Abstract：Bathe algorithm converts the locating of the phreatic surface to a nonlinear constitutive problem. And the implication of Signorini condition can simulate a seepage face as a head-fixed boundary through iterative calculation. Because an unsaturated seepage problem is also a nonlinear flow problem，the implication of Bathe algorithm and Signorini condition makes it possible to model both saturated and unsaturated seepage problems with a unified method by a minimal modification to an ordinary finite element method，and avoiding solving a variational inequality system. The followings are discussed mainly：(1) the improvements of Bathe algorithm in converge and its generalized form in a three-dimensional model；(2) the implement of the switching algorithm of Signorini condition to solving seepage problems；and (3) the under-relaxation scheme to improve the mass conservation and converge properties when an unsteady unsaturated problem is solved. Finally，some numerical examples are solved to evaluate the applicability of the proposed method；and the results are compared with those available in the literature.
BATHE K J，KHOSHGOFTAAR M R. Finite element free surface seepage analysis without mesh iteration[J]. International Journal for Numerical and Analytical Methods in Geomechanics，1979，3(1)：13-22.
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2013, Vol. 32 
