Seepage with nonlinear permeability by least square FEM

摘要

In seepage problems, for simplicity the coefficients of permeability in Laplace's equation are usually assumed to be constant in both space and time, but in reality these coefficients are variable. In this study, the effect of head variation in the consolidation process are considered. k_x and k_y can be defined as a function of unknown total head. The solution of the resulting nonlinear differential equation is found using the Least Square Finite Element Formulation. This method was used satisfactorily to solve several seepage problems and to examine the accuracy and convergence of the results. The effect of a variable coefficient of permeability may not be significant on small dams, but as the height of the dam increases the effect becomes more considerable. It is believed that a variable permeability analysis such as that described in this paper should be considered.