Analytical layer element solutions to plane strain problem of transversely isotropic multilayered soils

Based on the governing equations of plane strain problem, the transfer matrix of a single soil layer of transversely isotropic multilayered soils is obtained by using the Fourier transform and Cayley-Hamilton theorem. Then its exact stiffness matrix is deduced by means of the matrix transformation, which is called analytical layer element. The total stiffness matrix is established on the basis of the principle of finite layer method, and the solutions to the plane strain problem of transversely isotropic multilayered soils in the integral transform domain are obtained by solving it. The actual solutions in the physical domain are acquired by inverting the Fourier transform. The calculated results acquired by corresponding computer program agree fairly well with those by finite element analysis software. Numerical analysis shows that the influence of the stratification and transverse isotropy on the deformation of soils is significant.