岩石节理形貌粗糙度系数与分形维数及几个参数的关系分析
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摘要
为了更加准确地描述岩石节理形貌粗糙度系数(JRC),利用26组花岗岩试样劈裂形成模拟天然节理和20组人工预制具有不同JRC系数值的试样来模拟节理表面形貌,研究了节理三维形貌各向异性分形特征、JRC以及剖面线平均分形维数和节理表面分形维数之间的关系。并且在前人研究的基础上,分析了其他学者较少研究的几个参数,即节理剖面系数R_p、粗度轮廓的最大波谷深度R_v、粗度轮廓的均方根(RMS)的偏差R_q及峰度系数Sku几个统计参数和JRC之间的相关关系。结果表明,尽管各方向的分形维数差异较小,但是仍然存在各向异性特征。JRC与分形维数之间存在较为明显的指数关系,而剖面线平均分形维数和节理表面分形维数之间存在很强的线性相关关系,JRC与R_p、R_v、Sku之间的相关关系为线性关系,且R_p、R_v与JRC的相关关系拟合结果很相似,均为线性相关。而JRC与R_q之间存在抛物线的关系,拟合结果 JRC=3.80013+4.3267e43.3276Rq。通过运用分形和统计参数联合描述JRC更加全面。
In order to more accurately describe rock joint roughness coefficient( JRC),26 groups of granite samples containing crack profile simulated natural joints and 20 groups of numerical artificial prefabricated with different roughness JRC samples are used to simulate joint surface topography. Then,anisotropic fractal feature of joint 3D morphology,the relationship among JRC,the average fractal dimension and surface profile line fractal joint dimension are researched. On the basis of previous studies,correlation between several statistical parameters,including joint profile coefficient Rp,maximum trough depth of the roughness profile Rv,root mean square deviation RMS of roughness profile R_q,coefficient of kurtosis Skuand JRC are analyzed. The results show that there is the anisotropic characteristic although the difference of fractal dimension in each azimuth angle is small. There is the obvious exponential relationship between JRC and the fractal dimension,meantime,combined with the strongly linear relationship between the average profile fractal dimension and surface fractal dimension of joints. The linear relationship between JRC and R_p,R_v,Sku,R_p is found. The fitting correlation between Rp、Rvand JRC are very similar,but there is a parabola relationship between JRC and Rq,the fitting result is JRC = 3. 80013 +4. 3267e~(43. 3276) R_q. It is more comprehensive by using fractal theory and statistical parameters to describe the JRC.
In order to more accurately describe rock joint roughness coefficient( JRC),26 groups of granite samples containing crack profile simulated natural joints and 20 groups of numerical artificial prefabricated with different roughness JRC samples are used to simulate joint surface topography. Then,anisotropic fractal feature of joint 3D morphology,the relationship among JRC,the average fractal dimension and surface profile line fractal joint dimension are researched. On the basis of previous studies,correlation between several statistical parameters,including joint profile coefficient Rp,maximum trough depth of the roughness profile Rv,root mean square deviation RMS of roughness profile R_q,coefficient of kurtosis Skuand JRC are analyzed. The results show that there is the anisotropic characteristic although the difference of fractal dimension in each azimuth angle is small. There is the obvious exponential relationship between JRC and the fractal dimension,meantime,combined with the strongly linear relationship between the average profile fractal dimension and surface fractal dimension of joints. The linear relationship between JRC and R_p,R_v,Sku,R_p is found. The fitting correlation between Rp、Rvand JRC are very similar,but there is a parabola relationship between JRC and Rq,the fitting result is JRC = 3. 80013 +4. 3267e~(43. 3276) R_q. It is more comprehensive by using fractal theory and statistical parameters to describe the JRC.
引文
[1]贾洪强.岩石节理面表面形态与剪切破坏特性的实验研究[D].长沙:中南大学,2011.
[2]郭保华.岩石裂隙面粗糙度参数关系分析[J].采矿与安全工程学报,2011,28(2):241-246.
[3]BARTON N,CHOUBEY V.The shear strength of rock joints in theory and practice[J].Rock Mechanics,1977,10(1/2):1–54.
[4]MANDELBROT B B.How long is the coast of Britain?Statistical selfsimilarity and fractal dimension[J].1967,156(3775):636-638.
[5]TURK N,GREIG M J,DEARMAN W R,et al.Characterization of rock joint surfaces by fractal dimension[C].Proceeding of the 28th Symposium on Rock Mechanics.Tucson:Balkema,1987:1223-1236.
[6]LEE Y H,CARR J R,BARR D J,et al.The fractal dimension as a measure of the roughness of rock discontinuity profiles[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1990,27(6):453-464.
[7]谢和平,PARISEAU W G.岩石节理粗糙系数(JRC)的分形估计[J].中国科学(B辑),1994,24(5):524-530.
[8]曹平,贾洪强,刘涛影,等.岩石节理表面三维形貌特征的分形分析[J].岩石力学与工程学报,2011,30,(Z2):3839-3843.
[9]孙辅庭,佘成学,蒋庆仁.一种新的岩石节理面三维粗糙度分形描述方法[J].岩土力学,2013,34(8):2238-2242.
[10]王金安,谢和平.岩石断裂面的各向异性分形和多重分形研究[J].岩土工程学报,1998,20(6):16-21.
[11]BARTON N,BANDIS S.Effects of block size on the shear behavior of jointed rock[C].Proceedings of the 23rd U.S.Symposium on Rock Mechanics.Berkeley:Public New York,1982:739–760.
[12]TSE R,CRUDEN D M.Estimating joint roughness coefficients[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1979,16(5):303-307.
[13]MAERZ N H,FRANKLIN J A,BENNETT C P.Joint roughness measurement using shadow profilometry[J].International Joint Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1990,27(5):329-343.
[14]ODLING N E.Natural fracture profiles,fractal dimension and joint roughness coefficients[J].Rock Mechanics and Rock Engineering,1994,27(3):135-153.
[15]孙辅庭,佘成学,万利台.新的岩石节理粗糙度指标研究[J].岩石力学与工程学报,2013,32(12):2513-2519.
[16]吴月秀,刘泉声,刘小燕.岩石节理粗糙度系数与统计参数的相关关系研究[J].岩石力学与工程学报,2011,30(Z1):2593-2598.
[17]王卫华,李坤,严哲,等.基于BP神经网络方法研究岩石节理形貌粗糙度系数[J].世界科技研究与发展,2016,38(3):518-521.
[18]谢和平.岩石节理的分形描述[J].岩土工程学报,1995,17(1):18-23.
[19]MANDELBROT B B.The fractal geometry of nature[M].New York:W.H.Freeman and Company,1982.
[20]XIE Heping,WANG Jinan,XIE Weihong,et al.Fractal effects of surface roughness on the mechanical behavior of rock joints[J].Chaos,Solitons&Fractals,1997,8(2):221-252.
[21]丁增志.节理表面形貌研究及在非贯通节理岩体强度准则中的应用[D].上海:同济大学,2007.
[2]郭保华.岩石裂隙面粗糙度参数关系分析[J].采矿与安全工程学报,2011,28(2):241-246.
[3]BARTON N,CHOUBEY V.The shear strength of rock joints in theory and practice[J].Rock Mechanics,1977,10(1/2):1–54.
[4]MANDELBROT B B.How long is the coast of Britain?Statistical selfsimilarity and fractal dimension[J].1967,156(3775):636-638.
[5]TURK N,GREIG M J,DEARMAN W R,et al.Characterization of rock joint surfaces by fractal dimension[C].Proceeding of the 28th Symposium on Rock Mechanics.Tucson:Balkema,1987:1223-1236.
[6]LEE Y H,CARR J R,BARR D J,et al.The fractal dimension as a measure of the roughness of rock discontinuity profiles[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1990,27(6):453-464.
[7]谢和平,PARISEAU W G.岩石节理粗糙系数(JRC)的分形估计[J].中国科学(B辑),1994,24(5):524-530.
[8]曹平,贾洪强,刘涛影,等.岩石节理表面三维形貌特征的分形分析[J].岩石力学与工程学报,2011,30,(Z2):3839-3843.
[9]孙辅庭,佘成学,蒋庆仁.一种新的岩石节理面三维粗糙度分形描述方法[J].岩土力学,2013,34(8):2238-2242.
[10]王金安,谢和平.岩石断裂面的各向异性分形和多重分形研究[J].岩土工程学报,1998,20(6):16-21.
[11]BARTON N,BANDIS S.Effects of block size on the shear behavior of jointed rock[C].Proceedings of the 23rd U.S.Symposium on Rock Mechanics.Berkeley:Public New York,1982:739–760.
[12]TSE R,CRUDEN D M.Estimating joint roughness coefficients[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1979,16(5):303-307.
[13]MAERZ N H,FRANKLIN J A,BENNETT C P.Joint roughness measurement using shadow profilometry[J].International Joint Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1990,27(5):329-343.
[14]ODLING N E.Natural fracture profiles,fractal dimension and joint roughness coefficients[J].Rock Mechanics and Rock Engineering,1994,27(3):135-153.
[15]孙辅庭,佘成学,万利台.新的岩石节理粗糙度指标研究[J].岩石力学与工程学报,2013,32(12):2513-2519.
[16]吴月秀,刘泉声,刘小燕.岩石节理粗糙度系数与统计参数的相关关系研究[J].岩石力学与工程学报,2011,30(Z1):2593-2598.
[17]王卫华,李坤,严哲,等.基于BP神经网络方法研究岩石节理形貌粗糙度系数[J].世界科技研究与发展,2016,38(3):518-521.
[18]谢和平.岩石节理的分形描述[J].岩土工程学报,1995,17(1):18-23.
[19]MANDELBROT B B.The fractal geometry of nature[M].New York:W.H.Freeman and Company,1982.
[20]XIE Heping,WANG Jinan,XIE Weihong,et al.Fractal effects of surface roughness on the mechanical behavior of rock joints[J].Chaos,Solitons&Fractals,1997,8(2):221-252.
[21]丁增志.节理表面形貌研究及在非贯通节理岩体强度准则中的应用[D].上海:同济大学,2007.