Failure Mode and Failure-plane Angle in the Highly Porous Bentheim Sandstone Subjected to True Triaxial Stresses

We conducted a series of tests in Bentheim sandstone (24% porosity; 95% quartz), in which cuboidal rock specimens (19 x 19 x 38mm) were subjected to three independent principal stresses, using the University of Wisconsin true triaxial apparatus. The loading path used maintains a fixed deviatoric stress state, which exposes the separate dependence of failure on the mean (octahedral) stress, σ_oct, and the deviatoric stress state. During testing, σ₃ was constant (eight levels were attempted between 0 and 150 MPa) while Δσ₁ (= σ₁-σ₃) and Δσ₂ (= σ₂-σ₃) were raised in a fixed ratio (1:1; 3:4; 1:2; 1:3; 1:6; 0). Plotting the octahedral shear stress, τ_oct, at failure as a function of σ_oct for all tests conducted reveals a rising trend for σ_oct < 180 MPa, reaching a 'cap' at about σ_oct = 200 MPa, and beginning to drop for larger σ_oct. Data points can be loosely fitted by a quadratic equation. Failure mode varied from single shear band, or fault, at σ₃ = 0-80 MPa, to multiple parallel and conjugate faults at σ₃ = 80-100 MPa (brittle-ductile transition, Paterson and Wong, 2005), to shear-enhanced compaction bands at σ₃ = 120 MPa, to pure compaction bands at σ₃ = 150 MPa. Failure-plane angle decreased with the rise in σ_oct for each of the stress ratios, in a manner best fitted by a quadratic equation, from about 80° at the lowest σ_oct to nearly 45° as σ_oct approached brittle-ductile transition (σ_oct = 150-200 MPa), to below 45°, and approaching 0° at higher σ_oct (>200 MPa) for which shear-enhanced and pure compaction bands developed.