Approximate solution for deformation problems of transversely isotropic multi-layered soils

This study starts with the fundamental elastic equations for transversely isotropic plane problems by dividing the soil strata into a multi-layered finite region and an infinite region using the extended Rayleigh-Ritz method. Each layer of soil mass is treated as a block, and a function is constructed. The stationary values of the function are sought via the variation method in accordance with the principle of minimum potential. Boundary conditions are considered to seek the approximate solution. The solving process adopts higher-order polynomials and the transformation of infinite coordinates, achieving high accurate description of infinity boundary and overcoming the weakness of blindly truncating the infinity structures by the traditional finite element methods. A Mathematical computation program is compiled based on the formula and the solution to the plane strain problems of layered foundation under asymmetric loading is obtained. The sensitivity of the transversely isotropic parameters and layered properties to the deformation of the multi-layered soils is analyzed. Finally, it is applied to the calculation of ground deformation caused by the construction of a diaphragm wall. The research shows that the proposed program can quickly and easily calculate the ground deformation during slurry trench excavation, and is of engineering significance.