On the hyperbolic variation of elastic modulus in a non-homogeneous stratum

Abstract

An exact formulation is presented for the governing dual integral equations representing the mixed boundary-value problem of the static stress distribution under a long rigid rectangular body lying on the free surface of a non-homogeneous stratum. The shear modulus of the stratum increases in the depth direction y from a value G0 at the surface according to the hyperbolic variation. G(y)=Gohh−y It, therefore, simulates a practical soil, of arbitrary Poisson's ratio, which smoothly merges into a rigid bed at a depth h below the surface. The work shows that the problem is governed by both kinds of exponential integral function and that the effect of surface elastic properties is dominant in the solution of the governing equations. The limiting case of a homogeneous half-space is easily recovered from the general formulation as h tends to infinity.