Numerical techniques for fast generation of large discrete-element models

In recent years, civil engineers have started to use discrete-element modelling to simulate large-scale soil volumes thanks to technological improvements in both hardware and software. However, existing procedures to prepare ‘representative elementary volumes’ are unsatisfactory in terms of computational cost and sample homogeneity. In this work, a simple but efficient procedure to initialise large-scale discrete-element models is presented. Periodic cells are first generated with a sufficient number of particles (enough to consider the cell a representative elementary volume) matching the desired particle size distribution and equilibrated at the desired stress state, porosity and coordination number. When the cell is in equilibrium, it is replicated in space to fill the problem domain. And when the model is filled, only a small number of mechanical cycles is needed to equilibrate a large domain. The result is an equilibrated homogeneous sample at the desired initial state in a large volume

Géométrie et propriétés élastiques des matériaux granulaires

Nous étudions par simulation numérique (de type « éléments discrets») les propriétés géométriques et élastiques d'assemblages de grains sphériques obtenus par différents protocoles de préparation : compression isotrope de « gaz granulaires », vibration de configurations denses, dépôt sous gravité. Nous montrons que le nombre de coor- dination des contacts portant les forces, inaccessible à l'expérience, peut varier indépendamment de la compacité et constitue le paramètre déterminant pour les propriétés élastiques qui, elles, sont mesurables en laboratoire. La comparaison de valeurs numériques et expérimentales pour les modules élastiques des billes de verre, encore partielle, donne un bon accord

Distinct element geomechanical modelling of the formation of sinkhole clusters within large-scale karstic depressions

The 2-D distinct element method (DEM) code (PFC2D_V5) is used here to simulate the evolution of subsidence-related karst landforms, such as single and clustered sinkholes, and associated larger-scale depressions. Subsurface material in the DEM model is removed progressively to produce an array of cavities; this simulates a network of subsurface groundwater conduits growing by chemical/mechanical erosion. The growth of the cavity array is coupled mechanically to the gravitationally loaded surroundings, such that cavities can grow also in part by material failure at their margins, which in the limit can produce individual collapse sinkholes. Two end-member growth scenarios of the cavity array and their impact on surface subsidence were examined in the models: (1) cavity growth at the same depth level and growth rate; (2) cavity growth at progressively deepening levels with varying growth rates. These growth scenarios are characterised by differing stress patterns across the cavity array and its overburden, which are in turn an important factor for the formation of sinkholes and uvala-like depressions. For growth scenario (1), a stable compression arch is established around the entire cavity array, hindering sinkhole collapse into individual cavities and favouring block-wise, relatively even subsidence across the whole cavity array. In contrast, for growth scenario (2), the stress system is more heterogeneous, such that local stress concentrations exist around individual cavities, leading to stress interactions and local wall/overburden fractures. Consequently, sinkhole collapses occur in individual cavities, which results in uneven, differential subsidence within a larger-scale depression. Depending on material properties of the cavity-hosting material and the overburden, the larger-scale depression forms either by sinkhole coalescence or by widespread subsidence linked geometrically to the entire cavity array. The results from models with growth scenario (2) are in close agreement with surface morphological and subsurface geophysical observations from an evaporite karst area on the eastern shore of the Dead Sea

Periodic cells for large-scale problem initialization

In geotechnical applications the success of the discrete element method (DEM) in simulating fundamental aspects of soil behaviour has increased the interest in applications for direct simulation of engineering scale boundary value problems (BVP’s). The main problem is that the method remains relatively expensive in terms of computational cost. A non-negligible part of that cost is related to specimen creation and initialization. As the response of soil is strongly dependant on its initial state (stress and porosity), attaining a specified initial state is a crucial part of a DEM model. Different procedures for controlled sample generation are available. However, applying the existing REV-oriented initialization procedures to such models is inefficient in terms of computational cost and challenging in terms of sample homogeneity. In this work a simple but efficient procedure to initialize large-scale DEM models is presented. Periodic cells are first generated with a sufficient number of particles matching a desired particle size distribution (PSD). The cells are then equilibrated at low-level isotropic stress at target porosity. Once the cell is in equilibrium, it is replicated in space in order to fill the model domain. After the domain is thus filled a few mechanical cycles are needed to re-equilibrate the large domain. The result is a large, homogeneous sample, equilibrated under prescribed stress at the desired porosity. The method is applicable to both isotropic and anisotropic initial stress states, with stress magnitude varying in space

Rheophysics of dense granular materials : Discrete simulation of plane shear flows

We study the steady plane shear flow of a dense assembly of frictional, inelastic disks using discrete simulation and prescribing the pressure and the shear rate. We show that, in the limit of rigid grains, the shear state is determined by a single dimensionless number, called inertial number I, which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasi-static regime of soil mechanics, while large values of I correspond to the collisional regime of the kinetic theory. Those shear states are homogeneous, and become intermittent in the quasi-static regime. When I increases in the intermediate regime, we measure an approximately linear decrease of the solid fraction from the maximum packing value, and an approximately linear increase of the effective friction coefficient from the static internal friction value. From those dilatancy and friction laws, we deduce the constitutive law for dense granular flows, with a plastic Coulomb term and a viscous Bagnold term. We also show that the relative velocity fluctuations follow a scaling law as a function of I. The mechanical characteristics of the grains (restitution, friction and elasticity) have a very small influence in this intermediate regime. Then, we explain how the friction law is related to the angular distribution of contact forces, and why the local frictional forces have a small contribution to the macroscopic friction. At the end, as an example of heterogeneous stress distribution, we describe the shear localization when gravity is added.Comment: 24 pages, 19 figure

Numerical Modeling of Wedge Splitting Test by Discrete Element Approach: Flat Joint Contact Model

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Numerical modelling of the quasi-brittle behaviour of refractory ceramics by considering microcracks effect

In the steelmaking industry, the inner lining of ladles is made of refractory ceramics, which are constantly subjected to thermal shocks during their service. Experimentally, it is observed that pre-existing microcracks could significantly increase the thermal shock resistance of these ceramics. The presence of such microcracks network within the refractory microstructure could lead to a non-linear quasi-brittle mechanical behaviour.To model this quasi-brittle behaviour, a suitable numerical approach is the Discrete Element Method (DEM), which can circumvent the limitations of more conventional continuum approaches in capturing microstructural effects required to simulate multi-fracture propagation.Here, it is aimed to simulate such quasi-brittle behaviour by initial well-distributed damages, with a strength dispersion following a Weibull distribution. In this way, the microcracks effect on the quasi-brittle behaviour of a numerical sample under uniaxial and cyclic tensile tests is investigated. Ultimately, a quantitative DEM model to simulate such a complex behaviour is proposed

Investigation of different discrete modeling strategies to mimic microstructural aspects that influence the fracture energy of refractory materials

The mismatch between the coefficient of thermal expansion of the constituents within refractory ceramics could advantageously be used to tune the fracturing behavior by inducing numerous microcracks within the microstructure. The Wedge Splitting Test (WST) is thus commonly used to characterize such different fracturing behaviors. The present study aims to model the different fracture behaviors of refractory ceramics by proposing a Discrete Element Method (DEM) approach to reproduce fracture energy variation and crack branching during WSTs.Two model ceramics are used as references: a highly brittle pure Magnesia and a quasi-brittle Magnesia Hercynite. By using the proposed DEM approach for local strength randomization, a wide range of fracture behaviors is simulated and compared to the reference materials. Moreover, the crack branching obtained from these simulations was qualitatively compared to the experimental observations by Digital Image Correlation (DIC). Finally, a discrete/continuous hybrid model (DEM/FVM) was proposed to optimize the WST simulations

Periodic cells for large-scale problem initialization

In geotechnical applications the success of the discrete element method (DEM) in simulating fundamental aspects of soil behaviour has increased the interest in applications for direct simulation of engineering scale boundary value problems (BVP’s). The main problem is that the method remains relatively expensive in terms of computational cost. A non-negligible part of that cost is related to specimen creation and initialization. As the response of soil is strongly dependant on its initial state (stress and porosity), attaining a specified initial state is a crucial part of a DEM model. Different procedures for controlled sample generation are available. However, applying the existing REV-oriented initialization procedures to such models is inefficient in terms of computational cost and challenging in terms of sample homogeneity. In this work a simple but efficient procedure to initialize large-scale DEM models is presented. Periodic cells are first generated with a sufficient number of particles matching a desired particle size distribution (PSD). The cells are then equilibrated at low-level isotropic stress at target porosity. Once the cell is in equilibrium, it is replicated in space in order to fill the model domain. After the domain is thus filled a few mechanical cycles are needed to re-equilibrate the large domain. The result is a large, homogeneous sample, equilibrated under prescribed stress at the desired porosity. The method is applicable to both isotropic and anisotropic initial stress states, with stress magnitude varying in space