Uncertainty Evaluation of Water Inrush in Karst Tunnels Based on Epistemic Uncertainty with Possibility Theory

In the risk assessment of water inrush in karst tunnel, it is most important to provide an available theoretical model for qualifying the epistemic uncertainties due to a lack of knowledge and information. Firstly, a mechanical model dependent on geology is introduced associating with four parameters, i.e., the elastic modulus , the Poisson ratio , the water differential pressure , and the tunnel radius . Then, a mathematical model representing epistemic uncertainty is represented with probability theory and possibility theory. The methodology was computerized to calculate the distribution of the margin and uncertainty and then to determine the ratio of “margin/uncertainty.†Analyses involving possibility theory and possibility theory are illustrated with the same engineering example used in the presentation indicated above to illustrate the use of probability to represent aleatory and epistemic uncertainty in QMU analyses. The comparison between the uses of possibility theory and probability theory for the representation of aleatory and epistemic uncertainty indicates that the possibility is not only has a better mathematical structure than probability theory but also has some challenges.