Coupling Stable Node-Based Smoothed Finite Element Method with Machine Learning Approaches for Predicting the Stability of Horseshoe Tunnels
摘要
This study proposed a hybrid approach that integrated the stable node-based smoothed finite element method (SNS-FEM) with machine learning (ML) techniques to predict the stability of horseshoe-shaped tunnels in cohesive-frictional soils under surcharge loading. The SNS-FEM, formulated based on the upper-bound theorem and the Mohr-Coulomb failure criterion, generated a comprehensive dataset of 1,200 stability numbers (N = σₛ/c). This dataset incorporated four key parameters: cover-depth ratio (H/B), height-to-width ratio (h/B), internal friction angle (φ), and dimensionless soil unit weight (γB/c). Three machine learning models, including Support Vector Machine (SVM), Gradient Boosting Tree (GBT), and Artificial Neural Network (ANN), were trained and validated using a 5-fold cross-validation approach. The ANN model with eight hidden neurons achieved the highest performance (R² = 0.999, RMSE = 1.219), significantly outperforming the SVM and GBT models. Shapley Additive exPlanations (SHAP) analysis indicated that (φ) and (H/B) were the most influential factors affecting stability predictions. Stability results were presented as design tables and dimensionless charts, providing practical tools for engineers in the preliminary design phase of tunnels. The proposed hybrid approach demonstrated superior accuracy and computational efficiency, markedly reducing the need for resource-intensive numerical simulations.