True Triaxial Cyclic Loading of Sandstone Interpreted with a new Anisotropic Poroelastic Damage Model

Abstract

Crustal rocks undergo repeated cycles of stress over time. In complex tectonic environments where stresses may evolve both spatially and temporally, such as volcanoes or active fault zones, these rocks may experience not only cyclic loading and unloading, but also rotation and/or reorientation of stresses. In such situations, any resulting crack distributions form sequentially and may therefore be highly anisotropic. Thus, the tectonic history of the crust as recorded in deformed rocks may include evidence for complex stress paths, encompassing different magnitudes and orientations. Despite this, the ways in which variations in principal stresses influence the evolution of anisotropic crack distributions remain poorly constrained. In a previous study, we modelled the damage response of Darley Dale sandstone under true triaxial loading conditions. To do this, we extended the isotropic nonlinear damage rheology model with a scalar damage parameter to a more complex formulation by assuming orthotropic symmetry and introducing a second-order damage tensor, the principal values of which describe damage in three orthogonal directions associated with the orientations of the three principal loading axes. More recent experimental results have shown that damage, under true triaxial loading, is a distinctly directional phenomenon, and these results have also revealed a 3D directionally dependant Kaiser ‘damage memory’ effect. Here we build on the previous non-linear anisotropic damage rheology model by presenting a newly developed poroelastic rheological model which accounts for both coupled anisotropic damage and porosity evolution. The new model shares the main features of our previously developed anisotropic damage and scalar poroelastic damage models, including the ability to simulate the entire yield curve through a single formulation. In the new model, the yield condition is defined in terms of invariants of the strain tensor, and so the new formulation operates with directional yield conditions (different values for each principal direction) depending on the damage tensor and triaxial loading conditions. This allows us to discern evolving yield conditions for each principal stress direction and fit the measured amounts of accumulated damage from previous loading cycles. Coupling between anisotropic damage and anisotropic compaction along with the damage-dependent yield condition produces a reasonable fit to the experimentally obtained stress-strain curves. Furthermore, the simulated time-dependent cumulative damage is well correlated with experimentally observed acoustic emissions during cyclic loading in different directions. As such, we are able to recreate many of the features of the experimentally observed directional 3D Kaiser ‘damage memory’ effect.