Analysis of compressive fracture in rock using statistical techniques: Part I. A non-linear rule-based model

Abstract

Abstract A new non-linear rule-based model for the fracture in compression of heterogeneous brittle materials such as rock is presented and used to study crack nucleation and propagation at the grain scale. We have used the model to simulate uniaxial compression tests of rock samples and results underscore the importance of crack interaction in extensile cracking of rock in compression even at low crack densities. Moreover, the model produces non-linear stress–strain behavior similar to that observed in laboratory tests. We have analyzed the stress–strain behavior and found that in these simulations fracture occurs in the following way. First, initial damage occurs by random cracking. When approximately 15% of the sites are broken, cracks start to interact and coalesce to form larger cracks which then may propagate a significant fraction of the array length. Crack extension may be followed by crack arrest and subsequent formation of a damage zone ahead of a crack tip. Finally, a series of cracks will link and form a fracture that eventually causes failure. The model shows decreasing compressive strength with increasing size following a power-law relationship with an exponent that is similar to that determined from the study of laboratory and field-test results. The model can also incorporate heterogeneity in the strength and geometry of rock fabric; in part II, the model is used to investigate how microscale heterogeneity in these parameters affects extensile crack growth in compression.