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[SCG54-P04] Elastic Property Assessment of Rock Masses with Discrete Fracture Networks via Finite Element Analysis
Keywords:Finite element method, Discrete fracture network, Elasticity tensor, Averaging
Fracture networks in rock masses have a significant influence on the mechanical properties and permeability of a rock mass, requiring reliable modeling. The Discrete Fracture Network (DFN) has been widely adopted as an effective method to simulate fracture groups, and its fracture density and arrangement can be quantitatively evaluated using Dershowitz's Pij values together. Previously, numerous studies have investigated the effects of fracture network distributions on the macroscopic properties of rock masses both domestically and internationally. In Japan, research has accumulated on fractal characteristics and statistical analyses of fracture trace lengths and apertures [4][5][6][7][8]. Such studies have early highlighted the critical importance of fracture placement and provide essential insights for fracture modeling in rock engineering design.
In this study, fracture trace lengths were defined based on a probability density function ranging from 2 m to 100 m, and DFNs were generated according to this distribution. Finite element analyses were conducted on the generated DFNs to evaluate the macroscopic elastic moduli tensor. Periodic boundary conditions were applied, and an averaging method was adopted to calculate the macroscopic equivalent elastic moduli tensor by considering the stress-strain relationship over the DFN model. The Dershowitz Pij values were separately calculated for the DFNs, and the relationship between these values and the components of the elastic moduli tensor was investigated. The results showed that as the Pij values increased, the components of the elastic moduli tensor exhibited an inversely proportional decrease. This trend reflects the phenomenon where an increase in fracture density reduces the overall stiffness of the rock mass. Additionally, both the case of completely random fracture orientations and the case of fractures concentrated in specific orientations were analyzed. The finite element analyses were implemented using the general-purpose engineering software COMSOL Multiphysics.
The DFN-based analysis method adopted in this study allows for the quantitative evaluation of not only macroscopic anisotropic elastic properties but also other properties such as hydraulic conductivity and thermal conductivity when the physical properties of the crack and matrix are known. In the future, verification of the accuracy of this methodology is required through parameter adjustments for crack group generation, analysis at different scales, and comparison with measured data.
References
[1] W. S. Dershowitz and H. H. Herda, “Interpretation of Fracture Spacing and Intensity,” in Proc. 33rd U.S. Symp. Rock Mechanics (USRMS), 1992.
[2] D. Gottron and A. Henk, “Upscaling of Fractured Rock Mass Properties – An Example Comparing Discrete Fracture Network (DFN) Modeling and Empirical Relations Based on Engineering Rock Mass Classifications,” Eng. Geol., vol. 294, Dec. 2021, Art. no. 106382.
[3] Q. D. Boersma, “Natural Fracture Network Characterisation: Numerical Modelling, Outcrop Analysis and Subsurface Data,” Delft University Publishers, Delft, Netherlands, 2020.
[4] H. Ohno and K. Kojima, "Fractal on the Spatial Distribution of Fractures in Rock Mass, Part 1: Fractal Distribution," Journal of the Japan Society of Engineering Geology, vol. 33, no. 3, pp. 11-24, 1992. (in Japanese)
[5] H. Ohno and K. Kojima, "Fractal on the Spatial Distribution of Fractures in Rock Mass, Part 2: Fractal Characteristics and Variability of Fractal Distribution," Journal of the Japan Society of Engineering Geology, vol. 34, no. 2, pp. 12-26, 1993. (in Japanese) [6] Y. Ijiri, A. Sawada, and K. Akahori, Fracture Characteristics in Japanese Rock. JNC TN8400 99-091, Nov. 1999. (in Japanese)
[7] Y. Ijiri, A. Sawada, and K. Akahori, Hydrological Characteristics of Japanese Rock. JNC TN8400 99-090, Nov. 1999. (in Japanese)
[8] Y. Ijiri, A. Sawada, K. Sakamoto, M. Uchida, K. Ishiguro, H. Umeki, and Y. Ohnishi, "Evaluation of scale effects on hydraulic characteristics of fractured rock using fracture network model," Proceedings of the Japan Society of Civil Engineers, no. 694/III-57, pp. 179-194, 2001. (in Japanese)
In this study, fracture trace lengths were defined based on a probability density function ranging from 2 m to 100 m, and DFNs were generated according to this distribution. Finite element analyses were conducted on the generated DFNs to evaluate the macroscopic elastic moduli tensor. Periodic boundary conditions were applied, and an averaging method was adopted to calculate the macroscopic equivalent elastic moduli tensor by considering the stress-strain relationship over the DFN model. The Dershowitz Pij values were separately calculated for the DFNs, and the relationship between these values and the components of the elastic moduli tensor was investigated. The results showed that as the Pij values increased, the components of the elastic moduli tensor exhibited an inversely proportional decrease. This trend reflects the phenomenon where an increase in fracture density reduces the overall stiffness of the rock mass. Additionally, both the case of completely random fracture orientations and the case of fractures concentrated in specific orientations were analyzed. The finite element analyses were implemented using the general-purpose engineering software COMSOL Multiphysics.
The DFN-based analysis method adopted in this study allows for the quantitative evaluation of not only macroscopic anisotropic elastic properties but also other properties such as hydraulic conductivity and thermal conductivity when the physical properties of the crack and matrix are known. In the future, verification of the accuracy of this methodology is required through parameter adjustments for crack group generation, analysis at different scales, and comparison with measured data.
References
[1] W. S. Dershowitz and H. H. Herda, “Interpretation of Fracture Spacing and Intensity,” in Proc. 33rd U.S. Symp. Rock Mechanics (USRMS), 1992.
[2] D. Gottron and A. Henk, “Upscaling of Fractured Rock Mass Properties – An Example Comparing Discrete Fracture Network (DFN) Modeling and Empirical Relations Based on Engineering Rock Mass Classifications,” Eng. Geol., vol. 294, Dec. 2021, Art. no. 106382.
[3] Q. D. Boersma, “Natural Fracture Network Characterisation: Numerical Modelling, Outcrop Analysis and Subsurface Data,” Delft University Publishers, Delft, Netherlands, 2020.
[4] H. Ohno and K. Kojima, "Fractal on the Spatial Distribution of Fractures in Rock Mass, Part 1: Fractal Distribution," Journal of the Japan Society of Engineering Geology, vol. 33, no. 3, pp. 11-24, 1992. (in Japanese)
[5] H. Ohno and K. Kojima, "Fractal on the Spatial Distribution of Fractures in Rock Mass, Part 2: Fractal Characteristics and Variability of Fractal Distribution," Journal of the Japan Society of Engineering Geology, vol. 34, no. 2, pp. 12-26, 1993. (in Japanese) [6] Y. Ijiri, A. Sawada, and K. Akahori, Fracture Characteristics in Japanese Rock. JNC TN8400 99-091, Nov. 1999. (in Japanese)
[7] Y. Ijiri, A. Sawada, and K. Akahori, Hydrological Characteristics of Japanese Rock. JNC TN8400 99-090, Nov. 1999. (in Japanese)
[8] Y. Ijiri, A. Sawada, K. Sakamoto, M. Uchida, K. Ishiguro, H. Umeki, and Y. Ohnishi, "Evaluation of scale effects on hydraulic characteristics of fractured rock using fracture network model," Proceedings of the Japan Society of Civil Engineers, no. 694/III-57, pp. 179-194, 2001. (in Japanese)