摘要
对影响岩石摩擦滑动的因素进行了比较全面和系统的分析,从微细观层次对影响岩石摩擦滑动及其稳定性的机理进行了研究。
选取千枚岩、石英砂岩、石灰岩、大理岩、石英岩、岩屑砂岩、鲕状石灰岩、白云质灰岩、砾岩、含砾粗粒石英砂岩、中粒石英砂岩和中粒岩屑石英砂岩等12种试验岩样作为研究对象,采用自行设计的典型岩石摩擦滑动试验装置,在低正应力(σ≤5MPa)条件下,对自然状态、饱水状态和干燥状态的不同岩石摩擦滑动过程中的静、动摩擦系数以及速度-状态依赖性本构参数(a-b)等摩擦滑动特性进行了试验研究。
采用American MicroXAMTM ADE三维白光干涉表面形貌仪对试验岩样滑动面表面形貌中的粗糙度进行了试验研究。采用SHIMADZU XRD-6000型X-射线粉末衍射仪、μCT225kVFCB型高精度显微CT试验系统对试验岩样的矿物成分、粒度和孔隙结构进行了试验研究。分析研究了岩样的表面形貌、矿物成分、孔隙结构和粒度等因素与静、动摩擦系数和速度-状态依赖性本构参数(a-b)等岩石摩擦滑动特性之间的关系。得出了以下主要研究结论：
1、在对Amontons摩擦定律、微凸体理论和粘附理论,岩石摩擦滑动的试验方法,岩石摩擦滑动的研究尺度,稳滑和黏滑等岩石摩擦滑动方式,稳滑和黏滑的相互转换方式和条件,静、动摩擦系数等进行系统总结的基础上,从理论上分析了速度-状态依赖性本构关系、失稳准则和岩石系统内部各部分之间的相互作用等岩石摩擦滑动稳定性问题,得出了岩石滑动面表面形貌、矿物成分、孔隙结构和粒度等为影响岩石摩擦滑动方式的内在因素,且速度弱化是岩石摩擦滑动稳定性的必要条件。
2、采用统计学和分形几何学方法对岩石滑动表面的表面形貌进行了定量表征。抛光后的滑动表面其轮廓算术平均偏差、轮廓均方根偏差和表面粗糙度参数平均值等粗糙度参数取值范围相一致,轮廓最大谷深和轮廓最大峰高两个参数的取值范围相差较大。随着粗糙度参数平均值和滑动表面的分形维数值的增加,不同含水状态下各种岩石的静摩擦系数呈指数规律增加,速度-状态依赖性本构参数(a-b)呈线性规律增加。
3、在不同含水状态下,单一矿物组成的硅酸盐类岩石和碳酸盐类岩石的摩擦滑动方式为黏滑,水的作用对其滑动方式没有影响。多种矿物组成的硅酸盐类岩石和碳酸盐类岩石的摩擦滑动方式为稳滑或黏滑,水的作用使其摩擦滑动方式由稳滑转变为黏滑。单一矿物石英组成的硅酸盐类石英岩静摩擦系数小于多种矿物成分组成的硅酸盐类岩石在相应状态下的静摩擦系数。单一矿物方解石组成的碳酸盐类鲕状石灰岩静摩擦系数小于多种矿物组成的碳酸盐类岩石在相应状态下的静摩擦系数。在饱水状态下,硅酸盐类岩石随着延性黏土矿物含量的增加,碳酸盐类岩石随着脆性矿物方解石含量的增加,速度-状态依赖性本构参数(a-b)由正到负,呈负指数规律减小。
4、采用μCT225kVFCB型高精度显微CT试验系统和Matlab语言编制的图像处理程序,对12种不同岩石的孔隙结构和粒度进行计算分析,得到了基于显微CT图像岩石孔隙率随孔隙孔径的变化规律。岩样矿物成分和孔隙结构决定了滑动表面的轮廓算术平均偏差、轮廓均方根偏差和表面粗糙度参数平均值等粗糙度参数,粒度决定了滑动表面的轮廓最大谷深和轮廓最大峰高等粗糙度参数。随着粒度轮廓线平均高度的增加,滑动表面的轮廓最大峰高呈线性规律增加。在不同含水状态条件下,随着岩样滑动面表面孔隙率和粒度的增加,摩擦滑动过程中的静摩擦系数和动摩擦系数均呈线性规律变化。
The influencing factors about the frictional sliding rocks were systematic and generally analyzed. The influencing mechanism about frictional sliding of rocks and stabilization were studied from the microscomic degree.
The objects of study are twelve experimental samples, including phyllite, quartzite, quartz sandstone, lithic sandstone, marble, limestone, lite limestones, dolomitic limestone, conglomerate, gravelly coarse quartz sandstone, medium grained quartz sandstone, medium grained lithic sandstone, respectively. The typical friction experiment apparatus of rock frictional sliding was devised and reformed. The experimental condition was under nature state, moisture state and dry state at low normal force (σ<5MPa),. The properties of the rock frictional sliding including static frictional coefficient μ, dynamic frictional coefficient μd, and constitutive parameter (a-b) in different states were experimentally studied. The influencing factors are mainly inter factors of the samples, which are roughness parameters, mineralogical composition, pore structure, and grain.
The roughness parameters of the surface topography in the rock sliding were analysized by American MicroXAMTM ADE3dimension white light interferometry optical interferometer. The mineralogical composition, pore structure, and grain of the experimental samples were analysized by SHIMADZU XRD-6000X-ray diffactometer and μCT225kVFCB Micro-CT experimental system. The size of grain was computed with Scanning Probe Image Processor (SPIP). The relation between the properties of frictional sliding and the influencing factors were analyzed. The main research results are as follows:
1. The frictional theory, experimental method, scale of study, mode, experimental phenomena and the analysis for results were systematically summarized during the rock frictional sliding. The theory includes in Amontons law, Byerlee law, asperity, and adhesion. The experimental methods of the measurements of rock frictional sliding are respectively typical friction experiment, direct shear, double shear, rotary shear, and triaxial experiment. The analysis for the scale of experimental samples, the phenomena of steady sliding and stick slip, the conversion of the two sliding modes, static frictional coefficient μ and dynamic frictional coefficient μd, constitutive parameter (a-b), stability criterion, and the interreaction for internal system. The internal factors effecting the frictional sliding of rocks are the surface topography of rock sliding surfaces, mineralogical composition, pore structure, and size of grain. The necessary condition for the steady of rock frictional sliding is velocity-weakening.
2. The surface topography of rock sliding surfaces is characterized with statistic parameters and fractal dimensions. After the sliding surfaces were polished, the roughness parameters including in arithmetical mean deviation of the profile Ra, root mean square deviation of the profile Rq, and average value of the surface roughness parameter R are identical, however, the other parameters, such as, maximum depth of porfile valley Rm and maximum height of profile peak Rp are not identical. With the increment of R and the fractal dimension D, the static friciton coffeciment μ under different states exponentially increased, and the constitutive parameter (a-b) linearly increased.
3. Under different states, the mode of the mono-mineral rock frictional sliding about the silicate rock and carbonate rock is stick-slip, and water has no effect on the sliding mode. The mode of the multi-mineral rock frictional sliding about the two rocks is steady sliding and stick-slip, and water can transform the sliding mode from steady sliding to stick-slip. The static friciton coffeciment μ of the mono-mineral quartz silicate rock and calcite carbonate rock is less than that of multi-mineral rock under corresponding states, repecitvely. Under moisture state, with the contents of the brittle calcite mineral and the ductile clay mineral increased, the constitutive parameter (a-b) decreased in exponential law.
4. Micro-CT digital images are processed by Matlab processure. The law of the porosity variation with the pore aperture of rocks is estimated by the digital image processing. The parameters Ra, Rq, R for the surface roughness are governed by the mineralogical composition and pore structure of rocks, the two parameters Rm and Rp are governed by grain parameter, especially, mean height of the profile. With the increment of the mean height of the profile, the Rp increased as a linear law. With the increment of the porosity and grain of rock sliding surfaces, the frictional coefficient changes by linear law, under the nature, moisture, and drying states.
引文
[1]Edelbro C. Rock Mass Strength A Review[R].Lulea University of Technology,2003.
[2]郑林庆.摩擦学原理[M].北京：高等教育出版社,1994.
[3]傅征祥.中国大陆地震活动性力学研究[M].北京：地震出版社,1997.
[4]黄庭芳,陈顒.岩石物理学[M].北京：北京大学出版社,2001.
[5]陈立德,付虹.地震预报基础与实践[M].北京：地震出版社,2003.
[6]B.N米亚奇金(苏).地震理论与实验译文集[M].北京：地震出版社,1979.
[7]Scholz C H. Earthquakes and friction laws[J]. Nature.1998,391(1):37-42.
[8]Winkler K, Nur A, Gladwin M. Friction and seismic attenuation in rocks[J]. Nature.1979, 277(15):528-531.
[9]Spray J G. Friction phenomena in rock:an introduction[J]. Journal of Structural Geology.1989, 11(7):783-785.
[10]Tichy J A, Meyer D M. Review of solid mechanics in tribology[J]. International Journal of Solids and Structures.2000,37(1-2):391-400.
[11]陈铁民,陶振宇.岩石摩擦机制及基本摩擦角[J].武汉水利电力学院学报.1992,25(02)：25-30.
[12]陶振宇,陈铁民.岩石的基本摩擦角及高压摩擦特性[J].科学通报.1991,(20)：1567-1569.
[13]Byerlee J. Frictions of rocks[J]. Pageoph.1978,116(1):615-626.
[14]Scholz C H. The critical slip distance for seismic faulting[J]. Nature.1988,336(22/29): 761-763.
[15]张伯崇,姜光,韩风,等.房山大理岩的摩擦滑动试验[J].地球物理学报.1983,26(02)：193-197.
[16]Jaeger J C. The frictional properties of joints in rock[J]. Pure and Applied Geophysics.1959, 43(1):148-158.
[17]Byerlee J D. The mechanics of stick-slip[J]. Tectonophysics.1970,9(5):475-486.
[18]Spetzler H, Sobolev G, Koltsov A, et al. Some properties of unstable slip on rough surfaces[J]. Pure and Applied Geophysics.1991,137(1):95-112.
[19]Marone C, Hobbs B E, Ord A. Coulomb constitutive laws for friction:Contrasts in frictional behavior for distributed and localized shear[J]. Pure and Applied Geophysics.1992,139(2): 195-214.
[20]Tullis T E. Rock friction constitutive behavior from laboratory experiments and its implications for an earthquake prediction field monitoring program[J]. Pure and Applied Geophysics.1988,126(2):555-588.
[21]Marone C, Cox S J D. Scaling of rock friction constitutive parameters:The effects of surface roughness and cumulative offset on friction of gabbro[J]. Pure and Applied Geophysics.1994, 143(1):359-385.
[22]Louis Peselnick H L. Laboratory Measurement of Internal Friction in Rocks and Minerals at seismic frequencies[J]. Methods of Experimental Physics.1987,24(1):31-56.
[23]马胜利,嵨本利彦.蒙脱石的脱水作用对断层摩擦本构行为的影响[J].地震地质.1995,17(04)：289-304.
[24]Schellart W P. Shear test results for cohesion and friction coefficients for different granular materials:scaling implications for their usage in analogue modeIling[J]. Tectonophysics. 2000,324(1-2):1-16.
[25]Herrmann H J. Structures in deformed granular packings[J]. Granular Matter.2001,3(1): 15-18.
[26]Anthony L J, Marone C. Influence particle characterisitcs on granular friction[J]. Journal of Geophysical Research.2005,110(B08409):1-14.
[27]Frossard E. Effect of sand grain shape on interparticle friction; indirect measurements by Rowe's stress dilatancy theory[J]. Geotechnique.1979,29(3):341-350.
[28]Kanaori Y, Abiko. Surface textures of intrafault quartz grains[J]. Catena.1985,12:271-279.
[29]Fecker E. A new method for determining peak friction of rock joints[J]. Bulletin of Engineering Geology and the Environment.1977,16(1):198-200.
[30]Indraratna B, Haque A. Experimental study of shear behavior of rock joints under constant normal stiffness conditions[J]. International Journal of Rock Mechanics and Mining Sciences. 1997,34(3-4):141-155.
[31]黄平,温诗铸.摩擦学原理[M].北京：清华大学出版社,2002.
[32]Jaeger J C, Cook N G W, Zimmerman R W. Fundamentals of Rock Mechanics (4th Edition) [M]. Malden:Blackwell Publishing,2007.
[33]Martin H, Muser, Wenning L, et al. Simple microscopic theory of amontons's laws for static friction[J]. Physical Review Letters.2001,86(7):1925-1928.
[34]Chilingar G V E A. Effect of direct electrical current on permeability of sandstone cores[J]. Journal of Petroleum Technology.1970,22(7):830-836.
[35]Brace F P, Tabor D. The friction and lubrication of solids[M]. Oxford:Clarendon Press, 1964.
[36]Scholz C H, Engelder J T. The role of asperity indentation and ploughing in rock friction--Ⅰ: Asperity creep and stick-slip[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts.1976,13(5):149-154.
[37]Engelder J T, Scholz C H. The role of asperity indentation and ploughing in rock friction--Ⅱ: Influence of relative hardness and normal load[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts.1976,13(5):155-163.
[38]Mora P, Place D. Simulation of the frictional stick-slip instability[J]. Pure and Applied Geophysics.1994,143(1):61.
[39]Place D, Lombard F, Mora P, et al. Simulation of the micro-physics of rocks using LSMearth[J]. Pure and Applied Geophysics.2002,159(9):1911-1932.
[40]Carpick R W. Measurement of interfacial shear with an ultrahigh vacuum atomic force microscope[J]. Journal of Vacuum Science & Technology B.1995,14(2):1289-1296.
[41]Krim J. Atomic-scale origins of frictionf[J]. Langmuir.1996,12(19):4564-4566.
[42]Buzio R, Valbusa U. Morphological and tribological characterization of rough surfaces by atomic force microscopy[M]. Applied Scanning Probe Methods Ⅲ, Bhushan B, Fuchs H, Springer Berlin Heidelberg,2006.
[43]张人估.分子-原子级摩擦学的新进展[J].清华大学学报(自然科学版).1992(05)：101-108.
[44]温诗铸.纳米摩擦学(Nanotribology)研究现状和展望[J].仪器仪表学报.1995,16(1)：32-37.
[45]温诗铸,李娜.纳米摩擦学基础研究进展[J].材料研究学报.1997,11(1)：1-7.
[46]雒建斌,温诗铸,Lawrencek,等.纳米摩擦学研究进展与存在问题[J].科学通报. 1997(13)：1345-1354.
[47]聂时春,张嗣伟,王洪波,等.原子力显微镜在纳米摩擦学中应用的进展[J].摩擦学学报.1998(01)：88-96.
[48]张余平,杨生荣.原子力显微镜在纳米摩擦学研究中的应用[J].现代仪器.2000(06)：17-19.
[49]王慧,胡元中,邹鲲,等.纳米摩檫学的分子动力学模拟研究[J].中国科学A辑.2001(03)：261-266.
[50]李子存,冯新泸,宋世远,等.原子尺度上的摩擦[J].润滑与密封.2001(04)：72-73.
[51]Gourc J P, Ramirez R R. Dynamics-based interpretation of the interface friction test at the inclined plane[J]. Geosynthetics International.2004(6):439-454.
[52]钱鸣高,石平五.矿山压力与岩层控制[M].徐州：中国矿业大学出版社,2003.
[53]Yang S, Jing H, Li Y, et al. Experimental investigation on mechanical behavior of coarse marble under six different loading paths[J]. Experimental Mechanics.2011,51(3):315-334.
[54]Schneider H. The time dependence of friction of rock joints[J]. Bulletin of Engineering Geology and the Environment.1977,16(1):235-239.
[55]Byerlee J D. Static and kinetic friction of granite at high normal stress[J]. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts.1970,7(6): 577-582.
[56]Whittaker E J W. The characterization of serpentine minerals by X-ray diffraction[J]. Journal of theminralogical society.1956,4(233):107-126.
[57]Whittaker E J W. The characterization of serpentine minerals[J].The American Mineralogist. 1958,43(05):917-920.
[58]Horn H M, Deere D U. Frictional Characteristics of Minerals[J]. Geotechnique.1962,12(4): 319-335.
[59]Ramana Y V, Gogte B S. Dependence of coefficient of sliding friction in rocks on lithology and mineral characteristics[J]. Engineering Geology.1989,26(3):271-279.
[60]Reinen L A, Weeks J D, Tullis T E. The frictional behavior of lizardite and antigorite serpentinites:experiments, constitutive models, and implications for natural faults[J]. Pageoph.1994,143(1):317-358.
[61]Scruggs V J. Frictional Constitutive properties and related microstructures of albite, muscovite, biotite and talc[D]. Brown University,1997.
[62]Morrow C, Randney B, Byerlee J. Frictional strength and the effcetive pressure law of montmorillonite and illite clays[M]. Fault mechanics and transport properties of rocks:a festschrift in honor of W.F.Brace, California:Academic Press,1992.
[63]Hartl J, Ooi J. Experiments and simulations of direct shear tests:porosity, contact friction and bulk friction[J]. Granular Matter.2008,10(4):263-271.
[64]Hadizadeh J, Sehhati R, Tullis T. Porosity and particle shape changes leading to shear 1 ocalization in small-displacement faults[J]. Journal of Structural Geology.2010,32(11): 1712-1720.
[65]Homand F, Belem T, Souley M. Friction and degradation of rock joint surfaces under shear loads[J]. International Journal for Numerical and Analytical Methods in Geomechanics.2001, 25(10):973-999.
[66]Gokhale A, Underwood E. A general method for estimation of fracture surface roughness: Part I. Theoretical aspects[J]. Metallurgical and Materials Transactions A.1990,21(5): 1193-1199.
[67]A. M. Gokhale W J D. A general method for estimation of fracture surface roughness:part 2, practical considerations[J]. Metallurgical Transactions A.1990,21 A(l):1201-1207.
[68]Maerz N H, Franklin J A, Bennett C P. Joint roughness measurement using shadow profilometry[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts.1990,27(5):329-343.
[69]Myers N O. Characterization of surface roughness[J]. Wear.1962,5:182-189.
[70]Koura M M. The effect of surface texture on friction mechanisms[J]. Wear.1980,63(1): 1-12.
[71]Koura M M, Omar M A. The effect of surface parameters on friction[J]. Wear.1981,73(2): 235-246.
[72]Barton N. Review of a new shear-strength criterion for rock joints[J]. Engineering Geology. 1973,7(4):287-332.
[73]Abramov B K, Sapozhnikov V T. Friction at contacts between hard rocks[J]. Journal of Mining Science.1974,2:133-137.
[74]Barton N, Choubey V. The shear strength of rock joints in theory and practice[J]. Rock Mechanics and Rock Engineering.1977,10(1):1-54.
[75]Paterson M S, Wong T F. Experimental rock deformation--the brittle field [M]. Springer Berlin Heidelberg,2005:347.
[76]Clerici A. Some remarks on shear strength measurement along joints in rocks with a rigid behaviour[J]. Bulletin of Engineering Geology and the Environment.1990,41(1):57-62.
[77]Andrade P, Saraiva A. Estimating the joint roughness coefficient of discontinuities found in metamorphic rocks[J]. Bulletin of Engineering Geology and the Environment.2008,67(3): 425-434.
[78]Reeves M J. Rock surface roughness and frictional strength[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts.1986,23(3):429-442.
[79]Logan J M, Teufel L W. The effect of normal stress on the real area of contact during frictional sliding in rocks[J]. Pure and Applied Geophysics.1986,124(3):471-485.
[80]Odling N E. Natural fracture profiles, fractal dimension and joint roughness coefficients[J]. Rock Mechanics and Rock Engineering.1994,27(3):135-153.
[81]Kwafniewski M A, Wang J A. Surface roughness evolution and mechanical behavior of rock joints under shear[J]. International Journal of Rock Mechanics and Mining Sciences.1997, 34(3-4):151-157.
[82]Jiang Y, Li B, Tanabashi Y. Estimating the relation between surface roughness and mechanical properties of rock joints[J]. International Journal of Rock Mechanics and Mining Sciences.2006,43(6):837-846.
[83]Kulatilake P H S W, Um J, Pan G. Requirements for accurate estimation of fractal parameters for self-affine roughness profiles using the line scaling method[J]. Rock Mechanics and Rock Engineering.1997,30(4):181-206.
[84]Kabeya K K, Legge T F H. Relationship between grain size and some surface roughness parameters of rock joints[J]. International Journal of Rock Mechanics and Mining Sciences. 1997,34(3-4):141-146.
[85]Belem T, Homand-Etienne F, Souley M. Fractal analysis of shear joint roughness[J]. International Journal of Rock Mechanics and Mining Sciences.1997,34(3-4):130-131.
[86]Belem T, Homand-Etienne F, Souley M. Quantitative parameters for rock joint surface roughness[J]. Rock Mechanics and Rock Engineering.2000,33(4):217-242.
[87]何满潮,胡江春,段庆全,等.工程软岩表面形态及其摩擦特性研究[J1.煤田地质与勘探.2005,33(05)：37-40.
[88]Menezes P L, Kishore, Kailas S V. Influence of surface texture on coefficient of friction and transfer layer formation during sliding of pure magnesium pin on 080 M40 (EN8) steel plate[J]. Wear.2006,261(5-6):578-591.
[89]Schneider H J. The friction and deformation behaviour of rock joints[J]. Rock Mechanics and Rock Engineering.1976,8(3):169-184.
[90]Wang W. Micromechanics of rock friction and wear processes:A theoretical and experimental study[D]. Columbia University,1994.
[91]Moore D E, Lockner D A, Summers R, et al. Strength of chrysotile-serpentinite gouge under hydrothermal conditions:Can it explain a weak San Andreas fault?[J]. Geology.1996,24(11): 1041-1044.
[92]Moore D E, Summers R, Byerlee J D. The effects of sliding velocity on the frictional and physical properties of heated fault gouge[J]. Pure and Applied Geophysics.1986,124(1): 31-52.
[93]Yoshioka N, Iwasa K. The characteristic displacement in rate and state-dependent friction from a micromechanical point of view[J]. Pure and Applied Geophysics.1996,147(3): 433-453.
[94]Engelder T. Aspects of asperity-surface interaction and surface damage of rocks during experimental frictional sliding[J]. Pure and Applied Geophysics.1978,116(4):705-716.
[95]C. A. Morrow D E M D. The effect of mineral bond strength and adsorbed water on fault gouge frictional strength[J]. Geophysical Research Letters.2000,27(6):815-818.
[96]Demian M, Saffer C M. Comparison of smectite-and illite-rich gouge frictional properties:application to the updip limit of the seismogenic zone along subduction megathrusts[J]. Earth and Planetary Science Letters.2003,215(1):219-235.
[97]Sammis C G, Steacy S J. The micromechanics of friction in a granular layer[J]. Pure and Applied Geophysics.1994,142(3):777-794.
[98]Byerlee J, Summers R. A note on the effect of fault gouge thickness on fault stability[J]. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts. 1976,13(1):35-36.
[99]黄建国,张流.水对断层摩擦滑动稳定性的影响[J].地震地质.2002,24(3)：387-399.
[100]Stesky R M. Rock friction-effect of confining pressure, temperature, and pore pressure[J], Pure and Applied Geophysics.1978,116(4):690-704.
[101]Blanpied M L, Lockner D A, Byerlee J D. Frictional slip of granite at hydrothermal conditions[J]. Journal of Geophys Research.1995,100(B7):13045-13064.
[102]明亮.含水岩石摩擦滑动特征的初步研究[J].地震研究.1989,12(2)：155-160.
[103]Byerlee J D. The frictional characteristics of Westerly granite[D]. Cambridge: Massachusetts Institute of Technology,1966.
[104]Sanz Rehermann P F. Modeling Rock Folding with Large Deformation Frictional Contact Mechanics[D]. Stanford:Stanford University,2008.
[105]何昌荣.两种摩擦本构关系的对比研究[J].地震地质.1999,21(2)：137-146.
[106]Dieterich J H. Modeling of rock friction 1. Experimental results and constitutive equations[J]. Journal of Geophysical Research.1979,84(B5):2161-2168.
[107]Ruina A. Slip Instability and State Variable Friction Laws[J]. Journal of Geophysical Research.1983,88(B12):10359-10370.
[108]Dieterich J H. Fault stability under conditions of variable normal stress[J]. Geophysical Research Letters.1992,19(16):1691-1694.
[109]陈顺,耿乃光,姚孝新.不完整岩石样品的断裂与摩擦滑动[J].地球物理学报.1979,22(2)：195-200.
[110]耿乃光,刘晓红.四种岩石的摩擦滑动特征[J].岩土工程学报.1987,9(3)：27-32.
[111]谭文彬,何昌荣.高温高压及干燥条件下斜长石和辉石断层泥的摩擦滑动研究[J].地学前缘.2008,15(3)：297-286.
[112]中华人民共和国国家标准.表面粗糙度参数及其数值[S].1995.
[113]中华人民共和国国家标准.表面粗糙度、术语、表面及其参数[S].1983.
[114]杨松.表面粗糙度的三维motif评定方法研究[D].南京农业大学,2008.
[115]李成贵,董申,张国雄.表面粗糙度评定参数的分形表征[J].宇航计测技术.1998,18(4)：33-40.
[116]李成贵,董申.三维表面微观形貌的表征参数和方法[J].宇航计测技术.1999,19(6)：33-43.
[117]葛世荣,陈国安.磨合表面形貌变化的特征粗糙度参数表征[J].中国矿业大学学报. 1999,28(3)：204-207.
[118]陈国安,葛世荣,张晓云.机加工表面轮廓的分形插值[J].中国矿业大学学报.1999,28(2)：118-]21.
[119]尹自强.超精密直线度测量及表面微观形貌分析研究[D].国防科技大学,2003.
[120]刘小君.表面形貌的分形特征研究[J].合肥工业大学学报(自然科学版).2000,28(2)：236-239.
[[121]葛世荣.粗糙表面的分形特征与分形表达研究[J].摩擦学学报.1997,17(1)：73-80.
[122]张波.硬盘表面微观形貌的分形表征及模拟[D].吉林大学,2004.
[123]Majudar A, Bhushan. B. Fractal model of elastic-plastic contact between rough surfaces[J]. Tram of ASME.1991,113(1):1-11.
[124]陈国安,葛世荣,张晓云.分形几何与摩擦学进展[J].润滑与密封.1999,5：69-71.
[125]李成贵,董申.三维表面形貌的分形维数计算方法[J].航空精密制造技术.2000,36(4)：36-40.
[126]王炳成,褚祥志,任朝晖,等.磨损表面形貌分析中的小波变换和分形方法[J].组合机床与自动化加工技术.2005(01)：69-71.
[127]葛世荣,索双富.表面轮廓分形维数计算方法的研究[J].摩擦学学报.1997,17(4)：354-362.
[128]陈国安,葛世荣.粗糙表面测量轮廓的分形插值模拟[J].摩擦学学报.1998,18(4)：346-350.
[129]石米娜.基于分形几何的轴类零件表面粗糙度检测[D].吉林大学,2007.
[130]蒋书文,姜斌,李燕,等.磨损表面形貌的三维分形维数计算[J].摩擦学学报.2003,23(6)：533-536.
[131]郧建平.基于白光干涉的表面形貌接触和非接触两用测量系统的研究[D].华中科技大学,2008.
[132]刘建辉.基于数字图像处理技术的磨粒图像分析与识别方法的研究[D].北京交通大学,2007.
[133]全书海.基于表面灰度图像的加工表面形貌分形特征研究[D].武汉理工大学,2003.
[134]王淑珍.基于白光干涉超精密表面形貌测量方法与系统研究[D].华中科技大学,2010.
[135]Lttge A, Winkler U, Lasaga A C. Interferometric study of the dolomite dissolution:a new conceptual model for mineral dissolution[J]. Geochimica et Cosmochimica Acta.2003, 67(6):1099-1116.
[136]Koyuncu I, Brant J, Luttge A, et al. A comparison of vertical scanning interferometry (VSI) and atomic force microscopy (AFM) for characterizing membrane surface topography[J]. Journal of Membrane Science.2006,278(1-2):410-417.
[137]Schafer R, Seppanen H, Kassamakov I, et al. Bonding quality monitoring applying statistical modeling of scanning white light interferometry data[J]. Microelectronic Engineering.2007,84(11):2757-2768.
[138]Kassamakov 1 V, Seppanen H, Oinonen M J, et al. Scanning white light interferometry in quality control of single-point tape automated bonding[J]. Microelectronic Engineering. 2007,84(1):114-123.
[139]Sasajima K, Tsukada T. Measurement of fractal dimension from surface asperity profile[J]. International Journal of Machine Tools and Manufacture.1996,32(1-2):125-127.
[140]贾喜荣.矿山岩层力学[M].北京：煤炭工业出版社,1996.
[141]Constantine Douketis Wang Z H, Haslett T L, et al. Fractal character of cold-deposited silver films determined by low-temperature scanning tunneling microscopy [J]. Physical Review B.1995,51:11022-11031.
[142]Sun W, Xu G, Gong P, et al. Fractal analysis of remotely sensed images:A review of methods and applications[J]. International Journal of Remote Sensing.2006,27(22): 4963-4990.
[143]陈小梅,倪国强.基于局部分形维数的遥感图像分割[J].光电工程.2008,35(1)：136-139.
[144]Hyslip J P, Vallejo L E. Fractal analysis of the roughness and size distribution of granular materials[J]. Engineering Geology.1997,48(3-4):231-244.
[145]Jahn R, Truckenbrodt H. A simple fractal analysis method of the surface roughness[J]. Journal of Materials Processing Technology.2004,145(1):40-45.
[146]Martan J, Przybylski G, Tabaka R, et al. Fractal analysis of roughness profile induced by ion bombardment of metal surface[J]. Vacuum.2005,78(2-4):217-221.
[147]Tanaka M, Komagata M, Tsukada M, et al. Fractal analysis of the influence of surface roughness of toner particles on their flow properties and adhesion behavior[J]. Powder Technology.2008,186(1):1-8.
[148]李小兵,刘莹.表面形貌分形表征方法的比较[J].南昌大学学报(理科版).2006,30(1)：84-86.
[149]张乃娴.粘土矿物研究方法[M].北京：科学出版社,1990.
[150]沉积岩中粘土矿物总量和常见非粘土矿物X射线衍射定量分析方法[S].中华人民共和国石油天然气总公司,1997.
[151]黄继武.X射线衍射实验技术[M].长沙：中南大学出版社,2007.
[152]K. Norrish J P Q. crystalline swelling of montmorillonite[J]. nature.1954,173(4397): 255-257.
[153]谭罗荣,孔令伟.特殊岩土工程地质学[M].北京：科学出版社,2006.
[154]谭罗荣.蒙脱石晶体反常膨胀的电解质浓度效应[J].矿物学报.2002,22(04)：371-374.
[155]谭罗荣,孔令伟.蒙脱石晶体胀缩规律及其与基质吸力关系研究[J].中国科学,D辑,2001,31(02)：119-126.
[156]Madsen F T, Vonmoos M. The swelling behaviour of clays[J]. Applied Clay Science.1989, 4(2):143-156.
[157]Tuller M, Or D. Hydraulic functions for swelling soils:pore scale considerations[J]. Journal of Hydrology.2003,272(1-4):50-71.
[158]Schifano V C. Electrical treatment of clays[D]. United States--Illinois:University of Illinois at Urbana-Champaign,2001.
[159]Bernabeu A, Exp E, Montiel V, et al. A new electrochemical method for consolidation of porous rocks[J]. Electrochemistry Communications.2001,3(3):122-127.
[160]Nover G. Electrical properties of crustal and mantle rocks-A review of laboratory measurements and their explanation[J]. Surveys in Geophysics.2005,26(5):593-651.
[161]段黎明,刘元宝,吴志芳,等.基于工业计算机断层成像技术的三维CAD模型重构方法[J].计算机集成制造系统.2009,15(03)：479-485.
[162]郭丽萍,Carpinteri Andrea,孙伟,等.基于三维微焦点CT图像对高性能混凝土内部缺陷的测量和分析[J]. Journal of Southeast University.2009,25(01):1003-7985.
[163]刘学锋,孙建孟,王海涛,等.顺序指示模拟重建三维数字岩心的准确性评价[J].石油学报.2009,30(03)：391-395.
[164]张杰,沈霄云,刘明贵.智能化桩基超声波CT检测系统研究[J].岩土力学.2009, 30(04)：1197-1120.
[165]赵阳升,孟巧荣,康天合,等.显微CT试验技术与花岗岩热破裂特征的细观研究[J].岩石力学与工程学报.2008,27(01)：28-34.
[166]杨更社,刘慧.基于CT图像处理技术的岩石损伤特性研究[J].煤炭学报.2007,32(05)：463-468.
[167]宋卫卫,苏铁明,欧宗瑛,等.基于CT图像反求技术的人体股骨头修复建模[J].大连理工大学学报.2009,49(02)：221-227.
[168]练秋生,郝鹏鹏.基于压缩传感和代数重建法的CT图像重建[J].光学技术.2009,35(03)：422-425.
[169]张汝楠,孙丽萍.基于X-ray CT技术原木三维重建检测缺陷方法的初步探讨[J].森林工程.2008,24(05)：25-31.
[170]Gonzalez Rafael C数字图像处理[M].第二版.北京：电子工业出版社,2003.
[171]王鸣鹏.CT检查技术学[M].上海：复旦大学出版社,2004.
[172]赵俊,庄天戈.CT图像分块重建算法[J].上海交通大学学报.2004,38(02)：197-199.
