Molecular dynamics simulations of complex shaped particles using Minkowski operators

The Minkowski operators (addition and substraction of sets in vectorial spaces) has been extensively used for Computer Graphics and Image Processing to represent complex shapes. Here we propose to apply those mathematical concepts to extend the Molecular Dynamics (MD) Methods for simulations with complex-shaped particles. A new concept of Voronoi-Minkowski diagrams is introduced to generate random packings of complex-shaped particles with tunable particle roundness. By extending the classical concept of Verlet list we achieve numerical efficiencies that do not grow quadratically with the body number of sides. Simulations of dissipative granular materials under shear demonstrate that the method complies with the first law of thermodynamics for energy balance.Comment: Submitted to Phys. Rev.

Effect of frictional heat dissipation on the loss of soil strength

In the present paper through a shear test on a fully saturated granular medium, simulated by the discrete element method, the effect of the heat produced by friction on the internal pore water pressure is explored. It is found that the dissipated energy is enough to increase the pore pressure and reduce the soil strength. In adiabatic and impermeable conditions the heat builds up quickly inside the shear band, and the softening is more pronounced. It is found as well that for real geological materials, heat conduction is not enough to reduce the pore pressure, and the softening prevails. Nevertheless, it is observed that the hydraulic conduction may mitigate or completely eliminate the temperature growth inside the shear band. This result provides new understanding on the thermodynamic factors involved in the onset of catastrophic landslides

Characterization and Generation of 3D Realistic Geological Particles with Metaball Descriptor based on X-Ray Computed Tomography

The morphology of geological particles is crucial in determining its granular characteristics and assembly responses. In this paper, Metaball-function based solutions are proposed for morphological characterization and generation of three-dimensional realistic particles according to the X-ray Computed Tomography (XRCT) images. For characterization, we develop a geometric-based Metaball-Imaging algorithm. This algorithm can capture the main contour of parental particles with a series of non-overlapping spheres and refine surface-texture details through gradient search. Four types of particles, hundreds of samples, are applied for evaluations. The result shows good matches on key morphological indicators(i.e., volume, surface area, sphericity, circularity, corey-shape factor, nominal diameter and surface-equivalent-sphere diameter), confirming its characterization precision. For generation, we propose the Metaball Variational Autoencoder. Assisted by deep neural networks, this method can generate 3D particles in Metaball form, while retaining coessential morphological features with parental particles. Additionally, this method allows for control over the generated shapes through an arithmetic pattern, enabling the generation of particles with specific shapes. Two sets of XRCT images different in sample number and geometric features are chosen as parental data. On each training set, one thousand particles are generated for validations. The generation fidelity is demonstrated through comparisons of morphologies and shape-feature distributions between generated and parental particles. Examples are also provided to demonstrate controllability on the generated shapes. With Metaball-based simulations frameworks previously proposed by the authors, these methods have the potential to provide valuable insights into the properties and behavior of actual geological particles

Effect of the heating of the intergranular water on the softening of a shear band

When a landslide takes place, it is believed that a shear band of loose granular media acts as a lubricant between the descending block of soil and the basis on repose. The mechanism involved is known as softening: the granular skeleton looses its stiffness and the shear stress on the block is lost. In the hypothesis of Habib, the friction between grains heats the pore water, increasing its pressure and reducing the effective stress by the Terzagi criterion. Vardoulakis had constructed models on this hypothesis including thermal diffusion and Darcy’s law, plus a double dependence of the friction angle on the displacement and the velocity of the rolling block. Hereby we present a discrete element simulation of the process on a tilted shear band between two soil blocks: one bottom at rest and one upper at move. Soil blocks are assumed with uniform permeability and thermal conductivity. The shear band is modeled as a set of Voronoi polygons with elastic, frictional and damping forces between them. Pore water acts with hydrostatic pressure on the grains and on the upper and lower blocks, with a thermodynamic response that is reproduced by the Steam Tables provided by the International Association for the Properties of Water and Steam (IAPWS 97 report). At each time step, the forces on all grains are computed and all translational and rotational movements are integrated. Then, the heat is computed as the work done by all dissipative forces, distributing between water and grains according to their thermal capacities and increasing water temperature and pressure. Finally, this water pressure pushes the grains apart, reducing the shear stress on the upper block and speeding up the landslide. By this simulation procedure we obtain temperature increments on 10 C° that are strong enough to produce softening. Although the model is in two dimensions, it provides new insights on the study of catastrophic landslides evolutions

An efficient discrete element lattice Boltzmann model for simulation of particle-fluid, particle-particle interactions

In this study, an efficient Discrete Element Lattice Boltzmann Model (DE-LBM) is introduced to simulate mechanical behaviours of multiphase systems involving particle-fluid and particle-particle interactions. The LBM is based on the Multiple Relaxation Time (MRT-LBM) formalism for the fluid phase and the Discrete Element Method for particle motions. A novel algorithm is developed for detecting the particle contact base on particle overlapping areas computed directly from the grid-based LBM data. This contact algorithm achieves the same accuracy in determining the particle contact as provided by the Hertz contact model but is far more efficient computationally. The DE-LBM coupling approach is also modified to unify the different schemes developed previously. A modified Verlet List method for updating the solid occupation fraction is proposed to further speed up the simulation. The new model is validated by a series of simulations including the single particle settling and well-known ‘Drafting, Kissing and Tumbling’ (DKT) phenomenon found in suspensions. The settling of a large number (2500) of particles in a still fluid is also simulated with predicted concentration profiles matching well the analytic solution. These applications demonstrate the potential of the present DE-LBM model as a powerful numerical tool for simulating multiphase particulate systems encountered in many engineering and science disciplines

Microbubble transport in water-saturated porous media

Laboratory experiments were conducted to investigate flow of discrete microbubbles through a water-saturated porous medium. During the experiments, bubbles, released from a diffuser, moved upward through a quasi-2-D flume filled with transparent water-based gelbeads and formed a distinct plume that could be well registered by a calibrated camera. Outflowing bubbles were collected on the top of the flume using volumetric burettes for flux measurements. We quantified the scaling behaviors between the gas (bubble) release rates and various characteristic parameters of the bubble plume, including plume tip velocity, plume width, and breakthrough time of the plume front. The experiments also revealed circulations of ambient pore water induced by the bubble flow. Based on a simple momentum exchange model, we showed that the relationship between the mean pore water velocity and gas release rate is consistent with the scaling solution for the bubble plume. These findings have important implications for studies of natural gas emission and air sparging, as well as fundamental research on bubble transport in porous media

SPH-DEM Coupling for Debris Flows

Debris flows are natural events with a high potential of damage due to the materials, volume, and velocity they can reach once the flows were triggered. Mathematical models and numerical schemes constitute a transcendental way to get a deeper comprehension of these natural phenomena. Thus, the coupling of numerical methods is becoming more relevant to describe the behaviour of debris flows. The coupling of Smooth Particle Hydrodynamics (SPH) and Discrete Element Method (DEM) is presented in this work to show the capability to represent the interaction of several materials simultaneously. SPH is employed to represent the fluid and soil by using different constitutive models, from a continuum approach. On the other hand, DEM describes immersed objects to represent large boulders and unmoveable boundary conditions. Thus, it is possible to couple the behaviour occurring at very different scales, fines and water through the continuum approach, and boulders with the discrete one. A hypothetical case here presented shows the potential of our coupling method for simulating debris flows

Bottlenecks in granular flow: When does an obstacle increase the flowrate in an hourglass?

Bottlenecks occur in a wide range of applications from pedestrian and traffic flow to mineral and food processing. We examine granular flow across a bottleneck using particle-based simulations. Contrary to expectations we find that the flowrate across a bottleneck actually increases if an opti- mized obstacle is placed before it. The dependency of flowrate on obstacle diameter is derived using a phenomenological velocity-density relationship that peaks at a critical density. This relationship is in stark contrast to models of traffic flow, as the mean velocity does not depend only on density but attains hysteresis due to interaction of particles with the obstacle.Comment: Submitted to Phys. Rev. Let

An airblast hazard simulation engine for block caving sites

In this paper, a weakly compressible Lattice Boltzmann code is coupled with a realistic shape Discrete Element algorithm to create a simulation software to estimate the airspeed happening at airblast events in three dimensions. In an airblast event, air is compressed between falling rocks and the muckpile when the block caving method is used, creating potential hazardous air gusts compromising the safety of personnel and equipment. This work shows how the coupled code is capable of reproducing the key physical layers involved in this phenomenon such as the airspeeds attained by falling bodies in funnel geometries. After some validation examples, the code is used to evaluate the effect of the underground mine geometrical parameters on the potential airspeed. These examples show the potential of the software to be used by mining engineers to estimate accurately the impact of an airblast event