Reflection-transmission Matrix Method For The Consolidation Of A Layered Transversely Isotropic Saturated Soil

The natural soil has layered characteristics, and tends to be transversely isotropic. Therefore, the study on the consolidation of the layered transversely isotropic saturated soil(TISS) is of great significance in engineering practice. Throughout this study the static reflection transmission matrix(RTM) method for the layered TISS undergoing axisymmetric and non axisymmetric consolidation is developed. The RTM method has the advantage of small calculation quantity of the transfer matrix(TM) method, moreover, and overcomes numerical instability problems of the TM. Numerical results are given to show the influences of the moduli of the middle layer, modulus ratio()h vηE E, permeability of the middle layer and difference of the permeability in the horizontal and vertical directions of the soil. The main contents of this thesis are included as followed.(1) To develop RTMs for the layered TISS undergoing axisymmetric consolidation, first a system of partial differential equations is established based on the axisymmetric governing equations for the TISS. By means of the Hankel-Laplace integral transform method, the system of partial differential equations is reduced to a system of ordinary differential equations. Using the general solution to the system of ordinary differential equations, the static wave vector corresponding to the state vector of the TISS is introduced and the transfer matrices for the state and wave vectors are defined. The above transfer matrices of wave vectors are combined with the continuity conditions at the interface of layered saturated soil, to establish the RTMs for the aforementioned static wave vector of the layered TISS. It is worth noting that the state vector, static wave vector and transfer matrices for the state and wave vectors for the TISS are all defined in the global coordinate system, so the proposed RTM has a reasonable mechanical meaning.(2) To expand the static RTMs for the layered TISS undergoing asymmetric deformation, according to the features of asymmetric deformation, first the paper introducs an appropriate state vector, and then a partial differential equation of the state vector is established, based on the asymmetric governing equations for the TISS. Applying the Hankel-Laplace transform to this partial differential equation system yields the corresponding ordinary differential equation system. From the general solution of the ordinary differential equation system, the static wave vector, state vector and the transfer matrices for the state and wave vectors for the TISS are defined in the global coordinate system, and then the corresponding RTMs of the layered TISS are established. By means of the transfer matrix of wave vectors and the continuity conditions at the interface of layered saturated soil, the RTMs for the layered TISS undergoing asymmetric deformation are developed. Finally, the RTMs is used to derive solutions of the layered TISS for the asymmetric consolidation subjected to external sources.(3)With the proposed RTM method for the layered TISS, numerical results of axisymmetric and non axisymmetric consolidation are given. To prove the exactness and advantages of the proposed RTM method, our results are compared with some existing results. In the paper, the layered half space consists of three layers, and the stress, displacement and pore pressure of the layered TISS undergoing the vertical load, point fluild and horizontal load are calculated. Numerical results are given to show the influences of the moduli of the middle layer, modulus ratio, permeability of the middle layer and difference of the permeability in the horizontal and vertical directions of the soil.