Energy considerations in rock mechanics: fundamental results

If a transition from one equilibrium state to another occurs during the course of mining, energy transfer takes place in the rock mass, which is assumed to be an elastic continuum. The energy components are defined as follows: the work done by external and body forces, W; the increase in stored energy in the mass, Uc; the strain energy in the rock mined during the transition, Urn; the work done on mine support or backfill, Ws; and the released energy, Wr. The energy balance is defined as (W + Urn) - (Uc + Ws) = Wr> 0, where the first set of components in parentheses represents the sources of energy, while that of the second corresponds to the known modes of energy expenditure and the component on the right is the unaccounted-for energy surplus, which must be released and dissipated in some form. The inequality Wr ~ Urn> 0 applies. Expressions for the energy components are derived first for the general case and then for the 'slit' modal used to simulate tabular excavations. Through specific examples, the importance of the progressive nature of mining is emphasized. The size of the steps used to enlarge the excavations appears to play a significant role in the mode of energy transfer. This observation forms the basis of the second paper in this series of two papers.