Deformation evolves from shear to extensile in rocks due to energy optimization

Abstract Determining how fracture network development leads to macroscopic failure in heterogeneous materials may help estimate the timing of failure in rocks in the upper crust as well as in engineered structures. The proportion of extensile and shear deformation produced by fracture development indicates the appropriate failure criteria to apply, and thus is a key constraint in such an effort. Here, we measure the volume proportion of extensile and shear fractures using the orientation of the fractures that develop in triaxial compression experiments in which fractures are identified using dynamic in situ synchrotron X-ray imaging. The fracture orientations transition from shear to extensile approaching macroscopic, system-size failure. Numerical models suggest that this transition occurs because the fracture networks evolve in order to optimize the total mechanical efficiency of the system. Our results provide a physical interpretation of the empirical internal friction coefficient in rocks.