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Unraveling the details of fracture propagation leading to catastrophic rock failure is critical for understanding the precursors to earthquakes. Here we present numerical simulations of fracture growth using a work optimization criterion. These simulations apply work optimization to fracture propagation by finding the propagation orientation that minimizes the external work at each increment of fracture growth, repeating this process for each growing fracture tip in the model. We simulate published uniaxial compression experiments performed on a cylinder of marble with pre-cut fractures of varied lengths, orientations, and positions. This suite of experiments provides an ideal benchmark for the numerical simulations because of the relatively simple boundary conditions and the range of pre-cut fracture geometries that focus deformation. We compare the results of homogeneous, isotropic model material to results that incorporate hundreds of small randomly oriented and distributed microcracks representing internal weaknesses, such as grain boundaries. From these numerical models, we find that slip on and propagation of microcracks governs the non-linear stress-strain response observed before failure under axial compression. We use a suite of Monte Carlo realizations incorporating different initial seeding of microcracks to explore the range of fracture propagation paths that might result from inherent variation between rock samples. We find that while models that include microcracks begin to propagate fractures at smaller cumulative axial strains than an equivalent homogeneous isotropic model, ultimately, models including heterogeneity require more energy to reach failure than the homogeneous model. These results highlight the critical role of heterogeneity, such as microcracks, within the processes leading up to failure.

The Influence of Fracture Growth and Coalescence on the Energy Budget Leading to Failure