Risk analysis in tunneling with imprecise probabilities
Due to the inherent uncertainties in ground and groundwater conditions, tunnel projects often have to face potential risks of cost overrun or schedule delay. Risk analysis has become a required tool (by insurers, Federal Transit Administration, etc.) to identify and quantify risk, as well as visualize causes and effects, and the course (chain) of events. Various efforts have been made to risk assessment and analysis by using conventional methodologies with precise probabilities. However, because of limited information or experience in similar tunnel projects, available evidence in risk assessment and analysis usually relies on judgments from experienced engineers and experts. As a result, imprecision is involved in probability evaluations. The intention of this study is to explore the use of the theory of imprecise probability as applied to risk analysis in tunneling. The goal of the methodologies proposed in this study is to deal with imprecise information without forcing the experts to commit to assessments that they do not feel comfortable with or the analyst to pick a single distribution when the available data does not warrant such precision. After a brief introduction to the theory of imprecise probability, different types of interaction between variables are studied, including unknown interaction, different types of independence, and correlated variables. Various algorithms aiming at achieving upper and lower bounds on previsions and conditional probabilities with assumed interaction type are proposed. Then, methodologies have been developed for risk registers, event trees, fault trees, and decision trees, i.e. the standard tools in risk assessment for underground projects. Corresponding algorithms are developed and illustrated by examples. Finally, several case histories of risk analysis in tunneling are revisited by using the methodologies developed in this study. All results obtained based on imprecise probabilities are compared with the results from precise probabilities.