Stable and unstable damage evolution in rocks with implications to fracturing of granite

Hamiel, Y, Katz O, Lyakhovsky V, Reches Z, Fialko Y.  2006.  Stable and unstable damage evolution in rocks with implications to fracturing of granite. Geophysical Journal International. 167:1005-1016.

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acoustic-emission, cracked media, damage, deformation, earthquake, elastic-moduli, fractures, growth, model, rheology, saturated cracked solids, seismic velocities, shear, westerly granite


We address the relation between the rock rigidity and crack density by comparing predictions of a viscoelastic damage rheology model to laboratory data that include direct microscopic mapping of cracks. The damage rheology provides a generalization of Hookean elasticity to a non-linear continuum mechanics framework incorporating degradation and recovery of the effective elastic properties, transition from stable to unstable fracturing, and gradual accumulation of irreversible deformation. This approach is based on the assumption that the density of microcracks is uniform over a length scale much larger than the length of a typical crack, yet much smaller than the size of the entire deforming domain. For a system with a sufficiently large number of cracks, one can define a representative volume in which the crack density is uniform and introduce an intensive damage variable for this volume. We tested our viscoelastic damage rheology against sets of laboratory experiments done on Mount Scott granite. Based on fitting the entire stress-strain records the damage variable is constrained, and found to be a linear function of the crack density. An advantage of these sets experiments is that they were preformed with different loading paths and explicitly demonstrated the existence of stable and unstable fracturing regimes. We demonstrate that the viscoelastic damage rheology provides an adequate quantitative description of the brittle rock deformation and simulates both the stable and unstable damage evolution under various loading conditions. Comparison between the presented data analysis of experiments with Mount Scott granite and previous results with Westerly granite and Berea sandstone indicates that granular or porous rocks have lower seismic coupling. This implies that the portion of elastic strain released during a seismic cycle as brittle deformation depends on the lithology of the region. Hence, upper crustal regions with thick sedimentary cover, or fault zones with high degree of damage are expected to undergo a more significant inelastic deformation in the interseismic period compared to 'intact' crystalline rocks.