Geotechnical reliability analysis with limited data: Consideration of model selection uncertainty

• Importance of geotechnical model selection uncertainty is highlighted
• A versatile method is used to develop candidate probability models
• Model selection uncertainty is quantified based on Bayes’ theorem
• A model combination technique is used to consider model selection uncertainty.

The limited amount of data available in geotechnical practice makes it difficult to identify a unique probability model for the joint distribution of uncertain variables. Yet, the calculated failure probability can be sensitive to the probability model used, even if different models are calibrated based on the same data. The model selection uncertainty is a poorly understood area of research in current geotechnical practice. In this study, we show how to construct candidate probability models based upon the copula theory to more realistically model the soil data with explicit consideration of the possible non-linear dependence relationship between random variables. The authors used a Bayesian method to quantify the model selection uncertainty and to compare the validity of the candidate models. A model averaging method that combines predictions from competing models was then developed to deal with the situation when the effect of model selection uncertainty cannot be neglected. Averaging over the reliability index seems more plausible than averaging over the failure probability in geotechnical reliability analyses. To reduce the computational work, models with significantly less model probabilities can be removed from the model averaging process without an obvious effect on the prediction accuracy.