Pour étudier le comportement mécanique des massifs rocheux, en prenant en compte le réseau des discontinuités au sein de la roche intacte, cette recherche a pour objectif la représentation du massif par des modèles géométriques basés sur des relevés de terrain et l'analyse de ces modèles par l'utilisation d'outils informatiques adaptés pour les milieux granulaires. Le premier chapitre fait l'état de l'art des roches fracturées, des méthodes numériques de la mécanique des roches et des approches du calcul de structure d'un tunnel. Ces études conduisent à la proposition d'une méthodologie depuis les recherches in situ jusqu'à la modélisation et l'analyse mécanique, présentée dans le deuxième chapitre. Le massif rocheux est d'abord représenté géométriquement par la distribution de ses discontinuités, et l'utilisation du logiciel RESOBLOK basé sur la méthode du Réseau de Fractures Discrètes. Les modèles mécaniques de massifs rocheux sont ensuite présentés à partir des données sur les études de l'histoire du massif, et des mesures faites sur site et en laboratoire. Les modèles numériques en 3D sont analysés par l'utilisation du logiciel LMGC90 basé sur la méthode de la Dynamique des Contacts Non Réguliers. Les premières applications de la méthodologie sont exposées : la création d'une roche numérique pour simuler un essai de compression triaxiale, et la simulation d'une excavation multi phases d'un tunnel au rocher. La méthodologie proposée a été appliquée sur le marbre blanc de Saint Béat (Haute Garonne, France) et les résultats préliminaires sont donnés dans le chapitre trois. Les réponses mécaniques de la roche numérique sont analysées et son comportement est caractérisé. / Aimed at studying the mechanical behaviour of rock mass and considering the presence of the discontinuity network in the intact rock, this research concentrates on how the rock can be represented in suitable geometrical models, on the basis of site measurements, and then appropriately analysed using computer tools developed for the study of granular media. The first chapter deals with a bibliographical study on fractured rock and tunnel engineering. Different computational methods of rock mechanics are introduced. Simultaneously, three principal approaches for tunnel structural design are recalled. These studies lead to the proposition of a methodology from the in situ investigation to in-door modelling and mechanical analysis, presented in the second chapters. The rock mass is first geometrically represented through the distribution of discontinuities in the rock mass and the use of the RESOBLOK code based on the Discrete Fracture Network method. Mechanical models of rock mass are then presented from the data of historical studies on the rock mass and from laboratory and in situ measurements. The 3D computational models are analysed using the LMGC90 based on the Non Smooth Contact Dynamics method. The first two applications of the methodology are introduced: the generation of the numerical rock for the simulation of the triaxial compression test, and the simulation of multi-phase excavation of rock tunnel. The proposed methodology has been applied on the white marble of Saint Béat (Haute Garonne, France) and the initial results are given in the third chapter. The mechanical responses of the numerical rock mass are analysed and the bulk behaviour of the rock is evaluated.

Radio magnetotellurics (RMT), crosshole ground penetrating radar (GPR), and crosshole electrical resistance tomography (ERT) were applied in a range of hydrogeological applications where geophysical data could improve hydrogeological characterization. A profile of RMT data collected over highly resistive granite was used to map subhorizontal fracture zones below 300m depth, as well as a steeply dipping fracture zone, which was also observed on a coinciding seismic reflection profile. One-dimensional inverse modelling and 3D forward modelling with displacement currents included were necessary to test the reliability of features found in the 2D models, where the forward models did not include displacement currents and only lower frequencies were considered. An inversion code for RMT data was developed and applied to RMT data with azimuthal electrical anisotropy signature collected over a limestone formation. The results indicated that RMT is a faster and more reliable technique for studying electrical anisotropy than are azimuthal resistivity surveys. A new sequential inversion method to estimate hydraulic conductivity fields using crosshole GPR and tracer test data was applied to 2D synthetic examples. Given careful surveying, the results indicated that regularization of hydrogeological inverse problems using geophysical tomograms might improve models of hydraulic conductivity. A method to regularize geophysical inverse problems using geostatistical models was developed and applied to crosshole ERT and GPR data collected in unsaturated sandstone. The resulting models were geologically more reasonable than models where the regularization was based on traditional smoothness constraints. Electromagnetic geophysical techniques provide an inexpensive data source in estimating qualitative hydrogeological models, but hydrogeological data must be incorporated to make quantitative estimation of hydrogeological systems feasible.

>Magister Scientiae - MSc / Deformation of the western part of the Table Mountain Group rocks during the Cape Orogeny created a series of folds and associated fractures. The subsequent continental break-up of Gondwana led to the development of large fault systems. These exert a major influence on deep and shallow groundwater flow. There are 3 main types of structures that are investigated. The geological contacts between hydraulically different lithologies, the primary characteristics of the sediments comprising the main geological units and the secondary structures developed from the tectonic events. These inter-alia include lithological boundaries, bedding and conjugate joints and large faults. Compartmentalisation of the aquifers by lithological and fault boundaries are the main regional level controls on flow in the study area. Joints are important for local control of flow, but cumulatively exert a regional effect as well. These controls exert a strong 3 dimensional impact on flow patterns within the area. Geological cross sections and detailed fieldwork combined with the conceptual models proposed are used to determine groundwater flow and the extent of the flow constraints. There is heterogeneity in the fault characteristics whilst there is consistence in the impermeable aquitards. These effect boundaries at the base of the aquifer, divide the aquifer into upper and lower units and cap the top of the aquifer. Using water level data, EC and pH an attempt is made to establish patterns created by structures, mainly faults. There appears to be some control of these shown by patterns seen on contour plots of the data. Understanding of the structures can significantly alter the way the available data could be interpreted. The integration of all available data into the conceptual model provides an effective research tool, which opens up further avenues for new approaches and methods for continued research in this area.

Nesta tese o autor estabelece um método sistemático de quantificação de risco em obras subterrâneas em maciço rochoso fraturado utilizando de maneira eficiente conceitos de confiabilidade estrutural. O método é aplicado a um caso de estudo real da caverna da Usina Hidrelétrica Paulo Afonso IV, UHE-PAIV. Adicionalmente, um estudo de otimização de projeto com base em risco quantitativo também é apresentado para mostrar as potencialidades do método. A estimativa do risco foi realizada de acordo com as recomendações da Organização de Auxílio contra Desastres das Nações Unidas, UNDRO, onde o risco pode ser estimado como a convolução entre as funções de perigo, vulnerabilidade e perdas. Para a quantificação da confiabilidade foram utilizados os métodos de aproximação FORM e SORM com uso de acoplamento direto e de superfícies de resposta polinomial quadráticas. A simulação de Monte Carlo também foi utilizada para a quantificação da confiabilidade no estudo de caso da UHE-PAIV devido à ocorrência de múltiplos modos de falha simultâneos. Foram avaliadas as ameaças de convergência excessiva das paredes, colapso da frente de escavação e a queda de blocos. As funções de perigo foram estimadas em relação à intensidade da ameaça como razão de deslocamento da parede ou volume do bloco. No caso da convergência excessiva, um túnel circular profundo foi estudado com o intuito de comparar a qualidade de aproximação da técnica numérica (FLAC3D com acoplamento direto) em relação à solução exata. Erros inferiores a 0,1% foram encontrados na estimativa do índice de confiabilidade ß. Para o caso da estabilidade de frente foram comparadas duas soluções da análise limite da plasticidade contra a solução obtida numericamente. Já no caso de queda de bloco, verificou-se que as recomendações de parcialização do sistema de classificação geomecânica Q incrementa consideravelmente a segurança da escavação conduzindo a padrões da prática mais avançada, por exemplo, de um ß de 2,04 para a escavação a seção plena até 4,43 para o vão recomendado. No estudo de caso, a segurança da caverna da UHE-PAIV foi estudada perante a queda de blocos utilizando o software Unwedge. A probabilidade de falha individual foi integrada no comprimento da caverna e o conceito de sistema foi utilizado para estimar a probabilidade de falha global. A caverna apresentou uma probabilidade de falha global de 3,11 a 3,22% e um risco de 7,22x10-3 x C e 7,29x10-3 x C, sendo C o custo de falha de um bloco de grandes dimensões. O bloco mais crítico apresentou um ß de 3,63. No estudo de otimização foram utilizadas duas variáveis de projeto, a espessura do concreto projetado e o número de tirantes por metro quadrado. A configuração ótima foi encontrada como o par [t, nb] que minimiza a função de custo total. Também, um estudo de sensibilidade foi realizado para avaliar as influências de alguns parâmetros no projeto ótimo da escavação. Finalmente, os resultados obtidos sugerem que as análises quantitativas de risco, como base para a avaliação e gestão de risco, podem e devem ser consideradas como diretriz da prática da engenharia geotécnica, uma vez que estas análises conciliam os conceitos básicos de projeto como eficiência mecânica, segurança e viabilidade financeira. Assim, a quantificação de risco é plenamente possível. / In this thesis the author establishes a systematic method for quantifying the risk in underground structures in fractured rock masses using structural reliability concepts in an efficient way. The method is applied to the case study of the underground cavern of Paulo Afonso IV Hydroelectrical Power Station UHE-PAIV. Additionally, an optimization study was conducted in order to show a potential application of the method. The estimation of the risk was done according to the recommendations of the United Nations Disaster Relief Organization UNDRO where risk can be estimated as the convolution between the hazard, vulnerability and losses functions. FORM and SORM were used as approximation methods for the reliability quantification by means of Direct Coupling and Quadratic Polynomial Response Surfaces. A Monte Carlo simulation was also used to quantify the reliability of the cavern UHE-PAIV because of the presence of multiple failure modes in the numerical model. In this study 3 types of threads were evaluated: excessive wall convergence, face stability and wedge block fall. Hazard functions were built relative to the thread intensities such as wall convergence ratio or block size. In the case of excessive wall convergence a deep circular tunnel was studied meaning to compare the quality of the approximation of the reliability technique (FLAC3D with direct coupling) to the exact solution. Errors below 0.1% were found in the reliability index ß estimation. The reliability of the face stability was evaluated using two limit analysis solutions against the numeric estimation. For the block stability it was verified that the sequential excavation recommended by the Q system increases considerably the reliability of the excavation leading safety to modern standard levels, e.g. from a ß equal to 2.04 for a full section excavation to 4.43 for a partial excavation. In the case study of the UHE-PAIV, the reliability of the underground cavern was estimated using the commercial software Unwedge. The probability of failure of individual blocks was integrated along the length of the cavern and the concept of structural system was used to estimate the global probability of failure. The cavern presented a probability of failure of 3.11% to 3.22% and a risk of 7.22x10-3 x C and 7.29x10-3 x C - where C is the cost of failure of a large block. The critical individual block showed a ß equal to 3.63. The optimization was performed considering two design variables − liner thickness and number of bolt per square meter. The optimal design was found as the pair, [t, nb] which minimizes the total cost function. Also, a sensibility analysis was conducted to understand the influence of some parameters in the location of the optimal excavation design. Concluding, the results obtained here suggest that the quantitative risk analyses, as a base for the risk assessment and management, can and must be considered as a north for the practice of geotechnical engineering owing that these analyses reconcile the basic concepts of mechanical efficiency, safety and financial feasibility. Thus, risk quantification is fully affordable.

In this thesis, fractured rock masses are treated asequivalent continua for large-scale analyses of rockengineering projects. Systematic developments are made for thedetermination of equivalent mechanical and hydraulic propertiesof fractured rock masses using a hybrid discrete fracturenetwork - distinct element method (DFN-DEM) approach. Thedetermined equivalent properties are then used for a far-fieldfinite element analysis of the thermo-mechanical impacts on thestress, deformation and permeability of fractured rockssurrounding a hypothetical geological repository of nuclearwaste. The geological data were extracted from the results ofan extensive site investigation programme at Sellafield, UK,conducted by Nirex UK Ltd. The scale dependencies of the hydraulic and mechanicalproperties were investigated by using multiple realizations ofthe fracture system geometry with increasing model sizes untilproperly defined hydraulic and mechanical representativeelementary volumes (REVs) were reached. The validity of thesecond order permeability tensor and the fourth-ordermechanical compliance tensor were tested for continuum analysesat larger scales. The REV was determined to be around 5 m formechanical and hydraulic data in this study. Analysis of the stress-dependent mechanical and hydraulicproperties shows that the effect of rock stresses is crucial.The elastic moduli increase significantly with the increase ofstress and an empirical equation of stress-dependent elasticmodulus is suggested based on results of numerical experiments.Calculations of the Poisson's ratios suggest greater valuesthan are normally assumed in practice. Depending on the stateof stress, permeability decreases or increases with increasingcompressive stress. Stress-induced flow channeling effect iscaptured by numerical modeling for the first time and detailedmechanisms of shear dilation of fractures are provided. Basedon the numerical experiments, a set of empirical equations wassuggested for the stress-dependent permeability, consideringboth normal deformation and shear dilation of fractures. Thermo-mechanical impact on the performance of ahypothetical repository at a far-field scale (5 km by 1 km) wasinvestigated with the stress-dependent equivalent propertiesdetermined at the REV scale. This analysis shows thatmechanical responses vary significantly depending on how themechanical properties were determined. The change ofpermeability due to the thermal loading is, however, notsignificant in this particular case. The thesis provides a framework for systematic analysis oflarge-scale engineering applications in fractured rock masses,such as geological repositories of nuclear wastes. Keyword:Fractured rock masses, Equivalent Continuum,Discrete Fracture Network (DFN), Distinct Element Method (DEM),Finite Element Method (FEM), Nuclear Waste Disposal, CoupledThermo-Hydro-Mechanical Processes

<p>In this thesis, fractured rock masses are treated asequivalent continua for large-scale analyses of rockengineering projects. Systematic developments are made for thedetermination of equivalent mechanical and hydraulic propertiesof fractured rock masses using a hybrid discrete fracturenetwork - distinct element method (DFN-DEM) approach. Thedetermined equivalent properties are then used for a far-fieldfinite element analysis of the thermo-mechanical impacts on thestress, deformation and permeability of fractured rockssurrounding a hypothetical geological repository of nuclearwaste. The geological data were extracted from the results ofan extensive site investigation programme at Sellafield, UK,conducted by Nirex UK Ltd.</p><p>The scale dependencies of the hydraulic and mechanicalproperties were investigated by using multiple realizations ofthe fracture system geometry with increasing model sizes untilproperly defined hydraulic and mechanical representativeelementary volumes (REVs) were reached. The validity of thesecond order permeability tensor and the fourth-ordermechanical compliance tensor were tested for continuum analysesat larger scales. The REV was determined to be around 5 m formechanical and hydraulic data in this study.</p><p>Analysis of the stress-dependent mechanical and hydraulicproperties shows that the effect of rock stresses is crucial.The elastic moduli increase significantly with the increase ofstress and an empirical equation of stress-dependent elasticmodulus is suggested based on results of numerical experiments.Calculations of the Poisson's ratios suggest greater valuesthan are normally assumed in practice. Depending on the stateof stress, permeability decreases or increases with increasingcompressive stress. Stress-induced flow channeling effect iscaptured by numerical modeling for the first time and detailedmechanisms of shear dilation of fractures are provided. Basedon the numerical experiments, a set of empirical equations wassuggested for the stress-dependent permeability, consideringboth normal deformation and shear dilation of fractures.</p><p>Thermo-mechanical impact on the performance of ahypothetical repository at a far-field scale (5 km by 1 km) wasinvestigated with the stress-dependent equivalent propertiesdetermined at the REV scale. This analysis shows thatmechanical responses vary significantly depending on how themechanical properties were determined. The change ofpermeability due to the thermal loading is, however, notsignificant in this particular case.</p><p>The thesis provides a framework for systematic analysis oflarge-scale engineering applications in fractured rock masses,such as geological repositories of nuclear wastes.</p><p><b>Keyword:</b>Fractured rock masses, Equivalent Continuum,Discrete Fracture Network (DFN), Distinct Element Method (DEM),Finite Element Method (FEM), Nuclear Waste Disposal, CoupledThermo-Hydro-Mechanical Processes</p>

<p><font face="TimesNewRomanPSMT"> <p align="left">Groundwater in arid and semi-arid areas like the Karoo region of South Africa is an important source of domestic, agricultural and industrial source of fresh water. As a scarce resource, it requires extensive quality control and protection through innovative methods and efficient strategies. The town of Beaufort West and its vicinity use groundwater as a major source of municipal and private water supply. Forty nine groundwater samples were collected from spatially referenced boreholes located in and around the town of Beaufort West and were analyzed for <font face="TimesNewRomanPSMT">EC, pH, <font face="TimesNewRomanPSMT">TDS,<font face="TimesNewRomanPSMT">TH, SAR, TA, Ca</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">2+</font></font><font face="TimesNewRomanPSMT">, Mg</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">2+</font></font><font face="TimesNewRomanPSMT">, Na</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">+</font></font><font face="TimesNewRomanPSMT">, K</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">+</font></font><font face="TimesNewRomanPSMT">, HCO</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">3-</font></font><font size="3" face="TimesNewRomanPSMT">, Cl</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">-</font></font><font size="3" face="TimesNewRomanPSMT">, NO</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">3- </font></font><font size="3" face="TimesNewRomanPSMT">and SO</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">42- </font></font><font face="TimesNewRomanPSMT"><font size="3">according to&nbsp / <font face="TimesNewRomanPSMT">SANS 241 standards and tested for ionic balance. The groundwater of the study area was characterized using WHO and South African drinking water quality standards as well as TDS and Salinity hazard classifications. These comparisons and classifications characterized the groundwater of the study area as hard to very hard, with low to medium salinity hazard. These results are in accordance with the dominance of the ions Ca</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">2+</font></font><font face="TimesNewRomanPSMT">, Na</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">+</font></font><font face="TimesNewRomanPSMT">, HCO</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">3 - </font></font><font face="TimesNewRomanPSMT">and Cl</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">- </font></font><font face="TimesNewRomanPSMT">in the groundwater samples. Linear relationships between the hydrochemical variables were analysed through correlation and multiple regression analysis to relate the groundwater quality to the underlying hydrogeochemical processes. These linear relationships explained the contribution of the measured variables towards the salinity, hardness and anthropogenic contamination of the groundwater. The groundwater of the study area was also assessed using conventional trilinear diagrams and scatter plots to interpret the water quality and determine the major ion chemistry. The conventional methods highlighted the sources of the hydrochemical variables through analysis and interpretation of rock-water interaction and evaporations processes. To supplement <font face="TimesNewRomanPSMT">these conventional methods and reveal hidden hydrogeochemical phenomenon, multivariate statistical analyses were employed. Factor analysis reduced the hydrochemical variables into three factors (Hardness, Alkalinity and Landuse) that characterize the groundwater quality in relation to the source of its hydrochemistry. Furthermore, combination of Cluster (CA) and Discriminant analyses (DA) were used to classify the groundwater in to different hydrochemical facies and determine the dominant hydrochemical variables that characterize these facies. The classification results were also compared with the trilinear diagrammatic interpretations to highlight the advantages of these multivariate statistical methods. The CA and DA classifications resulted in to six different hydrochemical facies that are characterized by NO</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">3 -</font></font><font face="TimesNewRomanPSMT">, Na</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">+ </font></font><font face="TimesNewRomanPSMT">and pH. These three hydrochemical variables explain 93.9% of the differences between the water types and highlight the influence of natural hydrogeochemical and anthropogenic processes on the groundwater quality. All the univariate, bivariate, multivariate statistical and conventional hydrogeochemical analyses results were analyzed spatially using ArcGIS 10.0. The spatial analysis employed the Inverse Distance Weighted (IDW) interpolation method to predict spatial distribution of unmeasured areas and reclassification of the interpolation results for classification purposes. The results of the different analyses methods employed in the thesis illustrate that the groundwater in the study area is generally hard but permissible in the absence of better alternative water source and useful for irrigation.</font></font></font></font></font></font></p> </font></p>

<p><font face="TimesNewRomanPSMT"> <p align="left">Groundwater in arid and semi-arid areas like the Karoo region of South Africa is an important source of domestic, agricultural and industrial source of fresh water. As a scarce resource, it requires extensive quality control and protection through innovative methods and efficient strategies. The town of Beaufort West and its vicinity use groundwater as a major source of municipal and private water supply. Forty nine groundwater samples were collected from spatially referenced boreholes located in and around the town of Beaufort West and were analyzed for <font face="TimesNewRomanPSMT">EC, pH, <font face="TimesNewRomanPSMT">TDS,<font face="TimesNewRomanPSMT">TH, SAR, TA, Ca</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">2+</font></font><font face="TimesNewRomanPSMT">, Mg</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">2+</font></font><font face="TimesNewRomanPSMT">, Na</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">+</font></font><font face="TimesNewRomanPSMT">, K</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">+</font></font><font face="TimesNewRomanPSMT">, HCO</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">3-</font></font><font size="3" face="TimesNewRomanPSMT">, Cl</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">-</font></font><font size="3" face="TimesNewRomanPSMT">, NO</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">3- </font></font><font size="3" face="TimesNewRomanPSMT">and SO</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">42- </font></font><font face="TimesNewRomanPSMT"><font size="3">according to&nbsp / <font face="TimesNewRomanPSMT">SANS 241 standards and tested for ionic balance. The groundwater of the study area was characterized using WHO and South African drinking water quality standards as well as TDS and Salinity hazard classifications. These comparisons and classifications characterized the groundwater of the study area as hard to very hard, with low to medium salinity hazard. These results are in accordance with the dominance of the ions Ca</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">2+</font></font><font face="TimesNewRomanPSMT">, Na</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">+</font></font><font face="TimesNewRomanPSMT">, HCO</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">3 - </font></font><font face="TimesNewRomanPSMT">and Cl</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">- </font></font><font face="TimesNewRomanPSMT">in the groundwater samples. Linear relationships between the hydrochemical variables were analysed through correlation and multiple regression analysis to relate the groundwater quality to the underlying hydrogeochemical processes. These linear relationships explained the contribution of the measured variables towards the salinity, hardness and anthropogenic contamination of the groundwater. The groundwater of the study area was also assessed using conventional trilinear diagrams and scatter plots to interpret the water quality and determine the major ion chemistry. The conventional methods highlighted the sources of the hydrochemical variables through analysis and interpretation of rock-water interaction and evaporations processes. To supplement <font face="TimesNewRomanPSMT">these conventional methods and reveal hidden hydrogeochemical phenomenon, multivariate statistical analyses were employed. Factor analysis reduced the hydrochemical variables into three factors (Hardness, Alkalinity and Landuse) that characterize the groundwater quality in relation to the source of its hydrochemistry. Furthermore, combination of Cluster (CA) and Discriminant analyses (DA) were used to classify the groundwater in to different hydrochemical facies and determine the dominant hydrochemical variables that characterize these facies. The classification results were also compared with the trilinear diagrammatic interpretations to highlight the advantages of these multivariate statistical methods. The CA and DA classifications resulted in to six different hydrochemical facies that are characterized by NO</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">3 -</font></font><font face="TimesNewRomanPSMT">, Na</font><font size="1" face="TimesNewRomanPSMT"><font size="1" face="TimesNewRomanPSMT">+ </font></font><font face="TimesNewRomanPSMT">and pH. These three hydrochemical variables explain 93.9% of the differences between the water types and highlight the influence of natural hydrogeochemical and anthropogenic processes on the groundwater quality. All the univariate, bivariate, multivariate statistical and conventional hydrogeochemical analyses results were analyzed spatially using ArcGIS 10.0. The spatial analysis employed the Inverse Distance Weighted (IDW) interpolation method to predict spatial distribution of unmeasured areas and reclassification of the interpolation results for classification purposes. The results of the different analyses methods employed in the thesis illustrate that the groundwater in the study area is generally hard but permissible in the absence of better alternative water source and useful for irrigation.</font></font></font></font></font></font></p> </font></p>

Nesta tese o autor estabelece um método sistemático de quantificação de risco em obras subterrâneas em maciço rochoso fraturado utilizando de maneira eficiente conceitos de confiabilidade estrutural. O método é aplicado a um caso de estudo real da caverna da Usina Hidrelétrica Paulo Afonso IV, UHE-PAIV. Adicionalmente, um estudo de otimização de projeto com base em risco quantitativo também é apresentado para mostrar as potencialidades do método. A estimativa do risco foi realizada de acordo com as recomendações da Organização de Auxílio contra Desastres das Nações Unidas, UNDRO, onde o risco pode ser estimado como a convolução entre as funções de perigo, vulnerabilidade e perdas. Para a quantificação da confiabilidade foram utilizados os métodos de aproximação FORM e SORM com uso de acoplamento direto e de superfícies de resposta polinomial quadráticas. A simulação de Monte Carlo também foi utilizada para a quantificação da confiabilidade no estudo de caso da UHE-PAIV devido à ocorrência de múltiplos modos de falha simultâneos. Foram avaliadas as ameaças de convergência excessiva das paredes, colapso da frente de escavação e a queda de blocos. As funções de perigo foram estimadas em relação à intensidade da ameaça como razão de deslocamento da parede ou volume do bloco. No caso da convergência excessiva, um túnel circular profundo foi estudado com o intuito de comparar a qualidade de aproximação da técnica numérica (FLAC3D com acoplamento direto) em relação à solução exata. Erros inferiores a 0,1% foram encontrados na estimativa do índice de confiabilidade &#223;. Para o caso da estabilidade de frente foram comparadas duas soluções da análise limite da plasticidade contra a solução obtida numericamente. Já no caso de queda de bloco, verificou-se que as recomendações de parcialização do sistema de classificação geomecânica Q incrementa consideravelmente a segurança da escavação conduzindo a padrões da prática mais avançada, por exemplo, de um &#223; de 2,04 para a escavação a seção plena até 4,43 para o vão recomendado. No estudo de caso, a segurança da caverna da UHE-PAIV foi estudada perante a queda de blocos utilizando o software Unwedge. A probabilidade de falha individual foi integrada no comprimento da caverna e o conceito de sistema foi utilizado para estimar a probabilidade de falha global. A caverna apresentou uma probabilidade de falha global de 3,11 a 3,22% e um risco de 7,22x10-3 x C e 7,29x10-3 x C, sendo C o custo de falha de um bloco de grandes dimensões. O bloco mais crítico apresentou um &#223; de 3,63. No estudo de otimização foram utilizadas duas variáveis de projeto, a espessura do concreto projetado e o número de tirantes por metro quadrado. A configuração ótima foi encontrada como o par [t, nb] que minimiza a função de custo total. Também, um estudo de sensibilidade foi realizado para avaliar as influências de alguns parâmetros no projeto ótimo da escavação. Finalmente, os resultados obtidos sugerem que as análises quantitativas de risco, como base para a avaliação e gestão de risco, podem e devem ser consideradas como diretriz da prática da engenharia geotécnica, uma vez que estas análises conciliam os conceitos básicos de projeto como eficiência mecânica, segurança e viabilidade financeira. Assim, a quantificação de risco é plenamente possível. / In this thesis the author establishes a systematic method for quantifying the risk in underground structures in fractured rock masses using structural reliability concepts in an efficient way. The method is applied to the case study of the underground cavern of Paulo Afonso IV Hydroelectrical Power Station UHE-PAIV. Additionally, an optimization study was conducted in order to show a potential application of the method. The estimation of the risk was done according to the recommendations of the United Nations Disaster Relief Organization UNDRO where risk can be estimated as the convolution between the hazard, vulnerability and losses functions. FORM and SORM were used as approximation methods for the reliability quantification by means of Direct Coupling and Quadratic Polynomial Response Surfaces. A Monte Carlo simulation was also used to quantify the reliability of the cavern UHE-PAIV because of the presence of multiple failure modes in the numerical model. In this study 3 types of threads were evaluated: excessive wall convergence, face stability and wedge block fall. Hazard functions were built relative to the thread intensities such as wall convergence ratio or block size. In the case of excessive wall convergence a deep circular tunnel was studied meaning to compare the quality of the approximation of the reliability technique (FLAC3D with direct coupling) to the exact solution. Errors below 0.1% were found in the reliability index &#223; estimation. The reliability of the face stability was evaluated using two limit analysis solutions against the numeric estimation. For the block stability it was verified that the sequential excavation recommended by the Q system increases considerably the reliability of the excavation leading safety to modern standard levels, e.g. from a &#223; equal to 2.04 for a full section excavation to 4.43 for a partial excavation. In the case study of the UHE-PAIV, the reliability of the underground cavern was estimated using the commercial software Unwedge. The probability of failure of individual blocks was integrated along the length of the cavern and the concept of structural system was used to estimate the global probability of failure. The cavern presented a probability of failure of 3.11% to 3.22% and a risk of 7.22x10-3 x C and 7.29x10-3 x C - where C is the cost of failure of a large block. The critical individual block showed a &#223; equal to 3.63. The optimization was performed considering two design variables &#8722; liner thickness and number of bolt per square meter. The optimal design was found as the pair, [t, nb] which minimizes the total cost function. Also, a sensibility analysis was conducted to understand the influence of some parameters in the location of the optimal excavation design. Concluding, the results obtained here suggest that the quantitative risk analyses, as a base for the risk assessment and management, can and must be considered as a north for the practice of geotechnical engineering owing that these analyses reconcile the basic concepts of mechanical efficiency, safety and financial feasibility. Thus, risk quantification is fully affordable.

Magister Scientiae - MSc (Environ & Water Science) / Groundwater in arid and semi-arid areas like the Karoo region of South Africa is an important source of domestic, agricultural and industrial source of fresh water. As a scarce resource, it requires extensive quality control and protection through innovative methods and efficient strategies. The town of Beaufort West and its vicinity use groundwater as a major source of municipal and private water supply. Forty nine groundwater samples were collected from spatially referenced boreholes located in and around the town of Beaufort West and were analyzed for EC, pH, TDS,TH, SAR, TA, Ca2+, Mg2+, Na+, K+, HCO3-, Cl-, NO3- and SO42- according to SANS 241 standards and tested for ionic balance. The groundwater of the study area was characterized using WHO and South African drinking water quality standards as well as TDS and Salinity hazard classifications. These comparisons and classifications characterized the groundwater of the study area as hard to very hard, with low to medium salinity hazard. These results are in accordance with the dominance of the ions Ca2+, Na+, HCO3 - and Cl- in the groundwater samples. Linear relationships between the hydrochemical variables were analysed through correlation and multiple regression analysis to relate the groundwater quality to the underlying hydrogeochemical processes. These linear relationships explained the contribution of the measured variables towards the salinity, hardness and anthropogenic contamination of the groundwater. The groundwater of the study area was also assessed using conventional trilinear diagrams and scatter plots to interpret the water quality and determine the major ion chemistry. The conventional methods highlighted the sources of the hydrochemical variables through analysis and interpretation of rock-water interaction and evaporations processes. To supplement these conventional methods and reveal hidden hydrogeochemical phenomenon, multivariate statistical analyses were employed. Factor analysis reduced the hydrochemical variables into three factors (Hardness, Alkalinity and Landuse) that characterize the groundwater quality in relation to the source of its hydrochemistry. Furthermore, combination of Cluster (CA) and Discriminant analyses (DA) were used to classify the groundwater in to different hydrochemical facies and determine the dominant hydrochemical variables that characterize these facies. The classification results were also compared with the trilinear diagrammatic interpretations to highlight the advantages of these multivariate statistical methods. The CA and DA classifications resulted in to six different hydrochemical facies that are characterized by NO3 -, Na+ and pH. These three hydrochemical variables explain 93.9% of the differences between the water types and highlight the influence of natural hydrogeochemical and anthropogenic processes on the groundwater quality. All the univariate, bivariate, multivariate statistical and conventional hydrogeochemical analyses results were analyzed spatially using ArcGIS 10.0. The spatial analysis employed the Inverse Distance Weighted (IDW) interpolation method to predict spatial distribution of unmeasured areas and reclassification of the interpolation results for classification purposes. The results of the different analyses methods employed in the thesis illustrate that the groundwater in the study area is generally hard but permissible in the absence of better alternative water source and useful for irrigation.