Microcrack statistics, Weibull distribution and micromechanical modeling of compressive failure in rock

Statistics of the mechanical and failure properties on the grain scale are often assumed to follow the Weibull distribution in numerical simulations of failure and damage development. To investigate the microstructural basis for such a statistical model of compressive failure in a brittle rock, we consider the development of instability in a wing crack model and establish a methodology whereby the Weibull parameters can be inferred from microstructural data on microcrack density and length statistics for input into finite element simulations. Application of this methodology to six Yuen Long marble samples provides important insights into how different attributes of the microstructure may influence the progressive development of rock failure. The finite element simulations underscore the significant influence of microcrack length statistics, which has not been emphasized in continuum damage mechanics models that usually emphasize the roles of average crack size and crack density. The microstructural data indicate that strength heterogeneity increases with increasing grain size, and this plays a key role in lowering the uniaxial compressive strength, which contributes to the overall decrease of strength with increasing grain size.