Constrained optimization based F.E. mesh deforming algorithm for unconfined seepage problems

In this paper, a nonlinear programming technique is presented to calculate the location of the phreatic line in earth dams. Homogeneous and zoned earth dams with and without horizontal drain are considered in this study. A polynomial with unknown coefficients is assumed as equation of the phreatic line in the homogeneous dams. For zoned earth dams, phreatic line is considered as a multi-segment non smooth curve. Coefficients of the polynomials are calculated optimizing an objective function which is defined based on the physical conditions on the phreatic line. Seepage boundary conditions are introduced as constraints for the objective function. Linear finite elements method with adjustable mesh is used to calculate the distribution of the water pressure in the dam. An algorithm based on the location of the phreatic line is presented to construct the finite elements mesh. The result of the present method is verified by the results of the nonlinear finite elements and other mesh deforming methods.