Multi-region boundary element analysis of unconfined seepage problems in excavations

A multi-region boundary element method (BEM) is presented for the seepage analysis in deep excavations. In the formulation, soil foundation is regarded as a multilayered porous medium possessing the zoned inhomogeneous hydraulic conductivity. Based on Darcy's law, a two-dimensional steady state differential equation with transient free surface conditions is adopted. With a fundamental solution of the potential problem, a generalized multi-region boundary element method is developed. The transient boundary conditions are treated by means of the Galerkin scheme of the θ family approximation and are imposed into the boundary integral formulation. The essential features of the BEM are that it concerns the zoned inhomogeneous hydraulic conductivity of soil media, and that the assembly of each individual region can process in the same way as in finite element method (FEM) with much less computer memory storage. Several unconfined seepage problems are solved to demonstrate the performance of the multi-region BEM.