A coupled finite–hierarchic infinite element method for an inhomogeneous transversely isotropic soil layer under irregularly distributed strip load

In this paper, a coupled finite–hierarchic infinite element procedure is presented for an inhomogeneous transversely isotropic soil layer under irregularly distributed strip load. Elasticity and shear moduli follow a power law variation with depth. Quadratic quadrangular finite elements are coupled with a coordinate ascent hierarchic infinite element along the bounded edge using a least square approximation. The element mesh is fixed. Convergence is reached by increasing the polynomial degree. Novel results are presented for the vertical displacement and normal stress induced by uniform, parabolic, and triangular strip loads. The method is found to converge rapidly when the polynomial degree is increased. The calculated results for a homogeneous isotropic soil layer under a triangular strip load are compared with exact solutions and show excellent agreement. A parametric analysis reveals that inhomogeneity, transverse isotropy, layer depth, and form of strip load have an important effect on the soil layer physical behavior.