Finite deformation model of simple shear of fault with microrotations: apparent strain localisation and en-echelon fracture pattern

Abstract

Strain localisation is a widespread phenomenon often observed in shear and compressive loading of geomaterials, for example, the fault gouge. It is believed that the main mechanisms of strain localisation are strain softening and mismatch between dilatancy and pressure sensitivity. Observations show that gouge deformation is accompanied by considerable rotations of grains. In our previous work as a model for gouge material, we proposed a continuum description for an assembly of particles of equal radius in which the particle rotation is treated as an independent degree of freedom. We showed that there exist critical values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-surface layers of the fault, even in the absence of inelasticity. Here, we generalise the model to the case of finite deformations characteristic for the gouge deformation. We derive objective constitutive relationships relating the Jaumann rates of stress and moment stress to the relative strain and curvature rates, respectively. The model suggests that the pattern of localisation remains the same as in the linear case. However, the presence of the Jaumann terms leads to the emergence of non-zero normal stresses acting along and perpendicular to the shear layer (with zero hydrostatic pressure), and localised along the mid-line of the gouge; these stress components are absent in the linear model of simple shear. These additional normal stresses, albeit small, cause a change in the direction in which the maximal normal stresses act and in which en-echelon fracturing is formed.

Acknowledgement

EP acknowledges financial support from the ARC Postdoctoral Fellowship (2003–2006) and Discovery Grant DP0346148. The authors also acknowledge the support by the Australian Computational Earth Systems Simulator (ACcESS) – Major National Research Facility.

Notes

† The index notation we use is different from notation adopted in Mühlhaus and Hornby 36. Instead, we follow Nowacki 11, where the first index stands for the direction of the normal.

† Unlike the strain tensor in conventional non-linear continuum theories with three degrees of freedom.