Nonlinear Dilatancy Seepage Model of Single Rock Fracture with Shear Broken
Publication: International Journal of Geomechanics
Volume 25, Issue 2
Abstract
The seepage behavior of a single fracture under the coupled shear–seepage condition is important to the stability of rock mass, especially when shear broken. In this study, coupled shear–seepage tests are conducted on regular tooth single rock fracture with radial fluid flow. The shear failure and changes in the dilation angle were investigated with 1.27, 1.59, 1.91, 2.23, and 2.55 MPa normal stress; the nonlinear seepage behavior was analyzed with 0.2, 0.4, 0.6, and 0.8 MPa hydraulic pressure, and shear broken. The results show that during the shearing process, the nonlinear changes in shear strength, normal deformation, and the dilation angle show great differences with shear displacement, which could be divided into the peak shear, softening shear, and residual shear displacement sections under the influence of shear broken and gouge material. In the peak shear displacement section, normal deformation increased rapidly when the dilation angle was constant; in the softening shear displacement section, normal deformation increased slowly when the dilation angle rapidly decreased, and the normal deformation and dilation angle tended to be stable in the residual shear displacement section. The relationship between the hydraulic gradient and flow rate was consistent with Forchheimer’s law, and the linear and nonlinear term coefficients in Forchheimer’s law show a negative power and negative exponential function with shear displacement, because the joint surface roughness and the degree of the uneven aperture decreased with the influence of shear broken and gouge material. In addition, the values of the mechanical aperture were much larger than the hydraulic aperture, the ratio between the mechanical and hydraulic apertures increased, and decreased nonlinear taken peak shear displacement as the dividing point. Finally, the nonlinear dilatancy seepage model was established by considering the changed dilation angle and hydraulic gradient during the shear process. This study could be a basis for the coupled shear–seepage analysis of network rock mass and similar studies.
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Data Availability Statement
All data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This study received financial support from the National Natural Science Foundation of China (52209167, 52179143) and the China Postdoctoral Science Foundation (2023MD744254).
References
Alturki, A. A., B. B. Maini, and I. D. Gates. 2013. “The effect of fracture aperture and flow rate ratios on two-phase flow in smooth-walled single fracture.” J. Pet. Explor. Prod. Technol. 3: 119–132. https://doi.org/10.1007/s13202-012-0047-5.
Cao, C., Z. G. Xu, J. R. Chai, and Y. Q. Li. 2019. “Radial fluid flow regime in a single fracture under high hydraulic pressure during shear process.” J. Hydrol. 579: 124142. https://doi.org/10.1016/j.jhydrol.2019.124142.
Cao, C., Z. G. Xu, J. R. Chai, Y. Qin, and R. Tan. 2018. “Mechanical and hydraulic behaviors in a single fracture with asperities crushed during shear.” Int. J. Geomech. 18 (11): 04018148. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001277.
Chen, Z., J. Z. Qian, S. H. Luo, and H. B. Zhan. 2009. “Experimental study of friction factor for groundwater flow in a single rough fracture.” J. Hydrodyn. 21: 820–825. https://doi.org/10.1016/S1001-6058(08)60218-8.
Esaki, T., S. Du, Y. Mitani, K. Ikusada, and L. Jing. 1999. “Development of a shear-flow test apparatus and determination of coupled properties for a single rock joint.” Int. J. Rock Mech. Min. Sci. 36 (5): 641–650. https://doi.org/10.1016/S0148-9062(99)00044-3.
Fu, G., and Y. Yang. 2023. “A hybridizable discontinuous Galerkin method on unfitted meshes for single-phase Darcy flow in fractured porous media.” Adv. Water Resour. 173: 104390. https://doi.org/10.1016/j.advwatres.2023.104390.
Gan, L., Y. Liu, T. Xu, L. Xu, H. Y. Ma, and W. C. Xu. 2023. “Experimental investigation of the seepage characteristics of a single fracture in limestone with different roughness and seepage fluids.” J. Hydrol. 622: 129699. https://doi.org/10.1016/j.jhydrol.2023.129699.
Gan, L., Z. Z. Shen, and M. Xiao. 2020. “Experimental investigation of seepage characteristics in porous rocks with a single fracture.” Hydrogeol. J. 28: 2933–2946. https://doi.org/10.1007/s10040-020-02224-9.
Gudala, M., and S. K. Govindarajan. 2020. “Numerical modelling of coupled single-phase fluid flow and geomechanics in a fractured porous media.” J. Pet. Sci. Eng. 191: 107215. https://doi.org/10.1016/j.petrol.2020.107215.
He, G. H., E. Z. Wang, and X. L. Liu. 2016. “Modified governing equation and numerical simulation of seepage flow in a single fracture with three-dimensional roughness.” Arabian J. Geosci. 9: 81. https://doi.org/10.1007/s12517-015-2036-8.
Javadi, M., M. Sharifzadeh, K. Shahriar, and Y. Mitani. 2014. “Critical Reynolds number for nonlinear flow through rough-walled fractures: The role of shear processes.” Water Resour. Res. 50 (2): 1789–1804. https://doi.org/10.1002/2013WR014610.
Katende, A., J. Rutqvist, C. Massion, and M. Radonjic. 2023. “Experimental flow-through a single fracture with monolayer proppant at reservoir conditions: A case study on Caney Shale, Southwest Oklahoma, USA.” Energy 273 (15): 127181. https://doi.org/10.1016/j.energy.2023.127181.
Lavrov, A. 2023. “Flow of non-Newtonian fluids in single fractures and fracture networks: Current status, challenges, and knowledge gaps.” Eng. Geol. 321: 107166. https://doi.org/10.1016/j.enggeo.2023.107166.
Lee, J. G., and T. Babadagli. 2021. “Effect of roughness on fluid flow and solute transport in a single fracture: A review of recent developments, current trends, and future research.” J. Nat. Gas Sci. Eng. 91: 103971. https://doi.org/10.1016/j.jngse.2021.103971.
Li, B., Y. J. Jiang, T. Koyama, L. R. Jing, and Y. Tanabashi. 2008. “Experimental study of the hydro-mechanical behavior of rock joints using a parallel-plate model containing contact areas and artificial fractures.” Int. J. Rock Mech. Min. Sci. 45 (3): 362–375. https://doi.org/10.1016/j.ijrmms.2007.06.004.
Li, M., X. S. Liu, Y. Li, Z. L. Hou, and S. H. Qiao. 2022. “Effect of contact areas on seepage behavior in rough fractures under normal stress.” Int. J. Geomech. 22 (4): 04022019. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002330.
Matsuki, K., Y. Kimura, K. Sakaguchi, K. Kizaki, and A. A. Giwelli. 2010. “Effect of shear displacement on the hydraulic conductivity of a fracture.” Int. J. Rock Mech. Min. Sci. 47 (3): 436–449. https://doi.org/10.1016/j.ijrmms.2009.10.002.
Mirzaghorbanali, A., J. Nemcik, and N. Aziz. 2014. “Effects of cyclic loading on the shear behaviour of infilled rock joints under constant normal stiffness conditions.” Rock Mech. Rock Eng. 47 (4): 1373–1391. https://doi.org/10.1007/s00603-013-0452-1.
Mofakham, A. A., M. Stadelman, G. Ahmadi, K. T. Shanley, and D. Crandall. 2018. “Computational modeling of hydraulic properties of a sheared single rock fracture.” Transp. Porous Media 124: 1–30. https://doi.org/10.1007/s11242-018-1030-5.
Nicholl, M. J., and R. L. Detwiler. 2001. “Simulation of flow and transport in a single fracture: Macroscopic effects of underestimating local head loss.” Geophys. Res. Lett. 28 (23): 4355–4358. https://doi.org/10.1029/2001GL013647.
Qian, J.-z., M. Wang, Y. Zhang, X.-s. Yan, and W.-d. Zhao. 2015. “Experimental study of the transition from non-Darcian to Darcy behavior for flow through a single fracture.” J. Hydrodyn. 27: 679–688. https://doi.org/10.1016/S1001-6058(15)60530-3.
Rong, G., J. Yang, L. Cheng, J. Tan, J. Peng, and C. B. Zhou. 2018. “A Forchheimer equation-based flow model for fluid flow through rock fracture during shear.” Rock Mech. Rock Eng. 51: 2777–2790. https://doi.org/10.1007/s00603-018-1497-y.
Vilarrasa, V., T. Koyama, I. Neretnieks, and L. R. Jing. 2011. “Shear-induced flow channels in a single rock fracture and their effect on solute transport.” Transp. Porous Media 87 (2): 503–523. https://doi.org/10.1007/s11242-010-9698-1.
Wang, G., D. Y. Han, C. H. Jiang, and Z. Y. Zhang. 2020. “Seepage characteristics of fracture and dead-end pore structure in coal at micro- and meso-scales.” Fuel 266 (15): 117058. https://doi.org/10.1016/j.fuel.2020.117058.
Wang, S. M., Z. L. Wang, J. G. Wang, and P. Sun. 2024. “A theoretical model for nonlinear flow in a single marble fracture under high-stress conditions.” Int. J. Geomech. 24 (4): 04024044. https://doi.org/04024044.10.1061/IJGNAI.GMENG-9111.
Xu, W. T., X. Z. Li, Y. S. Zhang, X. Y. Wang, R. C. Liu, Z. C. He, and J. Fan. 2021. “Aperture measurements and seepage properties of typical single natural fractures.” Bull. Eng. Geol. Environ. 80: 8043–8058. https://doi.org/10.1007/s10064-021-02392-2.
Ye, Z. Y., Q. H. Jiang, C. B. Zhou, and Y. Z. Liu. 2017. “Numerical analysis of unsaturated seepage flow in two-dimensional fracture networks.” Int. J. Geomech. 17 (5): 04016118. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000826.
Zhang, X. B., Q. H. Jiang, N. Chen, W. Wei, and X. X. Feng. 2016. “Laboratory investigation on shear behavior of rock joints and a new peak shear strength criterion.” Rock Mech. Rock Eng. 49: 3495–3512. https://doi.org/10.1007/s00603-016-1012-2.
Zhang, Z. Y., and J. Nemcik. 2013. “Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures.” J. Hydrol. 477: 139–151. https://doi.org/10.1016/j.jhydrol.2012.11.024.
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Published In
International Journal of Geomechanics
Volume 25 • Issue 2 • February 2025
Copyright
© 2024 American Society of Civil Engineers.
History
Received: May 10, 2024
Accepted: Aug 28, 2024
Published online: Dec 6, 2024
Published in print: Feb 1, 2025
Discussion open until: May 6, 2025
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