Analysis of Three-Layer Viscoelastic Half-Space

The analysis of a three-layer linear viscoelastic half-space under a uniformly distributed circular load is presented. Such an analysis is an essential step in the development of a rational method of design for flexible pavements since such pavement systems respond in a markedly viscoelastic (time-dependent) fashion. The solution is obtained for the normal stress, radial stress, shear stress, vertical deflection and radial displacement, at any point within the half-space. These solutions are obtained by replacing the elastic constants in the elastic solution by integral operators derived from the hereditary form of the linear viscoelastic constitutive equations. This substitution results in integral equations involving multiple convolution integrals of the time-dependent quantities. The multiple convolution integrals are evaluated for a series representation of the creep functions, and then an associated technique is used for numerical solution of the integral equations. Sample numerical results are presented. The techniques used in this analysis were selected for their ease of application and because they allow realistic representations of the viscoelastic behavior of real materials over broad time intervals.