岩石节理面粗糙度的分形效应与试件尺寸影响分析
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摘要
岩石节理面的粗糙度是影响岩体形变、位移和强度的主要因素,准确量测岩石节理表面的粗糙度对评价岩石力学特性非常重要。根据分形理论,岩石节理表面具有分形特征,可用分形维数描述节理表面的起伏度,但是岩石节理表面粗糙度一般不具有严格的自相似分形性质,因此,表面分形参数(分形维数D和截距A)的量测结果受到尺度的影响。本文运用三维表面激光形貌仪扫描10个不同尺度的试件(尺寸为100mm×100mm—1000mm×1000mm),结果表明,D和A随试件尺寸增大而减小,两参数都有尺度效应,但存在一个极限尺寸。综合考虑岩石表面尺寸、试件长度以及测量尺度对岩石节理表面粗糙度的影响,提出可靠的分形测量途径。
The surface roughness of rock joints is a major factor that influences the rock mass deformation,displacement and strength.So its determination is very important for the evaluation of rock mechanical properties.The rock joint surface may be assumed to have fractal characteristics,and its fractal dimension can be used to describe the roughness of the surface joints,but the surface roughness of rock joints generally does not strictly have the nature of fractal self-similarity,so,the measurement results of surface fractal parameters(fractal dimension D and the intercept A)would be affected by the scale.In this study,the 3-D superficial laser topography instrument was used to scan samples of 10 different sizes(ranging from 100mm×100mm to 1000mm×1000mm).It is shown that both the fractal dimension D and the intercept A are indeed scale-dependent,but the scale effect and their values decrease with the increase of the size of the sampling windows,and a limit size exists.Considering the rock surface size,the sample length and the measurement scale on the rock joint surface roughness,an acceptable solution for fractal measurements is proposed to assess the properties of rocks.
The surface roughness of rock joints is a major factor that influences the rock mass deformation,displacement and strength.So its determination is very important for the evaluation of rock mechanical properties.The rock joint surface may be assumed to have fractal characteristics,and its fractal dimension can be used to describe the roughness of the surface joints,but the surface roughness of rock joints generally does not strictly have the nature of fractal self-similarity,so,the measurement results of surface fractal parameters(fractal dimension D and the intercept A)would be affected by the scale.In this study,the 3-D superficial laser topography instrument was used to scan samples of 10 different sizes(ranging from 100mm×100mm to 1000mm×1000mm).It is shown that both the fractal dimension D and the intercept A are indeed scale-dependent,but the scale effect and their values decrease with the increase of the size of the sampling windows,and a limit size exists.Considering the rock surface size,the sample length and the measurement scale on the rock joint surface roughness,an acceptable solution for fractal measurements is proposed to assess the properties of rocks.
引文
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[12]Mandelbrot B B.The fractal geometry of nature[M].New York:W H Freeman,1982.
[13]Brown S R,Scholz C H.Broad bandwidth study of the topography ofnatural rock surfaces[J].J Geophys Res,1985,90(B14):12575-12585.
[14]Huang S L,Oelfke S M,Speck R C.Application of fractal characterization and modelling to rock joint profiles[J].Int J Rock Meth Min Sci&Geomech Abstr,1992,29(2):89-98.
[15]王金安,谢和平,Kwasniewski M A.应用激光技术和分形理论测量和描述岩石节理表面粗糙度[J].岩石力学与工程学报,1997,16(4):354-361.Wang Jin′an,Xie Heping,Kwasniewski M A.Chinese Journal of Rock Mechanics and Engineering,1997,16(4):354-361.
[16]王金安,谢和平,Kwasniewski M A.剪切过程中岩石节理面粗糙度分形演化及力学特征[J].岩土工程学报,1997,19(4):2-9.Wang Jin'an,Xie Heping,Kwasniewski M A.Chinese Journal of Geotechnical Engineering,1997,19(4):2-9.
[17]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.Chinese Journal of Rock Mechanics and Engineering,2000,19(1):11-17.
[18]Burton N,Choubey V.The shear strength of rock joints in theory and practice[J].Rock Mech,1977,10(1-2):1-54.
[19]Malinverno A.A simple method to estimate the fractal dimensionof a self-affine series[J].Geophys Res Lett,1990,17(11):1953-1956.
[2]Patton F D.Multiple models of shear failure in rock[C]//First Congress of International Mechanics.Lisbon,Partugal,1966:509-513.
[3]Barton N,Chouhey V.The shear strength of rock joints in theory and practice[J].Rock Mechanics,1977,10(1-2):1-54.
[4]Barton W E.Suggested methods for the quantitative description of dis-continuities in rock masses[J].Int J Rock Mech Min Sci&Geomech Abstr,1978,15(6):319-368.
[5]杜守继,耿洪涛,周枝华.岩石节理剪切过程中应力与渗流性的数值模拟[J].岩石力学与工程学报,2008,27(12):2473-2481.Du Shouji,Geng Hongtao,Zhou Zhihua.Chinese Journal of Rock Mechanics and Engineering,2008,27(12):2473-2481.
[6]Carr J R,Warriner J B.Rock mass classification using fractal dimension[C].The28th US Symposium on Rock Mechanics,Tucson,June29-July1,1987:78-80.
[7]Turk N,Greig M J,Dearman W R,et al.Characterization of rock joint surfaces by fractal dimension[C].28th US Symposium on Rock Mechanics.Tueson,Tucson,June29-July1,1987:1223-1236.
[8]Carr J R.Fractal characterization of joint surface roughness in welded tuff at yucca mountain in Nevada,Rock Mechanics.As a Guide for Efficient Utilitation of Natural Resources[C]//Proc30th US Symp,on Rock Mech,Morgantown.West Virginia,Balkema,Rotterdam,1989:193-200.
[9]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].Int J Rock Mech Mm Sci&Geomech Abstr,1990,27(6):453-464.
[10]谢和平.分形-岩石力学导论[M].北京:科学出版社,1996.Xie Heping.Introduction to fractal rock mechanics[M].Beijing:Science Press,1996.
[11]Mandelbrot B B.How long is the coast of Britain?Statistical self-similarity and fractal dimension[J].Science,1967,156(3775):636-638.
[12]Mandelbrot B B.The fractal geometry of nature[M].New York:W H Freeman,1982.
[13]Brown S R,Scholz C H.Broad bandwidth study of the topography ofnatural rock surfaces[J].J Geophys Res,1985,90(B14):12575-12585.
[14]Huang S L,Oelfke S M,Speck R C.Application of fractal characterization and modelling to rock joint profiles[J].Int J Rock Meth Min Sci&Geomech Abstr,1992,29(2):89-98.
[15]王金安,谢和平,Kwasniewski M A.应用激光技术和分形理论测量和描述岩石节理表面粗糙度[J].岩石力学与工程学报,1997,16(4):354-361.Wang Jin′an,Xie Heping,Kwasniewski M A.Chinese Journal of Rock Mechanics and Engineering,1997,16(4):354-361.
[16]王金安,谢和平,Kwasniewski M A.剪切过程中岩石节理面粗糙度分形演化及力学特征[J].岩土工程学报,1997,19(4):2-9.Wang Jin'an,Xie Heping,Kwasniewski M A.Chinese Journal of Geotechnical Engineering,1997,19(4):2-9.
[17]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.Chinese Journal of Rock Mechanics and Engineering,2000,19(1):11-17.
[18]Burton N,Choubey V.The shear strength of rock joints in theory and practice[J].Rock Mech,1977,10(1-2):1-54.
[19]Malinverno A.A simple method to estimate the fractal dimensionof a self-affine series[J].Geophys Res Lett,1990,17(11):1953-1956.
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