Micromechanics of cataclastic pore collapse in limestone

Abstract

The analysis of compactant failure in carbonate formations hinges upon a fundamental understanding of the mechanics of inelastic compaction. Microstructural observations indicate that pore collapse in a limestone initiates at the larger pores, and microcracking dominates the deformation in the periphery of a collapsed pore. To capture these micromechanical processes, we developed a model treating the limestone as a dual porosity medium, with the total porosity partitioned between macroporosity and microporosity. The representative volume element is made up of a large pore which is surrounded by an effective medium containing the microporosity. Cataclastic yielding of this effective medium obeys the Mohr‐Coulomb or Drucker‐Prager criterion, with failure parameters dependent on porosity and pore size. An analytic approximation was derived for the unconfined compressive strength associated with failure due to the propagation and coalescence of pore‐emanated cracks. For hydrostatic loading, identical theoretical results for the pore collapse pressure were obtained using the Mohr‐Coulomb or Drucker‐Prager criterion. For nonhydrostatic loading, the stress state at the onset of shear‐enhanced compaction was predicted to fall on a linear cap according to the Mohr‐Coulomb criterion. In contrast, nonlinear caps in qualitative agreement with laboratory data were predicted using the Drucker‐Prager criterion. Our micromechanical model implies that the effective medium is significantly stronger and relatively pressure‐insensitive in comparison to the bulk sample.