Analysis of pumping in saturated multi-layered soil by using displacement function method

The problem of pumping in saturated multi-layered soil is solved by using the theory of Biot’s consolidation.Starting from the governing equations of axisymmetric Biot’s consolidation,introducing the displacement functions and taking the Laplace and Hankel transform to each variable,the transfer matrix relationship among displacement,stress,excess pore water pressure and flux at z = 0 and any arbitrary depth is obtained.The problem of pumping in saturated multi-layered soil in the transformed domain can be obtained by applying the relationship to each layer of multi-layered soil,and by considering the continuity conditions and boundary conditions of multi-layered soil and pumping horizon plane.The actual solutions can be acquired by inverting the Laplace-Hankel transform.The influence of Poisson’s ratio,pumping method and time on the surface displacement of multi-layered soil is analyzed.