Radial flow behaviors of a rough Beishan granite fracture under normal and thermal loadings

Abstract

During the operation of a deep geological repository in crystalline rocks for disposal of high-level radioactive waste, understanding the seepage behaviors of fractured crystalline rocks under coupled thermo-hydro-mechanical conditions is essential for the performance assessment of deep geological repositories. In this study, radial flow tests on cylindrical Beishan granite specimens with a single artificial fracture were conducted using the MTS 815 rock mechanics testing system to investigate the influence of normal stress and temperature on radial flow behaviors of rough rock fractures. Steady state method was used to measure fracture permeability, and an axial extensometer was used to measure fracture deformation during compression. A three-dimensional blue light scanner was used to characterize fracture surface morphology. Experimental results indicate that fracture permeability decreases nonlinearly with the increase of normal stress or temperature, and normal stress has a more significant influence on fracture permeability than temperature. The evolution of three-dimensional non-uniform distribution of voids under compression was numerically obtained, and the variogram was employed to quantify the non-uniform distribution characteristics of mechanical apertures. In addition, a radial flow model considering non-uniform distribution of apertures is proposed to predict the normal stress- and temperature-dependent seepage behaviors of rock fractures, and the predictions were found to be in good agreement with experimental data.

Keywords

Radial flow / Fracture / Permeability / Aperture / Variogram / Beishan granite

CRediT authorship contribution statement

Xingguang Zhao: Writing - review & editing, Writing - original draft, Investigation, Funding acquisition, Data curation, Conceptualization. Dongjue Fan: Writing - original draft, Methodology, Investigation, Data curation. Zhihong Zhao: Writing - review & editing, Writing - original draft, Methodology, Investigation, Funding acquisition, Data curation, Conceptualization. Liang Chen: Funding acquisition, Conceptualization. Ju Wang: Project administration, Funding acquisition, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work has been supported by the China Atomic Energy Authority through the geological disposal program and the National Natural Science Foundation of China (Grant Nos. 11972149, U2067203 and 42277140).

References

[1] Acuna, J. A., & Yortsos, Y. C. (1995). Application of fractal geometry to the study of networks of fractures and their pressure transient. Water Resources Research, 31, 527-540.

[2] Auradou, H., Drazer, G., Hulin, J. P., & Koplik, J. (2005). Permeability anisotropy induced by the shear displacement of rough fracture walls. Water Resources Research, 41(9), W09423.

[3] Barton, N., Bandis, S., & Bakhtar, K. (1985). Strength, deformation and conductivity coupling of rock joints. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 22(2), 121-140.

[4] Cao, C., Xu, Z., Chai, J., Qin, Y., & Tan, R. (2018). Mechanical and hydraulic behaviors in a single fracture with asperities crushed during shear. International Journal of Geomechanics, 18(6), 04018148.

[5] Cao, C., Xu, Z., Chai, J., & Li, Y. (2019). Radial fluid flow regime in a single fracture under high hydraulic pressure during shear process. Journal of Hydrology, 579, 124-142.

[6] Chang, J., & Yortsos, Y. C. (1990). Pressure-transient analysis of fractal reservoirs. SPE Formation Evaluation, 5(4), 31-38.

[7] Chen, Y., Selvadurai, A. P. S., & Zhao, Z. (2021). Modeling of flow characteristics in 3D rough rock fracture with geometry changes under confined stresses. Computers and Geotechnics, 130, 103910.

[8] Chen, Y., Liang, W., Selvadurai, A. P. S., & Zhao, Z. (2021). Influence of asperity degradation and gouge formation on flow during rock fracture shearing. International Journal of Rock Mechanics and Mining Sciences, 143, 104795.

[9] Delay, F., Porel, G., & Bernard, S. (2004). Analytical 2D model to invert hydraulic pumping tests in fractured rocks with fractal behavior. Geophysical Research Letters, 31(16), L16501.

[10] Dijk, P., Berkowitz, B., & Bendel, P. (1999). Investigation of flow in watersaturated rock fractures using nuclear magnetic resonance imaging (NMRI). Water Resources Research, 35(1), 347-360.

[11] Esaki, T., Du, S., Mitani, Y., Ikusada, K., & Jing, L. (1999). Development of a shear-flow test apparatus and determination of coupled properties for a single rock joint. International Journal of Rock Mechanics and Mining Sciences, 36(6), 641-650.

[12] Gale, J., MacLeod, R., & LeMessurier, P. (1990). Site characterization and validation-Measurement of flowrate, solute velocities and aperture variation in natural fractures as a function of normal and shear stress, stage 3 Stripa Project Report 90-11.

[13] Stockholm: Swedish Nuclear Fuel and Waste Management Company. Gentier, S., Lamontagne, E., Archambault, G., & Riss, J. (1997). Anisotropy of flow in a fracture undergoing shear and its relationship to the direction of shearing and injection pressure. International Journal of Rock Mechanics and Mining Sciences, 34(094), 1-16.

[14] Gutierrez, M., Øino, L. E., & Nygård, R. (2000). Stress-dependent permeability of a de-mineralized fracture in shale. Marine and Petroleum Geology, 17(7), 895-907.

[15] Hakami, E., & Larsson, E. (1996). Aperture measurements and flow experiments on a single natural fracture. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 33(4), 395-404.

[16] International Society for Rock Mechanics (ISRM) (1979). Suggested methods for determining water content, porosity, density, absorption and related properties and swelling and slake-durability index properties. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 16(1), 143-151.

[17] Keller, A. (1998). High resolution, non-destructive measurement and characterization of fracture apertures. International Journal of Rock Mechanics and Mining Sciences, 35(4), 1037-1050.

[18] Kranz, R. L., Frankel, A. D., Engelder, T., & Scholz, C. H. (1979). The permeability of whole and jointed Barre granite. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 16 (2), 225-234.

[19] Lavrov, A. (2014). Radial flow of Non-Newtonian power-law fluid in a rough-walled fracture: Effect of fluid rheology. Transport in Porous Media, 105(3), 559-570.

[20] Lee, H. S., & Cho, T. F. (2002). Hydraulic characteristics of rough fractures in linear flow under normal and shear load. Rock Mechanics and Rock Engineering, 35(3), 299-318.

[21] Leveinen, J. (2000). Composite model with fractional flow dimensions for well test analysis in fractured rocks. Journal of Hydrology, 430(1-4), 173-178.

[22] Li, B., Jiang, Y., Koyama, T., Jing, L., & Tanabashi, Y. (2008). Experimental study of the hydro-mechanical behavior of rock joints using a parallel-plate model containing contact areas and artificial fractures. International Journal of Rock Mechanics and Mining Sciences, 45(4), 362-375.

[23] Lin, T., Meng, W., Chen, Y., Zhao, Z., Liu, B., Zhang, J., Chen, S., & Zhao, X. (2023). Unloading-induced permeability recovery in rock fractures. Journal of Rock Mechanics and Geotechnical Engineering, 15 (4), 3148-3162.

[24] Liu, G., Zhao, Z., Chen, Y., Ma, F., & Wang, G. (2021). Comparison between typical numerical models for fluid flow and heat transfer through single rock fractures. Computers and Geotechnics, 138, 104341.

[25] Liu, M. M., Chen, Y. F., Hong, J. M., & Zhou, C. B. (2016). A generalized non-Darcian radial flow model for constant rate test. Water Resources Research, 52(9), 9325-9343.

[26] Louis, C. (1975). Rock hydraulics. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 12(1), 59-72.

[27] Luo, S., Zhao, Z., Peng, H., & Pu, H. (2016). The role of fracture surface roughness in macroscopic fluid flow and heat transfer in fractured rocks. International Journal of Rock Mechanics and Mining Sciences, 87, 29-38.

[28] Min, K. B., Rutqvist, J., & Elsworth, D. (2009). Chemically and mechanically mediated influences on the transport and mechanical characteristics of rock fractures. International Journal of Rock Mechanics and Mining Sciences, 46(1), 80-89.

[29] Olsson, R., & Barton, N. (1993). Hydromechanical response of a fracture undergoing compression and shear. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 30(6), 845-851.

[30] Olsson, R., & Barton, N. (2001). An improved model for hydromechanical coupling during shearing of rock joints. International Journal of Rock Mechanics and Mining Sciences, 38(3-4), 317-329.

[31] Peng, H., Zhao, Z., Chen, W., Chen, Y., Fang, J., & Li, B. (2020). Thermal effect on permeability in a single granite fracture: Experiment and theoretical model. International Journal of Rock Mechanics and Mining Sciences, 131, 104358.

[32] Rabczuk, T., & Belytschko, T. (2004). Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 61(13), 2316-2343.

[33] Rabczuk, T., Zi, G., Bordas, S., & Nguyen-Xuan, H. (2010). A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 199 (45-48), 2437-2455.

[34] Raven, K. G., & Gale, J. E. (1985). Water flow in a natural rock fracture as a function of stress and sample size. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 22(3), 251-261.

[35] Rutqvist, J., & Stephansson, O. (2003). The role of hydromechanical coupling in fractured rock engineering. Hydrogeology Journal, 11(1), 7-40.

[36] Song, C., & Elsworth, D. (2024). Stress sensitivity of permeability in highpermeability sandstone sealed with microbially-induced calcium carbonate precipitation. Biogeotechnics, 2(1), 100063.

[37] Song, D., Liu, Y., Dai, F., Jiang, R., & Li, A. (2024). Quantitative prediction of surrounding rock deformation via an energy-based damage model combining with microseismic monitoring. Tunnelling and Underground Space Technology, 147, 105711.

[38] Thompson, M. E., & Brown, S. R. (1991). The effect of anisotropic surface roughness on flow and transport in fractures. Journal of Geophysical Research: Solid Earth, 96(B11), 21923-21934.

[39] Tsang, Y. W., & Witherspoon, P. A. (1983). The dependence of fracture mechanical and fluid flow properties on fracture roughness and sample size. Journal of Geophysical Research: Solid Earth, 88(B4), 2359-2366.

[40] Wang, J., Chen, L., Su, R., & Zhao, X. G. (2018). The Beishan underground research laboratory for geological disposal of high-level radioactive waste in China: Planning, site selection, site characterization and in situ tests. Journal of Rock Mechanics and Geotechnical Engineering, 10(4), 411-435.

[41] Wang, Z., Liu, J., Zheng, T., Qiao, L., & Li, K. (2023). Macroscopic and mesoscopic characteristics of radial flow in rough rock fractures. Rock Mechanics and Rock Engineering, 56(5), 4881-4900.

[42] Xiong, X., Li, B., Jing, Y., Koyama, T., & Zhang, C. (2011). Experimental and numerical study of the geometrical and hydraulic characteristics of a single rock fracture during shear. International Journal of Rock Mechanics and Mining Sciences, 48(6), 1292-1302.

[43] Yeo, I. W. (2001). Effect of contact obstacles on fluid flow in rock fractures. Geosciences Journal, 5(2), 139-143.

[44] Yeo, I. W., de Freitas, M. H., & Zimmerman, R.W. (1998). Effect of shear displacement on the aperture and permeability of a rock fracture. International Journal of Rock Mechanics and Mining Sciences, 35(6), 1051-1070.

[45] Zhang, Y., Gao, Z., Li, Y., & Zhuang, X. (2020). On the crack opening and energy dissipation in a continuum based disconnected crack model. Finite Elements in Analysis and Design, 170, 103333.

[46] Zhang, Y., Huang, J., Yuan, Y., & Mang, H. A. (2021). Cracking elements method with a dissipation-based arc-length approach. Finite Elements in Analysis and Design, 195, 103573.

[47] Zhang, Y., Yang, X., Wang, X., & Zhuang, X. (2021). A micropolar peridynamic model with non-uniform horizon for static damage of solids considering different nonlocal enhancements. Theoretical and Applied Fracture Mechanics, 113, 102930.

[48] Zhang, Y., & Mang, H. A. (2020). Global cracking elements: A novel tool for Galerkin-based approaches simulating quasi-brittle fracture. International Journal for Numerical Methods in Engineering, 121(23), 2462-2480.

[49] Zhang, Y., & Zhuang, X. (2019). Cracking elements method for dynamic brittle fracture. Theoretical and Applied Fracture Mechanics, 102, 1-9.

[50] Zhao, Z., Dou, Z., Xu, H., & Liu, Z. (2019). Shear behavior of Beishan granite fractures after thermal treatment. Engineering Fracture Mechanics, 213, 223-240.

[51] Zhao, Z., Jing, L., Neretnieks, I., & Moreno, L. (2011a). Numerical modeling of stress effects on solute transport in fractured rocks. Computers and Geotechnics, 38(1), 113-126.

[52] Zhao, Z., Jing, L., Neretnieks, I., & Moreno, L. (2011b). Analytical solution of coupled stress-flow-transport processes in a single rock fracture. Computers and Geosciences, 37(9), 1437-1449.

[53] Zhou, D., Zhao, Z., Li, B., Chen, Y., & Ding, W. (2020). Permeability evolution of grout infilled fractures subjected to triaxial compression with low confining pressure. Tunnelling and Underground Space Technology, 104, 103539.

[54] Zimmerman, R. W., & Bodvarsson, G. S. (1996). Hydraulic conductivity of rock fractures. Transport in Porous Media, 23(1), 1-30.

[55] Zimmerman, R. W., Chen, D. W., & Cook, N. G. W. (1992). The effect of contact area on the permeability of fractures. Journal of Hydrology, 139(1-4), 79-96.

[56] Zou, L., Jing, L., & Cvetkovic, V. (2015). Roughness decomposition and nonlinear fluid flow in a single rock fracture. International Journal of Rock Mechanics and Mining Sciences, 75, 102-118.