Deformation prediction of surrounding rock in shallow buried biased tunnels based on PSO-LSSVM

Shallow-buried tunnels under unsymmetrical loading pose a high-risk scenario in urban underground engineering, yet accurate prediction of surrounding rock deformation is constrained by scarce field monitoring data and inadequate physical-mechanism integration. This study develops a novel physics-informed Particle Swarm Optimization–Least Squares Support Vector Machine (PSO-LSSVM) model, demonstrated on a shallow tunnel in Beijing, China. Nine cases varying in silty clay thickness and overburden depth characterize deformation. The model was calibrated and validated against in-situ measurements; physical insights from simulations were embedded into the machine learning framework to augment training data, coupling physical constraints with data-driven features. Predicted crown settlement and arch shoulder convergence agree with measurements, yielding a mean absolute percentage error (MAPE) of 1.09%, root mean square error (RMSE) of 0.48 mm, and mean absolute error (MAE) of 0.46 mm. Relative to the back propagation (BP) neural network, support vector machine (SVM), and LSSVM models, PSO-LSSVM reduces MAPE by 28.99%, 46.96%, and 25.34%; RMSE by 28.36%, 47.83%, and 29.41%; and MAE by 28.35%, 47.09%, and 26.02%. This stems from synergy between physics-informed simulations and nonlinear mapping. The "numerical simulation–field monitoring–machine learning" framework provides a robust solution to both challenges.