A Study On The Representative Elementary Volume Of Fractured Rock Masses And The Size Effects Of Mechanical Properties

The selection of research topic of this dissertation is based on significant item of Natural Science Fund [50239070] "Study on seepage characteristic and mechanical property of fractured rock masses ", and its purpose is to present a comprehensive description of the representative elementary volume (REV) of fractured rock masses, including the general mechanical implications of REV, the relationship between REV and mechanical models as well as mechanical parameters, the estimation of REV, the size effects of mechanical properties, and the REV-based finite element method. The major contributions of this paper are summarized as follows.The general mechanical meaning of REV is analyzed in detail by discussing its definition and then REV is considered as a fundamental conception in rock mechanics, which demonstrates the dialectic relationships of microstructure-macrostructure, discreteness-continuousness and randomness-determinacy and it reflects the size effects of mechanical properties. The close relationship between REV of fractured rock masses and the choice of rock mechanical models as well as the selection of mechanical parameters are elaborated in this dissertation. It is shown that REV can be regarded as a quantitative criterion for choosing equivalent continuum approach or discrete approach to solving rock engineering problems and for selecting appropriate parameters of the equivalent continuum models. For any rock engineering, large discontinuities (e.g., faults, large fissures, etc.) in the region of interest should be investigated and their mechanical properties should be established separately. As a result, the rock region is divided into several sub-regions by these large discontinuities. In each sub-region, the fracture information is investigated by in-situ measurements and the REV estimation method is applied to determine the REV size of that sub-region. If REV exists and is significantly smaller than the volume of the fractured rocks being investigated, equivalent continuum models are a suitable choice for analysis. Otherwise, discrete models should be applied. In additon, the following three major problems related to the mechanical parameters of the equivalent continuum models require further development: (1) evaluation of the REV size of fractured rock masses; (2) determination of the equivalent continuum properties of rock masses within REV; and (3) determination of the variation of the mechanical properties with the volume of the rock masses so as to provide a criterion for assigning appropriate mechanical parameters to the rock mass element with its volume smaller than the REV.Three methods, called Energy Superposition Method (ESM), Geological Statistic Method (GSM) and Numerical Simulation Method (NSM) are proposed to estimate theREV sizes of rock masses with stochastic fracture network system. Especially, modeling techniques of fracture network system is introduced in detail and Monte-Carlo simulation approach is employed to generate fracture nework system within rock masses for estimating the REV sizes of fractured rock masses. And the comprehensive scheme of numerical simulation method (NSM) based on modeling techniques of fracture network system is also presented. And the effectiveness of these three methods is demonstrated by explanatory examples respectively. The analysis results indicate that three methods are all effective for estimating the REV sizes of fractured rock masses. The numerical approach has the advantage of being able to consider the influence of irregular fracture system geometry and complex constitutive models of rock matrix and fractures. Therefore, numerical simulation method (NSM) based on modeling techniques of fracture network system is suggested to be the main approach to estimating the REV of fractured rock masses.Combined with modeling techniques of fracture network system, numerical method is applied to investigate the REV of fractured rock masses and the size effects of several important indices of rock mechanical properties, such as elastic modulus, compression strength and shear strength. Plenty of numerical tests are performed and computation results indicate that all the indices vary with the size of fractured rock masses. But when the size of rock mass is increased up to a certain value, they all approach constant values. Firstly, the Monte-Carlo simulation approach is used to generate the discrete fracture network models, based on distribution functions of location, orientation, trace-length and density of fractures. Considering a two-dimensional rock mass, which contains two sets of stochastic fractures, eight series of discrete fracture network models are generated by individual Monte-Carlo simulation and they have the same fracture statistics. The numerical analysis results indicate that the equivalent elastic moduli of eight discrete fracture network models are almost same and the REV size of this fractured rock masses is suggested to be 7mx7m. In addition, one of the eight discrete fracture network models are rotated in anticlockwise direction with a 30° intervals(0° ,30° ,60° ,90° ,120° ,150° ) and the anisotropy of elastic modulus of fractured rock masses is also analyzed. For the same discrete fracture network model, numercal tests are alse conducted to investigate the size effects of cohesion, friction angle and compression strength.To reflect the size effect of mechanical properties of fractured rock masses, a new approach named REV-based finite element method (FEM) is proposed and applied to simulate the mechanical behavior of rock masses. In rock engineering practices, researchers and engineers usually ignore the size effects of mechanical parameters, and the equivalent mechanical parameters are assigned to the whole geological region regardless of the FEM mesh sizes. This unreasonable treatment often leads to error results of FEM analysis. In fact, FEM meshes have significant impact on mechanicalparameters of rock masses. Firstly, to save computational cost for large or very large-scale problems, there generally exist elements with their sizes beyond the REV size of the considered region. The equivalent continuum properties should be determined within REV and the uniform parameters should be assigned to these elements. Secondly, to ensure reasonable calculation precision in some critical sub-regions, there also exist some elements with their sizes smaller than the REV. For these elements, special attention must be paid to the size effect of the rock mechanics parameters, and it is necessary to adopt different parameters for elements with distinct sizes. REV-based FEM is established exactly to solve these two problems. REV-based FEM is used to model the cavern excavation in a two-dimensional rock mass, and the analysis results demonstrate that the total displacement derived from traditional FEM is obviously larger than that derived from REV-based FEM. The underlying reason is that in traditional FEM, the same mechanical parameters are adopted for all elements regardless of their distinction in sizes, which essentially weakens the mechanical property of the rock mass. This implies that REV-based FEM should be more comprehensive and rational than traditional FEM, due to disregard of the size effects of mechanical parameters in the latter approach.