ch6.pdf

CHAPTER 6

SETRIC, a Mathematical Model forSediment Transport in Irrigation Canals

6.1 INTRODUCTION

Clogging of the structures that supply water to secondary and tertiaryunits, and sedimentation of the canal network are some of the main prob-lems in the operation and maintenance of irrigation systems. High annualinvestments are required for rehabilitation and maintenance to keep thesystems suitable for their purpose. To reduce these expenses and to pre-serve and sometimes improve the performance of the irrigation networks,the sediment transport should be properly estimated in terms of time andspace. An accurate prediction of the sediment deposition along the entirecanal network during the irrigation season will contribute to an improvedoperation of the canals in such a way that the irrigation needs are fullymet and at the same time a minimum deposition might be expected.

Although it is difficult to predict the quantity of sediment that willbe deposited in irrigation canals (Brabben, 1990), numerical modellingof sediment transport offers the possibility to predict and evaluate thesediment transport under very general flow conditions (Lyn, 1987).A mathematical model, which includes the latest sediment transport con-cepts for the specific conditions of irrigation canals, will be an importantand helpful tool for the designers and managers of these systems. Thischapter will describe the computer model SETRIC, which has been indevelopment at UNESCO-IHE since 1994 and which includes some ofthe specific characteristics of sediment transport in irrigation canals, asdiscussed in the previous chapter.

6.2 WATER FLOW EQUATIONS

Water flow in irrigation canals will be schematised as quasi-steady flowin which the governing equations are represented as: Continuity equation:

Q

x= 0 Q= constant (6.1)

2007 Taylor & Francis Group, London, UK

124 A New Approach to Sediment Transport

Continuity equation at confluences and/or bifurcations: Q ql = 0 (6.2)

Dynamic equation:

dh

dx= So Sf

1 Fr2 (6.3)Several methods are available to solve the dynamic equation of grad-ually varied flow for prismatic canals. Henderson (1966), Chow (1983),Depeweg (1993) and Rhodes (1995) present a comprehensive descriptionof the available methods, including graphical-integration, direct integra-tion, direct step, standard step, the Newton-Raphson solution and thepredictor-corrector method. A summary of those methods is given inChapter 2.

6.3 SEDIMENT TRANSPORT EQUATIONS

The numerical solution of the one-dimensional sediment equations thatinclude the friction factor predictor, continuity equation for sedimentand the sediment transport predictor (see Chapter 5) requires boundaryconditions for water flow and sediment transport. These conditions are: description of the geometrical variables of the canal during a time step:

width, slope and level of the bottom; description of the flow conditions along the entire canal during a time

step: discharge, velocity, roughness, water depth and slope of the energyline;

the characteristics of the incoming sediment, namely the sediment loadand sediment size at the upstream boundary;

the sediment transport rate along the entire canal; the changes in bottom level and/or bottom width; specific confluences and bifurcations can be incorporated by applying

continuity for water flow and sediment load.

In order to compute the sediment transport along the entire canal, it isnecessary to consider how the sediment load that is entering the canaladapts to the sediment transport capacity of the reaches; this is given interms of the sediment concentration C, which follows from Galappattisdepth-integrated model:

C = Ce (Ce C0)ex

LA with LA = f(uv

,wsu

, y)

(6.4)

Where:C = actual concentrationCe = equilibrium concentrationC0 = initial concentrationx= distance along the canal

LA = adaptation length


SETRIC, a Mathematical Model for Sediment Transport in Irrigation Canals 125

In order to determine the actual sediment concentration in the x-directionof the canal, the values of the variables C0, LA, x and Ce have to beknown. The first one, the initial concentration C0, does not depend onthe local flow condition, but instead depends on the source of water andsediment and on whether a sediment-trap is located at the head of theirrigation network. At boundaries between canal reaches, the sedimentload passing through the downstream boundary of the upstream reachwill become C0 for the next canal reach.

In a gradually varied flow the values of Ce, y, v, u and f are functionsof x. These variables may be known in advance at any point along thecanal network if the flow equations are solved first (using the uncoupledtechnique). That means that in any point of the canal, i= 0, 1, 2, . . . n aregiven Ce, y, v, u and the dimensionless parameters u/v and ws/u. Thesevariables are determined according to the following procedure: the x-value is fixed according to the required degree of accuracy

for the numerical solutions and the need for representing the adapta-tion of the actual non-equilibrium condition to the sediment transportcapacity (the equilibrium condition) of the canal. The x-value shouldbe much smaller than the adaptation length (LA) of the actual sedimenttransport to the sediment transport capacity of the canal;

computation of the LA-value. For the local flow conditions the values ofws/u, u/v and the water depth are known in advance. The maximumvalues of the parameter ws/u should satisfy the requirements for thevalidity of the depth-integrated model (Ribberink, 1986);

once the motion of sediment has been initiated, the values of thede Chzy coefficient can be estimated depending on the type ofroughness along the wetted perimeter of the canal by:

C = 18 log 12Rks

for single roughness (6.5)

C e = 18 log12R

ksefor composite roughness (6.6)

the value of the depth-averaged equilibrium concentration Ce will bedetermined by one of the sediment transport predictors, such asAckers-White, Brownlie or Engelund-Hansen. The predictors compute thesediment transport per unit width (qs), which is determined by thelocal flow conditions and the sediment properties. The total sedimenttransport across the whole canal section Qse is calculated by:

Qse = Bqs (6.7) Next, the equilibrium concentration Ce is calculated by:

Ce =(

s

QsQ

) 1, 000, 000 (in ppm) (6.8)



Some internal conditions along the canal can be taken into account forthe computation of the sediment transport distribution either at bound-aries between canal reaches or at boundaries at branches (bifurcationsor confluences). Application of the continuity for the water flow andfor the sediment transport rate is helpful when changes either in bot-tom width or bottom level, or at bifurcations or confluences have to beincorporated in the model. The distribution of water and sediment atbifurcations will depend on the local flow pattern at the branches.

6.4 GENERAL DESCRIPTION OF THE MATHEMATICAL MODEL

The computer program SETRIC simulates the water flow, sediment trans-port and changes of bottom level in an open networkwith amain canal andseveral laterals with or without tertiary outlets. Various flow conditionsalong the canal network and during the irrigation season can be simu-lated. Figure 6.1 shows the flow diagram for calculating the change ofthe bottom level in a canal reach during one time step. Flow diagrams ofthe computer program SETRIC for the water flow and sediment transportcalculations in a canal reach are shown in Figures 6.2 and 6.3.

The background for the hydraulic and sediment transport computationswas described in the previous chapter.

The general framework of the computer program consists of:

Hydraulic aspects The water flow can be modelled as a sub-critical, quasi-steady, uniform

or gradually varied flow (backwater as well as drawdown curves). Thewater profiles for the subcritical, gradually varied flow include: H2,M1, M2, C1, S1 and A2;

The water flow is in open channels with a rectangular or trapezoidalcross section; only friction losses are considered: no local losses dueto changes in the bottom level, cross section or discharge will be takeninto account. The canal sections are characterized by the followinggeometrical dimensions, namely: length (l) presents the length of a canal section (m); bottom width (B); side slope (1 vertical : m horizontal); the roughness is defined by the equivalent roughness coefficient (ks);

the total friction factor follows from the composite roughness for theentire cross section;

coordinates to give the relative location of a canal section; the mostupstream boundary is defined as x= 0m;

bottom slope (So in m/m); bottom elevation above a reference level (datum) at the beginning of

each canal section (zb).



Start

Time step > 0?

Next reach Repeat until end

Is there flowcontrol structure?

Calculate water depthupstream of the structure

Calculate water surface profileusing predictorcorrector method

Store all the output resultsto be used for next time step

Depending upon the equilibrium and actualconcentration, calculate morphological

change in the bed using Modified Lax method

Calculate modified Chzys coefficient,critical water depth and normal water depth

Input hydraulic and sedimentcalculation results ofprevious time step

Calculate critical water depth andnormal water depth using initial

value of roughness

For i = 1 to number of reaches

Read input filesand start calculation

for first period

N

Y

Y

N

Figure 6.1. Flow diagram of SETRIC for calculating the water flow, sediment transport and changes in bottom levelin main and/or lateral canals (after Paudel, 2002).



Calculate equivalentroughness of the section

Calculate water depthover control section

Calculate water depth (Y )2,1 at 2and test if Y2,1>0

Calculate change in depthDy2,2 = (dy/dx)av* length step

Calculate water depth at 2, (Y2,2 = Y1-Dy2,2)

Calculate (Bs, A, Fr2, P, dy/dx) at section 2

Calculate average (dy/dx) from (dy/dx)at 1 and (dy/dx) at 2

(Y )2,2 = 2Y2,1+1

With the parameters, calculate changein depth Dy2,1 at 2

Calculate (Bs, A, Fr2, P, dy/dx) at section 1

N

Y

Go

Y

Y

N

N

I Y2,2-Y2,1I >Accuracy

(dy/dx)2,1 = (dy/dx)av

Y2,2


Start

Read data fromwater flowcalculation

Calculation of the sediment transportcapacity for the entire reach

For i = 1 to total length of the reach

Is thereequilibriumcondition?

Deposition?

Next time step

Compute the sediment transport

Entrainment?

C(i ) = C(i1)

C(i ) = Ce

YesNo

No

No

Yes

Yes

Figure 6.3. Flow diagram of SETRIC for calculating the sediment transport in the main canal and lateral canals duringa time step.

Sediment aspects The sediment is characterized by:

sediment concentration (ppm) at the furthest upstream boundary ofthe main canal;

sediment size by the mean diameter d50. Variations of the roughness conditions over time are incorporated in the

model; sedimentation during the irrigation seasonwill induce the devel-opment of bed forms, which depend on the flow conditions (differentflow conditions will produce different types of bed form). The frictionfactor is computed for every time step and for each flow condition ineach cross section of the schematisation.

Irrigation aspects The model of the irrigation network can be most simply composed of

a main canal and secondary canals with tertiary outlets. Each canal isdivided into several reaches or sections;



the model can include changes in the bottom level at the upstreamboundary of a canal section;

control sections can be set at the downstream end of the main canal orsecondary canals; the type of structure located at the downstream endof a section sets the water level;

the network might include lateral inflow or outflow; these lateral flowsshould be located at the end of a canal section;

the flow control structures that can be incorporated, include: overflow type: crest width, crest level; undershot type: width and height of the rectangular opening; submerged culverts and inverted siphons: number and diameter of

pipes; flumes: constants of the upstream head-discharge relationship; drops: incorporated as a different bottom level at the boundary

between two reaches; the variation in crop water requirement during the irrigation season

can be incorporated and mainly depends on the climate, cropping pat-tern, stage of the crops, leaching requirement and water losses. Thegrowing season is divided into four stages depending on the crop devel-opment and climate (FAO, 1984). The water supply in the model canbe attuned to the varying water requirement and follows the changes inarea and time;

maintenance activities in view of weed growth on the banks can alsobe included and the growth is referred to by an obstruction degree. Theeffect of maintenance on the roughness can be expressed by: ideally maintained: negligible obstruction degree over time; well maintained: a maximum obstruction degree of 10% is assumed; poorly maintained: more than 75% obstruction degree is assumed.

6.5 INPUT AND OUTPUT DATA

Input dataFor the computation of the water flow and sediment transport, the programrequires several input data, which include: Simulation period: characteristics of the period to be simulated include:

number of periods in which the irrigation season is divided; type of maintenance to be expected during each period of the

irrigation season; number of days for each period and the number of irrigation hours

per day. Canal dimensions: the geometrical dimensions of main and secondary

canals contain: for each canal: number of sections, type of roughness data;



for each section: location from upstream boundary, length, slope,width and elevation of the bottom; roughness coefficient, sideslope.

Main and lateral discharges: the schedule of irrigation flows (inflow(+) and outflow ()) during each period of the irrigation season; thedischarge entering the main canal for each period together with thelateral flows at the furthest upstream boundary of each lateral and foreach period.

Sediment data: mean sediment concentration and mean diameter ofthe sediment particles entering the main canal; SETRIC computes thesediment concentration flowing to the laterals.

Control sections: the control section at the downstream end of themain canal and at each lateral has to be specified and they includethe water level and the location of each control section. Control struc-tures at the boundaries between canal-reaches are specified by the typeof structure and its main hydraulic characteristics. SETRIC computesthe upstream water level that will act as a control level for the nextcanal-reach.

Output dataThe computer program is able to present the results of the water flow andsuspended sediment transport calculations in tables or graphs dependingon the selected option. Moreover, the results can be presented on themonitor or on paper. The program can show the following tables: General information:

results related to thewater flow: normal and critical depth, discharge; results related to the sediment transport: fall velocity, length step,

minimum and maximum shear stress, shear velocity. Concentrations: table with the water depth, equilibrium concentration

and actual concentration for the entire canal. Bottom level: the initial bottom level and the change in bottom level at

the end of the period are presented.

6.6 CONCLUSIONS

The mathematical model SETRIC for predicting the water flow and thesediment transport together with the variation in bottom level of thecanal is based on an uncoupled solution of the water flow and sedimenttransport equations. The model can be used for simulating the sedimentdeposition in an irrigation network under changing flow conditions andsediment characteristics during the whole irrigation season and over oneor more years. The model can be used for evaluating the effects of theinterrelation between irrigation practice (operation and maintenance) and



sediment deposition. The direct effect of irrigation practices on the sedi-ment deposition may include changes in discharge, changes in sedimentload, flow control structures, controlled deposition, operation and main-tenance activities, diverted sediment load to the farmlands, etc. Sedimentdeposition in the canal reaches may affect the following hydraulic aspects,such as water level variation (overtopping of canals), water distribution atoutlets and flow control structures.


CHAPTER 6: SETRIC, a Mathematical Model for Sediment Transport in Irrigation Canals6.1 INTRODUCTION6.2 WATER FLOW EQUATIONS6.3 SEDIMENT TRANSPORT EQUATIONS6.4 GENERAL DESCRIPTION OF THE MATHEMATICAL MODELHydraulic aspectsSediment aspectsIrrigation aspects

6.5 INPUT AND OUTPUT DATAInput dataOutput data

6.6 CONCLUSIONS

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