Uncertainty analysis in rock mass classification and its application to reliability evaluation in tunnel construction

Abstract

Creation of underground infrastructures and facilities provides a viable solution to rapid urbanization and population growth with the limited and increasingly congested space on the surface, which has posed a critical challenge to urban population’s demands on the living environment. This includes road and rail transport systems, utility tunnels, water and sewage, parking, storage, and even living quarters. These underground structures are constructed in rock and soil materials, which are not precisely known before excavation. This means that there is intrinsic uncertainty due to the inherently heterogeneous nature of the ground, which can have adverse effects on the design and construction of underground works. Traditional deterministic design methods are based on a limited understanding of this inherent uncertainty, which may result in over- or under- design of underground structures. To address this issue, a systematic assessment of uncertainties in rock mass classification systems has been conducted in this study, in conjunction with a reliability-based approach, to evaluate the stability of underground openings. The rock mass quality Q-system has been used as an example of rock mass classification systems in this study, but the approach can also be applied to other rock mass classifications such as rock mass rating (RMR) and geological strength index (GSI). First, a Markovian prediction model based on the rock mass classification Q-system has been proposed to provide the probabilistic distribution of the rock mass quality Q for unexcavated tunnel sections using the Monte Carlo Simulation (MCS) technique. In addition, an analytical approximation approach has been proposed to derive the statistics (mean, standard deviation, and coefficient of variation) of the Q value based on statistics of Q-parameters (input parameters in the Q-system). The proposed prediction model and analytical approach were applied to a case study of a water tunnel and have been validated by the recorded Q data during tunnel construction. Next, an MCS-based uncertainty analysis framework has also been developed to probabilistically characterize the uncertainty in the rock mass quality Q-system and its propagation to rock mass characterization and ground response evaluation. The Shimizu highway tunnel was used as the case study for validation. The probabilistic distribution of the Q value was obtained using the MCS technique based on relative frequency histograms of the Q-parameters. Similarly, probabilistic estimates of rock mass parameters were also derived with Q-based empirical correlations, which were subsequently used as inputs in numerical models for the evaluation of excavation response. In addition, the probabilistic sensitivity analysis was also conducted in the MCS process to identify the most influential Q-parameters. The effects of the correlation and distribution types of uncertain Q-parameters on the Q value and associated rock mass parameters were also examined. Finally, a reliability assessment with a strain-based failure criterion has been performed using the First Order Reliability Method (FORM) algorithm. The probabilistic critical strain and Q-based empirically estimated tunnel strain were incorporated in the performance function. The Shimizu tunnel case study was also utilized to perform reliability analysis as a basis for the evaluation of tunnel excavation stability. Reliability analysis was also performed using the MCS technique for comparison. In addition, the effects of correlation, distribution types and coefficient of variation in input parameters on the reliability (reliability index and probability of failure) have also been studied. The reliability assessment results show that the Shimizu tunnel was not expected to experience instability after excavation. The excavation stability has also been evaluated using analytical and numerical approaches, and results were consistent with those derived from the reliability approach. Uncertainty and reliability assessment using rock mass classification systems, as presented in this thesis, can probabilistically characterize uncertainties and risks and provide an improved rock mass characterization and excavation response evaluation as compared to traditional use of safety factor. It can also offer insightful information and valuable input for the probabilistic analysis and design of excavation and support strategies as we as construction time and cost estimation for underground structures.