Analytical Elastic Solution Based on Fourier Series for a Laterally Confined Granular Column

Abstract

This paper presents an analytical solution methodology for the complete stress and displacement fields of a laterally confined granular column loaded from the top end. The granular column is idealized as a homogeneous isotropic elastic medium with Coulomb’s friction at the lateral boundary. The solution methodology consists of an analytical procedure that incorporates a potential approach with trigonometric series and Bessel functions, finite Fourier transforms and the superposition method, and an iterative algorithm to satisfy the Coulomb’s friction condition at the lateral boundary. Stress and displacement fields are computed for a specific example and found completely consistent with corresponding finite element results. Key characteristics, computational errors, the convergence behavior, and restrictions of the present approach are discussed. The methodology developed herein can be beneficially applied in the validation process of numerical simulation techniques in granular mechanics such as finite or discrete element methods.