Vlasov–Leont’ev Foundation Model for the Dynamic Analysis of a Laterally Loaded Pile in Homogeneous Viscoelastic Soil

Abstract

The Vlasov–Leont’ev foundation model describes the soil displacement field as a product of separable functions and utilizes the calculus of variation to obtain the governing differential equations describing the motion of the structure/substructure and the soil. In this paper, the model is employed to solve a lateral pile dynamics (in a homogeneous linear viscoelastic soil) problem. The step-by-step formulation is demonstrated, and the results obtained are compared with existing formulations (Winkler-, cone-, approximate continuum–, and rigorous continuum–based formulations) having varying degrees of rigor and accuracy in the literature. The comparison is performed to evaluate the applicability of the present formulation for two class of problems (theories): half-space and soil stratum on a rigid base. It is found that the present formulation is applicable to problems in which the pile is embedded in a soil stratum on a rigid base (relevant to practice). Further, from the comparative results, discussions on the accuracy, computational efficiency, and ability to capture the mechanics of a laterally loaded pile–soil interaction problem are also provided. The advantages and limitations of the formulations are also included in the paper.