On the Topology Update of the Numerical Manifold Method for Multiple Crack Propagation

Abstract

Crack initiation and propagation are the two key issues of concern in the geotechnical engineering. In this study, the numerical manifold method (NMM) is applied to simulate crack propagation and the topology update of the NMM for multiple crack propagation is studied. The crack-tip asymptotic interpolation function is incorporated into the NMM to increase the accuracy of the crack-tip stress field. In addition, the Mohr-Coulomb criterion with tensile cut off is adopted to be the crack propagation criterion to judge the direction of crack initiation and propagation. Then a crack tip searching method is developed to automatically update the position of the crack tips. The inapplicability of the original loop search method in the NMM is also illustrated and a novel loop search method based on manifold elements is developed for physical loop updating. Moreover, methods for the manifold element updating and physical cover updating are provided. Based on the above study, the developed numerical method is capable to simulate multiple crack propagation. At last, typical rock rupture problems are numerically simulated to manifest the effectiveness of the developed numerical method.