Characterization of model uncertainties for cantilever retaining walls in sand

Abstract

Because of our geotechnical heritage that is steeped in empirical calibrations, model uncertainties can be significant. Even a simple estimate of the average model bias is crucial for reliability-based design. If the model is conservative, it is obvious that the probabilities of failure calculated subsequently will be biased, because those design situations that belong to the safe domain will be assigned incorrectly to the failure domain, as a result of the built-in conservatism. This paper presents a critical evaluation of model factors for limit equilibrium analysis of cantilever retaining walls in sand. A total of 20 tests were collected from the literature to calibrate a theoretical model. It is important to note that there is no unique way of defining the model factor. Detailed statistical analyses showed that developing a regression equation using the theoretical embedment depth as the predictor variable can produce a significantly higher coefficient of determination, in contrast to other plausible methods. In addition, it was also shown that reasonable variations in theoretical details produce less effect on the degree of model uncertainty than variations in the definition of the model factor. This highlights the importance of choosing the definition of the model factor carefully. A practical reliability-based design approach for cantilever walls in cohesionless soils that can consistently account for the modelling error and uncertainties associated with soil friction angle and wall friction is presented. The proposed approach is very simple to use, as it is almost identical to the US Army Corps of Engineers (1996) approach. The key difference is that a range of rigorously calibrated factors of safety is applied on the friction angle to achieve a consistent reliability index, rather than the original empirically prescribed single value of 1.5.