A coupling peridynamic approach for the consolidation and dynamic analysis of saturated porous media

Abstract

A coupling peridynamic approach is developed for the consolidation and dynamic analyses of saturated porous media. In this method, the coupling state-based peridynamic equations of solid skeleton and pore fluid are derived based on the u–p form governing equations. Then, the corresponding implicit incremental formulations are obtained according to the linearization method on the basis of the first-order Taylor’s expansion technique and the Newton–Raphson method. There are two advantages of the present implicit algorithm comparing with the explicit one. First, the former can handily deal well with various boundary conditions without setting up additional boundary layers. Next, the former is more reasonable and efficient to solve the consolidation problems whereas it often needs very small time step for the explicit peridynamic method combining with an additional damping under a quasi-static loading. Finally, both the consolidation and dynamic examples are given out and the results certify the validity and accuracy of the developed method by comparing it with the finite element method.