Morris & Fan. Reservoir Sedimentation Handbook

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MODELING OF SEDIMENT TRANSPORT AND DEPOSITION IN RESERVOIRS 11.9

FIGURE 11.4 Modification of cross-section hydraulic geometry to eliminate

areas of ineffective flow during overbank flooding.

Test

ed three different sediment transport functions in a HEC-6 model of sediment

trapping in a debris basin. Different equations produced a four-fold variation in total

sediment transport and more than a two-fold difference in the amount of sediment

trapped during a single-event analysis. When measured bed material load data are

available, transport equations should be compared to the measured values to select the

applicable equation. In existing reservoirs with appreciable sediment accumulation or a

suitable calibration event, the historical depositional and scour process should be

simulated with different equations and the transport relation that best reproduces the

observed historical pattern should be selected.

MODELING OF SEDIMENT TRANSPORT AND DEPOSITION IN RESERVOIRS 11.10

TABLE 11.1 Relative Influence of Input Parameters on Sediment Routing Models

Relative importance of data

Description of Data High Medium Low

Physical parameters:

Roughness coefficients X

Sediment inflow X

Water inflow X

Variation of bed evaluation X

Sediment size distribution X

Water temperature X

Cross-section geometry X

Active layer thickness X

Coefficients of losses X

Operational parameters:

Sediment transport equation X

Time step duration X

Number of stream tubes X

Number of time iterations X

Stream power minimization X

Roughness equation X

Source: Molinas and Yang (1991).

Most numerical models allow a customized sediment transport equation to be used if

none of the equations provide a good fit. In this case, Simons and Senturk (1992)

suggest the following procedure. Using the existing data collected from a river station,

plot sediment load or concentration as a function of water discharge, velocity,

slope, depth, shear stress, stream power, and unit stream power. The least scattered

curve without systematic deviation from a one-to-one correlation between the

dependent and independent variables should be selected as the sediment rating curve

for the station. In constructing a rating curve, ensure that the time scales for

sediment transport and the hydrologic data series are compatible. For example, if the

sediment transport model uses a hydrologic series in which one day is the smallest time

step, the sediment rating curve and other hydrologic variables should be computed for

average daily values.

Often field data on transport rates are not available, and in the case of new reservoirs

there will be no historical deposition pattern to guide modeling. In these cases

measurements at other sites and engineering judgment can contribute to the

selection of are appropriate transport function. Comparisons have shown that some

transport equations tend to be better predictors of transport rates than others

when applied to diverse datasets. These comparisons provide one starting point

for the selection of an appropriate equation. Final selection of the transport equation

will depend on calibration results,

Brownlie (1981) compared the ability of 14 transport equations to predict measured

transport rates, in 5263 records from laboratory flumes and 1764 field data records, as

summarized in Fig. 11.5. The Brownlie equation gave the best fit of all equations for this

particular dataset because its parameter values were calibrated from this dataset, and it

would not be expected to perform as well when verified for an independent dataset. In a

comparison of measured sediment transport rates for field and laboratory datasets by

MODELING OF SEDIMENT TRANSPORT AND DEPOSITION IN RESERVOIRS 11.11

FIGURE 11.5 Comparison of the ability of 14 different sediment transport equations to predict

measured transport rates in rivers and laboratory flumes (Brownlie,1981).

onso (1980), ASCE (1982), and Yang and Wan (1991), the Yang equation gave the best

overall results. Brownlie also plotted the goodness of fit of each individual equation for

the test dataset. The plot for Yang's equation in Fig. 11.6 shows that a much better

agreement is achieved with the flume data than with the field data. This same pattern

occurred with most of the equations tested.

Transport equations may also be selected based on a comparison of conditions in the

study area against the dataset used in the development of each equation. The range of

the basic data used to develop selected equations is given in Table 11.2. Regime or

regression equations should be used only when the flow and sediment conditions are

similar to those from which the regression coefficients were derived. More formal

methods may be used to compare the applicability of specific transport equations to a

given fluvial environment. Williams and Julien (1989) suggested an applicability index

based on the relative roughness Z = d/D, Shields parameter F

, and dimensionless grain

size d

. The range of these parameter values in the calibration dataset for each

transport equation is compared to the range of each of these same parameters in the

prototype system to determine each equation's likely applicability.

When fine sediments are simulated by numerical models, recall that the settling is

controlled not by the grain size of individual particles, but by the extent of flocculation.

The settling rate or sedimentation diameter for fines should be analyzed in native water.

11.5.4 Calibration

In existing reservoirs, data may be available which document grain size and geometric

change over time. Calibration may be performed using these data (see Fig. 20.14).

However, calibration against a period of continuous deposition will not guarantee that

the model will accurately simulate the effect of a new operating rule that initiates scouring

of these deposits.

MODELING OF SEDIMENT TRANSPORT AND DEPOSITION IN RESERVOIRS 11.12

FIGURE 11.6 Ability of the Yang sand transport equation to predict sand transport rates

(top) measured in laboratory flumes and (bottom) measured in rivers (Brownlie, 1981)

In rivers lacking transport data, and at proposed reservoir sites, the model should be

calibrated by simulating the existing condition, reproducing the existing streambed slope

and grain size characteristics along the study reach, including any observed trends of bed

aggradation or degradation. For example, in the modeling of Waimea River on Kauai,

Hawaii, Copeland (1991) selected the transport equation for its ability to simulate the

MODELING OF SEDIMENT TRANSPORT AND DEPOSITION IN RESERVOIRS 11.13

TABLE 11.2 Range of Data Used to Construct Selected Sediment Transport Equation.

Equation Type

Uniform

grain

Size

range,

Data sources

(D= depth, ft)

Meyer-Peter and Muller Bed Load Yes 0.4-30 Flumes, D<1.2 m

Laursen BMT No 0.011-4.08 Flumes and rivers

Toffaleti BMT No Fine sand 0.1-

1.3

Flumes and rivers, 0.1<D<50

Ackers-White BMT Yes 1-3 Flumes and lowland rivers

Yang (sand) BMT Yes 0.152-1.35 Flumes and rivers, 0.1<D<50

Colby BMT Yes 0.1-0.8 Flumes and rivers, 1<D<100

Shen and Hung BMT Yes Sands Flumes and shallow rivers

Modified Einstein Total load No 0.28 Niobara and Middle Loup River,

flumes

Einstein BMT No 0.785-28.65

BMT = Bed Material Transport.

Source: Adapted from Williams (1990).

direction of bed aggradation and degradation observed in different reaches. In this case,

modeling results type indicated that equilibrium conditions did not prevail under all flow

conditions. Rather, the system was supply-limited at high discharges, causing the study

reach to degrade during infrequent large events. Aggradation occurred during smaller

events.

For a proposed reservoir site the numerical model may be used to simulate a similar

existing reservoir in the region. This exercise can demonstrate the model's ability to

simulate the pertinent processes, and aid in the selection of transport equations and para-

meter values. For example, Zarn (1992) modeled a chain of five planned hydro stations

along the upper Rhine River in Switzerland, using the MORMO one-dimensional steady-

flow numerical model (not publicly distributed) which uses 21 grain sizes to account for

bed material processes including transport, scour, deposition, sorting, and armoring of

sediment sizes ranging from 0.01 to 300 mm. Sediment release at the existing Reichenau

hydropower station, located 39 km upstream of the proposed project, was simulated by

modeling and verified against field data. The model was then used to simulate sediment

accumulation and the effects of different sediment pass-through options at the proposed

power stations.

In general, model construction should proceed by first entering several cross sections

and then running the model in a fixed-bed mode (hydraulics only, no sediment). Once the

first model segment functions, continue adding cross sections until the model is completed.

Use fixed-bed mode to perform hydraulic calibration for low, bankfull, and high flows

before calibrating for sediment. Roughness values can change as a result of sedimentation,

vegetative growth, and change in water depth. In enlongated reservoirs, the roughness

value selection can have a significant impact on upstream water levels, as described with

reference to the Three Gorges Dam in Chap. 13. Perform calibration adjustments

proceeding in the same direction as the computational sequence. Thus, for subcritical

standard step hydraulic computations, start hydraulic adjustments at the downstream limit

of the model and proceed upstream. In contrast, sediment is entered at the upstream end of

the model and is transported downstream by the computational sequence. Thus, when

calibrating for sediment, start adjustments at the upstream end of the model and work

downstream. The upstream limit of the model should consist of a reach having stable

characteristics throughout all simulations for both existing and proposed conditions.

MODELING OF SEDIMENT TRANSPORT AND DEPOSITION IN RESERVOIRS 11.14

11.6 DESCRIPTIONS OF SELECTED NUMERICAL

MODELS

Many mathematical models have been developed for simulation of sediment behavior. In

a compilation of U.S. models, Fan (1988) obtained information on 48 private and

government models in the following categories: 34 stream-, 18 watershed-, and 20

reservoir-sedimentation models. Multifunction models were listed in multiple categories.

Many additional models have been developed and are used in other parts of the world. In

summarizing the status of the available U.S. models, Fan (1988) made the following

generalizations. All computer stream sedimentation models include three major model

components: water routing, sediment routing, and special function modules. Most models

include the option of selecting alternative sediment transport formula, but none provides

criteria for making that selection. Most models use the finite difference method and

simulate unsteady flows as a series of steady flows. Most are equilibrium transport models in

which sediment transport is assumed to reach equilibrium conditions during each model

time step. Different models may produce significantly different results, even when run

with the same set of inputs. All models are strongly data-dependent and require adequate

data for calibration and verification, but in practice the field data required for this purpose

are often lacking. All models require a great deal of professional judgment and field

experience for interpretation of their outputs. Dawdy and Vanoni (1986) stated that

the choice of a modeler is probably more important than the choice of a model because of

the many judgmental factors involved.

The remainder of this section briefly describes several sediment transport models that

may be useful for analyzing sedimentation issues associated with reservoirs.

The models described illustrate the types of numerical tools currently available for use on

microcomputers, and show that each model will have certain features that can make it

attractive compared to others in certain situations. There is no general-purpose

model that is "best" for all conditions, and there are many good models in addition to

those mentioned here.

11.6.1 HEC-6

The U.S. Army Corps of Engineers HEC-6 model (U.S. Army, 1991) is probably the most

widely used model in the United States for the simulation of sediment transport in rivers

and reservoirs. Developed by William Thomas at the Army's Hydrologic Engineering

Center, it was first distributed for use within the Corps in 1973. The model has been

modified and enhanced through new releases, and the current version handles both

deposition and scour of sediment sizes from clay to boulders. A list of model vendors is

available from the Hydrologic Engineering Center, 609 Second St., Davis, California

95616.

HEC-6 is a one-dimensional movable-boundary open-channel flow model that com-

putes sediment scour and deposition by simulating the interaction between the hydraulics

of the flow and the rate of sediment transport. The model incorporates the assumption

that equilibrium conditions are achieved between the flow and the bed material transport

within each time step, an assumption also made in most other sediment transport models.

This assumption may be violated during rapidly rising and falling hydrographs, which can

limit the model's ability to simulate single events. For this reason the HEC-6 program

documentation specifically states that the model is designed for the analysis of long-term

river and reservoir behavior. However, in practice it has also been used to simulate single

events (for example, Gist et al., 1996)

HEC-6 can simulate a main river plus tributaries and local inflows. The hydraulic

MODELING OF SEDIMENT TRANSPORT AND DEPOSITION IN RESERVOIRS 11.15

profile is simulated by the standard step method and Manning's equation to solve the one-

dimensional energy equation, with the user specifying n values for both channel and

overbank areas at each cross section. It supports the use of both downstream and

internal rating curves, expansion and contraction losses, flow, containment by levees,

levee overtopping, ineffective flow areas, and conveyance limits in a fashion similar to

the HEC-2 model, but it does not handle split flow or have special routines for

bridges. Supercritical flow is approximated by normal depth, and sediment transport in

supercritical reaches is not explicitly computed.

At each time step, the hydraulic computations are initiated at the downstream boundary

of the model and proceed upstream. Then sediment computations are initiated at the

upstream boundary and proceed downstream. The bed elevation and grain size is

adjusted throughout the modeled reach, and hydraulic computations for the next

time step are initiated. Sediment transport capacity is calculated at each time

interval. Transport potential is calculated for each grain size class in the bed as

though that size comprised 100 percent of the bed material. This transport potential is then

multiplied by the fraction of each size class present in the bed to determine the

transport capacity for each size class.

HEC-6 model geometry is established by defining a series of cross sections, using the

same geometric input format as the HEC-2 hydraulic model. The user is required to

establish the limits of the erodible bed, which will not change over the course of the sim-

ulation. The initial bed geometry is assumed to raise and lower uniformly as a result

of deposition or sedimentation (Fig. 11.7), except that for simulating reservoir

sedimentation the model will allow all sediment to be focused into the bottom of each

cross section, producing horizontal sediment layers. Both sedimentation and scour can

occur within the movable channel limits, but only deposition can occur in the overbank

floodplain area. Armoring processes are simulated. The model incorporates 12

different transport equations or equation combinations, plus a user-specified transport

function. Gee (1992) notes that the impact of using different transport equations will

most likely be greater on transport rates than on geometry changes. Fines, consisting of

silt and clay-size particles, are scoured according to Ariathuri's (1976) adaptation

of Partheniades' (1965) method. Deposition of fine sediment is based on Krone's

(1962) relationship.

FIGURE 11.7 In the HEC-6 model, aggradation and degradation cause the entire movable bed to rais

or lower (U.S. Army, 1991).

Key advantages of this model include good documentation (U.S. Army, 1991; Gee,

1992), continuing support and development by the Hydrologic Engineering Center,

a long history of use, familiarity to many reviewing agencies, and the availability of

training through the Corps of Engineers and university short courses. A particular strength

MODELING OF SEDIMENT TRANSPORT AND DEPOSITION IN RESERVOIRS 11.16

of the HEC-6 model for reservoir analysis is its ability to simulate both deposition and

scour for a wide range of grain sizes, including silts and clays. Many other stream sed-

imentation models do not incorporate the capability to simulate fines.

In the future this model will be incorporated into the River Analysis System (HEC-

RAS), which consists of an integrated system of hydraulic analysis software consisting of

a graphical user interface, hydrologic and geometric database, separate hydraulic analysis

components, data storage and management capabilities, and graphics and reporting

facilities. When fully implemented the system will contain three one-dimensional

hydraulic analysis components: (1) steady-flow water surface profile computations,

replacing HEC-2 which will no longer be supported by the Corps; (2) unsteady-flow

simulation based on the UNET model; and (3) movable boundary sediment transport,

eventually replacing HEC-6. A key feature of this system is that all three computational

modules will use a common geometric and hydrologic database.

11.6.2 GSTARS

The General Stream Tube Model for Alluvial River Simulation (GSTARS) was devel-

oped by the U.S. Bureau of Reclamation (Molinas and Yang, 1986) and is available from

Ted Yang, MS D8540, U.S. Bureau of Reclamation, P.O. Box 25007, Denver, CO 80225.

GSTARS is a steady-, nonuniform-flow, one-dimensional model which simulates certain

aspects of two-dimensional flow by using the stream tube concept for hydraulic

computations. It is also capable of solving for channel width as an unknown variable,

based on the concept of stream power minimization. A version which will incorporate

routines specifically designed to simulate reservoir sedimentation processes is under

development.

Hydraulic computations may use the Manning, Darcy-Weisbach, or Chezy equation,

and computations can be carried through both subcritical and supercritical flows without

interruption. Geometry is specified by channel cross sections, and roughness coefficients

are specified as a function of distance across the channel.

The model uses stream tubes to compute the lateral variation in hydraulic and

sediment transport conditions within the cross section. Stream tubes are imaginary

channels within the wetted cross section bounded by streamlines. Since flow does not

cross streamlines, each stream tube has the same discharge (Fig. 11.8). The bed elevation

in each stream tube is allowed to move vertically up or down depending on transport con-

ditions, and one stream tube may be eroding while another parallel stream tube is

aggrading, providing a more realistic pattern of channel erosion and degradation than in

models in which bed geometry is fixed. Stream tube boundaries are computed at each

cross section at each time step to provide equal hydraulic conveyance within each stream

tube. The user determines the number of stream tubes to be used, and when a single

stream tube is used, the model becomes one-dimensional in the conventional sense.

The model simulates armoring by using a multiple-layer bed. Some transport equa-

tions (Yang, Ackers and White, Engelund and Hansen) compute total load without

breaking it into size fractions, but to track the composition of the bed and for armoring

computations it is necessary to determine transport rates by size class. In the GSTARS

model, the sediment load is computed for each size class individually as if the entire bed

consisted of that size. The resulting load is multiplied by the fraction of bed material

corresponding to that particle size to give the bed material load for each size class. Up to

10 user-specified size classes may be used in the model, but the model will not simulate

the scour and deposition of silts or clays.

MODELING OF SEDIMENT TRANSPORT AND DEPOSITION IN RESERVOIRS 11.17

FIGURE 11.8 Illustration of the stream tube concept used in the GSTARS model.

Changes in channel width can be computed by the model based on minimum stream

power theory which states (Chang,1980):

For all alluvial channels, the necessary and sufficient condition of equilibrium occurs when the

stream power per unit length of channel, QS, is a minimum subject to given constraints. Hence, an alluvial

channel with water discharge Q and sediment load Q as independent variables, tends to establish its

width, depth, and slope such that QS is a minimum.

This concept is implemented into the model by integrating the value of stream power

(QS) along the channel. At a given time step, if alteration of the channel width results

in lower total stream power than raising or lowering the channel bed, then channel

adjustments are made in the lateral direction instead of vertical. Thus, erosion can either

deepen or widen a channel. Similarly, depositing sediment accumulation can be placed

on the bottom or on the banks. Channel widening or narrowing computations are

restricted to the stream tubes adjacent to channel banks, and the bed of interior

stream tubes can move only vertically.

11.6.3 FLUVIAL

The FLUVIAL model is a private one-dimensional model developed by and available

from Howard Chang (P.O. Box 9492, Rancho Santa Fe, CA 92067; Fax (619) 756-9460;

email changh@mail.sdsu.edu

). The fundamental characteristics of the FLUVIAL model

are described by Chang (1988) and its use to analyze reservoir sedimentation is

described in the Feather River case study (Chap. 22).

The FLUVIAL model contains five major components: (1) hydraulic routing, (2)

sediment routing, (3) changes in channel width, (4) changes in channel bed profile, and

(5) changes in transverse bed geometry due to curvature. A particular feature of this

model is its ability to simulate the development of the transverse bed slope in a curved

MODELING OF SEDIMENT TRANSPORT AND DEPOSITION IN RESERVOIRS 11.18

reach, provided calibration data are available. The application of this feature is illus-

trated in the Feather River case study (Fig. 22.13).

Model geometry is specified by a series of cross sections. Bed material composition is

specified at the upstream and downstream boundaries of the model and may be specified

at other locations as well. Hydraulics, sediment transport, and bed and width adjustment

are simulated iteratively. Hydraulic routing can be performed as a series of steady

approximations by the computationally faster standard step method, or as dynamic-wave

unsteady flow. Bed roughness can be input in the form of Manning's n values, or

Brownlie's (1983) formula can be used to predict alluvial bed roughness. Six different

sediment transport formulas are incorporated into the model, and armoring computations

are performed. The model does not simulate silts and clays.

11.6.4 TABS

TABS-2 is a collection of generalized computer programs and utility codes integrated into

a numerical modeling system for analyzing two-dimensional hydraulics, transport, and

sedimentation problems in rivers, reservoirs, bays, and estuaries (Thomas and McAnally,

1985). There are three basic components: RMA-2 computes two-dimensional hydraulics,

STUDH computes sediment transport, and RMA-4 which computes water-quality

parameters.

RMA-2 is a finite element solution of the Reynolds form of the Navier-Stokes equa-

tions for turbulent flows. Friction is calculated by Manning's equation and eddy viscosity

coefficients are used to define turbulence characteristics. The model automatically

recognizes dry elements and corrects the mesh accordingly. The sedimentation model

STUDH solves the convection-diffusion equation with bed source terms, and is structured

for either sand or cohesive sediments. Clay erosion is based on work by Partheniades and

the deposition of clay utilizes Krone's equations. Deposited material forms layers, and

bookkeeping within the STUDH code allows up to 10 layers at each node for maintaining

separate material types, deposit thickness, and deposit age. Transport calculations with

RMA-4 are made with a form of the convection-diffusion equation that has general

source-sink terms. Up to seven conservative or decaying substances can be routed.

Whereas one-dimensional models specify geometry by cross sections, two- and three-

dimensional models use a finite element mesh to establish model geometry (Fig. 11.9).

Multidimensional models have much greater computational requirements than one-

dimensional models because they solve more, and more complex, equations at every node

and time step. Therefore, it is desired to minimize the number of nodes while adequately

reflecting the significant features of the hydraulic geometry. A microcomputer version of

TABS-2, with pre- and post-processing software for mesh generation and flow

visualization, is available from vendors such as Boss International, 6612 Mineral Point

Road, Madison, WI 53703 (Internet http://www.bossintl.com

11.6.5 SSIIM

The SSIIM model developed by Nils Olsen uses a finite volume method to solve the Navier

Stokes equations in three dimensions on a general nonorthogonal grid. Another three-

dimensional finite volume model is used to calculate sediment concentration within the

reservoir by solving the diffusion/convection equation for sediment concentration. The

primary motivation for development of this model was the difficulty of simulating fine sedi-

Morris &amp; Fan. Reservoir Sedimentation Handbook

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Morris & Fan. Reservoir Sedimentation Handbook