Efficient Scaled-Boundary Radial Point Interpolation Method for Unsteady Confined-Seepage Flow through Nonhomogeneous and Anisotropic Soils

Abstract

The two-dimensional unsteady confined-seepage flow through nonhomogeneous and anisotropic soils is studied in this paper. The study was based on a novel semianalytical method called scaled-boundary radial point interpolation method (SBRPIM). The proposed method combines the advantages of the scaled-boundary finite-element method (SBFEM) and the boundary radial point interpolation method (BRPIM). In this work, the SBFEM was developed and was called SBRPIM for unsteady confined-seepage flow through nonhomogeneous and anisotropic soils. Similar to the conventional SBFEM, the SBRPIM uses only boundary nodes and does not require the fundamental solution, but unlike the SBFEM, the SBRPIM uses BRPIM shape functions in the circumferential direction and does not require the element connectivity information. Because of the use of the BRPIM shape functions satisfying the Kronecker delta function property, the boundary conditions can be enforced accurately and easily in the SBRPIM. The proposed method was verified through four numerical examples comparing the new approach with the local radial basis function–based differential quadrature method (local RBF-DQ) as a meshless method, conventional SBFEM, and FEM. The obtained results showed the capability and efficiency of the SBRPIM in modeling unsteady seepage flow through nonhomogeneous and anisotropic media and the accuracy of the proposed method in dealing with singularities.