| Some classical problems of poroelastodynamics are studied systematically in the present paper. At the same time, wave propagation in multilayered poroelastic media is also investigated in the paper. The studies of the paper consist of the following parts.1. Fundamental solutions of poroelastodynamics in the frequency domain have been derived by cheng (1991) for the point force and fluid source singularities in2D and3D, using an analogy between poroelasticity and thermoelasticity. In this paper, a formal derivation is presented based on decomposition method. According the present paper, it is clear that the heat source and the fluid mass source are not equivalent, and only cheng (1991) correctly discerned the difference and correctly constructed the fluid source solution. The decomposition allows the derived fundamental solutions to be separated into a shear and two compressional wave components as well as decomposing a Diracδ function into a rotational and a dilatational part, before they are combined. For the point force solution, each of the isolated wave components contains a term that is not present in the combined wave field; hence can be observable only if the present approach is taken.2. The dynamic reciprocal relationships of poroelastodynamics in frequency-wavenumber domains are established firstly. Then, the relationships among dynamic Green’s functions for a poroelastic half space due to a buried point force and buried fluid source are determined. By using the fundamental solutions for a poroelastic full space, the relevant functions of a free field are obtained for buried vertical point force, buried horizontal point force, and buried fluid source, respectively. The superposition method is applied to obtain dynamic Green’s functions for a poroelastic half space. Dynamic reciprocal relationships can be derived in a frequency-wavenumber domain by the integral equation for dynamic poroelasticity in the frequency domain and by fundamental poroelastodynamic solutions. By these relationships, on one hand, the concise forms of dynamic Green’s functions are obtained in this paper and further we can easily verify the correction of these solutions. On the other hand, it can also give a simple and feasible approach to solve the buried fluid source Green’s functions.3. Based on Biot’s governing equations, through decoupling of the fast and slow dilational, the first-order differential simultaneous equations for the displacement-stress propagation were obtained, which satisfy the kinetics of wave propagation in the multilayer poroelastic saturated media. Both the simultaneous equations and the transfer functions could be degenerated to those for the multilayer single-phase media. With the displacement-stress continuity conditions at the interface between the poroelastic and single-phase media, the interfacial transitional transfer matrix was established by analysis of the propagation of displacement-stress from the poroelastic medium to single-phase medium. The4X6transfer matrix was derived from the6×6transitional transfer matrix of the multilayer poroelastic medium and could be combined with the4X4transfer matrix of single-phase medium.4. Based on Biot theory, using Fourier transform and combining solution matrix of displacement-stress differential equations obtained in the presented paper, we get the general solution form of displacement-stress function in wave number-frequency domain. Then using the interface transition transfer matrix eastablished in the presented paper, conbined the boundary conditions of moving load function and the radiation condition of elastic half-space, we obtained the analytical solutions of dynamic response of two-phase saturated overing on the elastic half-space under the moving load. Finally, using the fast algorithm of discrete Fourier inverse transform, we obtained the related numerical results for soil surface displacement. We also analyze the effect of speed, frequency of moving load and some parameters of soft soil to the surface vertical displacement. |
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