This thesis investigates a novel way to simulate cracks as an extension of the Mate- rial Point Method (MPM). Previous methods, like CRAMP (CRAcks with Material Points), often use an explicit crack representation to define the material crack. We use an implicit crack representation defined as the intersection between pieces of the original specimen created by a pre-fracture process. Material chunks are there- after forced together using massless particle constraints. The method has proven successful in tearing scenarios, and the main benefits are: (1) minor computational overhead compared to the initial MPM algorithm; (2) simple to implement and scales well in 3 dimensions; (3) gives easy and controllable setup phase for desired material failure mode. The development of the crack extension has required a fully general MPM solver that can handle arbitrarily many distinct bodies connected in the same simulation. Current collision schemes for MPM exists, however these are often focused on two-body collisions and does not scale well for additional objects due to inaccuracies in contact normal calculations. We present a method that uses an iterative pair-wise comparison scheme to resolve grid collisions that extends to any number of collision objects.

Understanding the deformation mechanisms and the impact forces generated by landslides on structures is essential for risk assessment and improving the design of mitigation measures. This thesis studies the effect of different basal sliding characteristics of biplanar compound landslides on the post-failure mechanics and the interaction with rigid structures. The Material Point Method (MPM), an advanced numerical tool capable of simulating large deformations, captures the whole instability and the impact process. A simple geometry of a biplanar compound landslide is considered with two different types of biplanar slope transitions along the basal surface – sharp transition (or "kink" geometry) and curved transition (with different radii). A comprehensive parametric study with more than 280 simulations is performed to analyze the landslide post-failure behavior in terms of the radii of transition, the basal friction angle, the distance to the rigid wall, the roughness of the rigid wall, and the scale of the landslide. The results are presented in terms of maximum impact force on the rigid wall and final runout (in the absence of the wall). Results show that the basal characteristics impact the landslide kinetics and energy dissipations, which in turn, influence the impact forces on the rigid wall as well as the final runout of the landslide. The basal friction amplifies the influence of slope geometry on maximum impact forces. In addition, the maximum impact force from numerical results is compared with the predictions from existing semi-empirical approaches. Finally, a preliminary empirical framework is proposed to incorporate the effects of basal sliding characteristics of compound landslides into predicting impact forces on retaining walls. / Master of Science / Landslides and slope failures are a major problem in the geotechnical field that causes significant damage to lives and infrastructure worldwide. It, therefore, becomes essential to understand the mechanisms and the deformation patterns from the standpoint of assessing the impact on infrastructure near the landslide. This thesis studies the effects of the geometry of compound landslides on the maximum impact forces exerted on a rigid structure at a given distance from the landslide. It uses the Material Point Method (MPM), a numerical method that simulates problems involving large deformations. MPM allows the study of the entire instability process from failure initiation to final runout and impact against barriers. Several theoretical models of generic landslides of different radii of slope transition, friction on the sliding surface, and different distances from the wall are presented to study the effects of these parameters on the maximum impact force exerted on the wall. Along with this, the effects of the scale of a landslide on the impact forces are also analyzed. Based on the results, an empirical framework is proposed to help calculate maximum impact forces on a vertical rigid wall while incorporating the basal failure surface characteristics.

This thesis examines the 2018 failure of the Northern Tailings Storage Facility at Cadia Valley Operations, located in New South Wales, Australia. First, the importance of examining and understanding failure mechanisms and post failure kinematics is described. Within which we understand that in the current state of affairs it is exceedingly difficult, or nigh impossible to perform without the use of large strain analyses, which have yet to permeate into the industry to a significant degree. Second, the initial construction and state of the dam just prior to failure is defined, with the materials and their properties laid out and discussed in depth as well as our means of modeling their behavior. Third, we validate and discuss our results of the base model of the dam based on key topographic features from initial and post-failure field measurements. After validation, we examine the influences of each of the different materials on the runout, comparing final topographies of different simulations with the actual final topography observed. This study was a valuable method of validating the Material Point Method as a means of modeling large deformations, as well as demonstrating its powerful applications towards catastrophic disaster prevention. The study validates and provides a greater understanding of the event of the Cadia Tailings Storage Facility Failure, and presents a framework of steps to perform similar examination on future tailings dams as a means of providing risk management in the event of failure. / Master of Science / Tailings dams are structures integral to the life cycle of mining and mineral processing. After mining and the processing of mined materials, the leftover material, known as "tailings" are pumped and stored behind these structures, usually indefinitely. These structures are unique because they are usually expanded as additional storage space for these materials is required. Over the past several decades, the rate at which catastrophic or serious tailings dam failures occur out of failures has been on the rise. Because of this, it becomes necessary to better understand the failure and post-failure movements of the dam. This thesis presents one such failure, the Cadia Tailings Dam Failure of 2018, which is located in New South Wales, Australia. It applies the Material Point Method, a numerical method which allows for largestrain deformations, to examine the post-failure mechanism and interpret various influences by the different materials on the final runout. Because of this, the paper provides insights on the importance of understanding large strain analyses, discussing and presenting the incidents of the failure. The model used for reference is validated using topographic and field data taken after the failure, allowing for a comparison with future models which vary the geometry and material characteristics of the event. A procedural plan is proposed to apply to future analyses, allowing for the analysis to be applied to other events and tailings dam structures, for further insight on influences of variability and material properties on post-failure topography and geometry.

Landslides cause significant damage worldwide and therefore epitomize the most important problems in geotechnical engineering. Hence, perceiving the mechanics involved in the deformation process of landslides is necessary for risk assessment. In addition to the resistance offered by basal shear surfaces, internal shearing also influences the stability and kinematics of compound landslides. For compound landslides, internal shearing is essential to develop feasible sliding mechanisms. The internal distortion is caused by the formation of shear bands that develop within the sliding mass. The strain localization is generally attributed to slope changes along the basal sliding surface (or topography) that constrain the strain field of the landslide. The development of these internal shear bands also controls the energy dissipation, and its distribution determines the final degradation of the material. This work focuses on the study of internal failure mechanisms that develop in compound landslides. A theoretical model of a compound landslide is numerically analyzed using the Material Point Method (MPM), a state-of-the-art numerical technique appropriate to model large deformation problems. The internal failure pattern is identified for different basal sliding geometries. Based on that, a generalized method is proposed to estimate the internal failure mechanism of bi-planar compound geometries. The material degradation and energy dissipation are evaluated in terms of the accumulated deviatoric strain and the reaction forces exerted by the landslide on a vertical wall. Moreover, preliminary studies are conducted to analyze the use of barriers as a mitigation strategy to counter landslide damage, and their efficiencies are investigated. / Master of Science / Landslides consist of movement of rock and debris down a slope. They cause substantial damage each year and therefore represent an important class of problems in geotechnical engineering. Understanding the deformation process and internal shearing pattern occurring in landslides is an important aspect for assessing the risk that a landslide poses. The internal shear is caused due to the formation of shear bands that develop within the mass flowing down the slope and originate at the points of slope change on an incline. These shear bands also affect the amount of energy dissipated and the degradation of flow material. In this work, the internal failure mechanism in landslides is analyzed and effects on landslide kinematics are studied. Material Point Method (MPM) is used to simulate slope instabilities which is an advanced numerical technique appropriate for modeling large deformation problems such as landslides. Several theoretical models of compound landslides are presented considering variation in geometry (roundedness), friction, and slope angle. A generalized failure mechanism of a landslide is proposed based on its geometry and physical parameters. Finally, accumulated strains and reaction forces impacted by moving mass on a wall are calculated for different landslide geometries, and subsequently correlated to energy dissipation material degradation. These results also serve as a precursor to studying the role of barriers in mitigating landslide damage.

Material point method (MPM) is a numerical tool which was originally used for modelling large deformations of solid mechanics problems. Due to the particle based spatial discretiza- tion, MPM is naturally capable of handling large mass movements together with topological changes. Further, the Lagrangian particles in MPM allow an easy implementation of history dependent materials. So far, however, research on MPM has been mostly restricted to explicit dynamic formu- lations with linear approximation functions. This is because of the simplicity and the low computational cost of such explicit algorithms. Particularly in MPM analysis of geomechan- ics problems, a considerable attention is given to the standard explicit formulation to model dynamic large deformations of geomaterials. Nonetheless, several limitations exist. In the limit of incompressibility, a significantly small time step is required to ensure the stability of the explicit formulation. Time step size restriction is also present in low permeability cases in porous media analysis. Spurious pressure oscillations are another numerical instability present in nearly incompressible flow behaviours. This research considers an implicit treatment of the pressure in MPM algorithm to simu- late material incompressibility. The coupled velocity (v)-pressure (p) governing equations are solved by applying Chorin’s projection method which exhibits an inherent pressure stability. Hence, linear finite elements can be used in the MPM solver. The main purpose of this new MPM formulation is to mitigate artificial pressure oscillations and time step restrictions present in the explicit MPM approach. First, a single phase MPM solver is applied to free surface incompressible fluid flow problems. Numerical results show a better approximation of the pressure field compared to the results obtained from the explicit MPM. The proposed formulation is then extended to model fully saturated porous materials with incompress- ible constituents. A solid velocity(v S )-fluid velocity (v F )-pore pressure (p) formulation is presented within the framework of mixture theory. Comparing the numerical results for the one-dimensional consolidation problem shows that the proposed incompressible MPM algorithm provides a stable and accurate pore pressure field even without implementing damping in the solver. Finally, the coupled MPM is used to solve a two-dimensional wave propagation problem and a plain strain consolidation problem. One of the important features of the proposed hydro mechanical coupled MPM formulation is that the time step size is not dependent on the incompressibility and the permeability of the porous medium.

[pt] Essa pesquisa usa o Método do Ponto Material (MPM), para avaliar diferentes aspectos de deslizamentos de encosta. Esse tema é de suma importância, visto que os deslizamentos de terra são o desastre natural que mais causa perdas humanas no Brasil. Esse método numérico foi verificado a fim de que fosse encontrado o fator de segurança e a superfície de ruptura em um talude infinito com solo representado pelo modelo constitutivo de Drucker-Prager. Além disso, foi validado para calcular a força de impacto em um anteparo, sendo o volume impactante um objeto qualquer elástico ou um solo com modelo de Drucker-Prager. Os cálculos foram executados com o código desenvolvido pela PUC-Rio e produziram excelentes resultados. Foi observada uma grande dependência dos resultados com a malha, e assim como no Método dos Elementos Finitos, o refinamento da malha gera convergência para um resultado. O método foi considerado satisfatório para cálculo de uma parede de retenção em locais de risco. / [en] This research uses a numerical method, the Material Point Method, to evaluate different aspects of slope landslides. This theme is of paramount importance since landslides are the natural disaster that shows the highest number of deaths in Brazil. The method was verified so that it could find the safety factor and rupture surface in an infinite slope with soil represented by the Drucker-Prager constitutive model. In addition, the method was validated to calculate impact force in a bulkhead; the impacting volume could be any elastic object or soil with the Drucker-Prager model. The calculations were performed using the code developed by PUC-Rio and showed excellent results. It was observed high dependence on the mesh discretization, as well as the Finite Element Method, the refinement of the mesh generates convergence for a result. The method was considered satisfactory for calculating a retention wall at risk locations.

Computer simulation using the Discrete Element Method (DEM) has emerged as a powerful tool in studying the behaviour of particulate systems during powder flow and compaction. Contact law between particles is the most important input to the Discrete Element simulation. However, most of the present simulations employ over-simplistic contact laws which cannot capture the real behaviour of particulate systems. For example, plastic yielding, material brittleness, sophisticated particle geometry, surface roughness, and particle adhesion are all vitally important factors affecting the behaviour of particle interactions, but have been largely ignored in most of the DEM simulations. This is because it is very difficult to consider these factors in an analytical contact law which has been the characteristic approach in DEM simulations. This thesis presents a strategy for obtaining the contact laws numerically and a comprehensive study of all these factors using the numerical approach. A numerical method, named as the Material Point Method (MPM) in the literature, is selected and shown to be ideal to study the particle interactions. The method is further developed in this work in order to take into account all the factors listed above. For example, to study the brittle failure during particle impact, Weibull’s theory is incorporated into the material point method; to study the effect of particle adhesion, inter-atomic forces are borrowed from the Molecular Dynamic model and incorporated into the method. These developments themselves represent a major progress in the numerical technique, enabling the method to be applied to a much wider range of problems. The focus of the thesis is however on the contact laws between extremely fine particles. Using the numerical technique as a tool, the entire existing theoretical framework for particle contact is re-examined. It is shown that, whilst the analytical framework is difficult to capture the real particle behaviour, numerical contact laws should be used in its place.

The Material Point Method (MPM) is a modern finite element method that is classified as a point based method or meshless method, while it takes the advantage of two kinds of spatial discretisation that are based on an arbitrary Eulerian-Lagrangian description of motion. The referenced continuum is represented by the material points, and the motions are tracked through a computational background mesh, that is an arbitrary constant mesh which does not move the material. Hence, in the MPM mesh distortion especially in the large deformation analysis is naturally avoided. However, MPM has been employed to simulate difficult problems in the literature, many are still unsatisfactory due to the lack of rigorous validation. Therefore, this thesis firstly provides a series of simple case studies which any numerical method must pass to test the validity of the MPM, and secondly demonstrate the capability of the MPM in simulating difficult problems such as degradation of highly swellable polymers during large swelling that is currently difficult to handle by the standard finite element method. Flory’s theory is incorporated into the material point method to study large swelling of polymers, and degradation of highly swellable polymers is modelled by the MPM as a random phenomenon based on the normal distribution of the volumetric strain. These numerical developments represent adaptability of the MPM and enabling the method to be used in more complicated simulations. Furthermore, the advantages of this powerful numerical tool are studied in the modelling of an additive manufacturing technology called Selective Laser Melting (SLM). It is shown the MPM is an ideal numerical method to study SLM manufacturing technique. The focus of this thesis is to validate the MPM and exhibit the simplicity, strength, and accuracy of this numerical tool compared with standard finite element method for very complex problems which requires a complicated topological system.

京都大学 / 0048 / 新制・論文博士 / 博士(工学) / 乙第13210号 / 論工博第4172号 / 新制||工||1706(附属図書館) / (主査)教授 三村 衛, 教授 渦岡 良介, 准教授 肥後 陽介 / 学位規則第4条第2項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

Within computational continuum mechanics there exists a large category of simulation methods which operate by tracking Lagrangian particles over an Eulerian background grid. These Lagrangian/Eulerian hybrid methods, descendants of the Particle-In-Cell method (PIC), have proven highly effective at simulating a broad range of materials and mechanics including fluids, solids, granular materials, and plasma. These methods remain an area of active research after several decades, and their applications can be found across scientific, engineering, and entertainment disciplines. This thesis presents a GPU driven PIC-like simulation framework created using the Vulkan® API. Vulkan is a cross-platform and open-standard explicit API for graphics and GPU compute programming. Compared to its predecessors, Vulkan offers lower overhead, support for host parallelism, and finer grain control over both device resources and scheduling. This thesis harnesses those advantages to create a programmable GPU compute pipeline backed by a Vulkan adaptation of the SPgrid data-structure and multi-buffered particle arrays. The CPU host system works asynchronously with the GPU to maximize utilization of both the host and device. The framework is demonstrated to be capable of supporting Particle-in-Cell like simulation methods, making it viable for GPU acceleration of many Lagrangian particle on Eulerian grid hybrid methods. This novel framework is the first of its kind to be created using Vulkan® and to take advantage of GPU sparse memory features for grid sparsity.