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
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摘要
适用于半迹长测线法的岩体结构面迹长与直径概率关系需要研究,基于弦端点在圆周上随机分布、弦中点在圆某一直径上随机分布、弦中点在扇形内随机分布、弦中点在扇形圆弧且直径上同时随机分布、弦中点在扇形直径上随机分布(广义模型)这5种不同等可能假设,得到未删截半迹长与直径的5种概率关系模型,理论与实例证明前4种模型在半迹长测线法中不适用或适用性不强、广义模型适用性强,5种模型填补未删截半迹长与直径概率关系方面的空白。当直径服从均匀分布形式时,提出广义模型直径新算法,在汶川地震中得到成功应用,值得推广。
Probability relation between trace length and diameter of rock discontinuities applicable for semi-trace scanline sampling needs to be studied.And five kinds of possibilities are assumed as follows:endpoints of chords are distributed randomly on circumference;midpoints of chords are distributed randomly on a circular diameter;midpoints of chords are distributed randomly in sector;midpoints of chords are distributed randomly both on sectorial arc and diameter;midpoints of chords are distributed randomly on sectorial diameter(generalized model),five models of probability relations between untruncated-uncensored semi-trace length and diameter are acquired.Theory and practice demonstrate that the former four models are not applicable or not quite applicable for semi-trace scanline sampling;while generalized model is quite applicable.The five models supply a gap in previous knowledge of relation between the probability densities of untruncated-uncensored semi-trace length and diameter.When diameters follow uniform distribution pattern,a new diameter algorithm of generalized model is proposed.The new algorithm is applied to Wenchuan earthquake successfully and worth popularizing.
Probability relation between trace length and diameter of rock discontinuities applicable for semi-trace scanline sampling needs to be studied.And five kinds of possibilities are assumed as follows:endpoints of chords are distributed randomly on circumference;midpoints of chords are distributed randomly on a circular diameter;midpoints of chords are distributed randomly in sector;midpoints of chords are distributed randomly both on sectorial arc and diameter;midpoints of chords are distributed randomly on sectorial diameter(generalized model),five models of probability relations between untruncated-uncensored semi-trace length and diameter are acquired.Theory and practice demonstrate that the former four models are not applicable or not quite applicable for semi-trace scanline sampling;while generalized model is quite applicable.The five models supply a gap in previous knowledge of relation between the probability densities of untruncated-uncensored semi-trace length and diameter.When diameters follow uniform distribution pattern,a new diameter algorithm of generalized model is proposed.The new algorithm is applied to Wenchuan earthquake successfully and worth popularizing.
引文
[1]SHI G H.Geometric method for the stability analysis of discontinuous rocks[J].Scientia Sinica,1982,25(3):318–336.
[2]HUDSON J A,PRIEST S D.Discontinuity frequency in rock masses[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1983,20(2):73–89.
[3]EINSTEIN H H,VENEZIANO D,BAECHER G B,et al.The effect of discontinuity persistence on rock slope stability[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,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 Mining Sciences 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.Model of rock mass structures and its applications[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 rock mass 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 rock mass[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 fissures network of jointed rock masses in one section of Three Gorges Reservoir[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.(HUANG Runqiu,XU Mo,CHEN Jianping,et al.Detailed description of complex rock structure and its application[M].Beijing:Science Press,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,2006:55–64.(GAO Lina.Application research of uncertain statistic model for discontinuities trace length[M.S.Thesis][D].Chengdu:Chengdu University of Technology,2006:55–64.(in Chinese))
[11]JOURDE H,FENART P,VINCHES M,et al.Relationship between the geometrical and structural properties of layered fractured rocks and 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 by hydraulic stimulation:natural fracture network simulation[J].Theoretical and 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 network simulation in rock mass and its application in Jijicao block,Beishan,Gansu Province[Ph.D.Thesis][D].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2008.(in Chinese))
[14]J?GER P,STEINMANN P,KUHL E.On local tracking algorithms for the simulation of three-dimensional discontinuities[J].Computational Mechanics,2008,42(3):395–406.
[15]SONG J J.Distribution-free method for estimating size distribution and volumetric frequency of rock joints[J].International Journal of Rock Mechanics and Mining Sciences,2009,46(4):748–760.
[16]BANKWITZ P.über Klüfte II.Die bildung der kluftfl?che und eine systematik 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 probabilistic model 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 in slope theory[C]//RENSBURG V P W J ed.Proceedings of Planning Open Pit Mines.Cape Town,South Africa:Balkema Press,1970:55–71.
[20]BAECHER G B,LANNEY N A,EINSTEIN H H.Statistical description of rock properties and sampling[C]//Proceedings of the 18th 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 of multiple 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 Zealand Conference on Geomechanics.Brisbane,Australia:RMIT University Press,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 rock masses[M].Wuhan:China University of Geosciences Press,1993:30–63.(in Chinese))
[24]KULATILAKE P H S W,WU T H.Relation between discontinuity size and trace length[C]//Proceedings of the 27th US Symposium on Rock Mechanics.Tuscaloosa,Alabama,USA:Society of Mining Engineers Publisher,1986:130–133.
[25]SONG J J,LEE C I.Estimation of joint length distribution using window sampling[J].International Journal of Rock Mechanics and Mining Sciences,2001,38(4):519–528.
[26]SONG J J.Estimation of a joint diameter distribution by an implicit scheme and interpolation technique[J].International Journal of Rock Mechanics and Mining Sciences,2006,43(4):512–519.
[27]VILLAESCUSA E,BROWN E T.Maximum likelihood estimation of joint sizes for trace length measurements[J].Rock Mechanics and Rock Engineering,1992,25(2):67–87.
[28]WARBURTON P M.A stereological interpretation of joint trace data[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics 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.(CHEN Jianping,XIAO Shufang,WANG Qing.Computer modeling theory of random discontinuities 3D network[M].Changchun:Press of Northeast Normal University,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 of Chengdu University of Technology,1998,25(4):552–557.(in Chinese))
[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].Journal of Baotou University of Iron and Steel Technology,1999,18(1):5–8.(in Chinese))
[32]KULATILAKE P H S W,WU T H.Estimation of mean trace length of discontinuities[J].Rock Mechanics and Rock Engineering,1984,17(4):215–232.
[33]CRUDEN D M.Describing the size of discontinuities[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1977,14(3):133–137.
[34]PRIEST S D,HUDSON J A.Estimation of discontinuity spacing and trace length using scanline surveys[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1981,18(3):183–197.
[35]KENDALL M G,MORAN P A P.Geometrical probability[M].New York:Hafner Pub.,Co.,1963:92.
[36]钱海涛,马平,秦四清.岩体不连续面迹长与直径间的概率关系模型分析[J].岩土力学,2007,28(9):1 828–1 832.(QIAN Haitao,MA Ping,QIN Siqing.Analysis of three probability models between trace length and diameter of rock discontinuities[J].Rock and Soil Mechanics,2007,28(9):1 828–1 832.(in Chinese))
[2]HUDSON J A,PRIEST S D.Discontinuity frequency in rock masses[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1983,20(2):73–89.
[3]EINSTEIN H H,VENEZIANO D,BAECHER G B,et al.The effect of discontinuity persistence on rock slope stability[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,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 Mining Sciences 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.Model of rock mass structures and its applications[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 rock mass 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 rock mass[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 fissures network of jointed rock masses in one section of Three Gorges Reservoir[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.(HUANG Runqiu,XU Mo,CHEN Jianping,et al.Detailed description of complex rock structure and its application[M].Beijing:Science Press,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,2006:55–64.(GAO Lina.Application research of uncertain statistic model for discontinuities trace length[M.S.Thesis][D].Chengdu:Chengdu University of Technology,2006:55–64.(in Chinese))
[11]JOURDE H,FENART P,VINCHES M,et al.Relationship between the geometrical and structural properties of layered fractured rocks and 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 by hydraulic stimulation:natural fracture network simulation[J].Theoretical and 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 network simulation in rock mass and its application in Jijicao block,Beishan,Gansu Province[Ph.D.Thesis][D].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2008.(in Chinese))
[14]J?GER P,STEINMANN P,KUHL E.On local tracking algorithms for the simulation of three-dimensional discontinuities[J].Computational Mechanics,2008,42(3):395–406.
[15]SONG J J.Distribution-free method for estimating size distribution and volumetric frequency of rock joints[J].International Journal of Rock Mechanics and Mining Sciences,2009,46(4):748–760.
[16]BANKWITZ P.über Klüfte II.Die bildung der kluftfl?che und eine systematik 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 probabilistic model 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 in slope theory[C]//RENSBURG V P W J ed.Proceedings of Planning Open Pit Mines.Cape Town,South Africa:Balkema Press,1970:55–71.
[20]BAECHER G B,LANNEY N A,EINSTEIN H H.Statistical description of rock properties and sampling[C]//Proceedings of the 18th 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 of multiple 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 Zealand Conference on Geomechanics.Brisbane,Australia:RMIT University Press,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 rock masses[M].Wuhan:China University of Geosciences Press,1993:30–63.(in Chinese))
[24]KULATILAKE P H S W,WU T H.Relation between discontinuity size and trace length[C]//Proceedings of the 27th US Symposium on Rock Mechanics.Tuscaloosa,Alabama,USA:Society of Mining Engineers Publisher,1986:130–133.
[25]SONG J J,LEE C I.Estimation of joint length distribution using window sampling[J].International Journal of Rock Mechanics and Mining Sciences,2001,38(4):519–528.
[26]SONG J J.Estimation of a joint diameter distribution by an implicit scheme and interpolation technique[J].International Journal of Rock Mechanics and Mining Sciences,2006,43(4):512–519.
[27]VILLAESCUSA E,BROWN E T.Maximum likelihood estimation of joint sizes for trace length measurements[J].Rock Mechanics and Rock Engineering,1992,25(2):67–87.
[28]WARBURTON P M.A stereological interpretation of joint trace data[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics 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.(CHEN Jianping,XIAO Shufang,WANG Qing.Computer modeling theory of random discontinuities 3D network[M].Changchun:Press of Northeast Normal University,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 of Chengdu University of Technology,1998,25(4):552–557.(in Chinese))
[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].Journal of Baotou University of Iron and Steel Technology,1999,18(1):5–8.(in Chinese))
[32]KULATILAKE P H S W,WU T H.Estimation of mean trace length of discontinuities[J].Rock Mechanics and Rock Engineering,1984,17(4):215–232.
[33]CRUDEN D M.Describing the size of discontinuities[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1977,14(3):133–137.
[34]PRIEST S D,HUDSON J A.Estimation of discontinuity spacing and trace length using scanline surveys[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1981,18(3):183–197.
[35]KENDALL M G,MORAN P A P.Geometrical probability[M].New York:Hafner Pub.,Co.,1963:92.
[36]钱海涛,马平,秦四清.岩体不连续面迹长与直径间的概率关系模型分析[J].岩土力学,2007,28(9):1 828–1 832.(QIAN Haitao,MA Ping,QIN Siqing.Analysis of three probability models between trace length and diameter of rock discontinuities[J].Rock and Soil Mechanics,2007,28(9):1 828–1 832.(in Chinese))
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