黄岛地下水封洞库裂隙岩体渗透性研究
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摘要
黄岛地下水封石油洞库位于山东省青岛市黄岛区,是我国在建的第一个大型国家战略石油储备库,洞库设计库容为300×104m3。本文以黄岛地下水封石油洞库工程为项目依托,在裂隙分布及成因、渗透性分析、离散裂隙网络模拟及离散裂隙连通性分析四个方面展开了较深入的研究。
低渗透性的裂隙介质是石油洞库的理想选址区。裂隙介质作为石油的赋存体,对其空间结构及基本水力学参数的研究将为后续的裂隙水渗流模拟及水封效果评价提供关键的水文地质数据。本研究区主要的岩性为元古界花岗片麻岩,岩脉以暗色煌斑岩为主。
岩体是在漫长的地质历史演变过程中经受了不同大小和不同方向的多期构造应力场的长期作用而形成的。这导致了岩体结构面分布的随机性、形态的多样性和空间组合的复杂性,以至于对岩体结构的研究变得非常复杂。但是从大量裂隙的统计意义上来讲,人们发现,岩体中的裂隙是具有一定的规律性,并受区域构造运动所控制的。因此,查明研究区构造运动,是进行裂隙结构面网络模拟和建立裂隙渗流模型的基础。
结构面网络模拟是根据现场测量所得的结构面各种几何参数的概率分布来生成服从这些分布规律的结构面网络几何图形,即根据有限天然露头或人工开挖面上结构面几何参数来推求岩体内部的结构面参数分布,实现这一过程通常采用的是Monte-Carlo法。
裂隙岩体渗流研究作为一个重要的科学研究和工程应用问题,随着许多应用性学科的发展和一些重大的急需解决的实际工程问题的显现,越来越受到广大学者的关注。该研究涉及诸多领域,如岩土工程、水利水电工程、石油工程以及岩体地下构筑物建设等项目。本论文是从裂隙渗透张量以及裂隙网络连通性两方面来分析研究区的渗流特征。
1.渗透张量是表征裂隙渗透性的基本参数,其是一个既有大小又有方向的量,在数学上通过矩阵来表示。本研究根据野外地表裂隙统计和钻孔裂隙统计结果,结合空间三维渗透张量理论求取研究区渗透张量,同时根据压水试验结果对渗透张量进行矫正,最后获得研究区平面及垂向上渗透张量变化规律。
2.裂隙连通性分析基于裂隙网络模拟。考虑裂隙连通性必然要弄清区域裂隙的隙宽、迹长、导水系数等。这些参数可以通过地表结构面调查以及钻孔裂隙统计分析得出。连通区实际上是根据裂隙网络模拟结果确定了一个有效的隔水边界,所有连通区内的裂隙是存在水力联系的,不同的连通区,裂隙不能直接导通。连通区分析的运算法则也是以相互切割的裂隙的逻辑关系为基础的。
在以上的理论以及研究方法基础上,本文针对黄岛地下水封石油洞库主要进行了以下三方面的研究：
1.裂隙成因及发育规律研究
本文结合断层成因及构造运动理论分析认为区域节理的分布特征是受燕山期太平洋板块向NW或向W俯冲的结果,并且经历了燕山早期、中期和晚期复杂的构造运动。
根据研究观察、岩体的分布与断层的相互切割关系分析,本次研究认为研究区及其周缘断层的形成总体来说是燕山期太平洋板块剧烈活动的结果,断层的活动性质复杂,经历了多期性质的转换,燕山早期,区域受到NNW方向的挤压应力,研究区主要断裂形成(包括F3、F4),同时次生NE向与NW向延伸的节理；燕山中期,在拉升引力环境下,岩浆上涌、岩脉形成；燕山晚期—现今,研究区总体受太平洋板块向W的挤压作用,F3呈现右行压扭的性质,而F4则呈现左行张扭的性质,研究区西侧部分裂隙在张应力作用下扩展,隙宽变大。
2.渗透张量变化规律研究
(1)通过研究区水文地质试验及物探成果,初步分析了研究区平面和垂向上渗透性的变化规律,从不同尺度上对渗透性作出评价。
(2)针对裂隙岩体渗透系数的重要性以及难确定性,本文运用了新的技术方法,不仅可以得出渗透主值水平上的变化规律,而且求出了垂向上渗透主值及渗透方向的变化规律。同时针对实际工程,数据多计算繁琐这一特点,本文在Excel中编制了计算渗透主值及倾向、倾角的VB程序,可以方便地得到了大量不同深度处的渗透张量。分析得出,洞库区平面上渗透张量变化与裂隙产状变化基本一致；垂向上,渗透性大小与隙宽的变化基本一致。
(3)用钻孔成像统计得出的渗透张量,受软件识别效果的影响,对于微裂隙隙宽的读取有一定的人为误差,所以得出的渗透主值有一定的偏差,但可以反映该处渗透主值的变化规律。对于这个不足,可以通过软件识别图像的最小像素做相对准确的估计。同时提出,在不同深度通过压水试验对渗透张量分别矫正的方法。本研究获得的矫正系数0.07～0.89之间,通过不同深度分别对应矫正后,渗透主值和压水试验数量级相一致,主渗透方向不变。
3.裂隙网络模拟及渗流研究
(1)本文在给出裂隙各参数概率统计分布类型及分布参数的基础上,对较小范围的洞库区做了二维结构面网络模拟,从不同剖面研究了裂隙的发育情况,给出了剖面上节理的密度图和RQD图。结果显示,洞库Ⅰ区主要分布有一个裂隙组,垂向上在-30m处产状有较大的变化,裂隙密度均小于1条/m,RQD分布在70～90%之间；洞库Ⅱ区主要发育有两组近于正交的裂隙,裂隙密度小于0.5条/m,RQD在90%以上,和Ⅰ区相比裂隙发育少,总体渗透性弱。
(2)对整个研究区在考虑断层发育的情况下做三维结构面网络模拟,得到了研究区的裂隙网络分布图、隙宽分布图、储水系数分布图、裂隙连通区图和钻孔连通区图。结合离散裂隙渗流的特征,对整个研究区做了连通性分析,认为整个模拟区的连通区具有南东方向的走向。同时对ZK13和ZK15做了钻孔连通性分析,模拟出了影响钻孔水位的裂隙范围。
Huangdao water sealed underground oil tank lies in Huangdao district, ShanDong province,which is one of strategic oil storages being build recently and is the first underground oil storage with the capacity of 300×104m3 in our country. In this paper,fracture causes and distribution、fracture permeability、discrete fracture network simulation and discrete fracture connectivity are analysed based on the projects of Huangdao water sealed underground oil tank.
The Proterozoic granite gneiss is the major lithology in the study area as Low-permeability fractured media is the ideal location for the underground oil tank. The research of spatial structure and basic hydraulic parameters can provide critical hydrogeological data for the following analysis of fracture flow simulation and water seal effect evaluation.
During the long process of geologic evolution, different quantity of tectonic stress displayed in size and directions have had so significant impact on the rock mass so that which shows the characteristics of heterogeneity,randomness,diversity and complexity.All of these characteristics makes the research of rock mass structure becomes more complex.However, it was found that the fracture of rock mass are regulared statistically and be controlled by regional tectonic movement.So,the identification of tectonic movement in study areas is basis for fracture network simulation and fracture flow model establishing.
With the development of computer technology,network simulation of rock mass discontinuities which is based on statistics and probability theory is improved and brought into practice gradually.Network geometric graphics are simulated with the probability distribution of the discontinuities geometric parameters that are Measured in-situ.The whole proeess will be completed by the Monte-Carlo method.
Seepage in fractured rock research is important for scientific research and application of engineering. With the development of engineering disciplines and the showing of actual engineering problems to be solved urgently,it is more and more concerned by researchers.The study involved a number of areas, such as geotechnical engineering, water conservancy and hydropower engineering, petroleum engineering, and construction of rock structures in underground projects. In this paper, flow characteristics of the study area are discussed in two sides:fracture permeability tensor and the fracture network connectivity.
1. Fracture permeability tensor which is the basic parameters in fissured area is expressed through the matrix in mathematically. three-dimensional fracture permeability tensor of study area was caculated based on the statistics of field surface cracks and drilling image fracture results.Meanwhile,the result was rectified by water pressure test to Reflect the horizontal and vertical variation of the fracture.
2. Fissure fracture network connectivity analysis based on fracture simulation.It is very significant to clarify fracture aperture, trace length, hydraulic conductivity coefficient and so on before the analysis of fracture connectivity.Components of the fracture network is based on the simulation results which to determine an effective impervious boundary, all the connected region share the same hydraulic fracture link within it. Connected component algorithm is also based on the logic cutting mutual relations.
According to the above theories and analysis, this paper did following three researches for Huangdao water sealed underground oil tank:
1. Law of fracture distribution analysis
In this paper, the causes of faults and tectonic theory was used to analyse the fracture distribution of the region which is characterized by the Yanshan Pacific Plate subduction to the W or to the NW direction.Complicated tectonic movements of early Yanshan,mid Yanshan and late Yanshan stage contribute to fracture formation.
In the early-Yanshan stage, main fault zone (including the F3, F4)formate in the area, while secondary to the NE and NW extension of the fracture; during the mid-Yanshan stage,in the pulling stress environment, dykes was forming while magma gushing up; during the late-Yanshan stage,study area was compressed W by the Pacific plate,while F3 show the nature of the right-transtension, and F4 are presented the left-transtensional,the fracture gap became larger in the west part of the study area in tensile stress.
2. Variation of permeability tensor
(1) A preliminary analysis of the study area on the plane and the vertical variation are sdudied from different scales to assess on the permeability.The hydrogeological and geophysical test results are used in this paper.
(2) Permeability coefficient is very importance for fracture rock mass,but it is also difficult to confirm. A new technicalness was exertioned in this paper to get permeability variety not only horizontally but also vertically.For much date and complicated calculation in field project, VB program in Excel was developed to caculate principal value and directions of hydraulic conductivity.The result is principal directions of hydraulic conductivity is in accord with dip direction and dip angle in horizontal and the principal value of hydraulic conductivity is in accord with changes of aperture in vertical.
(3)Permeability tensor derived from drilling imaging which could reasonably reflect the variation of the main value penetration,but human error is still exist because of the effect of recognition by the software. For this point, minimum pixel relatively estimation was used to make the correct estimation more accurate. And Also it is suggested that correct result through the water pressure test methods in different depths. The correction factor of this area is between 0.07 and 0.89. Through the correction in different depth, principal directions of hydraulic conductivity is stable and the principal value of hydraulic conductivity is in accord with water pressure test result quantitatively.
3. Fracture network simulation and seepage flow
(1)This paper made a two-dimensional structure network simulation for the reservoir area based on the probability of fracture parameter statistical distribution types and distribution parameters. Fracture density map and RQD map in different directions was used to analyse the fracture around the tank.the result is:fracture density is less than 1 piece per meter and RQD distribution is between 70～90% in sectionⅠ; fracture density is less than 0.5 piece per meter and RQD is more than 90% in sectionⅡ.
(2)Three-dimensional network simulation was used in the entire study area to analysis fracture network distribution,aperture distribution,transmissivity,coefficient of storage,fracture component and drilling connected zones.lt is find that connected direction of the area is in southeast base on the fracture seepage characteritics,meanwhile. Connectivity of ZK13 and ZK15 was simulated to make sure the range of infection area of water levels in boreholes.
低渗透性的裂隙介质是石油洞库的理想选址区。裂隙介质作为石油的赋存体,对其空间结构及基本水力学参数的研究将为后续的裂隙水渗流模拟及水封效果评价提供关键的水文地质数据。本研究区主要的岩性为元古界花岗片麻岩,岩脉以暗色煌斑岩为主。
岩体是在漫长的地质历史演变过程中经受了不同大小和不同方向的多期构造应力场的长期作用而形成的。这导致了岩体结构面分布的随机性、形态的多样性和空间组合的复杂性,以至于对岩体结构的研究变得非常复杂。但是从大量裂隙的统计意义上来讲,人们发现,岩体中的裂隙是具有一定的规律性,并受区域构造运动所控制的。因此,查明研究区构造运动,是进行裂隙结构面网络模拟和建立裂隙渗流模型的基础。
结构面网络模拟是根据现场测量所得的结构面各种几何参数的概率分布来生成服从这些分布规律的结构面网络几何图形,即根据有限天然露头或人工开挖面上结构面几何参数来推求岩体内部的结构面参数分布,实现这一过程通常采用的是Monte-Carlo法。
裂隙岩体渗流研究作为一个重要的科学研究和工程应用问题,随着许多应用性学科的发展和一些重大的急需解决的实际工程问题的显现,越来越受到广大学者的关注。该研究涉及诸多领域,如岩土工程、水利水电工程、石油工程以及岩体地下构筑物建设等项目。本论文是从裂隙渗透张量以及裂隙网络连通性两方面来分析研究区的渗流特征。
1.渗透张量是表征裂隙渗透性的基本参数,其是一个既有大小又有方向的量,在数学上通过矩阵来表示。本研究根据野外地表裂隙统计和钻孔裂隙统计结果,结合空间三维渗透张量理论求取研究区渗透张量,同时根据压水试验结果对渗透张量进行矫正,最后获得研究区平面及垂向上渗透张量变化规律。
2.裂隙连通性分析基于裂隙网络模拟。考虑裂隙连通性必然要弄清区域裂隙的隙宽、迹长、导水系数等。这些参数可以通过地表结构面调查以及钻孔裂隙统计分析得出。连通区实际上是根据裂隙网络模拟结果确定了一个有效的隔水边界,所有连通区内的裂隙是存在水力联系的,不同的连通区,裂隙不能直接导通。连通区分析的运算法则也是以相互切割的裂隙的逻辑关系为基础的。
在以上的理论以及研究方法基础上,本文针对黄岛地下水封石油洞库主要进行了以下三方面的研究：
1.裂隙成因及发育规律研究
本文结合断层成因及构造运动理论分析认为区域节理的分布特征是受燕山期太平洋板块向NW或向W俯冲的结果,并且经历了燕山早期、中期和晚期复杂的构造运动。
根据研究观察、岩体的分布与断层的相互切割关系分析,本次研究认为研究区及其周缘断层的形成总体来说是燕山期太平洋板块剧烈活动的结果,断层的活动性质复杂,经历了多期性质的转换,燕山早期,区域受到NNW方向的挤压应力,研究区主要断裂形成(包括F3、F4),同时次生NE向与NW向延伸的节理；燕山中期,在拉升引力环境下,岩浆上涌、岩脉形成；燕山晚期—现今,研究区总体受太平洋板块向W的挤压作用,F3呈现右行压扭的性质,而F4则呈现左行张扭的性质,研究区西侧部分裂隙在张应力作用下扩展,隙宽变大。
2.渗透张量变化规律研究
(1)通过研究区水文地质试验及物探成果,初步分析了研究区平面和垂向上渗透性的变化规律,从不同尺度上对渗透性作出评价。
(2)针对裂隙岩体渗透系数的重要性以及难确定性,本文运用了新的技术方法,不仅可以得出渗透主值水平上的变化规律,而且求出了垂向上渗透主值及渗透方向的变化规律。同时针对实际工程,数据多计算繁琐这一特点,本文在Excel中编制了计算渗透主值及倾向、倾角的VB程序,可以方便地得到了大量不同深度处的渗透张量。分析得出,洞库区平面上渗透张量变化与裂隙产状变化基本一致；垂向上,渗透性大小与隙宽的变化基本一致。
(3)用钻孔成像统计得出的渗透张量,受软件识别效果的影响,对于微裂隙隙宽的读取有一定的人为误差,所以得出的渗透主值有一定的偏差,但可以反映该处渗透主值的变化规律。对于这个不足,可以通过软件识别图像的最小像素做相对准确的估计。同时提出,在不同深度通过压水试验对渗透张量分别矫正的方法。本研究获得的矫正系数0.07～0.89之间,通过不同深度分别对应矫正后,渗透主值和压水试验数量级相一致,主渗透方向不变。
3.裂隙网络模拟及渗流研究
(1)本文在给出裂隙各参数概率统计分布类型及分布参数的基础上,对较小范围的洞库区做了二维结构面网络模拟,从不同剖面研究了裂隙的发育情况,给出了剖面上节理的密度图和RQD图。结果显示,洞库Ⅰ区主要分布有一个裂隙组,垂向上在-30m处产状有较大的变化,裂隙密度均小于1条/m,RQD分布在70～90%之间；洞库Ⅱ区主要发育有两组近于正交的裂隙,裂隙密度小于0.5条/m,RQD在90%以上,和Ⅰ区相比裂隙发育少,总体渗透性弱。
(2)对整个研究区在考虑断层发育的情况下做三维结构面网络模拟,得到了研究区的裂隙网络分布图、隙宽分布图、储水系数分布图、裂隙连通区图和钻孔连通区图。结合离散裂隙渗流的特征,对整个研究区做了连通性分析,认为整个模拟区的连通区具有南东方向的走向。同时对ZK13和ZK15做了钻孔连通性分析,模拟出了影响钻孔水位的裂隙范围。
Huangdao water sealed underground oil tank lies in Huangdao district, ShanDong province,which is one of strategic oil storages being build recently and is the first underground oil storage with the capacity of 300×104m3 in our country. In this paper,fracture causes and distribution、fracture permeability、discrete fracture network simulation and discrete fracture connectivity are analysed based on the projects of Huangdao water sealed underground oil tank.
The Proterozoic granite gneiss is the major lithology in the study area as Low-permeability fractured media is the ideal location for the underground oil tank. The research of spatial structure and basic hydraulic parameters can provide critical hydrogeological data for the following analysis of fracture flow simulation and water seal effect evaluation.
During the long process of geologic evolution, different quantity of tectonic stress displayed in size and directions have had so significant impact on the rock mass so that which shows the characteristics of heterogeneity,randomness,diversity and complexity.All of these characteristics makes the research of rock mass structure becomes more complex.However, it was found that the fracture of rock mass are regulared statistically and be controlled by regional tectonic movement.So,the identification of tectonic movement in study areas is basis for fracture network simulation and fracture flow model establishing.
With the development of computer technology,network simulation of rock mass discontinuities which is based on statistics and probability theory is improved and brought into practice gradually.Network geometric graphics are simulated with the probability distribution of the discontinuities geometric parameters that are Measured in-situ.The whole proeess will be completed by the Monte-Carlo method.
Seepage in fractured rock research is important for scientific research and application of engineering. With the development of engineering disciplines and the showing of actual engineering problems to be solved urgently,it is more and more concerned by researchers.The study involved a number of areas, such as geotechnical engineering, water conservancy and hydropower engineering, petroleum engineering, and construction of rock structures in underground projects. In this paper, flow characteristics of the study area are discussed in two sides:fracture permeability tensor and the fracture network connectivity.
1. Fracture permeability tensor which is the basic parameters in fissured area is expressed through the matrix in mathematically. three-dimensional fracture permeability tensor of study area was caculated based on the statistics of field surface cracks and drilling image fracture results.Meanwhile,the result was rectified by water pressure test to Reflect the horizontal and vertical variation of the fracture.
2. Fissure fracture network connectivity analysis based on fracture simulation.It is very significant to clarify fracture aperture, trace length, hydraulic conductivity coefficient and so on before the analysis of fracture connectivity.Components of the fracture network is based on the simulation results which to determine an effective impervious boundary, all the connected region share the same hydraulic fracture link within it. Connected component algorithm is also based on the logic cutting mutual relations.
According to the above theories and analysis, this paper did following three researches for Huangdao water sealed underground oil tank:
1. Law of fracture distribution analysis
In this paper, the causes of faults and tectonic theory was used to analyse the fracture distribution of the region which is characterized by the Yanshan Pacific Plate subduction to the W or to the NW direction.Complicated tectonic movements of early Yanshan,mid Yanshan and late Yanshan stage contribute to fracture formation.
In the early-Yanshan stage, main fault zone (including the F3, F4)formate in the area, while secondary to the NE and NW extension of the fracture; during the mid-Yanshan stage,in the pulling stress environment, dykes was forming while magma gushing up; during the late-Yanshan stage,study area was compressed W by the Pacific plate,while F3 show the nature of the right-transtension, and F4 are presented the left-transtensional,the fracture gap became larger in the west part of the study area in tensile stress.
2. Variation of permeability tensor
(1) A preliminary analysis of the study area on the plane and the vertical variation are sdudied from different scales to assess on the permeability.The hydrogeological and geophysical test results are used in this paper.
(2) Permeability coefficient is very importance for fracture rock mass,but it is also difficult to confirm. A new technicalness was exertioned in this paper to get permeability variety not only horizontally but also vertically.For much date and complicated calculation in field project, VB program in Excel was developed to caculate principal value and directions of hydraulic conductivity.The result is principal directions of hydraulic conductivity is in accord with dip direction and dip angle in horizontal and the principal value of hydraulic conductivity is in accord with changes of aperture in vertical.
(3)Permeability tensor derived from drilling imaging which could reasonably reflect the variation of the main value penetration,but human error is still exist because of the effect of recognition by the software. For this point, minimum pixel relatively estimation was used to make the correct estimation more accurate. And Also it is suggested that correct result through the water pressure test methods in different depths. The correction factor of this area is between 0.07 and 0.89. Through the correction in different depth, principal directions of hydraulic conductivity is stable and the principal value of hydraulic conductivity is in accord with water pressure test result quantitatively.
3. Fracture network simulation and seepage flow
(1)This paper made a two-dimensional structure network simulation for the reservoir area based on the probability of fracture parameter statistical distribution types and distribution parameters. Fracture density map and RQD map in different directions was used to analyse the fracture around the tank.the result is:fracture density is less than 1 piece per meter and RQD distribution is between 70～90% in sectionⅠ; fracture density is less than 0.5 piece per meter and RQD is more than 90% in sectionⅡ.
(2)Three-dimensional network simulation was used in the entire study area to analysis fracture network distribution,aperture distribution,transmissivity,coefficient of storage,fracture component and drilling connected zones.lt is find that connected direction of the area is in southeast base on the fracture seepage characteritics,meanwhile. Connectivity of ZK13 and ZK15 was simulated to make sure the range of infection area of water levels in boreholes.
引文
[1]夏喜林,刘烨.浅谈我国地下油库的建设[J].石油规划设计,2004,15(4)：26-28.
[2]柴军瑞,仵彦卿.岩体多重裂隙网络渗流模型研究[J].煤田地质与勘探,2000,4：33-35.
[3]孙蓉琳,梁杏,靳孟贵.裂隙岩体渗透系数确定方法综述[J].水文地质与工程地质,2006,6：120-123.
[4]周志芳,杨建,杨建宏.确定缓倾结构面渗透性参数的现场试验法[J].工程地质学报,1999,7(4)：375-379.
[5]张世殊,梁杏.平硐声波孔渗水试验确定岩体渗透系数[J].水电站设计,2002,18(1)：80-82.
[6]Louis.李世平,冯震海译.岩石力学(岩体水力学).北京：煤炭工业出版社,1981.254-330.
[7]Hsieh P A, Neuman S P. Field determination of the three-dimensional hydraulic conductivity tensor of anisotropic media[J].Water Resour.Res.1985,21 (11).
[8]Neuman S P. Determination of Horizontal aquifer anisotropy with three wells[J].Groudwater, 1984,22(1).
[9]Papadopulos I S. Nonsteady flow to a well in an infinite anisotropic aquifer[C]. Proc.Dubrovnik Symposium on the Hydrology,1966.
[10]Hantush M S. A method for analyzing a drawdown test in anisotropic aquifers[J].Water Resour.Res.1966,2 (2).
[11]周志芳,杨建,杨建宏.确定缓倾结构面渗透性系数的现场试验法[J].工程地质学报.1999,7(4)：37-41.
[12]周志芳,王锦国.裂隙介质水动力学[M].北京：中国水利水电出版社,2004.
[13]田开铭,万力.各向异性裂隙介质渗透性的研究与评价[M].学苑出版社,1989：7-18.
[14]A.F. Hrenandez, S.P.Neuman, A.Guadagnini. J.Carrera. Conditioning mean steady state flow on hydraulic head and conductivity through geostatistical inversion[J].Stochastic Environmental Research and Risk Assessment,2003,17:329-338.
[15]A.G. Hunt. Some comments on the scale dependence of the hydraulic conductivity in the presence of nested heterogeneity[J].Advances in water resources,2003,26:71-77.
[16]徐光黎,潘别桐,唐辉明等著.岩体工程模型与应用.中国地质大学出版社,1993.9.
[17]万力,李定方,李吉庆.三维裂隙网络的多边形单元渗流模型[J].水利水运科学研究.1993,(4)：347-353.
[18]王恩志,王洪涛,孙役.双重裂隙系统渗流模型研究[J].岩石力学与工程学报,1998,17(4)：400-406.
[19]Miller S.M.A statistical method to evaluate homogeneity of structural populations[J]. Mathematical geology.1983,15 (2):317-328.
[20]Mahtab M.A,Yegulap T.M.A similarity test for grouping orientation data in rock mechanics[A].25th U.S.Symposium on rock mechanics[C].1984,495-502.
[21]Bingham C.,Distributions on the sphere and on the projective Plane[D].New Haven, Connecticut,USA:Yale University,1964.
[22]Shanley R.J.,MAHTAB M A..Delineation and analysis of clusters in orieniation data [J]. Mathematical Geology,1976,8(1):9-23.
[23]Einstein H.H.,Veneziano D.,Baecher G.B.,et al.The effect of discontinuity persistence on rock slope stability [J].Int J Rock Mech Min Sci Geomech Abstr,1983,20(5):227-236.
[24]Priest S.D.,Hudson J.A.Discontitity Spacings in Rock[J].International Journal of Rock Mechanics and Mining Sciences.1976,13:135-148.
[25]Priest S.D.,Hudson J.A..Estimation of discontinuity spacing and trace length using scanline surveys[J].International Journal of Rock Mechanics and Mining Scienees and Geomechanics Abstracts,1981,18(3):183-197.
[26]Goodman R.E.,Smith H.R.RQD and fracture spacing[J].Journal of the Geotechnical Engineering Division.1980,106:191-193.
[27]Oda M.Fabric tensor for discontinuity geological materials[J].Soil and Foundation.1982,22 (4):96-108.
[28]Oda M.Permeability tensor for discontinuous rock asses[J].Geotechnique.1984,35:483-495.
[29]邬爱清,周火明.3-D岩体结构模拟分析系统及三峡船闸高边坡岩体结构概化模型研究[R].武汉：长江科学院,1998.
[30]王良奎,陈剑平,卢波.样本窗口中不连续面体积密度的评价与应用[J].煤田地质与勘探.2002,30(3)：42-44.
[31]Sen Z.,Kazi A.Discontinuity spacing and RQD estimates from finite length scanline[J].Inter. Journal Rock Mech.Min.Sci.and Geomech.Abstr.1984,21:203-212.
[32]Kulatilake P.H.S.W.,Wu T.H.Relation between discontinuity size and trace lenth[A]. Proceedings of the 27th U.S. symposium on rock mechanics[C].1986,130-133.
[33]Warburton P.A.A stereological interpretation of joint trace date[J].International Journal of Rock Mechanics and Mining Science and Geomechanics Abstract.1980,17:181-190.
[34]Warburton P.M. Stereological interpretation of joint trace data:influence of joint shape and implications for geological surveys[J].International Journal of Rock Mechanics and Mining Science and Geomechanics Abstract.1980,17:305-316.
[35]RouleauA.,Gale J.E..Stochastic discrete fracture simulation of groundwater flow into an underground excavation in granite[J].Int.J.Rock Mech.Min.Sci.&, Geomech.Abstr.,1987, 24(2):99-112.
[36]Hakami E. Aperture measurements and flow experiments using transparent replicas of rock joints.In:Barton&Stephanssoned.Rock Joint.1990.383-390.
[37]Tsang Y W.Channel model of flow through fractured media.Wat.Resour.Res.,1987,23(3): 467-479.
[38]周创兵,叶自桐,何炬林等.岩石节理张开度的概率模型与随机模拟[J].岩石力学与工程学报.1998,17(3)：267-272.
[39]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.
[40]庞作会,邓建辉,葛修润.在节理网络图上全自动生成有限元网格[J].岩石力学与工程学报,1999,118(2)：197-200.
[41]陶振宇,唐方福,张黎明,等.节理与断层岩石力学[M].武汉：中国地质大学出版社,1992.
[42]陶振宇,王宏.岩石力学中节理网络模拟技术[J].长江科学院院报,1990,7(4)：18-26.
[43]陈征宙,胡伏生.岩体节理网络模拟技术研究[J].岩土工程学报,1998,20(1)：22-25.
[44]周维垣,杨若琼,尹健民等.三维岩体构造网络生成的自协调法及其工程应用[J].岩石力学与工程学报,1997,16(1)：29-35.
[45]马宇,赵阳升,段康廉.岩体裂隙网络的二维分形仿真[J].太原理工大学学报,1999,30-52.
[46]仵彦卿.岩体水力学基础(一、二、三、四、五、六、七)—岩体水力学的基本问题[J].水文地质工程地质.
[47]万力,田开铭.交叉孔压水试验法确定三维各向异性渗透张量[J].水文地质工程地质,1990,4.
[48]张有天,张武功.裂隙岩石渗透特性渗流数学模型及系数量测.岩石力学.1982,(8)：41-52.
[49]田开铭,万力.各向异性裂隙介质渗透性的研究与评价.北京：学苑出版社,1989.3-21.
[50]田开铭.论裂隙岩石的水文地质模型.勘测科学技术.1984,(4)：27-34.
[51]王媛.单裂隙面渗流与应力的耦合特性[J].岩石力学与工程学报,2002,21(1)：83-87.
[52]汪旭涛,陈新国,王亮.某裂隙岩质边坡渗透张量的确定及应用[J].长江科学院院报,2008,25(2)：46-49.
[53]Nordqvist A W, Tsang Y W, Tsang C F. A variable aperture fracture network model for flow and transport in fractured rocks. Water Resources Research.1992,28(6):1703-1713.
[54]黄勇,周志芳.岩体渗流模拟的二维随机裂隙网络模型[J].河海大学学报,2004,32(1)：91-94.
[55]Dershowitz W S, Godron B M, Karfitsas J C. A new three dimensional model for flow of fractuerd rock[J],Men Int Assoc Hydrogeol.1985,17:441-448.
[56]黄润秋,许模,陈剑平,胡卸文,范留明.复杂岩体结构精细描述及其工程应用[J].北京科学出版社,2004
[57]于青春,刘丰收,大西有三.岩体连续裂隙网络三维面状渗流模型[J].岩石力学与工程学报,2005,24(4)：662-667.
[58]于青春,武雄,大西有三.非连续裂隙网络管状渗流模型及其校正[J].岩石力学与工程学报,2006,25(7)：1469-1473.
[2]柴军瑞,仵彦卿.岩体多重裂隙网络渗流模型研究[J].煤田地质与勘探,2000,4：33-35.
[3]孙蓉琳,梁杏,靳孟贵.裂隙岩体渗透系数确定方法综述[J].水文地质与工程地质,2006,6：120-123.
[4]周志芳,杨建,杨建宏.确定缓倾结构面渗透性参数的现场试验法[J].工程地质学报,1999,7(4)：375-379.
[5]张世殊,梁杏.平硐声波孔渗水试验确定岩体渗透系数[J].水电站设计,2002,18(1)：80-82.
[6]Louis.李世平,冯震海译.岩石力学(岩体水力学).北京：煤炭工业出版社,1981.254-330.
[7]Hsieh P A, Neuman S P. Field determination of the three-dimensional hydraulic conductivity tensor of anisotropic media[J].Water Resour.Res.1985,21 (11).
[8]Neuman S P. Determination of Horizontal aquifer anisotropy with three wells[J].Groudwater, 1984,22(1).
[9]Papadopulos I S. Nonsteady flow to a well in an infinite anisotropic aquifer[C]. Proc.Dubrovnik Symposium on the Hydrology,1966.
[10]Hantush M S. A method for analyzing a drawdown test in anisotropic aquifers[J].Water Resour.Res.1966,2 (2).
[11]周志芳,杨建,杨建宏.确定缓倾结构面渗透性系数的现场试验法[J].工程地质学报.1999,7(4)：37-41.
[12]周志芳,王锦国.裂隙介质水动力学[M].北京：中国水利水电出版社,2004.
[13]田开铭,万力.各向异性裂隙介质渗透性的研究与评价[M].学苑出版社,1989：7-18.
[14]A.F. Hrenandez, S.P.Neuman, A.Guadagnini. J.Carrera. Conditioning mean steady state flow on hydraulic head and conductivity through geostatistical inversion[J].Stochastic Environmental Research and Risk Assessment,2003,17:329-338.
[15]A.G. Hunt. Some comments on the scale dependence of the hydraulic conductivity in the presence of nested heterogeneity[J].Advances in water resources,2003,26:71-77.
[16]徐光黎,潘别桐,唐辉明等著.岩体工程模型与应用.中国地质大学出版社,1993.9.
[17]万力,李定方,李吉庆.三维裂隙网络的多边形单元渗流模型[J].水利水运科学研究.1993,(4)：347-353.
[18]王恩志,王洪涛,孙役.双重裂隙系统渗流模型研究[J].岩石力学与工程学报,1998,17(4)：400-406.
[19]Miller S.M.A statistical method to evaluate homogeneity of structural populations[J]. Mathematical geology.1983,15 (2):317-328.
[20]Mahtab M.A,Yegulap T.M.A similarity test for grouping orientation data in rock mechanics[A].25th U.S.Symposium on rock mechanics[C].1984,495-502.
[21]Bingham C.,Distributions on the sphere and on the projective Plane[D].New Haven, Connecticut,USA:Yale University,1964.
[22]Shanley R.J.,MAHTAB M A..Delineation and analysis of clusters in orieniation data [J]. Mathematical Geology,1976,8(1):9-23.
[23]Einstein H.H.,Veneziano D.,Baecher G.B.,et al.The effect of discontinuity persistence on rock slope stability [J].Int J Rock Mech Min Sci Geomech Abstr,1983,20(5):227-236.
[24]Priest S.D.,Hudson J.A.Discontitity Spacings in Rock[J].International Journal of Rock Mechanics and Mining Sciences.1976,13:135-148.
[25]Priest S.D.,Hudson J.A..Estimation of discontinuity spacing and trace length using scanline surveys[J].International Journal of Rock Mechanics and Mining Scienees and Geomechanics Abstracts,1981,18(3):183-197.
[26]Goodman R.E.,Smith H.R.RQD and fracture spacing[J].Journal of the Geotechnical Engineering Division.1980,106:191-193.
[27]Oda M.Fabric tensor for discontinuity geological materials[J].Soil and Foundation.1982,22 (4):96-108.
[28]Oda M.Permeability tensor for discontinuous rock asses[J].Geotechnique.1984,35:483-495.
[29]邬爱清,周火明.3-D岩体结构模拟分析系统及三峡船闸高边坡岩体结构概化模型研究[R].武汉：长江科学院,1998.
[30]王良奎,陈剑平,卢波.样本窗口中不连续面体积密度的评价与应用[J].煤田地质与勘探.2002,30(3)：42-44.
[31]Sen Z.,Kazi A.Discontinuity spacing and RQD estimates from finite length scanline[J].Inter. Journal Rock Mech.Min.Sci.and Geomech.Abstr.1984,21:203-212.
[32]Kulatilake P.H.S.W.,Wu T.H.Relation between discontinuity size and trace lenth[A]. Proceedings of the 27th U.S. symposium on rock mechanics[C].1986,130-133.
[33]Warburton P.A.A stereological interpretation of joint trace date[J].International Journal of Rock Mechanics and Mining Science and Geomechanics Abstract.1980,17:181-190.
[34]Warburton P.M. Stereological interpretation of joint trace data:influence of joint shape and implications for geological surveys[J].International Journal of Rock Mechanics and Mining Science and Geomechanics Abstract.1980,17:305-316.
[35]RouleauA.,Gale J.E..Stochastic discrete fracture simulation of groundwater flow into an underground excavation in granite[J].Int.J.Rock Mech.Min.Sci.&, Geomech.Abstr.,1987, 24(2):99-112.
[36]Hakami E. Aperture measurements and flow experiments using transparent replicas of rock joints.In:Barton&Stephanssoned.Rock Joint.1990.383-390.
[37]Tsang Y W.Channel model of flow through fractured media.Wat.Resour.Res.,1987,23(3): 467-479.
[38]周创兵,叶自桐,何炬林等.岩石节理张开度的概率模型与随机模拟[J].岩石力学与工程学报.1998,17(3)：267-272.
[39]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.
[40]庞作会,邓建辉,葛修润.在节理网络图上全自动生成有限元网格[J].岩石力学与工程学报,1999,118(2)：197-200.
[41]陶振宇,唐方福,张黎明,等.节理与断层岩石力学[M].武汉：中国地质大学出版社,1992.
[42]陶振宇,王宏.岩石力学中节理网络模拟技术[J].长江科学院院报,1990,7(4)：18-26.
[43]陈征宙,胡伏生.岩体节理网络模拟技术研究[J].岩土工程学报,1998,20(1)：22-25.
[44]周维垣,杨若琼,尹健民等.三维岩体构造网络生成的自协调法及其工程应用[J].岩石力学与工程学报,1997,16(1)：29-35.
[45]马宇,赵阳升,段康廉.岩体裂隙网络的二维分形仿真[J].太原理工大学学报,1999,30-52.
[46]仵彦卿.岩体水力学基础(一、二、三、四、五、六、七)—岩体水力学的基本问题[J].水文地质工程地质.
[47]万力,田开铭.交叉孔压水试验法确定三维各向异性渗透张量[J].水文地质工程地质,1990,4.
[48]张有天,张武功.裂隙岩石渗透特性渗流数学模型及系数量测.岩石力学.1982,(8)：41-52.
[49]田开铭,万力.各向异性裂隙介质渗透性的研究与评价.北京：学苑出版社,1989.3-21.
[50]田开铭.论裂隙岩石的水文地质模型.勘测科学技术.1984,(4)：27-34.
[51]王媛.单裂隙面渗流与应力的耦合特性[J].岩石力学与工程学报,2002,21(1)：83-87.
[52]汪旭涛,陈新国,王亮.某裂隙岩质边坡渗透张量的确定及应用[J].长江科学院院报,2008,25(2)：46-49.
[53]Nordqvist A W, Tsang Y W, Tsang C F. A variable aperture fracture network model for flow and transport in fractured rocks. Water Resources Research.1992,28(6):1703-1713.
[54]黄勇,周志芳.岩体渗流模拟的二维随机裂隙网络模型[J].河海大学学报,2004,32(1)：91-94.
[55]Dershowitz W S, Godron B M, Karfitsas J C. A new three dimensional model for flow of fractuerd rock[J],Men Int Assoc Hydrogeol.1985,17:441-448.
[56]黄润秋,许模,陈剑平,胡卸文,范留明.复杂岩体结构精细描述及其工程应用[J].北京科学出版社,2004
[57]于青春,刘丰收,大西有三.岩体连续裂隙网络三维面状渗流模型[J].岩石力学与工程学报,2005,24(4)：662-667.
[58]于青春,武雄,大西有三.非连续裂隙网络管状渗流模型及其校正[J].岩石力学与工程学报,2006,25(7)：1469-1473.