Potential fracture paths for cracked rocks under compressive-shear loading

An energy-based model on multiple cracks initiation from a crack tip has been proposed to capture the physical process of fracture, which can be used to predict and analyse the fracture behaviours of cracked rocks and rock-model materials under compressive-shear loading. The conservation law has been explored utilizing a partial integral path, from which an analytical solution of the energy release rate for multiple cracks initiation from a crack tip has been founded. Some underlying fracture behaviours on cracks initiation from a crack tip, including the crack kinking, side-branching, branching and tri-branching, have been theoretically investigated, which implies actually a degree of instability on a cracked rock under compressive-shear loading. The K-based criteria and fracture toughness for crack kinking, side-branching, branching and tri-branching have been defined. The predictions based on present modelling should help to refresh the understanding of some important experimental observations, such as so called wing cracks and secondary cracks observed in the experiments of cracked rock under compressive loading. As an alternative solution, the energy-based driving mechanism behind complex fracture phenomenon have been suggested.