适用于半迹长测线法的岩体结构面直径Priest-Zhang算法和修正算法适用性
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摘要
由概率论推导提出能够纠正截短偏差的修正算法,工程应用前为明确2种算法适用范围,先采用2种算法由实测半迹长分布估算直径期望,然后对比2种算法估算的直径期望与真实直径期望的相对误差,进行21组对比试验。结果表明:Priest-Zhang算法估算的直径期望是截短值的线性递增函数,修正算法估算的直径期望是截短值的水平线性函数;截短值较小时,2种算法接近,采用前者已能够获得较高精度,纠正截短偏差意义不大;截短值较大时后者明显更精确,纠正截短偏差能够大幅提高精度,应选用后者。汶川工程实例表明:当截短值为0.1 m时,2种算法具有高精度且估算结果接近,值得推广。
A new Priest-Zhang Algorithm was derived from the combination of Priest Equation and Zhang Equation.Priest-Zhang Algorithm brought in truncation bias,and Revised Priest-Zhang Algorithm was proposed from probability theory.Truncation bias was corrected in it.Applicability of both algorithms needs to be defined.First,mean diameter was estimated from distribution of observed semi-trace length by both algorithms.Secondly,the relative errors of estimated mean diameter were compared between both algorithms.21 sets of experiments were carried out.The results show that the estimated mean diameter by Priest-Zhang Algorithm is a linear increasing function of truncation threshold,while that by Revised Algorithm is a horizontal linear function.When truncation threshold is small the estimated mean diameters by both algorithms are similar,and Priest-Zhang Algorithm can be high of accuracy.When truncation threshold is large Revised Algorithm is more accurate,and the correction of truncation bias is significant.In this case Revised Algorithm is prior choice between the two algorithms.A case study in Wenchuan verifies that when truncation threshold is 0.1 m two algorithms are high of accuracy and similar in estimated diameters.The two new diameter algorithms are worth popularizing.
A new Priest-Zhang Algorithm was derived from the combination of Priest Equation and Zhang Equation.Priest-Zhang Algorithm brought in truncation bias,and Revised Priest-Zhang Algorithm was proposed from probability theory.Truncation bias was corrected in it.Applicability of both algorithms needs to be defined.First,mean diameter was estimated from distribution of observed semi-trace length by both algorithms.Secondly,the relative errors of estimated mean diameter were compared between both algorithms.21 sets of experiments were carried out.The results show that the estimated mean diameter by Priest-Zhang Algorithm is a linear increasing function of truncation threshold,while that by Revised Algorithm is a horizontal linear function.When truncation threshold is small the estimated mean diameters by both algorithms are similar,and Priest-Zhang Algorithm can be high of accuracy.When truncation threshold is large Revised Algorithm is more accurate,and the correction of truncation bias is significant.In this case Revised Algorithm is prior choice between the two algorithms.A case study in Wenchuan verifies that when truncation threshold is 0.1 m two algorithms are high of accuracy and similar in estimated diameters.The two new diameter algorithms are worth popularizing.
引文
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[19]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 Guo-ming,HUANG Run-qiu.Geometric description of complex rock mass structure[J].Journal of Chengdu University of Technology,1998,25(4):552-557.
[20]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 Shao-guo,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.
[21]Wines D R,Lilly P A.Measurement and analysis of rock mass discontinuity spacing and frequency in part of the Fimiston Open Pit operation in Kalgoorlie,Western Australia:A case study[J].International Journal of Rock Mechanics&Mining Sciences,2002,39:589-602.
[22]Grenon M,Hadjigeorgiou J.Drift reinforcement design based on discontinuity network modeling[J].International Journal of Rock Mechanics&Mining Sciences,2003,40:833-845.
[23]Brzovic A,Villaescusa E.Rock mass characterization and assessment of block-forming geological discontinuities during caving of primary copper ore at the El Teniente mine,Chile[J].International Journal of Rock Mechanics&Mining Sciences,2007,44:565-583.
[24]Priest S D,Hudson J A.Estimation of discontinuity spacing and trace length using scan line surveys[J].International Journal of Rock Mechanics and Mining Science and Geomechanics Abstract,1981,18(3):183-197.
[25]Zhang L,Einstein H H.Estimating the mean trace length of rock discontinuities[J].Rock Mechanics and Rock Engineering,1998,31(4):217-235.
[2]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.
[3]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[D].武汉:中科院武汉岩土力学研究所,2008:66-88.MEI Tao.Study on optimization of 3D joint network simulation in rock mass and its application in Jijicao block,Beishan,Gansu Province[D].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2008:66-88.
[4]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.
[5]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.
[6]Barton N.Some size dependent properties of joints and faults[J].Geophysical Research Letters,1981,8(7):667-670.
[7]Glynn E F,Veneziano D,Einstein H H.The probabilistic model for shearing resistance of jointed rock[C]//STATELINE N.19th US Symposium on Rock Mechanics.Reno:Press of University of Nevada,1978:66-76.
[8]Robertson A M.The interpretation of geological factors for use in slope theory[C]//RENSBURG V P W J.Proceedings of Planning Open Pit Mines.Cape Town,South Africa:Balkema Press,1970:55-71.
[9]Baecher G B,Lanney N A,Einstein H H.Statistical description of rock properties and sampling[C]//American Rock Mechanics Association.18th US Symposium on Rock Mechanics.Golden,Colorado,USA:Colorado School of Mines Press,1977:1-8.
[10]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.
[11]Bridges M C.Presentation of Fracture Data for Rock Mechanics[C]//BARTON A C T.2nd Australian-New Zealand Conference on Geomechanics.Brisbane,Australia:Institution of Engineers,1976:144-148.
[12]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 Fa-quan.Principles of statistical mechanics of rock masses[M].Wuhan:Press of China University of Geosciences,1993:30-63.
[13]Kulatilake P H S W,Wu T H.Relation between discontinuity size and trace length[C]//American Rock Mechanics Association.27th US Symposium on Rock Mechanics.Tuscaloosa,Alabama,USA:Society of Mining Engineers,1986:130-133.
[14]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.
[15]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.
[16]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.
[17]Warburton P M.A stereological interpretation of joint trace data[J].International Journal of Rock Mechanics and Mining Sciences&Geomechancis Abstracts,1980,17(4):181-190.
[18]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 Jian-ping,XIAO Shu-fang,WANG Qing.Computer modeling theory of random discontinuities 3-D network[M].Changchun:Press of Northeast Normal University,1995:122-233.
[19]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 Guo-ming,HUANG Run-qiu.Geometric description of complex rock mass structure[J].Journal of Chengdu University of Technology,1998,25(4):552-557.
[20]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 Shao-guo,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.
[21]Wines D R,Lilly P A.Measurement and analysis of rock mass discontinuity spacing and frequency in part of the Fimiston Open Pit operation in Kalgoorlie,Western Australia:A case study[J].International Journal of Rock Mechanics&Mining Sciences,2002,39:589-602.
[22]Grenon M,Hadjigeorgiou J.Drift reinforcement design based on discontinuity network modeling[J].International Journal of Rock Mechanics&Mining Sciences,2003,40:833-845.
[23]Brzovic A,Villaescusa E.Rock mass characterization and assessment of block-forming geological discontinuities during caving of primary copper ore at the El Teniente mine,Chile[J].International Journal of Rock Mechanics&Mining Sciences,2007,44:565-583.
[24]Priest S D,Hudson J A.Estimation of discontinuity spacing and trace length using scan line surveys[J].International Journal of Rock Mechanics and Mining Science and Geomechanics Abstract,1981,18(3):183-197.
[25]Zhang L,Einstein H H.Estimating the mean trace length of rock discontinuities[J].Rock Mechanics and Rock Engineering,1998,31(4):217-235.
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