Studies On Dynamic Interactions Of Saturated Soil-beam Or Saturated Soil-plate

The studies on dynamic interaction of saturated soil-foundation are related to many subjects, for example, mathematics, mechanics, geotechnical engineering, and so on. The studies are of not only importantly scientific values, but also extensively applied values in civil engineering.Using mechanics of continuum and the method of space average, the basic equations of transversely isotropic fluid-saturated poroelastic media are obtained in this article, in terms of stress-strain's relations, kinetics equations, continuity equations and generalized Darcy law. The basic equations are of strict basics, and are comprehended more easily. Comparing those equations with Biot's equations, the relations of elastic constants B\ with elastic constants c_ij are given, and the explicit expressions of Biot's parameters m_i and r_i, i.e., the relations of Biot's parameters with permeability, viscosity and porosity, are obtained. Those works will be helpful to bring the confusions in the present lituratures to an end.The interactions of transversely isotropic saturated poro-semiplane with beam are analized. By introducing the functionΦinto the basic equations of transversely isotropic saturated poro-semiplane, the basic equations are simplified to a 6-order governing equation. By use of Fourier transforms, the dynamic responses of the saturated poro-semiplane are studied, and the dynamic interactions between the saturated poro-semiplane and the infinite beams are analyzed. By the aid of Fourier sine series, the harmonic vibrations of the finite beams on the transversely isotropic saturated poro-semiplane are investigated. The effects of the vibration frequency, the inside friction and the beam's stiffness of beam on the beam's deflections are discussed. The interactions of transversely isotropic saturated porous half-space with rectangular plate are investigated, By introducing three scalar functions and using the double Fourier transforms, the basic equations of transversely isotropic saturated porous half-space are simplified to a 6-order and a 2-order governing equations. Solving the governing equations, the analytical solutions of the half-space are obtained. The double Fourier series with additional terms are selected as the solutions of rectangular plates and the settlement of the half-space's surface under the plates is expanded to the double Fourier series of the same formations. Using the former results and the continuous condition of plate-foundation displace, the dynamic responses of rectangle plates on transversely isotropic saturated porous half-space are analyzed.Dynamic interactions between thin circular plates or moderately thick circular plates, and transversely isotropic saturated porous half-space are also investigated in this paper. By introducing three scalar functions and using the Hankel transforms, the basic equations of transversely isotropic saturated porous half-space are simplified to a 6-order and a 2-order governing equations. Solving the governing equations, the analytical solutions of the half-space are obtained. After the deflection of plate, the load, the reactive force of soil ground, and the settlement of half-space's surface under the plate are all expanded to the double Fourier-Bessel series, the series solutions of the dynamic interactions are obtained.The methods of Fourier series used in this article are generized methods. When the problems of dynamic interaction between foundations are changed to the problems of numerical integral and integral equations, the same problems are all changed to the problems of numerical integral and algebraic equations in this artical. The methods of Fourier series are easier and simpler than the methods used in other lituratues.