隧洞围岩力学响应的物理信息神经网络模型及其工程应用

doi:10.3724/1000-6915.jrme.2025.0687

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摘要准确、高效把握围岩受力变形响应特征是确保隧洞安全开挖的核心基础，针对传统解析与数值方法中模型构建复杂、泛化能力差、计算效率与精度难以兼顾等难题，提出一种数物双驱动的隧洞围岩力学响应分析方法。首先，基于隧洞围岩二次应力叠加原理与Verruijt-Booker控制方程，构建以位移、应力等物理量为输出的神经网络近似解，并将其结构嵌入控制方程、边界条件与初始条件，从而形成一种无需网格离散的物理信息神经网络模型（Physics-Informed Neural Network，PINN）。训练过程中，通过优化数百万网络参数，寻找能够同时满足物理规律与数据约束的高维函数，使最终模型成为该偏微分方程组的智能代理求解器。其次，就隧洞赋存地质环境迥异、设计工况多变及监测数据稀缺等问题，提出迁移学习驱动的物理信息神经网络（Transfer Learning-Driven Physics-Informed Neural Networks，简称TL-PINNs），通过预训练–参数迁移策略，在隧洞埋深、洞径、岩体参数等多变量协同变化的大规模参数空间中实现快速收敛。研究结果表明：PINNs模型高度还原经典有限单元法（FEM）计算结果，在45个监测位移点与6 000个LHS配点共同约束下，PINNs横向位移最大绝对误差0.31 mm，竖向位移最大误差0.23 mm；对比有无迁移学习驱动的PINNs模型损失函数收敛性，目标域模型仅需5 000次迭代即可达到常规PINNs 50 000次迭代损失水平，训练时间由3 664 s缩短至420 s，位移绝对误差最大降低66.1%。迁移学习驱动的物理信息神经网络模型作为一种无网格智能算法，具有速度快、交互性强、泛化能力高等优点。本文提出的数物双驱动框架在“精度–效率–鲁棒性”三维指标上均满足实际工程应用需求，可为后续隧道与地下工程数物驱动智能仿真提供理论指导与参考依据。

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	贺鹏1
	江子豪1
	石少帅2
	3*
	王菲1
	胡杰4
	吴威涛5
	张盼盼1

关键词 ：隧道工程, 物理信息神经网络, 数物驱动, 围岩力学响应, 迁移学习

Abstract：Accurately and efficiently characterizing the mechanical response of surrounding rock is fundamental to ensuring safe tunnel excavation. To address the challenges associated with conventional analytical and numerical methods—such as complex model construction, limited generalizability, and difficulties in balancing computational efficiency with accuracy—this paper proposes a dual data- and physics-driven approach for analyzing the mechanical response of tunnel surrounding rock. First, based on the secondary stress superposition principle and the Verruijt-Booker governing equations, we construct a neural network approximation that outputs displacement and stress fields. This network architecture inherently embeds the governing equations, boundary conditions, and initial conditions, resulting in a mesh-free Physics-Informed Neural Network (PINN). During training, we optimize millions of network parameters to identify a high-dimensional function that simultaneously satisfies physical laws and data constraints, ultimately forming an intelligent surrogate solver for the system of partial differential equations. Second, to tackle issues such as highly variable geological conditions, diverse design scenarios, and sparse monitoring data, we introduce a Transfer Learning-Driven Physics-Informed Neural Network (TL-PINNs). By employing a pre-training and parameter transfer strategy, the model achieves rapid convergence within a high-dimensional parameter space involving multiple variables, including tunnel depth, diameter, and rock mass properties. Results demonstrate that the PINN model closely reproduces outcomes from classical Finite Element Method (FEM) simulations. Under constraints from 45 monitoring points and 6,000 Latin Hypercube Sampling (LHS) collocation points, the maximum absolute errors in horizontal and vertical displacements are 0.31 mm and 0.23 mm, respectively. Compared to the baseline PINN without transfer learning, the TL-PINNs model reaches the same loss level in only 5 000 iterations—a fraction of the 50 000 required by the conventional approach—while reducing training time from 3 664 seconds to 420 seconds, achieving up to a 66.1% reduction in absolute displacement error. As a mesh-free intelligent algorithm, the TL-PINNs framework offers high computational speed, strong interactivity, and excellent generalization capability. The proposed dual data- and physics-driven framework meets practical engineering requirements in terms of accuracy, efficiency, and robustness, providing theoretical guidance and a reference basis for future intelligent simulations in tunnel and underground engineering applications.

Key words： tunnelling engineering physical information neural networks numerical-physical coupling rockmass mechanical response transfer learning

引用本文:

贺鹏1，江子豪1，石少帅2，3*，王菲1，胡杰4，吴威涛5，张盼盼1. 隧洞围岩力学响应的物理信息神经网络模型及其工程应用[J]. 岩石力学与工程学报, 2026, 45(8): 2391-2412.
HE Peng1, JIANG Zihao1, SHI Shaoshuai2, 3*, WANG Fei1, HU Jie4, WU Weitao5, ZHANG Panpan1. Physical information neural network model for mechanical response of tunnel surrounding rock and its engineering applications. , 2026, 45(8): 2391-2412.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.3724/1000-6915.jrme.2025.0687 或 https://rockmech.whrsm.ac.cn/CN/Y2026/V45/I8/2391

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