[pt] As alterações no solo decorrentes de um elemento de fundação profunda e seus desempenhos sob a aplicação de carga axial são processos há muito tempo estudados na engenharia civil. Diversos fatores como, método de instalação utilizado, formato da estaca, interações solo-estrutura, mecanismos de transferências de carga, movimentação do solo e alterações na compressibilidade e tensões do solo adjacente, apresentam desafios importantes que ainda não foram totalmente compreendidos nos fenômenos de penetração e capacidade de suporte em estacas. Diversos avanços foram realizados ao longo das últimas décadas para se investigar estes comportamentos, a partir procedimentos experimentais e novas formas de instrumentação, assim como ferramentas numéricas sofisticadas com o emprego de complexos modelos constitutivos em elementos finitos. Apesar destes avanços, a modelagem numérica dos processos citados, com todas as suas complexidades, ainda encontra alguns desafios. Devido a facilidade em lidar com simulações de grandes deformações e de captar o comportamento dilatante e nãolinear de solos granulares, o Método dos Elementos Discretos apresenta uma excelente ferramenta para investigar estes processos, sem grandes complicações. O presente trabalho procurou avaliar os comportamentos obtidos a partir de diferentes processos de instalação da estaca e seus efeitos nos resultados da prova de carga estática em solos granulares. As alterações de tensão e deslocamento foram avaliadas nos diferentes modelos e discutindo sobre uma metodologia básica para obter correspondências qualitativas e quantitativas com os diferentes comportamentos de campo e laboratório. Para este estudo foram utilizados os programas PFC, na versão 2D, e o programa UDEC, da Itasca co. / [en] The disturbances experienced by the soil owing to the load applied to a deep foundation and its relative behavior consist of long time studied phenomena in civil engineering. Several factors such as the installation methods, the pile geometry, the interactions between soil and structure, the load-transfer mechanisms, the soil movements and the disturbances in the stress and compressibility fields present major challenges that have not yet been completely understood. Numerous advances have been observed throw-out the last decades, in order to investigate these behaviors starting from the different pile instrumentations, the use of calibration cameras and centrifuges and most recently the measurement of the stress and strain fields inside the soil mass in model tanks. Despite the advances the numerical modelling of those processes still faces major challenges. Due to simplified approach used by the Discrete Element Method to simulate large deformation and the dilant non-linear behavior of granular soils, it presents as an excellent tool to investigate these processes without further complications. The present work proposed to evaluate the different behaviors obtained with the variations of installation methods investigated as well as their effects in the results of the Pile Load Test. The disturbances were also evaluated in the different models considered and a basic method to achieve qualitative and quantitative comparisons was discussed. These studies were made possible with the help of the PFC2D and UDEC programs developed by Itasca co.

[pt] Diferentes mecanismos de ruptura são considerados no momento de avaliar a estabilidade de um maciço rochoso fraturado. Entre estes, os mecanismos de ruptura tipo planar, em cunha e tombamentos têm sido estudados intensivamente, existindo atualmente modelos matemáticos que permitem avaliá-los. Estes mecanismos de ruptura são restritos a taludes pequenos e com fraturas contínuas, nas quais o deslizamento ocorre ao longo destas descontinuidades. Em casos de taludes de grande altura ou quando a persistência das fraturas é pequena em relação à escala do talude, o fraturamento torna-se descontínuo. Neste caso, o mecanismo de ruptura mais provável é o tipo Step-Path, o qual, a superfície de ruptura é formada por fraturas que se propagam através da rocha intacta juntando-se entre elas. Este fenômeno de união de fraturas é chamado de coalescência. Análises de estabilidade, como os probabilísticos ou por equilíbrio limite, são usados atualmente para avaliar estes tipos de rupturas, não se tendo ainda o desenvolvimento de um modelo numérico que possa representá-lo e reforçar estas teorias. O presente trabalho avalia o uso do Método dos Elementos Discretos na modelagem do mecanismo de ruptura tipo step- path, realizando uma análise de estabilidade que permita comparar os seus resultados com o método de equilíbrio limite. Foi utilizado o programa PFC nas versões 2D e 3D, assim como o programa FracGen para a geração de fraturas tridimensionais. A análise tridimensional foi feita mediante um acoplamento PFC3D-FracGen. A pesquisa inclui a análise e modelagem dos fenômenos de coalescência em amostras, assim como a influência da anisotropia na resistência das rochas em ensaios triaxiais. / [en] Different failure mechanisms are considered when a fracturated rock mass is valued. Some of them are being subject of accurate study, like planar failure mechanism, wedges and toppling, which are currently valued by mathematical models. These failure mechanisms are restricted to small slopes and with continue fractures, where the sliding occurs along these discontinuities. To height slopes or when the fracture persistence is smaller than the slope scale, the fracturing becomes discontinuous. In this case, the most probable failure mechanism to happen is the step-path type, in which the failure surface is composed by fractures that propagate through the intact rock and that are joined together. This phenomenon of fracture union is known as coalescence. Stability analysis, like probability analysis or limit equilibrium analysis are currently utilized to evaluate this kind of failures, but its important to develop a numerical model to represent and reinforce these theories. This work aims to evaluate the use of Discrete Element Method to model step-path failure mechanism on a stability analysis and to compare the results with limit equilibrium method. The program used to simulate the slope is PFC (2D and 3D) and the program FracGen was used to generate three-dimensional fractures. Three-dimensional analysis was done by a coupling between PFC3D and FracGen. The research includes the analysis and modeling of coalescence phenomenon on rock samples, as well as the analysis of the anisotropy influence on rock strength obtained from triaxial tests.

[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.

Diese Forschung zielt darauf ab, den Einsatz realistischer Mineralmikrostrukturen in Mineralverarbeitungssimulationen Simulationen von Aufbereitungsprozessen zu ermöglichen. Insbesondere Zerkleinerungsprozesse, wie z.B. das Brechen und Mahlen von mineralischen Rohmaterialien, werden stark von der mineralischen Mikrostruktur beeinflusst, da die Textur und die Struktur der vielen Körner und ihre mikromechanischen Eigenschaften das makroskopische Bruchverhalten bestimmen. Ein Beispiel: Stellen wir uns vor, wir haben ein mineralisches Material, das im Wesentlichen aus Körnern zweier verschiedener Mineralphasen, wie Quarz und Feldspat, besteht. Wenn die mikromechanischen Eigenschaften dieser beiden Phasen unterschiedlich sind, wird sich dies wahrscheinlich auf das makroskopische Bruchverhalten auswirken. Unter der Annahme, dass die Körner eines der Minerale bei geringeren Belastungen brechen, ist es wahrscheinlich, dass sich ein Riss durch einen Stein dieses Materials durch die schwächeren Körner ausbreitet. Tatsächlich ist dies eine wichtige Eigenschaft für die Erzaufbereitung. Um wertvolle Mineralien aus einem Erz zu gewinnen, ist es wichtig, sie aus dem kommerziell wertlosen Material, in dem sie vorkommen, zu befreien. Dazu ist es wichtig zu wissen und zu verstehen, wie das Material auf Korngrößenebene bricht. Um diesen Bruch simulieren zu können, ist es wichtig, realistische Modelle der mineralischen Mikrostrukturen zu verwenden. Diese Studie zeigt, wie solche realistischen zweidimensionalen Mikrostrukturen auf der Grundlage der quantitativen Mikrostrukturanalyse am Computer erzeugt werden können. Darüber hinaus zeigt die Studie, wie diese synthetischen Mikrostrukturen dann in die gut etablierte Diskrete-Elemente-Methode integriert werden können, bei der der Bruch von mineralischem Material auf Korngrößenebene simuliert werden kann.:List of Acronyms VII List of Latin Symbols IX List of Greek Symbols XV 1 Introduction 1 1.1 Motivation for using realistic microstructures in Discrete Element Method (DEM) 1 1.2 Possibilities for using realistic mineral microstructures in DEM simulations . 4 1.3 Objective and disposition of the thesis . . . . . . . . . . . . . . . . . . . . 7 2 Background 9 2.1 Discrete Element Method (DEM) . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.1 Fundamentals of the Discrete Element Method (DEM) . . . . . . . . 9 2.1.2 Applications of DEM in comminution science . . . . . . . . . . . . . 21 2.1.3 Limitations of DEM in comminution science . . . . . . . . . . . . . . 26 2.2 Quantitative Microstructural Analysis . . . . . . . . . . . . . . . . . . . . . 29 2.2.1 Fundamentals of the Quantitative Microstructural Analysis . . . . . . 29 2.2.2 Applied QMA in mineral processing . . . . . . . . . . . . . . . . . . 49 2.2.3 Applicability of the QMA for the synthesis of realistic microstructures 49 3 Synthesis of realistic mineral microstructures for DEM simulations 51 3.1 Development of a computer-assisted QMA for the analysis of real and synthetic mineral microstructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.1.1 Fundamentals of the computer-assisted QMA . . . . . . . . . . . . 53 3.1.2 The requirements for the false-color image. . . . . . . . . . . . . . 54 3.1.3 The conversion of a given real mineral microstructure into a false-color image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.1.4 Implementation of the point, line, and area analysis . . . . . . . . . 59 3.1.5 Selection of appropriate QMA parameters for analyzing two-dimensional microstructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.1.6 Summary of the principles of the adapted Quantitative Microstructural Analysis (QMA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.2 Analysis of possible strategies for the microstructure synthesis . . . . . . . . 71 3.3 Implementation of the drawing method . . . . . . . . . . . . . . . . . . . . 76 3.3.1 Drawing of a single grain . . . . . . . . . . . . . . . . . . . . . . . 77 XVIII List of Greek Symbols 3.3.2 Drawing of multiple grains, which form a synthetic microstructure . . 81 3.3.3 Synthesizing mineral microstructures consisting of multiple phases . 85 3.4 The final program for microstructure analysis and synthesis . . . . . . . . . 89 3.4.1 Synthesis and analysis of an example microstructure . . . . . . . . . 90 3.4.2 Procedure for generating a realistic synthetic microstructure of a given real microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4 Validation of the synthesis approach 103 4.1 Methodical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.1.1 The basic idea of the validation procedure . . . . . . . . . . . . . . 103 4.1.2 The experimental realizations . . . . . . . . . . . . . . . . . . . . . 108 4.2 Basic indenter test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.2.1 Considerations for the basic indenter test . . . . . . . . . . . . . . . 109 4.2.2 Realization and evaluation of the real basic indenter test . . . . . . . 114 4.2.3 Realization and evaluation of the simulated basic indenter test . . . 127 4.2.4 Conclusions on the basic indenter test . . . . . . . . . . . . . . . . . 138 4.3 Extended indenter test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 4.3.1 Basic considerations for the extended indenter test . . . . . . . . . . 139 4.3.2 Realization and evaluation of the real extended indenter test . . . . 142 4.3.3 Realization and evaluation of the simulated extended indenter test . 154 4.3.4 Conclusions on the extended indenter test . . . . . . . . . . . . . . 171 4.4 Particle bed test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 4.4.1 Basic considerations for the particle bed test . . . . . . . . . . . . . 173 4.4.2 Realization and evaluation of the real particle bed test . . . . . . . . 176 4.4.3 Realization and evaluation of the simulated particle bed test . . . . . 188 4.4.4 Conclusions on the particle bed test . . . . . . . . . . . . . . . . . . 203 5 Conclusions and directions for future development 205 6 References 211 List of Figures 229 List of Tables 235 Appendix 237 / This research aims to make it possible to use realistic mineral microstructures in simulations of mineral processing. In particular, comminution processes, such as the crushing and grinding of raw mineral materials, are highly aff ected by the mineral microstructure, since the texture and structure of the many grains and their micromechanical properties determine the macroscopic fracture behavior. To illustrate this, consider a mineral material that essentially consists of grains of two diff erent mineral phases, such as quartz and feldspar. If the micromechanical properties of these two phases are diff erent, this will likely have an impact on the macroscopic fracture behavior. Assuming that the grains of one of the minerals break at lower loads, it is likely that a crack through a stone of that material will spread through the weaker grains. In fact, this is an important property for ore processing. In order to extract valuable minerals from an ore, it is important to liberate them from the commercially worthless material in which they are found. For this, it is essential to know and understand how the material breaks at grain-size level. To be able to simulate this breakage, it is important to use realistic models of the mineral microstructures. This study demonstrates how such realistic two-dimensional microstructures can be generated on the computer based on quantitative microstructural analysis. Furthermore, the study shows how these synthetic microstructures can then be incorporated into the well-established discrete element method, where the breakage of mineral material can be simulated at grain-size level.:List of Acronyms VII List of Latin Symbols IX List of Greek Symbols XV 1 Introduction 1 1.1 Motivation for using realistic microstructures in Discrete Element Method (DEM) 1 1.2 Possibilities for using realistic mineral microstructures in DEM simulations . 4 1.3 Objective and disposition of the thesis . . . . . . . . . . . . . . . . . . . . 7 2 Background 9 2.1 Discrete Element Method (DEM) . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.1 Fundamentals of the Discrete Element Method (DEM) . . . . . . . . 9 2.1.2 Applications of DEM in comminution science . . . . . . . . . . . . . 21 2.1.3 Limitations of DEM in comminution science . . . . . . . . . . . . . . 26 2.2 Quantitative Microstructural Analysis . . . . . . . . . . . . . . . . . . . . . 29 2.2.1 Fundamentals of the Quantitative Microstructural Analysis . . . . . . 29 2.2.2 Applied QMA in mineral processing . . . . . . . . . . . . . . . . . . 49 2.2.3 Applicability of the QMA for the synthesis of realistic microstructures 49 3 Synthesis of realistic mineral microstructures for DEM simulations 51 3.1 Development of a computer-assisted QMA for the analysis of real and synthetic mineral microstructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.1.1 Fundamentals of the computer-assisted QMA . . . . . . . . . . . . 53 3.1.2 The requirements for the false-color image. . . . . . . . . . . . . . 54 3.1.3 The conversion of a given real mineral microstructure into a false-color image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.1.4 Implementation of the point, line, and area analysis . . . . . . . . . 59 3.1.5 Selection of appropriate QMA parameters for analyzing two-dimensional microstructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.1.6 Summary of the principles of the adapted Quantitative Microstructural Analysis (QMA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.2 Analysis of possible strategies for the microstructure synthesis . . . . . . . . 71 3.3 Implementation of the drawing method . . . . . . . . . . . . . . . . . . . . 76 3.3.1 Drawing of a single grain . . . . . . . . . . . . . . . . . . . . . . . 77 XVIII List of Greek Symbols 3.3.2 Drawing of multiple grains, which form a synthetic microstructure . . 81 3.3.3 Synthesizing mineral microstructures consisting of multiple phases . 85 3.4 The final program for microstructure analysis and synthesis . . . . . . . . . 89 3.4.1 Synthesis and analysis of an example microstructure . . . . . . . . . 90 3.4.2 Procedure for generating a realistic synthetic microstructure of a given real microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4 Validation of the synthesis approach 103 4.1 Methodical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.1.1 The basic idea of the validation procedure . . . . . . . . . . . . . . 103 4.1.2 The experimental realizations . . . . . . . . . . . . . . . . . . . . . 108 4.2 Basic indenter test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.2.1 Considerations for the basic indenter test . . . . . . . . . . . . . . . 109 4.2.2 Realization and evaluation of the real basic indenter test . . . . . . . 114 4.2.3 Realization and evaluation of the simulated basic indenter test . . . 127 4.2.4 Conclusions on the basic indenter test . . . . . . . . . . . . . . . . . 138 4.3 Extended indenter test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 4.3.1 Basic considerations for the extended indenter test . . . . . . . . . . 139 4.3.2 Realization and evaluation of the real extended indenter test . . . . 142 4.3.3 Realization and evaluation of the simulated extended indenter test . 154 4.3.4 Conclusions on the extended indenter test . . . . . . . . . . . . . . 171 4.4 Particle bed test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 4.4.1 Basic considerations for the particle bed test . . . . . . . . . . . . . 173 4.4.2 Realization and evaluation of the real particle bed test . . . . . . . . 176 4.4.3 Realization and evaluation of the simulated particle bed test . . . . . 188 4.4.4 Conclusions on the particle bed test . . . . . . . . . . . . . . . . . . 203 5 Conclusions and directions for future development 205 6 References 211 List of Figures 229 List of Tables 235 Appendix 237

[pt] Esta dissertação tem como objetivo principal estudar o comportamento mecânico de um túnel, especificamente avaliando a degradação do maciço rochoso escavado de gnaisse ao longo do tempo, como se tem na região Sudeste do Rio de Janeiro. A maior cobertura da escavação subterrânea atinge a uma profundidade de 300m., com o um grau de alteração dos minerais da rocha escavada, seccionada por três famílias de descontinuidades que são de maior importância geológica com o potencial risco ao desabamento. Além disso, se avaliaram os cenários, em condições muito persistentes e moderadamente persistentes, com a finalidade de observar sua influência na estabilidade do túnel. Também foi avaliado o comportamento do maciço para três cenários de tensões in situ, K0= 1 (Condições Hidrostáticas), K0= 0.5 e K0= 1.5. Nas análises foram considerados a escavação com e sem elementos de suporte. Os suportes do maciço rochoso nas análises foram com concreto projetado com fibras metálicas (CPRF), reforço de cabos e a mistura dos dois. A análise numérica bidimensional da estabilidade da escavação, para os diferentes casos mencionados, foi feita utilizando o Método dos Elementos Discretos (MED), através do software comercial UDEC (Itasca, 2011). Nas análises dos mecanismos de ruptura com valores de deslocamentos cisalhantes máximos, foi observado que os efeitos do comportamento cisalhante do maciço são maiores na medida em que o ângulo de atrito vai diminuindo, tendo uma importante incidência na sua estabilidade o grau de persistência. Estes resultados mostram índices capazes de prever o comportamento de instabilidade da escavação para estes casos desenvolvidos. / [en] This thesis has the main objective to study the mechanical behavior of a tunnel, specifically assessing the degradation of gneiss rock mass excavated over time, as it has in the South-east region of Rio de Janeiro. The cover of the underground excavation reaches the depth of 300m. with a degree of alteration of minerals of the excavated rock, sectioned by three families of discontinuities that are of most geological importance with the potential risk of collapse. Moreover, scenarios are evaluated in conditions very persistent and moderately with the purpose of observing their influence on the stability of the tunnel. It was also rated the rock mass behavior for three scenarios of in situ stresses, K0= 1 (Conditions Hydrostatic), K0= 0.5 and K0= 1.5. In the analysis were considering the excavation with and without support elements. The supports of the rock mass in the analysis were with shotcrete with steel fibers (CPRF), reinforcement cable bolts and mixing the two. Two-dimensional numerical analysis of the stability of the excavation for the different cases mentioned was made using the Method of Discrete Elements (DEM) through the commercial software UDEC (Itasca, 2011). In the analysis of failure mechanisms with maximum shear displacement values, it was observed that the effects of mass shear behavior are larger in as far as than the friction angle decreases, with an important effect on their stability the degree of persistence. These results show indexes able to predict the behavior of instability of the excavation for these cases developed.

[pt] A perfuração de poços de petróleo em ambientes adversos requer especialistas dedicados a estuda-la a fim de garantir que ela ocorra de forma rápida, segura e com qualidade. Dentro desse contexto, há estudos experimentais e numéricos que avaliam a ação de corte feita por um cortador individual objetivando quantificar as forças de contato, propor soluções para aumentar o seu tempo de vida útil e a sua taxa de penetração, e entender o mecanismo de corte. Seguindo esta linha de pesquisa, a presente Tese visa oferecer uma melhor compreensão para o problema de interação rocha/cortador PDC (Polycrystalline Diamond Compact) ao longo da perfuração de depósitos evaporíticos de halita e de reservatórios de carbonatos. O estudo foi abordado através da modelagem numérica do ensaio de cortador único e da modelagem numérica de corte por múltiplos cortadores através do método dos elementos discretos. Resultados experimentais aferiram a calibração da amostra sintética e dos modelos numéricos de corte em rocha. Um estudo numérico paramétrico do ensaio de cortador único foi feito objetivando identificar parâmetros que controlam a ação de corte. Em seguida, foi desenvolvida uma equação analítica que quantifica a energia específica mecânica global resultante da ação de múltiplos cortadores, a fim de entender e quantificar qual a contribuição de cada cortador na eficiência global. A equação foi aplicada usando os resultados das modelagens numéricas de múltiplos cortadores. Constatou-se que o bom ajuste entre as previsões numéricas e os resultados experimentais validou o uso do método dos elementos discretos para modelar o processo de corte em diferentes tipos de rochas. A modelagem numérica desenvolvida neste estudo pode ser considerada uma ferramenta útil para projeto e otimização do desempenho de brocas de perfuração. / [en] Oil wells drilling in adverse environments requires specialists dedicated to study the drilling process to ensure a quickly, safely and quality performance. In this context, experimental and numerical studies can be find in technical literature that evaluate the cutting action done by a single cutter aiming to quantify the contact forces, proposing solutions to increase its useful life time and its rate of penetration, and to understand the cutting mechanism. Following this line of research, this Thesis aims to provide a better understanding regarding the rock / polycrystalline diamond compact cutter interaction during the halite deposits and carbonate reservoirs drilling. The study was approached through numerical modeling of the single cutter test and through numerical modeling of the cutting action by multiple cutters using the discrete element method. Experimental results were used to calibrate the synthetic sample and the rock cutting numerical models. A parametric numerical study of the single cutter test was done aiming to identify parameters that control the cutting action. Then, an analytical equation was developed that quantifies the global mechanical specific energy resulting from the cutting action of multiple cutters, in order to understand and quantify the contribution of each cutter to overall efficiency. The equation was applied using the results of numerical modeling of multiple cutters developed in this work. It was verified that the good agreement between numerical predictions and experimental results validated the use of the discrete element method to model the cutting process in different rock types. The numerical modeling developed in this study can be considered a useful tool for design and optimizing the performance of drill bits.