Sliding Crack Model for Nonlinearity and Hysteresis in the Triaxial Stress-Strain Curve of Rock, and Application to Antigorite Deformation

Under triaxial deviatoric loading at stresses below failure, rocks generally exhibit nonlinearity and hysteresis in the stress-strain curve. In 1965, Walsh first explained this behavior in terms of frictional sliding along the faces of closed microcracks. The hypothesis is that crack sliding is the dominant mode of rock inelasticity at moderate compressive stresses for certain rock types. Here we extend the model of David et al. (2012, ) to include (i) the effect of the confining stress; (ii) multiple load-unload cycles; (iii) calculation of the dissipated strain energy upon unload-reload; (iv) either frictional or cohesive behavior; and (v) either aligned or randomly oriented cracks. Closed-form expressions are obtained for the effective Young's modulus during loading, unloading, and reloading, as functions of the mineral's Young's modulus, the crack density, the crack friction coefficient and cohesion for the frictional and cohesive sliding models, respectively, and the crack orientation in the case of aligned cracks. The dissipated energy per cycle is quadratic and linear in stress for the frictional and cohesive models, respectively. Both models provide a good fit to a cyclic loading data set on polycrystalline antigorite, based on a compilation of literature and newly acquired data, at various pressures and temperatures. At high pressure, with increasing temperature, the model results reveal a decrease in friction coefficient and a transition from a frictionally to a cohesively controlled behavior. New measurements of fracture toughness and tensile strength provide quantitative support that inelastic behavior in antigorite is predominantly caused by shear crack sliding and propagation without dilatancy. We extend the crack sliding model of David et al. (2012, ) to a triaxial state of stress We obtain closed-form expressions for the stress-dependent Young's modulus during cyclic loading The model is able to fit a cyclic loading data set on antigorite at various conditions of pressure and temperature