Jackknife based generalized resampling reliability approach for rock slopes and tunnels stability analyses with limited data: Theory and applications

Abstract

An efficient resampling reliability approach was developed to consider the effect of statistical uncertainties in input properties arising due to insufficient data when estimating the reliability of rock slopes and tunnels. This approach considers the effect of uncertainties in both distribution parameters (mean and standard deviation) and types of input properties. Further, the approach was generalized to make it capable of analyzing complex problems with explicit/implicit performance functions (PFs), single/multiple PFs, and correlated/non-correlated input properties. It couples resampling statistical tool, i.e. jackknife, with advanced reliability tools like Latin hypercube sampling (LHS), Sobol's global sensitivity, moving least square-response surface method (MLS-RSM), and Nataf's transformation. The developed approach was demonstrated for four cases encompassing different types. Results were compared with a recently developed bootstrap-based resampling reliability approach. The results show that the approach is accurate and significantly efficient compared with the bootstrap-based approach. The proposed approach reflects the effect of statistical uncertainties of input properties by estimating distributions/confidence intervals of reliability index/probability of failure(s) instead of their fixed-point estimates. Further, sufficiently accurate results were obtained by considering uncertainties in distribution parameters only and ignoring those in distribution types.