無網格法在大地工程上之應用

Abstract

Numerical methods are often used to solve complex engineering problems. Among them, finite element method (FEM) is the most widely used method. However, FEM can only model problems with finite deformation as divergence of solution may occur if there is significant mesh distortion. Unlike FEM, meshfree method does not require a pre-defined mesh. It discretizes the problem domain by a set of particles and is not influenced by the deficiency of mesh distortion. In addition, meshfree method can be applied to solve crack and impact problems. Despite these advantages, meshfree method has not been widely used in the geotechnical engineering field. Therefore, the objective of this research is to demonstrate that meshfree method can be applied on geotechnical problems. In this study, meshfree method is used to obtain the factor-of-safety and deformation pattern at failure for several slope cases from Griffiths and Lane (1999). Moreover, meshfree method is used to compute the site response of a vertical array subjected to earthquake loading. The results are compared to those from FEM and found to have good agreement. In addition, meshfree method is used in this research to model the progressive failure of a slope and accumulation of soil at the bottom after the slope has slid down. This simulation showcases the capability of meshfree method as it involves large deformation which would not be possible to be simulated by FEM. Keywords: meshfree, RKPM, slope stability, post failure, ground response analysis