VOL. 7, NO. 2 WATER RESOURCES BULLETIN APRIL 1971

STABLE PROFILES OF PLUNGE BASINS'

S. P. Cheeand T, Kung2

ABSTRACT. The characteristics of scour holes were discussed including the problems created by them in relation to the hydraulic structures associated with their formation. The philosophy on the design and use of deflector buckets together with the need for plunge basins to dissipate the energy of the high velocity jets were reviewed.

Laboratory observations were made to study the erosion of beds of gravel caused by water jets projected from spillway buckets. Flip buckets with 15, 30, 45 and 60 degrees exit angles were utilized. One-quarter inch and %-inch nominal size bed materials were used in the investigation. The gravel was placed in a large comprehensive scour basin to observe their behavior when subjected to the water jets.

Besides the formula derived for the maximum depth of scour, a set of dimensionless equations were developed to describe the three-dimensional configuration of scour holes. The dimensions of stable plunge basins could be obtained from these profiles. (KEY WORDS: plunge basin; erosion; scour hole; flip bucket; water jet; energy dissipator)

INTRODUCTION

Curved deflector devices or better known as flip buckets are frequently used at the base of chute spillways to throw the high velocity jet of water a safe distance from the hydraulic structure to allow the dissipation of the energy of the water in the river. Its obvious economic advantages have been responsible for its wide use in hydroelectric and other water resources projects.

A scour hole would form at the jet impingement area in river beds composed of erodible material. The characteristics of the scour hole and the design of the bucket itself are common- ly investigated in a scale model before it is constructed. A homogeneous bed of granular material, such as gravel or sand, is normally used to simulate the river bed as it is considered to give the most critical scour condition; this always gives a stable, symmetrical, dish-shaped hole.

The performance of some full-size buckets revealed that the maximum depth of scour could exceed that extrapolated from model tests using non-cohesive materials and, further, the hole showed a tendency to erode upstream towards the spillway beyond the limits found in the model. Scour holes observed in nature could be very irregular and with steep sides when they are formed through successive strata of soft and hard rocks in river beds with a hetero- geneous composition. Secondary currents are generated in the irregularly shaped hole. The swirling water causes the breakup of the rocks by collision and abrasion in addition to under- mining the layers above it. The disintegrated fragments are subsequently transported from the hole by the water.

'Paper No. 71028 of the Wafer Resources Bulletin (Journal of the American Water Resources Associa-

Respectwely, Associate Professor, Department of Civil Engineering; Graduate Student; University of tion . Discussions are open until six months from date of publication.

Windsor, Windsor 11, Ontario, Canada. 2' ' :

303

304 Chee and Kung

In the light of these hazards which became apparent in the operation of the spillways, the old design philosophy of using uniform granular beds to represent the worst river bed condi- tion for the observation of scour hole characteristics could no longer be relied upon. A new design procedure is required. The destructive eddy currents could be eliminated by excavating in advance a plunge basin corresponding to the configuration and dimensions of the scour hole obtained in model tests using a granular bed. Besides the above function, plunge pools are also provided to avoid the accumulation of the products of erosion forming a weir control, which would cause the tailwater to rise, downstream of the hole.

This paper presents the study of the configuration of three-dimensional scour holes formed in beds of gravel using spillway buckets with flip angles of 15, 30, 45 and 60 degrees. Stable plunge basin dimensions could be obtained from the equations derived from this investigation.

EXPERIMENTAL PROGRAM

Observations were made using flip buckets with circular radii of 12 in. and 8 in. and having exit angles of 15, 30, 45 and 60 degrees. The ogee crest spillways have heights of 19.5 in. and 13 in. and crest lengths of 19.5 in. and 13 in. The spillway buckets were installed in a 6 ft. wide x 17 ft. long x 4 ft. high scour basin. At the outlet end of the basin, a weir control was installed to regulate the tailwater as well as a gravel trap and screen to prevent the gravel from being washed into the laboratory sump (Figure 1).

h CI IDDlV DIDC

1 1 I ,HEAD TANK

SCOUR BASIN

,

SCALE: 2 FT. TO 1 INCH GRAVEL .TRAP

I

Figure 1. Longitudinal section of test basin.

Granular beds of 19 in. thickness were provided. Quarter-inch and %-inch nominal size bed materials (specific gravity 2.65) were used. Water elevations were measured with manometers and point gages; discharges were determined by a magnetic flow meter.

STABLE PROFILES OF PLUNGE BASINS 305

RESULTS

Experiments were first made to determine the time required for the scour hole to reach a stable configuration when the time-average dimensions of the basin remained sensibly con- stant. Although the bed remained active, it had reached a state of dynamic equilibrium. Observations showed that limiting conditions were attained after two hours and this time was adopted for all the tests.

Maximum Scour Depth

The maximum scour depth is defined as the water depth measured from the tailwater level to the lowest point of the eroded bed. The maximum depth of scour is a function of the unit spillway discharge, the head difference between upstream spillway and tailwater levels, the mean size of the bed material, and the flip angle of the buckets. These five variables have been correlated (Figure 2) to give the non-dimensional equation,

Dm q 2 a3 H 0.1 (=) = 3.30 (- ) (-J (a)'.'

gH3 where Dm = maximum scour depth

q = unit spillway discharge H = head difference between headwater and tailwater elevations d = mean material size a = exit angle of flip bucket (radians)

The maximum scour depth is an important paramete1 in describing the shape of the hole.

D,/ H OBSERVED

Figure 2. Plot of observed versus calculated values of D,/H.

306 Chee and Kung

Scour Hole Configuration

The contours of the hole are symmetrical about the longitudinal axis with the point of maximum scour located downstream of the geometric center. The dimensions of the hole are defined by horizontal and vertical coordinates using the point on the original bed level directly above the deepest scour position as the origin with radius vectors radiating from it. The refer- ence axis is the radius vector (R,) pointing in the downstream direction where the periphery of the hole is closest to the origin.

The eroded depth, which is used to describe the distance between the hole bottom and the original bed level, at any position along a radius vector is related to D,, the ratio r/R and the tailwater depth. The eroded depth is given by the relationship,

Y = (D, - h)(l - r Z / R Z ) (2)

where Y = eroded depth at any point along a radius vector as measured from the scour hole bottom to the original bed.

D, = maximum scour depth as given by Eq. (1) h = tailwater depth r = distance at any point along a radius vector

R = length of the radius vector measured to the rim of the hole

Eq. ( 2 ) applies to any radius vector and determines the vertical dimensions of the hole. The length of the radius vector (Re) is required in order to determine the horizontal

coordinate. Radius vectors are expressed in terms of the angle measured from, and, the length of, the reference radius vector (Figure 3). The magnitudes of these radius vectors are given by the equations,

Re = R, (1 t 0.095 Oo.81) ( 3 )

R, = 1.55 (D,,, - h)0.24 (4)

where R, = reference radius vector Q = length of radius vector at the angle 6 measured to the rim of the hole

0 = angle in radians measured clockwise or anticlockwise from the reference radius vector

and the other variables are as defined previously.

Jct Trajrctop’ Distance

The throw distance of the jet is the horizontal length measured from the downstream edge of the spillway to the point of niasinium scour. The jet trajectory distance is made up of two components. namely. the horizontal flight length from the lip of the bucket to the point when it enters the tailwater together with the distance the submerged jet travels from the latter loca- tion t o the position of maximum scour. The first portion of the trajectory length is calculated using the theory of the simple projectile. The second part of the movement of the jet is determined by using the assumption that the submerged jet continues on a path tangent to its parabolic trajectory in air until it intersects the point of maximum bed erosion. Then, the horizontal tluow distance is given by,

S T A B L E PROFILES OF PLUNGE B A S I N S

and

L = La t L,

2 y g >I v,2 cos2 a

La = [tan (a) + (tan’a t g vO2 cos2a

L, = D, / [g L,/v, cos’ a - tan (a)]

where L = total horizontal trajectory distance La = horizontal flight length in air L, = submerged travel distance

V, = velocity of jet at the bucket lip

and the other symbols are as defined previously. y = vertical distance measured from the edge of the bucket to the tailwater

SCALE : 1 F T . TO 1 I N .

9 =1.15 cfs l f t . H =2.90f t B =2 .0 f t

h = 0 .70 f t . d =0.75in

d = 4 5 O

Figure 3. Typical computed scour hole contours.

DISCUSSION

307

(5)

(6)

(7)

Eq. (1) shows that the maximum depth of scour depends largely on the unit discharge and to a lesser degree to the difference in elevation between the reservoir and tailwater levels. It also indicated that it is not very sensitive to the bed material size for the range explored. These findings are confirmed by the empirical equations on limiting scour depth suggested by Veronese [U.S.B.R., 19611, Khosla [1954], Schoklitsch [Doddiah, 19531, and Chee and

308 Chee and Kung

Padiyar [ 19691 . Allen [ 19521 suggested a limiting material size below which the scour hole depth would cease to increase.

The scour hole configuration is determined by Eqs. (2) to (4). These equations were obtained for the dimensionless parameter q2 /gB3 describing the flow conditions falling be- tween 0.0003 and 0.0542. These equations do not apply to the case where an expanding spillway chute is used. Other researchers, not mentioned previously, who had conducted work on scour relevant to this subject, include Gunko [1965] and Smith and Strartg [1967].

Eq. (6) was derived based on the assumption that the jet was projected into a vacuum. An allowance for air resistance and wind drift should be made in ascertaining the throw distance in the prototype.

CONCLUSIONS

In utilizing Eqs. (1) to (4) to ascertain the configuration of scour holes in nature, geological data which are relevant and necessary to the solution of the problem include the following: size of the bed material lining the river or outlet channel, mode of stratification, durability of the rocks and anticipated final disintegrated size of the rocks.

The theoretical scour hole obtained by using Eqs. (1) to (4) would have curved profiles. For ease of construction of plunge basins, trapezoidal shapes could be circumscribed around these computed profiles.

In certain cases where the original river bed material is too small and would result in an uneconomically large plunge basin, the pool dimensions could be lessened by lining it with suitable size rocks.

ACKNOWLEDGEMENT

The research grant provided by the National Research Council of Canada is gratefully acknowledged.

LITERATURE CITED

Allen, J. 1952. Scale models in hydraulic engineering. Longmans, Green and Co. Ltd., London. Chee, S. P. and P. V. Padiyar. 1969. Erosion at the base of flip buckets. The Engineering Journal, Engineer-

ing Institute of Canada 52(11). Dodlah. D., M. L. Albertson and R. A. Thomas. 1953. Scour from jets. Proceedings, Minnesota Inter-

national Hydraulics Convention. G U I I ~ O , F.. A. F. Burkov, N. B. Isachenko, G. L. Rubenstein, A. G. Solovyova andG. A. Yuditsky. 1965.

Hydraulic regime and local scour of rock bed below spillways of high head hydroelectric stations. XI Congress. International Association for Hydraulic Research, v. 1.

Khosla, A. N.. N. I;. Bose and T. E. McKenzie. 1954. Design of weirs on permeable foundations. Central Board of Irrigation, India, Publication No. 12.

Smith, C. D. and D. K. Strang. 1967. Scour in stone beds. Twelfth Congress, International Association for Hydraulic Research, v. 3.

U.S.B.R. 1961. Design of small dams.