A PROPOSITION OF NUMERICAL ANALYTICAL METHOD FOR DETERMINATION OF FREE SURFACES IN AN EARTH DAM WITH PARTIALLY PENETRATING CUTOFF WALL

Abstract

It has been recognized that the Dupuit theory of unconfined flow is applicable to the determination of a free surface of flow in an earth dam which has a section with vertical slopes, and built on an impervious foundation. If the earth dam has a partially penetrating cutoff wall, there is no easy method to determine the free surfaces in the dam. For the above cases, the trial-and-error method has been carried out conventionally to determin the free surface in the earth dam with a penetrating cutoff wall. This paper describes a new numerical analytical method which enables us to easily obtain the free surfaces in the earth dam with a partially penetrating cutoff wall. In this method a curved boundary is transformed to a linear boundary by the Zhukovsky's function, and the solution of the Laplase's equation is obtained in the mapping area which satisfies the linear condition with regard to velocity potential. Then the actual free surface and length of cutoff wall in the definition diagram can be obtained by means of inverse mapping using the results of the above mentioned calculation. The authors made the experiments using sand-models with the same boundry condition as the case of analysis in order to validate the accuracy of the results of the analysis method.