Simplified solution for transverse deformation of segmental tunnels incorporating physics-data hybrid-driven nonlinear joint rotational behaviors

Abstract

Accurately evaluating the nonlinear rotational stiffness (NRS) of segmental joints is critical for predicting the load-induced transverse mechanical behaviors of shield tunnels. Existing analytical methods and machine learning techniques for joint NRS are limited by simplified assumptions and data volume, respectively, making accurate evaluation challenging. Furthermore, existing transverse mechanical solutions for tunnels are not applicable to arbitrary distributions of joint positions and loads. To this end, this study first develops physics-data hybrid-driven neural networks (PDNNs) for evaluating the NRS of segmental joints. The proposed analytical solutions for constructing physical constraints have been significantly improved in generality compared with existing methods, as they do not rely on known joint deformation paths and can easily incorporate complex material stress–strain relationships. The developed PDNNs are then employed for the iterative calculation of joint NRS in a beam-spring model resting on a tensionless Winkler foundation. Using an adaptive relaxation-iteration strategy and the state-space method, a simplified solution for the transverse mechanical response of shield tunnels with arbitrary joint layouts under arbitrary external loads is proposed. The effectiveness of the proposed methods is validated by comparing their results with those from high-fidelity finite element models (FEMs) in two application scenarios. Furthermore, the effects of concrete constitutive models on joint flexural performance, as well as those of key block position and top loading on tunnel mechanical performance, are investigated. The main conclusions drawn are as follows: (1) the developed PDNNs outperform purely analytical solutions and data-driven neural networks in predictive performance. When the training set contains only joint rotation angles corresponding to one set of axial force cases, the coefficients of determination (R²) of the PDNNs increase by approximately 2% and 46% under sagging and hogging moments, respectively, compared with the purely analytical methods, while the relative L₂ errors decrease by about 7% and 33%, respectively. (2) The simplified solution proposed exhibits good agreement between its predictions of displacement and internal force and the FEM results. Optimal deformation control is achieved when the key block is positioned 60° above the tunnel waist.

Keywords

Joint nonlinear rotational stiffness / Physics-data dual-driven / Neural network / Transverse deformation / Shield tunnel

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