TWO-PHASE DAMAGE THEORY AND CRUSTAL ROCK FAILURE: THE THEORETICAL 'VOID' LIMIT, AND THE PREDICTION OF EXPERIMENTAL DATA

Abstract

Using a classical averaging approach, we derive a two-phase theory to describe the deformation of a porous material made of a matrix containing voids. The presence and evolution of surface energy at the interface between the solid matrix and voids is taken into account with non-equilibrium thermodynamic considerations that allow storage of deformational work as surface energy on growing or newly created voids. This treatment leads to a simple description of isotropic damage that can be applied to low-cohesion media such as sandstone. In particular, the theory yields two possible solutions wherein samples can either 'break' by shear localization with dilation (i.e. void creation), or undergo shear-enhanced compaction (void collapse facilitated by deviatoric stress). For a given deviatoric stress and confining pressure, the dominant solution is that with the largest absolute value of the dilation rate, $|Γ|$, which thus predicts that shear-localization and dilation occur at low effective pressures, while shear-enhanced compaction occurs at larger effective pressure. Stress trajectories of constant $|Γ|$ represent potential failure envelopes that are ogive- (Gothic-arch-) shaped curves, wherein the ascending branch represents failure by dilation and shear-localization, and the descending branch denotes shear-enhanced compactive failure. The theory further predicts that the onset of dilation preceding shear-localization and failure necessarily occurs at the transition from compactive to dilational states and thus along a line connecting the peaks of constant-$|Γ|$ ogives. Finally, the theory implies that while shear-enhanced compaction first occurs with increasing deviatoric stress (at large effective pressure), dilation will occur at higher deviatoric stresses. All of these predictions in fact compare very successfully with various experimental data. Indeed, the theory leads to a normalization where all the data of failure envelopes and dilation thresholds collapse to a single curve.