A polymorphic uncertainty model is proposed considering the combined effect of aleatory and epistemic uncertainties of rock properties on the stability analysis of rock tunnels. The model incorporates fuzzy logic to represent epistemic uncertainties in the Geological Strength Index (GSI), transformational uncertainty of empirical models, systematic uncertainties due to discrepancy between field and laboratory conditions, and stochastic methods to represent aleatory uncertain properties. Further, detailed guidelines are proposed for the characterization and fuzzification of epistemic uncertain properties. An extended Convergence-Confinement Method (CCM) is proposed and illustrated by performing the stability analysis of a railway tunnel in Jammu and Kashmir, India under the framework of combined probabilistic and non-probabilistic methods. Further, the results obtained from the developed methodology were systematically compared with those of traditional reliability-based results and it was concluded that the proposed methodology is in order with the available input parameters having different uncertainty types.
Rock mechanics has always found it difficult and demanding to model uncertainties relating to rock characteristics and model parameters. In this discipline, the application of probabilistic analysis paired with reliability techniques such as First/Second-Order Reliability Method Point Estimate Methods (PEMs), Monte-Carlo Simulation (MCS), etc. (Hoek 1999 and Tiwari & Latha 2017) are the most renowned.
There are primarily two sorts of sources of uncertainty for intact rock and rock mass attributes. Aleatory uncertainty (caused by innate variability) and epistemic uncertainty (resulting from a lack of knowledge) (Bedi 2014). Systematic uncertainties resulting from variations in the laboratory and in-situ conditions and transformational uncertainties associated with the empirical relations are subcategories of epistemic uncertainty (Spross 2016 and Tiwari & Latha 2019). Because there is a lack of accurate or sufficient rock data, probabilistic approaches cannot accurately represent the uncertainties resulting from many sources. Numerous researchers have employed non-stochastic techniques to take into account epistemic uncertainties, such as fuzzy set theory and intervals (Alefeld & Mayer 2000; Park et al. 2012). However, accurate uncertainty modelling of structural response parameters of rock structure necessitates the complete uncertainty (epistemic + aleatory) quantification in intact rock and rock mass properties.
