A strain-based failure criterion for pillar stability analysis

Strain-based failure criteria have several advantages over stress-based failure criteria: they can account for elastic and inelastic strains; they utilise direct, observable effects instead of inferred effects (strain gauges versus stress estimates) and they model complete stress-strain curves, including prepeak, non-linear elasticity and post-peak strain weakening. In this study, a strain-based failure criterion derived from thermodynamic first principles utilising the concepts of continuum damage mechanics is presented. Furthermore, implementation of this failure criterion into a finite element simulation is demonstrated and applied to the stability of underground mining coal pillars.

In numerical studies, pillar strength is usually expressed in terms of critical stresses or stress-based failure criteria where scaling with pillar width and height is common. Previous publications have employed the finite element method for pillar stability analysis using stress-based failure criterion, such as Mohr-Coulomb and Hoek-Brown, or stress-based scalar damage models.

A novel constitutive material model, which takes into consideration anisotropy as well as elastic strain and damage as state variables, has been developed and is presented in this paper. The damage threshold and its evolution are strain-controlled, and coupling of the state variables is achieved through the damage-induced degradation of the elasticity tensor. This material model is implemented into the finite element software Abaqus and can be applied to 3D problems.

Initial results show that this new material model is capable of describing the non-linear behaviour of geomaterials commonly observed before peak strength is reached as well as post-peak strain softening. Furthermore, it is demonstrated that the model can account for directional dependency of failure behaviour (ie anisotropy) and has the potential to be expanded to environmental controls such as temperature or moisture.