Analysis of Beams on Heterogeneous and Nonlinear Soil

Abstract

A new method for nonlinear analysis of Euler-Bernoulli beams resting on heterogeneous, multilayered soil is presented. The governing differential equations for beam and soil displacements are obtained using the principle of virtual work, and these equations are solved using one-dimensional finite-element and finite-difference methods. Using the analysis, beam displacements can be obtained as a nonlinear function of applied loads if the beam and soil geometry and properties are known. The distinct feature of the analysis is that beam responses with accuracy comparable with those obtained from equivalent two-dimensional finite-element analysis are obtained within seconds. Examples illustrate how the proposed method can be applied in practice to obtain beam displacements in soil deposits that are characterized with nonlinear stress-strain relationships, have multiple layers, and have a modulus varying spatially within each soil layer. Parametric studies are performed that highlight the effects of soil layering and nonlinearity on the beam response.