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