Responses of a Transversely Isotropic Layered Half-Space to Multiple Horizontal Loads

Abstract

In this work, the displacements and stresses at any point in a transversely isotropic layered half-space under multiple horizontal loads are studied. The transversely isotropic plane is assumed to be parallel to the surface plane, and uniformly distributed circular loads with different magnitudes, radii and orientations are applied to the pavement surface. Based on the cylindrical system of vector functions in the transformed domain, the governing equations are first decoupled into two sets of equations related to the LM-type and N-type respectively. Solutions for the multilayered half-space in the transformed domain are then derived by virtue of the propagator matrix method. Solutions in the physical domain are then expressed in terms of the Bessel function integration. The method of superposition is finally utilized for multiple loads. We remark that while the propagator matrix method has been frequently used to solve the vertical loading problem in layered half-spaces, which only involve the LM-type equation, the corresponding horizontal loading problem involving multiple circular loads in a transversely isotropic layered half-space has not been addressed in the literature. A computer program has been coded by the authors' research group and numerical results obtained from this program for the isotropic layered half-space have been verified with existing ones. Further presented in this paper are the results for the transversely isotropic layered half-space, with examples elucidating clearly the effect of material anisotropy on the responses, especially on pavement failure. It is also observed that, in terms of computation, the developed program is very accurate, efficient and flexible. For instance, our program can easily handle more than 10,000 field points with more than 1,000 pavement layers.