A physics-informed framework for mechanical parameters inversion in tunnel engineering based on deep learning and Bayesian optimization

Zhiyong Pang, Yuequn Huang, Muwu Xie, Yaoru Liu,
A physics-informed framework for mechanical parameters inversion in tunnel engineering based on deep learning and Bayesian optimization,
Tunnelling and Underground Space Technology,
Volume 166,
2025,
106940,
ISSN 0886-7798,
https://doi.org/10.1016/j.tust.2025.106940.
(https://www.sciencedirect.com/science/article/pii/S0886779825005784)
Abstract: Accurately obtaining the mechanical parameters of surrounding rock is fundamental for the scientific support design and stability calculations of tunnels. To address the limitations in precision associated with traditional inversion methods, a mechanical parameter inversion framework based on deep learning and Bayesian optimization is proposed. By incorporating the time-dependent deformation characteristics and mechanical properties of rock masses, the physics-informed framework achieves efficient inversion of the mechanical parameters of surrounding rock. The framework employs a deep learning algorithm based on fully connected layers and a multi-layer GRU architecture to construct a surrogate model for tunnel deformation. A physical knowledge module related to tunnel deformation behavior is developed, and a composite loss function is encoded to guide the data-driven process by physical information. The elastic-viscoplastic creep constitutive model, which grounded in internal variable thermodynamics, is used to simulate the time-dependent evolution of surrounding rock deformation. Based on the surrogate model optimized through hyperparameter tuning, a complex nonlinear mapping relationship between mechanical parameters and time-dependent deformation of the surrounding rock is established. A Bayesian optimization algorithm incorporating physical constraints is employed to account for the physical interrelations among parameters. The optimal mechanical parameters of the surrounding rock are inversely obtained based on burial depth and measured time-dependent deformation data. The proposed framework is applied to the JLL tunnel project. Results demonstrate that the determination coefficients (R2) of all inversion outcomes exceed 0.8, with a maximum value of 0.99. Comparative analyses with baseline models and ablation experiments further confirm the superiority of the proposed framework over other models.
Keywords: Mechanical parameters inversion; Deep learning; Bayesian optimization; Physics-informed; Surrogate model; Time-dependent deformation