Data-driven and physics-informed neural network for predicting tunnelling-induced ground deformation with sparse data of field measurement

Accurately predicting tunnelling-induced ground deformation (TIGD) is crucial for the safety of tunnel construction and protection of surrounding environment. Existing analytical studies on the prediction of TIGD are typically limited by idealistic simplification, and popular machine learning (ML) methods suffer from poor out-of-distribution generalization. Nonetheless, the combination of the two methods promises complementary potential. The paper proposes a data-driven and physics-informed neural network (DPNN) to predict the real-time TIGD with sparse data of field measurement. An analytical method, considering effects of construction parameters, imposes physical constraints in the data-driven neural network, improving generalization and interpretability. Empirical boundary conditions are introduced and inputted to refine the coordination of predicted TIGD. Training on sparse field measurement increases the model accuracy. Data-driven loss, physics loss and coordinate loss are combined to form the total loss, and the weights of different losses are considered. Based on two case studies and comparisons with pure analytical methods and pure data-driven ML models, the DPNN is demonstrated to possess superior prediction performance with sparse monitoring data and reliability to invert geological parameters and ground volume loss. Finally, parametric analyses are conducted to reveal the influence of critical variables on the prediction performance of the DPNN. Key findings include: (1) The weight ratio of 1/3 to 1 can be considered as the optimal range for weight allocation. (2) The prediction model maintains good predictive capability even under the 20% data noise. (3) Even with only seven monitoring points, the correlation between predicted and observed values can reach over 90%. The proposed method, with superior robustness and generalization, benefits better ground deformation prediction, early warning systems, and adjustment of construction parameters.