Prediction of Probabilistic Settlements by the Perturbation-Based Spectral Stochastic Meshless Local Petrov–Galerkin Method

Originating an attempt of understanding the reliability and serviceability of foundations, an interest of comparing the difference between settlements predicted with and without considering the uncertainty in such as the spatial variability of soil properties is born. This study selectively compares between settlements predicted with and without considering the uncertainty in the spatial variability of Young’s modulus. The tool is a coupling of perturbation expansions of Young moduli and a two-dimensional meshfree weak-strong form in elastostatics. Two further examples show that the spatial variability of Young’s modulus causes apparent difference between probabilistic and deterministic settlement components along the direction of a surcharge. We can derive an autocorrelation function to describe the spatial variability of Young’s modulus and understand how it affects predicted settlements depending upon autocorrelation function values. In addition, the spectral stochastic meshless local Petrov–Galerkin method is a time-saving tool for predicting probabilistic settlements with the uncertainty in the spatial variability of soil properties.