Vertical Stress Isobars for Trenches and Mine Stopes Containing Granular Backfills

The vertical stresses within granular fills contained in trenches can be determined using Marston’s theory or numerical modeling. Marston’s theory gives only the average value of the vertical stress at a depth. Numerical modeling can be used for determining the vertical stress at any point within the fill. This paper presents vertical stress isobars for trenches filled with granular materials, developed from numerical modeling, and proposed in terms of dimensionless variables. These isobars are similar to the pressure isobars for uniformly loaded circular and strip footings found in literature. These isobars can be used for determining vertical stresses at any point within the granular material contained in trenches and can become a simple and valuable tool. The validity of the isobars was verified through several trenches with randomly selected dimensions and fill properties. It was found that the estimates using the isobars were within 9% of the estimates from the numerical model.