On the Vlasov-Leontev Foundation Model for Axial Dynamic Stiffness of a Pile Embedded in a Viscoelastic Soil

In this manuscript, the Vlasov-Leont ' ev foundation model is employed to develop a formulation for an axially loaded pile in a homogeneous linear viscoelastic soil. In the formulation, the soil displacement field because of pile deformation is expressed as a product of separable functions, and the Extended Hamilton's Principle in conjunction with variational calculus is applied to deduce the differential equations describing pile and soil motion along with the associated boundary conditions. Results (dynamic and static) obtained are compared with existing simplified, approximate continuum-based, and rigorous continuum-based formulations, available in literature, for two different types of problems - (i) pile embedded in a half-space and (ii) pile embedded in a soil stratum overlying a rigid-base. From the comparative study, it is found, the present formulation applies to the second type of problems - the problem in which the pile is embedded in a soil stratum overlying a rigid base, and is relevant to practice. The merits and demerits of the formulation procedure are also highlighted and discussed in the manuscript. Further, the effect of including the pile-damping ratio and density, and the varying depth of rigid base on the pile-head stiffness is studied. The effect of incorporating the compressibility coefficient in the formulation is also studied; it is shown by including the coefficient, the present formulation produces accurate results especially as the Poisson's ratio of soil deposit tends to 0.5.