Estimation of pillar loads in single and contiguous seam workings

Abstract

As opposed to the conventional theory of thin beams on elastic support, mine strata over pillar areas have to be treated as thick in those mining configurations where the oft-used ‘tributary area’ method gives incorrect estimates of pillar loads. Considering mine rock as a composite thick beam, comprising several rock beds of different elastic properties, pillar loads can be estimated by obtaining deflections produced in the beam. For this purpose a general differential equation in terms of over-burden deflections must be formulated. Having shown elsewhere that the method adopted by others to obtain a general differential equation for thick beams on elastic support does not appear to be acceptable, a derivation has been presented to deduce such an equation based on the modified theory of thick plates given by Reissner. The equation proper as obtained is ▪ and as derived by others was ▪ where D is the combined flexural rigidity of overburden strata, q is the loading on strata beam, h is the depth of mine from surface, k is the foundation modulus of the seam or pillars and E, μ are the elastic constants of overburden rocks. A satisfactory expression for the flexural rigidity D of stratified mine rock has been given converting the vertical section of rock layers into an equivalent section of a single rock material. Formulae for the foundation modulus k have been mentioned for various situations. A demarkation between the regions of applicability of the tributary area method and the thick beam method has been clearly indicated. Next in the sequel, an analytical method of estimating loads on pillars in contiguous seams has been presented. The method uses the thick beam equation so that the influence of nature and size of parting on pillar loads in contiguous workings can be obtained more rigorously.