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<p>The upward movement of an existing tunnel caused by excavation of a nearby foundation pit has emerged as a pressing issue in urban rail transit safety. Conventional data-driven prediction methods often lack physical interpretability, and their performance tends to deteriorate when only a small number of training samples are available. To fill this gap, the present study proposes a physics-guided gradient boosting regression tree (PG-GBRT) framework. This architecture integrates domain knowledge from geotechnical engineering into a machine learning model to achieve reliable tunnel deformation predictions. The framework consists of two hierarchical layers. In the first layer, a physics-based empirical formula captures the fundamental geometric relationships. It draws on three theoretical foundations: Gaussian settlement trough theory, the link between excavation depth and volume loss, and three-dimensional geometric effects. The second layer is a residual machine learning model designed to handle the complex nonlinear interactions that the physical component cannot adequately represent. The empirical formula adopts a multiplicative structure. Four key geometric parameters enter this formulation: excavation depth, vertical clear distance, crossing length, and intersection angle. The gradient boosting regression tree then learns systematic deviations from what the physical formula predicts. To validate the framework, we compile 154 engineering cases from major cities across China. On the training set, PG-GBRT achieves an R<sup>2</sup> of 0.9023, an RMSE of 0.6123&#xa0;mm, an MAE of 0.4567&#xa0;mm, and a MAPE of 8.23%. These results compare favorably with three baseline models: standalone GBRT, XGBoost, and LightGBM. Relative to the best performing baseline, PG-GBRT improves R<sup>2</sup> by 7.1% and reduces RMSE by 37.9%. Physical interpretability analysis reveals that the physical prediction component dominates feature importance. Residual learning compresses the prediction variance effectively, as reflected by a reduction in residual RMSE from 4.078&#xa0;mm to 0.477&#xa0;mm. Parameter sensitivity analysis further shows distinct sensitivity patterns across different physical parameters, with each pattern mirroring the parameter's specific role in the mathematical structure of the proposed formula. Overall, the PG-GBRT framework reconciles physical interpretability with the flexibility of machine learning, offering a practical prediction tool for excavation–tunnel interaction problems, particularly in data‑scarce scenarios.</p>

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Physics-guided gradient boosting regression tree for predicting tunnel deformation induced by foundation pit excavation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月1日

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  • Linlong Mu,
  • Yuxuan Li,
  • Zongyu Ma,
  • Kai Liu

摘要

The upward movement of an existing tunnel caused by excavation of a nearby foundation pit has emerged as a pressing issue in urban rail transit safety. Conventional data-driven prediction methods often lack physical interpretability, and their performance tends to deteriorate when only a small number of training samples are available. To fill this gap, the present study proposes a physics-guided gradient boosting regression tree (PG-GBRT) framework. This architecture integrates domain knowledge from geotechnical engineering into a machine learning model to achieve reliable tunnel deformation predictions. The framework consists of two hierarchical layers. In the first layer, a physics-based empirical formula captures the fundamental geometric relationships. It draws on three theoretical foundations: Gaussian settlement trough theory, the link between excavation depth and volume loss, and three-dimensional geometric effects. The second layer is a residual machine learning model designed to handle the complex nonlinear interactions that the physical component cannot adequately represent. The empirical formula adopts a multiplicative structure. Four key geometric parameters enter this formulation: excavation depth, vertical clear distance, crossing length, and intersection angle. The gradient boosting regression tree then learns systematic deviations from what the physical formula predicts. To validate the framework, we compile 154 engineering cases from major cities across China. On the training set, PG-GBRT achieves an R2 of 0.9023, an RMSE of 0.6123 mm, an MAE of 0.4567 mm, and a MAPE of 8.23%. These results compare favorably with three baseline models: standalone GBRT, XGBoost, and LightGBM. Relative to the best performing baseline, PG-GBRT improves R2 by 7.1% and reduces RMSE by 37.9%. Physical interpretability analysis reveals that the physical prediction component dominates feature importance. Residual learning compresses the prediction variance effectively, as reflected by a reduction in residual RMSE from 4.078 mm to 0.477 mm. Parameter sensitivity analysis further shows distinct sensitivity patterns across different physical parameters, with each pattern mirroring the parameter's specific role in the mathematical structure of the proposed formula. Overall, the PG-GBRT framework reconciles physical interpretability with the flexibility of machine learning, offering a practical prediction tool for excavation–tunnel interaction problems, particularly in data‑scarce scenarios.