A point interpolation method for simulating dissipation process of consolidation

Abstract

A Biot's consolidation problem in foundation engineering is numerically investigated using improved point interpolation method (PIM). A weak form of Biot's theory is first developed to consider the unbalanced forces at previous time-step and thus guarantees the global equilibrium at current step. Two independent variables in the weak form, displacement and excess pore water pressure, are approximated using the same shape functions through PIM technique. The PIM technique constructs its interpolation functions through a cluster of scattered points in problem domain and its shape function is of delta properties, thus implementation of essential boundary conditions is as easy in conventional finite element method. Crank-Nicholson's integration scheme is used to discretize time domain. Finally, examples are studied and compared with finite element methods to demonstrate its capability. © 2001 Elsevier Science B.V. All rights reserved.