Interpretable soft computing deep ensemble model for predicting deformation of surrounding rock in deep tunnels

Predicting tunnel crown settlement and convergence remains challenging due to uncertainties unaddressed by traditional methods. This study proposes an interpretable intelligent model to enhance surrounding rock deformation predictions. Six heuristic swarm intelligence optimization algorithms (HSIOAs) are applied to enhance the Deep Belief Network (DBN) model. Six DBN-based models are compared against classical machine learning models using metrics like RMSE, <i>R</i>², MAE, and VAF. The KOA-DBN achieves the best performance, with <i>R</i>² = 0.938, RMSE = 0.484 mm, and MAE = 0.381 mm for crown settlement, and <i>R</i>² = 0.949, RMSE = 0.947 mm, and MAE = 0.767 mm for tunnel convergence. KOA-DBN outperforms hybrid models, improving <i>R</i>² by 1.1%–4.3% and reducing RMSE by 7.6%–16.3% and MAE by 8.7%–29.5%. Its accelerated convergence boosts computational efficiency, while compatibility with monitoring systems enhances deformation prediction accuracy and safety. SHAP analysis identifies burial depth, lateral pressure coefficient, and support type as key deformation factors. This framework effectively addresses complex tunnel engineering challenges and offers a practical solution for deformation forecasting, with strong potential to support real-time decision-making and enhance safety standards in tunnel construction.