Hierarchical Bayesian Modelling for Uncertainty Quantification in Simplified Tunnel Deformation Models

When analysing the longitudinal performance of shield tunnels, simplified model assumptions are typically employed. As a result, deformation predictions exhibit significant uncertainty. Routine maintenance for tunnels allows for deformation measurements at the same locations at different points in time. By analysing these deformation measurements, we aim to infer and quantify the parameter uncertainty in the simplified models, thereby enabling more accurate probabilistic estimations of future tunnel deformations. The classical Bayesian approach, while powerful in integrating prior knowledge with observed data to update beliefs about uncertain parameters, faces limitations due to the assumption that all uncertainties are encapsulated within a single level of probability distributions. This can lead to biased results and underestimation of variability when dealing with complex and heterogeneous datasets typical in geotechnical engineering. These limitations highlight the need for a more flexible and comprehensive modelling framework that can account for the intricate nature of the simplified model's parameters and their impacts on tunnel deformation. The hierarchical Bayesian modelling framework addresses these issues by allowing for multiple levels of uncertainty and variation to be modelled simultaneously. This method structures the problem into different layers, where parameters at one level are treated as random variables that depend on the hyperparameters at a higher level. By adopting a hierarchical Bayesian framework, one can better quantify the uncertainties associated with the parameters of the simplified tunnel deformation model and improve the predictive accuracy of tunnel performance. In this contribution, we adapt the hierarchical Bayesian framework to the prediction of tunnel deformation with aim at enhancing the forecasting ability in tunnel maintenance. The approach is tested on a real-life example: an interval tunnel of Shanghai metro line 1, located in the city center in Shanghai.

Keywords: Hierarchical Bayesian modelling framework, Uncertainty quantification, Tunnel deformation, Simplified model.