Analysis of underground rock excavations accounting for uncertainty

• Main Author: Liu, Huaxin
• Other Authors: Low Bak Kong
• Format: Theses and Dissertations
• Language: English
• Published: 2018
• Subjects: DRNTU::Engineering::Civil engineering
• Online Access: http://hdl.handle.net/10356/73348
• Institution: Nanyang Technological University

In engineering practice, widely used methods for the analysis and design of underground projects are deterministic approaches, which overlook the stochastic nature of rock mass properties and in situ stress conditions. Probabilistic analysis is more reasonable since the uncertainties can be considered explicitly. Therefore, the main purpose of this thesis is to investigate the reliability analysis of underground excavation problems. A simple closed-form solution (the Duncan-Fama solution) for circular tunnels in Mohr-Coulomb grounds is used to illustrate various reliability methods, including the first-order reliability method (FORM), direct Monte Carlo simulation (MCS), Latin Hypercube Sampling (LHS), MCS with importance sampling and polynomial response surface method (RSM), which provides the basis for the content in later chapters. For a special case where the design point is far away from the mean value point, a numerical error problem is encountered for the linear RSM. The problem is caused by sampling in the unrealistic domain of the input parameters. A multiple-step response surface method (RSM) is proposed to solve this numerical error problem. The reliability analysis of single limit state is then extended to the system reliability evaluation which considers the interaction among different limit states. The iterative solution for a circular tunnel reinforced by end-anchored rockbolts is used to illustrate the system reliability analysis, in which the tensile force of the rockbolt, tunnel convergence and plastic zone size are considered as three performance functions. The bimodal bounds method and the multivariate normal cumulative distribution function (mvncdf) method are compared. It is shown that the second-order reliability method (SORM) can be used to refine the reliability indices from FORM and to improve the accuracy of the estimated system probability of failure. The optimal rockbolt installation position corresponds to the smallest system probability of failure. For problems where closed-form solutions are not available, a modified hybrid approach using the linear RSM to locate the design point and artificial neural network (ANN) to approximate the actual limit state surface (LSS) is proposed. Comparison with the second-order RSM shows that the proposed approach is efficient, accurate and robust for the system reliability evaluation. How reliability-based design (RBD) can provide insights to the partial factor design approach, such as the Eurocode 7 (EC7), is discussed and illustrated using various tunnelling problems. The first-order second-moment method (FOSM) and the point estimate method (PEM) may produce non-unique reliability indices for different but mathematically equivalent limit state functions. FORM is more consistent than FOSM and PEM and is suggested to be used in RBD. The intuitive expanding ellipsoid perspective and the efficient constrained optimization method for FORM help overcome the conceptual and computational barriers for practitioners. The structurally-controlled failure mechanism including the case of a symmetrical roof wedge and the stress-controlled failure mechanism including the cases of a lined circular tunnel and a rockbolt-reinforced tunnel are used to show the insights from RBD. RBD via FORM can determine the role (resistance or load factor) of input parameters on a case-by-case basis in ways that prescribed partial factors cannot. Besides, different case studies show that RBD can play a complementary role to the partial factor design approach when the correlation of the input parameters should be considered, when uncertainties of geometrical parameters are involved, when the rock parameters that are not covered in the design code are involved and when the same parameter has opposite effects on different performance functions. A real-life underground excavation project, Jurong Rock Cavern (JRC) in Singapore, is presented to show how reliability analysis is conducted for a real case study. The statistics of rock engineering properties are characterized using the site investigation and laboratory test results. The deterministic analysis using the finite difference software FLAC3D shows that the estimate of the rock mass Young’s modulus has a great influence on the cavern displacement. It is shown that the simplified 2D analysis using the stress reduction method can simulate the 3D excavation and support installation process. The longitudinal deformation profile (LDP) from 3D analysis using FLAC3D can be used to determine the stress reduction coefficient for the simplified 2D analysis. For JRC, the support system including fully-grouted rockbolts and shotcrete has limited effect on the cavern displacement because of the late installation of the support and the good quality of the rock mass. FORM and second-order RSM with cross terms are used to calculate the reliability index and design point for JRC project. The uniaxial compressive strength (UCS) and elastic modulus (EM) data summarized for JRC sedimentary rocks and some data collected for the igneous rocks are used to characterize the spatial variability of rock properties. The autocorrelation structures are selected using a Bayesian model class selection approach and the scales of fluctuation for these two parameters are estimated using a Bayesian updating method. The results show that the autocorrelation structures for UCS and EM could be described by a single exponential autocorrelation function. The scales of fluctuation for UCS and EM range from 0.3 m to 8.0 m and from 0.3 m to 8.4 m, respectively. These results serve as guidelines for selecting proper autocorrelation functions and autocorrelation distances for rock properties in the reliability analysis and could also be used as prior information for quantifying the spatial variability of rock properties in a Bayesian framework.