Three dimensional analysis of unconfined seepage in earth dams by the weak form quadrature element method

•Three dimensional unconfined seepage is analyzed by the weak form quadrature element method.•Grid lines are constructed in the element.•“Free points” are introduced by the interpolation of which the free surfaces are smoothly approximated.•An interpolatory scheme for locating the exit points is proposed.

SummaryIt remains challenging to determine the unknown free surface in three dimensional unconfined seepage in earth dams. A number of iterations are frequently required which make the problem computationally expensive. In the present research, a weak form quadrature element formulation is presented for three dimensional analysis of unconfined seepage which is an extension of the recently established method for two dimensional seepage problems. “Free points” are introduced by the interpolation of which the free surfaces are smoothly approximated. Grid lines are constructed in the element and the “free points” are confined to the lines when updated. An interpolatory scheme for locating the exit points is proposed. Formulations and procedures of the method are given in detail. Results of numerical examples are compared with available analytical solutions and numerical solutions in the literature and agreement is reached demonstrating the efficiency and reliability of the present formulation.