| Rock mass is defined as a geological body with particular composition and structure. It was formed in long geologic period and hosted in a certain geological environment. Natural jointed rock mass usually contains different types of discontinuities such as faults, joints, fractures and bedding planes. These discontinuities intersect, cutting rock mass into intact rocks with different shapes, sizes and components. The mechanical parameters of this complicate rock structure currently remain unclear. These parameters are crucial in the analysis, evaluation and design of practical rock engineering, and thus should not be excluded in theoretical research of rock mechanics. Investigation on the mechanical properties is a step toward obtaining proper strength and deformability parameters for jointed rock mass.Due to the existing discontinuities, mechanical parameters of jointed rock mass are featured with inhomogeneity, anisotropy and scale effect. Scale effect is an essential characteristic of rock mass mechanical parameters. To obtain these parameters, rock mass samples are usually tested. When these samples contain only a few joints, the sample parameter varies a lot from one to another, reflecting the inhomogeneity of rock mass. If sample size increases, more joints will be included and the sample mechanical parameters will decrease. Beyond a certain volume, rock mass parameters will not change significantly with respect to effect of fractures, and then rock mass can be treated as equivalent continuum material. This minimum rock mass volume is defined as "Representative Elementary Volume"(REV). REV can be used as an element volume to represent the equivalent property of a statistically homogeneous rock mass that contains a large number of joints. Methodology of equivalent continuum theory incorporated with REV mechanical property could chiefly simplify the analysis of jointed rock engineering, and thus it becomes a significant approach to evaluate stability of large-scale engineering rock mass.The fracture system should be first established to explore scale effect of jointed rock mass mechanical parameters. It is nearly impossible to carry out accurate description for fracture system in rock mass because of the probability, uncertainty and complexity of fractures, as well as the current limitation on fracture measuring technique. Fracture network simulation is an effective way to study on rock mass fracture system. Monte-Carlo simulation used in this method predict geometrical distribution of fractures in rock mass by similar probabilistic distribution of fracture geometrical parameters observed on natural or man-made outcrop.Several foreign and domestic scholars studied on stochastic fracture network simulation. The deficiencies of domestic researches in this area are as follow:a. there is a lack of reliability evaluation on fracture network model; b. little research has been done on further engineering application of fracture network model. Generated fracture network model was used to determine potential failure plane or unstable block of rock slope, however, effect of similar engineering application is not satisfactory. That is because the simulated fractures and natural fractures are not one-to-one correspondence. Instead, they only featured with similar probabilistic distribution. Owing to the probabilistic nature of simulated fracture network, it is a fantastic way to investigate macro mechanical parameters of jointed rock mass based on3D fracture network model, and then evaluate stability of engineering rock mass by the obtained mechanical parameters.Approaches to study on scale effect of rock mass mechanical parameters include in situ tests, analytical methods and numerical experiments. In situ tests are difficult to use in scale effect analysis in practice. That is because in situ tests are generally expensive and hard to perform. Analytical methods also have some restrictions in practical use because of the simplified joint conditions. The most operational way to explore scale effect of rock mass mechanical parameters should be numerical experiments. By this technique, complicated fracture system as well as samples with different sizes can be considered conveniently. Several explorations were done in this area by finite element method in two dimensions. Finite element method is problematic to simulate large displacements and rotations existing in jointed rock mass because it is based on continuum mechanics. Discontinuum method such as distinct element method is appropriate to be used to determine rock mass properties. Therefore, it is necessary to conduct research on scale effect of rock mass mechanical parameters by3D distinct element method.Procedures to build and validate3D stochastic fracture geometry model were discussed on the basis of in situ geological engineering investigation and fracture data measurement. Then, numerical experiments in3DEC were performed to look into scale effect and anisotropy of rock mass mechanical parameters by incorporating modified mechanical parameters of fictitious joints, physical and mechanical parameters of intact rock as well as self-defined constitutive model of real joints. The whole methodology was applied in scale effect analysis of jointed rock mass located in exit section of the diversion tunnel of Yujian River Reservoir in Guizhou province, China, and REV size was determined. Simultaneously, relationship between rock mass mechanical parameters and fracture tensor, as well as an elastic orthotropic constitutive model to represent the equivalent continuum pre-failure mechanical behavior of the REV size rock mass were built up. Finally, this orthotropic constitutive model was used to evaluate stability of exit section of the diversion tunnel by applying equivalent continuum method. The following research contents can be acquired for the conducted study:(1) Techniques to establish and validate3D stochastic fracture network model were introduced. The major research contents were as follow:a. Mean trace length was estimated by simplifying Kulatilake's equations using distribution of fracture apparent dip angle. Fracture data on an outcrop in Wenchuan area was used to verify the proposed equations and make comparison between estimation methods based on rectangular windows and circular windows. Shortcomings of estimation method based on circular windows were pointed out. b. The same outcrop was used to perform a thorough study on fracture areal density estimation. The research findings indicate that predictions based on the rectangular windows are more accurate than that of circular window method, c. Two issues to ensure the reliability of3D stochastic fracture model were proposed. One is to combine the qualitative geological engineering analysis with the quantitative mathematical methods in fracture network simulation, the other one is to validate and modify the generated3D fracture network by measured fracture data. d. Based on the aforementioned theory,3D stochastic fracture network model was established to represent fracture system of jointed rock mass located in the exit section of the diversion tunnel in Yujianhe River Reservoir. This model was then validated by measured fracture data from orientation, mean trace length and ID frequency.(2) Research was carried out to solve demanding problems in3DEC numerical experiment. The problems solved comprise:modeling of finite size joint, improvement of methods to estimate deformability parameters of fictitious joints as well as development of a program to build self-defined joint constitutive model. Fictitious joints that behave as intact rock are introduced to the domain to interact with actual joints so as to create finite size joints in3DEC. According to the procedure, a program to generate fictitious joints was developed by Visual Basic language. To acquire proper parameters for fictitious joints, analytical equations to determine normal stiffness and shear stiffness of fictitious joints were derived theoretically by considering effect of model size, stress boundary condition and geometry distribution of fictitious joints. These equations were then validated by numerical computing cases. Joint constitutive model affect rock mass mechanical properties significantly. A program of self-defined joint constitutive model was developed by FISH language. Through this program, users can define a particular joint constitutive model to represent the stress-strain characteristic of joints in3DEC numerical experiment.(3) Scale effect on mechanical parameters was explored for jointed rock mass located in exit section of the diversion tunnel in Yujian River Reservoir. The following factors are considered in the conducted research:a. To reduce the impact of model location, mean value of mechanical parameters obtained from different locations for the same block size was recognized as the final result of this block size. b. Normal and shear constitutive model of actual joints were built by laboratory test results, and then these constitutive models were used to represent the mechanical property of joints via the aforementioned self-developed program. c. Three stress paths were designed to estimate different mechanical properties in numerical experiments by distinct element method. Finally, scale effect on normalized rock block strength, deformability modulus, shear modulus, bulk modulus and Poisson's ratio were obtained and REV size of18m was determined to represent the mechanical properties of the studied rock mass by observing the variation of the aforementioned curves.(4) Relationship between rock mass strength/deformability parameters and fracture tensor components were developed. The fracture tensor was used to combine the effect of number of fracture sets, intensity, and distributions of orientation and size of the fracture sets. Taking the jointed rock mass located at exit section of the diversion tunnel of Yujian River Reservoir for example, the following relationships were obtained:a. Rock mass strength vs the summation of the fracture tensor components in the two perpendicular directions to the loading direction; b. Rock mass deformability modulus vs the fracture tensor component in the same direction; c. Rock mass shear modulus vs the summation of the fracture tensor components on the same two planes; d. Rock mass bulk modulus vs the first invariant of fracture tensor.(5) Numerical experiment was used to examine anisotropy of mechanical properties of jointed rock mass. The anisotropic mechanical behavior was studied in a more comprehensive way for jointed rock mass located at exit section of the diversion tunnel of Yujian River Reservoir. The REV block size of18m was rotated in every45degree in3D to determine mechanical parameters and fracture tensors in different directions. Anisotropy of fracture system for REV block was evaluated by the obtained fracture tensors. Based on the mechanical parameters estimated in different directions in3D, the principal parameter values, principal directions and tensors were obtained for rock mass mechanical parameters to represent the REV block size properties. Results indicated that mechanical parameters of the studied jointed rock mass featured with orthotropic characteristics.(6) An orthotropic constitutive model was suggested to represent the equivalent continuum pre-failure mechanical behavior of the jointed rock mass located at exit section of the diversion tunnel of Yujian River Reservoir. In this model, effect of joint geometry has been taken into account in terms of fracture tensor components; the scale-dependent and anisotropic behaviors of the rock mass are incorporated. Another orthotropic constitutive model obtained by anisotropy analysis of REV block size was used to validate the proposed orthotropic constitutive model.(7) Engineering application of the aforementioned study was explored. The3D linear elastic orthotropic constitutive model of REV block size of the studied jointed rock mass was used to investigate the elastic deformability characteristic of exit section of this diversion tunnel. The displacement distribution in different sections under lateral earth pressure coefficient of0.3,0.5,0.75,1.0,1.25and1.5was obtained. In addition, a fully discontinuum method was used as the second method to evaluate stability around the exit section of diversion tunnel. The displacement distribution pattern resulted from this approach was found to be influenced largely by the spatial distribution of the fractures compared to that resulted from the equivalent continuum method. For all cases studied, no failure zone was found around the tunnel and the displacements were small, which is coinciding with the real tunnel stability condition.The following innovation points can be reported for the conducted study:(1) Methods to estimate essential geometrical parameters in fracture network simulation were studied, simultaneously, procedure to validate the fracture model was proposed. Equations of mean trace length were modified by considering distribution of fracture apparent dip angle and corrected relative frequency of each trace appearing on the outcrop. Fracture data on an outcrop in Wenchuan area was used to validate the proposed equations and make comparison between estimation methods based on rectangular windows and circular windows respectively for mean trace length and areal density. To enhance the reliability of3D fracture network simulation, the generated fracture system was validated by measured fracture data from orientation,1D frequency and mean trace length.(2) Problems in finite size joints modeling were solved; methods were improved to estimate deformability parameters of fictitious joints. Fictitious joints that behave as intact rock are introduced to the domain to interact with actual joints so as to create finite size joints in3DEC. According to the procedure, a program to generate fictitious joints was developed by Visual Basic language. To acquire proper parameters for fictitious joints, analytical equations to estimate normal stiffness and shear stiffness of fictitious joints were derived theoretically by considering influence factors of model size, stress boundary condition and geometry distribution of fictitious joints.(3) A program was developed to create self-defined joint constitutive model. Constant normal stiffness and shear stiffness were usually used to represent the stress-strain features of fractures in numerical simulation of jointed rock mass. This is not applicable in general cases. Secondary development of3DEC was made by FISH language to develop a program of self-defined joint constitutive model. Basic procedure of this program and methods to avoid unexpected results were introduced.(4) Effect of fracture system on mechanical property of jointed rock mass was investigated systematically. By combing3D fracture network model with3D distinct element method, research on scale effect of mechanical parameters for jointed rock mass was fully conducted. The fracture tensor was used to combine the effect of joint geometry parameters. Relationships between fracture tensor and rock mechanical parameters were developed. Anisotropy of rock mass mechanical properties was then studied by rotating the numerical model in different directions in3-D. On the basis of the aforementioned research, an orthotropic constitutive model was proposed and applied in the stability evaluation of rock engineering.
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