S. A. Galindo-Torres

Breaking processes in three-dimensional bonded granular materials with general shapes

The paper presents an extension to the spheropolyhedra method for the simulation of granular materials comprising particles of general shapes with bonding. A bonding, cement, or cohesion model for particles sharing common faces is introduced. The bonding force is elastic and has a strain-based breaking threshold for modelling fracture. An initial study is conducted based on the Brazilian tensile test to check how the parameters of the proposed model affect the principal variables measured in this test. Afterwards, solid cubic blocks are then subjected to a triaxial test to explore the mathematical macroscopic failure model. It is found that the peak strength envelope is the product of the superposition of frictional and fracture failure mechanisms. The fracture failure is mainly produced by an avalanche of broken cohesive bonds. The intensity of the avalanche exhibits a power law distribution, as reported in previous studies. The method allows for random divisions of solid bodies without any pre-existing internal voids. It offers a natural, effective tool to model, simulate and study fragmentation processes in 3D

Minkowski-Voronoi diagrams as a method to generate random packings of spheropolygons for the simulation of soils

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.

Bottlenecks in granular flow: when does an obstacle increase the flow rate in an hourglass?

Bottlenecks occur in a wide range of situations from pedestrians, ants, cattle, and traffic flow to the transport of granular materials. We examine granular flow across a bottleneck using simulations of monodisperse disks. Contrary to expectations but consistent with previous work, we find that the flow rate across a bottleneck actually increases if an obstacle is optimally placed before it. Using the hourglass theory and a velocity-density relation, we show that the peak flow rate corresponds to a transition from free flow to congested flow, similar to the phase transition in traffic flow.

A Lattice Boltzmann model for studying transient effects during imbibition–drainage cycles in unsaturated soils

This paper presents a numerical model based on the Lattice Boltzmann Method (LBM), developed for studying dynamic responses of an unsaturated porous medium to periodic imbibition and drainage induced by a cyclic water table movement. The model includes gravity which helps defining an hydraulic head. The model predicted an incremental increase of the overall water content in the medium over each cycle prior to a quasi-steady oscillatory state, a hydraulic ratcheting effect that has been previously observed in laboratory experiments. An empirical model was proposed to combine the transient and harmonic variations of the volumetric water content. The parameters of this empirical model were examined against physical quantities including the frequency of the driving water table oscillations and the porosity of the porous medium. The findings presented here may help to improve the formulation of constitutive models that are able to describe hydraulic processes of unsaturated soils.

Probability of transportation of loose particles in suffusion assessment by self-filtration criteria

Suffusion occurs when soil particles are loosened, detached, and transported away by seepage flow through a series of pores and pore constrictions. While traditional suffusion assessment methods are often based on particle size distribution analysis only, modern assessment methods are focused on constriction size distributions, which are derived from particle size distributions based on certain assumptions. This paper provides a new assessment method, which employs the probability of loose particles being transported to the next pore. The new approach can introduce the influence of an overlapping zone between the two fractions of loose particles and soil primary fabric. This overlapping zone was often overlooked in prior studies. The constriction size distribution of the primary fabric can be calculated approximately by two-dimensional or three-dimensional methods. The three-dimensional method used in the presented study even offers the opportunity to study the influence of particle arrangements on suffusion. The results of the new assessment methods show satisfactory agreement with experimental results.

Micro-mechanical analysis on the onset of erosion in granular materials

The onset of internal erosion is a particle level phenomenon, and therefore, a numerical model capable of tracking the behaviour of particles at micro-scale is needed to exemplify most of the critical variables involved in the process. In this paper, a three-dimensional fully coupled fluid–solid model was utilized to explore the initiation of erosion. Particles were modelled on a micro-scale using the discrete element method (DEM), while the fluid was modelled at a meso-scale using the lattice Boltzmann method (LBM). Fluid was passed through a solid matrix in an opposing direction to gravity with the pore water pressure controlled in stepwise stages until internal erosion or bulk movement of the particles developed and progressed. The model was validated through experimental results found in the literature. Once validated, particle fluid properties were analyzed for the onset of erosion. Determination of a critical hydraulic gradient was obtained from the modelled scenario, which gave clear evidence that the coupled DEM-LBM scheme is a very effective tool for studying internal erosion phenomena in water retaining structures.

Numerical simulation of tank discharge using smoothed particle hydrodynamics

The study concerns the application of the smoothed particle hydrodynamics (SPH) method within computational fluid dynamics. In the present study, a tank discharge with a falling head is investigated. Water is modelled as a viscous fluid with weak compressibility. An enhanced treatment of the solid boundaries is used within the two-dimensional SPH scheme. The boundaries are represented by a special set of SPH particles that differ from the ones representing the fluid by being immovable, preventing the fluid from leaving the container. Particles with different colors are used to illustrate the sequence of the empting the tank as well as the velocity vectors to show stream lines. A code is developed using C++ to solve all equations explicitly by use of a Verlet algorithm. Results are compared to an analytical solution, and a good agreement is achieved.

Lattice Boltzmann simulations of settling behaviors of irregularly shaped particles.

We investigated the settling dynamics of irregularly shaped particles in a still fluid under a wide range of conditions with Reynolds numbers Re varying between 1 and 2000, sphericity ϕ and circularity c both greater than 0.5, and Corey shape factor (CSF) less than 1. To simulate the particle settling process, a modified lattice Boltzmann model combined with a turbulence module was adopted. This model was first validated using experimental data for particles of spherical and cubic shapes. For irregularly shaped particles, two different types of settling behaviors were observed prior to particles reaching a steady state: accelerating and accelerating-decelerating, which could be distinguished by a critical CSF value of approximately 0.7. The settling dynamics were analyzed with a focus on the projected areas and angular velocities of particles. It was found that a minor change in the starting projected area, an indicator of the initial particle orientation, would not strongly affect the settling velocity for low Re. Periodic oscillations developed for all simulated particles when Re>100. The amplitude of these oscillations increased with Re. However, the periods were not sensitive to Re. The critical Re that defined the transition between the steady and periodically oscillating behaviors depended on the inertia tensor. In particular, the maximum eigenvalue of the inertia tensor played a major role in signaling this transition in comparison to the intermediate and minimum eigenvalues.

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.

Scaling solutions for connectivity and conductivity of continuous random networks.

Connectivity and conductivity of two-dimensional fracture networks (FNs), as an important type of continuous random networks, are examined systematically through Monte Carlo simulations under a variety of conditions, including different power law distributions of the fracture lengths and domain sizes. The simulation results are analyzed using analogies of the percolation theory for discrete random networks. With a characteristic length scale and conductivity scale introduced, we show that the connectivity and conductivity of FNs can be well described by universal scaling solutions. These solutions shed light on previous observations of scale-dependent FN behavior and provide a powerful method for quantifying effective bulk properties of continuous random networks.