The post-failure characteristics of rock

A strain-softening constitutive relationship is introduced that describes the post-failure stress-strain curve for rock regardless of whether the rock is intact or broken. The core of this relationship is an “apparent friction” concept that relates the post-failure apparent cohesive and frictional characteristics of the rock to the strain. The relationship can be determined for a given rock via a series of triaxial strength tests establishing the peak strength and corresponding strain for a range of confining pressures, together with the determination of the base angle of friction via a simple tilt test. The postulates and assumptions used in deriving this relationship are verified from results of tri-axial tests on both intact and broken rock. This strain-softening relationship is then applied to coal. Having determined the post-failure stress-strain curve for coal specimens, this information can then be used in a finite element program, such as Phase 2, to examine the post-failure characteristics of coal pillars. Using example data, the strength of coal pillars of different width/height ratios are estimated and compared with well-known empirical pillar size-strength relationships. In addition, the post-failure stress-strain behaviour of a coal pillar is compared with an empirical relationship reported in the literature.