CC BY
49
Khazratov Alisher Normurodovich, Assistant Teacher in Karshi Engineering Economics Institute, Visiting student in Hohai University E-mail: Khazratov@gmail.com
A SEDIMENT TRANSPORT MODEL FOR IRRIGATION CANALS OF UZBEKISTAN
Abstract. This paper describes a dynamic morphological sediment transport model for determining the bed slope of dynamic stable irrigation canal. The model is supposed to help in designing process of irrigation canals.
Keywords: cohesive and non-cohesive sediments, dynamic stable irrigation canal, deposition, erosion rate.
1. Introduction
Currently, there are more than 196 thousand kilometers irrigation canals for around 4.3 million hectares of irrigated lands in Uzbekistan. Operation of big irrigation canals, like Mirishkor, Karshi that deliver water from Amudarya River, is requiring more and more expenses year-by-year. Parameters of the cross sectional geometry have changed and the capacity of the canals has decreased due to sedimentation problems.
On a worldwide scenario, sediment transport predictors of Ackers-White, Brownlie, Einstein, Engelund-Hansen, Van Rijn, Yang and others are available. However, the predictability of these methods is still poor [3, 142].
Many scientists, such as Karaushev, Poslavskiy, Cheku-laev, Xorst, Gostunskiy, Xachatryan, Zamarin, have developed a lot of empirical and semi-empirical formulas to evaluate sediment transport capacity having accuracy varying from 15% to 100% [10, 189]. Zamarin's formulas are being used to determine sediment transport capacity and permissible minimal velocity in the construction regulations of Uzbekistan. The fact that sedimentation has occurred in the main canals leads us to suspect that the canal design method in the construction regulations of our country lacks precision.
The existing canal design methods are based on the interrelation of equations for specific water flow and sediment transport conditions, leading to the design of stable canals. However, the input variables generally vary widely during the irrigation season and during the lifetime of the irrigation network. Most of the time, non-equilibrium conditions prevail in irrigation network and therefore, the basic assumptions for a stable canal design are no longer valid [3, 74].
The canal design methods do not directly use available information on sediment characteristics, such as the sediment size and its concentration. Nowadays, the design of irrigation canals involves complex and difficult to determine parameters such as water flow, required water levels, sediment load, control structure and operation and management strategies. No design package is available that deals with all these parameters at the same time. When analyzing the impact of one parameter, others are either ignored or assumed to be constant. Therefore, it is obvious that a mathematical model to take into
account important multiple parameters, specified for design of canals, will be an important tool for designers and managers of the irrigation systems [3, 75].
2. General description of the model
According to Van Rijn, depending upon whether the computation is for a single time step or multi time step, the combined model may be divided into two types:
- initial or sediment transport model that computes the sediment transport rate and bed level change for one time-step;
- dynamic morphological model, which computes the flow velocity, the sediment transport rates, the bed level change and computes again the new flow velocity: the process is continued for the next time step [5, 47].
A one-dimensional dynamic morphological model is being developed in JAVA programming language, which is used to find optimal bed slope to design an unbranched irrigation canal. One of the main peculiarities of the model is the usage of extensive available information such as properties of each sediment size class, flow and sediment parameters of every time interval. Sediment transport methods ofAckers - White and Brownlie are used for non-cohesive sediments. The calculations are carried out separately for every particle size class to get more accurate results. For cohesive sediments, however, equations of Krone (1962) and USDT Federal Highway administration report, (2015) are used.
After each time interval, the total volume of deposition or erosion is calculated. Then, based on this volume, the morphological changes are applied to the canal cross section by distributing equally the deposited/eroded sediment volume throughout the length of the canal and wetted perimeter. Calculations are repeated considering the changed canal cross-section and the new flow parameters of each time step.
General concept of the model is depicted in the flow diagram of (Fig. 1).
3. Input data to the model
One of the main purposes of the current model is to use as much available information as possible to get more accurate results. Therefore, in this part, after inputting constant data that does not change during the calculation period, a year is divided into number of time intervals. For each time step, long-
term average parameters, such as sediment concentration and water discharge are specified. Then, sediment size analyses, diameters and fall velocities of each size class are entered. Afterwards, from the topography of the canal construction site, possible canal bed slope values are inputted.
4. Cross section and flow parameters
Computations of the cross section and flow parameters for any bed slope starts from the first time-interval in which the biggest water discharge is observed over a long term.
Figure 1.
Relative width that is ¡3 = b / h ratio is computed with Girshkan's formula [1]. Shterenlicht's method is used to calculate the canal bed width and water flow depth [9]. The van Rijn method is implemented as bed roughness predictor, because, the van Rijn method shows good results over the whole range of measured friction factors [3, 119]. Calculation order is as follows:
1. ¡3 = b / h ratio with Girshkan's formula, dimensionless, [1, 243];
H= 3*Qm* -m; (1)
where:
Qmax - design flow discharge, m3 / s ; m - side slope;
2. Maximum water depth hmax and canal width b [9, 332].
h 2>5+7
Qmax = + m)
ß + m
\0.5+7
ß+ 2 VT
m
4S ; (2)
where y ~ 1/6..
From here we find the flow depth h
K = hmax =
Q • «
(ß + m )
ß + m
ß+ 2 VT
m
vs
(3)
(4)
b = p- hi; where
b - canal bed width, in m ;
h - design water flow depth, in m;
max
h1 - water flow depth in first time interval, in m ;
3. Then standard canal width is selected rounding the value of b to a next higher value of bt according to building regulations of Uzbekistan [1, 248].
4. Flow parameters are computed for first time interval assuming that there is a uniform flow.
5. Computing sediment transport
5.1. Computing cohesive sediment transport
Erodibility of cohesive sediment cannot be predicted on the basis of environmental parameters. Therefore, researchers have developed various test apparatus to empirically measure sediment erodibility [4, 371].
However, quantitative guidance for predicting erosion in cohesive soils has been presented by USDT Federal Highway Administration, so that erosion testing is not required for every project. Estimates of critical shear stress are based on the water content, fraction of fines, plasticity index, and the unconfined compressive strength. Coefficients and exponents of the method require to be calibrated to get more accurate results when applied at new places [7, 78].
In the model, for cohesive sediments, we use the equations of Krone (1962) and USDT Federal Highway admin-
istration report (2015). Values of settling velocities for cohesive sediment should be predetermined as input for each time interval. They can be determined from settling column measurements [2, 15].
Calculation order for first time step is as follows: 1. Critical shear stress for each time step, N / m2; [7, 72].
w
Tr =ad\F | PI13
(5)
2. Coefficient C1 for each time step, [7, 74];
C =«„ (<L f 0 PI-u (6)
3. Bed shear stress, N / m2, [4, 316];
Ti = PwgRs (7)
4. Probability of deposition, dimensionless [8, 13];
(' \
Pu =1 -5. Friction velocity;
6. Peclet number;
7. Coefficient ¡5 ;
p= 1 +
P = -6ws
KU
(8)
(9) (10)
(11)
(12)
1.25 + 4.75(p2f)
8. Near bed concentration, kg / m3 ;
cbi =P-c
9. If^bi <Tc, ,
• Deposition rate according to Krone, kg / m2 • s ;
SD1 = WCbi Pdi (13)
• Deposition volume, m3 ;
= SdiTlXil (14)
Pc
• Erosion volume, We = 0 ,m3;
10. If Tbi >rcr,
• Erosion rate in the first time step, m / s, [7, 70];
z1 = C1 (zb-zcr )18/3600*1000 (15)
• Erosion volume in the first time interval, m3;
W = Z1XIT1 (16)
• Deposition volume in the first time interval, Wd = 0 m3;
11. Total sediment erosion-deposition difference ,m3;
Waal1 = Wd - We (17)
where
F - fraction of fines by mass for each time step, dimen-sionless;
pc - density of fully saturated cohesive sediment for each time step, kg / m3 ;
PI - plasticity index of cohesive sediment for each time step, dimensionless
ws - settling velocity of cohesive sediment for each time step, m / s ;
qu - unconfined compressive strength of cohesive sediment for each time step, N / m2 ;
Sg = pc / pw - specific gravity of fully saturated cohesive sediment for each time step, dimensionless;
w = e / Sg - water content for each time step, dimension-less ratio.
K = 0.41 - Von Karman constant;
ad = 0.07 - coefficient, unit conversion constant for design;
Calculations for other time intervals are also carried out in this order except already computed parameters for every time step.
4.2. Computing non-cohesive sediment transport with Brownlie and Ackers-White method
In Brownlie method calculations are carried out for each sediment size class with a table method. Representative particle diameter d50 is replaced with the average particle diameter of each size class d.
Sediment transport potential for each size class, [3, 233];
qs = 727.6cf F - Fm)
/ N -0.3301
V d50 y
(18)
where
cf -coefficient;
cf = 1 for laboratory conditions, cf = 1.268 for field conditions;
S - bed slope; s = - relative gravity; Pw
pS - specific gravity of sediment, kg / m3 ; Pw - specific gravity of water, kg / m3 ; R - hydraulic radius, m ; v - cinematic viscosity, m2 / s ; 1. Water flow travel time 11, s ;
tl = l/9, (19)
where
l - canal length, m ;
- average flow velocity, m / s ; Sediment input volume of each size class;
W =-COT
input 100 1
Sediment transport of each size class;
W
output
= qJi
(20)
(21)
If W. > W
input output cient;
wt,
Continuity limiters for each size class, Coeft, [4, 342];
deposition efficiency coeffi-
(22)
erosion efficiency coefficient;
(23)
Coefi = Coefdeposition =h
IfW. < W
input output
C°efi = Coefer0SWn = 1.368 - e
30! I
J
Sediment input-output volume difference of each size class;
W ,= (W. - W )* Coef (24)
actual input output J'
Total sediment erosion-deposition difference ,m3 ;
W ,=VW , (25)
total actual
Calculations with Ackers-White method are carried out for each sediment size class with a table method. Representative particle diameters d50 and d35 are replaced with the average particle diameter of each size class di . The rest of the calculations are the same with as those presented above in Brownlie method.
5. Morphological changes of the cross-section parameters
Morphological changes are implemented based on total sediment erosion-deposition difference of the previous time step. Sediment continuity equation, that is Exner equation, is used to tackle this problem [4, 337]:
(26)
where
Qs - transported sediment load, m3 / s ;
B - canal width, m ;
n - canal elevation, m ;
x - distance, m ;
t - time, s ;
Xf - active layer porosity;
In this model, we distribute the eroded/deposited sediment volume equally throughout the canal length and the wetted perimeter.
Therefore, we computed morphological changes as follows:
1. Change at the canal bed with Exner equation, in m;
dh (27)
ix(i )
where
l - canal length, m;
X - wetted perimeter, m ;
Wtotal - deposited or eroded sediment volume of previous time step, m3 ;
2. Change in the cross section area, m2 ;
A = W /1
change total '
3. New canal cross section area, m2 ;
A = A - A
4. New canal depth, m2 ;
change
hnew = h1 - dh
(28)
(29)
(30)
5. Assuming constancy of side slope and bed slope, new canal bed width is determined;
"''2 (31)
b = Anew mKew
6. New wetted perimeter of canal, m ;
Znew = Kw + 2 • KwJ1 + m 2 ; (32)
7. New hydraulic radius of canal, m ;
Rnew = Anew ^ Xnew ; (33)
6. Flow parameters for the next time interval
Flow depth h2 of a next time step is computed with trial and error method considering changed cross section with following equations.
1. Cross section area, m2 ;
A2 = (Kw + m ■ K) ■ h2
2. Wetted perimeter, m ;
Z2 = Kw +2 • KJ1
3. Hydraulic radius, m ;
R2 = A2! X2
ks2 - k/2 + k/2
4. Total equivalent height is computed with van Rijn
method, m;
(37)
(38)
(39)
5. Chezy coefficient;
C 2 = 18 log
Г1ЩЛ
V ks 2
- m
6. Following condition must be fulfilled: Q = A2C;
7. Then flow parameters are determined from the equations (34-39).
Conclusion
The above-described model is one of the attempts to develop new calculation algorithms, which enables to determine the bed slope of dynamic stable irrigation canal in the design process to solve the problem of deformation.
References:
(34)
(35)
(36)
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