<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>This thesis studies the effect of-floor slabs on the static and dynamic behaviour of the shear wall structure. A single component has been analysed using the 'Matrix Transfer' technique along with Vlaspv's thin walled elastic beam theory. Experimental verification was done on a small scale plexiglas eight storey model in the form of a channel section for both static and dynamic loading. The thesis also deals with the ·analysis of the nonplanar shear walls coupled through floor beams subjected to static loading. The continuum approach along with Vlasov's theory h&s been used in the analysis. Experimental verification was done on a small scale plexiglas model in the form of two equal angles connected by eight floor beams at equal spacing.</p> / Thesis / Master of Engineering (ME)

The behavior of jointed rock mass is very complex and is influenced by many factors such as location of joints, joint frequency, joint orientation and joint strength. A thorough review of literature on different aspects of jointed rock mass indicate that the discontinuities or planes of weakness present in rock mass significantly influence its behavior. Numerous experimental tests were conducted to study the behavior of natural as well as artificial joints in rocks. Laboratory tests are time consuming and give results applicable to specific joint fabric and confining pressure. Numerical methods are the best alternative to laboratory tests to study the behavior of jointed rock mass. With the advent of computers numerical methods of analysis have become very popular, as they are highly flexible and can represent all complex geometries and material behavior. The accuracy of a numerical model depends upon the how well constitutive relations for the jointed rock mass are defined in the analysis. Empirical relationships for describing the mechanical behavior of discontinuities obtained from scaling the laboratory data is crucial unresolved problem, which will affect the quality of results obtained. One more important aspect in the numerical model is strength criteria used for jointed rock mass. The applicability of existing strength criteria to a particular jointed rock has to be carefully examined before they are used. Equivalent continuum approach simplifies the modeling of jointed rock mass as the joints are not modeled separately. Instead in equivalent continuum approach the jointed rock mass is represented by an equivalent continuum whose properties are defined by a combination of intact rock properties and joint properties. The accuracy of this kind of modeling depends upon the relationships used to define the jointed rock mass properties as a function of intact rock properties and joint properties. In the present study, an effort has been made (i) to establish empirical relations to define the properties of jointed rock mass as a function of intact rock properties and joint factor (ii) to develop a numerical model based on equivalent continuum approach using the empirical relations derived above, for easy and efficient modeling of jointed rock mass (iii) comparison of existing strength criteria for jointed rock masses using the equivalent continuum model developed above (iv) Modeling of joints explicitly and comparing these results with the equivalent continuum model results. Empirical relationships expressing the uniaxial compressive strength and elastic modulus of jointed rock as a function of corresponding intact rock properties and joint factor have been derived based on the statistical analysis of large amount of experimental data of uniaxial and triaxial tests collected from the literature. The effect of joints in the jointed rock is taken in to account by the joint factor. A comparative study of the empirical relationships arrived by the above analysis has been made to choose the best relation for the numerical analysis. Empirical relationships thus arrived for jointed rock mass are used in the equivalent continuum approach to represent the jointed rock properties as a combination of intact rock properties and joint factor. Equivalent continuum model developed is thoroughly tested, validated and applied for single, multiple and block jointed rocks. The equivalent continuum model developed has been applied for analysis of the power cavern for Shiobara power station. Different strength criteria available for jointed rock namely Mohr-Coulomb, Hoek and Drown, Yudhbir et al. and Rarnamurthy are incorporated in the equivalent continuum model to evaluate their applicability for jointed rock masses. Ramarnurthy's strength criterion gives the best values of failure stress for almost all the test cases and hence used in the equivalent continuum model. Alternatively, the joints in jointed rock mass are represented explicitly using interface element in the nonlinear finite element analysis. The explicit finite element model has been tested and validated using the experimental stress strain curves and failure stress values. Comparison of results obtained using equivalent continuum analysis and explicit modeling of joints has been given in the form of stress strain curves and failure stress plots for jointed rock masses along with the experimental results. Some of the major conclusions from the present study are as follows. Statistical relationships arrived to express the properties of the jointed rock as a function of intact rock and joint factor give a fair estimate of jointed rock in the absence of experimental data. Equivalent continuum model developed using statistical relations arrived above simplifies the numerical modeling of jointed rock to a large extent and also gives a fair estimate of jointed rock behavior with minimum input data. From the equivalent continuum analysis of Shiobara power cavern, it can be concluded that this approach is very advantageous for modeling highly discontinuous systems provided the joint factor is estimated properly so that it represents the real fabric of the joints present in the system. Comparison of different strength criteria shows that Ramamurthy's strength criterion is the best for jointed rocks. When the rock mass has one or two major joints it is advantageous to model it explicitly so that the behavior of the joint can be studied in detail. Explicit representation of the joints in the finite element analysis gives a lair estimate of the zones most susceptible to failure in a jointed rock. From comparison of experimental values, equivalent continuum model results and the explicit joint model results, it can be concluded that results obtained using equivalent continuum model are nearest to the experimental results in almost all the cases.

The vast majority of oil and gas reserves are trapped in fractured carbonate reservoirs. Most carbonate reservoirs are naturally fractured, with fractures ranging from millimeter- to kilometer-scale. These fractures create complex flow behaviors which impact reservoir characterization, production performance, and, eventually, total recovery. As we know, bridging the gas from plug to near-wellbore, eventually to field scales, is a persisting challenge in modeling Naturally Fractured Reservoirs (NFRs). This dissertation will focus on assessing the fundamental flow mechanisms in fractured rocks at the plug scale, understanding the governing upscaling parameters, and ultimately, developing fit-for-purpose upscaling tools for field-scale implementation. In this dissertation, we first focus on the upscaling of rock fractures under the laminar flow regime. A novel analytical model is presented by incorporating the effects of normal aperture, roughness, and tortuosity. We then investigate the stress-dependent hydraulic behaviors of rock fractures. A new and generalized theoretical model is derived and verified by a dataset collected from public experimental resources. In addition, an efficient coupled flow-geomechanics algorithm is developed to further validate the proposed analytical model. The physics of matrix-fracture interaction and fluid leakage is modeled by a high-resolution, micro-continuum approach, called extended Darcy-Brinkman-Stokes (DBS) equations. We observe the back-flow phenomena for the first time. Machine learning is then implemented into our traditional upscaling work under complex physics (e.g., initial and Klinkenberg effects). We finally consolidate the lab-scale upscaling tools and scale them up to the field scale. We develop a fully coupled hydro-mechanical model based on the Discrete-Fracture Model (DFM) in fractured reservoirs, in which we incorporate localized effects of fracture roughness at the field-scale.

La modélisation des massifs rocheux fracturés est un problèmes important dans de nombreux secteurs industriels, y compris, mais sans s'y limiter à l'exploitation pétrolière et gazière. Dans la littérature, les roches fracturées sont reconnues comme des milieux à double porosité et double perméabilité dans lesquels le réseau de fractures fournit la perméabilité primaire et la matrice rocheuse la perméabilité secondaire. L'idée de la dissociation de l'écoulement à l'intérieur du réseau de fractures et de la matrice,la double perméabilité, est toujours contestée pour les réservoirs fracturés. De nombreuses contributions sur cette question ont été présentées dans la littérature et les méthodes utilisées pourraient être classées dans deux approches principales : approches continues et discontinues. Chaque approche a ses avantages et ses limites. Pour surmonter les limites en gardant les avantages de ces deux approches, une approche nommée Embedded Fracture Continumm Approach (EFCA) qui emprunte le concept du modèle continu et intègre également l'effet des fractures explicites est considérée dans cette thèse. L'idée principale de cette approche repose sur le concept de la « cellule fracturée » représentant un milieu poreux qui a ses propres propriétés calculées à partir des propriétés de la matrice poreuse et des fractures qui la traversent. Le code de calcul développé dans le cadre de ce travail est basé sur la bibliothèque source DEAL.II. L'exactitude de l'EFCA a été étudiée à travers de différents tests. Plusieurs applications traitées dans ce travail comme la détermination des propriétés hydro-mécaniques effectives d'un site réel, estimation de la production de puits dans laquelle les fractures sont modélisées explicitement, démontrent la performance de l'EFCA dans la modélisation des roches fracturées ainsi que l'effet de la double porosité et de la double perméabilité aux comportements des réservoirs fracturés. / Fractured rock masses modeling is a challenge issue in many field of industry including but not limited to oiland gas exploitation. In the literature, fractured rock masse are in many cases recognized as double permeability medium in which fracture network provides the primary permeability and rock matrix plays asthe second one. The idea of dissociation of flow inside the fracture network and the matrix, the double permeability, is still challenged for fractured reservoirs. Numerous contributions on this issue have been presented in the past could be cast in two main approaches: continuum media approach and discontinuous approach. Each approach has its advantages and limitations. To overcome the limitation and to take advantage of these two approaches, the Embedded Fractured Continuum Approach (EFCA) which borrows the concept of continuum models and also incorporates the effect of explicit fractures is considered in this thesis. The principal idea of this approach lies on the concept of fracture cell representing a porous medium that has their own properties calculated from the properties of porous matrix and fractures intersecting it.The development in this work was conducted by using the library source code DEAL.II. The accuracy of EFCA was investigated through different verifications. Through some applications: determination of effective hydro-mechanical properties of an actual site, estimation of well production in which necessary fractures are modeled explicitly, we demonstrate the performance of the EFCA in the modeling fracture drock masses as well as the effect of double porosity and double permeability on behaviours of fractured reservoirs.