地下水封洞库岩体力学参数REV的各向异性研究
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摘要
岩体力学参数的合理取值是岩土工程中最根本的问题之一,参数选择的准确与否直接影响到工程的安全性及工程造价的合理性。地下水封洞库作为一种较为新颖的工程类型,“水封效果”及“围岩稳定性”是其需要解决的两个关键问题,而岩体力学参数的合理取值是解决这两个问题的核心内容。然而实际工程中的岩体内部都存在着大量的结构面,使得岩体力学性质错综复杂,具有显著的尺寸效应及各向异性。因此,岩体力学参数的合理取值离不开其尺寸效应及各向异性的研究。表征单元体(Representative Elementary Volume, REV)是岩体力学性质尺寸效应研究的核心内容,即尺寸效应的研究需要确定各力学参数REV的大小。且岩体具有各向异性,因此力学参数在不同方向上的REV尺寸必然不同,故本文开展岩体在不同方向上的力学参数REV研究,确定能够反映岩体各向异性的力学参数REV大小。
此外,REV的概念来源于等效连续介质理论,是该理论分析的最小体积单元。等效连续介质理论假设研究对象是由一系列这样的单元组成的等效连续介质体。将REV的概念引入到岩体力学当中,也是为了能够在岩体中找到这样一个单元体,使其能够从宏观上反映岩体的平均特性,那么就可以将岩体这种非连续介质看作由一系列这样的单元体组成的等效连续介质体。目前关于岩体REV的研究成果主要集中在岩体的渗流REV上,针对的是岩体的连续与非连续介质渗流分析,而针对岩体连续与非连续介质力学分析而研究岩体力学特性REV的成果还相对较少,且未形成一套系统的研究思路与方法。具体表现在：部分学者通过不同尺寸岩体试样的数值试验研究得到了岩体的各个等效力学参数REV,包括变形参数和强度参数,但却忽略了其等效变形参数是否具有张量特性的研究,而这却是等效连续介质力学分析的必要条件之一；部分学者通过数值试验得到了岩体等效变形参数REV,也进行了等效变形参数的张量特性研究,但工程中更加注重岩体的强度特征,因此还有必要进行其等效强度参数REV的研究,且强度参数REV的大小并不一定与变形参数REV相同；甚至还有部分学者只研究了岩体在一个方向上的力学参数REV,便将其用于等效连续介质力学分析当中。
鉴于此,论文依托国家战略石油储备黄岛地下水封洞库工程,主要开展花岗片麻岩体在不同方向上的力学参数REV研究及其等效连续性研究。首先,分析了洞库区主要构造体系的形成及演化历史,并根据结构面发育规模及工程地质意义对其进行了不同级别的划分；重点研究了影响洞库围岩完整性的Ⅳ级结构面,并根据其发育特征确定了花岗片麻岩体的结构类型；基于野外地质调查及钻孔摄像技术获得的结构面数据,统计了花岗片麻岩体发育的优势节理组及各组节理的几何要素概率密度函数,在此基础上采用Monte-Carlo方法进行了结构面网络模拟,建立了花岗片麻岩体结构模型,为其力学参数REV的研究奠定了基础。其次,对UDEC (Universal Distinct Element Code)离散元数值模拟软件开展岩体数值试验的适宜性进行了研究,确定了本文主要的研究手段；基于Monte-Carlo方法得到的岩体结构模型(20m×20m),从其中心依次选取不同尺寸(边长1m、2m、3m、...、14m)的正方形花岗片麻岩体试样,进行不同围压下的三轴压缩数值试验研究,得到了其等效变形参数(弹性模量、泊松比)及等效强度参数(粘聚力、内摩擦角)REV的大小。再次,旋转岩体结构模型,采用同样的研究思路得到了不同方向上的力学参数REV大小,研究了其各向异性特征,并根据各力学参数的变异系数变化规律确定了最终的REV大小。最后,对花岗片麻岩体等效变形参数张量特性进行了分析,并获得了花岗片麻岩的等效柔度矩阵及其采用连续介质力学分析的最小尺寸,在此基础上提出了岩体进行等效连续介质力学分析时的基本原则。
论文主要的研究内容及成果主要包括以下儿个方面：
一、洞库花岗片麻岩体结构模型研究
(1)结构面形成及演化历史
洞库区及其周围邻近地区分布的主要构造体系包括红崖山断裂、老君塔山断裂、前马连沟断裂以、孙家沟断裂以及柳花泊断裂,它们均属于脆性断裂,从区域构造演化历史来看,脆性断裂的产生主要发生在中生代板内活化阶段,受太平洋板块向NW或向W俯冲的影响,主要的构造运动为燕山运动。
(2)结构面的分级
距离工程区最近的三条大规模断裂——前马连沟断裂、老君塔山断裂及孙家沟断裂属于洞库区的Ⅰ级结构面；工程区规模较大F3断层横穿主洞室区,F4断层构成洞库稳定性分析的边界条件,属于Ⅱ级结构面；F1、F2、F7、F8、F9均为小型断层或破碎带,属于Ⅲ级结构面；花岗片麻岩体内发育的数量众多的构造节理、岩脉侵入节理以及物质分异面等属于Ⅳ级结构面；花岗片麻岩特有的片麻理属于V级结构面。Ⅳ级结构面的发育特征直接反应了岩体的完整性,是岩体结构划分的主要依据,并控制着岩体的强度及变形破坏方式。
(3)花岗片麻岩体结构类型及数值模型建立
花岗片麻岩体主要被软弱结构面F3、F4及F8切割成为Ⅰ级块裂结构(Ⅰ-1),被构造节理及岩脉侵入节理等坚硬结构面断续切割成为Ⅱ级块状断续结构(Ⅱ-2),具有断续结构的花岗片麻岩的力学性质与研究尺寸紧密相连,表现出了明显的尺寸效应。根据洞库区发育的三组陡倾角优势节理,考虑其倾向、倾角、迹长和间距四个几何要素,采用Monte-Carlo方法进行了结构面网络模拟,从而得到了花岗片麻岩体结构模型。
二、UDEC数值试验适宜性研究(1) UDEC求解岩体变形参数的可靠性
以含有两组正交节理的规则岩体为例,通过对比其在不同方向上的柔度矩阵解析解及数值解,验证了UDEC求解岩体等效变形参数的可靠性。研究表明不同方向上的等效变形参数数值解与解析解吻合较好,且其等效弹性模量及泊松比随研究方向的变化曲线近似于椭圆；等效剪切模量不随研究方向的改变而改变,其拟合曲线呈圆形。
(2) UDEC求解岩体强度参数的可靠性
以含一组结构面的岩体为例,利用Jaeger的单弱面强度理论求得结构面倾角β在0°、15°、30°、...、90°下的岩体抗压强度,并与数值计算结果进行对比以验证UDEC求解岩体抗压强度的可靠性。研究表明,除了β=75°的岩体抗压强度数值计算结果大于其解析解外,其它倾角下的抗压强度数值解与理论解非常接近,相对误差均小于1%。结构面倾角β=75°时数值计算误差较大的原因在于该倾角下的结构面出露于岩体上下边界,而数值压缩试验过程中施加在岩体上下边界的位移边界条件限制了岩体沿结构面的自由变形,从而导致结构面两端的岩块也发生了破坏,增大了岩体强度。此外,通过完整岩石三轴数值压缩试验求得其抗剪强度参数,并与室内试验得到的岩石强度参数进行对比验证了UDEC求解等效强度参数的可靠性。
三、花岗片麻岩体力学参数REV各向异性研究
(1)岩体尺寸效应研究及其力学参数REV
基于Monte-Carlo方法得到的花岗片麻岩体结构模型(20m×20m),由其中心依次选取边长lm、2m、3m、...、14m的正方形岩体试样,进行不同围压下的三轴压缩数值试验以确定各力学参数REV的大小。花岗片麻岩体等效弹性模量Ex、Ey,等效泊松比vxy、vyx及等效内摩擦角φ均随着岩体尺寸的增加波动性减小,趋于稳定时对应的岩样边长分别为5m、2m、5m、3m,6m,可知不同岩体力学参数的REV大小是不相同的,不能一概而论,表述时必须明确REV所指的对象。
(2)岩体力学参数REV各向异性
通过研究花岗片麻岩体在0°、30°、60°、90°、120°、150°方向上的岩体力学参数随岩体尺寸增加的变化规律可知,不同方向上的等效力学参数Ex、Ey、vxy、vyx及φ均随着岩体尺寸的增大而波动性减小,并逐渐趋于稳定,且同一力学参数在不同方向上达到稳定时对应的岩体尺寸不同,表明岩体的等效力学参数REV确实具有各向异性。最后通过计算不同尺寸岩体的各个等效力学参数在不同方向上的变异系数,并根据各参数变异系数随尺寸的变化规律确定了最终的各力学参数REV大小。
四、基于力学参数REV各向异性的花岗片麻岩体等效连续性研究
(1)等效变形参数张量特性研究
基于上述研究对岩体等效变形参数的张量特性进行了分析,当岩体尺寸达到6m×6m后,各等效变形参数的拟合曲线形状近似于椭圆,且其长轴与短轴的差别不大,各向异性特征不明显；等效弹性模量Ex、Ey的数值计算结果基本上都落在了相应的各条拟合曲线上,误差较小；而等效泊松比vxy、vyx的数值计算结果则较偏离各条拟合曲线,相对而言误差较大。此时由等效变形参数得到的柔度矩阵拟合误差基本接近于5%,低于10%的允许误差,表明花岗片麻岩的等效弹性模量Ex、Ey及泊松比vxy、vyx可以采用张量的形式近似表示。最后综合确定花岗片麻岩等效连续介质力学分析的最小尺寸为6m×6m。
(2)岩体的等效连续介质力学分析基本原则
力学参数REV各向异性研究的目的是确定岩体在不同方向上的各个力学参数都趋于稳定时的岩体尺寸；而岩体变形参数能够用张量形式近似表示这一条件的本质是确定不同方向上的岩体等效柔度矩阵均趋于稳定时的岩体尺寸,且其拟合误差在允许范围内。柔度矩阵是由等效变形参数计算得到的,不同方向上的柔度矩阵趋于稳定的实质即是不同方向上的等效变形参数趋于稳定,可见等效变形参数张量特性的研究包括了等效变形参数REV的各向异性研究。故岩体力学参数REV的各向异性与其等效变形参数张量特性在本质上具有共同之处,即都要研究岩体等效变形参数REV的各向异性,而它们的不同之处在于前者还包括了岩体强度参数REV的各向异性研究,后者则要进行等效柔度矩阵拟合误差的分析。根据两者之间的区别与联系,提出了岩体的等效连续介质力学分析基本原则,即首先进行岩体等效变形参数张量特性的研究,它包含了等效变形参数REV及其各向异性研究,其次再进行等效强度参数REV及其各向异性研究,并取它们中的较大值作为等效连续分析的最小尺寸。
通过以上研究主要得到以下认识：岩体的各力学参数REV大小是不相同的,在表述岩体REV时必须明确其所指的具体对象；各力学参数在不同方向上的REV大小是不同的,确定力学参数REV大小时必须研究其各向异性特征；力学参数REV的各向异性与等效变形参数张量特性在本质上存在共同之处,岩体的等效连续分析需要遵循一定的原则。本文的创新之处在于：(1)通过数值试验研究了岩体力学参数REV的各向异性,并根据各力学参数的变异系数变化规律确定了最终的各力学参数REV大小；(2)探讨了岩体力学参数REV的各向异性与等效变形参数张量特性之间的联系,并在此基础上提出了岩体进行等效连续介质力学分析的基本原则。
Determination of rock mass mechanical parameters is one of the most basic issues in geotechnical engineering. The accuracy of parameters is directly related to the safety of project and the reasonability of construction costs. Underground water sealed caverns, as a novel engineering construction mode, has two key issues need to be addressed, which are water sealed effects and surrounding rock stability. And the determination of mechanical parameters is the core contents during solving these two issues. However, there are a lot of discontinuities existing in rock mass in practice, leading to a complicate nature of its mechanical properties with scale dependent and anisotropy. Therefore, the research of rock mass's size effects and anisotropy characteristics cannot be separated from the determination of mechanical parameters. Representative Elementary Volume (REV) is the critical issue in the research of rock mass scale dependent, in other word, it is necessary to determine the REV size during studying mechanical property size effects. Moreover, rock mass has anisotropy characteristic, so mechanical parameters REV must be various in different directions. Therefore, the study of mechanical parameters REV in different directions was carried out in this thesis to achieve the final REV sizes that can reflect the rock mass's anisotropy characteristic.
Representative elementary volume (REV), the fundamental concept in the continuum theory, is the minimum element in the analysis based on this theory, which supposes that the research object is a continuum body composed by a series of such element. However, rock mass is ordinarily regarded as non-continuum medium because of the presence of the discontinuities. In order to apply the continuum theory into the rock (mass) mechanics, the element that can represents the average properties in a microscopic view should be found, and then the discontinuous rock mass can be equivalent to a continuous medium consists of such elements. And such an element is the REV of the rock mass. So far, the researches about the rock mass REV are mainly concerned the flow property REV for continuum and non-continuum flow analysis. However, fewer studies about the mechanical property REV are reported for continuum and non-continuum mechanical analyses of the rock mass. And there have not been a systematic research thoughts and methods for the latter. Some researchers obtained the mechanical parameters' REV by the numerical experiments on different rock mass samples sizes, including deformation and strength parameters. But they lose sight of the verification of the deformation parameters' tensor characteristics, which is one of the necessary conditions for continuum mechanics analysis. The other researches achieve rock mass deformation parameters'REV by numerical experiments and verify their tensor characteristics, while they omit the study of the equivalent strength parameters that are paid more attention in engineering. And the sizes of strength parameters' REV are not always the same as deformation parameters' REV. There are even also some researchers that just study the mechanical parameters' REV only in one direction.
The thesis attempted to solve the issues mentioned above, and the project of underground water sealed caverns, national strategic reserve for oil, Huangdao, in Shandong Province, is taken as an example to study the granite gneiss mechanical parameters REV. Firstly, the formation and evolution processes of major tectonic system were analyzed in the interesting area. And the discontinuities are classified by the development scale and engineering geological significance. The forth-class (Class IV) discontinuities, main factor of rock mass's integrity, were researched in detail, and the structure type of granite gneiss was determined based on the forth-class discontinuities' development characteristics. And then according to the discontinuities data obtained from field investigation and borehole camera technique, the superior joint groups were found and geometric elements' probability distribution models for each group were statistically analyzed. On this basis, discontinuity network simulation was conducted with Monte-Carlo mathematic method, and the structure model of granite gneiss was obtained, which laid a foundation for the further study of its mechanical parameters REV's anisotropy. Secondly, the suitability of UDEC (Universal Distinct Element Code) software to carry out numerical experiments was verified and made it as the main research means in this thesis. From the center of the obtained granite gneiss structure model, different sizes of square samples with side length of lm,2m,3m...14m were chosen to conduct triaxial numerical compression experiments under different confining pressures. And the sizes of equivalent deformation parameters (elastic modulus and Poisson's ratio) REV and equivalent strength parameters (cohesion and friction angle) REV of granite gneiss were finally achieved. The results indicated that each mechanical parameter have a distinct REV size. And then, the mechanical properties in different directions (30°,60°,90°,120°,150°) of the structure model were also analyzed in the same research thought, and the results revealed that there were various REV sizes in different directions for each mechanical parameter. Namely, mechanical parameters' REV indeed had an anisotropic characteristic. According to the mechanical parameters' coefficients of variation (CV) for each sample in various directions, their final REV sizes were determined. Lastly, the tensor characteristic of equivalent deformation parameters was analyzed. Based on this, the elastic compliance matrix and the minimum size for granite gneiss equivalent continuum mechanical analysis was obtained. Through the researches of mechanical parameters REV's anisotropy and equivalent deformation parameters'tensor characteristic, some common ground in essence between them was found, and their relation and difference were clearly posed. Finally, the necessary research contents and logical order for equivalent continuum mechanics analysis were determined.
The main works and achievements in this thesis are as follows.
1. Granite gneiss structure model
(1) Formation and evolution of discontinuities
Hongyashan Fault, Laojuntashan Fault, Qianmaliangou Fault, Sunjiagou Fault and Liuhuapo Fault, brittle ones, are the main tectonic system in research area. According to the analysis of regional tectonic evolution processes, these brittle faults were generally produced in Mesozoic intraplate activation phase, when Yanshan movement was the dominant tectonic movement influenced by the Pacific Plate subduction to northwest (NW) or west (W).
(2) Classification of the discontinuities
Qianmaliangou Fault, Laojuntashan Fault and Sunjiagou Fault, belonging to the first-class (Class Ⅰ) discontinuities, are the three large-scaled faults close to the engineering site. F3fault crosses all the proposed storage caverns and F4fault lying on the edge of caverns constitutes the boundary condition of in-situ stress field analysis, and they can be referred as to the second-class (Class Ⅱ) discontinuities. F1, F2, F7, F8, F9faults are small-scaled faults or fracture zones, they are the third-class (Class Ⅲ) discontinuities of the project. There are a large number of tectonic joints, dyke intrusion joints and substance differentiation planes developing in granite gneiss, they can be cataloged to forth-class (Class IV) discontinuities. And the fifth-class (Class V) discontinuities are the gneissic schistosities of the intact rock. The development characteristics of the forth-class discontinuities reflect the integrity of granite gneiss and are the major basis for the structure type classification, which control the deformation and failure modes of the rock mass.
(3) Structure type and numerical model of granite gneiss
F3, F4and F8fault with weak mechanical properties cut the granite gneiss into faulted structure type (Ⅰ.1), the first-class type. And it is further cut by the secondary discontinuities, tectonic joints and dyke intrusion joints with hard mechanical properties, into intermitted structure type (Ⅱ.2), the second-class type. Granite gneiss with the intermitted structure type has eminent scale dependent that the mechanical properties are close related to the size of the rock mass. Based on the three superior joints groups with steep dips, the numerical model of the rock mass is constructed with Monte-Carlo mathematic method considering four major geometric elements such as dip directions, dips, trace lengths and spaces.
2. Suitability of the UDEC software for numerical experiment
(1) Reliability of the deformation parameters obtained by UDEC
Taking the regular structure rock mass with two orthogonal joints as an example, the reliability of deformation parameters obtained by UDEC software is verified by contrasting the analytic solution and numerical solution of the elastic compliance matrix in different directions. And the numerical solutions agree well with the analytic solution. The curve shapes of elastic modulus and Poisson's ratio variation with research directions are similar to an ellipse. While the curve shape of shear modulus is a circle, namely the value of it does not change with the direction.
(2) Reliability of the strength parameters obtained by UDEC
Taking the rock mass with one group of discontinuity as an example, its compressive strengths are calculated by Jaeger's strength theory and UDEC software on the conditions that the discontinuity's angle is0,15,30...and90degree. The numerical solutions are close to the numerical solutions in each case and the relative errors are less than one percent except when the discontinuity angle is75degree. In that case, the numerical solution is much larger than the analytic solution, and the error reaches to one hundred and ten percent. The reason is that the displacement boundary conditions on upper and lower model edges limit the freedom of the rock mass's deformation and cause the failure of the rock block near the discontinuity. Therefore, the rock mass's strength becomes higher. In addition, the strength parameters of intact rock obtained by triaxial numerical compression tests using UDEC software are compared with the laboratory results.
3. Anisotropy of mechanical parameters REV
(1) Scale dependent and mechanical parameters REV
From the center of the obtained granite gneiss structure model (20m×20m), different sizes of square samples with side length of lm,2m,3m...14m were chosen to conduct triaxial numerical compression experiments under different confining pressures. The mechanical parameters of each rock mass sample can be achieved by numerical calculation results and the scale dependent rules and REV sizes can be determined. The fluctuation of elastic modulus(Ex, Ey), Poisson's ratio (vxy, vyx) and internal friction angle(φ) decreases with the sample size increasing, and the corresponding size length of samples are respectively are5m,2m,5m,3m,6m when they become stable. The results indicated that each mechanical parameter has a distinct REV size. So the meaning of REV's object must be clearly expressed.
(2) Anisotropy of mechanical parameters REV
The mechanical properties in different directions (30°,60°,90°,120°,150°) of the structure model were also analyzed in the same research thought, and the results revealed that the fluctuation of mechanical parameters (Exy, Eyx, vxy, vyx an φ) all decrease and finally are stable with size increasing. But there were various REV sizes in different directions for each mechanical parameter. Namely, the mechanical parameters' REV did have an anisotropic characteristic. According to the mechanical parameters' coefficients of variation (CV) for each sample in various directions, their final REV sizes were determined.
4. Analysis of equivalent continuum properties of granite gneiss based on REV's anisotropy
(1) Tensor characteristics of the deformation parameters
Based on the above researches in this thesis, tensor characteristics of the deformation parameters are analyzed. When the sample size reaches6m×6m, the shapes of deformation parameters' fitting curves are similar to ellipse and the difference between long axis and short axis is little, which indicates that the anisotropic feature of deformation parameters is not eminent. The numerical solutions of elastic modulus (Ex, Ey) almost all fall on the fitting curves and the errors are small. While the numerical solutions of Poisson's ratio (vxy, vyx) deviate from the fitting curves and have relatively larger errors. But the fitting errors of the equivalent elastic compliance matrix for granite gneiss deduced by them are acceptable after the sample size reaches6m×6m. The value of the error is close to five percent, less than ten percent (the allowable error), therefore, the equivalent elastic modulus (Ex, Ey) and Poisson's ratio (vxy, vyx) of granite gneiss can be approximately represented in tensor form. Finally the minimum size, 6m×6m, for granite gneiss equivalent continuum mechanical analysis was obtained.
(2) The principles of equivalent continuum mechanical analysis for rock mass
The research of mechanical parameters REV's anisotropy is in essence to determine the rock mass size in which the parameters in different directions are all stable. The necessary condition that deformation parameters can be expressed in tensor form for equivalent continuum analysis is in essence to determine the rock mass size in which the compliant matrixes in different directions are all stable and its fitting error is within the allowable range. The compliant matrix is calculated by deformation parameters, so the fact that rock mass compliant matrixes in different directions reach stable means that deformation parameters in different directions reach stable. Therefore, the research of equivalent continuum properties contains the research of deformation parameters REV's anisotropy. Through the above analysis, we can find that there is some common ground in essence between the researches of mechanical parameters REV's anisotropy and deformation parameters tensor characteristics. Namely, they both need to carry out the study about the anisotropy of deformation parameters REV. The difference between them is that the former includes the research of strength parameters REV, while the latter demand the error analysis of the equivalent compliance matrix. According to their relation and differences, the principle of equivalent continuum mechanical analysis for rock mass is proposed. The equivalent deformation parameters'tensor characteristics must be firstly researched, and then the strength parameters REV and its anisotropy. The larger one of them can be referred as to the minimum size for equivalent continuum mechanical analysis.
Some benefit conclusions have been drawn through the research in this thesis. Each mechanical parameter has a distinct REV size, so the meaning of REV's object must be clearly expressed. The sizes of the same mechanical parameter REVs in different direction are various, the anisotropy of REV must be considered during determination of sizes of mechanical parameters REV. There are some common ground in essence between the researches of mechanical parameters REV's anisotropy and deformation parameters tensor characteristics, and the equivalent continuum analysis for rock mass must conform to certain principle. There are two innovations in this thesis. One is that the anisotropy of mechanical parameters REV is posed and researched by numerical experiments and the final REV size for each parameter is determined according to its coefficient of variation (CV) of each sample in different directions. The other is that the relationship between the researches of mechanical parameters REV's anisotropy and deformation parameters tensor characteristics is discussed and the principle of equivalent continuum mechanical analysis for rock mass is proposed.
此外,REV的概念来源于等效连续介质理论,是该理论分析的最小体积单元。等效连续介质理论假设研究对象是由一系列这样的单元组成的等效连续介质体。将REV的概念引入到岩体力学当中,也是为了能够在岩体中找到这样一个单元体,使其能够从宏观上反映岩体的平均特性,那么就可以将岩体这种非连续介质看作由一系列这样的单元体组成的等效连续介质体。目前关于岩体REV的研究成果主要集中在岩体的渗流REV上,针对的是岩体的连续与非连续介质渗流分析,而针对岩体连续与非连续介质力学分析而研究岩体力学特性REV的成果还相对较少,且未形成一套系统的研究思路与方法。具体表现在：部分学者通过不同尺寸岩体试样的数值试验研究得到了岩体的各个等效力学参数REV,包括变形参数和强度参数,但却忽略了其等效变形参数是否具有张量特性的研究,而这却是等效连续介质力学分析的必要条件之一；部分学者通过数值试验得到了岩体等效变形参数REV,也进行了等效变形参数的张量特性研究,但工程中更加注重岩体的强度特征,因此还有必要进行其等效强度参数REV的研究,且强度参数REV的大小并不一定与变形参数REV相同；甚至还有部分学者只研究了岩体在一个方向上的力学参数REV,便将其用于等效连续介质力学分析当中。
鉴于此,论文依托国家战略石油储备黄岛地下水封洞库工程,主要开展花岗片麻岩体在不同方向上的力学参数REV研究及其等效连续性研究。首先,分析了洞库区主要构造体系的形成及演化历史,并根据结构面发育规模及工程地质意义对其进行了不同级别的划分；重点研究了影响洞库围岩完整性的Ⅳ级结构面,并根据其发育特征确定了花岗片麻岩体的结构类型；基于野外地质调查及钻孔摄像技术获得的结构面数据,统计了花岗片麻岩体发育的优势节理组及各组节理的几何要素概率密度函数,在此基础上采用Monte-Carlo方法进行了结构面网络模拟,建立了花岗片麻岩体结构模型,为其力学参数REV的研究奠定了基础。其次,对UDEC (Universal Distinct Element Code)离散元数值模拟软件开展岩体数值试验的适宜性进行了研究,确定了本文主要的研究手段；基于Monte-Carlo方法得到的岩体结构模型(20m×20m),从其中心依次选取不同尺寸(边长1m、2m、3m、...、14m)的正方形花岗片麻岩体试样,进行不同围压下的三轴压缩数值试验研究,得到了其等效变形参数(弹性模量、泊松比)及等效强度参数(粘聚力、内摩擦角)REV的大小。再次,旋转岩体结构模型,采用同样的研究思路得到了不同方向上的力学参数REV大小,研究了其各向异性特征,并根据各力学参数的变异系数变化规律确定了最终的REV大小。最后,对花岗片麻岩体等效变形参数张量特性进行了分析,并获得了花岗片麻岩的等效柔度矩阵及其采用连续介质力学分析的最小尺寸,在此基础上提出了岩体进行等效连续介质力学分析时的基本原则。
论文主要的研究内容及成果主要包括以下儿个方面：
一、洞库花岗片麻岩体结构模型研究
(1)结构面形成及演化历史
洞库区及其周围邻近地区分布的主要构造体系包括红崖山断裂、老君塔山断裂、前马连沟断裂以、孙家沟断裂以及柳花泊断裂,它们均属于脆性断裂,从区域构造演化历史来看,脆性断裂的产生主要发生在中生代板内活化阶段,受太平洋板块向NW或向W俯冲的影响,主要的构造运动为燕山运动。
(2)结构面的分级
距离工程区最近的三条大规模断裂——前马连沟断裂、老君塔山断裂及孙家沟断裂属于洞库区的Ⅰ级结构面；工程区规模较大F3断层横穿主洞室区,F4断层构成洞库稳定性分析的边界条件,属于Ⅱ级结构面；F1、F2、F7、F8、F9均为小型断层或破碎带,属于Ⅲ级结构面；花岗片麻岩体内发育的数量众多的构造节理、岩脉侵入节理以及物质分异面等属于Ⅳ级结构面；花岗片麻岩特有的片麻理属于V级结构面。Ⅳ级结构面的发育特征直接反应了岩体的完整性,是岩体结构划分的主要依据,并控制着岩体的强度及变形破坏方式。
(3)花岗片麻岩体结构类型及数值模型建立
花岗片麻岩体主要被软弱结构面F3、F4及F8切割成为Ⅰ级块裂结构(Ⅰ-1),被构造节理及岩脉侵入节理等坚硬结构面断续切割成为Ⅱ级块状断续结构(Ⅱ-2),具有断续结构的花岗片麻岩的力学性质与研究尺寸紧密相连,表现出了明显的尺寸效应。根据洞库区发育的三组陡倾角优势节理,考虑其倾向、倾角、迹长和间距四个几何要素,采用Monte-Carlo方法进行了结构面网络模拟,从而得到了花岗片麻岩体结构模型。
二、UDEC数值试验适宜性研究(1) UDEC求解岩体变形参数的可靠性
以含有两组正交节理的规则岩体为例,通过对比其在不同方向上的柔度矩阵解析解及数值解,验证了UDEC求解岩体等效变形参数的可靠性。研究表明不同方向上的等效变形参数数值解与解析解吻合较好,且其等效弹性模量及泊松比随研究方向的变化曲线近似于椭圆；等效剪切模量不随研究方向的改变而改变,其拟合曲线呈圆形。
(2) UDEC求解岩体强度参数的可靠性
以含一组结构面的岩体为例,利用Jaeger的单弱面强度理论求得结构面倾角β在0°、15°、30°、...、90°下的岩体抗压强度,并与数值计算结果进行对比以验证UDEC求解岩体抗压强度的可靠性。研究表明,除了β=75°的岩体抗压强度数值计算结果大于其解析解外,其它倾角下的抗压强度数值解与理论解非常接近,相对误差均小于1%。结构面倾角β=75°时数值计算误差较大的原因在于该倾角下的结构面出露于岩体上下边界,而数值压缩试验过程中施加在岩体上下边界的位移边界条件限制了岩体沿结构面的自由变形,从而导致结构面两端的岩块也发生了破坏,增大了岩体强度。此外,通过完整岩石三轴数值压缩试验求得其抗剪强度参数,并与室内试验得到的岩石强度参数进行对比验证了UDEC求解等效强度参数的可靠性。
三、花岗片麻岩体力学参数REV各向异性研究
(1)岩体尺寸效应研究及其力学参数REV
基于Monte-Carlo方法得到的花岗片麻岩体结构模型(20m×20m),由其中心依次选取边长lm、2m、3m、...、14m的正方形岩体试样,进行不同围压下的三轴压缩数值试验以确定各力学参数REV的大小。花岗片麻岩体等效弹性模量Ex、Ey,等效泊松比vxy、vyx及等效内摩擦角φ均随着岩体尺寸的增加波动性减小,趋于稳定时对应的岩样边长分别为5m、2m、5m、3m,6m,可知不同岩体力学参数的REV大小是不相同的,不能一概而论,表述时必须明确REV所指的对象。
(2)岩体力学参数REV各向异性
通过研究花岗片麻岩体在0°、30°、60°、90°、120°、150°方向上的岩体力学参数随岩体尺寸增加的变化规律可知,不同方向上的等效力学参数Ex、Ey、vxy、vyx及φ均随着岩体尺寸的增大而波动性减小,并逐渐趋于稳定,且同一力学参数在不同方向上达到稳定时对应的岩体尺寸不同,表明岩体的等效力学参数REV确实具有各向异性。最后通过计算不同尺寸岩体的各个等效力学参数在不同方向上的变异系数,并根据各参数变异系数随尺寸的变化规律确定了最终的各力学参数REV大小。
四、基于力学参数REV各向异性的花岗片麻岩体等效连续性研究
(1)等效变形参数张量特性研究
基于上述研究对岩体等效变形参数的张量特性进行了分析,当岩体尺寸达到6m×6m后,各等效变形参数的拟合曲线形状近似于椭圆,且其长轴与短轴的差别不大,各向异性特征不明显；等效弹性模量Ex、Ey的数值计算结果基本上都落在了相应的各条拟合曲线上,误差较小；而等效泊松比vxy、vyx的数值计算结果则较偏离各条拟合曲线,相对而言误差较大。此时由等效变形参数得到的柔度矩阵拟合误差基本接近于5%,低于10%的允许误差,表明花岗片麻岩的等效弹性模量Ex、Ey及泊松比vxy、vyx可以采用张量的形式近似表示。最后综合确定花岗片麻岩等效连续介质力学分析的最小尺寸为6m×6m。
(2)岩体的等效连续介质力学分析基本原则
力学参数REV各向异性研究的目的是确定岩体在不同方向上的各个力学参数都趋于稳定时的岩体尺寸；而岩体变形参数能够用张量形式近似表示这一条件的本质是确定不同方向上的岩体等效柔度矩阵均趋于稳定时的岩体尺寸,且其拟合误差在允许范围内。柔度矩阵是由等效变形参数计算得到的,不同方向上的柔度矩阵趋于稳定的实质即是不同方向上的等效变形参数趋于稳定,可见等效变形参数张量特性的研究包括了等效变形参数REV的各向异性研究。故岩体力学参数REV的各向异性与其等效变形参数张量特性在本质上具有共同之处,即都要研究岩体等效变形参数REV的各向异性,而它们的不同之处在于前者还包括了岩体强度参数REV的各向异性研究,后者则要进行等效柔度矩阵拟合误差的分析。根据两者之间的区别与联系,提出了岩体的等效连续介质力学分析基本原则,即首先进行岩体等效变形参数张量特性的研究,它包含了等效变形参数REV及其各向异性研究,其次再进行等效强度参数REV及其各向异性研究,并取它们中的较大值作为等效连续分析的最小尺寸。
通过以上研究主要得到以下认识：岩体的各力学参数REV大小是不相同的,在表述岩体REV时必须明确其所指的具体对象；各力学参数在不同方向上的REV大小是不同的,确定力学参数REV大小时必须研究其各向异性特征；力学参数REV的各向异性与等效变形参数张量特性在本质上存在共同之处,岩体的等效连续分析需要遵循一定的原则。本文的创新之处在于：(1)通过数值试验研究了岩体力学参数REV的各向异性,并根据各力学参数的变异系数变化规律确定了最终的各力学参数REV大小；(2)探讨了岩体力学参数REV的各向异性与等效变形参数张量特性之间的联系,并在此基础上提出了岩体进行等效连续介质力学分析的基本原则。
Determination of rock mass mechanical parameters is one of the most basic issues in geotechnical engineering. The accuracy of parameters is directly related to the safety of project and the reasonability of construction costs. Underground water sealed caverns, as a novel engineering construction mode, has two key issues need to be addressed, which are water sealed effects and surrounding rock stability. And the determination of mechanical parameters is the core contents during solving these two issues. However, there are a lot of discontinuities existing in rock mass in practice, leading to a complicate nature of its mechanical properties with scale dependent and anisotropy. Therefore, the research of rock mass's size effects and anisotropy characteristics cannot be separated from the determination of mechanical parameters. Representative Elementary Volume (REV) is the critical issue in the research of rock mass scale dependent, in other word, it is necessary to determine the REV size during studying mechanical property size effects. Moreover, rock mass has anisotropy characteristic, so mechanical parameters REV must be various in different directions. Therefore, the study of mechanical parameters REV in different directions was carried out in this thesis to achieve the final REV sizes that can reflect the rock mass's anisotropy characteristic.
Representative elementary volume (REV), the fundamental concept in the continuum theory, is the minimum element in the analysis based on this theory, which supposes that the research object is a continuum body composed by a series of such element. However, rock mass is ordinarily regarded as non-continuum medium because of the presence of the discontinuities. In order to apply the continuum theory into the rock (mass) mechanics, the element that can represents the average properties in a microscopic view should be found, and then the discontinuous rock mass can be equivalent to a continuous medium consists of such elements. And such an element is the REV of the rock mass. So far, the researches about the rock mass REV are mainly concerned the flow property REV for continuum and non-continuum flow analysis. However, fewer studies about the mechanical property REV are reported for continuum and non-continuum mechanical analyses of the rock mass. And there have not been a systematic research thoughts and methods for the latter. Some researchers obtained the mechanical parameters' REV by the numerical experiments on different rock mass samples sizes, including deformation and strength parameters. But they lose sight of the verification of the deformation parameters' tensor characteristics, which is one of the necessary conditions for continuum mechanics analysis. The other researches achieve rock mass deformation parameters'REV by numerical experiments and verify their tensor characteristics, while they omit the study of the equivalent strength parameters that are paid more attention in engineering. And the sizes of strength parameters' REV are not always the same as deformation parameters' REV. There are even also some researchers that just study the mechanical parameters' REV only in one direction.
The thesis attempted to solve the issues mentioned above, and the project of underground water sealed caverns, national strategic reserve for oil, Huangdao, in Shandong Province, is taken as an example to study the granite gneiss mechanical parameters REV. Firstly, the formation and evolution processes of major tectonic system were analyzed in the interesting area. And the discontinuities are classified by the development scale and engineering geological significance. The forth-class (Class IV) discontinuities, main factor of rock mass's integrity, were researched in detail, and the structure type of granite gneiss was determined based on the forth-class discontinuities' development characteristics. And then according to the discontinuities data obtained from field investigation and borehole camera technique, the superior joint groups were found and geometric elements' probability distribution models for each group were statistically analyzed. On this basis, discontinuity network simulation was conducted with Monte-Carlo mathematic method, and the structure model of granite gneiss was obtained, which laid a foundation for the further study of its mechanical parameters REV's anisotropy. Secondly, the suitability of UDEC (Universal Distinct Element Code) software to carry out numerical experiments was verified and made it as the main research means in this thesis. From the center of the obtained granite gneiss structure model, different sizes of square samples with side length of lm,2m,3m...14m were chosen to conduct triaxial numerical compression experiments under different confining pressures. And the sizes of equivalent deformation parameters (elastic modulus and Poisson's ratio) REV and equivalent strength parameters (cohesion and friction angle) REV of granite gneiss were finally achieved. The results indicated that each mechanical parameter have a distinct REV size. And then, the mechanical properties in different directions (30°,60°,90°,120°,150°) of the structure model were also analyzed in the same research thought, and the results revealed that there were various REV sizes in different directions for each mechanical parameter. Namely, mechanical parameters' REV indeed had an anisotropic characteristic. According to the mechanical parameters' coefficients of variation (CV) for each sample in various directions, their final REV sizes were determined. Lastly, the tensor characteristic of equivalent deformation parameters was analyzed. Based on this, the elastic compliance matrix and the minimum size for granite gneiss equivalent continuum mechanical analysis was obtained. Through the researches of mechanical parameters REV's anisotropy and equivalent deformation parameters'tensor characteristic, some common ground in essence between them was found, and their relation and difference were clearly posed. Finally, the necessary research contents and logical order for equivalent continuum mechanics analysis were determined.
The main works and achievements in this thesis are as follows.
1. Granite gneiss structure model
(1) Formation and evolution of discontinuities
Hongyashan Fault, Laojuntashan Fault, Qianmaliangou Fault, Sunjiagou Fault and Liuhuapo Fault, brittle ones, are the main tectonic system in research area. According to the analysis of regional tectonic evolution processes, these brittle faults were generally produced in Mesozoic intraplate activation phase, when Yanshan movement was the dominant tectonic movement influenced by the Pacific Plate subduction to northwest (NW) or west (W).
(2) Classification of the discontinuities
Qianmaliangou Fault, Laojuntashan Fault and Sunjiagou Fault, belonging to the first-class (Class Ⅰ) discontinuities, are the three large-scaled faults close to the engineering site. F3fault crosses all the proposed storage caverns and F4fault lying on the edge of caverns constitutes the boundary condition of in-situ stress field analysis, and they can be referred as to the second-class (Class Ⅱ) discontinuities. F1, F2, F7, F8, F9faults are small-scaled faults or fracture zones, they are the third-class (Class Ⅲ) discontinuities of the project. There are a large number of tectonic joints, dyke intrusion joints and substance differentiation planes developing in granite gneiss, they can be cataloged to forth-class (Class IV) discontinuities. And the fifth-class (Class V) discontinuities are the gneissic schistosities of the intact rock. The development characteristics of the forth-class discontinuities reflect the integrity of granite gneiss and are the major basis for the structure type classification, which control the deformation and failure modes of the rock mass.
(3) Structure type and numerical model of granite gneiss
F3, F4and F8fault with weak mechanical properties cut the granite gneiss into faulted structure type (Ⅰ.1), the first-class type. And it is further cut by the secondary discontinuities, tectonic joints and dyke intrusion joints with hard mechanical properties, into intermitted structure type (Ⅱ.2), the second-class type. Granite gneiss with the intermitted structure type has eminent scale dependent that the mechanical properties are close related to the size of the rock mass. Based on the three superior joints groups with steep dips, the numerical model of the rock mass is constructed with Monte-Carlo mathematic method considering four major geometric elements such as dip directions, dips, trace lengths and spaces.
2. Suitability of the UDEC software for numerical experiment
(1) Reliability of the deformation parameters obtained by UDEC
Taking the regular structure rock mass with two orthogonal joints as an example, the reliability of deformation parameters obtained by UDEC software is verified by contrasting the analytic solution and numerical solution of the elastic compliance matrix in different directions. And the numerical solutions agree well with the analytic solution. The curve shapes of elastic modulus and Poisson's ratio variation with research directions are similar to an ellipse. While the curve shape of shear modulus is a circle, namely the value of it does not change with the direction.
(2) Reliability of the strength parameters obtained by UDEC
Taking the rock mass with one group of discontinuity as an example, its compressive strengths are calculated by Jaeger's strength theory and UDEC software on the conditions that the discontinuity's angle is0,15,30...and90degree. The numerical solutions are close to the numerical solutions in each case and the relative errors are less than one percent except when the discontinuity angle is75degree. In that case, the numerical solution is much larger than the analytic solution, and the error reaches to one hundred and ten percent. The reason is that the displacement boundary conditions on upper and lower model edges limit the freedom of the rock mass's deformation and cause the failure of the rock block near the discontinuity. Therefore, the rock mass's strength becomes higher. In addition, the strength parameters of intact rock obtained by triaxial numerical compression tests using UDEC software are compared with the laboratory results.
3. Anisotropy of mechanical parameters REV
(1) Scale dependent and mechanical parameters REV
From the center of the obtained granite gneiss structure model (20m×20m), different sizes of square samples with side length of lm,2m,3m...14m were chosen to conduct triaxial numerical compression experiments under different confining pressures. The mechanical parameters of each rock mass sample can be achieved by numerical calculation results and the scale dependent rules and REV sizes can be determined. The fluctuation of elastic modulus(Ex, Ey), Poisson's ratio (vxy, vyx) and internal friction angle(φ) decreases with the sample size increasing, and the corresponding size length of samples are respectively are5m,2m,5m,3m,6m when they become stable. The results indicated that each mechanical parameter has a distinct REV size. So the meaning of REV's object must be clearly expressed.
(2) Anisotropy of mechanical parameters REV
The mechanical properties in different directions (30°,60°,90°,120°,150°) of the structure model were also analyzed in the same research thought, and the results revealed that the fluctuation of mechanical parameters (Exy, Eyx, vxy, vyx an φ) all decrease and finally are stable with size increasing. But there were various REV sizes in different directions for each mechanical parameter. Namely, the mechanical parameters' REV did have an anisotropic characteristic. According to the mechanical parameters' coefficients of variation (CV) for each sample in various directions, their final REV sizes were determined.
4. Analysis of equivalent continuum properties of granite gneiss based on REV's anisotropy
(1) Tensor characteristics of the deformation parameters
Based on the above researches in this thesis, tensor characteristics of the deformation parameters are analyzed. When the sample size reaches6m×6m, the shapes of deformation parameters' fitting curves are similar to ellipse and the difference between long axis and short axis is little, which indicates that the anisotropic feature of deformation parameters is not eminent. The numerical solutions of elastic modulus (Ex, Ey) almost all fall on the fitting curves and the errors are small. While the numerical solutions of Poisson's ratio (vxy, vyx) deviate from the fitting curves and have relatively larger errors. But the fitting errors of the equivalent elastic compliance matrix for granite gneiss deduced by them are acceptable after the sample size reaches6m×6m. The value of the error is close to five percent, less than ten percent (the allowable error), therefore, the equivalent elastic modulus (Ex, Ey) and Poisson's ratio (vxy, vyx) of granite gneiss can be approximately represented in tensor form. Finally the minimum size, 6m×6m, for granite gneiss equivalent continuum mechanical analysis was obtained.
(2) The principles of equivalent continuum mechanical analysis for rock mass
The research of mechanical parameters REV's anisotropy is in essence to determine the rock mass size in which the parameters in different directions are all stable. The necessary condition that deformation parameters can be expressed in tensor form for equivalent continuum analysis is in essence to determine the rock mass size in which the compliant matrixes in different directions are all stable and its fitting error is within the allowable range. The compliant matrix is calculated by deformation parameters, so the fact that rock mass compliant matrixes in different directions reach stable means that deformation parameters in different directions reach stable. Therefore, the research of equivalent continuum properties contains the research of deformation parameters REV's anisotropy. Through the above analysis, we can find that there is some common ground in essence between the researches of mechanical parameters REV's anisotropy and deformation parameters tensor characteristics. Namely, they both need to carry out the study about the anisotropy of deformation parameters REV. The difference between them is that the former includes the research of strength parameters REV, while the latter demand the error analysis of the equivalent compliance matrix. According to their relation and differences, the principle of equivalent continuum mechanical analysis for rock mass is proposed. The equivalent deformation parameters'tensor characteristics must be firstly researched, and then the strength parameters REV and its anisotropy. The larger one of them can be referred as to the minimum size for equivalent continuum mechanical analysis.
Some benefit conclusions have been drawn through the research in this thesis. Each mechanical parameter has a distinct REV size, so the meaning of REV's object must be clearly expressed. The sizes of the same mechanical parameter REVs in different direction are various, the anisotropy of REV must be considered during determination of sizes of mechanical parameters REV. There are some common ground in essence between the researches of mechanical parameters REV's anisotropy and deformation parameters tensor characteristics, and the equivalent continuum analysis for rock mass must conform to certain principle. There are two innovations in this thesis. One is that the anisotropy of mechanical parameters REV is posed and researched by numerical experiments and the final REV size for each parameter is determined according to its coefficient of variation (CV) of each sample in different directions. The other is that the relationship between the researches of mechanical parameters REV's anisotropy and deformation parameters tensor characteristics is discussed and the principle of equivalent continuum mechanical analysis for rock mass is proposed.
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