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Benha University
Faculty of Engineering, Shobra
Civil Engineering Department
Scour Evaluation at the Nile River Bends on Rosetta Branch
A Thesis Submitted in Partial Fulfillment of the Requirements For the MSc
Degree in Civil Engineering
Submitted By
Fatma Samir Ahmed Saad
B.Sc. in Civil Engineering (2010)
Supervised By
Cairo – Egypt
March 2015
Prof. Dr. Gamal Helmy Mohamed Elsaeed
Professor of Water Resources, Civil Engineering
Dept.
Faculty of Engineering, Shobra, Benha University
Dr. Hossam El-Din Mohamed El-Sersawy
Associate Prof, Nile Research Institute.
National Water Research Center
Dr. Mohammad Mahmoud Mohammed Ibrahim
Lecturer, Civil Engineering Dept.
Faculty of Engineering, Shobra, Benha University
Benha University
Faculty of Engineering, Shobra
Civil Engineering Department
APPROVAL SHEET
Scour Evaluation at the Nile River Bends on Rosetta Branch
Examiners Committee
Name and occupation Signature
Prof. Dr. Nahla M. AbdelHamid AboulAtta
Professor of Irrigation design, Head of the Irrigation & Hydraulics Dept,
Faculty of Engineering, Ain Shams University
Prof. Dr. Medhat Saad Aziz
Director, Nile Research Institute
National Water Research Center
Prof. Dr. Gamal Helmy Mohamed Elsaeed
Professor of Water Resources, Civil Engineering Dept,
Faculty of Engineering, Shobra, Benha University
Cairo – Egypt
March 2015
Benha University
Faculty of Engineering, Shobra
Civil Engineering Department
DECLARATION
I declare that this thesis entitled “Scour Evaluation at the Nile River Bends on
Rosetta Branch” is the result of my own research except as cited in the
references. It is being submitted to the degree of Master of Science of
Philosophy in the Faculty of Engineering at Shoubra, Benha University. The
thesis has not been accepted for any degree and is not concurrently submitted in
candidature of any other degree.
Signature : ……………………………….
Name : ……………………………………
Date : ……………………………………..
Cairo – Egypt
March 2015
To
My beloved parents, my sister and
brother Aalaa & Ahmed
i
ACKNOWLEDGEMENTS
First of all, I wish to give all my thanks to God for the completion of this work
I wish to express my deepest sense of gratitude and sincerest appreciation to Dr. Gamal
Helmy El-Saied, Irrigation and Hydraulics Department, Faculty of Engineering - Shobra, for
his excellent advice enthusiastic guidance and continuous encouragement towards the
successful completion of this study.
Special thanks to Dr. Hossam El-Din Mohamed El-Sersawy, Associate Professor, Nile
Research Institute, National Water Research Center, for his help, effort and support me
throughout this study.
Special thanks also to Dr. Mohamed Ibrahim, Researcher, Faculty of Engineering - Shobra,
for his outstanding valuable help and supervision.
Special thanks are due to Dr. Medhat Aziz, Director, Nile Research Institute for his
continuous support and encouragement through this research and for his help in providing the
materials for conducting this research and valuable comments and discussions.
I would like to express my thanks to colleagues in Nile Research Institute who helped me in
the preparation of field measurements.
Last but not least I wish to express my deepest thanks, gratitude, and appreciation to my
family for their love, warm caring, support, and, great patience throughout the time of this
study.
Finally, I want to thank everyone who helped or advised me during my work or even wished
me good luck.
ii
TABLE OF CONTENTS
LIST OF FIGURES
LIST OF TABLES
LIST OF SYMBOLS
LIST OF ABBREVIATIONS
ABSTRACT
VI
XI
XII
XV
XVI
Chapter 1
Introduction
1-1 General 1
1-2 Problem Definition 2
1-3 Study Objectives 2
1-4 Methodology and Scope of Work 2
1-5 Thesis Layout 3
Chapter 2
Literature Review
2-1 Introduction 5
2-2 The Nile River 5
2-3 Rosetta Branch 6
2-4 Basic Principals and Concepts 7
2-4-1 Channel Types 7
2-5 Meander Characteristics 9
2-6 Scour Holes 12
2-7 Types of Models 19
2-7-1 Physical Models 19
2-7-2 Numerical Models 19
2-8 Previous Works in Morphological Changes in Rivers 20
2-9 Dredging 23
2-10 Sediment Transport 24
2-10-1 Factors Affecting Sediment Transport 24
2-10-1-1 Bed Shear Stress 24
2-10-1-2 Incipient Velocity 26
2-11 Bank Revetment 28
iii
2-11-1 Stone protection 29
2-11-2 Design of Stone 31
2-11-3 Filter Design 32
Chapter 3
Data Collection
3-1 Introduction 34
3-2 Site Description 34
3-3 Hydrographic Survey 35
3-4 Velocity Measurements 37
3-5 Bed Material samples 39
3-6 Hydrological Data 43
Chapter 4
Mathematical Model Preparation
4-1 General 46
4-2 “SMS” 2-D Model Formulation 48
4-2-1 Model Description 48
4-2-2Governing Equations 48
4-2-3 Numerical Techniques and Limitation 52
4-3 Model Preparation 53
4-3-1 Data Assignment 53
4-3-1-1 Roughness estimation (Manning Coefficient) 55
4-3-2 Network Design 57
4-3-3 Calibration Results 62
4-3-4 Verification Results 64
4-4 Sensitivity Analysis 67
4-5 Summary 68
Chapter 5
Morphological Changes
5-1 Introduction 69
5-2 Study Reach General Description 69
iv
5-3 Bed Elevation Contour Map at Years 1982, 1998, 2003 and 2006 71
5-4 Morphology Comparison of Years 1982, 1998, 2003 and 2006 72
5-4-1 Comparison of Bed Profiles and Thalweg Lines 72
5-5 Scour Holes in the Area of Study 75
Chapter 6
Model Application and Scour Prediction
6-1 Model Application 87
6-1-1 Model Runs for Minimum Discharge 87
6-1-2 Average Discharge 89
6-1-3 Maximum Discharge 91
6-1-4 Emergency Discharge 93
6-2 Scour Prediction 95
6-2-1 The Local Scour at Bridge Piers Prediction 96
6-2-2 Contraction Scour 99
6-2-3 Bend Scour 100
6-2-4 General Scour 101
6-2-5 Evaluation of Total Scour 103
Chapter 7
Alternative Solutions and Testing Results
7-1 Introduction 108
7-2 The Modeled Reach 108
7-3 Simulation of the Proposed Solutions and Results 109
7-3-1 The First Alternative Simulation 109
7-3-1-1 First Alternative Model Run Results 111
7-3-2 The Second Alternative Simulation 117
7-3-2-1 Second Alternative Model Run Results 119
7-3-3 Comparisons of Bed Shear Stress between the Two Alternatives 127
7-4 Riprap Design 133
Chapter 8
Conclusion & Recommendations
v
9-1 Summary 137
9-2 Conclusions 138
9-3 Recommendations 139
REFERENCES 140
ARABIC SUMMARY
vi
LIST OF FIGURES
Figure (2-1) The River Nile Barrages 6
Figure (2-2) Rosetta Branch 7
Figure (2-3) Major Types of River 9
Figure (2-4) Sinuosity Ranges 9
Figure (2-5) Meander Geometrical Characteristics of Curved River Reach 10
Figure (2-6) Scour Holes Downstream Bridges (Linda, 1993) 12
Figure (2-7) Flow Profile around a Circular Bridge Pier. (HEC18, 2012) 13
Figure (2-8) Contraction Scour 15
Figure (2-9) Live Bed and Clear Water Scour 15
Figure (2-10) General Scour 17
Figure (2-11) Schematic Diagram of Cross Sections Dredging Concepts 23
Figure (2-12) Cross Section at Columbia River 23
Figure (2-13) Stream Load 24
Figure (2-14) Critical Shear Stress as a Function of Grain Size [Lane (1955)] 26
Figure (2-15) Chang’s Approximations to Neill’s Competent Velocity Curves 28
Figure (2-16) Bank Protection Layers 29
Figure (2-17) Typical Stone Revetment at the Nile River in Egypt 30
Figure (2-18) An Example of the Applied Design for Stone Revetment 30
Figure (2-19) Grain Size Distributions of the Protective Layers 33
Figure (3-1) Location of the Study Reach 35
Figure (3-2) Piers of the Bridges 35
Figure (3-3) River Bed Elevation Survey Year 1982 36
Figure (3-4) River Bed Elevation Survey Year 1998 36
Figure (3-5) River Bed Elevation Survey Year 2003 37
Figure (3-6) River Bed Elevation Survey Year 2006 37
Figure (3-7) The Measured Velocity Locations 1998 38
Figure (3-8) The Measured Velocity Locations 2006 38
Figure (3-9) Braystoke Type Current Meter 38
Figure (3-10) Sketch Illustrated the Vertical Positions in Cross Section to Measure Water
Velocity 39
Figure (3-11) Computation of the Average Velocity 39
Figure (3-12) The Used Grab Sediment Sampler 40
Figure (3-13) Bed Material Sampling Locations 40
Figure (3-14) Grain Size Distribution Curves at C.S. No. (1) 41
Figure (3-15) Grain Size Distribution Curves at C.S. No. (2) 42
vii
Figure (3-16) Grain Size Distribution Curves at C.S. No. (3) 42
Figure (3-17) River Nile Hydrograph in Years 1982, 1998, 2003 and 2006 43
Figure (3-18) Water Discharge D.S Rositta Barrage at Years 1982, 1998, 2003 and 2006 43
Figure (3-19) Relation Between Water Level at Kafr Al-Zayat and Discharge Down
Stream Rosetta Barrage in Years 1990, 1991, 1994, 1995, 1996 and 1997 44
Figure (3-20) Relation Between Water Level at Kafr Al-Zayat and Discharge Down
Stream Rosetta Barrage in Years 1998, 2000, 2001, 2002, 2003 and 2004 44
Figure (3-21) Relation Between Water Level at Kafr Al-Zayat and Discharge Down
Stream Rosetta Barrage in Years 2009, 2010 and 2011 45
Figure (4-1) Flowchart of Proposed Approaches in this Study 47
Figure (4-2) 3-D Coordinate System 49
Figure (4-3) Depth Average Velocity Definition 50
Figure (4-4) Modeling Steps 53
Figure (4-5) Study Reach Roughness Coefficient Classification 56
Figure (4-6) Study Reach Mesh Element Composition 58
Figure (4-7) Bridge Mesh Element Composition 58
Figure (4-8) Quadrilateral and Triangular Element Aspect Ratios 59
Figure (4-9) Inverse Distance Weighted Average Interpolation Criteria 60
Figure (4-10) Planer and 3D Contouring after Interpolation Process 60
Figure (4-11) Design Mesh Elevation Assignment 61
Figure (4-12) Location of the Calibration Cross Sections 62
Figure (4-13) Flow Velocity Calibration at Cross Section (1) 63
Figure (4-14) Flow Velocity Calibration at Cross Section (2) 63
Figure (4-15) Flow Velocity Calibration at Cross Section (3) 63
Figure (4-16) Comparison between the Measurement and Simulated Water Surface
Elevation
64
Figure (4-17) Location of the Verification Cross Sections 65
Figure (4-18) Flow Velocity Verification at Cross Section (1) 65
Figure (4-19) Flow Velocity Verification at Cross Section (2) 66
Figure (4-20) Flow Velocity Verification at Cross Section (3) 66
Figure (4-21) Comparison between the Measurement and Simulated Water Surface
Elevation
66
Figure (4-22) Data Relative Importance to Modeling 67
Figure (5-1) General Plan of the Study Reach 69
Figure (5-2) Meandering Planform Parameters 70
Figure (5-3) River Bed Elevation for Years 1982 and 2003 71
viii
Figure (5-4) River Bed Elevation for Years 1998 and 2006 72
Figure (5-5) Comparison of Bed Profiles at Cross Sections (1) to (8) 74
Figure (5-6) Variation of the Lowest Bed Levels 74
Figure (5-7) Scour Holes Location in Study Area at Years 1982 75
Figure (5-8) Scour Holes Location in Study Area at Years 2003 75
Figure (5-9) Comparison of Scour Holes in Study Area at Years 1982 and 2003 77
Figure (5-10) Scour Hole Length Change at Years 1982, 1998, 2003 and 2006 82
Figure (5-11) Scour Hole Width Change at Years 1982, 1998, 2003 and 2006 82
Figure (5-12) Scour Hole Depth Change from Years 1982, 1998, 2003 and 2006 83
Figure (5-13) Cross Sections Location for Scour Holes 83
Figure (5-14) Scour Holes Cross Sections for Years 1982, 1998, 2003 and 2006 85
Figure (5-15) Longitudinal Sections Location for Scour Holes 85
Figure (5-16) Scour Holes Longitudinal Sections for Years 1982, 1998, 2003 and 2006 86
Figure (6-1) Comparison between the Cross Sections Velocity Profiles in Case of
Minimum Discharge 89
Figure (6-2) Water Surface in Case of Minimum Discharges (6.65 Mm3/day) 89
Figure (6-3) Comparison between the Cross Sections Velocity Profiles in Case of Average
Discharge 91
Figure (6-4) Water Surface in Case of Average Discharges (13.92 Mm3/day) 91
Figure (6-5) Comparison between the Cross Sections Velocity Profiles in Case of
Maximum Discharge 93
Figure (6-6) Water Surface in Case of Maximum Discharges (69.90 Mm3/day) 93
Figure (6-7) Comparison between the Cross Sections Velocity Profiles in Case of
Emergency Discharge 95
Figure (6-8) Water Surface in Case of Emergency Discharges (220 Mm3/day) 95
Figure (6-9) Location of the Bridge Piers 96
Figure (6-10) Cross Sections Location for Contraction Scour 99
Figure (6-11) Cross Sections Location for Bend Scour 100
Figure (6-12) Cross Sections Location for General Scour 101
Figure (6-13) Evaluation of the Total Scour at Kafr El-Zayat 105
Figure (6-14) First Bridge Piers Location 105
Figure (6-15) Second Bridge Piers Location 105
Figure (6-16) Third Bridge Piers Location 105
Figure (7-1) River Bed Elevation in Case of Alternative 1 109
Figure (7-2) The Thalweg Line in Case of the Original and Alternative 1 110
Figure (7-3) Cross Sections Bed Profiles in Case of Original Year and Alternative1 111
Figure (7-4) Velocity along the Reach at Maximum Flow in Case of Alternative1 112
ix
Figure (7-5) Velocity Profile at the Deepest Points (Outer Curve) along the Reach in Case
of the Original & Alternative 1 at Max Flow 112
Figure (7-6) Cross Sections Velocity Profile of the Original & Alternative 1 at Max Flow 114
Figure (7-7) Water Surface Slope at the Deepest Points along the Reach of the Original &
Alternative 1 114
Figure (7-8) Velocity along the Reach in Case of Alternative 1 at Emergency Flow 115
Figure (7-9) Velocity Profile at the Deepest Points along the Reach in Case of Alternative
1 at Future Flow 115
Figure (7-10) Cross Sections Velocity Profile of the Original & Alternative 1 at Future
flow 117
Figure (7-11) Water Surface Slope at the Deepest Points along the Reach in Future Flow
of the Original & Alternative 1 117
Figure (7-12) River Bed Elevation in Case of Alternative 2 118
Figure (7-13) Cross Sections in Case of Original Year and Alternative 2 119
Figure (7-14) Velocity along the Reach in Case of Alternative 2 at Maximum Flow 120
Figure (7-15) Velocity Profile at the Deepest Points along the Reach in Case of Original,
Alternative 1 and Alternative 2 at Maximum Flow
121
Figure (7- 16) Cross Sections Velocity Profile of the Original, Alternative 1 and
Alternative 2 at Maximum Flow 122
Figure (7-17) Water Surface Slope at the Deepest Points along the Reach of the Original,
Alternative 1 and Alternative 2 at Maximum Flow 123
Figure (7-18) Velocity along the Reach in Case of Alternative 2 at Emergency Flow 124
Figure (7-19) Velocity Profile at the Deepest Points along the Reach in Case of Original,
Alternatives 1 and 2 at Emergency Flow 124
Figure (7- 20) Cross Sections Velocity Profile of the Original, Alternatives 1 and 2 at
Emergency Flow
126
Figure (7-21) Water Surface Slope at the Deepest Points along the Reach of the Original,
Alternatives 1 and 2 at Emergency Flow 126
Figure (7-22) Bed Shear Stress in Max Flow for Original Case 128
Figure (7-23) Bed Shear Stress in Max Flow for Alternative 1 128
Figure (7-24) Bed Shear Stress in Max Flow for Alternative 2 128
Figure (7-25) Cross Sections Shear Stress of the Original, Alternatives 1 and 2 at
Maximum Flow 130
Figure (7-26) Bed Shear Stress for Original Case at Emergency Flow 131
Figure (7-27) Shear Stress for Alternative 1 at Emergency Flow 131
Figure (7-28) Shear Stress for Alternative 2 at Emergency Flow 131
x
Figure (7-29) Cross Sections Shear Stress of the Original, Alternatives 1 and 2 at
Emergency Flow 133
Figure (7-30) Grain Size Distributions of the Proposed Filter Layers 136
Figure (7-31) The Designed Filter Layers Thickness 136
xi
LIST OF TABLES
Table (3-1) Hydrograph Survey of Study Area 36
Table (3-2) Characteristics of Bed Samples at C.S. (1,2&3) 41
Table (3-3) Discharge at Rosetta Bridge 45
Table (4-1) Data Needed for Model Validation 54
Table (4-2) Ranges of the Estimated Roughness Coefficients 56
Table (4-3) Boundary Condition of Calibration 62
Table (4-4) Calibration Values for Roughness Coefficients 64
Table (4-5) Boundary Condition of Verification 65
Table (5-1) Meandering Parameters of the Study Reach 71
Table (5-2) Scour Holes Variation from Year 1982 to 1998 78
Table (5-3) Scour Holes Variation from Year 1998 to 2003 79
Table (5-4) Scour Holes Variation from Year 2003 to 2006 80
Table (5-5) Scour Holes Variation from Year 1982 to 2003 81
Table (6-1) Boundary Condition 87
Table (6-2) Location and Diminutions of the Bridge Piers 97
Table (6-3) Boundary Condition 97
Table (6-4) The Used Parameters and The 2D Model Results of Scour Bridge Piers in
Case of Maximum Flow 98
Table (6-5) The Used Parameters and The 2D Model Results of Scour Bridge Piers in
Case of Emergency Flow 98
Table(6-6) Contraction Scour in Case of Maximum and Emergency Flow 100
Table (6-7) Bend Scour in Case of Maximum and Emergency Flow 101
Table (6-8) General Scour in Case of Maximum and Emergency Flow 102
Table (6-9) General Scour for Maximum and Emergency Flow Conditions 102
Table (6-10) Total Scour 104
Table (6-11) The Expected Increase of the Scour Holes around the Main Piers of Kfer El-
Zayat Bridges 106
Table (7-1) Grain Size Distribution of the Proposed Riprap and Filter Layers 135
Table (7-2) Sieve Analysis for the Designed Filters 135
xii
LIST OF SYMBOLS
Symbol Description Dimension
a Angle formed by the projection of the channel centerline from the point
of curvature to a point which meets a line tangent to the outer bank of
the channel. (degrees)
Ac
Am
a
B
Bs
bt
C
C
Di
D
z
g
H,h,ho
i
K
m
n
Р
Q
R*
R
r1
r2
rc
Sg
Sr
bx, by
sx, sy
xx , xy, yx,
yy
U
Ū
U*
V
Wetted cross section area
Mid-ship area
River bends amplitude
Channel bank full width
Ship width (the beam)
Isotropic momentum flux correction coefficient
Channel width at keel level
Chézy roughness coefficient
Izbach's turbulent coefficient
Grain size for which i percentage of a material by weight is finer
Mean size of riprap particle
Super elevation between outside and inside bank
Gravitational acceleration.
Flow water depth
Longitudinal hydraulic gradient
Roughness height
Roughness correction factor for channel meandering
Manning roughness coefficient
Meander channel sinuosity
Flow discharge
Reynolds No.
Radius of curvature
River bend inner radius
River bend outer radius
River bend center radius
Specific gravity
Transverse water slope
Bed shear stresses acting in (x and y) directions respectively
Surface shear stresses acting in (x and y) directions respectively
xy shear stress
acting in x direction on a plane that is perpendicular to the y
direction
Flow velocity
Cross-sectional average velocity
Beds shear velocity
Measured point velocity
(L2)
(L2)
(L)
(L)
(L)
(-)
(L)
(L2/T)
(-)
(L)
(L)
(L)
(L/T2)
(L)
(-)
(L)
(-)
(L-0.33
T)
(-)
(L3/T)
(-)
(L)
(L)
(L)
(L)
(-)
(L/L)
(M/LT2)
(M/LT2)
(M/LT2)
(L/T)
(L/T)
(L/T)
(L/T)
(M)
xiii
Symbol Description Dimension
W
ω
Z
zb
zs
λ
θ
U
V
Weight of the riprap stone in pounds
Fall velocity
Meander arc length
Bed elevation
Water surface elevation
Angle of repose
Bed slope angle in degrees
Meander Wavelength
Arc angle
Horizontal velocity in the x direction
Horizontal velocity in the y direction
Water mass density
(L/T)
(L)
(L)
(L)
(Degree)
(Degree)
(L)
(Degree)
(L/T)
(L/T)
(M/L3)
b Pier width. (L)
D50 Particle size in a mixture in which 50% are smaller. (L)
df Scoured depth below design floodwater level. (L)
di Average depth at bankfull discharge in incised reach. (L)
Dm Diameter of the smallest non-transportable particle in the bed material
(1.25xD50) in the contracted section. (L)
Fr1 Froude number directly upstream of the pier
K1 Exponent depending upon the mode of bed material transport.
K1, K2,K3, and K4 Correction factors.
KW Means there would be a 5% reduction in the estimated scour depth
approximately 0.95.
m Exponent varying from 0.67 for sand to 0.85 for coarse gravel.
Q Discharge through the bridge. (L3/T)
Q1 Flow in the upstream of bridge transporting sediment. (L3/T)
Q2 Flow in the contracted section. (L3/T)
qf Design flood discharge per unit width. (L3/T/L)
qi Bankfull discharge in incised reach per unit width. (L3/T/L)
se Upstream energy slope. (L/L)
V Velocity of upstream flow. (L/S)
VC Critical velocity. (L/T)
Vc Critical velocity. (L/T)
W Bottom width of the contracted section less pier width. (L)
W1 Bottom width upstream of bridge. (L)
W2 Bottom width in the contracted section. (L)
xiv
Symbol Description Dimension
y Maximum depth of upstream flow. (L)
Y0 Average depth of flow in the contracted section before scour. (L)
y0 Average existing depth in the contracted section. (L)
Y1 Depth of flow in the upstream of bridge. (L)
y1 Flow depth. (L)
Y2 Depth of flow in the contracted section. (L)
ya Average depth of flow upstream of the bridge. (L)
ygs General scour depth. (L)
Yh Hydraulic depth of upstream flow. (L)
Ys Average depth of scour. (L)
ys Equilibrium scour depth. (L)
Z Multiplying factor (0.5 for straight reach, 0.6 for moderate bend, 0.7 for
severe bend).
Zbs Bend scour component of total scour depth. (L)
xv
LIST OF ABBREVIATIONS
Aswan High Dam AHD
Average Avr.
Centimeter cm
Cross Section C.S
Downstream D.S
First Bend S1
First Bridge B1
Hydraulic Research Institute HHRI
Kfer El-Zayat Station K.St
Kilometer Km
Kilometer Square Km2
Maximum Max.
Mean Sea Level MSL
Meter m
Meter Cubic m3
Million Cubic Meter Mm3
Minimum Min
National Water Research Center NWRC
Nile Research Institute NNRI
North Direction N
Not Available Data N A
Old Aswan Dam OAD
Second Bend S2
Second Bridge B2
Surface Water Modeling System SMS
Third Bridge B3
Two Dimensional Model 2D
Upstream U.S
Water Level in m WL
xvi
ABSTRACT
The objectives of this research are to analyze and evaluate the effect of releasing flow
discharges on river meandering and the scour at the bridge piers. This part of river
meandering includes 13 piers distributed on 3 bridges. The meandering reach is located on
Rosetta branch. It is consisting of two successive bends of length of 9.0 Km from km 145.00
to km 154.00 D.S of El-Roda Gauge at Kfer El-Zayat City. This reach is selected to conduct
the current investigation. Several sorts of data were collected including site maps, velocity
measurements, bed samples, hydrographic survey data, water levels and discharges at several
years and seasons, as well as visual inspection photos. The developing of bed level, thalwege
line and scour holes were determined by comparing the surveyed entire reach of years 1982,
1998, 2003 and 2006. Study area was simulated four times by 2D mathematical model “SMS”
using a survey reach of years 1982, 1998, 2003 and 2006. This was done to estimate the
velocities and the water levels at different discharges on the entire reach. The flow was used
as upstream boundary condition and the water level was used as downstream boundary
condition. The model was calibrated and verified using the measured velocity data. The
model was run for sixteen times at different flow conditions (minimum, average, maximum
and emergency). The resulted velocities of these runs were compared. The obtained results
showed the local scour in bridge piers. The empirical equations used to predict the general
scour, contraction scour and bend scour of the whole reach and around bridge piers.
Two proposed alternatives were suggested and simulated separately by the SMS model. In the
first alternative, the outer bends were filled with layers of filter and riprap up to level -5.00 m
MSL. In additional to alternative 1, the inner sides of the bends were dredged to level -3.00 m
MSL as second alternative. The model was run for the two alternatives at maximum and
emergence flows with its corresponding water levels. The results illustrated that the second
alternative improved the flow conditions better than the first one. Based on the results, layers
of filter and riprap were designed to fill the scour holes.
The empirical equations were used to predict the long term degradation and bend scour of the
bed morphological changes along the entire reach of the Rosetta Branch. 2-D model was used
to scour at the bridge piers in the study area was predicted using 2-D (SMS) model
considering two scenarios of high river discharges. The results showed that in case of
xvii
discharges released were maximum (69.90, 220.00m.m3/day), the total scour evaluated at the
3 bridges were, (11.65, 16.93m) for bridge No.1, (9.08, 13.35m) for bridge No.2 and (9.11,
14.07m) for bridge No.3. The expected extend of the scour holes around the main piers of the
Bridges were also predicted. It is recommended to follow up the dimension of the scour holes
every year or after occurring high floods.
CHAPTER 1
INTRODUCTION
Chapter 1 Introduction
1
Chapter 1
Introduction
1-1 General
The water release from Aswan Dam is kept as far as possible equal to the water demand,
leaving no surplus water to be wasted into the sea except in emergency cases. During high
floods, the water managers in the Ministry of Water Resources and Irrigation may release
discharges greater than the annual maximum discharge in an average year. These high
discharges released from HAD are determined according to the regulation guidelines for
operating the High Aswan Dam. These peak discharges may cause damages to the water
control structures along the Nile and its branches. Relatively high discharges cause local scour
near bridges, harbors and other structures. Also, relatively high discharges may cause
inundation to former flood plains that are currently in use. Such inundation may cause damage
to agricultural properties, urban areas, roads and may put human lives into danger.
Meandering rivers are classified as either actively or passively meandering. An actively
meandering river has sufficient stream power to deform its channel boundaries through active
bed scour, bank erosion, and point bar growth. Conversely, while a passively meandering
stream is sinuous, it does not migrate or erode its banks.
The Nile River is relatively straight with some sinuous reaches over short distances that are
related to steeper slopes. The increase in sinuosity in turn increases the bed slope more than
10cm/km. Steeper portions become more active and bank erosive. Consequently, scouring
action was expected to continue in these areas.
The meander wavelengths of the River Nile varied from 2500m to 4500m. The meander
pattern was subsequent to the construction of the High Aswan Dam (H.A.D.) as a result of a
reduction in discharge and sediment load. These are low amplitude meanders of the river,
associated with the growth of alternate point bars and islands, and not meanders that
materially change the main riverbank alignment.
A comprehensive analysis of the fluvial characteristics of the River Nile has been
accomplished by the RNDP Project (RNDP, 1991a, 1992b). Before the construction of
H.A.D., the peak flows were quite constant down the river but after building H.A.D., the peak
flows decreases significantly downstream as irrigation water are withdrawn. After
Chapter 1 Introduction
2
constructing H.A.D., the Nile is considered as a very low energy river with low water surface
gradients.
From the Aswan Dam to the head of the Nile Delta, the river distance is about 950km, and the
river bed drops ranging from + 79m to + 11m MSL, giving rise to an average slope of
7.2cm/km. The average bed slope along the Damietta and Rosetta Branches of the Nile Delta
(240km from Delta Barrage) was 5.6cm/km. The suspended bed material loads for the Nile
downstream Aswan has changed substantially as a result of the creation of Lake Nasser, (HRI,
2005).
1-2 Problem Definition
Kfer El-Zayat city is located at the outer curve of a very sharp bend at Km 123 of Rosetta
Branch. A field investigation is carried out to the local scour downstream the railway and
Highway bridges just after the release of the emergency flood discharge in 1998. The lowest
bed level of the local scour increased from -16.0m MSL at year 1996 to level -18.0m MSL at
year 1998. This may lead to serious bank instability in front of the city and the local scour at
any pier of the railway bridge might affect the stability of the bridge foundation, which
consequently affects the stability of the bridge itself.
1-3 Study Objectives
The research objectives are summarized as the following:
1) Analyze and evaluate the effect of releasing different discharges including high and
emergency flow on the existing structures at Kafr El-Zayat City.
2) Prediction of the morphological changes and the scour holes at the outer curve of the
bends.
3) Simulation of the flow conditions to the reach in front of the city of Kfer El-Zayat
(including the meander and bridge piers) using the two dimensional model (2D
model). Proposed alternative solutions to redistribute the flow in the bend reach to
minimize deepening and widening the scour holes of Rosetta Branch at Kfer El-Zayat.
1-4 Methodology and Scope of Work
The “SMS” 2-D mathematical model would be employed, at first, to simulate the
morphological and hydrological characteristics in the meandering reach of Rosetta branch.
The present study would be carried out applying the following:
1. Collecting the available data to the study reach related to hydrographic and hydraulics.
Chapter 1 Introduction
3
2. Reviewing of the available scour hole information in the available literature.
3. Reviewing the previous available studies related to this subject. Determine the different
flows at several years passing in the Rosetta Branch from the HAD.
4. To study the development of the morphology on the bends, the reach available bed level
data at several years will be compared. This reach includes 2 bends located at Rosseta
Branch at Kfer El-Zayat city.
5. The reach will be simulated by 2-D mathematical model, 4 times using the surveyed
data at different years. The model will be calibrated and verified. Different runs at
several flow conditions will be carried out.
6. Using the convenient empirical formulae for prediction of the morphological changes
and the scour holes at the outer curve of the bends and around Bridge piers.
7. Simulating different proposed alternatives using 2-D model SMS to predict the
expected scour bed at whole reach including scour around the bridge piers.
8. Analysis of the results.
9. Conclusions and Recommendations.
1-5 Thesis Layout
This thesis includes 8 chapters as the following:
Chapter 1: Introduction
It describes the problem, the objectives, the procedure and methodology used in this study.
Chapter 2: Literature review
This chapter covered the survey of literature concerning river meandering included scour
around bridge piers, the outer curve and contraction areas.
Chapter 3: Data collection
Several sorts of data were collected including site location, bed level date maps, velocity
measurements, bed samples, hydrographic survey data, water level and annual discharges, as
well as visual inspection photos.
Chapter 4: Mathematical models formulation and preparation
The chapter includes the used mathematical model (SMS) and the collected data for the
fulfillment of the study reach model simulation. Also the applied principles and results for
model calibration and verification were illustrated.
Chapter 1 Introduction
4
Chapter 5: Morphological Changes
Comparison of study reach morphological plan form development through the last thirty years
was illustrated and analyzed. Moreover, Comparison between bed level cross sections and
discussions of morphological changes between years 1982, 1998, 2003 and 2006 was
achieved.
Chapter 6: Scour Prediction and Model Application
This chapter present the model application at different flows. It present also the scour
prediction and evaluation which includes general scour, local scour, contraction scour, and
bend scour. These scours were analyzed for the whole reach and bridges site.
Chapter 7: Alternative Solutions & Testing Results
This chapter provides effects of different scenarios of discharge and test results with respect
to differing configurations; velocity measurements, shear stress, expected heading up. It
presents a design of expected riprap.
Chapter 8: Conclusion and Recommendations
Encompasses the conclusions derived from the present study and suggests some
recommendations for future researches.
CHAPTER 2
LITERATURE REVIEW
Chapter 2 Literature Review
5
Chapter 2
Literature Review
2-1 Introduction
Flow in curved river reaches is usually under the influence of centrifugal acceleration, which
induces transverse velocity component (helical flow currents) and super elevation in water
surface. Although, these curved reaches are sometimes stable, there are general tendency of
bank failure and bed scour at the outer bend followed by sedimentation at the inner bend.
Therefore, lateral migration of the reach planform is occurred, consequently several
morphological and navigational problems take place. Due to these dynamic interactions, the
transverse velocity profile, shear stress on channel bed, lateral bed slope, sediment size
distribution, and energy expenditure will be changed. This revealed that in order to treat and
understand the meandering river mechanism, several emerged aspects should be reviewed
which will be the intention throughout this chapter.
2-2 The Nile River
The Nile River is the main source of water and life to Egypt and the Egyptians. The main flow
of the Nile comes through three main rivers in Sudan; the Blue Nile, the White Nile, and
Atbara River. These rivers originate from great lakes in the center and east of Africa.
Therefore, the River Nile flow income varies from one year to another according to the
amount of rain falling at the riverhead. However, the construction of High Aswan Dam gave
Egypt the opportunity to control the Nile River flow. Also, there are several control structures
(barrages) located along the Nile from Aswan to the Mediterranean Sea to control the flow
through the river (Figure (2-1)).
The Nile River is a natural river, thus it has many islands dividing its flow into two branches
and also has many bends and meanders along its course from Aswan to the Mediterranean
Sea. The Nile River bed from Aswan to Cairo is generally consisted of successive layers of
sandy soil. Meanwhile the upper layers of the river banks consisted of clayey silt to silty sand
soil layers. On the other hand, some islands on the rivers are consisted of sandy silt soils and
the others have the same formation as the river banks.
As mention earlier the discharge flow through the Nile River was controlled after the
construction of the High Aswan Dam. The maximum discharge flow was reduced and the
Chapter 2 Literature Review
6
suspended sediment concentration had greatly reduced. Thus, the Nile River subjected to
morphological changes in many locations along its course, particularly through the distance
between Aswan and Cairo.
Figure (2-1) The Nile River Barrages
2-3 Rosetta Branch
Nile River travels along Egypt for about 950 km starting from downstream High Aswan Dam
to upstream Delta Barrage, where it divides into two branches, Rosetta and Damietta branches
which, each of them runs separately to the Mediterranean Sea, forming the Delta region
between both branches, Figure (2-2).
Rosetta branch has an average width of 180m and depth from 2 to 4m. It ends at Edfina
Barrage, 30km upstream the sea, which releases excess water to the Mediterranean Sea. It is
estimated that the aquatic environment of this branch receives more than 3 million cubic meters
daily of untreated or partially treated domestic and industrial wastes and in addition to
agricultural drainage water.
Chapter 2 Literature Review
7
Figure (2-2) Rosetta Branch
2-4 Basic Principals and Concepts
To study the morphological changes in River, special definitions to identify these phenomena
should be illustrated.
2-4-1 Channel types
There are three basic types of channels, straight, meandering and braided. Describing the
channel by one of the mentioned terms does not mean that the entire channel is straight or
otherwise. It simply means that some portion of the channel can be described in such a way.
In fact, portions of a stream may be straight, some meandering and others braided.
Straight channel
Different definition of straight channel has been found in the literature for example in 1957
which reported by Leopold, and Wolman, defined that the straight reaches have negligible
sinuosity at bank full stage. At low stage the channel develops alternate sandbars and the
thalweg meanders around the sandbars in a sinuous fashion. Straight channels are often
considered as transitional stage to meandering. If the stream banks are stable, more than a one
channel will develop, and the reach will become braided. In 1988, Chang described Straight
River that it does not have a distinct meandering pattern; that is its sinuosity is less than about
1.5. Although a river may have a relatively straight alignment, its thalweg moves as Sinuous
(Chang, 1988).
Chapter 2 Literature Review
8
Braided channel
A braided channel is wide and the banks are poorly defined and unstable, and there are two or
more main channels. Between sub-channels there are sandbars and islands. The sub-channels
and sandbars change position rapidly with time. At low flow the braided river bed starts a
braided appearance. At flood stage, the flow straightens, most of the sandbars are inundated or
destroyed and the river becomes much wider. Such rivers often have relatively steep slopes
and carry large concentrations of sediment (Chang, 1988).
Meandering channel
A meandering river can be described as regular inflections that are sinuous in plan. It consists
of a series of bends connected by short straight reaches .In the bends, deep pools are carved to
the concave bank by the relatively high velocities because velocities are lower on the inside of
the bend, sediments are deposited in this region forming the point bar. Point bar building is
enhanced when large transfer’s velocities occur. The heavier concentrations of bed load
toward the convex bank and deposited to form the point bar. At low flow, large sandbars are
formed in the crossings if the channel is not well confined. Variations in factors such as bed
and bank material, width, cross sectional shape, curvature, history and period of development
of the bend, as well as gradient, are all likely to influence meander behavior and meander
morphology. The scour in the bend causes bend migration downstream and sometimes
laterally. Much of the sediment eroded from the outside bank is deposited in the crossing and
on the point bar in the next bend downstream. The configuration and geometry of meandering
channel are formed by erosion and deposition. Bed slopes are usually relatively flat. Figure (2-
3) shown that in 1988, Chang concluded that a meandering river has a sinuosity greater than
about 1.5, and it consists of alternating bends and a distinct sinuous plan form, (Chang, 1988).
In 1983 Brice put some classification for river types that is based on four major plan form
properties that are most readily observed on aerial photographs: sinuosity, point bars, braiding,
and an branching. River meandering consists of three types of sinuous rivers that are classified
on the basis of plan form properties: sinuous canal form, sinuous point-bar, and sinuous
braided. These are illustrated in Figure (2-4). The canal form tends to have the highest
sinuosity, the narrowest widths, the lowest rates of lateral erosion and high silt-clay content for
the banks (Brice, 1983).
Sinuous point-bar rivers are steeper and have more rapid rates of lateral migration at bends,
river tend to have greater width at bend apexes, and prominent point bars, although straight
reaches may remain stable for long period of time.
Chapter 2 Literature Review
9
Figure (2-3) Major Types of River
Sinuous braided rivers are steeper and wider than sinuous point-bar rivers with the same
discharge. Point bars are more irregular as the braiding Increases (Chang, 1988).
Figure (2-4) Sinuosity Ranges
2-5 Meander Characteristics
Derivations of motion and continuity equations for curved channels were mathematically
specified by Rozovskii (1957), Rouse (1959), and Schlichting (1968). Using the sub
critical flow restrictions with hydrostatic pressure distribution, the flow in curved channels
was deduced in terms of the super-elevation ∆Z between outside bank and inside bank which
would be approximated as follows:
c
r
r
r
rr
gr
BUdr
gr
UdrSZ
22
1
22
1 (2-1)
Figure (2-5) illustrates the meander geometrical characteristics of curved river reach which
can be described as follows:
Chapter 2 Literature Review
11
Figure (2-4) Geometrical Characteristics of Meandering Stream
Figure (2-5) Meander Geometrical Characteristics of Curved River Reach
1- Radius of curvature (rc): river forms a series of regular sinusoidal curves with an
average radius of 2.3 to 2.7 times the bank-full width.
2- Meander Wavelength (λ): A full meander wavelength is the distance between two
similar points along the channel between which waveform is complete. It was found to
occur between 6 and 15 times the bank-full width. The bank full width is the width of
the channel at water level during an average 1 to 2 year peak discharge event. The bank
full discharge is the dominant channel forming discharge. The bank full width can be
calculated by either using theoretical relationships or by on the ground measurements
using field indicators.
3- Sinuosity (Р): is the ratio of channel length along the center line of the channel to the
length of the valley measured along the center of the meander belt or center of the
valley. Sinuosity generates resistance to flow and alters the hydraulic slope of the
channel.
4- Arc angle (θ): the angle swept out by the radius of curvature between adjacent inflexion
points.
5- Meander arc length (Z): the distance measured along the meander path between
repeating (inflexion) points.
6- Amplitude (a): width of meander belt measured perpendicular to the valley or straight
line axis.
Wave length ()
Point
bar
Arc length = 0 Arc length = Z
Arc length =Z/2
Arc angle
Apex
Point of inflection
or crossover
Am
pli
tud
e (a
)
B
r c
Chapter 2 Literature Review
11
Additionally, empirical relationships are usually related the wavelength and amplitude of
meander bends to the bank-full width of the channel (Inglis, 1949; Leopold and Wolman,
1957, 1960; and Zaller, 1967). Also relation between wave length and radius of curvature
were treated by (Leopold and Woleman, 1960). Consequently, the following equations in
English units deduce the relations between the radius of curvature and meander wavelength:
λ = 10.77 B1.01
(2-2)
a = 3 B1.1
(2-3)
λ = 4.8 rc0.98
(2-4)
Where B is the surface width, from Eq. 2 and 4 one can deduce that:
rc = 2.4 B (2-5)
Equation (2-5) gives a good approximation of the maximum curvature for meander bends.
However, Hey (1976) indicated that the above equations are not applicable on bends of
sinuosity less than 1.5 where the radius of curvature is very large because the ratio rc/B will be
considerably greater than 2.4 or 3.
Furthermore, very relevant applied investigation was conducted in which statistical nature of
river bends along Damietta branch was highlighted and consequently some significant
geometrical relationships were developed. In this study, three bend types were defined as
free, limited and forced which were classified according to the physical and morphological
characteristics and degree of freedom to attain the lateral shifting. According to Attia and
El-Saied (2004), the three bend types were clarified as follow:
Free bend: This is usually related with broad flood plains that consist of relatively
erodible materials. In this case, the river bends follow the curves of the valley so that each
river bend includes a promontory of the parent plateau. It was noticed that this type is not
disturbed by the external factors and experienced the highest degree of freedom to form the
bend shape.
Limited bend: where the bend cut into solid rock or hard strata in deep gorges and exhibit
meandering pattern similar to that of rivers in flood plains. In this case the channel banks
are composed of consolidated parent material that limits the lateral erosion. Such rivers
are called incised rivers and these bends are called incised bends or entrenched bends.
Chapter 2 Literature Review
12
Forced bend: where the channel is highly restricted from external movements and the
bank line movements are mainly controlled by either natural or manmade activities.
Examples of these constrains are valley walls, protection works, developments of
croplands on island, mountains, infrastructures and towns Attia and Abdel-Bary(1998).
These constrains forced the river to grab a specific path according to their shape.
Sometimes in this type the river impinges onto an almost straight parent bank at large
angle (600 to 90
0).
2-6 Scour Holes
Scour is the hole left behind when sediment is washed away from the bottom of a river.
Although scour may occur at any time, scour action is especially strong during floods. The
different types of scour holes are indicated in Figure (2-6). Swiftly flowing water has more
energy than calm water to lift and carry sediment down river.
Figure (2-6) Scour Holes Downstream Bridges (Linda, 1993)
Types of Scour:
Scours are classified and defined as the following:
Local scour is removal of sediment from around bridge piers or abutments. Water flowing
past a pier or abutment may scoop out holes in the sediment; these holes are known as
scour holes.
Contraction scour is the removal of sediment from the bottom and sides of the river.
Contraction scour is caused by the increase in the water speed as it moves through bridge
opening which is narrower than the natural river channel.
Degradation scour is the general removal of sediment from the river bottom by the flow of
the river. This sediment removal is a natural process but may remove large amounts of
sediment over time and lowering the River bed.
Chapter 2 Literature Review
13
Scour is defined also as the erosion or removal of streambed or bank material from bridge
foundations due to flowing water, Federal Highway Administration, (2001). It is considered
one of the main factors affecting the stability of the highway bridge. Figure (2-7) shows flow
profile around a circular bridge pier, (HEC18, 2012).
Figure (2-7) Flow Profile around a Circular Bridge Pier. (HEC18, 2012)
Local Scour is defined as the erosion due to redirected and contracted flow lines around piers
or abutments (FCDMC, 2009). The evaluation of local scour was developed by Federal
Highway Administration criteria, (2001) and procedure set in (HEC-18). Local scour is
caused by flow obstruction and impingement - most local scour caused by man-made
structures such as bridge piers, bridge abutment, culverts, grade control, and drop structures.
The factor of safety for local scour is basely 1.3 (FCDMC, 2009), but it may be reduced to 1.0
due to excessive calculated local scour. However, the use of 1.0 for the factor of safety should
be considered by the (FCDMC, 2007).
There are many local scour depth prediction equations considered in the literature as well as a
number of review studies that used the comparison techniques between different equations
and methodologies involved in scour prediction. Most of these equations are empirical and
based primarily on small-scale laboratory data. Melville (1975) measured mean flow
directions, magnitude, and turbulent flow fluctuations and computed turbulent power spectra
around a circular pile for flatbed, intermediate, and equilibrium scour holes. He found that a
strong vertical downward flow developed ahead of the cylinder as the scour hole enlarged.
The size and circulation of the horseshoe vortex increased rapidly, and the velocity near the
hole bottom decreased as the scour hole was enlarged. As the scour hole develops further, the
intensity of the vortex decreases and reaches a constant value at the equilibrium stage. Large
Chapter 2 Literature Review
14
scour holes may also develop downstream from piers under certain circumstances (e.g. Shen
et al., 1966). More recently another potential scour mechanism was identified [Sheppard
(2004)]. This mechanism resulted from the pressure gradient field generated by the presence
of the structure in the flow.
Lança et al. (2013), collected new long-duration clear-water scour data for single cylindrical
piers with the objective of investigating the effect of sediment coarseness on the equilibrium
scour depth and improving the scour depth time evolution modeling by using the exponential
function suggested in the literature. Experiments were carried out for the flow intensity close
to the threshold condition of initiation of sediment motion, imposing wide changes of
sediment coarseness and flow shallowness. The effect of sediment coarseness on the
equilibrium scour depth was identified; existing predictors were modified to incorporate this
effect.
The effect of a single-peaked flood wave on pier scour was investigated theoretically and
experimentally by Hager and Unger (2010). The conditions considered involve clear-water
scour of a cohesion-less material for a given median sediment size and sediment non-
uniformity. An approach flow characterized by a flow depth and velocity, a circular-shaped
cylindrical bridge pier, and a flood hydrograph defined by its time to peak discharge. A
previously proposed formula for scour advance under a constant discharge was applied to the
unsteady approach flow.
Sheppard et al. (2014), employed twenty-three of the more recent and commonly used
equilibrium local scour equations for cohesion-less sediments which were evaluated using
compiled laboratory and field databases. This investigation assembled 569 laboratory and 928
field data. A method for assessing the quality of the data was developed and applied to the
data set. This approach reduced the laboratory and field data to 441 and 791 values,
respectively. Because the maturity of the scour hole at the time of measurement for the field
data was unknown, they were only used to evaluate under prediction by the equations. A
preliminary quality control screening of the equilibrium scour methods/equations reduced the
number of equations from the initial 23 to 17. The remaining 17 methods/equations were
analyzed using laboratory and field data.
Contraction scour is located at the flow area of the river at flood stages, Figure (2-8). It is
reduced due to the bridge construction. The contraction scour evaluation was developed by
Federal Highway Administration criteria. The higher value between the contraction scour
equation in this section and Neill’s general scour equation could be used for this component
(FCDMC, 2009). If there is a bend, then the higher value between Neill’s equation with a
Chapter 2 Literature Review
15
bend and the contraction scour equation and the bend scour equation could be used. The
following equation (for critical velocity) can be used to determine the contraction scour if the
flow upstream of the bridge is clear-water or live-bed (FHWA, 2001). The equation has the
following form:
Vc =11.17 ya1/6
D501/3
(2-6)
Clear-water when Vc> mean velocity, Live-bed when Vc< mean velocity.
Live-bed Contraction Scour Determination
y2/y1 =(Q2/Q1)6/7
* (W1/W2)k1
(2-7)
ys = y2 - y0
Clear-water Contraction Scour
Y2 = (0.0077Q2/Dm
2/3W
2)3/7
(2-8)
Ys= y2 - y0
Figure (2-9) show Live bed and Clear Water Scour
Figure (2-8) Contraction Scour
Figure (2-9) Live Bed and Clear Water Scour
Chapter 2 Literature Review
16
Bend scour is concentrated near the outside of the bend scour resulting from stream plan
form characteristics and scour at confluences (Flood Control District of Maricopa County,
2009). The equation has the form (Simons and Assoc 1989b):
Zbs = (0.0685*Y*V0.8
)[2.1*(sin²(a/2)/cos(a))0.2
-1]/(Yh0.4
*S*exp(0.3)) (2-9)
The general scour component is the scour caused by the passing of one flood, Figure (2-10).
The Flood Control District of Maricopa County (FCDMC) uses three general scour equations
(FCDMC, 2007): Lacey’s Equation, Neill’s Equation and Blench’s Equation, (Pemberton and
Lara, 1984). Neill’s Equation is applicable to streams where there is constriction of the
channels due to bridges or other structures. The equation has the form (Pemberton and Lara
1984):
ygs = Zdf = Zdi (qf/qi)m (2-10)
The wide pier problem is considered to be a concern when the relative depth, y/b, is too small
to allow the vortices to fully develop where y is the flow depth and b is the pier width. Earlier
investigations of the dependence of scour depth on y/b were performed with small piles and
very small water depths, Ettema (1980). Melville and Sutherland (1988) established an upper
threshold at y/b = 3 beyond which the scour depth is relatively independent of the relative
depth.
Recent data from J.Sterling Jones and D. Max Sheppard tests, (2000) on large piers indicated
that this threshold was closer to 2. HEC-18 is the standard used by most highway agencies for
evaluating scour at bridges. The pier scour equation was checked using laboratory data by
researchers at Colorado State University and was presented as the CSU equation in an earlier
FHWA publication, Highways in the River Environment. All of the data used for the original
equation was for circular piers in relatively uniform fine grain sands. Correction factors were
added later to account for various pier shapes, angle of attack, bed forms, and coarse bed
material fractions to produce the familiar pier scour equation that is currently in HEC-18:
yS/y1 = 2 K1K2K3K4 (b/y1)0.65
(Fr1)0.43
(2-11)
Johnson (1999) defined a wide pier as one situated in shallow, low velocity flows so that y/b
< 0.8 and Fr < 0.8. He isolated the data that met these conditions in the original data set used
in the CSU equation and added data from other sources to derive a new equation for wide
piers using the same parameters. That equation could be written as:
Chapter 2 Literature Review
17
yS/y1 = 2.08 K1K2K3K4 (b/y1)0.504
(Fr1)0.639
(2-12)
Then he divided the wide pier equation by the HEC-18 equation to express the difference as
another correction factor, KW, for the HEC-18 equation:
KW = 1.04(b/y1)-0.15
(Fr1)0.21
(2-13)
Which can be applied to the HEC-18 equation when y/b < 0.8 and Fr < 0.8 in case both of
these conditions were met. But if y/b = 0.5 and Fr =0.5, which could occur, then KW = 0.81
which is a 19% reduction.
Figure (2-10) General Scour
If sediment on which bridge supports rest is scoured by a river, the bridge could become
unsafe for travel. In 1987, the Interstate highway bridge over Schoharie Creek in New York
State collapsed during a flood. After this accident, the Federal Highway Administration
required every State to identify highway bridges over water which are likely to have scour
problems and to identify bridges where scour is severe. Knowledge of bridge sites where
scour is a potential problem will enable the States to monitor and improve conditions at these
bridges ahead of time before they become dangerous (Linda, 1993).
The process of bank erosion is much related to the general scour or river-bed-degradation. At
river cross sections where the bed level is lowered considerably, the bank height might be
higher than a critical value beyond which bank failure might occur. As river-bed-degradation
is investigated using numerical morphological modeling approach, therefore, bank scour
should be addressed in the context of river morphological modeling (Babaeyan and Valentine,
1999).
Chapter 2 Literature Review
18
In Egypt, local scour around the hydraulic structures located across the Nile River constitutes
a major concern. The two main hydraulic structures on the River Nile are bridges and
barrages. Scour downstream barrages seems to be more complex. The RNDP Project (RNDP,
1991a, 1992b) has accomplished a comprehensive analysis of the fluvial characteristics of the
River Nile. Before the construction of H.A.D., the peak flows were quite constant down the
river but after building H.A.D., the peak flow decreases significantly downstream as irrigation
water is withdrawn. During high floods, higher discharges than the annual maximum
discharge may be released in an average year. High discharges cause local scour near bridge
piers, especially the wide area.
When a bridge is built across an alluvial channel, the obstruction of the flow by the bridge
piers induces higher velocities and vortices that cause scour of the channel bed around the
piers. If this scour reaches the foundation level of bridge piers, the bridge might collapse.
Bridge pier scour is the leading cause of bridge failure. In the United States alone, bridge pier
scour is the leading cause of failure among more than 487,000 bridges over watercourses
(Melville, 1997). In Egypt, concerns about bridge pier scour may limit increasing the current
flow releases from Aswan High Dam (AHD) above the current maximum of 270 Mm3/day.
In order to release higher flows than the maximum current, knowledge is required about how
much scour is expected around bridges built on the Nile River (HRI, 1993).
Due to the importance of bridge pier scour, many investigators have worked on this critical
subject but most have built their analysis on laboratory data. This empirical approach suffers
from its associated simplified conditions and scale effects. When applying the existing
empirical equations for predicting bridge pier scour to field cases, the scour depths are over-
predicted.
Meander migration is a process in which water flow erodes soil on one bank and deposits it on
the opposite bank. Therefore, a gradual shift of bank line occurs over the long term. Bank
erosion undermines bridge piers and abutments, scours the foundations of parallel highways,
and causes loss of useful land, according to Jean-Louis Briaud et al. (2007).
Rossell and Ting (2013) used a 2-D depth-averaged river model based on finite element
theory (FESWMS) to simulate the hydraulic conditions at a contracted bridge site. The
studied area was located at James River bridges near Mitchell, South Dakota. The parallel
bridges were located in a crossing between the two bends of a meander. The validated model
was used to examine the site characteristics that influence the concentrated flow on the right
side of the main channel and the exchange of flow between the main channel and flood plains.
The scour analysis was performed using the equations mentioned in Hydraulic Engineering
Chapter 2 Literature Review
19
Circular No. 18 (HEC-18) and a method that accounts for the soil erodibility using the curve
of measured erosion rate versus shear stress. The study demonstrated that the channel
meandering, the no-flow boundary condition imposed by the walls of the river valley, skewed
roadway embankment, and the dense trees along the left bank were the three main factors
creating the unique hydraulic conditions at the bridge site. It was concluded that using the 2-D
flow model improved the estimation of contraction scour by providing more accurate
information on the hydraulic parameters. The predicted scour depth was highly sensitive to
the critical shear stress and curve slope of erosion rate versus shear stress.
2-7 Types of Models
Modeling has become a frequently used tool for studies in hydraulic and environmental
engineering. In the past many engineers were used physical models or simplified
descriptions for the support of engineering studies
A model is a physical or mathematical description of a physical system, including the
interaction with its outside world, which can be used to simulate the effect of changes in the
system itself or the effect of changes in the conditions imposed upon it.
2-7-1 Physical Models
Physical model in the laboratory are done primarily in a large flume. Much of the
laboratory's recent work has investigated scour at bridge installations. Physical Model
Studies are invaluable in designing hydraulic structures, improving the safety of existing
hydraulic structures and reducing construction costs. To do this, experimental setups are
designed and built on site and installed in the moveable stream bed of the large flume. Flow
regimes may be varied to simulate any almost flood event and the resulting scour measured.
Physical modeling results may be used directly by the laboratory's clients in the design of a
particular structure, or it may be used to develop predictive numerical models with potential
for general application in designing structures.
2-7-2 Numerical Models
The increasing availability of personal computers and the powerful developments in
computer graphics, data bases and on-line control software has brought computer support to
the desk of consulting engineers. In-line with these developments we also see a strongly
increased availability and use of mathematical molding software tools.
Chapter 2 Literature Review
21
Numerical (computational) analysis is widely used to solve mathematical expressions that
describe the physical phenomena. Numerical models are classified by number of spatial
dimensions over which variables are permitted to change. They provide much more detailed
results than other methods. Yet they need field data for verification. Numerical models have
been extensively and successfully applied to studies on sediment yield, river sedimentation
and morphological processes since the 1970s. The accuracy and reliability of a mathematical
model in predicting sediment processes depend to a large extent on understanding sediment
transport mechanism of effectiveness of numerical solution methods, calibration and
verification by field and experimental data as well as the user’s experience and art. There is,
obviously, plenty of room for improvement in these aspects.
a. One dimensional model
One dimensional model is mainly used in assessing long-term and averages in cross-section
processes along long distance.
b. Two dimensional and Three dimensional numerical-empirical models
Two and three dimensional models are mainly used in studying local and detailed phenomena
near structures.
2-8 Previous Works in Morphological Changes in Rivers
(RNPD) produced a study of the impact of projects on the Nile River (RNPD, 1991a) which
included an investigation of water levels, thalweg levels and known navigation bottlenecks.
(Moattassem et al.1990) defined the navigational bottlenecks as the locations where the water
depth is less than 1.55m when the discharge from Aswan dam is 75 Mm3/day. They calculated
the water depth as the difference between the water surface elevation obtained from rating
curves and the thalweg level. They calculated the required depth as 1.55m based on draft
1.3m plus 0.25m as clearance. They defined 14 locations from Aswan to Cairo to have
navigational bottlenecks. As their approach was a one-dimensional and the navigational path
does not follow the thalweg line exactly, this approach is not accurate enough and there might
be more bottlenecks than what they have defined.
(Motiee, et al 2003), reported that the morphological changes in River due to constructed
structures (case study of Sephidrood River) caused severe changes in riverbed as well as
riverbanks due to different reasons such as economical development, population growth, need
for more sand and construction materials and sediment removal from reservoirs. The Sefid-
Rud River has reached to its stable condition due to different reasons such as geological and
Chapter 2 Literature Review
21
alluvial formations, hydrological characteristics of the basin as well as hydraulic conditions of
the river.
(Sarker, et al 2003), studied the morphological changes at the Ganges River distributaries in
response to the Declining flow using remote sensing. They used three sets of landsat images
supported by hydrologic data. The images were classified with unsupervised classification
and knowledge based threshold to produce land, sand and water classes. The time series data
used to analyze the characteristics of erosion, accretion and planform changes. The changes of
sinuosity, rates of bank erosion and meander migration were derived from the image analysis.
(Fischer-Antze et al 2003), studied the morphological response of the Danube River. The
impact of the August 2002 flood on the morphological changes of the Danube River between
Vienna and the Austrian-Slovakian border. The river bed elevation changes were determined
in turns of volume differences and a number of morphological parameters including cross-
sectional shape and asymmetry parameters for both surveys. The results indicate that the
overall morphological features - sizes, shapes and locations of the gravel bars, thalweg
positions - have not changed. Volume differences indicate no significant overall change and
local changes occur of up to 1 meter. Further interpretations of these results will be provided
in the context of the long-term evolution of the river bed.
(Amadi et al 2004), studied the factors influencing morphological changes in an alluvial reach
of The Missuri River valley for River sensitivity to climate changes. Distinctions between the
meander morphologies are based on differences in their channel width, channel depth,
meander wavelength, meander radius, and bar grain size. High sensitively of the river to
climate change could have strong influence on ongoing efforts to plan reclamation of the river
to accommodate needs of both commerce and habitat because, (1) current river morphology
cannot be considered stable over very long time spans, and,(2) foundational substrate
materials for habitat are non-uniform in the valley.
Sadek, N., et al. (2006). Studied the impacts of the reduction of the flows downstream High
Aswan Dam due to the operation of new national projects for the fourth reach, and unsafe
stations are determined for different low flow conditions and the unsafe ranges are also
determined for each case.
( Sadek, N. et al, 2000), studied meandering geometry and the regime change of the river for
Rossetta Branch before and after the construction of Aswan High Dam by using mathematical
Chapter 2 Literature Review
22
model. The analysis of the study shows the effect of hydrological and morphological changes
such as meander parameters have changed after AHD, migrated bend occurred from Delta
Barrage to Kafr El-Zayat. (Sadek N., et al 2001), studied the morphological changes impact
on water surface profile predicted for the River Nile by using Mathematical model to
analyzing different hydraulic parameter. By comparing cross sections of year 1982 and year
1997 it found that sedimentation is more frequent than erosion, it found that the difference
between the predicted water surface profile for 1982 and 1997 lied within the range of 0.6m
and is considered relatively small. (El-Sersawy, 2001), studied the better identification and
prediction of the location of the bottlenecks that may affect navigation in the Nile River. In
this study he found that using two dimensional hydrodynamic flow and sediment transport
model lead to better handling of the input data, and improving the capabilities of the
numerical model. The modification gives also the link between hydrodynamic models, and
the sediment model increases the ability of the model to simulate long- term behavior of the
river reach under study. The proposed approach, is used for navigation studies in the Nile
River, to help the decision makers in planning and operation of the navigation system and to
evaluate the sedimentation processes and to predict their effects on the morphology of the
river reach.
(Enggrob, 2003), studied the morphological forecast simulation of Jamuna River in
Bangladesh. Described the set-up and results of a mathematical modeling tool applied in
connection with monitoring of the construction of bridge crossing and associated river
training works in a highly morphological active river: The Jamuna River in Bangladesh. The
objective of the model study was to provide forecasts of the morphological changes over the
coming monsoon period with sufficient lead time to enable the contractors to take remedial or
preventive actions should critical conditions occur. The model proved to be very useful not
only to provide morphological forecasts but also for impact studies. (Kapsimaisi et al 2004),
determined the long term morphological changes in a human affected coastal system using
GIS. Large-scale patterns of coastline evolution and sea-floor erosion and/or deposition were
investigated with the use of a Geographical Information System (GIS). The observed
morphological changes have been related to the deltaic processes, local hydrodynamic
conditions and human implications. Raslan Y., et al, (2008), studied the implications of
dredging in Damietta Branch on river regime and flow water level. Comparing river water
level after dredging with that before dredging downstream Delta and Zifta Barrage indicated
significant drop in the water level. Drop in water level may increase the capacity of the river.
Chapter 2 Literature Review
23
However, drop of water level might have impact on flow intake structures inside the reach.
The analysis of the results of the numerical models showed that aggradations will be
dominant over degradation. Aggradations will likely to happen at few local sites were
extensive dredging was carried out. Although navigation in the Nile has its merits, dredging
should not be the only solution for maintaining the navigable channel.
2-9 Dredging
Dredging is defined as a process by which sediment is removed from the bottom of streams,
lakes and rivers as shown in Figure (2-11). Permanent modifications and structures have not
succeeded in eliminating the requirement for the dredging of significant quantities of
sediment to maintain the desired navigation channel. Figure (2-12) shows the use of the
combination of dredging and the training structure in the river to reduce the deposition.
Dredging solution of a navigation channel has the advantage of being relatively simple and
direct in their application. Dredging operations on the river are closely related to the annual
cycle of high and low flow. Comparing river stage, average depth over crossings and dredging
requirements shows that, in general, crossings are built up and dredged cuts filled when river
stage falls after a period of high flow. Dredging of a channel through a crossing or shoal
should be considered successful if the dredged cut meets several criteria.
Figure (2-11) Schematic Diagram of Cross Sections Dredging Concepts
Figure (2-12) Cross section at Columbia River
Chapter 2 Literature Review
24
2-10 Sediment Transport
Once material is detached from the channel it can be transported. Transportation is the
movement of earth material, in this case, by water. As shown in Figure (2-13) once fine
particles are eroded, they can be transported under very low velocities. As particle size
increases, the velocity needed to transport it increases, the material transports through the
stream load. Stream load is composed of dissolved or solution load, suspended load, and bed
load. The dissolved load comes primarily from groundwater seepage into the stream. Ions in
solution also come from the solution of materials that line the channel (Demissie et al.,1992).
Suspended load is comprised of sediment suspended and transported through the stream.
Turbulent flow suspends clay and silt in the stream. Suspended load comes from material
eroded from the surface bordering the channel and deposited in the stream, as well as, erosion
of the channel bed itself.
Figure (2-13) Stream Load
Bed load is that which is moved across the bed of the channel. Bed load is transported in
two ways, traction, which is a scooting and rolling of particles along the bed. The second is
saltation, a bouncing-like movement. Saltation occurs when particles are suspended in the
stream for a short distance after which they fall to the bed, dislodging particles from the bed.
The dislodged particles move downstream a short distance where they fall to the bed, again
dislodging particles upon impact (Krone, 1962).
2-10-1 Factors Affecting Sediment Transport
2-10-1-1 Bed Shear Stress
The fluid shear stress depends on several factors such as the flow discharge (Q), water depth,
the grain size and the bed forms, the longitudinal hydraulic gradient (i), the ratio between the
bend radius (r) and the channel width (B), the cross sectional shape and the hydraulic
Chapter 2 Literature Review
25
roughness which can be represented by the Manning or Chezy roughness coefficients. While
river side slope resistance to erosion is mainly concerned with the properties of bank
materials. Considering river bed shear stress, the major variables that affect the incipient
motion of uniform sediment on a level bed include
c critical shear
d water depth
s - difference in sp.wt. between sol and water
density
kinematic viscosity respectively.
These variables may be grouped into the following dimensionless parameters:
(2-14)
Therefore the following relationship may be deduced:
(2-15)
Where U= (c/ρ)1/2
is the critical friction velocity.
This relationship was explicitly solved graphically by Shields (1936). This solution was
established based on experimental data on flumes with a flat bed and is generally referred to
as the Shields diagram. The Shields diagram may be divided into laminar, transition and
turbulent flow regions. In the laminar region where R is less than about 2, the particle size is
less than the thickness of the laminar sub-layer and, hence, is enclosed in the thin laminar
film. Since the boundary is hydraulically smooth, the movement is mainly caused by viscous
action. In turbulent region of Reynolds number ( R*> 400), the laminar sub-layer is
interrupted by the grain size and for this hydraulically rough boundary, the critical Shields
stress has a constant value of 0.06, independent of the Reynolds number. Additional criteria to
quantify critical shear stress in open channel was developed by Lane (1955) as illustrated in
Figure (2-14). In this figure, the adopted curve was attached to Shields curve which can be
applied to define the critical shear at the case of non-cohesive bed materials and clear water
sediment concentration.
Chapter 2 Literature Review
26
Moreover, the relation between the relative bend curvature and the maximum relative bank
erosion was tested by Nanson and Hichin (1986) which revealed that the maximum erosion
appear to occur in the range between 2.0 and 4.0. Therefore, the intensity of shear stress near
the outer bank would be considered as a function of bank erosion rate, while the shear stress
distribution along the bank determines the location of the maximum bank erosion and the
bend migration mechanism.
Figure (2-14) Critical Shear Stress as a Function of Grain Size [Lane (1955)]
2-10-1-2 Incipient Velocity
Incipient velocity is the velocity at which the bed particles are started to move the erosion
occurs only in the zones which subjected to velocity higher than incipient velocity. The
incipient velocity is dependent upon water depth and grain size diameter. Figure (2-15)
presents the values of the incipient velocity with respect to average water depth and average
bed size diameter D50 (Neill’s, 1973).
Neill presented a family of curves for estimating critical velocities for no cohesive sediments
at varying flow depths and with grain sizes ranging from 0.3 to 300 mm (0.0117 to 11.7
inches). Neill defined the critical velocity as the flow velocity just competent to move the bed
material. Neill used a combination of field data and laboratory data to develop his family of
curves. Neill used a critical velocity equation very similar to Laursen’s to estimate the critical
velocity for grain sizes greater than about 30 mm (1.17 inches). For a grain size of 0.3 mm
(0.0117 inch), Neill assumed that a regime theory equation for stable channels in sand would
be appropriate for estimating the critical velocity. Regime theory equations are design
equations developed from field data collected in the stable, fine sediment canals of Pakistan
Chapter 2 Literature Review
27
(Mahmood and Shen). Transition curves were hand drawn for grain sizes between 0.3 and 30
mm (0.0117 and 1.17 inches).
Chang transformed the plots of Neill’s curves into a set of equations for computing critical
velocity based on the flow depth and the median diameter of the particle. This set is given in
equations 15 through 18. For D50 greater than 0.03 m (0.1 ft), Neill’s critical velocity, VCN, is
given in equation 16.
(2-16)
where:
y2 is equilibrium scour flow depth (m or ft).
D50 is sediment size (m or ft).
Ku is 0.55217 for SI units, or 1.0 for U.S. customary units.
For D50 less than 0.03 m (0.1 ft) but greater than 0.0003 m (0.001 ft), Neill’s critical velocity
is given in equation 17.
(2-17)
The exponent, x, is calculated using equation 18:
(2-18)
where:
y2 is equilibrium flow depth (m or ft).
D50 is sediment size (m or ft).
KU1 is, for SI units, 0.3048 to the power of 0.65 minus x, or 1.0 for U.S. customary units.
X is the exponent as calculated in equation 17.
KU2 is 0.788 for SI units, or 1.0 for U.S. customary units.
For D50 less than 0.0003 m (0.001 ft), Neill’s critical velocity is given in equation 19.
(2-19)
where:
y2 is equilibrium flow depth (m or ft).
Chapter 2 Literature Review
28
D50 is sediment size (m or ft).
Ku is 0.55217 for SI units, or 1.0 for U.S. customary units.
Chang’s equations are plotted in Figure (2-15). Neill’s competent velocity curves are intended
for field conditions with flow depths of 1.5 m (5 ft) or greater. Chang’s equations were
extrapolated to flow depths below 0.30 m for these experiments and to curves for flow depths
of 0.305 and 0.15 m (1 and 0.5 ft) (Figure 2-15). Note that the sediment sizes used in the
experiments fell into the range described by equations 16 and 17.
Figure (2-15) Chang’s Approximations to Neill’s Competent Velocity Curves
2-11 Bank Revetment
Bank protection could be applied along river and island to protect its bank against high flow
velocity currents which might cause bank erosion. Continuous protection are the most widely
applied and successful method on river banks and bends in such a way that to form a smooth
bank alignment and least interference with river morphology. Also such rock revetment
would be essential to protect water intake structures, different type of bridges, dams, weirs,
barrages, shores, wave breaks, and diversion structures. The used materials for bank
protection usually consist of cemented layer of lime stones and sand which are economically
suitable and widely available in Egypt. This protection type can be successfully applied
above the minimum water levels while lower than that level, a freely depend stone is to be
used. But in some other cases, a rock protective layer consists of (un-cemented) particles can
be applied to allow water to percolate through the revetment.
Chapter 2 Literature Review
29
In this respect, different design criteria for rock protection can be applied including riprap,
rock trench, mattress, gabions, soil cement and concrete blocks (Searcy 1967; Norman,
1975). The main design criteria is that the top elevation of bank protection should be above
the highest design water level in straight reaches, while in case of curved reaches the super
elevation of water surface should be considered. Furthermore, for any structures built in
erodible materials, the toe elevation should be extended below the expected scour by a
minimum of about 2 vertical meters in medium to large streams as illustrated in Figure (2-16).
Figure (2-16) Bank Protection Layers
The purpose of the extended toe is only to prevent undermining and not to support the above
structure. While, on the concave bank of sharp river bends, severe local scour is expected and
the toe protection should be deeper than that in straight reaches. Additionally, and according
to practices carried out by many engineers the necessity of using appropriate filters between
the protection layers and the underlying permeable soil is recommended. Two types of bank
protections would be presented as stone revetment and riprap protection and the design of
filter layers would be also illustrated.
2-11-1 Stone protection
The river bank may be protected using hand placed particles of different sizes to form a layer
thickness of at least 0.5 m. This layer should be carefully arranged to provide river channel
bank protection in such a way as to form a smooth bank alignment and least interference with
river morphology. In order to fulfill stability of the protective layer board, stone toe should be
formed on the original river bed up to the minimum water surface level. While in order to
provide such primary stability to the eroded bank materials, a graded gravel filter (traditional
aggregate filter) can be applied underneath the rock protective layer.
In Egypt after the construction of the High Aswan Dam, many attempts have been made to
reduce the adverse impact of bank erosion. Therefore development and updating new
techniques for bank protection are representing high priorities to the country. Many aspects
Chapter 2 Literature Review
31
were taken into consideration; important amongst them are using local materials and labors,
inexpensive and the long life durability of the protection work. Different types of data are
collected through hydrographic survey to design the toe structure which would be
implemented during the period of the minimum water surface levels as shown in Figure (2-
17).
Figure (2-17) Typical Stone Revetment at the Nile River in Egypt
In addition to the designed filter and protective rock layers which would be applied on the
river bank board up to the top level using hand placed dry stones as shown in Figure (2-18)
which illustrates an example of the applied stone revetment at the Nile River.
Figure (2-18) An Example of the Applied Design for Stone Revetment
Additionally, complete stability analysis should also be performed. This analysis includes
geometry, geotechnical field and laboratory testing programs, surface and ground water levels
as well as all other hydrological and morphological data to represent each surveyed cross
section. The output of the stability analysis is given in terms of the factor of safety. This factor
is compared to the standard specification and when the resulted value does not meet the
specified criteria, the design should be improved till reaching the typical required values.
So far the presented design for stone revetment has proved to be the most suitable approach
for protecting river channel banks against erosion in Egypt which is due to the following
reasons:
Chapter 2 Literature Review
31
Availability of used materials as local product of Egypt.
Economic accessibility of such materials comparing with other bank protection required
materials, which can be disassembled and reused if necessary.
Minor interference with river morphology comparing with other methods such as spur
dikes or submerged vanes.
Easy to be monitored and maintained after construction to secure failures.
It can be successfully implemented using unqualified labors.
Long life with minimum maintenance requirements and good appearance.
Grass and vegetation usually grow on the top of the slope adding more stability.
2-11-2 Design of Stone
Riprap may be defined as a layer consists of discrete rock particles placed on stream banks,
slopes of dams and highway embankments to prevent erosion or scour of structures due to
flowing water. Rock material can be successfully employed as riprap, to meet certain
requirements such as sufficient weight for stability, porosity for drainage, roughness for
energy dissipation, availability in even the most remote areas, and finally low cost compared
with manufactured materials such as concrete. A number of design criteria for sizing riprap
have been developed by Lane (1955), Stevens and Simons (1971 and 1976), Ruh-Ming et.
al.,(1976 and 1979), Samad (1978) and Ahmed (1988). Some of these methods have been
derived from the viewpoint of equilibrium of a single particle in flowing water and referred to
as deterministic approach. While in the case of the others, which are referred to as the
probabilistic approaches, the fluctuating nature of the hydrodynamic forces acting on an
individual particle has been considered.
The earlier formula to design such riprap protection was adopted by the U.S. Army Corps of
Engineers (1970) which was based on the design criteria by Izbach (1936) for the movement
of stone in flowing water. The formula can be written as follows:
U = C {2g (S3 - 1) }½ D
½ (2-20)
In which U is the flow velocity (ft/s); S, is the specific gravity of the stone; g is the
gravitational acceleration (ft/s2); D is the mean particle diameter (ft); and C is the Izbach's
turbulent coefficient which was taken equal to 0.86 for high turbulent level flow and 1.2 for
low turbulent level flow. Latter, the ASCE Sedimentation Manual (1972) recommended the
formula proposed by Izbash for the construction of dams by depositing rock in running water.
Chapter 2 Literature Review
32
The formula was modified to take into account the slope of the bank and can be written as
follows:
33
65
cos)1(
101.4
s
s
S
UsxW (2-21)
In which W is the weight of the stone in pounds; and is the angle of repose. Furthermore
based on the experimental studies, the following formula for sizing riprap for river bed was
adopted by Stephensen, (1979):
2
1
)tan(tancos)1(
25.0
22
2
sSg
UD (2-22)
In which; D is the mean size of riprap particle (m); is the angle of repose; and is the bed
slope angle in degrees. Concerning size distribution of riprap layer, Simons and Senturk
(1977) suggested that riprap gradation should follow a smooth size distribution curve. This
would be fulfilled by applying the following criterion:
D0 = 0.2 D50
D20 = 0.5 D50
D100 = 2 D50
2-11-3 Filter Design
As mentioned in previous section, the appropriate filters between a riprap layers and the
underplaying permeable soil is deemed necessary. The filter layer is playing a considerable
rule in preventing leaching of the permeable soil through the riprap interstices. Herman
(1984) investigated the scour related to improper filter underneath the riprap downstream
hydraulic structures. It was proven during this study that piping and leaching were sometimes
the main cause for failure reassembly occurring before riprap erosion.
Criteria for such filters to prevent leaching as well as piping failure in alluvium have been
formulated by Terzaghi, and Peck (1948). On the basis of the tests, the Terzaghi criteria
were slightly modified by the U.S. Army Waterways Experiment Station at Vicksburg,
Mississippi, for application in dam design as reported by Posey (1969). Those modified
formulae can be described in the following subsections:
Chapter 2 Literature Review
33
A) Piping Criterion
To prevent washing of the underlying material through the filter, the smaller particles in the
filter should be small enough to trap the underlying materials. Therefore, for uneven shaped
riprap particles, the criterion is considered satisfactory if
4)(
)(
85
15 baseD
FilterD (2-23)
In which Di is the grain size for which i percentage of the material by weight is finer. Where
filter refers to the overlying material and base refers to the underlying material. This criterion
is applied to any two adjacent layers among the riprap, filter planet, and base material.
B) Segregation Criterion
To ensure that the fine particles are not separated from the filter mixture and washed out of
one layer into the one beneath, the particle size distribution curve for both layers should be
approximately parallel and not too far apart. This criterion could be considered satisfactory if
25)(
)(
50
50 baseD
filterD (2-24)
C) Permeability Criterion
The permeability of filter should be sufficient for the hydraulic gradient through it to be
negligible compared with that of the underlying material. The size D15 was selected to
represent the permeability of both filter and base material and the criterion is
40)(
)(5
15
15 baseD
filterD (2-25)
As the above mentioned three criteria were satisfied for the conventional filter design the
grain size distribution for every layer can be drown as depicted in Figure (2-19).
Figure (2-19) Grain Size Distributions of the Protective Layers
0
10
20
30
40
50
60
70
80
90
100
0.01 0.1 1 10 100 1000
Perc
enta
ge F
iner
By W
eig
ht
Particle Size (mm)
Riprap
Layer
Filter Layer
(2) Filter Layer (1)
Sand Base
CHAPTER 3
DATA COLLECTION
Chapter 3 Data Collection
34
Chapter 3
Data Collection
3-1 Introduction
This chapter is devoted to present the site description and to illustrate the comprehensive
arrangement of data collection which was achieved to fulfill the study objectives. These data
were preferred in such a way as to enable simulation of the three-dimensional bathymetric
features of the study reach as well as to highlight the emerged problems and difficulties due to
human interventions. The detailed description of the collected data, include the following sub-
titles:
Site description
Hydrographic survey
Velocity measurements
Bed material samples
Hydrological data
3-2 Site Description
Kafr El-Zayat city is located at the outer curve of a very sharp bend at Km 123 of Rosetta
Branch. The study area is approximately 9.0km long which located - as shown in Figure (3-1)
downstream of Delta Barrage km 145.00 to km 154.00 downstream of El-Roda Gauge
Station. The study area is a meander consisting of two bends and includes two highway
bridges and one railway bridge, as shown in Figure (3-2). The bridges are located 145.676,
145.928, 146.391km downstream El-Roda Gauge Station. The first highway bridge (new one)
has three rectangle piers with 16m width and 26.5m length, the distance between piers are
134.5m for each, The second highway bridge (old one) has six piers, 5 rectangle piers with
16m width and 26.5m length and one circular pier with diameter 14m, the distance between
piers is 70m and the distance between the circular pier and the next is 29m, the railway bridge
consists of four piers, 3 rectangle piers with 4m width and 13m length and one circular pier
with diameter 11m, the distance between piers is 70m and the distance between the circular
pier and the next is 35m.
Chapter 3 Data Collection
35
Figure (3-2) Location of the Study Reach
Figure (3-2) Piers of the Bridges
3-3 Hydrographic Survey
A hydrographic survey of the study reach was carried out by the Nile Research Institute
“NRI” and Hydraulic Research Institute “HRI”, the National Water Research Center during
years 1982, 1998, 2003 and 2006. The survey in years 1982 & 2003 were along the study
reach but the survey in years 1998 & 2006 were in the first 3.5km, as shown in Table (3-1)
and Figures (3-3) to (3.6).
Chapter 3 Data Collection
36
Table (3-1) Hydrographic Survey of Study Area
Km From El-Roda Gauge Station
Year Up Stream Down Stream Total Length (Km)
1982 145.00 156.11 11.09
1998 145.00 148.29 3.29
2003 145.00 154.93 9.93
2006 145.00 148.09 3.09
Figure (3-3) River Bed Elevation Survey Year 1982
a) Part1
b) Part2
c) Part3
Figure (3-4) River Bed Elevation Survey Year 1998
Chapter 3 Data Collection
37
Figure (3-5) River Bed Elevation Survey Year 2003
Figure (3-6) River Bed Elevation Survey Year 2006
3-4 Velocity Measurements
The measured velocity distribution by HRI in years of 1998 and 2006 are used in the study
area. The measured velocity are measured at three cross sections along the entire reach
located as shown in Figures (3-7) and (3-8).
Chapter 3 Data Collection
38
Figure (3-7) The Measured C. S Velocity
Locations 1998
Figure (3-8) The Measured C. S Velocity
Locations 2006
The velocity measurements were performed using a propeller type Braystoke current-meter
Figure (3-9). For each cross section, the velocity was measured at many points along the cross
section. At the each point the velocity was measured at three points along the vertical
direction and the average velocity for each point was determined, Figure (3-10).
Figure (3-9) Braystoke Type Current Meter
Chapter 3 Data Collection
39
Figure (3-10) Sketch Illustrated the Vertical Positions in Cross Section to Measure
Water Velocity
It should be mentioned that the flow velocities were measured on the 30th
of Sep 1998 and
11th
of Aug. The corresponding recorded discharge downstream Rosetta barrage was 72.58
million m3
/day and 19.25 million m3
/day respectively. For each measurement profile the
average velocity was estimated using Equation No. (3-1) and Figure ( 3-11 )
D
DV
DVV
DVV
DV
Vaverage
2.0*2
3.0*2
3.0*2
2.0* 332211
…….(3-1)
Figure (3-11) Computation of the Average Velocity
3-5 Bed Material samples
Manning coefficient (n) of bed roughness is considered an important parameter for calibrating
the mathematical models as well as for their verification process. Many factors are
interrelated to formulate the exact value of the Manning roughness; important amongst them
are the bed grain size distribution and the vegetation process in the channel. Grab Sediment
Sampler shown in Figure (3-12) was used to collect 9 bed material samples from three cross
Middle
Water surface
75% of Total Depth
.75 above bed
50% of Total Depth
25% of Total Depth
.50 Under W.S
Water surface
Eastern Third Western Third
Chapter 3 Data Collection
41
sections (sec1 ,sec2 & sec3) as illustrated in Figure (3-10). The location of bed material
sampling show in Figure (3-13).
Figure (3-12) The Used Grab Sediment Sampler
Figure (3-13) Bed Material Sampling Locations
Those locations were selected to cover the entire features of the study reach and to represent
the difference in the value of the Manning roughness. The samples were analyzed for grain
size distribution in the soil laboratory of Hydraulics Research Institute at Delta Barrages to be
dried up and the sieve analysis tests were performed according to the relevant specifications.
The obtained results of the grain size distributions for the nine collected samples are depicted
in Figures (3-14), (3-15) and (3-16) while the main characteristics of the samples are shown in
Table (3-2).
1 10 cm
Chapter 3 Data Collection
41
Table (3-2) Characteristics of Bed Samples at C.S. (1,2&3)
Sample No.
Sample properties
C.S. (1) C.S. (2) C.S. (3)
1 2 3 1 2 3 1 2 3
D84 (mm) 0.448 0.578 0.434 0.858 0.944 0.471 0.957 0.949 0.708
D50 (mm) 0.267 0.33 0.255 0.552 0.721 0.3 0.871 0.847 0.406
D16 (mm) 0.182 0.205 0.174 0.304 0.134 0.182 0.142 0.161 0.133
D84/D50 1.677 1.7515 1.7019 1.554 1.3092 1.57 1.0987 1.1204 1.7438
D50/D16 1.467 1.6097 1.4655 1.815 5.3806 1.6483 6.1338 5.2608 3.0526
Geometric mean
diameter (mm) 0.267 0.33 0.255 0.552 0.721 0.3 0.871 0.847 0.406
Geometric standard
deviation 1.568 1.681 1.577 1.681 2.657 1.606 2.599 2.426 2.307
Uniformity coefficient 2.198 2.06 2.053 2.41 8.321 2.407 8.221 7.862 4.777
Sorting coefficient 0.741 0.704 0.738 0.696 0.422 0.732 0.449 0.645 0.558
Curvature coefficient 1.096 0.953 1.023 0.991 0.383 1.265 1.055 3.354 1.254
Sample mean diameter
(mm) 0.307 0.379 0.298 0.571 0.576 0.33 0.649 0.676 0.421
Figure (3-14) Grain Size Distribution Curves at C.S. No. (1)
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Per
cen
t F
iner
by
Wei
gh
t
Particle Size (mm)
Bed Material Samples
Grain Size Distribution Curves
Cross-Section No. 1
Sample 1 Sample 2 Sample 3
Chapter 3 Data Collection
42
Figure (3-15) Grain Size Distribution Curves at C.S. No. (2)
Figure (3-16) Grain Size Distribution Curves at C.S. No. (3)
However, as they obtained samples from the outer curve contain such higher percentage of
sand grains than that of the inner curve which mainly consist of muddy grains with fines.
This would be an indication to the action of the surface transverse flow velocity components
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Per
cen
t F
iner
by
Wei
gh
t
Particle Size (mm)
Bed Material Samples
Grain Size Distribution Curves
Cross-Section No. 2
Sample 1 Sample 2 Sample 3
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Per
cen
t F
iner
by
Wei
gh
t
Particle Size (mm)
Bed Material Samples
Grain Size Distribution Curves
Cross-Section No. 3
Sample 1 Sample 2 Sample 3
Chapter 3 Data Collection
43
which attack the bank and bed of the outer curve causing fines to travel from outer curve to
sediment at the inner curve zone.
3-6 Hydrological Data
It is obvious that flow discharges and the corresponding water levels are essential data to
simulate the hydrological characteristics of the study reach. For this reason, daily monitoring
of passing discharges through the located hydraulic structures (barrages) and the upstream and
downstream corresponding water levels of those barrages as well as at different gauge stations
is essential. Figure (3-17) show the Nile river hydrograph in years 1982, 1998, 2003 and
2006. The discharges D.S Rosette barrage at years 1982, 1998, 2003 and 2006 are shown in
Figure (3-18). Figures (3-19), (3-20) and (3-21) show the relation between water level at Kafr
El-Zayat and discharge D.S Rosetta barrage from year 1990 to 2011. The different discharges
(min, max, avr and emergency flow) in the reach at last 20 years shown in Table (3-3).
Figure (3-17) Nile River Hydrograph in Years 1982, 1998, 2003 and 2006
Figure (3-18) Water Discharge D.S Rosetta Barrage at Years 1982, 1998, 2003 and 2006
1.5
1.7
1.9
2.1
2.3
2.5
2.7
2.9
3.1
3.3
3.5
JAN Feb MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
Wa
ter L
evel
(m
)
Time (month)
1982
1998
2003
2006
0
10
20
30
40
50
60
70
80
JAN Feb MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
Dis
cha
rge
(mil
lio
n.m
³/d
ay
)
Time (month)
1982
1998
2003
2006
Chapter 3 Data Collection
44
Figure (3-19) Relation Between Water Level at Kafr El-Zayat and Discharge Down
Stream Rosetta Barrage in Years 1990, 1991, 1994, 1995, 1996 and 1997
Figure (3-20) Relation Between Water Level at Kafr El-Zayat and Discharge D.S
Rosetta Barrage in Years 1998, 2000, 2001, 2002, 2003 and 2004
1990 R² = 0.7047 1991 R² = 0.1132 1994 R² = 0.0061 1995 R² = 0.1226 1996 R² = 0.0615
1997 R² = 0.1107
1
1.5
2
2.5
3
3.5
0 5 10 15 20 25 30 35
Wa
ter L
evel
(m
)
Discharge (m³/sec)
Rating Curve
1990
1991
1994
1995
1996
1997
Linear
(1990) Linear
(1991) Linear
(1994) Linear
(1995) Linear
(1996) Linear
(1997)
1998 R² = 0.0939 2000 R² = 0.1156
2001 R² = 0.1249
2002 R² = 0.3663
2003 R² = 0.0303
2004 R² = 0.0838
1.5
1.7
1.9
2.1
2.3
2.5
2.7
2.9
3.1
3.3
3.5
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
Wa
ter L
evel
(m
)
Discharge (m³/sec)
Rating Curve
1998
2000
2001
2002
2003
2004
Linear
(1998) Linear
(2000) Linear
(2001) Linear
(2002) Linear
(2003) Linear
(2004)
Chapter 3 Data Collection
45
Figure (3-21) Relation Between Water Level at Kafr El-Zayat and Discharge D.S
Rosetta Barrage in Years 2009, 2010 and 2011
Table (3-3) Discharge at Rosetta Bridge
Q(m.m³/month)
Year Min Average Max Emergence
1990 2.89 11.40 33.68 220.00
1991 3.32 11.62 27.46 220.00
1992 - - - 220.00
1993 - - - 220.00
1994 2.62 11.00 23.87 220.00
1995 2.05 7.23 15.05 220.00
1996 1.90 8.31 14.84 220.00
1997 3.51 8.28 17.10 220.00
1998 5.50 24.17 69.90 220.00
1999 11.89 13.01 13.77 220.00
2000 3.75 20.40 39.12 220.00
2001 5.41 22.84 69.09 220.00
2002 2.84 13.71 25.44 220.00
2003 2.81 11.05 20.14 220.00
2004 - - - 220.00
2005 4.75 12.52 21.36 220.00
2006 4.27 12.31 27.25 220.00
2007 - - - 220.00
2008 - - - 220.00
2009 7.23 14.27 21.74 220.00
2010 5.56 12.26 20.45 220.00
2011 4.40 12.42 20.06 220.00
R² = 0.0176
R² = 0.0019
R² = 0.2393
2
2.2
2.4
2.6
2.8
3
0 2 4 6 8 10 12 14 16 18 20 22 24
Wa
ter L
evel
(m
)
Discharge (m³/sec)
Rating Curve
2009
2010
2011
CHAPTER 4
MATHEMATICAL MODEL
PREPARATION
Chapter 4 Mathematical Model Preparation
46
Chapter 4
MATHEMATICAL MODEL PREPARATION
4-1 General
Numerical models could be considered as the most widely applied technique to solve
mathematical expressions that describe any physical phenomena. Those models are mainly
classified by number of spatial dimensions over which variables are permitted to provide
much more detailed results than others. However, collection of adequate and reliable field
data is highly required to fulfill suitable model calibration and verification leading to
successful application. For this respect, in case of large width to depth ratio of the water
body, the horizontal distribution of flow quantities might be the main interest and
two-dimensional solutions based on the depth-averaged flow approximations will provide an
acceptable description of flow motion. For this purpose, the finite element Surface Water
Modeling System “SMS” 2-D mathematical model would be used to simulate the water flow
along the study reach.
Furthermore, model calibration is the process of adjusting the dimensions of simplified
geometric elements and empirical hydraulic coefficients so that values computed by a model
reproduce as closely as possible the simulated reach. The ability of a model to reproduce and
predict measured values depends on the amount and quality of topographic and hydraulic data
collected such as velocity distributions, water-surface elevation, flow rates, and bed
roughness. Although model parameters can be adjusted to obtain close agreement between
computed and measured values, an adjustment may not be extended beyond physically
reasonable values. Consequently, the purpose of model calibration is to obtain an accurate
mathematical representation of reality, not a forced fit of a poorly constructed model.
A detailed description of the mentioned mathematical model and it’s preparation would be
provided in this chapter, as well as presenting the main steps of model calibration and
verification for the applied 2-D mathematical model under the following sub-titles:
Models Formulation
Model Preparation
Sensitivity analysis
A summary of the information needed and the suggested approach as well as the expected
outputs from the model is presented in Figure (4-1).
Chapter 4 Mathematical Model Preparation
47
Figure (4-1) Flowchart of Proposed Approaches in this Study
Proposed Approaches
Data Collection Modeling
and Organization
Geometry and
Topographic DataFlow Model
* Channel Cross Sections* FESWMS Model for
Flow Simulation
* Channel Morphology
Hydraulic Data
* Water Level Hydrograph
* Discharge Hydrograph Modeling Application
* Velocity Measurements
* Simulation of flow
Digital Data Sources
* Arial Photography
* Image Satellite
* Digital Terrain Model
* Applying of different
Scenarios of flow
Prediction of Navigation
Problems
* Prediction of bed
changes in the future.
* Prediction of new
thalwag line
Solutions and
Alternatives for
Navigation
*Fill Solution
*Fill & Dredging solution
* Determination the future
navigation bottlenecks.
* Determination the
erosion and deposition
* Determination the
morphological and
hydrological changes
Calibration and
Verification
* Determination the
velocity, water surface,
water depths, shear stress,
changes of bed elevation
under the actual flow
condition
Chapter 4 Mathematical Model Preparation
48
4-2 “SMS” 2-D Model Formulation
4-2-1 Model Description
The “SMS” 2-D mathematical model was developed by the Brigham Young University in
cooperation with the U.S. Army Corps of Engineers, Engineer Research and Development
Center (ERDC), and the U.S. Federal Highway Administration (FHWA). The model consists
of family of numerical models that provide multi-dimensional solutions for solving hydraulics
behavior, sediment transport problems, reservoirs, wetlands, estuaries and bays.
The model is a pre- and post-processor for surface water modeling, analysis, and design. It
includes tools for managing roughness assignment, editing and visualizing geometric and
hydraulic data, as well as creating and editing mesh data for use in numerical analysis. The
Finite Element Surface Water Modeling System “FESWMS” is a comprehensive environment
for two dimensional flows in horizontal plane model running under the SMS Interface. This
model simulates either steady or unsteady 2-D surface-water flows, including sub- and super-
critical conditions Lee and Froehlich (1986). FESWMS solves the vertically integrated
equations of motion and continuity with a finite element scheme.
4-2-2 Governing Equations
The SMS 2-D model is used to compute water surface elevation and horizontal velocity
components for sub critical, free surface flow in two dimensional flow fields. Friction is
calculated with the Manning or Chezy equation, while steady and unsteady state (dynamic)
problems can be analyzed. Equations that describe depth averaged surface water flow
account for the effects of bed friction, wind induced stress at the water surface, fluid stresses
caused by turbulence, and the effect of the earth rotation. With this in mind, the following
points may be illustrated:
A) Basic Equations
The depth averaged velocity components in horizontal x and y coordinate directions would be
respectively defined as follows:
dzuH
U1
(4-1)
dzvH
V1
(4-2)
zs = zb + H (4-3)
Chapter 4 Mathematical Model Preparation
49
In which:
H Flow water depth (m)
z vertical direction
zb bed elevation (+msl)
zs water surface elevation (+msl)
U horizontal velocity in the x direction at a point along the vertical coordinate (m/s)
V horizontal velocity in the y direction at a point along the vertical coordinate (m/s)
The coordinate system and variables are illustrated in Figure (4-2), while the depth averaged
velocity definition is shown in Figure (4-3). The depth-averaged surface water flow
relationships would be established by integrating the three dimensional mass and momentum
transport equations with respect to the vertical coordinate from the bed to the water surface.
Considering vertical velocities and accelerations to be negligible, the vertically integrated
mass transport equation or continuity equation can be derived as follows:
mw q
y
q
x
q
t
z
21 (4-4)
In which:
q1 = UH = unit flow rate in the x direction
q2 = VH = unit flow rate in the y direction
qm = mass inflow or outflow rate per unit area
Figure (4-2) 3-D Coordinate System
H
Zb
u
v w
X
Y Z
Water surface
Bed surface
Plane datum
Chapter 4 Mathematical Model Preparation
51
Figure (4-3) Depth Average Velocity Definition
Considering that the water mass density is constant throughout the modeled reach,
description of momentum transport in x and y directions would be respectively as follows:
0 )(H
- )(H
1
qy
Hz
gH 2
1
y )
qq(
yyyx
1b2
2
1212
yx
P
ygH
H
q
Hxt
q
syby
a
(4-5)
0 )(H
- )(H
1
q x
zgH
y
2
1
x
xyxx
2b212
2
11
yx
HgH
H
q
t
q
sxbx
(4-6)
In which
= isotropic momentum flux correction coefficient that accounts for the variation of
velocity in the vertical direction
g = gravitational acceleration
= water mass density
Pa = atmospheric pressure at the water surface
= Coriolis parameter
bx and by = bed shear stresses acting in x and y directions, respectively.
sx and sy = surface shear stresses acting in x and y directions, respectively.
xx, xy, yx, and yy = shear stresses caused by turbulence where, for example, xy is the shear
stress acting in x direction on a plane that is perpendicular to the y direction.
Chapter 4 Mathematical Model Preparation
51
B) Momentum Flux Correction Coefficient
Vertical velocity profiles can be approximated by the logarithmic function
K
zz
k
uu b
elog* (4-7)
In which
Ucu f* bed shear velocity or bed friction velocity
cf = bed shear-stress coefficient
k = von Karman's constant
K = roughness height
When vertical velocities follow the logarithmic profile, the momentum flux correction
coefficient is given by
21
k
c f (4-8)
Momentum flux correction coefficients in FESWMS are calculated as
fo cc (4-9)
where o and c are specified coefficients. Comparing the two expressions for gives o = 1
and c = 1/k2. For most open-channel flows, the coefficient k 0.4, which gives C = 6.25.
Constant momentum flux correction factors can be specified by setting o to the desired
value, and setting c to zero. Default values in Flo2DH are o = 1 and c = 0. Using these
default values means that vertical variations in velocity are considered negligible.
C) Bed Shear Stress
Directional components of bed shear stress are computed as follows:
2
2
2
2
11 H
qqqmc bfbx
(4-10)
2
2
2
2
12 H
qqqmc bfby
(4-11)
Chapter 4 Mathematical Model Preparation
52
where cf = dimensionless bed-friction coefficient, and
22
1
y
z
x
zm bb
b (4-12)
Where mb is a factor that accounts for increased shear stress caused by a sloping bed. Bed
friction coefficient cf is given by
23/12
2
c
g
H
gnc
n
f
(4-13)
Where n is Manning roughness coefficient, n = 1.486 for U.S. customary units, or 1.0 for SI
units, and c is Chézy roughness coefficient.
Both Manning and Chézy coefficients can be described by linear functions of water depth in
FESWMS. Variations in flow resistance with water depth might occur when short vegetation
is submerged and possibly bent by the flow, or where tree branches come into contact with
flow at high stages. Appropriate flow resistance coefficients for natural and constructed
channels and for floodplains can be estimated using references such as Chow (1959), Barnes
(1967), and Arcement and Schneider (1984).
4-2-3 Numerical Techniques and Limitation
The partial differential equations that govern two-dimensional surface-water flow in a
horizontal plane are derived from equations that govern three-dimensional flow by neglecting
fluid velocity in vertical direction. Therefore, pressure within the fluid is considered the same
as in a hydrostatic condition. The numerical technique used to solve the governing equations
is based on the Galerkin finite element method. This method is a numerical procedure which
could be applied to solve various differential equations encountered physics and engineering
problems. For this reason, continuous quantities are generally approximated by sets of
variables at discrete points that form networks or meshes. Therefore, due to the fact that the
finite element method can be modified to problems of great complexity and unusual
geometry, it is an extremely powerful tool to solve problems in the field of heat transfer, fluid
mechanics, and mechanical systems. In Addition, the availability of fast and reasonably priced
computers allows difficult problems using analytical or mathematical methods to be directly
solved by the finite element method. Conservation of momentum as described in classical
physics is an example of such a process.
Chapter 4 Mathematical Model Preparation
53
However FESWMS operates under the hydrostatic assumption; meaning accelerations in the
vertical direction are negligible. It is two-dimensional in the horizontal plane. It is not
intended to be used for near field problems where vortices, vibrations, or vertical
accelerations are of primary interest. Vertically stratified flow effects are beyond the
capabilities of FESWMS. Additionally FESWMS is a free-surface calculation model for sub
critical flow problems.
4-3 Model Preparation
The steps generally taken to simulate surface-water flow using Flo2DH are as follows:
Data assessment, network design, model calibration, model testing, and model
application. These five steps, illustrated in Figure (4-4), are common to the operation of
almost any type of numerical model and are described in this section. Additionally the
direction lines suggest modification or control of the application process is also shown in the
figure.
Figure (4-4) Modeling Steps
In order to reach the finest simulation of the model for the study reach, several sequential
steps are followed in order to fulfill its need which is the appropriate simulation for the
chosen river site and at the same time the model fit to different ideas for the proposed
solutions. To reach this goal the following points will be covered:
4-3-1 Data Assignment
As the surface-water flow problem has been defined, the first step in model operation is
making use of the gathered data mentioned in chapter 3. Needed data are classified as either
topographic or hydraulic data. Topographic data describe the geometry of the physical system
Data Assessment
Network Design
Model Calibration
Model Testing
Model Application
Chapter 4 Mathematical Model Preparation
54
including the assignment of the bed elevation to the study mesh, and evaluation of surface
roughness to be used in estimating bed friction coefficients. Additionally, hydraulic data
include measurements of discharges and the corresponding water levels, velocity cross
sections, and rating curves are also collected. The hydraulic data are used to establish the
model boundary conditions, model calibration, and model testing process. The overall data
needed for the different processes of the current study of modeling operation and their use and
source are summarized in Table (4-1).
Table (4-1) Data Needed for Model Validation
The type and amount of required data to design a network properly and to apply a model
mainly depend on the purpose of the model. The more data that can be obtained the better
simulation can be obtained and all of the data can be used to improve the quality of a model's
output. Theoretically, any surface-water flow can be simulated as accurately as wanted
provided the important physical processes are represented adequately by the governing
equations. However, the purpose of a model needs to be considered when deciding what and
how much data is needed to provide results of the desired accuracy. For example, a
computational resolution of centimeters or less might be needed to provide the desired results
for a model of a laboratory flume. On the other hand, a model of a tidal estuary might require
a computational resolution of a kilometer or more.
Several factors affect the choice of the adequate amount of data required to reach the ideal
modeling, these factors may be denoted as study objectives, the available period, required
DATA ITEM USE OF DATA SOURCE(S) OF DATA
Ground-surface
elevations
To define mesh node locations; layout of
a finite element network.
Topographic and
hydrographic maps, and
cross section surveys.
Channel and floodplain
surface characteristics,
vegetative cover, and
sediment composition.
Assessment and definition of bed friction
coefficients and eddy viscosity.
On site samples, Aerial
photographs, topographic
maps, on-site inspection,
and field experience.
Hydrological data ( water
surface elevations, and
discharge)
Establishment of boundary conditions,
calibration of model coefficients, and
testing model accuracy.
On-site measurements, and
historical data base from
stream gauge records.
Current velocity
Establishment of boundary conditions,
calibration of model coefficients, and
testing model accuracy.
On-site measurements and
database records.
Chapter 4 Mathematical Model Preparation
55
personnel experience, and financial considerations should be considered before model
construction. Therefore, decisions need to be made regarding how much detail to be
represented by the model and the extent of a calibration and testing to be carried out. If a high
level of detail is provided by a network, risk of not representing a physical system properly
will be reduced, but difficulty (in time and expense) of obtaining a solution will be increased.
On the hand, if a simple wide grid network is designed, the risk of inaccuracy representing the
physical system will be increased, but the difficulty of obtaining a solution will be reduced.
Knowledge of important physical processes that govern the response of a system under study
is needed to evaluate the transaction between risk of inaccuracy and difficulty of obtaining a
solution. Sometimes constraints on time, human resources, or funding will predetermine how
much detail can be included in a model and the amount of calibration and testing to be carried
out.
In order to calibrate the applied 2-D numerical model for the selected study reach, some
important hydraulic parameters would be prepared as follows:
4-3-1-1 Roughness estimation (Manning Coefficient)
Roughness coefficients of bed material and river configurations are empirical parameters that
could strongly influence model solution. Therefore, sufficient and accurate topographic data
should be collected; the initially predicted roughness coefficient values will not have to be
adjusted extensively during the calibration process. Adjusted roughness coefficients would be
carefully made according to the type and size of the materials that compose the bed and banks
of the channel as well as the channel configuration. With this respect, Cowan (1956)
developed a procedure for estimating the effects of these factors to determine a representative
Manning value n for a channel which may be computed as follows:
n = (nb +n1 +n2 +n3 +n4)m (4-14)
Where:
nb = base value of n for a straight, uniform, smooth channel in natural materials
n1 = correction factor for the effect of surface irregularities
n2 = value for variations in shape and size of the channel cross section,
n3 = value for obstructions
n4 = value for vegetation and flow conditions
m = correction factor for meandering of the channel
Chapter 4 Mathematical Model Preparation
56
Therefore, by applying the previous formula at different locations along the study reach, the
corresponding Manning roughness coefficient ranges could be estimated for each of the
banks, natural bed, and vegetative areas. These roughness values were then classified
according to their locations as illustrated in Figure (4-5) and listed in Table (4-2) which would
be used to calibrate the 2-D model.
Table (4-2) Ranges of the Estimated Roughness Coefficients
Region
No. Region Class
Estimated Manning factor (n)
Min. Max.
1
2
3
Original bed Profile
River banks
Vegetative areas
0.015
0.020
0.025
0.020
0.025
0.045
Figure (4-5) Study Reach Roughness Coefficient Classification
In which:
Region (1) is located at the original bed profiles where flow depth is sufficient to convey
the mainstream flow discharge. In this case the roughness would be due to bed
forms, type and gradation of bed materials.
Region (2) is located along the river banks where the roughness is mainly due to bank line
irregularities such as boulders, trees, and the existence of different types of training
works at different locations.
Region (1):
Original bed
Profile
Region (3):
Aquatic weed
Infestation
Region (2):
River banks
Reach
upstream
boundary
Reach
downstream
boundary
Chapter 4 Mathematical Model Preparation
57
Region (3) is located at shallow depths and deposition zones where flow depth is reduced
to minimum values which allow for sun rise penetration through the water. In this
case, the ability for vegetation and infested plants increased and consequently
roughness coefficient is rapidly raised.
4-3-2 Network Design
The next step in modeling is to design a finite element network. Network design can be
defined simply as the process by which the surface-water body being modeled is subdivided
into an assemblage of finite elements. The basic goal of network design is to create a
representation of the water body that provides an adequate approximation of the true solution
of the governing equations at a reasonable cost.
Decisions as to set the number, size, shape, and pattern of elements used is required to provide
an adequate representation of the water body that is to be modeled need to be made when
designing a finite element network. If the elements obey some basic requirements for a
convergent solution, the accuracy of the solution will improve as the size of the elements in a
network is reduced. However, increasing the number of elements in a network also increases
computational expenses. Elements need to be made small enough to provide a solution of
sufficient detail and accuracy, yet large enough to obtain the solution at a reasonable cost. So
in the study at hand the number of elements used for simulation was 9389 elements
distributed and assigned as subsequently demonstrated.
Next, the limits of the area to be modelled are defined. As a rule, model boundaries were
placed where water-surface elevations and flows at maximum conditions cannot reach as
close as possible so that any errors introduced at the boundaries will have little influence at
the points of interest. After defining boundaries the area is divided into regions that have
abruptly different topographic and surface cover characteristics, then every region is divided
into elements in a criteria at which the size and shape of which will depend on the desired
level of detail in that particular area. So referring to the study reach of different mesh density
as shown in Figure (4-6) and Figure (4-7) and illustrated as following:
Chapter 4 Mathematical Model Preparation
58
Figure (4-6) Study Reach Mesh Element Composition
Figure (4-7) Bridge Mesh Element Composition
Vertex node
Midside node
Center node
Quadrilateral
elements
Triangular
elements
60o : 120o
5
o : 120o
Upstream
boundary
Downstream
boundary
Chapter 4 Mathematical Model Preparation
59
In this case, the elements are defined by a series of node points for nine-node quadrilateral
elements at the element vertices, mid-side points, and at their centers, additionally triangular
elements joining different sizes of quadrilateral elements are composed of six nodes at the
element vertices, mid-side points. Values of dependent variables are approximated within
each element using the nodal values and a set of interpolation functions (also called shape
functions). Approximations of the dependent variables are substituted into the governing
equations, which generally will not be exactly satisfied, thus forming a residual. Because the
system of equations is nonlinear, a Newton iterative solution procedure performed, and the
resulting system of equations is solved using an efficient frontal solution scheme.
Some conditions regarding the shape of an element need to be satisfied so that to eliminate
any dimensional errors, it was taken in mind that internal angles of quadrilateral elements be
kept between 60o and 120
o as shown in Figure (4-6). For triangular elements it was assured to
keep interior angles between 5o and 120
o, which means avoiding long, thin elements that
come to a sharp point.
Another characteristic of network design that affects a finite element solution is the aspect
ratio of elements used in the network. The aspect ratio of a two-dimensional element is the
ratio of the longest element dimension to the shortest element dimension as shown in Figure
(4-8). The optimal aspect ratio for a particular element depends on the local gradients of the
solution variables, mainly aligning the longest element dimension to the direction of the
smallest gradient and the shortest element dimension to the direction of the largest gradient is
best. For example, in stream channels where the longitudinal variation of velocity and depth is
gradual and the transverse variation is large, elements can be much longer in the longitudinal
direction than in the transverse direction. If the interior angles of triangular elements are kept
between 5o and 120
o, the maximum aspect ratio that can result is about 12.5. So the mesh
creation in the study reach was carefully interpolated by elements of aspect ratio between 1:5
and 1:8.
Figure (4-8) Quadrilateral and Triangular Element Aspect Ratios
a
b
a
b
Element aspect ratio = a/b
Chapter 4 Mathematical Model Preparation
61
Till this point the mesh is in the planer form, therefore the bed elevations should be assigned
to each element composing nodal point at the same coordinates. Transforming coordinates of
each scatter point and mesh node is automatically interpolated by the SMS program as shown
below in Figure (4-9). Each mesh node is individually interpolated and a subset of bathymetry
scatter points within a user-defined region near that current mesh node is generated. The used
algorithm looks for a user-specifiable, minimum number of bathymetry points within
successively larger user-specifiable bounding regions. When the minimum number of points
is found, the mesh node elevation is calculated using an Inverse Distance Weighted average of
the elevations of only the selected bathymetry points.
Figure (4-9) Inverse Distance Weighted Average Interpolation Criteria
The stage of network design can be said to be finished when a contour of the whole reach can
be plotted by the SMS program, but further checks should be made for undefined nodes which
may occur from the lack of scatter points near the denoted nodes at the process of
interpolation. After that further investigations of the reach topography can easily be carried
out by changing the data range in contour options, as shown in the portion in Figure (4-10) it
can be deduced that a scour hole exists closer to the center of the channel, and for the whole
reach investigation Figure (4-11) shows the transformation process of changing the plan mesh
using the scatter data into the contour mapping.
Figure (4-10) Planer and 3D Contouring after Interpolation Process
SMS radial bounding region Node being
interpolated
Scatter points used for
interpolation
Scatter points
Mesh
Elements
Chapter 4 Mathematical Model Preparation
61
Figure (4-11) Design Mesh Elevation Assignment
Interp
ola
tion
Created Mesh
Scatter Points
Contour Map
Chapter 4 Mathematical Model Preparation
62
4-3-3 Calibration Results
Several model runs were made to achieve the best agreement between measured and resulted
values from the model. Measured values of water-surface elevation for year 1998, and
velocities will be used to calibrate the mode. This was carried out by adjusting roughness
coefficients at various locations along the modeled study reach according to the mentioned
ranges in Table (4-4) till the best results are achieved. The model was calibrated using the
inflow discharges at Delta Barrage and water levels at Kfer El-Zayat station as shown in
Table (4-3). Comparison of the measured field velocities and obtained velocity profiles at the
three cross sections located as shown in Figure (4-12), and its results are shown in Figures (4-
13 to 4-15).
The comparison between the measurements and simulated water surface elevations at Kfer-El
Zayat station showed that there is a good agreement as shown in Figure (4-16) for the
calibration.
Table (4-3) Boundary Condition of Calibration
Calibration Time Q(m³/day) WL(m)
30/09/1998 840 m³/sec 2.7
Figure (4-12) Location of the Calibration Cross Sections
Chapter 4 Mathematical Model Preparation
63
Figure (4-13) Flow Velocity Calibration at Cross Section (1)
Figure (4-14) Flow Velocity Calibration at Cross Section (2)
Figure (4-15) Flow Velocity Calibration at Cross Section (3)
0.00
0.25
0.50
0.75
1.00
1.25
1.50
0 50 100 150 200 250 300 350 400
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(1)
Model Field
0.00
0.25
0.50
0.75
1.00
0 50 100 150 200 250 300 350 400
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(2) Model Field
0.00
0.25
0.50
0.75
1.00
0 50 100 150 200 250 300 350
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(3) Model Field
Chapter 4 Mathematical Model Preparation
64
Figure (4-16) Comparison between the Measurement and Simulated Water Surface
Elevation
The three figures indicate good agreement between the measured and predicted velocity
profiles for the three cross sections which have the same trend and distributions. Moreover.
This comparison confirms the close equivalent of the calibration results where most points are
comparable with small percentage of less than 10% difference except two points. On the
other hand concerning the estimation of real roughness factor for the study reach, several
values were estimated within the listed limits which are illustrated in Table (4-4).
Table (4-4) Calibration Values for Roughness Coefficients
Region
No. Region Class Calibration values
1
2
3
4
5
Original bed Profile
River banks
Protection bank
Vegetative areas
Dikes
0.020
0.030
0.040
0.040
0.050
4-3-4 Verification Results
As calibration phase of the 2-D “SMS” mathematical model was considered satisfactory,
another testing stage is carried out which is the verification phase. The model was verified
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 WA
TE
R S
UR
FA
CE
EL
EV
AT
ION
(m)
DISTANCE (m)
Simulated
Measurement
B3
K.St
B1 B2
S2 S1
Flow
Chapter 4 Mathematical Model Preparation
65
using the inflow discharges at Delta Barrage and water levels at Kfer El-Zayat station as
shown in Table (4-5). Measured values of water-surface elevation for year 2006, and
velocities will be used in the verification phase.
The comparison between measured and simulated cross sections is shown in Figure.(4-18 to
4-20) which located as shown in Figure (4-17). The comparison between the measurements
and simulated water surface elevations at Kfer-El Zayat station showed that there is a good
agreement as shown in Figure (4-21) for the verification.
Table (4-5) Boundary Condition of Verification
Verification Time Q(m³/day) WL (m)
11/08/2006 222.8 m³/sec 2
Figure (4-17) Location of the Verification Cross Sections
Figure (4-18) Flow Velocity Verification at Cross Section (1)
0.00
0.25
0.50
0 50 100 150 200 250 300 350 400
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(1) Model Field
Chapter 4 Mathematical Model Preparation
66
Figure (4-19) Flow Velocity Verification at Cross Section (2)
Figure (4-20) Flow Velocity Verification at Cross Section (3)
Figure (4-21) Comparison between the Measurement and Simulated Water Surface
Elevation
0.00
0.25
0.50
0 50 100 150 200 250 300 350 400
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(2) Model Feild
0.00
0.25
0.50
0 50 100 150 200 250 300
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(3) Model Field
1.00
1.20
1.40
1.60
1.80
2.00
2.20
2.40
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
WA
TE
R S
UR
FA
CE
EL
EV
AT
ION
(m
)
DISTANCE (m)
Simulated
Measurement
B
3
K.St
B1 B2
S2 S1
Flow
Chapter 4 Mathematical Model Preparation
67
4-4 Sensitivity Analysis
Referring to the SMS specifications for the needed input data for calibration and the relative
importance of such data, the weight percentages of different parameters would be illustrated
as shown in Figure (4-22). This pie chart illustrates the approximate relative importance to the
simulation of the different aspects of any study. It can be denoted that the structure of the
geometry and overall study design which comprises an assemblage of nodes and elements are
the most significant which represents about 60% of the relative importance. Following that
by 20% for the boundary condition assignment which makes a total percentage of 80%. While
the other 20% of the relative importance is shared between the roughness assignments by
10%, internal fluid viscosity by 6%, and the rest 4% is devoted to the other factors which
includes field data issues, amount of time devoted for the effort, and approach chosen to
analyze data. (Wail Fahmy 2005 )
Figure (4-22) Data Relative Importance to Modeling
Bearing in mind the adopted hydraulic parameters to calibrate the 2-D model and the achieved
calibration and verification results, such sensitivity test was carried out on the calibrated
model. The objective of such test is to justify the reached calibration parameters and the
influence of any small variation of the input data on the attainable calibration results. This
sensitivity analysis was carried out by increasing the whole reach Manning roughness
coefficient values by an increment of 0.005 to assign the corresponding variation on the
longitudinal water surface profile as well as the corresponding sectional velocities. Several
tests were carried out to justify the application of different values of roughness coefficients.
(Wail Fahmy 2005 )
%61
%21
%11
%6 %
4
Geometry &
Study Design
Boundary
Conditions
Roughnes
s
Viscosity
Other
Chapter 4 Mathematical Model Preparation
68
4-5 Summary
It is obvious that satisfactory calibration and verification results are essentially needed to
adjust the dimensions of geometric elements and empirical hydraulic coefficients of the study
reach so that the produced model parameters represent as closely as possible the simulated
reach. In order to calibrate the applied 2-D mathematical model, the required hydraulic
parameters of the measured velocity distributions, water-surface elevation, total flow rates,
and bed roughness were provided. Those were prepared in the required input forms in such a
way as to suit the morphology of the modeled reach during the calibration stage. Several
model runs were conducted to achieve the best agreement between measured and resulted
parameters during which the roughness coefficients at various locations along the modeled
study reach were adjusted.
Since good were achieved, verification testing stage was carried out during which the
corresponding longitudinal water surface profiles to different flow conditions were used. This
test was carried out applying the same values that representing the minimum, average, and
maximum passing discharges through the study reach during the past ten years.
A third stage was carried out on the calibrated 2-D mathematical model, such sensitivity test
was carried out to justify the reached calibration parameters and the influence of any small
variation of the input data on the attainable results. In this study, the Manning roughness
coefficient increased by increment of 0.005 to assign the corresponding variation on the
longitudinal water surface profiles. Several tests were carried out to justify the application of
different values of roughness coefficients. This showed that, the minimum attainable
difference in the water surface profiles is achieved with the previously reached calibration
parameters. This revealed that the adopted calibration parameters of roughness coefficients
are the most suitable values which satisfy the best results.
At this stage of the study the model can be used to study the proposed training works on the
study reach.
CHAPTER 5
MORPHOLOGICAL CHANGES
Chapter 5 Morphological Changes
69
Chapter 5
Morphological Changes
5-1 Introduction
It is obvious that Nile River downstream the Old Aswan Dam (OAD) can be considered as a
very low energy river with low water surface gradient. Moreover, the average bed slope along
each of the Damietta and Rosetta branches of the Nile Delta of about 240 km long is about 5.6
cm/km. Bearing in mind the tremendous reduction which took place in suspended sediment
and flow discharges through the river after the construction of High Aswan Dam (HAD), this
leads to conclude that morphological changes took place and extended towards the
downstream direction where the study reach is located along Rosetta branch.
5-2 Study Reach General Description
The chosen reach for conducting the present study is approximately 9.000 km long of Rosetta
Branch with main features as shown in Figure (5-1). The reach is located in Kfer El-Zayat
City downstream of Delta Barrages Rosetta Branch which is corresponding to the distance
from km 145.00 to km 154.00 downstream of El-Roda Gauge Station. The selected reach
consists of two successive meandering curves where bed forms composed of a relatively
homogeneous combination of sand. The study area also consists of two highway bridges and
one railway bridge.
Figure (5-1) General Plan of the Study Reach
Chapter 5 Morphological Changes
71
Considering the meandering features of the selected study reach, the following two successive
sharp curved zones would be distinguished:
The upstream curved reach which is about 3.000km long located between km 145.00
and km 148.00 downstream of El-Roda Gauge Station. The curved reach is following anti
clock wise direction where the inner curve is situated on the west side and the outer curve
is located along the east side of the river.
The downstream curved reach which is about 2.455km long located between km 150.50
and km 153.00 downstream of El-Roda Gauge Station. The curved reach is following
clock wise direction where the inner curve is situated on the east side and the outer curve is
located along the west side of the river.
Therefore, using the geometrical definitions shown in Figure (5-2), parameters of the
meandering planform relevant to the study reach were deduced as illustrated in Table (5-1).
Figure (5-2) Meandering Planform Parameters
rc2
2 rc1
θ2
θ1
Z
(λ) is the meander wavelength
(Р) is the sinuosity
(θ) is the arc angle
(Z) is the meander arc length
(a) is the amplitude
(rc) is the radius of curvature
λ1/2
λ2/2
a
Chapter 5 Morphological Changes
71
Table (5-1) Meandering Parameters of the Study Reach
No. Curvature characteristics U.S. curve D.S. curve
1 Radius of curvature (rc) (km) 2.679 2.678
2 Meander Wavelength (λ) (km) 5.653 (average)
3 Sinuosity (Р) (-) 1.26 2.43
4 Arc angle (θ) (degree) 88 o 112
o
5 Meander arc length (Z) (km) 7.782
6 Amplitude (a) (km) 4.697
5-3 Bed Elevation Contour Map at Years 1982, 1998, 2003 and 2006
In order to understand the main character of the Nile River after the construction of HAD,
comparison of cross section profiles along the study reach during years 1982, 1998, 2003 and
2006 would be illustrated. The survey in years 1982 & 2003 were done along the study reach
but the survey in years 1998 & 2006 were done in the first 3.5km. as shown in Figure (5-3)
and Figure (5-4).
Figure (5-3) River Bed Elevation for Years 1982 and 2003
Chapter 5 Morphological Changes
72
Figure (5-4) River Bed Elevation for Years 1998 and 2006
5-4 Morphology Comparison of Years 1982, 1998, 2003 and 2006
The total number of 8 cross sections- as shown in Figure (5-1) was utilized in order to
understand the hydrological and morphological change along the study reach. Cross sections
1, 2 and 3 are located just upstream, downstream high way bridge 1 and downstream the
railway bridge respectively. Cross section 4 is located at the middle of curve one and cross
section 5 is located at transition zone between the two curves. Cross sections 6, 7 and 8 are
located at upstream, middle and downstream the second curve.
5-4-1 Comparison of Bed Profiles and Thalweg lines
Comparison between the deduced cross section profiles corresponding to the previous and
recent hydrographic measurements of years 1982, 1998, 2003 and 2006 are shown in Figure
(5-5). This description would be presented as follows:
Cross Section (1) It can be noticed that the section in different years have the same
profile. It’s clear also that the deepest point located in the same place and have a level of -
10.65 m MSL at survey 1982 and 1998 but it have a level of -6.15m MSL and -5.93 MSL
at survey of years 2003 and 2006 respectively. This mean that deposition was occurred by
the time. Also clear that the bank at the right side was filled.
Cross Section (2) It is clear that for all studied years, the deepest points are located in the
same place, at right side which consider unsafe to the bank. These deepest points were at
level of -1.86, -2.64, -4.82 and -1.78m MSL at years 1982, 1998, 2003 and 2006
respectively. This mean that scour was done until year 2003 and deposited again at year
2006.
Cross Section (3) It can be noticed that the deepest point of the scour hole at right side
(outer curve) was filled from level -14.5m MSL at years 1982 and 1998 until reached to
Chapter 5 Morphological Changes
73
about -7.8m MSL at years 2003 and 2006. It is also noticed that the deviation to the scour
hole of about 30m was done towards the inner curve in year 1998.
Cross Section (4) It is clear that the deepest point at year 1982 was -15.15m MSL which
is almost the same of year 1998, only deviation to the scour hole of about 40m to the
inner curve was done. The bed was deposited to level -12.82m MSL for year 2003 and
still stable until year 2006.
Cross Section (5) A little deposition was occurred in a year 2003 compared with a
surveyed of a year 1982. The deepest point almost in the same place and have a level of
-9.8m and -10.8m MSL in survey of years 1982 and 2003 respectively.
Cross Section (6) Scour at the whole section was occurred in survey of year 2003
compared with 1982. The deepest point didn’t move at a survey of years 2003 and 1982
and they have levels of -6.5 m and -6.0 m MSL respectively.
Cross Section (7) Scour was occurred of 30m distance towards the outer curve from a
survey of year 1982 to 2003 while deposition was done to the other side of the section.
The deepest point didn’t move at a survey of years 2003 and 1982 and they have levels of
-14.6 m and -18.1 m MSL respectively.
Cross Section (8) Comparing a survey of year 1982 to 2003, deposition was occurred to
the whole section except a distance of 60m at right hand side where scour was occurred.
The deepest point moved 20m to the right hand side from year 1982 to 2003 and have
levels -12.9m and -12.7m MSL respectively. Figure (5-6) shows the variation of the
lowest bed levels
-14.00 -12.00 -10.00
-8.00 -6.00 -4.00 -2.00 0.00 2.00 4.00
0 50 100 150 200 250 300
EL
EV
AT
ION
(m
)
DISTANCE (m)
Cross Section No.(1) 1982 1998 2003 2006
-6.00
-4.00
-2.00
0.00
2.00
4.00
0 50 100 150 200 250 300 350 400
EL
EV
AT
ION
(m
)
DISTANCE (m)
Cross Section No.(2) 1982 1998 2003 2006
Chapter 5 Morphological Changes
74
Figure (5-5) Comparison of Bed Profiles at Cross Sections (1) to (8)
Figure (5-6) Variation of the Lowest Bed Levels
-16.00
-12.00
-8.00
-4.00
0.00
4.00
0 50 100 150 200 250 300
EL
EV
AT
ION
(m
)
DISTANCE (m)
Cross Section No.(3) 1982 1998 2003 2006
-18.00
-14.00
-10.00
-6.00
-2.00
2.00
0 20 40 60 80 100 120 140
EL
EV
AT
ION
(m
)
DISTANCE (m)
Cross Section No.(4) 1982 1998 2003 2006
-12.00 -10.00
-8.00 -6.00 -4.00 -2.00 0.00 2.00 4.00
0 25 50 75 100 125 150 175 200 225
EL
EV
AT
ION
(m
)
DISTANCE (m)
Cross Section No.(5) 1982
2003
-8.00
-6.00
-4.00
-2.00
0.00
2.00
4.00
0 50 100 150 200 250 300 350 400 E
LE
VA
TIO
N (
m))
DISTANCE (m)
Cross Section No.(6) 1982
2003
-22.00
-18.00
-14.00
-10.00
-6.00
-2.00
2.00
0 25 50 75 100 125 150 175
EL
EV
AT
ION
(m
)
DISTANCE (m)
Cross Section No.(7) 1982
2003
-14.00 -12.00 -10.00
-8.00 -6.00 -4.00 -2.00 0.00 2.00 4.00
0 25 50 75 100 125 150 175 200 225
EL
EV
AT
ION
(m
)
DISTANCE (m)
Cross Section No.(8) 1982
2003
-20.00
-16.00
-12.00
-8.00
-4.00
0.00
4.00
8.00
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
LE
VE
L (
m)
DISTANCE (m)
1982 1998 2003 2006
K.St
Kfr Al zayat Bridges B1 B3 B2
S2 S1
N
Chapter 5 Morphological Changes
75
It can be concluded that the scour and thalweg line always locate at the outer bend while in
transition zone the scour locate approximately near the middle of the section. It is noticed that
in some places the recent survey recorded deepest point among the others surveys. The reason
of that was the human interfering by filling the critical scour holes after big floods.
5-5 Scour Holes in the Area of Study
Figure (5-7) shows the location of the scour holes in the study area. In the outer curve, the
velocity is higher than inner curve so, the scour holes are located in the outer curve of the
meander where, bank failure can occurring. Figures (5-7) and (5-8) show also the top width,
length and depth of the scour holes from year 1982 to 2003. Figure (5-9) show that the area of
scour holes no.1 and no.7 were wider in year 2003 than year 1982, but the scour holes no.2
&3 &4 &6 &9 &10 were deposited from year 1982 to year 2003, and scour hole no.5, 8
almost stable.
Figure (5-7) Scour Holes Location in Study Area at Year 1982
Figure (5-8) Scour Holes Location in Study Area at Year 2003
Chapter 5 Morphological Changes
76
1982 2003
Chapter 5 Morphological Changes
77
Figure (5-9) Comparison of Scour Holes in Study Area at Years 1982 and 2003
Table(5-2) shows the different variation in characteristics of scour holes no.1&2&3 from year
1982 to year 1998. The scour hole no.1 have length, width and depth of 122, 44 and -11m in
Chapter 5 Morphological Changes
78
year 1982 while it reached to 80, 44 and -13m in year 1998 respectively. It means that in year
1982, the length decreased by 42m, width didn’t change and the depth increased by 2m
comparing with year 1998.
The scour hole no.2 have length, width and depth of 195, 70 and -15m in year 1982 while it
reached to 145, 81 and -17m in year 1998 respectively. It means that in year 1982, the length
decreased by 50m, width increased by 11m and the depth increased by 2.5m comparing with
year 1998.
The scour hole no.3 have length, width and depth of 903, 58 and -16m in year 1982 while it
reached to 837, 76 and -15m in year 1998 respectively. It means that in year 1982, the length
decreased by 66m, width increased by 18m and the depth decreased by 1m comparing with
year 1998.
Table (5-2) Scour Holes Variation from Year 1982 to 1998
Table (5-3) shows the different variation in characteristics of scour holes no.1&2&3 from
year 1998 to year 2003. The scour hole no.1 have length, width and depth of 80, 44 and -13m
in year 1982 while it reached to 148, 53 and -11m in year 1998 respectively. It means that in
year 1998, the length decreased by 68m, width increased by 9m and the depth decreased by
2m comparing with year 1982.
The scour hole no.2 have length, width and depth of 145, 81 and -17.5m in year 1998 while it
reached to 113, 70 and -9m in year 2003 respectively. It means that in year 2003, the length
decreased by 32m, width decreased by 11m and the depth decreased by 8.5m comparing with
year 1998.
The scour hole no.3 have length, width and depth of 837, 76 and -15m in year 1998 while it
reached to 1009, 77 and -14m in year 2003 respectively. It means that in year 2003, the length
No.Of
HolesDifferece Differece Differece
Avr
Rate/Year
1982 1998 1982 1998 1982 1998
1 122.00 80.00 -42.00 44.00 44.00 - -11.00 -13.00 -2.00 -0.13
2 195.00 145.00 -50.00 70.00 81.00 11.00 -15.00 -17.50 -2.50 -0.16
3 903.00 837.00 -66.00 58.00 76.00 18.00 -16.00 -15.00 1.00 0.06
4
5
6
7
8
9
10
Hole Length (m)Hole Width
(m)
Hole Depth
(m)
No Data
Chapter 5 Morphological Changes
79
increased by 172m, width increased by 1m and the depth decreased by 1m comparing with
year 1998.
Table (5-3) Scour Holes Variation from Year 1998 to 2003
Table(5-4) shows the different variation in characteristics of scour holes no.1&2&3 from year
2003 to year 2006. The scour hole no.1 have length, width and depth of 148, 53 and -11m in
year 2003 while it reached to 147, 63 and -11.5m in year 2006 respectively. It means that in
year 2006, the length decreased by 1m, width increased by 10m and the depth increased by
0.5m comparing with year 2003.
The scour hole no.2 have length, width and depth of 113, 70 and -9m in year 2003 while it
reached to 98, 60 and -9m in year 2006 respectively. It means that in year 2006, the length
decreased by 15m, width decreased by 10m and the depth didn’t change comparing with year
2003.
The scour hole no.3 have length, width and depth of 1009, 77 and -14m in year 2003 while it
reached to 850, 84 and -14m in year 2006 respectively. It means that in year 2006, the length
decreased by 159m, width increased by 7m and the depth didn’t change comparing with year
2003.
No.Of
HolesDifferece Differece Differece
Avr
Rate/Year
1998 2003 1998 2003 1998 2003
1 80.00 148.00 68.00 44.00 53.00 9.00 -13.00 -11.00 2.00 0.40
2 145.00 113.00 -32.00 81.00 70.00 -11.00 -17.50 -9.00 8.50 1.70
3 837.00 1009.00 172.00 76.00 77.00 1.00 -15.00 -14.00 1.00 0.20
4
5
6
7
8
9
10
Hole Length (m)Hole Width
(m)
Hole Depth
(m)
No Data
Chapter 5 Morphological Changes
81
Table (5-4) Scour Holes Variation from Year 2003 to 2006
Table (5-5) shows the different variation in characteristics of all scours holes no.1 to 3 from
year 1982 to year 2006 and scour holes no.4 to 10 from year 1982 to 2003. The scour hole
no.1 have length, width and depth of 122, 44 and -11m in year 1982 while it reached to 147,
63 and -11.5m in year 2006 respectively. It means that in year 2006, the length increased by
25.5m, width increased by 19m and the depth increased by 0.5m comparing with year 1982.
The scour hole no.2 have length, width and depth of 195, 70 and -15m in year 1982 while it
reached to 98, 60 and -9m in year 2006 respectively. It means that in year 2006, the length
decreased by 97m, width decreased by 10m and the depth decreased by 6m comparing with
year 1982.
The scour hole no.3 have length, width and depth of 903, 58 and -16m in year 1982 while it
reached to 850, 84 and -14m in year 2006 respectively. It means that in year 2006, the length
decreased by 53m, width increased by 26m and the depth decreased by 2m comparing with
year 1982.
The scour hole no.4 have length, width and depth of 162, 44 and -10.5m in year 1982 while it
reached to 132, 53 and -10m in year 2003 respectively. It means that in year 2003, the length
decreased by 30m, width increased by 9m and the depth decreased by 0.5m comparing with
year 1982.
The scour hole no.5 have length, width and depth of 238, 67 and -14m in year 1982 while it
reached to 267, 65 and -14m in year 2003 respectively. It means that in year 2003, the length
increased by 29m, width decreased by 2m and the depth didn’t change comparing with year
1982.
No.Of
HolesDifferece Differece Differece
Avr
Rate/Year
2003 2006 2003 2006 2003 2006
1 148.00 147.00 -1.00 53.00 63.00 10.00 -11.00 -11.50 -0.50 -0.17
2 113.00 98.00 -15.00 70.00 60.00 -10.00 -9.00 -9.00 - -
3 1009.00 850.00 -159.00 77.00 84.00 7.00 -14.00 -14.00 - -
4
5
6
7
8
9
10
Hole Length (m)Hole Width
(m)
Hole Depth
(m)
No Data
Chapter 5 Morphological Changes
81
The scour hole no.6 have length, width and depth of 275, 55 and -11m in year 1982 while it
reached to 197, 46 and -10.8m in year 2003 respectively. It means that in year 2003, the
length decreased by 78m, width decreased by 9m and the depth increased by 0.2m comparing
with year 1982.
The scour hole no.7 have length, width and depth of 74, 35 and -7m in year 1982 while it
reached to 74, 26 and -7.5m in year 2003 respectively. It means that in year 2003, the length
didn’t change, width decreased by 9m and the depth increased by 0.5m comparing with year
1982.
The scour hole no.8 have length, width and depth of 572, 73 and -7m in year 1982 while it
reached to 615, 40 and -7m in year 2003 respectively. It means that in year 2003, the length
increased by 43m, width decreased by 33m and the depth didn’t change comparing with year
1982.
The scour hole no.9 have length, width and depth of 837, 108 and -19.2m in year 1982 while
it reached to 793, 87 and -17m in year 2003 respectively. It means that in year 2003, the
length decreased by 44m, width decreased by 21m and the depth decreased by 2.2m
comparing with year 1982.
The scour hole no.10 have length, width and depth of 846, 109 and -13.5m in year 1982 while
it reached to 840, 62 and -12.7m in year 2003 respectively. It means that in year 2003, the
length decreased by 6m, width decreased by 47m and the depth decreased by 0.8m comparing
with year 1982.
Table (5-5) Scour Holes Variation from Year 1982 to 2003
No.Of
HolesDifference Differece Differece
Avr
Rate/YearStates
1982 2006 1982 2006 1982 2006
1 122.00 147.50 25.50 44.00 63.00 19.00 -11.00 -11.50 -0.50 - Erosion
2 195.00 98.00 -97.00 70.00 60.00 -10.00 -15.00 -9.00 6.00 0.29 Deposition
3 903.00 850.00 -53.00 58.00 84.00 26.00 -16.00 -14.00 2.00 0.10 Deposition
1982 2003 1982 2003 1982 2003
4 162.00 132.00 -30.00 44.00 53.00 9.00 -10.50 -10.00 0.50 0.02 Deposition
5 238.00 267.00 29.00 67.00 65.00 -2.00 -14.00 -14.00 - - -
6 275.00 197.00 -78.00 55.00 46.00 -9.00 -11.00 -10.80 0.20 0.01 Deposition
7 74.00 74.00 - 35.00 26.00 -9.00 -7.00 -7.50 -0.50 -0.02 Erosion
8 572.00 615.00 43.00 73.00 40.00 -33.00 -7.00 -7.00 - - -
9 837.00 793.00 -44.00 108.00 87.00 -21.00 -19.20 -17.00 2.20 0.10 Deposition
10 846.00 840.00 -6.00 109.00 62.00 -47.00 -13.50 -12.70 0.80 0.04 Deposition
Hole Length
(m)
Hole Width
(m)
Hole Depth
(m)
Chapter 5 Morphological Changes
82
Figures (5-10 ), (5-11 ) and (5-12 ) illustrate the development of length, width and depth for
each of the scour holes in the surveys of 1982, 1998, 2003 and 2006.
It is clear that the scours length decreased from year 1982 to 1998, while the scour’s width for
no2&3 increased and there is no change in scour no1, and it show also that the depth of no
1&2 increased but no.1 almost didn’t change.
The scours length and width for no.1&3 increased from year 1998 to 2003 opposite of no.2,
and also the depth of no 1&2&3 decreased. The scours length decreased from year 2003 to
2006,while the scour’s width for no1&3 increased opposite of scour no2, and also the depth
of no.1 increased but no.2&3 didn’t change.
Figure (5-10) Scour Hole Length Change at Years 1982, 1998, 2003 and 2006
Figure (5-11) Scour Hole Width Change at Years 1982, 1998, 2003 and 2006
-200.00
-100.00
0.00
100.00
200.00
1 2 3
Len
gth
(m
)
Scour Hole No.
Different Length L1998 - L 1982
L2003 - L1998
L2006 - L2003
Dcc
rease
In
crea
se
-20.00
-10.00
0.00
10.00
20.00
1 2 3
Wid
th (
m)
Scour Hole No.
Different Width W1998 - W1982
W2003 - W1998
W2006 - W2003
Incr
ease
D
ccre
ase
Chapter 5 Morphological Changes
83
Figure (5-12) Scour Hole Depth Change from Years 1982, 1998, 2003 and 2006
Comparison Between Scour Hole Cross Sections for Years 1982, 1998, 2003 and 2006
Figure (5-13) and (5-15) show the location of cross and longitudinal sections from 1 to 10
which are chosen by such way to describe the scour hole development along the whole reach.
Figure (5-13) Cross Sections Location for Scour Holes
Figure (5-14) and (5-16) illustrated the comparison of cross and longitudinal sections on the
scour holes for years of 1982, 1998, 2003 and 2006. It is noticed that for cross section 1&2&3
the scour hole became the deepest and shifted to left hand side in year of 1998 with a
comparison with the other years. This was happened due to big flood in year 1998. For the
cross section of scour hole no.3 was shifted to the left hand side and the irregular longitudinal
section was existed at 1998 if it compared by the other years. This was done due to the big
flood in a year 1998 and the location of this scour hole which is just downstream the bridge
piers and narrow width. For cross and longitudinal sections no.4 to no.10, it is found that slide
-4.00
-2.00
0.00
2.00
4.00
6.00
8.00
10.00
1 2 3
Dep
th (
m)
Scour Hole No.
Different Depth D1998 - D1982
D2003 - D1998
D2006 - D2003
Ero
sion
D
eposi
tion
Chapter 5 Morphological Changes
84
deposition was existed along the section in year 2003 comparing with other years. This was
because filling work in the reach after 1998 flood.
-14.00
-10.00
-6.00
-2.00
2.00
0 40 80 120 160 200 240 280
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(1) 1982 1998 2003 2006
-18.00
-14.00
-10.00
-6.00
-2.00
2.00
0 40 80 120 160 200 240 280
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(2) 1982 1998 2003 2006
-18.00
-14.00
-10.00
-6.00
-2.00
2.00
0 20 40 60 80 100 120 140
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(3) 1982 1998 2003 2006
-12.00
-8.00
-4.00
0.00
4.00
0 40 80 120 160 200 240 280
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(4) 1982
2003
-16.00
-12.00
-8.00
-4.00
0.00
4.00
0 40 80 120 160 200 240
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(5) 1982
2003
-12.00
-8.00
-4.00
0.00
4.00
0 40 80 120 160 200 240
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(6) 1982
2003
-8.00
-6.00
-4.00
-2.00
0.00
2.00
4.00
0 40 80 120 160 200
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(7) 1982
2003
-8.00
-6.00
-4.00
-2.00
0.00
2.00
4.00
0 40 80 120 160 200 240
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(8) 1982
2003
Chapter 5 Morphological Changes
85
Figure (5-14) Scour Holes Cross Sections for Years 1982, 1998, 2003 and 2006
longitudinal Sections Combination Between Scour Holes
Figure (5-15) Longitudinal Sections Location for Scour Holes
-20.00
-16.00
-12.00
-8.00
-4.00
0.00
4.00
0 40 80 120 160
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(9) 1982
2003
-14.00
-10.00
-6.00
-2.00
2.00
0 40 80 120 160 200 240
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(10) 1982
2003
-14.00
-10.00
-6.00
-2.00
2.00
0 40 80 120 160 200 240
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(1) 1982 1998 2003 2006
-16.00
-12.00
-8.00
-4.00
0.00
0 50 100 150 200 250 300
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(2) 1982 1998 2003 2006
Chapter 5 Morphological Changes
86
Figure (5-16) Scour Holes Longitudinal Sections for Years 1982, 1998, 2003 and 2006
-16.00
-12.00
-8.00
-4.00
0.00
0 400 800 1200
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(3) 1982 1998 2003 2006
-14.00 -12.00 -10.00
-8.00 -6.00 -4.00 -2.00 0.00 2.00
0 40 80 120 160 200 240
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(4) 1982
2003
-14.00
-12.00
-10.00
-8.00
-6.00
-4.00
-2.00
0.00
0 60 120 180 240 300 360
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(5) 1982
2003
-14.00
-12.00
-10.00
-8.00
-6.00
-4.00
-2.00
0.00
0 60 120 180 240 300 360
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(6) 1982
2003
-8.00
-6.00
-4.00
-2.00
0.00
0 40 80 120 160 200 240 280
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(7) 1982
2003
-8.00
-6.00
-4.00
-2.00
0.00
0 100 200 300 400 500 600
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(8) 1982
2003
-20.00
-16.00
-12.00
-8.00
-4.00
0.00
0 200 400 600 800
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(9) 1982
2003
-16.00
-12.00
-8.00
-4.00
0.00
0 200 400 600 800 1000
LE
VE
L
(m)
DISTANCE (m)
Cross Section No.(10) 1982
2003
CHAPTER 6
MODEL APPLICATION AND SCOUR
CALCULATION
Chapter 6 Model Application and Scour Prediction
87
Chapter 6
Model Application and Scour Calculation
6-1 Model Application
After the calibration process the model can be used to run several cases of different flow
conditions such as minimum, average, maximum and emergency flow to predict the flow
pattern.
The reach was simulated 4 times using surveys of 1982, 1998, 2003 and 2006. The calibration
and verification were done as shown in chapter four. The model was run 4 times at minimum,
average, maximum and emergency flow for each of years 1982, 1998, 2003 and 2006. The
discharge and their corresponding water level were taken as upstream and downstream
boundary conditions respectively. The collected data indicated in Table (6-1) for the different
discharge and water level as follows:-
Minimum discharge 6.65 Mm3/day
Average discharge 13.92 Mm3/day
Maximum discharge 69.90 Mm3/day
Emergency discharge (future release) 220 Mm3/day
Table (6-1) Boundary Condition
WL
(m)
U.S
145 km
Kfer El-Zayat
Station
146 km
D.S
154 km Discharge
Q
(million.m³/day)
Q
(m³/sec)
WL min 1.57 1.57 1.54 Qmin 6.65 76.97
WL avr 2.09 2.08 2.04 Qavr 13.92 161.11
WL max 2.62 2.60 2.48 Qmax 69.90 809.03
WL
Emergency 6.01 5.90 5.06 QEmergancy 220.00 2546.30
For each run the water surface along the reach following the thalwege line and velocity
profiles at 8 cross sections were estimated. The location of these cross sections are shown in
Figure (5-1).
6-1-1 Model Runs for Minimum Discharge
Minimum discharge of 6.65Mm3/day and their corresponding water level of 1.57m at Kfer El-
Zayat station are considered as up and down stream boundary conditions. The model was runs
4 times at minimum flow for years of 1982, 1998, 2003 and 2006. The average velocity
Chapter 6 Model Application and Scour Prediction
88
profile at 8 cross sections for the above mentioned 4 runs in a comparison are shown in Figure
(6-1). The results show that:
The velocity average magnitudes at the study area where ranges from (0.02m/s to
0.4m/s) at left hand side, while the velocity at right hand side ranges from ( 0.04m/s to
0.16m/s).
Big difference in magnitude was appeared at a distance of 65m from left hand side of
the velocity in cross section no.1 at flood of year 1998 compared with other years. The
reason of this high velocity is that, the concerned area is shallow while the rest of the
section have big depths.
It is noticed that the velocity profile along some cross sections in year 2003 almost
bigger than the corresponding one in year 1982 such as cross sections no.4, 5, 7 and 8.
This means that the cross section area of those sections were bigger in year 1982 than
in year 2003.
Water surface level at the study area (above the thalwege line) in case of minimum
discharge is the highest in year 1998 from the beginning up to first bridge while the water
surface in year 1982 is the highest at the rest of the reach as shown in Figure (6-2).
0.00
0.15
0.30
0.45
0 50 100 150 200 250 300
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(1) 1982
1998
2003
2006
0.00
0.05
0.10
0.15
0.20
0.25
0 50 100 150 200 250 300 350 400
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(2) 1982
1998
2003
2006
0.00
0.10
0.20
0 50 100 150 200 250 300
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(3) 1982
1998
2003
2006
0.00
0.05
0.10
0 20 40 60 80 100 120 140
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(4) 1982
1998
2003
2006
Chapter 6 Model Application and Scour Prediction
89
Figure (6-1) Comparison between the C. S Velocity Profiles in Case of Min Discharge
Figure (6-2) Water Surface in Case of Minimum Discharges (6.65 Mm3/day)
6-1-2 Average Discharge
Average discharge is 13.92Mm3/day and the corresponding water level is 2.08m at Kfer El-
Zayat station are considered as up and down stream boundary conditions.
0.00
0.05
0.10
0 25 50 75 100 125 150 175 200 225
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(5) 1982
2003
0.00
0.05
0.10
0.15
0 50 100 150 200 250 300 350 400
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(6) 1982
2003
0.00
0.05
0.10
0 25 50 75 100 125 150 175
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(7) 1982
2003
0.00
0.05
0.10
0 25 50 75 100 125 150 175 200 225
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(8) 1982
2003
1.45
1.50
1.55
1.60
1.65
1.70
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
WA
TE
R S
UR
FA
CE
EL
EV
AT
ION
(m
)
DISTANCE (m)
1982 1998 2003 2006
K.St
Kfer El Zayat Bridges B1 B3 B2
S2 S1
Flow
Chapter 6 Model Application and Scour Prediction
91
The model was run 4 times at average flow for years of 1982, 1998, 2003 and 2006. The
average velocity profile at 8 cross sections for the above mentioned 4 runs in a comparison
are shown in Figure (6-3). The results shows that:
The velocity average magnitudes at the study area ranges from (0.05m/s to 0.6m/s) at
left hand side, while the velocity at right hand side ranges from (0.03m/s to 0.28m/s).
Big difference in magnitude appeared at a distance of 65m from left hand side of the
velocity in cross section no.1 at flood of year 1998 compared with other years. The
reason of this high velocity is that concerned area is shallow while the rest of the
section has big depths.
It is noticed that the velocity profile along some cross sections in year 2003 are bigger
than the corresponding one in year 1982 such as cross sections no.4, 5, 7 and 8. This
means that the cross section area of those sections were bigger in year 1982 than in
year 2003.
Water surface level at the study area (above the thalweg line) in case of average discharge is
the highest in year 1982 as shown in Figure (6-4).
0.00
0.25
0.50
0 50 100 150 200 250 300
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(1) 1982
1998
2003
2006
0.00
0.10
0.20
0.30
0 50 100 150 200 250 300 350
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(2) 1982
1998
2003
2006
0.00
0.10
0.20
0.30
0 50 100 150 200 250 300
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(3) 1982 1998 2003 2006
0.00
0.05
0.10
0.15
0 20 40 60 80 100 120 140
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(4) 1982
1998
2003
2006
Chapter 6 Model Application and Scour Prediction
91
Figure (6-3) Comparison between the C. S Velocity Profiles in Case of Ave. Discharge
Figure (6-4) Water Surface in Case of Average Discharges (13.92 Mm3/day)
6-1-3 Maximum Discharge
Maximum discharge is 69.90Mm3/day and the corresponding water level is 2.60m at Kfer El-
Zayat station are considered as up and down stream boundary conditions.
0.00
0.05
0.10
0.15
0.20
0 30 60 90 120 150 180 210
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(5) 1982
2003
0.00
0.05
0.10
0.15
0.20
0.25
0 50 100 150 200 250 300 350 400
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(6) 1982
2003
0.00
0.05
0.10
0.15
0 25 50 75 100 125 150 175
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(7) 1982
2003
0.00
0.05
0.10
0.15
0.20
0 30 60 90 120 150 180 210 V
EL
OC
ITY
(m
/s)
DISTANCE (m)
Cross Section No.(8) 1982
2003
2.00
2.05
2.10
2.15
2.20
2.25
2.30
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
WA
TE
R S
UR
FA
CE
EL
EV
AT
ION
(m
)
DISTANCE (m)
1982 1998 2003 2006
Kfer El Zayat Bridges
K.St
B1 B3 B2
S2 S1
Flow
Chapter 6 Model Application and Scour Prediction
92
The model was runs 4 times at maximum flow for years of 1982, 1998, 2003 and 2006. The
average velocity profile at 8 cross sections for the above mentioned 4 runs in a comparison
are shown in Figure (6-5). The results show that:
The velocity average magnitudes at the study area ranges from (0.4m/s to 1.6m/s) at
left hand side, while the velocity at right hand side ranges from (0.3m/s to 1.1m/s).
Big difference in magnitude was appeared at a distance of 65m from left hand side of
the velocity in cross section no.1 at flood of year 1998 compared with other years. The
reason of this high velocity is that concerned area is shallow while the rest of the
section have big depths.
It is noticed that the velocity profile along some cross sections in year 2003 are bigger
than the corresponding one in year 1982 such as cross sections no.4, 5, 7 and 8. This
means that the cross section area of those sections were bigger in year 1982 than in
year 2003.
Water surface level at the study area (above the thalwege line) in case of maximum discharge
is the highest in year 1982 as shown in Figure (6-6).
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
0 50 100 150 200 250 300
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(1) 1982 1998 2003 2006
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
0 50 100 150 200 250 300 350
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(2) 1982
1998
2003
2006
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 50 100 150 200 250 300
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(3) 1982 1998 2003 2006
0.00
0.20
0.40
0.60
0.80
0 20 40 60 80 100 120 140
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(4) 1982
1998
2003
2006
Chapter 6 Model Application and Scour Prediction
93
Figure (6-5) Comparison between the C. S Velocity Profiles in Case of Max. Discharge
Figure (6-6) Water Surface in Case of Maximum Discharges (69.90 Mm3/day)
6-1-4 Emergency Discharge
Emergency discharge is 220Mm3/day and the corresponding water level is 5.09m at Kfer El-
Zayat station are considered as up and down stream boundary conditions.
0.00
0.20
0.40
0.60
0.80
1.00
0 25 50 75 100 125 150 175 200 225
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(5) 1982
2003
0.00
0.20
0.40
0.60
0.80
1.00
0 50 100 150 200 250 300 350 400
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(6) 1982
2003
0.00
0.20
0.40
0.60
0 25 50 75 100 125 150 175
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(7) 1982
2003
0.00
0.20
0.40
0.60
0.80
0 25 50 75 100 125 150 175 200 225 V
EL
OC
ITY
(m
/s)
DISTANCE (m)
Cross Section No.(8) 1982
2003
2.20
2.30
2.40
2.50
2.60
2.70
2.80
2.90
3.00
3.10
3.20
3.30
3.40
3.50
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
WA
TE
R S
UR
FA
CE
EL
EV
AT
ION
(m
)
DISTANCE (m)
1982 1998 2003 2006
Kfer El Zayat Bridges
K.St
B1 B3 B2
S2 S1
Flow
Chapter 6 Model Application and Scour Prediction
94
The model was runs 4 times at emergency flow for years of 1982, 1998, 2003 and 2006. The
average velocity profile at 8 cross sections for the above mentioned 4 runs in a comparison
are shown in Figure (6-7). The results show that:
The velocity average magnitudes at the study area ranges from (0.77m/s to 1.84m/s) at
left hand side, while the velocity at right hand side ranges from (0.64m/s to 1.7m/s).
Big difference in magnitude appeared at a distance of 65m from left hand side of the
velocity in cross section no.1 at flood of year 1998 compared with other years. The
reason of this high velocity is that concerned area is shallow while the rest of the
section have big depths.
It is noticed that the velocity profile along some cross sections in year 2003 almost
bigger than the corresponding one in year 1982 such as cross sections no.4, 5, 7 and 8.
This means that the cross section area of those sections were bigger in year 1982 than
in year 2003.
Water surface level at the study area (above the thalwege line) in case of emergency
discharge is the highest in year 1998 from the beginning up to first bridge while the water
surface in year 1982 is the highest at the rest of the reach as shown in Figure (6-8).
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
0 50 100 150 200 250 300
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(1) 1982 1998 2003 2006
0.00
0.40
0.80
1.20
1.60
2.00
0 50 100 150 200 250 300 350
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(2) 1982 1998 2003 2006
0.00
0.40
0.80
1.20
1.60
2.00
0 50 100 150 200 250 300
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(3) 1982 1998 2003 2006
0.00
0.40
0.80
1.20
1.60
2.00
0 20 40 60 80 100 120 140
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(4) 1982
1998
2003
2006
Chapter 6 Model Application and Scour Prediction
95
Figure (6-7) Comparison between the C. S Velocity Profiles in Case of Emer. Discharge
Figure (6-8) Water Surface in Case of Emergency Discharges (220 Mm3/day)
6-2 Scour Prediction
The effect of releasing high and emergency discharges in the study reach were analysed. The
scour at the three bridge piers and the meander in Rosetta Branch in front of Kfer El-Zayat
city were evaluated. The potential magnitude and extent of scour that may occur at bridge
0.00
0.40
0.80
1.20
1.60
2.00
0 25 50 75 100 125 150 175 200 225
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(5) 1982
2003
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80
0 50 100 150 200 250 300 350 400
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(6) 1982
2003
0.00
0.40
0.80
1.20
1.60
0 25 50 75 100 125 150 175
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(7) 1982
2003
0.00
0.40
0.80
1.20
1.60
2.00
0 25 50 75 100 125 150 175 200 225
VE
LO
CIT
Y (
m/s
)
DISTANCE (m)
Cross Section No.(8) 1982
2003
5.00
5.10
5.20
5.30
5.40
5.50
5.60
5.70
5.80
5.90
6.00
6.10
6.20
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
WA
TE
R S
UR
FA
CE
EL
EV
AT
ION
(m
)
DISTANCE (m)
1982
1998
2003
2006
Kfer El Zayat Bridges
B3
K.St
B1 B2
S2 S1
Flow
Chapter 6 Model Application and Scour Prediction
96
sites during flood events in response to rapid changes in flow discharges in the river was
considered. The following sections show the scour prediction and evaluation which includes
general scour, local scour, contraction scour, and bend scour were analyzed for the whole
reach and bridges site.
6-2-1 The Local Scour at Bridge Piers Prediction
The study area consists of a meander includes two successive bends, two highway bridges and
one railway bridge. The location of the bridges is shown in Figure (6-9). The bridges are
located at 145.676, 145.928, 146.391km downstream of El-Roda Gauge Station. The first
highway bridge has three rectangle piers with 16m width and 26.5m length, the distance
between each two piers are 134.5m. The second highway bridge has six piers, five rectangle
piers with 16m width and 26.5m length and in the middle of them one circular pier with
diameter of 14m, the distance between each two piers is 70m and the distance between the
circular pier and the next one is 29m. The railway bridge consists of four piers, three rectangle
piers with 4m width and 13m length and one circular pier with diameter of 11m, the distance
between piers is 70m and the distance between the circular pier and the next one is 35m,
Table (6-2).
Figure (6-9) Location of the Bridge Piers
Highway Bridge 1
Highway Bridge 2
Railway Bridge 3
Chapter 6 Model Application and Scour Prediction
97
Table (6-2) Location and Diminutions of the Bridge Piers
Bridge
No. Bridge 1 Bridge 2 Bridge 3
Location
(km) 146.00 146.239 149.682
Pier No. Pier
1 Pier
2 Pier
3 Pier
4 Pier
5 Pier
6 Pier
7 Pier
8 Pier
9 Pier
10 Pier
11 Pier
12 Pier
13
Pier Shape Rec Rec Rec Rec Rec Cir Rec Rec Rec Rec Rec Cir Rec
Diameter
(m) ------ ------ ------ ------ ------ 14.00 ------ ------ ------ ------ ------ 11.00 ------
Width
(m) 16.00 16.00 16.00 4.00 4.00 ------ 4.00 4.00 4.00 4.00 4.00 ------ 4.00
Length
(m) 26.50 26.50 26.50 15.00 15.00 ------ 15.00 15.00 13.00 13.00 13.00 ------ 13.00
Dist.
(m) 41.25 182.1 300.9 77.64 147.3 170.0 206.1 276.8 347.7 58.11 132.04 157.61 195.90
Where: Location: downstream of El-Roda Gauge Station, Rec: rectangular, Cir: circular,
Dist. : distance from left bank.
The local piers' scour was calculated using the hydraulic parameters based on the water
velocities' magnitudes and water depths obtained from applying the 2D model in case of
maximum and emergency flow at Rosetta Branch, Table (6-3). The model results showed that
in case of maximum flow piers numbers 2, 6 and 12 had a maximum local scour depth for
each bridge. The interpretation of that is at piers no.2, 6 and 12, the point velocities were 0.7,
0.61 and 0.71m/sec and the depths were 6.53, 4.82 and 5.47m, which means that, it has
maximum point discharges (q) along the bridge piers no.1, 2 and 3 respectively. The same
interpretation was considered in case of emergency flow.
Tables (6-4) and (6-5) show the parameters which are used in calculation of the local scour at
each bridge piers. It shows also the local scour results.
Table (6-3) Boundary Condition
Flow Case Discharge (m.m3/day) Water Level (m)
Maximum 69.90 2.60
Emergency 220.00 5.90
Chapter 6 Model Application and Scour Prediction
98
Table (6-4) The Used Parameters and the 2D Model Results of Scour Bridge Piers in
Case of Maximum Flow
Pier
1
Pier
2
Pier
3
Pier
4
Pier
5
Pier
6
Pier
7
Pier
8
Pier
9
Pier
10
Pier
11
Pier
12
Pier
13
a (m) 16.00 16.00 16.00 4.00 4.00 14.00 4.00 4.00 4.00 4.00 4.00 11.00 4.00
L (m) 26.50 26.50 26.50 15.00 15.00 14.00 15.00 15.00 13.00 13.00 13.00 11.00 13.00
L/a 0.60 0.60 0.60 3.75 3.75 0.00 3.75 3.75 3.25 3.25 3.25 0.00 3.25
K1 1.10 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
K2 1.02 1.07 1.07 1.29 1.39 1.00 1.67 1.75 1.58 1.55 1.49 1.00 1.12
K3 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10
K4 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
V1 (m/s) 0.60 0.70 0.00 0.65 0.67 0.61 0.57 0.56 0.33 0.58 0.72 0.71 0.71
Y1 (m) 2.66 6.53 0.00 3.09 4.51 4.78 4.82 4.82 5.00 2.31 4.20 5.47 6.75
Fr1 0.12 0.09 0.00 0.12 0.10 0.09 0.08 0.08 0.05 0.12 0.11 0.10 0.09
[a/Y1]0.65
3.21 1.79 0.00 1.18 0.92 2.01 0.89 0.89 0.86 1.43 0.97 1.57 0.71
YS/Y1 3.16 1.48 0.00 1.34 1.06 1.56 1.12 1.16 0.81 1.97 1.24 1.27 0.61
YS (m) 8.40 9.64 0.00 4.15 4.77 7.48 5.38 5.60 4.04 4.56 5.22 6.95 4.15
Table (6-5) The Used Parameters and The 2D Model Results of Scour Bridge Piers in
Case of Emergency Flow
Pier
1
Pier
2
Pier
3
Pier
4
Pier
5
Pier
6
Pier
7
Pier
8
Pier
9
Pier
10
Pier
11
Pier
12
Pier
13
a (m) 16.00 16.00 16.00 4.00 4.00 14.00 4.00 4.00 4.00 4.00 4.00 11.00 4.00
L (m) 26.50 26.50 26.50 15.00 15.00 0.00 15.00 15.00 13.00 13.00 13.00 0.00 13.00
L/a 0.60 0.60 0.60 3.75 3.75 0.00 3.75 3.75 3.25 3.25 3.25 0.00 3.25
K1 1.10 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
K2 1.02 1.07 1.07 1.25 1.32 1.00 1.51 1.62 1.59 1.36 1.32 1.00 1.11
K3 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10
K4 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
V1 (m/s) 0.98 1.20 0.64 1.09 1.13 1.04 0.97 0.96 0.66 1.36 1.34 1.32 1.28
Y1 (m) 5.57 9.45 4.10 6.01 7.43 7.70 7.75 7.76 7.94 5.19 7.09 8.36 9.65
Fr1 0.13 0.12 0.10 0.14 0.13 0.12 0.11 0.11 0.07 0.19 0.16 0.15 0.13
[a/Y1]0.65
1.99 1.41 2.42 0.77 0.67 1.47 0.65 0.65 0.64 0.84 0.69 1.20 0.56
YS/Y1 2.05 1.35 2.13 0.91 0.81 1.30 0.84 0.90 0.73 1.23 0.91 1.15 0.58
YS (m) 11.39 12.77 8.75 5.49 6.04 10.03 6.52 6.96 5.81 6.40 6.45 9.60 5.56
Where:
a : Pier width 'V1 : Approach velocity, upstream
L : Pier length 'Y1 : Approach depth, upstream
K1 : Correction Pier nose shape Fr1 : Froude number
K2 : Correction angle of attack YS/Y1 = 2*K1*K2*K3*K4*(a/Y1)0.65
(Fr1)0.43
K3 : Correction bed forms YS : Scour depth
K4 : Correction armoring
Chapter 6 Model Application and Scour Prediction
99
6-2-2 Contraction Scour
To predict the contraction scour, first the mean velocities for the maximum and emergency
flow at the studied area were estimated using the numerical model. Secondly, the critical
velocities at the locations of the expected contraction scour at the studied reach were
calculated using empirical equations 2-6 and 2-7, (HEC-18). Figure (6-10) shows the five
cross sections location for expected contraction scour. Three of these cross sections located at
the three bridge piers respectively. Based on the results of the above mentioned methods, it is
noticed that the estimated velocities by the empirical equations (critical velocity) were less
than the estimated velocities using the numerical model (mean velocity). Hence the live bed
contraction scour technique was used in order to estimate the contraction scour at the bridges.
While the clear water contraction scour technique was used in order to estimate the
contraction scour at the other cross sections. The contraction scour was estimated in Table (6-
6). The results showed that cross section no.1, 2 and 3 have contraction scour. This is
expected because the bridge piers widths reduced the whole section widths by ratio of 15, 8.5
and 9% at bridges no.1, 2 and 3 respectively. The results showed also that cross sections no.4
and 5 have no contraction scour because they have enough cross section area to path the
maximum flow. It compensate the eroded area of the bank at the outer bend by deposition in
the inner side.
Figure (6-10) Cross Sections Location for Contraction Scour
Chapter 6 Model Application and Scour Prediction
111
Table(6-6) Contraction Scour in Case of Maximum and Emergency Flow
Contraction Scour (m)
C.S Maximum Flow Emergency Flow
C.S 1 0.48 0.87
C.s 2 0.25 0.41
C.S 3 0.34 0.57
C.S 4 0 0
C.S 5 0 0
6-2-3 Bend Scour
The bend scour was calculated at the studied area using empirical Equation (2-9), (Simons et
al. 1989b). Figure (6-11) shows five cross sections location for expected bend scour. The
results are shown in Table (6-7). Expected results were shown where cross section no.4 and 5
which located at head of the bend had maximum bend scour.
Figure (6-11) Cross Sections Location for Bend Scour
Chapter 6 Model Application and Scour Prediction
111
Table (6-7) Bend Scour in Case of Maximum and Emergency Flow
Bend Scour (m)
C.S Maximum Flow Emergency Flow
C.S 1 3.86 4.10
C.S 2 2.60 2.90
C.S 3 4.35 6.22
C.S 4 5.70 7.04
C.S 5 7.79 8.58
6-2-4 General Scour
To define the general and bend scour at the study area, the Neil’s incised Equation (2-10)
(Pemberton and Lara 1984) was applied to the two considered high discharges, aiming at
predicting the general river bed scour. Figure (6-12) shows the cross sections location for
general scour. The general scour was estimated and presented in Table (6-8).
The higher value between Neill’s equation with a bend and the contraction scour equation
plus the bend scour equation was considered as the general scour (Pemberton and Lara 1984)
and the results shows in Table (6-9). The results showed that contraction scour results gave
the lowest scour values when compared to the other types of scours, while the general scour
by Neil’s equation is higher than bend and contraction scours.
Figure (6-12) Cross Sections Location for General Scour
Chapter 6 Model Application and Scour Prediction
112
Table (6-8) General Scour in Case of Maximum and Emergency Flow
General Scour by Neil Incised Equation (m)
C.S Maximum Flow Emergency Flow
C.S 1 4.50 6.00
C.S 2 4.20 8.89
C.S 3 6.60 8.11
C.S 4 3.90 6.00
C.S 5 4.80 6.90
C.S 6 4.50 6.00
C.S 7 3.60 5.10
C.S 8 4.80 5.10
C.S 9 6.60 8.11
C.S 10 5.10 5.10
C.S B1 2.70 4.50
C.S B2 2.58 3.90
C.S B3 3.30 5.10
Table (6-9) General Scour for Maximum and Emergency Flow Conditions
C.S No. Discharge
(m.m3/day)
General Scour
by Neil’s
Equation (m)
Bend scour
(m)
Contraction
Scour
(m)
Bend + Contraction
Scour (m)
Considered
General
Scour (m)
Bridge 1 69.90 2.70 3.86 0.48 4.34 4.34
220.00 4.50 4.10 0.87 4.97 4.97
Bridge 2 69.90 2.58 2.60 0.25 2.85 2.85
220.00 3.90 2.90 0.41 3.31 3.90
Bridge 3 69.90 3.30 4.35 0.34 4.69 4.69
220.00 5.10 6.22 0.57 6.79 6.79
C.S1 69.90 4.50 - - - 4.50
220.00 6.00 - - - 6.00
C.S2 69.90 4.20 - - - 4.20
220.00 8.89 - - - 8.89
C.S3 69.90 6.60 5.70 - 5.70 6.60
220.00 8.11 7.04 - 7.04 8.11
C.S4 69.90 3.90 - - - 3.90
220.00 6.00 - - - 6.00
Chapter 6 Model Application and Scour Prediction
113
C.S No. Discharge
(m.m3/day)
General Scour
by Neil’s
Equation (m)
Bend scour
(m)
Contraction
Scour
(m)
Bend + Contraction
Scour (m)
Considered
General
Scour (m)
C.S5 69.90 4.80 - - - 4.80
220.00 6.90 - - - 6.90
C.S6 69.90 4.50 - - - 4.50
220.00 6.00 - - - 6.00
C.S7 69.90 3.60 - - - 3.60
220.00 5.10 - - - 5.10
C.S8 69.90 4.80 - - - 4.80
220.00 5.10 - - - 5.10
C.S9 69.90 6.60 7.79 - 7.79 7.79
220.00 8.11 8.58 - 8.58 8.58
C.S10 69.90 5.10 - - - 5.10
220.00 5.10 - - - 5.10
6-2-5 Evaluation of Total Scour
The total scour can be expressed as the summation of the general, local, contraction and bend
scours. The total scour was evaluated by the following Equation:
Total Scour = General Scour + Pier Scour + Contraction Scour + Bend Scour
The predicted flow pattern at the studied area indicated that the values of bend scour were
significant due to the meandering pattern in this area of river reach. The magnitudes of total
scour are presented in Table (6-10). Figure (6-13) shows the evaluation of the total scour at
Kafr El-Zayat bridge piers. The maximum expected scour for all piers and cross sections from
1 to 10 were estimated. It was found that Piers 2, 6 and 12 had a maximum scour depth. The
expected enlargement of the scour holes around Piers 2, 6 and 12 and the other cross sections
were computed as follows:
The expected enlargement of the scour holes around the bridge piers = Actual River Bed
Elevation - (Water Surface Elevation – Water Depth – Total Scour).
The results are presented in Table (6-11). Figures (6-14) to (6-16) show the location of the
bridge piers.
Chapter 6 Model Application and Scour Prediction
114
Table (6-10) Total Scour
Bridge No. Pier No. Discharge
(m.m3/day)
General Scour
(m)
Local Scour
(m)
Total Scour
(m)
Bridge 1 Pier 2 69.90 4.34 9.64 13.98
220.00 4.97 12.77 17.74
Bridge 2 Pier 6 69.90 2.85 7.48 10.33
220.00 3.90 10.03 13.93
Bridge 3 Pier 12 69.90 4.69 6.95 11.64
220.00 6.79 9.60 16.39
C.S1 69.90 4.34 - 4.50
220.00 4.97 - 6.00
C.S2 69.90 2.85 - 4.20
220.00 3.90 - 8.89
C.S3 69.90 5.69 - 6.60
220.00 5.74 - 8.11
C.S4 69.90 4.34 - 3.90
220.00 4.97 - 6.00
C.S5 69.90 2.85 - 4.80
220.00 3.90 - 6.90
C.S6 69.90 5.69 - 4.50
220.00 5.74 - 6.00
C.S7 69.90 5.69 - 3.60
220.00 5.74 - 5.10
C.S8 69.90 4.34 - 4.80
220.00 4.97 - 5.10
C.S9 69.90 7.79 - 7.79
220.00 8.58 - 8.58
C.S10 69.90 5.69 - 5.10
220.00 5.74 - 5.10
Chapter 6 Model Application and Scour Prediction
115
Water Level (5.90)m for Q = 220m.m^3/day
Max. Water Level(2.60)mMin. Water Level(1.57)m
Nourth South
Kfer El-Zayat Bridge
Q = 220m.m^3/day
Original Bed (-4.00)
General Scour = 4.97m
Local Scour = 12.77m
Total Scour = 17.74m
Bridge
Pier
(-21.74)m
Figure (6-13) Evaluation of the Total Scour at Kafr El-Zayat
Figure (6-14) First Bridge Piers Location
Figure (6-15) Second Bridge Piers Location
Figure (6-16) Third Bridge Piers Location
-5
-3
-1
1
3
5
0 50 100 150 200 250 300 350
Ele
vati
on
(m
)
Distance from Left Bank (m)
Pier 1 Pier 2 Pier 3
-5
-3
-1
1
3
5
0 100 200 300 400
Ele
vati
on
(m
)
Distance from Left Bank (m)
Pier 4 Pier 5 Pier 7
Pier 6 Pier 8 Pier 9
-7
-5
-3
-1
1
3
5
0 50 100 150 200 250 300
Ele
vati
on
(m
)
Distance from Left Bank (m)
Pier10 Pier11 Pier12
Pier13
Chapter 6 Model Application and Scour Prediction
116
Table (6-11) The Expected Increase of the Scour Holes around the Main Piers of Kafr
El-Zayat Bridges
Pier
No.
Discharge
(m.m3/day)
Water
Surface
Elevation
(m)
Water
Depth
(m)
Total
Scour
(m)
Expected
River
Bed
Elevation
(m)
Actual
River
Bed
Elevation
(m)
Magnitude
of Scour
Holes Depth
Enlargement
(m)
Pier 2 69.90 2.99 7.20 13.98 14.19 -4.00 -18.19
220.00 5.90 10.00 17.74 17.84 -4.00 -21.84
Pier 6 69.90 2.98 5.90 10.33 10.25 -3.00 -13.25
220.00 5.86 8.90 13.93 13.97 -3.00 -16.97
Pier
12
69.90 2.88 9.00 11.64 11.76 -6.00 -17.76
220.00 5.72 11.90 16.39 16.57 -6.00 -22.57
C.S1 69.90 2.96 14.00 4.50 4.54 -11.00 -15.54
220.00 5.99 17.00 6.00 6.01 -11.00 -17.01
C.S2 69.90 2.80 12.00 4.20 4.90 -8.50 -13.40
220.00 5.73 15.00 8.89 9.66 -8.50 -18.16
C.S3 69.90 2.76 17.00 6.60 6.34 -14.50 -20.84
220.00 5.62 19.50 8.11 7.49 -14.50 -21.99
C.S4 69.90 2.71 13.00 3.90 4.19 -10.00 -14.19
220.00 5.52 15.50 6.00 5.98 -10.00 -15.98
C.S5 69.90 2.71 16.50 4.80 5.09 -13.50 -18.59
220.00 5.52 19.50 6.90 7.38 -13.50 -20.88
C.S6 69.90 2.67 13.50 4.50 4.83 -10.50 -15.33
220.00 5.43 16.50 6.00 6.57 -10.50 -17.07
C.S7 69.90 2.66 10.00 3.60 3.64 -7.30 -10.94
220.00 5.40 12.90 5.10 5.30 -7.30 -12.60
C.S8 69.90 2.60 9.80 4.80 5.00 -7.00 -12.00
220.00 5.80 12.80 5.10 5.10 -7.00 -12.10
C.S9 69.90 2.56 20.00 7.79 8.23 -17.00 -25.23
220.00 5.18 22.50 8.58 8.90 -17.00 -25.90
C.S10 69.90 2.52 14.50 5.10 4.58 -12.50 -17.08
220.00 5.12 17.50 5.10 4.98 -12.50 -17.48
The general scour, local scour, contraction scour and bend scour were computed at the bridges
area. The following main conclusions may be drawn:
1. Unexpected velocity profiles resulted in complex flow, and the human interference
affects the geometry.
2. Maximum scour depth was located at the upstream piers.
3. The maximum scour depth was directly proportional to discharge.
Chapter 6 Model Application and Scour Prediction
117
4. The increase of the scour hole around the piers of the first bridge was higher than the
increase of the scour hole around the piers of the second and third bridges.
5. The local scour around the bridge piers estimated by the 2-D numerical model gave
higher scour values than the general scour (Neil’s equation) under the same
conditions.
6. The scour around the bridge piers calculated by the scour bend equation (Simons et al.
1989b) gave higher scour values than both general scour equation (Neil’s equation)
and contraction scour.
7. Contraction scour results gave the lowest scour values when compared to the other
types of scours.
8. The general scour by Neil’s equation is higher than bend and contraction scours.
CHAPTER 7
ALTERNATIVE SOLUTIONS AND
RESULT ANALYSIS
Chapter 7 Alternative Solutions and Result Analysis
118
Chapter 7
Alternative Solutions and Result Analysis
7-1 Introduction
A comparison of the previous and recent profiles of the study reach revealed that the ultimate
effect of river meandering is reached at outer bend where fully developed spiral and
transverse flow components are attain.
The measured hydraulic parameters and relevant collected data for the study reach would be
worked out to design different proposed solutions. It is obvious that due to economic reasons,
the proposed dredging and filling of the bed should be limited to specific selected locations to
maintain the required flow improvements near the inner bank as well as the outer bank.
Therefore, different alternatives of river bed dredging and filling would be designed to
redistribute the velocity profiles along the cross sections for protecting the outer curve along
the vulnerable locations of the upstream and downstream curved reaches. Using 2-D
numerical model, filling and dredging of the river bed would be tested.
Such higher velocities associated with the release of emergency discharges downstream High
Aswan Dam may cause degradation and scour to the entire bed of the reach particularly in the
outer curve of the reach where the city of Kfer El-Zayat is located. Consequently, a severe
damage to the bridges, agricultural properties, urban areas and roads is expected. So, it is
required to improve the velocities at the outer curve. To achieve that, two proposed
alternatives were suggested and simulated separately by the 2-D model.
7-2 The Modeled Reach
The total length of 9.00 km of the entire reach at Kfer El-Zayat are simulated using 2-D
mathematical model. The survey of year 2006 is used in the simulation as the original one.
Within this reach, the railway bridge and the two highway bridges are simulated; also, the
river bank in front of Kfer El-Zayat is included.
The calibration of the hydrodynamic model is carried out by comparing the velocity data
produced by the model and velocity obtained from field measurement at three cross sections
as shown at chapter 4. The results of water surface slope to the simulated reach is adjusted to
be close to survey of year 2006, as shown in Figure (4-19).
Chapter 7 Alternative Solutions and Result Analysis
119
7-3 Simulation of the Proposed Solutions and Results
Two proposed alternatives to improve the morphology of the study bend are suggested and
simulated separately by the SMS model. In the first alternative, the scour hole of the outer
curves is filled with layers of filter and riprap up to level -5.00m MSL. In additional to
alternative 1, dredging the inner sides to level -3.00m MSL is proposed as second alternative.
The model was run for the two alternatives at maximum and emergence flow with its
corresponding water levels which are 809.03m3/s, 2546.30m
3/sec, +2.60m MSL and +5.90m
MSL respectively. The flow was used as upstream boundary condition and the water level
was used as downstream boundary condition.
7-3-1 The First Alternative Simulation
The bed levels of the reach are filled to level -5.00 MSL to represent the first alternative. The
first alternative is simulated as the above mentioned description. Figure (7-1) shows the entire
reach bed elevation in case of alternative 1. Figure (7-2) shows the thalweg line before and
after the filling as a comparison between the bed level of the first alternative and the original
one. It is clear from Figure (7-1) that the most of the filling areas are concentrated at the outer
curves. These also are shown at Figure (7-3), which represents ten cross sections distributed
along the reach. The location of these sections is shown in Figure (7-1). The level of deepest
point of the scour holes at cross sections from 1 to 10 are -11, -9, -14, -10, -13, 8, -10.7, -7, -7,
-17 and -12.5 MSL, respectively. This means that the filling layers of some holes are more
than 12m.
Figure (7-1) River Bed Elevation in Case of Alternative 1
Chapter 7 Alternative Solutions and Result Analysis
111
Figure (7-2) The Thalweg Line in Case of the Original and Alternative 1
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Chapter 7 Alternative Solutions and Result Analysis
111
Figure (7-3) Cross Sections Bed Profiles in Case of Original Year and Alternative 1
7-3-1-1 First Alternative Model Run Results
Maximum Flow Run
In case of Maximum flow, the discharge is 809.03m3/s and its corresponding water level is
+2.60m MSL. The flow velocities along the reach are shown in Figure (7-4), which shows
that the maximum value of velocities were occurred at the outer curves. The resulted velocity
recorded by the figures are ranged from 0.45 and 1.05m/sec in the outer curve at sections no 1
to10. While the normal velocity of the reach is about 0.70m/s, as appeared in Figure (7-5).
Figure No (7-6) shows the velocity profiles of alternative 1 comparing to the original results
at cross sections No 1 to 10. The figure shows that the results of velocity profiles in case of
alternative 1 were similar to the profiles as the original case. It is clear that the values of the
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Chapter 7 Alternative Solutions and Result Analysis
112
velocities at cross sections 1, 3, 5, 6, 9 and 10 increased than its corresponding in case of
original case because of considerable part of those sections were filled, Figure (7-3). The
results of water surface slope at the location of the deepest points in case of alternative 1
became steeper than its corresponding of the original one. This is expected because of filling
the scour holes. Figure (7-7) shows the water surface slope at the deepest points along the
reach of the original and alternative 1.
Figure (7-4) Velocity along the Reach at Maximum Flow in Case of Alternative 1
Figure (7-5) Velocity Profile at the Deepest Points (Outer Curve) along the Reach in
Case of the Original & Alternative 1 at Max Flow
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Chapter 7 Alternative Solutions and Result Analysis
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Chapter 7 Alternative Solutions and Result Analysis
114
Figure (7- 6) Cross Sections Velocity Profile of the Original & Alternative 1 at Max Flow
Figure (7-7) Water Surface Slope at the Deepest Points along the Reach of the Original
& Alternative 1 at Max Flow
Emergency Flow Run
The model was run at emergency discharge with its corresponding water levels. The discharge
was 2546.30m3/s and its corresponding water level was +5.90m MSL. The flow velocities
along the reach are shown in Figure (7-8), which shows the maximum value of velocities are
occurred at the outer curves. The resulted velocity recorded by the figure are ranged between
1.00 and 2.20m/sec in the outer curve. While the normal velocity of the reach is about
1.50m/s, as appeared in Figure (7-9).
Figure No (7-10) shows the velocity profiles of alternative 1 in case of emergency flow
comparing to corresponding original results at cross sections No 1 to 10, The figure shows
that the results of velocity profiles in case of alternate 1 are similar to the profiles as the
original case. It is clear that the values of the velocities at cross sections 1, 3, 5, 6, 9 and 10
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2.60
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Chapter 7 Alternative Solutions and Result Analysis
115
increased than in case of original case because of considerable part of those sections were
filled, Figure (7-3). The results of water surface slope at the location of the deepest points in
case of alternative 1 became steeper than its corresponding of the original one. This is
expected because of filling the scour holes. Figure (7-11) shows the water surface slope at the
location of deepest points along the reach of the original and alternative 1 in case of
emergency flow.
Figure (7-8) Velocity along the Reach in Case of Alternative 1 at Emergency Flow
Figure (7-9) Velocity Profile at the Deepest Points along the Reach in Case of Alternative
1 at Emergence Flow
0.50
0.70
0.90
1.10
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1.70
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Chapter 7 Alternative Solutions and Result Analysis
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Chapter 7 Alternative Solutions and Result Analysis
117
Figure (7- 10) Cross Sections Velocity Profile of the Original & Alternative 1 at
Emergence Flow
Figure (7-11) Water Surface Slope at the Deepest Points along the Reach in Emergence
Flow of the Original & Alternative 1 at Emergence Flow
7-3-2 The Second Alternative Simulation
The bed levels of the reach are filled to level -5.00 MSL and the other part are dredged to
level -3.00 MSL to represent the second alternative. Figure (7-12) shows the entire reach bed
elevation in case of alternative 2. It is clear from Figure (7-12) that the most of the filling
areas are concentrated at the outer curves and the dredging area in the inner curve. These also
are shown at Figure (7-13), which represents ten cross sections distributed along the reach.
The location of these sections is shown in Figure (7-12). The deepest point of the scour holes
at cross sections from 1 to 10 are 2, 2, 2, 1.5, 1.5, 1.5, 1.01, 0.6, 0.9 and 1.5 above MSL,
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Chapter 7 Alternative Solutions and Result Analysis
118
respectively. This means that the filling layers of some holes are more than 12m and the
dredging layers of some area within 5m.
Figure (7-12) River Bed Elevation in Case of Alternative 2
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Chapter 7 Alternative Solutions and Result Analysis
119
Figure (7-13) Cross Sections in Case of Original Year and Alternative 2
7-3-2-1 Second Alternative Model Run Results
Maximum Flow Run
In case of Maximum flow, the discharge was 809.03m3/s and its corresponding water level
was +2.60m MSL. The flow velocities along the reach are shown in Figure (7-14), which
shows that the maximum value of velocities are occurred at the outer curves. The resulted
velocity recorded by the figure are ranged between 0.28 and 0.93m/sec at the concerned
section. While the normal velocity of the reach is about 0.55m/s, as appeared in Figure (7-15).
Figure No (7-16) shows the velocity profiles of alternative 2 comparing to the original results
at cross sections No 1 to 10. The figure shows that the results of velocity profiles in case of
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Chapter 7 Alternative Solutions and Result Analysis
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alternative 2 were redistributed along the sections to be more regular than in case of the
original at cross sections no 1, 3, 4, 7, 8 and 10. It is clear that the values of the velocities
increased at cross sections 3 and 9 and decreased at cross sections no 2, 4, 7 and 8 comparing
with the original case because of considerable part of those sections were filled and dredged
respectively, Figure (7-13). The results of water surface slope at the deepest points in case of
alternative 2 became almost the same as the original one. This is expected because of filling
the scour holes and dredging in other places. Figure (7-17) shows the water surface slope at
the location of the deepest points along the reach of the original and alternative 2 in case of
maximum flow.
Figure (7-14) Velocity along the Reach in Case of Alternative 2 at Maximum Flow
Chapter 7 Alternative Solutions and Result Analysis
121
Figure (7-15) Velocity Profile at the Deepest Points along the Reach in Case of Original,
Alternative 1 and Alternative 2 at Maximum Flow
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Chapter 7 Alternative Solutions and Result Analysis
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Figure (7- 16) Cross Sections Velocity Profile of the Original, Alternative 1 and
Alternative 2 at Maximum Flow
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Chapter 7 Alternative Solutions and Result Analysis
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Figure (7-17) Water Surface Slope at the Deepest Points along the Reach of the Original,
Alternative 1 and Alternative 2 at Maximum Flow
Emergency Flow Run
The model is run at emergency discharge with its corresponding water levels. The discharge is
2546.30m3/s and its corresponding water level is +5.90m MSL. The resulted velocity
recorded in this case are ranged between 0.80 and 2.00m/sec in the outer curve. While the
normal velocity along the reach is about 1.40m/s. Figure (7-18) shows velocity along the
reach at emergency flow in case of alternative 2. Figure (7-19) show the velocity profile at the
deepest points along the reach in case of original, alternatives 1 and 2 at emergency flow.
Figure (7-20) shows the velocity profiles at ten cross sections along the reach of alternative 2
in case of emergency flow comparing to the original results. The figure shows that the results
of velocity profiles in case of alternative 2 are redistributed along the cross sections to be
more regular than in case of the original at cross sections no 1, 4, 5, 6, 7 and 9. It is clear that
the values of the velocities increased at cross sections 3 and 9 and decreased at cross sections
no 2, 4, 7 and 8 comparing with the original case because of considerable part of those
sections were filled and dredged respectively, Figure (7-13). The results of water surface
slope at the deepest points in case of alternative 2 became almost the same as the original one.
This is expected because of filling the scour holes and dredging in other places. Figure (7-21)
shows the water surface slope at the location of the deepest points along the reach of the
original and alternative 2 in case of emergency flow.
2.20
2.30
2.40
2.50
2.60
2.70
2.80
2.90
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Chapter 7 Alternative Solutions and Result Analysis
124
Figure (7-18) Velocity along the Reach in Case of Alternative 2 at Emergency Flow
Figure (7-19) Velocity Profile at the Deepest Points along the Reach in Case of Original,
Alternatives 1 and 2 at Emergency Flow
0.50
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0.90
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1.90
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Chapter 7 Alternative Solutions and Result Analysis
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Chapter 7 Alternative Solutions and Result Analysis
126
Figure (7- 20) Cross Sections Velocity Profile of the Original, Alternatives 1 and 2 at
Emergency Flow
Figure (7-21) Water Surface Slope at the Deepest Points along the Reach of the Original,
Alternatives 1 and 2 at Emergency Flow
The original, alternatives 1 and 2 were simulated separately by SMS model. For each case the
model was run two times, during maximum and emergency flow. Based on the results and
analysis of those runs, the following can be concluded:
Big difference in velocities between outer and inner curve of the bend is appeared as a
result of the original case in the maximum and emergency flow.
When the scour holes (at the outer curve) are filled up to level of -5 MSL (Alternative 1),
the water surface slope increased, consequently the velocity profile along the cross
sections are increased.
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K.St
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S2 S1
Flow
Chapter 7 Alternative Solutions and Result Analysis
127
When the scour holes were filled up to level of -5 MSL and the other side dredged to -3
MSL (Alternative 2), slightly difference is appeared of water surface slope compared with
the original case.
In case of alternative 2 the results velocity profiles along the cross sections redistributed
and became more regular comparing to the alternative 1and original cases.
The results appeared in cases of maximum and emergency flow that the velocity take
similar profile, only the difference on values.
7-3-3 Comparisons of Bed Shear Stress between the Two Alternatives
Maximum Flow
Bed shear stress is estimated at the whole reach in the cases of original, alternatives 1 and 2.
For the original case, Figure (7-22) shows the locations of bed shear stress more than 2N/m2
and ranges between 2 and 15N/m2 and concentrated on the outer curves of the bend. For
alternative 1, Figure (7-23) shows the locations of bed shear stress more than 2N/m2 and
ranges between 2 and 6N/m2. For alternative 2, Figure (7-24) shows the locations of bed shear
stress more than 2N/m2 which ranges between 2 and 4N/m
2. It is noticed also that the value of
shear stress reduced in the case of alternative 2 compared with cases of alternative 1 and the
original. The bed shear stress is disappeared in some areas at the outer curve in case of
alternative 2 compared with alternative 1 and the original.
Figure (7-25) shows comparison of the bed shear stress along ten cross sections in the cases of
original, alternative 1 and 2.
After reviewing the shear stress distribution along the ten cross section the following can be
concluded:
The bed shear stress in case of alternative 2 became regular in cross sections 1, 3, 4, 5, 6,
7, 8 and 10 compared with alternative 1 and original. Also the shear stress beside the banks
reduced at section 2 comparing with the original and alternative 1. The shear stress of cross
section no 9 in case of alternative 2 increased than the original because this section have big
filling consequently the velocity is increased.
In general, in the case of alternative 2 the bed shear stress reduced beside the banks
compared with the other cases. This means that the bank failures become more safe than the
other cases.
Chapter 7 Alternative Solutions and Result Analysis
128
Figure (7-22) Bed Shear Stress in Max Flow for Original Case
Figure (7-23) Bed Shear Stress in Max Flow for Alternative 1
Figure (7-24) Bed Shear Stress in Max Flow for Alternative 2
Chapter 7 Alternative Solutions and Result Analysis
129
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Chapter 7 Alternative Solutions and Result Analysis
131
Figure (7-25) Cross Sections Shear Stress of the Original, Alternatives 1 and 2 at
Maximum Flow
Emergency Flow
Bed shear stress is estimated at the whole reach in the cases of original, alternatives 1 and 2.
For the original case, Figure (7-26) shows the locations of bed shear stress more than 2N/m2
and ranges between 2 and 30N/m2 and concentrated on the outer curves of the bend. For
alternative 1, Figure (7-27) shows the locations of bed shear stress more than 2N/m2 and
ranges between 2 and 18N/m2. For alternative 2, Figure (7-28) shows the locations of bed
shear stress more than 2N/m2 which ranges between 2 and 15N/m
2. It is noticed also that the
value of shear stress reduced in the case of alternative 2 compared with cases of alternative 1
and the original. The bed shear stress is disappeared in some areas at the outer curve in case of
alternative 2 compared with alternative 1 and the original.
Figure (7-29) shows comparison of the bed shear stress along ten cross sections in the cases of
original, alternative 1 and 2.
After reviewing the shear stress distribution along the ten cross section the following can be
concluded:
The bed shear stress in case of alternative 2 became regular in cross sections 1, 2, 3, 4, 5,
6 and 7 comparing with alternative 1 and original. Also the shear stress beside the banks
reduced at sections 1, 2, 5, 6 and 7 comparing with the original.
In general, in the case of alternative 2 the bed shear stress reduced beside the banks
compared with the other cases. This means that the bank failures become more safe than the
other cases.
The results of the runs at emergency flow condition for the original and the two
alternatives show that, a huge values at the whole reach were appeared. This means that bed
scours and bank instability will be occurred along the whole reach so failure of the bridge
piers and the road of Kfer El-Zayat city may expected.
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Chapter 7 Alternative Solutions and Result Analysis
131
Figure (7-26) Bed Shear Stress for Original Case at Emergency Flow
Figure (7-27) Shear Stress for Alternative 1 at Emergency Flow
Figure (7-28) Shear Stress for Alternative 2 at Emergency Flow
Chapter 7 Alternative Solutions and Result Analysis
132
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Chapter 7 Alternative Solutions and Result Analysis
133
Figure (7-29) Cross Sections Shear Stress of the Original, Alternatives 1 and 2 at
Emergency Flow
7-4 Riprap Design
In order to determine the suitable mean particle diameter for the riprap protective layer, the
mentioned three design methods for sizing riprap would be applied
U = C [ 2g (Ss - 1) ]1/2
D 1/2
(7-1)
In which U is the flow velocity (ft/s); Ss is the specific gravity of the stone; g is the
gravitational acceleration (ft/s2); D is the mean particle diameter (ft); and C is the Izbach’s
turbulent coefficient which was taken equal to 0.86 for high turbulent level flow and 1.2 for
low turbulent level flow.
33
65
cos)1(
101.4
s
s
S
USXW
In which W is the weight of the stone in pounds; and Φ is the angle of repose. Assume that
the particle is round; the average diameter can be defined as
3
1
))(
6(
ws
wD
(7-2)
In which γs and γw are the specific weight of the particle and water respectively
2
1
22
2
)tan(tancos)1(
25.0
sSg
UD
(7-3)
In order to determine the suitable mean particle diameter for the riprap protective layer, the
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Chapter 7 Alternative Solutions and Result Analysis
134
above design methods for sizing riprap will be applied with the following data:
Maximum flow velocity (U) = 1.32 m/s = 4.33 ft/s
Specific gravity of the stone (Ss) = 2.65
Gravitational acceleration (g) = 9.81 m/s2
= 32.4 ft/s2
Izbach turbulent coefficient (C) = 0.86
Angle of repose (Φ) = 36.5 degree
Angle of bed slope (θ) = 0.0
Specific weight of the water (γw) = 62.4 lb/ft3
Specific weight of the rock (γs) = 165.4 lb/ft3
Apply the various empirical methods for sizing riprap for the previously mentioned bed
protection methods, the following mean particle sizes was obtained as follows:
Apply method No. (1) D = 0.24 ft = 7.3 cm
Apply method No. (2) D = 0.18 ft = 5.5 cm
Apply method No. (3) D = 0.15 ft = 4.6 cm
Application of the available formula revealed a mean particle size of D= 0.073m. Therefore,
as the calculated mean particle size is rather small, a certain safety factor can be applied and
the average particle size of 0.15m was adopted for bank protection. On the other hand,
concerning size distribution of riprap layer, Simons and Senturk (1977) suggested that riprap
gradation should follow a smooth size distribution curve. This would be fulfilled by applying
the following criterion:
D0 = 0.2 D50 = 0.03 m
D20 = 0.5 D50 = 0.075 m
D100 = 2 D50 = 0.3 m
Where D0 and D100 are the minimum and maximum particle sizes respectively within the
riprap mixture. This grain size distribution would be utilized to design the under layer
protective layers of the conventional filter. On the other hand, according to the provided
analysis for the design of under layer filter, the conventional (inverted) granular type would
be applied.
While for the case of riprap protective layer with mean particle diameter of 0.15m the
following values were adopted:
D85 = 113 mm
D50 = 105 mm
Chapter 7 Alternative Solutions and Result Analysis
135
D15 = 65 mm
In case of large stone size and fine diameter of bed materials, multiple filter layers with
gradual size variations would be required. Therefore, it was suggested during the present
study to apply the provided filter design criteria which would be applied to any two adjacent
layers that comprising the riprap, filter planet and base material. Consequently, the mentioned
design criteria of protective layers were applied as depicted in Table (7-1) which were used to
prepare the grain size distribution of the filter layers (1) and (2) as shown in Figure (7-30).
Table (7-2) shows the sieve analysis for the designed filters. Figure (7-31) shows the designed
filter layers thickness.
Table (7-1) Grain Size Distribution of the Proposed Riprap and Filter Layers
Criterion Riprap Layer Filter Layer (2) Filter Layer (1)
4)(
)(
85
15 baseD
FilterD
25)(
)(
50
50 baseD
filterD
40)(
)(5
15
15 baseD
filterD
65.0/20.0 = 3.3
105.0/15.0 = 7.0
65.0/10.0 = 6.5
10.0/3.0 = 3.3
15.0/1.5 = 10.0
10.0/1.0 = 10.0
1.0/0.65 = 1.54
1.5/.33 = 4.55
1.0/0.18 = 5.56
Table (7-2) Sieve Analysis for the Designed Filters
D Sand Base Filter Layer (1) Filter Layer (2) Riprap Layer
D0 (mm) 0.11 0.60 6.00 30.00
D15 (mm) 0.18 1.00 10.00 65.00
D20 (mm) 0.24 1.20 11.00 75.00
D50 (mm) 0.33 1.50 15.00 105.00
D85 (mm) 0.65 3.00 20.00 113.00
D100 (mm) 0.80 4.00 33.00 300.00
Chapter 7 Alternative Solutions and Result Analysis
136
Figure (7-30) Grain Size Distributions of the Proposed Filter Layers
0.30 m
0.20 m
0.50 m
Base Layer
Filter Layer (2)
Riprap Layer
D50 = 0.33 mm
D50 = 1.50 mm
Stone D50 = 105 mm
Filter Layer (1)
D50 = 15.00 mm
Figure (7-31) The Designed Filter Layers Thickness
0
10
20
30
40
50
60
70
80
90
100
0.1 1 10 100 1000
Pe
rce
nt
Fin
er
by
We
igh
t
Particle Size (mm)
Base Filter 1 Filter 2 Riprap
CHAPTER 8
CONCLUSIONS AND
RECOMMENDATIONS
Chapter 8 Conclusions and Recommendations
137
Chapter 8
Conclusions and Recommendations
8-1 Summary
To understand and improve the behavior of flow, morphology and hydraulically to the
meandering of the Nile River in Egypt, two dimensional mathematical model “SMS”
was used to simulate meandering reach of 9.0km long on Rosetta branch at Kfer El-
Zayat city. This was achieved by studying the meandering river reach of Rosetta
branch including two successive bends located from km 145.00 to km 154.00
downstream El-Roda Gauge Station. The surveyed reach of years 1982, 1998, 2003
and 2006 were compared. The developing of bed level, thalwege line and scour holes
were determined.
The study area was simulated four times by the model using the survey reach of years
1982, 1998, 2003 and 2006. The flow and the water level were used as upstream and
downstream boundary conditions, respectively. The model was calibrated to actual
field water velocity measurements at different locations along the study area. The
model was run for sixteen times at different (minimum, average, maximum and
emergency) flow conditions. The resulted velocities were compared.
The model was run at maximum and emergency (69.90, 220.00m.m3/day) flow
conditions using survey of year 2006. The obtained results showed the variation of the
local scour at bridge piers. The empirical equations used to predict the general scour,
contraction scour and bend scour of the whole reach and around bridge piers.
Two proposed alternatives were suggested and simulated separately by the SMS
model. In the first alternative, the scour hole of the outer bends was filled with layers
of filter and riprap up to level -5.00m MSL. In additional to alternative 1, dredging the
inner sides to level -3.00m MSL was proposed as second alternative. The model was
run for the two alternatives at maximum and emergence flows with its corresponding
water levels. The results illustrated that the second alternative improved the flow
conditions better than the first one. The filling layers of filter and riprap were
designed.
Chapter 8 Conclusions and Recommendations
138
8-2 Conclusions
In this research, the following conclusions were obtained:
a) As a result of comparing different surveys reach and the results of the model runs at
different flow conditions, the following was concluded:
1. Unexpected velocity profiles resulted in some cross sections was appeared due to the
human interference.
2. Maximum scour depth was found at the piers located in the middle of the cross
section.
3. The maximum scour depth was directly proportional to discharge.
4. The increase of the scour hole around the piers of the first bridge (upstream) was
higher than the increase of the scour hole around the piers of the second and third
bridges (downstream).
b) As a result of studding the scours along the reach, the following was concluded:
5. The local scour around the bridge piers estimated by the 2-D numerical model gave
higher scour values than the general scour (Neil’s equation) under the same
conditions.
6. The scour around the bridge piers calculated by the scour bend equation (Simons et
al. 1989b) gave higher scour values than both general scour equation (Neil’s
equation) and contraction scour.
7. Contraction scour results gave the lowest scour values when compared to the other
types of scour.
8. The general scour by Neil’s equation was considered because it gave general scour
higher than bend and contraction scours.
c) Based on the results of comparing the two proposed solutions by surveying of year
2006, the following was obtained:
9. When the scour holes (at the outer curve) were filled up to level of -5 MSL
(Alternative 1), the water surface slope increased, consequently the velocity along
the cross sections was increased. This means that the probability of the expected
scour was increased.
Chapter 8 Conclusions and Recommendations
139
10. When the scour holes were filled up to level of -5m MSL and the other side dredged
to -3m MSL (Alternative 2), slightly difference was appeared of water surface slope
compared with the original case. This means that the probability of the expected
scour was reduced.
11. In case of alternative 2 the resulting velocity profiles along the cross sections were
redistributed and became more regular comparing to the alternative 1and original
case.
12. The results appeared that in case of maximum and emergency flows, the obtained
velocity had similar profile, only the difference on values.
8-3 Recommendations
Based on the results and conclusions of this study, the following are recommended:
Studying the impact of any construction on the river or on its banks and the impact
of the expected scour at the structure location is necessary.
The foundation level of Kfer El-Zayat bridges should be checked by designer
taking at consideration the expected total scour depth. Regular monitoring of the
study reach is recommended specially after each high flood.
The critical scour holes should be filled by filter and riprap until to the average bed
level.
Future studies are needed to apply three dimensional model or physical model to
give accurate and reliable estimations for the morphological changes.
Hydraulic structures to reduce the velocity such as weirs, vans and dikes should be
studied.
REFERENCES
References
141
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ARABIC SUMMARY
ملخص البحث
1
عنوان الرساله
تقييم النحر لمنحنيات نهر النيل علي فرع رشيد
:مقدمة ( 1
حفاظا علي مياه النهر تسمح وزاره الاشغال العامه والموارد المايه بمرور تصرفات المياه علي حسب الاحتياجات الفعليه
د العالي ولا تسمح بمرور تصرفات اكبر من الاحتياجات الا في حالات الفيضانات حتي لا يصل منسوب المياه خلال الس
. الي حد الخطوره علي منشات السد العالي
وهذه التصرفات العاليه وكذلك التصرفات خلال اقصي الاحتياجات يمكن ان تسبب مشاكل للمنشأت المقامه علي نهر النيل
ويمكن ايضا للفيضان . ثل النحر الموضعي حول دعامات الكباري والمواني والقناطر والمنشأت الاخريوفروعه وذلك م
تسبب النشط منها , تصنف الانهار نوعين نشطه وخامله. ان يسبب غرق لبعض الاراضي والطرق والقري حول نهر النيل
. جوانب النهر بها نحر بقاع النهر او تأكل الجسر بينما الخامله لا يتغير شكل القاع او
تم اجراء رفع . وتتعرض لكثير من مشاكل النحر 123تقع مدينه كفر الزيات علي المنحني الخارجي لفرع رشيد عند كم
وكان من نتائج هذا الرفع ان 1998مساحي للنحر خلف كوبري السكه الحديد وكوبري الطريق السريع بعد فيضان عام
والذي تم تسجيله عام -16.11رب من المنحني الخارجي للمنحنيات تغير من منسوب منسوب النحر لبعض البيارات بالق
وهذا سبب مشكله كبيره لاتزان الجسر امام المدينه وللنحر حول . متر من منسوب سطح البحر -18.11الي منسوب 1996
. دعامات الكباري في المنطقه مما سبب عدم امان للمدينه والكباري
ملخص البحث( 2
كيلومتر والذي يتميز بوجود 9.1يبلغ طوله حوالي رشيدإستخدام جزء منحني من مجري نهر النيل بمجري فرع تم
لنفس لرفع المساحي السابقالرفع المساحي الهيدروجرافي الحديث للمنطقه المذكورة ومقارنتها با وضح .منحنيان منعكسان
لإجراء هذه ناسبلهيدروليكية المختلفة أنه يمكن اعتبار هذا الحبس مالحبس علاوة علي البيانات الهيدرولوجية والقياسات ا
هذه القياسات . الدراسه لوضوح تأثير ظاهرتي النحر والترسيب علي كل من المنحني الخارجي والداخلي علي الترتيب
جانبيه بينما يحدث لنهر مما يهدد استقرار الميول اللالخارجي للمنحنيأوضحت حدوث نحر موضعي وإنتقال لمواد القاع
للنهر مما ادي الي عدم إنتظام سرعة التيار المائي وإزاجة المجري في إتجاه للمنحني الداخليترسيب ملحوظ في الجانبين
.المنحني الخارجي
حيث تم عمل مقارانات لقاع . 2116و 2113و 1998و 1982جي النهر في هذه المنطقه لعام وقد تم دراسه مورفولو
وتم ايضا امرار تصرفات مختلفه علي . ماكن النحر الموجوه في منطقه الدراسهالنهر في هذه السنين ودراستها ودراسه ا
وتم دراسه السرعات الناتجه علي القطاعات العرضيه علي طول ( منخفضه و متوسطه وعاليه و حاله الطواريء)النهر
.الحبس في الاعوام المختلفه
النحر الناتج من )نحر المحتمل علي كامل الحبس النحر المحتمل حول دعامات الكباري و حساب ال وتم حساب ايضا
وبناءا عليه تم حساب النحر الكامل لكل القطاعات (. المنحنيات والنحر الناتج عن ضيق عروض القطاعات و النحر العام
.الموجوده بطول الحبس والنحر المحتمل في حاله التصرفات العاليه وحاله الطواريء
ملخص البحث
2
حلول المقترحه لمنطقه الدراسه لتجنب النحر إختبار بدائل الفي (SMS) ضي ثنائي الأبعادتلي ذلك إستخدام النموذج الريا
متر فوق سطح البحر و البديل الاخر ردم البيارت 5-ردم البيارات الموجوده حتي مستوي , علي جوانب و قاع النهر ومنها
متر فوق سطح البحر وتم 3-رات حتي مستوي من سطح البحر مع تكريك للناحيه الاخري للقطاع من البيا 5-حتي مستوي
وتبين من خلال هذه . 2116محاكاه كل بديل علي حده علي البرنامج الرياضي ومقارنه نتائجهم بالرفع المساحي لعام
وبناءا عليه تم تصميم طبقات الحمايه .الاول ومن الحاله الاصليه للنهر عطي نتائج أفضل مني المقارنات ان الحل الثاني
.مستخدمه لردم البياراتال
محتويات الرسالة( 3
الباب الأول
المقدمة
يحتوى هذا الباب على المقدمة واسباب إختيارجزء من نهر النيل علي فرع رشيد عند منطقة كفر الزيات لهذه الدراسة كفر الزيات كما يوضح وفكرة عامة عن المشاكل المترتبة نتيجة للتغيرات المورفولوجية و الهيدروليكية الحادثة بمنطقة
.الاهداف الرئيسية للبحث وخطة الدراسة ومكونات البحث
الباب الثاني
مراجعة الأبحاث المتعلقة بالدراسه
علي نبذة تاريخية للدراسات والبحوث التي أجريت في مجال البحث وما يتعلق بها من خصائص وتكوٍن هذا الباب يحتوي
علاوة علي حنيهالأنهار و مراحل تطورها وما يتعلق بالأنهار ذات الأجزاء المن المجاري المائية الطبيعية وتصنيف
وتم عرض . لتوصيف العناصر الهيدروليكية الخاصة بمنحنيات الأنهار مناسبهالعلاقات والمعادلات الرياضية المختلفة ال
.مجالال هذا خلاصة البحوث والدراسات والخبرات السابقة في
وتم عرض ايضا انواع النماذج المختلفه . النحر وخواصه وانواعه المختلفه والنتائج المترتبه عليه تلي ذلك عرض لتعريف
كما عرض في هذا الباب ايضا تعريف التكريك والترسيب وتجميع . من نماذج رياضيه و نماذج طبيعيه وخواص كل منهما
علي حبيبات التربه المكونه لقاع ( Shear Stress) اهم العلاقات التي تستخدم في حساب القوه المؤثره من سريان المياه
. المجري
الباب الثالث
البيانات المطلوبه للبحث
للتعرف علي علي مدار السنين السابقه التي تم تجميعها المتاحه يعرض هذا الباب مختلف القياسات الحقلية والبيانات
دامها في تشغيل النموذج الرياضي ثنائي الأبعاد علاوة علي التغيرات المورفولوجية بالحبس موضوع البحث والتي تم استخ
شمل ذلك القياسات الهيدروجرافية التي تمت حديثا للحبس والأجهزة . تصميم الحماية اللازمة للمنحني الخارجي لهذا الحبس
ي ونتائج هذه القياسات الباب مواقع قياس توزيع سرعه التيار المائفي هذا كما عرض . المستخدمة وطريقة القياس ونتائجها
بالحبس موضوع البحث ونتائج تحليل هذه العينات وعلاقة نتائج كل منها بتغير ومواقعهاقاع ال من مواد علاوة علي عينات
ملخص البحث
3
تبع ذلك عرض الخصائص الهيدرولوجية الخاصة . في هذا الحبس النهر منحني شكل القطاع المائي علي إمتداد مسافة
. رشيدسيب المقابلة علي إمتداد الحبس الواقع من خلف قناطر الدلتا فرع بالتصرفات المارة والمنا
الباب الرابع
و معايرتهالمستخدم ج الرياضى ذالنمو
والذي تم إستخدامه لمحاكاة ( SMS)يتضمن هذا الباب شرح موجز للمعادلات المستخدمة في النموذج الرياضي ثنائي الأبعاد
لباب شرح تطبيقات النموذج الرياضي ومميزاته وأسباب إختياره علاوة علي كيفية إعداد كما شمل ا. الحبس موضوع البحث
شبكة العناصر التي تمثل الحبس موضوع البحث مع عرض كيفية تغذيته بالعناصر الهندسية والهيدروليكية الممثلة لطبيعة
الباب متطلبات معايرة النموذج وتحقيق بناءا عليه عرض . المجري وتشغيله والمخرجات التي تنتج عن تطبيق النموذج
. النموذج بحيث يحاكي الحبس المذكور لإجراء الدراسات المطلوبة
كما شمل هذا الباب ايضا عرض اسلوب معايرة وتحقيق وتجهيز النموذج الرياضي ثنائي الأبعاد للإستخدام في بحث أفضل
بناء عليه تم عرض البيانات الخاصة بكل . بس موضوع البحثتصميم لتحسين خواص التدفق المائي بالمنحني الداخلي بالح
من تقدير معاملات الإحتكاك المناسبة لطبيعة التربة والتغيرات المورفولوجية بالحبس موضوع البحث وكذلك القيم المتوسطة
عند الحدين الأمامي والخلفي لتوزيع سرعة التيار المائي بالقطاعات المختلفة علاوة علي بيانات التصرفات والمناسيب المقابلة
والتي يتم خلالها تغيير قيم ( SMS)تلي ذلك عرض نتائج معايرة النموذج الرياضي ثناءي الأبعاد . للحبس موضوع البحث
معاملات الإحتكاك بالمواقع المختلفة في حدود معينة بحيث تكون مخرجات النموذج بالنسبة لتوزيع سرعة التيار بالقطاعات
بناءا عليه تم إستخدام البيانات الخاصة بمختلف التصرفات المارة بالحبس . قرب ما يمكن من القياسات الحقليةالمختلفة أ
. موضوع الدراسة والمناسيب المقابلة لكل منها في تحقيق النموذج بعد نجاح مرحلة معايرته والتي أوضحت أفضل النتائج
إختبار مدي دقة إختيار قيم معامل الإحتكاك التي تم إستخدامها في تلي ذلك عرض نتيجة إستخدام النموذج الرياضي في
. معايرة النموذج
الباب الخامس
التغيرات المورفولوجيه لمنطقه الدراسه
عند رشيدكيلومتر من فرع 9.1يعرض هذا الباب خواص الحبس الذي تم إختيارة للبحث والذي يشكل جزء طوله حوالي
إختيار هذا الحبس لاجراء الدراسه وذلك لما يحتويه من منحنيين معكوسي الإتجاه وما يتطلبة من وأسباب مدينه كفر الزيات
تلي ذلك عرض الخصائص المورفولوجية والمميزات والأبعاد . تحسين خواص التدفق المائي بالمنحني الداخلي لكل منهما
عرض . وتأثير ذلك علي تغيرات مناسيب القاعالهندسية لكل من المنحنيين الأمامي والخلفي للحبس موضوع الدراسة
التي الكنتوريهأيضا هذا الباب التطور الزمني للتغيرات التي توضح شكل الحبس موضوع البحث وذلك من واقع الخرائط
تم تحديد . وعلاقة ذلك بالتغيرات التي طرأت علي مجري نهر النيل 2116 و 2113و 1998و 1981تمت خلال الأعوام
موزعة بصوره منتظمه علي كامل طول الحبس موضوع البحث وإستنتاج تغيرات مناسيب هعرضي اتقطاع 8دد مواقع ع
ثم تم تحديد مواقع البيارات الناتجه من نحر .المشار أليها عاليه الهيدروجرافي خلال الأعوام ام الرفع \باستخالقاع بكل منها
ملخص البحث
4
وتم مقارنه هذه البيانات علي مدار السنين المختلفه وتحليل كامل . جيحول دعامات الكباري و نتيجه النحر للمنحني الخار
.لها
السادسالباب
تشغيل النموزج الرياضي ودراسه الانواع المختلفه للنحر
( منخفضه و متوسطه و عاليه و حاله طواريء)تشغيل للنموزج ثنائي الابعاد لاربع تصرفات مختلفه يتضمن هذا الباب
وتم دراسه السرعات الناتجه ومقارنتها , (2116 و 2113و 1998و 1981)كونتوريه لاعوام مختلفه وذلك لاربع خرائط
. ببعضها وتحليل نتائجها
وتم حساب النحر المحتمل علي . وتم ايضا حساب النحر المحتمل حول دعامات الكباري عن طريق النموذج ثنائي الابعاد
وبناءا عليه تم حساب (. لنحر الناتج عن ضيق عروض القطاعات و النحر العامالنحر الناتج من المنحنيات وا)كامل الحبس
.أجمالى النحر لكل القطاعات الموجوده بطول الحبس والنحر المحتمل في حاله التصرفات العاليه وحاله الطواريء
الباب السابع
الحلول المقترحه وتحليل النتائج
حلول المقترحه لمنطقه الدراسه لتجنب النحر ثنائي الأبعاد في إختبار بدائل الإستخدام النموذج الرياضي في هذا الباب تم
متر أعلى سطح البحر ودراسه 5-وتم دراسه البديل الاول بملاء البيارات الموجوده حتي منسوب . علي جوانب و قاع النهر
راسه البديل الثاني المقترح بمليء البيارت وتم ايضا د. تأثير ذلك علي مجري النهر ومقارنه النتائج بالحاله الاصليه للنهر
متر أوطى سطح 3-متر أعلى سطح البحر مع تكريك للناحيه الاخري للقطاع من البيارات حتي منسوب 5-حتي منسوب
ن تم ايضا حساب تأثير القوه الناتجه من سريا. ج هذا المقترح مع البديل الاول والحاله الاصليه للنهرتم مقارنة نتائالبحر و
الاول ومن الحاله عطي نتائج أفضل مني وتبين من خلال هذه المقارنات ان الحل الثاني. المياه علي حبيبات التربه في القاع
. وبناءا عليه تم تصميم طبقات الحماية الازمة للبيارات .الاصليه للنهر
اثامنالباب
الخلاصه و التوصيات
صة النتائج التي توصل اليها البحث وتوصيات الأعمال المقترحة لحماية خلا ملخص ما سبق تقديمة و يتضمن هذا الباب
إزاحة تقليل معدل المنحنيين الخارجيين للحبس موضوع البحث والتي تحقق توزيع أفضل لسرعة التيار المائي بما يضمن
. لها باحثين التعرضكما يعرض الباب مقترحات لبعض الدراسات المستقبليه التي يمكن لل. نحو جوانب النهر المجري
جامعة بنها
كلية الهندسة بشبرا
المدنيهقسم الهندسة
تقييم النحر لمنحنيات نهر النيل علي فرع رشيد
المدنيهرسالة مقدمة كجزء من متطلبات الحصول علي درجة الماجستير في الهندسة
(هيدروليكا)
مقدمة من
فاطمه سمير أحمد سعد
(2111) هندسه المدنيهال بكالوريوس في
إشراف
جمهورية مصر العربية –القاهرة
2115مارس
السعيد محمد جمال حلمي /د.أ
الهندسة المدنيةقسم - الموارد المائية هندسة ستاذأ
جامعه بنها -كليه الهندسه بشبرا
السرساويالدين محمد حسام / د.م.أ
بمعهد بحوث النيل ستاذ مساعد أ
مي لبحوث المياهالمركز القو
محمد ابراهيم محمد محمود/ د
الهندسة المدنيةبقسم مدرس
جامعه بنها -كليه الهندسه بشبرا
جامعة ينها
كلية الهندسة بشبرا
قسم الهندسة المدنيه
القبول النهائي للرسالة
تقييم النحر لمنحنيات نهر النيل علي فرع رشيد
لجنة الحكم والمناقشة
جمهورية مصر العربية –القاهرة
2115مارس
الاسم الأمضاء
(مقررا –ممتحن خارجي ) نهله محمد عبدالحميد ابو العطا .د.أ رئيس قسم الري والهيدروليكا -عمال الري أأستاذ تصميم
جامعة عين شمس -كلية الهندسة
(عضوا –ممتحن خارجي ) مدحت سعدعزيز . د.أ
النيل حوث مدير معهد ب -أستاذ
هالمركز القومى لبحوث الميـا
( عضوا –عن لجنه الاشراف ) محمد السعيد جمال حلمي .د.أ الهندسة المدنية قسم - الموارد المائية هندسة ستاذأ
جامعه بنها -كليه الهندسه بشبرا