On microscale heterogeneity in granular media and its impact on elastic property estimation

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. D561-D571 ◽  
Author(s):  
Ratnanabha Sain ◽  
Tapan Mukerji ◽  
Gary Mavko
Keyword(s):  
Numerical Simulations ◽  
Contact Mechanics ◽  
Granular Media ◽  
Elastic Moduli ◽  
Effective Medium ◽  
Force Balance ◽  
Theoretical Treatment ◽  
Property Estimation ◽  
Stress Dependent ◽  
The Impact

We emphasize the existence of stress-dependent microscopic heterogeneities in granular media and their influence on macroscopic property estimation using numerical simulations. Although numerical simulations based on contact mechanics successfully reproduce experimental stress-dependent acoustic response of granular media, most contact-mechanics-based effective medium theories (EMTs) fail. We have determined that the main reason for this discrepancy is an inadequate theoretical treatment of micro-heterogeneities in structure, force, and stress. Under infinitesimal perturbations used for estimating elastic moduli, microheterogeneities lead to displacements or relaxations — typically ignored in EMT. These infinitesimal granular relaxations are necessary to comply with detailed force balance, but do not involve grain slip and hence do not depend on friction. Furthermore, we have found that these relaxations primarily depend on the “amount” of heterogeneity, which to a first order are dependent on stress only and are independent of mineralogy. In the absence of an effective medium framework to estimate such relaxation corrections, we have provided simulation-based corrections to account for the impact of heterogeneity on elastic moduli calculations in EMT.

On a Spring-Network Model and Effective Elastic Moduli of Granular Materials

1999 ◽  
Vol 66 (1) ◽  
pp. 172-180 ◽  
Author(s):  
K. Alzebdeh ◽  
M. Ostoja-Starzewaski
Keyword(s):  
Granular Materials ◽  
Disordered Systems ◽  
Granular Media ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Effective Medium ◽  
Solid State Physics ◽  
Two Phase ◽  
Effective Medium Theories ◽  
The Individual

Two challenges in mechanics of granular media are taken up in this paper: (i) development of adequate numerical discrete element models of topologically disordered granular assemblies, and (ii) calculation of macroscopic elastic moduli of such materials using effective medium theories. Consideration of the first one leads to an adaptation of a spring-network (Kirkwood) model of solid-state physics to disordered systems, which is developed in the context of planar Delaunay networks. The model employs two linear springs: a normal one along an edge connecting two neighboring vertices (grain centers) which accounts for normal interactions between the grains, as well as an angular one which accounts for angle changes between two edges incident onto the same vertex; edges remain straight and grain rotations do not appear. This model is then used to predict elastic moduli of two-phase granular materials—random mixtures of soft and stiff grains —for high coordination numbers. It is found here that an effective Poisson’s ratio, νeff, of such a mixture is a convex function of the volume fraction, so that νeff may become negative when the individual Poisson’s ratios of both phases are both positive. Additionally, the usefulness of three effective medium theories—perfect disks, symmetric ellipses, and asymmetric ellipses—is tested.

Estimating dry rock frame moduli of high-resolution 3D digital rock images using the contact-mechanics-based effective medium approach

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. MR235-MR243
Author(s):  
Abdulla Kerimov ◽  
Jennie Cook ◽  
Nathan Lane ◽  
Dmitry Lakshtanov ◽  
Glen Gettemy
Keyword(s):  
High Resolution ◽  
Contact Mechanics ◽  
Prediction Accuracy ◽  
Elastic Moduli ◽  
Effective Medium Theory ◽  
Contact Stiffness ◽  
Effective Medium ◽  
Contact Radius ◽  
Ambient Conditions ◽  
Digital Rock

We have developed a method to estimate the dry frame elastic moduli of high-resolution 3D digital rock images using the contact-mechanics-based effective medium theory (EMT) model. The existing EMT models often are used to predict the effective dry frame elastic moduli of granular aggregates as a function of porosity, average number of contacts per grain, grain radius, contact radius, and contact stiffnesses of an elastic two-grain combination. But, it is almost impossible to measure the number of contacts per grain, contact radius distribution, or contact stiffness distribution in complex rocks. Therefore, explicit assumptions based on simplified microstructural geometries often are made to predict these contact properties in granular aggregates. As a result, the predictions of dry frame elastic moduli using EMT models may fail to match the observed properties because of numerous simplified assumptions, which can be violated in complex rocks. Our method uses the morphological contact properties (i.e., the grain-to-grain contact radius distribution, grain radius distribution, and coordination number distribution) directly extracted from 3D digital rock images to improve the prediction accuracy of dry frame elastic moduli using the EMT models. With integration of digital rocks technology, there is no longer a need to assume the size and shape of the grains, contact size, and number of contacts. The prediction accuracy of our method is validated on high-resolution 3D micro-CT digital rock images of miniplugs extracted from plugs with ultrasonic velocity measurements under dry conditions at different confining pressures. Image-computed dry frame elastic moduli using the EMT model are consistent with laboratory-measured moduli extrapolated to ambient conditions.

scholarly journals Seismic waves in the asteroid environment

2021 ◽  
Vol 249 ◽  
pp. 13001
Author(s):  
Paul Sánchez ◽  
Daniel J. Scheeres
Keyword(s):  
Numerical Simulations ◽  
Seismic Wave ◽  
Granular Media ◽  
Wave Speed ◽  
Seismic Waves ◽  
Wave Transmission ◽  
Overburden Pressure ◽  
Wave Speeds ◽  
The Impact ◽  
Random Packings

Through numerical simulations, we investigate impact generated seismic wave transmission in granular media under extremely low pressure. This mimics the conditions in the interior of asteroids and other small planetary bodies. We find a dependency not only on the overburden pressure on the medium, but also on the velocity of the impact that generates the wave. This is, at extremely low values of overburden pressure, the wave speed depends no only on the imposed pressure, but also on the increment in pressure created by the passing of the wave. We study crystalline and random packings and find very similar behaviour though with different wave speeds as expected. We then relate our results to different mission-related events on asteroids.

scholarly journals Waterfall Algorithm as a tool of investigation the geometrical features of granular porous media

2021 ◽  
Author(s):  
Wojciech Sobieski
Keyword(s):  
Particle Size ◽  
Porous Media ◽  
Lattice Boltzmann ◽  
Granular Media ◽  
Density Ratio ◽  
Geometrical Features ◽  
Granular Porous Media ◽  
Collision Density ◽  
Boltzmann Method ◽  
The Impact

AbstractThe paper describes the so-called Waterfall Algorithm, which may be used to calculate a set of parameters characterising the spatial structure of granular porous media, such as shift ratio, collision density ratio, consolidation ratio, path length and minimum tortuosity. The study is performed for 1800 different two-dimensional random pore structures. In each geometry, 100 individual paths are calculated. The impact of porosity and the particle size on the above-mentioned parameters is investigated. It was stated in the paper, that the minimum tortuosity calculated by the Waterfall Algorithm cannot be used directly as a representative tortuosity of pore channels in the Kozeny or the Carman meaning. However, it may be used indirect by making the assumption that a unambiguous relationship between the representative tortuosity and the minimum tortuosity exists. It was also stated, that the new parameters defined in the present study are sensitive on the porosity and the particle size and may be therefore applied as indicators of the geometry structure of granular media. The Waterfall Algorithm is compared with other methods of determining the tortuosity: A-Star Algorithm, Path Searching Algorithm, Random Walk technique, Path Tracking Method and the methodology of calculating the hydraulic tortuosity based on the Lattice Boltzmann Method. A very short calculation time is the main advantage of the Waterfall Algorithm, what meant, that it may be applied in a very large granular porous media.

scholarly journals Benchmarking Quantum Computers and the Impact of Quantum Noise

2021 ◽  
Vol 54 (7) ◽  
pp. 1-35
Author(s):  
Salonik Resch ◽  
Ulya R. Karpuzcu
Keyword(s):  
Numerical Simulations ◽  
Computer Architecture ◽  
Quantum Noise ◽  
Computing System ◽  
Quantum Computers ◽  
Complicating Factors ◽  
The Impact

Benchmarking is how the performance of a computing system is determined. Surprisingly, even for classical computers this is not a straightforward process. One must choose the appropriate benchmark and metrics to extract meaningful results. Different benchmarks test the system in different ways, and each individual metric may or may not be of interest. Choosing the appropriate approach is tricky. The situation is even more open ended for quantum computers, where there is a wider range of hardware, fewer established guidelines, and additional complicating factors. Notably, quantum noise significantly impacts performance and is difficult to model accurately. Here, we discuss benchmarking of quantum computers from a computer architecture perspective and provide numerical simulations highlighting challenges that suggest caution.

scholarly journals The Impact of Initial Conditions in N-Body Simulations of Debris Discs

2015 ◽  
Vol 32 ◽  
Author(s):  
E. Thilliez ◽  
S. T. Maddison
Keyword(s):  
Numerical Simulations ◽  
Initial Conditions ◽  
Parent Body ◽  
Dust Trapping ◽  
Physical Context ◽  
Disc Width ◽  
Wide Range ◽  
Belt Width ◽  
New Generation ◽  
The Impact

AbstractNumerical simulations are a crucial tool to understand the relationship between debris discs and planetary companions. As debris disc observations are now reaching unprecedented levels of precision over a wide range of wavelengths, an appropriate level of accuracy and consistency is required in numerical simulations to confidently interpret this new generation of observations. However, simulations throughout the literature have been conducted with various initial conditions often with little or no justification. In this paper, we aim to study the dependence on the initial conditions of N-body simulations modelling the interaction between a massive and eccentric planet on an exterior debris disc. To achieve this, we first classify three broad approaches used in the literature and provide some physical context for when each category should be used. We then run a series of N-body simulations, that include radiation forces acting on small grains, with varying initial conditions across the three categories. We test the influence of the initial parent body belt width, eccentricity, and alignment with the planet on the resulting debris disc structure and compare the final peak emission location, disc width and offset of synthetic disc images produced with a radiative transfer code. We also track the evolution of the forced eccentricity of the dust grains induced by the planet, as well as resonance dust trapping. We find that an initially broad parent body belt always results in a broader debris disc than an initially narrow parent body belt. While simulations with a parent body belt with low initial eccentricity (e ~ 0) and high initial eccentricity (0 < e < 0.3) resulted in similar broad discs, we find that purely secular forced initial conditions, where the initial disc eccentricity is set to the forced value and the disc is aligned with the planet, always result in a narrower disc. We conclude that broad debris discs can be modelled by using either a dynamically cold or dynamically warm parent belt, while in contrast eccentric narrow debris rings are reproduced using a secularly forced parent body belt.

scholarly journals Sensitivity of Ultrasonic Coda Wave Interferometry to Material Damage—Observations from a Virtual Concrete Lab

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4033
Author(s):  
Claudia Finger ◽  
Leslie Saydak ◽  
Giao Vu ◽  
Jithender J. Timothy ◽  
Günther Meschke ◽  
...  
Keyword(s):  
Elastic Moduli ◽  
Concrete Specimen ◽  
Coda Wave ◽  
Velocity Change ◽  
Damage Scenarios ◽  
Different Types ◽  
Source Signal ◽  
The Impact ◽  
Structural Scale ◽  
Coda Wave Interferometry

Ultrasonic measurements are used in civil engineering for structural health monitoring of concrete infrastructures. The late portion of the ultrasonic wavefield, the coda, is sensitive to small changes in the elastic moduli of the material. Coda Wave Interferometry (CWI) correlates these small changes in the coda with the wavefield recorded in intact, or unperturbed, concrete specimen to reveal the amount of velocity change that occurred. CWI has the potential to detect localized damages and global velocity reductions alike. In this study, the sensitivity of CWI to different types of concrete mesostructures and their damage levels is investigated numerically. Realistic numerical concrete models of concrete specimen are generated, and damage evolution is simulated using the discrete element method. In the virtual concrete lab, the simulated ultrasonic wavefield is propagated from one transducer using a realistic source signal and recorded at a second transducer. Different damage scenarios reveal a different slope in the decorrelation of waveforms with the observed reduction in velocities in the material. Finally, the impact and possible generalizations of the findings are discussed, and recommendations are given for a potential application of CWI in concrete at structural scale.

scholarly journals Numerical models of slab migration in continental collision zones

Solid Earth ◽  
2012 ◽  
Vol 3 (2) ◽  
pp. 293-306 ◽  
Author(s):  
V. Magni ◽  
J. van Hunen ◽  
F. Funiciello ◽  
C. Faccenna
Keyword(s):  
Subduction Zone ◽  
Plate Tectonics ◽  
Numerical Models ◽  
Continental Collision ◽  
Force Balance ◽  
Small Scale ◽  
Dip Angle ◽  
External Forces ◽  
Stress Dependent ◽  
Subduction System

Abstract. Continental collision is an intrinsic feature of plate tectonics. The closure of an oceanic basin leads to the onset of subduction of buoyant continental material, which slows down and eventually stops the subduction process. In natural cases, evidence of advancing margins has been recognized in continental collision zones such as India-Eurasia and Arabia-Eurasia. We perform a parametric study of the geometrical and rheological influence on subduction dynamics during the subduction of continental lithosphere. In our 2-D numerical models of a free subduction system with temperature and stress-dependent rheology, the trench and the overriding plate move self-consistently as a function of the dynamics of the system (i.e. no external forces are imposed). This setup enables to study how continental subduction influences the trench migration. We found that in all models the slab starts to advance once the continent enters the subduction zone and continues to migrate until few million years after the ultimate slab detachment. Our results support the idea that the advancing mode is favoured and, in part, provided by the intrinsic force balance of continental collision. We suggest that the advance is first induced by the locking of the subduction zone and the subsequent steepening of the slab, and next by the sinking of the deepest oceanic part of the slab, during stretching and break-off of the slab. These processes are responsible for the migration of the subduction zone by triggering small-scale convection cells in the mantle that, in turn, drag the plates. The amount of advance ranges from 40 to 220 km and depends on the dip angle of the slab before the onset of collision.

The penetration and ricochet of ogive-nosed rigid projectiles obliquely impacting metallic targets

2021 ◽  
pp. 204141962110377
Author(s):  
Yaniv Vayig ◽  
Zvi Rosenberg
Keyword(s):  
Experimental Data ◽  
Numerical Simulations ◽  
Dynamic Pressure ◽  
Oblique Impacts ◽  
Simulation Results ◽  
The Impact ◽  
Penetration Depths ◽  
Resistance To Penetration ◽  
Good Agreement

A large number of 3D numerical simulations were performed in order to follow the trajectory changes of rigid CRH3 ogive-nosed projectiles, impacting semi-infinite metallic targets at various obliquities. These trajectory changes are shown to be related to the threshold ricochet angles of the projectile/target pairs. These threshold angles are the impact obliquities where the projectiles end up moving in a path parallel to the target’s face. They were found to depend on a non-dimensional entity which is equal to the ratio between the target’s resistance to penetration and the dynamic pressure exerted by the projectile upon impact. Good agreement was obtained by comparing simulation results for these trajectory changes with experimental data from several published works. In addition, numerically-based relations were derived for the penetration depths of these ogive-nosed projectiles at oblique impacts, which are shown to agree with the simulation results.

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