WATER RESOURCES BULLETIN VOL. 8, NO. 5 AMERICAN WATER RESOURCES ASSOCIATION OCTOBER 1972

SEDIMENTATION CHARACTERISTICS OF GORGE-TYPE RESERVOIRS'

S. P, Chee and A. P. Sweetman'

ABSTRACT. An investigation of the hydraulics of gorge-type reservoirs was conducted with scale models. Reservoir shapes were moulded within a large basin. Water was circulated using a centrifugal pump-motor unit and uniform sediment (specific gravity 2.65) with mean diameters of 0.20 mm and 0.60 mm were utilized. Observations were made to study sedimentation patterns from the com- mencement of sediment inflow until the final stage of a fully silted reservoir. In particular, the mode of deposition of the sediment beds, the mechanics of transportation and sediment bed slopes were investigated. These aspects of reservoir siltation were examined in relation to the factors which influence it, which included sediment characteristics and flow parameters. Bed slopes and flow depths were analyzed by various methods; the Kalinske equation in conjunction with the Manning and Einstein-Barbarossa relations as proposed by Doland-Chow produced the best results. (KEY TERMS: sedimentation; reservoir; siltation; sediment transport; bed load; silt; gorge; suspended load; sediment)

INTRODUCTION

In feasibility studies of water power, irrigation, water conservation, river basin development or other water resources projects, reservoir sedimentation is examined critically as it often determines the economic life of the project. The obvious detrimental aspect of reservoir silta- tion is the encroachment of sediment on reservoir storage and the extent and severity of this depends on the mode of disposition of the sediment beds.

The United States Bureau of Reclamation [1954] has classified reservoirs into four categories: gorge; hill; flood plain-foothill; and lake types based on reservoir configurations. Mathematically, these shapes can be described by the relationship,

in which h = reservoir height (depth); C = reservoir capacity; K = coefficient; m = a constant. Reservoir shapes are defined in terms of the values of m, that is, m = 1 .O to 1 S , gorge; m = 1.5 to 2.5, hill; m = 2.5 to 3.5, flood plain-foothill; and m = 3.5 to 4.5, lake. For any given in- crease in reservoir capacity, a large increase in reservoir depth is associated with a small value of the exponent m and vice versa. Hence, a reservoir with a small increase of capacity with a corresponding large increase in depth, that is a small value of m, is the gorge type. This paper deals with the sedimentation characteristics of the gorge-type of reservoirs.

'Paper No. 72081 of the Wafer Resources Bulletin Discussions are open until April 1 , 1973. 'Respectively, Associate Rofessor, Department of Civil Engineering; Graduate Student, University of

Wmdsor, Wmdsor 11, Ontario, Canada.

88 1

882 Chee and Sweetman

There are other factors which control the deposition of sediments besides reservoir shape. Sediment and flow characteristics are major parameters which exert a significant influence on siltation. Sediment distribution depends predominantly on the grading and size of the silt particles, sediment inflow, and water discharge. These variables have been examined in this investigation.

The important features of reservoir sedimentation studied included: (a) bed profiles (b) bed forms (c) mechanics of sediment transport and bed load equations (d) bed slopes which are required to predict the reduction of storage capacity

EXPERIMENTAL PROGRAM

The hydraulic characteristics of gorge-type reservoirs were investigated using a 5 ft. wide X 4 ft. high X 14 ft. long basin and provided with a similar size sump at the bottom. Reservoir configurations were moulded within the basin. Water and sediment were supplied from a head tank connected to an inlet channel which could be varied to study the effect of different entrance conditions. An overflow weir controlled the outlet water levels. A centrifugal pump- motor unit circulated the flow which was measured by a triangular weir. Sediment was fed at the upstream end through a calibrated hopper. Two sizes of uniform sediment (specific gravity 2.65) with mean diameters of 0.20 mm and 0.60 mm were utilized. Point gauges were used to measure water depths and bed slopes. Bedforms and profiles were photographed after sedi- ment contours have been properly defined.

ANALYSIS AND RESULTS

Sedimentation Mechanics

At the beginning of sediment flow, a delta initially formed at the inlet to the reservoir. The sediment bank filled the full width of the channel and gradually increased in size until stable hydraulic conditions were attain- ed. Sediment was then transported on the surface of the bed as bed load and deposited on the steep leading face. The sediment bed advanced rapidly in this manner until the entire reservoir was filled. Further addition of sediment resulted in its transportation over the outlet weir (Fig. 1). The deposition of the sediment was always very regular. The reservoir was able to self-adjust itself only with respect to its depth and bed slope but with its sides constrained. Blench [1966] described this phenomenon as one possessing two degrees of freedom. It is important to note that the reservoir width was such that it would not permit the flow to carve its own

8' 6 ' 4' 2'

a

4"

2

6'

13' 9' 7 '

Vert ical Exaggeration x 4

Conc = 2040 PPM , T = Elapsed time Flow - 0 . 4 4 c f s , d = 0.60mm

Fig. 1. Sediment bed profiles.

SEDIMENTATION CHARACTERISTICS OF GORGE-TY PE RESERVOIRS 883

channel and form meanders. If the latter were true, it would have represented a river in nature with four degrees of freedom. Gorge reservoirs in mountainous regions would likely exhibit two degrees of freedom as they would be constrained by the narrow walls. The hydraulic models, therefore, simulated this category of natural reservoirs.

Bedfoms

As the utilization of the bed load equations to calculate sediment discharge, bed slopes, and flow depths require a knowledge of bedforms, the ability to predict the type of bedform involved for given hydraulic conditions were necessary. Liu-Hwang [ 19591 described bedform mechanics by means of a diagram in terms of the dimensionless parameters V,/w and wd/u in which V , = m= shear ve1ocity;g = acceleration due to gravity; D = flow depth; S = energy slope (bed slope in uniform flow); w = fall velocity of spherical particles; d = mean size of sediment; u = kinematic viscosity. Graf [ 19711 presented Simons' diagram relating bedforms to stream power and grain diameter. Stream power is defined as TV in which T = shear stress; V = mean velocity.

The bedforms observed in the experiments were essentially dunes with a small proportion tending to be ripples. Using the criteria developed by Simons and Liu-Hwang, the bedforms predicted by these methods were mostly of the dune type.

Sedimenr Discharge Equation

In analysis of sediment deposition in reservoirs, it is necessary to calculate bed load dis- charge. A number of bed load equations are available for this purpose. In order to determine which was the most suitable formula for our study, four of the better known bed load equations have been evaluated using observed experimental data. The bed load equations given in Henderson [ 19661 and Brown [ 19591 are:

where qs = sediment discharge/width C, = sediment parameter T = shear stress T~ = critical shear stress S, = specific gravity of sediment q =water discharge per unit width G = ((2/3 + 36u2/gd3(SS - 1))'O - ((36u2/gd3)S, - 7 = specific weight of water p = density of water d = grain size s = energy gradient

884 G e e and Sweetman

Energy gradients were compared with bed slopes to determine their relationship. Both of these parameters were closely correlated. Thus either variable could be used in Eqs. (2) to (5).

Observed bed loads and those computed using Eqs. (2) to (5) were compared to determine which equation would give the best correlation. Kalinske’s equation proved to agree closest to observed values; the percentage mean error involved was 44%.

Bed Slopes

The slopes of sediment beds are important in estimating the loss of flood storage due to sedimentation. In computing bed slopes of reservoirs, it is common to use a flow resistance equation in conjunction with one of sediment transport to determine this parameter. The friction equations often used are those of Manning [1891], Chezy [King, 19541 and Liu- Hwang [ 19591 . The equations of Manning and Chezy, which were originally developed for rigid boundary hydraulics, have been extended to fluvial hydraulics by modifying Manning’s n and Chezy’s C to account for both surface rougnness as well as form roughness due to various types of bedforms.

The well-known Manning equation is given as,

in which V = mean velocity n = roughness coefficient R = hydraulic radius S = energy gradient or bed slope in uniform flow

Chow [ 19591 suggested that the strickler expression for Manning’s n could be written in the form,

where k = roughness height. Einstein and Barbarossa [ 19521 postulated that the hydraulic radius R comprises of two

parts, R’ and (R - R’) in which R’ = hydraulic radius due to surface roughness; (R - R‘) = hydraulic radius due to moving sediment beds. Doland and Chow [1952] extended the con- cept and defined the function @(R/k) to include both surface and bedform roughness and gave a relationship,

O($ R - - -- 00342 (R’/R)~”

Curves of values of (R’/R) were presented as functions of (R/k65)1” and kJ5/RS where k65 and k3, denote grain size just larger than 65% and 35% respectively of the material derived from a mechanical analysis curve. Eqs. (6)’ (7), and (8) could be combined to give,

The Chezy flow equation is given by,

SEDIMENTATION CHARACTHERISTICS OF GORGE-TYPE RESERVOIRS 885

To take into account surface and bedform roughness, Richardson and Simons [ 19671 pro- posed methods of calculating the coefficient C depending on the bedform encountered. For the case of dunes, the equation for C was given as,

-- D ARS 1i-2 - 7.4 log (- (1 - - g' a dB5 RS

in which D = flow depth; d,, = grain size just coarser than 85% of the material obtained from mechanical analysis. ARS represents the increase of RS owing to bedform roughness. A graph was provided to determine ARS from known values of RS. Substituting Eq. (1 1) into Eq. (10) gives,

la V = 7.4gla log(- D (1 - ARS -) In XRS) d85 RS

Based on laboratory studies of sediment transport, Liu-Hwang [1959] put forward a mobile bed flow equation,

v = cJP9 (13)

in which the coefficient C, and the exponents x and y take on different values depending on the type of bedform and sediment size. For dunes,

d = 0.20mm: C, = 11,x = 0 . 4 3 , ~ = 0.31

d = 0.60 mm: C, = 22, x = 0.59, y = 0.34

In attempting to evaluate the best flow equations, Eqs. (9), (12) and (13) were used separately in conjunction with Kalinske's bed load equation (Eq. 5 ) to calculate the sediment slopes. The bed slopes obtained by this procedure were compared with the observed bed slopes. The percentage mean errors involved in the use of these flow equations together with the Kalinske bed transport relation in deriving sediment slopes are: Einstein/Barbarossa- Doland/Chow (Eq. 9), 52%; Richardson-Simons (Eq. 12), 70%; Liu-Hwang (Eq. 13), 62%. These errors, although apparently large, are normal in sediment transport studies.

Flow Depths

Flow depths were examined using the same sets of equations used for the bed slopes; in this analysis energy slope parameters were eliminated from the relations. As in the case of bed slopes, the Kalinske equation used in conjunction with Eq. (9) gave the best results; the mean percentage error was 24%.

CONCLUSIONS

The use of the Kalinske bed load equation in conjunction with the Manning formula and taking into account bedform roughness as proposed by EinsteinlDoland [ 19591 consistently gave the closest correlation in the computation of sediment slopes and flow depths.

In the calculation of sediment slopes and flow depths in gorge reservoirs in nature, the type of bedform is not known initially. From these experiments, it appears that bedforms could be estimated by using the Kalinske and Manning equations ignoring bedform roughness. Once the

886 Chee and Sweetman

bedform has been determined, the calculation could be repeated taking into account bedform roughness.

The regime equations of Lacey [ 19581 and the stream geometry relations of Leopold and Maddock [ 19531 are sometimes used in computations involving this type of work. While the regime equations are strictly applicable to streams with three degrees of freedom, the applica- tion to these experiments in studying flow depths gave an expression very similar to that of the Lacey flow depth formula.

In estimating the reduced capacity of reservoirs due to sedimentation during the useful life of the project, a knowledge of the mode of sediment deposition, and the bed slopes of the sediment beds is required. In computing the bed slopes, a suitable bed load equation in con- junction with a flow resistance formula have to be utilized. It is hoped that the investigation presented in this paper will contribute towards a better understanding of the fluvial processes involved in reservoir siltation and the utilization of the necessary equations.

ACKNOWLEDGMENT

The research grant provided by the Department of Energy, Mines and Resources of Canada is gratefully acknowledged.

LITERATURE CITED

Blench, T. 1966. Mobile-bed fluviology. University of Alberta. pp. 54-56. Brown, C. B. 1950. Sediment transportation in Rouse, H. (ed.), Engineering Hydraulics. New York: John

Wiley and Sons, Inc. Chapter 12. chow, Ven Te. 1959. Open channel hydraulics. New York: McGraw-Hill Book Co. pp. 208-210. Doland, James J. and Ven Te Chow. 1952. Discussion of river channel roughness. Trans. A.S.C.E.,

Einstein, Hans A. and H. L. Barbarossa. 1952. River channel roughness. Trans. A.S.C.E., 117:1121-1132. Craf, Walter H. 1971. Hydraulics of sediment transport. New York: McCraw-Hill Book Co., p. 282. Henderson, F. M. 1966. Open channel flow. New York: The Macmillan Co. Chapter 10. King, Horace W. and E. F. Brater. 1954. Handbook of hydraulics. New York: McGraw-Hill Book Co.,

Lacey, Gerald. 1958. Flow in alluvial channels with sandy mobile beds. F’roc. Instn. Civ. Engrs., 9:145-164. Leopold, Luna B. and T. Maddock Jr. 1953. The hydraulic geometry of stream channels and some physie

Liu, Hsin-Kuan and Shoi-Yean Hwang. 1959. Discharge formula for straight alluvial channels. J. Hydraulics

Manning, Robert. 1891. Flow of water in open channels and pipes. Trans. Inst. Civil Engrs. Ireland,

Richardson, Everett V. and Daryl B. Simons. 1967. Resistance to flow in sand channels. Twelfth Congress,

U.S. Bureau of Reclamation. 1954. Interim report. Distribution of Sediment in Reservoirs. 15 pp.

117: 1121-1132.

pp. 7-15.

graphic implications. Geol. Survey Paper 252. 57 pp.

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I.A.H.R., 1~141-150.