Average Vertical Stresses in Underground Mine Stopes Filled with Granular Backfills

Marston’s theory and its modifications are being used to determine the average vertical stress variation with depth within a cavity with vertical wall, backfilled with granular material. In the past, this has been applied in trenches, mine stopes and silos of different cross sections. In all situations, at very large depths, the vertical stresses become asymptotic. The laboratory model tests clearly suggest that this is not the case and that the average vertical stresses continue to increase. In this paper, an attempt is made to improve Marston’s model, in the light of laboratory test data. It is shown that the problem with Marston’s equation is its inability to model the shear stress correctly, which leads to an asymptotic vertical stress after a certain depth. The proposed equation is of the same form as Marston’s equation, and has two coefficients α and β that have to be determined from a laboratory model test.