Abstract
In this paper tunnel probabilistic structural analysis (TuPSA) was performed using the first order reliability method (FORM). In TuPSA, a tunnel performance function is defined according to the boundary between the structural stability and instability. Then the performance function is transformed from original space into the standard normal variable space to obtain the design point, reliability index, and also the probability of tunnel failure. In this method, it is possible to consider the design factors as the dependent or independent random parameters with arbitrary probability distributions. A software code is developed to perform the tunnel probabilistic structural analysis (TuPSA) using the FORM. For validation and verification of TuPSA, a typical tunnel example with random joints orientations as well as mechanical properties has been studied. The results of TuPSA were compared with those obtained from Monte-Carlo simulation. The results show, in spite of deterministic analysis which indicates that the rock blocks are stable, that TuPSA resulted in key-blocks failure with certain probabilities. Comparison between probabilistic and deterministic analyses results indicates that probabilistic results, including the design point and probability of failure, are more rational than deterministic factor of safety.
Highlights
Structural instability is the most dominant failure mechanism of underground openings in moderately jointed rock masses
The results show the great capability of first order reliability method (FORM) method to reliability analysis of structural instability with low failure probability instead of Monte-Carlo simulation
By transforming the performance functions from the space spanned by physical random variables into the noncorrelated standard normal random variables space, the reliability index and probability of failure are calculated via optimization techniques
Summary
Structural instability is the most dominant failure mechanism of underground openings in moderately jointed rock masses. The inputs of this function are joints and tunnel axis orientations and the code indicating the block and the binary output indicates the removability of the block: Flag = removable (TO, JD, BC) ,. The results show the great capability of FORM method to reliability analysis of structural instability with low failure probability instead of Monte-Carlo simulation
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