Toward a Universal Energy Approach to Estimate Rate of Scour

Abstract

The paper presents a semiempirical method to estimate the rate of scour of earth materials, supplementing existing empirical and semiempirical methods that only quantify maximum scour depth. The premise is that the rate of scour equals the rate of removal of earth material that has already been dislodged by flowing water. A universal relationship between effective energy and the amount of dislodged material removed over a certain period is explored. Energy is defined as the product of stream power and flow duration and effective energy is the energy remaining after the energy required to dislodge the earth material has been consumed. An energy-based equation based on fundamental principles of physics is derived and its potential universality illustrated using laboratory and case study data. Analysis of volumes of gneiss scoured from the Kariba Dam plunge pool over a period of 20 years and analysis of experimental rate of scour data of soils occurring within minutes confirm the essential character of the equation. The ease by which the equation can be applied is demonstrated by an example calculation estimating the rate of scour at a bridge pier. Designing hydraulic structures to withstand the maximum scour depth can be unnecessarily costly if the time required to reach that depth exceeds the design life of the structure. Most of the empirical methods available to practicing engineers only estimate maximum scour depth and not the rate of scour, thereby hampering efforts to optimize designs. Implementing the energy-based equation presented in this paper offers a solution to this problem by following a two-step procedure. The first step is to estimate the maximum scour depth and the associated volume of material to be removed. This is done using existing empirical methods. Once the volume of material to be removed is known, the second step entails quantifying the rate of removal of the dislodged material. The principal objective of this paper is to enable the second step by offering an equation for calculating the rate of scour. The ease of application of this two-step procedure is illustrated by presenting an example calculation of scour at a bridge pier.