Calculation of a local scour depression near a protected concave bank of a gravel-pebble channel

Abstract

1. To predict the depth of a scour depression at the toe of a protected concave bank of a meander in gravel-pebble channels and to determine the rate of this scouring, a simplified calculation method was developed on the basis of analyzing the results of calculation by the complete method of the Institute of Fluid Mechanics, Academy of Science of the Ukrainian SSR. 2. The main conditions making it possible to use the simplified calculation method are: disregard of the balance of the bed load and the nonuniformity of the flow in the scour depression at the protected concave bank of meanders. To perform the calculation it is necessary to have the value of the average slope of the free surface of the water on the axis of the flow, which is assumed constant during deformation of the bottom of the meander. 3. In the calculation one determines the vertically averaged velocity of the nonuniform flow u2 and the friction velocity u*2 in the scour depression, which must be compared with the friction velocity u*p corresponding to the detachment of the erosion pavement of inhomogeneous soil composing the bottom of the meander. By assigning various values of deepening of the bottom Δzb in the scour depression, one finds the value of Δzb for which scouring of the bottom ceases (u*2=U*p). 4. To check whether the calculated deepening of the bottom can occur during the duration of the calcualted flood on the basis of the value of the bed-load discharge calculated by means of Einstein's graph, the rate of deepening of the bottom in the scour depression is determined with the use of the method given in [1] for this purpose. 5. The reliability of the recommended simplified calculation method is confirmed by the results of comparing the calculated and experimental values.