| 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 discontinuitiesHongyashan 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 discontinuitiesQianmaliangou 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 gneissF3, 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 UDECTaking 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 UDECTaking 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 REVFrom 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 REVThe 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 parametersBased 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 massThe 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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