Dynamic response of a multilayered half-plane under moving loads with analytical layer-element method

The analytical layer-element method owns higher computation efficiency and numerical stability. Hence, this method is utilized to analyze the dynamic response of an isotropic multilayered half-plane subjected to a moving load. It is assumed that the studied system moves synchronously with the moving load, therefore, the moving load is considered to be motionless relative to the moving system. Combining the governing equations of motion in the moving system and the Fourier transform, the analytical layer-elements for a single layer with a finite thickness and a half-plane are derived in the Fourier transform domain. The global matrix of the problem can be obtained by assembling the analytical layer-element of each layer. The solutions in the integral transform domain are obtained by combining with the boundary conditions. The corresponding solution in the frequency domain is further recovered by applying the inverse Fourier transform. Several examples are given to confirm the accuracy of the proposed method and to illustrate the influences of velocity, depth of the load, layering and reinforced thickness and effects on the dynamic response in layered soils. The following conclusions can be obtained. The vertical displacement and vertical stress increase with the increase of load velocity, and their increments increase rapidly when the load velocity gets close to the shear velocity of soils. Besides, the vertical displacement is affected by the layering of soils and the superstratum is the key factor. The reinforcement of the superstratum has a remarkable result in decreasing the settlement of foundation, but the decrease gets weak when the reinforcement effect increases.