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To simulate the moving boundary problems, the moving least square–based numerical manifold method, abbreviated as MLS-based NMM, was proposed. The MLS-based NMM has been applied successfully to open crack problems, which exhibits the high accuracy and strong robustness. In this study, we extend the MLS-based NMM to simulate the cracked rock considering the contact of the crack surface. Simultaneously, in order to simulate the progressive failure of the cracked rock, an improved strength-based criterion is proposed. The criterion is based on the Mohr–Coulomb criterion and maximum tensile stress criterion. Because rock can be regarded as a quasi-brittle material, a characteristic distance is used to calculate the crack tip stress and correct the crack propagation direction which avoids the phenomenon of “Zig-zag” for the crack propagation path based on the fracture mechanics criterion. The proposed strength-based criterion can acquire the crack tip stress and propagation direction and also realize the automatic determination of the crack propagation length in each step of the crack growth. A Brazilian disc problem and a rectangular plate problem are adopted to verify the numerical model. At last, the numerical model is applied to study the progressive failure process of the rock slope. The results indicate that the proposed method can deal with the crack propagation in the rock and the opening/sliding of rock blocks along discontinuities in a natural way.

MLS-Based Numerical Manifold Method for Modeling the Cracked Rock Considering the Contact of the Crack Surface