Strength testing under multi-axial stress states

Abstract

A true triaxial apparatus was designed and fabricated to apply mechanical loading to achieve multi-axial stress states. The University of Minnesota plane strain apparatus was equipped with piston assemblies that generated intermediate principal stress σ_II up to 100 MPa. The minor principal stress σ_III was limited by the pressure vessel to 24 MPa and the major principal stress σ_I was applied by a closed-loop, servo-hydraulic load frame. Calibration tests were conducted on an isotropic, linear elastic material (aluminum 6061) to confirm the performance of the piston assemblies. Results from strength testing of Dunnville sandstone under multi-axial stress states were used to evaluate the Mohr-Coulomb (MC), Hoek-Brown (HB), and Paul-Mohr-Coulomb (PMC) failure criteria. A series of conventional triaxial compression (σ_II=σ_III) and extension (σ_I=σ_II) experiments were performed to evaluate the necessary material parameters for each failure criterion. The true triaxial apparatus was used to conduct experiments under various states of stress (σ_I≠σ_II≠σ_III) at constant mean stress (p=(σ_I+σ_II+σ_III)/3) of 28.3 and 56.0 MPa. The three criteria were compared in principal stress space on a plane normal to the hydrostatic axis called the pi-plane. Even though MC and HB are independent of σ_II, the stress states at failure were reasonably predicted at p = 28.3 MPa. This was not the case at p = 56.0 MPa, and a plane fitting method using a failure criterion such as PMC that includes σ_II may be needed.