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<p>To address the limitations of existing three-dimensional fractured rock permeability models in accurately capturing complex connectivity and scale effects, this study employs electrical resistivity data to calibrate the scaling exponent <i>a</i> in the discrete fracture network (DFN) framework, thereby enabling a more realistic evaluation of the macroscopic permeability characteristics of three-dimensional fractured rock masses. Integrating the DFN with Oda’s fracture tensor theory enables the realistic simulation of hydraulic properties, such as permeability and transmissivity, within rock masses; however, this modeling approach imposes stringent requirements on parameter accuracy. Specifically, the scaling exponent <i>a</i> serves as a vital parameter in the DFN model, which exhibits exceptional sensitivity to changes in resistivity and directly determines the precise distribution of fracture lengths. To enhance the reliability of permeability estimation, this study proposes a three-dimensional dimensionless density calculation method to serve as a connectivity correction factor for fractures. Based on this, the asymmetric self-consistency (ASC) method and Oda’s fracture tensor theory are refined. Constraints on the exponent <i>a</i> are established by comparing the improved ASC-derived electrical resistivity with observed values. The refined fracture length distribution obtained from the DFN model is then incorporated into the modified Oda’s tensor theory to compute the three-dimensional permeability of the fractured rock mass. The results show that the DFN model, when calibrated with a constrained scaling exponent <i>a</i>, can accurately represent the spatial distribution of fractures (the error is maintained within 5%). The proposed method keeps the discrepancy between simulated and measured permeability within one order of magnitude, demonstrating its effectiveness in systematically linking electrical resistivity and permeability through DFN-based parameter optimization. Finally, a case study of a tunnel project in Sichuan Province, China, validates the applicability and reliability of the approach. This study not only enhances the precision of hydraulic simulations in fractured rock masses but also provides a feasible framework for parameter inversion and modeling in seepage prediction and geotechnical risk assessment for complex underground engineering.</p>

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Estimating three-dimensional permeability of fractured rock mass using electrical resistivity-constrained discrete fracture network

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • Bo Cai,
  • Linfeng Wang,
  • Mingjun Xie

摘要

To address the limitations of existing three-dimensional fractured rock permeability models in accurately capturing complex connectivity and scale effects, this study employs electrical resistivity data to calibrate the scaling exponent a in the discrete fracture network (DFN) framework, thereby enabling a more realistic evaluation of the macroscopic permeability characteristics of three-dimensional fractured rock masses. Integrating the DFN with Oda’s fracture tensor theory enables the realistic simulation of hydraulic properties, such as permeability and transmissivity, within rock masses; however, this modeling approach imposes stringent requirements on parameter accuracy. Specifically, the scaling exponent a serves as a vital parameter in the DFN model, which exhibits exceptional sensitivity to changes in resistivity and directly determines the precise distribution of fracture lengths. To enhance the reliability of permeability estimation, this study proposes a three-dimensional dimensionless density calculation method to serve as a connectivity correction factor for fractures. Based on this, the asymmetric self-consistency (ASC) method and Oda’s fracture tensor theory are refined. Constraints on the exponent a are established by comparing the improved ASC-derived electrical resistivity with observed values. The refined fracture length distribution obtained from the DFN model is then incorporated into the modified Oda’s tensor theory to compute the three-dimensional permeability of the fractured rock mass. The results show that the DFN model, when calibrated with a constrained scaling exponent a, can accurately represent the spatial distribution of fractures (the error is maintained within 5%). The proposed method keeps the discrepancy between simulated and measured permeability within one order of magnitude, demonstrating its effectiveness in systematically linking electrical resistivity and permeability through DFN-based parameter optimization. Finally, a case study of a tunnel project in Sichuan Province, China, validates the applicability and reliability of the approach. This study not only enhances the precision of hydraulic simulations in fractured rock masses but also provides a feasible framework for parameter inversion and modeling in seepage prediction and geotechnical risk assessment for complex underground engineering.