适用于半迹长测线法的岩体结构面直径新试算法
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摘要
当假定结构面形状为圆盘时,直径成为岩体结构面空间分布的重要参数,需由实测迹长推求。提出直径新试算法,以Monte Carlo法模拟结构面几何要素分布、解析几何学推导分布关系、Excel或C++等编程试算直径分布使试验逼近实测未删截半迹长分布,此时试算直径分布为最佳直径分布。由于结果具有离散性,进行降低离散性试验,发现多次试算取平均值能有效降低离散性。新试算法较Priest-Zhang算法更准确、容错能力更强、计算速度更快、硬件配置更低、文件和内存占用量更小、编程更简便、运行更稳定,且较Priest-Zhang算法、黄磊前期算法适用分布形式更广。新试算法填补了在半迹长测线法中能够适用于多种分布形式的直径准确算法鲜见的空白,在汶川地震区得到成功验证,值得推广。
The discontinuity in rock mass is assumed as a disc,and the diameter becomes an important parameter of its spatial distribution.The diameter can be deduced from the observed trace length.A new trial algorithm for diameter was proposed,which simulated discontinuity distribution with Monte Carlo method,deduced distribution relation with analytic geometry and programmed with Excel or C++.The best diameter distribution from the algorithm was that making the trial untruncated-uncensored semi-trace length approximate to the observed one.Experiments to reduce the discreteness of the algorithm result were conducted.It is shown that taking mean value of many trials can reduce the discreteness effectively.The new trial algorithm is more accurate,better in fault tolerance,faster in calculation,lower in hardware configuration,less in file size and memory occupancy,more convenient in programming and more stable in running than Priest-Zhang algorithm.Also it suits more distribution patterns than Priest-Zhang algorithm and Huang Lei?s previous one.The new trial algorithm supplies the gap in the accurate algorithms for universal distribution patterns in semi-trace line-sampling,which has been tested in Wenchuan earthquake area and is worth popularizing.
The discontinuity in rock mass is assumed as a disc,and the diameter becomes an important parameter of its spatial distribution.The diameter can be deduced from the observed trace length.A new trial algorithm for diameter was proposed,which simulated discontinuity distribution with Monte Carlo method,deduced distribution relation with analytic geometry and programmed with Excel or C++.The best diameter distribution from the algorithm was that making the trial untruncated-uncensored semi-trace length approximate to the observed one.Experiments to reduce the discreteness of the algorithm result were conducted.It is shown that taking mean value of many trials can reduce the discreteness effectively.The new trial algorithm is more accurate,better in fault tolerance,faster in calculation,lower in hardware configuration,less in file size and memory occupancy,more convenient in programming and more stable in running than Priest-Zhang algorithm.Also it suits more distribution patterns than Priest-Zhang algorithm and Huang Lei?s previous one.The new trial algorithm supplies the gap in the accurate algorithms for universal distribution patterns in semi-trace line-sampling,which has been tested in Wenchuan earthquake area and is worth popularizing.
引文
[1]SHI G H.Geometric method for the stability analysis ofdiscontinuous rocks[J].Scientia Sinica,1982,25(3):318–336.
[2]HUDSON J A,PRIEST S D.Discontinuity frequency in rockmasses[J].International Journal of Rock Mechanics and MiningSciences and Geomechanics Abstracts,1983,20(2):73–89.
[3]EINSTEIN H H,VENEZIANO D,BAECHER G B,et al.The effectof discontinuity persistence on rock slope stability[J].InternationalJournal of Rock Mechanics and Mining Sciences and GeomechanicsAbstracts,1983,20(5):227–236.
[4]KULATILAKE P H S W,WATHUGALA D N,STEPHANSSON O.Joint network modeling with a validation exercise in Stripa Mine,Sweden[J].International Journal of Rock Mechanics and MiningSciences and Geomechanics Abstracts,1993,30(5):503–526.
[5]徐光黎,潘别桐,唐辉明,等.岩体结构模型与应用[M].武汉:中国地质大学出版社,1993:89–144.(XU Guangli,PAN Bietong,TANG Huiming,et al.Modeling of rock mass structures and itsapplications[M].Wuhan:China University of Geosciences Press,1993:89–144.(in Chinese))
[6]陈剑平,王清,肖树芳.岩体裂隙网络分数维计算机模拟[J].工程地质学报,1995,3(3):79–85.(CHEN Jianping,WANG Qing,XIAO Shufang.Computer modeling of the fractal dimension of rockmass fracture network[J].Journal of Engineering Geology,1995,3(3):79–85.(in Chinese))
[7]李浩,吴晓玲,朱焕春.岩体裂隙线贯通率的计算机模拟计算[J].岩土力学,2001,22(3):350–352.(LI Hao,WU Xiaoling,ZHU Huanchun.Calculation of line-connectivity of fissure in rockmass[J].Rock and Soil Mechanics,2001,22(3):350–352.(in Chinese))
[8]荣冠,周创兵,朱焕春,等.三峡水库某库段岩体裂隙网络模拟研究[J].岩土力学,2004,25(7):1 122–1 126.(RONG Guan,ZHOU Chuangbing,ZHU Huanchun,et al.Research on fissuresnetwork of jointed rock masses in one section of Three GorgesReservoir[J].Rock and Soil Mechanics,2004,25(7):1 122–1 126.(in Chinese))
[9]黄润秋,许模,陈剑平,等.复杂岩体结构精细描述及其工程应用[M].北京:科学出版社,2004:192–204,306–365.(HUANGRunqiu,XU Mo,CHEN Jianping,et al.Detailed description ofcomplex rock structure and its application[M].Beijing:SciencePress,2004:192–204,306–365.(in Chinese))
[10]高丽娜.裂隙迹长非确定性统计模型的应用研究[硕士学位论文][D].成都:成都理工大学,2006.(GAO Lina.Applicationresearches of uncertain statistic model for discontinuities tracelength[M.S.Thesis][D].Chengdu:Chengdu University of Technology,2006.(in Chinese))
[11]JOURDE H,FENART P,VINCHES M,et al.Relationship betweenthe geometrical and structural properties of layered fractured rocksand their effective permeability tensor:a simulation study[J].Journal of Hydrology,2007,337(1/2):117–132.
[12]TRAN N H,RAHMAN S S.Development of hot dry rocks byhydraulic stimulation:natural fracture network simulation[J].Theoreticaland Applied Fracture Mechanics,2007,47(1):77–85.
[13]梅涛.岩体节理三维网络模拟优化及在甘肃北山芨芨槽岩块的应用研究[博士学位论文][D].武汉:中国科学院武汉岩土力学研究所,2008.(MEI Tao.Study on optimization of 3D joint networksimulation in rock mass and its application in Jijicao block,Beishan,Gansu Province[Ph.D.Thesis][D].Wuhan:Institute of Rock and SoilMechanics,Chinese Academy of Sciences,2008.(in Chinese))
[14]J GER P,STEINMANN P,KUHL E.On local tracking algorithmsfor the simulation of three-dimensional discontinuities[J].ComputationalMechanics,2008,42(3):395–406.
[15]SONG J J.Distribution-free method for estimating size distributionand volumetric frequency of rock joints[J].International Journal ofRock Mechanics and Mining Sciences,2009,46(4):748–760.
[16]BANKWITZ P.über Klüfte II.Die bildung der kluftfl che und einesystematik ihrer strukturen[J].Geologie,1966,15:896–941.
[17]BARTON N.Some size dependent properties of joints and faults[J].Geophysical Research Letters,1981,8(7):667–670.
[18]GLYNN E F,VENEZIANO D,EINSTEIN H H.The probabilisticmodel for shearing resistance of jointed rock[C]//STATELINE N ed.Proceedings of the 19th US Symposium on Rock Mechanics.Reno:Press of University of Nevada,1978:66–76.
[19]ROBERTSON A M.The interpretation of geological factors for use inslope theory[C]//RENSBURG V P W J ed.Proceedings of PlanningOpen Pit Mines.Cape Town,South Africa:Balkema Press,1970:55–71.
[20]BAECHER G B,LANNEY N A,EINSTEIN H H.Statisticaldescription of rock properties and sampling[C]//Proceedings of the18th US Symposium on Rock Mechanics.Golden,Colorado,USA:Colorado School of Mines Press,1977:1–8.
[21]NARENDRAN V M,CLEARY M P.Elastostatic interaction ofmultiple arbitrarily shaped cracks in plane inhomogeneous regions[J].Engineering Fracture Mechanics,1984,19(3):481–506.
[22]BRIDGES M C.Presentation of Fracture Data for Rock Mechanics[C]//BARTON A C T ed.Proceedings of the 2nd Australian-New ZealandConference on Geomechanics.Brisbane,Australia:RMIT UniversityPress,1975:144–148.
[23]伍法权.统计岩体力学原理[M].武汉:中国地质大学出版社,1993:30–63.(WU Faquan.Principles of statistical mechanics of rockmasses[M].Wuhan:China University of Geosciences Press,1993:30–63.(in Chinese))
[24]KULATILAKE P H S W,WU T H.Relation between discontinuitysize and trace length[C]//Proceedings of the 27th US Symposium onRock Mechanics.Tuscaloosa,Alabama,USA:Society of MiningEngineers Publisher,1986:130–133.
[25]SONG J J,LEE C I.Estimation of joint length distribution usingwindow sampling[J].International Journal of Rock Mechanics andMining Sciences,2001,38(4):519–528.
[26]SONG J J.Estimation of a joint diameter distribution by an implicitscheme and interpolation technique[J].International Journal of RockMechanics and Mining Sciences,2006,43(4):512–519.
[27]VILLAESCUSA E,BROWN E T.Maximum likelihood estimation ofjoint sizes for trace length measurements[J].Rock Mechanics andRock Engineering,1992,25(2):67–87.
[28]WARBURTON P M.A stereological interpretation of joint tracedata[J].International Journal of Rock Mechanics and Mining Sciencesand Geomechancis Abstracts,1980,17(4):181–190.
[29]陈剑平,肖树芳,王清.随机不连续面三维网络计算机模拟原理[M].长春:东北师范大学出版社,1995:122–233.(CHENJianping,XIAO Shufang,WANG Qing.Computer modeling theory ofrandom discontinuities 3D network[M].Changchun:Northeast NormalUniversity Press,1995:122–233.(in Chinese))
[30]黄国明,黄润秋.复杂岩体结构的几何描述[J].成都理工大学学报,1998,25(4):552–557.(HUANG Guoming,HUANG Runqiu.Geometric description of complex rock mass structure[J].Journal ofChengdu University of Technology,1998,25(4):552–557.(inChinese))
[31]袁绍国,王震.岩体节理迹长与节理真实长度的概率关系[J].包头钢铁学院院报,1999,18(1):5–8.(YUAN Shaoguo,WANG Zhen.Relation between joint size and its trace length on rock face[J].Journalof Baotou University of Iron and Steel Technology,1999,18(1):5–8.(inChinese))
[32]WINES D R,LILLY P A.Measurement and analysis of rock massdiscontinuity spacing and frequency in part of the Fimiston Open Pitoperation in Kalgoorlie,Western Australia:a case study[J].InternationalJournal of Rock Mechanics and Mining Sciences,2002,39(5):589–602.
[33]GRENON M,HADJIGEORGIOU J.Drift reinforcement design basedon discontinuity network modeling[J].International Journal of RockMechanics and Mining Sciences,2003,40(6):833–845.
[34]BRZOVIC A,VILLAESCUSA E.Rock mass characterization andassessment of block-forming geological discontinuities during cavingof primary copper ore at the El Teniente mine,Chile[J].InternationalJournal of Rock Mechanics and Mining Sciences,2007,44(4):565–583.
[35]黄磊,唐辉明,张龙,等.适用于半迹长测线法的岩体结构面迹长与直径关系新模型及新算法[J].岩石力学与工程学报,2011,30(4):733–745.(HUANG Lei,TANG Huiming,ZHANG Long,et al.New relation between rock discontinuities trace length anddiameter for semi-trace scanline sampling and new algorithm[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(4):733–745.(in Chinese))
[36]ZHANG L,EINSTEIN H H.Estimating the mean trace length of rockdiscontinuities[J].Rock Mechanics and Rock Engineering,1998,31(4):217–235.
[37]PRIEST S D,HUDSON J A.Estimation of discontinuity spacing andtrace length using scanline surveys[J].International Journal of RockMechanics and Mining Sciences and Geomechanics Abstracts,1981,18(3):183–197.
[38]赵鑫.运用三维非连续性裂隙网络模型研究裂隙产状误差[硕士学位论文].北京:中国地质大学,2006.(ZHAO Xin.Analyses oforientation errors of fractures using 3D discrete fracture network[M.S.Thesis][D].Beijing:China University of Geosciences,2006.(in Chinese))
[2]HUDSON J A,PRIEST S D.Discontinuity frequency in rockmasses[J].International Journal of Rock Mechanics and MiningSciences and Geomechanics Abstracts,1983,20(2):73–89.
[3]EINSTEIN H H,VENEZIANO D,BAECHER G B,et al.The effectof discontinuity persistence on rock slope stability[J].InternationalJournal of Rock Mechanics and Mining Sciences and GeomechanicsAbstracts,1983,20(5):227–236.
[4]KULATILAKE P H S W,WATHUGALA D N,STEPHANSSON O.Joint network modeling with a validation exercise in Stripa Mine,Sweden[J].International Journal of Rock Mechanics and MiningSciences and Geomechanics Abstracts,1993,30(5):503–526.
[5]徐光黎,潘别桐,唐辉明,等.岩体结构模型与应用[M].武汉:中国地质大学出版社,1993:89–144.(XU Guangli,PAN Bietong,TANG Huiming,et al.Modeling of rock mass structures and itsapplications[M].Wuhan:China University of Geosciences Press,1993:89–144.(in Chinese))
[6]陈剑平,王清,肖树芳.岩体裂隙网络分数维计算机模拟[J].工程地质学报,1995,3(3):79–85.(CHEN Jianping,WANG Qing,XIAO Shufang.Computer modeling of the fractal dimension of rockmass fracture network[J].Journal of Engineering Geology,1995,3(3):79–85.(in Chinese))
[7]李浩,吴晓玲,朱焕春.岩体裂隙线贯通率的计算机模拟计算[J].岩土力学,2001,22(3):350–352.(LI Hao,WU Xiaoling,ZHU Huanchun.Calculation of line-connectivity of fissure in rockmass[J].Rock and Soil Mechanics,2001,22(3):350–352.(in Chinese))
[8]荣冠,周创兵,朱焕春,等.三峡水库某库段岩体裂隙网络模拟研究[J].岩土力学,2004,25(7):1 122–1 126.(RONG Guan,ZHOU Chuangbing,ZHU Huanchun,et al.Research on fissuresnetwork of jointed rock masses in one section of Three GorgesReservoir[J].Rock and Soil Mechanics,2004,25(7):1 122–1 126.(in Chinese))
[9]黄润秋,许模,陈剑平,等.复杂岩体结构精细描述及其工程应用[M].北京:科学出版社,2004:192–204,306–365.(HUANGRunqiu,XU Mo,CHEN Jianping,et al.Detailed description ofcomplex rock structure and its application[M].Beijing:SciencePress,2004:192–204,306–365.(in Chinese))
[10]高丽娜.裂隙迹长非确定性统计模型的应用研究[硕士学位论文][D].成都:成都理工大学,2006.(GAO Lina.Applicationresearches of uncertain statistic model for discontinuities tracelength[M.S.Thesis][D].Chengdu:Chengdu University of Technology,2006.(in Chinese))
[11]JOURDE H,FENART P,VINCHES M,et al.Relationship betweenthe geometrical and structural properties of layered fractured rocksand their effective permeability tensor:a simulation study[J].Journal of Hydrology,2007,337(1/2):117–132.
[12]TRAN N H,RAHMAN S S.Development of hot dry rocks byhydraulic stimulation:natural fracture network simulation[J].Theoreticaland Applied Fracture Mechanics,2007,47(1):77–85.
[13]梅涛.岩体节理三维网络模拟优化及在甘肃北山芨芨槽岩块的应用研究[博士学位论文][D].武汉:中国科学院武汉岩土力学研究所,2008.(MEI Tao.Study on optimization of 3D joint networksimulation in rock mass and its application in Jijicao block,Beishan,Gansu Province[Ph.D.Thesis][D].Wuhan:Institute of Rock and SoilMechanics,Chinese Academy of Sciences,2008.(in Chinese))
[14]J GER P,STEINMANN P,KUHL E.On local tracking algorithmsfor the simulation of three-dimensional discontinuities[J].ComputationalMechanics,2008,42(3):395–406.
[15]SONG J J.Distribution-free method for estimating size distributionand volumetric frequency of rock joints[J].International Journal ofRock Mechanics and Mining Sciences,2009,46(4):748–760.
[16]BANKWITZ P.über Klüfte II.Die bildung der kluftfl che und einesystematik ihrer strukturen[J].Geologie,1966,15:896–941.
[17]BARTON N.Some size dependent properties of joints and faults[J].Geophysical Research Letters,1981,8(7):667–670.
[18]GLYNN E F,VENEZIANO D,EINSTEIN H H.The probabilisticmodel for shearing resistance of jointed rock[C]//STATELINE N ed.Proceedings of the 19th US Symposium on Rock Mechanics.Reno:Press of University of Nevada,1978:66–76.
[19]ROBERTSON A M.The interpretation of geological factors for use inslope theory[C]//RENSBURG V P W J ed.Proceedings of PlanningOpen Pit Mines.Cape Town,South Africa:Balkema Press,1970:55–71.
[20]BAECHER G B,LANNEY N A,EINSTEIN H H.Statisticaldescription of rock properties and sampling[C]//Proceedings of the18th US Symposium on Rock Mechanics.Golden,Colorado,USA:Colorado School of Mines Press,1977:1–8.
[21]NARENDRAN V M,CLEARY M P.Elastostatic interaction ofmultiple arbitrarily shaped cracks in plane inhomogeneous regions[J].Engineering Fracture Mechanics,1984,19(3):481–506.
[22]BRIDGES M C.Presentation of Fracture Data for Rock Mechanics[C]//BARTON A C T ed.Proceedings of the 2nd Australian-New ZealandConference on Geomechanics.Brisbane,Australia:RMIT UniversityPress,1975:144–148.
[23]伍法权.统计岩体力学原理[M].武汉:中国地质大学出版社,1993:30–63.(WU Faquan.Principles of statistical mechanics of rockmasses[M].Wuhan:China University of Geosciences Press,1993:30–63.(in Chinese))
[24]KULATILAKE P H S W,WU T H.Relation between discontinuitysize and trace length[C]//Proceedings of the 27th US Symposium onRock Mechanics.Tuscaloosa,Alabama,USA:Society of MiningEngineers Publisher,1986:130–133.
[25]SONG J J,LEE C I.Estimation of joint length distribution usingwindow sampling[J].International Journal of Rock Mechanics andMining Sciences,2001,38(4):519–528.
[26]SONG J J.Estimation of a joint diameter distribution by an implicitscheme and interpolation technique[J].International Journal of RockMechanics and Mining Sciences,2006,43(4):512–519.
[27]VILLAESCUSA E,BROWN E T.Maximum likelihood estimation ofjoint sizes for trace length measurements[J].Rock Mechanics andRock Engineering,1992,25(2):67–87.
[28]WARBURTON P M.A stereological interpretation of joint tracedata[J].International Journal of Rock Mechanics and Mining Sciencesand Geomechancis Abstracts,1980,17(4):181–190.
[29]陈剑平,肖树芳,王清.随机不连续面三维网络计算机模拟原理[M].长春:东北师范大学出版社,1995:122–233.(CHENJianping,XIAO Shufang,WANG Qing.Computer modeling theory ofrandom discontinuities 3D network[M].Changchun:Northeast NormalUniversity Press,1995:122–233.(in Chinese))
[30]黄国明,黄润秋.复杂岩体结构的几何描述[J].成都理工大学学报,1998,25(4):552–557.(HUANG Guoming,HUANG Runqiu.Geometric description of complex rock mass structure[J].Journal ofChengdu University of Technology,1998,25(4):552–557.(inChinese))
[31]袁绍国,王震.岩体节理迹长与节理真实长度的概率关系[J].包头钢铁学院院报,1999,18(1):5–8.(YUAN Shaoguo,WANG Zhen.Relation between joint size and its trace length on rock face[J].Journalof Baotou University of Iron and Steel Technology,1999,18(1):5–8.(inChinese))
[32]WINES D R,LILLY P A.Measurement and analysis of rock massdiscontinuity spacing and frequency in part of the Fimiston Open Pitoperation in Kalgoorlie,Western Australia:a case study[J].InternationalJournal of Rock Mechanics and Mining Sciences,2002,39(5):589–602.
[33]GRENON M,HADJIGEORGIOU J.Drift reinforcement design basedon discontinuity network modeling[J].International Journal of RockMechanics and Mining Sciences,2003,40(6):833–845.
[34]BRZOVIC A,VILLAESCUSA E.Rock mass characterization andassessment of block-forming geological discontinuities during cavingof primary copper ore at the El Teniente mine,Chile[J].InternationalJournal of Rock Mechanics and Mining Sciences,2007,44(4):565–583.
[35]黄磊,唐辉明,张龙,等.适用于半迹长测线法的岩体结构面迹长与直径关系新模型及新算法[J].岩石力学与工程学报,2011,30(4):733–745.(HUANG Lei,TANG Huiming,ZHANG Long,et al.New relation between rock discontinuities trace length anddiameter for semi-trace scanline sampling and new algorithm[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(4):733–745.(in Chinese))
[36]ZHANG L,EINSTEIN H H.Estimating the mean trace length of rockdiscontinuities[J].Rock Mechanics and Rock Engineering,1998,31(4):217–235.
[37]PRIEST S D,HUDSON J A.Estimation of discontinuity spacing andtrace length using scanline surveys[J].International Journal of RockMechanics and Mining Sciences and Geomechanics Abstracts,1981,18(3):183–197.
[38]赵鑫.运用三维非连续性裂隙网络模型研究裂隙产状误差[硕士学位论文].北京:中国地质大学,2006.(ZHAO Xin.Analyses oforientation errors of fractures using 3D discrete fracture network[M.S.Thesis][D].Beijing:China University of Geosciences,2006.(in Chinese))
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