Physics-informed machine learning has been a promising data-driven and physics-informed approach in geotechnical engineering. This study proposes a physics-informed extreme learning machine (PIELM) framework for analyzing tunneling-induced soil-pile interactions. The pile foundation is modeled as an Euler-Bernoulli beam, and the surrounding soil is modeled as a Pasternak foundation. The soil-pile interaction is formulated into a fourth-order ordinary differential equation (ODE) that constitutes the physics-informed component, while measured data are incorporated into PIELM as the data-driven component. Combining physics and data yields a loss vector of the extreme learning machine (ELM) network, which is trained within 1 second by the least squares method. After validating the PIELM approach by the boundary element method (BEM) and finite difference method (FDM), parametric studies are carried out to examine the effects of ELM network architecture, data monitoring locations and numbers on the performance of PIELM. The results indicate that monitored data should be placed at positions where the gradients of pile deflections are significant, such as at the pile tip/top and near tunneling zones. Two application examples highlight the critical role of physics-informed and data-driven approach for tunnelling-induced soil-pile interactions. The proposed approach shows great potential for real-time monitoring and safety assessment of pile foundations, and benefits for intelligent early-warning systems in geotechnical engineering.

翻译：物理信息机器学习已成为岩土工程中一种前景广阔的数据驱动与物理信息融合方法。本研究提出了一种物理信息极限学习机（PIELM）框架，用于分析隧道开挖诱发的土-桩相互作用。桩基础被建模为欧拉-伯努利梁，周围土体则采用帕斯捷尔纳克地基模型进行模拟。土-桩相互作用被表述为一个四阶常微分方程（ODE），构成物理信息部分；而实测数据则作为数据驱动部分融入PIELM。物理信息与数据相结合，形成了极限学习机（ELM）网络的损失向量，该网络通过最小二乘法在1秒内完成训练。在通过边界元法（BEM）和有限差分法（FDM）验证PIELM方法后，进行了参数化研究，以考察ELM网络结构、数据监测位置与数量对PIELM性能的影响。结果表明，监测数据应布置在桩身挠度梯度显著的位置，例如桩端/桩顶及隧道开挖区域附近。两个应用实例突显了物理信息与数据驱动方法在隧道开挖诱发土-桩相互作用分析中的关键作用。所提方法在桩基础实时监测与安全评估方面展现出巨大潜力，并有助于岩土工程智能预警系统的构建。