Quasi-static interaction between non-uniform beams and anisotropic permeable saturated multilayered soils with elastic superstrata

The soil above the water table is considered as elastic superstrata, and the soil below the water is regarded as a multilayered saturated soil with anisotropic permeability. The analytical layer element method is applied to obtain the fundamental solution of the soils, and the finite element method is used to solve the Timoshenko or non-uniform beam. Taking a Laplace transformation for the global matrix equation of the beam, the coupling equations for the soil-beam interaction are derived in the Laplace transformed domain by considering the displacement harmony conditions. By solving the coupling equations, the solution in the transformed domain can be achieved. With the aid of Laplace inverse transformation, the solution in the physical domain is obtained. Finally, the influence of the consolidation time and the thickness of the elastic superstrata as well as the application of varying cross-sections on the quasi-static interaction between the beams and the soils are investigated.