Three-dimensional numerical manifold method for seepage problems with free surfaces

A three-dimensional numerical manifold method for seepage problems with free surfaces is proposed. The hydraulic potential functions for arbitrarily shaped manifold element are constructed and the element conductivity matrix is derived in detail. The global governing equations for unconfined seepage analysis are established by minimizing the flow dissipation energy. The proposed method employs the tetrahedral mathematical meshes to cover the whole material volume. In the process of iterative solving for locating the free surface, the numerical manifold method can strictly realize the seepage analysis of the saturated domain on the condition of mathematical meshes keeping unchanged. Furthermore, the seepage force acting on the transitional elements cut by the free surface can be accurately calculated by the manifold method. Therefore, the proposed method is featured in high accuracy, fast convergence rate and simple programming, especially applicable to simulate the unconfined seepage problem with free surface.