Mathematical Modeling of Earth Dam Failures due to Overtopping

Abstract

A mathematical model for simulating the gradual failure of earthen dams, due to overtopping, was developed. The model was based on the water continuity, sediment transportation equations (sandy soil and clayey soil), and a breach shape geometric descriptor. The water continuity equation, elevation-storage relation and dischargeelevation equations, as a whole, were utilized via the Newton-Raphson iteration scheme to compute the pool elevation, reservoir storage and discharge during each computational increment. Commencement of erosion was based on the critical shear stress criterion. For sandy soil mixtures, a sediment transport equation developed by Smart (18) was used. And for clayey soil mixtures, a modified DuBoy’s type equation was used (2). Determination of the dimensions of the breach channel during each time increment is an iterative one. An algorithm, also based on the Newton-Raphson iteration scheme, was used to compute for every iteration that is completed, the length of the breach channel and the elevations of the upstream end and the downstream end of the breach channel. The assumed breach shape was trapezoidal. The validity of the model was successfully tested by simulating the failure of the Laurel Run Dam that occurred in July 1977, in Johnstown, Pennsylvania. Objective of Study The first objective of this study was to develop a trigonometric-geometricdescriptor in order to predict the dimensions of the breach channel in time and space via a Newton-Raphson iterative scheme. The second objective was to account for the volume of the eroded fill material and the ratio of the sediment discharge rate to the water discharge rate during every computational time increment.