Keywords: Biot theory, moving load, multilayered ground, semi-analytical approach, Fourier transform, wavenumber results.

The problem of determining the response of a soil under the action of moving loads has received considerable attention in the last few decades. Research activities in this area have been motivated by the need to determine the vibratory motion on the ground surface, and at depth, caused by moving vehicles. Moreover, high-speed trains are becoming increasingly common and freight trains increasingly heavier. Combined with this fact and the observation that the Rayleigh wave speeds are slower in soft soils, we note that the study of moving loads is of great importance for environmental and geotechnical engineering. Some problems of high vibrations induced by moving loads have been observed in different countries.

In the framework of moving loads, many authors have worked on ground modelled as viscoelastic homogeneous or multilayered viscoelastic media. Nevertheless, it can be of interest to model the ground more accurately. In fact, the soil is composed of a solid skeleton and pore space filled with fluid(s). The Biot theory is widely used to describe the macroscopic two-phase continuum. The interest in the moving load problem over poroviscoelastic grounds is quite recent and only a few papers are available on this subject.

In the past, the authors studied the case of viscoelastic multilayered media subjected to moving loads. They have recently extended this research to a poroviscoelastic half-space. The work presented in this paper is an extension of the previous approach to poroviscoelastic multilayered ground. The authors propose a three-dimensional semi-analytical approach to study the displacements induced by a harmonic rectangular load moving at constant speed over the surface of a poroviscoelastic multilayered half-space. The Biot theory including elastic, inertial and viscous couplings is considered. Moreover a modified hysteretic damping is used for the solid phase. Thus, the moving load speed range covers both sub- and super-Rayleigh regimes. The approach uses Helmholtz decompositions for the solid and relative displacements. Moreover, a double Fourier transform on the surface variables of the moving frame of reference is introduced to obtain displacements in the wavenumber domain. Transformed displacements are expressed in terms of incident and reflected waves in each layer and in terms of an incident wave in the half-space. They are written using an algebraic formulation. Boundary conditions are also established with a matrix formulation to link the stresses at each interface to the displacement vector. An assembly process, with continuity of displacements and stresses between each layer, is used for the multilayered system. Transformed displacements are then obtained numerically. Besides, inverse fast Fourier transform is performed to get the displacements in the spatial domain. Results are presented in the wavenumber domain for a stiff half-space and in the spatial domain for stiff and softer half-space and for a softer layer overlying a rigid half-space. Influence of the depth of the layer is studied.

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