Finite element modelling of rate-dependent ratcheting in granular materials

International audienceThe present paper introduces a comprehensive model that is capable of describing the behaviour, under cyclic loading, of the granular materials used in railway tracks and road pavement. Its main thrust is the introduction of the ''Chicago'' law in a continuum approach to account for the ratcheting effects. It also emphasizes rate-dependency as a dissipative mechanism that acts independently or jointly with the ratcheting effect as well as the non-associated plasticity. The numerical procedure is based on the return mapping algorithm, where Newton's method is used to calculate the nonlinear consistency parameter of the flow rule and to obtain a consistent tangent modulus. The model was applied to specific numerical examples including multi-axial and cyclic loading conditions

Modelling glass fibre-reinforced polymer reinforced geopolymer concrete columns

Glass fibre-reinforced polymer (GFRP) bar and stirrup reinforced geopolymer concrete (GPC) is increasingly recognised as a potential replacement to the conventional steel-reinforced ordinary Portland cement (OPC) concrete due to its superior durability. This paper proposed an analytical model to predict the load-displacement relationship of the concentrically and eccentrically loaded GFRP-GPC columns. The cross-section was divided into a number of strips and a strain gradient was assigned to determine the stresses in the cover, core and reinforcement. The theoretical predictions were then validated using experimental results from previous studies on the behaviour of GFRP-GPC, GFRP-OPC concrete and steel-GFRP concrete systems. It was found that the predicted peaks load, displacements at peak load and ductility indices were generally in close agreement with the experimental results of the GFRP-GPC columns. However, the model had a tendency to over-predict the stiffness of GFRP-OPC concrete and steel-OPC concrete columns in the elastic range. Overall, the proposed analytical model is suitable for GFRP-GPC systems and could facilitate the widespread use of this composite material

A strain-based failure criterion for pillar stability analysis

Strain-based failure criteria have several advantages over stress-based failure criteria: they can account for elastic and inelastic strains, they utilise direct, observables effects instead of inferred effects (strain gauges vs. stress estimates), and model complete stress-strain curves including pre-peak, non-linear elasticity and post-peak strain weakening. In this study, a strain-based failure criterion derived from thermodynamic first principles utilising the concepts of continuum damage mechanics is presented. Furthermore, implementation of this failure criterion into a finite-element simulation is demonstrated and applied to the stability of underground mining coal pillars. In numerical studies, pillar strength is usually expressed in terms of critical stresses or stress-based failure criteria where scaling with pillar width and height is common. Previous publications have employed the finite-element method for pillar stability analysis using stress-based failure criterion such as Mohr-Coulomb and Hoek-Brown or stress-based scalar damage models. A novel constitutive material model, which takes into consideration anisotropy as well as elastic strain and damage as state variables has been developed and is presented in this paper. The damage threshold and its evolution are strain-controlled, and coupling of the state variables is achieved through the damage-induced degradation of the elasticity tensor. This material model is implemented into the finite-element software ABAQUS and can be applied to 3D problems. Initial results show that this new material model is capable of describing the non-linear behaviour of geomaterials commonly observed before peak strength is reached as well as post-peak strain softening. Furthermore, it is demonstrated that the model can account for directional dependency of failure behaviour (i.e. anisotropy) and has the potential to be expanded to environmental controls like temperature or moisture

Interaction Diagram of Rubberised Concrete Filled Circular Hollow Sections

Concrete filled steel tube (CFST) is increasingly used in engineering construction as columns and beams. CFST is known to absorb large amounts of energy as a result of the composite effect. Internationally, there are increasing amounts of waste rubber. In this study recycled rubber is used as aggregate supplement in concrete. Rubberised concrete is known to be more ductile than conventional concrete however has a lower compressive strength. This study investigated the performance of thirty rubberised concrete-filled single-skin steel tubes under combined loading conditions and compared the results against six steel hollow tubular members. Three rubber replacement ratios, 0%, 15% and 30%, three load eccentricities and four tube sections with section slenderness (b/t, width/thickness) of 18 to 36 were examined. The results have shown that the composite section had greatly improved load carrying capacity. The ductile rubberised concrete was more effective in delaying the premature buckling failure of the steel tube compared to the normal concrete. The interaction diagrams were constructed from the experiments and theoretical calculations. It was found that the behaviours of the rubberised concrete filled steel tubes could be accurately predicted using existing design guidelines. This study demonstrated the potential of using rubberised concrete as a cost-effective solution to safe roadside barriers and structural members in buildings located in seismic active zones

Interaction Diagram of Rubberised Concrete Filled Square Hollow Sections

Rubberised concrete utilises waste material, prevents resource extraction and improves concrete ductility, however at the cost of reduced strength and stiffness. The performance of thirty rubberised concrete-filled single-skin steel tubes under combined loading conditions were systematically investigated and comparisons against six steel hollow tubular columns and beams were made. The experimental program consisted of three rubber replacement ratios, 0%, 15% and 30%, three load eccentricities and four tube sections with section slenderness (b/t, width/thickness) of 18 to 50. The results showed that the confined rubberised concrete and the restrained steel tube improved strength and ductility of the composite section. The rubberised concrete was more effective in delaying the premature buckling failure of the steel tube compared to the more brittle normal concrete. The rubberised concrete with 15% rubber replacement ratio showed a good balance of strength and ductility. The interaction diagrams obtained from the experiments and theoretical calculations were constructed and compared. The behaviours of the rubberised concrete filled steel tubes could be accurately predicted using existing design guidelines and safe designs can be produced. This study demonstrated the possibility of using rubberised concrete as a cost-effective solution to problems that require high moment and deformation capacity, such as the roadside barriers and columns in buildings located in seismic active zones

Evaluating force distributions within virtual uncemented mine backfill using discrete element method

This paper investigates the distribution of intergranular forces within uncemented mine backfills using the discrete element method (DEM) and compares it with the existing analytical method. The virtual backfilling is modeled via the DEM to simulate the underground mining stopes backfilling with uncemented granular materials. Normal and shear forces of all particle contacts within the model backfill are tracked and analyzed with particular attention to the effect of sidewall friction. The DEM evaluates normal force chains and reveals a concentration of high forces within the model backfill. The DEM shows profiles of forces that are distinctly different from those obtained from analytical solutions. Quantitative analyses of the spatial distribution of forces, number of contact points, and changes in the orientation of forces are presented. The DEM demonstrates its capacity as a good tool for looking closely into the backfill on a particle scale. It highlights potential force distribution and concentration within a backfill and shows the limitations of analytical solutions, which helps engineers in the mining industry to better understand the possible mechanisms within backfill

A discrete element study of settlement in vibrated granular layers: role of contact loss and acceleration

This paper deals with the vibration of granular materials due to cyclic external excitation. It highlights the effect of the acceleration on the settlement speed and proves the existence of a relationship between settlement and loss of contacts in partially confined granular materials under vibration. The numerical simulations are carried out using the Molecular Dynamics method, where the discrete elements consist of polygonal grains. The data analyses are conducted based on multivariate autoregressive models to describe the settlement and permanent contacts number with respect to the number of loading cycles

Comportement des matériaux granulaires sous vibration - Application au cas du ballast

Granular materials are discrete solid particles which are large enough to avoid any thermal fluctuations. These materials are widely encountered especially in construction, transportation and pharmaceutical industries. The behavior of these materials isgenerally out of the scope of the statistical and continuum mechanical approaches. In the first part of this thesis, we focus on the description of the discrete element model that we use, the effect of the simulation parameters on the sample quality and theirresponse under quasi-static axial loading. The second part is dedicated to the settlement of granular materials under periodic loading. An experimental study is conducted to investigate the effects of the physical factors on the settlement speed. These results are confronted and completed by numerical results based on the molecular dynamics. Moreover, the settlement mechanism, the effect of granular shape, the interaction and mode of confinement onthis phenomenon are described in details. At this level, we also introduced a computational method for the prediction of bed response under long term dynamic loading. The suggested approach usessequentially a molecular dynamics scheme, a time averaging technique, and a relaxation method in order to simulate long term granular materials settlement.Le comportement des matériaux granulaires est énéralement difficile à décrire par des approches tatistiques ou de mécanique des milieux continus. D'une part, il est difficile de trouver un volume élémentaire représentatif compte tenu des tailles des grains, d'autre part, les trajectoires des grains qui le constituent sont corrélées à cause de l'écoulement dense. Dans la première partie, nous nous penchons sur la description du modèle d'éléments discrets adopté dans cette étude. Nous nous intéressons également à l'effet des paramètres de simulation sur la qualité des échantillons et leurs réponses sous chargement axial quasi-statique. La deuxième partie est consacrée à l'étude du phénomène de tassement sous chargements périodiques. Une approche expérimentale est menée afin de comprendre les effets des grandeurs physiques qui peuvent, àpriori, influencer la vitesse de tassement. Ces résultats sont confrontés, par la suite, à l'approche numérique basée sur la dynamique moléculaire. Pour compléter l'étude du mécanisme de tassement, les effets de la granulométrie, de la forme des grains,du degré de confinement et des paramètres de simulation sur la vitesse de tassement sont étudiés en utilisant l'approche discrète. Confrontés au coût élevé de la dynamique moléculaire, une nouvelleapproche de calcul de tassement à long terme a été proposée. Elle consiste à utiliser séquentiellement un calcul de dynamique moléculaire, une technique de prolongement et une méthode de relaxation afin de simuler à long terme l'écoulement de la matière au cours des cycles de chargement

Comportement des matériaux granulaires sous vibration - Application au cas du ballast

Granular materials are discrete solid particles which are large enough to avoid any thermal fluctuations. These materials are widely encountered especially in construction, transportation and pharmaceutical industries. The behavior of these materials isgenerally out of the scope of the statistical and continuum mechanical approaches. In the first part of this thesis, we focus on the description of the discrete element model that we use, the effect of the simulation parameters on the sample quality and theirresponse under quasi-static axial loading. The second part is dedicated to the settlement of granular materials under periodic loading. An experimental study is conducted to investigate the effects of the physical factors on the settlement speed. These results are confronted and completed by numerical results based on the molecular dynamics. Moreover, the settlement mechanism, the effect of granular shape, the interaction and mode of confinement onthis phenomenon are described in details. At this level, we also introduced a computational method for the prediction of bed response under long term dynamic loading. The suggested approach usessequentially a molecular dynamics scheme, a time averaging technique, and a relaxation method in order to simulate long term granular materials settlement.Le comportement des matériaux granulaires est énéralement difficile à décrire par des approches tatistiques ou de mécanique des milieux continus. D'une part, il est difficile de trouver un volume élémentaire représentatif compte tenu des tailles des grains, d'autre part, les trajectoires des grains qui le constituent sont corrélées à cause de l'écoulement dense. Dans la première partie, nous nous penchons sur la description du modèle d'éléments discrets adopté dans cette étude. Nous nous intéressons également à l'effet des paramètres de simulation sur la qualité des échantillons et leurs réponses sous chargement axial quasi-statique. La deuxième partie est consacrée à l'étude du phénomène de tassement sous chargements périodiques. Une approche expérimentale est menée afin de comprendre les effets des grandeurs physiques qui peuvent, àpriori, influencer la vitesse de tassement. Ces résultats sont confrontés, par la suite, à l'approche numérique basée sur la dynamique moléculaire. Pour compléter l'étude du mécanisme de tassement, les effets de la granulométrie, de la forme des grains,du degré de confinement et des paramètres de simulation sur la vitesse de tassement sont étudiés en utilisant l'approche discrète. Confrontés au coût élevé de la dynamique moléculaire, une nouvelleapproche de calcul de tassement à long terme a été proposée. Elle consiste à utiliser séquentiellement un calcul de dynamique moléculaire, une technique de prolongement et une méthode de relaxation afin de simuler à long terme l'écoulement de la matière au cours des cycles de chargement

Comportement des matériaux granulaires sous vibration (application au cas du ballast)

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