Settlement predictions of footings on sands using probabilistic analysis

The design of footings on sands is often controlled by settlement rather than bearing capacity. Therefore, settlement predictions are essential in the design of shallow foundations. However, predicted settlements of footings are highly dependent on the chosen elastic modulus and the used method. This paper presents the use of probabilistic analysis to evaluate the variability of predicted settlements of footings on sands, focusing on the load curve (predicted settlements) characterization. Three methodologies, the first- and second-order second-moment (FOSM and SOSM), and Monte Carlo simulation (MCS), for calculating the mean and variance of the estimated settlements through Schmertmann (1970)'s equation, are presented and discussed. The soil beneath the footing is treated as an uncorrelated layered material, so the total settlement and variance are found by adding up the increments of the layers. The deformability modulus (ESi) is considered as the only independent random variable. As an example of application, a hypothetical case of a typical subsoil in the state of Espirito Santo, southeast of Brazil, is evaluated. The results indicate that there is a significant similarity between the SOSM and MCS methods, while the FOSM method underestimates the results due to the non-consideration of the high-order terms in Taylor's series. The contribution of the knowledge of the uncertainties in settlement prediction can provide a safer design.