May 25, 2007 - Chapter Three: Theoretical Basis of the Numerical Model. 3.1. General. 3.1 ..... Acceleration of gravity g. N pressure force in the x-direction. Fp m. m. -1. Slope of ...... Simplifying and dividing through by ÏÎx yields the final form of the continuity ...... 275.6. 33 48 44.23. 42 42 57.16. 62. 28600. 235. 33 48 53.85.
Republic of Iraq Ministry of Higher Education and Scientific Research University of Technology Building and Construction Engineering Department
Numerical Modeling of Flood Wave Behavior with Meandering Effects (Euphrates River, Haditha-Hit)
A THESIS SUBMITTED TO THE BUILDING AND CONSTRUCTION ENGINEERING DEPARTMENT, UNIVERSITY OF TECHNOLOGY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN BUILDING AND CONSTRUCTION ENGINEERING, WATER RESOURCES ENGINEERING.
By
SADIQ ALEIWI AL-FAHDAWI B. Sc. (Civil Eng.) 1993 M. Sc. (Water Resources Eng.) 2002
Supervised by Professor
Dr. RAFA H. AL-SUHAILY
Assist. Professor
Dr. MUHANNAD J. AL-KAZWINI 2009
To Those Who Helped Me During The Period of Study , My Parents, My Wife , My Brothers And Sisters, and My Lovely Daughters Dima and Reem With respect.
Sadiq
I
With deep sense of gratitude, I record my thanks to my supervisors, Prof. Dr. Rafa H. Al-Suhaily and Ass. Prof. Dr. Mohannad J. Al-Kazwini, for the valuable advices, guidance, and generous assistance that they gave to me throughout the period of research. Special thanks for prof. Dr. Karim K. Al-Jumaily for his unforgettable assistance pre and during the studying time. I sincerely thank Mr. Hassan H. Abdulla from General Directorate for Dams and Reservoirs and Mr. Qasim Sa'adallah from Dams and Water resources engineering of Al-Anbar University. I would like to express my deep thanks to the staff of the Building and Construction Department in the University of Technology. I am thankful for everyone who had helped me in this research.
II
No.
Descriptions
Chapter One: Introduction 1.1 1.2 1.3 1.4 1.5
General Problem definition Objective of the Present Work General description of the Euphrates river Limitation of the numerical model
1.1 1.2 1.3 1.4 1.5
Chapter Two: Literature Review 2.1 2.2 2.3
History of the river flood modeling Previous work on flood and meandering river models Model selection for the case study
2.1 2.2 2.3
Chapter Three: Theoretical Basis of the Numerical Model 3.1 3.2 3.3 3.3.1 3.3.2 3.3.2.1 3.3.2.2 3.4 3.5 3.6 3.6.1 3.6.1.1 3.6.1.2
General Unsteady flow equations Meandering rivers Development of meanders Meander parameters and their relationships Types of meanders Geometry of meander Floodplain Unsteady flow equations for meandering rivers with floodplain Finite difference form of unsteady flow equations Boundary conditions Upstream boundary conditions Downstream boundary conditions
3.1 3.2 3.3 3.3.1 3.3.2 3.3.2.1 3.3.2.2 3.4 3.5 3.6 3.6.1 3.6.1.1 3.6.1.2
Chapter Four: Basic Data Requirements 4.1 4.1.1 4.1.2 4.1.3
Geometric data The river system schematic Cross-section geometry Floodplain cross-section generation
III
4.1 4.1.1 4.1.2 4.1.3
No. 4.1.4 4.1.5 4.2 4.2.1 4.2.2 4.2.2.1 4.2.2.1.1 4.2.2.1.2 4.2.2.1.3 4.2.2.2
Descriptions Cross-section properties Reach length Hydraulic data Energy loss coefficient Unsteady flow data Boundary conditions Upstream boundary condition Downstream boundary condition Internal boundary condition Initial conditions
4.1.4 4.1.5 4.2 4.2.1 4.2.2 4.2.2.1 4.2.2.1.1 4.2.2.1.2 4.2.2.1.3 4.2.2.2
Chapter Five: Application, results, and discussion 5.1 5.2 5.3 5.4 5.4.1 5.4.1.1 5.4.1.2 5.4.1.3 5.5 5.6 5.6.1
Introduction Calibration of numerical model for the Euphrates river system (reach under study) Model verification Application of the numerical model Maximum flow, Maximum water surface elevation, and travel time Discharges Water levels Wave propagation Effect of meandering on the flood routing in study area Two-dimensional model Description of the two dimensional numerical model
5.1 5.2 5.3 5.4 5.4.1 5.4.1.1 5.4.1.2 5.4.1.3 5.5 5.6 5.6.1
Chapter Six: Conclusions and recommendations 6.1 6.2
Conclusions Recommendations
6.1 6.2
IV
Figure No.
Title
Page
1.1 1.2
Euphrates River Seasonal variation of flow in the Euphrates River
6 6
1.3
Euphrates river reach in the study area
7
2.1
12
3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.1 4.2 4.3 4.4 4.5 4.6
Section of a stream channel with force terms Definition plan of idealized meandering river with flood plain Cross-section 5-5 of idealized river Definition of sinuosity Elementary control volume for derivation of continuity and momentum equations Illustration of Terms Associated with Definition of Pressure Force Crossings in meandering river Typical meandering in a river Meander parameters Floodplain and stream channel Floodplain cross-section Channel and floodplain flows Weighted four-point implicit scheme River system schematic in the study area Surveying of the river banks Digital depth finder device Depth of river surveying Surveyed river cross-section in station No. (54) River centerline with limited cross sections
30 32 33 34 35 36 42 50 52 53 54 54 56
4.7
Stream centerline after increasing cross-sections
56
4.8 4.9 4.10
Cross-sections interpolated 3-D Mapping with interferometry Digital elevation model for the study area
57 59 60
2.2 2.3 2.4 3.1 3.2
V
15 15 17 24 26
Figure No. 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21-A 4.21-B 4.22 4.23 4.24 4.25 4.26 5.1 5.2 5.3 5.4-a 5.4-b 5.5
Title
Page
Digital elevation model cross-section data Surveyed cross-section of Euphrates River superimposed to (DEM) data Final combined cross-section Ineffective flow area in cross-section (62) River cross-section with levee interpolation between two adjacent cross-sections before correction Levees limitation Reach lengths between sec.(94) and (95) Reach lengths in meandering river
61
Manning's (n) value for (ROB) and (LOB) and main channel
horizontal variation of Manning's (n) horizontal variation of Manning's (n) Bridge on Euphrates River in study area Dam break scenario for foundation failure Upstream discharge hydrograph Rating curve at Hit gauge station Initial water surface elevation Daily discharge recorded in Husaiba gauge station for flood occurring in 1980 Comparison between observed and calculated water surface elevation at Hit gage station Observed and calculated stage of the Euphrates River at Hit gage station Locations of major cities along Euphrates River in study area Locations of cross-sections along Euphrates River in study area The peak flow and travel time of flood wave for section No. 189
61 62 63 64 65 65 66 67 70 71 71 73 78 79 80 81 85 86 88 90 91 95
5.6
The peak flow and travel time of flood wave for section No. 178
95
5.7
The peak flow and travel time of flood wave for section No. 166
96
VI
Figure No.
Title
Page
5.8
The peak flow and travel time of flood wave for section No. 120
96
5.9
The peak flow and travel time of flood wave for section No. 98
97
5.10 5.11 5.12 5.13
5.14
5.15
5.16
The peak flow and travel time of flood wave for section No. 59 The peak flow and travel time of flood wave for section No. 1 Maximum discharge along the river for various cases Maximum flood wave height for case A1 along study area Comparison of a peak flow and arrival time of flood wave between cases A1 and B1: a) At section No. 189 b) At section No. 178 c) At section No. 166 d) At section No. 120 e) At section No. 98 f) At section No. 59 g) At section No. 1 Comparison of a peak flow and arrival time of flood wave between cases A2 and B2: a) At section No. 189 b) At section No. 178 c) At section No. 166 d) At section No. 120 e) At section No. 98 f) At section No. 59 g) At section No. 1 Comparison of a peak flow and arrival time of flood wave between cases A3 and B3: a) At section No. 189 b) At section No. 178 c) At section No. 166 d) At section No. 120 e) At section No. 98 f) At section No. 59 g) At section No. 1 VII
97 98 99 101
104 104 104 105 105 106 106
107 107 107 108 108 109 109
110 110 110 111 111 112 112
Figure No.
5.17
5.18
5.19
5.20 5.21
Title Comparison of a water surface level of flood wave and its arrival time between cases A1 and B1: a) At section No. 189 b) At section No. 178 c) At section No. 166 d) At section No. 120 e) At section No. 98 f) At section No. 59 g) At section No. 1 Comparison of a water surface level of flood wave and its arrival time between cases A2 and B2: a) At section No. 189 b) At section No. 178 c) At section No. 166 d) At section No. 120 e) At section No. 98 f) At section No. 59 g) At section No. 1 Comparison of a water surface level of flood wave and its arrival time between cases A3 and B3: a) At section No. 189 b) At section No. 178 c) At section No. 166 d) At section No. 120 e) At section No. 98 f) At section No. 59 g) At section No. 1 Comparison of flood wave height along the Euphrates River in study area between cases A1 and B1 Comparison of flood wave height along the Euphrates River in study area between cases A2 and B2
Page
113 113 113 114 114 115 115
116 116 116 117 117 118 118
119 119 119 120 120 121 121 122 122
5.22
Comparison of flood wave height along the Euphrates River in study area between cases A3 and B3
122
5.23
Maximum top width of inundation area along the Euphrates River in study area for case No. A3
124
VIII
Figure No. 5.24 5.25 5.26 5.27 5.28 5.29 5.30 5.31 5.32 5.33 5.34 5.35 5.36
Title Maximum top width of inundation area along the Euphrates River in the study area for case No. B3 The relationship between Manning roughness ratio and time lag of peak discharge The relationship between Manning roughness ratio and time lag of peak level The relationship between Manning roughness ratio and discharge reduction The relationship between Manning roughness ratio and stage reduction Selected meander river reach in study area The available types of elements in SMS software Flow hydrograph at upstream study reach Rating curve at downstream study reach River and floodplain elevations in study reach Finite element mesh over all study reaches Discharge hydrograph at downstream of study reach for both one and two-dimensional model Velocity distributions over study reach
IX
Page 125 128 128 129 129 132 133 135 135 136 136 137 137
Table No. 3.1 3.2
Title Finite difference approximation of the terms in the continuity equation Finite Difference Approximation of the Terms in the Momentum Equation
Page 45 46
3.3
Coefficients of continuity equation
47
3.4
Coefficient of moment equation
47
4.1
Manning (n) values for different channels
69
4.2
Subcritical Flow Contraction and Expansion Coefficients
73
4.3
Reservoir outflow after Haditha dam failure
79
5.1
Flow discharges from Haditha Dam
87
5.2
Cases of the numerical model in study reach
92
5.3
Peak discharge after dam failure for various cases
93
5.5
Time lag between start of failure and arrival of peak discharge Maximum water level
100
5.6
Maximum wave height
100
5.7
Time lag between start of failure and occurrence of maximum water level
102
5.8
Time of flooding after start of failure
103
5.9
Computed parameters for different cases of routing
127
5.4
X
94
Symbols As
Definitions
Units
Off-channel dead storage area
m2
Kc
Conveyance of the channel
-
Kf
Conveyance of the left flood plain
-
Kr
Conveyance of the right flood plain
-
S
Storage from non conveyance portion of crosssection
m3
L
Discharge-weighted reach length
m
Llob
Reach length specified for flow in the left over bank
m
Lch
Reach length specified for flow in the channel
m
Lrob
Reach length specified for flow in the right over bank
m
ρ
Density of water
Kg.m-3
b
Width of finite element of water
m
H
Height of segment of water
m
u
Velocity of segment of water
m.s-1
0
Average boundary shear stress
N.m-2
S0
Bottom slope
m. m-1
Sf
Friction slope
m. m-1
Q
Discharge
m3.s-1
ql
Lateral flow
m3.s-1.m-1
XI
A
Cross section area
m2
∝
Velocity coefficient
-
P
Wetted perimeter
m
V
Mean velocity of the water in the stream
m.s-1
θ
Weighting factor
-
Momentum coefficient
-
h
Water surface elevation
m
x
Velocity in X-direction
m.s-1
B
Top width of the water surface
m
X
Distance along the channel
m
t
Time
s
g
Acceleration of gravity
m.s-2
pressure force in the x-direction
N
Se
Slope of energy grade line
m. m-1
Ce
expansion loss coefficient
-
R
Hydraulic radius
m
Vr
The velocity of the wind relative to the water surface
m.s-1
Ff
Frictional forces between the channel and the fluid
CD
Friction drag coefficient
N
λ
Length of a wave in the hydraulic system
m
n
Manning roughness coefficient
s.m-0.333
C
Chezy resistance factor
-
ܨ
XII
-
A Numerical model for routing flood in a meandering rivers is presented. It is based on modified form of the complete one-dimensional Saint-Venant equations of unsteady flow. These equations are modified such that flows in the meandering river channel, left overbank floodplain, and right overbank floodplain are all identified separately. Thus, the difference in hydraulic and geometric properties and flow-path distances are taken into account for all these three divisions of the valley cross-section. The numerical model was applied to the Euphrates River in its reach between Haditha Dam and Hit city along 124.4 km to make a sensitivity analysis of the effect of meandering on the following parameters: the river peak discharge, peak water level, lag time of peak discharge, and lag time of peak water level along the river reach under study for various values of Manning roughness coefficient of the floodplain. Six cases were taken to compare the effect of meandering in the above parameters, cases A1, A2, and A3 are made for straight river and cases B1, B2, and B3 for meandering river. For both cases, three values of Manning roughness coefficient were given for the flood plain, 0.05, 0.07, and 0.1 respectively. The corps of engineers computer programs HEC-RAS 3.1.3 was used to determine the above parameters from a given flood caused by a hypothetical foundation failure of Haditha Dam. A comparative analysis indicates that the peak flow of the flood wave in Hit city for case B1 is 11.2 % more than for case A1 under the effect of meandering when the flood wave moves between Haditha Dam and Hit city. It is found that the meandering of the river had increased the peak flow of the flood wave at Hit city for case B2 by 13.6% over the peak flow of case A2, and had increased the peak flow of case B3 by 15.1% over the peak flow of case A3. The time lag between the start of failure of Haditha dam and arrival of the peak flow to Hit city is 14:45 hours for case A1 and 12:10 hours for case B1, this means that the meandering of the river had reduced the time of arrival of the peak flow to Hit city by 2:35 hours comparing cases A1 and B1. The meandering of the river was reduced the time of arrival of the peak flow to Hit city with 3:10 hours and 3:30 hours XIII
when comparing cases A2 and B2 , A3 and B3 respectively. Comparing cases A1 and B1 showing that the maximum flood wave elevation in Hit city for case B1 is higher than that in case A1 with 0.97 m, and its time of arrival is lesser by 2:20 hours. Comparing cases A2 with B2, and A3 with B3 showing that the maximum flood wave elevation in Hit city for cases B2, and B3 are higher than that in cases A2, and A3 with 1.02 m, and 1.08 m respectively, while its time of arrival is lesser with (2:55), and (3:50) hours respectively. Dimensionless parameters: roughness ratio (nr), discharge reduction (Dr), and stage reduction (Sr) with other parameters such as time lag of peak discharge (TLD) and time lag of peak level (TLL) were developed to express graphically the relationship between the different cases of the flood wave routing of the case study. The dimensionless parameters: discharge reduction (Dr) and stage reduction (Sr), and the parameters of time lag of peak discharge (TLD) and time lag of peak level (TLL) were all increased with the increase of the dimensionless parameter roughness ratio (nr). The one-dimensional numerical model that used in this study was verified using a two-dimensional model over a selected small meandering reach in the study area. The two-dimensional model software (RMA-2) was used to calculate the velocity in two directions, water surface elevation, and discharge along the small meandering part in this reach. The results show a good agreement between the two-dimensional and the modified onedimensional models.
XIV
We certify that this thesis, titled “Numerical Modeling of Flood Wave Behavior with Meandering Effects (Euphrates River, Haditha-Hit)" was prepared by "Sadiq Aleiwi AlFahdawi" under our supervision at the Building and Construction Engineering Department in the University of Technology
in
partial fulfillment of the requirements for the degree of Doctor of Philosophy in Water Resources Engineering .
The Supervisors
prof. Dr. Rafa H. Al-Suhaily
Date
:
/
Asst.Prof. Dr. Mohanad J. Al-Kazwini
/ 2009
Date :
/
/ 2009
In view of the available recommendations ,I forward this thesis for debate by the Examining Committee .
Asst.Prof. Dr. Mohanad J. Al-Kazwini Chairman of the Branch of Dams & Water Resources Engineering . Date : / / 2009 .
XV
EXAMINATION COMMITTEE CERTIFICATE We certify that we have read this thesis titled (Numerical
Modeling of Flood Wave Behavior with Meandering Effects (Euphrates River, Haditha-Hit)) and as an examining committee , examined the student (SADIQ ALEIWI AL-FAHDAWI) in its content and what is connected with it ,and its meets the standard of a thesis for the degree of doctor Philosophy in Dams and Water Resources Engineering. Signature :Prof .Dr. Ahmed M. Ali (Chairman) Date :- / / 2009 Signature:Professor. Dr .Karim K. AL-jumaily. (Member) Date :- / / 2009 .
Signature :Assistant Professor. Dr . Hassan A. Omran. (Member) Date :- / / 2009
Signature :Assistant Professor. Dr. Rasul M. Khalaf (Member) Date :- / /2009 .
Signature :Assistant Professor. Dr. Basim Sh. Abed (Member) Date :- / / 2009.
Signature :Professor Dr. Rafa H. Al-Suhaily (Supervisor) Date :- / /2009 .
Signature :Assistant Professor Dr .Muhannad J. AL-kazwini. (Supervisor) Date :- / / 2009 .
Approved by the Head of Building and Construction Engineering Department . Signature :Professor Dr.Namir K.S.AL-saoudi Date : / /2009
ཱི ི ཱ ༡
َ
َْ ْ َ ﱠ َ َ َ َ ْ َ ﻪ ﺃﻧﻚ ﺗﺮﻯ ﺍﻷﺭﺽ ﺎﺗ ِ ﻣﻦ ﺁﻳ ِ ﻭ ِ َ ً َ َ َ َ ْ َ َ َ ْ َ َ ﺎﺷﻌﺔ ﻓ ِﺈﺫﺍ ﺃﻧﺰﻟﻨﺎ ﻋﻠﻴﻬﺎ ﺧ ِ
ْ َﱠ ْ َ َ َ ْ ﱠ ﱠ ْ َ ﺬﻱ ﺍﻟﻤﺎء ﺍﻫﺘﺰﺕ ﻭﺭﺑﺖ ِﺇﻥ ﺍﻟ ِ ﱠ ُ ْ َ ْ َ َ ْ َ َ َ ُ ْ ﺃﺣﻴﺎﻫﺎ ﻟﻤﺤ ِﻴﻲ ﺍﻟﻤﻮﺗﻰ ِﺇﻧﻪ ٌ ُ ﱢ َ ْ َ َ َ ﺪﻳﺮ ءﻗ ِ ﻋﻠﻰ ﻛﻞ ﺷﻲ ٍ ﺻدق ﷲ اﻟﻌظﯾم
ﺳورة ﻓﺻﻠت-
اﻵﯾﺔ ) ( 39
Chapter One
Introduction
CHAPTER ONE
INTRODUCTION 1.1 General Flooding is one of the most severe natural disasters. It is extremely important to know when it happens, how it propagates, and how large the magnitude will be. Frequently, there are reports of submerged catchments or regions, lives that have been lost, properties flushed away, traffic halted, electricity cut, community activities disrupted, etc., (Wang, et.al, 2000; Jiang, et.al, 2002). The propagation of flow in space and time through a river or network of rivers is a complex problem. The desire to build and live along rivers creates the necessity for accurate calculation of water levels, and flow rates and provides the impetus to develop complex flow routing models. The computation of flood water level is needed because this level delineates the floodplain and determines the required height of structures such as bridges and levees. (Smith, 1995; Miller, 1997). Flow routing is a procedure to determine the time and magnitude of flow (i.e., the flow hydrograph) at a point on a stream from known or assumed hydrographs at one or more points upstream. If the flow is a flood, the procedure is specifically known as flood routing. Flooding is a result of heavy or continuous rainfall exceeding the absorptive capacity of soil and the flow capacity of rivers or streams. This causes a watercourse to overflow its bank onto adjacent lands. Flood analysis assists decision makers with the prediction and prevention of flood events. (Snead, 2000). In this study one of the most important unsteady flow phenomena the engineer has to deal with is considered. It is the movement of the flood wave down a natural river. The associated problem is the tracing of this movement and any related changes in the magnitude and height of the wave. 1
Chapter One
Introduction
Unsteady flow in a natural river which meanders through a wide floodplain is complicated by large differences in hydraulic resistance and crosssectional geometry of the river channel and the floodplain. The unsteady flow is further complicated by the tendency for a portion of the flow to short-circuit along the more direct route afforded by the floodplain rather than following the longer route along the meandering channel. Thus, the wave attenuation and the time of travel of the portion of the flow in the channel differ from that in the floodplain due to differences in the hydraulic properties and flow-path distances of the channel and floodplain. Developments in fully dynamic, unsteady models have provided engineers with highly accurate hydraulic modeling methods that result in graphical two- and three dimensional visualizations for the purpose of analysis. The key to graphical visualizations in dynamic modeling is the inclusion of timeseries data within a spatial interface, like the Geographic Information System (GIS). The mathematical model for routing floods in meandering rivers with floodplains for Euphrates River in selected area is developed. The technique is based on a modified form of the complete one-dimensional equations for unsteady flow. The one-dimensional equations are modified in such a way that the flow in the meandering channel and the flood plain are identified separately. Thus, the differences in both hydraulic properties and flow-path distance are taken into account in a physically meaningful way, onedimensional in concept. This development differs from conventional onedimensional treatment of unsteady flows in rivers with floodplains wherein the flow is either averaged across the total cross-sectional area (channel and floodplain) or the floodplain is treated as off-channel storage, and the reach lengths of the channel and floodplain are assumed to be identical. The modified equations contain the same two unknowns (discharge and water surface elevation) as the conventional equations; hence the same numerical 2
Chapter One
Introduction
solution technique applicable to the conventional one-dimensional unsteady flow equations may be used. A weighted four-point implicit finite difference technique is used for its versatility and computing efficiency. The fundamental assumptions underlying the development of the SaintVenant equations for unsteady flow in rivers caused by the motion of long waves are, (Fread, 1971, and Smith, 1978): 1. This motion can be considered one-dimensional, that is the acceleration and velocity components of the wave in the transverse and vertical directions are neglected since they are small relative to the components in the direction of the longitudinal axis of the water way. 2. The water surface is horizontal across any section perpendicular to the longitudinal axis. 3. The flow is gradually varied with hydrostatic pressure prevailing at all points in the flow. 4. The longitudinal axis of the channel can be approximated as a straight line between any two adjacent cross-sections. 5. The bottom slope of the channel is small. 6. The bed of the channel is fixed, that is, no scouring or deposition is assumed to occur. 7. The flow is incompressible and homogeneous in density. Computer modeling techniques have assisted engineers in determining more accurately where and when flooding may occur. The army corps of engineers' Hydraulic Engineering Center is one of the world-leading software developers for incorporating water resources related time-series data into modeling. HEC-RAS 3.13 hydrodynamic model uses 1-D implicit, dynamic wave routing based on the Saint-Venant equations for unsteady flow. It is a 1-D unsteady flow model that can simulate flow in a complex 3
Chapter One
Introduction
network of open channels and it can include off-channel storage and flood plain storage areas and flow in meandering rivers. In the literature of the most of researchers in flood routing, it is evident that the one dimensional mathematical models proposed for simulating unsteady flows in natural rivers have, for the most part, ignored the above flow complexities. Most either treat the floodplain or some portion of it as off-channel dead storage, or the main river channel and the floodplain are lumped together to form a composite channel in which the significantly different particle velocities and wave speeds of the flows in the main channel and in the floodplain are averaged together. Each of these techniques provides only a rough approximation of the actual flow. A numerical model was applied to the Euphrates River in the reach between Haditha Dam and Hit city (124.4 Km) long. A flood risk map explained maximum height, maximum discharge, and arrival time of flood wave along the river in this study area was obtained. The results of the application of a numerical model on the meandering river was compared with the application of the same model for the same river but with assumption that the reach lengths of the channel and the floodplain are identical. It is found that the channel meander led to increase the wave attenuation and decrease its travel time.
1.2 Problem definition This research presents development and application of unsteady flow model for a flood wave in the study area mentioned above and evaluates the effect of river meandering on it.
1.3 Objectives of the present work 1- Apply an unsteady flow model for a reach in Euphrates River between Haditha dam and Hit city, (124.4 km length). 4
Chapter One
Introduction
2- Analyze the effect of meandering along this river on the flood wave characteristics. 3- Analyze flood impact in flood prone areas on roads, land use and strategic projects. 4- Prepare the maps and its output, which can be used during flood emergency in flood inundated area. 5- Developing a dimensionless parameters (nr, Sr, and Dr) to evaluate the effect of various values of Manning roughness coefficient for flood plains on the stage reduction and discharge reduction of flood wave for various cases.
1.4 General description of the Euphrates river The Euphrates River is the main water course on the territory of the Middle East. It rises at the mountains between the Black Sea and Lake Van in Turkey, 3000-3500 m (a.s.l). The Euphrates River originates at the confluence of the Karasu (470 km) and Murad (650 km) rivers. The length of the Euphrates River from the confluence of Murad and Karasu to the confluence with Tigris River is (2220 km) as shown in figure (1.1). The Euphrates River crosses the territory of Turkey, Syria, and Iraq. While 28% of the Euphrates basin lies in Turkey, 17% in Syria and 40% in Iraq, approximately 88.7% of the Euphrates water originates in Turkey, Syria contributes 11.3%. The consumption of Euphrates water is inversely proportional to contributions: Syria and Iraq are using 22% and 43% respectively. In addition, water flow is highly seasonal, in dry, normal, and wet years the flow is concentrated during April and May months. July through November is low water months, figure (1.2), (Lorenz, 1997).
5
Chapter One
Introduction
Discharge (cms)
Figure (1.11) Euphrates River (after Lorenz F.M. 1997)
8000 6000
Dry year
4000
Normal year
2000
Wet year
0 .Oct .Nov .Dec .Jan
.Feb .Mar
.Apr
.May
.Jun
.Jul
.Aug
.Sep
Time (month)
Figure (1.2)) Seasonal variation of flow in the Euphrates Rive River 6
Chapter One
Introduction
The river enters Iraq in Al-Qaim town, the site of Haditha city is at km 239.7 from the Syria – Iraq border along the Euphrates River. Hit city is situated at about (120 km) downstream Haditha city along the Euphrates River. (Kashif Al-Ghita'a. 1959). At the reach from the state border with Syria to the town of Ana the river flows eastwards with a mean gradient of 0.00021; at the reach from Ana to Hit the Euphrates flows in south-east direction with a mean gradient of 0.00033. From Hit to Ramadi the mean gradient of river decreases to 0.0001. The hydrographic network of the Euphrates River within the territory of Iraq is represented by dry wadies with water flow only during heavy rains. The largest wadies diffuse at the Euphrates River in the western region of Iraq are Horan, El-Fehaimi, and Zaghdan, (Ministry of Irrigation 1980). Figure (1.3) shows the Euphrates river reach in the study area.
Figure (1.3) Euphrates river reach in the study area 7
Chapter One
Introduction
1.5 Limitation of the numerical model 1- The motion of flood wave can be considered one-dimensional, that is, the acceleration and velocity components of the wave in the transverse and vertical directions are neglected since they are relatively small compared with the components in the direction of the longitudinal axis of the water way. 2- The water surface is horizontal across any section perpendicular to the longitudinal axis. 3- The energy loss due to the interaction of channel and flood plain flows is not considered in the proposed model. 4- The problems of simulating helicoidally flow, traveling eddies at river bends, and wind resistance effects are neglected. 5- The bed of the channel is fixed and has a small slope. 6- The flow is incompressible and homogeneous in density.
8
Chapter Two
Literature review
CHAPTER TWO
Literature Review 2.1 History of the river flood modeling In 1968, Congress in U.S.A established the National Flood Insurance Program (NFIP) in response to rising costs associated with taxpayer funded disaster relief for flood victims. Through the NFIP, federally backed flood insurance became available in communities that enacted and enforced floodplain management ordinances aimed at reducing flood damage. The need to delineate floodplains for the NFIP spawned a massive national floodplain-mapping project in the 1970s, (FEMA, 1999). During (1970-1976), the U.S. National Weather Service’s (NWS) developed DWOPER (Dynamic Wave Operational Model) and DAMBRK models. The DWOPER and DAMBRK models use the implicit finite difference method for solving the Saint-Venant equations for unsteady flow. The DAMBRK model was used by the NWS to analyze floods resulting from dam breaks. In 1976, the DAMBRK model has been applied to reconstruct the downstream flood wave caused by the failure of the Teton dam in Idaho. The NWS models eventually led to the development of the FLDWAV model by Fread (1982). It is a synthesis of DWOPER and DAMBRK, and adds significant modeling capabilities not available in either of the other models. FLDWAV is a dynamic wave model for 1-D unsteady flows for a single stream or a stream network. Like the DWOPER and DAMBRK models, it is based on an implicit finite-difference solution of the Saint-Venant equations. Expanding on Fread’s work, Barkau (1982) defined a new set of equations that were more convenient to be solved by computational methods. He combined the convective terms for both the floodplain and channel using a velocity distribution factor. Barkau also replaced the friction slope (bed 9
Chapter Two
Literature review
resistance term) with equivalent force terms. His work is the basis of the Hydrologic Engineering Centre’s 1-D, unsteady flow model called UNET. HEC recently improved upon HEC-RAS by including unsteady flow using the UNET program as an extension to the software. The unsteady flow option currently exists for HEC-RAS version 3.1.3 in 2005. In Europe, the Danish Hydraulic Institute (DHI) developed the MIKE11 hydraulic model in 1987 and it became a widely applied 1-D dynamic modeling tool for rivers and channels. Its ability to simulate unsteady stream flows for specified time durations and time steps currently makes it a powerful graphical tool. Two-dimensional models, compared with 1-D models, require a significant amount of additional data (especially topographic data) and time to set up and run. Any change in topography like addition of dike or road will require a change in topographic data and incorporating such changes, in general, is more time consuming compared to 1-D modeling. Due to significant requirements of topographic data and computational time for two-dimensional modeling, one-dimensional approach was a preferred choice for modeling floods, especially in very large basins, and limited available data.
2.2 Previous works on floods and meandering river models Hydraulic engineers and scientists have used various approaches to analyze fluvial environments. With advances in computer technology, a majority of analysis of rivers and their floodplains have been conducted with numerical models. These efforts have utilized a wide variety of techniques and methods, including the use of one-dimensional finite difference hydraulic models, two- dimensional finite difference and finite element hydraulic models, and two-dimensional finite element hydraulic models coupled with hydrologic models. 10
Chapter Two
Literature review
In 1871, Saint-Venant derived the continuity and momentum equations for 1-D unsteady flow in an open channel, known as the Saint-Venant equations. The equations he derived assume uniform cross-sections and bed slope for a segment of open channel with no flow above the banks. Fread (1976) further investigated the Saint-Venant equations and developed an implicit method of solving the dynamic wave for the modeling of meandering streams. He distinguished left and right flood plains from the flow channel in a stream’s cross-section. The method was used to solve for the unknowns h (water surface elevation) and Q (stream flow) for specified points along the stream over a series of time steps. Fread first approached the problem by dividing stream channels into two conceptual channels; the stream channel and floodplain. He made four additional assumptions to simplify the 1-D flow problem: 1) The water surface at each cross-section is horizontal (normal to the direction of flow) 2) The momentum exchange between the stream channel and floodplain is negligible 3) The flow is distributed to the stream channel and floodplain according to conveyance 4) The bed channel slope is small (denoting subcritical flow). These assumptions led Fread to an implicit method to solve the SaintVenant equations using a finite difference solution. For the finite segment of the stream shown in figure (2.1), there are five acceleration and pressure terms that act on the control volume: convective acceleration, local acceleration, hydrostatic pressure, bed resistance, and gravity. The convective acceleration, local acceleration, and hydrostatic pressure terms are important to dynamic wave motion because they account for pressure and inertial forces
11
Chapter Two
Literature review
which characterize the movement of a large flood wave in the stream (Chow, et.al, 1988).
Figure (2.1) Section of a stream channel with force terms (after Chow et.al, 1988) The equations simplify to the following: Continuity equation డொ
డ௫
+
డ
డ௧
= ݍ-----------------------------------------------(2-1)
Momentum equation డொ
డ௧
+
ഁೂ మ ൰ ಲ
డ൬
Where
డ௫
+ ܣ
డ
డ௫
+
ொ|ொ| మோ
= 0 -------------------------(2-2)
Q: discharge along the river axis, x. A: cross-section area. q: lateral inflow per unit distance. h: stage above datum. C: Chezy resistance coefficient R: hydraulic radius. g: acceleration of gravity. β: momentum coefficient for velocity correction. t: time. 12
Chapter Two
Literature review
For Fread’s methodology, the above equations were separated between stream channel and floodplain. The momentum coefficient, also known as the Boussinesq coefficient, accounts for uniform distribution of velocity at a cross-section. Its value ranges from 1.01 for straight prismatic channels to 1.33 for river valleys with floodplains. Although the proposed model is also an approximation of the complex flow in such a natural watercourse, it does directly consider the influence of the unequal flow velocities and different degrees of roughness in the main river channel and the flood plain, the influence of different lengths and slopes of the flow paths of the channel and the flood plain, and the influence of dead storage areas. The energy loss due to the interaction of channel and flood-plain flows, as well as the problems of simulating helicoidally flow at river bends, traveling eddies, etc., which are associated with natural river channels are not considered in the proposed model. The basic concept of the model is to treat the flows in the river channel and flood plain separately and from a one-dimensional point of view. In order to treat the flows in the channel and flood plain separately, it is important that the geometric, roughness, and flow-path characteristics of both the river channel and flood plain be preserved in the governing onedimensional equations. Using a subscript “c” to denote variables pertaining to the river channel, the complete one-dimensional equation of unsteady flow in a prismatic or non-prismatic river channel of arbitrary cross-sectional shape are: డொ డ
డொ డ௧
+ +
డ డ௧
= 0 ----------------------------------------------------------(2-3)
డ(ொ) డ
+ ݃ܣ(
డ௭
డ
+ ܵ) = 0 --------------------------------(2-4)
Where: ܸ = velocity of main channel cross-section
ܵ = friction slope at the main channel cross-section 13
Chapter Two
Literature review
Likewise, using a subscript “f” to denote variables pertaining to the floodplain, the one dimensional equations of unsteady flow can be written for the floodplain flow as follows: డொ డ௫
డொ డ௧
+ +
డ డ௧
+
డೞ డ௧
డ(ொ ) డ௫
− = ݍ0 ----------------------------------------------------(2-5)
+ ݃ܣ ൬
డ௭
డ௫
+ ܵ ൰− ݒݍ௫ = 0 ----------------------------(2-6)
Where: ܣ௦ = the off-channel dead storage area.
ݒ௫ = the velocity of the lateral inflow in the direction of x-axis of the flood plain.
ܵ = friction slope at the flood plain cross-section
Upon adding the flows in the channel and the floodplain, the equations of unsteady flow for the combined flow become: డ൫ ାାೞ൯ డ௧
ࣔ൫ࡽ ାࡽ ࢌ൯ ࢚ࣔ
+
+
డொ డ௫
ࡽ ࣔቆ ࢉቇ ࢉ
ࣔ࢞ࢉ
+
+
డொ డ௫
ࡽ ࢌ
ࣔ൭
൱
ࢌ
ࣔ࢞ࢌ
− = ݍ0 ------------------------------------------(2-7) ࣔࢎࢉ
+ ࢍࢉ ቀ
ࣔ࢞ࢉ
ࣔࢎࢌ
+ ࡿࢌࢉቁ+ ࢍࢌ ൬
ࣔ࢞ࢌ
+ ࡿࢌࢌ൰− ࢜࢞ = -(2-8)
The stated above equations contain only four unknown, Qc , Qf , hc , and hf, because A can be expressed as a function of h, S can be expressed as a function of Q and h, and q, Vlx, g, x, t are known quantities. An idealized meandering river with a significant flood plain, figure (2.2), and uniform cross section, figure (2.3), is used for the simulation model. (Chang, 1985) developed and applied a mathematical model for water and sediment routing through a curved alluvial channels. This model which is for alluvial stream with non erodible banks may be employed to simulate stream bed changes during a given flow, thereby providing the necessary information for the design of dikes, levees, or other bank protection. He found that the river flow through curved channels is characterized by the 14
Chapter Two
Literature review
Figure (2.2) Definition plan of idealized meandering river with flood plain
Figure (2.3) Cross-section 5-5 of idealized river 15
Chapter Two
Literature review
changing curvature, to which variations of flow pattern and bed topography are closely related. A mathematical model, “FLUVIAL-12” was developed to simulates time and spatial variations in water level, sediment transport, and bed topography. Application of this model is limited to alluvial channels with non erodible banks, large width-depth ratio, and mild curvature. A case study using this model on San-Lorenzo River in California during a flood event is presented. (Ikeda and Nashimura, 1985) presented a mathematical model for defining three-dimensional flow and bed topography in sinuous channels with suspendable bed material. The three-dimensionality of turbulent flow in sinuous channels is mainly associated with the secondary flow, which can be nullified if the flow is depth-average. Therefore, the three-dimensional flow is separated into the depth-averaged two-dimensional flow component and the secondary flow component. The model for bed topography is derived by considering the sediment balance for bed load and suspends load, the transport rate and direction, all of which are governed by the threedimensional flow. A laboratory test supports the model. This study has made it possible to predict the large-scale bed topography of meandering sand-silt rivers, including such features as the magnitude and the location of local scour and point-bar deposits. (Odgaard, 1989) described a development and application of a rivermeander model. The basis is steady, two dimensional model of flow and bed topography in an alluvial channel with variable curvature. The model is developed from the equations for conservation of mass (water and sediment) and momentum, and from a stability criterion for sediment particles on the stream bed. Formulas are thereby developed for calculation of: 1) Velocity and depth distribution in meandering channels; and 2) Rate and direction of channel migration.
16
Chapter Two
Literature review
The analytical model is tested with data from rivers in India and the United State. (Fukuoka, et.al, 1997) have been performing experiments using a flume with a mobile main channel bed and a flood channel bed with high roughness. For the case of a channel having constant sinuosity, the positions of maximum flow velocity filament in the main channel, the mixing of main channel and flood plain flows, and bed variation such as scouring and deposition have been studied. They explain that, in the experimental channel, sinuosity was defined as the ratio of meander wavelength to straight downstream distance, but in rivers where embankments also meander, this definition of sinuosity cannot adequately express the effects of embankment meandering. For this reason, sinuosity is, instead, defined as the ratio of main channel center distance to embankment center distance or: ܵ݅݊= ݕݐ݅ݏݑ
௧ ௧……….
௧ ௧ ௧௪ ௩௦ିିି
as shown in figure (2.4).
Levee Flood plain
Main channel
Flood plain Levee
Figure (2.4) Definition of sinuosity The study clearly demonstrated, as was observed in experiments that for a doubly meandering compound river course, there is a high flow velocity at the outer bank of river bends characteristic of simple meandering flow, and a
17
Chapter Two
Literature review
high flow velocity at the inner bank of river bends characteristic of compound meandering flow. (Tate, 1998) presents that a significant deficiency of most computer models used for stream floodplain analysis, is that the locations of structures impacted by floodwaters, such as bridges, roads, and buildings, cannot be effectively compared to the floodplain location. His research presents a straightforward approach for processing output of a one-dimensional hydraulic model, to enable two- and three-dimensional floodplain mapping and analysis in the Arcview GIS. The methodology is applied to a reach of Waller Creek, location in Texas. The results of this research indicate that GIS is an effective environment for floodplain mapping and analysis. (Khan, et.al, 2000) had investigated in his study the applicability of the two-dimensional depth-averaged models to river bend reaches. Three models: CCHE2D; RMA-2; and FESWMS-2DH are applied to the river Dommel in Netherlands. The study area consists of two consecutive bends with long straight reaches upstream and downstream of the two bends. The mesh consists of quadrilateral elements and the number of elements for all of the three models is same. The boundary conditions for flow at the upstream end and water surface elevation at the downstream end are specified for all of the three models. A constant and same value of manning’s coefficient is specified throughout the whole domain for these three models. The computed water surface elevations and velocity profiles across various sections specifically in the bends are compared with the measurements in the field. (Snead, 2000) develops a one-dimensional unsteady flow hydraulic model used for flood routing and visualization for a section of the stream network within the Mill-Creek Watershed using a MIKE-11 hydraulic model software. Discharge hydrographs from the HEC-HMS hydrologic model were extracted and imported into his model. The time-series results from the unsteady flow model are imported into Arcview GIS using corresponding 18
Chapter Two
Literature review
Arcview extensions to develop floodplain determination and visualization in a spatial environment. He creates two- and three-dimensional flood animations of specific storm from model for future analysis and public presentations. (Hammarsmark, 2002) used a one-dimensional unsteady hydraulic model to evaluate the flood stage impacts of seven management scenarios for the McCormack-Williamson Tract, located in California, USA. Scenario features include weirs, levee breaches, levee removal, and internal levee construction in a variety of configurations. In addition to quantifying flood impacts, the model results are used to quantify the potential areal extent of sub tidal, intertidal habitat zones within the project area and the volume of tidal exchange for each of the scenarios. (Khayyun, 2006) used a numerical model software (FLDWAV) which is a one-dimensional unsteady flow hydraulic model to evaluate a hypothetical failure of multiple dams and his case study was Mosul and Mackhool Dams located across Tigris river. Four scenarios are used in this study; statuses for these scenarios are the gates, the floodplain (conveyance and composite options) and the probability of inflow hydrograph. The effects of five parameters (distance, breach base width, breach depth, failure time and side slope of breach) are investigated for determining the peak flow, water surface elevation and travel time of wave. A range of various laboratory experiments were presented. The observations were compared with numerical models. Experiments were carried out by using a digital imaging technique for measuring the water surface level and the steady flow velocity. A velocimeter sensor was used for measuring the unsteady flow velocity of the flood wave. The conveyance option gives results more conservative as regards emergency planning. It leads to higher flow levels, while the composite option leads to high peak flow and shorter time of flood arrival. It was found that the maximum elevation of water level at cross – 19
Chapter Two
Literature review
section just upstream Makhool dam is above the design crest elevation of the dam by about 6.74m. A case which means that hypothetical collapse for Mosul dam had not taken into consideration. The most critical flood areas were descending within Mosul, Sharqat, Qaiyara and Fatha cities respectively. The computed depth showed no dangerous situations for Beiji and Tikrit cities. The travel times of wave were 4.86 hr, 11.4 hr, 14.6 hr, 22.64 hr, 24.78 hr and 35.12 hr for the above mentioned cities respectively.
2.3 Model selection for the case study Both one-dimensional and two-dimensional hydrodynamic models can be used to simulate floods in river basin or any stream channel. However, each modeling approach has its own advantages and limitations. Two most commonly used one-dimensional modeling tools are HEC-RAS and MIKE 11. The main objective of HEC-RAS program is to compute water surface elevation at locations of interest for a given flow value. The basic assumptions underlying HEC-RAS are: (HEC-RAS River Analysis System, 2005) flow is gradually varied, flow is one-dimensional i.e. velocity component in direction other than the direction of flow is not accounted and, river channel has small slope Main inputs to the model include flow regime, starting elevation, discharge, loss coefficient, cross-section geometry and reach length for both river main channel and floodplain. Model can handle bridges, weir flow, meander in streams and split flow options. The computational procedure is based on solution of the one-dimensional energy and momentum equations using the standard step method.
20
Chapter Two
Literature review
MIKE 11 one-dimensional hydraulic model has a GIS interface and can handle unsteady flows. Cost of MIKE 11 is very high but it comes with very good technical support. Considering the size of river floodplains and characteristics like flat slopes and complex topography due to the presence of infrastructure, HEC-RAS is probably the best available one-dimensional modeling tool. However, there are certain aspects of modeling that cannot be resolved using a 1-D model e.g. determining the flow path of flood wave, velocity and flow in floodplains perpendicular to the flow in the main river, and determination of flooded areas based on topography. In these particular situations a fully two dimensional model is required. DHI develops the twodimensional software MIKE 21, to simulate the river flow in two-dimensions. Despite tremendous developments in computer software the interoperability of different software components is still a major area of concern with every change in topography e.g. size, height or location of dike the whole process has to be repeated. (Danish Hydraulic Institute 2005). Some important points derived from the comparison of 1-D and 2-D hydrodynamic modeling approaches are, (Simonovic, 1999; HEC-RAS River Analysis System, 2005; Kamel, 2008): (a) The one-dimensional model is warranted since the purpose of the model is to route floods and thus determine the celerity and transformation of the flood wave as it proceeds downstream through the river channel and flood plain. These characteristics of the flood wave are influenced predominantly by the one-dimensional motion of the flood along the longitudinal axes of the river and the flood plain. The model is based on a modified form of the one-dimensional equations of unsteady flow and thereby avoids the obvious use of the more complex and computationally time-consuming two-dimensional equations. (b) Two-dimensional models, compared with 1-D models, require a significant amount of additional data (especially topographic data) and 21
Chapter Two
Literature review
time to set up and run. Any change in topography like addition of dike or road will require a change in topographic data and incorporating such changes, in general, is more time-consuming compared to 1-D modeling. (c) Due to detailed description of topography and additional terms in mass and momentum equations the 2-D models require more time and computational resources to simulate same hydrological event. Therefore, for the above reasons the HEC-RAS 3.1.3 model was used to simulate the flood flow for the Euphrates River in study area.
22
Chapter Three
Theoretical Basis of Mathematical Model CHAPTER THREE
Theoretical Basis of the Numerical Model 3.1 General In the latest years there is an increasing demand for helping and supporting environmental planning decisions with simulation models because of the development of regulatory and planning tools. For example River basin development plans have a close link between the definition of physical phenomena such as floods and the characteristics of land planning limitations. Generally geomorphologic analyses are used in the definition of river floodplain, but definition of a risk or definition of a flooding of an area for a return period needs to use hydraulic and hydrologic models. Estimation of flood inundation and its risk is increasingly a major task in relevant national and local government bodies in world-wide. When river flow depth is reached in a flood event, water ceases to be contained solely in the main river channel and water spreads onto adjacent floodplains. These make the flood prediction a very complex process in both spatial and temporal contexts.
3.2 Unsteady flow equations The physical laws which govern the flow of water in a stream are: (1) the principle of conservation of mass (continuity), and (2) the principle of conservation of momentum. These laws are expressed mathematically in the form of partial differential equations, which will hereafter be referred to as the continuity and momentum equations, (Liggett, and Cunge, 1975). 1) Continuity equation Conservation of mass for a control volume states that the net rate of flow into the volume be equal to the rate of change of storage inside the control volume. Figure (3.1) illustrates elementary control volume. 23
Chapter Three
Theoretical Basis of Mathematical Model
Q(x,t)
ΔX h(x,t) inflow outflow X
Figure (3.1) Elementary control volume for derivation of continuity and momentum equations The rate of inflow to the control volume may be written as: ܳ−
డொ Δ
------------------------------- (3-1)
డ௫ ଶ
ܳ+
the rate of outflow as:
డொ Δ డ௫ ଶ
and the rate of change in storage as: where:
------------------ (3-2) డ డ௧
∆ܺ -------- (3-3)
X = distance measured along the channel Q = flow at midpoint of the control volume AT = total flow area at midpoint of the control volume S = off-channel storage area A = Active area. Assuming that Δx is small, the change in mass in the control volume is equal to: ߩ
డ డ௧
డொ Δ௫
∆ߩ = ݔቂቀܳ − డ௫
డொ Δ௫
ቁ− ቀܳ + డ௫ ଶ
24
ଶ
ቁ+ ܳቃ---------- (3-4)
Chapter Three
Theoretical Basis of Mathematical Model
where ܳ is the lateral flow entering the control volume and ρ is the fluid
density. Simplifying and dividing through by ρΔx yields the final form of the continuity equation: డ డ௧
+
డொ
డ௫
− ݍ = 0
---------------------------------------(3-5)
in which ݍ is the lateral inflow per unit length. 2) Momentum equation
Conservation of momentum is expressed by Newton's second law as: ∑ ܨ௫ =
ሬ⃗ ௗெሬ ௗ௧
-----------------------------------------(3-6)
Conservation of momentum for a control volume states that the net rate of momentum entering the volume (momentum flux) plus the sum of all external forces acting on the volume be equal to the rate of accumulation of momentum. This is a vector equation applied in the x-direction. The momentum flux (MV) is the fluid mass times the velocity vector in the direction of flow. Three forces will be considered: (a) pressure, (b) gravity and (c) boundary drag, or friction force. a) Pressure forces: Figure (3.2) illustrates the general case of an irregular cross section. The pressure distribution is assumed to be hydrostatic (pressure varies linearly with depth) and the total pressure force is the integral of the pressure-area product over the cross section. After Shames (1962), the pressure force at any point may be written as:
ܨ = ∫ ߩ݃(ℎ − ݕ݀)ݕ(ܶ)ݕ
----------------------------(3-7)
25
Chapter Three
Theoretical Basis of Mathematical Model
Where h is the depth, y the distance above the channel invert, and T(y) a width function which relates the cross-section width to the distance above the channel invert. T(y)
(h-y) dy
h
y Datum
Figure (3.2) Illustration of terms associated with definition of pressure force If ܨ is the pressure force in the x-direction at the midpoint of the control
volume, the force at the upstream end of the control volume may be written as: ܨ −
డி Δ௫ డ௫ ଶ
----------------------------------------------------------(3-8)
and at the downstream end as: ܨ +
డி Δ௫ డ௫ ଶ
----------------------------------------------------------(3-9)
The sum of the pressure forces for the control volume may therefore be written as: ܨ = ቚܨ −
డி Δ௫ డ௫ ଶ
ቚ− ቚܨ +
డி Δ௫ డ௫ ଶ
ቚ+ ܨ
--------------------------(3-10)
Where ܨ is the net pressure force for the control volume, and ܨ is the force exerted by the banks in the x-direction on the fluid. This may be simplified to: 26
Chapter Three ܨ = −
డி డ௫
Theoretical Basis of Mathematical Model
߂ ݔ+ ܨ --------------------------------------------------(3-11)
Differentiating equation (3-7) using Leibnitz's Rule and then substituting in equation (3-11) results in: డ
ܨ = −ߩ݃∆ݔቂ ∫ ܶ( ݕ݀)ݕ+ ∫ (ℎ − )ݕ డ௫
డ்(௬) డ௫
݀ݕቃ+ ܨ ------(3-12)
The first integral in equation (3-12) is the cross-sectional area, A. The second integral (multiplied by -ρgΔx) is the pressure force exerted by the fluid on the banks, which is exactly equal in magnitude, but opposite in direction to FB. Hence the net pressure force may be written as: ܨ = −ߩ݃ܣ
డ
డ௫
∆ ݔ-----------------------------------------------------(3-13)
b) Gravitational force: The force due to gravity on the fluid in the control volume in the xdirection is: Fg =ρgA sinθΔx -----------------------------------------------------------(3-14) here θ is the angle that the channel invert makes with the horizontal. For natural rivers θ is small and sin θ≈ tan θ= -∂Z0 / ∂X , where z0 is the invert elevation. Therefore the gravitational force may be written as: ܨ = −ߩ݃ܣ
డబ డ௫
∆ ݔ------------------------------------------------------(3-15)
This force will be positive for negative bed slopes. c) Boundary drag (Friction force):
Frictional forces between the channel and the fluid may be written as: Ff =−τ0PΔx ----------------------------------------------------------------(3-16)
27
Chapter Three
Theoretical Basis of Mathematical Model
Where τ0 is the average boundary shear stress (force/unit area) acting on the fluid boundaries, and P is the wetted perimeter. The negative sign indicates that, with flow in the positive x-direction, the force acts in the negative x-direction. From dimensional analysis, τ0 may be expressed in terms of a drag coefficient, CD, as follows: 2
τ0 =ρ CD V
-------------------------------------------------------------(3-17)
The drag coefficient may be related to the Chezy coefficient, C, by the following: ܥ =
మ
--------------------------------------------------------------------(3-18)
Further, the Chezy equation may be written as: ܸ = ܥඥ ܴܵ
--------------------------------------------------------------(3-19)
Substituting equations (3-17), (3-18), and (3-19) into (3-16), and simplifying yields the following expression for the boundary drag force: Ff = −ρg ASf Δx -----------------------------------------------------------(3-20) Where Sf is the friction slope, which is positive for flow in the positive xdirection. The friction slope must be related to flow and stage. Traditionally, the Manning and Chezy friction equations have been used. Since the Manning equation is predominantly used in the engineering calculated, it is also used in our hydraulic model. The Manning equation is written as: ܵ =
ொ|ொ|మ ర
ோ యమ
-------------------------------------------------------------(3-21)
Where R is the hydraulic radius and n is the Manning friction coefficient.
28
Chapter Three
Theoretical Basis of Mathematical Model
d) Momentum flux: With the three force terms defined, only the momentum flux remains. The flux entering the control volume may be written as: ߩቂܸܳ −
డொ Δ௫
ߩቂܸܳ +
డொ Δ௫
డ௫ ଶ
ቃ -----------------------------------------------------(3-22)
and the flux leaving the volume may be written as: డ௫ ଶ
ቃ ------------------------------------------------------(3-23)
Therefore the net rate of momentum (momentum flux) entering the control volume is: −ߩ
డொ డ௫
∆ ݔ------------------------------------------------------------(3-24)
Since the momentum of the fluid in the control volume is ߩQΔx, the rate of accumulation of momentum may be written as: డ
డ௧
(ߩܳ∆ݔ∆ߩ = )ݔ
డொ
డ௧
----------------------------------------------- (3-25)
Restating the principle of conservation of momentum: The net rate of momentum (momentum flux) entering the volume (3-24) plus the sum of all external forces acting on the volume [(3-13) + (3-14) + (3-20)] is equal to the rate of accumulation of momentum (3-25). Hence: ߩ∆ݔ
డொ
డ௧
= −ߩ
డொ డ௫
∆ ݔ− ߩ݃ܣ
డ
డ௫
∆ ݔ− ߩ݃ܣ
డ௭బ డ௫
∆ ݔ− ߩ݃ܵܣ∆ ݔ-----(3-26)
The elevation of the water surface, z, is equal to ݖ + h. Therefore: డ௭
డ௫
=
ப୦
ப୶
+
డబ డ௫
---------------------------------------------------------------(3-27)
Where ∂z/ ∂x is the water surface slope. Substituting (3-27) into (3-26), dividing through by ρΔx and moving all terms to the left yields the final form of the momentum equation: డொ
డ௧
+
డொ డ௫
డ
+ ݃ ܣቄ + ܵቅ= 0 ---------------------------------------(3-28) డ௫
29
Chapter Three
Theoretical Basis of Mathematical Model
3.3 Meandering Rivers Meandering causes the river to leave its original course and adopt a new course. Meandering rivers follow a winding, crooked course. They consist of a series of bends of alternate curvature in the plan. The successive curves are connected by small straight reach of the river, called crossover or crossings, figure (3.3), (Arora, 1996). Unsteady flow in natural river which meanders through a wide floodplain is complicated by large differences in hydraulic resistance and crosssectional geometry of the river channel and the floodplain. The unsteady flow is further complicate by the tendency for apportion of the flow to “short-circuit" along the more direct route afforded by the floodplain rather than flowing the longer route along the meandering channel. Thus, the wave attenuation and the time of travel of the portion of the flow in the channel differ from that in the floodplain due to differences in the hydraulic properties and flow-path distances of the channel and floodplain, (Fread, 1976).
convex side (inner)
Straight reach crossing
Concave side (outer) Figure (3.3) Crossings in meandering river
30
Chapter Three
Theoretical Basis of Mathematical Model
3.3.1 Development of meanders Once a bend in river has been developed, either due to its own characteristics or due the impressed external forces, the process continues further downstream. Shoals are built up on the convex side due to secondary currents. The formation of these shoals on the convex side cause further shifting of the concave side because of erosion. Thus successive bends of the reverse order are formed. It ultimately leads to the development of a complete S-curve, called a meander. When a large number of such consecutive curves of reverse order connected by straight reach have been developed, the river is called a meandering river, figure (3.4). 3.3.2 Meander parameters and their relationships Meander parameters can be summarized as: 3.3.2.1 Types of meanders a- Meanders can be classified as regular or irregular. If there are a series of bends of approximately the same curvature and frequency (i.e. number of bends per unit length), the meander is said to be regular. On the other hand, if the meanders are irregular and deformed in shape and vary in amplitude and frequency, they are said to be irregular. b- Meanders may also be classified as simple or compound. If the bend has a single radius of curvature, it is called a simple. On other hand, a compound meander is made of segments of different radii and varying angles.
31
Chapter Three
Theoretical Basis of Mathematical Model
Figure (3.4) Typical meandering in a river 3.3.2.2 Geometry of meanders The geometry of meanders is usually described by the meander length (ML ) and meander width (MB ). A meander when fully developed has a definite pattern. Various parameters are used to define the characteristics of the meanders, figure (3.5), (Arora, 1996). a- Meander length (ML): is the tangential distance between the two consecutive corresponding points of the meander. The meander length is also called the axial length. b- Meander width (MB ): is the distance between the outer edges of the one clockwise loop and the adjacent anti-clockwise loop of the meander. c- Meander ratio: is the ratio of the meander width to the meander length. Thus: 32
Chapter Three
Theoretical Basis of Mathematical Model ా
Meander ratio=
ெಽ
d- Crossing: the short straight reaches of the river connecting two consecutive clockwise and anti-clockwise loops are called crossings or crossovers. e- Sinuosity: is the ratio of thalweg length to valley length. The thalweg length is the length of the river along the line of the maximum depth. In general, every meander depends upon the combined effect of the following factors: 1- Discharge and hydraulic parameters of the river 2- Sediment load and its characteristics. 3- Relative erodibility of bed and banks of the river. 4- Slope of the river.
Meandering length (ML)
Meanderng width(MB)
River width (W) Cross over
Figure (3.5) Meander parameters 33
Chapter Three
Theoretical Basis of Mathematical Model
3.4 The floodplain A floodplain is the normally dry land area adjoining rivers, streams, lakes, or oceans that are inundated during flood events, figure (3.6). The most common causes of flooding are the overflow of streams and rivers and abnormally high tides resulting from severe storms. The floodplain can include the full width of narrow stream valleys, or broad areas along streams in wide, flat valleys. The floodplain carries flow in excess of the channel capacity and the greater the discharge, the further the extent of flow over the floodplain, (Kamel, 2008)
Figure (3.6) Floodplain and stream channel Floodplain can be looked at from different perspective. Srivastava et.al, (1968) has defined floodplain as a flat topographic category lying near the stream, geomorphologically, it is a landform composed primarily of adjacent depositional material derived from sediments being transported by the related stream; hydrologically, it can be defined as a landform subjected 34
Chapter Three
Theoretical Basis of Mathematical Model
to periodic flooding by a parent stream. A combination of these (characteristics) perhaps comprises the essential criteria for defining the floodplain. Frequency of inundation depends on the climate, the material that makes up the banks of the stream, and the channel slope, where substantial rainfall occurs in a particular season each year, or where the annual flood is derived principally from snowmelt, the floodplain may be inundated nearly each year, even along large streams with very small channel slopes. Flood usually occurs in the season of highest precipitation. A floodplain can be divided to floodway and fringe, figure (3.7). The floodway is the stream channel and that portion of the adjacent floodplain which must remain open to permit passage of the base flood. Floodwaters generally are deepest and swiftest in the floodway, and anything in this area is in greatest danger during a flood. The fringe is the remainder of the floodplain where water may be shallower and slower, (FEMA, 1999).
Figure (3.7) Floodplain cross-section
35
Chapter Three
Theoretical Basis of Mathematical Model
3.5 Unsteady flow equations for the meandering rivers with floodplain When the river is rising, water moves laterally away from the channel, inundating the floodplain and filling available storage areas. As the depth increases, the floodplain begins to convey water downstream generally in natural meander river along a shorter path than that of the main channel. When the river stage is falling, water moves toward the channel from the overbank supplementing the flow in the main channel. Figure (3.8) illustrates the interaction between the channel and meander river floodplain flows. Because the primary direction of flow is oriented along the channel, this two-dimensional flow field can often be accurately approximated by a one-dimensional representation. Off-channel pounding areas can be modeled with storage areas that exchange water with the channel. Flow in the overbank can be approximated as flow through a separate channel.
Δxf
Δxc
jJ
j+1 J+1 Figure (3.8) Channel and floodplain flows
36
Chapter Three
Theoretical Basis of Mathematical Model
This channel/floodplain problem has been addressed in many different ways. A common approach is to ignore overbank conveyance entirely, assuming that the overbank is used only for storage. This assumption may be suitable for large streams such as the Mississippi River where the channel is confined by levees and the remaining floodplain is either heavily vegetated or an off-channel storage area. Fread (1976) and Smith (1978) approached this problem by dividing the system into three separate channels and writing continuity and momentum equations for each channel. Thus, both dynamic and storage effects of the main river channel and overbanks portion of the flood plain are considered. Problems of simulating energy losses due to large scale eddies formed in the flow at river bends and wind resistance effects were not considered in this study. By using the subscript "C" to denote variables pertaining to the main river channel, the unsteady flow equations (3.5) and (3.28) can be written as follows (assuming the momentum correction factor, β=1): ࣔࢉ ࢚ࣔ
ࣔࡽ ࢉ ࢚ࣔ
+ +
ࣔࡽ ࢉ ࣔ࢞ࢉ
= ------------------------------------------------------ (3.29)
ࡽ ࣔ( ࢉ൘ ) ࢉ ࣔ࢞ࢉ
ࣔࢠࢉ
+ ࢍࢉ ቀ
ࣔ࢞ࢉ
+ ࡿࢌ ቁ = ࢉ
-------------------------( 3.30)
Likewise, using the subscript "f" to denote variables pertaining to the left flood plain, the unsteady flow equations can be written as follows: డ డ௧
ࣔࡽ ࢌ ࢚ࣔ
+ +
డೞ డ௧
+
డொ డ௫
ࡽ ࣔ( ࢌ൘ ) ࢌ ࣔ࢞ࢌ
− ݍ = 0 --------------------------------------- (3.31) ࣔࢠࢌ
+ ࢍࢌ ൬
ࣔ࢞ࢌ
+ ࡿࢌ ൰− ݍܸ௫ = ---------------- ( 3.32) ࢌ
Likewise, using the subscript "r" to denote variables pertaining to the right overbank flood plain, the unsteady flow equations can be written as follows: 37
Chapter Three ࣔ࢘ ࢚ࣔ
ࣔࡽ ࢘ ࢚ࣔ
࢙ࣔ
+
࢚ࣔ
+
+
ࣔࡽ ࢘ ࣔ࢞࢘
ࡽ ࣔ( ࢘൘ ) ࣔ࢞࢘
Theoretical Basis of Mathematical Model
࢘
− ࢘ = -------------------------------------- (3.33) ࣔࢠ࢘
+ ࢍ࢘ ቀ
ࣔ࢞࢘
+ ࡿࢌ ቁ− ࢘ࢂ࢞࢘ = ------------------ ( 3.34) ࢘
The terms in equations (3.29) to (3.34) are defined as:
x = Distance along the longitudinal axis of the channel or flood plain. t = time, A = cross-sectional area of active flow, z = water surface elevation, Q = discharge, Sf = friction slope, g = acceleration of gravity, As = off-channel dead storage area, q = lateral inflow. Vx = velocity of lateral inflow in the direction of the x-axis of the flood plain. After adding the flows in the river channel and in the left and right overbank flood plains, the unsteady flow equations for the combined flow became: డ(ାାೝାೞ) డ௧
డ(ொାொ ାொೝ) డ௧
డ௭
+
+
డொ డ௫
ொమ డ( ൘ )
డ௫
+
+ డ(
డொ డ௫
+
ொమ ൘ ) డ௫
+
డொೝ డ௫ೝ
− (ݍ + ݍ) = 0 ------------- (3.35)
ொమ డ( ೝ൘ ) ೝ డ௫ೝ
డ௭
డ௭
+ ݃ܣ ቀడ௫ + ܵ ቁ+ ݃ܣ ൬డ௫ + ܵ ൰+
݃ܣ ቀడ௫ೝ + ܵ ቁ− (ݍܸ௫ + ݍܸ௫) = 0 ----------------------------------( 3.36) ೝ
The above equations contain six unknowns Qc, Qf, Qr, zc, zf, and zr. The other quantities are known or can be expressed as functions of discharge or elevation. Some assumptions are needed to reduce the number of unknowns to two. First the water surface is assumed to be horizontal across the entire flood plain; therefore: 38
Chapter Three
Theoretical Basis of Mathematical Model
zc = zf = zr =z ----------------------------------------------- (3.37) Second, it is assumed that the friction slope in the main river channel, and in the left and right overbank portion of the flood plain can be expressed by Manning's equation, in which the slope Sf is approximated as: Sf ≈ Δz / Δx
----------------------------------------------- (3.38)
An approximate ratios (kf) of the flow in the left overbank flood plain to that in the river channel and (kr) of the flow in the right overbank flood plain to that in the river channel can be found using Manning's equation with (Sf) approximated by equation (3.38). Therefore,
Where,
ொ
ொ
ொೝ
ொ
ೝ
ೝ
ோ మ ோ
య
ோೝ మ ோ
య
௫ భ మ
௫
Δ௫ భ
Δ௫ೝ
మ
-------------------- (3.39)
----------------
(3.40)
n = Manning's roughness coefficient, R = Hydraulic radius, R=A/P or approximated by A/B when B>> 10 y, P = wetted perimeter, y = flow depth, and B = top width of the water surface. The total flow in the river channel and left and right overbank portions of the flood plain is the sum of the separate flows, i.e., Q = Qc + Qf + Qr ------------------------------------------------(3.41) From equation (3.39) and (3.40) the left and right overbank discharge are: ܳ = ܭܳ ------------------------------------------------------ (3.42)
ܳ = ܭܳ
--------------------------------------------------- (3.43) 39
Chapter Three
Theoretical Basis of Mathematical Model
Substituting equations (3.42) and (3.43) into equation (3.41) and solving for Qc , Qf , and Qr yields, Qc = Ø Q
-------------------------- (3.44)
Qf = τ Q
where Ø = 1 /( 1+ Kf + Kr )
where τ = Kf /( 1+ Kf + Kr )
-------------------------- (3.45)
Qr = ψ Q
where ψ = Kr /( 1+ Kf + Kr )
------------------------- (3.46)
Since Ø, τ, and ψ are all functions of Kf and Kr which are a functions of z. Thus, by substitute equations (3.44), (3.45), and (3.46) into equations (3.35) and (3.36) yields: డ
డ௧
డொ
డ௧
డ(Øொ)
+
+
డ௫
∅మொ మ൘ డ( )
డ௭
డ௫
+ +
డ(ఛொ) డ௫
డ(
+
ఛమொ మ൘ ) డ௫
డ(ట ொ)
+
డ௫ೝ
− (ݍ + ݍ) = 0 ------------------ (3.47)
ట మொ మ൘ డ( ) ೝ
డ௫ೝ
డ௭
డ௭
+ ݃ܣ ቀడ௫ + ܵ ቁ+ ݃ܣ ൬డ௫ + ܵ ൰+
݃ܣ ቀడ௫ + ܵ ቁ− (ݍܸ௫ + ݍܸ௫) = 0 --------------------------------------- (3.48) ೝ
Where,
A = Ac + Af + Ar + As Equations (3.47) and (3.48) are the governing differential equations of onedimensional flow in natural meandering river with left and right overbank flood plains. Equation (3.47) conserves the mass of the flow and equation (3.48) conserves the momentum. The boundary between the main channel and the overbank section is taken as a vertical line above the bank of the main channel. The length of this line is included as part of the wetted perimeter of the main channel, but it is not included as part of the wetted perimeter of the overbank section. The reason for doing this, as suggested by Posey (1967), is that the banks of most natural streams are lined with
40
Chapter Three
Theoretical Basis of Mathematical Model
trees and other vegetation which effectively prevents the transfer of positive shear to the over bank sections. Equations (3.47) and (3.48) constitute a system of partial differential equations of the hyperbolic type. They contain two independent variables, x and t, and two dependent variables, z and Q; the remaining terms are either functions of x, t, z, and/or Q, or they are constants. These equations cannot be solved analytically except in special cases. However, these equations may be solved numerically by performing two basic steps. First, the partial differential equations are represented by a corresponding set of finite difference algebraic equations; and second, the system of algebraic equations is solved in conformance with prescribed initial and boundary conditions.
3.6 Finite difference form of the unsteady flow equations The most successful and accepted procedure for solving the onedimensional unsteady flow equations is the weighted four-point implicit finite difference scheme, also known as the box scheme, figure (3.9). Letting K represent any variable, the time derivative at point M is approximated by the following difference quotient: ࣔࡷ
࢚ࣔ
=
శ
శ
(ࡷ శ ା ࡷ )ି (ࡷ శ ି ࡷ ) ∆࢚
------------------------------- (3.49)
The spatial derivatives and non-derivative terms are positioned between adjacent time lines at point M according to weighting factors of θ and (θ-1), where θ is defined as difference quotients: డ
డ௫
శ
శ
(ࡷ శି ࡷ )
= ࣂ
శ
∆࢞
శ
(ࡷ శା ࡷ )
ࣂ = ܭ
∆ُ࢚◌
∆࢚
. they are approximated by the following
(ࡷ శି ࡷ )
൨+ (1 − ߠ)
∆࢞
(ࡷ శା ࡷ )
൨+ (1 − ߠ)
41
൨ --------------- (3.50)
൨ -----------------(3.51)
Chapter Three
Theoretical Basis of Mathematical Model
t
డ డ௫
ߠ=
J+1
Δݐᇱ Δݐ
M ᇱ
Δݐ
j
Δݐ
Δݔ 2
డ డ௧
i
Δݔ
Δݔ 2 i+1
x
Figure (3.9) Weighted four-point implicit scheme Substituting equations (3.49), (3.50), and (3.51) into the modified SaintVenant equations (3.47) and (3.48), the following weighted four-implicit finite difference equations are obtained: ೕశభ
ೕశభ
ೕ
ೕ
శభ ା ି శభ ି + ଶ∆௧ೕ ೕశభ
ೕశభ
(∅ொ)శభ ି(∅ொ)
ߠ൜
ାଵ
∆௫
+
ೕశభ
ೕ
∆௫
ೕ
(∅ொ)శభି(∅ொ)
ݍ ത )ൠ + (1 − ߠ) ൜
ݍ ത)ൠ= 0
ೕశభ
(ఛொ)శభ ି(ఛொ) ∆௫
+
+
ೕశభ
ೕశభ
(ట ொ)శభ ି(ట ொ) ೕ
∆௫ೝ
ೕ
(ఛொ)శభି(ఛொ) ∆௫
+
ାଵ
− (ݍ ത ೕ
+
ೕ
(ట ொ)శభି(ట ொ) ∆௫ೝ
------------------------------------------------------------ (3.52) 42
− (ݍ ത +
Chapter Three ାଵ
Theoretical Basis of Mathematical Model
ାଵ
ܳାଵ + ܳ
− ܳାଵ − ܳ 2∆ݐ + ߠ
ାଵ
ାଵ
ଶ ଶ ଶ ଶ ⎧൬∅ ܳ ൰ − ൬∅ ܳ ൰ ⎪ ܣ ାଵ ܣ
߬ଶܳ ଶ ାଵ ߬ଶܳ ଶ ାଵ ( ) ܣାଵ − ( ) ܣ + ∆ݔ
∆ݔ
⎨ ⎪ ⎩
߰ ଶܳ ଶ ାଵ ߰ ଶܳ ଶ ାଵ ( ) ܣାଵ − ( ) ܣ + ∆ݔ ାଵ
ାଵ
ݖ− ݖ ାଵ തതത + ݃ܣ ߠቆ ାଵ ∆ݔ ାଵ
ାଵ
ାଵ
ାଵ
ݖ− ݖ തതതାଵ ߠ ቆ ାଵ + ݃ܣ ∆ݔ
ݖ− ݖ തതതାଵ ߠ ቆ ାଵ + ݃ܣ ∆ݔ
+ ܵഥ
+ ܵഥ
ݖ− ݖ ቇ + (1 − ߠ) ቆ ାଵ + ܵഥ ቇ൩ ∆ݔ
ାଵ
+ ܵഥ
ݖ− ݖ ቇ + (1 − ߠ) ቆ ାଵ + ܵഥ ቇ൩ ∆ݔ
ାଵ
ݖ− ݖ ቇ + (1 − ߠ) ቆ ାଵ + ܵഥ ቇ൩ ∆ݔ
ାଵ
തതതത തതାଵ + ݍ തതതത തതାଵ)ൢ + − (ݍ ܸത௫ ܸത௫ ೕ ೕ ∅మೂ మ ∅మೂ మ ൬ ൰ ି൬ ൰ ಲ శభ ಲ
(1 − ߠ) ൞
∆௫
ೕశభ
ೕశభ
௭శభ ି௭ തതത ݃ܣ + ܵഥ ߠ ൬ ∆௫
ೕశభ
ೕశభ
തതത ߠ ൬௭శభ ି௭ + ܵഥ ݃ܣ ∆௫ ೕశభ
ೕశభ
∆௫
ೕ
ାଵ
௭
ାଵ
௭
തതതାଵ ߠ൬௭శభ ି௭ + ܵഥ ݃ܣ ∆௫ೝ
+
ೕ ೕ ഓమೂ మ ഓమೂ మ ቇ ିቆ ቇ ಲ ಲ శభ
ቆ
+
ೕ
ೕ
ି௭
∆௫ೝ
ೕ
ି௭
൰+ (1 − ߠ) ൬ శభ ∆௫
శభ ൰+ (1 − ߠ) ൬ ∆௫
ೕ ೕ ഗ మೂ మ ഗ మೂ మ ൰ ି൬ ൰ ಲ ೝ శభ ಲೝ
൬
ೕశభ
+ ܵഥ ൰൨+
+ ܵഥ ൰൨+ ೕశభ
௭శభ ି௭
ାଵ
൰+ (1 − ߠ) ൬
+
∆௫ೝ
+ ܵഥ ൰൨−
തതതത തത + ݍ തതതത തത)ቑ = 0 ---------------------------------------------- (3.53) (ݍ ܸത௫ ܸത௫ Where,
43
Chapter Three
ܵ̅ =
మொ|ொ| ర
̅మோതయ
Theoretical Basis of Mathematical Model ------------------------------------------------------------ (3.54)
In Which,
ܳത = 0.5 (ܳାଵ + ܳ) ---------------------------------------------------- (3.55)
= ̅ܣ0.5 (ܣାଵ + ܣ) ---------------------------------------------------(3.56) ܴത =
̅ ത
ܴ ݎത =
̅
݂݅ ≫ ܤ10 ݕ--------------------------------- (3.57)
ܲത = 0.5 (ܲାଵ + ܲ) ------------------------------------------------ (3.58)
ܤത = 0.5 (ܤାଵ + ܤ) ------------------------------------------------- (3.59)
Equations (3.52 ) and (3.53 ) constitute a system of algebraic equations that are nonlinear with respect to the unknowns, that is, the values of the dependent variables z and Q at the net points i and i+1 at the time line j+1. The terms associated with the jth time line are known from either the initial conditions or previous computations. The initial value refer to values of z and Q at each node along the x-axis for the first time line (j=1). They are obtained from a previous unsteady flow solution, or they can be estimated by a steady flow solution since small errors in the initial conditions dampen out within a few time steps. Equations (3.52) and (3.53) cannot be solved directly since there are four unknowns. However, if they are applied to each of the (N-1) rectangular grids between the upstream and downstream boundaries, a total of (2N-2) equations with (2N) unknown are formulated (N denotes the total number of nodes). Then the prescribed conditions at the upstream and downstream boundaries provide the necessary two additional equations required for the system to be determinate. Amein and Fang (1970), Chen (1973), Fread (1974, 1976), and others have solved the nonlinear equations using the Newton-Raphson iteration technique.
44
Chapter Three
Theoretical Basis of Mathematical Model
The finite difference approximations are listed term by term for the continuity equation in Table (3.1) and for the momentum equation in Table (3.2). Table (3.1) Finite difference approximation of the terms in the continuity equation (After HEC-RAS 2005)
Term
Finite difference approximation
ΔQ
൫ܳାଵ − ܳ൯+ ߠ(∆ܳାଵ − ∆ܳ)
߲ܣ ∆ܺ ߲ ݐ ߲ܣ ∆ܺ ߲ ݐ ߲ܵ ∆ܺ ߲ ݐ
0.5∆ܺ 0.5∆ܺ
( (
݀ܣ ݀ܣ )∆ݖ + ( )ାଵ ∆ܼାଵ ݀ݖ ݀ݖ ∆ݐ
݀ܣ ݀ܣ )∆ݖ + ( ) ∆ܼ ݀ݖ ݀ ݖାଵ ାଵ ∆ݐ
0.5∆ܺ
(
݀ܵ ݀ܵ )∆ݖ + ( )ାଵ ∆ܼାଵ ݀ݖ ݀ݖ ∆ݐ
45
Chapter Three
Theoretical Basis of Mathematical Model
Table (3.2) Finite Difference Approximation of the Terms in the Momentum Equation (After HEC-RAS 2005) term
Finite difference approximation
∂(ܳ∆ܺ + ܳ∆ܺ) ∂ܺ∆ݐ
0.5 (߲ܳ∆ܺ + ߲ܳ∆ܺ + ߲ܳାଵ∆ܺ ∆ܺ ∂ݐ + ߲ܳାଵ∆ܺ
∆(ߚܸܳ) ∆ܺ ഥ gA
∆z ∆ܺ
തതത) ݃ܵ(̅ܣഥ + ܵ ഥ
1 ൣ(βVQ)୨ାଵ − (βVQ)୨൧ ∆ܺ θ + ൣ(βVQ)୨ାଵ − (βVQ)୨൧ ∆ܺ z − z୨ θ ഥ ቈ ୨ାଵ gA + (∆z୨ାଵ − ∆z୨) ∆xୣ୨ ∆ܺ (z − z୨) ഥ ୨ାଵ + θg∆A ∆ܺ തതത൯ ݃̅ܣ൫ܵഥ + ܵ + 0.5ߠ݃̅ܣൣ൫∆ܵାଵ + ∆ܵ൯ + ൫∆ܵାଵ + ∆ܵ൯൧ തതത൯(∆ܣ + ∆ܣାଵ) + 0.5ߠ݃൫ܵഥ + ܵ 0.5(ܣ + ܣାଵ)
ത ࡿതࢌത
ࣔ
ࣔࡿࢌ ഥ ࣔ
0.5(ܵାଵ + ܵ)
(
(
݀ܣ ) ∆ݖ ܼ݀
−2ܵ ݀ܭ 2ܵ ) ∆ݖ + ( )∆ܳ ݖ݀ ܭ ܳ 0.5(∆ܣ + ∆ܣାଵ)
If the unknown values are grouped on the left-hand side, the following linear equations result: CQ1j ΔQ j+CZ 1j ∆ z j+CQ2j ΔQ j+1+CZ 2 j ∆ z j+1=CBj -------------(3-60) MQ1j ΔQ j + MZ1 j ∆ z j + MQ2 j ΔQ j+1+ MZ 2 j ∆ z j+1= MB j ---(3-61) The values of the coefficients are defined in tables (3.3) and (3.4). 46
Chapter Three
Theoretical Basis of Mathematical Model
Table (3.3) Coefficients of continuity equation (After HEC-RAS 2005) Term ܳܥ1 ܼܥ1
ܳܥ2 ܼܥ2 ܤܥ
Value −ߠ ∆ݔ
݀ܣ ݀ܵ 0.5 ݀ܣ ቈ൬ ൰ ∆ݔ + ൬ + ൰ ∆ ݔ ∆ݔ∆ݐ ݀ ݖ ݀ ݖ݀ ݖ ߠ ∆ݔ ݀ܣ ݀ܵ 0.5 ݀ܣ ቈ൬ ൰ ∆ݔ + ൬ + ൰ ∆ ݔ ∆ݔ∆ݐ ݀ ݖାଵ ݀ ݖ݀ ݖାଵ ܳାଵ − ܳ ܳଵ − + ∆ݔ ∆ݔ
Table (3.4) Coefficient of moment equation (After HEC-RAS 2005) Term ܳ ܯ1 ܼ ܯ1
ܳ ܯ2
ܼ ܯ2
ܤ ܯ
Value ∆ݔ∅ + ∆ݔ൫1 − ∅൯ ߚܸߠ ൫ܵ + ܵ൯ 0.5 − + ߠ݃̅ܣ ∆ݔ∆ݐ ∆ݔ ܳ −݃ߠܣ ݀ܣ ߠ + 0.5݃൫ܼାଵ − ܼ൯൬ ൰ ቆ ቇ ∆ݔ ܼ݀ ∆ݔ ܵ ܵ ݀ܭ ݀ܣ − ݃ ߠ ̅ܣቈ൬ ൰ ቆ ቇ + ൬ ൰ ቆ ቇ ݀ ݖ ܭ ܼ݀ ܣ ݀ܣ + 0.5ߠ݃ ൬ ൰ ൫ܵഥ − ത ܵതത൯ ܼ݀
1 ߠ 0.5ൣ∆ݔ∅ାଵ + ∆ݔ൫1 − ∅ାଵ൯൧ቆ ቇ + ߚାଵܸାଵ ቆ ቇ ∆ݔ∆ݐ ∆ݔ ߠ݃ܣ + + ܵାଵ൯ ൫ܵ ܳାଵ ାଵ ݃ߠ̅ܣ ݀ܣ ߠ + 0.5݃൫ܼାଵ − ܼ൯൬ ൰ ቆ ቇ ∆ݔ ܼ݀ ାଵ ∆ݔ ܵାଵ ܵାଵ ݀ܭ ݀ܣ − ݃ ߠ ̅ܣቈ൬ ൰ ቆ ቇ+ ൬ ൰ ቆ ቇ ݀ ݖାଵ ܭାଵ ܼ݀ ାଵ ܣାଵ ݀ܣ + 0.5ߠ݃ ൬ ൰ ൫ܵഥ − ത ܵതത൯ ܼ݀ ାଵ
1 ݃̅ܣ − ቈ(ߚାଵܸାଵܳାଵ − ߚܸܳ) +ቆ ቇ൫ ݖ− ݖ൯ ∆ݔ ∆ݔ ାଵ തതത൯ + ݃̅ܣ൫ܵഥ + ܵ 47
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3.6.1 Boundary Conditions For a reach of river there are N computational nodes which bound (N-1) finite difference cells. From these cells (2N-2) finite difference equations can be developed. Because there are 2N unknowns (ΔQ and Δz for each node), two additional equations are needed. These equations are provided by the boundary conditions for each reach. 3.6.1.1 Upstream Boundary Conditions The upstream boundary condition can be specified as a known discharge hydrograph in which Q1 is known as a function of time express mathematically as: ାଵ
ܳଵ
− ܳ ُ◌ ൫ݐାଵ൯= 0 -------------------------------------- (3.62)
In which ܳ ُ◌ ൫ݐାଵ൯is the known discharge at the upstream boundary at time ݐାଵ . If this boundary condition is denoted as B1 then : డ డ௭
డ
డொ
= 0 -------------------------------------------------------- (3.63) = 1 -------------------------------------------------------- (3.64)
3.6.1.2 Downstream Boundary Conditions
The downstream boundary condition is required at the downstream end of all reaches which are not connected to other reaches or storage areas. The downstream boundary condition can be specified as a stage-discharge rating curve. This can be expressed mathematically as: ାଵ
ܳே
ାଵ
− (ܳ + ܳ + ܳ)ே
= 0 ---------------------------- (3.65)
If the downstream boundary condition was denoting as, BN then: డಿ
డொಿ
= 1 -------------------------------------------------------- (3.66)
48
Chapter Four
Basic Data Requirements Chapter Four
Basic Data Requirements The data used in this research are classified as: geometric data, and hydraulic data.
4.1 Geometric data The basic geometric data include establishing the connectivity of the river system (River network); cross sections; reach lengths, and hydraulic structures such as bridges piers. 4.1.1 The River system schematic The river schematic allows to: 1) Define river network and reference cross-sections and control structures to the river; and 2) Graphically obtains an overview of model information in the current simulation. The river system schematic should be developed before any other data can be entered. The river centerline of the study area contains x- and ycoordinate data in a 2-D plane so as to spatially connect the unsteady flow models to the corresponding terrain models. The software (HEC-RAS) will automatically look for a companion file to the image, called a world file. This file contains information about the image, including the coordinate system and the extents of the image. Figure (4.1) illustrate Euphrates River system schematic in the study area. 4.1.2 Cross-section geometry After the river system schematic is completed, the next step is to obtain the cross-sections data. The cross-sections data represent the geometric boundary of the river. Cross-sections are located at relatively short intervals 49
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Figure (4.1) Euphrates River system schematic in the study area
along the river to characterize the flow carrying capacity of the river and its adjacent floodplain. Cross-sections are required at representative locations throughout a river reach and at locations where changes occur in a discharge, slope, shape, or roughness, at locations where levees begin or end, and at bridges or any other control structures. Boundary geometry for the analysis of flow in a natural river is specified in terms of ground surface profiles (cross-sections) and the measured distances between them (reach lengths). They should extend across the entire floodplain and should be perpendicular to the anticipated flow lines. Occasionally it is necessary to layout cross-sections in a curved or dog-leg alignment to meet this requirement, (HEC-RAS Hydraulic Reference Manual 2005). Where abrupt changes occur, several cross-sections should be used to describe the change regardless of the distance. Cross-section spacing is also a function of the river size, slope, and the uniformity of cross-section shape. In general, large uniform rivers of flat slope normally require a fewest 50
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number of cross sections per kilometer. For instance, navigation studies on a rivers may require closely spaced (e.g., 200 m) cross-sections to analyze the effect of local conditions on low flow depths, whereas cross-sections for sedimentation studies, to determine deposition in reservoirs, may be spaced at intervals on the order of kilometers, (Lancaster 1998). Each cross-section in a numerical model data set is identified by a River, Reach, and River Station label. The cross-section is described by entering the station and elevation (X-Y data) from left to right, with respect to looking in the downstream direction. The River Station identifier may correspond to stationing along the channel, kilometer points, or any fictitious numbering system. The numbering system must be consistent, in that the program assumes that higher numbers are upstream and lower numbers are downstream. Each data point in the cross-section is given a station number corresponding to the horizontal distance from a starting point on the left. Up to 500 data points may be used to describe each crosssection. Stationing must be entered from left to right in increasing order. However, more than one point can have the same stationing value. The left and right bank stations which separating the main channel from the overbank areas must be specified on the cross-section data editor. Other data that are required for each cross section consist of: downstream reach lengths; roughness coefficients; and contraction and expansion coefficients. These data will be discussed in detail later in this chapter. In this study, (197) cross-sections were surveyed along the Euphrates River between Hit city and Haditha Dam along (124.4 Km) river reach distance. The distance between the cross-sections ranged from (150 m) to (1 Km). These distance depended on the nature of every reach along the river. The distance between the cross-sections was decreased in river meandering and bends locations; and increased when the river is approximately straight. The Global Positioning System (GPS) device was used to locate position of each 51
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cross-section along river centerline. Table (A1) in Appendix (A) illustrates the positions of the cross-sections along Euphrates River in the study area. Theodolite, depth sounder, and GPS instruments were used by the surveying working team, figure (4.2). The surveying started at Hit gage station, and ended at Haditha Dam. Since the cross-section location and water surface elevation of the same location was detected, the depth of water was measured along the crosssection of the river perpendicular to the flow direction by using a digital depth sounder device shown in figure (4.3).
Figure (4.2) Surveying of the river banks
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Figure (4.3) Digital depth finder device Table (A2) in Appendix (A) shows the details of some of these crosssections along Euphrates River in the study area. The massive depth read-out of (24 m) allows the use of the sonar for an instant reading of the depth below so a reading every 15 m along river cross-section was taken, figure (4.4). The specification of the left bank and right bank of each cross section were obtained by using a theodolite device depending on an abrupt change (when occur) in the slope of the floodplain or the border of floodplain that if water exceed it, flood will take place and inundate farms and houses. Figure (4.5) shows a surveyed cross-section of the river in station No.(54) with bank stations.
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Figure (4.4) Depth of river surveying
67.00 66.00 65.00 64.00 63.00 62.00 61.00 60.00 59.00 58.00
surveyed cross-section
57.00 56.00 0.00
50.00
100.00
150.00
200.00
250.00
300.00
Figure (4.5) Surveyed river cross-section in station No. (54) 54
350.00
400.00
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Basic Data Requirements
The accuracy of simulation will increase when the numbers of crosssections along the river in the study area were increased so more crosssections were made with short distance in the meander regions of the river, but the highly cost and the security troubles in some parts of the study area cause to adopt such reach lengths between cross-sections. The river reach between Haditha Dam and Haqlaniyya city about (16 Km) long was not surveyed because of unavailable security license so a surveying which carried by the head office of Haditha dam in (2002) was adopted. The floodmap utility was limited to define the 3-D stream centerline and bank lines from the imported cross-section locations, as a straight line from cross-section to cross-section, as shown in figure (4.6). If the number of cross-sections is limited and the cross-sections do not account for every bend in the stream, then the stream centerline location with respect to the terrain model will be inaccurate. By increasing the number of cross-sections along the stream centerline, the straight line segments derived by the floodmap utility would get smaller and smaller, creating a more accurate depiction of curves in the stream for the model. More cross-sections were required, especially along curved sections of the stream centerline. To compensate for this, cross-sections between surveyed cross-section data were interpolated in the HEC-RAS model. The development of interpolated cross-sections between the surveyed cross-sections in HEC-RAS when defining the stream centerline and bank lines was an iterative process. If they did not match, then additional cross-sections were interpolated until the stream derived stream centerline overlapped the actual centerline, figure (4.7). Spacing between interpolated cross-sections was typically around 100 meters in stream centerline length, (HEC-GeoRAS 2000). Figure (4.8) shows the addition of the interpolated cross-sections to the surveyed cross-section data.
55
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Figure (4.6) River centerline with limited cross sections
Figure (4.7) Stream centerline after increasing cross-sections
56
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Figure (4.8) Cross-sections interpolated 4.1.3 Floodplain cross-section generation For this study, surveying data of the streambed cross-section was incorporated into the floodplain. The surveying operation of floodplain cross-sections along river in the study reach is not an easy task and required a large surveying team and long time. Hence aerial photogrammetry was used for this purpose. Analysis of aerial photography in form of digital elevation model was used to obtain the floodplain cross-sections. A digital elevation model (DEM) describes the height of an area, including all objects on the surface including vegetation and buildings. Compared with two-dimensional images like those offered by airphotographs and satellite pictures, digital elevation models have the advantage of representing the vertical extension of the earth's surface by 57
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giving height values for every pixel. Having information on the Z-value, a three-dimensional image and analysis of the surface is possible. Completely new possibilities for the production of digital elevation models arise when using radar systems. Due to the fact that radar systems actively send out signals (microwaves), they are independent of external source of radiation, unlike optical systems that depend on the radiation of the sun. This means that these signals can be recorded even at night, (Tate 1998). It is not possible to measure the three-dimensional position of point on the ground using only one radar image. Therefore, in analogy to optical stereoscopy, two images taken from different positions are combined. One possible technique to record two images is to simultaneously use one sending-receiving antenna and a second spatially separated antenna, this technique is called single pass interferometry, figure (4.9). The shuttle radar topography mission (SRTM) allows recording both images simultaneously using two antennas, (USGS 2008). In the present study a digital elevation model (SRTM_DEM) for the study area is acquired and a software program called (Global Mapper-10) was used to open it. The above software has a capability of identifying the height of any point and delineation of cross-section at any given location, but unfortunately the digital elevation model did not contain information about streambed elevations in a river channel. It considers the water surface as a ground surface. An image with extension of DEM for the study area was shown in figure (4.10).
58
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Figure (4.9) 3-D Mapping with interferometry (after USGS 2004) 59
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Figure (4.10) Digital elevation model for the study area Figure (4.11) demonstrate a cross-section No.(54) upstream Hit city generated by (DEM ) opened with Global-Mapper software. The surveyed cross-section data of the river bed was combined with the floodplain crosssection obtained from the (DEM) to produce the final cross-section in each river stations. Figure (4.12) demonstrate cross-section (54) which surveyed to Euphrates river incorporating with floodplain cross-section that obtained from (DEM) for the same location. It is observed that there is a difference between the surveyed cross-sections and floodplain cross-sections (DEM) data comes from the low accuracy of digital elevation model and the climatic, erosion, and deposition effects for the period between the time of capture of (DEM) data and the present time. So it is considered that the surveyed cross-section is the extraction data and it will integrate with digital elevation model data, figure (4.13). 60
61
Figure (4.12) Surveyed cross-section of Euphrates River superimposed to (DEM) data
Surveyed river channel cross-section
Flood plain cross-section from DEM
Figure (4.11) Digital elevation model cross-section data
Chapter Four Basic Data Requirements
Figure (4.13) Final combined cross-section
Chapter Four Basic Data Requirements
62
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4.1.4 Cross-Section Properties There are some properties of the cross-section that needs to restrict flow to the effective flow areas of this cross-section, these properties are: 1- Ineffective Flow Areas: Ineffective flow areas are often used to describe
portions of a cross-section in which water will pond, in which the velocity of that water, in the downstream direction, is close to zero. This water is included in the storage calculations and other wetted cross-section parameters, but it is not included as part of the active flow area. When using ineffective flow areas, no additional wetted perimeter is added to the active flow area. An example of an ineffective flow area is shown in figure (4.14). The cross-hatched area on the right of the plot represents what is considered to be the ineffective flow. Such area were found in the reach of the case study at cross-sections (6), (20), (33), (85), (116), (145), (163) and (172).
right ineffective flow station
Main river channel
Figure (4.14) Ineffective flow area in cross-section (6) 2- Levees: In some portion of the river reach a left and/or right levee and elevation was found. When levee are established, no water can 63
Chapter Four
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go to the left of the left levee station or to the right of the right levee station until either of the levee elevations are exceeded. Levee stations must be defined explicitly, or the program assumes that water can go anywhere within the cross-section. An example of a cross-section with a levee on the left side in case study is cross-section no. (144) as shown in figure (4.15). In this example the levee station and elevation are associated with an existing point on the cross-section. Occasionally an interpolation between any two certain cross-sections should be done and a levee should be defined in each bank of cross-section so that the model assumes no separation in a levee between two cross-sections permitting intromission of water to floodplain as shown in figure (4.16) and figure (4.17).
Left levee station
Figure (4.15) River cross-section with levee
64
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Main river channel
Figure (4.16) Interpolation between two adjacent cross-sections before correction
Main river channel
Figure (4.17) Levees limitation 65
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4.1.5 Reach length The measured distances between cross-sections are referred to as reach lengths. The reach lengths for the left overbank, right overbank and channel are specified on the cross-section data editor.
Channel reach
lengths are typically measured along the thalweg. Overbank reach lengths should be measured along the anticipated path of the center of mass of the overbank flow (HEC-RAS 2002). These three lengths will be of similar value when the river channel and the overbanks are straight as shown in figure (4.18). They will differ significantly when the river channel is meanders at its valley as shown in figure (4.19).
Lob Ch
Rob
Figure (4.18) Reach lengths between section (94) and (95)
66
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Figure (4.19) Reach lengths in meandering river
4.2 Hydraulic data Unsteady flow model require, at minimum two forms of hydraulic data: 1) energy loss coefficients, and 2) unsteady flow data. 4.2.1 Energy loss coefficients In this study, several types of loss coefficients are utilized by the numerical model to evaluate energy losses: (1) Manning coefficient values or equivalent roughness “k” values for friction loss, (2) contraction and expansion coefficients to evaluate transition (shock) losses, and bridge loss
67
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coefficients to evaluate losses related to weir shape, pier configuration, pressure flow, and entrance and exit conditions. 1-Manning coefficient: Selection of an appropriate value for Manning’s n is very significant to the accuracy of the computed water surface profiles. The value of Manning coefficient is highly variable and depends on a number of factors including: channel bed surface roughness; vegetation; channel irregularities; channel meandering; scour and deposition; obstructions; size and shape of the channel; stage and discharge; seasonal changes; temperature; and suspended material and bed load. In general, Manning coefficient values should be calibrated whenever observed water surface profile information (gauged data, as well as high water marks) is available. When gauged data are not available, values of Manning's n computed for similar stream conditions or values obtained from experimental data should be used as guides in selecting n values (Chow, 1959). There are several references a user can access that show Manning's n values for typical channels. Table (4.1) illustrate the Manning roughness coefficient for the most common types of channels. Although there are many factors that affect the selection of the Manning's (n) value for the channel, some of the most important factors are the type and size of materials that compose the bed and banks of a channel, and the shape of the channel. Cowan (1956) developed a procedure for estimating the effects of these factors to determine the value of Manning’s n of a channel.
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Table (4.1) Manning (n) values for different channels, after (Chow 1959) Type of Channel and Description
Minimum Normal Maximum
A. Natural Streams 1. Main Channels a. Clean, straight, full, no rifts or deep pools b. Same as above, but more stones and weeds c. Clean, winding, some pools and shoals d. Same as above, but some weeds and stones e. Same as above, lower stages, more ineffective slopes and sections f. Same as "d" but more stones g. Sluggish reaches, weedy. deep pools h. Very weedy reaches, deep pools, or floodways with heavy stands of timber and brush 2. Flood Plains a. Pasture no brush 1. Short grass 2. High grass b. Cultivated areas 1. No crop 2. Mature row crops 3. Mature field crops c. Brush 1. Scattered brush, heavy weeds 2. Light brush and trees, in winter 3. Light brush and trees, in summer 4. Medium to dense brush, in winter 5. Medium to dense brush, in summer d. Trees 1. Cleared land with tree stumps, no sprouts 2. Same as above, but heavy sprouts 3. Heavy stand of timber, few down trees, little undergrowth, flow below branches 4. Same as above, but with flow into branches 5. Dense willows, summer, straight 3. Mountain Streams, no vegetation in channel, banks usually steep, with trees and brush on banks submerged a. Bottom: gravels, cobbles, and few boulders b. Bottom: cobbles with large boulders 69
0.025 0.030 0.033 0.035 0.040
0.030 0.035 0.040 0.045 0.048
0.033 0.040 0.045 0.050 0.055
0.045 0.050 0.070
0.050 0.070 0.100
0.060 0.080 0.150
0.025 0.030
0.030 0.035
0.035 0.050
0.020 0.025 0.030
0.030 0.035 0.040
0.040 0.045 0.050
0.035 0.035 0.040 0.045 0.070
0.050 0.050 0.060 0.070 0.100
0.070 0.060 0.080 0.110 0.160
0.030 0.050 0.080
0.040 0.060 0.100
0.050 0.080 0.120
0.100 0.110
0.120 0.150
0.160 0.200
0.030 0.040
0.040 0.050
0.050 0.070
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Basic Data Requirements
In this study, the Manning coefficient values were assumed for each cross-section depending on the field investigations and previous study in this region of Euphrates River. Various range of Manning’s n values between (0.023 to 0.039) were used to calibrate a suitable value of Manning coefficient for river channel in study area, (Technopromexport 1978, Swiss consultants 1985a, AL-Eoubaidy and Salman 1997,AL-Eoubaidy 1999, Ayoub 1999, AL-Ani 2001, AL-Fahdawi 2002). When three values of Manning coefficient are sufficient to describe the channel and overbanks, the three n values will be entered directly onto the cross-section editor for each cross-section, figure (4.20). When three values are not enough to adequately describe the lateral roughness variation in the cross-section; in this case the horizontal variation of (n) value should be making to cross-section, figure (4.21-A, B). The values of Manning’s (n) used for floodplain are significant to vary between 0.05 to 0.1 according to the field investigations and previous studies, (Technopromexport 1978, Federal Highway Administration 1984, Swiss consultants 1985b).
LOB
Ch
ROB
Figure (4.20) Manning's (n) value for (ROB) and (LOB) and main channel 70
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LOB
Ch
ROB
Figure (4.21-A) horizontal variation of Manning's (n)
Figure (4.21-B) horizontal variation of Manning's (n)
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2- Contraction and Expansion Coefficients: The energy head loss (ℎ) between two cross-sections is comprised of
friction losses and contraction or expansion losses. Contraction or expansion of flow due to changes in the cross section is a common cause
of energy losses within a reach (between two adjacent cross-sections). Whenever this occurs, the loss is computed from the contraction and expansion coefficients specified on the cross-section data editor. The coefficients, which are applied between cross-sections, are specified as part of the data for the upstream cross-section. The coefficients are multiplied by the absolute difference in velocity heads between the current cross-section and the next cross-section downstream, which gives the energy loss caused by the transition. The equation for the energy head loss is as follows: మ
మ
∝ ∝ ℎ = ܵܮ̅ + ܥቚ మ మ − భ భ ቚ ------------------------- (4.1) ଶ
ଶ
Where: L = discharge weighted reach length, L, is calculated as: =ܮ
್ ொത್ା ொത ାೝ್ ொതೝ್ ொത್ାொത ାொതೝ್
ܮ, ܮ , ܮ = cross-section reach lengths specified for flow in the left
overbank, main channel, and right overbank respectively.
ܳത, ܳത , ܳത = arithmetic average of the flows between sections for the left overbank, main channel, and right overbank respectively. ܵ̅ = friction slope between two sections.
= ܥexpansion or contraction loss coefficient. ∝ = velocity coefficient.
Where the change in river cross section is small, and the flow is subcritical, coefficients of contraction and expansion are typically on the order of 0.1 and 0.3, respectively. When the change in effective cross-section area is abrupt such as at bridges, contraction and expansion coefficients of 0.3 and 0.5 are often used. Typical values for contraction and expansion 72
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coefficients, for subcritical flow, are shown in Table (4.2) below, (Hydrologic Engineering Center (RD-42), 1995). Table (4.2) Subcritical Flow Contraction and Expansion Coefficients (after Hydrologic engineering center RD-42, 1995) Contraction 0.0 0.1 0.3 0.6
No transition loss computed Gradual transitions Typical Bridge sections Abrupt transitions
expansion 0.0 0.3 0.5 0.8
In the case study, a concrete bridge was crossing the river between cross-sections (173 and 174), figure (4.22). The coefficients of expansion and contraction between any adjacent cross-sections were assumed to be 0.1 and 0.3 respectively for all of the study area except at the location of bridges; it was assumed to be 0.3 and 0.5 respectively upstream and downstream bridge cross-sections. Additional details about expansion and contraction coefficients were found in appendix (B).
Figure (4.22) Bridge on Euphrates River in study area 73
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4.2.2 Unsteady Flow Data Unsteady flow data are required in order to perform an unsteady flow analysis. Unsteady flow data consists of boundary conditions (external and internal), as well as initial conditions. 4.2.2.1 Boundary Conditions To solve the nonlinear partial differential equations presented by Saint-Venant, the upstream and downstream boundary conditions must be specified. Boundary conditions must be established at all of the open ends of the river system being modeled. Upstream ends of a river system can be modeled with the following types of boundary conditions: -flow hydrograph; -stage hydrograph; -flow and stage hydrograph. Downstream ends of the river system can be modeled with the following types of boundary conditions: -rating curve, -normal depth (Manning’s equation); -stage hydrograph; -flow hydrograph; -stage and flow hydrograph. Boundary conditions can also be established at internal locations within the river system. The following types of boundary conditions can be specify at the internal cross-sections: lateral inflow hydrograph; uniform lateral inflow hydrograph; groundwater interflow. 4.2.2.1.1 The upstream boundary condition The upstream boundary condition for the study reach is the hourly discharge hydrograph. The flood wave discharge caused by foundation failure is used for the inflow at the upstream end of study reach, downstream Haditha dam
74
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which is obtained from the scenarios of failure of Haditha dam. For more details about Haditha Dam analysis, see appendix (C). Regarding the hydraulic of the out flow wave, the actual cause of dam failure is of minor importance since the outflow wave is dependent upon: 1) The reservoir content at the moment of failure and the inflow volume. 2) The breach size and erosion velocity. Therefore, possible failure scenarios can be simplified to two cases: a) A failure where reservoir is at normal maximum operating level and reservoir inflow may be height but not excessive. These conditions occur for different foundation failures, enemy attack, earth quake, construction deficit or similar. They are including in the scenario called foundation failure. b) A failure where the reservoir rises to the crest or even above thus causing the overtopping of the dam. This can only occur if the reservoir inflow is extremely high and spillway and/or bottom outlets are blocked. The foundation failure caused by embankment failure is the most likely type of failure for Haditha dam. The development of a breach caused by a defect in the embankment is described hereafter with the phases 1 through 4, giving the sequence of events, possible time spans and breach geometry.
Phase 1: seepage By impounding the reservoir, a steady flow of water is created seeping through the embankment along the interface between embankment and foundation and through the foundation. Within the embankment, this flow would preferably pass through joints of the asphalt diaphragm. This flow of water will, on one hand, start to dissolve dolomites’ core material and thus enlarge the flow paths and, on the other hand, it will start at the downstream side to dislodge the firm soil particles. Since at this stage, the outflow is 75
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very small, the resulting seepage quantity is neglected in studying the flood waves. The duration of the process may be in the range of months or years. Therefore, this phase is not included in the simulation.
Phase 2: formation of pipes The flow tends to concentrate at various points within the zone where solution and erosion started, thus accelerating the destruction process. Distinct pipes will be formed. Such pipes will create local failure within the embankment material. This process is growing exponentially and may finally affect a 40 m wide dam section. The last part of this phase, giving effectively a countable amount of water outflow, is estimated to last 1 hour. It is simulated by opening a gate of 40 m in width and final height of 5 m. Five meters corresponding to approximately 10% of the dam height. By the time collapse occur (phase 3), a noticeable percentage of the dam material should have already been removed. The sum of openings in the weakened zone, therefore, is assumed to be 10% just prior to collapse. However, in the final phase the process is very quick. The purpose of the gate opening in one-hour is to create an exponentially increasing outflow in the phase immediately prior to collapse.
Phase 3: collapse The relatively large area of perforated embankment finally leads to a collapse of the embankment and the washout of a primary breach. This phase of collapse is simulated by superimposing two movements: first by closing all pipes with in the affected area and secondly by opening an initial breach reaching from the affected area to the dam crest. This phase is assumed to last half an hour. It is simulated in the mathematical model by closing the original gate 76
Chapter Four
Basic Data Requirements
and by simultaneously opening a trapezoidal gap down to elevation 100 m a.s.l. Phase 4: breach enlargement Once a first breach is open, the huge flow of water will rapidly enlarge the breach to its final shape, which will be limited at the bottom by the surrounding valley bottom elevation and to the sides by the powerhouse block and by the left valley side. The phase of breach enlargement is simulated by widening of the trapezoidal gap with decreasing speed due to backwater effects in to the breach during three and a half hours. In this scenario, it was assumed that almost the complete dam to the left of the powerhouse block will be eroded. The final breach has a bottom width of 420 m and side angle of 34° at the left valley side and a vertical delimitation at the powerhouse block. It is assumed that material is eroded down to an elevation of 100.0 m a.s.l. A sketch of this scenario is presented in figure (4.23). Within this scenario, the initial wave was calculated for the dam site and a flow hydrograph are given in figure (4.24), and selected values for the reservoir outflow are given in table (4.3). Peak out flow for the initial wave scenario occurs before the breach is completely formed indicating that the backwater effects are important. The reservoir level is lowered to 108 m a.s.l. within 32 hours.
77
Chapter Four
Basic Data Requirements
PHASE 1 : SEEPAGE 147
154
POWERBLOCK TIME : LONG DURATION
100
AREA: NEGLECTED IN COMPUTATION
75.9
PHASE 2 : INTERNAL EROSION, PIPING 147
154 SIMULATION BY OPENING A GATE :
100
110
TIME :
0:00
1:00
h
WIDTH:
40
40
m
HEIGHT:
0
5
m
PHASE 3 : COLLAPSE AND BREACH DEEPENING 147
154 SIMULATION BY CLOSING THE GATE AND OPENING AN INITIAL 100
BREACH SIMULTANEOUSLY:
PHASE 4 : BREACH ENLARGEMENT
TIME :
1:00
1:30
h
WIDTH:
40
40
m
HEIGHT:
5
0
m
(BREACH SEE BELOW)
154 100 TIME
:
1:00
1:30
2:00
3:30
5:00
h
TOP WIDTH
:
40
120
340
440
500
m
BOTTOM WIDTH:
40
40
300
400
420
m
SILL ELEVATION :
147
100
100
100
100
m a.s.l.
0
3760
15040
19740
AREA
:
21620 m 2
Figure (4.23) Dam break scenario for foundation failure (after Swiss consultant 1985c)
78
Chapter Four
Basic Data Requirements
Foundation Failuer Discharge Hydrograph 250000
Discharge (m3/s)
200000
150000
100000
50000
0 0
10
20
30
40
50
60
70
Hours after start of breach
Figure (4.24) Upstream discharge hydrograph (after Swiss consultant 1985)
Table (4.3) Reservoir outflow after Haditha dam failure (after Swiss consultant 1985) Hour Discharge x 1000 m3/s 0 2.1 0.5 3.7 1.0 5.2 1.5 98 2 208 2.2 209 2.5 208 3 205 3.5 203 4 198 4.5 193 5 187 6 168 8 139 10 115 12 93 18 41 24 17 79
Chapter Four
Basic Data Requirements
4.2.2.1.2 Downstream boundary condition The downstream boundary condition for the Euphrates river in this study is a single value rating curve at Hit city (124.4 (12 Km) downstream Haditha dam which is obtained from head office of Al-Ramadi Barrage, Fig Figure (4.25).
57.5 57.0 56.5 56.0
Stage (m)
55.5
y = 2.220ln(x) ln(x) +0.00015x+ + 40.26 R² = 0.908
55.0 54.5 54.0
Observed
53.5
Rating curve
53.0 52.5 52.0 0
200
400
600
800
1000
Discharge
1200
1400
1600
1800
(m3/s)
Figure (4.25)) Rating curve at Hit gauge station,, after head office of Al AlRamadi barrage (2008). 4.2.2.1.3 Internal boundary conditions condition It is the boundary conditions that found in the internal cross cross-sections of river except that at the upstream and downstream of river, such as tributary those diffuse in the river, groundwater inflow, evaporation, and using water for irrigation and municipalities’ use. us Whereas no permanent tributary or hydraulic structure such as dam or weir or gates are found along the Euphrates River in a reach of study so the internal boundary conditions
80
2000
Chapter Four
Basic Data Requirements
were estimated to be a uniform distributed discharge with 440 m3/s along the case study,(after ,(after ministry of irrigation 1992) 4.2.2.2 Initial Conditions In addition to boundary conditions, it is required to establish the initial conditions (flow and stage) at all nodes in the system at the beginning of the simulation. Initial conditions can be established in two different ways. The most common way is to enter flow data for each reach, and then have the program compute water surface elevations by performing a steady flow backwater analysis. A second method can only be done if a previous run was made. This method allows writing a file of flow and stage from a previous run, which can then be used as the initial conditions for a subsequent run. The initial condition for this reach study was a flow of 500 m3/s for each cross-section section in study area. Figure Fig (4.26)) shows the initial water surface elevation along the reach of study by use a steady flow of 500 m3/s.
Figure (4.26) (4. Initial water surface elevation 81
Chapter Five
Application, Results, and Discussion Chapter Five
Application, Results, and Discussion 5.1 Introduction The numerical model used in this research was calibrated by using previous data of flood happened in 1980. Simulation of this flood wave was used to select the sufficient value of Manning roughness coefficient for the Euphrates river reach in the study area. Verification of the numerical model was done by using observed data in this river reach between 1/5/2008 to30/6/2008. Six cases of simulation were applied to the Euphrates River reach under study. The results were obtained from the model, and discussion is based on these results.
5.2 Calibration of the numerical model for the Euphrates River system (reach under study) The objective of the calibration is to control the model by simulation of an observed flood, and for this reasons, the flood occurred in 1980 have been chosen because it is the nearest recorded flood happened in the river at study reach. The peak discharge in the study reach occurring in 1980 have been comparatively low due to the regulating effect of the upstream dams such as Keban Dam in Turkey and Tabaqa Dam in Syria. This limits the value of the calibration which should serve as a basis for extrapolation in case of the extreme event of the dam break flood. The main parameter to be calibrated is the roughness value according to the Manning-Strickler formula which was incorporated in the mathematical model. When judging the results of the calibration, the following facts should be considered:, (Swiss consultant 1985a, Khayyun 2006):
82
Chapter Five
Application, Results, and Discussion
1- There is no way to determine reliably the roughness value which could be valid for such extreme floods as a dam break wave. It is a common hypothesis to use extrapolation of the same value as obtained from the highest observed floods. However, the dam break floods exceed by far all historic observed values and will inundate areas which might be cultivated or inhabited having different hydraulic characteristics than the actual river courses. It is, therefore, conservative to assume higher flow resistance for this extreme type of floods than obtained from calibration. 2- Although results obtained from calibration are not directly applicable for dam break wave calculation, the calibration is necessary to show that at least for the known range of floods, the model may give reliable results. Only when historic basis is known, values applied in the extrapolation can be discussed and meaningful sensitivity test can be carried out. 3- Any model serves for certain purposes. In this case, calibration is carried out for extreme floods. 4- There is no possibility to obtain a 100% agreement between measured and observed values since: a) Each discharge measurement contains errors. b) Discharge and water level are only seldom measured at the same time. For most of the cases the discharge is derived from rating curves which frequently have a standard deviation of 20 cm to 40 cm c) River bed geometry changes with time. Even if the river regime is in equilibrium over the long range, erosion and aggradations occurs locally, changing the rating curves of the main hydrological stations which, therefore, are adapted annually.
83
Chapter Five
Application, Results, and Discussion
During calibration, it was tried to obtain a roughness value which is valid for a longer river reach and for a wide range of water levels. This more general value may lead locally to larger deviations between the observed and the calculated flood. However, it has the better chance to be valid for extrapolation than any adjustment realized for short reaches. For the Euphrates River in the case study, a Manning's coefficients of 0.023, 0.025, 0.028, 0.03, 0.033, 0.035, and 0.039 were used in previous studies. To calibrate a numerical model to get a suitable value of Manning coefficient the flood that occurred in 1980 was simulated. Daily discharge obtained from Ministry of water resources for Huseiba gauge station as shown in figure (5.1) which were used as the model inflow in Haditha site after reduction by 5% as a losses due to seepage, irrigation, and evaporation as adopted by Swiss consultant research. The records from Hit gauge station used as an observed data in the calibration process. Three values for Manning coefficient (0.028, 0.033, 0.039) were used here for the main river channel to obtain which one is the most suited for the calibration. A value of 0.05 was used for flood plain roughness for all cases of calibrations. Figure (5.2) shows a good convergence between the stages and discharges observed in Hit gauge station and those calculated by routing from Haditha using the numerical model. The influence of the irrigation demand and evaporation between Haditha city and Hit gauge station is small compared to the flood discharges but generally not negligible. For that reason a reduction in discharge of the Euphrates River has been included in the calibration. Figure (5.2) shows that Manning's value n=0.033 led to the best agreement between the calculated and observed data for the Euphrates river in the study area.
84
Chapter Five
Application, Results, and Discussion
85
Figure (5.2) Comparison between observed and calculated water surface elevation at Hit gage station
Chapter Five Application, Results, and Discussion
86
Chapter Five
Application, Results, and Discussion
5.3 Model verification Discharge obtained from the Ministry of Water Resources which were used as the model inflow are illustrated by daily value of Haditha dam discharge recorded between 1\5\2008 to 30\6\2008 as shown in table (5.1). The application of the numerical model with Manning roughness coefficient equal to 0.033 for river channel shows a good agreement between the stage of river observed in Hit gauge station and those calculated by using the numerical model, as shown in figure (5.3). Table (5.1) Flow discharges from Haditha Dam, (after Ministry of Water Resources, 2008) Date
Discharge
Date
Discharge
Date
Discharge
Date
Discharge
(day)
3
(m /s)
(day)
3
(m /s)
(day)
3
(m /s)
(day)
(m3/s)
1/5
358
17/5
490
1/6
350
17/6
450
2/5
474
18/5
480
2/6
350
18/6
450
3/5
500
19/5
500
3/6
390
19/6
450
4/5
375
20/5
500
4/6
358
20/6
488
5/5
350
21/5
515
5/6
350
21/6
500
6/5
343
22/5
500
6/6
425
22/6
500
7/5
350
23/5
505
7/6
425
23/6
500
8/5
350
24/5
500
8/6
425
24/6
500
9/5
365
25/5
500
9/6
425
25/6
500
10/5
350
26/5
500
10/6
450
26/6
500
11/5
323
27/5
374
11/6
450
27/6
500
12/5
350
28/5
371
12/6
450
28/6
500
13/5
350
29/5
350
13/6
470
29/6
500
14/5
350
30/5
388
14/6
470
30/6
540
15/5
350
31/5
350
15/6
450
16/5
350
16/6
450
87
Figure (5. 3) Observed and calculated stage of the Euphrates River at Hit gage station
Chapter Five Application, Results, and Discussion
88
Chapter Five
Application, Results, and Discussion
5.4 Application of the numerical model There are several cities, strategic project, and agricultural area along the Euphrates River in the study area. Information about the important cities must be known before predicting the propagation of flood wave downstream Haditha dam. Downstream Haditha dam is located at the upstream of the study reach, its elevation is about (103 m) above sea level and cross-section No. (198) passes through it. Haditha city is located (8.9 Km) downstream of Haditha dam and its elevation is about (116 m) above sea level. Cross-section No. (189) passes through this city. Haglaniyya city is (16 Km) downstream Haditha dam and its elevation is about (127 m) above sea level. Cross-section No. (178) passes through this city. Alus island is (24.2 Km) downstream Haditha dam and cross-section No. (166) passes through this town which is (95 m) above sea level. AL-Baghdadi city is located (59 km) downstream of Haditha dam and is (91 m) above sea level. Cross section No.(120) passes through this city. Doulab city is (73.8 km) downstream Haditha dam corresponds to cross section No.(98) and it is (76 m) above sea level. Zkhaikha village is located (97 km) downstream Haditha dam, cross-section No.(59) passes through it and its elevation is (73 m) above sea level. Finally, Hit city is located (124.4 km) downstream of Haditha dam and it is (67 m) above sea level. Cross section No.(1) passes through this city. Figures (5.4a-b) shows the locations of these cities along the river in the reach of study. 5.4.1 Maximum flow, maximum water surface elevation, and travel time The results of the numerical model are the maximum flow, the maximum water depth, the travel time of maximum flood wave between each crosssections. Six cases were used in this study to obtain the effect of the meandering along the Euphrates River in the study area on the discharge, elevation, and speed of travel of flood wave. 89
Chapter Five
Application, Results, and Discussion
Figure (5.4-a) Locations of major cities along Euphrates River in study area
90
Chapter Five D/S Haditha dam Haditha city
Haqlanyyah city
Alus Island
Baghdadi city
Dulab city
Zkhaikhah village
Hit town
Application, Results, and Discussion km 0 km 8.9
km 16
km 24.2
km 59
km 73.8
km 97
km 124.4
Figure (5.4-b) Locations of cross-sections along Euphrates River in study area 91
Chapter Five
Application, Results, and Discussion
The cases were divided to two parts A and B. In part A the effect of meandering will be neglected so that, the left and right over bank length between any two adjacent cross-sections will be the same as that length of the main river channel reach. Part A have a three cases A1, A2, and A3, the difference between these three cases are the values of Manning roughness coefficient of flood plain, the values of 0.05, 0.07, and 0.1 were used for flood plains in cases A1, A2, and A3 respectively. In part B the effect of meandering will be taken so that, the left over bank and right over bank length between any two adjacent cross-sections will differ from that of the river channel length in meandering region. Part B have a three cases B1, B2, and B3, the values of Manning roughness coefficient of flood plain in these cases are 0.05, 0.07, and 0.1 respectively. Table (5.2) shows summary of these cases. Table (5.2) Cases of the numerical model in study reach
A1
Part A Straight River Manning Coefficient for the Flood plain 0.05
A2 A3
Cases
B1
Part B Meandering River Manning Coefficient for the Flood plain 0.05
0.07
B2
0.07
0.1
B3
0.1
Cases
It was assumed that the initial conditions, boundary conditions, internal boundary conditions, and Manning roughness coefficient for the main river channel are the same for all the cases. Under these assumptions the numerical model was run for routing the flood wave through these six cases.
92
Chapter Five
Application, Results, and Discussion
5.4.1.1 Discharges Peak discharges for selected locations along the Euphrates river downstream Haditha dam in the study reach for the various cases are given in Table (5.3). The time lag between start of failure and arrival of the maximum discharge is recapitulated in Table (5.4). Figures (5.5, 5.6, 5.7, 5.8, 5.9, 5.10, and 5.11) show the peak flows and travel time of the flood wave for a selective locations in the study area for the various cases. Maximum discharges along the river in study reach for various cases can be shown in Figure (5.12). 5.4.1.2 Water levels The maximum wave height is defined as the difference between maximum water level and initial water level. Initial water level on its side is defined as the water level of a constant discharge of Q=500 m3/s which corresponding to the discharge from dam prior to the dam failure. Tables (5.5), (5.6) show the maximum water levels and maximum wave height along the river in the study area for selective locations. The maximum flood wave height for case A1 can be observed in the longitudinal profiles shown in figure (5.13). By analyzing the longitudinal profile of water level, local breaks in the slope of the maximum water level can be observed. They correspond to contraction of the valley where flow is accelerated causing backwater effects upstream and a sudden drop in the water level at the narrow cross-section; therefore, the wave height does not continuously decrease in the downstream direction. The average slope of maximum water level between Haditha Dam and Hit city is 0.00043 for case A1 and it is 0.00041 for case B1. The slope of the maximum water level at a singular places may differ from the above average due to local narrowing or enlargements of the river valley.
93
Chapter Five
Application, Results, and Discussion
Table (5.3) Peak discharge after dam failure for various cases
Location
Distance from Haditha dam (Km)
A1
A2
A3
B1
B2
B3
0.0
208
208
208
208
208
208
Downstream Haditha dam Haditha city Haqlaniyya city Alus island Baghdadi city Dulab city Zkhaikha village Hit city
(Case) Peak discharge in 1000 m3/s
8.9
183.85 181.95 181.75 188.34 186.69 184.92
16
180.95 178.45 178.02 186.59 184.62 182.36
24.2
178.16 174.38 173.54 184.69 181.56 177.73
59
149.88 142.69 136.51 164.12 160.27 150.51
73.8
143.08 135.08 127.74 156.12 151.95 141.49
97
132.40 123.40 114.72 146.37 140.28 129.75
124.4
121.04 111.43 100.96 134.76 126.66 116.21
Table (5.4) Time lag between start of failure and arrival of peak discharge
Location
Distance from Haditha dam (Km)
(Case) Lag time ∆t (h : min) A1
A2
A3
B1
B2
B3
Downstream Haditha dam Haditha city
0.0
02:00 02:00 02:00 02:00 02:00 02:00
8.9
04:35 04:40 04:40 04:25 04:30 04:35
Haqlaniyya city
16
05:10 05:15 05:10 04:50 04:55 05:00
Alus island AL-Baghdadi city Dulab city
24.2
05:35 05:35 05:30 05:05 05:10 05:20
59
08:45 09:10 09:35 07:25 07:35 08:10
73.8
09:50 10:30 11:00 08:20 08:40 09:20
Zkhaikha village
97
12:25 13:35 14:25 10:25 11:25 12:10
Hit city
124.4
14:45 16:50 19:15 12:10 13:40 15.45 94
Chapter Five
Application, Results, and Discussion
Figure (5.5) The peak flow and travel time of flood wave for section No. 189
Figure (5.6) The peak flow and travel time of flood wave for section No. 178 95
Chapter Five
Application, Results, and Discussion
Figure (5.7) The peak flow and travel time of flood wave for section No. 166
Figure (5.8) The peak flow and travel time of flood wave for section No. 120 96
Chapter Five
Application, Results, and Discussion
Figure (5.9) The peak flow and travel time of flood wave for section No. 98
Figure (5.10) The peak flow and travel time of flood wave for section No. 59
97
Figure (5.11) The peak flow and travel time of flood wave for section No. 1
Chapter Five Application, Results, and Discussion
98
Figure (5. 12) Maximum discharge along the river for various cases
Chapter Five Application, Results, and Discussion
99
Chapter Five
Application, Results, and Discussion Table (5.5) Maximum water level (Case) Max. flood wave elevation (m a.s.l.)
Distance from Location
Haditha dam
Elevation (m a.s.l.)
A1
A2
A3
B1
B2
B3
(Km) Downstream Haditha dam
0.0
154
130.09
132.28
134.74
128.92
131.33
133.59
Haditha city
8.9
116
130.97
132.00
133.24
130.3
131.29
132.21
Haqlaniyya city
16
127
125.08
126.02
127.23
124.59
125.53
126.51
Alus island
24.2
95
118.88
120.66
122.60
118.23
120.31
121.84
Baghdadi city
59
91
104.68
105.70
106.90
105.32
106.56
107.64
Dulab city
73.8
76
96.73
98.29
99.87
97.43
98.32
100.31
Zkhaikha village
97
73
87.01
88.04
88.96
87.27
88.54
89.51
Hit city
124.4
67
76.62
77.26
78.03
77.59
78.28
79.11
Table (5.6) Maximum wave height
Location
Downstream Haditha dam Haditha city
Distance from Haditha dam (Km)
(Case) Maximum flood wave height (m) A1
A2
A3
B1
B2
B3
0.0
28.43 30.62 33.08
27.26
29.67
31.93
8.9
34.81 35.84 37.08
34.14
35.13
36.05
Haqlaniyya city
16
32.74 33.68 34.89
32.25
33.19
34.17
Alus island AL-Baghdadi city Dulab city
24.2
31.27 33.05 34.99
30.62
32.7
34.23
59
29.91 30.93 32.13
30.55
31.79
32.87
73.8
26.88 28.44 30.02
27.58
28.47
30.46
Zkhaikha village
97
25.2
25.46
26.73
27.7
Hit city
124.4
23.46
24.33
24.98
26.23 27.15
22.49 23.13
100
23.9
Chapter Five
Application, Results, and Discussion
140 130 Minimum river bed elevation 120
Maximum wave height
Elevation (m)
110 100 90 80 70 60 50 40 0
10
20
30
40
50
60
70
80
90
100
110
120
Main channel distance (Km) Figure (5.13) Maximum flood wave height for case A1 along study area Table (5.7) gives the time lag between start of failure and occurrence of maximum water level. Owing to the decreasing slope upstream of the wave front, maximum water level never occurs at the same time as maximum discharge as seen when comparing table (5.7) with table (5.4). At certain locations such as downstream Haditha Dam and Haditha city, the time of peak water level at the downstream side of the dam may be delayed compared to Haditha city caused by the influences of backwater due to the narrowing of the river valley and existence of the concrete bridge with its abutments and embankments downstream Haditha city.
101
Chapter Five
Application, Results, and Discussion
Table (5.7) Time lag between start of failure and occurrence of maximum water level
Location
Distance from Haditha dam (Km)
(Case) Lag time ∆t (h : min) A1
A2
A3
B1
B2
B3
Downstream Haditha dam
0.0
05:45 05:55 05:40 05:35 05:30 05:25
Haditha city
8.9
05:20 05:30 05:30 05:00 05:05 05:20
Haqlaniyya city
16
05:40 05:55 06:10 05:15 05:30 05:55
Alus island
24.2
06:55 07:25 07:40 05:55 06:15 07:05
AL-Baghdadi city
59
09:25 10:20 11:15 08:00 08:30 09:30
Dulab city
73.8
11:30 12:25 13:30 09:40 10:25 11:10
Zkhaikha village
97
13:30 15:05 16:35 11:25 12:15 13:40
Hit city
124.4
18:00 19:25 21:00 15:40 16:30 17:10
5.4.1.3 Wave propagation Time of flooding was defined when discharge exceeds 6000 m3/s, since the 1969 flood with its peak of about 6000 m3/s caused already serious damages along the Euphrates valley. Table (5.8) below gives the arrival time of flood discharges for selected downstream locations for various cases. Propagation of the front wave is in average (4.365) m/s, (4.154) m/s, (3.926) m/s, (5.196) m/s, (4.855) m/s, and (4.659) m/s for cases A1, A2, A3, B1, B2, and B3 respectively. It is strongly influenced by roughness assumptions. The celerity of front wave is not identical with the flow velocities. The flow velocity is varying considerably with cross-section geometry, downstream slope and roughness of river valley, and time. Flow velocities founded varying widely from (0.21) m/s to (10.81) m/s. 102
Chapter Five
Application, Results, and Discussion
Table (5.8) Time of flooding after start of failure
Location
Distance from Haditha dam (Km)
(Case) Time of flooding (h : min) A1
A2
A3
B1
B2
B3
Haditha dam
0.0
00:40 00:40 00:40 00:40 00:40 00:40
Haditha city
8.9
01:16 01:16 01:18 01:15 01:15 01:15
Haqlaniyya city
16
01:34 01:35 01:37 01:33 01:33 01:34
Alus island
24.2
01:56 02:02 01:59 01:54 01:55 01:57
AL-Baghdadi city
59
03:48 03:51 03:57 03:22 03:27 03:31
Dulab city
73.8
04:40 04:47 05:05 04:09 04:20 04:27
Zkhaikha village
97
06:29 06:45 07:09 05:34 05:59 06:10
Hit city
124.4
08:35 08:59 09:28 07:19 07:47 08:05
5.5 Effect of meandering on the flood routing in the study area The pervious selected parts for different cases of meandering and straight river and for various Manning roughness coefficients were used to run the numerical model to obtain the downstream discharges, water surface elevations, and the time of arrival of flood wave through the dam break flood routing. Comparison of a maximum flood wave height, peak flow, and arrival time of maximum height and discharge of flood wave between a straight and meandering river were shown in figures (5.14), (5.15), (5.16), (5.17), (5.18), and (5.19) for selective locations along the Euphrates river in the study area. Figures (5.20), (5.21), and (5.22) illustrate a comparison between a maximum flood wave height along the longitudinal profile of the study area for both straight and meandering river for the flood plain Manning roughness coefficient values of 0.05, 0.07, and 0.1 respectively. 103
Chapter Five
Application, Results, and Discussion
Figure (5.14) Comparison of a peak flow and arrival time of flood wave between cases A1 and B1: a) At section No. 189
b) At section No. 178
c) At section No. 166 104
Chapter Five
Application, Results, and Discussion
d) At section No. 120
e) At section No. 98 105
Chapter Five
Application, Results, and Discussion
f) At section No. 59
g) At section No. 1 106
Chapter Five
Application, Results, and Discussion
Figure (5.15) Comparison of a peak flow and arrival time of flood wave between cases A2 and B2: a) at section No. 189
b) At section No. 178
c) At section No. 166 107
Chapter Five
Application, Results, and Discussion
d) At section No. 120
e) At section No. 98 108
Chapter Five
Application, Results, and Discussion
f) At section No. 59
g) At section No. 1 109
Chapter Five
Application, Results, and Discussion
Figure (5.16) Comparison of a peak flow and arrival time of flood wave between cases A3 and B3: A) at section No. 189
b) At section No. 178
c) At section No. 166 110
Chapter Five
Application, Results, and Discussion
d) At section No. 120
e) At section No. 98 111
Chapter Five
Application, Results, and Discussion
f) At section No. 59
g) At section No. 1 112
Chapter Five
Application, Results, and Discussion
Figure (5.17) Comparison of a water surface level of flood wave and its arrival time between cases A1 and B1: a) at section No. 189
b) at section No. 178
c)
at section No. 166 113
Chapter Five
Application, Results, and Discussion
d) at section No. 120
e)
at section No. 98
114
Chapter Five
f)
Application, Results, and Discussion
at section No. 59
g) at section No. 1
115
Chapter Five
Application, Results, and Discussion
Figure (5.18) Comparison of a water surface level of flood wave and its arrival time between cases A2 and B2: a) at section No. 189
b) at section No. 178
c) at section No. 166 116
Chapter Five
Application, Results, and Discussion
d) at section No. 120
e) at section No. 98
117
Chapter Five
Application, Results, and Discussion
f) at section No. 59
g) at section No. 1 118
Chapter Five
Application, Results, and Discussion
Figure (5.19) Comparison of a water surface level of flood wave and its arrival time between cases A3 and B3: a) at section No. 189
b) at section No. 178
c) at section No. 166 119
Chapter Five
Application, Results, and Discussion
d) at section No. 120
e) at section No. 98 120
Chapter Five
Application, Results, and Discussion
f) at section No. 59
g) at section No. 1 121
Chapter Five
Application, Results, and Discussion
Figure (5.20) Comparison of flood wave height along the Euphrates River in study area between cases A1 and B1
Figure (5.21) Comparison of flood wave height along the Euphrates River in study area between cases A2 and B2
Figure (5.22) Comparison of flood wave height along the Euphrates River in study area between cases A3 and B3 122
Chapter Five
Application, Results, and Discussion
The maximum top width of the inundation area along the Euphrates River in the study area was estimated in figures (5.23) and (5.24) for cases A3 and B3 respectively. It is clearly seen in figures and tables that the peak flow increase by 11.2 % over the 124.4 km between Haditha dam and the town of Hit under effect of meandering between case A1 and case B1. The meandering of river was increased the peak flow of the flood wave at Hit city in case B2 by 13.6 % over the peak flow of case A2, and it was increased the peak flow of case B3 by 15.1 % over the peak flow of case A3. The time lag between start of failure and arrival of the maximum discharge in Hit town occurs after start of dam failure with about (14:45) hours for case A1 and (12:10) hours for case B1, this means that the meandering of the river was reduced the time lag the peak discharge to Hit town (2:35) hours between case A1 and B1when the Manning roughness coefficient of the flood plain equal to 0.05. The lag time of the peak discharge that arrival to Hit town after failure of Haditha Dam for cases A2 and B2 are 16:50, 13:40 hours after the beginning of dam failure. This is means that the meandering of the river was reduced the time lag of the peak discharge to Hit town with about (3:10) hours between case A2 and B2 when the Manning roughness coefficient of the flood plain equal to 0.07. The arrival time of peak discharge to Hit town after beginning of Haditha dam failure are
19:15 and 15:45 hours
respectively. This is means that the meandering of the river was reduced the arrival time of the peak discharge to Hit town with about (3:30) hours between case A3 and B3 which it have a Manning coefficient equal to 0.1. Maximum water levels always occur delayed to the peak discharges as may be seen from tables (5.4), (5.7) and figures from (5.5) to (5.11).
123
Figure (5. 23) Maximum top width of inundation area along the Euphrates River in study area for case No. A3
Chapter Five Application, Results, and Discussion
124
Chapter Five
Application, Results, and Discussion
Main river channel Flooded area
Figure (5.24) Maximum top width of inundation area along the Euphrates River in the study area for case No. B3 125
Chapter Five
Application, Results, and Discussion
For case A1 the peak water level in Haditha city is reached about 05:20 hours after start of the dam failure and 25 minute before the corresponding peak water level at the downstream of Haditha Dam due to the effect of backwater and narrowing of the river valley. This is 45 minutes after corresponding the moment of peak discharge. The peak water level in Hit city is reached with 18:00 hours after start of the Dam failure or 3:15 hours after the moment of peak discharge. For case B1 the lag time of peak water level in Haditha city is 05:00 hours after start of the dam failure and 35 minute before occurrences of peak water level at the downstream of Haditha Dam, this delay is due to the effect of backwater and narrowing of the river valley. The peak water level at Haditha city is 35 minutes after moment of peak discharge. The peak water level in Hit city is reached with 15:40 hours after start of the Dam failure or 3:30 hours after the moment of peak discharge. When comparing between case A1 with case B1, it is shown that the maximum flood wave elevation in Hit city for case B1 is higher than that in case A1 with 0.97 m, and its time of arrival is lesser with 2:20 hours. When comparing between cases A2 with B2, and A3 with B3 it is shown that the maximum flood wave elevation in Hit city for cases B2, and B3 are higher than that in cases A2, and A3 with 1.02 m, and 1.08 m respectively, and its time of arrival is lesser with (2:55), and (3:50) hours respectively. It is clearly seen that the time of peak water elevation is much more affected by roughness than the elevation itself because of that the flow hydrograph is nearly flat after the first steep rise and often influenced by the downstream backwater effects. The following parameters can be used to express the relationship between the different cases of the flood wave in this study. a) Roughness ratio (nr): The ratio of Manning roughness coefficient of flood plain to the main river channel Manning roughness coefficient. b) Discharge reduction (Dr): Percent reduction in peak discharge of the flood wave between downstream Haditha Dam and Hit city: 126
Chapter Five ܦ =
Application, Results, and Discussion
ܲ݁ܽ݇ ݀݅ܿݏℎܽݐ݅݀ܽܪݐܽ݁݃ݎℎܽ ݉ܽܦ− ܲ݁ܽ݇ ݀݅ܿݏℎܽݕݐ݅ܿݐ݅ܪݐܽ݁݃ݎ ܲ݁ܽ݇ ݀݅ܿݏℎܽݐ݅݀ܽܪݐܽ݁݃ݎℎܽ ݉ܽܦ
c) Stage reduction (Sr): Percent reduction in peak height of the flood wave between downstream Haditha Dam and Hit city: ܵ =
ܲ݁ܽ݇ ݁ݒܽݓℎ݁݅݃ℎݐ݅݀ܽܪݐܽݐℎܽ ݉ܽܦ− ܲ݁ܽ݇ ݁ݒܽݓℎ݁݅݃ℎݕݐ݅ܿݐ݅ܪݐܽݐ ܲ݁ܽ݇ ݁ݒܽݓℎ݁݅݃ℎݐ݅݀ܽܪݐܽݐℎܽ ݉ܽܦ
d) Time lag of peak discharge (TLd): Difference in time between the peak flows of flood wave computed D/S Haditha Dam and the peak flood wave flow at Hit city. e) Time lag of peak level (TLL): Difference in time between the peak level of flood wave computed D/S Haditha Dam and the peak flood wave level at Hit city. The computed parameters for the results of the different cases of the numerical model were shown in table (5.9). These parameters are summarized graphically in figures (5.25) through (5.28).
nr
Dr
Sr
TLD (hours)
TLL (hours)
Straight river
A1
1.51
0.418
0.2089
12:45
12:15
A2
2.12
0.464
0.244
14:50
13:30
A3
3.03
0.514
0.277
19:10
15:20
Meandering river
Table (5.9) Computed parameters for different cases of routing Cases
B1
1.51
0.352
0.139
10:10
10:05
B2
2.12
0.391
0.1799
11:40
11:00
B3
3.03
0.441
0.2176
13:45
11:45
127
Chapter Five
Application, Results, and Discussion
Time lag of peak dischage (TLD) (hour)
25
A3
20
A2
15
A1
B3
B2
B1 10
Straight river Meandering river
5
0 1
1.5
2
2.5
3
3.5
Manning roughness ratio (nr)
Figure (5.25) The relationship between Manning roughness ratio and time lag of peak discharge
Time lag of peak level (TLL) (hours)
20
A3 15
A2 A1 B3 B2
10
Straight river Meandering river
B1
5 1
1.5
2
2.5
3
Manning roughness ratio (nr)
Figure (5.26) The relationship between Manning roughness ratio and time lag of peak level 128
3.5
Chapter Five
Application, Results, and Discussion
Discharge reduction % (Dr)
60
A3 50 A2 A1
B3
40 Straight river
B2
Meandering river B1 30 1
1.5
2
2.5
3
3.5
Manning roughness ratio (nr)
Figure (5.27) The relationship between Manning roughness ratio and discharge reduction 30 A3
A2
Stage reduction % (Sr)
25
A1 B3
20
Straight river Meandering river
B2 15 B1
10 1
1.5
2
2.5
Manning roughness ratio (nr)
3
Figure (5.28) The relationship between Manning roughness ratio and stage reduction 129
3.5
Chapter Five
Application, Results, and Discussion
It can be seen from the figures between (5.25) through (5.28) that the dimensionless parameters discharge reduction (Dr) and stage reduction (Sr), and the parameters time lag of peak discharge (TLD) and time lag of peak level (TLL) are all increase with increasing of the dimensionless parameter roughness ratio (nr). There was a little difference in a stage reduction (Sr) compared with a discharge reduction (Dr) due to a small variation in hydrograph stage level with discharge in a high flood events.
5.6 Two-dimensional model The one-dimensional numerical model that used in this study was tested by using the two-dimensional numerical model over a small meandering reach selected from the study area and comparing the result with this in one-dimensional model. The two-dimensional flood modeling cannot be applied for all the river reach under study because of the lack of the information required. Hence the two-dimensional model was applied for a small part of the reach of the river, where the required information is available. The two-dimensional model software (RMA-2) was used to calculate the velocity in two directions, water surface elevations, and discharges along the small meandering part of the study area between crosssections No. (10) and (54), 14.1 km long as shown in figure (5.29). 5.6.1 Description of the two dimensional numerical model The two-dimensional depth averaged numerical model (RMA-2) under Surface Water Modeling System software (SMS) is a finite element hydrodynamic numerical model. It computes the water surface elevations and the horizontal velocity components for sub-critical free surface flow in a twodimensional flow fields. The original RMA2 model was developed by Norton, et.al, (1973). This software has been applied to calculate water levels and flow distribution around islands; flow at bridges having one or more relief openings; in 130
Chapter Five
Application, Results, and Discussion
Figure (5.29) Selected meander river reach in the study area
131
Chapter Five
Application, Results, and Discussion
contracting and expanding reaches; into and out of off-channel hydropower plants; at river junctions; and at river bending, etc. This software is a general purpose model designed for far –field problems in which vertical acceleration are negligible and velocity vectors point in the same direction over the entire depth of the water column at any instant of time. It expects a vertically homogenous fluid with a free surface. (SMS8.1 2003). The capability of RMA2 model may be listed as: 1 Simulate wetting and drying events. 2 Applying wind stress involving frontal passages. 3 Model up to 5 different types of flow control structures. 4 Accepts a wide variety of boundary conditions. The physical laws which govern the flow of water in a river are the principle of conservation of Mass (continuity) and the principle of conservation of Momentum. These equations are solved by the finite element method using the Galerkin Method of Weighted residuals. RMA2 is capable of supporting different types of quadratic basis elements within the same computational finite element mesh. The types of elements fit into three categories: onedimensional, two dimensional and special elements as shown in figure (5.30). The SMS (Surface Water Modeling System) software is a comprehensive environment for one, two and three dimensional models. A pre- and postprocessor for surface water modeling and design, SMS includes different numerical techniques as modeling tools. SMS is a powerful graphical tool for creation and visualization of results. Model can built using digital maps and elevation models for reference and source data. RMA2 model may be used to compute variety of information applicable to surface water modeling.
132
Chapter Five
Application, Results, and Discussion
Figure (5.30) The available types of elements in SMS software The required data in the RMA2 model are: 1. The topographical map or maps, digital elevation model map (if possible) of the study area, including all the existing hydraulic structures within the area and the location of the existing inlets and outlets. 2. The discharges and stages (according to the type of the boundary conditions) of inflow and out flow at the same recording time. 3. The wind speed, the bed materials, water temperature and the water density may be considered in the RMA2 models if the required data are available. 4. The values of roughness and turbulence coefficients. The last one may be evaluated from the one of the different methods within the software when the eddy viscosity is known. This model contains the following input data: 133
Chapter Five
Application, Results, and Discussion
1. The flow hydrograph or inflow discharge of water in cross-section (54), this can be obtained from an operation of one-dimensional model and uses the resultant of flow in this cross-section as an upstream boundary condition in two-dimensional model. A flow hydrograph used as upstream boundary condition in section (54) can show in figure (5.31). 2.
Rating curve at cross section No. 10, it is also obtained from the operation of one dimensional model and used as a downstream boundary condition in two-dimensional model. A rating curve used in section (10) can be shown in figure (5.32)
3. Forty-four cross-sections were surveyed for the river in study reach with distance about 150 m to 300 m between them. 4. Import the floodplain elevations for both left and right over bank along the study reach from the digital elevation model map. Figure (5.33) shows the river channel with floodplains of study area. 5. Manning roughness coefficient will take equal to 0.033 for river channel and 0.05 for both floodplains. The mesh of finite elements were made to study reach; the mesh was concentrate beside the banks of river to increase the accurate of flood routing as shown in figure (5.34). The result of discharge hydrograph from two-dimensional model at section No. 10 shows a good uniformity with those obtained from case B1 in one dimensional model for the same location as shown in figure (5.35). Figure (5.36) shows the velocity distribution in two-dimensional model, it clearly shown that the direction of velocity over a flood plain is making a short-cut along the meandering area but with magnitude less than this in the main river channel.
134
Chapter Five
Application, Results, and Discussion
160000 140000
Discharge (cms)
120000 100000 80000 Flow hydrograph 60000 40000 20000 0 12:00 AM
12:00 PM
12:00 AM
12:00 PM
12:00 AM
12:00 PM
Time (hr)
Figure (5.31) Flow hydrograph at upstream study reach 85 80
Stage (m) a.s.l
75 70 65 60 55 50 0
20000
40000
60000
80000
100000
120000
140000
Discharge (cms)
Figure (5.32) Rating curve at downstream study reach
135
160000
Chapter Five
Application, Results, and Discussion
Figure (5.33) River and floodplain elevations in study reach
Figure (5.34) Finite element mesh over all study reaches
136
Chapter Five
Application, Results, and Discussion
160000 140000
Discharge (cms)
120000 100000 Flow hydfrograph from one-dimensional model 80000
Flow hydrograph from Two-dimensional model
60000 40000 20000 0 12:00:00 AM
12:00:00 PM
12:00:00 AM
12:00:00 PM
12:00:00 AM
12:00:00 PM
Time (hr)
Figure (5.35) Discharge hydrograph at downstream of study reach for both one and two-dimensional model
Figure (5.36) Velocity distributions over study reach 137
Chapter Six
Conclusions and Recommendations CHAPTER SIX
Conclusions and Recommendations 6.1 Conclusions From the information that collected during this study, and from the analysis of results, the following conclusions are extracted: 1.
The results of the flood wave height, discharge, and time of arrival for various cases shows that the presence of meandering in river leading to increase flood wave height and discharge, and decrease the time of arrival along the river.
2.
It was found that the maximum flood wave elevation in Hit city for cases B1, B2, and B3 is higher than that in cases A1, A2, and A3 with 0.97 m, 1.02 m, 1.08 m respectively, and its time of arrival is lesser with (2:20 hours), (2:55 hours), and (3:50 hours) respectively.
3.
The peak flow of the flood wave was increased by 11.2%, 13.6%, and 15.1% when the meandering of the Euphrates river in the study area was taken in the cases B1, B2, B3 and neglected in cases A1, A2, A3 respectively.
4.
The meandering in river in cases B1, B2, and B3 had reduced the time lag between start of failure and arrival of maximum discharge to Hit city by 2:35 hours, 3:10 hours, and 3:30 hours lesser than for cases A1, A2, and A3 where the effect of meandering in river was neglected.
5.
Time of flooding after start of Haditha dam failure for a major cities along the Euphrates river in study area shows that there is a little difference between cases dealing with meandering in river and that 138
Chapter Six
Conclusions and Recommendations
neglect meandering in river in the cities that locate upstream study area such as Haditha city and Alus island, but the differences between them become more visible in Baghdadi city, Dulab city, Zkhaikhah village, and Hit city. 6.
The dimensionless parameters, discharge reduction (Dr) and stage reduction (Sr) were increased when the Manning roughness ratio increase.
7.
The parameters, time lag of peak discharge (TLD) and time lag of peak level (TLL) were increased when the dimensionless parameter manning roughness ratio (nr) was increased.
8.
The most critical flooded areas were descending with Haditha, Alus, Baghdadi, Duolab, Zkhaikhah, and Hit cities respectively. The computed depth showed no dangerous situations for center of Haqlanyyah city.
9.
A good agreement between one-dimensional model and two-dimensional model in peak flows and travel time on a part of study area has been shown.
6.2 Recommendations The following recommendations are suggested for future studies: 1.
For more accurate of analysis of flood wave, modification of HEC-RAS numerical model to deal with movable bed of river is required.
2.
More accurate digital elevation model (DEM) for study area must be provided to increase the accuracy of flood plain simulation.
3.
Because of the effect of meandering in rivers on the peak discharge, maximum water surface elevation, and arrival time of flood wave, reevaluation of flood warning system must be achieved for various dams in Iraq. 139
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Department,
The
University of Texas at Austin. 53. Srivastava, Y.K., Binod Doley, D.K. Pal., R.K. Das., S. Sudhakar., S. Adiga., K.V. Venkatachary.1968, http://www.iirsnrsa.gov.in 13/7/2008. 54. Swiss Consultants, 1985a, "Calculation of Flood Wave Caused by a Failure of Qadisiyah Dam", Ministry of Irrigation, State Organization of Dams, Haditha Flood Wave, Volume 3. 55. Swiss Consultants, 1985b, "Summary of Calculations in Case of a Failure of Qadisiyah Dam", Ministry of Irrigation, State Organization of Dams, Haditha Flood Wave, Volume 1. 56. Swiss Consultants, 1985c, "The Mathematical Model of the Euphrates River From Qadisiyah Dam to AL-Hindiyah Town", Ministry of Irrigation, State Organization of Dams, Haditha Flood Wave, Volume 2. 57. Tate E.C., 1998, "Photogrammetry Applications in Digital Terrain Modeling and Floodplain Mapping", Final Project Report for GRG 393, Research in Remote Sensing, University of Texas at Austin. 58. Technopromexport, USSR, 1978, "Natural Conditions", Ministry of Irrigation, Haditha Project on the Euphrates River, Technical Design, Volume 2. 59. Technopromexport, USSR, 1978, "Summary Report", Ministry of Irrigation, Haditha Project on the Euphrates River, Technical Design, Vol.1. 60. USGS (United State Geological Survey), 2004, "Shuttle Radar Topography
Mission
(SRTM)",
http://edcsns17.cr.usgs.gov/srtmbil/ 8/9/2007.
Internet
Web
Site,
REFERENCES
61. USGS (United States Geological Survey)., 2008, Internet Sites, http://www.usgs.gov/research/gis/title.html., http://eros.usgs.gov/products/elevation/strmbil.php 27/3/2008. 62. Wang, and Jiang, et.al, 2000, "Review of Global Catastrophes in the 20th Century", Journal of Natural Disasters, Vol. 9, No. 4.
Appendix (C) Analysis of Haditha Dam The typical cross section of Haditha dam is given in figure (C-1), general layout of Haditha dam is given in figure (C-2), all significant data on the reservoir, dam, structures and hydrology are summarized in table (C-1). Flood control at Haditha dam is accomplished with a spillway integrated in the powerhouse and equipped with six radial gate of 16 m width and 13 m height each. Sill level of the spillway is at level 134.00 m a.s.l. and top elevation of radial gate in closed position is at 147.00 m a.s.l., which is the normal height water level. The storage volume of the reservoir at this elevation amount to approximately 8.2 x109 m3, whereas at maximum design reservoir level of 150.20 m a.s.l., i.e., 16.20 m above sill elevation of spillway, approximately 9.7x109 m3 of water will be stored in the reservoir, as shown in figure (C-3). The spillway and bottom outlet rating curves are given in figure ( C-4) and (C-5), respectively. If all six gate are opened, the capacity of the spillway amounts to 7900 m3/s for normal operating reservoir level, which represents approximately a 100-year flood.
Figure (C-1) Typical dam cross section C-1-
Appendix (C)
Figure (C-2) General layout of Haditha dam
Figure (C-3) Reservoir surface area and storage curve C-2-
Appendix (C) Table (C-1) Significant data on dam and reservoir
C-3-
Appendix (C)
Figure (C-4) spillway rating curves
Figure (C-5) Rating curves of bottom outlets C-4-
Appendix (A) Table (A-1) The position of the cross-sections, river width, and distance above Hit gage station along Euphrates river in study area Crosssection No.
Distance above Hit gage station (m)
River width (m)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
0 1800 2550 3600 4650 5800 6500 6700 6900 8000 8500 9000 9250 9500 9850 10150 10450 10700 11000 11300 11600 11900 12100 12350 12600 12850 13100 13400 13700
220.2 211.8 455.1 269.6 145.5 243 293.4 303.5 290.3 254.3 310.5 260.9 230.1 235.1 247.3 300 300.2 250.4 300.3 300.5 300.5 300.2 200.2 250 250.7 250.6 250.5 300.4 300.6 A-1
G.P.S at middle of crosssection N
E
33 38 17.36 33 38 42.17 33 39 00.82 33 39 18.63 33 39 42.51 33 40 09.94 33 40 31.8 33 40 36.91 33 40 44 33 41 19.17 33 41 32.82 33 41 45.66 33 41 50.33 33 41 55.00 33 41 58.45 33 41 58.42 33 41 57.97 33 41 57.82 33 42 00.06 33 42 03.30 33 42 08.15 33 42 14.74 33 42 19.00 33 42 24.52 33 42 29.75 33 42 33.2 33 42 36.16 33 42 39.07 33 42 41.36
42 50 34.89 42 49 31.77 42 49 08.31 42 48 32.37 42 48 04.53 42 47 40.63 42 47 29.42 42 47 27.62 42 47 24.68 42 47 13.92 42 47 03.15 42 46 49.94 42 46 41.94 42 46 33.88 42 46 21.01 42 46 09.34 42 45 57.37 42 45 47.58 42 45 35.77 42 45 25.03 42 45 14.76 42 45 06.17 42 45 00.69 42 44 53.22 42 44 46.02 42 44 37.05 42 44 28.19 42 44 16.87 42 44 05.55
Appendix (A) 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
14000 14350 14700 14940 15270 15570 15870 16200 16500 16750 17000 17300 17600 17950 18300 18525 18750 19050 19350 19600 19850 20050 20250 21000 21950 22950 24000 25000 26000 27000 28000 28300 28600 28900 29200
300.5 350.7 350.4 240.9 330.3 300.2 300.5 330.5 300.2 250.1 250.3 300.2 300.8 350.8 350.4 225.1 450.2 300.5 285.2 285.6 230.9 240.5 220 207.1 350.7 290.7 340.5 325.9 310.2 323.1 305.4 275.6 235 270 315.9 A-2
33 42 42.91 33 42 44.06 33 42 47.29 33 42 51.35 33 43 00.37 33 43 09.92 33 43 19.66 33 43 30.11 33 43 39.55 33 43 47.20 33 43 54.05 33 44 02.07 33 44 09.01 33 44 16.70 33 44 23.80 33 44 27.80 33 44 30.20 33 44 30.65 33 44 30.07 33 44 31.57 33 44 35.29 33 44 40.47 33 44 46.91 33 45 10.49 33 45 36.15 33 46 03.42 33 46 34.31 33 47 03.57 33 47 33.35 33 48 03.13 33 48 34.22 33 48 44.23 33 48 53.85 33 49 02.99 33 49 09.32
42 43 53.89 42 43 39.89 42 43 26.75 42 43 18.78 42 43 11.36 42 43 11.05 42 43 01.11 42 43 10.95 42 43 14.02 42 43 17.52 42 43 21.98 42 43 29.35 42 43 37.14 42 43 46.80 42 43 57.68 42 44 04.85 42 44 13.78 42 44 25.16 42 44 36.54 42 44 46.15 42 44 54.75 42 44 58.83 42 45 00.59 42 44 54.14 42 44 35.21 42 44 21.75 42 43 55.23 42 43 39.07 42 43 23.55 42 43 08.09 42 42 56.72 42 42 57.16 42 42 59.56 42 43 03.45 42 43 12.24
Appendix (A) 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
29500 29800 30300 30600 31100 31600 32100 33100 34100 35100 35600 35750 35900 36050 36200 36500 37200 37500 38500 39500 39800 40800 41800 42500 43500 44500 45500 46500 47500 48200 48900 49200 49500 50500 51500
265.8 260.1 145.5 230.2 475.2 370.8 278.4 301.2 192.5 215.9 155.8 159.4 156.2 179.9 185.1 200.6 125.1 181.2 355.4 137.5 222.3 210.2 270.4 285.3 360.8 275.4 392.2 300.1 228.9 275.6 265.4 391.9 400.1 310.5 303.5 A-3
33 49 11.29 33 49 10.18 33 49 03.04 33 49 01.86 33 49 07.45 33 49 20.41 33 49 33.25 33 49 57.89 33 50 20.04 33 50 47.47 33 51 01.46 33 51 05.46 33 51 10.50 33 51 14.44 33 51 17.93 33 51 22.75 33 51 30.72 33 51 35.01 33 52 00.72 33 52 26.08 33 52 32.44 33 52 43.84 33 52 53.99 33 53 07.04 33 53 17.56 33 53 30.53 33 53 42.22 33 53 59.55 33 54 10.46 33 54 12.23 33 54 04.73 33 54 03.34 33 54 03.27 33 54 04.84 33 53 55.40
42 43 23.66 42 43 35.11 42 43 52.73 42 44 03.90 42 44 22.83 42 44 34.77 42 44 46.09 42 45 11.63 42 45 40.36 42 46 00.57 42 46 10.51 42 46 13.43 42 46 13.98 42 46 11.88 42 46 07.73 42 45 57.22 42 45 31.74 42 45 20.50 42 44 56.80 42 44 32.53 42 44 24.03 42 43 47.48 42 43 10.37 42 42 48.80 42 42 11.94 42 41 36.57 42 41 00.09 42 40 27.42 42 39 51.05 42 39 23.34 42 38 57.56 42 38 45.86 42 38 34.23 42 37 55.54 42 37 18.32
Appendix (A) 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134
52200 52700 53200 54200 55200 55500 55900 56350 56800 57800 58200 58600 59400 60200 60800 61800 62800 63800 64500 64900 65400 65900 66400 66700 67000 67500 68500 69000 69500 70000 70500 71100 71850 72350 72850
295.4 332.2 280.5 290.6 217.5 250.7 345.2 400 310.5 265.4 285.5 281.1 429.9 540 384.2 375.1 400.2 479.8 474.7 425.1 430 428.7 380.2 351.3 355.3 339 313.5 350.1 318.6 364.5 350.1 437.7 330 358.6 270.1 A-4
33 53 40.46 33 53 27.12 33 53 11.95 33 52 39.54 33 52 07.13 33 51 57.55 33 51 45.02 33 51 31.56 33 51 19.60 33 50 59.10 33 50 51.96 33 50 49.17 33 50 53.74 33 51 00.52 33 51 06.26 33 51 16.10 33 51 29.62 33 51 40.98 33 51 51.76 33 52 03.44 33 52 19.70 33 52 30.18 33 52 39.66 33 52 58.40 33 52 58.40 33 53 13.77 33 53 39.99 33 53 54.93 33 54 11.48 33 54 25.25 33 54 33.04 33 54 31.21 33 54 20.69 33 54 16.22 33 54 19.46
42 36 57.14 42 36 46.88 42 36 40.24 42 36 38.13 42 36 35.66 42 36 33.58 42 36 30.36 42 36 23.67 42 36 13.76 42 35 43.52 42 35 30.99 42 35 15.56 42 34 44.67 42 34 14.97 42 33 51.93 42 33 15.16 42 32 39.66 42 32 03.15 42 31 40.98 42 31 34.22 42 31 35.85 42 31 50.04 42 32 05.42 42 32 11.04 42 32 10.74 42 32 05.11 42 31 42.25 42 31 34.38 42 31 34.84 42 31 44.47 42 32 01.59 42 32 24.71 42 32 51.21 42 33 09.47 42 33 27.94
Appendix (A) 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169
73350 73850 74850 75850 76850 77850 78850 79450 79850 80850 81850 82850 83850 84850 85600 86350 87350 88350 89350 90350 91350 92050 93050 93700 94700 95700 96700 97700 98700 99450 99850 100250 100550 100800 101600
325.2 327.4 212.8 255.6 276.9 240.1 301.1 422.5 367.4 220.8 220.1 352.8 390.2 310.2 276.3 270.5 275.8 280.6 250.6 401.2 359.8 393.6 376.2 494.9 354.4 400.5 390.6 415.8 380.8 440.7 574.2 564.8 515 469.8 305.8 A-5
33 54 30.45 33 54 45.60 33 55 18.35 33 55 50.76 33 56 22.63 33 56 54.27 33 57 24.02 33 57 41.10 33 57 54.11 33 58 25.58 33 58 48.92 33 58 59.64 33 59 14.48 33 59 31.52 33 59 48.72 34 00 11.74 34 00 43.42 34 01 14.47 34 01 41.93 34 02 00.80 34 02 08.50 34 02 06.50 34 01 51.79 34 01 40.78 34 01 16.10 34 00 57.08 34 00 44.52 34 00 40.43 34 00 40.75 34 00 48.63 34 00 57.54 34 01 08.22 34 01 18.64 34 01 26.62 34 01 49.80
42 33 42.40 42 33 47.99 42 33 46.55 42 33 45.32 42 33 39.30 42 33 48.90 42 34 04.36 42 34 15.28 42 34 16.54 42 34 08.25 42 33 41.09 42 33 04.64 42 32 29.58 42 31 56.22 42 31 35.03 42 31 26.66 42 31 18.31 42 31 07.90 42 30 47.95 42 30 16.16 42 29 38.36 42 29 10.80 42 28 35.56 42 28 14.68 42 27 48.99 42 27 17.81 42 26 41.94 42 26 03.48 42 25 24.33 42 24 56.42 42 24 44.56 42 24 37.83 42 24 38.69 42 24 41.32 42 24 55.30
Appendix (A) 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198
101800 102000 103000 104000 105000 106000 107000 108000 108500 109000 109500 110000 110500 111500 112000 112500 113500 114500 115000 115500 116500 118500 119500 120000 121000 121500 122500 123500 124400
322 330.4 510.2 430.5 465.3 504.8 500.7 476.1 366.1 490.9 471.8 432.1 370.6 340.5 299.8 416.1 397.5 444.2 605.2 460.7 339.7 408.1 302.4 321.4 420 354.7 367.2 372.5 384
A-6
34 01 56.15 34 02 02.34 34 02 34.45 34 03 05.01 34 03 31.27 34 03 53.95 34 04 15.94 34 04 35.65 34 04 47.93 34 05 00.44 34 05 14.65 34 05 30.49 34 05 45.67 34 06 06.59 34 06 16.82 34 06 30.95 34 07 03.53 34 07 35.87 34 07 51.79 34 08 08.85 34 08 40.38 34 09 44.13 34 10 15.39 34 10 31.53 34 11 03 .02 34 11 16.54 34 11 38.27 34 11 51.84 34 12 13.47
42 24 57.54 42 24 59.89 42 24 58.95 42 24 46.51 42 24 24.21 42 23 55.97 42 23 26.84 42 22 56.06 42 22 41.84 42 22 29.86 42 22 19.96 42 22 16.02 42 22 23.20 42 22 52.80 42 23 08.17 42 23 17.21 42 23 20.70 42 23 19.07 42 23 14.90 42 23 17.17 42 23 21.29 42 23 07.57 42 23 17.07 42 23 20.90 42 23 13.39 42 23 02.02 42 22 10.11 42 22 56.47 42 21 35.66
Appendix (A) Table (A-2) Details of some of surveyed cross-sections along Euphrates River in the study area: a) Cross-section No. 1
Cross-section No. ……………………….……….=( 1 ) Down-stream study area River width ……………………………………..……=( 220 m) Water surface elevation (a.s.l) ……………..=( 53.62 m) Distance upstream Hit gauge station ……=( 0 Km) G.P.S reading for middle of cross-section: N ( 33 38 17.36 ); E ( 42 50 34.8 ) Distance from left bank (m) 0 15 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300
Elevation (a.s.l) 58.5 53.62 53.12 52.52 52 51.9 51.8 51.6 51.2 50.3 49.9 49.5 49.6 49.6 49.4 49.2 49.3 48.7 48.3 49.1 49.2 50.2 53.62 60
Notice Left bank
Right bank
Distance from left bank (m) 310 320 330 340 350 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600
A-7
Elevation (a.s.l)
Notice
Appendix (A) b) cross-section No. 23 Cross-section No. ……………………….……….=( 23 ) River width ……………………………………..……=( 315 m) Water surface elevation (a.s.l) ……………..=( 57.5 m) Distance upstream Hit gauge station ……..=( 12.100 Km) G.P.S reading for middle of cross-section: N ( 33 42 19.00 ); E ( 42 45 00.60 ) Distance from left bank (m) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300
Elevation (a.s.l) 62.6 57.5 56.3 56.1 55.8 55.1 55.3 55.6 55.4 55.8 56.1 56.3 56.5 56.2 55.7 55.3 54.9 54.5 54.6 54.8 55.2 55.5 55.9 56.1 55.9 56 56.1 55.7 55.5 55.8 56.1
Notice Left bank
Distance from left bank (m) 310 320 330 340 350 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600
A-8
Elevation (a.s.l) 56.2 56.6 61.7
Notice
Right bank
Appendix (A) c) cross-section No. 28 Cross-section No. ……………………….……….=( 28 ) River width ……………………………………..……=( 420 m) Water surface elevation (a.s.l) ……………..=( 57.86 m) Distance upstream Hit gauge station ……=( 13.400 Km) G.P.S reading for middle of cross-section: N ( 33 42 39.07 ); E ( 42 44 16.87 ) Distance from left bank (m) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300
Elevation (a.s.l) 62.9 59 58.2 57.86 55.7 55.2 55.5 55.6 55.4 55.87 56.1 55.6 55.7 55.6 55.7 55 55.8 55.9 55.6 55.4 55.3 55.7 55.9 56.3 56.2 55.9 56.1 56.4 56.9 57.9 58.8
Notice Left bank
Distance from left bank (m) 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600
A-9
Elevation (a.s.l) 59.4 59.5 59.8 59.2 58.8 58.7 58.8 58 57.1 56.2 56.1 57.8 62.1
Notice
Right bank
Appendix (A) d) cross-section No. 30 Cross-section No. ……………………….……….=( 30 ) River width ……………………………………..……=( 380 m) Water surface elevation (a.s.l) ……………..=( 58.04 m) Distance upstream Hit gauge station ……=( 14.000 Km) G.P.S reading for middle of cross-section: N ( 33 42 42.91 ); E ( 42 43 53.89 ) Distance from left bank (m) 0 13 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300
Elevation (a.s.l) 62.5 58.04 57.1 56.4 56.6 56.4 56.5 55.7 55.6 55.9 56.6 56.1 56.2 56.9 57.2 57.6 57.1 56.4 56.9 56.6 56.1 56 56.1 56.7 56.7 55.7 56.4 56.1 56.3 56.8 56
Notice Left bank
Distance from left bank (m) 310 320 330 340 350 360 370 380 390 405 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600
A-10
Elevation (a.s.l) 55.8 55.9 56.6 56.1 55.6 55.7 55.9 56.8 58.04 61.5
Notice
Right bank
Appendix (A) e) Cross-section No. 36 Cross-section No. ……………………….……….=( 36 ) River width ……………………………………..……=( 325 m) Water surface elevation (a.s.l) ……………..=( 58.62 m) Distance upstream Hit gauge station ……=( 15.870 Km) G.P.S reading for middle of cross-section: N ( 33 43 19.66 ); E ( 42 43 10.11 ) Distance from left bank (m) 0 15 21 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300
Elevation (a.s.l) 62.3 59.9 58.62 57.25 57 56.3 56.3 56.4 56.9 57.3 57 56.4 57.1 57.2 56.7 57.3 56.9 56.8 57.5 57.3 57.1 57.7 57.3 57.5 57.5 57.5 57.6 57.3 56.5 57.2 57.1
Notice Left bank
Distance from left bank (m) 310 320 330 340 350 360 590 600 610 650
A-11
Elevation (a.s.l) 57.5 57.4 57.6 57.8 58.8 60.3 60.5 58 60.1 63.7
Notice
Right bank
Appendix (A) f) Cross-section No. 56 Cross-section No. ……………………….……….=( 56 ) River width ……………………………………..……=( 341 m) Water surface elevation (a.s.l) ……………..=( 61.1 m) Distance upstream Hit gauge station ……=( 24.000 Km) G.P.S reading for middle of cross-section: N ( 33 46 34.31 ); E ( 42 43 55.23 ) Distance from left bank (m) 0 15 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300
Elevation (a.s.l) 65.87 62.3 61.96 61.1 60.2 58.7 59.2 58.5 58.7 58.9 59.1 59.7 59.3 59.8 58.7 58.6 57.3 57.7 58.2 59.1 59.8 59.7 60.2 59.8 58.4 58.2 58.9 59.3 59.5 58.52 58.8
Notice Left bank
Distance from left bank (m) 310 320 330 340 350 360 370 384 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600
A-12
Elevation (a.s.l) 59.4 59.9 59.6 59.7 60.2 59.9 61.1 65.3
Notice
Right bank
Appendix (A) g) cross-section No. 60 Cross-section No. ……………………….……….=( 60 ) River width ……………………………………..……=( 305 m) Water surface elevation (a.s.l) ……………..=( 62.5 m) Distance upstream Hit gauge station ……=( 28.000 Km) G.P.S reading for middle of cross-section: N ( 33 48 34.22 ); E ( 42 42 56.72 ) Distance from left bank (m) 0 15 20 26 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300
Elevation (a.s.l) 67.4 63.2 62.9 62.5 61.5 61.3 61.2 61 60.6 59.5 60 60.2 59.3 58.9 58.7 59.3 59.9 59.3 60.5 60.3 61.3 61.4 60.8 60.2 61.4 60.5 61.3 61.2 61 60.9 60.3
Notice Left bank
Distance from left bank (m) 310 320 330 347 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600
A-13
Elevation (a.s.l) 61.2 61.5 62.6 68.5
Notice
Right bank
Appendix (A) h) cross-section No. 129 Cross-section No. ……………………….……….=( 129 ) River width ……………………………………..……=( 364 m) Water surface elevation (a.s.l) ……………..=( 75.54 m) Distance upstream Hit gauge station ……=( 70.000 Km) G.P.S reading for middle of cross-section: N ( 33 54 25.25 ); E ( 42 31 44.47 ) Distance from left bank (m) 0 15 25 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300
Elevation (a.s.l) 80.5 77.2 75.45 74.1 74.3 74.4 73.8 73.5 73.2 73.5 73.2 73.9 73.8 73.5 73.4 73.9 73.8 73.5 73.5 73.6 73.2 73.4 73.8 73.6 73.6 73.1 73.5 72.7 72.8 73.4 73.7
Notice Left bank
Distance from left bank (m) 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600
A-14
Elevation (a.s.l) 73.8 73.9 74.1 73.5 73.2 73.7 73.9 73.9 75.6
Notice
Right bank
Appendix (A) i)
cross-section No. 137
Cross-section No. ……………………….……….=( 137 ) River width ……………………………………..……=( 212 m) Water surface elevation (a.s.l) ……………..=( 77.05 m) Distance upstream Hit gauge station ……=( 74.850 Km) G.P.S reading for middle of cross-section: N ( 33 55 18.35 ); E ( 42 33 46.55 ) Distance from left bank (m) 0 10 22 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 243 250 260 270 280 290 300
Elevation (a.s.l) 81.4 78.9 77.05 75.5 75.1 74.8 74.5 74.2 73.7 73.5 73.8 73.6 74.3 74.5 74.5 74.2 74.8 73.6 73.7 73.4 74.8 74.3 75.7 74.7 77.1 79.3 81.8
Notice Left bank
Right bank
Distance from left bank (m) 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600
A-15
Elevation (a.s.l)
Notice
Appendix (A) j) cross-section No. 162 Cross-section No. ……………………….……….=( 162 ) River width ……………………………………..……=( 415 m) Water surface elevation (a.s.l) ……………..=( 87.16 m) Distance upstream Hit gauge station ……=( 97.700 Km) G.P.S reading for middle of cross-section: N ( 34 00 10.43 ); E ( 42 26 03.48 ) Distance from left bank (m) 0 12 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300
Elevation (a.s.l) 93.7 87.16 86.1 85.8 85.6 86 85.4 85.4 85.8 85.3 84.8 84.7 85 85.1 84.5 84.7 84.4 84.4 84.3 85.2 84.9 84.2 84.5 84.4 84.6 85.3 85.2 84.6 84.5 85.3 85.1
Notice Left bank
Distance from left bank (m) 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600
A-16
Elevation (a.s.l) 84.7 84.8 85.4 85.5 85.8 85.3 85.3 85.7 85.4 85.5 85.8 86.1 87.2 87.9 88.4 92.1
Notice
Right bank
Appendix (B) Contraction and Expansion Coefficients In constructed trapezoidal and rectangular channels, designed for supercritical flow, the value of contraction and expansion coefficients should set equal to zero in the reaches where the cross sectional geometry is not changing shape such as in physical model. In reaches where the flow is contracting and expanding, we should select contraction and expansion coefficients carefully. Typical values for gradual transitions in supercritical flow would be around 0.05 for the contraction coefficient and 0.10 for the expansion coefficient. As the natural transitions begin to become more abrupt, it may be necessary to use higher values, such as 0.1 for the contraction coefficient and 0.3 for the expansion coefficient. The value of 0.3 and 0.5 were used as contraction and expansion coefficients respectively upstream and downstream bridge cross-sections. On occasion, the coefficients of contraction and expansion around bridges and culverts may be as high as 0.6 and 0.8, respectively.
These values may be
changed at any cross section. The maximum value for the contraction and expansion coefficient is one (1.0). In general, the empirical contraction and expansion coefficients should be lower for supercritical flow. In supercritical flow the velocity heads are much greater, and small changes in depth can cause large changes in velocity head.
Using
contraction and expansion coefficients that would be typical for subcritical flow can result in over estimation of the energy losses and oscillations in the computed water surface profile. The coefficients of expansion and contraction at the location of bridges will be 0.3 and 0.5 respectively for the cross-sections with
B-1-
Appendix (B) distance Lc (the contraction reach length) upstream bridge and Le (the expansion reach length) downstream bridge as shown in figure (B-1).
Figure (B-1) cross section location at bridge The values of expansion ratio (ER) can be obtained from table (B-1) to limitation the location of additional cross-section (1) downstream the bridge. Where: ( b/B) is the ratio of the bridge opening width to the total floodplain width, (nob) is the Manning (n) value for the overbank, (nc ) is the Manning (n) value for the main channel, and (S) is the longitudinal slope.
The values in the interior of the table are the ranges of the
expansion ratio.
B-2-
Appendix (B) Table (B-1) range of expansion ratio (ER)
Once an expansion ratio (ER) is selected, the distance to the downstream end of the expansion reach (Le) is found by multiplying the expansion ratio by the average obstruction length (the average of the distances A to B and C to D from figure (B-1)). In upstream of bridge cross-section 4 must be restrict to defining the beginning of flow contractions. In general, flow contractions occur over a shorter distance than flow expansions. The distance between cross section 3 and 4 (the contraction reach length, Lc) should generally be determined by field investigation during high flows. Traditionally, the Corps of Engineers used a criterion to locate the upstream cross section one times the average length of the side constriction caused by the structure abutments (the average of the distance from A to B and C to D on figure (B-1). The contraction distance will vary depending upon the degree of constriction, the shape of the constriction, the magnitude of the flow, and the velocity of the flow.
B-3-
ﺗﻢ دراﺳﺔ وﺗﺤﻠﯿﻞ ﺗﺄﺛﯿﺮ اﻟﺘﻤﻨﺪر )اﻟﺘﻤﻌﺞ( اﻟﻤﻮﺟﻮد ﻓﻲ اﻷﻧﮭﺎر ﻋﻠﻰ اﺳﺘﺘﺒﺎع اﻟﻤﻮﺟﺎت اﻟﻔﯿﻀﺎﻧﯿﺔ .اﻟﺪراﺳﺔ ﺗﻤﺖ ﺑﺎﺳﺘﺨﺪام ﻧﻤﻮذج ﻋﺪدي أﺣﺎدي اﻟﺒﻌﺪ ﯾﻌﺘﻤﺪ ﻋﻠﻰ ﺗﻄﻮﯾﺮ ﻣﻌﺎدﻻت ) (Saint-Venantﺑﺤﯿﺚ إن أﺟﺰاء اﻟﻨﮭﺮ اﻟﻤﺘﻤﻨﺪر )اﻟﻤﺘﻤﻌﺞ( أي ﻗﻨﺎة اﻟﻨﮭﺮ اﻟﺮﺋﯿﺴﯿﺔ واﻟﻀﻔﺘﯿﻦ اﻟﯿﻤﻨﻰ واﻟﯿﺴﺮى ﻟﮫ ﺗﻌﺎﻣﻞ ﻛﺄﺟﺰاء ﻣﻨﻔﺼﻠﺔ ,ﻟﮭﺬا ﻓﺎن اﻻﺧﺘﻼف ﻓﻲ اﻟﺨﺼﺎﺋﺺ اﻟﮭﯿﺪروﻟﯿﻜﯿﺔ واﻟﮭﻨﺪﺳﯿﺔ وطﻮل ﺧﻂ اﻟﺠﺮﯾﺎن ﺳﻮف ﺗﺄﺧﺬ ﻓﻲ اﻟﺤﺴﺒﺎن ﻓﻲ ﻛﻞ ﻗﺴﻢ ﻣﻦ أﻗﺴﺎم ﻣﻘﻄﻊ وادي اﻟﺠﺮﯾﺎن ﻓﻲ اﻟﻨﮭﺮ. ﺗﻢ ﺗﻄﺒﯿﻖ اﻟﻨﻤﻮذج اﻟﻌﺪدي ﻋﻠﻰ ﻧﮭﺮ اﻟﻔﺮات ﻓﻲ اﻟﻤﻨﻄﻘﺔ اﻟﻮاﻗﻌﺔ ﺑﯿﻦ ﺳﺪ ﺣﺪﯾﺜﺔ وﻣﺪﯾﻨﺔ ھﯿﺖ وﻟﻤﺴﺎﻓﺔ ) ( 124.4 kmﻟﻠﺤﺼﻮل ﻋﻠﻰ ﺗﺤﻠﯿﻞ دﻗﯿﻖ ﻋﻦ ﺗﺄﺛﯿﺮ اﻟﺘﻤﻨﺪر ﻓﻲ اﻟﻨﮭﺮ ﻋﻠﻰ اﻟﻤﻌﺎﻣﻼت اﻟﺘﺎﻟﯿﺔ :اﻟﺘﺼﺮﯾﻒ اﻷﻗﺼﻰ ,اﻟﻤﻨﺴﻮب اﻷﻗﺼﻰ ,وﻗﺖ اﻟﺘﺨﻠﻒ ﻟﻠﺘﺼﺮﯾﻒ اﻷﻗﺼﻰ ,و وﻗﺖ اﻟﺘﺨﻠﻒ ﻟﻠﻤﻨﺴﻮب اﻷﻗﺼﻰ ﻋﻠﻰ اﻣﺘﺪاد اﻟﻨﮭﺮ وﻟﻘﯿﻢ ﻣﺨﺘﻠﻔﺔ ﻣﻦ ﻣﻌﺎﻣﻞ ﻣﺎﻧﻨﻚ ﻟﻠﺨﺸﻮﻧﺔ ﻟﻀﻔﺎف اﻟﻨﮭﺮ .ﺗﻢ إﻋﺪاد ﺳﺖ ﺣﺎﻻت ﻻﺳﺘﺘﺒﺎع اﻟﻤﻮﺟﺔ اﻟﻔﯿﻀﺎﻧﯿﺔ ﻟﻤﻘﺎرﻧﺔ ﺗﺄﺛﯿﺮ وﺟﻮد اﻟﺘﻤﻌﺞ واﺧﺘﻼف ﻗﯿﻢ ﻣﻌﺎﻣﻞ ﻣﺎﻧﻨﻚ ﻟﻠﺨﺸﻮﻧﺔ ﻋﻠﻰ اﻟﻤﻌﺎﻣﻼت أﻋﻼه ﺣﯿﺚ ﺗﻢ اﻋﺘﺒﺎر إن اﻟﺤﺎﻻت A3, A2, A1ھﻲ ﻟﻠﻨﮭﺮ ﻋﻨﺪ إھﻤﺎل ﺗﺄﺛﯿﺮ اﻟﺘﻌﺮﺟﺎت وﺑﻘﯿﻢ ﻣﻌﺎﻣﻞ ﻣﺎﻧﻨﻚ ﻟﻠﻀﻔﺎف ,0.07 ,0.05و 0.1ﻋﻠﻰ اﻟﺘﻮاﻟﻲ ,أﻣﺎ اﻟﺤﺎﻻت B3, B2, B1ﻓﮭﻲ ﺗﻤﺜﻞ اﻟﻨﮭﺮ ﺑﻮﺟﻮد اﻟﺘﻤﻌﺠﺎت وﻟﻘﯿﻢ ﻣﻌﺎﻣﻞ ﻣﺎﻧﻨﻚ ﻟﻠﺨﺸﻮﻧﺔ ﻟﻠﻀﻔﺎف ﺗﺴﺎوي ,0.07 ,0.05و 0.1ﻋﻠﻰ اﻟﺘﻮاﻟﻲ. ﺗﻤﺖ اﻟﺤﺴﺎﺑﺎت ﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﺤﺎﻻت اﻟﺴﺘﺔ ﺑﺎﺳﺘﺨﺪام ﺑﺮاﻣﺞ )( HEC-RAS 3.1.3 ﻟﻤﻮﺟﺔ ﻓﯿﻀﺎﻧﯿﮫ ﻧﺎﺗﺠﺔ ﻣﻦ اﻧﮭﯿﺎر اﻓﺘﺮاﺿﻲ ﻟﺴﺪ ﺣﺪﯾﺜﺔ .إن ﻣﻘﺎرﻧﺔ اﻟﻨﺘﺎﺋﺞ أظﮭﺮت ﺑﺎن ھﻨﺎك زﯾﺎدة ﻓﻲ اﻟﺘﺼﺮﯾﻒ اﻷﻗﺼﻰ اﻟﻮاﺻﻞ ﻟﻤﺪﯾﻨﺔ ھﯿﺖ ﻋﻨﺪ اﺧﺬ اﻟﺘﻤﻌﺠﺎت ﻓﻲ اﻟﻨﮭﺮ ﺑﻨﻈﺮ اﻻﻋﺘﺒﺎر ﻓﻲ اﻟﺤﺎﻻت B3, B2, B1ﺑﻤﻘﺪار ,%13.6 ,%11.2و %15.1 ﻋﻨﮭﺎ ﻋﻨﺪ إھﻤﺎل وﺟﻮد اﻟﺘﻤﻌﺠﺎت ﻛﻤﺎ ﻓﻲ اﻟﺤﺎﻻت . A3, A2, A1ﺗﺸﯿﺮ اﻟﻨﺘﺎﺋﺞ ﻛﺬﻟﻚ
إﻟﻰ أن اﻟﻮﻗﺖ اﻟﻼزم ﻟﻮﺻﻮل أﻋﻈﻢ ﺗﺼﺮﯾﻒ ﻟﻠﻤﻮﺟﺔ اﻟﻔﯿﻀﺎﻧﯿﺔ اﻟﻨﺎﺗﺠﺔ ﻣﻦ اﻧﮭﯿﺎر ﺳﺪ ﺣﺪﯾﺜﺔ إﻟﻰ ﻣﺪﯾﻨﺔ ھﯿﺖ ﻟﻠﺤﺎﻻت B3, B2, B1ﯾﻘﻞ ﺑﻤﻘﺪار 3:30 ,3:10 , 2:35ﺳﺎﻋﺔ ﻋﻦ وﻗﺖ وﺻﻮل اﻟﺘﺼﺮﯾﻒ اﻷﻋﻈﻢ ﻓﻲ اﻟﺤﺎﻻت A3, A2, A1ﻋﻠﻰ اﻟﺘﻮاﻟﻲ .أﻣﺎ ﺑﺎﻟﻨﺴﺒﺔ ﻟﻼرﺗﻔﺎع اﻷﻗﺼﻰ ﻟﻤﻮﺟﺔ اﻟﻔﯿﻀﺎن اﻟﻮاﺻﻠﺔ إﻟﻰ ﻣﺪﯾﻨﺔ ھﯿﺖ ﻓﻘﺪ أﻋﻄﺖ اﻟﺤﺎﻻت B3, B2, B1ارﺗﻔﺎع ﻣﻮﺟﺔ أﻋﻠﻰ ﺑﻤﻘﺪار 1.08m, 1.02m, 0.97ﻋﻨﮫ ﻓﻲ اﻟﺤﺎﻻت A3, A2, A1ﻋﻠﻰ اﻟﺘﻮاﻟﻲ .ﻛﺬﻟﻚ ﻛﺎن اﻟﺘﺄﺧﯿﺮ ﻓﻲ وﻗﺖ وﺻﻮل اﻻرﺗﻔﺎع اﻷﻗﺼﻰ ﻟﻠﻤﻮﺟﺔ اﻟﻔﯿﻀﺎﻧﯿﺔ إﻟﻰ ﻣﺪﯾﻨﺔ ھﯿﺖ ﻋﻨﺪ اﺧﺬ اﻟﺘﻤﻌﺠﺎت اﻟﻤﻮﺟﻮدة ﻓﻲ اﻟﻨﮭﺮ ﻓﻲ اﻟﺤﺴﺎﺑﺎت ﻓﻲ اﻟﺤﺎﻻت B3, B2, B1اﻗﺼﺮ ﻣﻨﮫ ﻋﻨﺪ إھﻤﺎل اﻟﺘﻤﻌﺠﺎت ﻓﻲ اﻟﺤﺎﻻت A3, A2, A1ﺑﻤﻘﺪار 3:50 ,2:55 ,2:20ﺳﺎﻋﺔ ﻋﻠﻰ اﻟﺘﻮاﻟﻲ. ﺗﻢ اﺳﺘﻨﺒﺎط ﻣﻌﺎﻣﻼت ﻻﺑﻌﺪﯾﺔ وھﻲ اﻟﺨﺸﻮﻧﺔ اﻟﻨﺴﺒﯿﺔ ) (nrواﻟﺘﺼﺮﯾﻒ اﻟﻤﺨﻔﺾ )(Dr واﻟﻤﻨﺴﻮب اﻟﻤﺨﻔﺾ ) (Lrوﻛﺬﻟﻚ ﻣﻌﺎﻣﻼت ﺗﻤﺜﻞ وﻗﺖ ﺗﺨﻠﻒ اﻟﺘﺼﺮﯾﻒ اﻷﻗﺼﻰ ) (TLDو وﻗﺖ ﺗﺨﻠﻒ اﻟﻤﻨﺴﻮب اﻷﻗﺼﻰ ) (TLLﻟﺘﻤﺜﯿﻞ اﻟﻌﻼﻗﺔ ﺑﯿﻦ ﺣﺎﻻت اﻟﺪراﺳﺔ اﻟﺴﺘﺔ ﺑﺎﺳﺘﺨﺪام اﻟﺮﺳﻮم اﻟﺒﯿﺎﻧﯿﺔ ﺣﯿﺚ ﺑﯿﻨﺖ ھﺬه اﻟﻌﻼﻗﺎت ﻋﻠﻰ إن ﻗﯿﻢ ﻛﻞ ﻣﻦ اﻟﺘﺼﺮﯾﻒ اﻟﻤﺨﻔﺾ ) (Drواﻟﻤﻨﺴﻮب اﻟﻤﺨﻔﺾ ) (Lrوﻛﺬﻟﻚ اﻟﻤﻌﺎﻣﻼت اﻟﺘﻲ ﺗﻤﺜﻞ وﻗﺖ ﺗﺨﻠﻒ اﻟﺘﺼﺮﯾﻒ اﻷﻗﺼﻰ ) (TLDو وﻗﺖ ﺗﺨﻠﻒ اﻟﻤﻨﺴﻮب اﻷﻗﺼﻰ ) (TLLﺗﺰداد ﺟﻤﯿﻌﮭﺎ ﺑﺰﯾﺎدة ﻗﯿﻤﺔ اﻟﺨﺸﻮﻧﺔ اﻟﻨﺴﺒﯿﺔ ).(nr ﺗﻢ اﺳﺘﻌﻤﺎل ﻧﻤﻮذج رﯾﺎﺿﻲ ﺛﻨﺎﺋﻲ اﻟﺒﻌﺪ ﺑﺎﺳﺘﺨﺪام ﺑﺮﻧﺎﻣﺞ RMA-2ﻋﻠﻰ ﻣﻘﻄﻊ ﻣﺘﻤﻌﺞ ﺻﻐﯿﺮ ﻣﻦ اﻟﻨﮭﺮ ﻓﻲ ﻣﻨﻄﻘﺔ اﻟﺪراﺳﺔ ﻟﺘﺪﻗﯿﻖ ﻧﺘﺎﺋﺞ اﻟﻨﻤﻮذج اﻟﺮﯾﺎﺿﻲ أﺣﺎدي اﻟﺒﻌﺪ وﻛﺎﻧﺖ اﻟﻨﺘﺎﺋﺞ ﻣﺘﻮاﻓﻘﺔ ﺑﺸﻜﻞ ﺟﯿﺪ.
وزارة اﻟﺗﻌﻠﯾم اﻟﻌﺎﻟﻲ واﻟﺑﺣث اﻟﻌﻠﻣﻲ اﻟﺟﺎﻣﻌﺔ اﻟﺗﻛﻧوﻟوﺟﯾﺔ ﻗﺳم ھﻧدﺳﺔ اﻟﺑﻧﺎء واﻹﻧﺷﺎءات
ﻧﻤﻮذج ﻋﺪدي ﻻﺳﺘﺘﺒﺎع ﺗﺼﺮف اﻟﻤﻮﺟﺔ أﻟﻔﻴﻀﺎﻧﻴﻪ ﺗﺤﺖ ﺗﺄﺛﻴﺮ اﻟﺘﻤﻨﺪر)ﻧﻬﺮ اﻟﻔﺮات ﺣﺪﻳﺜﺔ -ﻫﻴﺖ( رﺳﺎﻟﺔ ﻣﻘدﻣﺔ إﻟﻰ ﻗﺳم ﻫﻧدﺳﺔ اﻟﺑﻧﺎء واﻹﻧﺷﺎءات ﻓﻲ اﻟﺟﺎﻣﻌﺔ اﻟﺗﻛﻧوﻟوﺟﯾﺔ وﻫﻲ ﺟزء ﻣن ﻣﺗطﻠﺑﺎت ﻧﯾل درﺟﺔ دﻛﺗوراﻩ ﻓﻠﺳﻔﺔ ﻓﻲ ﻫﻧدﺳﺔ اﻟﺑﻧﺎء واﻹﻧﺷﺎءات -ﻫﻧدﺳﺔ اﻟﻣوارد اﻟﻣﺎﺋﯾﺔ إﻋداد
ﺻﺎدق ﻋﻠﯾوي ﺳﻠﯾﻣﺎن اﻟﻔﮭداوي ﺑﻛﺎﻟورﯾوس ) ﻫﻧدﺳﺔ ﻣدﻧﯾﺔ (1993 ﻣﺎﺟﺳﺗﯾر )ﻫﻧدﺳﺔ ﻣدﻧﯾﺔ – ﻣوارد ﻣﺎﺋﯾﺔ( 2002
ﺑﺄﺷراف
أ.م.د .ﻣﮭﻧد ﺟﻌﻔر اﻟﻘزوﯾﻧﻲ
أ.د .راﻓﻊ ھﺎﺷم اﻟﺳﮭﯾﻠﻲ
2009
