Seepage analysis using the weak form quadrature element method

Seepage analysis has found wide application in many areas. In practice, the conventional numerical tools such as the finite element method are mainly used in the seepage analysis, which often demand large computational resources and therefore impose restrictions on the problem scale. The weak form quadrature element method is a simple and efficient numerical tool which has been applied to structural analysis. Based on the weak form description of a problem, it has the characteristics of global approximation and enjoys rapid convergence. The method is used for simulation of two- and three-dimensional confined and unconfined seepage. For the unconfined seepage, the adaptive mesh method is employed, and the free surface is expressed by polynomial interpolation at integration points. The results are compared with those of other methods and good agreement is reached. It is shown that a relatively small number of degrees of freedom are needed to attain convergence by the quadrature element formulation as compared with those of the finite element method. The weak form quadrature element method is expected to be an effective numerical tool for seepage analysis.