Statistical Analysis of the Q-system in Different Tunnelling Conditions

R.A. Ziebarth, A.G. Corkum

In the proceedings of: GeoSt. John's 2019: 72nd Canadian Geotechnical Conference

Session: Rock Mechanics

ABSTRACT: Understanding of the quality of a rock mass is essential in determining the expected mode of failure and the support requirement for tunnel and cavern designs. The Q-system quantifies the quality of a rock mass, but due to the complex and varied mechanisms related to ground structure interaction, a single value is unlikely to classify the variety in a rock mass correctly. Statistical methods can account for uncertainty to select the suitable design value for Q instead of a deterministic value, based on estimated Q input parameters. In this study, the Monte Carlo simulation (MCS) method is used to apply statistical analysis to the Q-system. The paper describes the basis and methodology, in conjunction with a case study, to present the use of MCS analysis, of the Q-system, to associate a quantitative level of risk with determining ground support needs for tunnel and cavern excavations.

RÉSUMÉ: La compréhension de la qualité d'une masse rocheuse est essentielle pour déterminer le mode de rupture prévu et les exigences de soutien pour la conception des tunnels et des cavernes. Le système Q quantifie la qualité d'une masse probable qu'une seule valeur puisse classer correctement la variété dans une masse rocheuse. Les méthodes statistiques peuvent tenir compte de l'incertitude pour choisir la valeur de calcul appropriée pour Q au lieu d'une valeur déterministe, en fonction des paramètres d'entrée Q estimés. Dans cette étude, la méthode de simulation de Monte Carlo (MCS) est utilisée pour appliquer l'analyse statistique au système qualité. Le document décrit la base et la méthodologie, en conjonction avec une étude de cas, pour présenter l'utilisation de l'analyse MCS, du système Q, afin d'associer un niveau quantitatif de risque à la détermination des besoins d'appui au sol pour les excavations en tunnel et en caverne. 1. INTRODUCTION In tunnel and cavern design, identifying the quality of a rock mass is essential to both determining the dominant mode of failure and adequate ground support to manage it. Empirical classification systems present a quantifiable representation of the rock mass which recommends ground support measures; however, is it advisable to place a single value that classifies the quality of an entire rock mass? Multiple conservative estimations of input parameters to determine rock quality can lead to redundancy, and overestimation of support requirements. Two of the most widely used empirical classification systems are the Rock Mass Quality Index (Q) (Barton et al. 1974) and Rock Mass Rating (RMR) (Bieniawski, 1989). The Q-system considers multiple parameters, such as joint characteristics and stress regime, to classify the overall quality of a rock mass and provide ground support recommendations. A single Q input parameter, such as joint roughness (Jr), does not wholly define an entire rock mass, but it can significantly affect the overall rating. The Q-system relies on visual observation, instead of an analytical calculation or numerical modelling, which introduces greater potential for human error to affect the estimation. Complex and varied mechanisms related to ground interaction make considering a single value for a Q parameter impractical and can lead to over, or under, evaluation of Q. If a design is believed to be conservative, to decrease the quantity of rock support provides no accurate measurement of its effectiveness. Facilitating the planning process of ground support with statistical analysis reduces the potential to under, or over, estimate the quality of the rock mass. Ground support recommendations, for Q, are directly correlated to the performance of historical case data, and the majority of the existing data for the Q-system are tunnels from the Scandinavia region. Different conditions can significantly affect the performance of ground support, which can be problematic, leading to the question of how conservative a designer should be (Potvin, 2015). Palmstrom and Broch (2006) performed a detailed review of the limitations of the Q-system, and one major takeaway was that the classification system was most accurate in moderately fractured rock. Specific scenarios can see a substantial alteration in the support installed to recommendations by the Q-system, such as Hawkesbury Sandstone, where Q recommended substantially lower support than what was adopted at five specific sites (Pells, 2002). Overall, empirical analysis is reliant on the capabilities of the investigator. Statistical methods can provide an alternative which can enhance the classification system by allowing a quantifiable level of risk to be estimated instead of relying on judgement alone. In this paper, the idea of statistical analysis methods to facilitate the planning process of ground support will be discussed. Monte Carlo Simulation (MCS), considering all measured Q input parameters as independent variables, was implemented to develop probability (PDF) and cumulative distribution function (CDF) curves of Q, creating an intuitive method for determining the rock mass quality. A case study on the Norwegian Underground

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