A logarithmic model for predicting fracture trajectory of pre-cracked rock specimen under compression

Researches on the fracture trajectory of pre-cracked specimen are mostly focused on experiments and numerical simulations, and theoretical studies are usually limited to the fracture criterion, crack initiation angle and load, with few theoretical studies on the prediction of the complete fracture trajectory. This work first derives stress intensity factor (SIF) and T-stress expressions related to crack geometry, friction and deformation parameters, and physical properties of the rock. Then, the classical maximum tangential stress (MTS) fracture criterion is modified, followed by the development and validation of a logarithmic model for predicting the fracture trajectory of pre-cracked specimen made of diverse brittle or quasi-brittle rock materials under compression. The results shown that the crack geometry, friction and deformation parameters have significant effects on SIF and Tstress under compression. The present study demonstrates a strong concurrence between the anticipated fracture trajectory of pre-cracked specimens subjected to compressive loading and diverse experimental outcomes. Furthermore, the fracture trajectory is predominantly influenced by the crack geometry, friction and deformation parameters, and the mechanical characteristics of the specimen.