Probabilistic analysis of tunnel loads using variance reduction

Abstract

Selection of input parameters for numerical modelling of geotechnical structures is problematic due to their variability and uncertainty. Generally parametric studies are required to evaluate the impact of input parameters on the modelling results. Utilisation of various statistical methods can bring significant benefits, such as probabilistic distributions of the modelling outputs, the probability of failure, etc. This paper presents a variance reduction method known as Latin Hypercube Sampling (LHS). Special attention is paid to the LHS mean method representing a more efficient sampling scheme within the LHS framework. Performance of the LHS mean method is evaluated by comparison with the standard LHS median method and the necessary number of simulations is recommended. To take the statistical dependency of input variables into consideration the LHS mean is combined with the Simulated Annealing method. The effectiveness of LHS methods and their practical application is demonstrated by static calculations for the Brusnice tunnel. The Brusnice tunnel is a part of the Blanka tunnel complex on the Prague City Circle Road in the Czech Republic excavated by the New Austrian Tunnelling Method (NATM). The 2D numerical model was prepared using FEM. The modelling results were evaluated in terms of confidence intervals.