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<p>Foaming polymers are widely used in trenchless rehabilitation because of their rapid expansion and high bonding strength. However, grouting in highly permeable media such as sand–gravel deposits is typically characterized by high pressure and short duration, making it difficult to continuously capture the internal pressure field and the evolving diffusion front. This limitation hampers performance evaluation and the rapid selection of grouting parameters. To address this issue, we formulate a physics-informed neural network (PINN) framework in which the governing seepage equation during the quasi-steady stage of grouting is imposed as a physical constraint, together with multiple boundary conditions. The model is trained by jointly minimizing the residuals of the governing equation and boundary-condition constraints. Three representative working conditions are investigated using visualized physical-model tests and numerical simulations. The PINN predictions of the pressure response during grouting and the effective diffusion distance obtained from post-curing measurement of the consolidated grout body are analyzed. The results show that: (1) the proposed PINN accurately reconstructs the pressure field under sparse observations; the deviations at the injection point and critical boundaries are negligible, with relative errors below 0.3%, indicating that the boundary constraints and physical consistency are well preserved. (2) The pressure patterns predicted by the PINN agree well with the numerical results. Compared with experimental measurements, the overall discrepancy remains within an engineering-acceptable range, with most errors concentrated between 5 and 11%. (3) The effective diffusion distances predicted from the PINN pressure fields agree well with the experimentally measured diffusion ranges, with relative errors below 7% in the tested cases, and show consistent trends with the numerical simulations. These findings demonstrate that the proposed PINN framework can provide physically consistent predictions of both the pressure field and the grouting influence zone.</p>

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Physics-informed Reconstruction of Pressure Fields and Diffusion Range in Foaming Polymer Grouting

  • 期刊论文

  • 发表日期：

    2026年7月9日

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  • Longbin Cao,
  • Jianzhao Wang,
  • Peng Zhao,
  • Hui Xue,
  • Yanbin Xue,
  • Hao Jiang,
  • Xueming Du,
  • Xiaohua Zhao

摘要

Foaming polymers are widely used in trenchless rehabilitation because of their rapid expansion and high bonding strength. However, grouting in highly permeable media such as sand–gravel deposits is typically characterized by high pressure and short duration, making it difficult to continuously capture the internal pressure field and the evolving diffusion front. This limitation hampers performance evaluation and the rapid selection of grouting parameters. To address this issue, we formulate a physics-informed neural network (PINN) framework in which the governing seepage equation during the quasi-steady stage of grouting is imposed as a physical constraint, together with multiple boundary conditions. The model is trained by jointly minimizing the residuals of the governing equation and boundary-condition constraints. Three representative working conditions are investigated using visualized physical-model tests and numerical simulations. The PINN predictions of the pressure response during grouting and the effective diffusion distance obtained from post-curing measurement of the consolidated grout body are analyzed. The results show that: (1) the proposed PINN accurately reconstructs the pressure field under sparse observations; the deviations at the injection point and critical boundaries are negligible, with relative errors below 0.3%, indicating that the boundary constraints and physical consistency are well preserved. (2) The pressure patterns predicted by the PINN agree well with the numerical results. Compared with experimental measurements, the overall discrepancy remains within an engineering-acceptable range, with most errors concentrated between 5 and 11%. (3) The effective diffusion distances predicted from the PINN pressure fields agree well with the experimentally measured diffusion ranges, with relative errors below 7% in the tested cases, and show consistent trends with the numerical simulations. These findings demonstrate that the proposed PINN framework can provide physically consistent predictions of both the pressure field and the grouting influence zone.