一种新的岩石节理面三维粗糙度分形描述方法
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摘要
研究并提出一种新的岩石节理面三维粗糙度分形描述方法。首先,基于激光扫描数据将节理表面离散成三角网,并建立与剪切方向相关的三维均方根抵抗角的计算方法。其次,运用分形数学理论,提出一种新的基于三维均方根抵抗角的节理面粗糙度分形描述方法。最后,采用新方法对天然玄武岩节理和花岗岩张拉型节理的粗糙特性进行分析。研究结果表明,提出的新方法能够较全面地反映节理面的三维几何形貌信息,并能描述节理粗糙度的各向异性特性。研究成果为进一步建立岩石节理面的三维剪切强度公式和剪切本构理论奠定了基础。
A new fractal description method for three-dimensional roughness characteristics of rock joint is proposed and researched.Firstly,based on the scanning data of joint surface morphology,the joint surface is reproduced in the discrete form of triangular nets;and then the calculation method of 3D root mean square resistance angle is established.Secondly,fractal theory is applied to propose a new fractal description method to describe 3D roughness characteristics of rock joint on the basis of 3D root mean square resistance angle.Finally,the new method is used to characterize the roughness of natural basalt joint and tensile granite joint.Research results show that the new method can well reflect the 3D morphology of joint and it can also describe the anisotropy of roughness.Research results offer the foundation for further studying the shear strength and shear constitutive law of rock joints.
A new fractal description method for three-dimensional roughness characteristics of rock joint is proposed and researched.Firstly,based on the scanning data of joint surface morphology,the joint surface is reproduced in the discrete form of triangular nets;and then the calculation method of 3D root mean square resistance angle is established.Secondly,fractal theory is applied to propose a new fractal description method to describe 3D roughness characteristics of rock joint on the basis of 3D root mean square resistance angle.Finally,the new method is used to characterize the roughness of natural basalt joint and tensile granite joint.Research results show that the new method can well reflect the 3D morphology of joint and it can also describe the anisotropy of roughness.Research results offer the foundation for further studying the shear strength and shear constitutive law of rock joints.
引文
[1]杜世贵.岩体结构面的工程性质[M].北京:地震出版社,1999.
[2]夏才初,孙宗颀.工程岩体节理力学[M].上海:同济大学出版社,2002.
[3]BARTON N,CHOUBEY V.The shear strength of rockjoints in theory and practice[J].Rock Mechanics,1977,10:1-54.
[4]TSE R,CRUDEN D M.Estimating joint roughnesscoefficients[J].Int.J.Rock Mech.Min.Sci.&Geomech.,1979,16:303-307.
[5]RASOULI V,HARRISON J P.Assessment of rockfracture surface roughness using Riemannian statistics oflinear profiles[J].International Journal of RockMechanics&Mining Sciences,2010,47:940-948.
[6]GRASSELLI G,EGGER P.Constitutive law for the shearstrength of rock joints based on three-dimensional surfaceparameters[J].International Journal of RockMechanics&Mining Sciences,2003,40:25-40.
[7]MANDELBROT B.B.The fractal of nature[M].NewYork:FREEMAN W H,1983.
[8]ODLING N E.Natural fracture profiles,fractal dimensionand joint roughness coefficient[J].Rock MechanicsRock Engineering,1997,27(3):135-153.
[9]KULATILAKE P H S W,BALASINGAM P,PARK J,et,al.Natural rock joint roughness quantification throughfractal techniques[J].Geotechnical and GeologicalEngineering,2006,24:1181-1202.
[10]YANG Z Y,LO S C.An index for describing anisotropyof joint surfaces[J].International Journal of RockMechanics&Mining Sciences,1997,34(6):1031-1044.
[11]YANG Z Y,DI C C,YEN K C.The effect of asperityorder on the roughness of rock joints[J].InternationalJournal of Rock Mechanics&Mining Sciences,2001,38:745-752.
[12]XIE He-ping,WANG Jin-an,XIE Wei-hong.Fractaleffects of surface roughness on the mechanical behaviorof rock joints[J].Chaos,Solitons&Fractals,1997,8(2):221-252.
[13]KEITH C,CLARKE.Computation of the fractaldimension of topographic surfaces using the triangularprism surface area method[J].Computers&Geo-sciences,1986,12(5):713-722.
[14]XIE He-ping,WANG Jing-an.Direct fractal measurementof fracture surfaces[J].International Journal of Solidsand Structures,1999,36:3073-3084.
[15]易成,张亮,陈忠辉,等.一种新的描述粗糙表面形貌尺度分维参数Rd的研究[J].中国矿业大学学报,2007,36(1):75-80.YI Cheng,ZHANG Liang,CHEN Zhong-hui,et al.Anovel description of roughness surface with a modifiedfractal index Rd[J].Journal of China University ofMining&Technology,2007,36(1):75-80.
[16]RE F,SCAVIA C.Determination of contact areas in rockjoints by X-ray computer tomography[J].InternationalJournal of Rock Mechanics and Mining Sciences,1999,36:883-890.
[17]GENTIER S,RISS J,ARCHAMBAULT G,et al.Influence of fracture geometry on shear behavior[J].International Journal of Rock Mechanics and MiningSciences,2000,37:161-174.
[18]KENNETH FALCONER,分形几何——数学基础及其应用[M].曾文曲译.北京:人民邮电出版社,2007.
[19]ESAKI T,DU S,JIANG Y,et al.Effect of the asperitydamage on the shear behavior of irregular rock joints[C]//Proceedings of the Second International Conference onAnalysis of Discontinuous Deformation.Kyoto:[s.n.],1997:459-464.
[2]夏才初,孙宗颀.工程岩体节理力学[M].上海:同济大学出版社,2002.
[3]BARTON N,CHOUBEY V.The shear strength of rockjoints in theory and practice[J].Rock Mechanics,1977,10:1-54.
[4]TSE R,CRUDEN D M.Estimating joint roughnesscoefficients[J].Int.J.Rock Mech.Min.Sci.&Geomech.,1979,16:303-307.
[5]RASOULI V,HARRISON J P.Assessment of rockfracture surface roughness using Riemannian statistics oflinear profiles[J].International Journal of RockMechanics&Mining Sciences,2010,47:940-948.
[6]GRASSELLI G,EGGER P.Constitutive law for the shearstrength of rock joints based on three-dimensional surfaceparameters[J].International Journal of RockMechanics&Mining Sciences,2003,40:25-40.
[7]MANDELBROT B.B.The fractal of nature[M].NewYork:FREEMAN W H,1983.
[8]ODLING N E.Natural fracture profiles,fractal dimensionand joint roughness coefficient[J].Rock MechanicsRock Engineering,1997,27(3):135-153.
[9]KULATILAKE P H S W,BALASINGAM P,PARK J,et,al.Natural rock joint roughness quantification throughfractal techniques[J].Geotechnical and GeologicalEngineering,2006,24:1181-1202.
[10]YANG Z Y,LO S C.An index for describing anisotropyof joint surfaces[J].International Journal of RockMechanics&Mining Sciences,1997,34(6):1031-1044.
[11]YANG Z Y,DI C C,YEN K C.The effect of asperityorder on the roughness of rock joints[J].InternationalJournal of Rock Mechanics&Mining Sciences,2001,38:745-752.
[12]XIE He-ping,WANG Jin-an,XIE Wei-hong.Fractaleffects of surface roughness on the mechanical behaviorof rock joints[J].Chaos,Solitons&Fractals,1997,8(2):221-252.
[13]KEITH C,CLARKE.Computation of the fractaldimension of topographic surfaces using the triangularprism surface area method[J].Computers&Geo-sciences,1986,12(5):713-722.
[14]XIE He-ping,WANG Jing-an.Direct fractal measurementof fracture surfaces[J].International Journal of Solidsand Structures,1999,36:3073-3084.
[15]易成,张亮,陈忠辉,等.一种新的描述粗糙表面形貌尺度分维参数Rd的研究[J].中国矿业大学学报,2007,36(1):75-80.YI Cheng,ZHANG Liang,CHEN Zhong-hui,et al.Anovel description of roughness surface with a modifiedfractal index Rd[J].Journal of China University ofMining&Technology,2007,36(1):75-80.
[16]RE F,SCAVIA C.Determination of contact areas in rockjoints by X-ray computer tomography[J].InternationalJournal of Rock Mechanics and Mining Sciences,1999,36:883-890.
[17]GENTIER S,RISS J,ARCHAMBAULT G,et al.Influence of fracture geometry on shear behavior[J].International Journal of Rock Mechanics and MiningSciences,2000,37:161-174.
[18]KENNETH FALCONER,分形几何——数学基础及其应用[M].曾文曲译.北京:人民邮电出版社,2007.
[19]ESAKI T,DU S,JIANG Y,et al.Effect of the asperitydamage on the shear behavior of irregular rock joints[C]//Proceedings of the Second International Conference onAnalysis of Discontinuous Deformation.Kyoto:[s.n.],1997:459-464.
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