i

PREDICTION OF BED PROFILE IN THE

LONGITUDINAL AND TRANSVERSE

DIRECTIONS IN ASWAN HIGH DAM

RESERVOIR

By

Tarek Mohamed Abdel-Aziz Ismail

A Thesis Submitted to the

Faculty of Engineering at Cairo University

in Partial Fulfillment of the

Requirements for the Degree of

DOCTOR OF PHILOSOPHY

in

CIVIL ENGINEERING

FACULTY OF ENGINEERING, CAIRO UNIVERSITY

GIZA, EGYPT

March 1997

ii

PREDICTION OF BED PROFILE IN THE

LONGITUDINAL AND TRANSVERSE

DIRECTIONS IN ASWAN HIGH DAM

RESERVOIR

By

Tarek Mohamed Abdel-Aziz Ismail

A Thesis Submitted to the

Faculty of Engineering at Cairo University

in Partial Fulfillment of the

Requirements for the Degree of

DOCTOR OF PHILOSOPHY

in

CIVIL ENGINEERING

Under the Supervision of

Prof. Dr. M. Mokhles Abou-Seida Head

Of Irrigation and Hydraulics Department

Faculty of Engineering, Cairo University

Dr. Magdy M. Saleh Prof. Dr. M. ELMoattassem Lecturer Professor

Irrigation & Hydraulics Nile Research Institute

Faculty of Engineering National Water Research

Cairo University Center

FACULTY OF ENGINEERING, CAIRO UNIVERSITY

GIZA, EGYPT

March 1997

iii

PREDICTION OF BED PROFILE IN THE

LONGITUDINAL AND TRANSVERSE

DIRECTIONS IN ASWAN HIGH DAM

RESERVOIR

By

Tarek Mohamed Abdel-Aziz Ismail

A Thesis Submitted to the

Faculty of Engineering at Cairo University

in Partial Fulfillment of the

Requirements for the Degree of

DOCTOR OF PHILOSOPHY

in

CIVIL ENGINEERING

Approved by the

Examining Committee:

Prof. Dr. M. Mokhles Abou-Seida Thesis Main Advisor

Prof. Dr. Farouk M. Abdel-Aal Member

Prof. Dr. Mahmoud A. Abou Zeid Member

FACULTY OF ENGINEERING, CAIRO UNIVERSITY

GIZA, EGYPT

March 1997

iv

ACKNOWLEDGMENTS

The author would like to express his gratitude to his promoter Prof. Dr. Eng.

Mohamed Mokhles Abou-Seida, Head of Irrigation and Hydraulics Department,

Faculty of Engineering, Cairo University, for his permanent guidance, invaluable

suggestions, patience and understanding during this work.

The author appreciates deeply Prof. Dr. Eng. Mohamed El-Moattassem Mohamed

El-Kotb, Professor, Nile Research Institute, National Water Research Center, for his

keen interest, his support, guidance and positive encouragement through this work.

Thanks are also due to Dr. Eng. Magdy Mohamed Saleh, Lecturer, Irrigation and

Hydraulics Department, Faculty of Engineering, Cairo University, for his support,

comment, and guidance throughout this work.

Great thanks are mainly to Prof. Dr. Eng. Mahmoud Abdel-Halim Abou Zeid,

Chairman of the National Water Research Center, Ministry of Public Works and Water

Resources, for his keen interest in the topic of the study and accepting to be a member

of the examining committee.

The author would like to thank Porf. Dr. Eng. Farouk Mostafa Abdel-Aal, Professor,

Irrigation and Hydraulics Department, Faculty of Engineering, Cairo University, for

his great effort, as a member of the examining committee, and his valuable guidance

and comments.

Sincere thanks to all staff members of the Nile Research Institute (NRI), National

Water Research Center (NWRC), Ministry of Public Works and Water Resources

(MPWWR), for providing the hydrological data especially Prof. Dr. Eng. Mohamed

Rafik Abdel-Bary, Director of the Nile Research Institute, for his positive

encouragement and his keen interest in this work.

v

ABSTRACT

Estimating sediment deposition volumes in reservoirs is one of the major problems

faced by engineers involved in river regulation. The accumulated sedimentation helps

in getting the effective volume of the reservoir and the life time of the project.

A new methodological approach is developed to simulate and predict the changes of

the deposition and scour areas in space and time and to determine the movement

sediment front in the longitudinal and transverse directions. Contour maps of the bed

profile are predicted as a function of space and time using the developed approach.

The life time of the Aswan High Dam reservoir is also estimated.

The present approach is based on the field data analysis considering the limited

collected data of water flow velocity and suspended sediment concentration. It

considers the temporal and spatial changes of bed density that affects the deposited

and eroded depth. The present study shows good agreement between the measured and

predicted cross sections for the period from 1980 to 1995 and consequently provides

reliable prediction mechanism for the cross sections and bed contours for the Aswan

High Dam reservoir. Prediction computer runs show that the deposition will continue

until year 2000 in the first 140 km of the reservoir and the bed level will rise 1.5 m in

average to reach the level 160 m above mean sea level. This deposition will be

followed by an erosion period until year 2010 and the bed level will reach 150 m in

the same reach. The eroded sediment will move to the next 60 km towards the dam

direction. The life time of dead zone of Aswan High Dam Reservoir is expected to be

311 years and 1202 years for the live zone. A rough estimation of bed sediment to

reach the entrance of the South Valley Canal (Toushka) is about 40 years.

vi

CONTENTS

Page

ACKNOWLEDGMENTS ............................................................................................ ii

ABSTRACT ................................................................................................................ iii

LIST OF TABLES .................................................................................................... viii

LIST OF FIGURES ...................................................................................................... x

LIST OF SYMBOLS AND ABBREVIATIONS ..................................................... xiii

1. INTRODUCTION .................................................................................................. 1

1.1 The Aswan High Dam .............................................................................. 1

1.2 The Aswan High Dam Reservoir (AHDR) ............................................... 1

1.3 Inflow ........................................................................................................ 3

1.4 Outflow ..................................................................................................... 3

1.5 The Suspended Solids in The Reservoir ................................................... 5

1.6 Toushka Spillway ...................................................................................... 6

1.7 South Valley Canal ................................................................................... 6

1.8 Problem Identification .............................................................................. 6

1.9 Research Objectives .................................................................................. 7

2. DATA PRESENTATION ...................................................................................... 9

2.1 Introduction ............................................................................................... 9

2.2 The Cross Sections .................................................................................... 9

2.3 Water Velocities ...................................................................................... 12

2.4 Suspended Sediment Concentration ....................................................... 12

2.5 Water Level Measurements .................................................................... 16

2.6 Grain Size Distribution of Bed Material ................................................ 21

vii

2.7 Discharges at Dongola ............................................................................ 21

3. LITERATURE REVIEW .................................................................................... 27

3.1 The Deposited Sediment in AHDR ......................................................... 27

3.2 Suspended Sediment Constituents .......................................................... 28

3.3 The Water Flow and Sediment Interaction ............................................. 28

3.4 Numerical Models for Sedimentation in Reservoirs ............................... 30

3.5 Review of The Studies Related to The AHDR ....................................... 34

3.6 Consolidation of Deposited Sediment .................................................... 38

4. DATA ANALYSIS ............................................................................................... 45

4.1 Introduction ............................................................................................. 45

4.2 Cross Sections Characteristics ................................................................ 45

4.3 Flow Velocities ....................................................................................... 45

4.4 Transverse Currents Distribution ........................................................... 47

4.5 Discharges Passing Different Cross Sections ......................................... 52

4.6 Suspended Sediment Concentrations ...................................................... 58

4.7 Grain Size Distribution ........................................................................... 61

5. METHODOLOGY ............................................................................................... 62

5.1 Introduction ............................................................................................. 62

5.2 Estimation of The Sediment Load .......................................................... 62

5.3 The Adjustment Factor for The Discharge (Ri) ...................................... 63

5.4 Estimation of The Deposited Sediment Volume..................................... 65

5.5 Estimation of The Deposited Area .......................................................... 67

5.6 Adjustment Factor for The Deposited Area (Zi) ..................................... 68

5.7 Estimation of The Deposited Depth ........................................................ 72

5.8 Comments on The Adjustment Factors ................................................... 75

5.9 Verification of Results ............................................................................ 76

5.10 Prediction of Bed Profile ...................................................................... 76

viii

6. DISCUSSION OF RESULTS .............................................................................. 81

6.1 Discharge and Sediment Adjustment Factors ......................................... 81

6.2 Contour Maps for 1995 and 2000 ........................................................... 84

6.3 Prediction of AHDR Life Time .............................................................. 91

6.4 Predictions of Bed Profile ....................................................................... 92

7. CONCLUSIONS AND RECOMMENDATIONS ............................................. 97

7.1 Conclusions ............................................................................................. 97

7.2 Recommendations ................................................................................... 98

REFERENCES ....................................................................................................... 100

APPENDICES ........................................................................................................ 107

ix

Appendices

Appendix 1 The Measured Cross Sections .......................................... (On diskette)

Appendix 2 The Measured Velocities .................................................. (On diskette)

Appendix 3 The Measured Suspended Sediment Concentrations ....... (On diskette)

Appendix 4 The Computer Program REGULAR.FOR ....................... (On diskette)

Appendix 5 The Relative Distribution of Currents and their Coefficients .......... 107

Appendix 6 The Relation between Discharge at Dongola and

Suspended Sediment Concentration at Each Section ...................... 137

Appendix 7 The calculation Procedure of Lag Time .......................................... 142

Appendix 8 The Calculated and Measured Cross Sections of 1992 .................... 144

Appendix 9 The Calculated and Measured Cross Sections of 1993 .................... 150

Appendix 10 The Calculated and Measured Cross Sections of 1995 .................... 155

Appendix 11 The Predicted Cross Sections of 2000 ............................................. 162

Appendix 12 The Computer Program CONTOUR.FOR ....................... (On diskette)

x

LIST OF TABLES

Page

Table 2.1 Distances of Fixed Cross Sections Upstream AHD ........................... 10

Table 2.2 Average Suspended Sediment Concentration at Kajnarity

Station (1929-1955) ........................................................................... 14

Table 2.3 The Average Monthly Water Level just

Upstream AHD in meter (1964-1995) ............................................... 17

Table 2.4 Median Diameter D50 of Measured Bed Material

Samples in Micron ............................................................................. 22

Table 2.5 Percentage of Sand, Silt, and Clay in Bed Material

(October 81) as an example ................................................................ 23

Table 2.6 10 Day Mean of Discharge at Dongola in Million m3/Day ............... 24

Table 3.1 Lane Constants for Estimating The Density of

Reservoir Sediments ........................................................................... 40

Table 3.2 Trask Coefficients for The Initial Density ......................................... 40

Table 4.1a Measured C.Sec.19 (Year 1993) at Irregular Distances ..................... 46

Table 4.1b Corresponding C.Sec.19 (Year 1993) at Regular Distances .............. 46

Table 4.2 Velocity Measurements During The Period (1980-1992) .................. 48

Table 4.3 The Coefficients of The Velocity Distribution Curve

at Each Section .................................................................................. 51

Table 4.4 Discharge Calculation Procedure C.Sec.19 (Date 28.10.1981) ......... 57

xi

Table 4.5 Measured Suspended Sediment Concentrations in mg/l .................... 59

Table 4.6 Coefficients of The Discharge and Suspended Sediment

Concentration Curves ......................................................................... 60

Table 4.7 Calculation of Minimum and Maximum Density for

Various Cross Section Using Lane-Koelzer equation

& Trask Constants .............................................................................. 61

Table 5.1 The Adjustment Factor for The Discharge (Ri) ................................. 64

Table 5.2 Lag Time between Dongola Station and Each Section ...................... 65

Table 5.3 Calculated Density of Deposited Sediment (kg/m3) Using

The Approach Presented by Abdel-Aziz, T.M. in 1991 .................... 66

Table 5.4 The Length of The Different Reaches Represented by

The Given Cross Section .................................................................... 67

Table 5.5 The Adjustment Factor for The Deposited Area (Zi) ......................... 69

Table 5.6 Steps of Calculation of The Deposited Depth

(C.Sec.23 from 1990 to 1992) ............................................................ 73

Table 6.1 Volume of The Deposited Sediment From 1964 to 1995 .................. 91

xii

LIST OF FIGURES

Page

Figure 1.1 Map Showing The Location of The Nile AHD and AHDR ........................ 2

Figure 1.2 10 Day Mean of Discharge at Dongola

(750 km u/s AHD) Year 1985 .............................................................. 4

Figure 1.3 Comparison between measured and calculated

by 1-D model (C.Sec. 6) ...................................................................... 8

Figure 2.1 Map Showing The Locations of Fixed Cross Sections

Upstream AHD ................................................................................... 11

Figure 2.2 Points of Measured Velocity at Each Cross Section ................................. 13

Figure 2.3 A Typical Diagram for The Velocity Distribution

in The Vertical Direction.................................................................... 13

Figure 2.4 The Distribution of Suspended Sediment Concentration

During The Year At Kajnarity ........................................................... 15

Figure 2.5 The Average Monthly Water Level Upstream AHD ................................. 19

Figure 2.6 The Relation Between Water Level U/S AHD and

The Surface Area of Reservoir ........................................................... 20

Figure 2.7 The Relation Between Water Level U/S AHD and

The Water Contents of Reservoir ....................................................... 21

Figure 2.8 10 Day Mean of Discharge at Dongola

(750 km Upstream AHD) ................................................................... 26

Figure 4.1 Relative Distribution of Currents in Transverse Direction

xiii

(C.Sec.23 Km 487.5 U/S AHD) ......................................................... 54

Figure 4.2 First Coefficient in Transverse Direction

(C.Sec.23 Km 487.5 U/S AHD) ......................................................... 54

Figure 4.3 Second Coefficient in Transverse Direction

(C.Sec.23 Km 487.5 U/S AHD) ......................................................... 55

Figure 4.4 Third Coefficient in Transverse Direction

(C.Sec.23 Km 487.5 U/S AHD) ......................................................... 55

Figure 4.5 Fourth Coefficient in Transverse Direction

(C.Sec.23 Km 487.5 U/S AHD) ......................................................... 56

Figure 4.6 Fifth Coefficient in Transverse Direction

(C.Sec.23 Km 487.5 U/S AHD) ......................................................... 56

Figure 4.7 Correlation Between Discharge at Dongola and Suspended

Sediment Concentration at C.Sec.23 ................................................. 60

Figure 5.1 Deposited Depth at Calculated C.Sec.19 from

Year 1990 to Year 1992 ..................................................................... 74

Figure 5.2 C.Sec.13 (Km 431.0 U/S AHD) Year 1992............................................... 77

Figure 5.3 C.Sec.8 (Km 403.5 U/S AHD) Year 1993................................................. 78

Figure 5.4 C.Sec.10 (Km 415.5 U/S AHD) Year 2000............................................... 79

Figure 5.5 Flow Chart of The Calculation Procedure ................................................. 80

Figure 6.1 C.Sec.16 (Km 448.0 U/S AHD) Year 1992............................................... 82

Figure 6.2 C.Sec.D (Km 372.0 U/S AHD) Year 1992 ................................................ 83

xiv

Figure 6.3 C.Sec.23 (Km 487.5 U/S AHD) Year 1993............................................... 85

Figure 6.4 C.Sec.3 (Km 378.0 U/S AHD) Year 1993................................................. 86

Figure 6.5 C.Sec.19 (Km 466.0 U/S AHD) Year 1995............................................... 87

Figure 6.6 C.Sec.6 (Km 394.0 U/S AHD) Year 1995................................................. 88

Figure 6.7 Contour Map of AHDR (Year 1995) ......................................................... 89

Figure 6.8 Contour Map of AHDR (Year 2000) ......................................................... 90

Figure 6.9 C.Sec.23 (Km 487.5 U/S AHD) Year 2000............................................... 94

Figure 6.10 C.Sec.3 (Km 378.0 U/S AHD) Year 2000 ......................................... 95

Figure 6.11 Changes in Bed Profile for AHDR

For estimated period (1964 - 2010) .................................................... 96

xv

LIST OF SYMBOLS AND ABBREVIATIONS

A1, A2, A3,

A4, A5 Coefficients of the Velocity Distribution Curves

A, B The Coefficients of the Discharge and Suspended Sediment

Concentration Curves

AHD Aswan High Dam

AHDR Aswan High Dam Reservoir

B1, B2, B3

B4, B5 Coefficients of the Velocity Distribution Curves

C1, C2, C3 The First, The Second, The Third, The fourth, and The Fifth Coefficient

C4, C5 of the Relative Distribution of Currents in the Transverse direction

Css Suspended Sediment Concentration

C.Sec. Cross Section

D50 Median Diameter

PPM Part Per Million

Qs Total Sediment Load

Qw Water discharge

xvi

Ri The Adjustment Factor for the Discharge

T Time

U/S Upstream

V Water velocity

X Distance in the Transverse Direction

Zi The Adjustment Factor for the Deposited Area

1

CHAPTER 1

INTRODUCTION

1.1 The Aswan High Dam

The Aswan High Dam (AHD) is a rockfill dam, closing the Nile at a distance of 6.5

km upstream of the old Aswan Dam, about 950 km south of Cairo as shown in

Figure (1.1). The dam is 3600 m long and has a width of 40 m at the top and 980 m

at the bed level. The maximum height of the dam is 111 m above the river bed. The

water is discharged downstream the dam through 6 tunnels located at the eastern side

where the water flow is used for the operation of the Francis turbines for electrical

power generation. These turbines were designed to work at their full power as long

as the upstream water level is higher than 150 m above sea level, therefore this level

was considered as the critical water level. On the western side there is a spillway to

release the water that exceeds the maximum storage capacity when the water level

reaches more than 182 m level. The spillway was designed to release the flow

whenever the level of 182 m is exceeded with a maximum discharge of 2400 m3/sec.

Construction began on the Aswan High Dam in 1960. By 1964 the river was blocked

with a coffer dam, and the upstream reservoir began to fill. The construction of the

Dam itself was completed in 1970.

1.2 The Aswan High Dam Reservoir (AHDR)

The construction of the AHD upstream of the old Aswan Dam, made it possible to

have an overyear water storage and thus create a reservoir upstream the dam. The

length of the AHD reservoir is about 500 km at its maximum storage level, which is

182 m, with an average width of about 12 km and a surface area of 6540 km2. This

reservoir is considered to be the second largest man-made lake in the world, where

the storage capacity of the reservoir has a volume of 162 km3 divided into three

zones: dead storage capacity of 31.6 km3 between levels 85 m and 147 m, live

2

storage capacity of 90.7 km3 from level 147 m to 175 m, and flood protection

capacity of 39.7 km3 ranging between levels 175 m and 182 m that is the maximum

level of the reservoir.

Figure 1.1 Map showing the location of the AHD and AHDR.

Hydrology of the Nile Basin, p. 448 (M. Shahin, 1985)

3

1.3- Inflow

The continuous record of discharge at Dongola station (750 km upstream AHD)

shows that there are two stages for the Nile river namely: (1) The rising stage which

is distinguished by the sharp increase in the discharge, and an increase in the river

levels. This stage starts by the end of July and reaches its peak around the middle of

September and (2) The falling stage where the discharge starts to have lower values

during the months October to June. Figure 1.2 indicates the 10 day mean of

discharge at Dongola during the year 1985 as an example. The measured discharges

during the period (1964-1995) at Dongola were collected and presented in chapter 2,

where it is noticed that the maximum discharge reached 11397 m3/s in September

1975 and the minimum discharge was 582 m3/s for the month of March 1975. In

general, most of the measured discharges range between 6000 and 2000 m3/s.

1.4- Outflow

Before the construction of the AHD water was running in the Nile and its branches

on its way to the Mediterranean Sea following the normal flow hydrograph shown in

Figure (1.2). A certain part of this flow was used for land irrigation and for domestic

purposes and the rest was discharged to the Mediterranean Sea. Before the

construction and operation of the storage works on the Nile, agriculture in Egypt

depended almost entirely on the natural supply of the river. A short distance

downstream Cairo, the river bifurcates into two branches: Damietta and Rosetta.

These branches are the main source of water feeding the irrigation canals in Lower

Egypt. They were also used in the pre-Aswan High Dam period to convey the excess

flood water to the Mediterranean Sea. This is no longer the case after exercising full

control of the Nile water by means of the AHD. From the measured outflow at

Elgaafra station (34 km downstream AHD) during the period (1964-1995), It is

noticed that the outflow in the period (1964-1970) was high in the range of 5000

m3/s because the flow was partially under control during the construction period of

the AHD, and it decreased to the normal range (1000-2400) m3/s when it became

completely under control.

4

5

1.5- The suspended sediment in the reservoir

Under natural flow conditions, high concentrations of suspended sediments were

transported by the Nile as it crossed the northeastern desert of Africa, and deposited

in its lower course as rich alluvial soil. The main source of suspended matter are the

two main tributaries of the Nile, the Atbara and Blue Nile Rivers. Ninety five percent

of sediments originate from the Ethiopian Plateau through the Blue Nile and Atbara

River and less than 5% from Equatorial Lakes through the White Nile and its

tributaries.

Before operation of AHD in 1964, all major hydraulic structures including the old

Aswan Dam were designed and built in such a way as to permit the suspended

sediments, during flood flow to be carried through the reservoirs and to the

downstream along the river course to the sea. As The AHD was designed as an over

year storage reservoir, most of the river’s suspended sediments are deposited in the

upstream reservoir. The life span of the Aswan High Dam reservoir (AHDR) was

estimated by some investigators to be 450 years. This is the time period in which

suspended sediments would fill the dead storage zone of the reservoir.

Prior to the construction and operation of AHD, in 1964, 9-10 million tons of

suspended sediment were deposited annually on the flood plains of the Nile, while

about 93% of the total average annual suspended load of 124 million tons was

carried out to the Mediterranean Sea. Since the full operation of AHD in 1970, the

flood discharge of the Nile, downstream the dam, has been greatly modified and

more than 98% of the total suspended load was retained within the reservoir and the

total amount of sediment transported downstream the reservoir dropped to only 2.5

million tons/year.

1.6- Toushka spillway

Toushka spillway (260 km upstream AHD) was constructed to release the excess

6

water when water level reaches 178 m. The excess water is discharged to a natural

depression located at the western side. This flow will help in limiting the outflow

behind the dam to values ranging for 350 or 400 million m3/day which are the

discharge values that cause no harm to the Nile bed. The water flows over the

spillway to a channel called Toushka canal of a length 22 km until it reaches the

depression. The lowest level of the depression is 150 m above sea level while the

highest level is 190 m. The surface area of the depression is about 6000 km2 and it

can contain about 120*109 million m3.

1.7- South valley canal

The south valley canal aims to create a new civilization and society around a valley

parallel to the present Nile valley where it is expected to serve water for the

agriculture of about 3.4 million feddan in the first stage. The entrance of this canal is

located 10 km downstream Toushka spillway (250 km upstream AHD). A pump

station is designed to lift water from the lowest water level in the Aswan High Dam

reservoir that is 147 m. This means that the flow through this canal will not depend

on the presence of high floods. The pump station will lift the water for about 73 m to

reach the highest natural level close to the canal then the water will flow by gravity

through the entire length of the canal. The length of the south valley canal is about

320 km in the first stage then it will extend in different directions to reach about 800

km.

1.8- Problem identification

A well-known problem associated with the construction of any dam is the creation of

a reservoir that traps sediments supplied by the contributing river. In general a delta

formation occurs in the reservoir. The trapped sediment transported towards the dam

through moving waves of erosion and deposition. This deposition will affect the

storage capacity of the reservoir. Also the movement of sediment in the transverse

and longitudinal directions will affect any development projects that may take place

7

at the banks of the reservoir such as the new valley canal. The erosion will affect the

stability of the banks and in turn the planning for development of these banks.

The problem of sediment transport in reservoirs has been tackled using One-

dimensional model for example by EL-Manadely, M.S. (1991) and Abdel-Aziz, T.M.

(1991). These models give a global overview and approximate values for the

sediment movement in the longitudinal direction only. The One-dimensional model

may give good estimation of the total amount of sediment load that deposits in the

reservoir, but it does not give information about the distribution of such deposits in

the longitudinal and transverse directions.

A typical measured cross section at distance 394 km upstream AHD and the

distribution of the deposited sediment during the period (1990-1992) are indicated in

Figure (1.3). The calculated cross section using the one-D model of Abdel-Aziz,

T.M. (1991) is shown as compared to the measured ones. This figure demonstrates

the limitation of information resulting from the application of the one-D models.

1.9- Research objectives

Determination of the amounts and distributions of sediment in the longitudinal and

transverse directions in AHDR is needed. This is not only for getting reservoir

capacity, but also for possible utilization of these deposited sediments in the future.

Therefore the objectives for this research are to:-

1- Develop a new methodological approach for analyzing the field data taking into

consideration the limited collected data of flow velocity and suspended sediment

concentration.

2- Estimate the life time of the reservoir considering the effect of sediment

consolidation and the actual shape of bed profile in the longitudinal and transverse

directions.

3- Simulate the spatial and temporal changes of deposition and erosion in the AHDR

to predict the sediment front location in the longitudinal and transverse directions.

8

4- Develop the bed contour maps as a function of time.

5- Present an approach to estimate the temporal and spatial changes of bed sediment

density that affect the deposited and eroded depth in the reservoir.

Regular field trips being conducted in the reservoir for monitoring sediment

accumulation are rather expensive, time consuming. The use of the results of the

present study may help in getting the needed information. However, the number of

trips and the amount of work conducted per trip should continue for verification and

modification of the developed approach.

9

CHAPTER 2

DATA PRESENTATION

2.1- Introduction

Before the construction of AHD, the collection of data started at the expected

location of the reservoir and at several control stations such as Kajnarity (399 km

upstream AHD) and Dongola (750 km upstream AHD). After the construction of

AHD and by year 1975, regular field trips take place once a year to measure several

variables at fixed locations along the reservoir. These data include the cross sections,

velocities, suspended sediment concentrations, bed material and water levels.

The data used for this study were gathered from the files of the following authorities:

Nile Research Institute (NRI), National Water Research Center (NWRC), High and

Aswan Dam Authority (HADA), and Nile Control Authority (NCA), Ministry of

Public Works and Water Resources (MPWWR).

2.2- The cross sections

Field survey of 13 cross sections was carried out after the construction of AHD along

the expected backwater curve, extending from km 487.5 to km 325.1 upstream the

dam. The main purposes of these measurements are:

1- To establish fixed locations where measurements of bed levels in the transverse

direction can be carried out to compare the change of the river morphology before

and after the dam construction and between any successive years.

2- To establish fixed locations where measurements of deposited sediment,

suspended sediment, bed material characteristics, as well as velocity values in the

vertical direction can be done periodically (once per year) as part of the regular

hydrographic survey.

3- To use the collected data to get the deposited sediment in the reservoir as a

10

function of time and space. The cross sections locations related to distances upstream

the dam are shown in Table 2.1 and Figure 2.1.

Table 2.1 Distances of fixed cross sections upstream AHD

Series No. Cross section name Distance upstream

AHD (km)

1

2

3

4

5

6

7

8

9

10

11

12

13

(El-Daka) CS-23

(Okma) CS-19

(Malek El-Nasser) CS-16

(El-Dowaishat) CS-13

(Ateere) CS-10

(Semna) CS-8

(Kajnarity) CS-6

(Morshed) CS-3

(Gomai) CS-D

(Amka) CS-27

(Elgandal Elthany) CS-26

(Doghame) CS-24

(Sara) CS-20

487.5

466.0

448.0

431.0

415.5

403.5

394.0

378.0

372.0

364.0

357.0

347.0

325.1

The depth of water is measured using an echo-sounder. Water depths of the measured

cross sections during the period from 1980 to 1995 were summarized in appendix 1. It is

realized that the width of the cross sections between km 487.5 and km 403 upstream

AHD are relatively small and in the range of (500-1000) m and the depth is in the range

of (10-20) m. The cross sections in the middle reach between km 403 and km 368

upstream AHD are wide where the width is in the range of (1000-2200) m and the depth

is in the range of (20-30) m. between km 368 and km 325.1 upstream AHD the cross

sections are very wide where the width varies between (2200-8500) m and the depth is

between (30-45) m.

11

Figure 2.1 Map showing the locations of fixed cross sections upstream AHD

12

2.3- Water velocities

Velocities were measured at three positions across the width of the section, namely at

1/3, ½, 2/3 of water surface width. The vertical points selected for velocity

measurements were located at 0.25, 0.5, 0.65, 0.8 of the water depth measured from

the water surface as a datum. Another two points at 50 cm below the water surface

and at 75 cm above the bottom of the channel were also selected for velocity

measurements. The velocity is measured using a propeller type current meter for a

period of 60 seconds for each point. Therefore, for each cross section there are 18

measurements. Figure 2.2 indicates these points for a typical cross section. The

measurements of velocity at different cross sections during the period (1980-1995)

were summarized and presented in appendix 2. It is noticed that the velocity is high in

the first five cross sections, between km 487.5 and km 415.5 upstream AHD, where

the width of the channel is narrow and the depths are small. The velocities may reach

up to 1.2 m/sec. The velocities decrease in the reach between km 403 and km 368

upstream AHD where the widths and depths are relatively large and they may reach a

maximum value of 0.6 m/sec. The velocities are very small and may reach 0.1 m/sec

or lower at the large cross sections in the reach between km 368 and km 325.1

upstream AHD. A typical diagram for the velocity distribution in the vertical

direction is indicated in figure 2.3.

2.4- Suspended sediment concentration

Time integrated suspended sediment samples were collected for three positions

across the width of the section, namely at 1/3, ½, 2/3 of stream width. The vertical

points selected for suspended sediment concentrations were located at 0.25, 0.5,

0.65, 0.8 of the depth. Another two points at 50 cm below the water surface and at 75

cm above the bottom of the channel were selected for suspended sediment

concentrations measurements. These are the same positions of measuring the

velocities. Suspended sediment concentration were obtained for each sample and the

mean suspended sediment concentration was determined

13

14

for each section. It is noted that the suspended sediment concentration is high at the

reservoir entrance, then decreases in the middle reach of the reservoir and reaches its

low levels close to the dam, similar to the velocity distribution in the longitudinal

direction. Also the suspended sediment concentration is high during the rising stage

and low for the falling stage, similar to the discharge distribution for different

months of the year. The average values of the suspended sediment concentration at

Kajnarity (399 km upstream AHD) during the period (1929-1955) is shown in Table

2.2 and Figure 2.4. It is noted that the highest values occur in August and may reach

up to 2820 parts per million (Milligram per liter), and the lowest value takes place in

May and is about 41 Milligram per liter. The collected data for suspended sediment

concentrations during the period from 1980 to 1995 at different cross sections are

given in Appendix 3.

Table 2.2 Average suspended sediment concentration at Kajnarity station (1929-

1955)

Month

Average suspended sediment

concentration (ppm)

January

February

March

April

May

June

July

August

September

October

November

December

84

60

53

50

41

44

278

2820

2497

1034

294

121

15

16

2.5- Water level measurements

The 10 day means of water level for the period from 1964 to 1995 upstream the dam

are shown in Table 2.3 and Figure 2.5. It is noticed that the water level increases in a

systematic way until year 1978 (except year 1973) with a high rate in the first five

years. The annual inflow was very high and it reached a level of 177.47 m. Then the

water level decreased during the period from 1979 to 1986 until it reached a value of

150.50 m which is very close to the critical water level where the turbines will not

be able to work at their full capacity. This period was the dry period for Africa. The

water level increased again during the period from 1986 to 1996 until it reached a

level more than 178 m. This indicates that there are almost regular cycles of wet and

dry between the two levels 178 m and 150 m. Therefore, in the present study it is

assumed that this cycle of wet and dry will continue and consequently the record data

of discharge at Dongola will be repeated again in the future.

The water level upstream the dam defines the surface area and the volume of water in

the reservoir. Figure 2.6 indicates the relation between the water surface area of the

reservoir and the water level upstream the dam. This relation may be written as:

(2.1)

Where A is the surface area in km2, and W is the water level just upstream AHD in

m.

Figure 2.7 indicates the relation between the water volume of the reservoir (V) and

the water level upstream the dam. This relation is written as:

(2.2)

Where V is the water content in billion m3,

and W is the water level just upstream the dam in m.

Table 2.3 The average monthly water level just upstream AHD in meter (1964-1995)

W*10*6.493=A 6.1911-

W*10*8.578=V 8.09817-

17

Month

Year

1964

1965

1966

1967

1968

1969

1970

1971

January

0.00

127.36

132.67

141.90

151.16

156.34

160.61

164.60

February

0.00

127.16

132.31

142.34

150.92

155.68

160.17

164.25

March

0.00

126.59

131.37

141.33

150.23

154.88

159.32

163.82

April

0.00

126.19

130.22

139.96

149.54

154.36

158.59

163.17

May

120.89

123.64

129.41

139.16

148.84

154.17

158.02

162.73

June

119.13

120.82

126.07

137.29

147.25

152.85

156.48

161.53

July

112.75

116.75

119.94

134.30

145.54

151.12

154.57

160.01

August

116.07

120.15

123.96

138.16

148.27

152.86

155.36

160.86

September

121.46

129.92

136.23

147.38

153.32

158.88

161.35

165.09

October

124.02

131.95

139.78

150.92

155.37

161.17

164.08

167.21

November

127.15

132.66

140.38

150.97

156.50

161.09

164.75

167.58

December

128.26

132.43

140.96

151.13

156.41

160.81

164.78

167.61

Table 2.3 The average monthly water level upstream AHD in meter (continued) Month

Year

1972

1973

1974

1975

1976

1977

1978

1979

January

167.48

164.45

165.82

170.28

175.59

175.85

176.63

176.78

February

167.17

163.80

165.55

169.94

175.35

175.42

176.26

176.47

March

166.59

162.97

164.76

169.31

174.97

174.78

175.66

175.94

April

166.00

162.17

163.97

168.65

174.46

174.17

174.83

175.46

May

165.53

161.47

163.31

168.17

174.01

173.69

174.21

175.06

June

164.32

160.28

162.30

167.19

173.40

172.92

173.42

174.31

July

162.91

158.76

161.24

165.93

172.58

171.93

172.57

173.34

August

162.82

159.33

163.37

166.91

173.09

172.93

173.51

173.48

September

164.30

163.17

167.59

171.62

175.47

175.74

175.76

175.06

October

165.03

165.50

170.06

174.99

176.44

176.82

176.98

175.78

November

165.17

166.29

170.60

175.66

176.44

177.11

177.40

175.89

December

164.84

166.17

170.48

175.69

176.20

177.04

177.08

175.61

Table 2.3 The average monthly water level upstream AHD in meter (continued)

18

Month

Year

1980

1981

1982

1983

1984

1985

1986

1987

January

175.29

175.51

175.09

171.50

169.11

162.65

163.50

161.46

February

174.80

175.06

174.62

170.83

168.74

161.91

162.93

160.81

March

174.22

174.53

174.06

170.12

168.06

161.00

162.11

159.88

April

173.62

173.93

173.44

169.48

167.31

160.28

161.23

158.85

May

173.13

173.47

172.97

168.92

166.72

159.46

160.51

157.96

June

172.42

172.62

172.05

167.86

165.53

158.00

159.10

156.45

July

171.42

171.49

170.83

166.46

164.04

156.39

157.36

155.12

August

172.38

171.91

170.41

165.94

163.90

157.28

158.20

154.82

September

175.23

174.16

171.76

168.26

164.56

161.66

161.07

157.59

October

176.12

175.64

172.27

169.44

164.48

164.17

162.46

158.15

November

176.17

175.88

172.52

169.82

164.01

164.22

162.61

158.44

December

175.88

175.47

172.02

169.64

163.33

163.90

162.05

158.21

Table 2.3 The average monthly water level upstream AHD in meter (continued) Month

Year

1988

1989

1990

1991

1992

1993

1994

1995

January

157.83

168.62

169.45

167.81

168.96

170.59

174.26

176.86

February

157.30

168.52

169.08

167.35

168.68

170.31

173.86

176.52

March

156.43

168.04

168.47

166.61

168.03

169.82

173.20

176.02

April

155.61

167.47

167.79

165.85

167.38

169.24

172.52

175.38

May

154.77

166.98

167.33

165.22

166.92

168.81

171.98

174.78

June

152.87

165.95

166.09

163.83

165.69

167.88

170.96

173.80

July

151.06

164.61

164.43

162.50

164.28

167.38

169.77

172.66

August

155.20

165.08

164.18

163.58

164.38

168.53

171.07

173.03

September

162.58

167.63

166.37

167.32

167.68

171.62

174.92

175.37

October

166.66

169.30

168.02

169.21

169.48

173.65

177.06

176.19

November

168.41

169.77

168.36

169.25

170.52

174.25

177.13

176.10

December

168.75

169.67

168.14

169.14

170.69

174.32

176.96

175.93

19

20

21

2.6- Grain size distribution of bed material

Samples of freshly deposited sediment that were collected at the different cross

sections along the sedimentation zone from 1980 until 1992, and mechanical analysis

was carried out to determine the grain size distribution. The average diameter of the

deposited sediment at each cross section was estimated and indicated in Table 2.4. It

is noticed that the average diameter at the inlet section (cross section 23, km 487.5

upstream AHD) is 361 microns, and at cross section 27, km 364 upstream AHD is 7

microns. Table 2.5 indicates the percentages of the deposited sediment in AHDR in

October 1981. The general trend is the decrease in the average diameter towards the

dam. The main constituents of the deposited sediment in the inlet zone are sand and

silt without any clay. But at the end of the sedimentation zone (cross section 20 at

325.1 km upstream AHD) the sediment is only clay.

2.7- Discharges at Dongola

The continuous record of discharge is available only at Dongola station (750 km

upstream AHD). The 10 day mean of discharge at Dongola for the period from 1980

to 1995 was summarized and indicated in table 2.6 and figure 2.7.

22

Table 2.4 Median diameter D50 of measured bed material samples in micron

C.Sec.

June

1980

May

1983

July

1985

November

1986

November

1987

23

19

16

13

10

8

6

3

D

27

-

55

82

34

40

30

25

-

55

-

620

594

166

86

95

139

69

-

594

-

200

242

217

95

92

145

79

-

242

-

-

341

288

146

98

102

86

-

341

-

470

530

410

11

6

11

6

7

9

8

Table 2.4 Median diameter D50 of measured bed material samples in micron

(continued)

C.Sec.

November

1988

December

1989

March

1990

May

1992

Average

D50

23

19

16

13

10

8

6

3

D

27

388

212

262

183

109

-

-

-

-

-

345

300

242

165

12

17

10

9

6

7

261

316

187

197

98

213

26

6

47

6

244

261

222

148

144

148

184

142

-

-

361

317

231

118

77

101

61

41

185

7

23

Table 2.5 Percentage of sand, silt, and clay in bed material (October 81) as an

example

C.Sec.

Left side

Middle side

Sand

Silt

Clay

Sand

Silt

Clay

23

19

16

13

10

8

6

3

D

27

100

100

0

0

7

10

8

8

7

9

0

0

32

56

54

64

48

38

37

11

0

0

68

44

39

26

44

54

56

80

100

72

10

0

7

7

10

0

7

5

0

25

80

52

79

45

45

43

45

24

0

3

10

48

11

48

45

57

48

71

Table 2.5 Percentage of sand, silt, and clay in bed material (October 81) continued

C.Sec.

Right side

Mean

Sand

Silt

Clay

Sand

Silt

Clay

23

19

16

13

10

8

6

3

D

27

100

100

15

0

12

8

6

0

10

4

0

0

72

36

63

68

64

33

24

20

0

0

13

64

25

24

30

67

66

76

100.0

90.7

8.3

0.0

8.7

8.3

8.0

2.7

8.0

6.0

0.0

8.3

61.3

48.0

65.3

59.0

52.3

38.0

35.3

18.3

0.0

1.0

30.3

52.0

25.0

32.7

39.7

59.3

56.7

75.7

24

Table 2.6: 10 day mean of discharge at Dongola in million m3/day

10-d Period

1981

1982

1983

1980

1984

1985

1986

1987

1

86.0

90.2

90.8

80.0

71.2

56.4

80.2

60.1 2

74.5

86.8

85.3

63.6

88.6

56.9

76.1

56.2

3

64.3

84.5

85.3

60.2

100.0

56.4

64.3

51.8 4

52.8

71.9

85.1

56.5

88.6

55.2

62.3

50.3

5

53.0

66.3

82.6

56.0

81.4

52.3

64.0

68.1 6

55.7

61.4

73.9

51.8

68.2

52.1

57.9

68.1

7

52.4

58.5

63.2

51.8

55.8

51.5

54.2

44.8 8

50.1

59.7

59.1

51.8

54.2

52.3

52.1

44.8

9

54.0

59.7

60.6

60.2

59.5

59.6

52.1

44.1 10

68.3

76.1

74.6

92.4

78.4

70.3

65.7

52.1

11

86.0

96.3

88.4

100.0

89.5

76.4

80.2

60.3 12

86.3

103.0

106.0

100.0

92.5

72.5

92.1

71.9

13

86.3

100.0

94.8

84.0

89.8

77.4

95.9

80.1 14

96.4

102.0

82.5

70.6

84.1

77.5

87.8

78.3

15

110.0

82.8

64.4

69.5

70.4

72.5

80.1

76.2 16

94.6

66.1

65.2

69.1

61.3

70.3

60.5

62.1

17

73.8

69.8

71.8

76.8

58.8

72.1

48.2

106.0 18

70.1

76.3

82.3

72.2

65.1

75.2

45.6

125.0

19

80.1

82.1

93.2

64.3

76.1

104.0

80.1

159.0 20

143.0

98.5

93.6

76.5

122.0

190.0

206.0

139.0

21

268.0

222.0

141.0

114.0

267.0

256.0

220.0

159.0 22

530.0

445.0

197.0

195.0

258.0

304.0

358.0

199.0

23

605.0

567.0

360.0

384.0

336.0

508.0

500.0

284.0 24

734.0

580.0

452.0

492.0

302.0

560.0

398.0

460.0

25

720.0

700.0

520.0

592.0

272.0

712.0

520.0

508.0 26

540.0

540.0

296.0

484.0

118.0

780.0

521.0

290.0

27

326.0

470.0

240.0

364.0

190.0

460.0

300.0

144.0 28

174.0

452.0

238.0

245.0

166.0

284.0

216.0

136.0

29

183.0

311.0

222.0

198.0

144.0

202.0

208.0

160.0 30

203.0

239.0

256.0

240.0

100.0

158.0

187.0

180.0

31

166.0

167.0

188.0

196.0

79.6

130.0

144.0

132.0 32

140.0

134.0

120.0

146.0

76.2

120.0

103.0

111.0

33

116.0

116.0

92.2

120.0

79.6

112.0

72.1

93.0 34

100.0

107.0

80.1

112.0

68.2

104.0

64.2

80.1

35

101.0

105.0

105.0

88.3

56.2

89.3

66.8

74.3 36

79.5

104.0

106.0

68.6

56.5

95.8

66.1

71.8

25

Table 2.6: 10 day mean of discharge at Dongola in million m3/day (continued)

10-d Period

1988

1989

1990

1991

1992

1993

1994

1995

1

69.5

108.0

88.5

64.8

92.8

88.2

83.6

78.3 2

66.3

114.0

81.5

62.2

88.2

82.4

75.8

79.5

3

64.1

95.8

67.8

51.8

76.5

79.8

116.0

76.4 4

60.3

80.2

62.7

43.8

72.5

76.1

59.7

68.3

5

51.1

72.5

60.2

43.8

66.8

74.5

58.5

61.8 6

50.2

66.3

59.9

39.2

60.5

74.0

58.1

59.0

7

50.0

60.4

47.2

40.7

62.5

67.8

55.4

61.2 8

50.0

52.6

46.0

44.2

62.2

64.2

52.5

63.3

9

60.1

55.7

49.5

48.9

61.9

65.9

55.2

61.5 10

78.3

76.1

67.8

62.3

76.5

82.4

63.8

57.7

11

84.1

82.3

108.0

76.2

92.8

88.2

74.2

60.2 12

78.1

87.8

112.0

81.8

112.0

92.3

87.5

65.3

13

65.1

108.0

108.0

76.4

100.0

102.0

97.4

89.7 14

60.1

96.3

106.0

76.5

84.6

102.0

81.2

86.0

15

54.2

86.2

80.0

65.2

72.8

79.8

77.4

79.3 16

48.5

70.2

52.4

54.2

61.9

82.0

74.2

68.7

17

45.2

68.6

47.5

62.1

64.2

128.0

67.8

59.3 18

68.1

70.2

46.2

70.4

64.8

164.0

64.3

62.9

19

100.0

88.2

52.4

70.2

84.5

156.0

63.7

63.6 20

176.0

122.0

52.4

178.0

106.0

232.0

138.0

163.5

21

430.0

264.0

132.0

290.0

204.0

304.0

316.0

150.0 22

584.0

356.0

270.0

448.0

203.0

475.0

564.4

455.0

23

876.0

383.0

380.0

396.0

460.0

592.0

744.5

635.0 24

964.0

540.0

494.0

712.0

660.0

692.0

855.1

664.0

25

960.0

666.0

460.0

680.0

700.0

680.0

908.0

575.0 26

808.0

540.0

512.0

620.0

596.0

680.0

916.8

475.0

27

692.0

364.0

364.0

520.0

396.0

532.0

626.8

280.0 28

560.0

324.0

236.0

292.0

270.0

380.0

456.4

235.0

29

348.0

320.0

246.0

136.0

252.0

332.0

242.8

202.0 30

432.0

210.0

172.0

160.0

372.0

280.0

162.3

140.0

31

356.0

172.0

126.0

172.0

308.0

195.0

126.6

133.0 32

196.0

142.0

105.0

124.0

168.0

174.0

113.3

105.0

33

168.0

114.0

82.1

108.0

148.0

138.0

108.8

92.3 34

148.0

100.0

70.2

100.0

126.0

128.0

101.5

80.7

35

110.0

88.5

76.3

96.5

104.0

116.0

90.7

77.8 36

80.2

80.0

72.1

96.5

96.5

94.5

82.0

72.2

26

27

CHAPTER 3

LITERATURE REVIEW

3.1- The deposited sediment in AHDR

Under natural flow conditions suspended solids are transported by the water course as

it crosses the northeastern desert of Africa, these solids are to be deposited in the lower

course as rich alluvial soil. The major source of suspended matter is the two main

tributaries of the Nile, Atbara and Blue Nile rivers. During the rainy season, July-

September, these rivers erode the surface soil of the Ethiopian mountains, and carry

the material northward under flood conditions. Most of sediments that being carried

by the river Nile during the flood seasons originate in the Ethiopian plateau which

represent about 95% of the total sediment loads. Less than 5% of the load originates

from the Equatorial lakes through the White Nile and its tributaries.

Before partial operation of the AHD in 1964, all major hydraulic structures including

the old Aswan Dam were designed and built in such a way to permit flow of suspended

solids, during flood season, to be carried along the river course towards the sea. The

AHD was constructed to act as an over year storage reservoir where the water volume

and load of sediment are to be stored year by year upstream the dam and the release of

the discharge for irrigation and other uses is carried out according to actual needs.

Prior to the construction of the AHD, in 1964, about 9 to 10 million tons of

suspended sediment were deposited annually in the flood plain of the Nile. This

amount represents about 7% of the total yearly sediment load carried by the river. The

total average annual suspended load of 124 million tons was transported to the

Mediterranean Sea during the flood season. Since the full operation of the AHD in

1970, the flood discharge of the Nile, downstream the dam, has been greatly modified

and more than 98% of the total suspended load has been retained within the reservoir

and the total amount of sediment transported downstream the reservoir dropped to 2.5

million tons/year.

28

3.2- Suspended sediment constituents

The results of size analysis on samples of suspended sediment taken at Kajnarity

station 399 km upstream AHD indicate that the sediments are composed of 30% fine

sand, 40% silt, and 30% clay (Hurst, Black, and Simiaka 1965). A research analysis of

the suspended sediment constituents was conducted by Makary 1982 and it was found

that the main distribution of sand, silt, and clay fractions, indicated a slight increase of

sand concentration with depth, while the distribution of silt and clay are nearly constant

along the whole depth. This means that in general there is no change in the size

distribution of suspended sediment before and after the construction of AHD.

3.3- The water flow and sediment interaction

The water flow affects the sediment transport and deposition/scour patterns along the

river course. This causes changes in the boundary roughness and channel geometry

which in turn affect the flow. This interdependency makes it difficult to analyze and

simulate flow and sediment transport. Several attempts have been made to study the

sediment-flow interaction in order to establish valid and practical correlations.

Forces exerted by the flow on a sediment particle have been investigated to study the

initiation of particle motion. Einestien and El-Samni (1949) measured pressure

difference between the bottom and the top of half-spheres forming a rough bed.

Coleman (1967), and Fenton and Abbott (1976) measured average lift and drag forces

on similar spheres.

To measure particle trajectories and to analyze fluid forces acting on sediment

transport, Bagnold (1973, 1974), Francis (1973), Luque and Beek (1976), Abbott and

Francis (1977), White and Schultz (1977), Murphy and Hooshiari (1982), have tried

to visualize different modes of particle movement. These studies have shown that

sediment particles either slide or roll over the bed or they are entrained into the flow

further from the bed.

29

Lane and Kalinske (1939), Van Rijn (1984), Akiyama and Fukushima (1986), Cutwick

and Philip (1986), and others attempted to explain and quantify the entrainment and

settlement of a particle in reservoirs. They investigated the exchange between

suspended load and bed load particles

Spasojevic and Holly (1990) incorporated the exchange between suspended load and

bed load in their model, which simulate the 2-D unsteady water and sediment

movement in natural rivers.

As summarized by Onishi (1993), the various bed forms were taken into account by

many stage-discharge predictors such as: Einstein and Barbarossa (1952), Engelund

(1966), Garde and Raju (1966), Znamenskaya (1967), Raudkivi (1967), Simons and

Richardson (1966), Haynie and Simons (1968), Kennedy and Alam (1969), Lovera

and Kennedy ((69), Maddock (1969), Mostafa and McDermid (1971), and Brownlie

(1983). Most of these predictors are based on the concept that a specific variable (e.g,

friction factor, hydraulic radius, or cross sectional area) can be divided into two

components, one corresponding to the grain roughness, and the other accounting for

bed forms. He concluded that Brownlie (1983) reveals the best presentation of the

measured data.

Vanoni (1975) compared the results of different methods against measured data and

showed a wide variation among predictors, resulting from incomplete understanding

of the relationship between bed forms and hydraulic roughness.

Many relationships have been developed to get the rate of sediment load as a function

of shear stress, water velocity, or stream power as well as fluid and sediment

properties. The major challenge for engineers is the selection of the proper sediment

discharge formula to be applied to a specific problem. After comparing 23 sediment

discharge formulas applicable to non-cohesive bed sediment, Onishini (1993)

demonstrated a wide range of variations and limitations of these formulas. He

classified the Engelund-Hansen (1967), Toffaleti (1969), Ackers-White (1973) and

Yang (1979) formulas as the most acceptable ones over a wide range of flow and

sediment conditions.

30

3.4- Numerical models for sedimentation in reservoirs

Sedimentation in reservoirs is one of the most complex problems encountered in river

hydraulics. This is due to the fact that water and sediment variables are involved in the

process of accumulation of sediment. Size and texture of the sediment particles, water

properties, variation in water and sediment flow, geometry of the reservoir, and

reservoir operation rules are considered as some of these major variables. To predict

the river-bed evolution, engineers generally resort to physical modeling and/or

numerical modeling. The latter is getting popular for its economy, time-saving,

flexibility in changing boundary and initial conditions of the problem itself, and for

increase in computational power. Most of the numerical models of sediment transport

may be classified into coupled or uncoupled models, and unsteady or quasi-steady flow

models. Uncoupled models are those in which the water-flow equations and the

sediment continuity equation are uncoupled together during a given time step, whereas

in the coupled models, all governing equations are solved simultaneously. In the

unsteady flow models, full St. Venant equations are solved but in quasi-steady flow

models, the water flow is assumed steady during the computation of bed level

variations.

HEC-6 (1977) is a model for scour and deposition developed by Thomas, W.A. and

Prasuhn, A.L. It is being used by the crops of engineering, United State Army, for

many years. It is a one-dimensional model, which does not consider the distribution of

sediment in transverse direction. The location of the channel banks and the flood plains

were considered fixed. The water flow was approximated by a series of steady flow

discharges, each of which flows for a specified period of time. The water surface

profile is calculated by solving the energy equation using standard step method and

friction losses are calculated using Manning equation. The sediment load is calculated

according to hydraulic and geometric characteristics. The new bed profile is calculated

using equation of sediment continuity with an explicit computation scheme. Sediment

transport formulas are being used to run this model.

31

Chang (1982) developed a one dimensional model called FLUVIAL-II. In this model

he computes the residual transport capacity, i.e., the ability of the stream to carry any

additional load of a particular size fraction in the presence of all of the size fractions

already present in the flow. He also determined the change of sediment discharge or

concentration with distance due to erosion and deposition. The model computes the

separate cases of erosion and deposition, update sediment concentration and update

channel bed profiles.

Karim et al. (1983) developed a one dimensional model for sediment transport. They

related the depth of degradation or aggradation to the corresponding volume of non-

moving sediment size fractions and then converted the volume of accumulated

sediment into a distributed area by assuming a diameter-thick top layer. They presented

different relations that determine the effect of the new bed profile on sediment

discharge and friction factor.

Holly, F.M., and Karim, M.F. (1986), developed a one dimensional model for

simulation bed degradation and aggradation known as (IALLUVIAL) where they

comprised the laboratory and field observations for unarmored, equilibrium transport.

The sediment discharge was considered as one of the independent variables in the

formulation of the friction factor. Because of the interdependence of the sediment

discharge and the friction factor on each other, simultaneous solution was necessary to

obtain their values for given discharge, slope, and mean sediment diameter. They used

energy equation with discharge and friction factor equations, bed-evolution

calculations using four point finite difference scheme of the sediment continuity

equation, bed material sorting and bed armoring.

One of the common and widely used models is HEC-2SR which is a combination of a

water flow model, HEC-2 developed by hydraulic Engineering Center (HEC),

USA.1982, and a sediment flow model developed by (Simons, Li and Associates

1980). The model uses a step backwater computation method for water flow, Mayer

peter-Muller formula for the bed load and Einstein method to calculate suspended

sediment capacity.

32

Molinas (1983) developed a model called STARS. He used the stream tubes to divide

each cross section into multiple equal discharge sections. This allows lateral variation

of flow and sediment movements; thus the model can simulate simultaneous erosion

and deposition within the cross section. Molinas and Yang (1986) extended the use of

stream tubes to handle one, semi-two, and semi-three dimensional cases of super

critical, critical, and subcritical flows. They used Manning, Darcy-Weisbach, and

Chezy equations to determine the energy loss along the river reach.

Chen (1988) developed REDSED model. It is a quasi-steady model to simulate water

and sediment flow for a reservoir. He used Engelund-Hansen and Colby methods to

calculate the sediment transport capacity, and Manning n for the friction, but updated

the value of n internally, depending on the reservoir’s bed elevation change.

Holley et al. (1990) extended IALLUVIAL model to CHARIMA to solve flow and

sediment routing unsteady multiple-connected fluvial channels with reverse flow. The

model simulates also cohesive sediment routing.

Bhallamudi and Chudary (1991) developed an unsteady, coupled deformable bed

model, in which the complete St. Venant equations for water and the sediment

continuity equation are solved simultaneously by the MacCormack explicit finite

difference scheme. The model is applied to predict bed level changes due to over

loading, base level lowering, and the migration of nick points.

The 2-D models generally solve the Rynolds form of the Navier-Stocks equations,

instead of the St. Venant equations.

TWODSR is an unsteady, uncoupled, finite-difference water and sediment model,

developed by Simons et al. (1979). It uses the Reynolds form of the Navier Stocks

equations with the continuity equation to simulate flow hydrodynamics.

TABS-2 is a series of unsteady, finite-element hydrodynamic and sediment transport

computer codes developed by Thomas and Hoath (1988). These codes are applicable

33

to rivers, reservoirs, and estuaries. The sediment transport component solves the

Reynolds form of the Navier Stocks equations, and does not take into account the

interaction between the bed form and friction factor.

Shimizu and Itakura (1989) developed a steady, 2-D hydrodynamic and sediment

transport model to deal with symmetric and unsymmetrical meandering channel flow.

They used Mayer Peter and Muller formula for the longitudinal sediment load, and

Hasegawa’s (1984) formula for the lateral sediment load.

Odgaard (1989) developed a steady, 2-D hydrodynamic and sediment transport model

to solve meandering flow with the associated meandering development and sediment

transport. He assumed vertical distribution of the longitudinal and lateral velocities.

By linearing velocities, he can cast the momentum equations into two variables, lateral

gradient velocity and lateral bed slope along the centerline. Qiwei et al. (1989)

developed 2-D model governed by a system of equations and boundary conditions,

which is capable of describing a variety of non-equilibrium transport of nonuniform

sediments. Olsen (1992) developed 2-D morphological model for river application.

The model includes a description of helical flow and space lag between the flow and

the suspended load transport. The model is composed of four components: a

hydrodynamic model, a sediment transport model, a bed form flow resistance model,

and a large scale morphological model.

McAnally et al. (1993) developed 3-D model called RAM10-WES. The model

computes time-varying open channel flow in 1-D, 2-D and/or 3-D by using a finite

element method to solve the Reynolds form of Navier-Stocks momentum conservation

equations, Mass continuity equation, convection-diffusion equation, and an equation

of the state for water density. The equations are fully 3-D, except for the assumption

that vertical accelerations are negligible.

Sheng (1993) developed an unsteady, finite difference model to simulate the water

flow, salinity, water temperature and sediment parameters. The model is applicable to

rivers, lakes, estuaries, coastal waters, and Oceans. He used Darcy-Weisbach,

34

Manning n, or Chezy C for the friction factor. He used a two-mode hydrodynamic

calculation with internal and external modes. For the external mode, it calculates the

water surface elevations by solving the depth averaged hydrodynamic equations with

a small time step. With the calculated water surface, the internal mode then calculates

3-D velocity distributions with a much larger time step.

M. Elfiky (1993) developed a quasi-3D model for estimating the effects of structures

or dredging activities on river systems. The flow pattern has been represented as the

discharge and velocity distributions in three dimensions along the simulated river

reach. The fluid velocities have been represented by applying a 2-D depth averaged

model, (HYD-2) in combination with the logarithmic velocity profiles to obtain a

quasi-3-D flow field.

These models demonstrated the usefulness of the mathematical approach as a decision-

making tool. However, there have been few attempts where several flow-sediment

models are tested against each other and the field data. Shou (1989) found that most

models include the option of choosing a sediment transport formula but non of them

provides the criteria needed to make a choice. All models may give different results

even when run with the same set of input data. He concluded that the computer

modeling, at present, is not a real representation but can be considered as an

approximation for the problems that it was designed for. Also Onishi (1993) concluded

that no single flow-sediment model can be selected as the best model to analyze

sediment transport for all conditions.

3.5- Review of the studies related to the AHDR

Previous studies to simulate and predict the sediment deposition/ scour in the Aswan

High Dam reservoir may be divided into two stages; the first stage started before the

construction of the Dam till year 1985 and the second stage from 1985 till present.

Investigators concentrated during the first stage on collecting and analyzing the field

data to study the characteristics of the reservoir and to get relationships between the

35

flow and the sediment load. While in the second stage they started to develop

mathematical models to describe the motion of both water and sediment flow to

simulate the water surface and bed profile in the longitudinal direction.

Hurst, Black, and Simiaka, (1965), estimated the average proportions for the

suspended matter carried by the flood based on the measured sediment concentrations

during the period 1929-1955. They concluded that there is no presence of coarse sand,

and there are 30% by weight as sand fraction, 40% silt, and 30% clay. The coarse sand

are those particles of diameter larger than 0.2 mm, fine sand particles range from 0.2

mm to 0.02 mm, the silt particle has a diameter from 0.02 mm to 0.002 mm, and the

clay size particles are less than 0.002 mm diameter.

Shalash, S., (1980), used the measured suspended sediment concentration during the

period from 1958 to 1979 to study the sediment transport along the AHDR. He

concluded that the average annual rate of sediment inflow is 142 million tons, the

average annual rate of outflow is 6 million tons, and therefore the average annual

deposited sediment is 136 million tons. He used also the available data of the total

discharge and sediment passing Kajnarity station during the period 1929-1955 to

develop a formula relating the sediment discharge to the water discharge. This formula

is used to calculate the sediment discharge flowing into the reservoir during the period

1964-1979. Using the data of the sediment discharge passing downstream the dam in

the same period, he estimated the deposited sediment to be 1570 million tons during

the 15 years. Based on average specific gravity of compacted sediment and average

annual inflow and outflow of sediment load. Shalash estimated also the life time of the

dead zone of the reservoir to be 362 years approximately.

Makary, A.Z., (1982), used the data collected between 1964 to 1980 for sediment

parameters in the Aswan High Dam reservoir, to define the Suspended sediment trend,

the deposited sediment trend, the actual useful reservoir life. He found that the bed

material fractions changed before, during, and after the flood season. Also, such

fraction changed according to the distance from the inlet of the reservoir. The fractions

for sand, silt, and clay were 30%, 40%, and 30% before the flood season; 34%, 41%,

36

and 25% during the flood season; and 20%, 50%, and 30% after the flood season. He

estimated the mean annual suspended sediment load as about 130 million tons. The

mean annual average bed level rise for the zone considered between cross section 23

(km 487.5 upstream AHD) and cross section 27 (km 364 upstream AHD) is about 0.7

m. The maximum value 0.97 m was found at cross section 3 (km 378 upstream AHD),

while the minimum value of 0.2 m was found at cross section 27. He also reported that

the maximum average annual minimum bed level height of 3.03 m was recorded at

cross section 6 (km 394 upstream AHD), and the minimum average annual minimum

bed level height of 0.65 m was that observed at cross section 27. The average annual

sediment yield was about 85 billions m3, loaded with about 80 million tons of

sediments, which when deposited their volume was about 92 millions m3. Based on

the principles proposed by Koelzer and Lane (1943), the average yearly density of the

deposited sediment was calculated and it is expected that the designed dead storage

capacity 31.6 billions m3 will be occupied by the deposited sediments in about 408

years and the total reservoir life is about 1580 years.

Dahab, A. H., (1982), compared the cross sections of the storage zone upstream the

AHD before and after the dam. He found that the total deposited sediment between km

450 and 372 upstream the dam equals 242 million m3 during the period (1968-1973),

which represents an average deposition of 48.4 million m3 per year. He assumed a

yearly deposit of 24.6 million m3 of sediments in the reach between km 372 and km

281 upstream the dam per year. Dahab compared the cross sections for the periods

from August, 1973 to November, 1979 and from November 1979 to June, 1982. The

total deposited sediment in the region between km 487 and 281 upstream the dam was

calculated to be 713.75 million m3 and 206.73 million m3 during the two periods,

respectively, Based on these calculations, he estimated the time taken to fill the dead

storage zone of the reservoir to be 310 years.

El-Moattassem, M., and Makary, A. Z., (1988), studied the sediment balance in AHDR

during the period from May 1964 to December 1985. They used the sediment and

water discharge data at Dongola during the period (1968-1973) to develop a formula

that relates the sediment load and the discharge on daily and yearly values. Using this

37

formula, and Lane-Koelzer formula for density of deposited sediment, they estimated

the deposited volume to be 1650 million m3. The calculated deposited volume from

the hydrographic survey for the same period is 1657 which is very close to the

estimated one.

Salem et al., (1987), developed a one dimensional numerical model based on the

continuity equation, the momentum equation, and the sediment continuity equation to

estimate the change in the bed profile in the longitudinal direction. The model has been

applied on the reach from km 365 to km 280 upstream AHD, and the flow conditions

assumed to be similar to the measured during the flood of 1973. The model still needs

modifications to be used for long periods or for the entire reservoir.

El-Manadely, M.S., (1991), developed a one-dimensional mathematical model to

simulate the transport of sediment in the longitudinal direction in the AHDR. The

governing equations of the model are: The water continuity equation, the momentum

equation for water, the sediment continuity equation, Brownlie (1981) frictions slope

equation, and Brownlie (1981) sediments concentration equation. The explicit finite

element technique was used to solve the continuity and momentum equations for

water. In explicit techniques, only known flow conditions at time (t) were used to

advance the solution to time (t+dt). The finite difference technique of the explicit four

point types was used to solve the sediment continuity equation. The model results of

the total volume of deposits accumulated inside the reservoir were nearly equal to the

estimated values based on field observations.

Abdel-Aziz, T. M., (1991), developed a one dimensional model to simulate and predict

the bed profile in AHDR in the longitudinal direction. The model is based on the

principle equations of water volume conservation, water momentum conservation and

a general sediment transport equation, based on an improved rating curve for Dongola

station at the inlet and a modified Bagnold’s sediment transport equation at the

reservoir. The average bed density is calculated as a mass balance of the existing

consolidating sediments influenced by deposition or erosion. The model gave good

results for the accumulated deposited sediment compared to the actual measurements

38

in the period (May 1964-November 1988). The two models of El-Manadely, M.S.

(1991), and Abdel-Aziz, T. M., (1991) gave a global overview and an approximate

values for the sediment movement in the longitudinal direction only. These models

may give good information about the total amount of sediment load that deposits in

the reservoir, but it does not give any information about the location and distribution

of this deposited sediment.

As a result of the literature review presented shows that the majority of numerical

models for open channel flow with movable bed are 1-D, while few models of 2-D and

3-D have been developed. Also, there is no model that can be used to simulate all

natural conditions of flow-sediment transport. In addition, natural watercourses are

seldom straight and prismatic. AHDR cross sections are highly irregular especially in

the transverse direction and the change in water depth is large. Therefore, in order to

predict the sediment deposition in the transverse and longitudinal directions, there is a

need to develop a new approach based on the analysis of the actual measurements.

3.6- Consolidation of deposited sediment

When the consolidation of deposited sediment occurs, the grains compacted together

and compaction occurs due to the applied water pressure. At the same time, the water

is squeezed out of the pores between grains. The analytic treatment of the problem

considers the relation between the loads on a deposit due its weight, the pressure of the

water in the pores between the grains, the resistance of the water to being squeezed

from the pores, and the stress on the grains themselves. This problem was treated by

Terzaghi (1943) for the case of a load applied to a deposit that was already well

compacted. The resulting reduction in deposited volume is small compared to the

original volume. This theory is not applicable to the case in which the compaction is

larger, e.g., for clays in reservoirs, which may have an initial density of only a fraction

its ultimate value. The problem of large compaction in sediments has been studied

theoretically and experimentally by Long (1961). He derived a nonlinear partial

differential equation describing the void ratio of the deposit in depth and time in terms

39

of the relations between void ratio and permeability and void ratio and intergranular

stress. Although the theoretical work previously outlined is useful, yet it needs more

analysis to be used to predict densities of reservoir deposits as a function of time.

Lane and Koelzer have presented a relation for estimating the density of deposit in

reservoirs, taking into account the grain size of the sediment, the method of operating

the reservoir, and time. These relationships may be written as

(3.1)

Where : the density of a deposit at the end of T years of consolidation in kg/m3

i: its initial density, usually taken to be the value after one year of

consolidation in kg/m3

B: a constant with dimensions of kg/m3

T: is time in years

(3.2)

Where Psa, Psi, Pcl : are the percentages of sand, silt, and clay

Wsa, Wsi, Wcl : are constants defined by Lane

The constants Wsa, Wsi, Wcl , and B are functions of method operating the reservoir

and are given in Table 3.1.

TB+=i

log

P*W+P*W+P*W= clclsisisasai

40

Table 3.1 Lane constants for estimating the density of reservoir sediments

Reservoir operation

Type of material

Sand

Silt

Clay

W

B

W

B

W

B

Sediment always or

nearly submerged

1488

0

1040

91

480

256

Normally moderate

reservoir drawdown

1488

0

1184

43

736

160

Considerable

reservoir drawdown

1488

0

1264

16

960

96

Reservoir normally

empty

1488

0

1312

0

1248

0

Table 3.2 Trask coefficients for the initial density

Range of sediment size (mm)

Initial density in kg/m3

0.5 - 0.25

1424

0.25 - 0.125

1424

0.125 - 0.064

1376

0.064 - 0.016

1264

0.016 - 0.004

880

0.004 - 0.001

368

0.001 - 0

48

Lane and Koelzer formula and the quantities in table 3.1 are based on measurements

of the weights of reservoir sediments and, therefore represent average results. When

41

the sediment contains material in more than one size class, the weight for each class

given by the above formula should be combined in proportion to their relative weights.

Colby (1963) proposed that the density of a sediment deposit containing several size

classes should be calculated by combining the various fractions according to their

relative volumes instead of weights because, the clay and silt are less compacted than

sand. This formula gives the density of material that has consolidated for a period of

T years after having reached its initial density in a short period of about one year.

The average density of the sediments in a reservoir after T years of operation during

which deposits accumulated at a uniform rate is obtained by integrating of Lane and

Koelzer formula with respect to time. Performing the integration from one to T years

and dividing by (T-1) years gives Miller formula as follows

(3.3)

Based on extensive studies, Miller was led to believe that the initial densities proposed

by Lane and Koelzer in table 3.1 were too large for the finer sediment and that the

values compiled by Trask were more appropriate, particularly for the finer sediments.

The values suggested by Trask are shown in table 3.2.

Marc Sas and Jean E. Berlamont, (1990), developed a mathematical model to enable

reliable predictions of mud consolidation at the port of Antwerp on the river Scheldt

in Belgium. This model was developed to get a one-dimensional consolidation of fine-

grained material, including the effects of evaporation, shrinkage and crust formation.

The model is based on a description of pore water fluxes due to different hydraulic

potentials and to settlement of the mud layers both in saturated and unsaturated

conditions. The model is based on the hydraulic conductivity function (permeability

vs, void ratio), the retention function (water content vs. void ratio) and the

consolidation function (effective stress vs. void ratio). The partial differential equation

was solved using the finite difference technique. They concluded that the consolidation

B*0.434-T*]1-T

T[*B+= i log

42

behavior of fine grained material is the most relevant characteristic with respect to the

efficiency of mud deposits.

Toorman and Jean E. Berlamont, (1990), combined both theoretical and experimental

consideration to develop a model for the prediction of settling and consolidation of

cohesive sediment that can be used in sediment transport modeling. The model solves

the sediment mass balance equation. Numerical tests on the proposed model, have

shown that it suffices to subdivide the sediment into two fractions, i.e. fine cohesive

(clays) and coarse non-cohesive (mainly sand) material. For each fraction the mass

balance equation has to be solved. They came to the conclusion that the advantages of

solving the solids mass balance instead of the fluid balance is that it enables a

distinction between different particle fractions, for as many fractions as the user wishes

to consider. Particle size measurements of mud samples from settling columns have

shown that the coarse, non-cohesive particles are concentrated in the regions where

large density peaks are measured.

Erik A. Toorman and Jean E. Berlamont, (1990), proved that the prediction of the

settling and consolidation behavior of mixtures of cohesive and non-cohesive sediment

is possible using a numerical model that solves the solids' mass balance for each

fraction. To develop a semi-empirical formulation of the settling term, the mass

transport equation has been reduced to a one-dimensional vertical mass balance

equation. A finite element is used for solution. They concluded that in general, it is

possible to calibrate the equation that relates the settling rate and the density for each

type of sediment.

Y.L. Lau, (1994), carried out experimental studies for mud deposition in an annular

flume. The experiments showed that as temperature decreased, most of the material

initially suspended would settle out. The effective settling velocity is also higher when

temperature decreases, in direct contrast to published results from settling tube

experiments. The only published report of the effect of temperature on cohesive

sediment settling, was by Owen (1972) who investigated the settling of an estuary mud

in a settling tube. It was concluded that temperature effected the settling velocity only

through the change in viscosity of the water, according to Stockes law in which the

settling velocity is inversely proportional to the kinematic viscosity. Thus it has been

common practice to correct for the effect of temperature by assuming the settling

43

velocity is inversely proportional to the kinematic viscosity. He concluded that there

is an increased deposition with larger settling velocity as temperature is lowered and

that it is likely due to the effect of electrochemical forces on the properties of the

flocks. Thus, for turbulent flows, it would be erroneous to correct for the effect of

temperature on settling velocity by assuming that the settling velocity is inversely

proportional to the kinematic viscosity as given by Stockes law.

In the present study, the density of the deposited sediment at any time step is required

to get the sediment load. The theoretical work previously mentioned has not

progressed to the point at which it can be used to predict densities of reservoir deposits,

therefore, empirical relations will be used for this purpose. The empirical relations

such as Lane and koelzer formula (1943) and Miller formula (1953) give the density

of deposits in reservoirs at the end of T years or the average density of the sediments

in reservoir after T years of operation during which deposits accumulated at a uniform

rate. In the study, the density of sediments is needed for each time step where the rate

of deposition is not uniform. An approach presented by Abdel-Aziz, T.M. in (1991)

was utilized. A formula to the estimation of the density of the deposited sediment at

any time step was derived. The relation between the density of deposits and time is

assumed to follow exponential equation given by

(3.4)

(3.5)

Where min: is the initial density at the time of sedimentation or the start of the

consolidation, max: is the maximum density of the accumulated sediments at the end

of consolidation, and : is a characteristic consolidation time.

This equation may be rearranged to be written as

(3.6)

e-1=-

-t/-

minmax

min

e]-

[=dt

d t/-

minmax

)e-)(1-(+= -t/ minmaxmin

44

Therefore, the consolidation rate is given by

(3.7)

The relative consolidation during a period dt may be evaluated as:

(3.8)

Or

) (3.9)

Where M is mass of deposited sediment, V is volume of the deposited sediment, Zb is

the bed level at any time step, Zb0 is the initial bed level, and h is thickness between Zb

and Zb0.

(3.10)

(3.11)

(3.12)

Hence, at all times the change in bed level due to consolidation can be calculated if the

density is known. It is not necessary to have the time of the sedimentation, but it

becomes necessary to simulate the density of the bed.

-=e)-(

1=

dt

d t/- maxminmax

)dt

)(-

(=d

max

)Z-Z

1d()

h

1d()

V

1d()

V

Md(d

bb 0

)d

-(dZ1

)Z-Z(2bbb

0

1)-)(Z-Z(1

-=dt

dZbb

b

max

0

dt1)--(=)

d-(=

Z-Z

dZ

bb

b max

0

45

CHAPTER 4

DATA ANALYSIS

4.1- Introduction

The different measurements of cross sections, water flow velocities, suspended

sediment concentrations, bed materials and water levels were collected and presented

in chapter 2. Among the objectives of the study is to develop a new methodological

approach for analyzing the field data. Therefore, each set of data has been treated in

a special way to help at the end to get the sediment transport in the longitudinal and

the transverse directions in AHDR.

4.2- Cross sections characteristics

The depth of water is measured at irregular distances at each cross section. In the

present study the depth of the bed level is needed at regular distances which was

selected to be 20 m. Therefore a computer program called REGULSEC.FOR was

developed to get the bed profile of any cross section for any year at regular distances

of 20 m. This program is given in appendix 4. Table 4.1a gives an example of

measured cross section, where the measurements of bed level were taken at irregular

distances and Table 4.1b gives the same cross section but at regular distances after

using the developed program.

4.3- Flow velocities

Since the velocity is the most important factor that affects the sediment transport

either in the longitudinal or the transverse direction, It was assumed that the sediment

distribution will be similar to the velocity distribution in the transverse direction.

Therefore, it is important to simulate the velocity distribution at each cross section in

the transverse direction, the developed curves will be called the relative distribution

of currents in the transverse direction.

Table 4.1a Measured C.Sec.19 Table 4.1b Corresponding

C.Sec.19

(Year 1993) at irregular distances (Year 1993) at regular distances

46

Distance (m)

from left bank

Bed level

(m)

Distance (m)

from left bank

Bed level

(m)

0.00

21.60

48.77

57.76

87.40

114.63

129.44

142.17

161.52

183.44

194.63

213.66

236.33

279.51

285.31

332.09

347.78

379.94

381.32

406.37

417.68

442.28

447.86

461.50

470.63

500.00

185.00

174.51

165.71

167.21

164.71

161.71

161.21

160.71

161.21

161.71

158.21

152.71

150.21

157.71

160.21

164.21

164.71

165.91

166.21

168.21

169.21

169.71

169.71

170.71

174.51

175.00

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

420

440

460

480

500

185.00

175.29

167.40

167.03

165.34

161.61

161.53

160.80

161.17

161.63

156.66

146.41

150.85

154.32

157.92

162.38

163.69

164.46

165.17

165.92

167.82

168.82

169.60

170.60

174.67

175.00

47

4.4- Transverse currents distribution

The calculated mean velocity at the three vertical lines for the whole cross sections

during the period from 1980 to 1992 were collected and presented in Table 4.2,

where data for years 1983, 1984, and 1985 are missing. The horizontal velocity

distribution is presented using these values assuming zero values of velocities at the

banks. The distribution is similar in shape for each cross section and was found to

have the following characteristics:

1) Similarity of distribution for the different years and for same cross sections.

2) The distribution is almost symmetrical around an axis in the middle of section.

3) It follows a polynomial distribution of fourth degree and is given by

(4.1)

in which V is the velocity at the distance X, C 1, C 2, C 3, C 4, and C 5 are coefficients.

Therefore, there are ten equations for each cross section, each of them corresponds to

one year. This means that there are ten values for C1, C2, C3, C4, and C5 as a function

of time. From these ten values a relationship was deduced for each coefficient as

function of time for each cross section. The developed relations for each cross

section have the following forms,

(4.2)

(4.3)

(4.4)

(4.5)

(4.6)

XC+XC+XC+XC+C=V 45

34

2321

B+(T)A=C 111 Ln

B+(T)A=C 222 Ln

B+(T)A=C 333 Ln

B+(T)A=C 444 Ln

B+(T)A=C 555 Ln

48

In which T is time in years, A1 , B1, A2 , B2, A3 , B3, A4, B4, A5 , and B5 are

coefficients. These factors represent the irregularity and orientation of each cross

section. They represent also the variation of the water surface width and water depth

of the different cross sections. These coefficients for the different sections were

calculated and presented in table 4.3. The developed curves for cross section 23 are

shown in figures 4.1 to 4.6. The developed curves for the other cross sections are

presented in appendix 5.

The same trend of velocity distribution is valid for all sections, i.e., C 1 is decreasing

with time for each cross section, while C 2 is increasing with time for all sections.

Therefore, it can be concluded that the same procedure for estimation the velocity

distribution may be applied at any other cross section between the existing sections

or for other ones in the dam direction.

Table 4.2 Velocity measurements during the period (1980-1992)

C.Sec. Transverse

dist. (m)

Velocity (m/sec)

Year 1992

Year 1991

Year 1990

Year 1989

Year 1988

23

0.0

0.000

0.000

0.000

0.000

0.000

135.0

0.300

0.750

0.830

0.423

0.480

202.5

0.490

0.740

0.780

0.566

0.585

270.0

0.615

0.780

0.510

0.529

0.375

405.0

0.000

0.000

0.000

0.000

0.000

19

0.0

0.000

0.000

0.000

0.000

0.000

150.0

0.433

0.630

0.760

0.423

0.370

225.0

0.478

0.750

0.740

0.459

0.525

300.0

0.330

0.470

0.690

0.413

0.230

450.0

0.000

0.000

0.000

0.000

0.000

16

0.0

0.000

0.000

0.000

0.000

140.0

0.580

0.450

0.300

0.520

210.0

0.450

0.520

0.380

0.280

280.0

0.440

0.480

0.258

0.156

420.0

0.000

0.000

0.000

0.000

49

Table 4.2 Velocity measurements during the period (1980-1992) (continued)

C.Sec. Transverse

dist. (m)

Velocity (m/sec)

Year 1992

Year 1991

Year 1990

Year 1989

Year 1988

13

0.0

0.000

0.000

0.000

0.000

0.000

280.0

0.342

0.240

0.300

0.170

0.395 420.0

0.387

0.460

0.450

0.292

0.575

560.0

0.136

0.082

0.360

0.246

0.380 840.0

0.000

0.000

0.000

0.000

0.000

10

0.0

0.000

0.000

0.000

0.000

0.000 325.0

0.196

0.240

0.300

0.166

0.275

487.5

0.235

0.330

0.340

0.198

0.385 650.0

0.229

0.250

0.170

0.096

0.520

975.0

0.000

0.000

0.000

0.000

0.000

8

0.0

0.000

0.000

0.000

0.000

0.000 270.0

0.090

0.360

0.060

0.104

0.153

405.0

0.790

0.070

0.270

0.168

0.345 540.0

0.185

0.037

0.120

0.066

0.210

810.0

0.000

0.000

0.000

0.000

0.000

6

0.0

0.000

0.000

0.000

0.000 460.0

0.350

0.240

0.126

0.250

690.0

0.170

0.240

0.139

0.200 920.0

0.180

0.180

0.075

0.200

1380.0

0.000

0.000

0.000

0.000

3

0.0

0.000

0.000

0.000

0.000

0.000 363.3

0.105

0.140

0.120

0.017

0.063

545.0

0.115

0.200

0.180

0.106

0.158 726.7

0.157

0.260

0.200

0.128

0.063

1090.0

0.000

0.000

0.000

0.000

0.000

D

0.0

0.000

0.000

0.000

0.000 520.0

0.180

0.160

0.077

0.102

780.0

0.190

0.200

0.110

0.151 1040.0

0.160

0.080

0.108

0.135

1560.0

0.000

0.000

0.000

0.000

27

0.0

0.000

0.000

0.000

1506.7

0.030

0.090

0.043

2260.0

0.030

0.060

0.043

3013.3

0.030

0.090

0.207

4520.0

0.000

0.000

0.000

50

Table 4.2 Velocity measurements during the period (1980-1992) (continued)

C.Sec.

Transverse

dist. (m)

Velocity (m/sec)

Year 1987

Year 1986

Year 1982

Year 1981

Year 1980

23

0.0

0.000

0.000

0.000

0.000

0.000

135.0

0.905

0.320

0.360

0.647

0.343

202.5

0.915

0.640

0.488

0.818

0.414

270.0

0.752

0.320

0.425

0.702

0.354

405.0

0.000

0.000

0.000

0.000

0.000

19

0.0

0.000

0.000

0.000

0.000

0.000

150.0

1.066

0.700

0.117

0.476

0.171

225.0

1.075

0.830

0.380

0.437

0.156

300.0

0.989

0.700

0.496

0.288

0.163

450.0

0.000

0.000

0.000

0.000

0.000

16

0.0

0.000

0.000

0.000

0.000

0.000

140.0

0.756

0.400

0.430

0.267

0.073

210.0

0.742

0.500

0.263

0.304

0.113

280.0

0.655

0.400

0.111

0.270

0.177

420.0

0.000

0.000

0.000

0.000

0.000

13

0.0

0.000

0.000

0.000

0.000

0.000

280.0

0.920

0.650

0.208

0.346

0.139

420.0

1.076

0.750

0.242

0.303

0.186

560.0

0.693

0.650

0.068

0.162

0.145

840.0

0.000

0.000

0.000

0.000

0.000

10

0.0

0.000

0.000

0.000

0.000

0.000

325.0

0.953

0.550

0.073

0.128

0.043

487.5

0.946

0.650

0.171

0.222

0.137

650.0

0.955

0.550

0.170

0.195

0.053

975.0

0.000

0.000

0.000

0.000

0.000

8

0.0

0.000

0.000

0.000

0.000

0.000

270.0

0.686

0.300

0.228

0.323

0.154

405.0

0.564

0.360

0.194

0.086

0.136

540.0

0.509

0.300

0.014

0.108

0.051

810.0

0.000

0.000

0.000

0.000

0.000

6

0.0

0.000

0.000

0.000

0.000

0.000

460.0

0.530

0.350

0.049

0.162

0.066

690.0

0.641

0.460

0.117

0.200

0.099

920.0

0.261

0.350

0.076

0.214

0.093

1380.0

0.000

0.000

0.000

0.000

0.000

51

Table 4.2 Velocity measurements during the period (1980-1992) (continued)

C.Sec.

Transverse

dist. (m)

Velocity (m/sec)

Year 1987

Year 1986

Year 1982

Year 1981

Year 1980

3

0.0

0.000

0.000

0.000

0.000

0.000

363.3

0.670

0.250

0.021

0.073

0.017

545.0

0.693

0.310

0.134

0.128

0.071

726.7

0.669

0.250

0.209

0.096

0.097

1090.0

0.000

0.000

0.000

0.000

0.000

D

0.0

0.000

0.000

0.000

0.000

0.000

520.0

0.507

0.150

0.192

0.146

0.015

780.0

0.596

0.210

0.041

0.137

0.038

1040.0

0.639

0.150

0.014

0.077

0.031

1560.0

0.000

0.000

0.000

0.000

0.000

27

0.0

0.000

0.000

0.000

0.000

1506.7

0.038

0.033

0.074

0.053

2260.0

0.048

0.039

0.151

0.063

3013.3

0.038

0.022

0.129

0.036

4520.0

0.000

0.000

0.000

0.000

Table 4.3 The coefficients of the velocity distribution curve at each section

C.Sec.

A1

B1

A2

B2

A3

23

19

16

13

10

8

6

3

D

27

-2.2E-14

-0.43

-0.11

-0.94

0.14

-1.83

0.03

2.07

-0.06

0.15

1.71

3.28

0.86

7.12

-1.09

13.87

-0.26

-15.74

0.49

-1.13

1.41

1.07

1.43

0.20

0.26

-0.18

0.31

0.10

-0.10

0.02

-10.70

-8.12

-10.86

-1.49

-2.00

1.36

-2.36

-0.73

0.77

-0.19

-1.5E-02

-4.5E-03

-1.2E-02

-6.6E-04

-7.6E-04

1.1E-03

-9.6E-04

2.0E-03

3.3E-04

-3.7E-05

Table 4.3 The coefficients of the velocity distribution curve at each section

(continued)

52

C.Sec.

B3

A4

B4

A5

B5

23

19

16

13

10

8

6

3

D

27

1.2E-01

3.4E-02

9.4E-02

5.0E-03

5.7E-03

-8.6E-03

7.3E-03

-1.5E-02

-2.5E-03

2.8E-04

6.3E-05

1.1E-05

3.6E-05

1.1E-06

8.4E-07

-1.6E-06

9.8E-07

6.9E-07

-3.1E07

1.4E-08

-4.8E-04

-8.3E-05

-2.7E-04

-8.1E-06

-6.4E-06

1.2E-05

-7.5E-06

-5.3E-06

2.4E-06

-1.1E-07

-7.9E-08

-8.4E+01

-3.9E-08

-6.5E-10

-3.4E-10

5.8E-10

-3.1E-10

-4.0E-10

8.2E-11

-1.6E-12

6.0E-07

5.7E-08

2.9E-07

4.9E-09

2.6E-09

-4.4E-09

2.4E-09

3.1E-09

-6.2E-10

1.2E-11

4.5- Discharges passing different cross sections

The discharge for each cross section was calculated using the velocity area method

from the indicated measurements of velocity and the measured cross section. In this

method the area of the cross section is determined from soundings; the mean flow

velocity is deduced from velocities measured at points distributed systematically

over the cross section. The discharge is then defined as:

Qw = Aj*Vj (4.7)

where Qw is the discharge, Aj is the area of strip j, and Vj is the mean velocity of

strip j.

The number of strips is three because the velocities were measured only in three

vertical locations. The used method to determine the mean velocity in the vertical

direction is the point method. It consists of taking measurements, during a certain

time interval, of the flow velocity at a selected number of points in the vertical

direction and hence determination of the mean velocity.

An example of calculating the discharge for one of the cross sections for one of the

53

regular trips is indicated in Table 4.4. Where

X is the measured distance in the transverse direction starting from the first

point of the cross section in meter.

Y is the measured bed level at distance X in meter.

W.L. is the measured water level at the cross section in meter.

dd is the calculated depth in meter under the water level, where the equation

used

dd = W.L. - Y (4.8)

dA is the calculated area in m2 of any strip between two successive points

from the relationship

dA = ½ (ddi + ddi+1)*(Xi+1 - Xi) (4.9)

Sum dA is the calculated area of the three strips

Avg. V is the calculated mean velocity at 1/3, ½ , 2/3 of the cross section width in

m/sec.

dQ is the calculated discharge in m3/sec of each strip where

dQ = Sum dA * Avg.V (4.10)

These values of discharge have been used in calculation of the sediment load at each

cross section as follows:

(4.11)

Where Qs is sediment load in kg, Qw is the calculated discharge in m3/sec, Css is the

suspended sediment concentration in kg/m3, and T is time in sec.

T*C*Q=Q ssws

54

55

56

57

Table 4.4 Discharge calculation procedure C.Sec.19 (Date 28.10.1981)

X

Y

W.L.

dd

dA Sum dA

Avg. V

dQ

m

m

m

m

m2

m2

m/sec

m3/sec

0.00

179.00

20.00

176.08

176.08

0.00

30.40

30.00

170.00

176.08

6.08

78.30

40.00

166.50

176.08

9.58

83.30

50.00

169.00

176.08

7.08

90.80

60.00

165.00

176.08

11.08

256.60

80.00

161.50

176.08

14.58

654.00

130.00

164.50

176.08

11.58

120.80

140.00

163.50

176.08

12.58

128.30

150.00

163.00

176.08

13.08

133.30

160.00

162.50

176.08

13.58

148.30

170.00

160.00

176.08

16.08

185.80

180.00

155.00

176.08

21.08

64.37

183.00

154.25

176.08

21.83

407.24 2381.50

0.48

1133.59

200.00

150.00

176.08

26.08

521.60

220.00

150.00

176.08

26.08

481.60

240.00

154.00

176.08

22.08

107.90

245.00

155.00

176.08

21.08

278.70

260.00

160.00

176.08

16.08

150.80

270.00

162.00

176.08

14.08

377.40 1918.00

0.44

837.21

300.00

165.00

176.08

11.08

251.60

320.00

162.00

176.08

14.08

291.60

340.00

161.00

176.08

15.08

291.60

360.00

162.00

176.08

14.08

565.20

400.00

161.90

176.08

14.18

511.50

450.00

169.80

176.08

6.28

185.40

480.00

170.00

176.08

6.08

96.60

500.00

172.50

176.08

3.58

77.40

530.00

174.50

176.08

1.58

26.60

550.00

175.00

176.08

1.08

5.80

560.00

176.00

176.08

0.08

1.60 2304.90

0.29

663.35

600.00

176.08

176.08

0.00

Sum=2634.15

Qw calculated at C.Sec.19 = 2634.15 m3/sec = 227.59 million m3/day

Qw measured at Dongola = 207.00 million m3/day, Lag time = 2.3 days

58

4.6- Suspended sediment concentrations

In the new methodological approach for prediction of sediment transport in the

transverse direction, it is essential to have continuous records of sediment loads, this

means that continuous records of discharge are necessary. But the only continuous

records of discharges are available at Dongola. This is in addition to one

measurement for suspended sediment concentration for each year for any cross

section. Therefore, it is necessary to identify the link between the suspended

sediment concentration at each cross section and the corresponding discharges at

Dongola. The suspended sediment concentrations at each cross section during the

period (1980-1992) were collected and indicated in Table 4.5. Using these values and

the corresponding discharges at Dongola, a relationship was deduced for each cross

section in the form :

(4.12)

In which C ss is the suspended sediment concentration at cross section in ppm, Q w

is the corresponding discharge at Dongola in million m3/day, and A, B are two

constants. The values of these constants for each cross section are indicated in Table

4.6.

It was noticed that when the discharge at Dongola is high, the suspended sediment

concentration is high at each cross section, and for low discharge values at Dongola,

the suspended sediment concentration at each cross section is low. Therefore it is

expected that similar trend for this relationship is valid at each cross section. So it is

concluded that a general formula can be developed for any other cross section in the

reservoir. One of these relations is indicated in figure 4.7 for cross section 23 where

(4.13)

The developed curves for the other cross sections are indicated in appendix 6.

B+)Q(A.=C wss Ln

613.13-)Q(*161.672=C wss Ln

59

Table 4.5 Measured suspended sediment concentrations in mg/l

C.Sec. June 1980 Oct. 1981 June 1982 Nov. 1986 Nov. 1987

23

19

16

13

10

8

6

3

D

27

65.02

46.25

36.41

27.77

27.65

28.82

27.05

16.54

17.65

16.88

285

234

177

121

106

95

81

70

66

46

33.2

33.7

34.3

32.0

26.6

26.3

21.2

21.0

13.5

12.6

152

166

211

229

172

149

223

213

132

144

274.3

281.0

283.0

205.0

186.0

138.0

157.0

192.0

117.0

196.0

Table 4.5 Measured suspended sediment concentrations in mg/l (continued)

C.Sec. Nov. 1988 Dec. 1989 Mar. 1990 Nov. 1991 May 1992

23

19

16

13

10

8

6

3

D

27

151

203

192

174

111

88

103

112

78

120

88.9

78.8

69.2

60.5

41.7

38.4

36.3

24.5

24.7

25.9

54.7

48.4

37.1

35.7

33.0

26.8

27.0

26.0

24.9

16.8

207.0

174.6

153.0

141.9

121.0

103.9

86.2

89.0

77.3

58.0

49.50

77.80

52.00

47.11

42.99

21.00

16.00

8.10

24.60

18.00

Table 4.6 Coefficients of the discharge and suspended sediment concentration curves

C.Sec. A B

23

19

16

13

10

8

6

3

D

27

161.67

151.61

133.88

99.24

75.69

64.09

64.54

69.77

48.68

62.81

-613.13

-568.23

-495.88

-352.48

-263.94

-225.48

-221.29

-246.08

-168.00

-225.64

60

61

4.7- Grain size distribution

The percentages of sand, silt, and clay of bed material samples were used in

determining the initial density at each cross section according to Lane-Koelzer

equation (3.1). The maximum densities were determined using Lane-Koelzer

equation and Trask coefficients assuming that the density will reach its maximum

value after 50 years and the results are indicated in Table 4.7. The minimum density

in section 20, where the sediment is almost clay, is 606 kg/m3; while in section 23,

where the sediment is only sand, is 1424 kg/m3. The maximum density in section 23

is the same as the initial density, which means that in case of sand there is no

difference between the minimum and the maximum densities. In section 20 the

maximum density is 921 kg/m3 about 30% higher than the initial density which

indicates that there is a considerable difference between the minimum and maximum

densities in case of clay.

Table 4.7 Calculation of minimum and maximum density for various cross sections

using Lane-Koelzer equation & Trask constants

C.Sec. Mean Fractions Minimum

density

Trask

constant

Maximum

density

Sand % Silt % Clay % Kg/m3 Kg/m3 Kg/m3

23

19

16

13

10

8

6

3

D

27

26

24

20

100

100

100

75

51.5

24

46

41

39

22

10

3.5

7

0

0

0

19

41

43

31

36

45.5

48

47

39

32

0

0

0

6

7.5

33

23

23

15.5

30

43

57.5

61

1424

1424

1424

1257

1122

842

1012

985

1013

846

714

605

606

0

0

0

33

57

124

87

92

81

120

153

183

185

1424

1424

1424

1313

1218

1052

1160

1141

1151

1051

974

915

921

62

CHAPTER 5

METHODOLOGY

5.1- Introduction

There is hardly any rainfall from Aswan to Cairo. Therefore, the main source of

water for land irrigation and domestic purposes is AHDR. Consequently,

determination of the amounts and distributions of sediment in the longitudinal and

transverse directions in AHDR is needed. This is not only for getting reservoir

capacity, but also for possible utilization of these deposited sediment in the future. In

addition, the movement of sediment will affect any development project that may

take place at the banks of the reservoir. As a result of the limited results obtained by

the one-dimensional models, there is a need to develop a new methodological

approach to simulate and predict the bed profile in the longitudinal and transverse

directions. To estimate the deposited/ eroded sediment volumes that take place at

each cross section as a result of the sediment transport associated with water flow,

the following procedure will be used.

5.2- Estimation of the sediment load

The sediment load is a function of water discharge, suspended sediment

concentration, and time. The following equation may be used to get the value of

sediment load (El-Moattassem, M., and Makary, A.Z., 1988)

(4.11)

Where: Qs is sediment load in Kg, Q w is discharge at the section in m3/sec, C ss is

suspended sediment concentration in ppm (kg/m3), and T is time in sec.

The estimation of sediment load Qs for a certain time period needs a continuous

T*C*Q=Q ssws

63

record of discharge and the corresponding suspended sediment concentration for the

whole period at each section. Since there is no continuous record of discharge or

suspended sediment concentration at each cross section, and knowing that the only

available continuous record of discharge is at Dongola station, then the records of

Dongola station will be used to estimate the corresponding suspended sediment load

at different downstream cross sections. The relationship was formed to have the

following form as explained in chapter 4.

(4.12)

The sediment load at any section is to be corrected considering the ratio of the

discharge at Dongola to the corresponding discharge at a specific section. This ratio

will be introduced as an adjustment factor for the discharge (Ri).

5.3- The adjustment factor for the discharge (Ri)

The discharge at each section at a certain time was calculated using the measured

profile of the section, the water level, and the measured velocities at the three

vertical lines for the period from 1980 to 1988. Applying the equation of the form,

(Jansen, P.Ph., 1979)

(4.7)

Where Qw is the discharge in m3/sec, Aj is

the area of one strip of the three strips of the section in m2; Vj is the mean velocity at

this strip in m/sec.

The results of the calculated discharge are shown in Table 3.4 as an example. The

ratio between the discharge at each cross section and the discharge at Dongola for

the above-mentioned years was obtained. The arithmetic mean of these ratios was

calculated to get the average Ri at each section as shown in Table 5.1. Knowing the

discharge at Dongola, the corresponding discharge at any section can be obtained

using the factor Ri (I is the section number) and considering the lag time of discharge

B+)Q(*A=C wss Ln

)V*A(=Q jjw

64

between Dongola and each section. Dongola station (750 km upstream AHD) is far

from the first section in the sedimentation zone (section 23, km 487.5 upstream

AHD) with 262.5 km. This indicates that there is a lag time between the discharge at

Dongola and the discharge at each cross section. The calculation procedure of lag

time is explained in appendix 7 and the result is presented in Table 5.2. This lag time

was used to get the corresponding value of the flow for each section related to the

value of flow at Dongola.

Table 5.1 The adjustment factor for the discharge (Ri)

C.

Sec.

Year 1980

Year 1981

Year 1982

Year 1986

Year 1987

Year 1988

Qsec.

Qd

Qsec.

Qd

Qsec.

Qd

Qsec.

Qd

Qsec.

Qd

Qsec.

Qd

23

80.94

70.60

223.96

233

57.00

71

103.18

103

199.21

167

129.91

165

19 58.02

62.20

227.59

226

112.14

74

122.16

120

182.97

167

119.33

169

16 66.78

62.20

223.86

219

58.80

75

137.01

120

195.56

167

131.19

169

13 100.93

65.40

174.83

207

105.90

75

119.68

120

145.17

167

207.52

169

10 79.40

65.40

207.00

196

82.17

76

100.21

103

180.53

147

215.78

169

8 121.32

70.10

266.66

190

73.19

77

110.34

104

144.92

147

153.30

149

6 97.15

70.10

251.98

184

96.66

76

149.02

104

145.46

147

179.15

149

3 106.24

70.10

165.05

181

159.13

77

135.83

104

162.05

147

115.21

149

D 62.35

70.10

251.97

175

162.63

75

117.74

104

138.30

147

166.54

149

27 403.71

70.10

879.25

171

187.66

74

Qsec. = Qw calculated at each section Qd = Qw measured at Dongola

Table 5.1 The adjustment factor for the discharge (Ri) (continued)

C.Sec.

R1

1980

R2

1981

R3

1982

R4

1986

R5

1987

R6

1988

Ri

Ratio

23

1.15

0.96

0.80

1.00

1.19

0.79

0.98 19

0.93

1.01

1.52

1.02

1.10

0.71

1.05

16

1.07

1.02

0.78

1.14

1.17

0.78

0.99 13

1.54

0.84

1.41

1.00

0.87

1.23

1.15

10

1.21

1.06

1.08

0.97

1.23

1.28

1.14 8

1.73

1.40

0.95

1.06

0.99

1.03

1.19

6

1.39

1.37

1.27

1.43

0.99

1.20

1.28 3

1.52

0.91

2.07

1.31

1.10

0.77

1.28

D

0.89

1.44

2.17

1.13

0.94

1.12

1.28 27

5.76

5.14

2.54

4.48

65

Table 5.2 Lag time between Dongola station and each section

C.Sec.

Distance Km

u/s AHD

L

(Km)

T (Day)

for Q1

T (Day)

for Q2

23

19

16

13

10

8

6

3

D

27

487.5

466.0

448.0

431.0

415.5

403.0

394.0

378.0

372.0

364.0

262.5

284.0

302.0

319.0

334.5

347.0

356.0

372.0

378.0

386.0

2.1

2.3

2.4

2.5

2.7

2.8

2.8

3.0

3.0

3.1

0.7

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.1

Where L = The distance between Dongola station and the section, Q1 (minimum

value) = 60 million m3/day, and Q2 (maximum value) = 800 million m3/day.

5.4- Estimation of the deposited sediment volume

The density of the deposited sediment at any time step is required to get the sediment

volume. The theoretical work has not progressed to the point at which it can be used

to predict densities of reservoir deposits. Therefore, an empirical relation will be

used for this purpose. The empirical relations such as Lane and koelzer formula

(1943) and Miller formula (1953) give the density of deposits in reservoirs at the end

of T years or the average density of the sediments in reservoir after T years of

operation during which deposits accumulated at a uniform rate. In the present study,

the density of sediments is needed for each time step where the rate of deposition is

not uniform. An approach presented by Abdel-Aziz, T.M. in 1991 was utilized. The

calculated density of deposited sediment for each cross section for same dates of the

field trips during the period from 1980 to 1995 and the predicted density for the

years 1997, 2000, and 2010 using that approach is indicated in Table 5.3.

66

Table 5.3 Calculated density of deposited sediment (kg/m3) using the approach

presented by Abdel-Aziz, T.M. in 1991

C.Sec. June

1980

Oct.

1981

June

1982

Nov.

1986

Nov.

1987

Nov.

1988

Dec.

1989

March

1990

23

19

16

13

10

8

6

3

D

27

1085

1091

1090

1091

1093

1098

1098

1098

1094

1094

1087

1095

1093

1095

1098

1103

1104

1105

1102

1094

1093

1100

1097

1100

1102

1107

1108

1109

1107

1097

1106

1117

1111

1118

1125

1125

1130

1121

1117

1114

1108

1121

1113

1122

1128

1127

1130

1117

1115

1116

1112

1125

1117

1125

1130

1125

1129

1116

1114

1119

1098

1127

1130

1131

1133

1128

1130

1114

1117

1121

1100

1128

1131

1132

1134

1129

1131

1116

1119

1122

Table 5.3 Calculated density of deposited sediment (kg/m3) using the approach

presented by Abdel-Aziz, T.M. in 1991 (continued)

C.Sec. Nov.

1991

May

1992

Dec.

1993

Jan.

1995

Jan.

1997

Jan.

2000

Jan.

2010

23

19

16

13

10

8

6

3

D

27

1093

1123

1126

1127

1130

1129

1132

1122

1123

1127

1097

1126

1128

1130

1132

1131

1135

1124

1126

1130

1100

1127

1129

1130

1132

1134

1138

1130

1132

1136

1102

1128

1131

1132

1135

1136

1141

1134

1137

1141

1098

1125

1122

1128

1129

1127

1134

1123

1127

1135

1106

1133

1130

1137

1141

1137

1144

1131

1135

1129

1122

1153

1146

1157

1166

1156

1165

1143

1147

1144

5.5- Estimation of the deposited area

67

The locations of fixed cross sections are presented in Figure 3.1. It is assumed that

each cross section represents a certain reach considering that the section is in the mid

distance of this reach. It is assumed that the calculated deposited volume for each

cross section will be distributed uniformly along the reach represented by this

section. The length of each reach is indicated in Table 5.4. Using the estimated

deposited volume and the lengths of different reaches, we get the deposited thickness

area as follows:

(5.1)

Where A: is the deposited area at each cross section in m2, Vol: is the deposited

volume along the reach represented by this section in m3, and L is the length of this

reach in m.

Table 5.4 The length of the different reaches represented by the given cross section

C.Sec. Distance upstream AHD

(km)

Length of the reach

(km)

23

19

16

13

10

8

6

3

D

27

487.5

466.0

448.0

431.0

415.5

403.5

394.0

378.0

372.0

364.0

23.25

19.75

17.50

16.25

13.75

10.75

12.75

11.00

7.00

7.50

5.6- Adjustment factor for the deposited area (Zi)

L

Vol=A

68

The calculated deposited area at each cross section should represent the measured

area during the same period. In order to satisfy this condition the calculated

deposited area is to be adjusted accordingly. The calculated deposited area was

compared to the measured one during successive periods of two years starting 1980

to 1992 and indicated in Table 5.5.

As the field trips usually do not take place at the same date every year, the measured

and estimated deposited areas were calculated for different time periods depending

on the actual dates of the field trips planned for data collection. For example, a

period of 17 months from 20th of June 1980 to 10th of October 1981 was used for

calculation as a first time span and 8 months from 10th of October 1981 to 20th of

June 1982 were used as a time span for second calculation. The first time span (17

months) contains two periods of the rising stage, where most of the sediment loads

come with water flow and one period of the falling stage, where the sediment load is

low. While the second time span (8 months) does not contain any rising stage,

therefore the sediment load was low. This may explain the difference between the

estimated deposited areas in the successive periods. To overcome this condition it

was proposed to add the calculated deposited area of two successive years and

compare it with the measured values for the same period. This has been done for four

periods namely the years from 1980 to 1982, 1986 to 1988, 1988 to 1990, and from

1990 to 1992 to get the ratios Z1, Z2, Z3, and Z4 respectively. The arithmetic mean

of these ratios were calculated to get the average value. This is called the adjustment

factor for the deposited area Zi (I is the section number). This factor adjusts the

calculated deposited area at any section during any period. So the calculated

deposited area will be divided by this adjustment factor to get the corrected deposited

area that will be distributed in the transverse direction as:

Ad = A/Zi = (Vol / L) / Zi (5.2)

Where Ad is the adjusted calculated deposited area in m2

A is the calculated deposited area in m2

Zi is the adjustment factor for the deposited area

Vol is the deposited volume in m3

70

L is the length of the reach in m

Table 5.5 The adjustment factor for the deposited area (Zi)

Measured Cross section area in m2 up to water level = 175 m

C.Sec.

1980 1981

1982

1986

1987

1988

1990

1991

1992

23

4323

3791

3355

5001

4939

5182

4679

4676

4532

19

6733

7144

6746

5714

6120

6521

4893

5860

5824

16

11002

10235

10404

8222

10120

8070

7082

7940

6985

13

11154

7751

10505

9137

11771

10784

10908

10955

9227

10

15502

9915

11839

11925

14300

13668

12274

13166

11141

8

17082

14321

16087

12298

14388

13922

12154

12867

10105

6

19414

16375

15659

18264

18868

12340

15596

13781

14164

3

25067

19659

20205

17027

18188

21387

16725

17710

15641

D

32188

24286

29502

23055

26618

29019

21430

20787

20429

27

108376

99770

101137

68719

59065

55238

Table 5.5 The adjustment factor for the deposited area (Zi) (continued) Measured deposited area in m2

C.Sec. (80-81)

(81-82)

(86-87)

(87-88)

(88-90)

(90-91)

(91-92)

23

532

435

62

-243

503

3

144

19

-411

398

-406

-401

1628

-967

36 16

767

-169

-1897

2050

987

-858

956

13

3403

-2754

-2634

988

-125

-47

1728 10

5587

-1924

-2375

632

1395

-893

2025

8

2760

-1766

-2089

465

1769

-714

2762 6

3039

716

-604

6528

-3256

1815

-383

3

5408

-546

-1161

-3199

4662

-985

2068 D

7902

-5216

-3563

-2401

7589

643

358

27

8607

-1367

9654

3826

Table 5.5 The adjustment factor for the deposited area (Zi) (continued) Calculated Deposited area in m2

C.Sec. (80-81)

(81-82)

(86-87)

(87-88)

(88-89)

(89-90)

(90-91)

(91-92)

71

23 2010.95 63.00 596.51 1856.91 702.85 19.65 2158.33 52.15

19 1816.66 64.94 930.89 2865.21 723.02 19.97 2115.21 71.98

16 1579.15 62.46 1071.94 3082.82 716.57 17.86 2008.71 60.17

13 1215.80 53.01 841.18 2979.20 674.99 18.02 2024.80 59.18

10 1330.57 53.37 890.75 2246.38 547.29 18.35 2082.44 61.94

8 1634.88 64.00 850.99 2285.79 643.71 19.68 2252.77 50.71

6 1234.42 44.67 824.48 2246.84 515.44 16.44 1666.64 34.04

3 1043.00 47.99 1168.72 2869.84 417.72 17.37 1968.56 32.09

D 1640.68 59.07 1121.95 3140.17 650.76 26.41 2769.22 73.32

27 1265.93 44.58 1776.25 4601.23 652.86 18.28 1868.32 50.45

Table 5.5 The adjustment factor for the deposited area (Zi) (continued)

C.Sec. Measured

(80-82)

Calculated

(80-82)

Z1

Ratio

Measured

(86-88)

Calculated

(86-88)

Z2

Ratio

23 967.68 2073.95 2.14 -181.08 2453.42 -13.55

19 -12.81 1881.60 -146.89 -806.99 3796.10 -4.70

16 598.68 1641.61 2.74 152.77 4154.76 27.20

13 648.47 1268.81 1.96 -1646.50 3820.38 -2.32

10 3663.45 1383.94 0.38 -1743.26 3137.13 -1.80

8 994.38 1698.88 1.71 -1623.91 3136.78 -1.93

6 3755.25 1279.09 0.34 5924.00 3071.32 0.52

3 4861.63 1090.99 0.22 -4360.58 4038.56 -0.93

D 2686.35 1699.75 0.63 -5964.22 4262.12 -0.71

27 7239.91 1310.51 0.18

Table 5.5 The adjustment factor for the deposited area (Zi) (continued)

C.Sec. Measured

(88-90)

Calculated

(88-90)

Z3

Ratio

Measured

(90-92)

Calculated

(90-92)

Z4

Ratio

23 503.04 722.50 1.44 146.57 2210.48 15.08

72

19 1628.05 742.99 0.46 -930.97 2187.19 -2.35

16

987.34

734.43

0.74

97.83

2068.88

21.15

13

-124.59

693.01

-5.56

1681.14

2083.98

1.24

10

1394.74

565.64

0.41

1132.44

2144.38

1.89

8

1768.77

663.39

0.38

2048.23

2303.48

1.12

6 -3256.22

531.88

-0.16

1432.02

1700.68

1.19

3

4661.94

435.09

0.09

1083.82

2000.65

1.85

D

7589.12

677.17

0.09

1000.84

2842.54

2.84

27

13480.49

1918.77

0.14

Table 5.5 The adjustment factor for the deposited area (Zi) (continued)

C.Sec.

Z1

(80-82)

Z2

(86-88)

Z3

(88-90)

Z4

(90-92)

Zi

Ratio

23

2.14

-13.54

1.44

15.08

8.05

19

-146.89

-4.70

0.46

-2.35

2.50

16

2.74

27.20

0.74

21.15

12.96

13

1.96

-2.32

-5.56

1.24

2.77

10

0.38

-1.80

0.41

1.89

1.12

8

1.71

-1.93

0.38

1.12

1.28

6

0.34

0.52

-0.16

1.19

0.55

3

0.22

-0.93

0.09

1.85

0.77

D

0.63

-0.71

0.09

2.84

1.07

27

0.18

0.14

0.16

5.7- Estimation of the deposited depth

It is assumed that the calculated deposited area will be distributed in the transverse

direction similar to the velocity distribution. The velocity distribution at each cross

section is a function of the longitudinal distance, the transverse distance, and time.

73

Each cross section is divided into strips of equal widths of 20 m. The average of the

two depths at the beginning and the end of each strip is calculated and considered

constant along the total width of the strip, Figure 5.1. An example for the

calculations of the deposited depth from March 1990 to May 1992 for one of the

cross sections is indicated in Table 5.6. Where

Distance (X): is the measured distance in the transverse direction starting from the

left bank in meter.

Velocity (V): is the calculated velocity in m/sec according to the developed

equation:

V = C1 + C2X + C3X2 + C4X3 + C5X4 (4.1)

Where C1‘ C2 ‘ C3 ‘ C4 ‘ and C5 are coefficients (function of time) represented by

developed curves are given in appendix 5.

Velocity strip Area is the area of each strip under the calculated velocity distribution

curve, where:

Velocity strip Area = ½(Vi +Vi+1)*(Xi+1 - Xi) (5.3)

Sediment strip Area is the corresponding area of the deposited area of the specific

strip, where:

Sediment strip Area = Velocity strip Area * (Ad/Av) (5.4)

Ad is the adjusted calculated deposited area

Av is the area under the curve of the velocity distribution in the transverse direction,

Figure 4.1

Ad = A/Zi = (Vol/L) / Zi (5.5)

Sediment strip depth is the thickness of the deposited/ eroded depth for the specific

strip, where Sediment strip depth = Sediment strip Area/b (5.6)

Where b = 20 m is the width of each strip.

The thickness of the deposited/ eroded depth will be added/ subtracted to the depth of

each strip to get the new depth of the strip. These new depths of the different strips

74

will give the new cross section. This calculated cross section will be compared to the

measured cross section in the same date. The one-dimensional model presented in

1991 by Abdel-Aziz, T.M. was first applied to check wether deposition or erosion

will take place at each section of AHDR during any period.

Table 5.6 Steps of calculation of the deposited depth (C.Sec.23 from 1990 to 1992)

Distance (X)

(m)

Velocity (V)

(m/sec)

Velocity Strip

Area (m2)

Sediment strip

Area (m2)

Sediment strip

depth (m)

0

0.00

2.96

3.22

0.16 20

0.30

7.94

8.63

0.43

40

0.50

11.26

12.23

0.61 60

0.63

13.30

14.44

0.72

80

0.70

14.41

15.66

0.78 100

0.74

14.90

16.19

0.81

120

0.75

15.01

16.31

0.82 140

0.75

14.94

16.23

0.81

160

0.74

14.84

16.12

0.81 180

0.74

14.81

16.09

0.80

200

0.74

14.90

16.18

0.81 220

0.75

15.10

16.41

0.82

240

0.76

15.38

16.70

0.84 260

0.78

15.62

16.97

0.85

280

0.79

15.69

17.05

0.85 300

0.78

15.38

16.71

0.84

320

0.76

14.45

15.70

0.79 340

0.69

12.60

13.69

0.68

360

0.57

9.48

10.30

0.52 380

0.38

4.70

5.11

0.26

400

0.09

0.24

0.26

0.01 405

0.00

75

76

5.8- Comments on the adjustment factors

The different steps of the proposed procedure start from the estimation of sediment

load until the calculation of deposited depth and then comparison between the

calculated and measured cross sections. These were carried out for each cross section

for successive periods of two years from 1980 to 1992. It is required to get the values

for the adjustment factors of discharge and the adjustment factors of the deposited

thickness area. These calculations have been repeated until we reached the most

appropriate values of these factors which are indicated in Tables 5.1 and 5.5.

For the adjustment factors of the discharge, it is noticed that these factors are

sometimes higher and sometimes lower than unity for the group of cross sections

except cross section 27. There are different conditions that may cause these

differences. These differences may be due to evaporation, seepage to the banks or to

the ground, as well as due to the lack of accuracy of velocity and cross section

measurements. For cross section 27, the width is about 4500 m that is too wide to

consider that the whole cross section will carry the discharge. The discharge will be

carried by the main channel, which is a part of the total cross section. Also having

the velocity measurements at three vertical lines in such, a wide section does not

represent the actual conditions. This may explain the large value of the adjustment

factor of discharge for cross section 27.

For the adjustment factors of the deposited thickness area, it is noticed that the values

for the cross sections 23 and 16 are high compared to other factors, and the rest are

ranging around unity except cross section 27. The movement between deposition and

erosion occurred mostly in the first three cross sections where the sediment load is

not yet stable, while at the next sections the sediment load is either deposited or

eroded. This can explain the high values of the adjustment factors of deposited

thickness area for these two sections. For cross section 27, again, it is not correct to

consider the whole section to carry the deposited or eroded sediment but only part of

the section will act as the main channel. This may explain the low value of this factor

for cross section 27. The calculated cross section 13 in May 1992 based on the

77

measured one in March 1990 is compared to the measured in May 1992 and

indicated in Figure 5.2. The calculated and measured cross sections in May 1992 are

shown in appendix 4. It is noticed that there is a good agreement between the

calculated and measured cross section for each one.

5.9- Verification of results

The measured cross sections in May 1992 were taken as reference, and the calculated

cross sections in December 1993 were calculated with the proposed methodology

without any change in the adjustment factors. The calculated cross sections were

compared to the measured ones as indicated in appendix 5. A sample is presented in

Figure 5.3 for cross section 8. From these figures, it is noticed that there is good

agreement between the calculated and the measured values for each cross section.

For other time span, the measured cross sections in December 1993 were considered

as a reference. The calculated cross sections were compared to the measured and

indicated in appendix 6. These figures also show good agreement between the

calculated and measured ones.

5.10- Prediction of bed profile

Based on the measured cross sections in January 1995 and assuming that the

discharges at Dongola will continue in the same way of filling the reservoir to reach

a water level of 178 m and then decreasing until water level 150 m, the predictions

for the sediment load, the density of the deposited sediment, and the velocity

distribution at each cross section have been calculated to get the predicted cross

sections in January 1997 and January 2000. These predicted cross sections are

indicated in appendix 7. An example for the prediction of cross section 10 is

indicated in Figure 5.4. The prediction shows that the deposition will continue until

year 1997 at every cross section and then this deposition will be followed by an

erosion period until year 2000. A summary of the steps to be followed to get the

deposited or scoured depth for any cross section is shown in Figure 5.5.

78

79

80

81

81

CHAPTER 6

DISCUSSION OF RESULTS

6.1- Discharge and sediment adjustment factors

The measured cross sections for year 1990 have been taken as reference and the

different steps of calculations were carried out to get the distribution of deposited

sediment in the transverse direction from 1990 until 1992. The calculated cross

sections were compared to the measured cross sections in 1992 and indicated in

appendix 8. For cross sections 23, 10, and 6 there is a good agreement between the

calculated and the measured sections. For cross sections 19, 8, and 27 there is a

slight difference between the measured and the calculated ones. The adjustment

factors for discharge and deposited thickness area have been fine-tuned until good

agreement was reached as indicated in Tables 5.1 and 5.5. For cross sections 16, 13,

3, and D the calculated cross sections are almost coincide with the measured ones.

The calculated and measured cross sections 16 and D are indicated in Figures 6.1 and

6.2.

To apply the results obtained from the analysis of the present approach to other

periods than those used for simulation (1980-1992), the changes in cross sections

were estimated between years 1992 and 1993 and between 1993 to 1995. For the

calculation of the cross sections in 1993, the measured cross sections in 1992 were

considered as reference. The different steps of calculations that include the sediment

load, the deposited volume, the deposited area, and the deposited depth were done to

get the cross sections in 1993. The calculated and the measured cross sections were

indicated in appendix 9. For cross sections 23, 16, 8, 3, and D the calculated cross

sections were very close to the measured ones. For cross sections 13, 10, 6, and 27

there is a slight difference between the calculated and the measured sections. For the

cross section 19, the measured cross section contains a sudden deep change in the

bed level, and the calculated cross section gives the same trend of the bed level

distribution but it does not show that sudden deep change in the bed level. This is

because that the deposited sediment distribution in the transverse direction is similar

82

83

84

To the velocity distribution which is a smooth curve. In order to be able to represent

any sudden change in the bed level, the locations of measuring the velocity should

increase in the transverse direction. The calculated and measured cross sections 23

and 3 are indicated in Figures 6.3 and 6.4.

The cross sections in 1995 have been calculated based on the measured cross

sections in 1993. The calculated and the measured cross sections in 1995 were

indicated in appendix 10. For all cross sections, the calculated areas are very close to

the measured ones except cross sections 13 and 27 where there is a slight difference

between the measured and the calculated sections. The calculated and measured

cross sections 19 and 6 are indicated in Figures 6.5 and 6.6.

6.2- Contour maps for 1995 and 2000

The measured cross sections in 1995 were used to develop the contour map using

computer software called ‘surfer’. The software assumes that the cross sections are

parallel; therefore, it was necessary to develop a computer program to consider the

actual inclination angles of the cross sections. The developed computer program is

called CONTOUR.FOR and indicated in appendix 11. After using this program, the

contour map of the actual cross sections was developed to simulate the riverbed

morphology as indicated in Figure 6.7. The same procedure has been used to develop

the contour map for the year 2000 using the predicted cross sections as indicated in

Figure 6.8. The comparison between the contour maps in 1995 and 2000 indicates

the expected change in the riverbed morphology during this period. The deposition is

expected to concentrate on the left side of the reservoir between km 460 and km 420

u/s AHD while it will settle in the middle of AHDR in the reach between km 390 and

km 365 u/s AHD.

The length of the sedimentation zone is about 150 km while the average width of the

above-mentioned cross sections is about 1.5 km except cross section 27, i.e. the

length of the contour map is about 100 times of its width, which is not suitable for

presentation. In order to overcome this problem a distorted scale has been used,

where the horizontal scale is 1: 5000 while the vertical scale of the contour map is 1:

500.

85

86

87

88

89

90

91

6.3- Prediction of AHDR life time

The measured cross sections in 1964 and the calculated ones in 1995 were compared

to calculate the deposited area at each cross section and to calculate the deposited

volume along the reservoir. Table 6.1 indicates the calculated deposited volume

during the period from 1964 to 1995. The variables shown in the table are defined as

follows:

Length (km): is the length of the reach represented by the given cross section.

Area-64 (m2): is the area of the measured cross section in 1964.

Area-95 (m2): is the area of the calculated cross section in 1995 except sections 26,

25, 22, and 20 are measured.

Dep.area (m2): is the calculated deposited area at each cross section during the period

from 1964 to 1995) = (Area-95) - (Area-64)

Dep.vol (1000 m3): is the volume of the deposited sediment at each reach where

Dep.vol (1000 m3) = Dep.area (m2) * length (km)

Table 6.1 Volume of the deposited sediment from 1964 to 1995

C.Sec.

Dist.km

u/s AHD

Length

km

Area-64

m2

Area-95

m2

Dep.area

m2

Dep.vol

1000 m3

23

487.5

23.5

6803

3510

3293

77386 19

466.0

19.8

10375

5248

5127

101264

16

448.0

17.5

14550

6602

7948

139097 13

431.0

16.3

21425

9405

12020

195320

10

415.5

13.8

26433

9027

17406

239336 8

403.5

10.8

25350

10709

14641

157386

6

394.0

12.8

30250

11925

18325

233647 3

378.0

11.0

37008

14244

22764

250401

D

372.0

5.0

42275

15340

26935

134675 28

368.0

4.0

55795

19916

35879

143518

27

364.0

5.5

118109

38571

79537

437455 26

357.0

6.0

155100

84257

70843

425057

25

352.0

13.0

203103

180645

22458

290826 22

331.1

13.5

218289

192380

25908

348469

20

325.1

3.0

252672

224624

28049

84146

Sum = 3,257,982

92

Number of years from 1964 to 1995 = 32 years

Deposited volume = 3,257,982*1000 m3

Dead zone capacity = 31.6*109 m3

Live zone capacity = 90.7*109 m3

Life time of dead zone =

Years

Life time of live zone =

Years

The life time of dead zone is about 311 years and the life time of live zone is about

1202 years. This is comparable to other investigators results (Shalash, 1980),

(Makary, 1982), and (Dahab, 1982).

6.4- Predictions of bed profile

One of the main objectives of the study is to predict the future evolution of the

sediment transport in the longitudinal and the transverse directions. Year 2000 and

year 2010 have been chosen for the prediction. The predicted cross sections are

shown in appendix 12. The predicted cross sections 23 and 3 are indicated in Figures

6.9 and 6.10.

311=32*)1000*3,257,982

10*31.6(=

9

1202=311+32*)1000*3,257,982

10*90.7(=

9

93

It is assumed that the discharges at Dongola in the period from 1978 to 1995 will be

repeated in the same way for the next 17 years. Starting from the water level of 1995,

it is assumed that there will be a slight increase in the water level until the reservoir

will be full and water level reaches 178 m, this increasing will be followed by a

decreasing period until the water level reaches 150 m. This assumption is similar to

the measurements of the average monthly water level upstream AHD as indicated in

Table 2.3 and Figure 2.5.

Forecasts show that the deposition will continue in the same way until the year 2000

in the inlet zone (from km 500 to km 360 upstream AHD). This deposition will be

followed by an erosion period in the same zone till the year 2010. Consequently, the

eroded sediment will move closer to the dam and will be deposited up to km 300

upstream AHD. The prediction in the longitudinal section is indicated in Figure 6.11.

The prediction shows that the deposited sediment will take about 11 years (from year

2000 to year 2010) to move about 60 km (from km 360 to km 300 u/s AHD). The

volume of the reach between km 300 u/s AHD to the entrance of the south valley

canal (250 km u/s AHD) is about three times the volume of the reach between km

360 and km 300 u/s AHD. Therefore, it is concluded that the deposited sediment

needs about 40 years to reach the entrance of the south valley canal. This conclusion

needs more investigation.

94

95

96

97

CHAPTER 7

CONCLUSIONS AND RECOMMENDATIONS

7.1- Conclusions

A new methodological approach is developed to simulate the change of the

deposition and the scour locations with time and space to predict the sediment front

in the longitudinal and the transverse directions of AHDR. By means of this new

approach, the contour maps of the bed profile are predicted as a function of space

and time and the life time of the reservoir is predicted. The proposed methodology is

applied to get the sedimentation depth and the time of arrival of bed sediment at the

location of the entrance of the South Valley Canal (Toushka).

The new approach depends on analyzing the field data considering the limited

collected data of water flow velocity and suspended sediment concentration. It

considers also the temporal and spatial changes of bed density that affects the

deposited and eroded depth.

The calculated cross sections in 1992, 1993, and 1995 are compared to the measured

ones to verify and demonstrate the capability of the proposed approach for analyzing

sediment transport and consolidation conditions.

The data pertaining to the cross sections, velocity measurements, suspended

sediment concentrations and the proposed computer program developed for data

analysis and carrying out the sediment deposition and scour in the longitudinal and

transverse directions is given on a computer diskette accompany this text.

Investigators and researchers may make use of this valuable information for future

studies.

Finally the following conclusions are reached:

1- The developed approach can be used for prediction of bed profile in the

98

longitudinal and the transverse directions taking into consideration the limited field

measurements such as velocity of water flow and suspended sediment concentration.

2- The total amount of the accumulated deposited sediment and its distribution on the

bed of the reservoir in the longitudinal and transverse directions during any period

may be deduced using the developed approach that takes the spatial and temporal

variations of density as a factor in the analysis and using the proposed correction

factors (Ri) for the discharge and deposited area (Zi).

3- The irregularity in the cross sections were considered as well as the changes in the

orientation of the sections with respect to the main reservoir longitudinal axis.

4- The present study identifies locations of scour and deposition across each section

in the transverse direction.

5- A contour map of bed profile can be produced for any year to define the change of

the riverbed morphology.

6- The calculated cross sections show good agreement with the field measurements

along the whole sedimentation zone.

7- The sediment deposition will continue until year 2000 in the first 140 km and the

bed level will rise 1.5 m in the average to reach level 160 m. This deposition will be

followed by an erosion period until year 2010 and the bed level will reach level 150

m. The eroded sediment will move to the next 60 km in the dam direction.

8- The life time of the dead zone of AHDR is expected to be 311 years and for the

live zone is expected to be 1202 years.

7.2- Recommendations

In order to assess the ability of the developed approach and to modify the proposed

coefficients it is recommended that:-

1-The field investigations to be extended to other cross sections between the existing

sections (almost every 5 km) to improve the contour map of bed profile.

2- The velocities and suspended sediment concentrations are to be measured at least

in 20 vertical lines instead of 3 for each cross section, as recommended by (ISO,

99

1968).

3- The field investigation may be carried out three times per year instead of one

(before, during, and after the flood period) to have measurements during the rising as

well as the falling stage. These data will be used for refining the finding of this

study.

4- Continuous measurements of suspended sediment concentration are to be carried

out at Dongola station together with the discharge to get more precise estimation of

the input sediment load.

5- Construction of a new control station at Shalal Dal (500 km upstream AHD)

which is very near to the sedimentation zone and suitable for installation of

measuring devices for discharge and sediment load is needed to give reliable values

of the input variables to the AHDR.

6- Measurements of variables for new cross sections in the dam direction to

investigate the nature of the deposition in the vicinity of the dam are necessary for

the follow up of the results of the proposed methodology.

7- Complete hydrographic survey for AHDR every 10 years using GPS (Global

Positioning System) to have a global overview for the movement of the deposited

sediment and to check the results obtained by the proposed approach may be carried

out.

8- Automatic recording for the water level at the locations of the existing cross

sections and any other new cross section using telemetry system to have a complete

control for the water level measurements is needed. This will help in accurately

calculating the discharge at each cross section and consequently comparing the

results with the present study for any modifications in the future.

100

References

1- A. Azim Abou-Elata, 1978, Egypt and the Nile after the construction of the Aswan

High Dam, Cairo, Egypt.

2- Abbott, J.E., and Francis, J.R.D., 1977, Saltation and suspension trajectories of

solid grains in a water stream. Proc. R. Soc. Lond., A. 284, pp.225-254.

3- Abdel-Aziz, T.M., 1991, Numerical modeling of sediment transport and

consolidation in the Aswan High Dam Reservoir, M.Sc. Thesis, Laboratory of

hydrology, Free University of Brussels, VUB, Belgium.

4- Akiyama, J., and Fukushima, Y., 1986, Entrainment of non cohesive bed sediment

into suspension, Third International Symposium on river sedimentation, The

university of Mississippi, March 31-April 4, pp.804-813.

5- Alam, A.M.Z., and Kennedy, J.F., 1969, Friction factors for flow in sand bed

channels, J. Hydr. Div., ASCE, Vol. 95, No.6, pp. 1973-1992.

6- Brownlie, W.L., 1983, Flow depth in sand bed channels, J. Hydraulic engineering,

ASCE, Vol. 109, No.7, pp. 959-990.

7- Chang, H.H., 1982, Mathematical model for erodible channel, J. Hydraulic

engineering, ASCE, Vol.108, No.5, pp.678-689.

8- Chen, Y.A., Lagasse, P.F., Shumm, S.A., and Simons, D.B., 1966, The river

environment, Colorado State University, Fort Collins.

9- Curwick, and Philip, B., 1986, Model of diffusion and settling for suspended

sediment transport, Third International Symposium on river sedimentation, The

university of Mississippi, March 31-April 4, pp.1690-1700.

10- Djordjevic, S., 1993, Mathematical model of unsteady transport and its

experiment verification in a compound open channel flow, J. Hydr. Research, Vol.

31, pp. 229-248.

11- Dole Whittington and Giorgio Guariso, Water management models in practice,

1983, A case study of the Aswan High Dam, Amsterdam.

101

12- Einstein and, H.A., and Barbarossa, N., 1952, River channel roughness, Trans.,

ASCE, Vol. 117, Paper No.2528.

13- El-Korany, M., 1985, Computer-based flow sediment models for Nile river

degradation, Ph.D. dissertation, Cairo university, Egypt.

14- El-Manadely, M.S., 1991, Simulation of sediment transport in the Aswan High

Dam Lake, Ph.D. Dissertation, Irrigation and Hydraulic department, Cairo

University, Egypt.

15- El-Moattassem, M., and Abdel-Aziz, T.M., 1988, A study of the characteristics

of sediment transport in the Aswan High Dam Reservoir, Report 117 NRI, Cairo,

Egypt.

16- El-Moattassem, M., and Makary, A.Z., 1988, Sedimentation balance in the

Aswan High Dam Reservoir, Report 110 NRI, Cairo, Egypt.

17- Engelund, F., 1966, Hydraulic resistance of alluvial streams, J. Hydr. Div.,

ASCE, Vol. 92, No.2, pp. 315-327.

18- Erik, A. Toorman, and Jean, E. Berlamont, 1990, Mathematical modeling of

cohesive sediment settling and consolidation, Paper, Hydraulics Laboratory,

Katholicke University Leuven, Belgium.

19- Erik, A. Toorman, and Jean, E. Berlamont, 1991, A Hindered settling model for

the prediction of settling and consolidation of cohesive sediment, Paper, Hydraulics

Laboratory, Catholic University Leuven, Belgium.

20- Fan, J., and Morris, G., 1992, Reservoir sedimentation I, Delta and Density

current deposits, J. Hydr. Engineering, ASCE, Vol. 118, No.3, pp. 354-369.

21- Francis, J.R.D., 1973, Experiments on the motion of solitary grains along the bed

of a water-stream, Proc. R. Soc. Lond., A. 332, pp. 443-471.

22- Garde, R.J., and Raju, K.G.R., 1966, Resistance relationship for alluvial channel

flow, J. Hydr. div., ASCE, Vol. 92, No.2, pp. 77-100.

23- Graf, 1971, W.H., Hydraulics of sediment transport, New York.

102

24- Graf, W.H., and Mortimer, C.H., 1979, Hydraulics of lakes, Development in

Water Science 11, Amsterdam.

25- Haynie, R.B., and Simons, D.B., 1968, Design of stable channels in alluvial

materials, J. Hydr. Div., ASCE, Vol. 94, No.6, pp. 1399-1420

26- Hurst, Black, and Simiaka, 1965, The Nile Basin, Vol. IX.

27- Hydrologic Engineering Center, 1977, HEC-6 Scour and deposition in rivers and

reservoirs, U.S. Army corps of engineering, Davis, CA, USA.

28- International Association for Hydraulic Research, IAHR, 1980, Hydraulic

Research and River Basin Development in Africa.

29- ISO, 1968, Liquid flow measurement in open channels by velocity area method,

Recommendation R748 (1st. Edn), ISO, Geneva.

30- Jansen, P.Ph., L. Van Bondegom, J. Van den Berg, M. De Vries, and A. Zanen,

1979, Principles of river engineering, The non-tidal alluvial river, London.

31- Karim, M.F., Holly, F.M., and Kennedy, J.F. 1983, Bed armoring procedures in

IALLUVIAL and application to the Missouri river, IIHR report No.269, University of

Iowa, Iowa City, USA.

32- Karim, M.F., Holly, F.M., and Yang, J.C., 1986, IALLUVIAL numerical

simulation of mobile-bed rivers, IIHR report No.309, Institute of Hydraulic Research,

University of Iowa, Iowa City, USA.

33- Lane, E.W., and Kalinske, A.A., 1939, The relation of suspended to bed material

in rivers, EOS Trans., No.20, pp.637-641.

34- Lau, Y.L., 1994, Temperature effect on settling velocity and deposition of

cohesive sediments, J. Hydr. Research, IAHR, Vol. 32. pp. 48-60.

35- Lovera, F., and Kennedy, J.F., 1969, Friction factors for flat-bed flows in sand

channels, J. Hydr. Div., Vol. 95, No.4, pp. 1227-1234.

103

36- Luque, R.F., and Vann Beek, R., 1976, Erosion and transport of bed load

sediment, J. Hydr. Res., Vol. 14, No.2, pp. 127-144.

37- Maddock, T., 1969, The behavior of straight open channels with movable beds,

Professional Paper 622-A, United States Geological survey, Washington, D.C., USA.

38- Makary, A.Z., 1982, Sedimentation in the Aswan High Dam Reservoir, Ph.D.,

dissertation, Ain Shams University, Cairo, Egypt.

39- Mamdouh Shahin, Hydrology of the Nile Basin, 1985, Developments in Water

Science: 21, Amsterdam.

40- Marc Sas, and Jean, E. Berlamont, 1990, Research on the consolidation of mud,

Paper, University of Leuven, Belgium.

41- Mostafa, M.G., and McDermid, R.M., 1971, Discussion of sediment transport

mechanics: Hydraulic relation for alluvial streams, J. Hydr. Div., ASCE, Vol. 97,

No.10, pp. 1777-1780.

42- Murphy, P.J., and Hooshairi, H., 1982, Saltation in water dynamics, J. Hydr.

Div., ASCE, Vol. 108, No.11, pp. 1251-1267.

43- Odgaard, A.J., 1989, Meander flow model. I: Development, J. Hydraulic

division, ASCE, Vol.112, No.12, pp.1117-1150.

44- Olsen, N.R.B., and Skoglund, M., 1994, Three-dimensional numerical modeling

of water and sediment flow in a sand trap, J. Hydr. Research, IAHR, Vol. 32, No.6,

pp. 833-844.

45- Onishi, Y., 1993, Sediment transport models and their testing, Proc. NATO

advanced study Inst., June 28-July 9, Washington State University, Pullman, WA.

46- Qiwei, H., 1989, Two-Dimensional non-equilibrium transport of nonuniform

sediment, Proc. Intr. Symp. Sediment transport modeling, ASCE, August 14-18, New

Orleans, Louisiana, pp. 575-580.

47- Raudkivi, A.J., 1967, Loose boundary hydraulics, Pergamon press, New York.

104

48- Rouse, H., Engineering hydraulics, Proc. 4th. Hydr. Conference, IOWA Institute

of Hydraulic Research, June 12-15, London.

49- Salem et. al., 1987, Prefeasiblity study on utilization of Nile sediments in Aswan

High Dam Lake, Development Research and Technological Planning Center, Cairo

University, Egypt.

50- Shalash, S., 1980, Effect of sedimentation on storage capacity of Aswan High

Dam Lake, NRI, Cairo, Egypt.

51- Shen, H.W., 1973, Environmental impact on rivers, Colorado. USA.

52- Shimizu, y., and Itakura, T., 1989, Calculation of bed variation in alluvial

channels, J. Hydraulic division, ASCE, Vol.115, No.3, pp.367-384.

53- Shou, S.F., 1989, An Overview of computer stream sedimentation models, Proc.

Intr. Symp. Sediment transport modeling, August 14-18, New Orleans, Louisiana,

pp.362-367.

54- Simons, D.B., and Richardson, E.V., 1966, Resistance to flow in alluvial

channels, Professional Paper 422 J, United States Geological Survey, Washington,

D.C.

55- Slay, P.G., 1984, Proc., The 3rd. Intr. Symp. Interactions between sediments and

water, Geneva, Switzerland, August 27-31, London.

56- Spasojevic, M., and Holly, F.M., 1990, 2-D Bed evolution in natural water

courses, New simulation approach, J. Waterway, Port, Coastal, and Ocean Enger,

ASCE, Vol.116, No.4, PP.425-443.

57- Traver, R.G., 1988, Transition modelingof unsteady one dimensional open

channel flow through the subcritical-supercritical interface, Ph.D. Dissertation, The

Pennsylvania State University, USA.

58- Van Rijn, L.C., 1984, Sediment transport, Part II, Suspended load transport, J.

Hydraulic engineering, ASCE, Vol.110, No.11, pp.1613-1641.

59- Vanoni, V.A., 1975, Sedimentation engineering, ASCE manuals and report on

engineering practice, ASCE, 54, New York.

105

60- Vanoni, V.A., 1977, Sedimentation engineering, prepared by the ASCE Task

Committee for the preparation of the manual on sedimentation of the sedimentation

committee of the Hydraulics Division, New York.

61- Walling, D.E., Yair, A., and Berkowicz, S., Erosion, 1990, transport and

deposition processes, IAHS, Publication 189, Oxfordshire.

62- White, B.R., and Schultz, J.C., 1977, Magnus effect in saltation, J. Fluid mech.,

ASCE, Vol.81, N0.3, pp. 497-512.

63- Williams, M.A.J., and Adamson, D.A., 1982, A land between two Niles,

Quaternary geology and biology of the central Sudan, Rotterdam.

64- Yalin, M.S., 1971, Theory of Hydraulic Models, London.

65- Yalin, M.S., 1977, Mechanics of sediment transport, Queens University, Ontario,

Canada.

66- Znamenskaya, N.S., 1967, The analysis of estimating of energy losses by

instantenous velocity distribution of stream with movable bed, Proc. 12th. Congress

IAHR, Vol. 1, pp.27-30.

References in Arabic

ة حبرية السد العاىل بني جندل دال وأبو مسبل )دراسة مورفولوجية(، ، منطق 1891حسن دهب ، أمحد -1 ، جامعة عني مشس .رسالة دكتوراة ، قسم اجلغرافيا ، كلية األداب

، معهد حبوث النيل ، 1881حىت 1891تقارير عن أعمال بعثة البحرية ، عن السنوات من جمموعة -1 وزارة الرى. العامة للسد العاىل وخزان أسوان ،املركز القومى لبحوث املياة ، باإلشرتاك مع اهليئة