Application of Bayesian Inference and Observational Method for Uncertainty Reduction in the Bearing Pressure–Settlement Relationship of Spread Footings on Clay

Abstract

The design of spread footings on a clayey soil bed are usually governed by the allowable settlement criterion at a serviceability limit state (SLS). Therefore, the bearing pressure against settlement curve obtained from the plate load test (PLT)s are used for such designs. This paper presents a probabilistic hyperbolic model for the bearing pressure–settlement curve. A database of 61 PLTs performed at various locations were collected from the literature and were used to prepare the global probabilistic model. For the likelihood function, a site-specific local data was prepared by performing a PLT at a site. Subsequently, the global model was updated with the local data by means of Bayesian inference. A footing load test (FLT) was also performed at the same site at a distance of 32 meters from the location of the PLT. The first few data points of the FLT were used to apply observational method to predict the behavior of the footing at higher loadings. Finally, the Bayesian inference was performed along with the observational method to further reduce the uncertainties of the model parameters. A comparison of all the methods showed a close prediction of the actual footing behavior by the combination of Bayesian inference and observational method. The uncertainties of the model parameters were also found to be reduced. When a spread footing lies on a clayey soil bed, its allowable bearing pressure is governed by a permissible settlement value fixed by the serviceability requirements. This paper presents four models for estimating the bearing pressure corresponding to a given settlement value. The proposed models are: (1) the global probabilistic model, (2) Bayesian inference with plate load test (PLT), (3) observational method, and (4) Bayesian inference with observational method. The first model uses a global database. For the second model, a PLT is performed at the site and the global model is updated with the local data. In the third method, the response of an actual footing at the initial loads of a staged construction is used to predict its future behavior at higher loads. In the fourth method, a combination of the second and the third method is done to get the most accurate prediction.