MOBILE CONTROLS FOR WATER RESOURCES PROJECTS

WATER RESOURCES BULLETIN VOL. 14, NO. 1 AMERICAN WATER RESOURCES ASSOCIATION FEBRUARY 1978

MOBILE CONTROLS FOR WATER RESOURCES PROJECTS'

S. P. Chee'

ABSTRACT: An investigation of the erosion mechanics and washout time rates of erodible control embankments were made with hydraulic scale models in the laboratory. The water control dams have both homogeneous and clay cores. A wide range of configurations and layouts were tested and equations were developed to make possible the computation of erosion rates. Model scale relationships were analyzed from the developed equations and compared with the results obtained analytically from sediment transport equations. (KEY TERMS: erodible dams; breaching; fuse plugs; sediment transport; granular dams; breaching; washout.)

INTRODUCTION In most water resources projects, excess water must be spilled during floods due to a

lack of storage. The smaller the reservoir capacity available to accommodate flood waters, the larger the quantity of water that has to be released over the spillway. Large concrete spillways are expensive structures and substantial savings could be realized by reducing their sizes.

One method of reducing the size of permanent spillways without sacrificing spilling capacity, is to add an auxiliary waterway by using erodible embankments for controls. Fuse plug spillways, as referred to by Tinney and Hsu (1961), are sometimes designed so that in combination with the main spillway, they could pass the probable maximum flood. After breaching and washed away by the flood waters, the erodible embankments are built again at a relatively much lower cost than a concrete structure.

A better control of reservoir water elevations could be obtained by using multiple erodible controls located at different sill elevations. The erodible dams would be washed off at predetermined water levels. I f the erodible plugs are used as auxiliary spillways, it is advantageous to locate them at the upstream end of a concrete apron. In the case of erodible dams used as emergency spillways, described by Binnie, et a]., (1967), an unlined channel is frequently used. The earth plugs could be made solely of a homogeneous material or with a clay core and granular material on both shoulders. Breaching of the embankment could be attained by overtopping or side erosion.

'Paper No. 77072 of the Wafer Resources Bulletin. Discussions are open until October 1. 1978. 'Professor of Civil Engineering, University of Windsor, Windsor, Ontario, Canada.

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EXPERIMENTAL PROGRAM

The washout of fuse plugs were investigated in the laboratory using model embankments installed in flumes and scour basins with widths of 0.2 m to 2.3 m and heights of from 0.3 m to 1.5 m. The flumes have clear plexiglass on at least one side to provide visual observation and photographic recording of the erosion process. The floor inclinations and elevations of the flumes could be altered by installing temporary bottoms for apron sills and channel beds.

Fifteen sizes of granular materials with mean diameters ranging from 0.14 mm to 10 mm were utilized to form the embankment dams. To observe the effect of the washout rates due to different specific weights of the embankment fill, silica, granite, olivine, and zircon sands with specific gravities varying from 2.65 to 4.50 were employed in the tests. Rounded shapes predominate in the sand size materials while the larger size crushed gravels were more angular. The range of porosities of the granular materials varied from 0.32 to 0.44.

A wide range of embankment configuration shapes were utilized to observe the nature of form in erosion mechanics. These shapes were built up by appropriate combinations of width to height ratios of the central stem of the dam in conjunction with varying inclinations of the sides. The upstream face of the granular banks varied from 2:l to 7: 1 and the downstream slope range from 2 : 1 to 4: 1.

The method of breaching the embankments was by overtopping. Erodible plugs were washed away at a constant discharge. The laboratory arrangement to obtain this condi- tion was to maintain a constant control discharge valve opening during the entire scouring process when single embankments were involved. In multiple control dam arrangements successive larger constant openings for specified periods of time were initiated which would simulate sensibly a rising flood. Discharges used ranged from 1 m3/sec./m to 18 m3/sec./m.

The experimental investigation consisted of two test series. In the first series of observations, only single embankments with and without clay cores were used. Multiple erodible control dams were tested in the second series.

A centrifugal pump-motor unit was used to circulate clear water for the washout process. An electronic flow meter with an automatic recording pen and chart provided continuous flow measurements. Weirs were used to record the separate flows in the multiple control arrangements. Water level point gages and manometers were employed to determine the water elevations. Erosion patterns were photographed to capture all the significant phases of the scouring process through the plexiglass walls which have graduated markings. Washout rates were computed from the enlarged photographs.

MECHANICS OF WASHOUT

There were three phases involved in the mechanics of washout of a homogeneous embankment.

The failure of the embankment by overtopping was initiated by breaching and rapid surface slip of the downstream face of the dam. As the water cascaded over the crest, surface slip occurred on the downstream portion and the scoured material was rapidly transported away by the water. The erosion of the fuse plug caused a rapid lowering of the crest with progressive back erosion and a flattening of the slope. It simulated the

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Mobile Controls for Water Resources Projects

flow of water of a weir with variable coefficients of discharge and a continuous lowering of the crest control.

After the rapid scour of the embankment by surface slip, a transitional stage followed where the mechanics of erosion was a mixed surface slip and bed load transportation. Material was removed at a considerably slower rate during the transitional phase.

The final stage of the scouring process was one of bed load transportation and was the slowest of the three stages. The erosion face of the plug acquired a more gentle slope and this mode of material transportation continued till the scour of the plug was com- plete.

Figure 1 illustrates the typical erosion of an embankment under constant discharge. Material with a larger angle of repose was associated with a steeper eroding face.

In all experiments on the washout of fuse plugs it was essential that all the material eroded from the model embankments did not deposit immediately downstream and hinder the transport of solids. This was accomplished by constructing the dams at the outlet end of the flumes; the eroded material fell into a collecting box without any being left behind. An alternative procedure which could have achieved the same objective would be to provide a steep chute downstream of the plug to obtain supercritical flow at all times; this method would be adaptable readily to prototype arrangement.

ANALYSIS AND DISCUSSION

The hydraulics of an embankment washout represents the case of unsteady, non- uniform flow when viewed from the point that the velocity at the section of the dam varies with time as the cross-section enlarges due to progressive erosion of the embankment. In formulating the dimensionless equation on the rate of washout, the parameters were chosen so they could be easily measured in the experiment and readily usable in practice. To this end, time averaged values were used in developing the equation.

In the first series of experiments, single granular homogeneous embankments were first tested and this was followed by dams with clay cores. In the second series, observations were made on multiple control dams.

First Series: Single Embankments Washout of Single Control Embankments - In formulating the dimensionless equation for the washout rate of an erodible homogeneous control under constant discharge the following parameters were used (Figure 2 ) :

mean solids discharge per unit width

constant water discharge per unit width

critical flow depth calculated from q

initial height of control measured from sill

distance between channel bottom and control crest before erosion

mean design width of dam

mean grain size specific gravity of grains

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t = 6 9 seconds

t =84 seconds

t =93 seconds

t =elapsed time

Figure 1. Erosion Pattern.

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ERODIBLE CONTROL

I

FLUME

Figure 2. Definition Sketch.

t9 = angle of repose of material in degrees

m = thickness of clay core

The following functional relationship can be written:

in which C = coefficient, K1 = f(e), K 2 = f(H/B), K 3 = f(E/H), K 4 = f(m/H), a and b are constants. The coefficient C and the exponents a and b, have been found experimentally to have the following numerical values:

C = 1/73, a = - 2 , b = 1/8

The values of K 1 , K 2 , K 3 , and K 4 are given in Tables 1 t o 4 as functions of 8, H/B, E/H, and m/H, respectively. Equation ( 1 ) takes the final form:

(2) qs/q = 1/73 K1 K 2 K 3 K 4 (SS - (Yc/d) 118

From Equation (2), the mean solids discharge can be computed. The time required to washout completely the erodible control can be calculated from the volume of the

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TABLE 1. Values of K1.

8 Degrees K1

20 25 30 35 40

0.83 0.86 0.89 0.91 0.94


0.2 0.3 0.4 0.5

0.67 0.74 0.80 0.84

~~


1 .o 1.2 1.4 1.6

1 .oo 1.07 1.14 1.20


K4 flay Core Thickness Ratio m/H

0.000 0.025 0.050 0.075 0.100 0.150

1 .oo 0.53 0.69 0.73 0.74 0.75

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granular embankment taking into account the porosity of the material from the equation:

in which t = washout time of the control; Vvol = volume of granular embankment per unit width; n = porosity of the material; qs = mean solids discharge rate per unit width as given by Equation ( 2 ) . Figure 3 illustrates the comparison of the observed time oferosion with the time calculated using Equations ( 2 ) and (3).

t CALCULATED (SECS.) I -

Figure 3. Results.

It is clear from Table 4 that the inclusion of a clay core increased the erosion time of the embankment. Beginning with a homogeneous granular dam, the washout time increased as the clay core thickness ratio, calculated relative to the height of the dam,

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increased up to a core thickness ratio of 0.025 and decreased beyond this value. To ex- plain this phenomenon, observations of the mechanics of washout of the clay core indi- cated a tendency to bend in the flow direction and this configuration provided a protec- tive covering for the sand grains when the core thickness ratio was equal to or less than 0.025. When the thickness ratio exceeded this value, the core sheared off neatly and was transported from the embankment by the stream without impeding the erosion of the grains.

Second Series: Multiple Erodible Controls In nature, the washout of erodible control dams would result from a flood. To enable

a closer control of upstream pond water elevations, it would be necessary to employ more than one control embankment located at different sill levels. Depending on the magni- tude of the flood, one or more of the dams would be eroded away. The highest control embankment would be washed away by the project design flood.

The routed outflow of a reservoir could be approximated by successive mean constant discharges corresponding to relatively short time intervals. These mean flows could then be applied to compute mean solids discharge and with the time intervals of the flood, corresponding volumes of each control could be determined until the flood has been passed. Breaching and washout of erodible banks under these conditions could be sensibly considered as washout under constant discharge.

To simulate the washout of multiple controls in the laboratory, up to three embankments were built at different elevations with a different outlet channel and measuring weir for each dam. Successive constant discharges were passed through the controls. From these known time intervals and using Equations (2) and (3), washout rates were determined and upstream water elevations known.

Model Scales It is a frequent practice to test models to prove and improve the design of prototypes.

In this respect, the washout time ratio of the erodible control is the principal parameter to be determined. For the predominant case in which the water discharge rate is operated according to the gravity law in the model, and using materials sensibly of the same porosity as the prototype, Equations ( 2 ) and (3) give:

1); (dr)0.13 (4)

in which suffix r refers to the ratio of prototype to model values and 1/M is the model scale.

As the washout of erodible dams involves bed load transportation, an erosion time scale ratio could be derived analytically by using a bed load transport equation such as Kalinske’s equation as given by Brown (1950), together with the flow resistance equation of Manning (1 891); Strickler’s expression of Manning’s roughness coefficient given by Henderson (1966); and the tractive force equation used in channel stability analysis developed by the U.S. Bureau of Reclamation under Lane (1952).

Kalinske: qs < h / d & ? h = 10(T/y(Ss - l)d)2

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Manning:

Strickler: n = 0.1 1 2 d1/6 (7)

Tractive Force: T = y DS (8)

in which 7 = bed shear stress; y = unit weight of water; s = energy gradient; D = flow depth; n = Manning's roughness coefficient. Equations (6) and (8) are based on the wide channel approximation in which the flow depth is used in place of the hydraulic radius. In the Manning and the Strickler equations, the flow depth D and the mean grain size d are expressed in meters, and the unit discharge in cubic meters per meter width of channel. Equations (S), (6), and (7) in combination with Equation (3) give the Kalinske washout time ratio as:

1); (dr)0.17 (9)

Comparison of Equation (9) and Equation (4) shows that there is good agreement between these equations. Tinney and Hsu (1961) found in their study of the washout of large fuse plugs by side erosion, the time ratio was proportional t o M113.

CONCLUSIONS 1 . In the design of erodible controls washout times for preliminary designs to be made

for feasibility studies could be obtained using Equations ( 2 ) and (3) together with Tables 1 t o 4. The use of multiple erodible controls sited at suitable sill elevations would enable a closer control of upstream pond water levels.

2. Adequate hydraulic scale model studies should always be conducted t o verify erodible control embankment designs t o ascertain their washout behavior before they are constructed particularly with less familiar configurations and layouts.

3. Erodible controls constructed from materials which contain a significant amount of clay mixed with it, require careful investigation as the erosion characteristics of such materials are uncertain and difficult t o determine.

ACKNOWLEDGMENT

The financial supported provided by The National Research Council of Canada is gratefully acknowledged.

LITERATURE CITED

Binnie, G . M., et a[.. 1967. Mangla. Proc. Inst. Civ. Engrs., London, 38:439442. Brown, C. B., 1950. Sediment Transportation. H. Rouse (Ed.)., Engineering Hydraulics, John Wiley

Henderson, F. M., 1966. Open Channel Flow. The Macmillan Co., New York, p. 98. Lane, E. W., 1952. Progress Report on Results of Studies on Design of Stable Channels. U. S. Bureau

and Sons, Inc., New York, Chapter 12.

of Reclamation Hyd. Lab. Report Hyd-352.

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Manning, R., 1891. Flow of Water in Open Channels and Pipes. Trans. Inst. Civ. Engrs., Ireland,

Tinney, E. R. and H. Y. Hsu, 1961. Mechanics of Washout of an Erodible Fuse Plug. J . Hydraulics 20: 161 -207.

Div., A.S.C.E., 87:l-29.

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