Modeling Fault Angle in Novel True Triaxial Tests on a Compactive Porous Sandstone

Ma and Haimson (see accompanying Abstract) have conducted true triaxial tests on a compactive porous sandstone (Coconino) using a novel loading path consisting of keeping the minimum (least compressive) principal stress (σ₃) constant but increasing the other two stresses in a fixed ratio. For stress ratios Δσ₂/Δσ₁ = 1:1; 1:2; 1:3; 1:6; 0 (where Δσ_i = σ_i-σ₃, and 0 implies σ₂ = σ₃), the parameter R, describing the deviatoric stress state or Lode angle (and equal to √3N, where N is the parameter used by Rudnicki and Rice (1975)), varies from -1 (axisymmetric extension), to 0 (deviatoric pure shear), to 0.36, 0.71 and +1 (axisymmetric compression). For each value of R, the fault angle decreases roughly linearly with increasing mean stress. A straight line fits plots of the slopes and intercepts of these lines (omitting the points for axisymmetric compression) as a function of R. The resulting bi-linear relationship fits all the data well although for axisymmetric compression the predicted line is slightly offset to the fit to the data. Fault angles are also compared to predictions of a theory that treats fault formation as an alternative to (bifurcation from) homogeneous deformation (Rudnicki and Rice, 1975). Results are based on an inferred dependence of the sum of a friction coefficient μ and dilatancy factor β with mean stress for a single value of R. Using a linear fit to the data for R = 0, gives a plausible variation of μ + β with mean stress: a linear decrease, except at lower values (below about 150 MPa) where the slope decreases. Predictions of the fault angle based on this variation of μ + β agree well with observations for R = 0.36 and R = 0.71. Predictions for axisymmetric compression are slightly offset from the line fitted to the data. For axisymmetric extension the predictions do not agree well with data. For higher mean stress, predicted angles are similar to the data but the variation with mean stress is clearly different. At lower mean stress (below 200 MPa), the theory predicts a dilation band (perpendicular to least compressive stress). Although the observed angles between the fault and the least compressive stress do get larger with lower mean stress (70 to 80 degrees), the failure is still a shear fault. The reason for these discrepancies is unclear. One possibility is that predictions are based on a two invariant (octahedral shear stress and mean stress) description of non-elastic behavior. A three invariant description may improve predictions but introduces additional parameters that are only loosely constrained by the data. Another possibility is that predictions of this theory for smooth yield surface models are known to have deficiencies for axisymmetric deformation states (Rudnicki and Rice, 1975).