Abstract
AbstractUnder 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, https://doi.org/10.1016/j.ijrmms.2012.02.001) 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.
Highlights
It is well known that the mechanical behavior of polycrystalline brittle rocks under confined compressive loading is to a great extent controlled by the presence of crack-like flaws or voids located within grains and along grain boundaries
We examine here the hypothesis that, under deviatoric loading, inelastic deformation is predominantly accommodated by shear-induced sliding of preexisting microcracks, without in- or out-of-plane crack growth
The second reason is that a substantial portion of the unloading segments for the data obtained in the Griggs' apparatus yield unphysically large Young's moduli that are well above that extracted from the elastic portion of the loading segments; modification of the data processing strategy to extract more physically plausible stress-strain data during unloading appears to be an excessively subjective and ad hoc process
Summary
It is well known that the mechanical behavior of polycrystalline brittle rocks under confined compressive loading is to a great extent controlled by the presence of crack-like flaws or voids located within grains and along grain boundaries. Bruno and Kachanov (2013) incorporated the effect of the nonclosable pores in addition to crack closure and frictional sliding during a uniaxial load-unload cycle Their model, which uses approximate schemes to account for crack and pore interactions, was applied to stress-strain as well as microstructural data on ceramic. (i) in contrast to the case of uniaxial compression, if a confining stress is applied, there is no need to include a cohesion term in the constitutive law for crack sliding in order to predict yield-type behavior; (ii) we wish to minimize the number of parameters used to fit the experimental data; and (iii) “friction” and “cohesion” have different physical origins, and a cohesion-only model may be used to simulate intracrystalline slip, whereas friction (i.e., normal stress-dependent slip) should require a minimum degree of crack roughness and the presence of interface asperities at the microscale or nanoscale (Bowden & Tabor, 2001). The model is fit to cyclic loading stress-strain data on polycrystalline antigorite from David et al (2018) at 150 MPa confining pressure and room temperature, and from newly conducted experiments at 1 GPa at room temperature, 400◦C and 500◦C in a Griggs apparatus
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