Characterizing geotechnical model uncertainty

There are two types of uncertainty that could affect the credibility of a geotechnical analysis, i.e., uncertainty in model input parameters, and uncertainty associated with the prediction model. This research provides theories, solutions, and application examples on model uncertainty characterization utilizing observed performance data from similar geotechnical systems when model input parameters are uncertain and when observed performance cab be subjected to measurement error. This research starts with a literature review on model uncertainty characterization and computational techniques for implementing Bayesian methods. A Bayesian framework is then proposed to identify geotechnical model uncertainty considering both uncertainty in model input parameters and observation uncertainty. In the proposed framework, the model uncertainty parameters are modeled as random variables, and their distributions are updated simultaneously with uncertain model input parameters and uncertain system performance using the observed performance data. To facilitate professional application, a simplified Bayesian formulation involves less computational work is also suggested to characterize model uncertainty approximately. Three methods are developed for model uncertainty characterization, i.e., (1) a maximum posterior density method in the simplified Bayesian framework, (2) a grid calculation method in the simplified Bayesian framework, and (3) Markov chain Monte Carlo (MCMC) simulation in the original Bayesian framework. Among the three methods, MCMC simulation in the original Bayesian framework is most accurate as it depends on fewer assumptions. The maximum posterior density method is less accurate than the grid calculation method as it is not only based on the approximate formulation but also based on the large sample approximation, whereas the grid calculation method only depends on the approximate formulation. The advantage of the maximum posterior density method resides in its ease of implementation. The three methods are of various degrees of theoretical stringency and application convenience. Three application examples are used to thoroughly illustrate these methods for model uncertainty characterization utilizing different types of observed data, and to demonstrate how model uncertainty characterization can help the current geotechnical practice. Particularly, in the first example the model uncertainty of limit equilibrium methods is characterized using point observed data. It is found the knowledge on model uncertainty is crucial for a site-specific back analysis of slope failure. If such knowledge is poor, most observed information would be allocated to update the model uncertainty parameters rather than model input parameters. When there is good knowledge on model uncertainty, most information would be allocated to update the site-specific model input parameters. In such a case, model uncertainty parameters will not be updated much even when they are incorporated in the updating process. Nevertheless, the back analysis of slope failure can be implemented in a simpler manner by excluding the model uncertainty parameters from the updating process. Based on this idea, two easy-to-apply procedures for back analysis of multiple slope stability parameters are suggested. The second example shows the prediction of pile capacity is dominated by model uncertainty. How to treat those piles that were not loaded to failure in pile load tests has important effect on model uncertainty characterization. To incorporate the model uncertainty in daily design, partial factors are developed based on the characterized model uncertainty using a two stage procedure, i.e., (1) calculating the partial factors based on reliability analysis, and (2) adjusting these partial factors to be in compliance with partial factors for loads specified in the structural design codes. After the partial factors are obtained, regression analyses are further conducted to reveal the relationship between the partial factors and the uncertainty structure in the design. In the third example, the model uncertainty of a liquefaction model is evaluated using fully censored data. In particular, how to consider the bias in the database is addressed. This example also illustrates the conceptual difference between reliability analyses with and without considering model uncertainty. If the model uncertainty is not considered, a single limit state surface is drawn to separate the failure region from the safe region in the space of design parameters. If model uncertainty is considered, multiple limit state surfaces with varying probabilities are drawn. If model uncertainty is neglected, the results from the reliability analysis would be over-confident