An extended polygon scaled boundary finite element method for the nonlinear dynamic analysis of saturated soil

Abstract

In this paper, the polygon scaled boundary finite element method is extended to analyze saturated soil based on the generalized Biot's dynamic consolidation theory. The displacement shape functions of the polygon element are obtained by elastic static theory while the pore pressure shape functions are constructed from steady-state seepage theory. A scaled boundary polygon equations for saturated soil is established by applying Galerkin method. Two sets of Gauss points are adopted, including Gauss points of line utilized to compute the shape functions and Gauss points of area employed to realize material nonlinearity. In order to verify and assess the reliability and accuracy of the presented method, a saturated elastic half space subjected to a uniform cyclic dynamic loading is simulated and the results are compared with the analytical solution. Moreover, a liquefaction analysis of a breakwater built on saturated sand soil with generalized plastic model is subsequently carried out. The results correspond well with those calculated by finite element method (FEM), which indicates the significant capability of the current method in solving nonlinear problems. The proposed method processes extraordinary mesh flexibility and fast reconstruction, which will make it a promising tool in liquefaction analysis.