A progressive S-shaped yield criterion and its application to rock pillar behavior

Yielding of hard rock pillars under moderate to high stresses involves the formation of excavation-parallel extensile fractures. In recent decades, researchers have found that this behavior can be best replicated by a Cohesion-Weakening-Frictional-Strengthening (CWFS) model which captures the non-simultaneous mobilization of cohesion and friction; this is a mechanism that has been experimentally proved to occur in rocks undergoing brittle failure. In the context of rock pillars, the extensile fracturing process is limited only to the surficial portions. The inner core of rock pillars, on the other hand, fails through a shear mechanism. A realistic rock strength criterion must therefore account for the two different failure behaviors. To this end, this study introduces an improved yield criterion that represents small-scale damage processes (extensile cracking under low confinement and semi-brittle shear under higher confinement) while exhibiting an emergent pillar behavior consistent with what has been observed in the field. The failure criterion was implemented in the finite difference software FLAC3D which was then used to investigate the effect of width to height and length to width ratios on the strength of pillars.