Numerical Simulation of True 3D Rock Tests with Classical and New Three-Invariant Constitutive Models Focusing on the End Effects

Abstract

True 3D rock tests have revealed more complex (than axisymmetric conventional tests) constitutive behaviors of geomaterials which depend on the Lode angle and intermediate principal stress $\sigma_{2}$. These tests, however, are subject to significant errors related to the end effects. It is important to understand which part of the stress–strain measurements is due to the actual rock properties, and which is caused by the end friction. We perform 3D finite-difference numerical simulations of true 3D tests approaching the real test conditions as closely as possible. Two constitutive models are used, one is the classical Mohr–Coulomb model, and the other is a recently developed 3-invariant 3ICM model calibrated with true 3D data for Castlegate sandstone. The results obtained with both models strongly depend on the end friction coefficient or friction angle $\phi$ (notably along the $\sigma_{2}$-normal specimen faces), but the 3ICM model fits the data much better. At each constant $\sigma_{3}$ and $\phi > 0$, the measured (calculated) specimen model strength grows with $\sigma_{2}$ increase, the growth rate being proportional to $\phi$. The $\phi$ increase also leads to an increase in the measured (apparent) stiffness. These results suggest that the experimentally defined typical arc-shaped curves $\sigma_{1} (\sigma_{2}$) at constant $\sigma_{3}$ are progressively uplifted (with respect to real/intrinsic curves) when $\sigma_{2}$ varies from $\sigma_{3}$ to $\sigma_{1}$.