A solution procedure using the Green's function based finite element method (FEM) is presented for two-dimensional nonlinear steadystate seepage analysis with the presence of free surface in isotropic dams. In the present algorithm, an iteration strategy is designed to convert the over-specified free surface problem to a regular partial differential equation problem. Then, at each iteration step, the Green's function for isotropic linear seepage partial differential equation is employed to construct the element interior water head field, while the conventional shape functions are used for the independent element frame water head field. Then these two independent fields are connected by a double-variable hybrid functional to produce the final solving equation system. By means of the physical definition of Green's function, all two-dimensional element domain integrals in the present algorithm can reduce to one-dimensional element boundary integrals, so that versatile multinode element is constructed to simplify mesh reconstruction during iteration. Finally, numerical results from the present Green's function based FEM with isotropic Green's function kernels are compared with other numerical results to verify and demonstrate the performance of the present method.

A solution procedure using the hybrid finite element method is presented for two-dimensional steady-state linear seepage analysis of orthotropic dams. In the present algorithm, fundamental solutions for orthotropic seepage problems are employed to construct the element interior hydraulic head field and the conventional shape functions are used for the element frame hydraulic head field, then these two independent fields are connected by a hybrid functional. According to the physical definition of fundamental solutions, the elemental interior field can naturally satisfy the orthotropic seepage governing equation and as a result, all twodimensional element domain integrals in the present algorithm can reduce to one-dimensional element boundary integrals. Finally, the present hybrid finite element method with orthotropic fundamental solution kernels is verified by way of analytical solutions and subsequently, numerical experiment is carried out for a practical seepage problem of an orthotropic dam.