Finite element-based probabilistic framework including Bayesian inference for predicting displacements due to tunnel excavation
Jocelyn Minini, Yi Zhang, Marc Groslambert, Stéphane Commend
Abstract
Excessive settlements due to tunnel excavation in urban sites may affect the stability of sensitive buildings, and additional design costs are needed to prevent these effects. In this article, a finite element-based probabilistic framework is presented and applied to a real-world case study to estimate tunnel-induced settlements. This probabilistic analysis framework consists of the following four fundamental elements: a sensitivity analysis to identify key parameters, an a priori reliability analysis using metamodels to calculate reliability indices and probabilities of failure, field monitoring results (e.g., settlements) and a Bayesian inverse analysis using the field measurements to update the probabilities of failure a posteriori. This framework is materialized through the linking of ZSOIL, a non-linear finite element soil–structure interaction software, and UQLab, a MATLAB®-based uncertainty quantification toolbox. With the application of this framework to a real-world case study in the Grand Paris Express project, key geotechnical parameters can be identified, reliability indices and probabilities of failure can be computed using metamodelling-powered Monte Carlo (MCS) and adaptive kriging Monte Carlo simulations (AKMCS). Finally, using Bayesian inverse analyses to update prior knowledge and refine posterior prediction, the probability that the settlements exceed acceptable values can be reduced, potentially leading to design cost savings.