Seepage with Nonlinear Permeability by Least Square FEM

In seepage problems, the coefficients of permeability in Laplace equation are usually assumed to be constant vs. both space and time; but in reality these coefficients are variable. In this study, the effect of material deformation due to external loads (consolidation) and variation of head in the consolidation process are considered. For the first case, formulation of kx and ky can be defined by a second order binominal equation in order to take into account the material changes due to volume changes. For the second case, kx and ky can be defined as a function of unknown total head. The solution of the resulting non-linear differential equation is found using the Least Square Finite Element formulation. In order to increase the accuracy of the solution, eight nodal (isoperimetric) elements were obtained. 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 the one described in this paper should be taken into account.