Finding the right place in Mohr circle space: Geologic evidence and implications for applying a non-linear failure criterion to fractured rock

The ability to relate patterns of brittle rock failure to stress conditions permits geologists to better understand the nature of rock deformation in natural geologic settings. In the field of structural geology, the relationship between shear and normal stress at the time of rock failure, a critical element of any failure criterion, is most commonly assumed to be linear in compressive stress environments. However, derivation and utilization of linear and non-linear failure criteria have been debated and variably invoked in past laboratory, field, and modeling-based analyses. In a study of fractured Jurassic Moab Tongue Member sandstone (Entrada Formation) bordering Arches National Park (Utah), we have documented field evidence for a system of shear fractures whose character and kinematics are best explained by a non-linear failure criterion. This field setting is distinguished by lateral subjacent juxtaposition of a salt-wall diapir (to the northeast) and the fractured sandstone (to the southwest). The shear fracture system reveals conjugate dihedral angles that systematically decrease northeastward reflecting decreasing critical differential stress magnitudes along a non-linear failure criterion, driven by a reduction in mean normal stress closer to the salt-sediment interface. These stress conditions are most likely associated with the mechanical response of the adjacent salt body to tectonic loading. Augmented by experimental rock failure testing, we provide novel field-based evidence that a non-linear failure criterion is most applicable in this natural geologic environment. We also present a pathway to gain insight into paleostress magnitudes utilizing observed failure angles and a geomechanically constrained non-linear failure criterion.