Correlation length or scale of fluctuation (SOF) is often used as a primary parameter in defining the spatial correlation characteristics of varying soil properties. However, geotechnical site investigations are rather limited so that proper determination of correlation length is not always possible. The concept of a worst-case correlation length thus has important implications in reliability-based designs. In the case of insufficient information, the worst-case correlation length can be used to conservatively estimate the reliability or probability of failure of geotechnical structures. However, the definition of the worst-case correlation length in the literature is not very clear and has been seen in some investigations to not exist. This paper, in the context of bearing capacity of 3D spatially varying soils, investigates the worst-case correlation length based on different definitions to clarify past findings. Further analyses provide insight into practical applications, where the impact of site sampled data and realistic uncertainties are considered. Using realistic values of the coefficient of variation, and taking account of the distance at which site investigation is likely to occur from the loaded area, a worst-case SOF is identified and found to be similar using all definitions.

The bearing capacity of square and/or rectangular footings in geotechnical foundation designs traditionally is determined based on experimental observations and/or deterministic analysis assuming uniform soil profiles. However, soils are spatially varying, and this spatial variability can significantly affect the bearing capacity of the foundation soils. Probability-based design methods can address this problem explicitly. However, a full three-dimensional (3D) probabilistic simulation, such as that involving the random finite-element method, generally is prohibitive, because it involves numerous Monte Carlo runs of a complicated nonlinear elastoplastic algorithm. This paper developed and validated an approximate analytical method based on local averaging theory and geometric averages of soil properties directly under the footing. It was found that the theoretical prediction of the first two moments of a square footing bearing capacity agrees very well with crude Monte Carlo simulation. The analytical prediction of the probability of a design failure was validated through simulation and can be used directly in reliability-based designs against bearing failure.