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| Study on stochastic method for modeling rough joints based on fractal theory |
| SONG Yu，LIU Baoguo，REN Darui，YU Mingyuan，HUANG Rui |
| (School of Civil Engineering，Beijing Jiaotong University，Beijing 100044，China) |
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Abstract The three-dimensional morphology is the key factor affecting the shear mechanical properties of rock joints. 3D scanning is performed to reconstruct the surface morphology model of the sandstone tension joint obtained by the Brazilian splitting test. The stochastic methodology of generating fractal digital elevation models，which is widely used in topography，is introduced to construct surface models with different rough morphological features based on the statistical self-similarity of rough joint surfaces. By adjusting the random parameter d，a series of fractal rough joints with different morphological features are generated using the “diamond-square” algorithm，and compared with the natural sandstone tension joint obtained by the Brazilian splitting test. 3D box-counting method is used to calculate the fractal dimensions of both kinds of joint surfaces，and the statistical distribution of apparent dip angles along a specific shear direction is analyzed. Considering the fractal dimension and the standard deviation of the statistical distribution of apparent dip angles as characterization parameters of 3D joint roughness，it is confirmed that the morphological feature of the natural sandstone tension joint conform to that of the artificial surface with the random parameter d ranging from 2 mm to 3 mm，verifying the feasibility of the stochastic method of constructing digital elevation model based on fractal theory for modelling rough joints with different morphologies.
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[1] 孙洪泉. 分形几何与分形插值[M]. 北京：科学出版社，2011：153–183.(SUN Hongquan. Fractal geometry and fractal interpolation[M]. Beijing：Science Press，2011：153–183.(in Chinese))
[2] XIE H，WANG J，STEIN E. Direct fractal measurement and multifractal properties of fracture surfaces[J]. Physics Letters A，1998，242：41–50.
[3] 孙洪泉，谢和平. 断层粗糙表面的分形模拟[J]. 中国矿业大学学报，1999，28(5)：433–436.(SUN Hongquan，XIE Heping. Fractal simulation of the fault surface[J]. Journal of China University of Mining and Technology，1999，28(5)：433–436.(in Chinese))
[4] 王金安，谢和平，田晓燕，等. 岩石断裂表面分形测量的尺度效应[J]. 岩石力学与工程学报，2000，19(1)：11–17.(WANG Jin¢an，XIE Heping，TIAN Xiaoyan，et al. Scale effect on fractal measurement of rock fracture surfaces[J]. Chinese Journal of Rock Mechanics and Engineering，2000，19(1)：11–17.(in Chinese))
[5] BARTON N. Rock mechanics review，the shear strength of rock and rock joints[J]. International Journal of Rock Mechanics and Mining Science and Geomechanics Abstracts，1973，13：255–279.
[6] HUDSON J A，PRIEST S D. Discontinuities and rock mass geometry[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1979，16(6)：339–362.
[7] 夏才初. 岩石表面形貌学与节理力学研究[博士学位论文][D]. 长沙：中南大学，1992.(XIA Caichu. Study of rock surface topography and joint mechanical properties[Ph. D. Thesis][D]. Changsha：Central South University，1992.(in Chinese))
[8] 伍法权. 统计岩体力学原理[M]. 武汉：中国地质大学出版社，1993：59–63.(WU Faquan. Principles of statistical mechanics of rock[M]. Wuhan：China University of Geosciences Press，1993：59–63.(in Chinese))
[9] 孙洪泉，谢和平. 岩石断裂表面的分形模拟[J]. 岩土力学，2008，29(2)：347–352.(SUN Hongquan，XIE Heping. Fractal simulation of rock fracture surface[J]. Rock and Soil Mechanics，2008，29(2)：347–352.(in Chinese))
[10] 汤国安，那嘉明，程维明. 我国区域地貌数字地形分析研究进展[J]. 测绘学报，2017，46(10)：1 570–1 591.(TANG Guoan，NA Jiaming，CHENG Weiming. Progress of digital terrain analysis on regional geomorphology in China[J]. Acta Geodaetica et Cartographica Sinica，2017，46(10)：1 570–1 591.(in Chinese))
[11] 周志富. 地形建模中的分形应用及分析[J]. 测绘与空间地理信息，2019，42(12)：107–110.(ZHOU Zhifu. Application and analysis of fractal theory in mining area terrain modeling[J]. Geomatics and Spatial Information Technology，2019，42(12)：107–110.(in Chinese))
[12] 郭敬磊. 基于DEM数据的三维地形地类可视化研究[博士学位论文][D]. 南京：东南大学，2016.(GUO Jinglei. The 3D visualization of terrain and terrain category based on DEM[Ph. D. Thesis][D]. Nanjing：Southeast University，2016.(in Chinese))
[13] LAI F，HUANG Y. Probability- and curve-based fractal reconstruction on 2D DEM terrain profile[J]. Chaos Solitons and Fractals，2009，41(2)：970–978.
[14] HE W，ZHENG N，LIANG L. An improved fractal construction on 3D DEM terrain profile[C]// IEEE International Geoscience and Remote Sensing Symposium. [S. l.]：[s. n.]，2009：654–657.
[15] 徐琼燕，李俊峰，吴印华. 基于分形理论的三维地形生成算法研究与实现[J]. 计算机与现代化，2011，(5)：74–77.(XU Qiongyan，LI Junfeng，WU Yinhua. Research and application of 3D terrain generation algorithm based on fractal theory[J]. Computer and Modernization，2011，(5)：74–77 (in Chinese))
[16] 赵敏荣，张曦文. 局部区域地形地貌生成方法[J]. 工程图学学报，2011，32(6)：62–65.(ZHAO Minrong，ZHANG Xiwen. Method of creating camouflage physiognomy for a local region[J]. Journal of Engineering Graphics，2011，32(6)：62–65.(in Chinese))
[17] ZHOU X，XIAO N. A hierarchical-fractal approach for the rock reconstruction and numerical analysis[J]. International Journal of Rock Mechanics and Mining Sciences，2018，109：68–83.
[18] 贺晶晶，师俊平. 冻融后不同含水状态砂岩的剪切破坏特性[J]. 岩石力学与工程学报，2018，37(6)：1 350–1 358.(HE Jingjing，SHI Junping. Shear failure properties of sandstone with different moisture contents after cyclic freezing-thawing[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(6)：1 350–1 358.(in Chinese))
[19] 向 高，刘建锋，李天一，等. 基于声发射的盐岩变形破坏过程的分形与损伤特征研究[J]. 岩土力学，2018，39(8)：2 905–2 912. (XIANG Gao，LIU Jianfeng，LI Tianyi，et al. Study of fractal and damage characteristic in the deformation and failure process of salt rack based on acoustic emission[J]. Rock and Soil Mechanics，2018，39(8)：2 905–2 912.(in Chinese))
[20] 张 科，刘享华，李 昆，等. 含孔多裂隙岩石力学特性与破裂分形维数相关性研究[J]. 岩石力学与工程学报，2018，37(12)： 2 785–2 794.(ZHANG Ke，LIU Xianghua，LI Kun，et al. Investigation on the correlation between mechanical characteristics and fracturing fractal dimension of rocks containing a hole and multi-flaws[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(12)：2 785–2 794.(in Chinese))
[21] 张蓉蓉. 不同温度处理后深部砂岩动态力学及损伤特性试验与分析[J]. 岩石力学与工程学报，2018，37(增2)：3 879–3 890.(ZHANG Rongrong. Test and analysis of dynamic mechanics and damage characteristics of deep sandstone after different temperatures[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(Supp.2)：3 879–3 890.(in Chinese))
[22] ZHOU H，XIE H. Direct estimation of the fractal dimensions of a Fracture Surface of Rock[J]. Surface Review and Letters，2003，10(5)：751–762.
[23] 冯夏庭，王泳嘉. 岩石节理力学参数的非线性估计[J]. 岩土工程学报，1999，21(3)：12–16.(FENG Xiating，WANG Yongjia. Nonlinear estimation of rock joint mechanical parameters[J]. Chinese Journal of Geotechnical Engineering，1999，21(3)：12–16.(in Chinese))
[24] 李 淼，乔 兰，周 明，等. 节理粗糙度对应力波传播的影响研究[J]. 岩石力学与工程学报，2019，38(增1)：2 840–2 847.(LI Miao，QIAO Lan，ZHOU Ming，et al. Research of joint roughness effects on stress wave propagation[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(Supp.1)：2 840–2 847.(in Chinese))
[25] 申林方，王志良，曾 叶，等. 基于粗糙岩体裂隙表面反应的格子Boltzmann渗流–溶解耦合模型[J]. 岩石力学与工程学报，2019，38(8)：1 615–1 626.(SHEN Linfang，WANG Zhiliang，ZENG Ye，et al. A coupled seepage and dissolution model of rough rock fractures considering surface reaction based on lattice Boltzmann method[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(8)：1 615–1 626.(in Chinese))
[26] 邹先坚，王益腾，王川婴. 钻孔图像中岩石结构面三维形貌特征及优势抗滑方向研究[J]. 岩土力学，2020，41(增1)：1–9.(ZOU Xianjian，WANG Yiteng，WANG Chuanying. Three-dimensional morphological feature of rock structural surfaces and dominant anti-slip direction using the borehole images[J]. Rock and Soil Mechanics，2020，41(Supp.1)：1–9.(in Chinese))
[27] PARK J，SONG J. Numerical method for the determination of contact areas of a rock joint under normal and shear loads[J]. International Journal of Rock Mechanics and Mining Sciences，2013，58：8–22.
[28] GRASSELLI G. Manuel rocha medal recipient shear strength of rock joints based on quantified surface description[J]. Rock Mechanics and Rock Engineering，2006，39(4)：295–314.
[29] LIU Q，TIAN Y，JI P，et al. Experimental investigation of the peak shear strength criterion based on three-dimensional surface description[J]. Rock Mechanics and Rock Engineering，2018，51(4)：1 005–1 025.
[30] DANG W，WU W，KONIETZKY H，et al. Effect of shear-induced aperture evolution on fluid flow in rock fractures[J]. Computers and Geotechnics，2019，114：DOI: 10.1016/j.compgeo.2019.103152
[31] GOODMAN R E. Methods of geological engineering in discontinuous rocks[M]. [S. l.]：West Pub. Co.，1976：158–208.
[32] LIU Q，TIAN Y，LIU D，et al. Updates to JRC-JCS model for estimating the peak shear strength of rock joints based on quantified surface description[J]. Engineering Geology，2017，228：282–300.
[33] TIAN Y，LIU Q，HAO M，et al. New peak shear strength model for cement filled rock joints.[J]. Engineering Geology，2018，233：269–280.
[34] MANDELBROT B B. The fractal geometry of nature[M]. New York：[s. n.]，1982：1–24.
[35] CLARKE K C. Computation of the fractal dimension of topographic surfaces using the triangular prism surface area method[J]. Computers and Geosciences，1986，12(5)：713–722.
[36] 张亚衡，周宏伟，谢和平. 粗糙表面分形维数估算的改进立方体覆盖法[J]. 岩石力学与工程学报，2005，24(17)：3 192–3 196. (ZHANG Yaheng，ZHOU Hongwei，XIE Heping. Improved cubic covering method for fractal dimensions of a fracture surface of rock[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(17)：3 192–3 196.(in Chinese))
[37] 刘庆元，易柳城，刘 莉. 基于diamond-square算法的数字地形模型构建与三维可视化研究[J]. 测绘工程，2014，23(2)：1–4.(LIU Qingyuan，YI Liucheng，LIU Li. Digital terrain model construction and 3D visualization based on diamond square algorithm[J]. Engineering of Surveying and Mapping，2014，23(2)：1–4.(in Chinese))
[38] DOUILLET N. 3D fractal mountain[CP/OL]. [2020–05–10]. https://www.mathworks.com/matlabcentral/fileexchange/73544-3d- fractal-mountain. |
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2021, Vol. 40 
