Geological and mathematical framework for failure modes in granular rock

Abstract We synthesize all the available data on failure processes in granular rock and provide a geological framework for the corresponding structures. We describe two categories: (1) sharp discontinuities made up of two surfaces similar to elastic crack models, and (2) tabular structures resulting from strain localization into narrow bands. Each of these categories includes types predominated by shear and/or volumetric deformation. While shear failure can be in two different modes as sliding and tearing, the volumetric failure has two diametrically opposite types: compaction (contraction) and dilation (extension). Thus, we distinguish among bands predominantly by shearing, shortening, and extension. Slip surfaces, pressure solution surfaces, and joints represent corresponding sharp discontinuities. A survey of observations and measurements from naturally occurring structures indicates that although isochoric shear and pure volumetric deformation types represent end members, a complete spectrum of combined shear and volumetric deformation occurs in nature. Field observations also show that sharp structures overlap older narrow tabular structures in the same rock. This switch in failure modes is attributed to changing rock rheology and/or loading conditions. In the mathematical modeling, we focus on the strain localization into narrow tabular bands using classical bifurcation theory combined with nonlinear continuum mechanics and plasticity. We formulate a family of three invariant plasticity models with a compression cap and capture the entire spectrum of failure of geomaterials. In addition, we draw an analogy between the concepts of ‘strong’ and ‘sharp’ discontinuity and classic elastic crack representations to complement the mathematical treatment of the failure modes.