Interaction Between Structure And Saturated Multi-layered Transversely Isotropic Soils In Cylindrical Coordinate System

This paper presents a systematic research on the interaction between saturated layered transversely isotropic soils and foundation structure such as pile and plate in the cylindrical coordinate system.Firstly, this paper studies on the non-axisymmetric Biot consolidation of saturated layered homogeneous isotropic and transversely isotropic soils, respectively. From the basic governing equations of homogeneous isotropic and transversely isotropic soils in the cylindrical coordinate system, a matrix ordinary differential equation of three-dimensional consolidation is obtained by employing the Laplace transform to the variable of time t together with the technique of the Fourier expansions with respect to coordinateθand the Hankel transform with respect to coordinate r. By solving the matrix ordinary differential equation, the obvious transfer matrix for a single layered homogeneous isotropic soil and the hidden transfer matrix for a single layered transversely isotropic soil are obtained. Based on the continuity and the boundary conditions, the transfer matrix method is utilized to derive the solution for the multi-layered soils in the transformed domain. By the inversion of the Hankel transform and the Laplace transform, the solution for the three-dimensional consolidation problems in the physical domain is obtained. Moreover, the calculation of Biot consolidation of saturated layered transversely isotropic soils is simplified, i.e. a 8x8 transfer matrix is transformed into a 6x6 transfer matrix and a 2x2 transfer matrix to reduce the calculation work.Based on the fundamental solution for Biot consolidation of saturated layered transversely isotropic soils, the interaction between saturated layered transversely isotropic soils and the axially loaded single pile is studied by the virtual pile method. By decomposing the problem system into an extended saturated soil system and a virtual pile system, through the strain compatibility condition between the extended saturated soil system and the virtual system at an arbitrary depth z along the pile, and combined the Laplace transform and its convolution, a Fredholm intergral equation of the second kind of the single pile in saturated layered transversely isotropic soils is established. The axial force and diaplacement of the pile are obtained by solving the Fredholm intergral equation. Based on theory of analysing the single pile, the interaction between saturated layered transversely isotropic soils and the axially loaded pile groups is studied. The calculation and analysis are carried out by the computer program.Starting with the basic solution for Biot consolidation of the saturated layered transversely isotropic soils, and using the classical theory of the elastic thin plate, the contact stress formulation is obtained by considering the displacement compatibility and the smooth contact condition. Finally, the analytic solution for the asymmetric loaded plate of any rigidity on the transversely isotropic foundation is obtained. The corresponding computer program is worked out, and the problem for the asymmetric loaded elastic plate on the transversely isotropic foundation is analyzed by this program.Finally, the summary is made out by pointing out some deficiencies and discussing the research prospect for this problem.