Two new three-dimensional rock mass strength criteria are developed in this dissertation by extending an existing rock mass strength criterion. These criteria incorporate the effects of the intermediate principal stress, minimum principal stress and the anisotropy resulting from these stresses acting on the fracture system. In addition, these criteria have the capability of capturing the anisotropic and scale dependent behavior of the jointed rock mass strength by incorporating the effect of fracture geometry through the fracture tensor components. Another significant feature of the new rock mass strength criterion which has the exponential functions (equation 6.7) is having only four empirical coefficients compared to the existing strength criterion which has five empirical coefficients; if the joint sets have the same isotropic mechanical behavior, the number of the empirical coefficients reduces to two in this new strength criterion (equation 6.10). The new criteria were proposed after analyzing 452 numerical modeling results of the triaxial, polyaxial and biaxial compression tests conducted on the jointed rock blocks having one or two joint sets by the PFC3D software version 5. In this research to have several samples with the same properties a synthetic rock material that is made out of a mixture of gypsum, sand and water was used. In total, 20 joint systems were chosen and joint sets have different dip angles varying from 15 to 60 at an interval of 15 with dip directions of 30 and 75 for the two joint sets. Each joint set also has 3 persistent joints with the joint spacing of 42 mm in a cubic sample of size 160 mm and the joints have the same isotropic mechanical behavior. The confining stress combination values were chosen based on the uniaxial compressive strength (UCS) value of the modeled intact synthetic rock. The minimum principal stress values were chosen as 0, 20, 40 and 60 percent of the UCS. For each minimum principal stress value, the intermediate principal stress value varies starting at the minimum principal stress value and increasing at an interval of 20 percent of the UCS until it is lower than the strength of the sample under the biaxial loading condition with the same minimum principal stress value. The new rock mass failure criteria were developed from the PFC3D modeling data. However, since the joint sets having the dip angle of 60 intersect the top and bottom boundaries of the sample simultaneously, the joint systems with at least one of the joint sets having the dip angle of 60 were removed from the database. Thus, 284 data points from 12 joint systems were used to find the best values of the empirical coefficients for the new rock mass strength criteria. λ, p and q were found to be 0.675, 3.16 and 0.6, respectively, through a conducted grid analysis with a high R2 (coefficient of determination) value of 0.94 for the new criterion given by equation 6.9 and a and b were found to be 0.404 and 0.972, respectively, through a conducted grid analysis with a high R2 value of 0.92 for the new criterion given by equation 6.10. The research results clearly illustrate how increase of the minimum and intermediate principal stresses and decrease of the joint dip angle, increase the jointed rock block strength. This dissertation also illustrates how different confining stress combinations and joint set dip angles result in different jointed rock mass failure modes such as sliding on the joints, failure through the intact rock and a combination of the intact rock and joint failures. To express the new rock mass strength failure criteria, it was necessary to determine the intact rock strengths under the same confining stress combinations mentioned earlier. Therefore, the intact rock was also modeled for all three compression tests and the intact rock strengths were found for 33 different confining stress combinations. Suitability of six major intact rock failure criteria: Mohr-Coulomb, Hoek-Brown, Modified Lade, Modified Wiebols and Cook, Mogi and Drucker-Prager in representing the intact rock strength was examined through fitting them using the aforementioned 33 PFC3D data points. Among these criteria, Modified Lade, Modified Mogi with power function and Modified Wiebols and Cook were found to be the best failure criteria producing lower Root Mean Square Error (RMSE) values of 0.272, 0.301 and 0.307, respectively. Thus, these three failure criteria are recommended for the prediction of the intact rock strength under the polyaxial stress condition. In PFC unlike the other methods, macro mechanical parameters are not directly used in the model and micro mechanical parameter values applicable between the particles should be calibrated using the macro mechanical properties. Accurate calibration is a difficult or challenging task. This dissertation emphasized the importance of studying the effects of all micro parameter values on the macro mechanical properties before one goes through calibration of the micro parameters in PFC modeling. Important effects of two micro parameters, which have received very little attention, the particle size distribution and the cov of the normal and shear strengths, on the macro properties are clearly illustrated before conducting the said calibration. The intact rock macro mechanical parameter values for the Young’s modulus, uniaxial compression strength (UCS), internal friction angle, cohesion and Poisson's ratio were found by performing 3 uniaxial tests, 3 triaxial tests and 5 Brazilian tests on a synthetic material made out of a mixture of gypsum, sand and water and the joint macro mechanical parameter values were found by conducting 4 uniaxial compression tests and 4 direct shear tests on jointed synthetic rocks with a horizontal joint. Then the micro mechanical properties of the Linear Parallel Bond Model (LPMB) and Modified Smooth Joint Contact Model (MSJCM) were calibrated to represent the intact rock and joints respectively, through the specific procedures explained in this research. The similar results obtained between the 2 polyaxial experiments tests of the intact rock and 11 polyaxial experimental tests of the jointed rock blocks having one joint set and the numerical modeling verified the calibrated micro mechanical properties and further modification of these properties was not necessary. This dissertation also proposes a modification to the Smooth Joint Contact Model (SJCM) to overcome the shortcoming of the SJCM to capture the non-linear behavior of the joint closure varying with the joint normal stress. Modified Smooth Joint Contact Model (MSJCM) uses a linear relation between the joint normal stiffness and the normal contact stress to model the non-linear relation between the joint normal deformation and the joint normal stress observed in the compression joint normal stiffness test. A good agreement obtained between the results from the experimental tests and the numerical modeling of the compression joint normal test shows the accuracy of this new model. Moreover, another shortcoming associated with the SJCM application known as the interlocking problem was solved through this research by proposing a new joint contact implementation algorithm called joint sides checking (JSC) approach. The interlocking problem occurs due to a shortcoming of the updating procedure in the PFC software related to the contact conditions of the particles that lie around the intended joint plane during high shear displacements. This problem increases the joint strength and dilation angle and creates unwanted fractures around the intended joint plane.

Prior to an underground excavation a site investigation is carried out. This includes reviewing and analysing existing data, field data collected through outcrop mapping, drill core logging and geophysical investigations. These data sources are combined and used to characterise, quantify and classify the rock mass for the tunnel design process and excavation method selection. Despite the best approaches used in a site investigation, it cannot reveal the required level of detail. Such gaps in information might become significant during the actual construction stage. This can lead to; for example, over-break due to unfavourable geological conditions. Even more so, an underestimation of the rock mass properties can lead to unplanned stoppages and tunnel rehabilitation. On-the-other-hand, the excavation method itself, in this case, drill and blast, can also cause severe damage to the rock mass. This can result in over-break and reduction of the strength and quality of the remaining rock mass. Both of these attributes pose risks for the tunnel during excavation and after project delivery. Blast damage encompasses over-break and the Excavation Damage Zone (EDZ). In the latter irreversible changes occur within the remaining rock mass inside this zone, which are physically manifested as blast fractures. In this thesis, a number of methods to determine blast damage have been investigated in two ramp tunnels of the Stockholm bypass. Herein, a comparison between the most common methods for blast damage investigation employed nowadays is performed. This comparison can be used to select the most suitable methods for blast damage investigation in tunnelling, based on the environment and the available resources. In this thesis Ground Penetrating Radar, core logging (for fractures) and P-wave velocity measurements were applied to determine the extent of the blast damage. Furthermore, the study of the two tunnels in the Stockholm bypass shows a significant overestimation of the actual rock mass quality during the site investigation. In order to gain a more accurate picture of the rock mass quality, Measurement While Drilling (MWD) technology was applied. The technology was investigated for rock mass quality prediction, quantifying the extent of blast damage, as well as to investigate the potential to forecast the required rock support. MWD data was collected from both grout and blast holes. These data sets were used to determine rock quality indices e.g. Fracture Indication and Hardness Indicator calculated by the MWD parameters. The Fracture Index was then compared with the installed rock support at the measurement location. Lastly, the extent of the damage is investigated by evaluating if the MWD parameters could forecast the extent of the EDZ. The study clearly shows the capability of MWD data to predict the rock mass characteristics, e.g. fractures and other zones of weakness. This study demonstrated that there is a correlation between the Fracture Index (MWD) and the Q-value, a parameter widely used to determine the required rock support. The study also shows a correlation between the extent of the blast damage zone, MWD data, design and excavation parameters (for example tunnel cross section and charge concentration).

Una caracterización precisa y el modelamiento de la heterogeneidad geomecánica del macizo rocoso conducen a una planificación y diseño de mina eficientes. El uso de técnicas convencionales como el Kriging para el modelamiento del macizo rocoso es limitado, pues no considera la variabilidad espacial y la heterogeneidad del macizo rocoso, dando como resultado estimaciones que no representan el comportamiento real del macizo rocoso. En este contexto, se propone como alternativa de solución usar la Simulación Gaussiana para estimar la heterogeneidad espacial del macizo rocoso basado en el análisis de los valores de UCS, RQD, Condición de aguas y condición de juntas para el modelado del RMR, esta técnica consiste en simular diferentes valores a partir de datos conocidos, además permite analizar la incertidumbre de las simulaciones obtenidas. La metodología que se propone en esta investigación considera el análisis variográfico de las variables regionalizadas geomecánicas en diferentes direcciones, con el fin de determinar su comportamiento anisotrópico; asimismo, se desarrolla el análisis de la incertidumbre mediante la técnica de la validación cruzada que consiste en dividir los datos originales en dos subconjuntos al azar. El 85% de la base de datos se usó para estimar los valores de RMR, mientras que el 15% se utilizó como subconjunto de prueba. El caso de estudio es el tramo crítico con presencia de aguas hidrotermales del túnel de acceso principal de un proyecto minero al sur de Perú, se utilizaron los datos de registro geomecánico tomados en campo, con ellos se produjeron un total de 5 simulaciones por cada variable, produciéndose aproximadamente 3 millones de valores por cada variable. El error medio absoluto del modelo generado con Simulación Gaussiana es de solo 6.58%, que es considerado admisible comparado con el 38.01% obtenido con Kriging. / Accurate characterization and modeling of the rock mass geomechanical heterogeneity leads to efficient mine planning and design. The use of conventional techniques such as Kriging for modeling the rock mass is limited, since it does not consider the spatial variability and heterogeneity of the rock mass, resulting in estimates that do not represent the real behavior of the rock mass. In this context, it is proposed as an alternative solution to use the Gaussian Simulation to estimate the spatial heterogeneity of the rock mass based on the analysis of the values of UCS, RQD, Water condition and joint condition for the RMR modeling, this technique consists in simulating different values from known data, in addition to allowing to analyze the uncertainty of the obtained simulations. The methodology proposed in this research considers the variographic analysis of the regionalized geomechanical variables in directions, in order to determine their anisotropic behavior; Likewise, the uncertainty analysis is developed using the cross-validation technique that consists of dividing the original data into two subsets at random. 85% of the database was used to estimate the RMR values, while 15% was used as a test subset. The case study is the critical section with the presence of hydrothermal waters of the main access tunnel of a mining project in southern Peru, the geomechanical record data taken in the field was used, with them a total of 5 simulations were produced for each variable, producing approximately 3 million values for each variable. The mean absolute error of the model generated with Gaussian Simulation is only 6.58%, which is considered admissible compared to the 38.01% obtained with Kriging. / Tesis

Construction of rock slopes is needed in many civil work projects. It is for example very common in road and railway cuts, but other applications include excavation for tunneling or building foundations, where perhaps sensitive constructions are present in the immediate vicinity. In Sweden the majority of the rock is hard crystalline bedrock of relatively good quality, and the fracture orientation have a large effect of the stability of the rock slope.If the geology is not properly considered for when the design of the slope is carried out, it can result in slope failure, with severe consequences. This applies especially if the rock slope is high, but unwanted effects like increased excavation and construction costs, could occur also in smaller slopes if the risks are not identified and managed. However, it is difficult to standardize design of rock slopes in fractured hard crystalline rock because of the uncertainties and variations in the geological conditions during the design phase.Rock mass characterization systems like Rock mass rating, RMR (Bieniawski 1989) and the Qsystem (Barton, Lien och Lunde 1974) are commonly used to describe the general rock mass quality. Whilst a good rock mass quality is generally easier to construct in, stability problems do occur due to structural geology in rock slopes even in good rock mass quality. The application of these systems in rock slopes can be problematic as they do not describe the geometry of the slope and how the fractures daylight in the slope face. Instead, stereonets can be used to visualize this, but fracture parameters of large importance for stability (persistence, roughness and alteration) are traditionally not presented in a stereonet analysis. Additionally, these parameters and the structural geological conditions can be difficult to predict and can vary significantly over short distances, why it can be difficult to forecast and predict failure in the design face.Slope instability due to large sliding and wedge failures have been observed in a large number of slopes in crystalline rock, and a standard method for design of rock slopes is lacking. This has given rise to the research question of how best to describe rock mass conditions, how to design slopes in crystalline rock and how to manage these risks during construction.To investigate this, three rock slopes where large failure had occurred were selected for the case study and were mapped, characterized and analyzed. The results from the case study showed that all rock slopes investigated had in common that failure had occurred along fractures of large persistence. This highlights the importance of evaluating the geology in the correct scale and suggest that lineament studies and other elevation based interpretation are perhaps more useful than previously thought. It also came to light that the planning and design process is inflexible which in many cases lead to large risks being overlooked or left unnoticed.A flow chart for risk classification was produced and suggested for aid in decision making aiming at simplifying project management of rock slopes, as well as aiding in visualization of the risk that rock slopes can be associated to.

[pt] O objetivo deste trabalho foi o de verificar a influência da modificação no campo de tensões ao redor de uma escavação em um maciço rochoso fraturado, observando a ocorrência do fechamento de fraturas e a redução da condutividade hidráulica na região ao redor da escavação. São apresentadas inicialmente as características básicas que devem ser consideradas ao analisar problemas em maciços rochosos fraturados e apontados os possíveis efeitos de uma escavação neste tipo de material. Uma breve revisão bibliográfica mostra alguns tipos de técnicas de análises numéricas disponíveis para simulação de problemas em meios descontínuos, com ênfase no método dos elementos discretos e, em especial, no método dos elementos distintos (DEM), empregado no software UDEC da Itasca Consulting Group Inc., utilizado neste trabalho. As simulações utilizam um acoplamento hidromecânico, onde o maciço é representado por um conjunto de blocos e as descontinuidades são tratadas como contornos dos blocos, sendo o fluxo permitido apenas no interior das fraturas. Foi utilizado um modelo hipotético com escavação circular para validação da modelagem a partir de soluções analíticas presentes na literatura. Além disso, foi realizado um estudo de caso real, de dois túneis localizados em uma importante via na cidade do Rio de Janeiro. A análise paramétrica do problema mostra a influência da modificação de algumas variáveis importantes neste tipo de fenômeno. Por fim, foram analisados os resultados de todos os casos, com suas considerações finais e sugestões para trabalhos futuros. / [en] This work aims to verify the influence of the stress field changing around an excavation in a jointed rock mass, noticing the fracture closure and the hydraulic conductivity decrease in the region surrounding the excavation. At first, the basic characteristics that should be considered in jointed rock masses analyses are presented, pointing out the potential effects caused by excavations in such materials. A brief literature review presents some types of numerical analysis techniques available for discontinuous medium modeling, focusing on the discrete elements methods and, specifically, in the distinct element method (DEM), applied in the UDEC software by Itasca Consulting Group Inc., which was utilized in this work. The simulations make use of a hydromechanical coupling, being the rock mass represented by an assembly of blocks. The water flow takes place among the discontinuities, which are treated as blocks’ boundaries. A hypothetical model was used for modeling validation by comparison with analytical solutions from the literature. Besides that, it was accomplished a real case study of two tunnels located at an important road in Rio de Janeiro city. The parametric analyses of the problem show the influence of changing some important variables in this type of phenomenon. At last, all the results have been discussed, with final considerations and future works suggestions.

When two parallel tunnels are excavated under high to moderate horizontal in-situ stresses combined with minor deformations in the pillar between the tunnels, the in-situ stresses can be redistributed over the tunnels in form of two compressive arches and are transferred from the roof to the abutments of the two tunnels. At additional deformations in the pillar, a new redistribution of the stresses can occur creating one compressive arch over both of the tunnels. This leads to lower vertical stresses in the pillar between the two tunnels. Today, this effect is normally not accounted for in the design of rock support. By accounting for this arching effect, it is possible to design the pillars for a lower load. The aim of this thesis is to analyze how to optimize the rock support (rock bolts) in the pillar by accounting for this potential arching effect in the rock mass. To study this, a sensitivity analyses is performed where the rock mass is represented by three different qualities (very good, good and fair). The geometry of the rock pillar is defined by a height of 6 m and two width dimensions of 3 m and 6 m are used. The in-situ stresses are categorized in three levels: minimal, typical and maximal according to typical conditions in the Stockholm region. Numerical models are analyzed in PLAXIS based on these different conditions. Stress redistribution in the rock is simulated by reducing the modulus of elasticity of the pillar in five stages. Based on the results from the numerical simulations and comparisons against analytical solutions it can be concluded that it is possible to design the pillar for a lower load, which accounts for this secondary arching effect over the two tunnels. The number of bolts could be reduced with at least 1-5 units per meter tunnel for the analyzed cases; thereby reducing the costs and also contribute to a more sustainable use of natural resources. / När parallella tunnlar tas ut i en bergmassa under höga eller måttliga horisontella in-situ spänningar omfördelas de över de båda tunnlarna i form av två tryckbågar och överförs från taket till stöden. Vid ytterligare deformationer i pelaren kan istället ytterligare en omfördelning ske och en tryckbåge över båda tunnlarna skapas. Detta leder till en minskning av de vertikala spänningarna i pelaren mellan de båda tunnlarna. Idag beaktas normalt inte denna effekt vid dimensioneringen av pelarens förstärkning. Genom att beakta denna valveffekt är det möjligt att dimensionera pelarens förstärkning för en lägre last. Syftet med detta arbete är att analysera hur förstärkningen kan optimeras i pelaren genom att beakta denna valveffekt i bergmassan. För att studera detta har en känslighetsanalys genomförts där bergmassan representeras av tre olika kvaliteter (mycket bra, bra och acceptabel). Geometrin för bergpelaren definieras av en höjd på 6 m och två olika bredder på 3 m och 6 m har analyserats. In-situ spänningarna kategoriseras i tre nivåer: minimala, typiska och maximala enligt typiska förhållanden för Stockholmsregionen. Olika numeriska modeller har analyserats i PLAXIS utifrån dessa olika förutsättningar. Spänningsfördelningen i berget simulerades genom att pelarens elasticitetsmodul reducerades i fem steg. Baserat på resultaten från de numeriska analyserna och jämförelser mot analytiska lösningar kan slutsatsen dras att det är möjligt att dimensionera förstärkningen för en lägre last genom att beakta den sekundära valvverkan som kan uppstå i bergmassan över de båda tunnlarna. I de utförda analyserna kunde antalet bergbultar reduceras med mellan 1-5 stycken per meter tunnel; vilket därmed kan bidra till läge kostnader och en mer hållbar användning av naturresurser.

[pt] Com base nos frequentes relatos de problemas associados à alteração hidrotermal, durante a escavação de túneis na cidade do Rio de Janeiro, com destaque para a ação de argilas expansivas e/ou minerais secundários, decidiu-se estudar profundamente os aspectos petrográficos-genéticos básicos das rochas que afloram num túnel da região de Jacarepaguá e avaliar até que ponto a influência da alteração hidrotermal favorece as modificações de resistência dos maciços que afloram naquela região. Para isso foram realizadas investigações detalhadas das amostras coletadas dentro do túnel e no bota fora. No laboratório as amostras foram submetidas à análise petrográfica na lupa e microscópio, análises por difração de raios-x e ensaio de resistência. Foram estabelecidas correlações entre as transformações químicas mineralógicas ocorridas nos litotipos que afloram no túnel com a sua resistência. Com os resultados obtidos foi constatada a importância da alteração hidrotermal nos projetos de túneis e desta forma pode-se concluir que pequenas abordagens geológicas podem minimizar vários problemas de engenharia. / [en] Based on the frequent problems of reports associated with hydrothermal alteration, during the excavation of tunnels in the city of Rio de Janeiro, especially the action of swelling clays and/or secondary mineral, it decided to deeply study the basic aspects petrographic-genetic this rocks appear in the tunnel of Jacarepaguá region and assess to what extent the influence of hydrothermal alteration favors changes massive resistance that appear in the region. For that were conducted detailed investigations of the samples collected in the tunnel and the slag heap. In the laboratory, the samples were subjected to petrographic analysis on the magnifying glass and microscope, analysis by diffraction of x-rays and strength test. Correlations were established between the mineralogical chemical transformations in rock types that appear in the tunnel with their resistance. With the results, it was found the importance of hydrothermal alteration in the projects of tunnels and thus it can be concluded that small geological approaches can minimize various engineering problems.

The properties of the surrounding rock mass in underground projects have significant impacts on the design and construction. However, it is quite challenging to evaluate rock mass properties due to the great uncertainties of the geological conditions. Besides, even if techniques of field test have obtained a well development, the high expense of tests and scattering results always make it difficult to cover a large domain in a complex project. In recent years, because of the maturity of numerical analysis as well as the wide use of tunnel deformation measurements, displacement-based back analysis has become a popular and effective indirect method to estimate rock mass properties.The main purpose of this thesis was to perform a displacement-based back analysis on the in-situ stress ratio and Young’s modulus of the exploratory tunnel BP201, which constitutes the passage under the Lake Mälaren in the Stockholm Bypass project. The back analysis was carried out using the Pattern search method and the Simplex method. The error function was built according to the least square method, and the commercial finite element software Plaxis 2D was used to calculate theoretical deformations. Moreover, a sensitivity analysis was performed to study the influence of starting point and how other numerical model parameters affects the results of the back analysis.The two optimization algorithms used in this study provided an in-situ stress ratio and Young’s modulus with close estimations to the measured deformations. For the specific problem analysed in this thesis, it was found that the Simplex method was more suitable than the Pattern search method. It was also concluded that a better choice of starting point can improve the precision and efficiency of the back analysis. / Bergmassans egenskaper har en stor påverkan vid dimensioneringen och utformningen av förstärkningen i tunnlar och vid indelningen av uttagssekvenser vid tunneldrivning. Det är emellertid svårt att utvärdera bergmassans egenskaper till följd av stora osäkerheter i de geologiska förhållandena. Även om tekniker för provning i fält har utvecklats är de relativt kostsamma och det är svårt att täcka in hela den geologiska domänen i stora projekt. På senare år har utvecklingen av numeriska metoder och deformationsmätningar i tunnlar möjliggjort bestämning av bergmassans egenskaper genom deformationsbaserad bakåtanalys.Syftet med detta examenarbete var att utföra en deformationsbaserad bakåtanalys av in-situ spänningstillståndet och bergmassans elasticitets-modul i bypass tunneln BP 201 under passagen av sjön Mälaren i Stockholm, vilket är en del av projektet Förbifart Stockholm. I bakåt-analysen användes metoderna ”the Pattern Search Method” och ”the Simplex Metod”. Minsta kvadratmetoden användes som felfunktion. Tvådimensionella numeriska beräkningar av deformationerna i tunneln utfördes med det finita elementprogrammet Plaxis 2D. En känslighets-analys gjordes för att studera inverkan på resultatet vid val av startpunkt i bakåtanalysen och hur osäkerheter i övriga parametrar påverkade resultatet.De två optimeringsalgoritmerna som användes i denna studie resulterade i in-situ spänningar och en elasticitetsmodul som genererade beräknade deformationer nära de uppmätta. For det studerade problemet i detta arbete var ”the Simplex Method” lämpligare att använda än ”the Pattern Search Method”. Genom att välja ett lämpligare startvärde kunde också precisionen och effektiviteten i bakåtanalysen förbättras.

The distinct element method (DEM) is a useful tool in rock engineering to model jointed rock masses. To simulate a jointed rock mass realistically, the main challenge is to be able to capture its complex geometry which consists of blocks with various shapes and sizes, and to model the interactions between these blocks. The main contribution of this thesis is the development of novel algorithms in the DEM to model jointed rock masses, namely rock slicing procedures for block generation, and algorithms for contact detection between polygonal blocks in 2-D or polyhedral blocks in 3-D. These algorithms make use of convex optimisation techniques, for which there exist efficient solution procedures. They do not rely on conventional vertex-edge-face hierarchical data structures and tedious housekeeping algorithms. The algorithms have been verified against analytical and numerical solutions, as well as validated against experimental results published in the literature. Among those, the results of DEM simulations were compared against the experimental model tests and numerical simulations of jointed beams carried out by Talesnick et al. (2007) and Tsesarsky & Talesnick (2007) respectively. Emphasis was placed on modelling the stiffness of the block interfaces accurately, and this was accomplished by reinterpreting the laboratory data published by the investigators. The capabilities of the numerical tools are also examined and demonstrated in areas for which the DEM has found practical application. A substantial fraction of this thesis is devoted to illustrating how these tools can assist the engineer in designing support systems; for example, designing the length and spacing of rock bolts and the lining thickness for a tunnel. Algorithms to model rock bolt and lining support were implemented for this purpose. Interesting comparisons with elastic solutions for supported openings were obtained. Further, it is shown that the relative benefit of introducing more rock bolts or thicker lining can be evaluated using the numerical tools with the aid of an interaction diagram. In the final part of this thesis, the case history of the 1963 Vaiont rock slide in Italy is studied. The 2-D analyses led to useful insights concerning the influence of the reservoir water level, the rock mass strength and deformability, and the slide surface shear stiffness. 3-D analyses were undertaken to investigate the influence of the eastern boundary of the slope, and interesting insights were obtained concerning the slope kinematics. Overall, the case study shows that the tools are capable of modelling problems with specific physical and geometrical detail in both 2-D and 3-D.

Ancoragens são muito utilizadas na estabilização do maciço rochoso pela rapidez e baixo custo, embora sua análise não seja completamente entendida devido à interação de diferentes materiais como rocha, graute e aço. Este documento apresenta os resultados de um estudo realizado em juntas lisas reforçadas com ancoragens. Foram ensaiadas ancoragens com barras de diferentes diâmetros e diferentes orientações em relação ao plano da descontinuidade. Os ensaios realizados para avaliar o comportamento deste tipo de reforço foram o ensaio de arrancamento em tubo duplo e o ensaio de cisalhamento em juntas lisas reforçadas. Os ensaios de arrancamento em tubo duplo demonstraram que a resistência ao arrancamento é dependente da resistência à tração da barra. As deformações internas no sistema foram idealizadas através da obtenção de um comprimento livre hipotético de uma barra livre submetida a tração. Nos ensaios de cisalhamento, avaliou-se a melhora da resistência ao cisalhamento de descontinuidades lisas reforçadas com barras ancoradas. Observaram-se dois picos de carga mobilizada antes da ruptura do sistema no caso de barras perpendiculares ao plano da descontinuidade. Este fato introduz significativa ductilidade ao sistema e é importante do ponto de vista de confiabilidade do sistema. A ruptura das ancoragens se produz devido a uma combinação de efeitos de tração, flexão, e cortantes. Os sistemas reforçados com áreas maiores de aço apresentaram maior ductilidade, e, portanto oferecem maior segurança. Os resultados sugerem que uma vez superado o comprimento mínimo ancorado a ruptura das ancoragens acontecerá por ruptura das barras de aço e não por aderência na interface barra-graute, concluindo-se que a resistência das ancoragens é dependente da resistência de ruptura e da área de aço utilizada. Finalmente, esta pesquisa contribui ao entendimento dos mecanismos de ruína que acontecem num maciço reforçado com ancoragens. / Rock anchors are widely used to stabilize rock masses due to their rapid installation and low cost. Their behavior is not fully understood because of the interaction of different elements such as rock, grout and steel. This document presents the results of both pull-out and shear tests on steel bar reinforced discontinuities. Tests were carried out with different diameters and orientations of bars with respect to the discontinuity plane. Double-pipe pullout tests and smooth-joint anchor-reinforced shear tests were performed. The results of double-pipe pull-out tests were analyzed in terms of both strength and deformations. Internal strains were idealized through a model based on hypothetical length of a free bar. In the smooth-joint anchor-reinforced shear tests, both increase in shear strength and ductility were evaluated. Two load peaks were observed in test with bars perpendicular to the joint plane. Ductility is significantly increased with respect to joints reinforced with inclined bars. This is important for reliability evaluation. The failure of anchors is produced by a combination of tensile, bending, and shear internal forces. The systems reinforced with a greater amount of steel presented more ductile behavior than those less reinforced. The results suggest that since the minimum anchor length is exceeded, the system failure is governed by the rebar failure and not by the adhesion in the rebar-grout interface. From this, it is concluded that the anchor strength is dependent on the strength and cross section area of the rebar. Finally, this research contributes to better understanding of the failure mechanisms of anchor-reinforced rock masses.