Experimental study of compaction localization in carbonate rock and constitutive modeling of mechanical anisotropy

Sedimentary rocks are inherently anisotropic and prone to strain localization. While the influence of rock anisotropy on the brittle/dilative regime has been studied extensively, its influence on the ductile/compactive regime is much less explored. This paper discusses the anisotropic behavior of a high-porosity carbonate rock from central Europe (the Maastricht Tuffeau). A set of triaxial tests with concurrent x-ray tomography has been performed at different confining pressures. The anisotropic characteristics of this rock have been investigated by testing samples cored at different inclinations of the bedding, thus revealing non-negligible effects of the coring direction on yielding and compaction behavior. Specifically, samples cored perpendicular to bedding display higher strength and longer stages of post-yielding deformation before manifesting re-hardening. Despite such alterations of the inelastic response, Digital Image Correlation has revealed that the strain localization mode is independent of the coring direction, thus being primarily affected by the confinement level. To capture the observed interaction between material anisotropy and compaction behavior at the continuum-scale, an elastoplastic constitutive law has been proposed. For this purpose, a set of tensorial bases has been introduced to replicate how the oriented rock fabric modulates the yielding and plastic flow characteristics of the material. The analyses show that the impact of the coring direction on yield function and plastic flow rule is fundamentally different, thus requiring the use of distinct projection strategies (a strategy here defined heterotopic mapping). The performance of the model, studied through parametric analyses and by calibrating the experimental results, illustrates the improved capability of the proposed constitutive approach when applied to strongly anisotropic porous rocks.