Reliability based analysis and design of slopes and tunnels in rock mass

Abstract

Structures in rock mass such as slopes and tunnels form an important segment in the infrastructure development of a country. Rock mass consists of intact rock matrix with numerous discontinuities that can be represented using discontinuum modeling approaches that are capable of simulating the combined interaction of fracturing of intact rock matrix and sliding along the discontinuities when rock mass is subjected to an external force. Discontinuum modeling is adopted for sparsely jointed rock mass, whereas heavy to moderately jointed rock mass is represented as an equivalent continuum material. The thesis focuses on developing methodologies for probabilistic characterization of rock mass response under applied loads for both equivalent continuum and discontinuum approaches, which can then be used for estimating the probability of failure of structures in rock mass. The work conducted in this thesis begins with stability analysis based on rock mass classification system on a jointed rock slope and a tunnel using the deterministic factor of safety approach and two probability approaches – random variable and random field. A comparative study is conducted to assess the ability of these methods to identify failure mechanisms and computational complexity needed for estimation of probability of failure. This is followed by a global sensitivity analysis to obtain the ranking of rock mass parameters (for equivalent continuum approach) according to their impact on the performance measure of the structure that helps in prioritizing data acquisition and gaining insights into the underlying failure mechanism. The study also addresses the challenging issue of probabilistic characterization of rock mass based on rock mass classification system for cases involving limited availability of field and laboratory tests data for both random variable and random field representations and associated reliability analysis. Since limited data causes uncertainty in parameters that govern the probabilistic description of rock mass, a reliability based robust geotechnical design methodology (RGD) is proposed, which provide design parameters that are the least sensitive to the unforeseen variations in the statistics of rock mass parameters. Reliability based RGD ensures the cost-effectiveness of the robust design and is illustrated for selecting a rock bolt design for reinforcement of jointed rock slope and support selection for circular tunnel driven in weak rock mass. A synthetic rock mass obtained by embedding stochastic fracture networks in intact rock matrix is simulated using distinct element method (discontinuum approach) for quantification of uncertainty in strength and deformation parameters of a sparse and non-persistently jointed rock mass. The distinct element method does not require prescribing the constitutive model based on rock mass classification system; instead, the response (stress-strain curves) of the rock mass emerges as a result of the simulation under the prescribed loading conditions. The simulations are conducted under uniaxial loading conditions for increasing sizes of the synthetic rock mass to understand the scale effects and obtain a representative elemental volume (REV). For each size, simulations are performed for different realizations of fracture networks (realizations of orientation, location and length of fractures), which quantifies the uncertainty in strength and deformation parameters. The methodologies presented in this thesis aims to provide a systematic process involving characterization of rock mass parameters and subsequently, reliability based analysis and design of slopes and tunnel in rock mass.