Localized Failure in Brittle Rock

Failure characteristics of two porous sandstones subjected to true triaxial stresses: Applied through a novel loading path

“…The two‐invariant model and equation , or its equivalent, were used to model the failure plane angle variations by Rudnicki and Olsson [] for Castlegate sandstone, by Rudnicki [] for Westerly granite, and by Ma [] for Coconino and Bentheim sandstones. However, in no case was the agreement between the theoretical predictions and experimental results satisfactory.…”

“…In particular, the yield function is given by F ( τ oct,f , σ oct,f , Θ ) = 0 and plastic potential by G ( τ oct,f , σ oct,f , Θ ) = 0, where the subscript “ f ” denotes the value at failure. ( Rudnicki [, ] used τ Mises = (3/2) 1/2 τ oct and σ kk = −3 σ oct ). As a consequence yield and material parameters such as the frictional coefficient μ and the dilatancy factor β are dependent on Θ .…”

“…However, in no case was the agreement between the theoretical predictions and experimental results satisfactory. Consequently, an analysis incorporating a three‐invariant model, introduced by Rudnicki [] and detailed by Rudnicki [], is used here. In particular, the yield function is given by F ( τ oct,f , σ oct,f , Θ ) = 0 and plastic potential by G ( τ oct,f , σ oct,f , Θ ) = 0, where the subscript “ f ” denotes the value at failure.…”

“…The bifurcation theory was previously employed to compare results with experimental observations of failure plane angle in Westerly granite [ Rudnicki , , ] and TCDP siltstone [ Haimson and Rudnicki , ]. Although the bifurcation theory can describe the stress state at the onset of failure and the failure plane angle, comparison with the experimental data has concentrated on the failure plane angle, where the required constitutive parameters are fewer.…”

“…We summarize failure mechanism similarities and differences between the two sandstones. We then compare our experimental data with the bifurcation theory framework by Rudnicki and Rice [], as extended by Rudnicki [, ] to a three‐invariant model and applied by Haimson and Rudnicki [], which relates the stress states at failure to the failure plane angles. This comparison of theory and experiment concentrates on predicting the failure plane angle with the experimentally derived failure stress conditions and material constants.…”