Physics-informed neural networks for stress field reconstruction in roadway surrounding rock

To address the problems of the high computational cost of traditional numerical simulations and the heavy reliance of data-driven models on vast amounts of data, this study proposes a method for reconstructing the stress field of roadway surrounding rock based on Physics-informed Neural Networks (PINNs). The method incorporates the solid mechanics equilibrium equations in the form of displacement and Dirichlet/Neumann boundary conditions into the loss function, constructing a joint constraint framework that integrates physical mechanisms and sparse monitoring data. It enables the synchronized high-precision inversion of the surrounding rock displacement and stress fields using only deformation data near the roadway boundary. A training and optimization process for multi-constraint loss functions is developed using the MATLAB platform. The computational domain is discretized using collocation points, and the displacement gradient is parsed through automatic differentiation. The strain and stress fields are output by combining geometric and constitutive relationships. Verification with finite element solutions as the benchmark shows that in 2D plane strain scenarios, the errors of displacement and stress fields solved by the PINN are less than 1.5% in the optimal scenario, while the maximum error in scenarios with sparse collocation points does not exceed 6%. From the perspective of pure computational mechanics, the prediction accuracy of 2D plane and 3D PINNs reaches the level of finite elements. The network structure with 8 hidden layers and 15 nodes per layer has the optimal convergence efficiency. The internal collocation point density of 20×20 is required to ensure the error is less than 5%. In typical scenarios without measured data or with fused sparse deformation data, the method can reconstruct the stress field with high precision. In addition, the reconstruction based on roadway deformation data can effectively capture stress concentration areas without the need for dense collocation points. This method breaks through the reliance of traditional methods on mesh generation and dense data, providing an efficient and low-cost numerical tool for the stability analysis of surrounding rock.