Monte Carlo simulation (MCS)-based uncertainty analysis of rock mass quality Q in underground construction

Abstract

Uncertainties in a rock mass quality measure are due largely to the inherently heterogeneous nature of the rock mass itself. Traditional deterministic methods for the assessment of rock mass quality are not based upon a complete understanding of these inherent uncertainties, which can result in adverse impact on overall design performance. To address this problem, a Monte Carlo simulation (MCS)-based uncertainty analysis framework is proposed in this study to probabilistically quantify the uncertainties in the Q-system of rock mass classification. The proposed framework is then implemented in a highway tunnel case study. The probability distribution of the Q-value is obtained using the MCS technique in which the relative frequency histograms of the input parameters are used to probabilistically assess the rock mass properties and responses with appropriate empirical correlations. The probabilistic estimates of the rock mass properties are also adopted as the input for a finite element model for probabilistic evaluation of the excavation-induced tunnel displacement. In addition, a probabilistic sensitivity analysis is conducted to rank the relative importance of the input parameters in the Q-system according to the regression coefficients, Spearman’s rank-order correlation coefficients, contributions to variance and effects on output mean. The effects of the distribution types of uncertain input parameters in the Q-system are also examined. The proposed framework is shown to be capable of systematically assessing the uncertainty in the rock mass quality measure before construction as well as providing insightful information for the probabilistic evaluation of the ground response and support performance of underground structures. Although applied specifically to the Q-system, the proposed probabilistic framework should also be applicable to other rock mass classification systems.