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<p>To enable the non-destructive detection of reinforcing bars and cracks within concrete structures civil engineering, we implement a numerical framework integrating an unstructured FEM for forward modelling and L-BFGS algorithm for inversion in Electrical Resistance Tomography (ERT). Given that the target surface is exposed to air, we adopt Neumann boundary conditions to accurately represent the physical scenario. The unstructured FEM offers greater adaptability to complex geometries compared to structured grids, enabling localized mesh refinement and more flexible control over mesh density. This enables the accurate computation of the electric potential distribution throughout the entire observation domain. Results from these simulations and comparisons indicate that the forward modelling algorithm can precisely simulate the electrical properties of reinforcing bars and cracks in concrete. Since the three-dimensional conductivity distribution of the target is reconstructed from boundary voltage measurements, we further apply 3D ERT imaging to typical structural concrete models using the L-BFGS inversion algorithm. A comparative evaluation with the NLCG algorithm highlights the computational efficiency and practical advantages of L-BFGS algorithm in this study. This study assesses the feasibility of employing ERT as non-destructive testing (NDT) method for concrete structures. The findings affirm the potential of ERT as a viable and effective imaging modality for the inspection and assessment of concrete integrity.</p>

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Three-dimensional modelling and inversion of reinforcing bars and cracks in concrete models using ERT

  • 期刊论文

  • 发表日期：

    2026年4月7日

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  • Shi-jie Gao,
  • Han-dong Tan,
  • Huan Ma,
  • Jian-ping Wu,
  • Xiao Liu

摘要

To enable the non-destructive detection of reinforcing bars and cracks within concrete structures civil engineering, we implement a numerical framework integrating an unstructured FEM for forward modelling and L-BFGS algorithm for inversion in Electrical Resistance Tomography (ERT). Given that the target surface is exposed to air, we adopt Neumann boundary conditions to accurately represent the physical scenario. The unstructured FEM offers greater adaptability to complex geometries compared to structured grids, enabling localized mesh refinement and more flexible control over mesh density. This enables the accurate computation of the electric potential distribution throughout the entire observation domain. Results from these simulations and comparisons indicate that the forward modelling algorithm can precisely simulate the electrical properties of reinforcing bars and cracks in concrete. Since the three-dimensional conductivity distribution of the target is reconstructed from boundary voltage measurements, we further apply 3D ERT imaging to typical structural concrete models using the L-BFGS inversion algorithm. A comparative evaluation with the NLCG algorithm highlights the computational efficiency and practical advantages of L-BFGS algorithm in this study. This study assesses the feasibility of employing ERT as non-destructive testing (NDT) method for concrete structures. The findings affirm the potential of ERT as a viable and effective imaging modality for the inspection and assessment of concrete integrity.