西康铁路秦岭隧道区岩体结构面分布规律的混沌特征及围岩分级预测
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摘要
西安安康铁路秦岭特长隧道区域地质环境条件复杂,岩体结构面空间分布规律的评价与预测是指导工程设计和保障施工安全的重要基础因素。铁路隧道围岩基本分级主要由岩石的硬度和岩体的破碎程度决定,而岩体的破碎程度与岩体中结构面的分布状态和发育程度直接相关。岩体中的结构面是复杂地质构造运动的产物,它的分布具有典型的非线性特点。论文应用非线性系统科学中的混沌理论,研究了秦岭隧道区结构面空间分布非线性规律,建立了结构面预测的混沌模型,进一步从结构面分布的混沌特征入手,应用数据挖掘方法预测了秦岭隧道的围岩分级。
(1)应用时间序列概念及分析方法,建立了结构面序列。为满足时间序列等间距采样要求,将结构面在测线上的间距逐一排列形成一个序列,依次可建立结构面倾向和倾角序列。由这三个序列共同确定结构面在空间的位置、倾向和倾角。用混沌等非线性研究方法,研究了结构面序列特征及其分形结构。
(2)以实测数据为基础,应用非线性科学的混沌理论,研究了结构面的空间分布特征。功率谱图中低频部分负幂现象的存在、结构面发育与断层关系负幂存在、结构面分布的分形现象、Kolmogorov熵大于0等特征都证明了结构面混沌分布的存在性,Lyapunov指数趋于0、主分量分析图中先斜后趋平、功率谱负幂出现与消失又说明了结构面分布不完全是混沌,而是位于混沌的边缘。
(3)相空间重构揭示结构面空间分布非线性规律,根据混沌时间序列相空间重构原理,用C-C法、预测误差最小法计算嵌入维和空间延迟量,可张显结构面在岩体中的分布特征。明确了嵌入维实际上是岩体中主要相似结构面发育的平均组数,而空间延迟是主要相似结构面之间的平均间隔等混沌学指标的物理意义。
(4)通过结构面混沌特征量的计算,建立了混沌学预测模型,对结构面位置及产状进行了混沌预测,结构面序列化提供了预测的基础,相空间重构决定了混沌预测的方法。一阶局域预测法算法简单,使用方便,其预测精度不但取决于结构面序列嵌入维和空间延迟,而且与最临近相点、训练样本大小和预测步长等有关。
(5)基于结构面混沌特征,进行了围岩分级预测,用已知围岩分级岩体中的结构面作为训练样本,预测出的结构面作为预测样本,以结构面切割权密度、结构面间距、倾向和倾角四个属性为预测因子,按数据挖掘理论离散化结构面数据,以基本贝叶斯分类法预测未知样本的围岩分级,工程实践结果证明是可行的。
论文以非线性系统科学的混沌理论为理论基础,以知识挖掘和基本贝叶斯分类法为手段,预测了西安安康铁路秦岭特长隧道的围岩分级,研究成果不仅为该工程的设计施工提供了技术支撑,而且为其他工程中该类问题的解决探索了一个新的途径。
The guiding engineering for the regional geology,complicated environmental situation,rock mass structural planes,and space pattern evaluation and surveying of the Qinling Extra-Long Tunnel of the Xi'an-Ankang Railroad is an important factor in design and construction safety.The basic classification of the surrounding rock of a railroad is determined by rock hardness and the crushing degree of rock mass,which is directly related to the distribution and development of its structural planes.The structural plane of the rock is the product of a complicated tectonic process,which has the characteristics of a non-linear distribution.This paper uses the non-linear system science of chaos theory to research the non-linear spatial distribution patterns of the Qinling Tunnel area structural planes and construct a model of chaos.Advancement will be made beginning from the chaos characteristics of structural planes and the utilization of data to develop new surveying methods for the rock masses in the Qinling Tunnel area.
(1) The structural series was constructed using the concept of time series analysis.In order to satisfy distance requirements such as time series,we formed an arrangement from surveys of the structural plane distances.From this,we could construct the structural plane dipdirect and rake series.From the combination of these three series we could determine the spatial orientation,dipdirect and rake of the structural plane.Using non-linear research methods including chaos theory,we studied the characteristics of the structural plan series and its structural formation.
(2)Using surveying as the basis of our data,we utilized the non-linear science of chaos theory to research the characteristics of spatial distribution within the structural plane.The phenomenon of the existence of low frequency negative power within the power spectrum,the existence of the relationship between structural plane development and faults,and the phenomenon of the Kolmogoroc entropy structural plane distribution fractal environment greater than 0 all explain the existence of chaotic distribution within the structural plane.The Lyapunov index that tends towards 1,the principal component graded analysis,the appearance of the power spectrum and the disappearance of negative power also lead us to believe that the distribution of the structural plane is not completely chaotic,but is at the edge of chaos.
(3) phase-space reconfiguration reveal the spatial distribution of non-linear law based on chaotic time series phase-space reconstruction theory.Using the CC method,the smallest methods of error prediction in the embedding dimension and delays the amount of space showing the distribution of the rock structure.Explicit embedding dimension of the is similar to the structure of the main rock face in the development of the average group number,and the main space delay structure is similar to the average interval between the chaos,such as the physical meaning of parameters.
(4) Through the calculation of the amount of chaos in the structural plane,we establish the predicative chaos models for the structural plane locations and a chaotic occurrence predicted sequence structure prediction provides the basis for the decision to phase-space reconstruction of chaotic prediction method.The single-order local-region method algorithm is simple and easy to use,the sequence prediction accuracy not only depends on the embedded dimension of structure and spatial delay,it is also related to the closest related points,training sample size and estimations such as step size.
(5) Based on the chaotic characteristics of the structural planes we predicted the surrounding rock mass classifications.Using the known classification of rock masses surrounding the structural planes as training samples,the structural plane samples as a prediction to the structure of the cutting weight density,the structure of surface spacing length of structural planes,and the orientation and inclination for the four predictor attribute factors according to the theory of excavation discretization data structure to basic Bayes's classification,we predicted unknown samples of rock classification.The results of the engineering project proved to be feasible.
This thesis uses the nonlinear systems of chaos theory as a scientific theoretical foundation,and uses basic knowledge from Bayesian classification as a means to predict the rock classification of the Xi'an-Ankang Railway Qinling Tunnel.The results not only provide technical support for the design and construction works,they also can be used to explore these issues a new way for other projects.
(1)应用时间序列概念及分析方法,建立了结构面序列。为满足时间序列等间距采样要求,将结构面在测线上的间距逐一排列形成一个序列,依次可建立结构面倾向和倾角序列。由这三个序列共同确定结构面在空间的位置、倾向和倾角。用混沌等非线性研究方法,研究了结构面序列特征及其分形结构。
(2)以实测数据为基础,应用非线性科学的混沌理论,研究了结构面的空间分布特征。功率谱图中低频部分负幂现象的存在、结构面发育与断层关系负幂存在、结构面分布的分形现象、Kolmogorov熵大于0等特征都证明了结构面混沌分布的存在性,Lyapunov指数趋于0、主分量分析图中先斜后趋平、功率谱负幂出现与消失又说明了结构面分布不完全是混沌,而是位于混沌的边缘。
(3)相空间重构揭示结构面空间分布非线性规律,根据混沌时间序列相空间重构原理,用C-C法、预测误差最小法计算嵌入维和空间延迟量,可张显结构面在岩体中的分布特征。明确了嵌入维实际上是岩体中主要相似结构面发育的平均组数,而空间延迟是主要相似结构面之间的平均间隔等混沌学指标的物理意义。
(4)通过结构面混沌特征量的计算,建立了混沌学预测模型,对结构面位置及产状进行了混沌预测,结构面序列化提供了预测的基础,相空间重构决定了混沌预测的方法。一阶局域预测法算法简单,使用方便,其预测精度不但取决于结构面序列嵌入维和空间延迟,而且与最临近相点、训练样本大小和预测步长等有关。
(5)基于结构面混沌特征,进行了围岩分级预测,用已知围岩分级岩体中的结构面作为训练样本,预测出的结构面作为预测样本,以结构面切割权密度、结构面间距、倾向和倾角四个属性为预测因子,按数据挖掘理论离散化结构面数据,以基本贝叶斯分类法预测未知样本的围岩分级,工程实践结果证明是可行的。
论文以非线性系统科学的混沌理论为理论基础,以知识挖掘和基本贝叶斯分类法为手段,预测了西安安康铁路秦岭特长隧道的围岩分级,研究成果不仅为该工程的设计施工提供了技术支撑,而且为其他工程中该类问题的解决探索了一个新的途径。
The guiding engineering for the regional geology,complicated environmental situation,rock mass structural planes,and space pattern evaluation and surveying of the Qinling Extra-Long Tunnel of the Xi'an-Ankang Railroad is an important factor in design and construction safety.The basic classification of the surrounding rock of a railroad is determined by rock hardness and the crushing degree of rock mass,which is directly related to the distribution and development of its structural planes.The structural plane of the rock is the product of a complicated tectonic process,which has the characteristics of a non-linear distribution.This paper uses the non-linear system science of chaos theory to research the non-linear spatial distribution patterns of the Qinling Tunnel area structural planes and construct a model of chaos.Advancement will be made beginning from the chaos characteristics of structural planes and the utilization of data to develop new surveying methods for the rock masses in the Qinling Tunnel area.
(1) The structural series was constructed using the concept of time series analysis.In order to satisfy distance requirements such as time series,we formed an arrangement from surveys of the structural plane distances.From this,we could construct the structural plane dipdirect and rake series.From the combination of these three series we could determine the spatial orientation,dipdirect and rake of the structural plane.Using non-linear research methods including chaos theory,we studied the characteristics of the structural plan series and its structural formation.
(2)Using surveying as the basis of our data,we utilized the non-linear science of chaos theory to research the characteristics of spatial distribution within the structural plane.The phenomenon of the existence of low frequency negative power within the power spectrum,the existence of the relationship between structural plane development and faults,and the phenomenon of the Kolmogoroc entropy structural plane distribution fractal environment greater than 0 all explain the existence of chaotic distribution within the structural plane.The Lyapunov index that tends towards 1,the principal component graded analysis,the appearance of the power spectrum and the disappearance of negative power also lead us to believe that the distribution of the structural plane is not completely chaotic,but is at the edge of chaos.
(3) phase-space reconfiguration reveal the spatial distribution of non-linear law based on chaotic time series phase-space reconstruction theory.Using the CC method,the smallest methods of error prediction in the embedding dimension and delays the amount of space showing the distribution of the rock structure.Explicit embedding dimension of the is similar to the structure of the main rock face in the development of the average group number,and the main space delay structure is similar to the average interval between the chaos,such as the physical meaning of parameters.
(4) Through the calculation of the amount of chaos in the structural plane,we establish the predicative chaos models for the structural plane locations and a chaotic occurrence predicted sequence structure prediction provides the basis for the decision to phase-space reconstruction of chaotic prediction method.The single-order local-region method algorithm is simple and easy to use,the sequence prediction accuracy not only depends on the embedded dimension of structure and spatial delay,it is also related to the closest related points,training sample size and estimations such as step size.
(5) Based on the chaotic characteristics of the structural planes we predicted the surrounding rock mass classifications.Using the known classification of rock masses surrounding the structural planes as training samples,the structural plane samples as a prediction to the structure of the cutting weight density,the structure of surface spacing length of structural planes,and the orientation and inclination for the four predictor attribute factors according to the theory of excavation discretization data structure to basic Bayes's classification,we predicted unknown samples of rock classification.The results of the engineering project proved to be feasible.
This thesis uses the nonlinear systems of chaos theory as a scientific theoretical foundation,and uses basic knowledge from Bayesian classification as a means to predict the rock classification of the Xi'an-Ankang Railway Qinling Tunnel.The results not only provide technical support for the design and construction works,they also can be used to explore these issues a new way for other projects.
引文
[1]Sharma V.M.,Saxena K.R.eds.,A.A.In In-situ characterization of rocks.Balkema publishers,2001,49-97.
[2]郑颖人,刘兴华.近代非线性科学与岩石力学问题,岩土工程学报,1996,18(1):98-100.
[3]谢和平,刘夕才,王金安.关于21世纪岩石力学发展战略的思考.岩土工程学报,1996,18(4):98-10.
[4]Turcotte D L.Fractal in geology and geophysics.Pure Appl Geophys,1989,131:171-196.
[5]Meng X G,Zhao P D.Fractal method for statistical analysis of geological data.J of China University of Geoscience,1991,2(1):111-116.
[6]孟宪国.试论非线形科学在数学地质中的地位和作用.地球科学进展,1993,8(1):67-71
[7]於崇文.地质作用的自组织临界过程动力学—地质系统在混沌边缘分形生长.地学前缘,2000,7(1):13-42.
[8]於崇文.地质作用的自组织临界过程动力学—地质系统在混沌边缘分形生长(下).地学前缘,2000,7(2):555-586.
[9]於崇文.大型成矿和成矿区(带)在混沌边缘(上).地学前缘,1999,6(1):89-102.
[10]於崇文.大型成矿和成矿区(带)在混沌边缘(下).地学前缘,1999,6(2):195-230.
[11]於崇文.成矿动力系统在混沌边缘分形生长—一种新的成矿理论与方法论(上).地学前缘,2001,8(3):9-27.
[12]於崇文.成矿动力系统在混沌边缘分形生长—一种新的成矿理论与方法论(下).地学前缘,2001,8(4):19-36.
[13]中华人民共和国建设部.工程岩体分级标准(GB50218-94).北京:中国计划出版社,1995.
[14]谢和平,Pariseau W G.岩石节理粗糙度系数(JRC)的分形估计.中国科学(B 辑),1994,24(5):524-530.
[15]Maerz,N.H.,and Zhou,W.Multivariate analysis of bore hole discontinuity data.Rock Mechanics for Industry,Proceedings of the 37th US Rock Mechanics Symposium,Vail Colorado:1999,1:431-438.
[16]Maerz,N.H.,and Zhou,W.Discontinuity data analysis from oriented boreholes.Proceedings of the Fourth North American Rock Mechanics Symposium,Seattle, Washington:2000,667-674.
[17]W.Zhou and N.H.Maerz.Multivariate Clustering Analysis of Discontinuity Data:Implementation and Applications.Rock Mechanics in the National Interest;Proceedings of the 38th U.S.Rock Mechanics Symposium,Washington,D.C.:2001,861-868
[18]赵奎,蔡美峰.岩体节理面延展性的概率分析.矿冶,2002,11(1):1-3.
[19]袁绍国,王震.岩体表面节理迹长与节理真实尺寸的概率关系.水文地质工程地质,1999,(1):5-22.
[20]Zhang Wohua,Valliapan S.Analysis of randam anisotropic damage mechanics problems of rockmass.Rocking,1990,23:91-112
[21]保长江.节理迹长的概率统计分析.武汉水力水电大学(宜昌)学报,1998,20(1):7-11.
[22]Huang,Q.,and J.Angelier,Fracture spacing and its relation to bed thickness,Geol.Mag.,1989,126:355-362.
[23]Rives,T.,M.Razack,J.P.Petit,and K.D.Rawnsley,Joint spacing:Analogue and numerical simulation,J.Struct.Geol.,1992,14:925-937.
[24]Dershowitz,W.S.,and H.H.Herda,Interpretation of fracture spacing and intensity,Proc.U.S.Symp.Rock Mech..,1992,33:757-766.
[25]Zhang,X.,and D.J.Sanderson,Anisotropic features of geometry and permeability in fractured rock masses,Eng.Geol.,1995,40:65-75.
[26]Palmstrom.Block size and block size distribution,GeoEng2000 conference,Melbourne,18 - 24,November 2000.
[27]Mandelbrot B B.The fractal geometry of nature.New York,Preeman W H,1982,16-22.
[28]Xie H.Fractals in rock mechanics.Balken a A A Publishers,Netherlands:1993,357-397.
[29]Xie H.Fractals-rock mechanics.Lecture Notes given at the University of U tah,USA:1990,1-50.
[30]Turk N.Characterization of rock joints surfaces by fractal dimension.Tucson:On Rock Mechanics,1987,1223-1236.
[31]Carr J R.Fractal characterization of joints surface roughness in welded tuff at Yucca.Tucson:28~(th) US Symp,On Rock Mechanics,1987,1223-1236.
[32]徐光黎.岩体结构面几何特征的分形与分维.水文地质工程地质,1993,20(2):20-22.
[33]陈颙等.分形与混沌在地球科学中的应用.北京:学术期刊出版社,1990,115-118.
[34]易顺民,唐辉明,龙昱.基于分形理论的岩体工程分类初探.地质科技情报,1994,13(1):101-106.
[35]Odling,N.E..Network properties if a two-dimensional natural fracture pattern,Pure Appl.Geophys.,1995,138:9-114.
[36]Gillespie,P.A.,C.B.Howard,J.J.Walsh,and J.Watterson.Measurement and characterization of spatial distrition of fractures,Techononphysics,1993,226:113-141.
[37]Barton,C.C.Fractal analysis of scaling and spatial clustering of fractures,in Fractals in the Earth Sciences,edited by C.C.Barton and P.R.La Pointe,Plenum,New York,1995:141-178.
[38]Berkowitz,B.and A.Hadad.Fractal and multifractal measures of natural and synthetic fractures at depth in crystalline rock in the Cajon Pass scientific drill hole,J.Geophys.Res.,1992,97:5181-5200.
[39]Bour,O.,and P.Davy,Connectivity of random fault networks following a power law fault length distribution,Water Resour.Res.,1997,33:1567-1583.
[40]Bour,O.,and P.Davy.Clustering and size distributions of fault pattern:Theory and measements,Geophys.Res.Lett.,1999,26:2001-2004.
[41]S.K.Pal and D.Chakravarty.Rock-mass characterization using fractals.National conference on nonlinear system & dynamics,NCNSD-2003.
[42]秦四清,张倬元,王士夭,黄润秋.节理岩体损伤及分形耦合分析.成都理工学院学报,1994,21(1):84-90.
[43]杨太华.节理岩体断裂的分形机理研究.西北地震学报,1995,17(1):10-14.
[44]Maerz,N.H.,Germain,P.,Block size determination around underground openings using simulations.Proceedings of the FRAGBLAST 5 Workshop on Measurement of Blast Fragmentation,Montreal,Quebec,Canada,23-24 Aug.,1996:215-223.
[45]Jun Lu,Systematic identification of polyhedral rock blocks with arbitrary joints and faults,computers and geotechnics.2002,29:49-72.
[46]R.Windsor,Block stability in jointed rock masses.Proceedings of the conference on fractural and jointed rock masses.Lake Tahoe,USA,1992:59-66.
[47]P.M.Warburton.Vector stability analysis of an arbitrary polyhedral rock block with any number of free faces.Int.J.Rock Mech.Min.& Geomech.Abst.,1981,18(5):415-427.
[48]R.E.Goodman and Gen-hua Shi,Block theory and its application to rock enginecring,Engewood Cliffs,New Jersey:Prentice-Hall,Inc.,1985,338.
[49]S.D.Priest,Hemispherical projection methods in rock mechanics,London:George Allen &Unwin,1985,124.
[50]J.L.Delport and D.H.Martin.A multiplier method for identifying keyblocks in excavations through jointed rock.Society for Industrial and Applied Mathematics,J.of Alg.Disc.Meth.1986,7(2):321-330.
[51]D.Lin.,C.Fairhurst and A.M.Starfield,Geometrical identification of three-dimensional rock block systems using topological techniques.Int.J.Rock Mech.Min.Sci.& Geomech.Abstr.,1987,24:331-338.
[52]Hellot D.Generating a blocky rock mass.Int.J.Rock Mech.Min.Sci.& Geomech.Abstr.,1988,25(3):127-138
[31]Hart R etal.Formulation of a three-dimentional discrete elemental odel-part.mechanical calculation form otion and interaction of a system composed of m any polyhedral blocks.Int.J.Rock Mech.Min.Sci.& Geomech.Abstr.,1988,25(3):127-138.
[53]Hart R etal.Formulation of a three-dimentional discrete elemental odel-part.mechanical calculation form otion and interaction of a system composed of m any polyhedral blocks.Int.J.Rock Mech.Min.Sci.& Geomech.Abstr.,1988,25(3):127-138.
[54]刘志刚、赵勇编著,隧道隧洞施工地质技术,北京:中国铁道出版社,2001.
[55]谢和平.岩石节理的分形描述.岩土工程学报,1995,17(1):18-23.
[56]Turk N,Fearman W R.Investigation of Some Rock Joint Properties:Roughness Angle Determination and Joint Closure.In:Proc Int Symp on Fundamentals of Rock Jointed.Sweden,Bjorhliden,1985:197-204.
[57]王振龙,时间序列分析.北京:中国统计出版社,2003.
[58]刘顺兰,吴杰,数字信号处理.西安:西安电子科技大学出版社,2003.
[59]A.Karzulovic,R.E.Goodman.Technical note:Determination of principal joint frequencies,International journal of rock mechnics and mining science and geomechnics abstracts,22:471-473.
[60]S.D.Priest and J.A.Hudson.Discontiouity spacings in rock,International journal of rock mechanics and mining science and geomechanics abstracts,13:135-148.
[61]李后强,汪富全.分形理论及其在分子科学中的应用.北京:科学出版社,1993.
[62]林振山.非线性科学及其在地学中的应用.北京:气象出版社.2003.
[63]陈士华,陆君安.混沌动力学初步.武汉:武汉水利电力大学出版社.1998.
[64]许清海.混沌时间序列的相关性及其应用.泉州师范学院学报(自然科学),2000,18(6):4-7.
[65]陈予恕,唐云等.非线性动力学中的现代分析方法.北京:科学出版社.2000.
[66]C.尼科里斯,L.普里高津.非平衡系统的自组织.北京:科学出版社,1986.
[67]仪垂祥.非线性科学及其在地学中的应用,北京:气象出版社,1995.
[68]申维,自组织理论和耗散结构理论及其地学应用.地质地球化学,2001,5(3):1-7.
[69]West B J,Deering B.The Lure of Modern Science[M].Singapore World Science,1995,1-421.
[70]Schroeder M.Fractals,Chaos,Power Laws(Minutes from an Infinite Paradise)[M].New York:W.H.Freeman and Company,1991,1-429.
[71]Bak P,Tang C,Wisenfeld K.Self-organized criticality[J].Physical Review A,1988,38(1):364-374.
[72]Bak P.How Nature Works[M].(The Science of Self-Organized Criticality).New York:Copernicus,1996,1-212.
[73]Jensen H J.Self-Organized Criticality[M].Cambridge:Cambridge University Press,1998,1-153.
[74]Grassberger P.Self-organized criticality[A].Livi R,Nadal J P,Packerd N.Complex Dynamics[M].New York:Nova Science Publishers,Inc.,1993,31-45.
[75]Langton C G Studying artificial life with cellular automa ta.Physica,1986,22D:120-149.
[76]Packard N.Adaptation toward the edge of chaos.In:Technical Report,Center for Complex Systems Research.Illinois:University of Illinois,CCSR- 85-5,1988.
[77]Kauffman S A.Origins of order in evolution:self-organization and sele ction.In:Goodwin B,Saunders P,eds.Theoretical Biology.Baltimore,Maryland:Jo hns Hopkins University Press,1989:67-88.
[78]Kauffman S A.Antichaos and adaptation.Sci Am,1991(8):64-70.
[79]Kauffman S A,Johnson S.Coevolution to the edge of chaos:coupled fitn ess landscapes,poised states,and revolutionary avalanches.J Theor Biol,1991,149:467-505.
[80]Kauffman S A.Requirements for evolvability in complex systems:orderly dynamics and frozen components.In:Stein W D,Varela F J,eds.Thinking About Biology.Reading,Mass:Addison-Wesley Publishing Company,1993:269-301.
[81]Kauffman S A.Origins of Order:Self-Organization and Selection in E volution. Oxford:Oxford University Press,1993:1-709.
[82]Bak P,Chen K.Self-organized criticality.Sci Am,1991(1):26-33.
[83]Anderson P W.The eight fold way to the theory of complexity:a prologu e.In:Cowan G A,Pines D,Meltzer D,eds.Complexity,Metaphors,Models,and Reality.Reading,Mass:Addison-Wesley Publishing Company,1994:7-16.
[84]D.L.特科特.陈顒,郑捷等.分形与混沌—在地质学和地球物理学中的应用.北京:地震出版社.1993.
[85]秦四清,张倬元等.非线性工程地质学导引.成都:西南交通大学出版社,1993.
[86]张筑生.微分动力系统原理.北京:科学出版社,1987.
[87]Takens F.Dynamical systems and turbulence.In:RandD,YoungLS,eds.Lecture Notesin Mathematics.Berlin:Springer,1981:366-381.
[88]Sauer T,YorkeJ A,Casdagli M.Embedology.J Stat Phys,1991,65:579-616.
[89]Ding M,Grebogi C,OttE,etal.Estimating correlation dimension from chaotic time series:when does plateau onset occur.Physica D,1993,69:404-424.
[90]D.Broomhead and G P.King.Extracting qualitative dynamics from experimental data,Physica 20D,1986:217-236.
[91]D.Kugiurmtzis.State space reconstruction parameters in the analysis of chaotic time series-the role of the time window length,Physica D,1996,95:13-28.
[92]H.S.Kim,R.Eykholt and J.D.Salas,Nonlinear dynamics,delay times,and embedding windows,Physica D,1999,127:48-60.
[93]Lai Y C,Lerner D.Effectives scaling regime for computing the correlation dimension form chaotic time series.Phyica D,1998,115:1-18.
[94]王海燕,盛昭瀚.混沌时间序列相空间重构参数的选取方法.东南大学学报(自然科学版),2000,30(5):113-117.
[95]M.T.Rosenstein,J.J.Collins and C.J.De luca.A Practical method for calculation largest Lyapunov exponents from small data sets.Physica D,1993,65:l 17-187.
[96]J.Bhattacharya,P.P.Kanjilal.Revisiting the role of correlation coefficient to distinguish chaos from noise.Eur.Phys.J.B 2000,13:399-403.
[97]沈明荣.岩体力学.上海:同济大学出版社,1999.
[98]孙广忠.岩体结构力学.北京:科学出版社,1988.
[99]温权,张勇传,程时杰.负荷预报的混沌时间序列分析方法.电网技术.2001,25(10):13-16.
[100]孙海云,曹庆杰.混沌时间序列建模及预测.系统工程理论与实践.2001,5:106-113.
[101]温权,张勇传,程时杰.混沌时间序列预测技术.水电能源科学.2001,19(3):76-78.
[102]贺太纲,郑崇勋.混沌序列的非线性预测.自然杂志.19(1):10-13.
[103]于国新,白明洲,许兆义.工程岩体结构面间距空间分布的ARIMA模型及应用.工程地质学报,2006,14(6):819-823.
[104]Arild Palmstrom.The weight joint density method leads to improved characterization of jointing.Paper published in conference on recent advances in tunneling technology,New Delhi,1996.
[105]Norbert H.Maerz,Paul Germain.Block size determination around underground openings using simulations.Proceedings of the FRAGBLAST 5 Workshop on Measurement of blast Fragmention,Montreal,Quebec,Canada,23-24 Aug.,1996:215-223.
[106]Palmstrom A RMi-a rock mass characterization system for rock engineering purpose.PhD thesis.1995.
[107]Arild Palmstrom.Collection and use of geological data in rock engineering.Published in ISRM News Journal,1997:21-25.
[108]T.Ramamurthy,A geo-engineering classification for rocks and rock masses.Rock mechanics and ming sciences 2004(41):89-101.
[109]孙建国,李天斌,黄润秋,王芳其.地下工程围岩分类模糊推理系统设计 工程地质学报,2003,11(3):269-273.
[110]杨朝晖,刘浩吾。地下工程围岩稳定性分类的人工神经网络模型。四川联合大学学报(工程科学类),1999,3(4):68-72.
[111]何发亮 谷明成 王石春,TBM施工隧道围岩分级方法研究。岩石力学与工程学报,2002,21(9):1350-1354.
[112]杜时贵,周庆良,孙有法。公路隧道围岩稳定的结构面影响。1997,10(2):64-69。
[2]郑颖人,刘兴华.近代非线性科学与岩石力学问题,岩土工程学报,1996,18(1):98-100.
[3]谢和平,刘夕才,王金安.关于21世纪岩石力学发展战略的思考.岩土工程学报,1996,18(4):98-10.
[4]Turcotte D L.Fractal in geology and geophysics.Pure Appl Geophys,1989,131:171-196.
[5]Meng X G,Zhao P D.Fractal method for statistical analysis of geological data.J of China University of Geoscience,1991,2(1):111-116.
[6]孟宪国.试论非线形科学在数学地质中的地位和作用.地球科学进展,1993,8(1):67-71
[7]於崇文.地质作用的自组织临界过程动力学—地质系统在混沌边缘分形生长.地学前缘,2000,7(1):13-42.
[8]於崇文.地质作用的自组织临界过程动力学—地质系统在混沌边缘分形生长(下).地学前缘,2000,7(2):555-586.
[9]於崇文.大型成矿和成矿区(带)在混沌边缘(上).地学前缘,1999,6(1):89-102.
[10]於崇文.大型成矿和成矿区(带)在混沌边缘(下).地学前缘,1999,6(2):195-230.
[11]於崇文.成矿动力系统在混沌边缘分形生长—一种新的成矿理论与方法论(上).地学前缘,2001,8(3):9-27.
[12]於崇文.成矿动力系统在混沌边缘分形生长—一种新的成矿理论与方法论(下).地学前缘,2001,8(4):19-36.
[13]中华人民共和国建设部.工程岩体分级标准(GB50218-94).北京:中国计划出版社,1995.
[14]谢和平,Pariseau W G.岩石节理粗糙度系数(JRC)的分形估计.中国科学(B 辑),1994,24(5):524-530.
[15]Maerz,N.H.,and Zhou,W.Multivariate analysis of bore hole discontinuity data.Rock Mechanics for Industry,Proceedings of the 37th US Rock Mechanics Symposium,Vail Colorado:1999,1:431-438.
[16]Maerz,N.H.,and Zhou,W.Discontinuity data analysis from oriented boreholes.Proceedings of the Fourth North American Rock Mechanics Symposium,Seattle, Washington:2000,667-674.
[17]W.Zhou and N.H.Maerz.Multivariate Clustering Analysis of Discontinuity Data:Implementation and Applications.Rock Mechanics in the National Interest;Proceedings of the 38th U.S.Rock Mechanics Symposium,Washington,D.C.:2001,861-868
[18]赵奎,蔡美峰.岩体节理面延展性的概率分析.矿冶,2002,11(1):1-3.
[19]袁绍国,王震.岩体表面节理迹长与节理真实尺寸的概率关系.水文地质工程地质,1999,(1):5-22.
[20]Zhang Wohua,Valliapan S.Analysis of randam anisotropic damage mechanics problems of rockmass.Rocking,1990,23:91-112
[21]保长江.节理迹长的概率统计分析.武汉水力水电大学(宜昌)学报,1998,20(1):7-11.
[22]Huang,Q.,and J.Angelier,Fracture spacing and its relation to bed thickness,Geol.Mag.,1989,126:355-362.
[23]Rives,T.,M.Razack,J.P.Petit,and K.D.Rawnsley,Joint spacing:Analogue and numerical simulation,J.Struct.Geol.,1992,14:925-937.
[24]Dershowitz,W.S.,and H.H.Herda,Interpretation of fracture spacing and intensity,Proc.U.S.Symp.Rock Mech..,1992,33:757-766.
[25]Zhang,X.,and D.J.Sanderson,Anisotropic features of geometry and permeability in fractured rock masses,Eng.Geol.,1995,40:65-75.
[26]Palmstrom.Block size and block size distribution,GeoEng2000 conference,Melbourne,18 - 24,November 2000.
[27]Mandelbrot B B.The fractal geometry of nature.New York,Preeman W H,1982,16-22.
[28]Xie H.Fractals in rock mechanics.Balken a A A Publishers,Netherlands:1993,357-397.
[29]Xie H.Fractals-rock mechanics.Lecture Notes given at the University of U tah,USA:1990,1-50.
[30]Turk N.Characterization of rock joints surfaces by fractal dimension.Tucson:On Rock Mechanics,1987,1223-1236.
[31]Carr J R.Fractal characterization of joints surface roughness in welded tuff at Yucca.Tucson:28~(th) US Symp,On Rock Mechanics,1987,1223-1236.
[32]徐光黎.岩体结构面几何特征的分形与分维.水文地质工程地质,1993,20(2):20-22.
[33]陈颙等.分形与混沌在地球科学中的应用.北京:学术期刊出版社,1990,115-118.
[34]易顺民,唐辉明,龙昱.基于分形理论的岩体工程分类初探.地质科技情报,1994,13(1):101-106.
[35]Odling,N.E..Network properties if a two-dimensional natural fracture pattern,Pure Appl.Geophys.,1995,138:9-114.
[36]Gillespie,P.A.,C.B.Howard,J.J.Walsh,and J.Watterson.Measurement and characterization of spatial distrition of fractures,Techononphysics,1993,226:113-141.
[37]Barton,C.C.Fractal analysis of scaling and spatial clustering of fractures,in Fractals in the Earth Sciences,edited by C.C.Barton and P.R.La Pointe,Plenum,New York,1995:141-178.
[38]Berkowitz,B.and A.Hadad.Fractal and multifractal measures of natural and synthetic fractures at depth in crystalline rock in the Cajon Pass scientific drill hole,J.Geophys.Res.,1992,97:5181-5200.
[39]Bour,O.,and P.Davy,Connectivity of random fault networks following a power law fault length distribution,Water Resour.Res.,1997,33:1567-1583.
[40]Bour,O.,and P.Davy.Clustering and size distributions of fault pattern:Theory and measements,Geophys.Res.Lett.,1999,26:2001-2004.
[41]S.K.Pal and D.Chakravarty.Rock-mass characterization using fractals.National conference on nonlinear system & dynamics,NCNSD-2003.
[42]秦四清,张倬元,王士夭,黄润秋.节理岩体损伤及分形耦合分析.成都理工学院学报,1994,21(1):84-90.
[43]杨太华.节理岩体断裂的分形机理研究.西北地震学报,1995,17(1):10-14.
[44]Maerz,N.H.,Germain,P.,Block size determination around underground openings using simulations.Proceedings of the FRAGBLAST 5 Workshop on Measurement of Blast Fragmentation,Montreal,Quebec,Canada,23-24 Aug.,1996:215-223.
[45]Jun Lu,Systematic identification of polyhedral rock blocks with arbitrary joints and faults,computers and geotechnics.2002,29:49-72.
[46]R.Windsor,Block stability in jointed rock masses.Proceedings of the conference on fractural and jointed rock masses.Lake Tahoe,USA,1992:59-66.
[47]P.M.Warburton.Vector stability analysis of an arbitrary polyhedral rock block with any number of free faces.Int.J.Rock Mech.Min.& Geomech.Abst.,1981,18(5):415-427.
[48]R.E.Goodman and Gen-hua Shi,Block theory and its application to rock enginecring,Engewood Cliffs,New Jersey:Prentice-Hall,Inc.,1985,338.
[49]S.D.Priest,Hemispherical projection methods in rock mechanics,London:George Allen &Unwin,1985,124.
[50]J.L.Delport and D.H.Martin.A multiplier method for identifying keyblocks in excavations through jointed rock.Society for Industrial and Applied Mathematics,J.of Alg.Disc.Meth.1986,7(2):321-330.
[51]D.Lin.,C.Fairhurst and A.M.Starfield,Geometrical identification of three-dimensional rock block systems using topological techniques.Int.J.Rock Mech.Min.Sci.& Geomech.Abstr.,1987,24:331-338.
[52]Hellot D.Generating a blocky rock mass.Int.J.Rock Mech.Min.Sci.& Geomech.Abstr.,1988,25(3):127-138
[31]Hart R etal.Formulation of a three-dimentional discrete elemental odel-part.mechanical calculation form otion and interaction of a system composed of m any polyhedral blocks.Int.J.Rock Mech.Min.Sci.& Geomech.Abstr.,1988,25(3):127-138.
[53]Hart R etal.Formulation of a three-dimentional discrete elemental odel-part.mechanical calculation form otion and interaction of a system composed of m any polyhedral blocks.Int.J.Rock Mech.Min.Sci.& Geomech.Abstr.,1988,25(3):127-138.
[54]刘志刚、赵勇编著,隧道隧洞施工地质技术,北京:中国铁道出版社,2001.
[55]谢和平.岩石节理的分形描述.岩土工程学报,1995,17(1):18-23.
[56]Turk N,Fearman W R.Investigation of Some Rock Joint Properties:Roughness Angle Determination and Joint Closure.In:Proc Int Symp on Fundamentals of Rock Jointed.Sweden,Bjorhliden,1985:197-204.
[57]王振龙,时间序列分析.北京:中国统计出版社,2003.
[58]刘顺兰,吴杰,数字信号处理.西安:西安电子科技大学出版社,2003.
[59]A.Karzulovic,R.E.Goodman.Technical note:Determination of principal joint frequencies,International journal of rock mechnics and mining science and geomechnics abstracts,22:471-473.
[60]S.D.Priest and J.A.Hudson.Discontiouity spacings in rock,International journal of rock mechanics and mining science and geomechanics abstracts,13:135-148.
[61]李后强,汪富全.分形理论及其在分子科学中的应用.北京:科学出版社,1993.
[62]林振山.非线性科学及其在地学中的应用.北京:气象出版社.2003.
[63]陈士华,陆君安.混沌动力学初步.武汉:武汉水利电力大学出版社.1998.
[64]许清海.混沌时间序列的相关性及其应用.泉州师范学院学报(自然科学),2000,18(6):4-7.
[65]陈予恕,唐云等.非线性动力学中的现代分析方法.北京:科学出版社.2000.
[66]C.尼科里斯,L.普里高津.非平衡系统的自组织.北京:科学出版社,1986.
[67]仪垂祥.非线性科学及其在地学中的应用,北京:气象出版社,1995.
[68]申维,自组织理论和耗散结构理论及其地学应用.地质地球化学,2001,5(3):1-7.
[69]West B J,Deering B.The Lure of Modern Science[M].Singapore World Science,1995,1-421.
[70]Schroeder M.Fractals,Chaos,Power Laws(Minutes from an Infinite Paradise)[M].New York:W.H.Freeman and Company,1991,1-429.
[71]Bak P,Tang C,Wisenfeld K.Self-organized criticality[J].Physical Review A,1988,38(1):364-374.
[72]Bak P.How Nature Works[M].(The Science of Self-Organized Criticality).New York:Copernicus,1996,1-212.
[73]Jensen H J.Self-Organized Criticality[M].Cambridge:Cambridge University Press,1998,1-153.
[74]Grassberger P.Self-organized criticality[A].Livi R,Nadal J P,Packerd N.Complex Dynamics[M].New York:Nova Science Publishers,Inc.,1993,31-45.
[75]Langton C G Studying artificial life with cellular automa ta.Physica,1986,22D:120-149.
[76]Packard N.Adaptation toward the edge of chaos.In:Technical Report,Center for Complex Systems Research.Illinois:University of Illinois,CCSR- 85-5,1988.
[77]Kauffman S A.Origins of order in evolution:self-organization and sele ction.In:Goodwin B,Saunders P,eds.Theoretical Biology.Baltimore,Maryland:Jo hns Hopkins University Press,1989:67-88.
[78]Kauffman S A.Antichaos and adaptation.Sci Am,1991(8):64-70.
[79]Kauffman S A,Johnson S.Coevolution to the edge of chaos:coupled fitn ess landscapes,poised states,and revolutionary avalanches.J Theor Biol,1991,149:467-505.
[80]Kauffman S A.Requirements for evolvability in complex systems:orderly dynamics and frozen components.In:Stein W D,Varela F J,eds.Thinking About Biology.Reading,Mass:Addison-Wesley Publishing Company,1993:269-301.
[81]Kauffman S A.Origins of Order:Self-Organization and Selection in E volution. Oxford:Oxford University Press,1993:1-709.
[82]Bak P,Chen K.Self-organized criticality.Sci Am,1991(1):26-33.
[83]Anderson P W.The eight fold way to the theory of complexity:a prologu e.In:Cowan G A,Pines D,Meltzer D,eds.Complexity,Metaphors,Models,and Reality.Reading,Mass:Addison-Wesley Publishing Company,1994:7-16.
[84]D.L.特科特.陈顒,郑捷等.分形与混沌—在地质学和地球物理学中的应用.北京:地震出版社.1993.
[85]秦四清,张倬元等.非线性工程地质学导引.成都:西南交通大学出版社,1993.
[86]张筑生.微分动力系统原理.北京:科学出版社,1987.
[87]Takens F.Dynamical systems and turbulence.In:RandD,YoungLS,eds.Lecture Notesin Mathematics.Berlin:Springer,1981:366-381.
[88]Sauer T,YorkeJ A,Casdagli M.Embedology.J Stat Phys,1991,65:579-616.
[89]Ding M,Grebogi C,OttE,etal.Estimating correlation dimension from chaotic time series:when does plateau onset occur.Physica D,1993,69:404-424.
[90]D.Broomhead and G P.King.Extracting qualitative dynamics from experimental data,Physica 20D,1986:217-236.
[91]D.Kugiurmtzis.State space reconstruction parameters in the analysis of chaotic time series-the role of the time window length,Physica D,1996,95:13-28.
[92]H.S.Kim,R.Eykholt and J.D.Salas,Nonlinear dynamics,delay times,and embedding windows,Physica D,1999,127:48-60.
[93]Lai Y C,Lerner D.Effectives scaling regime for computing the correlation dimension form chaotic time series.Phyica D,1998,115:1-18.
[94]王海燕,盛昭瀚.混沌时间序列相空间重构参数的选取方法.东南大学学报(自然科学版),2000,30(5):113-117.
[95]M.T.Rosenstein,J.J.Collins and C.J.De luca.A Practical method for calculation largest Lyapunov exponents from small data sets.Physica D,1993,65:l 17-187.
[96]J.Bhattacharya,P.P.Kanjilal.Revisiting the role of correlation coefficient to distinguish chaos from noise.Eur.Phys.J.B 2000,13:399-403.
[97]沈明荣.岩体力学.上海:同济大学出版社,1999.
[98]孙广忠.岩体结构力学.北京:科学出版社,1988.
[99]温权,张勇传,程时杰.负荷预报的混沌时间序列分析方法.电网技术.2001,25(10):13-16.
[100]孙海云,曹庆杰.混沌时间序列建模及预测.系统工程理论与实践.2001,5:106-113.
[101]温权,张勇传,程时杰.混沌时间序列预测技术.水电能源科学.2001,19(3):76-78.
[102]贺太纲,郑崇勋.混沌序列的非线性预测.自然杂志.19(1):10-13.
[103]于国新,白明洲,许兆义.工程岩体结构面间距空间分布的ARIMA模型及应用.工程地质学报,2006,14(6):819-823.
[104]Arild Palmstrom.The weight joint density method leads to improved characterization of jointing.Paper published in conference on recent advances in tunneling technology,New Delhi,1996.
[105]Norbert H.Maerz,Paul Germain.Block size determination around underground openings using simulations.Proceedings of the FRAGBLAST 5 Workshop on Measurement of blast Fragmention,Montreal,Quebec,Canada,23-24 Aug.,1996:215-223.
[106]Palmstrom A RMi-a rock mass characterization system for rock engineering purpose.PhD thesis.1995.
[107]Arild Palmstrom.Collection and use of geological data in rock engineering.Published in ISRM News Journal,1997:21-25.
[108]T.Ramamurthy,A geo-engineering classification for rocks and rock masses.Rock mechanics and ming sciences 2004(41):89-101.
[109]孙建国,李天斌,黄润秋,王芳其.地下工程围岩分类模糊推理系统设计 工程地质学报,2003,11(3):269-273.
[110]杨朝晖,刘浩吾。地下工程围岩稳定性分类的人工神经网络模型。四川联合大学学报(工程科学类),1999,3(4):68-72.
[111]何发亮 谷明成 王石春,TBM施工隧道围岩分级方法研究。岩石力学与工程学报,2002,21(9):1350-1354.
[112]杜时贵,周庆良,孙有法。公路隧道围岩稳定的结构面影响。1997,10(2):64-69。