Research on Size Effect and Directionality of Roughness of Natural Rock Fracture Surface
Received date: 2023-10-06
Revised date: 2024-01-31
Online published: 2024-05-21
To delve into the size-related effects and directional properties of the roughness on rock fracture surfaces，this paper focus on analyzing the roughness correction coefficient C within the refined formula of the cubic law，as it effectively characterizes the roughness of natural rock fractures. Since Louis first introduced the cubic law，numerous scholars have since proposed numerous modified formulas，including those by Zhang Youtian，Zimmerman，and Xiong et al. Through conversion，we acquire the calculation formula for the roughness correction coefficient and utilize collected natural fractures for related computations.High-precision 3D scanning technology was used to scan natural rock samples and acquire roughness data of fracture surfaces. By combining this data with publicly available high-precision CT scan data of rough rock fractures，we generate spatial coordinates.Both formulaic and numerical methods were used to calculate and analyze the roughness correction coefficient C. Using the formulaic approach，the roughness correction coefficient for sample sizes ranging from 10% to 100% of the fracture surface were calculated and varying results were obtained，which indicates that roughness exhibits a scale effect. According to the numerical method，a well-fitting ellipse was obtained，indicating that the roughness correction coefficient possesses directionality and can be expressed using tensor notation. This conclusion is further supported by calculating the JRC value of rough fractures and their surface and crack width fractal dimensions，revealing that the roughness of fracture surfaces exhibits scale effects and anisotropy. Upon further investigation，it is discovered that the roughness correction coefficient tensor or roughness tensor，when combined with average crack width，can be utilized to form a single crack permeability tensor that quantifies the rough surface in complex rough crack network models
Qianwei MEI , Gang CHEN , Fengqiang LUO , Ling MA , Hongsheng GONG , Yanzhu LONG . Research on Size Effect and Directionality of Roughness of Natural Rock Fracture Surface[J]. Gold Science and Technology, 2024 , 32(2) : 290 -305 . DOI: 10.11872/j.issn.1005-2518.2024.02.137
| null | Barton N， Choubey V，1978.The shear strength of rock joints in theory and practice［J］.Rock Mechanics Felsmechanik Mécanique des Roches，10（1/2）：1-54. |
| null | Brown S R，1995.Simple mathematical-model of a rough fracture［J］.Journal of Geophysical Research-Solid Earth，DOI：10.1029/94JB03262 . |
| null | Candela T， Renard F， Yann K，et al，2012.Roughness of fault surfaces overnine decades of length scales［J］.Journal of Geophysical Research-Solid Earth，117：B08409.DOI：10.1029/2011JB009041 . |
| null | Chen Gang， Xu Shiguang， Ma Ling，et al，2022.Study on Fractured Permeability of Rough Rock Mass Based on Multi-Scale Three-Dimensional Spatial Fractured Distribution［M］.Beijing：Metallurgical Industry Press. |
| null | Cheng Huihui， Gao Yue， Guo Fengjuan，et al，2023.Research on seepage test model of rough rock fracture［J］.Water Resources and Power，41（1）：137-141. |
| null | Chen Shijiang， Zhu Wancheng， Wang Chuangye，et al，2017. Review of research progresses of the quantifying joint roughness coefficient［J］. Chinese Journal of Theoretical and Applied Mechanics，49 （2）：239-256. |
| null | Du S G， Lin H， Yong R，et al，2022.Characterization of joint roughness heterogeneity and its application in representative sample investigations［J］.Rock Mechanics and Rock Engineering，55：3253-3277 . |
| null | Fardin N， Jing L R， Stephansson O，2001.The scale dependence of rock joint surface roughness［J］.International Journal of Rock Mechanics and Mining Sciences，38（5）：659-669. |
| null | Hakami E， Larsson E，1996.Aperture measurements and flow experiments on a single natural fracture［J］.International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，33（4）：395-404. |
| null | He Yulong， Tao Yujing， Yang Lizhong，2010.Experimental research on hydraulic behaviors in a single joint with various values of JRC［J］.Chinese Journal of Rock Mechanics and Engineering，29（Supp.1）：3235-3240. |
| null | Jiang Yujing， Li Bo， Wang Gang，et al，2008.New advances in experimental study on seepage characteristics of rock fractures［J］. Chinese Journal of Rock Mechanics and Engineering，27（12）：2377-2386. |
| null | Ju Yang， Zhang Qingang， Yang Yongming，et al，2013.Experimental study on the seepage mechanism of rough single fractured fluid in rock mass［J］.Scientia Sinica （Technological），43（10）：1144-1154. |
| null | Ketcham R A， Slottke D T， Sharp J M，2010.Three-dimensional measurement of fractures in heterogeneous materials using high-resolution X-ray computed tomography［J］.Geosphere，6（5）：1-54. |
| null | Lang P S， Paluszny A， Zimmerman R W，2014.Permeability tensor of three-dimensional fractured porous rock and a comparison to trace map predictions（Article）［J］.Journal of Geophysical Research：Solid Earth，119（8）：6288-6307. |
| null | Lee S H， Yeo I W， Lee K K，et al，2017.The role of eddies in solute transport and recovery in rock fractures：Implication for groundwater remediation［J］.Hydrological Processes，31（20）：3580-3587. |
| null | Li B， Jiang Y J， Koyama T，et al，2008.Experimental study of the hydro-mechanical behavior of rock joints using a parallel-plate model containing contact areas and artificial fractures［J］.International Journal of Rock Mechanics and Mining Sciences，45（3）：362-375. |
| null | Liu R C， Li B， Jiang Y J，et al，2018.A numerical approach for assessing effects of shear on equivalent permeability and nonlinear flow characteristics of 2-D fracture networks［J］. Advances in Water Resources，111：289-300. |
| null | Liu Richeng， Jiang Yujing， Li Bo，et al，2014.Numerical calculation of directivity of equivalent permeability of fractured rock masses network［J］.Rock and Soil Mechanics，35（8）：2394-2400. |
| null | Liu Weiqun， Wang Dongni， Su Qiang，2016.Dual media model of shale layer with anisotropy involved and its simulation on gas migration［J］.Natural Gas Geoscience，27（8）：1374-1379. |
| null | Long J C S， Remer J S， Wilson C R，et al，1982.Porous media equivalents for networks of discontinuous fractures［J］.Water Resources Research，18（3）：645-658. |
| null | Louis C，1969. A Study of Groundwater Flow in Jointed Rock and Its Influence on The Stability of Rock Masses［D］. London：Imperial College. |
| null | Marcus H，1962.The permeability of a sample of an anisotropic porous medium［J］.Journal of Geophysical Research，67（13）：5215-5225. |
| null | Matsuki K， Lee J J， Sakaguchi K，et al，1999.Size effect in flow conductance of a closed small-scale hydraulic fracture in granite［J］.Geothermal Science and Technology，6：113-138. |
| null | Olsson R， Barton N，2001.An improved model for hydromechanical coupling during shearing of rock joints［J］.International Journal of Rock Mechanics and Mining Sciences，38（3）：317-329. |
| null | Patir N，1978.A numerical procedure for random generation of rough surfaces［J］.Wear，47（2）：263-277. |
| null | Qin Yuan， Zhang Xin， Chai Junrui，et al，2020.Simulating the influence of different joint roughness on single-fracture seepage［J］.Chinese Journal of Applied Mechanics，37（1）：455-462，500. |
| null | Rasouli V， Hosseinian A，2011.Correlations developed for estimation of hydraulic parameters of rough fractures through the simulation of JRC flow channels［J］.Rock Mechanics and Rock Engineering，44（4）：447-461. |
| null | Renshaw C E， Pollard D D，1995.An experimentally verified criterion for propagation across unbounded frictional interfaces in brittle， linear elastic materials［J］.International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，32（3）：237-249. |
| null | Richard K，2016.Fracture in tuff［EB/OL］.Digital Rocks Portal （April 2016）.：. |
| null | Richard K， Matthew C， Zhou J Q，et al，2018.Fracture in granite［EB/OL］.Digital Rocks Portal（December 2）.：. |
| null | Waite M E， Ge S M， Spetzler H，et al，1998.The effect of surface geometry on fracture permeability：A case study using a sinusoidal fracture［J］. Geophysical Research Letters，25（6）：813-816. |
| null | Walsh J B，1981.Effect of pore pressure and confining pressure on fracture permeability［J］.International Journal of Rock Mechanics and Mining Sciences，18（5）：429-435. |
| null | Wang Bao， Wang Yuan， Niu Yulong，2017.Determinateion on hydraulic aperture of single rough fractures based on standard curves of discrete joint roughness coefficien［J］.Water Resources and Power，35（4）：77-80，62. |
| null | Wang Gang， Jiang Yujing， Li Shucai，2014.Coupled Characteristics of Stress Seepage and Anchorage Theory of Fractured Rock Mass［M］.Beijing：Science Press. |
| null | Wang Ke， Sheng Jinchang， Gao Huicai，et al，2020. Study on seepage characteristics of rough crack under coupling of stress-seepage erosion［J］. Rock and Soil Mechanics，41（Supp.1）：30-40. |
| null | Wang L C， Cardenas M B， Zhou J Q，et al，2020.The complexity of nonlinear flow and non-fickian transport in fractures driven by three-dimensional recirculation zones［J］.Journal of Geophysical Research（Solid Earth），125（9）. DOI：10.1029/2020JB020028 . |
| null | Wang Yuan， Su Baoyu，2002.Research on the behavior of fluid flow in a single fracture and its equivalent hydraulic aperture［J］.Advances in Water Science，13（1）：61-68. |
| null | Wu Jimin， Chen Ling， Sun Shaorui，et al，2003.Joint roughness coefficients and their fractal dimension［J］.Journal of Hohai University（Natural Sciences），31（2）：152-155. |
| null | Xie L Z， Gao C， Ren L，et al，2015.Numerical investigation of geometrical and hydraulic properties in a single rock fracture during shear displacement with the Navier-Stokes equations ［J］.Environmental Earth Sciences，73（11）：7061-7074. |
| null | Xiong X B， Li B， Jiang Y J，et al，2011.Experimental and numerical study of the geometrical and hydraulic characteristics of a single rock fracture during shear［J］.International Journal of Rock Mechanics and Mining Sciences，48（8）：1292-1302. |
| null | Xiong Xiangbin， Zhang Chuhan， Wang Enzhi，2009.A review of steady state seepage in a single fracture of rock［J］.Chinese Journal of Rock Mechanics and Engineering，28（9）：1839-1847. |
| null | Zhang Ge， Tian Yuan， Li Yingjun，2019. Numerical study on the mechanism of fluid flow through single rough fractures with different JRC［J］. Scientia Sinica：Physica，Mechanica et Astronomica，49（1）：014701.. |
| null | Zhang Youtian，2005.Rock Hydraulics and Engineering［M］.Beijing：China Water and Power Press. |
| null | Zhong Zhen， Yan Jinxiu， Xu Congqiang，et al，2021.Study on size effect of permeability of single rough fracture and its corresponding influencing factors［J］.Water Resources and Hydropower Engineering，52（4）：192-201. |
| null | Zhou Chuangbing， Xiong Wenlin，1996.Relation between joint roughness coefficient and fractal dimension［J］. Journal of Wuhan University of Hydraulic and Electric Engineering，29（5）：1-5. |
| null | Zimmerman R， Bodvarsson G S，1996.Hydraulic conductivity of rock fractures［J］.Transport in Porous Media，23（1）：1-30. |
| null | 陈刚，徐世光，马玲，等，2022.基于多尺度三维空间裂隙分布的粗糙岩体裂隙渗透性研究［M］.北京：冶金工业出版社. |
| null | 陈辉辉，高悦，郭凤娟，等，2023.岩石粗糙裂隙渗流试验模型研究［J］.水电能源科学，41（1）：137-141. |
| null | 陈世江，朱万成，王创业，等，2017.岩体结构面粗糙度系数定量表征研究进展［J］.力学学报，49 （2）：239-256. |
| null | 贺玉龙，陶玉敬，杨立中，2010.不同节理粗糙度系数单裂隙渗流特性试验研究［J］.岩石力学与工程学报，29（增1）：3235-3240. |
| null | 蒋宇静，李博，王刚，等，2008.岩石裂隙渗流特性试验研究的新进展［J］.岩石力学与工程学报，27（12）：2377-2386. |
| null | 鞠杨，张钦刚，杨永明，等，2013.岩体粗糙单裂隙流体渗流机制的实验研究［J］.中国科学（技术科学），43（10）：1144-1154. |
| null | 刘日成，蒋宇静，李博，等，2014.岩体裂隙网络等效渗透系数方向性的数值计算［J］.岩土力学，35（8）：2394-2400. |
| null | 刘卫群，王冬妮，苏强，2016.基于页岩储层各向异性的双重介质模型和渗流模拟［J］.天然气地球科学，27（8）：1374-1379. |
| null | 覃源，张鑫，柴军瑞，等，2020.模拟不同节理粗糙度对单裂隙渗流的影响［J］.应用力学学报，37（1）：455-462，500. |
| null | 王报，王媛，牛玉龙，2017.基于离散标准节理粗糙度系数曲线的粗糙单裂隙等效水力隙宽的确定［J］.水电能源科学，35（4）：77-80，62. |
| null | 王刚，蒋宇静，李术才，2014.裂隙岩体应力渗流耦合特性及锚固理论［M］.北京：科学出版社. |
| null | 王珂，盛金昌，郜会彩，等，2020.应力—渗流侵蚀耦合作用下粗糙裂隙渗流特性研究［J］.岩土力学，41（增1）：30-40. |
| null | 王媛，速宝玉，2002.单裂隙面渗流特性及等效水力隙宽［J］.水科学进展，13（1）：61-68. |
| null | 吴继敏，陈玲，孙少锐，等，2003.裂隙粗糙度系数及其分数维研究［J］.河海大学学报（自然科学版），31（2）：152-155. |
| null | 熊祥斌，张楚汉，王恩志，2009.岩石单裂隙稳态渗流研究进展［J］.岩石力学与工程学报，28（9）：1839-1847. |
| null | 张戈，田园，李英骏，2019.不同JRC粗糙单裂隙的渗流机理数值模拟研究［J］.中国科学（物理学力学天文学），49（1）：014701.. |
| null | 张有天，2005.岩石水力学与工程［M］.北京：中国水利水电出版社. |
| null | 钟振，闫金秀，徐从强，等，2021.粗糙单裂隙渗透性尺寸效应及其影响因素研究［J］.水利水电技术，52（4）：192-201. |
| null | 周创兵，熊文林，1996.节理面粗糙度系数与分形维数的关系［J］.武汉水利电力大学学报，29（5）：1-5. |
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