Assessing Coal Bumps From Excess Energy in Finite Difference Models

A numerical investigation is made into unstable failures of coal pillars (i.e. coal bumps) using the finite difference software FLAC3D. A static energy balance is first derived to calculate the excess energy released as a consequence of unstable failure in rock. Two- and three-dimensional mining layouts are then assessed on their bump-potential based on the magnitudes of excess energy released during simulated pillar failures. A three dimensional pillar model is developed to represent tributary area loading of an infinite room-and-pillar layout. Pillar strength and brittleness characteristics are calibrated using a Mohr-Coulomb strain-softening constitutive law to simulate width-to-height ratio coal pillars ranging from 1:1 to 5:1. Width-to-height ratio pillars 1:1 to 3:1 release large magnitudes of excess energy as the pillars fail, representing massive collapse of room-and-pillar layouts. The larger pillars maintain their residual strength during failure; however significant excess energy is still released during temporary reductions in pillar strength. A two-dimensional model is then constructed of a gate road pillar failing due to elastic rebound of the surrounding rock mass. Soft loading conditions initiate unstable failure for all pillar widths, while the total magnitudes of excess energy increase with the size of pillar being modeled. The results from these tests indicate that excess energy may be used as a direct assessment of the bump potential of simulated mine layouts.