A PD-FEM Coupling Approach for Modeling Cracks Propagation in Brittle Rock Under Compressive Load

Abstract

ABSTRACT Considering the low computational efficiency and accuracy of peridynamics (PD), a concurrent multiscale method coupling PD and finite element method (FEM) is proposed for modeling crack propagation of brittle rock under compressive load. In the coupling method, the fracture behavior is solved by the ordinary state-based peridynamics (OSBPD), while the elastic deformation of the rock mass is simulated by FEM. The implementation of the approach is as the following steps: first, a hybrid region is introduced in the framework to realize the strain energy equivalence between PD and FEM and eliminate the boundary effect. Then, the short-range force is utilized in PD to model the contact of the crack surface and prevent the particles from penetrating each other. In addition, the tangential force of the short-range force is introduced to simulate the friction sliding effect of the crack surface. Finally, the dynamic relaxation method is used to solve the displacement in the PD-FEM coupling model. The crack propagation of rock samples with a single pre-existing closed fracture under uniaxial compression is simulated by the PD-FEM coupling approach, and the numerical calculation results are in good agreement with the rule of the experimental results. The proposed coupling approach can capture the failure process of rocks under uniaxial compression and reduce the computational cost, simultaneously. INTRODUCTION The failure of rock can lead to structural damage, landslides, and rock bursts, which can endanger human life and property. Therefore, studying the fracture behavior of rock is essential for ensuring the safety of engineering projects. The law of crack growth in the brittle rock remains a great challenge in rock mechanics. In order to predict crack growth, many numerical methods have been developed. The numerical methods often used in the field of rock fracture mechanics include continuous methods and discontinuous methods. Common continuous methods include the extended finite element method (Eftekhari et al., 2016), the cohesive force element method (Zhou & Molinari, 2004), and the phase field method (Zhou et al., 2018). However, traditional continuum mechanics theory-based modeling makes it difficult to deal with complex crack propagation problems. The discrete element method (Cundall, 1971) is a commonly used technique in discontinuous methods to simulate fracture problems in rocks. However, the microscopic parameters of the discrete element method lack physical meaning and need to be calibrated through experiments.