Surface subsidence associated with long wall mining: Two and three dimensional boundary element model

Abstract

Abstract Systematic measurements of surface displacements associated with longwall mining made by British Coal (formerly National Coal Board - NCB) are compared with NCB results calculated in the present study. Three aspects of subsidence are considered: maximum subsidence, surface configuration and applicability of two-dimensional models to three-dimensional cases. The model presented in this paper is based on elementary solution presented by Golecki (1978, 1979) for stresses and displacements in an infinite homogeneous elastic halfplane or half space, subjected at its boundary by a discontinuous uniform displacement. Two and three dimensional models were developed using those solutions. The model was used for an analysis of ground subsidence as a function of the span and height of the mined openings, assuming various Poisson’s ratios. Results of two-dimensional models, representing openings of infinite length were compared with measurements compiled by the NCB which correspond to longwall mines. The comparison shows that for deep mines, use of small Poisson’s ratios renders close agreement between calculated and measured subsidence, whereas for shallow mines use of large Poisson’s ratios gives the best agreement. These results lead to the conclusion that subsidence in shallow mines is associated with a state of failure extending to the ground surface. This entails an increase in volume (dilatancy) and is therefore best represented by a model with a large Poisson’s ratio. On the other hand failure in deep mines is confined to a relatively limited zone above the subsiding roof. Computed subsidence over the longwall face (rib subsidence) appears to be consistently larger than that measured in the field. This may be attributed to one fundamental difference between the model and the prototype; while the model assumes closure over the entire longwall span (using a step function) actual closure occurs only at some distance behind the longwall face. Results of the three dimensional model indicate that subsidence associated with a square groundplan is smaller than that associated with a two dimensional opening. Subsidence over square openings amounts to less than 70% of that calculated in two dimensional models of equal relative span. For openings with a rectangular groundplan, subsidence increases rapidly with increasing length. For shallow openings with a length to width ratio exceeding 2.5, maximum subsidence is more than 95% of that in an opening of equal width but of infinite length.