Estimation of Rock Damage Induced by Stress Relief Based on Viscoelastic Behavior of Grain Boundaries

Abstract

Based on the viscoelastic behavior of grain boundaries, we proposed a new mechanism for rock damage induced by stress relief. In this mechanism, the normal and shear stiffnesses of grain boundaries change with geological time so that the state of stress becomes more uniform, and elastic response of the grain boundaries during stress relief produces tensile residual stress that induces damages in rock. The residual stress was determined with finite element method for three specimen models of polycrystalline rock in a general state of compressive stress, and the degree of damage and the crack density were estimated according to the extended Coulomb criterion to compare the results with the assumptions in the differential strain curve analysis (DSCA) for determining rock stress. The damages are induced only for the grain boundaries having a normal direction that is not much deviated from the directions of the principal stresses with the maximum value. As a result, the maximum crack density increases with the maximum principal stress, while the intermediate crack density does not always increase with the intermediate principal stress and furthermore, the minimum crack density decreases with the minimum principal stress, which does not agree to the assumptions in DSCA. However, the directions of all the principal crack densities approximately coincide with those of the principal stresses for about half of all possible regime of compressive rock stress when the mean stress is large, since the principal crack densities are indirectly determined from the principal strains that are determined by the contribution of all intergranular cracks including those inclined from the principal stresses. Although the assumptions in DSCA are not supported by the mechanism proposed in this study, there is a stress region for which both the magnitudes and directions of the principal stresses can be accurately estimated from those of the principal crack densities and this region becomes wider as the mean stress increases with depth.