Reliability analysis of beams on random elastic foundations

The classical problem of a beam on an elastic foundation has long been of practical interest to geotechnical engineers, because it provides a framework for computing deflections not only of foundations, but also of vertically oriented laterally loaded piles. The supporting soil can be modelled as an elastic medium, which can be calibrated to represent the stiffness of the soils adjacent to the beam (or pile). The objective of this paper is to study the influence of spatially random soil stiffness on deformations of transversely loaded homogeneous piles and beams, using a combination of finite-element analysis, random field theory and Monte Carlo simulations. Following code validation against alternative solutions, the method investigates how the statistically defined soil stiffness (mean, standard deviation and spatial correlation length) influences the mean and standard deviation of pile or beam deflection. The goal of such an approach is to estimate the probability of deflections exceeding some design threshold.