Predicting tunnel squeezing with incomplete data using Bayesian networks

Tunnel squeezing or time-dependent large deformations due to creep are common in tunnels constructed in weak rock masses at large depth or subjected to high horizontal in situ stresses in tectonically active regions. Squeezing can produce tunnel collapses, budget overruns and construction delays, and being able to predict squeezing is therefore important. This study presents a novel application of Bayesian networks (BNs) to predict squeezing. In particular, we employ a Naive Bayes classifier based on five parameters – support stiffness (K), Rock Tunneling Quality Index (Q), tunnel depth (H), tunnel diameter (D), and strength–stress ratio (SSR) – about which information is commonly available at early design stages. The Naive Bayes classifier is “learned”, using the Expectation Maximization algorithm, with a database of 166 tunneling case histories from 7 countries compiled by the authors which is provided as Supplementary material. Then, the Junction Tree algorithm is employed for “belief updating”; i.e., to predict the probability of tunnel squeezing for a given set of (probably incomplete) evidence. The model is validated using 10-fold cross-validation and also using an additional set of case-histories that had not been originally employed to learn the network. Results show that, when compared with other available criteria, the error rate of our BN is among the lowest, but with the advantage that it is able to provide predictions even with incomplete data. Results of a sensitivity analysis to assess the importance of input parameters on the squeezing outcome are also presented. And, finally, a web-based implementation of the proposed BN is provided to improve the ease-of-use of our approach.