Photoelastic Analogy for Nonhomogeneous Foundations

The stress distributions in a semi-infinite body–in which Poisson's ratio is constant but in which the modulus of elasticity varies with depth–are considered herein. The general equations of elasticity for such a point-isotropic material are derived. These equations establish the fact that superposition of correct solutions is permissible. There is shown to be an analogy between the stresses in a constrained slice, which has a modulus of elasticity that varies with depth, and the stresses in a plate whose thickness varies in the same manner if the state of stress in the plate can be considered to be two-dimensional. Thus, the stress distributions beneath infinite line loads or infinite strip loads on such a foundation can be determined experimentally by the use of photoelasticity. The photoelastic analogy is confirmed by experiments, and its u se is outlined.