Numerical Manifold Method for Simulating of Multi-crack Propagation in Rock Mass

Abstract

The expansion and penetration of the structural planes under stress is an important cause of rock mass failure. Based on the principle of linear elastic fracture mechanics, a multi-crack propagation simulation algorithm of higher-order numerical manifold method (NMM) is proposed. The singularity of the crack tip displacement field is considered by adding key terms of the crack tip displacement field function to the basis function of the NMM. The stress intensity factor at the crack tip was calculated by J integral. The cracking and propagation directions of I-II mixed cracks are judged by the maximum circumferential tensile stress criterion. Hypothesis-modified multi-crack propagation algorithm is used to solve the problem of multi-crack propagation. When a single physical cover contains two or more crack tips, the influence of the singularity of the displacement field at each crack tip will be considered simultaneously in the physical cover displacement function. For those integral functions which do not conform to the simplex integral form, Taylor series expansion method is used to calculate the approximate solution. The rationality and accuracy of the calculation method are verified by numerical simulation of two classical static crack propagation problems and physical model test.