Research On Interaction Between Structure And Transversely Isotropic Saturated Multi-layered Soils In Cartesian Coordinate System

This paper presents a systematical research on Biot's consolidation problem of multi-layered soils, and the interactions between transversely isotropic saturated multi-layered soils and foundations structures such as pile and plate in the Cartesian coordinate system.Starting from the governing equations of three dimensional Biot's consolidation of homogeneous isotropic saturated soils, the ordinary differential equations in matrix form comprising of eight coupled state variables are obtained by taking the Laplace transform with respect to the time t and the double Fourier transform with respect to the coordinate x and y. The transfer matrix relationship of three dimensional Biot's consolidation for homogeneous isotropic saturated soils described by the eight coupled state variables can be obtained by employing the Cayley-Hamilton theorem. Then the method to analyze homogeneous isotropic saturated soils is extended to solve three dimensional Biot's consolidation of transversely isotropic single layer soil. The transfer matrix relationship of three dimensional Biot's consolidation for transversely isotropic single layer soil is acquired by using the same method mentioned above. According to the transfer matrix relationship of basic variables for a single layer soil and combined with the boundary conditions and continuous conditions between layers, the solutions for three dimensional Biot's consolidation of transversely isotropic saturated multi-layered soils are obtained by using the transfer matrix method. Since plane-strain problem can be treated as a special case of three dimensional problem, the solutions for plane-strain problem can be obtained by taking off a variable referred to any of x, y and z.Meanwhile, this paper makes a rewarding attempt to analyze three dimensional Biot's consolidation of saturated multi-layered soils in an uncouple state variables, namely, translating one set of state variables of 8 order into a simpler form including two sets of state variables of 6 order and 2 order, respectively, by introducing intermediate variables. The solutions in the uncoupled state variables presented in this paper reduce the elements of transfer matrix, simplify the deriving process and increase the speed of calculation.Finally, based on the fundamental solutions of Biot's consolidation of transversely isotropic saturated multi-layered soils, the Fredholm integral equation of second kind for the interaction between transversely isotropic saturated multi-layered soils and rectangular piles is established, the relevant numerical analysis is also carried out. When referred to the interaction between transversely isotropic saturated multi-layered soils and rectangular rigid plate, we divide the contacted area between transversely isotropic saturated multi-layered soils and rectangular rigid plate into several smaller sub-areas, the flexible coefficients of each sub-area can be obtained based on the solutions of a uniform loading obtained above. Combining with the contact conditions and equilibrium conditions, the solutions for this problem are derived.