Abstract: Signorini-type variational inequality has the advantage to eliminate the singularity of the infiltration point and to overcome the mesh dependency when solving the seepage free surface problem. Constraint iteration method is used in the iterative process, and the mathematical constraint is more stringent. For the free surface through the unit calculation, it is not easy to converge and even results in a shock between two kinds of solutions. On the basis of the variational inequality, the authors modify the iterative formula. The mathematical constraints are revised, and an iterative method with variable bandwidth is developed. Modifying the iterative algorithm improves the numerical stability of the variational inequality formulation of Signorini, and reduces the iteration time. After the excavation of underground powerhouse, the groundwater normally leaks from the side wall of the cavern, the determination of critical percolation point plays a key role in the analysis of leakage and the effect of drainage hole. The modified Signorini-type variational inequality is applied to simulate the seepage flow in the excavation boundary and the drainage hole of a typical project, which proves that the modified method has better convergence in the complex nonlinear three-dimensional seepage calculation.

Key words: variational inequality, variable bandwidth iteration, outlet seepage, boundary condition