Deformation of Sand in Hydrostatic Compression

The deformational behavior of a granular soil under hydrostatic compressive stress is studied. A theoretical model consisting of regular arrays of uniform spheres, but with a probabilistic distribution of holes in the arrays, is postulated. When Hertzian behavior of the points of contact between the spheres is assumed and the holes are made to close under increasing pressure, a theoretical hydrostatic stress-strain relationship is derived. The theory is used to predict the compression of an Ottawa sand at various densities, and is found to give good agreement with the measurements obtained by testing the soil in a new apparatus. The behavior is found to be nonlinear but almost completely elastic.