Statistical Volume Elements for the Characterization of Angle-Dependent Fracture Strengths

The fracture response of rock, a quasi-brittle material, is very sensitive to its microstructural defects. Herein, we use statistical volume elements (SVEs) to characterize rock fracture strength at the mesoscale, based on the distribution of microcracks at the microscale. The use of SVEs ensures that the material randomness is maintained upon “averaging” of microscale features. Certain fracture strengths, such as uniaxial tensile strength, uniaxial hydrostatic strength, shear strength, and uniaxial compressive strength, are obtained and characterized for different angles of loading. Thus, a material with anisotropic fracture strength can be characterized. Statistics of the characterized strengths are analyzed, as well as their auto- and cross-correlation functions of these random fields to shed light on the length scales, relative to the volume element size, at which homogenized properties vary. While crack interaction is not included, the analysis provides insight on the distribution and correlation of different strengths. Finally, the asynchronous spacetime discontinuous Galerkin method is used for macroscopic fracture analyses of two rock domains homogenized by SVEs.