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    Volume 51 Issue 2
    Feb.  2026
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    Song Zhenyu, Yan Bingming, Li Bo, Zou Liangchao, Shi Zhenming, 2026. Study on Time-Dependent Closure Behavior of Rock Fractures Subject to Normal Stress. Earth Science, 51(2): 496-512. doi: 10.3799/dqkx.2025.241
    Citation: Song Zhenyu, Yan Bingming, Li Bo, Zou Liangchao, Shi Zhenming, 2026. Study on Time-Dependent Closure Behavior of Rock Fractures Subject to Normal Stress. Earth Science, 51(2): 496-512. doi: 10.3799/dqkx.2025.241

    Study on Time-Dependent Closure Behavior of Rock Fractures Subject to Normal Stress

    doi: 10.3799/dqkx.2025.241
    • Received Date: 2025-07-15
    • Publish Date: 2026-02-25
    • This study conducted time-dependent compression tests on asperities with different height-to-radius ratios using ultra-hard gypsum. According to Hertz contact theory, the attenuation laws of the elastic modulus of different asperities over time were fitted. Time-dependent closure tests were performed on fresh fracture surfaces of red sandstone and limestone under varying normal stresses. By integrating wavelet analysis, region growth algorithms, and the reference surface method, a novel approach was developed for identifying the mesoscale asperity morphology of rock fractures, and compared the differences in the number, height, and height-to-radius ratio of asperities before and after the experiment. Utilizing Boussinesq's solution, an influence matrix was constructed to account for interactions between asperities. Based on the law of the elastic modulus decaying over time, enabling time-dependent closure calculations for different rock fractures under variable stress conditions. This approach precisely analyzes the temporal evolution of strain, contact area, and contact stress for individual asperity, with simulation results matching experimental data in terms of damage area and creep deformation. The study reveals the pivotal role of asperities with distinct mesoscale morphological features in the time-dependent closure process of rock fractures under compression.

       

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    • Alamos, F. J., Philo, M., Go, D. B., et al., 2022. Rough Surface Contact under Creep Conditions. Tribology International, 176: 107916. https://doi.org/10.1016/j.triboint.2022.107916
      Brot, C. C., Etsion, I., Kligerman, Y., 2008. A Contact Model for a Creeping Sphere and a Rigid Flat. Wear, 265(5/6): 598-605. https://doi.org/10.1016/j.wear.2007.12.003
      Brown, S. R., Scholz, C. H., 1985. Closure of Random Elastic Surfaces in Contact. Journal of Geophysical Research: Solid Earth, 90(B7): 5531-5545. https://doi.org/10.1029/JB090iB07p05531
      Chen, L., Zhao, X. G., Liu, J., et al., 2023. Progress on Rock Mechanics Research of Beishan Granite for Geological Disposal of High-Level Radioactive Waste in China. Rock Mechanics Bulletin, 2(3): 100046. https://doi.org/10.1016/j.rockmb.2023.100046
      Chung, J. C., 2010. Elastic-Plastic Contact Analysis of an Ellipsoid and a Rigid Flat. Tribology International, 43(1/2): 491-502. https://doi.org/10.1016/j.triboint.2009.08.005
      Ciavarella, M., Delfine, V., Demelio, G., 2006. A "Re-Vitalized" Greenwood and Williamson Model of Elastic Contact between Fractal Surfaces. Journal of the Mechanics and Physics of Solids, 54(12): 2569-2591. https://doi.org/10.1016/j.jmps.2006.05.006
      Goedecke, A., Jackson, R. L., Mock, R., 2010. Asperity Creep under Constant Force Boundary Conditions. Wear, 268(11/12): 1285-1294. https://doi.org/10.1016/j.wear.2010.01.025
      Greenwood, J. A., 2006. A Simplified Elliptic Model of Rough Surface Contact. Wear, 261(2): 191-200. https://doi.org/10.1016/j.wear.2005.09.031
      Greenwood, J. A., Williamson, J. B. P., 1966. Contact of Nominally Flat Surfaces. Proceedings of the Royal Society of London Series A, Mathematical and Physical Sciences, 295(1442): 300-319
      Huang, K., Yu, F., Zhang, W., et al., 2023. Experimental and Numerical Simulation Study on the Influence of Gaseous Water on the Mechanical Properties of Red-Layer Mudstone in Central Sichuan. Rock Mechanics and Rock Engineering, 56(4): 3159-3178. https://doi.org/10.1007/s00603-023-03228-z
      Kang, F. C., Li, Y. C., Tang, C. A., et al., 2022. Competition between Cooling Contraction and Fluid Overpressure on Aperture Evolution in a Geothermal System. Renewable Energy, 186: 704-716. https://doi.org/10.1016/j.renene.2022.01.033
      Kang, H., Einstein, H., Brown, S., et al., 2020. Numerical Simulation for Rock Fracture Viscoelastic Creep under Dry Conditions. Geofluids, 2020(1): 8879890. https://doi.org/10.1155/2020/8879890
      Kling, T., Vogler, D., Pastewka, L., et al., 2018. Numerical Simulations and Validation of Contact Mechanics in a Granodiorite Fracture. Rock Mechanics and Rock Engineering, 51(9): 2805-2824. https://doi.org/10.1007/s00603-018-1498-x
      Kumamoto, K. M., Thom, C. A., Wallis, D., et al., 2017. Size Effects Resolve Discrepancies in 40 Years of Work on Low-Temperature Plasticity in Olivine. Science Advances, 3(9): e1701338. https://doi.org/10.1126/sciadv.1701338
      Li, B., Cui, X. F., Mo, Y. Y., et al., 2021. Deformation Behavior of Dislocated Sandstone Fractures Subject to Normal Stresses. Rock and Soil Mechanics, 42(7): 1850-1860 (in Chinese with English abstract).
      Li, B., Mo, Y. Y., Zou, L. C., et al., 2022. An Extended Hyperbolic Closure Model for Unmated Granite Fractures Subject to Normal Loading. Rock Mechanics and Rock Engineering, 55(7): 4139-4158. https://doi.org/10.1007/s00603-022-02862-3
      Li, B., Zhao, Z. H., Jiang, Y. J., et al., 2015. Contact Mechanism of a Rock Fracture Subjected to Normal Loading and Its Impact on Fast Closure Behavior during Initial Stage of Fluid Flow Experiment. International Journal for Numerical and Analytical Methods in Geomechanics, 39(13): 1431-1449. https://doi.org/10.1002/nag.2365
      Ma, H. C., Cao, Y., Qian, J. Z., et al., 2023. Theoretical Study of the Mesoscopic Mechanism of Rock Fractures during Normal Deformation. Rock Mechanics and Rock Engineering, 56(8): 5719-5733. https://doi.org/10.1007/s00603-023-03372-6
      Malamut, S., Kligerman, Y., Etsion, I., 2009. The Effect of Dwell Time on the Static Friction in Creeping Elastic-Plastic Polymer Spherical Contact. Tribology Letters, 35(3): 159-170. https://doi.org/10.1007/s11249-009-9445-3
      Matsuki, K., Wang, E. Q., Sakaguchi, K., et al., 2001. Time-Dependent Closure of a Fracture with Rough Surfaces under Constant Normal Stress. International Journal of Rock Mechanics and Mining Sciences, 38(5): 607-619. https://doi.org/10.1016/S1365-1609(01)00022-3
      Ovcharenko, A., Halperin, G., Etsion, I., 2009. Experimental Study of a Creeping Polymer Sphere in Contact with a Rigid Flat. Journal of Tribology, 131: 011404. https://doi.org/10.1115/1.3002330
      Pyrak-Nolte, L. J., Nolte, D. D., 2016. Approaching a Universal Scaling Relationship between Fracture Stiffness and Fluid Flow. Nature Communications, 7: 10663. https://doi.org/10.1038/ncomms10663
      Qu, J. K., Xue, Y. G., Kong, F. M., et al., 2025. Multi-Scale Analysis of the Influence of Red-Bed Lithological Interface on Tunnel Deformation and Instability. Engineering Geology, 357: 108314. https://doi.org/10.1016/j.enggeo.2025.108314
      Rohmer, J., Pluymakers, A., Renard, F., 2016. Mechano-Chemical Interactions in Sedimentary Rocks in the Context of CO2 Storage: Weak Acid, Weak Effects? Earth-Science Reviews, 157: 86-110. https://doi.org/10.1016/j.earscirev.2016.03.009
      Rostami, A., Goedecke, A., Mock, R., et al., 2014. Three-Dimensional Modeling of Elasto-Plastic Sinusoidal Contact under Time Dependent Deformation Due to Stress Relaxation. Tribology International, 73: 25-35. https://doi.org/10.1016/j.triboint.2013.12.020
      Serati, M., Alehossein, H., Williams, D. J., 2015. Estimating the Tensile Strength of Super Hard Brittle Materials Using Truncated Spheroidal Specimens. Journal of the Mechanics and Physics of Solids, 78: 123-140. https://doi.org/10.1016/j.jmps.2015.02.011
      Song Z. Y., Li B., Yan B. M., et al., 2024. Time-Dependent Closure Calculation Method of Rock Fractures Considering the Attenuation of Relaxation Modulus. In: China Rock Mechanics and Engineering Society, International Association for Geohazards and Risk Reduction. Proceedings of the 21st Chinese Rock Mechanics and Engineering Academic Conference, CHINA ROCK 2024. Department of Underground Architecture and Engineering, Tongji University; Department of Environmental Science and Engineering, Royal Institute of Technology, Sweden, 2024: 42-48 (in Chinese with English abstract).
      Song, Z. Y., Li, B., Chen, X. W., et al., 2025. Time-Dependent Deformation of Fracture Asperities with Different Height-to-Radius Ratios Subject to Normal Loading. Rock Mechanics and Rock Engineering, 2025: 1-18. https://doi.org/10.1007/s00603-025-04858-1
      Sun, J., 2007. Rock Rheological Mechanics and Its Advance in Engineering Applications. Chinese Journal of Rock Mechanics and Engineering, 26(6): 1081-1106 (in Chinese with English abstract).
      Tang, Z. C., Zhang, Q. Z., 2021. Elliptical Hertz-Based General Closure Model for Rock Joints. Rock Mechanics and Rock Engineering, 54(1): 477-486. https://doi.org/10.1007/s00603-020-02275-0
      Tian, X. F., Bhushan, B., 1996. A Numerical Three-Dimensional Model for the Contact of Rough Surfacesby Variational Principle. Journal of Tribology, 118(1): 33-42. https://doi.org/10.1115/1.2837089
      Viswanathan, H. S., Ajo-Franklin, J., Birkholzer, J. T., et al., 2022. From Fluid Flow to Coupled Processes in Fractured Rock: Recent Advances and New Frontiers. Reviews of Geophysics, 60(1): e2021RG000744. https://doi.org/10.1029/2021RG000744
      Wang, Z., Shen, M. R., Tian, G. H., et al., 2017. Characteristics of Aging Strength of Structural Planes with Different Roughness. Chinese Journal of Rock Mechanics and Engineering, 36(S1): 3287-3296 (in Chinese with English abstract).
      Wen, Y. Q., Tang, J. Y., Zhou, W., et al., 2022. New Analytical Model of Elastic-Plastic Contact for Three-Dimensional Rough Surfaces Considering Interaction of Asperities. Friction, 10(2): 217-231. https://doi.org/10.1007/s40544-020-0419-7
      Xue, Y. C., Xu, T., Heap, M. J., et al., 2023. Time-Dependent Cracking and Brittle Creep in Macrofractured Sandstone. International Journal of Rock Mechanics and Mining Sciences, 162: 105305. https://doi.org/10.1016/j.ijrmms.2022.105305
      Zhang, L. L., Wang, X. J., 2020. Viscoelastic-Plastic Damage Creep Model for Rock. Chinese Journal of Geotechnical Engineering, 42(6): 1085-1092 (in Chinese with English abstract).
      Zhang, Q. Z., Wu, C. Z., Fei, X. C., et al., 2019. Time-Dependent Behavior of Rock Joints Considering Asperity Degradation. Journal of Structural Geology, 121: 1-9. https://doi.org/10.1016/j.jsg.2019.01.004
      Zhang, W. G., Lin, S. C., Wang, L. Q., et al., 2024. A Novel Creep Contact Model for Rock and Its Implement in Discrete Element Simulation. Computers and Geotechnics, 167: 106054. https://doi.org/10.1016/j.compgeo.2 023. 106054 doi: 10.1016/j.compgeo.2023.106054
      Zou, L. C., Li, B., Mo, Y. Y., et al., 2020. A High-Resolution Contact Analysis of Rough-Walled Crystalline Rock Fractures Subject to Normal Stress. Rock Mechanics and Rock Engineering, 53(5): 2141-2155. https://doi.org/10.1007/s00603-019-02034-w
      李博, 崔逍峰, 莫洋洋, 等, 2021. 法向应力作用下砂岩错位裂隙变形行为研究. 岩土力学, 42(7): 1850-1860.
      宋振宇, 李博, 颜炳明, 等, 2024. 考虑松弛模量衰减的岩石裂隙时变闭合计算方法. 见: 中国岩石力学与工程学会, 国际地质灾害与减灾协会. CHINA ROCK 2024第二十一次中国岩石力学与工程学术年会论文集. 同济大学地下建筑与工程系; 瑞典皇家理工学院环境科学与工程系, 2024: 42-48.
      孙钧, 2007. 岩石流变力学及其工程应用研究的若干进展. 岩石力学与工程学报, 26(6): 1081-1106.
      王振, 沈明荣, 田光辉, 等, 2017. 不同粗糙度结构面时效强度特征. 岩石力学与工程学报, 36(S1): 3287-3296.
      张亮亮, 王晓健, 2020. 岩石黏弹塑性损伤蠕变模型研究. 岩土工程学报, 42(6): 1085-1092.
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