Development of a computer program for gradual failure of earthen dams due to overtopping

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 continuity, sediment transportation equations (sandy soil and clayey soil), and a breach shape geometric descriptor. The water continuity equation, elevation-storage relation, and discharge-elevation 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. As the water overtopped the dam and surpassed the permissible shear stress of the dam protective cover, erosion of the dam began. The rate of erosion was considered according to two different approaches. For sandy soil mixtures, a sediment transport equation developed by Smart (65) was used, and for clayey soil mixtures, a modified Du Boy's type equation was used (75). 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 ends of the breach channel. The assumed breach shape was trapezoidal. The side slope of the trapezoid was set equal to the angle of repose of the fill material and the breach channel slope is assumed to be equal to the internal friction angle of the fill material. 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.