CHAPTER 1 INTRODUCTION GENERAL When a dam is constructed on a river to store water

CHAPTER 1
INTRODUCTION
GENERAL
When a dam is constructed on a river to store water, sediments transported by the water flow are also stored and reservoir capacity is gradually reduced by sediment accumulation. The loss of capacity of reservoir due to deposition of silt and sediment resulted less availability of water for irrigation, decreased ability to generate hydroelectricity. Apart from loss of capacity sediment deposit in reservoir also lead to increase flood risks, interruption in hydropower generation, downstream river bed degradation, deterioration of water quality, increased complexity in reservoir operation, maintenance lead to increase in associated cost. Prediction of sediment distribution in reservoirs is an important issue for dam designers to determine the reservoir active storage capacity, outlet sill elevation, dam stability, recreational facilities, and backwater conditions. It is therefore necessary to monitor sediment deposit in different storage zones of reservoir which may be helpful to know the current status of availability of water, modification in reservoir operation plan, need for soil conservation measures in catchment areas, life of reservoir, environmental hazards etc. Considering great plans regarding construction of reservoir dams and great investments in this part, awareness of status and a precise estimation of sedimentation in such dams is necessary. The sediment in reservoirs is computed by conventional techniques such as hydrographic surveys, inflow-outflow methods or recent technique of digital image classification of remote sensing data. If total sediment deposit is known, the sediment distribution in a reservoir can be computed with the help of empirical area-reduction method suggested by Borland & Miller, 1958 and 1960 which subsequently revised by Lara, 1962. In this method, the parameters C, m and n are computed with the help of original area-elevation-capacity curve of the reservoir.

Although empirical method of area-reduction is one of the most common methods of estimating sediment distribution, but survey of previous researches show that, since parameters used’ in this method are obtained from information under study by Borland and Miller on 30 dams in America, which, in most of the dams, these parameters were not the best parameters to estimate sediment distribution and needs to be calibrated. Following this, empirical method parameters of area-reduction concerning Bhatghar reservoir dam were calibrated and this method was optimized. Eventually and through the optimized method, a more precise estimation of sediments amount was predicted for coming years.

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AIM
The aim is to determine sedimentation in reservoir using area reduction method and establish volume/surface area/depth relationship for reservoir after sediment has been deposited.

OBJECTIVE
The objectives of my study are as
1.Determine type of reservoir on the basis of shape factor M.

2.Determine total sediment volume to be distributed in the reservoir.
3.Calibrating the parameters c, m, n by genetic algorithm.

4.Predict the elevation-area-capacity curve for next few years.
THEORY OF SEDIMENTATION
1.4.1 BACKGROUND
Dams are constructed in rivers for various amounts of reasons. Hydropower can be generated and fresh water can be stored for drinking water or for agricultural purposes. Also, river floods can be controlled in order to increase the river safety. However, the consequences for the environment can be severe, and extensive research is necessary to investigate what the effects of such a structure are. Especially the sediment blockage in the river can be a serious problem. The capacity of the reservoir reduces as a consequence of this blockage and it also has a big influence on the river morphology.

Sedimentation is known as the process which fills up natural lakes and man-made reservoir by sediments to become the end land again. The main reason for this process is the sediment yield transported by the rivers as suspended or bead load into the reservoir. Bed and suspended sediment load originate from soil and rock erosion in the catchment area of the reservoir.

1.4.2 MECHANICS OF RESERVOIR SEDIMENTATION
1.4.2.1 RIVER HYDRAULICS
A river system starts with precipitation that falls down in the mountains. This water is collected by small streams that discharge their water into bigger streamlets. The streamlets will end up discharging their water into a river, which keeps on growing in size. While the volume of the river keeps on growing, the river leaves the mountains and the surface below the river flattens out. The velocity of the river decreases and the river is now in a meandering state, where it curves its way through a flat landscape. Eventually, the river ends up in a delta where it will discharge the water into a lake, sea or ocean.

The amount of water that is transported by the river grows from a few liters per second in the stream to a substantial amount of cubical meters of water per second or even more, depending on the size of the river. This means that besides a considerable amount of water, the flow is now also carrying a lot of energy. It is this amount of water and the energy potential of the river, especially in the mountainous regions, that interests dam engineers. It can be used to generate hydropower and to store fresh water. A side effect is that the river collects a lot of sediment throughout this process, due to the friction of the water with the subsurface. Especially in the mountains, where the flow velocities are higher, the water takes a lot of sediments along the way. When the river calms down and starts to meander, the nutrient rich sediment particles start to settle and provide fertile grounds that can be used for agriculture. This process of sediments that are picked up in the mountains and deposited in the lower areas and at the river mouth has been going on since the first water drop fell in the mountains. It results in a balance between erosion and accretion in the river morphology. The supply of sediment is approximately equal to the amount of sediment that erodes away, keeping in mind that there are some (seasonal) fluctuations. This process is schematized in Figure 1, where S is the sediment transported by the river. The same process yields for the coastline, where there is a balance between the supply of sediments from the river and the erosion of the coastline.

If S1 = S2, the river bottom is in an equilibrium state
If S1; S2, the river bottom is accumulating
If S1; S2, the river bottom is eroding
Figure 1 shows that erosion or accretion will get the upper hand if this balance is disturbed. This will influence the river morphology until equilibrium is found.

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FIG. 1.4.2.1: Dynamics of the river morphology
Constructing a dam in the river will block the sediment flow in the river and will disturb this sediment balance in the river considerably. Upstream of the dam, the sediment inflow ?1 will be higher than the amount of sediment ?2 that is taken away due to the blockage. This results in sediment accumulation close to the dam.

1.4.2.2 RESERVOIR SEDIMENTATION
Reservoir sedimentation is a process that has been going on since the first dams were build and is a consequence of creating a calm reservoir lake where there used to be a fast flowing river. It eventually starts to influence the reservoir capacity and the river morphology. The siltation of the reservoir could hinder the usage of the dam and interfere with the functionality of the reservoir. With the sediments taking up space in the reservoir, the storage capacity of the reservoir is decreasing. If the sediments settle all the way towards the dam structure, the hydropower installation can be influenced by the sedimentation process as well. The sedimentation problems strongly depend on the local circumstances of the reservoir. Sedimentation in reservoirs is also of big influence downstream of the dam. A river system consists of a continuous balance between erosion and accretion, where sand is picked up due to the river flow and deposited elsewhere in the river. If the inflow of sediment is blocked due to a dam structure, the equilibrium of the river morphology is disturbed and the river channel downstream of the dam starts to erode.

1.4.3 SEDIMENT DEPOSTION PATTERN IN RESERVOIR
Region of sediment deposition is important to a hydraulic engineer for several reasons.
FIG. 1.4.3.1 General deposition Pattern (CWPRS Report. 4626, 2009)
Firstly, the elevations of the outlets in the dam must be such that, in future they will not be in sediment deposition zone. Secondly the areas of deposition are required for computing the reduction in live storage capacity with the passage of time. Also it is important to know how much sediment will be deposited in the backwater reach of the reservoir, for determination of the raised flood levels. Fig 1.4.3.1 presents a general deposition pattern of sedimentation in the reservoir showing Qs (incoming discharge of sediment) and Qw (incoming discharge of water).

FIG. 1.4.3.2: Generalized depositional zones in a reservoir
The sediment is deposited in form of toposet, forest and bottom set beds. Top set beds correspond to delta deposits of rapidly settling sediment. Forest deposits represent the face of the delta advancing into the reservoir and are differentiated from topset beds by an increase in slope and decrease in grain size. Bottom set beds consist of fine sediments which are deposited beyond the delta by turbidity currents or non -stratified flow. Delta deposits contain both coarse and fine material, whereas bottom set contains only fine grained particles.

1.4.3.1 LONGITUDINAL DEPOSITION PATTERN
Longitudinal deposition pattern is the deposition of sediment along L-section of the reservoir. It varies from one reservoir to another due to difference in pool geometry, discharge and grain size characteristics of the inflowing load, and reservoir operation. (Morris and Fan 2008) Deposits exhibit four basic types of patterns depending on the characteristic of inflowing sediment and reservoir operation (Fig. 1.4.3.1.1)

FIG 1.4.3.1.1: Longitudinal deposition pattern
1.4.3.1.1 DELTA DEPOSITS:
It contains the coarsest fraction of the sediment load, which is rapidly deposited at the zone of inflow. It may consist entirely of coarse sediment (d ; 0.062 mm) or may also contain a large fraction of finer sediment such as silt.
1.4.3.1.2 WEDGE-SHAPED DEPOSITS
They are thickest at the dam and become thinner moving upstream. This pattern is typically caused by the transport of fine sediment to the dam by turbidity currents. Wedge-shaped deposits are also found in small reservoirs with a large inflow of fine sediment, and in large reservoirs operated at low water level during flood events, which causes most sediment to be carried into the vicinity of the dam.

1.4.3.1.3 TAPERING DEPOSITS
They occur when deposits become progressively thinner moving toward the dam. This is a common pattern in long reservoirs normally held at a high pool level, and reflects the progressive deposition of fines from the water moving toward the dam.
1.4.3.1.4 UNIFORM DEPOSITS
They are unusual but do occur. Narrow reservoirs with frequent water level fluctuation and a small load of fine sediment can produce nearly uniform deposition depths.
1.4.3.2 LATERAL DEPOSITION PATTERN
Lateral deposition pattern is the deposition of sediment in the lateral section (cross section) of the reservoir. Sediment is initially deposited in the deepest part of each of the cross section, creating deposits having a near-horizontal surface regardless of the original cross section shape.

1.4.4 PHASES OF SEDIMENT TRANSPORT
Sediment at rest
The entrainment
The motion
The deposition phase
These phases of sediment transport regime are given by the ratio between the tractive force and the resistance forces which act upon the sediment particles. The tractive forces is the hydrodynamic forces exerted by the flowing water, which tend to move the sediments, and the resistance forces is exerted by the weight, cohesion or contact forces, which oppose their movement (Batuca 2000).(Reference-CWPRS report-4626, 2009).

Case 1. Tractive force; resistance force (Rest regime): No movement of sediment
Case2. Tractive force=resistance force (critical entrainment regime): Unstable equilibrium condition.

Case 3. Tractive force;resistance force (transportation regime): Sediment in suspension
Yalin (1972) gave a functional and dimensionless relationship that gives the factors affecting the sediment entrainment and the sediment transport.

1.4.5 METHODS TO CONTROL RESERVOIR SEDIMENTATION
In order to increase the life of a reservoir, it is necessary to control the deposition of sediment. Various measures can be adopted in order to achieve this aim. The various methods which can be adopted can be divided into two parts
(a) Pre- construction measures
Selection of reservoir site
Design of dam in stages
Construction of under sluice in the dam
Vegetation screen
Construction of check dam
(b) Post- construction measures
1) Removal of post flood water
2) Mechanical stirring of the sediment
3) Erosion control and soil conservation
1.4.6 ILL EFFECT OF RESERVOIR SEDIMENTATION
Different effect of reservoir sedimentation as mentioned follow
Reduced live storage capacity, which affects power generation/ irrigation/ water supply
Increase in backwater levels in head reaches of the reservoir
Increase flood level in upstream reaches/ water logging
Formation of island/ deltas
Choking of irrigation, navigation and power outlets
Increased weed growth resulting in more evaporation
Increase rate of evaporation of same storage volume
Reduction in dissolved oxygen at lower depth due to decomposition of organic sediment deposition
Stratification of reservoir due to density currents affecting water quality
Degradation of river bed in the reach downstream of dam which in turn will have following ill effect
Lowering the tail water level may affect performance of energy dissipation arrangement and cause serve erosion
Increase uplift pressure
Formation of bridge and intake on river bed may be exposed
Intakes and locks in downstream reach affected due to lowering of water levels
Hence, to optimize the benefits from any project it is necessary to have knowledge of likely progressive reduction in reservoir storage during planning stage.
CHAPTER 2
REVIEW OF LITERATURE
2.1 Mohammad Gharaghezlou, Mohsen Masoudian, RobabehFendereski “Calibrating the Experimental Area Reduction Method in Assessing the Distribution of Sediments in Droodzan Reservoir Dam in Iran” Journal of Civil Engineering and Urbanism Volume 4, Issue 1: 54-58 (2014).In this paper, the experimental area reduction method is a technique for predicting sediment distribution in dam’s reservoir. Its parameters (C, m, n) have been obtained by Borland and Miller on the information from a limited number of dams. After calculating these parameters, the sediment distribution has been predicted. The result that calibrated parameters makes 30% reduction on the amount of errors in predicting sediment distribution.

2.2 SepidehTorabi, Hojjat Allah Yonesi1, Babak Shahinejad presented paper on “Calibration the area-reduction method in sediment distribution of Ekbatan reservoir dam using genetic algorithms” Model. Earth Syst. Environ. (2015) 1:21, pp 1-9.Sedimentation in dam’s reservoirs is one of the destructive phenomena which leads to reduction of useful volume of reservoirs and also damages the installations and disturbs their functions. Area reduction method is the most common experimental method to measure the sediment distribution in reservoirs. C, m, n parameters were optimized with genetic algorithms to reduce sedimentation estimate error and resulted elevation area–capacity curves was compared with 2011 Hydrography curves. Elevation–area–capacity curves of Ekbatan dam in 2021, 2026, 2031, 2036, 2041 and 2046 were predicted through optimized parameters. The results showed that 50 % of volume of Ekbatan dam will be ?lled by sediment in 2046.

2.3 Kosit Lorsirirat, Kazurou Nakane, Panya Ponsane presented paper on “Catchment erosion and reservoir sedimentation-prediction for Khwae Noi Reservoir lifespan project in Thailand” Inter prevent 2002 in the Pacific Rim(IPR) Mastumoto /Japan, Congress Publication, Volume 1,pp 156-163.In this study author use the empirical area reduction method for distribution of sediments deposition in reservoir. As the result, the annual sediment inflow is accounted as 0.480392 mcm. The author suggested that the lifespan of reservoir predicted at 437 years since its completion.

2.4 G. W. Annandale presented paper on “Predicting the distribution of deposited sediment in southern African reservoirs” Challenges in African Hydrology and Water Resources (Proceedings of the Harare Symposium, July 1984). IAHS Publ. no. 144. In this paper author use method proposed by Borland ; Miller (1958) i.e. area reduction method to predict distribution of deposited sediment in reservoirs was evaluated by testing it against observed South African data. According to researcher’s Sediment deposition in reservoirs does not only result in loss of storage, but also influences placement of sluices, design of structures such as dam walls and intake towers and effects flood lines upstream of reservoirs. By using this method author found that the method was unreliable and did not present the user with sufficient information to assess the influence of sediment deposition on flood lines. A new semi-empirical method based on the principle of minimum stream power was then proposed. This method allows distribution of sediment as a function of distance from the dam wall for various rates of change in reservoir width with distance.

2.5 Amir hossein Shafiee, MajidSafamehr presented paper on “Study of Sediments Water Resources System of Zayanderud Dam through Area increment and Area reduction Methods, Isfahan Province, Iran” Procedia Earth and Planetary Science 4 (2011) 29 – 38 .In this paper authors study the Zayandehrud dam’s lake with the capacity of 1.6 *109 cum is located 115 Km from Isfahan city at the center of Iran. Due to occurrence of drought in recent years reduced the capacity to 150 MCM and had harmful impacts on the different water resources system of the area such as dryness of dam, reduction of agricultural and industrial water availability. y. In this study, the different aspects of Zayanderud Dam through Area increment and Area reduction Methods are evaluated. The author found that the level reduce Model 7 is the best model for estimating distribution of sediment in ZayandehRud dam reservoir because it has the lowest error and standard deviation.

2.6 H. Hosseinjanzadeh, K. Hosseini, K. Kaveh, S.F. Mousavinpresented paper on “New proposed method for prediction of reservoir sedimentation distribution” International Journal of Sediment Research(2015) pp1-6.In this paper, to determine the reservoir active storage capacity, prediction of sediment distribution in reservoirs is an important issue. Among all the methods currently available, only area-reduction and area increment methods are considered as the principal methods for prediction of sediment distribution. In this paper, author study data of 16 reservoirs in the United States are used to propose a new empirical method for prediction of sediment distribution in reservoirs. In the proposed method, reservoir sediment distribution is related to sediment volume and original reservoir characteristics. Kaveh, Hosseinjanzadeh and Hosseini (2013) proposed new equations for reservoir’s dimensionless depth–capacity and regular depth–capacity curves. The obtained results are compared with survey data for two reservoirs. The results of this investigation showed that the proposed method has an acceptable accuracy.

CONCLUDING REMARKS
In the reviewed papers it was seen how sedimentation in reservoirs reduce the useful volume of reservoirs and also damages the installations and predict the distribution of sedimentation by using area reduction method. The papers also discussed about the new method for prediction of distribution of sediment in reservoir comparing with survey data.
CHAPTER 3
METHODOLOGY
3.1 INTRODUCTION TO EMPIRICAL AREA REDUCTION METHOD
Empirical Area-Reduction method was developed by Borland and Miller in 1958. The basis of this method is the shape of the reservoir, which is determined by using the reservoir depth and the reservoir capacity. The method divides the reservoirs in 4 standard types. Within these standard reservoir types, the parameter “M” divides the types in different classes and it represents the reciprocal of the slope of the line obtained by plotting the reservoir depth at the vertical axis against reservoir capacity at the horizontal axis on log-log paper as shown in fig. 3.1.1. This result in the classification presented in Table 3.1.1
TABLE 3.1.1: TYPES OF RESERVOIRS
Reservoir type “M” Standard classification
Gorge 1.0-1.5 IV
Hill 1.5-2.5 III
Flood plain –foothill 2.5-3.5 II
Lake 3.5-4.5 I

FIG. 3.1.1: Determination of the different types of reservoirs (Borland W.M. and Miller C.R., 1958)
28575168592500 These types of reservoirs can then be linked to the sediment distribution within these reservoirs. It is important to know where sediment settles if a decision has to be made between the different reservoir preservation techniques. The reservoir percent depth plotted against percent sediment deposition shown in fig. 3.1.2. A reservoir depth percentage of 100 means that the reservoir is at its full depth, so that is the depth just before the dam.

FIG. 3.1.2: Sediment distribution within a reservoir (Borland W.M. and Miller C.R.)
The situation of a type I reservoir, the sediment already starts to settle at shallower depths, close to the point where the river enters the reservoir as shown in fig.3.1.2. This makes sense since a type I reservoir is described as a “Lake” reservoir and has a relatively flat bottom slope. It reduces the flow velocity and therefore facilitates the settling of sediments. For type IV reservoirs, sediment starts to settle at the deeper parts of the reservoir, much closer to the dam. This is due to the steeper bottom slope of the reservoir, which results in a faster flow in the reservoir. Sediments will be kept longer in suspension and will settle further away from the point where the river enters the reservoir.
-3619501174115The majority of the sediments also settles close to the dam with type III reservoirs, but not as extreme as with type IV. A type II reservoir has a more or less constant dispersion of sediment throughout the reservoir.
FIG. 3.1.3: Area Design curve
Experimental area-reduction method, first presented by Borland and Miller (1958) was subsequently revised by Moody (Blanton and Ferrari 1992). The aim of the Borland and Miller technique is to establish volume/surface area/ depth relationships for reservoirs after sediment has been deposited therein (Annandale 1987).

The main equation in this method is:

Where,
S is the total input sediments to the reservoir during life span of reservoir and the bottom and above limits of the first integral count for the primary level of the river bed at the place of construction before and after sediment settlement, respectively.
A is the reservoir area in the different elevations.
dy is height increment,
H is the reservoir height at normal water level.
a is the approximate area of sediments which is measurable according to a difference, for the approximate of p,
h(p) is the dimensionless function of the whole settled sediments, and the capacity depth and area of reservoir.
V(y) is the reservoir capacity in level y and A(y) in the reservoir area in level of y and
k is the proportion coefficient to change the sediment in the approximate area into the real area obtained from Eq. (5).

In which,
A0 is the reservoir area in height h0.

a0 is the sediment in the approximate area in the new height zero.
The approximate area is obtained through Eq. (6).

Where the measures C, m and n are fixed coefficients determined according to the type of reservoir from Table no. 3.2
Table 3.2: Values of C, m, n on type of reservoir
Types C M n
I 5.074 1.85 0.36
II 2.487 0.57 0.41
III 16.967 -1.15 2.32
IV 1.486 -0.25 1.34
3.2. PROCEDURE
In the area reduction method, for determining the profile of sediment distribution, the following steps should be taken:
From the catchment area, siltation index (sediment volume/ unit area/ year) and period for sediment deposition compute total sediment yield. Siltation index could be available from earlier hydrographic survey or from isoerodant map of the region derived by R. J. Grade (1985).

From the trap efficiency of the reservoir as defined by Brune (1953) and total sediment yield compute sediment volume likely to be deposited in the reservoir.

Determine reservoir type and corresponding deposition pattern by plotting depth-capacity relation.

Take suitable interval (2 to 5 m) and find the levels over the total depth at dam (up to FRL). Compute relative depth at different levels starting from FRL to river bed.

Depth above bed at any elevation
Relative Depth =
Total depth at dam (FRL-bed level)
For these relative depths, compute relative sediment area factor ‘Ap’ from fig.3.1.3 using appropriate type curve.
Assume a new bed level (ho) near the dam after siltation. Compute reservoir area, capacity, relative depth and factor ‘Ap’ at level ‘ho’. Compute ‘K’ as
area at level (ho)
K =
‘Ap’ at level (ho)
Multiply ‘Ap’ at each level computes in step 5 by ‘K’ to obtain sediment area at each level.

Compute sediment volume deposited between two successive levels and cumulative sediment volume deposited below each level.

If computed sediment volume below FRL or highest water level is equal to the total sediment volume likely to be deposited in assumed duration then stop the computations. Else, assume a new value of ho and repeat step 6 to 9 till the above condition is satisfied.

10. Compute revised elevation-area-capacity curve by deducting sediment area and volume from initial area and volume at respective levels.

3.3 INTRODUCTION TO GENETIC ALGORITHMS
GAs was first presented systematically by Holland, the basic ideas of analysis and design based on the concepts of biological evolution can be found in the work of Rechenberg (Mitchell 1998; Antoniou and Lu 2007). The Solution of an optimization problem by GAs starts with a population of random strings denoting several (population of) design vectors. The population size in GAs is usually fixed. Each string (or design vector) is evaluated to find its fitness value. The population (of designs) is operated by three operators-selection, crossover, and mutation-to produce a new population of points (designs).

3.3.1 SELECTION
The selection component of a GA is designed to use fitness to guide the evolution of chromosomes by selective pressure (Kia 2009). Chromosomes are therefore selected for recombination on the basis of fitness. Those with higher fitness should have a greater chance of selection than those with lower fitness, thus creating a selective pressure towards more highly fit solutions. This allocates each chromosome a probability of being selected proportional to its relative fitness, which is its fitness as a proportion of the sum of fitness’s of all chromosomes in the population (Goldberg 1989). There are many different selection schemes. Random stochastic selection explicitly selects each chromosome a number of times equal to its expectation of being selected under the fitness proportional method. Tournament selection first selects two chromosomes with uniform probability and then chooses the one with the highest fitness. Truncation selection simply selects at random from the population having first eliminated a fixed number of the least fit chromosomes (Davis 1991).

3.3.2 CROSSOVER
The crossover operator represents the mixing of genetic material from two selected parent chromosomes to produce one or two child chromosomes. After two parent chromosomes have been selected for recombination, a random number in the interval (0, 1) is generated with uniform probability and compared to a pre-determined ”crossover rate”. If the random number is greater than the crossover rate, no crossover occurs and one or both parents pass unchanged on to the next stage or recombination. If the crossover rate is greater than or equal to the random number, then the crossover operator is applied. One commonly used crossover operator is one-point crossover. A crossover point between 0 and n is chosen with uniform probability. Child chromosomes are then constructed from the characters of the first parent occurring before the crossover point and the characters of the second parent occurring after the crossover point. We illustrate this on a length 10 bit-string encoding as follows:
Parent one: 1 1 1 0 1 0 0 1 1 0
Parent two: 0 0 1 0 0 1 1 1 0 0
Crossover point:
Child one: 1 1 1 0 0 1 1 1 0 0
Child two: 0 0 1 0 1 0 0 1 1 0
There are many alternative forms of crossover operation. One-point crossover generalises straightforwardly to 2- and multi-point crossover operations, where a sequence of crossover points is chosen along the chromosome length and the child chromosomes are constructed from the allele values of the two parents, interchanging at each crossover point. Uniform crossover constructs a child by selecting uniformly between parent allele values at each locus. Algorithms also differ with respect to whether one or more children are created from the crossover operation. After crossover, the resultant chromosome(s) will be passed on to the mutation stage.

3.3.3 MUTATION
Mutation operators act on an individual chromosome to flip one or more allele values. In the case of bit-string chromosomes, the normal mutation operator is applied to each position in the chromosome. A random number in the interval (0, 1) is generated with uniform probability and compared to a predetermined ”mutation rate”. If the random number is greater than the mutation rate, no mutation is applied at that position. If the mutation rate is greater than or equal to the random number then the allele value is flipped from 0 to 1 or vice versa. Mutation rates are typically very small (McCall 2005). The new population is further evaluated to find the fitness values and tested for the convergence of the process. One cycle of production, crossover, and mutation and the evaluation of the fitness values are known as a generation in GAs. If the convergence criterion is not satisfied, the population is iteratively operated by the three operators and the resulting new population evaluated for the fitness values. The procedure is continued through several generations until the convergence criterion is satisfied and the process is terminated (Rao 2009).

In the genetic algorithms the following steps should be taken (Chambers 2001):
Step 1: Randomly generate a population of genomes represented as bit strings.

Step 2: Assign a fitness value to each individual in the population.

Step 3: Selection:
(a) Retain the top 5 % of the current population
(b) Randomly choose mating-pairs
Step 4: Crossover: randomly exchange genetic material between the two genomes in each mating pair to produce one child.

Step 5: Mutation: randomly mutate (invert) bit(s) in the genomes of the children.

Step 6: Repeat from step 2 with this new population until some termination criteria is fulfilled.
In this study, first based on area reduction method a model was made by using MATLAB software, area reduction method is added as a function to the genetic algorithms and calibrated by GA. Then sediment distribution profile of 2017 was estimated through area reduction method before and after calibration. Figure 3.3.3 shows flowchart of method that used in this study.

FIG. 3.3.3 Flowchart of calibration the area-reduction method using genetic algorithms
CHAPTER 4
STUDY AREA
4.1. BHATGHAR RESERVOIR
Bhatghar dam is constructed on Yelwandi River in Pune district of Maharashtra. It is one of the highest dams in India Built in 1969. The dam is 1,625 m long, FRL is 623.28 m and storage capacity 672.58 million m3.

The dam is used for irrigation, drinking water supply and hydro power generation. The river at the dam site has a catchment area of 336 km2. Maximum length of the reservoir is 45 km and the mean depth is 24.02 m.

FIG. 4.1.1: Location of Bhatghar reservoir
Pune district lies in the Western Ghats or Sahyadri mountain range and it extends on to the Deccan Plateau on the west. Pune stands on the leeward side of the Western Ghats. The climate of this district is characterized by high humidity nearly all the year round, an oppressive summer season, and well-distributed and heavy rainfall during the south-west monsoon season. Average annual rainfall in this area is around 700 mm. Highest temperature of 41o C in summer and the minimum temperature is 8oC is recorded winter. The nearest meteorological station is in Pune, which is 60 km from the dam.
4.1.2 SALIENT FEATURES OF BHATGHAR DAM
1 Name of reservoir Bhatghar2 River Yelwandi3 Year of Impoundment 1927
4 Location
Nearby village Bhatghara. TalukaBhorb. District Pune
c. Latitude 180 10″33’N
d. Longitude 73o52″14E
5 Catchment Area 331.50 km2
6 Year of construction 1927
7 Storage (Mm3)
a. Gross 672.65
b. Live 672.65
c. Dead NIL
8. Purpose of Project Irrigation
9. Earthen dam details
a. Maximum height 57.92m
b. Length of dam 1625m
10 Spillway a. Spillway Length 100.5m
b. Type Ogee,Masonary11. Year of Completion 1927
12 Reservoir Level (m)
a. F.R.L. 623.28m
b. M.W.L. 623.28m
c. R.B.L. 576.04m
d. MDDL 578.48m
13. Max. Spillway Discharge 832.40 m3/s
14 Total area of submergence at F.R.L. 3790 Ha

The geological formation consists of recent-shores sand, Pleistocene-laterite and eocene- basalt flows. Basalt flows from the predominant formation capped at a few places by laterite at higher levels and covered by shore sands along the coast. Seismically Pune district lies in the Zone –III, Moderate Hazard Zone.

The soil of Bhatghar reservoir is sandy and neutral to alkaline in reaction. The soil quality is poor in terms of organic carbon, available phosphorus and available nitrogen there is not much agriculture activity in the area.
The Nira Right Bank Canal system is fed by Bhatghar dam. This canal system provides irrigation facilities to the Malshiras taluka and irrigates about 50,000 acres in the district. The important crops irrigated by this system are sugarcane, cotton and wheat. Almost 90% of the population is in the rural area. Backward communities account for about 6 % of the population. There are industries in the region. Majority of the local people are involved in agriculture and / or work in the industries.
13335027940
FIG. 4.1.2: Bhatghar dam site
CHAPTER 5
DATA ANALYSIS
5.1 DATA ANALYSIS BY AREA REDUCTION METHOD BEFORE CALIBRATION
For assessment of sediment distribution at different levels Bhatghar reservoir is selected as a study area. This reservoir is on Yelwandi River in Pune District of Maharashtra. It is one of the highest dams in India Built in 1969. The dam is 1,625 m long, FRL is 623.28 m and storage capacity, 672.58 million m3. The dam is used for irrigation, drinking water supply and hydro power generation. The river at the dam site has a catchment area of 336 km2. Maximum length of the reservoir is 45km and the mean depth is 24.02 m.

Estimation of type of reservoir in respect of possible sedimentation pattern is most crucial. The linear slope of depth capacity curve on log scale is provided to decide the type of deposition pattern of Bhatghar Reservoir. Fig 5.1, fig 5.2, fig 5.3 shows the depth capacity area curve for Bhatghar Reservoir. As per the criteria of Borland and Miller the Bhatghar Reservoir falls under type III. As per this type the major part of sediments, nearly 80% of sediments, trapped in the reservoir should settle in upper 40% depth.

TABLE .5.1.1: ORIGINAL AREA CAPACITY AT IMPORTANT LEVELS FOR THE YEAR 1981
Sr. No Level Elevation
(m) Area
(Mm2 ) Capacity
(Mm3) Remark
1 RBL 576.04 0.00 0.00 Zero content level
2 MDDL 578.84 – – Dead Storage
3 FRL 623.28 37.91 672.65 Gross Storage
(Dead + Live)
4 MWL 623.28 37.91 672.65 Gross + Flood
Storage

TABLE .5.1.2: ORIGINAL ELEVATION AREA – CAPACITY (1981)
R.L CAPACITY AREA
(m) (Mm3) (Mm2)
576.04 0 0
595.94 38.8 13.86
598.10 57.12 15.71
600.21 81,24 17.50
603.74 140.82 20.48
614.69 412.34 29.76
618.59 525.62 33.06
618.81 532.13 33.27
623.01 663.82 37.63
623.16 672.6 37.78
623.19 672.65 37.82
623.22 672.6 37.85
623.22 671.47 37.85
623.25 670.62 37.88
623.28 670.62 37.91
623.28 669.48 37.91
623.28 668.64 37.91

FIG. 5.1.1: Elevation area curve for Bhatghar reservoir for the year 1981

FIG. 5.1.2: Elevation- Capacity curve for Bhatghar Reservoir for year 1981
TABLE 5.1.3: RESERVOIR AREA AND CAPACITY DATA OF BHATGHAR RESERVOIR FOR YEAR 1981
1981 R.L
(m) Capacity
(Mm3 ) Area
(Ha) Log Capacity Log Depth
576.04 0 0 1 1
JUNE 595.94 38.8 2173172.193 1.58883 1.299
595.94 27.75 2173172.193 1.44326 1.299
595.94 38.23 2173172.193 1.58240 1.299
JULY 597.37 49.56 2394671.567 1.69513 1.329
614.69 412.34 5077447.193 2.61526 1.587
618.59 525.62 5681536.393 2.72067 1.629
AUGUST 618.81 532.13 5715613.22 2.72602 1.631
623.01 663.82 6366170.82 2.82205 1.672
623.28 672.6 6407992.38 2.82776 1.674
SEPTEMBER 623.28 672.65 6407992.38 2.82779 1.674
OCTOBER 623.28 672.6 6407992.38 2.82776 1.674
623.25 671.47 6403345.54 2.82703 1.674
623.22 670.62 6398698.7 2.82648 1.674
NOVEMBER 623.22 670.62 6398698.7 2.82648 1.674
623.19 669.48 6394051.86 2.82574 1.673
623.16 668.64 6389405.02 2.82519 1.673

FIG. 5.1.3: Curve to determine the type of Bhatghar Reservoir
From the given data the important levels were determined and elevation – area – capacity curves are plotted as shown in fig 5.1 ; fig 5.2. Computation of the sediment volume is done by comparing and analyzing the data acquired from the Bhatghar Reservoir for the years 1981 and 2017. Thus by comparing the values from the respective years for important levels as shown in table 5.5, total volume of sediments is calculated. The total sediments deposition was 981.7 ha-m for duration of 36 years.

Thus for applying the Area Reduction Method, the type of reservoir is found out by plotting the graph for depth and capacity is plotted and the slope is calculated.

Calculation for slope:
??? ?=?.???
??y=?.???
?=?.??
??? ?=?.???
??x=?.??
?=?.??
Slope (n) = ?/?=0.56
?=?/?=?.???
TABLE 5.1.4: RESULT FROM ANALYSIS OF DATA FROM 1981
Slope (n) 0.56
M 1.785
Type Of curve III (Hill)
As the value of M (1.785) lies between 1.5 to 2.5, the type of reservoir is Hill (Type III) as per the table 1. Thus equation of Ap is selected as equation of Type III from fig.3.1.3 (Area design curves)
Ap = C × pm (1-p) n
Ap =16.967 × p-1.15 × (1-p) 2.32
Where
Ap = Approximate area.

C,m,n = fixed coefficients determined according to the type of reservoir.

P = relative depth.

TABLE 5.1.5: COMPUTATION OF RESERVOIR SEDIMENTATION FROM COLLECTED DATA
Elevation in (m) Area in (Mm2) 1981 Capacity (Mm3) 2017 Capacity (Mm3) Measured sediment volume (Ha-m) Percentage (%) of measured sediment
623.28 37.91 672.65 665.5 71.5 100
620.57 35.09 586.5 579.36 71.4 99.86
617.76 32.37 501.34 494.21 71.3 99.72
614.76 29.84 415.14 407.16 79.8 111.60
611.72 27.26 331.34 324.22 71.2 99.58
608.99 24.94 260.17 253.07 71 99.30
605.9 22.33 186.77 179.67 71 99.30
602.85 19.74 124.18 117.09 70.9 99.16
599.81 17.16 76.38 69.35 70.3 98.32
596.76 14.58 44.88 38.06 68.2 95.38
593.74 5.2 26.77 19.71 70.6 98.74
591.3 1.95 17.03 9.97 70.6 98.74
588.56 1.09 9.39 2.32 70.7 98.88
586.71 0.74 5.32 0 53.2 74.40
576.04 0 0 0 0 0
Total=981.7 TABLE 5.1.6: SEDIMENT COMPUTATION BY AREA REDUCTION METHOD
Elevation (m) Area (Ha) Capacity (Ha-m) Relative Depth Ap for type III Sediment area
(Ha) Sediment volume (Ha-m) Accumulated sediment volume
(Ha-m) Revised Area 2017 Revised capacity 2017
1 2 3 4 5 6 7 8 9 10
621 3554 5926.9 1 0 0 0 972.776 3554 4954.1
619 3349 5316 0.9285 0.00004 0.01417 0.01417 972.762 3348.9 4343.6
617 3173 4717 0.8571 0.0002 0.0776 0.09178 972.67 3172.9 3744.3
615 3005 4148 0.7857 0.0006 0.21972 0.29733 972.372 3004.7 3176.3
613 2835 3589 0.7142 0.001 0.4779 0.69763 971.675 2834.5 2617.4
611 2664 3046 0.6428 0.002 0.90531 1.38322 970.292 2663 2075.7
609 2496 2538 0.5714 0.004 1.58242 2.48774 967.804 2494.4 1570.4
607 2326 2048 0.5 0.007 2.63834 4.22077 963.5835 2323.3 1084.5
605 2157 1600 0.4285 0.012 4.29399 6.93234 956.6512 2152.7 643.54
603 1987 1198 0.3571 0.019 6.95975 11.2537 945.3974 1980 253.2
601 1816 858.3 0.2857 0.032 11.4867 18.4465 926.9509 1804.5 0
599 1647 595.8 0.2142 0.05 19.9484 31.4351 895.5157 1627 0
597 1476 398.4 0.1428 0.11 38.9119 58.8603 836.655 1437 0
595 1310 264.2 0.0714 0.29 103.97 142.883 693.7717 1206 0
593 1139 163.4 0 0 113.9 217.871 475.9 1025.1 0
591 970 90.3 0 0 97 210.9 265 873 0
589 840 34.8 0 0 84 181 0 756 34.8
588 0 9.99 0 0 0 84 0 0 9.99
          Total 972.776    
Referring to Table 6.6, the data given in column 1, 2 and 3 are calculated from original area capacity curves.
The relative depth ratio for different levels to the total depth from the spillway crest (or FRL) to the stream bed is entered in column 4.
Ap in column 5 is obtained from relevant curve of figure 4.3. Assumed zero elevation which is in this case is 593.00 m. Surface area corresponding to this elevation is 1139 ha.

Find out K, the ratio of original area at assumed new zero elevation (col 2) to the corresponding Ap value (col 5).
? = 1139/0.3255
= 3498.9
For this value of K the computed volume of sediments is 972.77 ha-m which is near to actual sediment deposited in the reservoir
Sediment area is calculated by multiplication of K and Ap values at each succeeding increment and is shown in column 6.
Column 7 is the increment of sediment volume.

Column 8 gives the sediment accumulation volume in hectare meters.
Revised areas in col 9 are obtained by subtracting the values in col 6 to col 2.
Revised capacity in col 10 is obtained by subtracting the values in col 8 from col 3.
TABLE 5.1.7: COMPUTATION OF % SEDIMENT AND % DEPTH OF BHATGHAR DAM
Elevation (m) Depth % sediment % depth
621 33 100 100
619 31 99.99 93.93
617 29 99.98 87.87
615 27 99.95 81.81
613 25 99.87 75.75
611 23 99.72 69.69
609 21 99.44 63.63
607 19 98.96 57.57
605 17 98.18 51.51
603 15 96.91 45.45
601 13 94.84 39.39
599 11 91.30 33.33
597 9 84.68 27.27
595 7 68.60 21.21
593 5 44.093 15.15
591 3 20.36 9.09
589 1 0 3.03
588 0 0 0

FIG. 5.1.4: Sediment Deposition Curve for Bhatghar Dam for year 2017
TABLE 5.1.8: ACCUMULATION OF SEDIMENT IN BHATGHAR DAM
Elevation (m) Accumulated sediment volume (Ha-m)
621 972.77
619 972.76
617 972.67
615 972.37
613 971.67
611 970.29
609 967.80
607 963.58
605 956.65
603 945.39
601 926.95
599 895.51
597 836.65
595 693.77
593 475.9
591 265
589 0
588 0

FIG. 5.1.5: Sediment accumulation curve for Bhatghar Dam for year 2017
5.2 TOTAL SILTATION IN RESERVOIR
The sedimentation study of Bhatghar reservoir by Area Reduction Method covered entire reservoir portion and hence siltation in reservoir at different elevation could be estimated. The present study reveals that gross storage capacity of the reservoir is reduced by 972.77 ha-m which is about 14.5% of total capacity. This implies that sedimentation in the reservoir in a span of 36 years is 972.77 ha-m. The percentage annual losses in capacity are 0.402% only. The live storage capacity of the reservoir is reduced by 972.77 ha-m which is 5753.73 ha-m against the original live storage capacity (6726.5 ha-m).

5.3 PRESENT GROSS STORAGE CAPACITY OF THE RESERVOIR
Due to sedimentation the original gross storage capacity changed (592.69Mm3). The revised gross storage capacity of the reservoir is 495.4123 Mm3.The storage capacity with respect to the elevation is shown in Table no.6.1.

TABLE 5.1.9: COMPARISON OF CAPACITY
Elevation (m) Capacity (Ha-m) 2017 Revised capacity (Ha-m) 2017
621 5316.4 4954.12
619 5316.4 4343.63
617 4717 3744.32
615 4148.7 3176.32
613 3589.1 2617.42
611 3046 2075.70
609 2538.3 1570.49
607 2048.1 1084.51
605 1600.2 643.54
603 1198.6 253.20
601 858.3 0
599 595.8 0
597 398.4 0
595 264.2 0
593 163.4 0
591 90.3 0
589 34.8 34.8
588 9.99 9.99

FIG. 5.1.6: Revised Elevation-Capacity Curve
TABLE 5.1.10: COMPARISON OF AREA
Elevation (m) Area (Ha) Revised Area (Ha) 2017
621 3554 3554
619 3349 3348.98
617 3173 3172.92
615 3005 3004.78
613 2835 2834.52
611 2664 2663.09
609 2496 2494.41
607 2326 2323.36
605 2157 2152.70
603 1987 1980.04
601 1816 1804.51
599 1647 1627.05
597 1476 1437.08
595 1310 1206.02
593 1139 1025.1
591 970 873
589 840 756
588 0 0

FIG.5.1.7: Revised Elevation-Area Curve
TABLE 5.1.11: DISTRIBUTION OF SEDIMENTS IN RESERVOIR
Elevation (m) Sediment volume (Ha-m)
621 0
619 0.0141
617 0.0917
615 0.2973
613 0.6976
611 1.3832
609 2.4877
607 4.2207
605 6.9323
603 11.2537
601 18.4465
599 31.4351
597 58.8603
595 142.8836
593 217.8717
591 210.9
589 181
588 84

FIG.5.1.8: Sediment Distribution at different elevation
From the Sediment Distribution graph, it is observed that the maximum sediments get accumulated in the elevation range of 590 m to 595 m. Area Reduction Method is thus useful for assessment of sediment distribution in reservoir.

TABLE 5.1.12: SEDIMENT DISTRIBUTION ESTIMATION IN YEAR 2017
Elevation (m) Revised Area (Ha) 2017 Revised capacity
(Ha-m) 2017 Sediment deposition (Ha-m) Cumulative sediment volume (Ha-m)
621 3554 4954.12 0 972.77
619 3348.98 4343.63 0.0141 972.75
617 3172.92 3744.32 0.0917 972.66
615 3004.78 3176.32 0.2973 972.36
613 2834.52 2617.42 0.6976 971.66
611 2663.09 2075.70 1.3832 970.28
609 2494.41 1570.49 2.4877 967.79
607 2323.36 1084.51 4.2207 963.57
605 2152.70 643.54 6.9323 956.64
603 1980.04 253.20 11.2537 945.39
601 1804.51 0 18.4465 926.94
599 1627.05 0 31.4351 895.50
597 1437.08 0 58.8603 836.64
595 1206.02 0 142.8836 693.76
593 1025.1 0 217.8717 475.89
591 873 0 210.9 264.99
589 756 34.8 181 0
588 0 9.99 84 0
TABLE 5.1.13: LOSS OF GROSS STORAGE
Year Reservoir capacity (Ha-m) Loss of capacity
(Ha-m) Period
Year % loss of capacity from1981 % Annual loss
1981 6008 0 0 0 0
2017 4954.1237 972.77 36 14.5 0.402
From the above table it can be seen that there is a capacity loss of 972.77 ha-m during 1981 to 2017 (36 years). By Area Reduction Method the reservoir capacity of Bhatghar Dam in the year 2017 was 4954.1237 ha-m. The percentage loss of capacity from 1981 was 14.5% and % average annual loss of capacity was 0.402%.

Siltation Index
For catchment area= 331.50 km2
Loss of capacity in 36 years = 97.277 Mm3
SILTATION INDEX = 97.277×106/331.50×36
= 8151.2485 m3/ km2/ year
= 8151.245×1.199 T/km2/year
= 9780.7857 T/km2/year
Siltation index computed considering total sediment deposition since 1981 up to 2017 (36 years) was about 8151.2485 m3/km2/year, which was equivalent to 9780.7857 T/km2/year and is higher than siltation index of 2000 T/km2/year indicated in Iso erosion map of Garde and Kothari (1990).
5.4 DATA ANALYSIS BY AREA REDUCTION METHOD AFTER CALIBRATION BY GENETIC ALGORITHM
5.4.1 CODING FOR AREA REDUCTION METHOD
For Genetic Algorithm, I have to create a code for area reduction method which is added as a function to the genetic algorithms and calibrated by GA. The coding is as following:
filename = ‘test.xlsx’;
Elevation = xlsread(filename, ‘A:A’);
Area = xlsread(filename, ‘B:B’);
Capacity = xlsread(filename, ‘C:C’);
Length = length(Elevation);
TotalMeasuredSedimentVolume = 981.7;
%if Area(Length) == 0
% Length = Length – 1;
%end
%depth = Length;
Iteration = Length;
totalSedimentVolumeFinal = 0;
for inty=1:Length

if inty == 1
SedimentAreaIteration = zeros(Length,1);
end maxEle = Elevation(1);
minEle = Elevation(Iteration);

%if minEle == 595
% nonMin = 1;
% break;
%end

totalDepthDam = maxEle – minEle;
relativeDepth = zeros(Length,1);
for intx=1:(Iteration)
relativeDepth(intx) = double((Elevation(intx) – minEle)/ totalDepthDam);
end
approximateArea = zeros(Length,1);

for intx=1:(Iteration)
approximateArea(intx) = double((16.967* relativeDepth(intx).^(-1.15)) * ((1 – relativeDepth(intx)).^(2.32) )/1000);
if isinf(approximateArea(intx)) == 1
approximateArea(intx) = 0;
end end
ApproximateArea = approximateArea;

sum = 0;
for intx=1:(Iteration)
sum = sum + approximateArea(intx);
end
%Index = 0;
%if Area(Length -15) == 0 || approximateArea(Length -15) ==0
% Index = Length -16;
%end

%K = double(Area(Index)/approximateArea(Index));
if inty == 1
approximateArea_old = 0;
end %approximateArea_old;
if Area(Iteration) == 0
approximateArea_old = 0;
approximateArea_old = approximateArea(Iteration – 1);
Iteration = Iteration – 1;
SedimentArea = zeros(Length,1);

else
K = double(Area(Iteration)/approximateArea_old);
sedimentArea = zeros(Length,1);

for intx=1:(Length)
if approximateArea(intx) == 0 ;; Area(intx) ~= 0 ;; intx ==(Iteration)
sedimentArea(intx) = double((approximateArea_old * K) / 10);
else if intx ; Iteration
sedimentArea(intx) = SedimentArea(intx);
else sedimentArea(intx) = double((approximateArea(intx) * K) / 10);
end end %in first iteration no need to add this value
%sedimentArea(Iteration +1) = 84; % as Iteration decreases the Ineration + 1 values are constant so need to copy from last iteration.

end
sedimentVolume = zeros(Length,1);

for intx=2:(Length)
sedimentVolume(intx) = double(sedimentArea(intx) + sedimentArea(intx – 1));
end totalSedimentVolume = 0;
for intx=1:(Length)
totalSedimentVolume = double(totalSedimentVolume + sedimentVolume(intx));
end SedimentArea = sedimentArea;
approximateArea_old = approximateArea(Iteration – 1);
Iteration = Iteration – 1;
totalSedimentVolumeFinal = totalSedimentVolume;
end SedimentAreaIteration = SedimentAreaIteration SedimentArea;

%if totalSedimentVolumeFinal ; 900
if ((totalSedimentVolumeFinal/TotalMeasuredSedimentVolume)) ; 0.9
final =1;
break;
end
endAccumulatedSedimentVolume = zeros(Length, 1);
for intx=1:Length
if intx == 1
AccumulatedSedimentVolume(intx) = totalSedimentVolume;
else AccumulatedSedimentVolume(intx) = AccumulatedSedimentVolume(intx – 1) – sedimentVolume(intx);
end
endRevisedArea = zeros(Length,1);
for intx=1:Length
RevisedArea(intx) = Area(intx) – sedimentArea(intx);
endRevisedCapacity = zeros(Length,1);
for intx=1:Length
RevisedCapacity(intx) = Capacity(intx) – AccumulatedSedimentVolume(intx);
endFinalTable = Elevation Area Capacity relativeDepth approximateArea sedimentArea sedimentVolume AccumulatedSedimentVolume RevisedArea RevisedCapacity;
%figure % AccumulatedSedimentVolume vs Elevation
figure(‘units’,’normalized’,’outerposition’,0 0 1 1) %To full screen the plot window
plot(AccumulatedSedimentVolume, Elevation, ‘:r*’);
xlabel(‘AccumulatedSedimentVolume’);
ylabel(‘Elevation’);
%To Add the point(X,Y) in the figure following two lines
strValues = strtrim(cellstr(num2str(AccumulatedSedimentVolume(:) Elevation(:),'(%.2f,%.2f)’)));
text(AccumulatedSedimentVolume,Elevation,strValues,’VerticalAlignment’,’bottom’);
%figure % RevisedCapacity vs Elevation
figure(‘units’,’normalized’,’outerposition’,0 0 1 1) %To full screen the plot window
plot(RevisedCapacity,Elevation, ‘:r*’);
xlabel(‘RevisedCapacity’);
ylabel(‘Elevation’);
%To Add the point(X,Y) in the figure following two lines
strValues = strtrim(cellstr(num2str(RevisedCapacity(:) Elevation(:),'(%.2f,%.2f)’)));
text(RevisedCapacity,Elevation,strValues,’VerticalAlignment’,’bottom’);
%figure % RevisedArea vs Elevation
figure(‘units’,’normalized’,’outerposition’,0 0 1 1) %To full screen the plot window
plot(RevisedArea,Elevation, ‘:r*’);
xlabel(‘RevisedArea’);
ylabel(‘Elevation’);
%To Add the point(X,Y) in the figure following two lines
strValues = strtrim(cellstr(num2str(RevisedArea(:) Elevation(:),'(%.2f,%.2f)’)));
text(RevisedArea,Elevation,strValues,’VerticalAlignment’,’bottom’);
%figure % sedimentVolume vs Elevation
figure(‘units’,’normalized’,’outerposition’,0 0 1 1) %To full screen the plot window
plot(sedimentVolume, Elevation, ‘:r*’);
xlabel(‘sedimentVolume’);
ylabel(‘Elevation’);
%To Add the point(X,Y) in the figure following two lines
strValues = strtrim(cellstr(num2str(sedimentVolume(:) Elevation(:),'(%.2f,%.2f)’)));
text(sedimentVolume,Elevation,strValues,’VerticalAlignment’,’bottom’);
%figure % sedimentVolume vs Elevation vs Area
figure(‘units’,’normalized’,’outerposition’,0 0 1 1) %To full screen the plot window
plot3(sedimentVolume, Elevation, RevisedArea, ‘:r*’);
xlabel(‘sedimentVolume’);
ylabel(‘Elevation’);
zlabel(‘RevisedArea’);
%To Add the point(X,Y) in the figure following two lines
strValues = strtrim(cellstr(num2str(sedimentVolume(:) Elevation(:) RevisedArea(:),'(%.2f,%.2f,%.2f)’)));
text(sedimentVolume,Elevation, RevisedArea, strValues,’VerticalAlignment’,’bottom’);
5.4.2 CODING FOR CALIBRATION
After giving the area reduction method as a function to genetic algorithm, there is another code for calibrating the value of c, m, and n. This is as follow:
%FitnessFunction = @simple_fitness;
%options= gaoptimset(‘PlotFcns’,@gaplotbestf);
options= gaoptimset(‘PopulationSize’, 50, ‘EliteCount’,ceil(0.05*50),’Display’,’final’,’CrossoverFraction’,0.8,’SelectionFcn’,@selectionroulette,’CrossoverFcn’,@crossoversinglepoint,’Generation’, 100,’MutationFcn’,{@mutationuniform,0.5},’PlotFcns’,@gaplotbestf);
FitnessFunction = @ARM_FINAL_GA;
numberOfVariables = 3;
LB = 1.486, -1.15, 0.36;
UB = 16.976, 1.85, 2.32;
%x,fval = ga(FitnessFunction,numberOfVariables);
x,Fval, reason, Output, population,scores = ga(FitnessFunction,numberOfVariables,,,,,LB,UB,,options);
%gaplotbestf;
fprintf(‘The number of generations was : %d
‘, Output.generations);
fprintf(‘The number of function evaluations was : %d
‘, Output.funccount);
fprintf(‘The best function value found was : %g
‘, Fval);
fprintf(‘Calibrated paramaters of Area Reduction Method was C:%g, m:%g, n:%g
‘, x(1),x(2),x(3));
load(‘SedimentData’);
AccumulatedSedimentVolume = zeros(Length, 1);
for intx=1:Length
if intx == 1
AccumulatedSedimentVolume(intx) = totalSedimentVolume;
else AccumulatedSedimentVolume(intx) = AccumulatedSedimentVolume(intx – 1) – sedimentVolume(intx);
end
endRevisedArea = zeros(Length,1);
for intx=1:Length
RevisedArea(intx) = Area(intx) – sedimentArea(intx);
endRevisedCapacity = zeros(Length,1);
for intx=1:Length
RevisedCapacity(intx) = Capacity(intx) – AccumulatedSedimentVolume(intx);
endFinalTable = Elevation Area Capacity relativeDepth approximateArea sedimentArea sedimentVolume AccumulatedSedimentVolume RevisedArea RevisedCapacity;
figure % AccumulatedSedimentVolume vs Elevation
plot(AccumulatedSedimentVolume, Elevation, ‘:r*’);
xlabel(‘AccumulatedSedimentVolume’);
ylabel(‘Elevation’);
%To Add the point(X,Y) in the figure following two lines
strValues = strtrim(cellstr(num2str(AccumulatedSedimentVolume(:) Elevation(:),'(%.2f,%.2f)’)));
text(AccumulatedSedimentVolume,Elevation,strValues,’VerticalAlignment’,’bottom’);
figure % RevisedCapacity vs Elevation
plot(RevisedCapacity,Elevation, ‘:r*’);
xlabel(‘RevisedCapacity’);
ylabel(‘Elevation’);
%To Add the point(X,Y) in the figure following two lines
strValues = strtrim(cellstr(num2str(RevisedCapacity(:) Elevation(:),'(%.2f,%.2f)’)));
text(RevisedCapacity,Elevation,strValues,’VerticalAlignment’,’bottom’);
figure % RevisedArea vs Elevation
plot(RevisedArea,Elevation, ‘:r*’);
xlabel(‘RevisedArea’);
ylabel(‘Elevation’);
%To Add the point(X,Y) in the figure following two lines
strValues = strtrim(cellstr(num2str(RevisedArea(:) Elevation(:),'(%.2f,%.2f)’)));
text(RevisedArea,Elevation,strValues,’VerticalAlignment’,’bottom’);
figure % sedimentVolume vs Elevation
plot(sedimentVolume, Elevation, ‘:r*’);
xlabel(‘sedimentVolume’);
ylabel(‘Elevation’);
%To Add the point(X,Y) in the figure following two lines
strValues = strtrim(cellstr(num2str(sedimentVolume(:) Elevation(:),'(%.2f,%.2f)’)));
text(sedimentVolume,Elevation,strValues,’VerticalAlignment’,’bottom’);
figure % sedimentVolume vs Elevation vs Area
plot3(sedimentVolume, Elevation, RevisedArea, ‘:r*’);
xlabel(‘sedimentVolume’);
ylabel(‘Elevation’);
zlabel(‘RevisedArea’);
%To Add the point(X,Y) in the figure following two lines
strValues = strtrim(cellstr(num2str(sedimentVolume(:) Elevation(:) RevisedArea(:),'(%.2f,%.2f,%.2f)’)));
text(sedimentVolume,Elevation, RevisedArea, strValues,’VerticalAlignment’,’bottom’);
;
After calibrating the area reduction method, value of c, m and n are as
TABLE 5.4.1: COMPARING THE PARAMETERS OF AREA REDUCTION METHOD BEFORE AND AFTER CALIBRATION BY GENETIC ALGORITHM
Area reduction parameters C M N
Before calibration 16.967 -1.15 2.32
After calibration by G.A 8.77 -0.74 0.97
Table 5.4.1 shows the value of C, m and n for sediment distribution using the Area Reduction method before and after calibrating parameters (C, m, n) for the sediment distribution in Bhatghar dam. According to the table, the parameters of area reduction method decreased around 52.66 %.

TABLE 5.4.2: REVISED AREA AND CAPACITY AFTER CALIBRATING THE PARAMETERS OF AREA REDUCTION METHOD
Elevation (m) Sediment volume (Ha-m) Accumulated sediment volume (Ha-m) Revised Area 2017 (Ha) Revised capacity 2017 (Ha-m)
621 0 1053.14 3554 4873.76
619 4.85 1048.28 3344.15 4267.72
617 11.48 1036.8 3166.38 3680.2
615 14.76 1022.01 2996.83 3125.99
613 17.86 1004.15 2825.31 2584.85
611 20.99 983.16 2652.7 2062.84
609 24.38 958.78 2482.92 1579.22
607 28.19 930.58 2310.88 1117.42
605 32.66 897.92 2139.45 702.08
603 38.11 859.81 1966.44 338.19
601 45.06 814.76 1791.5 43.54
599 54.47 760.29 1617.03 0
597 68.35 691.54 1437.63 0
595 91.88 600 1256.5 0
593 145.79 455.28 1046.72 0
591 189.28 265 873 0
589 181 84 756 0
588 84 0 0 9.99

FIG.5.4.1: Sediment accumulation curve

FIG. 5.4.2: Sediment distribution at different elevation

FIG.5.4.3: Revised elevation-capacity curve

FIG.5.4.4: Revised elevation area curve
CHAPTER 6
RESULT AND DISCUSSION
In area reduction method previous year’s elevation–area– capacity curves are used in order to calculate sedimentation distribution. In this study by using data of the 1981 elevation–capacity–area curves of Bhatghar dam reservoir and through area reduction method, the sediment distribution profile was estimated for the year 2017. The volume of sediment that entered into Bhatghar dam reservoir from year 1981 to year 2017 is 972.77 Ha-m.

The shape factor was adopted as the major criteria for development of empirically derived design curves for use in distributing sediment (Ferrari 2008). The shape of the reservoir is defined by the depth to capacity relationship where ”M” is the reciprocal of the slope of the depth versus capacity plot on a logarithmic paper (USBR 1962). Considering that M = 1.785 the reservoir is from type III(Hill).

The value of C, m and n for sediment distribution using the Area Reduction method before and after calibrating parameters (C, m, n) by genetic algorithm for the sediment distribution in Bhatghar dam decreased around 52.66 %.

6.1 PREDICTED ELEVATION–AREA–CAPACITY CURVES FOR NEXT YEARS
The useful life or design life is a period that the sediment deposited does not affect the economic feasibility and sustainability of water resources demand. In general, useful life of the reservoir is the time period when the reservoirs depleted 50 % of its storage capacity or the dead storage is completely filled with sediment (Gill 1979). Figure 7.1 shows elevation–capacity curves predicted in years 2017, 2053 and 2089 with optimized coefficients. According to Fig. 7.1, 50 % of volume of Bhatghar dam will be filled by sediment in 2089.

FIG.6.1: Predicted elevation capacity curve for different year
TABLE 6.1 PREDICTED ELEVATION-CAPACITY FOR DIFFERENT YEAR
Elevation Capacity 1981 Revised capacity 2017 Revised capacity 2053 Revised capacity 2089
621 615.216 487.376 386.0993 305.8679
619 558.11 426.772 326.4806 249.7577
617 501.34 368.02 270.4947 198.8136
615 443.873 312.599 220.3823 155.3695
613 387.2 258.485 172.4095 114.9971
611 331.34 206.284 128.5149 80.06478
609 283.89 157.922 87.80463 48.81937
607 235.7 111.742 52.96571 25.10575
605 186.77 70.208 26.39821 9.925727
603 145.04 33.819 7.879827 1.836
601 108.24 4.354 0.17416 0.0069664
599 76.38 0 0 0
597 55.38 0 0 0
595 38.84 0 0 0
593 26.77 0 0 0
591 17.03 0 0 0
589 11.93 0 0 0
588 9.39 0 0 0
REFERENCES
Mohammad Gharaghezlou, Mohsen Masoudian, Robabeh Fendereski “Calibrating the Experimental Area Reduction Method in Assessing the Distribution of Sediments in Droodzan Reservoir Dam in Iran”Journal of Civil Engineering and Urbanism Volume 4, Issue 1: 54-58 (2014).

Sepideh Torabi , Hojjat Allah Yonesi1 , Babak Shahinejad, “Calibration the area-reduction method in sediment distribution of Ekbatan reservoir dam using genetic algorithms” Model. Earth Syst. Environ. (2015) 1:21,pp 1-9.

Kosit Lorsirirat, Kazurou Nakane,Panya Ponsane, “Catchment erosion and reservoir sedimentation-prediction for Khwae Noi Reservoir lifespan project in Thailand” Intrepraevent 2002 in the Pacific Rim(IPR) Mastumoto/Japan, Congress Publication, Volume 1,pp 156-163.

G. W. Annandale, “Predicting the distribution of deposited sediment in southern African reservoirs” Challenges in African Hydrology and Water Resources (Proceedings of the Harare Symposium, July 1984). IAHS Publ. no. 144.
Amir hossein Shafiee, Majid Safamehr, “Study of Sediments Water Resources System of Zayanderud Dam through Area increment and Area reduction Methods , Isfahan Province, Iran” Procedia Earth and Planetary Science 4 ( 2011 ) 29 – 38.

H. Hosseinjanzadeh, K. Hosseini, K. Kaveh, S.F. Mousavinpresented, “New proposed method for prediction of reservoir sedimentation distribution” International Journal of Sediment Research (2015) pp1-6.

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