<p>The equivalent continuum approach uses equivalent propertiesof rock mass as the input data for a continuum analysis. Thisis a common modeling method used in the field of rock mechanicsand hydrogeology. However, there are still unresolvedquestions; how can the equivalent properties be determined andis the equivalent continuum approach suitable for modeling thediscontinuous fractured rock mass.</p><p>The purpose of this paper is to establish a methodology todetermine the equivalent hydraulic and mechanical properties offractured rock masses by explicit representations of stochasticfracture systems, to investigate the scale-dependency of theproperties, and to investigate the conditions for theapplication of the equivalent continuum approach for thefractured rock masses. Geological data used for this study arefrom the site characterization of Sellafield, Cumbria, UK. Aprogram for the generation of stochastic Discrete FractureNetwork (DFN) is developed for the realization of fractureinformation and ten parent DFN models are constructed based onthe location, trace length, orientation and density offractures. Square models with the sizes varying from 0.25 m× 0.25 m to 10 m × 10 m are cut from the center ofthe each parent network to be used for the scale dependencyinvestigation. A series of the models in a parent network arerotated in 30 degrees interval to be used for investigation oftensor characteristic. The twodimensional distinct elementprogram, UDEC, was used to calculate the equivalentpermeability and compliance tensors based on generalizedDarcy’s law and general theory of anisotropic elasticity.Two criteria for the applicability of equivalent continuumapproach were established from the investigation: i) theexistence of properly defined REV (Representative ElementaryVolume) and ii) existence of the tensor in describing theconstitutive equation of fractured rock The equivalentcontinuum assumption cannot be accepted if any one of the abovetwo criteria is not met. Coefficient of variation and meanprediction error is suggested for the measures toquantitatively evaluate the errors involved in scale dependencyand tensor characteristic evaluation.</p><p>Equivalent permeability and mechanical properties (includingelastic modulus and Poisson’s ratios) determined onrealistic fracture network show that the presence of fracturehas a significant effect on the equivalent properties. Theresults of permeability, elastic moduli and Poisson's ratioshow that they narrow down with the increase of scale andmaintain constant range after a certain scales with someacceptable variation. Furthermore, Investigations of thepermeability tensor and compliance tensor in the rotated modelshow that their tensor characteristics are satisfied at acertain scale; this would indicate that the uses of theequivalent continuum approach is justified for the siteconsidered in this study.</p><p>The unique feature of the thesis is that it gives asystematic treatment of the homogenization and upscaling issuesfor the hydraulic and mechanical properties of fractured rockswith a unified approach. These developments established a firmfoundation for future application to large-scale performanceassessment of underground nuclear waste repository byequivalent continuum analysis.</p><p><b>Keywords :</b>Equivalent continuum approach, Equivalentproperty, Representative Elementary Volume (REV), DistinctElement Method, Discrete Fracture Network (DFN)</p>

The equivalent continuum approach uses equivalent propertiesof rock mass as the input data for a continuum analysis. Thisis a common modeling method used in the field of rock mechanicsand hydrogeology. However, there are still unresolvedquestions; how can the equivalent properties be determined andis the equivalent continuum approach suitable for modeling thediscontinuous fractured rock mass. The purpose of this paper is to establish a methodology todetermine the equivalent hydraulic and mechanical properties offractured rock masses by explicit representations of stochasticfracture systems, to investigate the scale-dependency of theproperties, and to investigate the conditions for theapplication of the equivalent continuum approach for thefractured rock masses. Geological data used for this study arefrom the site characterization of Sellafield, Cumbria, UK. Aprogram for the generation of stochastic Discrete FractureNetwork (DFN) is developed for the realization of fractureinformation and ten parent DFN models are constructed based onthe location, trace length, orientation and density offractures. Square models with the sizes varying from 0.25 m× 0.25 m to 10 m × 10 m are cut from the center ofthe each parent network to be used for the scale dependencyinvestigation. A series of the models in a parent network arerotated in 30 degrees interval to be used for investigation oftensor characteristic. The twodimensional distinct elementprogram, UDEC, was used to calculate the equivalentpermeability and compliance tensors based on generalizedDarcy’s law and general theory of anisotropic elasticity.Two criteria for the applicability of equivalent continuumapproach were established from the investigation: i) theexistence of properly defined REV (Representative ElementaryVolume) and ii) existence of the tensor in describing theconstitutive equation of fractured rock The equivalentcontinuum assumption cannot be accepted if any one of the abovetwo criteria is not met. Coefficient of variation and meanprediction error is suggested for the measures toquantitatively evaluate the errors involved in scale dependencyand tensor characteristic evaluation. Equivalent permeability and mechanical properties (includingelastic modulus and Poisson’s ratios) determined onrealistic fracture network show that the presence of fracturehas a significant effect on the equivalent properties. Theresults of permeability, elastic moduli and Poisson's ratioshow that they narrow down with the increase of scale andmaintain constant range after a certain scales with someacceptable variation. Furthermore, Investigations of thepermeability tensor and compliance tensor in the rotated modelshow that their tensor characteristics are satisfied at acertain scale; this would indicate that the uses of theequivalent continuum approach is justified for the siteconsidered in this study. The unique feature of the thesis is that it gives asystematic treatment of the homogenization and upscaling issuesfor the hydraulic and mechanical properties of fractured rockswith a unified approach. These developments established a firmfoundation for future application to large-scale performanceassessment of underground nuclear waste repository byequivalent continuum analysis. <b>Keywords :</b>Equivalent continuum approach, Equivalentproperty, Representative Elementary Volume (REV), DistinctElement Method, Discrete Fracture Network (DFN) / NR 20140805

<p>QC 20140428</p>

In this thesis, the effects of size and stress on permeability, deformability and strength of fractured rock masses are investigated. A comparison study was carried out to examine the effects of considering, or not considering, the correlation between distributions of fracture apertures and fracture trace lengths on the hydro-mechanical behavior of fractured rocks. The basic concepts used are the fundamental principles of the general theory of elasticity, Representative Elementary Volume (REV), the tensor of equivalent permeability, and the strength criteria of the fractured rocks. Due to the size and stress dependence of the hydro-mechanical properties of rock fractures, the overall effective (or equivalent) hydro-mechanical properties of the fractured rocks are also size and stress-dependent. However, such dependence cannot be readily investigated in laboratory using small samples, and so numerical modeling becomes a necessary tool for estimating their impacts. In this study, a closed-form relation is established for representing the correlation between a truncated lognormal distribution of fracture apertures and a truncated power law distribution of trace lengths, as obtained from field mapping. Furthermore, a new nonlinear algorithm is developed for predicting the relationship between normal stress and normal displacement of fractures, based on the Bandis model and the correlation between aperture and length. A large number of stochastic Discrete Fracture Network (DFN) models of varying sizes were extracted from some generated large-sized parent realizations based on a realistic fracture system description from a site investigation programme at Sellafield, UK, for calculating the REV of hydro-mechanical properties of fractured rocks. Rotated DFN models were also generated and used for evaluation of the distributions of directional permeabilities, such that tensors of equivalent permeability could be established based on stochastically established REVs. The stress-dependence of the permeability and the stress-displacement behaviour were then investigated using models of REV sizes. The Discrete Element Method (DEM) was used for numerical simulation of the fluid flow, deformability properties and mechanical strength behavior of fractured rocks. The results show significant scale-dependency of rock permeability, deformability and strength, and its variation when the correlation between aperture and trace length of fractures are concerned, with the overall permeability and deformability more controlled by dominating fractures with larger apertures and higher transmissivity and deformability, compared with fracture network models having uniform aperture. As the second moment of aperture distribution increases, a fractured rock mass shows more discrete behavior and an REV is established in smaller value of second moment with much larger model size, compared with the models with uniform fracture aperture. When the fracture aperture pattern is more scattered, the overall permeability, Young’s modulus and mechanical strength change significantly. The effect of stress on permeability and fluid flow patterns in fractured rock is significant and can lead to the existence or non-existence of a permeability tensor. Stress changes the fluid flow patterns and can cause significant channeling and the permeability tensor, and REV may be destroyed or re-established at different applied stress conditions. With an increase in the confining stress on the DEM models, the strength is increased. Compared with the Hoek-Brown criterion, the Mohr-Coulomb strength envelope provides a better fit to the results of numerical biaxial compression tests, with significant changes of the strength characteristic parameters occurring when the second moment of the aperture distribution is increased. / QC 20100702

This thesis presents a systematic numerical modeling framework to simulate the stress-deformation and coupled stress-deformation-flow processes by performing uniaxial and biaxial compressive tests on fractured rock models with considering the effects of different loading conditions, different loading directions (anisotropy), and coupled hydro-mechanical processes for evaluating strength and deformability behavior of fractured rocks. By using code UDEC of discrete element method (DEM), a series of numerical experiments were conducted on discrete fracture network models (DFN) at an established representative elementary volume (REV), based on realistic geometrical and mechanical data of fracture systems from field mapping at Sellafield, UK. The results were used to estimate the equivalent Young’s modulus and Poisson’s ratio and to fit the Mohr-Coulomb and Hoek-Brown failure criteria, represented by equivalent material properties defining these two criteria. The results demonstrate that strength and deformation parameters of fractured rocks are dependent on confining pressures, loading directions, water pressure, and mechanical and hydraulic boundary conditions. Fractured rocks behave nonlinearly, represented by their elasto-plastic behavior with a strain hardening trend. Fluid flow analysis in fractured rocks under hydro-mechanical loading conditions show an important impact of water pressure on the strength and deformability parameters of fractured rocks, due to the effective stress phenomenon, but the values of stress and strength reduction may or may not equal to the magnitude of water pressure, due to the influence of fracture system complexity. Stochastic analysis indicates that the strength and deformation properties of fractured rocks have ranges of values instead of fixed values, hence such analyses should be considered especially in cases where there is significant scatter in the rock and fracture parameters. These scientific achievements can improve our understanding of fractured rocks’ hydro-mechanical behavior and are useful for the design of large-scale in-situ experiments with large volumes of fractured rocks, considering coupled stress-deformation-flow processes in engineering practice. / <p>QC 20141111</p>

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