muda rivers (Ab. Ghani et al., 2011)
Predicted Total bed material load (kg/s)
25
Langat
Kurau
20
Muda
Ideal fit
15
10
5
0
0
5
10
15
20
Obseved Total bed material load (kg/s)
25
Figure 2.7: Observed versus predicted sediment load by GEP for Langat, Kurau and
Muda rivers (Ab. Ghani and Azamathulla, 2012; Azamathulla et al., 2010a; Chang et al.,
2012; Zakaria et al., 2010)
35
2.8
River Channel Confluence
In recent years various aspects of flow and sedimentation at river confluences
have been an interesting subject of investigation for hydraulicians, geomorphologists,
sedimentologists, and engineers. River channel confluences are highly complex
environments in which the combination of material (water and sediment) and energy
(power flow) of two different channels occur. The interaction of these components
creates a unique environment in the fluvial system in which the operation is of
fundamental importance for river management (Stevaux et al., 2009).
The dynamics of confluences have been the subject of a long-standing research
provided insight into the complex flow structure and distinct geomorphic features at
natural confluences (Ashmore, 1993; Biron et al., 1993; Boyer et al., 2006;
Kenworthy and Rhoads, 1995; Lane et al., 1999; Rhoads and Sukhodolov, 2001;
Rhoads and Sukhodolov, 2004) and at laboratory junctions (Best, 1986, 1987; Best,
1988; Best and Roy, 1991; Mosley, 1976). This experiential research has been
complemented by attempts to investigate confluence hydrodynamics through
numerical modelling (Baranya and Masa, 2007; Bradbrook et al., 1998; Bradbrook et
al., 2000; Bradbrook et al., 2001; Đorđević, 2012; Weerakoon and Tamai, 1989).
The characteristics of flow and associated processes and phenomena in river
confluences depend on hydrological and hydraulic characteristics of the two rivers
(discharge and momentum ratios of the combining flows), channel geometry (cross
sectional and planform), sediment transport and sediment characteristics of the
material (grain-size distribution of the sediment load) (Đorđević, 2012; Leite Ribeiro
et al., 2012).
36
Flow at river confluences is three-dimensional and often characterized by the
presence of helical flow cells. The number of these cells, their presence or absence,
and their intensity depends on the confluence characteristics. The characteristics of
these cells have been studied in a long-standing contest (Ashmore and Parker, 1983;
Biron and Lane, 2008; Bradbrook et al., 1998; Fujita and Komura, 1988; Mosley,
1976; Parsons et al., 2007; Rhoads and Kenworthy, 1995; Rhoads and Sukhodolov,
2001).
The principal factors controlling the flow structure and channel morphology
are (1) the confluence angle and plan view (asymmetrical or symmetrical ) (Ashmore
and Gardner, 2008; Best, 1987; Best, 1988; Leite Ribeiro et al., 2012; Mosley, 1976),
(2) the discharge, and/or momentum ratios of flow and sediment between the two
confluent channels (Rhoads, 1996) , and (3) the bed elevation discordance between
the two confluent rivers (Best and Roy, 1991; Biron et al., 1993).
Channel confluences often have been reflected by bed morphology of
confluences (Szupiany et al., 2009) such as (1) a scour hole that is normally adjusted
along the region of maximum velocity where both flows begin to converge and mix;
(2) avalanche faces at the mouth of both river channels, which dip into a central
scour hole; (3) sediment deposition within the stagnation zone at the upstream
junction corner; and (4) bars formed within the flow separation zone at the
downstream junction corner or mid-stream in the main channel of confluences. A
summary of the foremost previous investigations of the hydrodynamic and
sedimentary processes in channel confluences is as shown in Table 2.9.
37
Table 2.9: Summary of the major foregoing studies considering the morphodynamics of channel confluences (Leite Ribeiro et al., 2012)
Confluence
Bayonne-Berthier
confluence.
Angle of 65° and width ratio
Bt/Bm = 1 (Low gradient
rivers)
38
Reference
Bed Discordance
(Mild/Moderate/
Pronounced)
(1) Discharge Ratio
(Qt/Qm);
(2) Momentum Flux
Ratio (Mt/Mm)
Sediment
Supply
Biron et al. (1993a)
Moderate (ratio between the (1) No information
height of the step and the
(2) 0.68–2.02
flow depth is around 0.35)
Biron et al. (1993b)
Moderate (ratio between the (1) 0.38–1.33
height of the step and the
(2) 0.18–2.04
flow depth is around 0.35)
Leclair and Roy (1997)
Moderate (ratio between the (1) 0.29–1.87
height of the step and the
(2) 0.20–10.4
flow depth is around 0.35)
De Serres et al. (1999)
Moderate (ratio between the (1) 0.38–1.33
height of the step and the
(2) 0.18–2.02
flow depth is around 0.35)
Bed morphology,
flow velocity and
turbulence
Roy et al. (1999)
Moderate (ratio between the (1) No information
height of the step and the
(2) No information
flow depth is around 0.35)
Turbulence and bed
load transport
Biron et al. (2002)
Moderate (ratio between the (1) 0.57–1.48
height of the step and the
(2) 0.71–2.22
flow depth is around 0.35)
Boyer et al. (2006)
Moderate (ratio between
(1) 0.38–1.33
the height of the step and the (2) 0.18–2.03
flow depth is around 0.35)
Natural
regime
Natural
regime
Measurements
Bed morphology
and shear layer
turbulence
Comments
Two investigated
situations:
1) Bed load transport
in both rivers and
2) bed load transport only
in the tributary
Bed morphology and Measurements during the
dry season. Bed load
shear layer
turbulence
transport only in the
tributary
Bed morphology
t
Bed morphology,
turbulence and water
surface topography
Bed morphology,
3D velocity,
turbulence and bed
load transport
Transport-effective flow
conditions
Table 2.9: Continue
Confluence
Reference
Bed Discordance
(Mild/Moderate/
Pronounced)
Ruisseau du Sud
confluence.
Angle of 60° and
width ratio Bt/Bm = 1
Kaskaskia–Copper
Slough confluence.
Angle of 60° and width
ratio Bt/Bm = 1
(Low gradient rivers)
Roy and Bergeron
(1990)
Mild
Kenworthy and
Rhoads (1995)
Mild
(1) Discharge Ratio Sedimen
(Qt/Qm);
t Supply
(2) Momentum
Flux Ratio
(1) 0.45–0.65 (2)
0.28–0.50
(1) 0.64–6.64
(2) 0.46–42
39
Rhoads and
Kenworthy (1995)
(1) 0.75–1.74
(2) 0.55–3.64
Rhoads and
Sukhodolov(2004)
(1) 1.24
(2) 1.67
Rhoads [1996]
Natural
regime
(1) KRCS 0.95
SA 1.24
KRTMS 0.47
Tracking of
different gravel
size particles
Bed morphology
and 3D velocity
Suspended sediment
transport
3D velocities and
turbulence
Bed morphology,
3D velocity, water
temperature and
bed load transport
(1) 0.2–30
(2) No information
Mild
Bed morphology,
flow velocity and
particle tracking
Comments
Bed morphology
and sediment
concentration
No bed discordance at low (1) No information
(2) 0.35–3–54
momentum flux ratios
and mild bed discordance
at high momentum flux
ratios
Rhoads et al.
(2009)
Kaskaskia–Copper Slough Rhoads and
Sukhodolov (2001)
(KRCS).
Angle of 60° and width ratio
Bt/Bm = 1
Natural
regime
Measurements
Transport-effective
flow conditions
Bed morphology and
bed constitution
Natural
regime
Transport-effective
Bed morphology,
3D velocities and water flow conditions with
negligible changes in
temperature
bed morphology
Table 2.9: Continue
Confluence
Saline Ditch - Unnamed tributary
(SA) Angle of 70° and width ratio
Bt/Bm = 1
40
Kaskaskia–Two-Mile
Slough (KRTMS) Angle
of 36° and width ratio
Bt/Bm = 1 (Low gradient rivers)
Colorado State University
(Fort Collins, USA).
Angles between 15 and
180° and width ratio
(Bt/Bm =1)
Reference Bed
(1) Discharge
Sediment Supply
Discordance
Ratio (Qt/Qm);
(Mild/Moderate (2) Momentum
/ Pronounced) Flux Ratio
(Mt/Mm)
Measurements
Sukhodolov
and Rhoads
(2001)
Turbulence
Comments
Mosley
(1976)
Mild
Bed load transport
Laboratory
of uniform material
(1) 0.33–1.00
(2) No information in both confluents
Bed morphology
Two series of tests:
1) All sections in the confluence
zone were free to adjust to the
imposed hydro-sedimentary
conditions and 2) only the
confluence and the downstream
channel were adjustable
Birkbeck College,
University of London (UK).
Angles between 15 and 105° and
width ratio Bt/Bm = 1
Best (1988)
Mild
(1) 0.5–1.6
(2) 0.25–2.42
Bed load transport
of uniform material
in both confluents
Bed morphology
and particle
tracking
Low gradient channels with
Sub critical flow conditions.
Include a case study of a small
confluence in UK
Ecole Polytechnique Fédérale
de Lausanne (Lausanne,
Switzerland). Angle of 90° and width
ratio Bt/Bm = 0.30
Leite
Ribeiro
(2012)
Pronounced
(1) 0.11
(2) 0.21
Bed load transport
of poorly sorted
sediments. Tributary
Qst = 0.3 kg/min; Main
channel Qsm = 0
Bed morphology,
water levels, 3D
velocities,
turbulence and bed
Small tributary with steep
slope and transcritical flow
(Fr ≈ 1), larger main
channel with subcritical flow
Ecole Polytechnique Fédérale
de Lausanne (Lausanne,
Switzerland). Angle of 90°
and width ratio Bt/Bm = 0.30
Leite
Ribeiro
(2011)
Pronounced
(1) 0.11–0.23
(2) 0.21–0.45
constitution
Bed morphology,
water
levels and bed
constitution
Small tributary with steep
slope and transcritical
flow (Fr ≈ 1), larger main
channel with subcritical flow
2.9
Sediment Transport Modelling
River engineering studies typically are needed for analyse some level of spatial
and temporal sediment transport and morphology change dependencies. Multidimensional sediment transport models are valuable tools for river engineering
investigations.
Sediment transport models are employed by engineers to evaluate the effects of
naturally occurring or man made changes to river systems. The understanding of
long-term channel response is used to predict future project operations and needs
while an evaluation of short-term channel response in the affected river reach is
required for planning and design purposes. A more specific approach is required for
both short and long term channel response evaluating in complex alluvial channels
that exhibit widely varying channel planform, morphology, and bed composition.
Multi-dimensional hydrodynamic and sediment transport models can potentially
provide this level of analysis (Scott and Jia, 2005).
Mathematical hydrodynamic/sediment transport models, usually solves
numerically, one or more of the governing differential equations of energy of the
fluid, continuous, and momentum along with the differential equation for sediment
continuity. An advantage of mathematical models is that they can be adapted to
different physical fields easier than physical models, which are typically constructed
to represent site specific circumstances. Another advantage of mathematical models
is that they are not subject to deformation effects of physical models, when a solution
can be obtained for the same flow condition that are present in the field
(Papanicolaou et al., 2008).
41
The following capabilities are required for the ideal hydrodynamic/sediment
transport model:
Fully unsteady and steady or quasi-steady simulation capability
Proficient analysis of variable flow regimes from subcritical to supercritical
flow
Bed sorting capability
Capable of performing multiple grain size analysis for both cohesive and noncohesive sediments
Wide selection of sediment transport relationships namely bed, suspended,
and total load transport
Provides a selection of turbulence modelling schemes for enhanced
hydrodynamic simulation
Capable of computing the effects of bend way hydrodynamics on sediment
transport and provide a suitable interface for mesh generation and
visualization of results.
Numerous computational hydrodynamic/sediment transport models have
become very popular and developed over the past three decades, mostly due to the
increasing availability of more powerful and economical computing platforms (Fan,
1988; Rodi, 2006). Many computer models are now available for users to purchase
(FLOW-3D, FLUENT). Some of the models are in the public domain and can be
obtained free of charge (SSIIM). Automatic grid generators, graphical user
interfaces, improved data collection techniques, and geographic information systems
comfort to further advance the use of numerical models as a popular tool for solving
practical river engineering problems. Great reviews of different hydrodynamic and
42
sediment transport models can be found in Onishi (1994), Blazejewski et al. (1995),
Spasojevic and Holly (2000), ASCE (2008) Sedimentation Engineering Manual no.
110 and Papanicolaou et al. (2008).
Table 2.10 provides the information on the model formulation, the spatial and
temporal
characteristics,
the
linkage
of
the
sediment
components
and
hydrodynamics, and the model’s predictive capabilities. This table provides useful
information about the model capabilities to handle unsteady flows, bed load and
suspended load, sediment exchange processes, type of sediment (cohesive and
noncohesive), and multi fractional sediment transport. Information about model
abbreviations, language, availability, and distribution is also provided in Table 2.10
and examples of the different model applications are summarized in Table 2.11.
43
Table 2.10: Summary of Some 3D hydrodynamic/sediment transport Models (Papanicolaou et al, 2008)
44
Suspended
sediment
transport
Sediment
mixtures
Sediment
Cohesive
exchange
sediment
processes
Unsteady Yes
Yes
No
Yes
RMA-10: Resource
Management
--Associates; King (1988)
Unsteady Yes
Yes
No
Yes
GBTOXe: Green Bay
TOXic enhancement;
Bierman et al. (1992)
Unsteady No
Yes
No
Yes
Last
Model and references
update
Flow
ECOMSED: Estuarine,
Coastal, and Ocean
V.1. 3
Model—Sediment
transport; Blumberg and (2002)
Mellor (1987)
EFDC3D:
Environmental Fluid
Dynamics code;
Hamrick (1992)
---
---
ROMS: Regional Ocean
V.1. 7 .2
Modelling System; Song
and Haidvogel (1994) (2002)
CH3D-SED:
Computational
Hydraulics 3D--SEDiment; Spasojevic
and Holly (1994)
Bed
sediment
transport
Executable
Entrainment
PD
and
deposition
Entrainment
and
C
deposition
Entrainment
and
NA
deposition
Source
code
Language
PD
F77
P
F77
NA
F77
P
F77
Unsteady Yes
Yes
Yes
Yes
Entrainment
and
PD
deposition
Unsteady Yes
Yes
Yes
No
Entrainment
and
LD
deposition
LD
F77
Yes
Entrainment
and
C
deposition
C
F90
Unsteady Yes
Yes
Yes
Note: V= version; C= copyrighted; LD= Limited distribution; P= proprietary; PD= public domain; F = FORTRAN
Bed
sediment
transport
Last
Model and references
update
Flow
SSIIM: Sediment
Simulation In Intakes V.2.0
(20011)
with Multiblock
options; Olsen (1994)
Unsteady Yes
45
MIKE 3: Danish
acronym of the word
Microcomputer;
--Jacobsen and
Rasmussen (1997)
FAST3D: Flow
Analysis Simulation
Tool; Landsberg et al.
(1998)
Unsteady Yes
V.Beta-1.1
Unsteady Yes
(1998)
Table 2.10: Continue
Suspended
Sediment
Sediment Cohesive
sediment
exchange
mixtures
sediment
transport
processes
Yes
yes
Executable
V.3.25.00
Unsteady Yes
(2005)
Entrainment
PD
and
deposition
P
CLanguage
P
F90
P
F90
LD
F77
P
F90
P
F90
No
No
Yes
Entrainment
C
and
deposition
Yes
No
No
Entrainment
LD
and
deposition
Yes
No
Language
No
Entrainment
C
and
deposition
Entrainment
TELEMAC; Hervouet
--Yes
Unsteady Yes
C
and
No
Yes
and Bates (2000)
deposition
Entrainment
Zeng et al. (2005)
--Unsteady Yes
P
Yes
and
No
No
deposition
Note: V= version; C= copyrighted; LD= Limited distribution; P= proprietary; PD= public domain; F = FORTRAN
Delft 3D; Delft
Hydraulics (1999)
Source
code
Yes
Table 2.11: Applications for selected 3D models (Papanicolaou et al, 2008)
Model and references
Applications
ECOMSED:
Simulation of the flow and sediment transport processes of Lavaca Bay,
(Blumberg and Mellor, 1987) Texas (HydroQual 1998)
46
RMA-10:
Associates; (King, 1988)
Simulation of the flow and sediment transport processes of the Klarälven River east and west channels at the
bifurcation, Sweden (Admass 2005) Modelling of the Nisqually River Delta to evaluate habitat restoration
alternatives, Washington
GBTOXE:
(Bierman, 1992)
Modelling the hydrodynamics of flow and sediment of the Los Angeles and Long Beach harbors California
(Tetra Tech 2004) Simulation of fate and transport of PCBs in Green Bay, Wisconsin
EFDC3D:
(Hamrick, 1992)
Modelling of the hydrodynamic and sediment processes in Moro Bay, California
Simulation of flow and sediment transport of Lake Hartwell reservoir on the Savannah River between South
ROMS:
Carolina and Georgia Modelling of sediment transport and estuary turbidity maximum of the Hudson River
(Song and Haidvogel, 1994)
Estuary, New York
Simulation of flow and sediment quality of the Southern California Bight, California
CH3D-SED:
Evaluation of the relative impact of different sediment sources on the shore areas of the western basin of Lake
(Spasojevic and Holly, 1994) Erie, Ohio (Velissariou et al. 1999) Simulation of sedimentation on bends, crossings, and distributaries on
the lower Mississippi River and Atchafalaya River, Lousiana
Table 2.11: Continue
Model and references
SSIIM:
(Olsen, 1994)
MIKE 3:
(Jacobsen and Rasmussen,
1997)
Applications
Tested against experimental data from Colorado State University (Olsen 2003)
Simulation of the flow, sediment transport processes, and water quality of Upper Klamath Lake, Oregon
Simulation of the flow, sediment transport processes, and water quality of Tampa Bay, Florida Tested against the
experimental data of Odgaard and Bergs (1988)
Delft 3D;
(Delft3D, 1999)
Simulation of contaminated regions resulting from hypothetical airborne agent releases in major urban areas at
Washington D.C., Maryland, and Chicago, Illinois (Pullenet al. 2005)
Simulation of the flow, sediment transport processes and water quality of Tolo Harbor and Mirs Bay, Hong Kong
(Delft Hydraulics 1999)
Morphodynamic modelling of the German Wadden Sea and Duck, North Carolina (Delft Hydraulics 1999)
TELEMAC;
Hervouet and Bates (2000)
Development of a mesoscale hydrodynamic and sediment transport model for the Peru Basin in the Southeast
Pacific Ocean (Zielke et al. 1995)
Simulation of transport and Fate of Toxic Chemicals in Shasta Reservoir, California (Gu and Chung 2003)
(Zeng et al., 2005)
Tested against the experimental data of Odgaard and Bergs _1988)
47
FAST3D:
(Landsberg et al., 1998)
2.9.1
SSIIM
Generally there are two types of 'Computational Fluid Dynamic' (CFD)
programs, the first type such as PHOENICS, STAR-CD, CFX, FLUENT and
FLOW-3D are general purpose programs and the second type include TELEMAC,
MIKE3, DELFT-3D, CH3D, TABS and SSIIM are absolutely developed for river
engineering.
SSIIM is an abbreviation for Sediment Simulation in Intakes with Multiblock
Option. It is developed by Dr. Nils Reider B. Olsen, Professor at NTNU, Norway
and complete software is freely available over the net with user manual (Olsen,
2011).
SSIIM solves the Navier-Stokes equations using the control volume method
with the SIMPLE algorithm and the k-epsilon turbulence model that is based on an
unstructured grid system. It also solves the convection-diffusion equation for
sediment transport, using van Rijn's formula for the bed boundary (Olsen, 2011).
SSIIM has the capability of simulating sediment transport with a moveable
river bed in complex geometry. It also includes bed load and suspended load
transport modelling with multiple sediment sizes, bed forms and associated sorting
and armoring processes (Olsen, 2011).
The program has an interactive graphical grid editor creating a structured grid.
The post-processor includes vector graphics, contour plots, profiles etc. which can
48
run simultaneously with the solver, enabling viewing of intermediate result. A postprocessor viewing coloured surface in 3D is also made, as a separate program.
The model has been extended to other hydraulic engineering applications such
as spillway modelling, head loss in tunnels, meandering in rivers, and turbidity
currents. The model has also been used for water quality and habitat studies in rivers.
The User's Manual (Olsen, 2011) gives more information about the SSIIM.
2.9.1.1 SIMPLE Algorithm
SIMPLE is an acronym for Semi-Implicit Method for Pressure Linked
Equations. The SIMPLE algorithm was developed in the early 1970s. Since then it
has been extensively used by many researchers to solve different kinds of fluid flow
and heat transfer problems (Ghia et al., 1982; Karp et al., 2003).
2.9.1.2 Control Volume Scheme
Several well-established numerical schemes have been employed in the past for
solving flow and sediment transport model governing equations. The streamlineupstream Petrov-Galerkin finite element method (SUPG-FEM), the classical finite
element method (C-FEM), the fully upwind finite element method (FU-FEM), and
the control-volume method based on some type of gridded discretization of the
problem are more useful techniques available to solve numerically the fluid flow and
sediment transport equations. Detailed review of these methods was provided by
Helmig (1997).
49
The control volume method is in substance a finite volume formulation that
uses the integral forms of the governing equations. The domain of calculation is
divided into a random number of control volume and the equations are discretized by
calculating the number of streams that crosses the volume control boundaries
(Chung, 2002).
The main advantage of the control volume method is the flexibility of the
method that can be employed in both structured and unstructured grid systems.
Momentum, mass and energy can automatically conversed by the numerical scheme
because the method is based on physical conservation principles (Reclamation and
Interior, 2011).
2.9.1.3 SSIIM Application
The sediment transport model applications take various capabilities of different
models. Each sediment transport model that is used as engineering tools has some
limitation for solving fluvial hydraulic problem. For that reason, selection of the
correct model requires a comprehensive knowledge of capabilities of available
model. In this section some of the SSIIM applications for sediment transport
modelling and general hydraulics are summarised.
A fully three-dimensional numerical model for reservoir flushing was tested
against field measurements for the Angostura reservoir in Costa Rica (Haun and
Olsen, 2012). The applied numerical model (SSIIM 2) solved the Reynolds-averaged
Navier-Stokes (RANS) equations in three dimensions and used to discretize the finite
volume method together with a second-order upwind scheme. The used grid was
50
adaptive and unstructured grid, which moved with the time-dependent changes for
both water and bed levels. Results from the numerical simulation of the deposition
and the flushing were compared with bathymetry data of the bed level from the
prototype.
The computations demonstrated that the deposition was easier to model than
the flushing. The amount of flushing out sediments shows reasonable agreement
compared with the measured data from the prototype. Therefore the simulation of a
reservoir flushing in a prototype became possible due to the increasing development
of three-dimensional SSIIM model (Haun and Olsen, 2012). Figure 2.8 shows the
measured and simulated bed level after flushing.
SSIIM was applied to compute uniform and nonuniform sediment transport and
bed deformation in an S-shaped laboratory channel with two bends, a trapezoidal
cross section, and a slope of S = 0.005 (Feurich and Olsen, 2011). The sediment size
of 4.2 mm (gravel) was used as movable bed material. Significant good agreement
was found between the measured and computed bed elevations for Wu’s formula and
Vain Rijn's formula. Several parameters were tested in modelling such as grid
distribution in vertical, lateral, and longitudinal direction, time step, number of inner
iterations/time step, active sediment layer thickness, and the Shields coefficient. The
overall pattern variation of parameters tested gave some differences in the results, but
the total bed elevation changes gained the same value. The comparison of simulation
and measured longitudinal bed level changes are shown in Figure 2.9 and Figure 2.10
for selected cross sections.
51
Figure 2.8: (a) Measured bed levels after the flushing (b) Simulated bed levels after the
flushing (Haun and Olsen, 2012)
52
Figure 2.9: Comparison of bed level changes: (a) measurements; (b) numerical simulation
with uniform sediment; and (c) nonuniform sediment (Feurich and Olsen, 2011)
Figure 2.10: Comparison between measured values and simulation results at: (a) cross
section 80; (b) cross section 60; and (c) cross section 20 (Feurich and Olsen, 2011)
The morphological bed changes in a 6 km long section of the river Danube
located between Vienna and the Austrian-Slovakian border were computed using a
SSIIM model (Fischer-Antze et al., 2008). A time series of discharges during the
flood in 2002 was used for modelling. The Wu et al. (2000) formula was used to
53
compute the nonunniform sediiment transsport with hiding exxposure alg
gorithms
considerattion. The SSIIM perfoormed well in computinng the bed changes du
ue to the
reasonablee accuracy of the com
mparison results with field
f
measuurement. Th
he study
indicated the
t model is
i able to reepresent the relevant morphodynam
m
mic processses, such
as creation of a bar due to depposition pro
ocesses andd appearancce the scour on the
s
due to the related erosion pro
ocesses. Figgure 2.11 shows the measured
m
opposite side
and compuuted water and
a bed levvel in Dunub
b River befoore and after flood 2000.
M model in confluencee hydrodynaamics modeelling by
Appplication off the SSIIM
using the published field and laboratory
l
data of diffferent studdy was asseessed by
Đorđević (2012). Reyynolds averraged Navieer-Stokes eqquations weere used to compute
c
a 3D orthoogonal/non-orthogonall unstructurred, multiblock grid, w
which is suittable for
the discrettisation of thhe dendriticc flow domaains such ass the flow inn river confl
fluences.
Figuree 2.11: Meassured water depths
d
beforee (a) and afteer (b) the floood, together with
w
measuured (c) and computed (dd) bed elevatiion changes (Fischer-Antze et al., 2008).
54
4
SIMPLE algorithm is used to achieve the coupling of the continuity and
momentum equations in SSIIM. Due to high pressure and velocity gradients in the
confluence, the second-order upwind scheme is used for discrete convective terms in
the momentum equations. Đorđević (2012) validated the model SSIIM2 with using
both the experimental and field data and concluded that transfer of the momentum
from the tributary to the main river can be described satisfactorily using the 3D
model with the k-ε type turbulence model closure. Therefore, variations of the
recirculation zone width throughout the flow depth were predicted correctly.
2.10 Summary
Natural rivers are usually in a state of morphological equilibrium where the
sediment inflow on average balances the sediment outflow. A river, in effect, can be
considered a body of flowing sediments as much as one of flowing water. To clarify
the causes and consequences of changes in fluvial form and also to make informed
management decisions that affect a river’s function, it will require a good knowledge
regarding the role of bedload movement in forming and maintaining channel
geometry.
Bedload transport in rivers is basically a process of movement of individual
particles. The individual sediment size and the characteristic of the bed sediment
influence sediment transport. Bedload size distribution and bed material particle size
specifications are required to determine the sediment transport process. The extracted
parameter from affective factors on sediment transport can be used as a basis for the
prediction of sediment transport rates.
55
Various bed load transport equations have been formulated under limited
laboratory or field conditions as mentioned in section 2.4. The river flow condition
and river environment have most effect on the bedload transport rate in different
rivers, and the computed results from various equations often differ from each other
and even from the measured data set. Consequently the recent proposed equations
need to be adopted for the new conditions.
Soft computing technique such as artificial neural networks (ANNs) and
genetic programming (GP) have been successfully applied for water engineering
problems since the last two decades. The good performance of ANN and GP
methods demonstrated its predictive capability and the possibility of generalization
of the modelling to nonlinear problems for river engineering applications. The
regression method also has been widely used to analyse and develop relationship
between variables specifically in water sciences. The Application of GP and ANN
was mentioned in section 2.6 indicate these models which are particularly useful in
modelling processes about data interpretation without any restriction to an extensive
database predict well the bedload transport in different locations with different
circumstances.
A more specific approach is required for short and long term channel response
evaluating in complex alluvial channels such river channel confluences that exhibit
widely varying channel plan form, morphology, and bed composition. Multidimensional hydrodynamic and sediment transport models can potentially provide
this level of analysis. Each sediment transport model has its limitations for solving
the fluvial hydraulic problem. Therefore, the selection of right model under certain
56
constraints requires a satisfactory knowledge of the capabilities and features of
available models. The sediment transport model applications illustrate the capability
of SSIIM model for improving our understanding of river channel confluence
morphological processes as complex phenomena in river engineering.
Bedload transport characteristic study at small streams and investigating the
bedload transport in Ara -Kurau river channel confluence has been implemented. The
data collection and analysis will be discussed in Chapter 4 and result of sediment
transport model in river channel confluence will also present in Chapter 5.
57
3
CHAPTER 3
METHODOLOGY
3.1
Introduction
Study area, the methodology includes the study flowchart, data collection such
as hydrologic data, geometry data and sediment data were described in this chapter.
This chapter also provides information on the setting up of different methods that
include nonlinear regression, artificial neural network and genetic programming for
predicting the bedload transport rate. Figure 3.1 illustrates the research framework as
a study guide.
Literature review
Study the morphology of area
Data collection
1. Geometry
2. Sediment
3. Hydrology
Bedload transport
determination
SSIIM Model
Preparation
Define boundary
condition
NLR
ANN
GP
Modification of
model equation
Simulation
Calibration and
validation model
Conclusions
Figure 3.1: Research framework for present study
58
3.2
Study Area
Kurau River sub-basin lies between latitude 530,000 (N) and 570,000 (N),
longitude 683,300 (E) and 723,300 (E) in Zone 47 in UTM coordinate system. The
catchment area is approximately 1600 Km2, consisting of two main river tributaries
namely Kurau River and Ara River. The river starts partly in the Bintang Range and
partly in the Main Range where the territory in the upper reaches is steep and
mountainous. Mid valleys of the river are characterized by low to undulating terrain,
which give way to broad and flat floodplains. Ground elevations at the river
headwaters are moderately high, being 1,200 m and 900 m. The slopes in the upper
6.5 km of the river averaged 12.5% whilst those lower down the valleys are much
lower, of the order of 0.25% to 5%. Kurau River sub basin and data collection sites
included the Kurau- Ara confluence are shown in Figure 3.2 and Figure 3.3.
Land use distribution in the year 2004 shows that primary forests contribute
most at about 50% of the total area of Kurau River sub-basin, followed by rubber
dominate at about 24% of the total area, oil palm at about 11.28% of the total area. It
can be concluded that Kurau River sub basin is an undeveloped area with the
majority of the land being used for agriculture.
Rapid development in the Kurau River basin has led to an increased demand
for river sand as a source of construction material, which has resulted in the increase
in river sand mining activities that have rise to various problems. Kurau River is one
of selected river based on previous studies (DID, 2009) that sand mining activities
occurred in the river basin. The bed material sizes are in the sand-gravel range.
59
Figuree 3.2: Kurau River sub-basin and dataa collection ssites
Figure 3..3: Ara -Kuraau river conffluence
60
0
3.3
3.3.1
River Hydrology and Hydraulic
Stream Flow Data
The Pondok Tanjung streamflow station is a telemetry station that is located in
Pondok Tanjung (Ara- Kurau confluence) and it has been operating since 1960 as
shown in Figure 3.4. The station is a well hydrometric site for low and high flow
measurement.
The historical streamflow data at the Pondok Tanjung streamflow station is
provided by the DID Hydrology Division from year 1960 to the year 2008. The
hydrographs for year 1970, 1972, 1986, 2006 and 2007 which present the highest
discharge at the Pondok Tanjung streamflow station are shown in Figure 3.5.
Figure 3.4: Pondok Tanjung stream flow station (5007421)
3.3.2
Water Level Record
The historical water level record at the Pondok Tanjung streamflow station is
provided by the DID Hydrology Division from year 1960 to the year 2008. Figure
3.6 shows the water level chart for year 1970, 1972, 1986, 2006 and 2007 which
present the highest year the Pondok Tanjung streamflow station.
61
Figure 3.5: Discharge hydrograph for Kurau River at Pondok Tanjung
Figure 3.6: Water level chart for Kurau River at Pondok Tanjung
3.3.3
Stage Discharge Data
Figure 3.7 shows the flow rating curve for years 1996 to 2007. The shift in the
flow rating curve association reflects the variability of flow at the Pondok Tanjung
62
station at Kurau River. The rating curve for the year 2007 and 2002 are defined for
higher flow.
20
19
Stage (m)
18
17
16
1996
1998
2000
2002
2004
15
14
0
20
40
60
80
100
120
1997
1999
2001
2003
2005
140
160
180
200
Discharge (m³/s)
Figure 3.7: Stage-discharge relationship at Pondok Tanjung for 1996-2007
3.3.4
Flood Frequency Analysis
The ranking of flood over 48 years are given in Table 3.1. The review indicates
that the 2007 flood at the Pondok Tanjung streamflow station had the highest
discharge measured in 48 year period. Flood frequency analysis was carried out for
48 years of stream flow data using Normal distribution, Generalized extreme value, 3
Parameter Pearson, 3 Parameter lognormal, Gumbel Min, Log Pearson type III and 2
Parameter lognormal (Table 3.2).
63
Table 3.1: Flood ranking for Kurau River at Pondok Tanjung
Rank
Q(m3/s)
Year
Date
Rank
Q(m3/s)
Year
Date
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
191.322
175.807
156.943
147.956
138.167
132.491
125.095
123.611
115.681
100.436
99.733
97.685
96.725
93.182
92.502
92.288
90.807
85.732
84.294
83.833
83.429
83.136
80.979
80.588
2007
1970
1986
2006
1972
1995
1997
2003
1998
1991
1978
1971
1999
1983
2005
1977
1994
1969
2001
1973
1990
1993
1984
1975
23-Oct
11- Oct
09-May
26-Mac
31- Oct
31- Oct
12-Nov
05- Oct
17-Agu
03-Jun
25- Oct
12-Agu
25- Oct
10-Sep
15-Dec
07-Nov
27-Nov
13-Oct
01-Nov
01-Nov
03-Nov
03-Jul
09-Nov
08-Dec
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
78.692
78.035
77.817
70.685
70.648
68.81
67.866
65.884
65.348
64.548
58.462
58.462
55.015
53.116
53.116
46.463
45.417
44.793
32.574
27.822
18.542
9.344
8.577
7.448
1979
2004
1989
2000
1987
1980
1981
1985
1988
1982
1960
1961
1962
1963
1664
1974
1992
1665
1976
2002
1996
1967
1966
1968
22-Nov
03-Feb
13-Apr
22-Nov
25- Oct
06-Jun
01-Jun
01-Oct
22-Jun
16-nov
31-Dec
01-Oct
21-Oct
13-Dec
11-Dec
24-Dec
29-Oct
29-Apr
01-Jan
18-Oct
13-Dec
18-Sep
22-Nov
30-Dec
Figure 3.8 shows the measured stream flow data for the different type of
distributions. The most valid model was determined with the goodness of fit tests.
Chi-Squared test the most popular goodness of fit tests was used to compare the
fitted distributions. Since the goodness of fit test statistical indicates the distance
between the data and the fitted distributions, it is obvious that the distribution with
the lowest statistic value is the best fitting model. The generalized extreme value has
the lowest Chi- squared statistic value with better agreement with the measured
streamflow data (Table 3.2).
64
The goodness of fit tests can be used to compare the fitted distributions. Table
3.3 shows the value of Chi Squared indicating the best distribution for flood analysis.
The Generalized extreme value distribution with the lowest Chi squared was used for
the flood frequency analysis. Consequently the discharge of 195.83 should be
considered as the design peak discharge and sediment transport study for Kurau
River.
Table 3.2: Summary of flood frequency analysis for Kurau River at Pondok Tanjung
Discharge (m3/s)
Return
period
Generalized
Extreme
Value
Pearson
3
Parameter
Log
normal 3
Parameter
Normal
Distribution
Gumbel
Min
Log
Pearson
Type III
Log
normal 2
Parameter
200
211.006
222.3811
223.939
189.270
151.989
239.966
505.324
100
195.834
202.6552
204.063
178.006
147.053
223.900
407.830
50
179.215
182.5206
183.706
165.698
141.310
205.078
322.673
25
160.935
161.7328
162.633
152.015
134.445
183.027
248.701
10
133.597
132.5348
132.981
130.834
122.652
147.924
166.198
5
109.534
108.0684
108.141
110.971
110.044
115.853
113.886
2
68.612
67.88854
67.549
72.972
80.389
63.433
55.262
Table 3.3: Goodness of fit test with chi-squared statistic value
Distribution
Chi- Squared
1
Generalized Extreme Value
0.36421
2
Pearson 3 Parameter
1.6383z
3
Lognormal 3 Parameter
1.6602
4
Normal Distribution
2.6298
5
Gumbel Min
3.379
6
Logpearson Type III
11.354
7
Lognormal 2 Parameter
11.638
65
0
discharge Q (m³/s)
discharge Q (m³/s)
Normal Distribution
actual data
prediction
220
200
180
160
140
120
100
80
60
40
20
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
0
discharge Q (m³/s)
discharge Q (m³/s)
Lognormal 2 Parameter
actual data
prediction
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
actual data
prediction
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Weilbull Probability
Weilbull Probability
220
200
180
160
140
120
100
80
60
40
20
0
Lognormal 3 Parameter
220
200
180
160
140
120
100
80
60
40
20
0
Pearson 3 Parameter
220
200
180
160
140
120
100
80
60
40
20
0
1
actual data
prediction
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
discharge Q (m³/s)
actual data
prediction
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Log-Pearson 3
220
200
180
160
140
120
100
80
60
40
20
0
actual data
prediction
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Weilbull Probability
Weilbull Probability
Generalized Extreme Value
220
200
180
160
140
120
100
80
60
40
20
0
actual data
prediction
0
0.1
0.2
1
Weilbull Probability
Gumbel Min
220
200
180
160
140
120
100
80
60
40
20
0
discharge Q (m³/s)
discharge Q (m³/s)
Weilbull Probability
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Weilbull Probability
Figure 3.8: Flood frequency analysis using difference types of distribution
66
1
3.4
Field Data Measurement
The current study was conducted at six cross sections of the Kurau River from
January 2010 to January 2013 because of the difficulty in sampling and possibility of
wading in the water in these areas. Owing to bank erosion and severe bed
degradation, other locations were either inaccessible or impossible to wade into the
water. These sites and the data collected by Ariffin (2004) from two other sites in Lui
and Semenyih rivers were selected for development of bedload equation.
The confluence zone of Kurau and Ara Rivers was also selected for the
modelling part of this study. Hydraulic and sediment measurements were made along
a series of cross sections in April 2012, with each reach being separated by
approximately 15 to 20 meters.
Figure 3.9: Langat River basin and data collection sites by Ariffin (2004)
67
3.4.1
Flow Measurement
Flow discharges were measured at six sites using an electromagnetic current
meter (Figure 3.10). The procedure for discharge measurement is based on
Hydrology Procedure No.15: River Discharge measurement by Current Meter (DID,
1976). Measurement taken includes flow depth (y0), velocity (V) and river width (B).
The flow velocities on the confluence zone of Kurau and Ara River at
approximately the same time as the river depth were also measured. A Hydroboard
Acoustic Doppler Profiler, ADP (SonTek River Surveyor core system; S5), and a
sub-meter-accurate, differential GPS (DGPS) system integrated with PCM (Power
and Communications Module) connected to a laptop computer were used for this
measurement (Figure 3.11).
Figure 3.10: Electromagnetic current meter
68
Transect coordinates were received by the PCM at 10-Hz and transferred to the
ADP internal memory for integration and processing. It is then transmitted along
with the ADP data from the PCM to the laptop for navigation to transect start and
end points. As much of the wetted width of each transect was sampled as possible.
Due to the blanking distance (0.2 m) and mounting depth (0.2 m) of the transducer,
measured velocities include all but the top 0.5m of the water column. Survey data
was processed using SonTek’s River Surveyor (v3.10) software. River Surveyor was
used to create discharge summaries, export transects positional data (profile number,
distance, and latitude/longitude) and to provide screenshots of cross-sectional
velocity profiles for each transect. Data exported from the program for each transect
was individually examined.
Figure 3.11: SonTek River Surveyor Hydroboard with optional GPS
69
3.4.2
Geometry Data
The six cross sections and confluence zone of Kurau and Ara rivers were
surveyed using Electronic Distance Meter (EDM) (Table 3.4). Water surface and
bed elevation during different flow were also observed. The geometry data along a
series of cross sections were collected by using Sontek River Surveyor for sediment
transport modelling (Figure 3.12).
Table 3.4: Typical cross sections along Kurau River (19 June 2010)
Locations Present condition
Cross-section
KRU1
28.0
Elevation(m)
27.0
26.0
25.0
24.0
23.0
0
5
10
15
20
25
30
35
40
Distance(m)
KRU2
Elevation(m)
20
19
18
17
16
0
2
4
6
8
10
12
14
16
18
20
Distance(m)
40
KRU3
Elevation(m)
39
38
37
36
35
0
70
5
10
15
20
Distance(m)
25
30
Table 3.4: Continue
Locations Present condition
Cross-section
40
KRU4
Elevation(m)
39
38
37
36
35
0
5
10
15
20
25
30
Distance (m)
36
KRU5
35
Elevation(m)
34
33
32
31
30
0
4
8
12
16
20
24
28
32
36
Distance(m)
55
ARA1
Elevation(m)
54
53
52
51
50
0
10
20
Distance(m)
71
30
40
50
Figure 3.12: River surveying at Ara River with river surveyor (ADP)
3.4.3
Sediment Data
Bedload and bed material particle size distributions were selected to represent
material transported and stored in the Kurau River.
3.4.3.1 Bed Material
River bed materials were collected by Van Veen grab sampler (Figure 3.13).
The width of the river was divided into seven spaced measuring points from left bank
to the right bank. The spacing between measuring points differs for one cross section
to the other and depends on the river width at different water levels.
72
Figure 3.13: Van Veen grab for bed material sampling
3.4.3.2 Bedload
In the last decade there has been an increase in interest in the measurement and
visualization of bed load movement in streams. As a result, there have been a series
of new developments in bed load movement sensing apparatus including: devices
based on repeated measurements of the stream cross-section (Ergenzinger, 1992),
repeated bed load sampling using Helley-Smith samplers (Bunte, 1990; Claude et al.,
2012; Helley and Smith, 1971; Ryan and Emmett, 2002; Sear, 2003), Brikbeck-type
slot samplers with pressure pillows (Garcia et al., 2000; Laronne et al., 2003; Sear et
al., 2000), magnetic induction devices (Bunte, 1996; Ergenzinger et al., 1994)
acoustic Doppler velocity devices (Claude et al., 2012; Ramooz, 2007; Rennie et al.,
2002) and hydrophones and impact sensing devices (Banzinger and Burch, 1990;
Barton, 2006; Froehlich, 2003).
73
These devices could sample the pattern of movement across the stream width,
or the pattern and quantity of movement through time. Direct and indirect methods
used to measure rates of bedload transport and the characteristics of different
sampling technologies and their applications can be found in Ryan et al. (2005)
The type of sampler was used based on the ease of handling, the sampling
efficiency and its operating cost (Ariffin, 2004). The hand Helley- Smith sampler
was selected in this research due to its ability to capture a wide sample material range
(0.5 to 16 mm), the high sediment trapping efficiency (Helley and Smith, 1971;
Yuqian, 1989) easy handling, suitable for short term measurement and low operating
cost.
In the field study, each section was sampled eight times. At the beginning of
each sampling event, water surface height was surveyed. The channel cross section
was then divided into eight equal spaced increments based on flow width at sampling
time. At each increment, flow depth and velocity were measured. Bedload was
sampled immediately after velocity at each increment. Bedload was collected with a
Helley-Smith bedload sampler made up of a square 7.6 cm orifice and 0.25 mm mesh
bag with frame and sampling durations ranging from 3-10 minutes, depending on the
intensity of bedload activity (Figure 3.14).
74
Figure 3.14: Hand held Helley-Smith sampler for bed load sampling
3.5
Techniques for Bedload Prediction
The new mathematical modelling methods will be used to improve the
sensitivity and performance of prediction equations in overcoming the difficulties of
developing such equations based on a balance between simplicity and accuracy. The
simple formula can estimate the bedload transport of small streams. Genetic
75
programming (GP) and artificial neural network (ANN) are powerful tools for
pattern recognition and data interpretation. They were employed and compared with
the nonlinear regression (NLR) method to present an explicit predictive equation for
bedload transport in small streams.
3.5.1
Performance of Bedload Transport Equation
Most of the equations depend on a lack of field data, a limited database, and
untested model assumptions. Consequently, the application of many equations is
limited to special conditions developed; only a few are generally accepted for
practical use.
The Meyer-Peter and Muller (1948) Rottner (1959), Chang (2002), Julien
(2002), Wong and Parker (2006) and vanRijn (1993) are some of the most common
and popular equations used to estimate the bedload transport rate in rivers and are
summarized in Table 3.5. Selection of formulas was based on their applicability to
sandy bed rivers and that the boundary conditions suit those of the Kurau River.
76
Table 3.5: The common bedload transport equations
Equation
Name
s g n
qb 8
( s ) nt
Meyer-Peter
and Muller
( 1948)
s 2R
nt
V
1
d 6
n 90
26
1
2
2
3
d
0.14 0.778 50
Rh
0.05 s 2 R
exp 1.5
V
b 13
Julien
( Julien, 2002)
b
Wong and
Parker (2006)
ϕb=4.93(θ-0.047)1.6
3.5.2
0.047 s d 50
1
1.5
2
2
3
3
(3-2)
3
18 g d 50 2 2
b
2
(3-1)
Chang
(Cheng, 2002)
vanRijn (1993)
2
No
3
3
d
qb s Rh v av 0.667 50
Rh
Rottner
(Yang, 1996)
3
(3-3)
3
g Gs 1d 50
(3-4)
3
0.088≤ d50 ≤ 4 (mm)
0.053 1.5 c r
( 1) 2.1
D*0.3
(3-5)
(3-6)
Dimensional Analysis
The Buckingham π theorem is one of the approaches that researchers used in
developing a general bedload equation (Khorram and Ergil, 2010). Based on the
theorem, the proposed influential parameter is the general form of the intensity of the
bed-load rate, b :
b = f (θ, Dgr, R/s, Gs)
(3-7)
b qb
(3-8)
G s 1gd 50 3
θ= RS0/ ((Gs-1).d50)
G 1 g
Dgr d50 s 2
(3-9)
1
3
(3-10)
77
where qb (m2 ⁄s) is the volumetric bed-load sediment rate per unit width, Dgr is
dimensionless grain size. In this study the median grain-size diameter, d50, assumed
as the grain diameter ds. The terms Rh ⁄ds and Gs are embedded in the Shields’
parameter θ, and taking θ = f (Re), one can generate a rather simple relationship:
b = f (θ)
(3-11)
And it can be expressed in the form of power law:
b = αθ
(3-12)
The bedload transport rate at Kurau River sites found to be similar to Barry et al.
(2004) and generally well described in log10 space (0.50 < R2<0.9) by a simple power
function of total discharge (Q).
Tb= αQ β
(3-13)
where Tb is bedload transport rate and α and β are empirical values.
3.5.3
Nonlinear Regression Method (NLR)
Nonlinear regression is a method of finding a nonlinear model characterized by
the fact that the prediction equation depends nonlinearly on one or more unknown
parameters. This method can be employed when there is the relationship between the
response and the predictors that satisfy a particular functional form.
NLR can estimate models with random relationships between independent and
dependent variables, whereas traditional linear regression is limited to estimating
linear models.
Based on the fundamental data and the relationship between the variables, the
following function is suggested:
78
b m.qn . i .Dgr h
s
0
Gs 1 .g.d503
(3-14)
where the following hydraulic parameters were used in the regression analysis: S0,
water surface slope, θ, Shields parameter, q stream discharge per unit width (m2/s),
dimensionless grain size Dgr, g, acceleration gravity, Gs, sediment specific gravity
and m, n, i, h are empirical parameters that can be obtain by NLR method.
3.5.4 Artificial Neural Network (ANN)
A neural network toolbox contained within the MATLAB package was used in
this study. Bedload transport equations were integrated into a multilayer feedforward network with an error back propagation algorithm. A two-layer feed-forward
network with sigmoid hidden neurons and linear output neurons (fitnet) can fit
multidimensional mapping problems arbitrarily well, given consistent data and
sufficient neurons in its hidden layer. Field data were provided and an appropriate
neural network structure was selected for training purposes. Training was performed
using the Levenberg–Marquardt backpropagation, where the input and output were
presented to the neural network as a series of learning. The network was set up with
the four parameters as the input pattern of discharge (Q), water surface slope (S0),
mean grain size (d50), and Shields parameter for the initiation of motion (θ) as most
influential parameters were widely used in bedload transport equations, and the bed
load transport rate Tb as the output pattern. In other words, the input layer contains
four neurons while the output layer contains one. Between the two layers, there is
another hidden layer that contains a suitable number of neurons under investigation
(Figure 3.15).
79
Inputs
Hidden layer
10
Output
Q
S0
Tb
d50
θ
Figure 3.15: Feed-forward multilayer network
3.5.5
Genetic Programming Method (GP)
A GPTIPS run with the following settings was performed: Population size =
500, Number of generations = 25, Tournament size = 7 (with lexicographic selection
pressure), Dmax = 3, Gmax = 4, Elitism = 0.01 % of the population, function node set =
(plus, minus, times, protected). The default GPTIPS multigene symbolic regression
function was used in order to minimize the root mean squared prediction error on the
training data (Searson, 2009a).
The following (default) recombination operator event probabilities were used:
Crossover events = 0.85, mutation events = 0.1, direct reproduction = 0.05. The
following sub-event probabilities were used: high level crossover = 0.2, low level
crossover = 0.8, subtree mutation = 0.9, replace input terminal with another random
terminal = 0.05, Gaussian perturbation of randomly selected constant = 0.05 (with a
standard deviation of Gaussian = 0.1) (Table 3.6). These settings are not considered
‘optimal’ in any sense but were based on experience with modelling different data
sets of similar size.
80
The selection of appropriate model input variables in GP, as with any datadriven prediction model is extremely important. The choice of input variables is
generally based on a previous knowledge for most influential variables and physical
insight into the problem (Khorram and Ergil, 2010). Four input parameters including
discharge (Q), water surface slope (S0), mean grain size (d50) and Shields’ parameter
for initiation of motion(θ) as a most influential parameters were widely used in
bedload transport equations as variable data and Tb (bedload rate) as invariable data
are used in the current study.
Table 3.6: Multigene GP range of initially defined parameters
Parameter
Range
Population size
500
Function set
+, -, *, /
Number of generations
25
Maximum number of genes
4
Maximum number of nodes per tree
13
Maximum depth of trees
3
Probability of GP tree mutation
0.1
Probability of GP tree cross over
0.85
Probability of GP tree direct copy
0.05
81
4
CHAPTER 4
BEDLOAD TRANSPORT CHARACTERISTICS
4.1
Introduction
Understanding the spatial distribution of bed material transport is essential for
many aspects of river management. Also the development of a relation to describe
the bedload transport rate is of high importance for detailed study and improvement
of models for prediction of bedload transport rate, prediction of channel change, and
analysis of stability of engineered structures such as bridges in rivers (Rennie and
Millar, 2004).
In this section detailed analyses for bedload and bed material characteristics
were performed for upstream and downstream of Kurau River. Size gradation of
bedload and bed material was analysed in relation to shear stress, and flow
discharges. Differences in bed load size distributions depending on the type of the
flow are explained according to intrinsic characteristics of transport processes. The
fractional transport rate was determined for each location as a function of the particle
size to assess the relative mobility of various size classes in the upstream and
downstream of Kurau River.
In this section NLR, ANN and GP river system models were used to simulate
and predict bedload transport in Kurau River. These models were employed for other
small streams. Data from six sediment stations on Kurau River in Perak and two
sediment stations in Lui and Semenyih River in Selangor (Ariffin, 2004), were
compiled to obtain the formula as well as for comparison with other existing bedload
82
transport formulas. The performances of the GP, ANN, and statistical (NLR) models
for small streams were evaluated and compared with five bedload transport formulas
such as Meyer-Peter and Muller (1948) based on the energy slope method; Rottner
(1959), Yang (1996), Chang (Cheng, 2002), van Rijn (1993), and Julien (2002) based
on the regression method; and Wong and Parker (2006) based on the shear stress
method.
4.2
4.2.1
River Characteristics
Summary of River Data Collection
Data of the six channel criteria ranged from 20000 km long in the drainage
area and included a variety sand–gravel bed channels. Discharges ranged from 0.55
m3/s to 12.79 m3/s. All cross sections in the Kurau River have a single thread channel
width. The top width ranged from 7 m to 19 m; the stream gradients ranged from
0.0007 to 0.001; median particle size of bed material (d50) ranged from 0.65 mm to
1.84 mm. Most channels were bounded by flood plains or alluvial terraces and were
able to adjust freely to discharge sediment inputs. The dynamics of the river are
relatively natural because the structures (i.e., bridges and some bank protection
structures) have some influence on lateral channel mobility. Bedload discharge,
hydraulics parameter and sediment data (grain size distribution, d50), were gathered
from the Lui River, Semenyih River (Ariffin, 2004) and Kurau River as small
streams. The range of measured data is shown in Table 4.1. Figure 4.2 to Figure 4.6
show cross sectional changes at different flow discharges. Lower bed elevations
suggest bed erosion occurs at higher flow discharges.
83
Molinas and Wu (2001) categorized the rivers in large and medium by flow
depth, flow discharge and flow velocities. They pointed out that large rivers refer to
those with yearly average flow depths greater than 4 m, and medium rivers refer to
those with yearly average flow depths between 2 m and 4 m. They mentioned that
large rivers have flow discharges more than 134 m3/s for, flow velocities bigger than
0.21 m/s, flow depths more than 3 m, water surface slopes in the range of 0.02×l04 to
1.8×104 and median bed material diameters in the range of 0.09 mm to 0.99 mm. The
flow discharges for medium rivers are between 13 m3/s to 4791 m3/s, flow velocities
in the range of 0.20 m/s to 2.30 m/s, flow depths in the range of 1.50 m to 9.29 m,
water surface slopes in the range of 0.06×104 to 25×104, median bed material
diameters in the range of 0.02 mm to 2.60 mm. The summary of some rivers (large
and medium) data is shown in Table 4.2. The range of data in Kurau, Semenyih and
Lui rivers such as flow discharge (0.55-17.2), flow depth (0.23-1.15) and etc... are
not the in the range of large and medium rivers as mentioned above. Consequently
these three rivers are considered as small rivers. Details of the present data for Kurau
River are shown in Appendix A.
84
Table 4.1: Range of field data for Kurau , Lui and Semeneyih
River
Kurau
Location
No
of
data
KRU1
Q
(m3/s)
V (m/s)
So×10-2
B (m)
Y0 (m)
A (m2)
R (m)
d50 (mm)
Tb (kg/s)
8
3.18-12.8
0.53-0.82
0. 05-07
17-19
0.47-1.15
6-15.51
0.412-0.885
0.65-1.044
0.23-2.10
KRU2
8
1.6-6.1
0.5-0.73
0. 07-1.85
9-10.3
0.42-1.15
2.87-8.37
0.313-0.76
0.699-1.084
0.17-0.86
KRU3
8
0.55-1.52
0.31-0.52
0. 06-0. 96
7-9.2
0.28-0.38
1.39-2.89
0.166-0.303
0.99-1.404
0.03-0.26
KRU4
8
0.56-4.7
0.15-1.22
0. 1-0. 62
13-Dec
0.27-0.52
1.99-6.03
0.161-0.286
1.02-1.83
0.01-0.50
KRU5
8
2.32-6.6
0.49-1.56
0. 03-0. 51
13-Dec
0.37-1.03
3.46-9.78
0.224-0.699
0.74-1.51
0.13-1.52
ARA1
8
0.77-5.25
0.4-0.69
0. 03-3.12
11.3-13
0.27-0.86
1.94-7.57
0.167-0.567
1.29-1.84
0.12-1.04
92
0.7 – 17.2
0.2 – 1.0
0.03 - 0.93
15-15.5
0.23– 0.99
3.42-16.84
0.221-0.887
0.50 – 1.74
0.04-1.55
2.6 – 8.0
0.4 – 0.9
0.23 – 1.5
13-15
0.36 – 0.82
5.42-11.49
0.345-0.735
0.88 – 2.29
0.65-3.15
(present data)
85
Lui
Kg Lui
(Ariffin, 2004)
Semenyih
Kg.
(Ariffin , 2004) Rinching
50
Data source
Table 4.2: Summary of large and medium rivers (Monalis and Wu, 2001)
Flow
Flow
Flow
Water
Median
Discharge
Velocity
Depth
Surface
Diameter
3
4
(m /s)
(m/s)
(m)
Slope×l10 (mm)
Bed-Material
Concentration
(ppm)
(a) Large Rivers (dyr (i)> 4.0 m)
86
Amazon and Orinoco River Systems (Posada 1995)
134-235000
0.37-2.42
3.56-62.33 0.14-1.8
0.093-0.90
0.1-2360
Mississippi River System (Posada 1995)
332-4100
0.37-1.77
3.17-21.80 0.03-1.8
0.18-0.99
0.2-370
Atchafalaya River at Simmesport (Toffaleti 1968)
382-14188
0.21-2.03
6.10-14.75 0.02-0.51
0.091-0.31
0.6-570
Mississippi River at Tarbert Landing (Toffaleti 1968)
4228-48830
0.62-1.61
6.74-16.40 0.18-0.43
0.18-0.33
12-260
Mississippi River at St. Louis (Toffaleti 1968)
1512-21608
0.62-2.42
4.66-17.28 0.25-1.34
0.18-1.15
7-510
Red River at Alexandria (Toffaleti 1968)
190-1538
0.37-1.14
3.00-7.38
0.10-0.22
8-500
Total of Large Rivers
134-235000
0.21-2.42
3.00-62.33 0.02-1 .8
0.091-0.99
0.1-2360
0.66-0.82
(b) Medium Rivers ( 2.0 m < dyr< 4.0 m, d > 1.5 m)
ACOP Canal Data of Mahmood et al. (1979)
30-529
0.50-1.30
1.50-4.30
0.55-1.7
0.083-0.36
17-2083
Chop Canal Data of Chaudhry et al. (1970)
28-428
0.69-1.60
1.68-3.41
0.51-2.5
0.10-0.31
116-1 317
Canal Data of Chitale et al. (1966)
13-242
0.51-1.06
1.57-3.56
0.57-1.2
0.02-0.082
512-5759
Colorado River (US Bureau of Reclamation, (1958)
River Data of Leopold (1969)
South American River and Canal Data of NEDCO
(1973)
97-500
109-499
0.53-1 .27 1.51-3.89
0.56-1 .26 1.50-4.11
0.37-4.1
0.37-3.5
0.16-0.70
0.14-0.81
18-769
11-564
29-4791
0.20-1 .64 1.53-9.29
0.06-6.2
0.10-1.08
3-3000
Portugal River Data of Peterson and Howells (1973)
107-660
0.93-1.44
1.50-2.44
6.1 -9.7
2.20-2.60
54-351
Rio Grande River Data of Nordin and Beverage (1965) 79-286
13-4791
Total of Medium Rivers
1.25-2.30
1.50-3.12
13-25
0.31-1.91
1300-5310
0.20-2.30
1.5-9.29
0.06-25
0.02-2.60
3-5759
(i)dyr Yearly avrage flow depth
4.2.2
Typical Cross-Sections for the River Study Site
Kurau River surveyed cross sections are shown in Figure 4.1 to Figure 4.6.
The figures indicate the changes in bed morphology during the data collection time.
The maximum degradation occurred in KRU1 around 0.8 m during the minimum
discharge and maximum discharge that measured in this cross section.
28
27
26
Elevation(m)
25
24
23
22
0
5
10
15
20
distance (m)
28/04/2010 Q=7.21 mᵌ/s
29/12/2010 Q=5.58 mᵌ/s
24/02/2011 Q=12.79 mᵌ/s
25
30
35
40
11/11/2010 Q=5.21 mᵌ/s
19/01/2011 Q=3.99 mᵌ/s
9/3/2011 Q=4.91 mᵌ/s
Figure 4.1: Cross section KRU1 along Kurau River
20
19
Elevation(m)
18
17
16
15
0
2
4
6
8
10
12
14
16
18
Distance(m)
19/05/2010 Q=1.6(mᵌ/s)
1/12/2010 Q=6.1(mᵌ/s)
16/02/2011 Q=1.65(mᵌ/s)
12/10/2010 Q=2.1(mᵌ/s)
19/01/2011 Q=2.25(mᵌ/s)
3/03/2011 Q=1.95(mᵌ/s)
Figure 4.2: Cross section KRU2 along Kurau River
87
20
20
19
Elevation(m)
18
17
16
15
0
2
4
6
8
10
Distance(m)
5/7/2010 Q=0.79 mᵌ/s
29/12/2010 Q=1.03 mᵌ/s
16/2/2011 Q=1.32 mᵌ/s
11/05/2011 Q=1.52 mᵌ/s
12
14
16
18
20
5/10/2010 Q=0.55 mᵌ/s
6/1/2011 Q=0.66 mᵌ/s
9/3/2011 Q=0.62 mᵌ/s
2/06/2011 Q=0.72 mᵌ/s
Figure 4.3: Cross section KRU3 along Kurau River
40
39
Elevation(m)
38
37
36
35
0
5
10
15
Distance(m)
19/05/2010 Q=0.73 mᵌ/s
20/12/2010 Q=0.56 mᵌ/s
8/2/2011 Q=2.59 mᵌ/s
5/5/2011 Q=4.7 mᵌ/s
20
25
5/10/2010 Q=1.33 mᵌ/s
26/01/2011 Q=1.18 mᵌ/s
16/02/2011 Q=1.41 mᵌ/s
9/6/2011 Q=2.21 mᵌ/s
Figure 4.4: Cross section KRU4 along Kurau River
88
30
35
34
Elevation(m)
33
32
31
30
0
2
4
6
8
10
12 14 16 18 20 22 24 26 28
Distance(m)
28/06/2010 Q=6.44mᵌ/s
26/05/2011 Q=4.6 mᵌ/s
12/10/2010 Q=2.32 mᵌ/s
20/12/2010 Q=4.06 mᵌ/s
6/1/2011Q=5.68 mᵌ/s
8/2/2011 Q=5.39 mᵌ/s
24/02/2011 Q=6.6 mᵌ/s
21/06/2011 Q=2.23 mᵌ/s
30
Figure 4.5: Cross section KRU5 along Kurau River
55
54
Elevation(m)
53
52
51
50
0
5
10
15
Distance (m)
12/5/2010 Q=1.27 mᵌ/s
1/12/2010 Q=5.25 mᵌ/s
1/2/2011 Q=1.19mᵌ/s
5/5/2011 Q=1.68 mᵌ/s
20
25
27/10/2010 Q=0.776 mᵌ/s
6/1/2011 Q=2.29 mᵌ/s
3/3/2011 Q=1.02mᵌ/s
2/6/2011 Q=2.29 mᵌ/s
Figure 4.6: Cross section A1 along Ara River
89
30
4.2.3
Parameter Affecting Bedload Transport
All measured variables were plotted against the bedload transport to indicate
the correlations of different parameters and to be used as basis for developing new
bedload transport equation. The scatter plots of this variable against bedload
transport rate are shown in Figure 4.7 to Figure 4.15.
10
Bedload transport rate Tb(kg/s)
kurau River
Lui River
Semenyih River
1
0.1
0.01
0.1
1
Discharge Q (m3/s)
10
Figure 4.7: Scatter plot of bedload transport rate against discharge
10
Bedload transport rate Tb(kg/s)
Kurau
Lui
Semenyih
1
0.1
0.01
0.01
0.1
Velocity V ( m/s )
1
10
Figure 4.8: Scatter plot of bedload transport rate against velocity
90
10
Bedload transport rate Tb(kg/s)
Kurau
Lui
Semenyih
1
0.1
0.01
1
10
Width B (m)
100
Figure 4.9: Scatter plot of bedload transport rate against width
10
Bedload transport rate Tb(kg/s)
Kurau
Lui
Semenyih
1
0.1
0.01
0.01
0.1
1
Water depth Yo (m)
10
Figure 4.10: Scatter plot of bedload transport rate against water depth
10
Bedload transport rate Tb(kg/s)
Kurau
Lui
Semenyih
1
0.1
0.01
1
10
100
B/Y ratio
Figure 4.11: Scatter plot of bedload transport rate against B/Y ratio
91
10
Bedload transport rate Tb(kg/s)
Kurau
Lui
Semenyih
1
0.1
0.01
0.01
0.1
1
Hydraulic radus R (m)
10
Figure 4.12: Scatter plot of bedload transport rate against hydraulic radius
10
Bedload transport rate Tb(kg/s)
Kurau
Lui
Semenyih
1
0.1
0.01
0.1
1
Area A ( m2 )
10
100
Figure 4.13: Scatter plot of bedload transport rate against area
Bedload transport rate Tb(kg/s)
10
1
0.1
0.01
0.0001
Kurau
Lui
Semenyih
0.001
0.01
Slope S0
0.1
1
Figure 4.14: Scatter plot of bedload transport rate against slope
92
Bedload transport rate Tb(kg/s)
10
1
0.1
Kurau
Lui
Semenyih
0.01
0.1
1
10
Median grain size d50 (mm)
100
Figure 4.15: Scatter plot of bedload transport rate against median grain size
4.3
Particle Size Distribution
Analysis of particle size distributions of bedload and bed material for different
discharges ensure better understanding of sediment transport processes for each
particular river and generally increase information about parameters affecting
bedload transport rates.
The particle size distributions of bedload and bed material are illustrated in
Figure 4.17. The results show that the bedload material is finer than the surface bed
material for all analyzed sites. The median bedload particle size and median particle
of bed material are less than unity in the upstream of the Kurau River. This finding
demonstrates the size selectivity of bedload transport during the different water
discharges (Ashworth et al., 1992; Wathen et al., 1995).
In most of the samples analysed, sand and fine gravel were the main fractions
of the bedload transport rate for the measured range of discharges, and the size
93
fractions enlarged with the increase in discharge. The source of fine material could
be from external sources or material from the bed surfaces (i.e., fine material
transported over a stable bed).
The bedload frequency curves obtained from the upstream of the river were
mainly bimodal and were unimodal only in a few cases. The unimodal bedload
frequency curve indicates that uniform fine material is present in the bedload sample,
whereas the bimodal curve shows sand and gravel modes with some concentration in
special sizes because of the mobilization of coarser bed particles during higher
discharges (Muskatirovic, 2008). Most bedload curves in the downstream were
unimodal, and the size of fractions was enlarged, following approximately the same
range.
The presence of sand and fine gravel in most of the bedload particle size
distributions in the downstream was caused by the fine sediment coming from the
upstream network during flood events. The coarser fractions of bedload particles
were transported by higher discharges, but they were generally smaller than those
formed on the bed surface. The median particle size of the bedload sample, even for
the highest measured values of the bedload transport rate, was equal or smaller than
the median particle size of bed material. Comparison of the distribution size of the
bedload in a medium frequency discharge between the upstream (KRU5) and
downstream (KRU1) of the Kurau River (Figure 4.18) indicates that the amount of
sediment particles of each fraction size in the upstream is greater than that in the
downstream in the same fractions Figure 4.16.
94
30
Upstream
Percentage retained (%)
25
20
15
6.44 (m³/s)
5.39 (m³/s)
10
4.6 (m³/s)
5
2.23 (m³/s)
0
0.01
0.1
1
10
Particle size (mm)
30
Downstream
Percentage retained (%)
25
20
15
7.21 (m³/s)
5.58 (m³/s)
10
12.79 (m³/s)
3.18 (m³/s)
5
4.91 (m³/s)
0
0.01
0.1
1
10
Particle size (mm)
Figure 4.16: Bedload frequency distribution size of upstream (KRU5) and downstream
(KRU1) of Kurau River
95
100
90
Upstream
Percentage passing (%)
80
70
60
50
3.18 (m³/s)
40
4.91 (m³/s)
30
5.58 (m³/s)
7.21 (m³/s)
20
12.79 (m³/s)
10
bed material
0
0.001
0.01
0.1
1
10
Particle size (mm)
100
90
Downstream
Percentage passing (%)
80
70
60
50
2.23 (m³/s)
40
4.6 (m³/s)
30
5.39 (m³/s)
20
6.44 (m³/s)
10
bed material
0
0.001
0.01
0.1
1
10
Particle size (mm)
Figure 4.17: Particle size distributions of bedload and bed material samples for Kurau River.
96
100
90
Percentage passing (%)
80
70
60
50
40
30
20
Downstream
10
Upstream
0
0.01
0.1
1
10
Particle size (mm)
Figure 4.18: Comparison of particle size distributions of bedload samples for upstream and
downstream of Kurau River in same discharge.
4.4
Evaluation of Bedload Size Distribution with Increasing Shear Stress
Figure 4.19 shows the size distribution of bedload sampled at different shear
stresses and discharges. Unlike in the following analyses, all material in the upstream
and downstream was included, and no upper size truncation was applied. To clarify
the emerging pattern, the grain size distributions for all discharges and all samples
were demonstrated in each shear stress, and an average size distribution was derived
for each shear stress. Individual size classes were classified into five groups to
represent fine sand (<0.3 mm), medium sand (0.3 mm to 0.71 mm), very coarse sand
(0.71 mm to 2 mm), granules (2 mm to 5.3 mm), and fine pebbles (5.3 mm to 25
mm) from the classification sediment size(Wentworth, 1922)
97
.
Table 4.3: The classifiication of seddiments by particle
p
size according
a
to the Wentworth scale
Sedimeent name
pebble
Granulle
Sand
Mud
Aggregate name
Size range
r
(Wentworth Class)
(metrric)
Boulder
Cobble
Very coarsse gravel
Coarse graavel
Medium grravel
Fine graveel
Very fine gravel
g
Vary coarsse sand
Coarse sannd
Medium saand
Fine sand
Very fine sand
s
Silt
Clay
Colloid
256 mm
m <
64–2556 mm
32–644 mm
16–322 mm
8–16 mm
m
4–8 mm
2–4 mm
m
1–2 mm
m
0.5–11 mm
0.25––0.5 mm
125–2250 µm
*
scalee
−8 <
−6 to −8
62.5–
–125 µm
3.906
625–62.5 µm
m
< 3.90
0625 µm
< 1 µm
-5 to-6
-4 to -5
-3 to -4
-2 to -3
-1 to -2
0 to -1
1 to 0
2 to 1
3 to 2
4 to 3
8 to 4
>8
>10
* = lo
og2D/D0 whhere is the Krumbein phhi scale,
is the diamete
er of the particcle,
and
is a referencee diameter, eqqual to 1 mm (to
( make the equation
e
dimeensionally
consistent).
100%
Percentage passing (%)
90%
80%
70%
60%
50%
40%
5.33-25 mm
30%
2-5.3 mm
20%
0.771-2 mm
0.33-0.71 mm
10%
<00.3 mm
0%
Shhear stress (N//m² )
Figure 4.119: Mean bedd load grain size distributtions for shear stress bannds arranged in order
of incrreasing shearr stress (upstrream of Kuraau River KR
RU5).
98
8
At the lowest flow in the upstream of the Kurau River ( = 5.4 N/m2), around
50% of the load was medium sand. The remainder was dominated by coarse sand
(30%) and granules (18%); only 2% accounted for sediment coarser than 5.3 mm.
With increasing shear stress, the grain size distribution became coarser. The
proportion of bedload in fine sand and medium sand reduced, and the proportion of
granules and fine pebbles increased. Interestingly, the proportion of coarse sand did
not change significantly over the range of monitoring flows. However, from the point
at which shear stress was 13.5 N/m2 and 14.2 N/m2 by increasing the flow, the
granule size increased and the transience of fine pebbles was observed. In the
upstream, the movement of fine size sand depended largely on its availability within
the channel, leading to the decrease in transport rates after the peak discharge.
Similar to the upstream at the lowest flow, in the downstream of the Kurau
River (Figure 4.20), most of the material load was medium sand and coarse sand,
with only 30% granules and approximately 5% fine pebbles. As shear stress
increased, the grain size distribution became coarser. The proportion of bedload in
fine sand and medium sand decreased, and the proportion of granules and fine
pebbles increased, but the amount of coarse sand did not change in all shear stresses.
The increase in the movement of sand at high flow and high shear stress in the Kurau
River was caused by the unavailability of coarse granules and fine pebbles in the
river. As mentioned previously, the Kurau River is a sand–gravel bed river with a
mean particle size (d50) in the range of 0.5 mm to 1.9 mm.
99
100%
g ppassing
g ((%))
Percentage
90%
80%
70%
60%
50%
5.3-25 mm
40%
2-5.3 mm
30%
0.71-2 mm
0.3-0.71 mm
m
20%
<0.3 mm
10%
0%
60.77
34.87
3.70
3 07
3.07
2.82
Shear stress (N
N/m²)
Figure 4.220: Mean bedd load grain size distributtions for shear stress bannds arranged in order
of increaasing shear stress
s
(downsstream of Kuurau River K
KRU1).
The changes in
i distributtion size frrom fine sand
s
to coaarser fractiion with
increasingg shear stresss can be evvaluated usin
ng the diam
meter of the bedload at different
d
percentiles (dx) of thee size distriibution. Fig
gure 4.21 shhows how thhe 10th, 16th, 30th,
t bedloadd grain sizee distributio
ons vary
50th, 60thh, 84th, andd 90th perccentiles of the
with shearr stress in thhe upstream
m and down
nstream of thhe river. Inn each samp
pling, the
grain size of each perrcentile incrreased gradu
ually with thhe increase in shear strress. The
increase inn size of cooarse sand became
b
lesss constant at
a high sheaar stress than
n that of
fine sand. For exampple, d30 incrreased to 0..1 mm in thhe upstream
m, but d84 in
ncreased
from 1.5 mm
m at low flow
f
to 3 mm
m at high fllow.
In thhe downstreeam, the chaanges increaased but beccame more constant th
han those
in the upsttream of thee river. To describe beetter the deppendence off grain size on shear
stress for each dx, thee trend line is illustrateed in this study. As shoown in Figu
ure 4.21,
the gradieent of trend line from d10 to d90 off each sampple increasees by increaasing the
shear stresss, indicatinng that the size
s of the particle
p
shiffts to becom
ming coarseer. In the
100
0
upstream, the trend of fine size (i.e., d10, d16, and d30) is mostly straight, and the trend
of coarse size is soft. However, in the downstream, the increasing grain size is
steady. The gradients are steeper than those upstream because of the existence of
each grain size in the locations.
10
Particle size (mm)
Upstream
d10
1
d16
d30
d50
d60
d84
d90
0.1
5
7
9
11
13
15
Shear stress( N/m²)
10
Particle size (mm)
Downstream
d10
d16
1
d30
d50
d60
d84
d90
0.1
0
20
40
60
80
Shear stress( N/m²)
Figure 4.21: Variation in grain size at the10th, 16th, 30th, 50th, 84th and 90th percentiles of
the bedload size distribution with increasing shear stress.
101
4.5
Fractional Transport Rate
The previous analysis demonstrates that bedload grain size varies with
increasing shear stress. However, these changes cannot be understood without
referring to the size distribution of bed material available for transport in the same
section. Wilcock and Southard (1989) normalized the fractional transport rates by
dividing all the various fractions by the corresponding proportion f in the sediment
i
bed to obtain equal mobility. Therefore, the ratio of the fractional transport rate of a
given size fraction to the proportion of the given size fraction in the bed sediment is
the same for all of size fractions.
The fractional transport rate piqb, was determined for each location as a
function of the particle size to assess the relative mobility of various size classes for
all samples in the locations. The results describe the comparison between bedload
and bed material grain size. The fraction of bedload particle size in the ith size range
is pi, and qb is the total transport, calculated as the mean for the sampling period.
Results of pi/fi for different values of Q were plotted, as the overall transport
rate varies with the applied discharges (Figure 4.22 and Figure 4.23). Figure 4.22a
and Figure 4.23a show the range of sediment sizes present in all recorded discharges.
The degree to which the curves revolve from the horizontal indicates how much the
particle size distribution of the bedload departs from that of the bed material
(Wilcock and McArdell, 1993).
Based on Figure 4.22a, the middle range sediment size has an equal rate of
bedload transport and bed material. Fine sediment was loaded less in the upstream
and downstream compared with the bed material. However, the fine sediment size
102
loaded more at low flow and less at high flow compared with the bed material
distributions because the flow moves finer sediment more easily than coarser
sediment from the bed. In contrast, at high flow, the fine sediment loaded less than
the coarser sediment. In this condition, the increase in flow increased in shear stress
and load of the coarser sediments.
10.00
a
Pi/Fi
1.00
2.23 (m³/s)
0.10
4.6 (m³/s)
5.39 (m³/s)
6.44 (m³/s)
0.01
0.01
0.1
1
Particle size (mm)
10
Scaled Fractional transport rate (kg/ms)
b
10
1
2.23 (m³/s)
4.6 (m³/s)
0.1
5.39 (m³/s)
A
B
6.44 (m³/s)
0.01
0.01
0.1
1
10
Particle size (mm)
Figure 4.22: Transport ratio as a function of grain size at upstream (a) the transport ratio Pi/fi
where pi is the proportion of each size fraction i present in transported material and fi is the
proportion of each size fraction in the bed material (b) the scaled fractional transport rate
computed as qbpi/fi, where qb is the sediment transport rate.
103
10.00
a
Pi/Fi
1.00
3.18 (m³/s)
0.10
4.91 (m³/s)
5.58 (m³/s)
7.21 (m³/s)
12.79 (m³/s)
0.01
0.01
0.1
1
10
Particle size (mm)
10
Scaled Fractional transport rate (kg/ms)
b
1
3.18 (m³/s)
0.1
5.58 (m³/s)
4.91 (m³/s)
7.21 (m³/s)
B
A
12.79 (m³/s)
0.01
0.01
0.1
1
10
Particle size (mm)
Figure 4.23: Transport ratio as a function of grain size at downstream (a) the transport ratio
Pi/fi (b) the scaled fractional transport rate qbpi/fi.
The range of 0.7< pi/fi <2 was selected to define the balance condition
approximately. This range indicates that the transport proportion of the bedload is the
same as that of bed material of this size. The departure from the value pi/fi range was
statistically significant compared with that of other sizes.
104
Figure 4.22b and 4.23b demonstrate that the fractional sediment transport ratios
for the given flows have a similar range, except the fine sediment side and the coarse
sediment side (i.e., outside of lines A and B). Fractions finer than line A on the fine
sediment side are relatively rare in the bedload than in the bed material. The
condition of equal mobility may seem confusing because transporting the coarser
fractions is more difficult than transporting the finer fractions for a flow. Larger
particles are more difficult to move because they are heavier. This condition is
known as the particle–weight effect in mixed-sized sediment transport. Two
important countervailing effects tend to offset the particle–weight effect. First is the
hiding–sheltering effect, in which larger particles are more exposed to the flow, and
thus a greater fluid force is exerted on them. However, smaller particles tend to be
sheltered from the forces of the flow by the larger particles (Einstein, 1950 ). Second
is the rollability effect, in which larger particles can roll easily over a bed of smaller
particles but not the other way around. The relative importance of the particle–
weight's effect and the combination of the hiding–sheltering' s effect and the roll
ability's effect are essential factors in mixed-sized sediment transport (Southard,
2006). The hiding -sheltering and rollability effect usually occurred on the armored
bed surface. Armoring is a small-scale sorting process that results in a thin layer of
coarse grains at the bed surface (Sutherland, 1987). The presence of an armor layer
on the bed surface is a common phenomenon in rivers. Two types of armor layers
can be distinguished: stable armor layers and dynamic armor layers. Dynamic armor
layers develop if the bed shear stress is large enough to transport both the fine and
the coarse grain-size fractions (involving a continuous supply of sediment from
upstream) and the innate difference in mobility between coarse and fine grains
causes the fine grains to be winnowed from the bed surface, overexposing the coarse
105
grains on the bed surface. Dynamic armor layers may disappear at high bed shear
stresses, but this is not necessarily the case (Gomez, 1995; Wilcock and DeTemple,
2005).
The dynamic armored bed condition at the downstream of Kurau River can be
exist as a results of frequency curve of discharges and an extended period of flows
over a mixed sand and gravel bed. It is described by the distribution size of bed
material samples in different discharges and the condition of equal mobility in
downstream of Kurau River. Therefore, because of this dynamic armored bed with
coarse sediment the fine sediment is relatively rare in the bedload than in the bed
material.
The change in the range of fractional transport rate, as a function of particle
size to assess the relative mobility of various sizes of classes, shows that fractional
transport rates decreases with the decrease in sediment loading in the first part (i.e.,
left side of line A). The reason is that the fine fraction is present in the bedload
because of the overpass in the suspension at high flows, not at low flows. In the
second part (i.e., between lines A and B), the fractional transport rates are
approximately equal. Sediments are present in the load in proportions similar to those
present in the bed. In the third part (i.e., right side of line B) in the coarse material,
the fractional transport ratio decreases with the increase in particle size and moves in
the partial transport system.
The horizontal part of the data points (i.e., between lines A and B) indicates
that the transport of variously sized sediment particles approaches equal mobility.
106
The transported bedload is composed approximately of the same value of sediment
as bed material. The fractional transport ratio depends regularly on the proportion in
the bed in the Kurau River and the transport rate of fraction independent of the
particle size. In comparison, the range of fractions in equal mobility in the upstream
within 0.4<dx<4.5 was found to be greater than that in the downstream equal
mobility range (0.55< dx < 3). This finding demonstrates the stable condition of
sediment transport of the upstream compared with that in the downstream. The low
amount of Pi/fi in the downstream shows the sedimentation in the section caused by
the geomorphology of the Kurau River in the downstream.
4.6
4.6.1
Performance of Bedload Transport Equation
Assessment of Existing Equation for Kurau River
Predicted bedload transport rates by Meyer-Peter and Muller (1948), Rottner
(1959), Chang (Cheng, 2002), Julien (2002), Wong and Parker (2006) and van Rijn
(1993) were compared with observed values from Kurau River. The performances of
the equations were measured using the discrepancy ratio (DR), which is the ratio of
the predicted bedload to measured bedload (DR = predicted/measured). A
discrepancy ratio of 0.5-2.0 (0.5<DR <2.0) was used as a criterion in the evaluation
of the selected equations. Based on the relationship within measured and predicted
values the formulas in most cases performed disconcert and they over predicted and
under predicted of the measured values (Table 4.4). All equations produced an
average discrepancy ratio out of range 0.5-2. Figure 4.24 depicts comparisons of
bedload transport predictions and measurements from Kurau River study sites.
107
Table 4.4: Summary of bedload transport equations assessment
Discrepancy ratio between
0.5 and 2
No data
%
1
3.33
No data
Coefficient of
determination, (R2 )
Average
Discrepancy
ratio (DR )
Rottner
48
0.70
7.36
MPM
Wong
48
48
0.38
0.09
0.11
9.10
1
8
4.00
37.78
Chang
48
0.02
16.27
6
18.18
Julien
48
0.07
5.35
6
18.18
vanRijn
48
0.03
33.40
2
6.45
Equation
10
Rottner
Meyer-Peter and Muller
Predicted Tb(kg/s)
1
Predicted Tb(kg/s)
1
0.1
0.1
0.01
0.01
0.001
0.01
0.1
1
10
0.01
0.1
Measured Tb(kg/s)
1
10
Measured Tb(kg/s)
10
wong
julien
Predicted Tb(kg/s)
Predicted Tb(kg/s)
1
0.1
0.01
0.001
1
0.1
0.01
0.01
0.1
1
10
0.01
0.1
1
Measured Tb(kg/s)
Measured Tb(kg/s)
10
10
Chang
Van Rijn
1
Predicted Tb(kg/s)
Predicted Tb(kg/s)
10
0.1
0.01
1
0.1
0.01
0.01
0.1
1
Measured Tb(kg/s)
10
0.01
0.1
1
Measured Tb(kg/s)
10
Figure 4.24: Comparison of predicted and measured bedload rates for Kurau River
108
4.6.2
Prediction of Bedload Transport in Kurau River with Nonlinear
Regression Method
Blizard and Wohl (1998) reported the relationship between bedload transport
and hydraulic variables, thus, multiplication of the hydraulic variables in the form of
power law based on Equation (3-12) and (3-13) can better describe the behaviour of
the bedload transport rate (Tb). Figure 4.25 shows the bedload rating curve and fit of
this function at study sites. Power function of flow discharge, Shields’ parameter (θ),
median grain size (d50) and the channel gradient assumed as the variables of the
bedload transport rate function in the Kurau River sites. The average flow rate and
the sediment movement are strongly coupled in a highly non-linear manner (Wang et
al., 2011). Therefore new equation was extracted based on the relationship between
intensity bedload rate and hydraulic data where parameters α and
in terms of
Bed load Transport rate Tb(kg/s)
channel characteristics were evaluated quantitatively by nonlinear regression method.
10
y = 0.144x1.1
R² = 0.88
1
KRU1
KRU2
0.1
KRU3
KRU4
0.01
KRU5
A1
0.001
0.001
0.01
0.1
1
Discharge Q (m3/s)
10
Figure 4.25: Bedload rating curve along Kurau River
109
The nonlinear regression method was used to assess the relationship between
each independent variable and the bedload transport rate. The coefficients obtained
to produce a significant relationship between bedload transport and other parameters.
Partial R2 values were calculated for each variable included in the models. Based on
equation (3.7) several runs were performed with various initial settings and the
performance of the developed equation was analysed and calibrated for each run. The
best value estimated parameters are listed in Table 4.5. Table 4.6 shows the statistical
analysis of experimental data and correlation coefficient (R2).
Table 4.5: Parameter estimates of experimental data based on equation (3-14)
Parameter
m
n
i
h
Estimate
2.46×10-8
1.81×10-6
1.000
1.000
Std.
Error
0.000
0.000
0.000
0.000
95% Confidence Interval
Lower Bound Upper Bound
2.461×10-8
2.462×10-8
-1.201×10-5 1.564×10-5
1.000
1.000
1.000
1.000
Table 4.6: Statistical analysis of experimental data based on equation (3-14)
Source
Sum of Squares df
Mean Squares
Regression
0.000
4
0.000
Residual
0.000
32
0.000
Uncorrected Total 0.000
36
Corrected Total
0.000
35
Dependent variable: qb
a. R squared = 1 - (Residual Sum of Squares) / (Corrected Sum
of Squares) = 1.
Based on the first accurate analysis the value of n was rounded to 0.2, h=1
where simplify the final approximation equation, the value i=1.00 applied to the
equation. Equation (4-1) was entered as a base for the next run of nonlinear
regression with the new adjusted invariables. Table 4.7 shows the briefly parameter
110
estimate for coefficient and Table 4.8 shows that this equation is significant with the
R2 value of 0.948.
b m.q0.2 . .Dgr
s
0
Gs 1 .g.d503
(4-1)
Table 4.7: Parameter estimates of experimental data base on equation (4-1)
Parameter
Estimate
Std.
Error
m
3×10-8
0.000
95% Confidence Interval
Lower Bound
2.93×10-8
Upper Bound
3.06×10-8
Table 4.8: Statistical analysis of experimental data base on equation (4-1)
Source
Sum of Squares df
Mean Squares
Regression
0.000
4
0.000
Residual
0.000
32
0.000
Uncorrected Total 0.000
36
Corrected Total
0.000
35
Dependent variable: qb
a. R squared = 1 - (Residual Sum of Squares) / (Corrected Sum
of Squares) = 0.98.
The unit of parameters follow the SI unit. Therefore, the value of Tb was found
in the same scale of the other variables in SI unit (kg/s). The nonlinear equation was
Gs 1 .g.d503
derived from the analysis expressed in equation (4-2).
b 3108.q0.2 . .Dgr
s0
(4-2)
The predictive abilities of the NLR equation (4-2) are assessed through
validation the model by the set of data of the Kurau River of present study and
previous study (DID, 2009). The assessment of Equation (4-2) is shown in Table 4.9
with acceptable average discrepancy ratio of 1 ,and Figure 4.26 shows the best fitting
model of total data with acceptable R2= 0.89.
111
Table 4.9: Assessment of NLR equation
Data
No Data
Coefficient of Average
determination, Discrepancy ratio
(R2 )
(0.5<DR <0.2)
Present study
48
0.98
0.85
DID 2009
20
0.82
1.16
Total
60
0.90
1.00
predicted Tb (kg/s)~[Eq 4-2]
10
1
0.1
Present study
DID 2009
0.01
0.01
0.1
Measured Tb(kg/s)
1
10
Figure 4.26: Validation of NLR equation in Kurau River
4.6.3
Prediction of Bedload Transport in Kurau River by Genetic
Programming
Multiple sets of training, testing, and validation data were randomly selected
and numerous runs were performed with various model setting such as number of
generation and genes and depth of trees by the trial and error. From 69 available data
50% were used for training (present study) and 25 % were used for testing and 25 %
112
(DID, 2009) for validation. Consequently, the models were selected according to
statistical criteria such as R2, RMSE, and MAE.
The best relationship was selected from the optimum R2, RMSE and MAE for
each training, test and validation to prevent from over fitting of the model by
selecting the high R2 of the training. The following relationship was selected to
model the bedload transport:
Tb= 0.09427 Q + 35.81 S + 0.06682 Q (d50 + θ) - 38.02 Q S0 - 0.06172
(4-3)
where Tb is the bedload transport rate (kg/s), d50 median grain size (mm), S0 water
surface slope (m/m) and θ Shield's parameter. Figure 4.27 shows the expression of
genes for GP formulation.
113
Gene 1and base term
*
C
*
C
S
Q
*
Gene
*
C
+
Q
θ
d50
Gene
*
S
C
*
Gene
+
C
*
Q
*
C
S
C
Figure 4.27: Expression genes for GP formulation
The accuracy of the developed equation is examined by plotting the measured
versus predicted values of bedload rate for training, testing, and all data as shown in
Figure 4.28, Figure 4.29 and Figure 4.31, respectively. The values of R2, RMSE, and
MAE are equal to 0.96, 0.083 and 0.067, respectively, for training sets (Figure 4.28)
and 0.78, 0.159 and 0.099, respectively, for testing sets (Figure 4.29).
114
10
Predicted Tb (kg/s)
R²=0.96 RMSE=0.083
1
0.1
0.01
0.01
0.1
1
10
Measured Tb(kg/s)
Figure 4.28: Measured versus predicted values of Tb for the training data set.
The predictive abilities of the GP equation (4-3) were assessed through modle
validation using Kurau River data sets of the present study and previous study (DID,
2009). The measured versus predicted values of bedload rate for validation set is
illustrated in Figure 4.31. The values of R2, RMSE, and MAE for this data set were
obtained equal to 0.89, 0.110, and 0.082, respectively. The R2 is equal to 0.90 while
RMSE and MAE are equal to 0.116 and 0.080 respectively for all data sets (Figure
4.31). In fact, the evolved model has achieved higher accuracy for both testing and
validation sets in order to confirm that enough generalization obtained.
115
10
predicted Tb (kg/s)
R²=0.78 RMSE=0.159
1
0.1
0.01
0.01
0.1
1
10
Measured Tb(kg/s)
Figure 4.29: Measured versus predicted values of Tbfor testing data set.
10
predicted Tb (kg/s)
R²=0.89 RMSE=0.110
1
0.1
0.01
0.01
0.1
1
10
Measured Tb(kg/s)
Figure 4.30: Measured versus predicted values of Tb for validation data set.
116
10
predicted Tb (kg/s)~[Eq 4-3]
R²=0.90 RMSE=0.116
1
0.1
Present study
DID 2009
0.01
0.01
0.1
1
10
Measured Tb(kg/s)
Figure 4.31: Measured versus predicted values of Tb for all data set.
4.6.4
Combination of ANN and GP
The combination of GP and ANN was suggested for best prediction result for
predicting the sediment transport (Singh et al. (2007). The combination of GP and
ANN was performed for the modelling of bedload transport rate in Kurau River.
First the bedload transport rate was calculated using GP Equation (4-3), and
then the outcome was given as input to the ANN, which consisted of one input node,
one output node and 10 hidden layers. Figure 4.32 shows the test result in the form
of a scatter plot of predicted against measured bedload transport. The underlying
error measures are R2 = 0.92, RMSE = 0.11 kg/s. The results show the combination
of GP-ANN can be applied to provide predictions of bedload transport rate which
performed better than GP application. As an alternative, a neural network consisting
117
of the input of four variables (Q, S, d50, θ) and one output Tb was trained and
validated. For this purpose, the data were shuffled and divided in two parts; one part
of them was used in the learning process by random, the other part was used for the
verification. Often this can be done in more than one way by changing the percentage
of data for training process and verification. Finally from 69 available data 50% were
used for training and 25 % were used for testing and validation. The number of
neurons in the hidden layer was determined by calibration using several computer
run tests on random data sets.
10
predicted Tb (kg/s)
R²=0.92 RMSE=0.11
1
0.1
Present study
DID 2009
0.01
0.01
0.1
1
10
Measured Tb(kg/s)
Figure 4.32: Measured versus predicted values of Tb by GP-ANN
The best fit of the obtained and given data for bedload transport rate is shown
in Figure 4.33 to Figure 4.36 where the number of neurons in the hidden layer is 15.
The correlation of determination, root mean square error and mean absolute error of
118
training, testing and validation of modelling shows in Table 4.10. The result shows
the acceptable network obtain but not as well as GP.
Table 4.10: Summary of results of ANN
Data
Percentage of
R2
RMSE
MAE
total data
Training
50%
0.9
0.16
0.088
Testing
25%
0.81
0.16
0.013
Validation
25%
0.9
0.10
0.085
Total
100%
0.86
0.15
0.1
10
predicted Tb (kg/s)
R²=0.90 RMSE=0.16
1
0.1
0.01
0.01
0.1
1
10
Measured Tb(kg/s)
Figure 4.33: Measured versus predicted values of Tb by ANN for training data set
The outcome of the ANN was calibrated with GP and the result shows an
expected success with improving the R2, and the indicating errors (R2= 0.94,
119
RMSE=0.1 and MAE= 0.075). The plot scatter of measured against the predicted
bedload transport rate is shown in Figure 4.37.
The combined ANN-GP model results thus appear to be more acceptable than
the single ANN or GP models. The combination shows that the ANN first carries out
a good function approximation; thereby GP was made the search of an optimum
solution easier and improve the accuracy of the single ANN and GP results.
10
Predicted Tb (kg/s)
R²=0.81 RMSE=0.16
1
0.1
0.01
0.01
0.1
1
10
Measured Tb(kg/s)
Figure 4.34: Measured versus predicted values of Tb by ANN for testing data set
120
10
predicted Tb (kg/s)
R²=0.90 RMSE=0.1
1
0.1
0.01
0.01
0.1
1
10
Measured Tb(kg/s)
Figure 4.35: Measured versus predicted values of Tb by ANN for validation data set
10
predicted Tb (kg/s)
R²=0.86 RMSE=0.15
1
0.1
Present study
DID 2009
0.01
0.01
0.1
1
10
Measured Tb(kg/s)
Figure 4.36: Measured versus predicted values of Tb by ANN for total data set
121
10
predicted Tb (kg/s)
R²=0.95 RMSE=0.10
1
0.1
Present study
DID 2009
0.01
0.01
0.1
1
10
Measured Tb(kg/s)
Figure 4.37: Measured versus predicted values of Tb by ANN-GP
4.6.5
Comparison of Bedload Equations for Kurau River
Many measures for model evaluation have been documented in the literature of
the sediment transport application. Several conventional measures such as correlation
coefficient (r or R2), index of agreement (d), root mean squared error RMSE, and so
on, were critically reviewed by (Legates and McCabe, 1999), and suggested that it is
inappropriate to use only correlation coefficient for model evaluation. The authors
suggested a complete assessment of model performance should include at least one
‘goodness-of-fit’ or relative error measure like d and at least one absolute error
measure (e.g., RMSE or MAE) with additional supporting information. Accordingly,
two conventional evaluation criteria, RMSE (root mean square error) and U
(inequality coefficient), are used in the present study to measure the performances of
models based on training data and testing data.
122
RMSE provides a quantitative indication of the model absolute error in terms
of the units of the variable, with the characteristic that larger errors receive greater
attention than smaller ones. This characteristic can help eliminate approaches with
significant errors (Wu et al., 2008). The inequality coefficient (U) was used to
determine how accurate a bedload equation predicted the actual value of bedload
discharge in the Kurau River of similar bedload-transport conditions. The inequality
coefficient (U) is defined as:
U
2
1 n
n i 1 Tbo i
2
1 n
i 1 Tbp
i
n
rmse
1
2
1
2
(4-4)
where RMSE is the root-mean-square error, define as
2
n Tbo Tbp i
RSME i 1
n
MAE
n
i 1
1
2
(4-5)
Tboi Tbpi
(4-6)
n
where Tbi is the measured bed load rate, Tbo is the predicted bedload rate, i
denotes a given flow, and n is the number of flows. The scaling of the denominator is
such that U always falls between 0 and 1. If U = 0, then Tbi= Tbo and there is a perfect
fit. If U = 1, then Tbo Tbp and the equation lacks a predictive value. For the purpose
of this study, the GP, NLR methods can represent the measured data when U is very
small and closed in 0. For the Meyer-Peter and Muller, Rottner, Wong, Chang, Julien
and vanRijn equations, U near to 1.This demonstrates that the predicted value does
not fit the measured bedload (Table 4.11).
123
The results in Table 4.11 show that the observed transport data are not very
well predicted by the existing bedload transport formulae. Furthermore, the observed
transport data are best fitted with GP, ANN based and nonlinear regression functions.
Figure 4.38 shows the comparison of the bedload rating curve with different
equation and methods. Figure 4.39 demonstrates observed versus predicted transport
rate from Kurau River study sites, and indicates that, predicted values by GP, GPANN, ANN, ANN-GP and NLR methods are typically within an order of magnitude
of observed values. However the ANN-GP model shows a better performance with
0.95 as the correlation coefficient, but the function of NLR has the minimum errors
and is fundamental and not complex.
Table 4.11: Comparison of bedload transport equations for Kurau River
Models
Coefficient of Root mean
determination, square error
(R2)
(RMSE)
Mean
Absolute
error,
(MAE)
Inequality Equation
coefficient number
(U)
NLR
0.98
0.00
0.00
0.00
GP
0.90
0.083
0.08
0.07
(4-2)
(4-3)
ANN
0.86
0.15
0.10
0.08
-
ANN-GP
0.95
0.10
0.07
0.09
-
GP_ANN
0.92
0.11
0.07
0.08
-
Rottner
0.84
2.25
1.95
0.66
(3-2)
MPM
0.38
0.61
0.46
0.91
(3-1)
Wong
0.10
3.3
1.71
0.81
(3-5)
Chang
0.02
4.64
2.68
0.85
(3-3)
Julien
0.07
2.09
1.22
0.72
(3-4)
vanRijn
0.03
5.96
3.99
0.87
(3-6)
124
Calculated bedload Tb (kg/s)
Present study(R² = 0.89)
NLR (R² = 0.98)
GP (R² = 0.90)
Rottner (R² = 0.76)
MPM (R² = 0.35)
chang (R² = 0.22)
Julien (R² = 0.18)
Wong (R² = 0.19)
Van Rijn (R² =0.2)
10
1
0.1
0.01
0.01
0.1
1
10
Discharge Q ( mᵌ/s)
Figure 4.38: Comparison of bedload rating curve for Kurau River
predicted Tb (kg/s)
10
1
GP
0.1
GP-ANN
ANN
ANN-GP
NLR
0.01
0.01
0.1
1
10
Measured Tb(kg/s)
Figure 4.39: Comparisons of predicted and measured bedload rates for Kurau River
125
4.7
Development of Bedload Equation for Small Rivers (Kurau, Lui,
Semenyih)
Sediment transport in small streams is diverse and highly variable due to the
various characteristics of channel morphology. The hydraulic geometry of channels
in small rivers is affected by various parameters. Each channel section is in many
ways unique because it is influenced by its own particle history of flow conditions,
sediment transport and distribution of channel roughness elements, and management
activities, all of which should be considered in bedload transport estimation (Beschta
and Platts, 1986).
As shown in Figure 4.40, the bedload transport rate for these rivers has good
relation with discharge in power function. All these rivers can be represented by the
following relationship; Tb=0.164 Q1.314 with R2=0.926 where Tb is the bedload
transport rate (kg/s) and Q is the flow discharge (m3/s).
Bedload transport rateTb(kg/s)
10
y = 0.17x1.31
R² = 0.95
1
0.1
Present study (Kurau)
Ariffin 2004(Lui, Semenyih)
0.01
0.1
1
Discharge Q (m³/s)
Figure 4.40: Bedload rating curve for three rivers
126
10
4.7.1
Assessment of Existing Equations for Small Rivers (Kurau, Lui and
Semenyih)
The predicted bedload transport rates by Meyer-Peter and Muller (1948),
Rottner (1959), Chang (Cheng, 2002), Julien (2002), Wong and Parker (2006) and
vanRijn (1993) were compared with observed values with a log10 transformation
applied to all equations. A discrepancy ratio of 0.5-2.0 (0.5<DR <2.0) was used as a
criterion in the evaluation of the selected equations (Table 4.12). The results of the
comparisons between bedload transport predictions and measurements from the
study sites are shown in Figure 4.41. Based on the relationship between measured
and predicted values, the formula results were disconcerted, and the measured values
were overpredicted and underpredicted.
Table 4.12: Summary of bedload transport equations assessment for three rivers
Equation
No Data
Coefficient of
determination,
R2
Average
Discrepancy
ratio DR
Discrepancy ratio between
0.5 and 2
No data
%
MPM
136
0.35
0.10
1
0.68
Rottner
136
0.35
3.23
45
30.82
Chang
136
0.22
2.54
58
39.72
Wong
136
0.19
11.88
54
36.99
Julien
136
0.18
13.72
20
13.72
vanRijn
136
0.085
0.49
15
10.27
127
10
1.000
Predicted Tb(kg/s)
Rottner
Meyer-Peter and Muller
Predicted Tb (kg/s)
1
0.100
0.1
0.01
0.010
0.01
0.1
1
Measured Tb(kg/s)
10
0.001
wong
10
julien
100
Predicted Tb (kg/s)
10
Predicted Tb (kg/s)
0.01
0.1
1
Measured Tb (kg/s)
1
0.1
10
1
0.1
0.01
0.01
0.001
0.01
0.1
1
10
0.001
Measured Tb (kg/s)
10
10
10
VanRijn
Predicted Tb(kg/s)
Chang
Predicted Tb (kg/s)
0.01
0.1
1
Measured Tb (kg/s)
1
0.1
1
0.1
0.01
0.01
0.01
0.1
1
Measured Tb (kg/s)
0.01
10
0.1
1
Measured Tb(kg/s)
10
Figure 4.41: Performance of existing bedload transport formula in Kurau, Lui and Semenyih
rivers.
128
4.7.2
Nonlinear Regression Result for Small Rivers (Kurau, Lui and
Semenyih)
Based on the section 4.6.2 and the relationship between the variables, the
following function as same as a function for Kurau River is suggested for data of
small streams:
b m.qn . i .Dgr h
s
0
Gs 1 .g.d503
(4-7)
where the following hydraulic parameters were used in the regression analysis: S0,
water surface slope, θ, Shields parameter, q, stream discharge per unit width (water
discharge was calculated for each increment, and stream discharge was obtained by
summing the individual increments) Dgr, is dimensionless grain size.
Based on Equation (4-7), several runs were performed with various initial
settings for power and constant values, and the performance of the developed
equation was analysed for each run. The best values of estimated parameters are
listed in Table 4.13.
Table 4.13: Parameter estimates of experimental data based on equation (4-7)
Parameter Estimate
Std. Error
m
n
i
h
0.000
0.000
0.000
0.000
2.47E-8
0.001
1.001
0.998
95% Confidence Interval
Lower Bound Upper Bound
2.445E-8
2.503E-8
-0.002
0 .004
0.999
1.002
0.995
1.001
Based on the first accurate analysis, the value of n was rounded to 0.1, h = 1,
where the final approximation equation was simplified by applying the value i = 1.00
129
to the equation. Equation (4-8) was entered as a base for the second run of NLR with
the new adjusted invariables. Table 4.14 shows the brief parameter estimate for the
coefficient. Table 4.15 shows that this prediction is significant with the R2 value of
s
0.99.
b m.q0.1. .Dgr
0
Gs 1 .g.d503
(4-8)
Table 4.14: Parameter estimates of experimental data based on equation (4-8)
Parameter
m
Estimate
2.71E-8
Std.
Error
0.000
95% Confidence Interval
Lower Bound Upper Bound
2.699E-8
2.730E-8
Table 4.15: Statistical analysis of experimental data base on equation (4-7)
Source
Sum of Squares
Regression
0.000
Residual
0.000
Uncorrected Total
0.000
Corrected Total
0.000
df
4
160
164
Mean Squares
0.000
0.000
163
Dependent variable: qb
a. R squared = 1 - (Residual Sum of Squares) / (Corrected Sum
of Squares) = 0.995.
The unit of the parameters follow the SI unit. Therefore, the value of Tb was
found in the same scale as the other variables in SI unit (kg/s).
The nonlinear equation was derived from the analysis expressed in Equation
(4-9).
b 2.71108 q0.1. .Dgr
s
0
Gs 1 .g.d503
130
(4-9)
The predictive abilities of the NLR, Equation (4-9) were assessed by the total
data gathered from the Kurau, Lui, and Semenyih rivers. Figure 4.42 shows the best
fitting model of data by acceptable R2 = 0.99.
Predicted Tb (kg/s)~[Eq 4-9]
10
1
0.1
Present study (Kurau)
Ariffin 2004 (Lui, Semenyih)
0.01
0.01
0.1
1
10
Measured Tb(kg/s)
Figure 4.42: Measured versus predicted values of Tb for total data set modelled by NLR
4.7.3
Artificial Neural Network Results
It is well known that the bedload transport predictions are of higher accuracy
when more measured data are taken into consideration. The best configuration may
be determined by the trial and error method. For this purpose, the data were shuffled
and divided in two parts; one part of them was used in the learning process by
random, the other part was used for the verification. Also, the data from all rivers
were uniformly distributed among the training and test data sets. Often this can be
done in more than one way by changing the percentage of data for training process
and verification. Finally from 190 available data 60% were used for training and
131
40 % were used for testing and validation. The number of neurons in the hidden layer
was determined by calibration using several computer run tests on random data sets.
There is no generally accepted standard for evaluating model performance for
ANN model performance. The common procedure is the use of the coefficient of
determination R2, when evaluating the goodness of fit of models. The best fit of the
model obtained and given data for bedload transport rate is shown in Figure 4.43 to
Figure 4.46, where the number of neurons in the hidden layer is 15. Figure 4.46
shows the verification between the measured and estimated values for these new
patterns, which clearly show that the linear coefficient of correlation is very high
between the observed data and the values predicted through neural nets. The values
are 0.99 and 0.93 in training and testing. Overall, the linear coefficient of correlation
is 0.978.
10
Estimated bedload transport rate Tb(kg/s)
R²=0.99 RMSE=0.047
1
0.1
0.01
0.01
0.1
1
Measured bedload tranport rateTb(kg/s)
132
10
Figure 4.43: Measured versus predicted values of Tb by ANN for the training data set
10
Estimated bedload transport rate Tb(kg/s)
R²=0.93 RMSE=0.114
1
0.1
0.01
0.01
0.1
1
10
Measured bedload tranport rateTb(kg/s)
Figure 4.44: Measured versus predicted values of Tb by ANN for testing data set
Estimated bedload transport rate Tb(kg/s)
10
1
0.1
R²=0.95 RMSE=0.118
0.01
0.01
0.1
1
Measured bedload tranport rateTb(kg/s)
133
10
Figure 4.45: Measured versus predicted values of Tb by ANN for validation data set
10
Estimated bedload transport rate Tb(kg/s)
R²=0.97 RMSE=0.161
1
0.1
0.01
0.01
0.1
1
10
Measured bedload tranport rateTb(kg/s)
Figure 4.46: Measured versus predicted values of Tb by ANN with for total data set.
4.8
Sensitivity Analysis
Sensitivity analysis was carried out to identify the dominant parameters
influencing the bedload transport.
Table 4.16 shows the result of the sensitivity analysis for 5 parameters with
the reduced data set. In the process of the sensitivity analysis, the parameters were
excluded one by one from the list of input variables. Then, the parameter with the
least relative importance compared to all of the other parameters is extracted from
the model construction, based on the highest correlation coefficient. This procedure
is repeated for all parameters one by one. In the first stage, the least effective
parameter was determined to be P ((1-Gs).g.d503), since the highest correlation is
obtained when P is excluded from the input list. Therefore, in the second stage, P
134
was omitted, and the analysis repeated for the rest of the variables. In Table 4.15, the
results also are given for different hidden nodes, and it can be seen for getting better
results, increasing the number of hidden nodes is not necessary. In summary, the
parameters can be listed from the most effective to the least effective as follows: Q,
d50, θ, S0 and P.
Table 4.16: Sensitivity analysis results for parameters
Model
parameters
Hidden nod 5
Hidden node 10
Train
R2
Test
R2
Q,S,d50,θ,P
0.99
0.99
0.16
0.98
0.98
Q, S, d50, θ
0.98
0.97
0.18
0.99
S, d50, θ, P
0.97
0.93
0.177
Q, S, θ, P
0.99
0.97
Q, d50, θ, P
0.98
Q, d50, S, P
0.98
RMSE
Train Test RMS
R2
R2
E
Model with variables Q, S,d50, θ
Hidden node 15
Train
R2
Test
R2
RMSE
0.16
0.98
0.99
0.17
0.98
0.16
0.99
0.99
0.17
0.98
0.96
0.162
0.97
0.89
0.21
0.155
0.99
0.94
0.18
0.99
0.96
0.186
0.98
0.19
0.99
0.98
0.201
0.99
0.98
0.176
0.96
0.22
0.98
0.97
0.198
0.98
0.98
0.195
Model with variables Q, S, d50, θ
S, d50, θ
0.91
0.91
0.3
0.87
0.89
0.335
0.91
0.93
0.3
Q, S, θ
0.98
0.98
0.202
0.98
0.97
0.184
0.99
0.96
0.184
Q, S, d50
0.97
0.97
0.2
0.98
0.97
0.21
0.98
0.98
0.18
Q, d50, θ
0.98
0.98
0.196
0.99
0.98
0.176
0.99
0.98
0.174
Model with variables Q, d50, θ
Q, d50
0.98
0.98
0.205
0.98
0.98
0.194
0.98
0.97
0.194
Q, θ
0.98
0.97
0.206
0.99
0.97
0.185
0.97
0.97
0.194
d50, θ
0.88
0.94
0.3
0.92
0.87
0.31
0.93
0.89
0.29
Model with variables Q, d50
Q
0.92
0.94
0.203
0.92
0.94
0.199
0.97
0.94
0.202
d50
0.11
0.42
0.450
0.15
0.36
0.460
0.16
0.72
0.466
135
4.9
Genetic Programming Result
Multiple sets of training, testing, and validation data were randomly selected
and numerous runs were performed with various model setting such as number of
generation and genes and depth of trees by the trial and error. A GPTIPS run with the
following settings was performed: population size = 500, number of generations =
10, tournament size = 7 (with lexicographic selection pressure), Dmax = 3, Gmax =
4, Elitism = 0.01% of the population, function node set = (plus, minus, times,
protected). As same as Kurau River four input parameters as variable data, including
discharge (Q), water surface slope (s0), mean grain size (d50), and Shields parameter
for the initiation of motion (θ), as well as the bed load rate (Tb) as invariable data
were used to estimate the bedload transport rate, where
Tb = f (Q, S0, d50, θ)
(4-10)
The performance of the developed equation was analysed for each run.
Consequently, the best models were selected according to statistical criteria such
as R2, root mean square error (RMSE), and mean absolute error (MAE).
The best relationship was selected from the optimum R2 for each training, test,
and validation to prevent from over fitting of the model by selecting the high R2 of
the training. The following relationship was selected to model the bedload transport:
Tb= 0.2269 Q + 0.131d50 + 0.0606 θ - 0.6375Q S0 - 0.2514
(4-11)
where Tb is the bedload transport rate (kg/s), Q is discharge m3/s, θ is Shield's
parameter and S0 is water surface slope .
136
The precision of the developed equation is examined by plotting the measured
versus predicted values of bedload rate for training and testing. All of the data are
shown in Figure 4.47 to Figure 4.48. The values of R2, RMSE, and MAE are equal to
0.97, 0.079, and 0.063, respectively, for the training sets (Figure 4.47), and 0.90,
0.13, and 0.098, respectively, for the testing sets (Figure 4.48).
For all of the data sets, R2 = 0.93, RMSE = 0.11, and MAE = 0.085 (Figure
4.49). Figure 4.50 illustrates the measured versus predicted values of bedload rate
for the validation data set. The obtained values of R2, RMSE, and MAE for this data
set were equal to 0.92, 0.124, and 0.093, respectively. In fact, the evolved model
achieves high accuracy for both testing and validation sets in order to confirm that
enough generalization was obtained.
10
Estimated bedload transport rate Tb (kg/s)
R²=0.97 RMSE=0.08
1
0.1
0.01
0.01
0.1
1
Measured bedload transport rateTb(kg/s
10
Figure 4.47: Measured versus predicted values of Tb for the training data set.
137
Estimated bedload transport rate Tb (kg/s)
10
R²=0.90 RMSE=0.14
1
0.1
0.01
0.01
0.1
1
10
Measured bedload transport rate Tb(kg/s)
Figure 4.48: Measured versus predicted values of Tb for testing data set
10
Estimated bedload transport rate Tb (kg/s)
R²=0.93 RMSE=0.11
1
0.1
0.01
0.01
0.1
1
10
Measured bedload transport rateTb(kg/s
Figure 4.49: Measured versus predicted values of Tb for total dataset
138
10
Estimated bedload transport rate Tb (kg/s)
R²=0.92 RMSE=0.12
1
0.1
0.01
0.01
0.1
1
10
Measured bedload transport rateTb(kg/s)
Figure 4.50: Measured versus predicted values of Tb for validation dataset
4.9.1
Comparison of Bedload Equations for Small Streams
The results in Table 4.17 show that the observed bedload transport data do not
have a consistent relationship with the performances of the bedload transport
formulas; otherwise, the observed bedload transport data best fitted by the GP and
ANN estimates and the NLR function result. The predicted bedload transport rates
from the GP method, ANN, and NLR were compared to the observed values.
Comparison of the bedload rating curve for different formula and methods is shown
in Figure 4.51.
139
Table 4.17: Bedload equations assessment
Coefficient of
determination
R2
Root mean
square error
RMSE
Mean absolute
error
MAE
Inequality
coefficient
U
Equation
number
GP
0.93
0.12
0.09
0.11
(4-11)
NLR
0.99
0.00
0.00
0.00
(4-9)
ANN
0.97
0.16
0.11
0.09
-
MPM
0.35
0.94
0.76
0.83
(3-1)
Rottner
0.35
1.54
1.21
0.45
(3-2)
Chang
0.22
1.61
1.08
0.51
(3-3)
Wong
0.19
0.91
0.64
0.41
(3-5)
Julien
0.18
1.02
0.83
1.00
(3-4)
vanRijn
0.085
0.88
0.68
0.87
(3-6)
Models
Figure 4.52 provides the observed versus predicted transport rate of the small
rivers, and indicates that the predicted values by GP, ANN, and NLR are typically
within an order of magnitude of observed values. The ANN model actually shows a
better performance with a 0.97 coefficient of determination. A major advantage of
the GP and ANN approach to bedload transport modelling is the automatic ability of
the GP and ANN to select input variables that contribute beneficially to the model
and to ignore those that do not, and also the GP does not assume any a priori
functional form of the solution but in NLR, the model structure is specified in
advance (which is in general difficult to do) and the model coefficients are
determined.
140
Predicted Tb(kg/s)
Present Study (R=0.92)
GP (R² = 0.93)
NLR(R² = 0.88)
ANN(R² = 0.84)
Rottner (R² =0.83)
MPM (R² =0.48)
Chang (R² =0.18)
Julien(R² =0.14)
Wong (R² =0.13)
VanRijn(R² =0.06
10
1
0.1
0.01
0.01
0.1
1
Discharge Q( m3/s)
10
Figure 4.51: Comparison of bedload rating curve for small streams
Predicted Tb(kg/s)
10
1
0.1
NLR
GP
ANN
0.01
0.01
0.1
1
10
Measured Tb(kg/s)
Figure 4.52: Comparisons of predicted and measured bedload rates for small streams by
different models
141
5
CHAPTER 5
RIVER CONFLUENCE SEDIMENT TRANSPORT MODELLING
5.1
Introduction
Modelling river systems by using computers is a powerful tool for river
engineering, habitat evaluation and flood forecasting. Accordingly modifications can
be tested on the model before they are constructed.
As mentioned in site description Kurau River is important as main domestic
water supply and main sources for irrigating the paddy areas in some part of the state
of Perak. Human activity includes the recently railway construction, changes in land
use and river sand mining make changes to river morphology and perturbation in
river equilibrium. Changes in the sediment load affect the efficiency of reservoir as
most of the transported sediment in the river will be deposited in the reservoir and
this problem require the river management at the upstream of river such as
controlling the sediment transport and consideration changes in river morphology.
The different morphology and geometry in each section of the river provide the
different potential of sediment transport where need detail studies.
The Kurau sub basin is consisting of two main river tributaries namely Kurau
River and Ara River. These two rivers join together at Pondok Tanjung. River
channel confluence morphology needs to be studied because it is an important and
complex place due to rapid changes in sediment discharge, flow structure, and
channel morphology. The changes usually occur to accommodate the convergence of
sediment and water from combining tributaries.
142
Various alternative techniques have been developed to provide quantitative
predictions of the complexity of the flow movement and its interaction with its
boundaries. Modelling is one such technique.
In recent year multi-dimensional computer programs for computing several
different processes such as sediment transport, water quality, and water surface
profiles etc has been developed. These multi-dimensional programs may be twodimensional, three dimensional with hydrostatic pressure assumption, fully threedimensional. Two- and three-dimensional models are based on the detailed
topography survey, bed roughness data and boundary conditions such as water level
and discharge.
In this part of the study the sediment flow in Ara and Kurau confluence was
simulated by SSIIM, three-dimensional software to evaluate the changes in bedload
transport, bed morphology and bed material in channel confluence.
5.2
SSIIM
SSIIM is an abbreviation for Sediment Simulation In Intakes with Multiblock
option. The program is designed for use generally in research for hydraulic, river,
sedimentation and environmental engineering. It solves the Navier-Stokes equations
in a three-dimensional non-orthogonal grid, using the "k-ε" model for turbulence, the
control volume method with the SIMPLE algorithm and it solves the convectiondiffusion equation for several parameters, including sediments (Olsen, 2011).
143
The advantage of using SS
SIIM, comp
pared to othher CFD proograms is th
hat it can
model seddiment transport with a movable bed in a complex
c
geoometry. SSIIM can
compute time dependdent changes in bed and
d surface levels employy multiple sediment
s
sizes and can handle wetting andd drying off cells resultting in a chhanging grid
d (Olsen,
2011). Thiis makes the program ideal
i
for thee modelling to be done in this stud
dy.
5.3
ns
SSIIIM version
Therre are two different versions
v
of SSIIM: SS
SIIM1 and SSIIM2. The main
differencee between the
t two verrsions is th
hat SSIIM1 uses a strructured grid (cells
(nodes) arre arrangedd in rows and column
ns (Figure 5.1)) whille SSIIM2 uses an
unstructurred grid (ceells and nodes are nott arranged in rows annd columns (Figure
5.2)). In an
a unstructuured 3D gridd, each celll will have one index, it is not possible to
identifyingg of the grrid locationn by two in
ndex whichh is random
mly generatted. The
inflow andd outflow areas
a
are sppecified by the use of the graphiccal discharg
ge editor
while thiss editor doees not exist in SSIIM1 version. Also
A
in SSIIIM2 generaating and
connectingg multiple blocks
b
is poossible by the
t grid ediitor. The strructured griid editor
just workss on one bloock.
Fiigure 5.1: Strructured gridd
144
4
Figure 5.2: Unstructured grid
SSIIM 1 is easier to use, but cannot apply wetting and drying of cells (Olsen,
2011). The main strength of the unstructured version is capability of modelling
complex geometry and its algorithms for wetting and drying. For the simulations to
be done in this study, only SSIIM 2 will be used due to the complex geometry and
wetting and drying of cells. In the rest of this thesis, when the name SSIIM is used, it
is referring to the Windows version of SSIIM 2.
5.4
Theoretical Basis
Brief theoretical background of the model is discussed below. The SSIIM
program solves the Navier-Stokes equations with the k-epsilon model for velocity
and turbulence on a three-dimensional almost general non-orthogonal grid. A control
volume method is used for the power-law scheme or the second order upwind
scheme together with the discretization. The SIMPLE method is used for the pressure
coupling. The velocity field in the geometry obtains with an implicit solver. The
convection-diffusion equations for different sediment sizes are solved by using the
velocities.
145
5.4.1
Water Flow Calculation
The Navier-Stokes equations for turbulent flow are solved to obtain the water
velocity in a general three-dimensional geometry. The Navier-Stokes equations for
constant density and non-compressible flow can be modelled as follow:
Ui
Ui 1
Ui
Pij ui u j
t
xi xi
(5-1)
The left most term on the left side is transient term and the next term is
convective term. The first term on the right hand side is pressure term and the next
term on the right side of the equation is the Reynolds stress term. A turbulence model
is required for evaluating this term. The transient term is neglected in the default
algorithm in SSIIM. To include this term, time steps and a number of inner iterations
in the calculations, different data sets are used in the control file. For transient
calculations it is possible to give the water levels and discharges as input time series.
5.4.1.1 The k-ε turbulence model
The eddy viscosity concept with the k-ε turbulence model is introduced with
the Boussinesq approximation to model the Reynolds stress term:
U Ui
ui u j vT i
xi x j
2
k ij
3
(5-2)
The first term on the right side of the equation forms the diffusive term in the
Navier- Stokes equation. The second term is often neglected, but can be included in
SSIIM 1 by adding some data set in the control file. The third term on the right side
is incorporated into the pressure.
The eddy viscosity in the k-ε is as:
vT c
2
k
(5-3)
146
Turbulent kinetic energy k, defined by:
1
k ui u j
2
(5-4)
k is modelled as
k
k
vT k
U j
P
t
x j x j k x j k
(5-5)
where Pk is given by:
Pk vT
U j
xi
U j Ui
xi x j
(5-6)
The dissipation of k is denoted ε, and modelled as:
vT
2
U j
C 1 Pk C 2
t
x j xi k x j
k
k
(5-7)
In all above equations C's are different constants. The k- ε model is the default
turbulence model in SSIIM.
5.4.1.2 Wall laws
The default wall law in SSIIM for rough as is given by Schlichting (1979)
defined as:
U 1 30 y
ln
u x k ks
(5-8)
The shear velocity is denoted ux and k is a constant equal to 0.4. y is the
distance to the wall and the roughness, ks, is equivalent to a diameter of particles on
the bed.
147
5.4.2
Sediment Flow Calculation
Sediment transport is generally divided in bedload and suspended load. The
suspended load can be calculated with the convection-diffusion equation for the
sediment concentration, c
c
c
c c
U j
w
t
xj
z x j T x j
(5-9)
where w is the fall velocity of the sediment particles and Г diffusion coefficient,
which is taken from the k-εmodel.
vT
Sc
(5-10)
Where Sc is the Scmidth number, set to 1.0 as default in model, but different
value can be adopted in the model.
SSIIM calculates sediment transport by size fractions. Each fraction is
specified in the control file, where the diameter and fall velocity is given. A vertical
sediment concentration distribution according to the Hunter-Rouse Equation will
then be used. The Rouse number (Whipple, 2004) commands the mode of sediment
transport. It is the ratio of particle settling velocity to the shear velocity (rate of fall
versus strength of turbulence acting to suspend particles):
Rouse number
Bedload:
50% Suspended:
100% Suspended:
Wash Load:
#=
ws
; k = 0.4 (Von Karman’s constant)
ku*
ws
2.5
ku*
w
1.2 s 2.5
ku*
w
0.8 s 1.2
ku*
ws
0.8
ku*
148
Van Rijn (1984) formula is used in SSIIM for calculating the suspended load
for the equilibrium sediment concentration, cbed, close to the bed:
c
0.3
d
c
0.015
a s w g 0.1
2
w
1.5
Cbed
(5-11)
where d is the sediment particle diameter, a is a reference level set equal to the
roughness height, is the bed shear stress, c is the critical bed shear stress for
movement of sediment particles according to Shield’s curve, and s are water and
w
sediment density, is the viscosity of the water and g is the acceleration of gravity.
The empirical parameters in the equation (0.015, 1.5 and 0.3) may be changed by
using the some data set in the control file.
The bed load, qb, also can be calculated by using van Rijn’s formula:
c
c
0.053
0.1
0.3 s w g
D50
2
w
2.1
qb
1.5
D50
5.5
s w g
w
(5-12)
Graphical Interface
In the windows version of SSIIM's user interface, grids can be created,
discharges specified and simulations can be started for water flow or for water flow
with sediments. It is also possible to follow the simulations and to view the results
after a simulation. Different variables can be shown by choosing different sub-option
in the view option of the menu. The different views are Map graphics with contour
plots or vectors, Longitudinal or cross-sectional profiles, Grid Editor and Discharge
149
Editor. Some of the most important variables are velocity vectors, water level, bed
changes a sediment concentration. The results are shown as plots of the different
variables (Olsen, 2011). Figure 5.3 shows SSIIM's graphical interface. In this figure,
the interface is showing a map of Kurau- Ara influence, and the chosen variable is
bed level.
Figure 5.3: SSIIM graphical interface
5.6
Input Files
In general, a SSIM run starts by reading input files, or generating the grid using
the Grid Editor. After generation of the grid, the inflow and outflow should be
defined using the Discharge Editor. Then the data was saved in the Unstruc or
koordina files, before the computations are started and the results are viewed.
150
As an input for model four main things are needed as follow:
1. Geometry data of the hydraulic structure
2. Water inflow/outflow data
3. Sediment data
4. Different controlling parameters
To run the program a file called Control is necessary. Control file controls all
parameters. Most of the parameters used in the simulations are in the Control file.
This file include physical parameters like water level, discharge and friction factors,
also the other parameters like time step, number of iterations and parameters that
decides what kind of formulae to be used. SSIIM have default values for most of the
parameters, so for simple situations, the program can be run without a complicated
Control file.
Transient calculations run with parameters in a file called Timei. This file
contains parameters which can vary over time such as water level, discharge, and
sediment concentrations. All inputs and outputs of the SSIIM model are given in SI
units (Olsen, 2011).
The Control file is made with data sets, all the data sets such as F, G, W, S, I
which can be used are explained in the SSIIM manual (Olsen, 2011).
5.7
Output Files
The 'boogie' file is an intermediate file which shows a print-out of intermediate
results from the calculation. It shows parameters as average water velocity, water
151
depth and shear stress in the initialization. Trap efficiency and sediment grain size
distribution are also written in this file. If any error occurs during the run of program,
the explanation is written in 'boogie" before the program terminates.
After simulation when prescribed number of iterations have been calculated or
when the solution has converged, the results are written to 'result' file and 'bedres'
file. The result file stores the information about the water flow simulation. This
information includes velocities in three dimensions, k, ε, pressure, and fluxes. The
bedres file is written only after sediment simulation. It stores information about bed
roughness, grain size distribution, sediment thickness, and bedform height. SSIIM
can read the result and bedres files later to show all the graphical results from the
simulation (Olsen, 2011).
Figure 5.4 shows flowchart included the various files are used in each SSIIM
run. Most of the files are only used for special purposes and they are normally not
required. The program can also produce many of the input files. All the necessary
input files can be generated by the program for simpler cases.
152
unstruc
control
koordina
SSIIM2
result
geodata
timei
koomin
timeo
boogie
compres
interpol
interres
Figure 5.4: SSIIM flowchart (Olsen, 2011)
5.8
Making a Grid in SSIIM
The grid generation is a time consuming part of the numerical modelling
process. The grid generation has done by using three softwares: Gridmeister, Matlab
and SSIIM for this study.
The Gridmeister program usually applies to support the CFD and especially the
SSIIM user working in the field of hydraulic engineering with the structured grid
generation. The input data is the geometry data of Kurau and Ara confluence
boundary that represented by x-and y- coordinates. The geometry data was saved by
"DXF" format in a CAD program and used in gridmeister. The outputs are koordina
and a control file. The control file includes the correct grid information and koordina
file includes i and j that are the cells number in X and Y direction, X and Y the
coordinates of the cells and Z equal to zero (Figure 5.5).
153
Figure 5.5: Koordina file
After generating a 2D structure grid, the output files used in MATLAB
software for making a 3D unstructured grid. The koordina file and the field geometry
cross section were used in MATLAB for making a 3D surface grid by using the
TriscatterdInterp function. The format of output file was change for using in SSIIM
that named koosurf to generate the 3D mesh (Figure 5.6). Figure 5.7 shows a koosurf
file included i, j, X, Y, Z (bed), Z (water surface).
154
Ara
Kurau
Figure 5.6: 3D grid generation
Figure 5.7: Koosurf file
155
5.8.1
Grid Editor
When the koosurf file is present, the grid for the xy- plane of Kurau and Ara
confluence can be viewed in the graphical interface of SSIIM by choosing the add
block from koosurf in blocks menu. The program generates the grid in the vertical
direction according to the z-coordinates by selecting the 3D grid from Generate
menu. The grid can either be multiblock or the simpler version with only one block.
With the most recent wetting/drying algorithm, it may be more suitable to make a
single block of the geometry (Olsen, 2011).
5.8.2
Multiblock and One Block Grid
A multiblock grid is an unstructured grid made up of several structured grids
which are glued together. For the simulations of sediment flow in Ara and Kurau
river confluence, experiments have been made with both the two blocks and the one
block grids (Figure 5.8 and Figure 5.9).
For making grid with 2 blocks, one block was added by choosing the Add
block from koosurf in the Block menu. The next step was to make the grid 3D, this is
done by choosing Generate 3D grid in the interface. After having the grid the content
has written to the Unstruc file. This is done in the File option of the main menu. The
next step was reading Unstruc file by the new SSIIM window then the second block
was added from the Block menu. Then the blocks were glued together. The water
surface was first covered with blocks, and then the boxes were connected. In the end
there will be an unstructured grid covering the entire water body. The program then
generates the grid in the vertical direction according to the bed levels given in the
koosurf file. A three-dimensional multiblock grid for the given water body has then
been generated.
156
Block 2
Block 1
Ara River
Kurau River
70.0 m
Level 2
Block 2
Block 1
70.0 m
Level 2
Figure 5.8: Two block grid
157
Outblocked
Ara River
Outblocked
Kurau River
70.0 m
Level 1
Figure 5.9: One block grid
The location and magnitude of inflow and outflow is specified in discharge
editor. There can be several groups of inflows and outflows in the grid, but for
making continuity, total inflow discharges and total outflow discharge should be
equal to each other. The information about the grid, including the discharges was
stored in the Unstruc file by choosing the write unstruc from File menu.
158
For the simulations of sediment flow in river confluence two type grids (two
blocks and one block) was tested for equal situations and the conclusion was that the
simulation gave better results and converged faster for the grid with only one block.
A disadvantage of using two block grids was that the time needed for the simulation
will increase because of the extra boundaries.
The sum of all the water inflow and outflow in the geometry is shown in
Boogie file that start with the word "Cont:". This should be a very low value,
typically under 10-7. This value for simulation with 2 blocks increased by time but
with one block the value is acceptable. The solutions were diverged with increasing
Cont value by time or have not got reasonable results.
Table 5.1 shows some Cont value for one and 2 blocks simulation. Due to this,
only the one-block grid has been used for the simulations in this study.
Table 5.1: Comparison of Cont value for one and two block grid
Iteration
Cont value
One block
Two block
1
-2.28013164e-011
-3.09416937e-011
100
-4.34141612e-012
-5.91961575e+001
500
6.78315043e-012
1.66492505e+002
1000
-1.03997366e-012
2.22419433e+002
2000
-5.50826051e-012
1.91046643e+002
3000
-1.79767312e-012
1.90132543e+002
4800
-7.26496641e-012
2.17529220e+002
159
During the grid generation, some considerations have been taken to ensure a
well functioning grid that will be given stable calculations. The grid cells are almost
orthogonal. Nonorthogonality makes the simulation to be slow down. For decreasing
false diffusion, the grid lines are aligned with the direction of the flow, especially
close to inflow and outflow areas. The distortion ratio (the dimension of a grid cell in
one direction divided by the dimension of the cell in the other direction) is not too
big. The size of a grid cell does not differ too much from the size of the neighbouring
cells. This could lead to physically impossible results (Olsen, 2011).
For this purpose the grid sensitivity has done by choosing a different size of
the grid cell. The best results have achieved by the grid size of 0.75×0.75 m for each
cell. The grid for Ara-Kurau river confluence has about 64138 cells at the start of the
calculations. The grid has up to 11 cells in the vertical direction depending on the
depth of the specific location in the river confluence. The number of cells may
decrease during calculations due to wetting and drying algorithm. If the water level
goes down, or if the bed level goes up due to sedimentation, there might be a
decrease of cells in the vertical direction. As cells dry up there will also be a decrease
of cells in the xy-plane.
5.9
Sediment Flow Simulation in Confluence of Kurau and Ara River
The simulation of river channel confluence is one of the most complex
situations that can be modelled in SSIIM. This is an unsteady water flow
computation with sediments, moving surface, and moving bed. It also has to include
the wetting and drying of cells, as the flow is changed and many cells will dry up due
to sedimentation. The simulation carried out at Ara and Kurau river confluence that
160
is located between 691915.7559 and 691874.4946 North Latitude and 554178.7400
and 554212.3463 East Longitude in Zone 47 in UTM coordinate system with
approximately 141.5 m in length and 111.5 m in width. The coordinate was changed
with deducting 691800 from latitude and 554000 from longitude coordinate for easy
using in software.
5.9.1
Characteristics of Kurau -Ara Confluence
The field site for this study is the confluence of the Kurau and Ara rivers in
Pondok Tanjung at the upstream of the Bukit Merah reservoir in Perak (Figure 3.2).
The two confluent channels have different widths and different bed height. The Ara
width is around 28 m and Kurau around 23 meters and the bed of Ara is
approximately 0.45 m higher than the bed of the Kurau channel and goes through the
confluence at an angle of 135o. The width of confluence at its apex is 36 m reducing
to 26 m in width further downstream. The confluence is a sand bed junction and this
sandy bed making the most of the likelihood of active sediment movement and
change in bed morphology as flow stage varied (Figure 5.10).
The morphology of this confluence with discordant bed is dominated by
avalanche slopes, a central scour, and a bar formed below the downstream junction
corner (Figure 5.11). The deepest zone within the two confluent channels is an
extension of the Kurau channel thalweg in to the confluence. The finest bed
sediments (d50 = 0.5 mm) are found the left side of the Ara mouth while the coarsest
bed sediments (d50 = 1.5 mm) are located on downstream from the region of
maximum scour. The two confluent channels have same grain size distributions and
sediment pattern is moderately sorted with a d50 of 1 mm.
161
Kurau
Ara
Lateral bar
Figure 5.10: View of the confluence of the Kurau and Ara rivers
16.4
260
16.2
240
16
Lateral bar
15.8
Ara
220
Latitude N
15.6
200
15.4
180
Scour zone
15.2
160
15
140
14.8
120
14.6
Kurau
80
100
120
140
160
Longitude E
180
200
220
Figure 5.11: Contour bed level of the Kurau-Ara confluence
162
14.4
Elevation (m)
5.9.2
Input Data
SSIIM needs input data for sediment sizes, sediment fall velocities, and
sediment concentrations. For the simulation, eight sediment sizes of bedload samples
in Kurau and Ara River were used. Figure 5.12 to Figure 5.14 shows the distribution
grain size of bedload sample in Kurau and Ara River. The fall velocities (Vanoni,
2006) and sediment sizes are given in Table 5.2.
The concentrations were calculated from the percentages of each sediment size
for the given water discharge and its sediment load. The calculation made and
concentration value for different flow is explained in appendix. The sediment
concentrations results are given as cubic meters sediments per cubic meters water.
100
90
Percentage Passing (%)
80
70
60
50
40
30
20
10
D50=1 mm
0
0.01
0.1
1
10
100
Particle size (mm)
Figure 5.12: Sediment distribution size of bedload in Kurau River branch
163
100
Percentage Passing (%)
90
80
70
60
50
40
30
20
10
D50=1.1 mm
0
0.01
0.1
1
10
Particle size (mm)
100
Figure 5.13: Sediment distribution size of bedload in Ara River
100
90
Percentage Passing (%)
80
70
60
50
40
30
20
10
D50=1.8 mm
0
0.01
0.1
1
10
100
Particle size (mm)
Figure 5.14: Sediment distribution size of bedload in main Kurau River
164
Table 5.2: Sediment characteristics
5.9.3
No
dx
Size (mm)
Fall velocity
(ωs) (m/s)
1
d90
3.67
0.29
2
d85
2.84
0.25
3
d75
2.22
0.21
4
d65
1.37
0.18
5
d50
1
0.14
6
d25
0.7
0.085
7
d15
0.47
0.068
8
d10
0.38
0.055
Input Files
The most important input files were prepared for the sediment flow simulation
is Control and Timei file. The control file was made after several tests concluded in
what algorithms would give a good and stable solution. The timei file was prepared
by the chosen values for discharges, water levels and sediment concentrations.
In addition to these files, the Unstruc file included the grid information has
been used in the simulations. The information about cells outside of the grid has been
stored in a file called koordina. This file is also used in case new cells become wet.
5.9.3.1 Control File
Some parts of the data set in the control file are explained in this section. For
more details on the data sets, see the SSIIM manual (Olsen, 2011). The simulation
uses van Rijn's formula to calculate the concentrations at the bed. This is given in the
F 10 data set. The F 6 data set gives the coefficients for this formula. This data set
has been used to calibrate the model to give a total bed change as close to the
165
measured amount as possible. The roughness in the rivers were measured and used as
input for the simulations. The value is set to 0.063 metres in the F 16 data set. In the
F 33 data set the time step of the simulation is set to 30 seconds, with 10 inner
iterations per time step. This simulation is a transient sediment computation with free
water surface, specified on the F 36 and F 37 data sets. Since wetting and drying may
happen for this simulation, an algorithm that changes the shape of the grid cells close
to the boundaries is necessary, this is given in the F 102 data set. Algorithms that
help to stabilise triangle cells are also included in data sets F 113 and F 235. The
chosen sediment sizes and their fall velocities are given in the S data sets. The N data
set gives the percentage size fraction of the bed sediments which is taken from
different samples for different flow discharges.
G 13 data set was used for outblocking option in this study. Two parts of Ara
and Kurau confluence were blocked out for using 1 block to ensure getting better
results (Figure 5.9). The sediment flow simulation uses a 30 second time step. To
simulate 3 days, 86400 iterations are necessary. This is given in the K 1 data set in
the control file. The control file was used in this study is shown in Figure 5.15.
5.9.3.2 Timei File
The timei file used in this simulation gives the concentrations of sediment
loading in Kurau and Ara River. The timei file is shown in Figure 5.16. The data
given in the file are upstream water levels, and downstream water levels, and
different water discharge. The file specifies the concentrations of the 8 sediment
groups for both Kurau and Ara rivers given in the control file.
166
Figure 5.15: Control file used in SSIIM modelling
167
Figure 5.16: Time File
168
5.9.4
Numerical Algorithms
Several numerical algorithms were chosen to be able to model the sediment
flow of Kurau and Ara river confluence simulation. The combination of algorithms
in the control files leads to a successful simulation. The simulation may give
different result or may lead to crashing by choosing other algorithms. The algorithms
were used in this study describe as below:
Data set F 36 7 was used for the computation of the vertical elevation of the
water surface. The data set reads one integer. If the integer is 7, as it is in this
simulation, the water surface is updated based on the pressure in only its
neighbouring cells.
Data set F 64 was used for the grid generation to generate the grid lines in the
longitudinal and lateral direction. The algorithm used in these simulations is F 64
11that is the most tested options for sediment transport computations in rivers. The
algorithm gives a body fitted grid with priority to close to the bed. While most of
sediments are transported close to the bed, the hexahedral cells will give better
results in sediment computations than tetrahedral cells would.
The F 102 1 algorithm is also employed for the sediment flow simulation. This
algorithm is used to change the shape of the grid cells close to the boundary for the
wetting and drying simulations.
The F 113 data set was implemented to stabilize the solution in the shallow
areas close to the side walls. The algorithm used in these simulations is the F 113 4.
169
The algorithm uses second-order interpolation instead of third-order interpolations
for pressure gradients.
The F 222 data set invokes algorithms which prevents the downstream bed
level to rise to a height which may block the outflow.
The F 233 data set invokes an algorithm that, instead of using the pressure in
the surface cells to compute the water level, uses a depth-averaged pressure field.
The F 235 data set was used to improve the stability in triangular cells. F 235
10 which is used in this case, is the most successful of these algorithms. This option
invokes an algorithm that gives extra relaxation in the triangular cells.
The F 244 data set was implemented to reduce instabilities in triangular cells.
Two relaxation factors used in the algorithms, the first floating point is used for the
velocities in the cells, in the F235 10 algorithms. The second integer is used for the
fluxes on the cell surfaces, if F 235 is between 8 and 23.
5.9.5
Sensitivity Analysis
Sensitivity analysis was performed to determine the influence of parameters on
predicting velocity, water level and bed elevation for the confluence. A sensitivity
analysis was conducted to provide parameter estimation guidance for the calibration.
Large numbers of parameters were tested, from grid size, turbulence models,
discretization schemes, values for critical bed shear stress parameters, parameters in
170
bed form and roughness prediction formulas, and empirical coefficients in the
sediment transport capacity formula etc. It is not possible to go into further detail due
to dearth of space. The summary of obtained mentioned parameters after sensitivity
analysis that was used to calibrate the model is shown in Table 5.4.
5.9.6
Calibration and Validation
5.9.6.1 Model Calibration
SSIIM model first is tested with sensitivity analysis and calibrated using field
data from one time and then validated with a different set of data in different time.
Calibration of SSIIM was primarily accomplished by adjusting model parameter
until a reasonable match was found between model predictions and field data.
Validation for the model was carried out by comparing measured, water level and
bed level with different discharges to the prediction average velocity, water level and
bed level by model.
Calibration of SSIIM was performed using the flow and bed elevation data in
April 2012. In order to calibrate flow several roughness coefficient and relaxation
factor for the tree velocity equations, the pressure correction equation and k and e
equation are adjusted to gain the correct observe velocity and water level, meanwhile
for suspended and bedload sediment calibration, parameter of sediment transport
response need to be adjusted to fit with the observed sediment data. Coefficients in
van Rijn's formula for bedload and suspended sediment transport were adjusted to
gain a good fit with the observed sediment transport. Also several algorithms as
mentioned in section 5.9.4 were used in a SSIIM program for obtaining the correct
result from the simulation.
171
The vanRijn's bedload transport parameter was calibrated for different
discharge flow and bedload transport rate with the value of calculating bedload
transport from genetic programming derived equation for Kurau River in section 4.9.
The estimate of bedload transport rate with GP formula and van Rijn formula are
shown in Figure 5.17 and Table 5.3.
The parameters of the van Rijn formula were determined for calibration
follows:
c
c
420
0.1
g
D500.5 s w2
w
1.115
qb
D50
s w g
w
(5-13)
100.000
Eq. 4.11
Van Rijn formula
Bed load transport rate Tb (kg/s)
1.5
10.000
1.000
0.100
0.1
1
10
Discharge Q(m³/s)
Figure 5.17: Comparison of Bedload transport rate
172
100
Table 5.3: Comparison of Bedload transport rate
Bedload transport rate (kg/s)
Discharge
(m3/s)
GP formula
van Raijn' formula
4
0.781
0.886
-0.104
5
1.007
1.065
-0.058
6
1.232
1.248
-0.016
7
1.457
1.433
0.024
8
1.683
1.621
0.062
9
1.908
1.811
0.097
10
2.134
2.004
0.130
11
2.356
2.233
0.123
12
2.582
2.432
0.150
14
3.009
3.066
-0.057
15
3.235
3.295
-0.061
18
3.895
3.960
-0.065
20
4.346
4.217
0.129
23
5.013
4.880
0.133
Difference
The parameters after calibration are summarized in Table 5.4. The simulated
flow average velocity, water level and bed elevation were compared with observed
data and coefficient of determination was calculated for measured and simulated
water level and bed level as shown in Figure 5.18 to Figure 5.30.
173
Table 5.4: Parameter calibrated in SSIIM
No Description
1
Roughness coefficient (R)
0.063
2
Schumidt's coefficient
1
3
Relaxation factor for horizontal velocity ( u)
0.8
4
Relaxation factor for longitudinal velocity (v)
0.8
5
Relaxation factor for vertical velocity (w)
0.8
6
Relaxation factor for pressure correction equation
0.02
7
Relaxation factor for k correction equation
0.05
8
Relaxation factor for e correction equation
0.05
9
Parameters to decrease the eddy-viscosity as a function of the
water density gradients and the Richardson number
10
Relaxation factors used in the algorithms to reduce instabilities
in triangular cells for velocity and fluxes on the cell surface
-0.5
10.0
-1.5
3.33
0.5
0.8
11
Parameter in Brook’s formula for reduction of the critical
sediment particle shear stress when the bed slopes
12
Relaxation factor for second order interpolation of bed
concentration
Coefficient for van Rijn' formula for bed concentration
13
14
Coefficient for van Rijn' formula for bed load sediment
transport
174
1.23
0.78
0.2
0.5
9
0.3
0.02
420
1.115
-0.5
1.5
1.2
Measured
Velocity (m/s)
1
Simulated
0.8
0.6
0.4
0.2
0
0
5
10
15
Distance (m)
20
25
30
Figure 5.18: Measured and simulated average velocity in Ara mouth
0.7
Measured
0.6
Simulated
Velocity (m/s)
0.5
0.4
0.3
0.2
0.1
0
0
5
10
15
Distance (m)
20
25
Figure 5.19: Measured and simulated average velocity in Kurau mouth
175
(a)
Depth (m)
0.8
0.6
0.4
0.2
0
5
0
100
1
15
20
25
30
Distancce (m)
(b)
Figure 5.20:
5
Compaarison cross-ssectional bed
d level and avverage velocity a) simulaated b)
Measuured, April 2012 at Ara River
R
176
6
1.5
Depth (m)
(aa)
1
0.5
0
0
5
10
1
15
20
Distance (m)
(
(b)
Figure 5.21:
5
Compaarison cross-ssectional bed
d level and avverage velocity a) simulaated b)
Measurred, April 2012 at Kurau River
177
7
Ara
A'
Legend
A
16.466812
16.133136
15.799461
15.465785
15.132109
14.798434
14.464758
Kurau
90.0 m
Bed levels, min= 14.465 m, max= 16.467 m
Figure 5.22: Measured bed level (April 2012)
Ara
RSK7
RSK6
RSK5
RSK4
RSK3
RSK2
RSK1
RSA
Legend
16.460000
16.130000
15.800000
15.450000
15.130000
14.800000
14.450000
Kurau
90.0 m
Bed levels, min= 14.450 m, max= 16.460 m
Figure 5.23: Simulated contour bed level
178
16.5
16.5
RSK1
16.0
Elevation(m)
Elevation(m)
RSA
15.5
15.0
Measured BL
Simulated BL
14.5
0
10
Distance (m)
20
15.5
15.0
Measured BL
Simulated BL
14.5
0
30
10
30
17.0
RSK2
Elevation(m)
Elevation(m)
15.5
15.0
14.5
30
15.5
15.0
Measured BL
Simulated BL
14.0
14.0
10Distance20(m)
16.0
14.5
Measured BL
Simulated BL
0
RSK3
16.5
16.0
0
40
16.5
16.5
10
Distance (m)
20
30
RSK5
RSK4
16.0
Elevation(m)
16.0
15.5
15.0
14.5
0
10
20
15.5
15.0
14.5
Measured BL
Simulated BL
14.0
Measured BL
Simulated BL
14.0
30
0
10
Distance (m)
16.5
RSK6
Elevation(m)
16.0
15.5
15.0
14.5
20
30
Distance (m)
16.5
Elevation(m)
20
Distance (m)
16.5
Elevation(m)
16.0
Measured BL
Simulated BL
RSK7
16.0
15.5
15.0
14.5
14.0
Measured BL
Simulated BL
14.0
0
10
20
30
0
Distance (m)
10
20
Distance (m)
30
40
Figure 5.24: Comparison cross sectional bed level in different condition of Ara and Kurau
confluence (Measured BL, April 2012)
179
16.0
15.8
15.6
Elevation(m)
15.4
15.2
15.0
14.8
14.6
14.4
Measured BL
Simulated BL
14.2
14.0
0
10
20
30
40
50
60
70
Distance (m)
Figure 5.25: Comparison of measured and simulated Longitudinal bed level at downstream
of confluence (AA') (Measured BL, April 2012)
Simulated bed level(m)
16.0
R² = 0.98
15.5
15.0
14.5
14.0
14.0
14.5
15.0
15.5
16.0
Measured bed level (m)
Figure 5.26: Scatter plot of measured bed level against simulated bed level (April 2012)
180
16.44
16.42
16.40
Elevation(m)
16.38
16.36
16.34
16.32
16.30
16.28
16.26
16.24
Measured wl
16.22
Simulated wl
16.20
0
10
20
30
40
50
60
70
Distance (m)
Figure 5.27: Comparison of measured and simulated water level at downstream of
confluence (AA') (April 2012)
Simulated water level (m)
16.5
R² = 0.97
16.4
16.3
16.2
16.2
16.3
16.4
Measured water level (m)
16.5
Figure 5.28: Scatter plot of measured water level against simulated water level (April 2012)
181
Legend
16.580581
16.528214
16.475847
16.423481
16.371114
16.318747
16.266380
80.0 m
Water levels, min= 16.27 m, max= 16.58 m
Figure 5.29: Measured water level (April 2012)
Legend
16.563013
16.515460
16.467906
16.420353
16.372799
16.325246
16.277692
80.0 m
Water levels, min= 16.28 m, max= 16.56 m
Figure 5.30: Simulated water level
182
5.9.6.2 Model Validation
Sediment transport process was validated for the Ara- Kurau confluence. The
simulation SSIIM was carried using surveyed cross section and flow discharge
measurement for three events: low flow, moderate flow and high flow at the
confluence. As part of the validation, measured bed level profiles, water levels
during July to October were compared to the prediction bed level profiles and water
levels by SSIIM model (Table 5.5 to Table 5.7 and Figure 5.31to Figure 5.33).
Table 5.5: Comparisons of water and bed level for Q=15 m3/s (19 July 2012)
Location
Water level (m)
Observed
Predict
Bed level (m)
Difference
Observed
Predict
Difference
RSA
16.45
16.46
-0.02
15.73
15.66
0.07
RSK1
16.44
16.47
-0.03
14.86
14.88
-0.02
RSK2
16.42
16.46
-0.04463
14.58
14.39
0.187
RSK3
16.40
16.46
-0.05393
14.47
14.64
-0.166
RSK4
16.38
16.45
-0.06612
14.72
14.63
0.089
RSK5
16.36
16.43
-0.07151
14.72
14.73
-0.004
RSK6
16.33
16.42
-0.08551
14.81
15.13
-0.328
Table 5.6: Comparisons of water and bed level for Q=43 m3/s (27 Sept 2012)
Location
Water level (m)
Bed level (m)
RSA
Observed
17.300
Predict
17.290
Difference
0.010
Observed
15.560
Predict
15.520
RSK1
17.290
17.271
0.019
14.970
14.920
0.050
RSK2
17.213
17.260
-0.047
14.516
14.478
0.038
RSK3
17.207
17.246
-0.039
14.468
14.315
0.153
RSK4
17.193
17.210
-0.017
14.584
14.512
0.072
RSK5
17.181
17.194
-0.013
14.465
14.507
-0.042
RSK6
17.177
17.144
0.033
14.459
14.615
-0.155
183
Difference
0.040
18.00
Elevation (m)
17.00
16.00
15.00
14.00
Water level
Bed level
Observed water level
Observed bed level
13.00
0
10
20
30
40
50
60
70
Distance (m)
Figure 5.31: Comparisons of water and bed level (AA') for Q=15 m3/s (19 July 2012)
18.00
Elevation (m)
17.00
16.00
15.00
14.00
Water level
Bed level
Observed water level
Observed bed level
13.00
0
10
20
30
40
50
60
70
Distance (m)
Figure 5.32: Comparisons of water and bed level (AA') for Q=15 m3/s (20 July 2012)
184
Table 5.7: Comparisons of water and bed level for Q=11 m3/s (8 Oct 2012)
Location
Water level (m)
Bed level (m)
RSA
Observed
16.430
Predict
16.460
Difference
-0.030
Observed
15.710
Predict
15.660
Difference
0.050
RSK1
16.421
16.460
-0.039
14.921
14.880
0.041
RSK2
16.410
16.449
-0.038
14.460
14.560
-0.100
RSK3
16.396
16.442
-0.046
14.456
14.424
0.032
RSK4
16.360
16.430
-0.070
14.560
14.651
-0.091
RSK5
16.344
16.410
-0.066
14.814
14.686
0.128
RSK6
16.310
16.400
-0.090
14.850
14.737
0.113
18.00
Elevation (m)
17.00
16.00
15.00
14.00
Water level
Bed level
Observed water level
Observed bed level
13.00
0
10
20
30
40
50
60
70
Distance (m)
Figure 5.33: Comparisons of water and bed level (AA') for Q=11 m3/s (8 Oct 2012)
185
5.9.7
Short Term Changes in Bedload Transport, Bed Morphology and Bed
Material Characteristics
The morphology and sedimentology of sand bed river channel confluences are
complex and subject to important temporal variations caused by the different
hydrological responses of the two incoming rivers.
Short term variation in bed morphology and spatial patterns of bed material
was documented in detail over a period of 7 days. During this short event water level
varied from 1.7 m to 2.8 m of bankfull depth, and the momentum ratio Mr =
(ρQU)Ara /( ρQU)Kurau, where Q is discharge, and U is the section averaged velocity in
each channel ranged from 0.8 to 2.6 (Table 5.8).
The simulation was started with the low flows with Mr < 1 during the first 2
days and then followed a high flow event when the confluence was characterized by
a high momentum ratio. For analysing the bed change and characteristic of sediment
patterns, result of flow and bedload transport from six of the flow stage with Mr>1
and Mr<1 will be presented. This simulation is representative of morphological
change during an event in Kurau and Ara confluence at the end of September and
first week of October data collection. The morphology changes will be shown in 8
cross sections, two at Ara and Kurau mouth (RSA, RSK1) and the other six cross
sections (RSK2, RSK3, RSK4, RSK5, RSK6, RSK7) along the main Kurau at the
downstream of confluence (Figure 5.34).
186
Table 5.8: Hydraulic condition during an event at Kurau _Ara confluence
a
Water Level, m
1.7
1.85
2.35
2.8
2.5
2.2
1.8
Flow discharge, m3/s
Kurau
5
8
14
15
12
10
7
Ara
4
7
17
28
23
15
6
Flow Depth, m
Flow Velocity, m/s
Kurau
0.45
0.71
1.01
1.05
0.92
0.82
0.61
Kurau
0.39
0.49
0.6
0.62
0.57
0.53
0.5
Ara
0.42
0.5
0.93
1.17
1.1
0.86
0.5
aMain Kurau
b Mr= (Q.U.ρ) Ara/ (Q.U.ρ) Kurau
Figure 5.34: Morphology of Kuaru -Ara confluence
187
Ara
0.43
0.5
0.65
0.85
0.75
0.62
0.43
Mrb
0.8
0.9
1.3
2.6
2.5
1.7
0.7
5.9.7.1 Morphological Changes
The confluence morphology during the first step (Q=9 to Q=15 m3/s) was
drastically modified. The bed morphology at Q=15 m3/s is shown in Figure 5.37,
cross sectionals change are shown in Figure 5.39 and longitudinal change in Ara and
Kurau are shown in Figure 5.35 and Figure 5.36. The valance face for both of Kurau
and Ara is illustrated in the longitudinal profile of confluence. Low flow condition
(Mr<1), privileged the expansion of the Ara mouth bar over 4 meters and extended
by ~ 2m into the confluence and constrained the principal flow at the confluence in
the middle of the channel, as indicated by expansion of the deepest zone of the bed
(Figure 5.38). The angel of the avalanche face changed from 50 o to 30o at the end of
the Ara mouth bar. During this period bed erosion occurred on the right hand of
main Kurau in lateral bar and along the channels in downstream of confluence
(RSK3, RSK4). This erosion was followed by a deposition phase at the downstream
of the lateral bar in the secondary bar (RSK5, RSK6, RSK7) and at the left hand of
confluence downstream.
188
16.2
16.0
15.8
Elevation(m)
15.6
15.4
15.2
15.0
14.8
14.6
14.4
Measured BL April 2012
Q= 15 (mᵌ/s)
14.2
14.0
0
20
40
60
80
100
120
140
160
Distance (m)
Figure 5.35: Longitudinal bed change profile of Ara and downstream of confluence after
Q=15m3/s
15.8
15.6
Elevation(m)
15.4
15.2
15.0
14.8
14.6
14.4
Measured BL April 2012
14.2
Q= 15 (mᵌ/s)
14.0
0
20
40
60
80
100
120
140
160
Distance (m)
Figure 5.36: Longitudinal bed change profile of Kurau and downstream of confluence after
Q=15m3/s
189
Ara
Legend
16
6.777551
16
6.364626
15
5.951700
15
5.538775
15
5.125850
14
4.712925
14
4.360000
Kurau
u
80.0 m
Bed levells, min= 14.3
360 m, max= 16.778 m
Figure 5.37: Bed morph
hology after Q=15
Q
m3/s
Ara
Kurau
Figure 5.38: Change in bed morpphology afterr Q=15m3/s. Zone of erossion and deposition
m white as deeposition to black
b
as
during eaach period arre illustrated with colour change from
erosion.
190
0
16.5
16.5
RSK1
16
Elevation(m)
Elevation(m)
RSA
15.5
15
Measured
Q= 15 (mᵌ/s)
14.5
0
10
20
16.0
15.5
15.0
Measured
Q= 15 (mᵌ/s)
14.5
0
30
10
Distance (m)
16.5
16.5
RSK2
Elevation(m)
Elevation(m)
16
15.5
15
14.5
0
10
20
Distance (m)
30
15.5
15
Measured
Q= 15 (mᵌ/s)
14
0
10
Distance (m)
20
30
16.5
RSK4
RSK5
Elevation(m)
16
Elevation(m)
16
40
16.5
15.5
15
14.5
0
10
Distance (m)
16.5
20
15.5
15
Measured
Q= 15 (mᵌ/s)
14
0
30
16.5
Elevation(m)
16
15.5
15
14.5
10
20
30
20
RSK7
16
15.5
15
14.5
Measured
Q= 15 (mᵌ/s)
14
10
Distance (m)
RSK6
0
16
14.5
Measured
Q= 15 (mᵌ/s)
14
Elevation(m)
30
RSK3
14.5
Measured
Q= 15 (mᵌ/s)
14
20
Distance (m)
Measured
Q= 15 (mᵌ/s)
14
0
30
Distance (m)
10
Distance (m)
20
30
Figure 5.39: Channel cross section profiles, Q=15m3/s (Measured bed level April 2012)
191
The erosion in downstream of confluence continued with increasing flow and
changing the momentum ration from Mr<1 to Mr>1. The bed morphology after this
event is shown in Figure 5.40. During this period deposition occurred in the Ara
mouth bar and at the right hand of the post confluence entrance (Figure 5.42 and
Figure 4.41). The cross sectional changes in bed morphology during this period are
shown in Figure 5.41 and the plan of erosion and deposition is shown in Figure 5.44.
In this event the lateral bar and also the sediment deposition in the downstream of
main bar were scoured in the inner bank (RSK5, RSK6 and RSK7). Increasing the
discharge was not great enough to obviously change the shape of the downstream
channel bed of confluence (RSK2 and RSK3). The channel morphology changes and
sediment transport in this period largely reflected sustained next high flow
conditions.
Ara
Legend
16.590823
16.233427
15.876031
15.518635
15.161239
14.803843
14.446447
Kurau
80.0 m
Bed levels, min= 14.446 m, max= 16.591 m
Figure 5.40: Bed morphology after Q=31 m3/s
192
16.5
16.5
RSK1
16
16.0
Elevation (m)
Elevation (m)
RSA
15.5
15.5
15
15.0
Q=15 (mᵌ /s)
Q= 31 (mᵌ/s)
Q=15 (mᵌ /s)
Q= 31 (mᵌ/s)
14.5
14.5
0
10
20
Distance (m)
30
0
16
Elevation (m)
Elevation (m)
30
RSK3
RSK2
16
15.5
15
14.5
0
10
20
Distance (m)
30
15
Q=15 (mᵌ /s)
Q= 31 (mᵌ/s)
14
40
16.5
0
10
Distance (m)
20
30
16.5
RSK4
RSK5
Elevation (m)
16
15.5
14.5
Q=15 (mᵌ /s)
Q= 31 (mᵌ/s)
14
Elevation (m)
20
16.5
16.5
15.5
16
15.5
15
14.5
Q=15 (mᵌ /s)
Q= 31 (mᵌ/s)
15
Q=15 (mᵌ /s)
Q= 31 (mᵌ/s)
14.5
14
14
0
10
Distance (m)
20
30
16.5
0
16.5
Elevation (m)
15.5
10
Distance (m)
20
30
RSK7
RSK6
16
Elevation (m)
10
Distance (m)
16
15.5
15
14.5
0
10
Distance (m)
20
Q=15 (mᵌ /s)
Q= 31 (mᵌ/s)
14.5
Q=15 (mᵌ /s)
Q= 31 (mᵌ/s)
14
15
14
30
0
10
Distance (m)
Figure 5.41: Channel cross section profiles, Q=31m3/s
193
20
30
16.2
16.0
15.8
Elevation(m)
15.6
15.4
15.2
15.0
14.8
14.6
Measured
Q= 15 (mᵌ/s)
Q= 31 (mᵌ/s)
14.4
14.2
14.0
0
20
40
60
80
100
120
140
160
Distance (m)
Figure 5.42: Longitudinal bed change profile of Ara and downstream of confluence between
Q=15m3/s and Q=31m3/s (Measured bed level April 2012)
15.8
15.6
Elevation(m)
15.4
15.2
15.0
14.8
14.6
14.4
Measured
Q= 15 (mᵌ/s)
Q= 31 (mᵌ/s)
14.2
14.0
0
20
40
60
80
100
120
140
160
Distance (m)
Figure 5.43: Longitudinal bed change profile of Kurau and downstream of confluence
between Q=15m3/s and Q=31m3/s (Measured bed level April 2012)
194
Ara
Kurau
Figure 5.44: Change in bed morphology between Q=15m3/s and Q=31m3/s. Zone of erosion
and deposition during each period are illustrated with colour change from white as
deposition to black as erosion.
High flows occurred in next step and discharge flow changed from 31 to 43
m3/s, and the water depth changed from 2.35 to 2.8 m. At this larger discharge ratio
(Mr=2. 6), the influence of the Ara River into the confluence and the curvature of
flows through tributary increase. This, aided by larger flow separation, generates
maximum sediment transport pathways which are constricted to smaller zones
around the confluence rather than through the centre of the confluence. The
morphological effect of these changes is larger bed scour, larger bar formed within
the separation zone (Figure 5.45 and Figure 5.46) and the retreat of the tributary
channel avalanche face from the confluence.
195
Ara
1.7299 m/s
10.0 m
Level 11
Kurau
Figure 5.45: Flow separation Mr>1
Ara
Kurau
Figure 5.46: Flow separation at Ara- Kurau confluence (Mr>1)
196
During this high flow event the Ara mouth bar was eroded over and the scour
zone at the entrance the Kurau River increased in the direction of the Ara side. This
led to the retraction of the front of the Ara mouth bar and the development of a
steeper avalanche face. The steepest part of the face was located close to the edge of
the shear layer and appeared to be maintained by the presence of the shear layer
along the side of the Ara mouth bar and the lateral bar (Boyer et al., 2006). The bed
morphology after Q=43m3/s shows in Figure 5.47
Ara
Legend
17.391625
16.864688
16.337750
15.810813
15.283875
14.756938
14.280000
Kurau
80.0 m
Bed levels, min= 14.280 m, max= 17.392 m
Figure 5.47: Bed morphology after Q=43m3/s
197
This high momentum flow was directed toward the main channel side of
downstream channel after the Ara mouth. The deepest part of the main channel
extended further downstream through the confluence and near to the bars due to
acceleration of flow along the mixing interface. This acceleration corresponds to
increase in bed shear stress over distance and high bed shear stresses in the centre of
the confluence both of which advance scour zone (Rhoads and Sukhodolov, 2008).
The cross sectional and longitudinal changes during this flood event is shown in
Figure 5.48 , Figure 5.49 and Figure 5.50. The central portion of the confluence was
scoured and cross sections profile reshaped through erosion of the inner channels
(RSK2, RSK3) and the scour hole align itself in the direction of Ara River (RSK4).
Excavation of bed material decreased bed elevation by 0.5 and shifted the face of this
part of the cross section toward the outer bank of the downstream confluence by 1
meter (RSK4, RSK5).
Over this period, a bar complex developed along the inner bank that include
the lateral bar and a secondary bar created at the downstream end of the lateral bar
due to deposition of suspended and eroded sediments in a separation zone in the lee
of the lateral bar (Figure 5.51). Deposition along the front of the protruding lateral
bar in downstream of confluence increased the bed elevation by about 0.5 m within
the outer bank (RSK4, RSK5 and RSK6).
198
16.6
17.0
RSK1
RSA
16.5
Elevation (m)
Elevation (m)
16.1
16.0
15.6
15.5
15.1
15.0
Q= 31 (mᵌ/s)
Q= 43 (mᵌ/s)
14.6
0
10
20
Distance (m)
14.5
0
30
RSK2
Elevation (m)
Elevation (m)
20
30
15.5
15
14.5
Q= 31 (mᵌ/s)
Q= 43 (mᵌ/s)
14
0
RSK3
16.5
16
10
20
Distance (m)
30
16
15.5
15
Q= 31 (mᵌ/s)
Q= 43 (mᵌ/s)
14.5
14
40
0
17
10
Distance (m)
20
30
17
RSK4
16
15.5
15
16
15.5
15
Q= 31 (mᵌ/s)
Q= 43 (mᵌ/s)
14.5
10
Distance (m)
20
14
0
30
17.5
10
Distance (m)
20
30
16.5
RSK6
17
Q= 31 (mᵌ/s)
Q= 43 (mᵌ/s)
14.5
14
0
RSK5
16.5
Elevation (m)
16.5
Elevation (m)
10
Distance (m)
17
16.5
RSK7
16.5
Elevation (m)
Elevation (m)
Q= 31 (mᵌ/s)
Q= 43 (mᵌ/s)
16
15.5
15
Q= 31 (mᵌ/s)
Q= 43 (mᵌ/s)
14.5
16
15.5
15
Q= 31 (mᵌ/s)
Q= 43 (mᵌ/s)
14.5
14
14
0
10
Distance (m)
20
30
0
10
Distance (m)
Figure 5.48: Channel cross section profiles, Q=43m3/s
199
20
30
16.2
16.0
15.8
Elevation(m)
15.6
15.4
15.2
15.0
14.8
14.6
Measured
Q= 31 (mᵌ/s)
Q= 43 (mᵌ/s)
14.4
14.2
14.0
0
20
40
60
80
100
120
140
160
Distance (m)
Figure 5.49: Longitudinal bed change profile of Ara and downstream of confluence between
Q=31m3/s and Q=43m3/s (Measured bed level April 2012)
15.8
15.6
15.4
Elevation(m)
15.2
15.0
14.8
14.6
Measured
14.4
Q= 31 (mᵌ/s)
14.2
Q= 43 (mᵌ/s)
14.0
0
20
40
60
80
100
120
140
160
Distance (m)
Figure 5.50: Longitudinal bed change profile of Kurau and downstream of confluence
between Q=31m3/s and Q=43m3/s (Measured bed level April 2012)
200
Ara
Kurau
Figure 5.51: Change in bed morphology between Q=31m3/s and Q=43m3/s. Zone of erosion
and deposition during each period are illustrated with colour change from white as
deposition to black as erosion.
From this temporal change in high flow and discharge momentum ratio Mr>1,
it was possible to demarcate the location on the Ara side were more responsive and
active in its morphological change and it responded to the migration of the shear
layer within the confluence as flow stage changes from Mr<1 to Mr>1.
The bed morphology of confluence after Q=35 m3/s is shown in Figure 5.54.
Erosive event during high flow was followed by a deposition phase as the discharge
decreased to 35 m3/s and water level decreased from 2.8 to 2.5 m (Figure 5.52 and
Figure 5.53). The bed elevation was increased at the entrance of Kurau (RSK1) by
~0.4 m on the right hand and erosion occurred along the outer of lateral bar and
201
deposition was concentrated along the inner bank of RSK4, RSK5 and RSK6 and in
the downstream of main Kurau , RSK7 (Figure 5.56). The scour hole migrated to the
centre of the channel. Bed change morphology which included the deposition of a
bar in the inner bank and weak scour at the outer bank during this period is shown in
Figure 5.55.
16.0
15.8
15.6
Elevation(m)
15.4
15.2
15.0
14.8
14.6
Measured
Q= 43 (mᵌ/s)
Q= 35 (mᵌ/s)
14.4
14.2
14.0
0
20
40
60
80
100
120
140
160
Distance (m)
Figure 5.52: Longitudinal bed change profile of Ara and downstream of confluence between
Q=43m3/s and Q=35m3/s (Measured bed level April2012)
15.8
15.6
Elevation(m)
15.4
15.2
15.0
14.8
14.6
Measured
14.4
Q= 43 (mᵌ/s)
14.2
Q= 35 (mᵌ/s)
14.0
0
20
40
60
80
100
120
140
160
Distance (m)
Figure 5.53: Longitudinal bed change profile of Kurau and downstream of confluence
between Q=43m3/s and Q=35m3/s (Measured bed level April2012)
202
Ara
Legend
17.500000
16.500000
16.000000
15.500000
15.000000
14.500000
14.310000
Kurau
80.0 m
Bed levels, min= 14.310 m, max= 17.500 m
Figure 5.54: Bed mophology after Q=35m3/s
Ara
Kurau
Figure 5.55: Change in bed morphology between Q=43m3/s and Q=35m3/s. Zone of erosion
and deposition during each period are illustrated with colour change from white as
deposition to black as erosion.
203
16.6
16.6
RSK1
16.1
16.1
Elevation(m)
Elevation(m)
RSA
15.6
15.1
15.6
15.1
Q= 43 (mᵌ/s)
Q= 35 (mᵌ/s)
14.6
0
10
Distance (m)
20
30
0
RSK2
20
30
RSK3
16.5
Elevation(m)
Elevation(m)
16
15.5
15
16
15.5
15
Q= 43 (mᵌ/s)
Q= 35 (mᵌ/s)
14.5
Q= 43 (mᵌ/s)
Q= 35 (mᵌ/s)
14.5
14
14
0
10
20
Distance (m)
30
40
0
17
10
Distance (m)
20
30
17
RSK4
16
15.5
15
Q= 43 (mᵌ/s)
Q= 35 (mᵌ/s)
14.5
16
15.5
15
10
Distance (m)
20
Q= 43 (mᵌ/s)
Q= 35 (mᵌ/s)
14.5
14
14
0
RSK5
16.5
Elevation(m)
16.5
Elevation(m)
10
Distance (m)
17
16.5
0
30
10
Distance (m)
20
30
17
17.5
RSK6
17
16.5
16
15.5
15
Q= 43 (mᵌ/s)
Q= 35 (mᵌ/s)
14.5
14
0
RSK7
16.5
Elevation(m)
Elevation(m)
Q= 43 (mᵌ/s)
Q= 35 (mᵌ/s)
14.6
10
Distance (m)
20
16
15.5
15
Q= 43 (mᵌ/s)
Q= 35 (mᵌ/s)
14.5
14
0
30
10
20
Distance (m)
Figure 5.56: Channel cross section profiles, Q=35m3/s
204
30
40
Next step the total discharge was decreased (Q=13m3/s) and discharge ratio
dropped below 1, the Kurau flow discharge was the dominant flow. The bed
morphology after change of flow momentum is shown in Figure 5.57. The low
momentum flow ratio prompted migration of flow separation to the centre of
confluence (Figure 5.58). Comparisons of channel cross sections confirm that bed
morphology is similar to Q= 35 and Q=13 m3/s but that some minor changes can be
identified (Figure 5.59 and Figure 5.60). These minor changes and low discharge
ratio flow eroded the Kurau mouth at the cross section RSK1 and lateral and
secondary bars along the inner bank (RSK6 and RSK7). The deposition occurred in
left hand of the Ara mouth (RSA) and outer bank of the lateral bar in cross sections
RSK5 and RSK6 (Figure 5.62).
Ara
Legend
16.615858
16.241548
15.867239
15.492929
15.118619
14.744310
14.360000
Kurau
80.0 m
Bed levels, min= 14.360 m, max= 16.616 m
Figure 5.57: Bed morphology after Q=13 m3/s
205
Ara
1.6078 m/s
10.0 m
Level 11
Kurau
Figure 5.58: Flow separation Mr<1
16.0
15.8
15.6
Elevation(m)
15.4
15.2
15.0
14.8
14.6
Measured
14.4
Q= 35 (mᵌ/s)
14.2
Q= 13 (mᵌ/s)
14.0
0
20
40
60
80
100
120
140
160
Distance (m)
Figure 5.59: Longitudinal bed change profile of Ara and downstream of confluence between
Q=35m3/s and Q=13m3/s (Measured bed level April 2012)
206
15.8
15.6
15.4
Elevation(m)
15.2
15.0
14.8
14.6
Measured
14.4
Q= 35 (mᵌ/s)
14.2
Q= 13 (mᵌ/s)
14.0
0
20
40
60
80
100
120
140
160
Distance (m)
Figure 5.60: Longitudinal bed change profile of Kurau and downstream of confluence
between Q=35m3/s and Q=13m3/s (Measured bed level April 2012)
Ara
Kurau
Figure 5.61: Change in bed morphology between Q=35m3/s and Q=13m3/s. Zone of erosion
and deposition during each period are illustrated with colour change from white as
deposition to black as erosion.
207
16.6
16.5
RSK1
16.1
Elevation (m)
Elevation (m)
RSA
15.6
15.1
16.0
15.5
15.0
Q= 35 (mᵌ/s)
Q= 13 (mᵌ/s)
14.6
0
10
Distance (m)
20
0
30
RSK2
Elevation (m)
Elevation (m)
10
15
Distance (m)
20
25
15.5
15
14.5
30
15
Q= 35 (mᵌ/s)
Q= 13 (mᵌ/s)
14
14
10
20
Distance (m)
15.5
14.5
Q= 35 (mᵌ/s)
Q= 13 (mᵌ/s)
0
RSK3
16
16
0
40
16.5
10
Distance (m)
20
30
16.5
RSK4
RSK5
Elevation (m)
16
Elevation (m)
5
16.5
16.5
15.5
16
15.5
15
14.5
15
Q= 35 (mᵌ/s)
Q= 13 (mᵌ/s)
14.5
Q= 35 (mᵌ/s)
Q= 13 (mᵌ/s)
14
14
0
10
Distance (m)
20
30
0
17
10
20
Distance (m)
30
16.5
RSK6
RSK7
Elevation (m)
16.5
Elevation (m)
Q= 35 (mᵌ/s)
Q= 13 (mᵌ/s)
14.5
16
15.5
15
Q= 35 (mᵌ/s)
Q= 13 (mᵌ/s)
14.5
16
15.5
15
Q= 35 (mᵌ/s)
Q= 13 (mᵌ/s)
14.5
14
14
0
10
Distance (m)
20
30
0
10
20
Distance (m)
Figure 5.62: Channel cross section profiles, Q=13 m3/s
208
30
40
5.9.7.2 Lateral bar
At Kurau-Ara asymmetrical planform confluence the frequently occurring bar
is that formed just below the downstream junction corner. The origin of this bar is
linked to the formation of a large zone of separated flow (Best and Reid, 1984). Flow
separation occurs at the downstream junction corner where fluid of the Ara channel
cannot remain attached to the channel wall. This creates a zone of low velocity,
recirculating flow which provides a favourable site for sediment deposition.
Sediment predominantly from the Ara channel is concentrated along a distinct
pathway and is carried into this zone. Because of the low flow velocities present
material quickly comes to rest. An examination of natural channel confluences
reveals that this bar is composed of relatively fine grained sediment, another
indication of the low velocities within the region. The separation zone bar dips into
the central scour but grades into the general bed elevation downstream where the
effects of the flow separation zone diminish beyond the point at which the combined
flow reattaches itself to the stream bank. The size of this bar is therefore related to
the size of the separation zone which grows both at higher confluence angles and
higher discharge ratios (Best and Reid, 1984; McGuirk and Rodi, 1978). Erosion of
the far bank may cause channel widening opposite this bar because of the
constriction of the effective channel width through which the combined discharges
must flow (Best and Reid, 1984). Figure 5.63 and Figure 5.64 show the change of
lateral bar during the event longitudinally and cross sectional. The Figures indicate
that the morphological change in lateral bar completely depend on flow momentum.
209
16.6
16.5
Elevation (m)
16.4
16.3
16.2
16.1
16.0
15.9
0
5
10
Q=15(mᵌ/s)
15
20
Latral bar distance (m)
Q=31(mᵌ/s)
25
Q=43(mᵌ/s)
30
35
Q=35(mᵌ/s)
Figure 5.63: longitudinal profile of lateral change in different flow momentum
16.5
RSK4
Elevation (m)
16.0
15.5
Q=12 (m3/s)
Q=15 (mᵌ /s)
15.0
Q= 31 (mᵌ/s)
Q= 43 (mᵌ/s)
Q= 35 (mᵌ/s)
14.5
Q= 25 (mᵌ/s)
Q= 13 (mᵌ/s)
14.0
0
5
10
15
20
25
Distance (m)
Figure 5.64: Cross sectional lateral change in different flow momentum
210
30
5.9.7.3 Bedload Transport Rates
The Bedload transport rating curve of Ara and Kurau at upstream of confluence
is obtained with SSIIM is shown in Figure 5.65. The figures depict the good
accuracy of prediction of bedload transport by SSIIM and significant of coefficient
determination (R2= 0.98) of bedload transport rate by SSIIM shows the ability of
good prediction of bedload transport (Figure 5.66).
Bedload transport rate Tb (kg/s)
10
Ara
1
Eq 4.11
SSIIM
0.1
1
10
Discharge (m³/s)
100
Bedload transport rate Tb (kg/s)
10
Kurau
1
Eq 4.11
SSIIM
0.1
1
10
Discharge (m³/s)
100
Figure 5.65: Bed load transport rating curve in Ara and Kurau River branch
211
Bedload transport rate (SSIIM)Tb (kg/s)
10
R² = 0.981
1
Kurau
Ara
0.1
0.1
1
Bedload transport rate (Eq.4.11)Tb (kg/s)
10
Figure 5.66: Bed load transport rate value by SSIIM against the calculated bedload transport
rate with Eq. 4.11
The relationship between sediment loads and the discharges in the main
channel and the tributary is an important factor for confluence morphology,
including the development, relative importance and location of erosion, deposition
and change in bed elevation (Leite Ribeiro et al., 2012).
The simulation of flow sediment in the confluence of Ara and Kurau shows
that for each flow discharge, bed load transport rates varied throughout the
confluence, laterally and longitudinally, and also from one event to the other. In the
first step, bed load transport rates were found to increase at the entrance of the
confluence (RSK2, RSK3) and then decrease in the downstream direction at cross
section RSK5 and RSK6 (Figure 5.67).
Bed load transport rates were higher in the upstream portion of the confluence
than in the Kurau and Ara channels, corresponding with erosion within the
212
confluencee. For this flow dischaarge and wiith the mom
mentum ratiio less than
n one the
location of the maxim
mum bedloaad transport rate at eachh cross sectiion is on the side of
the Kurau channel aloong the connfluence.
Araa
Bed load
l
transportt rate
0.4 kg s-1m-11
Leg
gend
16.777
7551
16.364
4626
15.951700
15.538
8775
15.125
5850
14.712
2925
14.360
0000
Flow directiion
Shear layerr
Kurrau
8
80.0
m
Bed
d levels, min=
m
14.360 m, max=
= 16.778 m
Figure 5.67:
5
Bed moorphology annd spatial disstribution of bedload
b
trannsport rate Mr=0.9.
M
Nexxt event thee flow dischharge increased to 31m
m3/s and thhe flow mo
omentum
ratio channge from Mr<1
M
to Mrr>1. The bed
b load traansport ratee slightly in
ncreased
further doownstream particularly
p
y along the edge of thhe shear layyer (RSK5, RSK6).
The locatiion of maxiimum bed load
l
transport rates off each crosss section is the Ara
side alongg the confluence. Bed load
l
transpo
ort is high inn the Ara m
mouth whilee there is
213
3
some trannsport of seediment from
m Kurau. At
A upstream
m maximum
m bedload transport
t
rate is obsserved in thee Ara side (Figure
(
5.68
8).
Araa
Beed load transpport rate
0.4 kg s-11m-1
Flow dirrection
Legend
16.777551
16.364626
15.951700
15.538775
15.125850
14.712925
14.300000
Shear laayer
Ku
urau
80.0 m
Bed leve
els, min= 14.300
1
m, max=
m
16.778 m
Figure 5.68:
5
Bed moorphology annd spatial disstribution of bedload
b
trannsport rate Mr=1.3.
M
Bedload transpoort for highh flow disch
harge with high
h
momenntum ratio (Mr=2.6)
(
is shown in Figure 5.69. Thiis figure illlustrates thhe high beedload tran
nsport in
comparisoon with thee other flow
w occurred within the confluencee, however bedload
transport rate
r
in Kurrau River iss very low, and may be
b explainedd by the fact that a
most propportion of the
t bed seddiment is trransported in suspension rather than the
bundled.
214
4
Thesse relativelly high bedd load tran
nsport rates are continnuing, conssiderably
increased at the entrrance of coonfluence (RSK2, RSK
K3) and thhen decrease in the
R
and RSK6). The location
l
of maximum bed
b load
downstreaam directionn (RSK4, RSK5
transport rates
r
at eacch cross sections are the
t Ara sidde along the confluencce. The
distributioon of bed load transporrt rates in crross sections shows thaat the highesst values
at the coonfluence (ccross sectioons RSK2 and RSK33) are gennerally nearr to the
boundaries of the shhear layer, and these patterns arre changedd depending
g on the
momentum
m ratio. Thhe forms off bedload transport
t
allso define tthat deposittion and
erosion arre happeninng at diffeerent locatio
ons in the confluencee according
g to the
magnitudee of the mom
mentum ratiio.
Ara
Bed looad transport rrate
0.4 kg s-1m-1
Flow directioon
Leg
gend
17.3916
625
16.8646
688
16.3377
750
15.8108
813
15.2838
875
14.7569
938
14.2800
000
Shear layer
Kurau
K
8
80.0
m
Bed
d levels, min
n= 14.280 m,
m max= 17..392 m
Figure 5.69
5
: Bed moorphology annd spatial disstribution of bedload trannsport rate Mr=2.6.
M
215
5
Nexxt event the flow dischaarge come down
d
and also
a the dom
minant flow
w is from
the Kurauu River witth flow moomentum raatio less thaan one andd the shear layer is
moved neear to the Ara side. The bed
dload transpport in thiis event decreases
d
considerabbly. Like thhe other eveent the max
ximum bed load transpport rates take place
near and on both sides of the shear layeer (Figure 5.70).
5
The maximum bedload
i both Araa and Kurauu Rivers hap
ppened in the middle oof channelss (RSK1,
transport in
RSA). In the upstreaam region of
o the conffluence (crooss sectionss RSK2, RS
SK3 and
RSK4), higher
h
sedim
ment transpport rates occurred
o
onn the Ara side whilee further
downstreaam (RSK7) higher rate is along thee Kurau sidee.
Ara
Bed load
l
transportt rate
0.025 kg s-1m-1
Lege
end
Flow directiion
16.61585
58
16.23821
15
15.86057
72
15.48292
29
15.10528
86
14.72764
43
14.35000
00
Shear layerr
Kuraau
80
0.0 m
Bed levels, min= 14.350 m,
m max= 16..616 m
Figure 5.70:
5
Bed moorphology annd spatial disstribution of bedload
b
trannsport rate Mr=0.7.
M
216
6
The shear layer that develops along the interface of two merging flows is a
common hydrodynamic feature of channel confluences (Figure 5.71). Shear layer is
characterized by increased turbulence levels at the junction of the flows coming from
the main channel and the tributary (Rhoads and Sukhodolov, 2008).
As shown in Figure 5.72 the shear layer is tridimensional as it develops both
vertically and laterally in the downstream of a region of flow separation. The
position of shear layer varies according to the discharge ratio and the height of the
bed discordance. As shown in Figure 5.67 to Figure 5.70 this position is critical for
the dynamics of the confluence as it influences flow mixing and sediment transport
pathways thus affecting the resulting bed morphology (Boyer et al., 2006).
Rhoads (1996) explained that dual surface-convergent helical cells develop on
either side of the mixing interface at the entrance to the downstream channel (Figure
5.71), which sweeps sediment laterally away from the centre of the confluence,
contributing to scour and separation of sediment loads. The locus of the zone of high
bed shear stress near the centre of the channel leads to degradation of accumulated
sediment over the inner part of the downstream channel (edge the shear layer).
217
Shear layer
Shear layer
helicoidal flow cells
Figure 5.71: Shear layer and distinct vortices about vertical axes at RSK1
Ara
Kurau
Figure 5.72: Shear layer in the confluence of Ara and Kurau
218
Figure 5.73 shows the variation of bedload transport rate in the cross sections
at the downstream of confluence with changing the discharge and flow momentum.
This figure depicted the increasing of bedload capacity through the confluence zone
between RSK2 and RSK4. The increases in bedload transport capacity from the Ara
sediment supply though the confluence was provided by some hydro-morphological
interactions (Rhoads and Sukhodolov, 2001). The existing of the lateral bar at the
inner bank of the downstream channel caused a reduction in the local flow depth, an
acceleration of the near-bed flow, and outward deflection of this flow by topographic
steering. The bed discordance between Ara and Kurau gave rise to a two-layer flow
structure and to three-dimensional flow patterns that were characterized by near-bed
cores of high velocity with increased bedload transport capacity. The coincidence of
the shear layer that was generated the considerable turbulence indicated that the
increased turbulence levels contribute substantially to the required increase in
bedload transport capacity.
11
Q=15 m³/s Mr=0.9
Q=31 m³/s Mr=1.3
Q=43 m³/s Mr=2.6
Q=13 m³/s Mr=0.7
Bedload transport rate Tb (kg/s)
10
9
8
7
6
5
4
3
2
1
0
RSK2
RSK3
RSK4
Cross section
RSK5
RSK6
Figure 5.73: Bedload rate in cross sections at downstream of confluence
219
The spatial distribution of bed load transport rates consequently seems to be
varied with the changes in bed morphology. For low flow condition, the extent of the
bed load transport pathway on the Kurau side responds to the migration of the Ara
mouth bar and the lateral bar into the confluence (Figure 5.67), this migration in turn
being controlled by the change in the position of the shear layer. As the shear layer
invades on the lateral bar and secondary bar (high momentum ratio), it causes their
regular erosion and may explain the high bed load transport rates occurred between
RSK3 and RSK6 along the Ara side (Figure 5.68). These forms are interrelated with
the boundaries of the shear layer and respond to the movement of the shear layer as
momentum ratio alterations.
5.9.7.4 Sediment Pattern
Patterns of sediment distribution within the confluence respond not only to the
flow dynamics but also control the bed morphology: this in turn affects both the flow
and sediment transport pathways. An understanding of the behaviour of sediment
within channel confluences therefore has fundamental implications for the
investigation of junction bed morphology (Best, 1988).
The bedload transport between the Ara and the Kurau River as mentioned in
previous section mainly occurs near the downstream junction corner of the
confluence due to the formation of depression in the upstream junction corner that
causes an asymmetric distribution of the flow and sediment transport. Bedload
provided by the Ara to the Kurau channel is mainly transported by the near-bed flow
originating from the Kurau branch channel. This near-bed flow has an element that is
focused on the slope of the bar. The interaction between the near-bed flow and the
220
downward slope gravitational impinges on the sediment particles conditions the
slope of the bar and causes sediment sorting. Moreover, this near-bed flow prevents
deposition of fine sediment at the inner-bank and the formation of a zone of flow
recirculation (Rhoads et al., 2009).
The spatial distribution of bed material was evaluated for tree flow conditions
as Mr <1 with total discharge Q=15m3/s, at high flow Mr>1 and Q=43 m3/s and low
flow Q=13 m3/s, Mr<1.
At the apex of the junction when the momentum flux ratio is less than 1
(Q=15m3/s), the distribution of bed material reveals separate zones of fine and coarse
sediment within the confluence (Figure 5.74). A zone of fine gravel from the Ara
extends laterally across the downstream confluence channel from the RSK2 and the
inner bank of the lateral bar into the base of a scour hole (RSK3). Figure 5.74
illustrates the lateral displacement of fine gravel by the position of limit of the 3 mm
curve moving from the Ara right bank toward the centre of the confluence. This
movement of coarse sediment seems to be related to the position of the mixing layer
which is controlled by the momentum flow and sediment ratio. The sediment near
the inner bank of the downstream channel consists mainly of sand (d50=1.5 mm) that
extends along the top of the bar. A track of coarse sand extends along the front of the
lateral bar near the outer bank. This track of sediment, presumably comprised of
material from the Kurau River, located within the downstream channel where it is
replaced by the fine gravel-dominated sediment from the Ara River. The median
grain size in upstream junction as a flow stagnation zone where the two incoming
flows diverge towards the outer banks is fine sand (d50=1.5 mm) and it could
221
explained by the low bed shear stresses in the stagnation zone (Best, 1988) (Figure
5.75).
Ara
Legend
0.003505
0.003012
0.002519
0.002025
0.001531
0.001038
0.000545
Kurau
80.0 m
Bed grain size distribution, D50, layer 2, min=
0.54 mm, max=
3.51 mm
Figure 5.74: Distribution of bed median size, D50 Q=15 m3/s, Mr<1
222
Ara
Legend
2.756875
2.326643
1.896410
1.466178
1.035946
0.605714
0.175482
Kurau
80.0 m
Bed shear stress, min=1.754817e-001, max=2.756875e+000
Figure 5.75: Bed shear stress in confluence Q=15m3/s
The high flow in the next step cussed re adjustment of the grain size pattern to
reflect the dominant flow of the Ara River. At high flow with Mr>1 the Ara flow
penetrates slightly into the main channel, allowing the Ara sediments to be deposited
on the Kurau side (Figure 5.76). As the momentum flow ratio increased, finer
particles from the Kurau are found on the Ara bed at the upstream junction.the
median grain size increased from 3 mm to 3.5 mm at the lateral moving from the Ara
to the left bank of downstream confluence included the maximum depth zone (Figure
5.76) .
223
The increase in the median grain size appears to be the result of the increasing
bed shear stress as flow in Ara and Kurau rises (Figure 5.77). For high momentum
ratio the coarser sediments are located near to the left bank while in low flow ratio
the coarser sediment is located in centre of the channel. A sudden transition from fine
gravel to coarse sand occurred along the inner bank, between the outer bank and the
top of the lateral bar. Mix gravel and sand cover the channel bed near the outer bank
of the lateral bar (cross section RSK4). The area along the inner bank of secondary
bar at the right hand of downstream main Kurau is underlain by fine and coarse sand
material.
Ara
Coarse
Fine
Legend
0.003506
0.003012
0.002519
0.002025
0.001532
0.001038
0.000545
Kurau
80.0 m
Bed grain size distribution, D50, layer 2, min=
0.54 mm, max=
3.51 mm
Figure 5.76: Distribution of bed median size at high flow, D50 Q=43 m3/s, Mr>1
224
Ara
Legend
3.100000
2.636577
2.173153
1.709730
1.246306
0.782883
0.319459
Kurau
80.0 m
Bed shear stress, min=3.194591e-001, max=3.100000e+000
Figure 5.77: Bed shear stress in confluence Q=43m3/s
A sustained change in flow discharge and momentum ratio from Mr>1 to Mr
<1 redistributed the surficial bed material through the confluence. The pattern of the
bed sediment differs from the high flow condition in that input of sediment from
Kurau and Ara River remain segregated well downstream of confluence (Figure
5.78). During this period a wedge of sediment advanced to the confluence of the
Kurau River. Medium to coarse sand cover the outer bank along the lateral bar and
fine gravel is shifted toward the inner bank of lateral bar. The coarse material is
confined to the mouth of Ara and a narrow track in outer bank of lateral bar and
continued to farther downstream. Fine sediment also is present along the inner bank
225
of secondary bar and the inner channel and extended far down stream. This
movement of fine sediment from Kurau and coarse sediment from Ara in low flow is
because of high bed shear stresses in the centre of the confluence and an increase in
bed shear stress over distance (Figure 5.79) due to acceleration of flow along the
mixing interface (Rhoads and Sukhodolov, 2008).
Ara
Coarse
Fine
Legend
0.003505
0.003012
0.002519
0.002025
0.001531
0.001038
0.000545
Kurau
80.0 m
Bed grain size distribution, D50, layer 2, min=
0.54 mm, max=
3.51 mm
Figure 5.78: Distribution of bed median size at low flow, D50 Q=13 m3/s, Mr<1
226
For the three discharge flow, the grain size distribution on the bar at the
downstream junction corner was considerably constant compared to the other part of
confluence such as scour hole and upstream of the junction. The particle size of
lateral bar was usually finer than the average median grain size of the post
confluence channel. However, the particle size in the upstream part of the bar is more
affected by the changes in flow conditions than the downstream end where the
median diameters not varied during the period. During high discharge-ratio the flow
curvature from the Ara into the downstream channel produces two effects that
influence bed material patterns. First, the magnitude of bed shear stress along the
inner bank appears to decrease rapidly leading to deposition along the inner bank and
a downstream fining of bed material on the bar surface. On the other hand, the
magnitude of bed shear stress increases rapidly near the outer bank along the bar
edge, downstream coarsening of the bed material. Second, curvature of the flow from
the Ara leads to the development of helical motion of flow within the downstream
channel that is characterized by outward near-surface flow and inward near-bed flow
(Rhoads and Kenworthy, 1995).
During low discharge-ratio events, the main flow of the Kurau River causes
penetration of a wedge of fine sediment in the downstream channel along the outer
bank. Fine material from the Kurau River and coarse material from the Ara are
confined within the confluence to opposing sides of the scour hole before combining
in the downstream channel (Figure 5.78). This combination is influenced by the
transformation of the pattern of secondary circulation from dual surface-convergence
cells, which separate the sediment loads of the two incoming streams, into a single
dominant helical cell that extends over most of the downstream channel, which leads
227
to connect bedload transport from the Kurau River toward the inner bank of the
downstream channel (Rhoads, 1996).
Ara
Legend
2.000000
1.695345
1.390691
1.086036
0.781382
0.476727
0.172072
Kurau
80.0 m
Bed shear stress, min=1.720723e-001, max=2.000000e+000
Figure 5.79: Bed shear stress at low flow Q=13m3/s
228
5.9.8
High Flow Modelling
The 2007 flood is the largest flood for Kurau River since 1960, where this
flood event is slightly lower than the 100 ARI. Therefore, the high discharge at
191.32 m3/s of the event occurred on 23 October 2007 was considered as the design
peak discharge. Figure 5.80 shows the hydrograph for the October 2007. The
morphology variation and bedload transport analysis was carried out in this flood
event. The grid was created with105437 cells and discharge specified for Ara and
Kurau rivers.
250
Discharge (m³/s)
200
191.322 m3/s
150
100
50
32.708
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Time (day)
Figure 5.80: Hydrograph of the October 2007 flood
229
Figure 5.81: The morphology of Kurau-Ara confluence before flood
Figure 5.82 depicts peak water surface and changes of the channel geometry
due to erosion and deposition by the simulated changes in the channel bed profile.
The original channel geometry was based on survey in April 2012. The result shows
the erosion of the bed occurred at all cross sections along the downstream of the
confluence (Figure 5.83) and flood level was higher at the downstream compare to
upstream of the confluence.
230
Ara
Legend
20.256214
19.226845
17.500000
16.500000
15.500000
14.500000
14.080000
Kurau
90.0 m
Bed levels, min= 14.080 m, max= 20.256 m
Figure 5.82: Bed morphology of Kurau-Ara confluence after flood
231
Ara
Kurau
Figure 5.83: Change in bed morphology after Q=191.32m3/s. Zone of erosion and deposition
during each period are illustrated with colour change from white as deposition to black as
Elevation(m)
erosion.
20.0
19.5
19.0
18.5
18.0
17.5
17.0
16.5
16.0
15.5
15.0
14.5
14.0
13.5
13.0
Befor flood
After flood
Peak W.s.
0
10
20
30
40
50
60
Distance (m)
Figure 5.84: Longitudinal bed change profile of downstream of confluence
232
70
Figure 5.85 shows the cross section changes for the location along the
confluence of Kurau and Ara rivers. In general erosion has occurred at most inner
bank of cross sections after flood 2007, while the high flow favoured the progression
of the Ara mouth bar at the left side of Ara River. The high junction angle between
Ara and Kurau rivers made deep scour hole and segregation of bedload from each
confluent channel became more prominent.
Bed load transport during this flood event as expected increased but not
surprising in amount and may be explained by the fact that a large proportion of the
bed sediment is transported in suspension rather than the bedload (Figure 5.86). The
distribution of bed load transport in the Kurau river mouth is more than Ara mouth
and the bed load transport rate slightly decreased further downstream particularly
along the edge of the shear layer (RSK5, RSK6). The location of maximum bed load
transport rates of each cross section is varied along the both sides of confluence.
233
19
20.0
RSA
Elevation(m)
Elevation(m)
17
16
15
18.0
17.0
16.0
15.0
Befor flood
After flood
14
0
10
20
Distance (m)
30
0
40
20
30
Distance (m)
40
50
18
17
16
15
Befor flood
After flood
14
13
0
RSK3
19
Elevation(m)
Elevation(m)
10
20
RSK2
19
10
20
Distance (m)
30
18
17
16
15
14
Befor flood
After flood
13
40
0
20
10
20
Distance (m)
30
40
20
RSK4
19
18
17
16
15
Befor flood
After flood
14
13
0
RSK5
19
Elevation(m)
Elevation(m)
Befor flood
After flood
14.0
20
10
20
Distance (m)
30
18
17
16
15
Befor flood
After flood
14
13
0
40
10
20
Distance (m)
30
40
20
20
RSK6
19
RSK7
19
18
Elevation(m)
Elevation(m)
RSK1
19.0
18
17
16
15
Befor flood
After flood
14
13
18
17
16
15
Befor flood
After flood
14
13
0
10
20
Distance (m)
30
40
0
10
20
Distance (m)
30
Figure 5.85: Modelled cross section changes before and after flood 2007
234
40
Ara
Legend
d
B load transsport rate
Bed
1 kg s-1m-1
20.25621
14
19.22684
45
17.50000
00
16.50000
00
15.50000
00
14.50000
00
14.08000
00
Flow diirection
Shear llayer
Ku
urau
90.0
0m
Bed lev
vels, min= 14.080
0 m, max=
= 20.256 m
Figuure 5.86: Bed morphologgy and spatiaal distributionn of bedloadd transport ratte
(Q=191.3
32m3/s)
235
5
6
CHAPTER 6
CONCLUSIONS AND RECOMMENDATIONS
6.1
Conclusion
The bedload transport characteristics in a sand–gravel bed Kurau River was
studied the conclusion of this study is as follows.
6.1.1
Bedload Transport Characteristics
The bedload transport in the Kurau River is low; movement of large sediments
(i.e., granules and pebbles) of bed material are rare, and it occurs at a relatively high
discharge. At a low discharge, sand was transported over the bed. By increasing
flow, the pattern of the mobile sediment changed, and distribution became more
bimodal. Comparison of the distribution size of the bedload in a medium frequency
discharge between the upstream and downstream of the Kurau River indicates that
the amount of sediment particles of each fraction size in the upstream is greater than
that in the downstream in the same fractions. This finding demonstrates the size
selectivity of bedload transport during the observed water discharges.
The equal mobility of the bedload and bed material in the Kurau River is
achieved at moderate flows in streams, even when the size distribution of the bedload
is finer than the size distribution of the bed material at high flow. The frequency of
the discharge shows that the mean size distribution of the bedload is similar to that of
the bed material distribution.
236
6.1.2
Estimating Bedload Transport
Hydraulic and sediment data from Kurau River in Malaysia were used to
predict bedload transport and to evaluate the performance of available bedload
transport equations. The performances of empirical bedload transport equations such
as Meyer-Peter and Muller, Wong and Parker, as well as Chang, Julien and van Rijn
were evaluated. No consistent relationship was observed between the predicted and
observed bedload at the sites. Moreover, based on the relationship between the
bedload transport (Tb) and discharge (Q) and the Shields parameter (θ), the power
function of the hydraulic variable best described the observed bedload transport at
the small streams. This power function was subsequently developed into a predictive
transport equation. The NLR, ANN and GP methods were used to predict bedload
transport at first for Kurau River and then were updated by feeding networks by
more data from the other small streams for obtaining simple equation.
In NLR (Eq 4.2), maximum likelihood estimates of the regression parameters
were obtained using the iterative estimation algorithm procedure. The RSME (0.069)
and coefficient of determination (R2 = 0.99) suggest a good agreement between
observed and predicted bedload transport rates for Kurau River. The Eq 4.2 was
updated by adding the Semenyih and Lui river data. The bedload transport predicted
by Equation 4.9 shows a good result by RMSE equal to 0.00 kg/s and U= 0.00.
The results show that the ANN and GP model with four input nodes Q, S, θ,
and d50 can accurately not surprisingly estimate the bedload transport rate. The
combination of ANN with GP shows better agreement between computed and
observed bedload transport rate. The developed equations for small streams by GP
237
(Eq 4.11) and ANN after updating the GP and ANN by feeding the networks with the
Lui and Semeniyh data also show reasonable performance under field conditions.
The predicted bedload transport was compared with observed values, and the
minimum RMSE and inequality ratio (U) were used to select the best performing
model. In this case, the ANN and GP models performed better than the NLR-based
model and other equations. It should be considered that specific condition and
complex behaviour of small streams affect the bedload transport rate. So, the
obtained equations may require reanalyzing in some highly different condition to
correct the equation coefficients. In general, unlike the other transport equations that
were tested, the equation derived using the GP model mostly predicted the bedload
transport rate to within an order of magnitude of the measured values in small
streams and had the lowest RMSE. However, it is not much simpler than the NLR
equation.
6.1.3
Sediment Transport in River Channel Confluence
The sediment transport and morphology characteristic of river confluence are
very complex and include various associations between flow structure, bed
morphology and sediment transport which will change over differing temporal and
spatial scales.
SSIIM2 a three dimensional numerical model, was used successfully to
investigate the morphodynamics of Ara- Kurau confluence. The sediment transport
modelling in the confluence gave more understanding about the changes in
238
morphology, sediment pattern and bedload transport within and at the downstream of
the confluence.
SSIIM2 was calibrated and validated for average velocity, water surface and
bed elevation profile, bedload transport at upstream of confluence with using the
calibrated vanRijn equation for several times. Good agreement was obtained for
bedload transport rate, and bed level and water profiles between the measured data
and predicted results by SSIIM.
The study has demonstrated that the short term hydrologic variability can
considerably influence the morphodynamics of Ara-Kurau channel confluence. For
low flow with momentum ratio, Mr, less than 1, the shear layer is in the middle of
the confluence, the input sediment loads are separated around the scour hole before
mixing, the bed load mostly travels through the confluence near the edge of shear
layer in the left side of the post confluence channel (Kurau side), the Ara mouth bar
is created and lateral bar is eroded, the sediment deposited on the downstream of the
lateral bar (secondary bar). A zone of fine gravel from the Ara extends laterally
across the downstream confluence channel. This movement of coarse sediment is
related to the position of the mixing layer which is controlled by the momentum flow
and sediment ratio.
For flow condition when momentum ratio is greater than 1, the shear layer is
near the Kurau channel side, the bedload transport follow the flow coming from Ara
in to the confluence, moving from the Ara side toward the downstream of the
confluence. The erosion occurs in the Kurau mouth and right side of Ara at the
239
entrance of confluence and inner bank of lateral bar. Sediment deposition occurs at
the outer bank of lateral bar and at secondary bar.
For the different flow condition, the grain size distribution on the bar at the
downstream junction corner is remarkably constant compared to the other part of
confluence such as scour hole and upstream of the junction. The particle size of
lateral bar is usually finer than the average median grain size of the Kurau channel.
However, the particle size in the upstream part of the bar is more affected by the
changes in flow conditions than the downstream end where the median diameters not
varied during the period.
SSIIM2 has been used to simulate the river channel confluence for flood event
with 100 ARI. Bed load transport during flood event as expected increased but not
surprisingly in amount and may be explained by the fact that a large proportion of the
bed sediment is transported in suspension rather than the bedload. The channel bed
degradation had occurred at most cross sections and deposition had occurred at the
upstream part of confluence.
6.2
Recommendations
More study is required into the nature of a range of differing size
confluence.
More study is required to quantify the suspended and dissolved load
transport at confluence.
240
7
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8
APPENDIX A
BEDLOAD TRANSPORT DATA FOR KURAU RIVER
Table A.1: The measured data of Kurau River
locatin
KRU1
KRU2
Batu 14
KRU3
Kg
Bechah
KRU4
Kg Perak
KRU5
Cherok
Pelandok
ARA1
Sg Ara
Date
28/04/2010
11/11/2010
29/12/2010
19/01/2011
24/02/2011
9/03/2011
26/05/2011
21/06/2011
19/05/2010
12/10/2010
01/12/2010
19/01/2011
16/02/2011
03/03/2011
11/05/2011
02/06/2011
05/07/2010
05/10/2010
29/12/2010
26/01/2011
16/02/2011
09/03/2011
11/05/2011
02/06/2011
19/05/2010
05/10/2010
20/12/2010
26/01/2011
8/02/2011
16/02/2011
05/05/2011
09/06/2011
28/06/2010
12/10/2010
20/12/2010
06/01/2011
08/02/2011
24/02/2011
26/05/2011
21/06/2011
12/05/2010
27/10/2010
01/12/2010
06/01/2011
01/02/2011
03/03/2011
05/05/2011
02/06/2011
Q
(m3/s)
V
(m)
Y
(m)
B
(m)
A
(m2)
R
(m)
S
(m/m)
d50
(mm)
Tb
(kg/s)
7.21
5.21
5.58
3.99
12.79
4.91
3.18
7.69
1.6
2.10
6.10
2.25
1.65
1.95
3.14
2.97
0.79
0.55
1.03
0.66
1.32
0.62
1.52
0.72
0.73
1.33
0.56
1.18
2.59
1.41
2.21
4.7
6.44
2.32
4.06
5.68
5.39
6.6
2.23
4.6
1.27
0.776
5.25
2.29
1.19
1.02
1.68
2.29
0.6
0.54
0.56
0.55
0.82
0.56
0.53
0.73
0.56
0.5
0.73
0.58
0.55
0.54
0.61
0.58
0.37
0.31
0.48
0.42
0.47
0.45
0.52
0.37
0.37
0.45
0.15
0.45
1.22
0.6
0.55
0.78
0.66
0.53
0.58
0.6
1.56
0.68
0.49
0.62
0.49
0.4
0.69
0.58
0.51
0.52
0.56
0.54
0.87
0.65
0.88
0.52
1
0.8
0.47
0.85
0.42
0.53
1.15
0.5
0.45
0.52
0.63
0.7
0.3
0.33
0.37
0.28
0.6
0.37
0.38
0.3
0.27
0.3
0.45
0.35
0.3
0.33
0.36
0.52
0.94
0.39
0.57
1.04
0.34
1.03
0.37
0.62
0.46
0.4
0.86
0.64
0.5
0.5
0.27
0.5
19
17.5
17
17.3
17
17.2
15
14
9
9.5
10.3
9
9
9
9.3
8.8
7.7
7
7
7.6
9.2
8.3
8.8
7.5
12.32
12.7
13
12.4
12
12.32
12.2
12.8
12.1
13.4
14
13.4
12.8
13.2
12.8
13.3
11.4
11.3
13
12.4
11
11.7
11.7
12
12.07
9.68
9.96
7.20
15.51
8.77
6.00
10.59
2.87
4.19
8.37
3.90
2.98
3.58
5.15
5.17
2.15
1.75
2.14
1.59
2.84
1.39
2.89
1.97
1.99
2.93
3.75
2.65
2.12
2.36
4.03
6.03
9.78
4.39
6.95
9.50
1.56
9.64
4.56
7.43
2.57
1.94
7.57
3.95
2.32
1.97
3.00
4.23
0.626
0.547
0.574
0.412
0.885
0.503
0.395
0.735
0.313
0.428
0.760
0.421
0.326
0.388
0.530
0.559
0.242
0.274
0.300
0.207
0.303
0.166
0.322
0.259
0.161
0.230
0.286
0.213
0.176
0.188
0.320
0.464
0.688
0.324
0.487
0.690
0.268
0.699
0.352
0.548
0.242
0.169
0.567
0.314
0.209
0.167
0.253
0.346
0.0005
0.0005
0.0005
0.0027
0.0070
0.00075
0.0090
0.0046
0.00076
0.00076
0.00076
0.00300
0.01850
0.00070
0.00130
0.00120
0.0060
0.0006
0.0010
0.0010
0.0096
0.0066
0.0001
0.0020
0.0010
0.0010
0.0010
0.0062
0.0048
0.0051
0.0008
0.0008
0.0021
0.0021
0.0021
0.0020
0.0051
0.0003
0.0020
0.0010
0.0010
0.0010
0.0010
0.0003
0.0057
0.0312
0.0040
0.0050
1.04
0.87
0.80
1.04
0.98
0.97
1.22
0.67
0.91
0.75
0.90
0.98
1.08
0.69
0.7
0.75
1.17
0.99
0.87
1.21
1.40
1.17
1.70
0.80
1.31
1.02
1.20
1.83
1.12
1.22
1.1
0.98
0.75
0.87
0.80
0.79
0.74
0.86
0.85
0.80
1.51
1.29
1.10
1.52
1.84
1.56
1.5
1.53
1.9
0.66
0.88
0.63
2.098
0.72
0.745
1.407
0.168
0.299
0.859
0.304
0.253
0.346
0.75
0.44
0.064
0.128
0.113
0.073
0.265
0.081
0.247
0.086
0.09
0.223
0.13
0.092
0.347
0.14
0.813
0.9
0.89
0.341
1.473
0.728
0.876
1.051
0.527
0.896
0.128
0.174
1.04
0.293
0.116
0.133
0.337
0.523
9
APPENDIX B
RIVER SURVEYOR CROSS SECTIONAL DATA FOR ARA- KURAU
CONFLUENCE
Figure B.1: Survoyed boundry and cross sections in Ara-Kurau confluence (9 April
2012)
Table B.1: The measured data with river surveyor of Ara River in Ara-Kurau confluence
Discharge Measurement Summary
Date Measured: Tuesday, April 09, 2012
Site I nformation
Measurement I nformation
Site Name
Station Number
Location
Party
Boat/ Motor
Meas. Number
Ara-Kurau Junction
Ara Branch
System I nformation
System Setup
System Type
Serial Number
Firmware Version
Software Version
RS-S5
515
2.00
3.01
Units
Transducer Depth (m)
Salinity (ppt)
Magnetic Declination (deg)
Discharge Calculation Settings
Track Reference
Depth Reference
Coordinate System
Distance
Velocity
Area
Discharge
Temperature
0.13
0.0
-6.0
m
m/ s
m2
m3/s
degC
Discharge Results
GPS-VTG
Bottom-Track
ENU
Left Method
Right Method
Top Fit Type
Bottom Fit Type
Distance
Mean Vel
Sloped Bank
Sloped Bank
Power Fit
Power Fit
Width (m)
Area (m2)
Mean Speed (m/ s)
Total Q (m3/s)
22.21
10.1
1.281
6.432
Measurement Results
Tr
#
Time
Discharge
%
Time Duration Temp. Track DMG Width Area Boat Water Left Right Top Middle Bottom Total MBTotal Measured
1L
2:17:16
PM
0:03:10
30.9
34.70
23.75
25.75
10.5
0.183
0.629
0.00
0.01
3.01
2.76
0.86
6.635
--
41.6
2R
2:20:40
PM
0:02:25
30.7
33.44
26.98
28.58
11.4
0.231
0.535
0.00
0.00
2.73
2.63
0.76
6.116
--
43.0
2:41:56
3L
PM
0:02:12
30.2
23.24
20.15
21.35
11.5
0.176
0.563
0.00
-0.02
2.61
3.06
0.82
6.468
--
47.0
2:44:32
4R
PM
0:02:13
30.2
24.91
21.62
22.82
12.0
0.187
0.634
0.00
-0.02
3.13
3.54
0.94
7.591
--
46.4
2:56:46
5L
PM
0:01:55
30.2
20.18
16.86
17.66
9.5
0.175
0.684
0.00
0.00
2.40
3.06
1.03
6.500
--
47.1
2:58:56
6R
PM
0:01:48
30.2
20.40
17.64
18.44
10.3
0.189
0.666
0.00
0.00
2.50
3.22
1.15
6.871
--
46.9
3:11:49
7L
PM
0:01:27
30.2
16.15
15.24
16.04
9.7
0.186
0.611
0.00
0.01
1.78
2.99
1.14
5.920
--
50.4
3:13:28
PM
0:01:07
30.1
17.23
14.75
15.55
9.7
0.257
0.537
0.00
0.00
1.36
2.64
1.21
5.220
--
50.6
3:15:06
9R
PM
0:01:50
30.1
16.50
14.91
15.71
0.7
0.150
9.543
0.00
0.07
1.99
3.31
1.09
6.459
--
51.2
3:29:08
10 L
PM
0:01:58
30.0
28.00
24.13
24.93
10.0
0.237
0.593
0.00
0.03
2.40
2.73
0.76
5.919
--
46.2
3:31:32
11 R
PM
0:01:40
30.0
27.74
24.04
24.84
10.5
0.277
0.650
0.00
0.03
2.82
3.21
0.78
6.841
--
47.0
3:38:59
12 L
PM
0:02:33
29.9
33.00
27.47
28.37
12.2
0.216
0.509
0.00
0.00
2.62
2.78
0.78
6.188
--
45.0
3:41:47
PM
0:02:07
29.9
32.73
27.84
28.74
13.7
0.258
0.500
0.01
0.00
2.83
3.20
0.85
6.881
--
46.4
Mean
30.2
25.25
21.18
22.21
10.1
0.209
1.281
0.00
0.01
2.48
3.01
0.94
6.432
0.000
46.8
Std Dev
0.3
6.58
4.72
4.87
3.0
0.038
2.386
0.00
0.02
0.48
0.27
0.16
0.562
0.000
2.7
COV
0.0
0.261
0.223
0.219
0.293
0.180
1.862 2.461
2.729 0.194
0.091
0.172
0.087
0.000
0.057
8R
13 R
Exposure Time: 0:26:25
FigureB.2: Surveyed cross sections in Ara branch (9 April 2012)
TableB.2: The measured data with river surveyor of Kurau River in Ara-Kurau confluence
Discharge Measurement Summary
Site I nformation
Site Name
Station Number
Location
Ara-Kurau Junction
Party
Boat/ Motor
Meas. Number
Kurau Branch
System I nformation
System Type
Serial Number
Firmware Version
Software Version
Date Measured: Tuesday, April 09, 2012
Measurement I nformation
System Setup
RS-S5
515
2.00
3.01
Units
Transducer Depth (m)
Salinity (ppt)
Magnetic Declination (deg)
Discharge Calculation Settings
Track Reference
Depth Reference
Coordinate System
Distance
Velocity
Area
Discharge
Temperature
0.16
0.0
-6.0
m
m/ s
m2
m3/s
degC
Discharge Results
GPS-VTG
Bottom-Track
ENU
Left Method
Right Method
Top Fit Type
Bottom Fit Type
Sloped Bank
Sloped Bank
Power Fit
Power Fit
Width (m)
Area (m2)
Mean Speed (m/ s)
Total Q (m3/s)
25.12
23.4
0.594
6.331
Measurement Results
Tr
#
Time
Distance
Mean Vel
Discharge
%
Time Duration Temp. Track DMG Width Area Boat Water Left Right Top Middle Bottom Total MBTotal Measured
1R
11:56:14
AM
0:01:44
29.7
26.88
24.59
25.99
22.5
0.259
0.360
0.04
0.00
2.24
4.97
0.86
8.122
--
61.2
2L
11:58:26
AM
0:01:36
29.3
29.42
24.70
26.10
21.7
0.306
0.278
0.03
0.00
1.74
3.52
0.73
6.030
--
58.4
3L
12:02:57
PM
0:02:15
28.8
22.04
20.50
21.90
1.3
0.163
5.060
0.06
0.04
1.63
4.14
0.62
6.491
--
63.8
4R
12:05:37
PM
0:01:08
28.7
20.81
20.24
21.64
20.0
0.306
0.397
0.01
0.02
2.02
5.15
0.73
7.923
--
65.0
5L
12:07:54
PM
0:03:32
28.6
23.94
20.83
22.83
18.8
0.113
0.359
0.03
0.03
1.83
4.23
0.64
6.760
--
62.5
6R
12:11:55
PM
0:01:17
28.5
22.14
20.31
22.31
19.9
0.287
0.411
0.03
0.04
2.25
4.86
0.98
8.155
--
59.5
7R
12:55:16
PM
0:01:34
31.2
25.09
23.33
24.83
17.2
0.267
0.390
0.00
0.00
1.81
4.08
0.82
6.717
--
60.8
8L
12:57:17
PM
0:01:31
30.6
23.72
23.13
24.63
16.4
0.261
0.342
0.01
0.00
1.58
3.33
0.67
5.600
--
59.5
9R
1:00:53
PM
0:01:18
30.1
22.31
20.87
22.87
18.9
0.286
0.396
0.00
0.00
2.06
4.54
0.88
7.483
--
60.6
10 L
1:02:37
PM
0:01:16
29.9
22.73
21.22
23.22
19.1
0.299
0.329
0.00
0.00
1.58
4.07
0.63
6.268
--
64.8
11 R
1:06:31
PM
0:01:22
29.5
24.06
21.78
24.28
21.9
0.293
0.361
0.02
0.00
2.11
4.74
1.04
7.901
--
59.9
12 L
1:08:15
PM
0:01:32
29.4
23.20
21.88
24.38
22.2
0.252
0.306
0.03
-0.01
1.61
4.54
0.65
6.815
--
66.5
13 L
1:35:09
PM
0:01:31
29.0
23.47
21.30
23.30
26.1
0.258
0.214
0.04
0.04
1.30
3.44
0.76
5.588
--
61.6
14 R
1:37:05
PM
0:01:10
29.0
23.40
21.54
23.54
25.8
0.334
0.303
0.04
-0.06
1.72
5.33
0.77
7.815
--
67.3
15 L
1:44:24
PM
0:03:07
28.8
42.07
27.34
29.04
28.8
0.225
-0.090
0.03
0.03 -0.34
-1.87
-0.43
-2.581
--
69.4
16 R
1:48:17
PM
0:01:23
28.6
41.97
38.89
41.09
74.1
0.506
0.084
0.02
0.00
0.94
3.85
1.40
6.208
--
62.0
Mean
29.3
26.08
23.28
25.12
23.4
0.276
0.594
0.02
0.01
1.63
3.93
0.74
6.331
0.000
62.7
Std Dev
0.8
6.34
4.45
4.50
14.3
0.080
1.160
0.02
0.02
0.61
1.61
0.36
2.453
0.000
3.0
COV
0.0
0.243
0.191
0.179
0.611
0.290
1.954 0.693
2.748 0.371
0.409
0.486
0.387
0.000
0.049
Exposure Time: 0:27:16
FigureB.3: Surveyed cross sections in Kurau branch (9 April 2012)
Table B.3: The measured data with river surveyor at main Kurau in Ara-Kurau confluence
Discharge Measurement Summary
Site I nformation
Date Measured: Tuesday, April 09, 2012
Measurement I nformation
Site Name
Station Number
Location
Party
Boat/ Motor
Meas. Number
Ara-Kurau Junction
M a i n Ku r a u
System I nformation
System Setup
System Type
Serial Number
Firmware Version
Software Version
RS-S5
515
2.00
3.01
Units
Transducer Depth (m)
Salinity (ppt)
Magnetic Declination (deg)
Discharge Calculation Settings
Track Reference
Depth Reference
Coordinate System
Distance
Velocity
Area
Discharge
Temperature
0.16
0.0
-6.0
m
m/ s
m2
m3/s
degC
Discharge Results
GPS-VTG
Bottom-Track
ENU
Left Method
Right Method
Top Fit Type
Bottom Fit Type
Distance
Mean Vel
Sloped Bank
Sloped Bank
Power Fit
Power Fit
Width (m)
Area (m2)
Mean Speed (m/ s)
Total Q (m3/s)
27.10
19.9
0.638
12.571
Measurement Results
Tr
#
Time
Discharge
%
Time Duration Temp. Track DMG Width Area Boat Water Left Right Top Middle Bottom Total MBTotal Measured
3:14:29
PM
0:06:44
30.4
54.14
27.74
28.74
19.5
0.134
0.597
0.00
0.00
3.08
6.57
2.01 11.654
--
56.4
3:21:23
2R
PM
0:03:05
30.5
47.47
32.49
33.49
22.9
0.257
0.575
0.00
0.00
3.68
7.15
2.34 13.175
--
54.3
3:24:44
3L
PM
0:02:03
30.4
34.53
27.75
28.75
21.0
0.281
0.525
0.00
0.00
3.04
6.11
1.88 11.029
--
55.4
3:26:59
4R
PM
0:02:00
30.4
36.77
27.31
28.31
20.2
0.306
0.620
0.00
0.00
3.50
6.98
2.05 12.519
--
55.7
3:30:14
5L
PM
0:02:10
30.3
33.96
26.42
27.42
20.7
0.261
0.561
0.00
0.00
2.73
6.78
2.10 11.619
--
58.4
3:33:16
6R
PM
0:01:30
30.4
30.48
25.43
26.73
20.6
0.339
0.600
0.00
0.00
2.90
7.47
2.02 12.385
--
60.3
3:43:02
PM
0:01:11
30.3
18.14
16.50
22.70
17.1
0.255
0.787
-0.02
0.00
3.44
7.76
2.29 13.476
--
57.5
3:46:22
8L
PM
0:01:23
30.4
22.32
19.99
22.99
18.0
0.269
0.699
0.01
0.00
3.43
6.97
2.22 12.617
--
55.2
3:48:04
9R
PM
0:01:35
30.5
25.14
20.63
23.63
18.3
0.265
0.697
0.02
0.00
3.39
7.21
2.11 12.732
--
56.6
4:39:39
10 R
PM
0:02:16
32.7
29.34
26.72
27.72
19.8
0.216
0.735
0.08
0.00
5.01
7.32
2.13 14.538
--
50.3
4:42:18
11 L
PM
0:01:44
32.3
29.05
26.65
27.65
20.3
0.279
0.617
0.00
0.00
4.14
6.55
1.85 12.539
--
52.2
Mean
30.8
32.85
25.24
27.10
19.9
0.260
0.638
0.01
0.00
3.49
6.99
2.09 12.571
0.000
55.7
Std Dev
0.8
10.03
4.27
2.97
1.5
0.050
0.077
0.03
0.00
0.61
0.45
0.15
0.917
0.000
2.6
COV
0.0
0.305
0.169
0.110
0.077
0.191
0.121 2.859
-2.680 0.175
0.064
0.071
0.073
0.000
0.047
1L
7R
Exposure Time: 0:25:41
FigureB.4: Surveyed cross sections in main Kurau (9 April 2012)
Table 9.4: The measured data with river surveyor at Ara-Kurau confluence
Discharge Measurement Summary
Date Measured: Thursday, July 19, 2012
Site I nformation
Measurement I nformation
Site Name
Station Number
Location
Ara-Kurau Junction
System I nformation
System Type
Serial Number
Firmware Version
Software Version
Party
Boat/ Motor
Meas. Number
System Setup
RS-S5
515
2.00
3.01
Units
Transducer Depth (m)
Salinity (ppt)
Magnetic Declination (deg)
Discharge Calculation Settings
Track Reference
Depth Reference
Coordinate System
Distance
Velocity
Area
Discharge
Temperature
0.16
0.0
-6.0
m
m/ s
m2
m3/s
degC
Discharge Results
GPS-VTG
Bottom-Track
ENU
Left Method
Right Method
Top Fit Type
Bottom Fit Type
Sloped Bank
Sloped Bank
Power Fit
Power Fit
Width (m)
Area (m2)
Mean Speed (m/ s)
Total Q (m3/s)
21.63
18.9
0.393
9.396
Measurement Results
Tr
#
Time
Distance
Mean Vel
Discharge
%
Time Duration Temp. Track DMG Width Area Boat Water Left Right Top Middle Bottom Total MBTotal Measured
1L
11:19:48
AM
0:02:00
27.9
20.42
18.93
20.93
13.5
0.170
0.410
0.00
0.00
2.11
2.78
0.63
5.520
--
50.4
2R
11:22:06
AM
0:01:19
27.7
20.80
19.50
21.50
13.6
0.263
0.497
0.00
-0.01
2.60
3.41
0.75
6.749
--
50.4
3L
12:23:36
PM
0:01:08
28.4
19.15
1.86
2.36
0.9
0.282
-1.098
-0.02
0.00 -0.46
-0.49
-0.06
-1.030
--
47.8
4L
12:24:52
PM
0:01:09
28.2
22.04
20.93
21.93
14.5
0.319
0.439
0.01
0.00
2.38
3.24
0.75
6.379
--
50.8
5R
12:26:30
PM
0:01:57
28.0
27.70
21.90
22.90
15.1
0.237
0.483
0.02
-0.01
2.71
3.78
0.79
7.297
--
51.7
6R
12:29:19
PM
0:01:22
27.9
24.04
21.74
22.74
15.2
0.293
0.515
0.02
0.00
2.92
4.06
0.85
7.845
--
51.7
7L
1:22:00
PM
0:01:55
27.6
24.06
22.28
23.78
25.6
0.209
0.452
0.00
0.00
2.12
7.44
2.03 11.590
--
64.2
8R
1:24:07
PM
0:01:09
27.7
24.33
22.18
23.68
25.9
0.353
0.574
0.00
0.00
2.76
9.50
2.61 14.878
--
63.9
9L
1:26:17
PM
0:01:00
27.7
20.31
19.40
20.90
28.1
0.338
0.472
-0.04
0.00
2.28
8.84
2.16 13.248
--
66.4
10 R
1:27:27
PM
0:01:08
27.7
21.02
18.45
19.95
27.2
0.309
0.571
-0.02
0.00
2.68
10.19
2.69 15.536
--
65.4
11 L
1:34:39
PM
0:01:30
27.9
27.80
26.61
27.61
16.3
0.309
0.484
0.00
0.00
2.96
4.04
0.89
7.898
--
51.2
12 R
1:36:21
PM
0:01:07
27.9
28.80
27.08
28.08
18.7
0.430
0.497
0.00
0.00
3.29
4.74
1.25
9.274
--
51.1
13 L
1:38:47
PM
0:01:23
28.0
27.08
25.51
26.51
14.6
0.326
0.580
0.00
0.00
3.38
4.04
1.05
8.483
--
47.7
14 L
1:48:27
PM
0:02:53
27.9
21.57
19.58
20.58
26.6
0.125
0.462
-0.03
-0.01
2.37
7.86
2.09 12.290
--
63.6
15 R
1:51:38
PM
0:01:02
27.9
21.04
20.05
21.05
26.8
0.339
0.558
-0.02
0.00
2.82
9.97
2.22 14.981
--
66.3
Mean
27.9
23.34
20.40
21.63
18.9
0.287
0.393
-0.01
0.00
2.46
5.56
1.38
9.396
0.000
56.2
Std Dev
0.2
3.08
5.61
5.71
7.4
0.074
0.402
0.02
0.00
0.86
3.07
0.81
4.295
0.000
7.3
COV
0.0
0.132
0.275
0.264
0.393
0.259
1.022
3.065
-2.550 0.350
0.551
0.589
0.457
0.000
0.130
Exposure Time: 0:22:02
T 1 20120719111948 i
T 2 20120719112205 i
T 3 20120719122334 i
T 4 20120719122451 i
T 5 20120719122629 i
T 6 20120719122917 i
FigureB.5: Surveyed cross sections in Ara -Kurau confluence (19 July 2012)
FigureB.6: Surveyed cross sections in Ara -Kurau confluence (19 July 2012)
Table B.5: The measured data with river surveyor at Ara-Kurau confluence
Discharge Measurement Summary
Site I nformation
Measurement I nformation
Site Name
Station Number
Location
Ara-Kurau Junction
System I nformation
System Type
Serial Number
Firmware Version
Software Version
Date Measured: Monday, Oct ober 08 , 2012
Party
Boat/ Motor
Meas. Number
System Setup
RS-S5
515
2.00
3.01
Units
Transducer Depth (m)
Salinity (ppt)
Magnetic Declination (deg)
Discharge Calculation Settings
Track Reference
Depth Reference
Coordinate System
Distance
Velocity
Area
Discharge
Temperature
0.15
0.0
-6.0
m
m/ s
m2
m3/s
degC
Discharge Results
GPS-VTG
Bottom-Track
ENU
Left Method
Right Method
Top Fit Type
Bottom Fit Type
Sloped Bank
Sloped Bank
Power Fit
Power Fit
20.04
12.7
0.484
7.064
Width (m)
Area (m2)
Mean Speed (m/ s)
Total Q (m3/s)
Measurement Results
Tr
#
Time
Distance
Discharge
%
1R
10:58:30
AM
0:01:59
26.7
20.23
19.25
20.75
10.0
0.170
0.500
0.00
-0.01
2.32
2.05
0.64
4.999
--
40.7
2L
11:02:21
AM
0:02:15
26.7
23.00
20.71
22.21
11.2
0.170
0.378
0.00
0.00
1.86
1.81
0.55
4.213
--
42.8
3R
11:04:49
AM
0:01:45
26.7
22.05
20.18
21.18
11.5
0.210
0.442
0.00
0.00
2.17
2.23
0.66
5.061
--
44.0
4L
11:23:33
AM
0:02:15
26.8
27.36
24.29
25.29
17.4
0.203
0.540
0.00
0.00
2.51
5.13
1.73
9.370
--
54.7
5R
11:26:03
AM
0:01:44
26.9
26.68
22.97
23.97
16.3
0.257
0.639
0.00
0.00
2.80
5.44
2.18 10.424
--
52.2
6R
11:34:50
AM
0:01:44
27.1
28.74
24.92
25.92
11.2
0.276
0.435
0.00
0.00
2.16
1.98
0.72
4.863
--
40.8
7L
11:36:43
AM
0:01:34
27.2
29.04
25.27
26.27
10.5
0.309
0.426
0.00
0.00
2.10
1.73
0.66
4.494
--
38.5
8R
11:39:23
AM
0:01:46
27.2
26.28
22.78
23.78
10.1
0.248
0.464
0.00
0.00
2.05
2.04
0.62
4.701
--
43.3
9L
11:41:25
AM
0:01:26
27.3
24.79
22.77
23.77
9.4
0.288
0.398
0.00
0.00
1.54
1.68
0.51
3.726
--
45.0
10 R
11:52:25
AM
0:01:32
27.3
24.60
20.66
21.66
15.4
0.267
0.622
0.00
0.00
2.07
5.47
2.05
9.581
--
57.1
11 L
11:58:41
AM
0:02:36
27.4
24.45
21.98
22.98
15.4
0.157
0.475
0.00
0.00
1.53
4.32
1.49
7.337
--
58.9
12 R
12:01:28
PM
0:01:19
27.4
24.13
22.04
23.04
15.8
0.305
0.666
0.00
0.00
2.46
5.96
2.13 10.553
--
56.5
13 L
12:03:15
PM
0:01:27
27.4
18.12
16.78
18.28
16.9
0.208
0.554
-0.02
0.00
1.91
5.67
1.79
9.352
--
60.4
14 R
12:04:55
PM
0:01:00
27.4
17.88
16.92
18.42
16.7
0.298
0.647
0.01
0.00
2.18
6.82
1.80 10.808
--
63.1
15 L
12:22:04
PM
0:01:19
27.4
19.92
18.30
19.30
18.1
0.252
0.548
0.02
0.00
2.42
5.78
1.70
9.916
--
58.3
16 R
12:23:33
PM
0:00:49
27.4
19.92
18.13
19.13
17.9
0.407
0.700
0.03
0.00
2.98
7.25
2.24 12.508
--
58.0
17 L
12:25:41
PM
0:01:16
27.5
24.47
19.68
20.68
16.9
0.322
0.562
0.04
0.00
2.38
5.57
1.54
9.529
--
58.5
18 R
12:27:07
PM
0:01:01
27.5
23.90
19.93
20.93
17.4
0.392
0.739
0.06
0.00
3.38
7.19
2.21 12.838
--
56.0
19 L
1:01:04
PM
0:02:55
24.4
0.00
0.00
0.55
0.0
0.000
0.000
0.00
0.00
0.00
0.00
0.00
0.000
--
0.0
20 L
12:13:27
PM
0:01:17
26.8
4.20
1.18
2.18
0.0
0.055
0.000
0.00
0.00
0.00
0.00
0.00
0.000
--
0.0
21 L
12:15:21
PM
0:02:09
26.7
21.91
19.59
20.64
9.6
0.170
0.424
0.00
0.00
1.93
1.66
0.48
4.068
--
40.8
Mean
27.0
21.51
18.97
20.04
12.7
0.236
0.484
0.01
0.00
2.04
3.80
1.22
7.064
0.000
46.2
Std Dev
0.7
7.03
6.41
6.47
5.1
0.095
0.187
0.02
0.00
0.79
2.32
0.75
3.684
0.000
COV
0.0
0.327
0.338
0.323
0.404
0.404
0.386 2.515
-3.085 0.386
0.612
0.614
0.521
0.000
Exposure Time: 0:35:08
.
Mean Vel
Time Duration Temp. Track DMG Width Area Boat Water Left Right Top Middle Bottom Total MBTotal Measured
16.8
0.365
FigureB.7: Surveyed cross sections in Ara -Kurau confluence (8 October 2012)
FigureB.8: Surveyed cross sections in Ara -Kurau confluence (8 October 2012)
10 APPENDIX C
INPUT FILE FOR SSIIM
Table C.1: Calculation of sediment input for SSIIM
Q (m3/s)
Tb (kg/s)
Tb (Ton/s)
Tb /γs
(Ton/s/m3)
(Tb /γs)/Q
Ton
Kurau
4
0.781240297
0.00078124
0.000294808
7.37019E-05
5
1.006646488
0.001006646
0.000379867
7.59733E-05
6
1.232052678
0.001232053
0.000464926
7.74876E-05
7
1.457458869
0.001457459
0.000549984
7.85692E-05
8
1.682865059
0.001682865
0.000635043
7.93804E-05
9
1.90827125
0.001908271
0.000720102
8.00114E-05
10
2.13367744
0.002133677
0.000805161
8.05161E-05
11
2.356464916
0.002356465
0.000889232
8.08393E-05
12
2.581871195
0.002581871
0.000974291
8.11909E-05
14
3.009115796
0.003009116
0.001135515
8.11082E-05
15
3.234523065
0.003234523
0.001220575
8.13716E-05
18
3.89503179
0.003895032
0.001469823
8.16569E-05
20
4.345841887
0.004345842
0.00163994
8.1997E-05
23
5.01289886
0.005012899
0.00189166
8.22461E-05
27
5.919773243
0.005919773
Ara
0.002233877
8.27362E-05
4
0.793262937
0.000793263
0.000299345
7.48361E-05
5
1.021404503
0.001021405
0.000385436
7.70871E-05
6
1.250642744
0.001250643
0.000471941
7.86568E-05
7
1.490787633
0.001490788
0.000562561
8.03659E-05
8
1.72022527
0.001720225
0.000649142
8.11427E-05
9
1.949662908
0.001949663
0.000735722
8.17469E-05
10
2.168692387
0.002168692
0.000818374
8.18374E-05
11
2.396541592
0.002396542
0.000904355
8.22141E-05
12
2.626406505
0.002626407
0.000991097
8.25914E-05
14
3.06808168
0.003068082
0.001157767
8.26976E-05
15
3.298827851
0.003298828
0.001244841
8.29894E-05
18
3.976515616
0.003976516
0.001500572
8.33651E-05
20
4.434056699
0.004434057
0.001673229
8.36614E-05
23
5.133188694
0.005133189
0.001937052
8.42197E-05
27
6.060891318
0.006060891
0.002287129
8.47085E-05
Table C. 2: Fractional sediment input for SSIIM (Kurau)
Size (mm)
3.67
2.34
2.22
1.37
1
0.7
0.47
0.38
0.099745682
0.062509271
0.046679693
0.166047007
0.121483118
0.132082221
0.212459885
0.158993123
0.162588153
0.170485464
0.109354695
0.215291484
0.104558858
0.092083149
0.111765134
0.033873062
4
0.000007351
0.000004607
0.000003440
0.000012238
0.000008954
0.000009735
0.000015659
0.000011718
5
0.000007578
0.000004749
0.000003546
0.000012615
0.000009229
0.000010035
0.000016141
0.000012079
6
0.000007729
0.000004844
0.000003617
0.000012867
0.000009413
0.000010235
0.000016463
0.000012320
7
0.000007837
0.000004911
0.000003668
0.000013046
0.000009545
0.000010378
0.000016693
0.000012492
8
0.000007918
0.000004962
0.000003705
0.000013181
0.000009643
0.000010485
0.000016865
0.000012621
9
0.000007981
0.000005001
0.000003735
0.000013286
0.000009720
0.000010568
0.000016999
0.000012721
10
0.000008031
0.000005033
0.000003758
0.000013369
0.000009781
0.000010635
0.000017106
0.000012802
11
0.000008063
0.000005053
0.000003774
0.000013423
0.000009821
0.000010677
0.000017175
0.000012853
12
0.000013201
0.000013842
0.000008879
0.000017480
0.000008489
0.000007476
0.000009074
0.000002750
14
0.000013187
0.000013828
0.000008870
0.000017462
0.000008481
0.000007469
0.000009065
0.000002747
15
0.000013230
0.000013873
0.000008898
0.000017519
0.000008508
0.000007493
0.000009095
0.000002756
18
0.000013276
0.000013921
0.000008930
0.000017580
0.000008538
0.000007519
0.000009126
0.000002766
20
0.000013332
0.000013979
0.000008967
0.000017653
0.000008574
0.000007551
0.000009164
0.000002777
23
0.000013372
0.000014022
0.000008994
0.000017707
0.000008600
0.000007573
0.000009192
0.000002786
27
0.000013452
0.000014105
0.000009048
0.000017812
0.000008651
0.000007619
0.000009247
0.000002803
Fraction %
3
Q (m /s)
Table C. 3: Fractional sediment input for SSIIM (Ara)
Size (mm)
3.67
2.34
2.22
1.37
1
0.7
0.47
0.38
Fraction %
0.084424126
0.068001208
0.0667869
0.125382672
0.136256792
0.131892238
0.237721259
0.149534805
0.162588153
0.170485464
0.109354695
0.215291484
0.104558858
0.092083149
0.111765134
0.033873062
4
0.000006318
0.000005089
0.000004998
0.000009383
0.000010197
0.000009870
0.000017790
0.000011191
5
0.000006508
0.000005242
0.000005148
0.000009665
0.000010504
0.000010167
0.000018325
0.000011527
6
0.000006641
0.000005349
0.000005253
0.000009862
0.000010718
0.000010374
0.000018698
0.000011762
7
0.000006785
0.000005465
0.000005367
0.000010076
0.000010950
0.000010600
0.000019105
0.000012018
8
0.000006850
0.000005518
0.000005419
0.000010174
0.000011056
0.000010702
0.000019289
0.000012134
9
0.000006901
0.000005559
0.000005460
0.000010250
0.000011139
0.000010782
0.000019433
0.000012224
10
0.000013306
0.000013952
0.000008949
0.000017619
0.000008557
0.000007536
0.000009147
0.000002772
11
0.000013367
0.000014016
0.000008991
0.000017700
0.000008596
0.000007571
0.000009189
0.000002785
12
0.000013428
0.000014081
0.000009032
0.000017781
0.000008636
0.000007605
0.000009231
0.000002798
14
0.000013446
0.000014099
0.000009043
0.000017804
0.000008647
0.000007615
0.000009243
0.000002801
15
0.000013493
0.000014148
0.000009075
0.000017867
0.000008677
0.000007642
0.000009275
0.000002811
18
0.000013554
0.000014213
0.000009116
0.000017948
0.000008717
0.000007677
0.000009317
0.000002824
20
0.000013602
0.000014263
0.000009149
0.000018012
0.000008748
0.000007704
0.000009350
0.000002834
23
0.000013693
0.000014358
0.000009210
0.000018132
0.000008806
0.000007755
0.000009413
0.000002853
27
0.000013773
0.000014442
0.000009263
0.000018237
0.000008857
0.000007800
0.000009467
0.000002869
3
Q (m /s)
Figure C.1: Timei file for Q=15 m3/s
Figure C.2: Timei file for Q=31m3/s
Figure C.3: Timei file for Q=43m3/s
Figure C.4: Timei file for Q=35 m3/s
Figure C.5: Timei file for Q=25 m3/s
Figure C.6: Timei file for Q=13 m3/s
16.6
16.5
Ara
RSK1
16.0
Elevation (m)
Elevation (m)
16.1
15.6
15.1
15.5
15.0
Q= 35 (mᵌ/s)
Q= 25 (mᵌ/s)
Q= 35 (mᵌ/s)
Q= 25 (mᵌ/s)
14.5
14.6
0
10
Distance (m)
20
0
30
RSK2
Elevation (m)
Elevation (m)
30
RSK3
16
16
15.5
15.5
15
Q= 35 (mᵌ/s)
Q= 25 (mᵌ/s)
14.5
15
14.5
Q= 35 (mᵌ/s)
Q= 25 (mᵌ/s)
14
14
0
10
20
Distance (m)
30
10
Distance (m)
20
30
16.5
RSK4
RSK5
Elevation (m)
16
0
40
16.5
Elevation (m)
20
16.5
16.5
15.5
16
15.5
15
Q= 35 (mᵌ/s)
Q= 25 (mᵌ/s)
14.5
15
Q= 35 (mᵌ/s)
Q= 25 (mᵌ/s)
14.5
14
14
0
10
Distance (m)
20
0
30
17
10
Distance (m)
20
30
16.5
RSK6
16.5
RSK7
16
Elevation (m)
Elevation (m)
10
Distance (m)
16
15.5
15.5
15
Q= 35 (mᵌ/s)
Q= 25 (mᵌ/s)
14.5
15
Q= 35 (mᵌ/s)
Q= 25 (mᵌ/s)
14.5
14
14
0
10
Distance (m)
20
30
0
10
20
Distance (m)
Figure C.7: Channel cross section profiles, Q=25m3/s
30
40
16.6
16.5
RSK1
16.1
Elevation (m)
Elevation (m)
Ara
15.6
15.1
10
Distance (m)
20
30
5
10
15
Distance (m)
20
25
RSK3
RSK2
16
Elevation (m)
16
Elevation (m)
0
16.5
16.5
15.5
15.5
15
Q= 25 (mᵌ/s)
Q= 13 (mᵌ/s)
14.5
15
14.5
14
Q= 25 (mᵌ/s)
Q= 13 (mᵌ/s)
14
0
10
20
Distance (m)
30
40
0
16.5
10
Distance (m)
20
30
17
RSK4
RSK5
16.5
Elevation (m)
16
Elevation (m)
Q= 25 (mᵌ/s)
Q= 13 (mᵌ/s)
14.5
0
15.5
15
Q= 25 (mᵌ/s)
Q= 13 (mᵌ/s)
14.5
16
15.5
15
Q= 25 (mᵌ/s)
Q= 13 (mᵌ/s)
14.5
14
14
0
10
Distance (m)
20
0
30
10
Distance (m)
20
30
17
17
RSK6
16
15.5
15
14
10
Distance (m)
20
16
15.5
15
Q= 25 (mᵌ/s)
Q= 13 (mᵌ/s)
14.5
Q= 25 (mᵌ/s)
Q= 13 (mᵌ/s)
14.5
0
RSK7
16.5
Elevation (m)
16.5
Elevation (m)
15.5
15.0
Q= 25 (mᵌ/s)
Q= 13 (mᵌ/s)
14.6
16.0
14
30
0
10
20
Distance (m)
Figure C.8: Channel cross section profiles, Q=13m3/s
30
40
Aminuddin Ab Ghani