The solution of unconfined water seepage problem in saturated-unsaturated soil using Bathe algorithm and Signorini condition

Bathe algorithm converts problem of determining inner infiltration face into a material nonlinearity problem, and Signorini condition coverts outflow boundary into conventional water boundary. Because an unsaturated seepage problem is also a nonlinear flow problem, through the joint application of this 2 methods, solving variational inequalities is avoided. In conventional material nonlinearity finite element framework with small modification, using NR algorithm, the solving of unconfined water seepage problems including unsteady and unsaturated water seepage problems is realized. The followings are discussed: (1) the improvement of convergence of Bathe method and its generalized form in a three-dimensional model; (2) use Switching Algorithm of Signorini condition to solve water seepage problems; (3) the under-relaxation methods of improving the convergence and mass conservation when solving unsaturated and unsteady water seepage problems. At last, through classic calculation examples, the calculating accuracy and application fields of the proposed methods are evaluated.