Load and Resistance Separation for Reliability Based Design in Rock Engineering

摘要

The existence of variability in rock mass properties is ubiquitous in rock engineering. As such, probabilistic analysis is required for accurate evaluation of the safety of designs, rather than the use of working-stress design with factors of safety. The fundamental problem in reliability-based design of structures is the evaluation of the probability of the resistance of the structure being less than the effect of applied loads. Customary approaches to this assume the resistance and effect of load to be independent (i.e. one is not a function of the other). However, in rock engineering this elementary characteristic of independence may not be valid, as both the load and the strength of rock may be functions of the minor principal stress. In this paper, and using the example of a tunnel in rock, we show how this problem may be resolved through a novel interpretation of the elementary structural problem. We develop and present a non-iterative technique that allows calculation of the probability of attaining rock peak strength and the evaluation of the design point (i.e. the conditions giving the greatest probability of failure). Using scenarios of differing rock strength and variability, we demonstrate the efficacy of the proposed method by comparing it to the recognised techniques of Monte Carlo simulation and the first-order reliability method.