The influence of pore geometry and orientation on the strength and stiffness of porous rock
Résumé
The geometry of voids in porous rock falls between two end-members: very low aspect ratio (the ratio of the minor to the major axis) microcracks and perfectly spherical pores with an aspect ratio of unity. Although the effect of these end-member geometries on the mechanical behaviour of porous rock has received considerable attention, our understanding of the influence of voids with an intermediate aspect ratio is much less robust. Here we perform two-dimensional numerical simulations (Rock Failure Process Analysis, RFPA2D) to better understand the influence of pore aspect ratio (from 0.2 to 1.0) and the angle between the pore major axis and the applied stress (from 0 to 90°) on the mechanical behaviour of porous rock under uniaxial compression. Our numerical simulations show that, for a fixed aspect ratio (0.5) the uniaxial compressive strength and Young's modulus of porous rock can be reduced by a factor of ~2.4 and ~1.3, respectively, as the angle between the major axis of the elliptical pores and the applied stress is rotated from 0 to 90°. The influence of pore aspect ratio on strength and Young's modulus depends on the pore angle. At low angles (~0-10°) an increase in aspect ratio reduces the strength and Young's modulus. At higher angles (~40-90°), however, strength and Young's modulus increase as aspect ratio is increased. At intermediate angles (~20-30°), strength and Young's modulus first increase and then decrease as pore aspect ratio approaches unity. These simulations also highlight that the influence of pore angle on compressive strength and Young's modulus decreases as the pore aspect ratio approaches unity. We find that the analytical solution for the stress concentration around a single elliptical pore, and its contribution to elasticity, are in excellent qualitative agreement with our numerical simulations. The results of our numerical modelling are also in agreement with recent experimental data for porous basalt, but fail to capture the strength anisotropy observed in experiments on sandstone. We conclude that the alignment of grains or platy minerals such as clays exerts a greater influence on strength anisotropy in porous sandstones than pore geometry. Finally, we show that the strength anisotropy that arises as a result of preferentially aligned elliptical pores is of a similar magnitude to that generated by bedding in porous sandstones and foliation in low-porosity metamorphic rocks. The modelling presented herein shows that porous rocks containing elliptical pores can display a strength and stiffness anisotropy, with implications for the preservation and destruction of porosity and permeability, as well as the distribution of stress and strain within the Earth's crust.