PINN-Swell: Physics-informed neural networks for modeling of coupled hydro-mechanical-chemical swelling processes in clay-sulfate rocks

粘土-硫酸盐岩溶胀是各种地下工程如隧道或地热钻井中遇到的主要岩土灾害。了解膨胀现象背后的水-机械-化学（HMC）过程对于制定适当的对策至关重要。膨胀过程可用耦合偏微分方程（PDEs）来描述。它们的解可以通过离散化方案在数值上近似，例如使用有限元法（FEM），这是固体力学中首选的数值方法。然而，有限元法仍然存在一些不足，如解的鲁棒性很大程度上取决于网格质量、离散化方法和用于近似未知场的多项式的阶数。物理信息神经网络（PINN）是一种可以近似求解偏微分方程的无网格方法。总的来说，PINN是一种新的和有前途的方法来解决控制土工材料和其他复杂系统耦合行为的偏微分方程。它们提供了一种高效的数据和基于物理的方法来模拟复杂的现象，并有可能促进我们对岩土工程中膨胀岩石行为的理解。计划中的研究有三个主要目标：(1)开发一个统一的、无网格的、鲁棒的PINN框架来模拟膨胀粘土-硫酸盐岩石中的耦合HMC过程；(2)总体上提高了我们用PINN方法模拟复杂耦合过程的能力；(3)提高了我们目前对粘土-硫酸盐岩石溶胀过程中耦合HMC过程的认识。研究地点Staufen和Freudenstein隧道提供了全面的数据集，包括水力、化学和力学数据来参数化模型，以及地面和隧道底板的隆起观测来仔细检查PINN模型。

Swelling of clay-sulfate rocks is a major geotechnical hazard, which is encountered in various underground engineering projects such as tunneling or geothermal drilling. It is crucial to understand the underlying hydro-mechanical-chemical (HMC) processes of swelling phenomena in order to plan appropriate countermeasures. The swelling processes can be described by coupled partial differential equations (PDEs). Their solution can be approximated numerically by means of a discretization scheme, e.g. using the finite element method (FEM), the preferred numerical approach in solid mechanics. However, FEM still suffers from some shortcomings, e.g. the robustness of the solution depends strongly on the mesh quality, the discretization method and the order of the polynomials used to approximate the unknown fields. The physics-informed neural network (PINN) is a meshless method that can approximate solutions to PDEs. Overall, PINN is a new and promising method for solving PDEs governing the coupled behavior of geo-materials and other complex systems. They offer a data-efficient and physics-based approach to model complex phenomena, and have the potential to advance our understanding of the behavior of swelling rocks in geotechnical engineering. The planned research has three main objectives: (1) developing a unified, meshless and robust PINN framework to model the coupled HMC processes in swelling clay-sulfate rocks; (2) advance our ability to model complex coupled processes by the PINN approach in general; (3) advance our present understanding of the coupled HMC processes in swelling of clay-sulfate rocks. The study sites Staufen and Freudenstein tunnel provide comprehensive data sets including hydraulic, chemical and mechanical data to parameterize the models, as well as heave observations at the land surface and tunnel floor to scrutinize the PINN models.