Swarm-Based Extreme Gradient Boosting Models for Predicting the Undrained Stability Factor of Twin Circular Tunnels

This study examines the undrained stability of twin circular tunnels in anisotropic and heterogeneous clays using three-dimensional adaptive finite-element limit analysis (3D-AFELA). Four design variables are considered in the study. They are the cover-depth ratio (C/D), the spacing ratio (S/D), the anisotropy ratio (re), and the undrained shear strength gradient ratio (ρD/suTC0). A detailed parametric study, utilizing various design charts and contour plots, is conducted to discuss the impacts of these variables on the stability factor (N) and the failure mechanism. Using the data set from 3D-AFELA, three hybrid machine-learning models are proposed for stability predictions: GWO-XGBoost, WOA-XGBoost, and SHO-XGBoost. These models combine nature-inspired optimization algorithms (gray wolf optimizer, whale optimization algorithm, and sea-horse optimizer) with Extreme Gradient Boosting (XGBoost). Compared to XGBoost's default settings, hybrid approaches can reduce the model's error by nearly 60%. Among these, the SHO-XGBoost model notably lowers computational costs. Additionally, permutation feature importance and the cosine amplitude method are applied in the sensitivity analysis, revealing that ρD/suTC0 is the most important variable. The findings from this study provide a comprehensive and practical approach to addressing the undrained stability of 3D twin circular tunnels in anisotropic and heterogeneous clays.