Stresses and Displacements in Nonlinear Soil Media

A method is presented for determining the vertical stresses and displacements in semi-infinite nonlinear soil media under circular loaded areas. The soil is assumed to be incompressible with an elastic modulus varying with the state of the stresses. The medium is arbitrarily divided into seven layers in which the stresses and displacements are determined by a high speed computer using Burmister's layered theory and the principle of successive approximations. The results of this study reveal that the nonlinear behavior of soils has a relatively small effect on stresses but a large effect on displacements. This may explain why Boussinesq's solution of stresses based on linear theory has been applied to soils with great success even though soils themselves are basically nonlinear. Because the differences in stresses between linear and nonlinear theory are not too significant, the displacement in a nonlinear medium can be estimated by a simplified method based on Boussinesq's stress distribution. It is found that this simplified method checks closely with the method presented, especially at large radial distances.