A nalytical layer-element method for axisymmetric problem of transversely isotropic multi-layered soils

An analytical layer-element method is proposed to solve the axisymmetric problem of transversely isotropic multi-layered soils. From the basic equations of elasticity and by using the Hankel transform, the transfer matrix of a single soil layer is obtained. Based on the transfer matrix, a precise stiffness matrix of a single soil layer is deduced. By employing the finite element method, we can further get the total stiffness matrix of multi-layered soils. A numerical inversion technique of the Hankel transform is adopted to obtain the exact solutions of axisymmetric problems of transversely isotropic multi-layered soils in the physical domain. Because of no existence of positive functions and the symmetry of the matrix, we can not only simplify the calculation but also improve its accuracy. Finally, a numerical example is given to prove the accuracy of the present results.