Multibody failure criterion for the four-dimensional lattice spring model

Gao-Feng Zhao, Zhi-Qiang Deng, Ben Zhang

Although lattice spring models (LSMs) have been increasingly applied in the study of rock fracturing and rock failure, it is still difficult to accurately reproduce high ratios of the uniaxial compressive strength to the tensile strength of rock materials. In this work, a feasible solution is developed for the four-dimensional lattice spring model (4D-LSM) that overcomes this shortcoming by incorporating a multibody failure criterion. The stress tensor of a spring bond is determined by the local deformation state between this bond and its neighboring spring bonds, which is further used to judge its failure state using a stress-based strength model. Then, a cohesive zone model is introduced to describe the postfailure stage of the spring bond. The performance of the proposed solution in reproducing the high ratio of the uniaxial compressive strength to the tensile strength of rock materials is demonstrated via numerical tests. Enriched by the multibody failure criterion, 4D-LSM is demonstrated to solve a broader range of practical problems that involve rock failure.