隧道施工诱发地表沉降估算方法及其规律分析

地表沉降是城市复杂环境下盾构隧道施工重点关注的问题。传统机器学习方法在预测隧道施工诱发地表沉降时忽略了其内在的物理机理，存在对训练样本需求量较大的弊端。基于深度神经网络 (deep neural networks, DNN) 对Verruijt-Booker解的围岩位移因子进行修正，构建地表沉降与隧道开挖面空间位置的关联。将修正后的Verruijt-Booker解的物理方程耦合至另一并行的DNN框架中，构建数据-物理双驱动的物理信息神经网络模型 (physics-informed neural networks, PINN)，从而约束神经网络在满足物理机制的空间中进行训练。算例分析的结果表明：在同等配置的条件下，提出的PINN模型的预测效果显著优于单一数据驱动的传统DNN模型，其外推泛化性能得到显著提升。工程应用的结果表明：PINN模型可以利用施工前期的实测数据，准确预测后续施工过程中开挖面在不同位置时监测断面的地表沉降值。提出的方法有助于提高盾构隧道施工过程中地表沉降控制的智慧化程度，可为工程的潜在风险及施工决策提供预警和指导。

Estimation method and laws analysis of surface settlement due to tunnelling

Tunnelling-induced surface settlement is a significant concern due to the complexity of urban environment. For the prediction of surface settlements, traditional machine learning methods ignore the underlying physical mechanism, resulting in the requirement of excessive training samples. Based on the framework of a DNN, the classical Verruijt-Booker solution is modified to connect tunnelling-induced surface settlements with the position of a tunnel face. The modified solution is integrated into a paralleled DNN framework to build the data-driven and physics-informed PINN model, in which the physical mechanism can constrain the neural network. The results of illustrative examples show that: compared to the traditional DNN model, the generalization capability of a PINN model has apparently increased. The results of engineering applications show that: based on the monitoring data at the early stage of a shield tunnel project, the PINN model can accurately predict the surface settlement in the process subsequent to construction; in addition, it increases the intelligence of surface settlement control, which can provide early warnings for potential risks and construction suggestions.