A probabilistic Q-system using the Markov chain to predict rock mass quality in tunneling

Uncertainty in rock mass conditions is mainly caused by the inherently inhomogeneous nature of rock masses. Assessment of rock mass quality without accounting for inherent uncertainty often leads to unnecessary conservatism in design and construction, resulting in excessive cost and schedule overrun. In this study, to advance rock mass quality assessment, a rock mass classification Q-based prediction model to assess probabilistic rock mass quality has been proposed using the Markov chain framework with Monte Carlo simulation. In addition, an analytical approximation approach has also been developed to derive the statistics (mean, standard deviation, and coefficient of variation) of the Q value given statistics of Q parameters in the Markov chain model. The proposed prediction model and analytical calculation approach were applied to a water tunnel. The probabilistic prediction results have been validated by the field recorded Q data during tunnel construction in a probabilistic framework with the use of the accuracy plot where uncertainties are explicitly quantified in the predicted probabilistic model. The proposed Q-based prediction model can assess the rock mass quality in unexcavated tunnel sections using a probabilistic approach to serve as a preliminary site condition indicator.