Brittle Failure of a Compactive Porous Sandstone under True Triaxial Conventional and Novel Stress Paths

We conducted two series of true triaxial tests in Coconino Sandstone (17.5% porosity; 96% quartz), in which square cuboidal rock specimens (19 x 19 x 38mm) were independently compressed in three principal directions, using the UW-Madison true triaxial testing apparatus. In the conventional series of true triaxial tests the least and intermediate principal stresses (σ₃ and σ₂) were maintained constant, while the largest stress (σ₁) was raised at a rate of 0.1 MPa/s until brittle failure occurred in the form of shear fracture or fault. Eight different σ₃ levels were attempted (between 0 and 150 MPa), to cover the full range of brittle behavior up to the point of brittle-ductile transition. σ₂ varied between σ₂ = σ₃ and σ₂ = σ₁. The results reinforced previous findings in crystalline rocks that both resistance to faulting and fault angle increase as σ₂ rises above σ₃ (Haimson and Chang, 2000; Chang and Haimson, 2000), albeit at a reduced rate. This is contrary to the Mohr-Coulomb model, which predicts no σ₂ effect on either. Plotting all the data points as τ_oct vs. σ_oct (where τ_oct is the octahedral shear stress and σ_oct is the mean normal stress, both at fault initiation) reveals a trend that can be loosely fitted by a quadratic equation (R = 0.95). A better fit is obtained if the mean stress σ_oct is reduced to its 2D equivalent (σ₁+σ₃)/2 (R = 0.99). Brittle failure characteristics varied from single fault at σ₃ lower than 120 MPa, to multiple parallel and conjugate faults at σ₃ = 120-150 MPa (a characteristic of brittle-ductile transition, Paterson and Wong, 2005). Conventional true triaxial tests, however, do not maintain constant any of the three principal stress invariants during loading. Tests using a novel loading path with fixed deviatoric stress state facilitate comparison with a theory that predicts failure as a bifurcation from homogeneous deformation (Rudnicki and Rice, 1975). We conducted a series of tests in which σ₃ (between 0 and 150 MPa) was maintained constant while Δσ₁ (= σ₁-σ₃) and Δσ₂ (= σ₂-σ₃) were raised in a fixed Δσ₂/Δσ₁ ratio (1:1; 1:2; 1:3; 1:6; 0, where 0 implies σ₂ = σ₃), enabling the study of brittle failure and fault angle as a function of the mean stress for different constant deviatoric stress states. The novel loading path test results showed that τ_oct at fault initiation consistently increased with the correspondent σ_oct, following a trend that can be fitted by a quadratic equation (or equally well by a power function) for each of the Δσ₂/Δσ₁ stress ratios. In addition, a quadratic equation (or power function) could also be fitted to all test data in term of τ_oct vs. σ_oct. The latter is similar to that obtained in the conventional tests. Fault angle decreased linearly with the rise in σ_oct for each of the stress ratios. Generally the decrease was from approximately 80° at the lowest σ_oct to about 50° as σ_oct approached brittle-ductile transition. Notably, for the same σ_oct fault angle increased by 10°-14° as the stress ratio rose from 0 to 1:1 (corresponding to σ₂ rising from σ₂ = σ₃ to σ₂ = σ₁).