[pt] Esta tese apresenta o fenômeno de ruptura por tombamento bloco-flexural, que acontece na zona NW da mina Tintaya. O objetivo do presente estudo é contribuir o conhecimento de este tipo de fenômeno de ruptura, quantificando as características do maciço rochoso com as técnicas da mecânica das rochas. O trabalho inicia-se por uma caracterização geral da zona de estudo, com especial relevo das propriedades geomecánicas das descontinuidades presentes, pelo que foram desenvolvidos mapeamentos das caras de bancada e a amostragem da rocha intacta, esta data permitiu estabelecer correlações dos parâmetros geomecânicos e fazer a análise cinemática da zona de estudo. Após de fazer a caracterização e avaliação das características das descontinuidades, foi definido o tombamento bloco-flexural, pelo jeito das descontinuidades presentes no maciço, já que este tipo de ruptura é mais complexo do que os outros tipos de tombamento, porque é uma combinação de tombamento e deslizamento dos blocos. Em vez da ruptura flexural de colunas contínuas, neste caso o tombamento é resultado de deslocamentos acumulados das juntas transversais. Com o objetivo de fazer uma análise numérica, obtou-se por um modelo contínuo- equivalente que inclui os efeitos de orientação e espaçamento das juntas é o modelo de plasticidade de Cosserat. O contínuo de Cosserat, conhecido também como contínuo micropolar acrescenta os graus de liberdade de rotação ao contínuo convencional. Pelo que foi analisado este tipo de ruptura através de uma modelagem computacional com um programa de elementos finitos feito na PUC-Rio, assim, tornar possível a modelagem computacional com a teoria do continuo de Cosserat. / [en] This thesis presents the block - flexural toppling failure phenomenon, which happens at NW zone of the Tintaya´s mine. The objective of the present study is to contribute the knowledge of this type of phenomenon of failure, quantifying the characteristics of rock mass with the techniques of the rock mechanics. The work begins for a general characterization of the zone, with special relief of the geomechanical properties of the discontinuities, which were developed the window sampling (bench face mapping) and sampling of the intact rock, this information allowed to establish correlations of the geomechanical parameters and make feasible kinematics analysis from the zone of study. After doing the rock mass characterization and evaluation of the characteristics of the discontinuities, the block - flexural toppling failure was defined, on those long column rocks crossed by numerous huge subhorizontal joints. The block-flexural type failure is a complex phenomenon compared with other types of toppling failure, because it is a combination of pure toppling and sliding. With the intention of numerical analysis, I have been proposed analyzing this rupture for a continuum - equivalent model of Cosserat, that includes the orientation and the discontinuity´s spacing. This model is known also as continuum micropolar, which adds the degrees of freedom of rotation to a conventional continuum. It was analyzed this type of failure through a computational modeling with a program of finite elements made in the PUC-Rio, so, the computational modeling possible with the theory of continuum of Cosserat.

Taludes escavados em filitos muitas vezes estão sujeitos à instabilidade, principalmente quando há outras famílias de descontinuidades presentes na estrutura. Este problema está presente na mina de Candiota, onde foi identificado, em um dos taludes, potencialidade para ruptura por tombamento. Este trabalho aborda uma discussão sobre métodos analíticos e numéricos aplicado a tombamento primário, com objetivo de avaliar o fator de segurança do talude em estudo por meio de método numérico por elementos finitos, utilizando o Phase2 da Rocscience, e métodos analíticos. Também são apresentadas doze simulações para avaliar se o movimento de tombamento em modelagens numéricas obedece a um efeito de escala. Com uso de métodos numéricos dois modelos foram construídos: um contínuo equivalente e outro contínuo (mas com as descontinuidades inseridas no modelo). No modelo com as descontinuidades a rocha foi tratada como elástica por meio do critério de Hoek-Brown e as descontinuidades foram tratadas como elasto-plásticas por meio do critério de Mohr-Coulomb. Os resultados das modelagens da mina de Candiota foram semelhantes e mostraram fatores de segurança em níveis de estabilidade, sendo que no modelo contínuo (mas com descontinuidades inseridas) se observou de forma mais clara as tensões cisalhantes induzidas nas descontinuidades quando ocorre o movimento de tombamento. O uso dos métodos analíticos mostrou-se ineficientes para o problema apresentado. Os resultados das doze modelagens sugerem que o aumento do espaçamento das descontinuidades influencia nos fatores de resistência dos taludes e na forma do movimento de tombamento. / Slopes in phyllites are often subject to instability, especially when there are other families of discontinuities in the structure. This problem is present in Candiota mine, which was identified in one of the slopes potential to toppling. This work show a discussion of analytical and numerical methods applied to toppling, to evaluate the slope safety factor being studied by numerical method finite element using the Phase2 of Rocscience, and analytical methods. Also shown are twelve simulations to evaluate if the toppling in numerical modeling follows a scaling effect. With use of numerical methods two models were built: an equivalent continuous and another solid (but with discontinuities inserted in the model). In the model with the discontinuities the rock was treated as elastic by the Hoek-Brown criterion and discontinuities were treated as elastic-plastic by the Mohr-Coulomb criterion. The results of Candiota mine were similar and showed safety factors in stability levels, and in the continuous model (with discontinuities) was observed more clearly the shear stress induced in discontinuities when the movement of overturning occurs. The use of analytical methods proved inefficient for the problem presented. The results of the twelve modeling suggests increasing the spacing of the discontinuities of slope influences the resistance factor and the form of the toppling movement.

Taludes escavados em filitos muitas vezes estão sujeitos à instabilidade, principalmente quando há outras famílias de descontinuidades presentes na estrutura. Este problema está presente na mina de Candiota, onde foi identificado, em um dos taludes, potencialidade para ruptura por tombamento. Este trabalho aborda uma discussão sobre métodos analíticos e numéricos aplicado a tombamento primário, com objetivo de avaliar o fator de segurança do talude em estudo por meio de método numérico por elementos finitos, utilizando o Phase2 da Rocscience, e métodos analíticos. Também são apresentadas doze simulações para avaliar se o movimento de tombamento em modelagens numéricas obedece a um efeito de escala. Com uso de métodos numéricos dois modelos foram construídos: um contínuo equivalente e outro contínuo (mas com as descontinuidades inseridas no modelo). No modelo com as descontinuidades a rocha foi tratada como elástica por meio do critério de Hoek-Brown e as descontinuidades foram tratadas como elasto-plásticas por meio do critério de Mohr-Coulomb. Os resultados das modelagens da mina de Candiota foram semelhantes e mostraram fatores de segurança em níveis de estabilidade, sendo que no modelo contínuo (mas com descontinuidades inseridas) se observou de forma mais clara as tensões cisalhantes induzidas nas descontinuidades quando ocorre o movimento de tombamento. O uso dos métodos analíticos mostrou-se ineficientes para o problema apresentado. Os resultados das doze modelagens sugerem que o aumento do espaçamento das descontinuidades influencia nos fatores de resistência dos taludes e na forma do movimento de tombamento. / Slopes in phyllites are often subject to instability, especially when there are other families of discontinuities in the structure. This problem is present in Candiota mine, which was identified in one of the slopes potential to toppling. This work show a discussion of analytical and numerical methods applied to toppling, to evaluate the slope safety factor being studied by numerical method finite element using the Phase2 of Rocscience, and analytical methods. Also shown are twelve simulations to evaluate if the toppling in numerical modeling follows a scaling effect. With use of numerical methods two models were built: an equivalent continuous and another solid (but with discontinuities inserted in the model). In the model with the discontinuities the rock was treated as elastic by the Hoek-Brown criterion and discontinuities were treated as elastic-plastic by the Mohr-Coulomb criterion. The results of Candiota mine were similar and showed safety factors in stability levels, and in the continuous model (with discontinuities) was observed more clearly the shear stress induced in discontinuities when the movement of overturning occurs. The use of analytical methods proved inefficient for the problem presented. The results of the twelve modeling suggests increasing the spacing of the discontinuities of slope influences the resistance factor and the form of the toppling movement.

Taludes escavados em filitos muitas vezes estão sujeitos à instabilidade, principalmente quando há outras famílias de descontinuidades presentes na estrutura. Este problema está presente na mina de Candiota, onde foi identificado, em um dos taludes, potencialidade para ruptura por tombamento. Este trabalho aborda uma discussão sobre métodos analíticos e numéricos aplicado a tombamento primário, com objetivo de avaliar o fator de segurança do talude em estudo por meio de método numérico por elementos finitos, utilizando o Phase2 da Rocscience, e métodos analíticos. Também são apresentadas doze simulações para avaliar se o movimento de tombamento em modelagens numéricas obedece a um efeito de escala. Com uso de métodos numéricos dois modelos foram construídos: um contínuo equivalente e outro contínuo (mas com as descontinuidades inseridas no modelo). No modelo com as descontinuidades a rocha foi tratada como elástica por meio do critério de Hoek-Brown e as descontinuidades foram tratadas como elasto-plásticas por meio do critério de Mohr-Coulomb. Os resultados das modelagens da mina de Candiota foram semelhantes e mostraram fatores de segurança em níveis de estabilidade, sendo que no modelo contínuo (mas com descontinuidades inseridas) se observou de forma mais clara as tensões cisalhantes induzidas nas descontinuidades quando ocorre o movimento de tombamento. O uso dos métodos analíticos mostrou-se ineficientes para o problema apresentado. Os resultados das doze modelagens sugerem que o aumento do espaçamento das descontinuidades influencia nos fatores de resistência dos taludes e na forma do movimento de tombamento. / Slopes in phyllites are often subject to instability, especially when there are other families of discontinuities in the structure. This problem is present in Candiota mine, which was identified in one of the slopes potential to toppling. This work show a discussion of analytical and numerical methods applied to toppling, to evaluate the slope safety factor being studied by numerical method finite element using the Phase2 of Rocscience, and analytical methods. Also shown are twelve simulations to evaluate if the toppling in numerical modeling follows a scaling effect. With use of numerical methods two models were built: an equivalent continuous and another solid (but with discontinuities inserted in the model). In the model with the discontinuities the rock was treated as elastic by the Hoek-Brown criterion and discontinuities were treated as elastic-plastic by the Mohr-Coulomb criterion. The results of Candiota mine were similar and showed safety factors in stability levels, and in the continuous model (with discontinuities) was observed more clearly the shear stress induced in discontinuities when the movement of overturning occurs. The use of analytical methods proved inefficient for the problem presented. The results of the twelve modeling suggests increasing the spacing of the discontinuities of slope influences the resistance factor and the form of the toppling movement.

In this thesis, the dynamic modeling of a wheelchair-human system is performed, and the effects of steering action and sudden slope changes along the path on the system stability are analyzed for different road and driving conditions. For the cases where the wheelchair system is unstable three methods are proposed for stability augmentation. This study is performed to improve the stability of the wheelchair system under varying road conditions so as to increase the limit of independency for wheelchair users and enhance their life quality. Two separate mathematical models are obtained for the wheelchair driven on constant sloped and changing sloped roads. Matlab Simulink models are constructed with the obtained mathematical models and control structure. The stability of the system is analyzed by case studies and it is seen that the system is unstable in some of these cases. Three methods are used for enhancement of the stability. One is the speed reduction via joystick module during steep turns, by which the speed of the wheelchair is reduced automatically for a safe steering, but the wheelchair follows the desired course. The second method is the use of a shape filter in order to obtain a less jerky response for the speed. As a final method, the center of mass of the wheelchair-human system is shifted gently in a controlled manner to the side where the reaction force on the wheels decreases.

This thesis explores the structure of games, including both the internal structure of various games and also the structure of classes of games as partially ordered sets. Internal structure is explored through consideration of juxtapositions of game positions and how the underlying games interact. We look at ordinal sums and introduce side-sums as a means of understanding this interaction, giving a full solution to a Toppling Dominoes variant through its application. Loopy games in which only one player is allowed a pass move, referred to as Oslo games, are introduced and their game structure explored. The poset of Oslo games is shown to form a distributive lattice. The Oslo forms of Wythoff’s game, Grundy’s game and octal .007 are introduced and full solutions given. Finally, the poset of option-closed games is given up to day 3 and all are shown to form a planar lattice. The option-closed game of Cricket Pitch is also fully analyzed.

Following the 22 February 2011, MW 6.2 earthquake located on a fault beneath the Port Hills of Christchurch, fissuring of up to several hundred metres in length was observed in the loess and loess-colluvium of foot-slope positions in north-facing valleys of the Port Hills. The fissuring was observed in all major valleys, occurred at similar low altitudes, showing a contour-parallel orientation and often accompanied by both lateral compression/extension features and spring formation in the valley floor below. Fissuring locations studied in depth included Bowenvale Valley, Hillsborough Valley, Huntlywood Terrace–Lucas Lane, Bridle Path Road, and Maffeys Road–La Costa Lane. Investigations into loess soil, its properties and mannerisms, as well as international examples of its failure were undertaken, including study of the Loess Plateau of China, the Teton Dam, and palaeo-fissuring on Banks Peninsula. These investigations lead to the conclusion that loess has the propensity to fail, often due to the infiltration of water, the presence of which can lead to its instantaneous disaggregation. Literature study and laboratory analysis of Port Hills loess concluded that is has the ability to be stable in steep, sub-vertical escarpments, and often has a sub-vertically jointed internal structure and has a peak shear strength when dry. Values for cohesion, c (kPa) and the internal friction angle, ϕ (degrees) of Port Hills loess were established. The c values for the 40 Rapaki Road, 3 Glenview Terrace loess samples were 13.4 kPa and 19.7 kPa, respectively. The corresponding ϕ values were thought unusually high, at 42.0° and 43.4°.The analysed loess behaved very plastically, with little or no peak strength visible in the plots as the test went almost directly to residual strength. A geophysics resistivity survey showed an area of low resistivity which likely corresponds to a zone of saturated clayey loess/loess colluvium, indicating a high water table in the area. This is consistent with the appearances of local springs which are located towards the northern end of each distinct section of fissure trace and chemical analysis shows that they are sourced from the Port Hills volcanics. Port Hills fissuring may be sub-divided into three categories, Category A, Category B, and Category C, each characterised by distinctive features of the fissures. Category A includes fissures which display evidence of, spring formation, tunnel-gullying, and lateral spreading-like behaviour or quasi-toppling. These fissures are several metres down-slope of the loess-bedrock interface, and are in valleys containing a loess-colluvium fill. Category B fissures are in wider valleys than those in Category A, and the valleys contain estuarine silty sediments which liquefied during the earthquake. Category C fissures occurred at higher elevations than the fissures in the preceding categories, being almost coincident with bedrock outcropping. It is believed that the mechanism responsible for causing the fissuring is a complex combination of three mechanisms: the trampoline effect, bedrock fracturing, and lateral spreading. These three mechanisms can be applied in varying degrees to each of the fissuring sites in categories A, B, and C, in order to provide explanation for the observations made at each. Toppling failure can describe the soil movement as a consequence of the a three causative mechanisms, and provides insight into the movement of the loess. Intra-loess water coursing and tunnel gullying is thought to have encouraged and exacerbated the fissuring, while not being the driving force per se. Incipient landsliding is considered to be the least likely of the possible fissuring interpretations.

[pt] Em um maciço rochoso, as fraturas apresentam-se de forma irregular e descontínua. A complexidade na distribuição espacial destas descontinuidades faz com que o mecanismo de ruptura por tombamento ocorra mais frequentemente por uma combinação de dois tipos de fenômenos: Tombamento de blocos e flexural. Assim, a ruptura por tombamento do tipo bloco-flexural pode ser considerada a forma mais comum presente neste tipo de mecanismo. Trabalhos utilizando o método de equilíbrio limite ou modelos físicos estudam a influência desta combinação, mas a literatura relata poucos trabalhos numéricos que possam ajudar na compreensão dos fenômenos envolvidos neste processo de ruptura. O presente trabalho procura modelar o mecanismo de ruptura por tombamento bloco-flexural através do método dos elementos discretos (DEM), utilizando o software PFC (Particle Flow Code). Em particular, procura-se avaliar as potencialidades do método para estudos deste tipo, utilizando um novo modelo de contato entre partículas e a calibração das propriedades elásticas do material sintético. Apresentam-se também detalhes da metodologia utilizada e exemplos de validação, incluindo comparações com soluções analíticas e semi-analíticas disponíveis na literatura. / [en] Joints exhibit an irregular and discontinuous behavior inside the rock mass. The spatial distribution complexity of these discontinuities causes the toppling failure occurs more often by a combination of two types of toppling phenomena: toppling of rock blocks and flexural toppling. Thus, the block-flexural toppling can be considered the most common when a toppling process is being developed in rock slopes. Analytical and physical models approach, were presented in order to study each process individually, but the literature reports few works that may help to understand the influence of the two processes together. The present work aims to represents the mechanism of block-flexural toppling through the discrete elements method (DEM) using the PFC (Particle Flow Code) software. In particular, the objective is to assess the potential of the method for studies of this type, using a new model of contact between particles and the elastic properties calibration of the synthetic material. In order to do that, the work shows the methodology details and validation examples, including comparisons with analytical and semi-analytical solutions that are available in the literature.