Probabilistic Approach for Q-based Ground Support Design

Abstract

For tunnel, cavern, and shaft design, the inherent variability in a given rock mass domain makes accurately estimating rock quality and support requirements difficult. The Q system developed by Barton provides a method of quantifiably classifying rock quality. However, the input parameters are somewhat subjective and variable within a rock mass, thus introducing uncertainty. A methodology was developed incorporating a statistical analysis of measured Q input parameters and Monte Carlo Simulation (MCS) to perform a probabilistic ground support design with a measure of quantifiable uncertainty. In the statistical analysis, histograms of logged field data were used to estimate the distribution type and calculate the mean and standard deviation for each parameter, becoming the inputs for the MCS. Using the mathematical program MATLAB, probability and cumulative density functions were developed and used to perform a probabilistic assessment of Q and subsequent ground support. The method was applied to two case studies, illustrating the approach to estimate rock quality considering uncertainty within a given rock mass domain. Finite Element Modelling (FEM) was used to evaluate the mean Q rock support performance in a range of rock conditions for a specific case study. The Discrete Fracture Network concept was used to model the interaction of individual blocks in the rock mass, with a direct correlation to Q. The approach presents a methodology for analyzing the variability and uncertainty in a rock mass and provide insight into the design criteria for ground support in underground excavations.