Study On Theory Of Saturated Elastic Half-Space For Soil-Foundation Dynamic Interaction

Soil-structure dynamic interaction is the dynamic responding of soils, foundation and superstructures excited by wave propagation in soils and structure virtually and, dynamic analysis of soil-foundation interaction is the key problem in studying soil-structure interaction. In the dissertation, a systematic study on the 3-D dynamic responding of transversely isotropic saturated half-space/layered saturated strata produced by harmonic loading and seismic loading and dynamic interaction of saturated soils- foundation (circular plate) based on Biot's theory for fluid-saturated porous media and the model of elastic half-space.The dissertation starts with the analysis for Biot's theory for transversely isotropic fluid-saturated porous media. A group of governing equations and parameters is presented. Thereafter, the 3-D Biot's wave equations in cylindrical coordinate for transversely isotropic saturated poroelastic media are transformed into the two uncoupling governing different equations of 6-order and 2-order respectively by means of the displacement functions. Then, the differential equations are solved by the Fourier expanding and Hankel integral transform method. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media are obtained. Furthermore, a systematic study on Lamb's problems in transversely isotropic saturated half-space is performed. Integral solutions for surface radial, vertical and tangentical displacements are obtained both in the case of drained surface and in the case of undrained surface excited by vertical and tangentical harmonic resources respectively. Numerical results show the obvious difference between the model of isotropic saturated poroelastic media and that of transversely isotropic saturated poroelastic media.Secondly, the work is extended to the case of a general harmonic source distributing on arbitrary surface zone of the half-space with transversely isotropic saturated poroelastic half-space. Using the displacement functions and the technique of double Fourier transform, the governing differential equations for transverselyisotropic saturated poroelastic media are easily solved and , the Fourier transformed stress and displacement solutions coorespondingly are obtained. Then, under the boundary conditions, the analytical solutions for half-space are presented.Thirdly, the method to calculate the 3-D dynamic responding of layered transversely isotropic saturated soils to an arbitrary buried source in cylindrical coordinate as well as to an arbitrary harmonious source in rectangular coordinate is presented respectively. Based on Biot's wave theory, the 3-D wave equations in cylindrical coordinate for transversely isotropic saturated poroelastic media are transformed into a group of governing different equations with 1-order by the Fourier expanding with respect to azimuth and Hankel integral transform method or by the double Fourier transform method with respect to horizontal coordinates in rectangular coordinate. Then, transfer matrixes within layered media are derived under the continuous conditions, drainage conditions and the boundary conditions. By the transfer matrixes, the solutions of 3-d dynamic response of layered transversely isotropic saturated soils are presented.Fourthly, the solutions for non-axisymmetical dynamic responding of elastic circular plate (thin and thick plate)rested on transversely isotropic saturated half-space/layered ground subjected to arbitrary harmonic loading are presented. Under the contact conditions, the problem leads to a pair of dual integral equations which describs the mixed boundary-value problem. Furthermore, the dual integral equations can be reduced to the Fredholm integral equations of the second kind and solved by numerical procedure. At the end of this chapter, the numerical analysis for dynamic interaction characters of saturated half-space/layered ground and circular plate is evaluated.Finally, the solutions for 3-D dynamic responding of elastic rect...