Unconfined Seepage Analysis Using Moving Kriging Mesh-Free Method with Monte Carlo Integration

The unconfined seepage problem is a classic moving boundary problem, in which the position of phreatic surface is unknown at the beginning of solution and should be determined through iteration. Mesh-free methods are especially suitable for solving this problem. In this work, the moving Kriging mesh-free method with Monte Carlo integration is proposed. Additionally, a corresponding procedure for handling material discontinuity is presented, which extends the approach to inhomogeneous medium. The present method is a true mesh-free method, which does not require a mesh for either shape function construction or numerical integration. Another advantage of the present method is the convenient numerical implementation. Numerical examples show that the present method can achieve better convergence and higher accuracy with rational computation cost when compared with the original mesh-free method. The present method is also verified to be applicable in analyzing transient seepage through homogeneous and inhomogeneous media.