Статті в журналах: "Representative elementary volumes"

1

Lukas, M. Keller. "On the representative elementary volumes of clay rocks at the mesoscale." Journal of Geology and Mining Research 7, no. 6 (June 19, 2015): 58–64. http://dx.doi.org/10.5897/jgmr2015.0224.

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2

Yoon, Hongkyu, and Thomas A. Dewers. "Nanopore structures, statistically representative elementary volumes, and transport properties of chalk." Geophysical Research Letters 40, no. 16 (August 19, 2013): 4294–98. http://dx.doi.org/10.1002/grl.50803.

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3

Montagne, David, Isabelle Cousin, Lydie Le Forestier, Joël Daroussi, and Sophie Cornu. "Quantification of soil volumes in the Eg & Bt-horizon of an Albeluvisol using image analysis." Canadian Journal of Soil Science 87, no. 1 (January 1, 2007): 51–59. http://dx.doi.org/10.4141/s05-029.

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In this study, we provide a strategy to quantify the effects on soil evolution of driving forces such as human activities or global change. This strategy was developed for situations in which soil evolution resulted in the formation of a complex juxtaposition of soil volumes with distinct properties including soil colours. It is based on image analysis. Our approach proceeds in two steps: (1) to find the minimum sample size over which the soil anisotropy can be neglected and (2) to define a Representative Elementary Volume (REV) of that sample. This approach was developed on the Eg & Bt horizon of a drained Albeluvisol in which three decimetric soil monoliths were sampled at 60, 110 and 210 cm from a drain. The monoliths were sliced into 1.5-cm horizontal layers. Each slice was photographed and studied by image analysis. At the monolith scale, there was neither lateral nor vertical anisotropy. The sampled monoliths were larger than the REV allowing quantification of the different soil volumes constituting this particular horizon. We quantified significant evolutions of the abundance of the different soil volumes characterized by their colour as a function of the distance to the drain. Such a quantification of the effects on soil evolution of human activities or global change equally applies for Podzols, Calcisols or Gleysols for which pedogenesis also resulted in contrasted soil colour evolutions. Key words: Soil change, pedogenesis quantification, artificial drainage, image analysis, Albeluvisol, representative elementary volume

4

Ukrainczyk, N., and E. A. B. Koenders. "Representative elementary volumes for 3D modeling of mass transport in cementitious materials." Modelling and Simulation in Materials Science and Engineering 22, no. 3 (February 28, 2014): 035001. http://dx.doi.org/10.1088/0965-0393/22/3/035001.

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5

Milani, Marco, J. Germán Rubino, Tobias M. Müller, Beatriz Quintal, Eva Caspari, and Klaus Holliger. "Representative elementary volumes for evaluating effective seismic properties of heterogeneous poroelastic media." GEOPHYSICS 81, no. 2 (February 18, 2016): D21—D33. http://dx.doi.org/10.1190/geo-2015-0173.1.

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6

Milani, Marco, J. Germán Rubino, Tobias M. Müller, Beatriz Quintal, Eva Caspari, and Klaus Holliger. "Representative elementary volumes for evaluating effective seismic properties of heterogeneous poroelastic media." GEOPHYSICS 81, no. 2 (March 1, 2016): D169—D181. http://dx.doi.org/10.1190/geo2015-0173.1.

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Understanding and quantifying seismic energy dissipation in fluid-saturated porous rocks is of considerable interest because it offers the perspective of extracting information with regard to the elastic and hydraulic rock properties. An important, if not dominant, attenuation mechanism prevailing in the seismic frequency band is wave-induced fluid pressure diffusion in response to the contrasts in elastic stiffness in the mesoscopic-scale range. An effective way to estimate seismic velocity dispersion and attenuation related to this phenomenon is through the application of numerical upscaling procedures to synthetic rock samples of interest. However, the estimated seismic properties are meaningful only if the underlying sample volume is at least of the size of a representative elementary volume (REV). In the given context, the definition of an REV and the corresponding implications for the estimation of the effective seismic properties remain largely unexplored. To alleviate this problem, we have studied the characteristics of REVs for a set of idealized rock samples sharing high levels of velocity dispersion and attenuation. For periodically heterogeneous poroelastic media, the REV size was driven by boundary condition effects. Our results determined that boundary condition effects were absent for layered media and negligible in the presence of patchy saturation. Conversely, strong boundary condition effects arose in the presence of a periodic distribution of finite-length fractures, thus leading to large REV sizes. The results thus point to the importance of carefully determining the REV sizes of heterogeneous porous rocks for computing effective seismic properties, especially in the presence of strong dry frame stiffness contrasts.

7

Teruel, Federico E., and Rizwan-uddin. "Numerical computation of macroscopic turbulence quantities in representative elementary volumes of the porous medium." International Journal of Heat and Mass Transfer 53, no. 23-24 (November 2010): 5190–98. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.07.041.

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8

Bruns, S., S. L. S. Stipp, and H. O. Sørensen. "Statistical representative elementary volumes of porous media determined using greyscale analysis of 3D tomograms." Advances in Water Resources 107 (September 2017): 32–42. http://dx.doi.org/10.1016/j.advwatres.2017.06.002.

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9

Khassanov, Damir I., and Marat A. Lonshakov. "The investigation of the scale effect on porosity in Bashkirian limestones." Izvestiya of Saratov University. New Series. Series: Earth Sciences 21, no. 2 (June 24, 2021): 137–47. http://dx.doi.org/10.18500/1819-7663-2021-21-2-137-147.

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The article presents the methodology of the representative elementary volume definition for two 1 m long whole core segments. Scientific articles focused on practical methods of representative volume calculations using various physical parameter fluctuations have been studied. Porosity values of every whole core fragment evaluated in two ways using the 7.3 cm diameter core samples in the first approach and the 3 cm diameter core samples in the second one have been compared. Particularities of the scale effect occurring in core samples and depending on core size and porosity type have been analyzed. The cause of porosity increase in big core samples has been determined. The reason due to which porosity changes are explained by fracture porosity occurring in core samples having big volumes has been found. The comparison between neutron log porosity and core porosity has been made. Reasons of similarities or differences of core and log data have been established.

10

Hendrick, A. G., R. G. Erdmann, and M. R. Goodman. "Practical Considerations for Selection of Representative Elementary Volumes for Fluid Permeability in Fibrous Porous Media." Transport in Porous Media 95, no. 2 (August 2, 2012): 389–405. http://dx.doi.org/10.1007/s11242-012-0051-8.

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11

Godwal, U., S. Bhagavath, B. Ghaffari, M. Li, P. D. Lee, and S. Karagadde. "Numerical modelling of porosity with combined gas and shrinkage effects in HPDC." IOP Conference Series: Materials Science and Engineering 1274, no. 1 (January 1, 2023): 012028. http://dx.doi.org/10.1088/1757-899x/1274/1/012028.

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Abstract High-pressure die casting is a manufacturing process in which near-net-shape components are produced rapidly under a pressurized environment. However, due to the relatively higher cooling rate prevailing during the process, isolated liquid pockets form at certain locations, leading to increased porosity formation. A one-dimensional deformable grid numerical model has been developed for predicting the evolution of a single pore in an elementary volume, which combines the diffusion model with the shrinkage affected growth. The model accounts for the change in pore size due to shrinkage and inter-granular growth. This model can provide predictions in representative volumes and be used for component level predictions by combining with a macroscopic model.

12

Rahman, Taufiq, Hamed Lamei Ramandi, Hamid Roshan, and Stefan Iglauer. "Representative Elementary Volume of Rock Using X-Ray Microcomputed Tomography: A New Statistical Approach." Geofluids 2020 (September 1, 2020): 1–13. http://dx.doi.org/10.1155/2020/8866486.

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Rock heterogeneity is a key parameter influencing a range of rock properties such as fluid flow and geomechanical characteristics. The previously proposed statistical techniques were able to rank heterogeneity on a qualitative level to different extents; however, they need to select a threshold value for determination of representative elementary volumes (REV), which in turn makes the obtained REV subjective. In this study, an X-ray microcomputed tomography (μCT) technique was used to obtain images from different porous media. A new statistical technique was then used to compute REV, as a measure of heterogeneity, without the necessity of defining a threshold. The performance of the method was compared with other methods. It was shown that the calculated sum of the relative errors of the proposed method was lowest compared to the other statistical techniques for all tested porous media. The proposed method can be applied to different types of rocks for more accurate estimation of a REV.

13

Zakirov, T. R., and M. G. Khramchenkov. "Representative elementary volumes for various characteristics of two-phase flows in porous media: A statistical approach." Geoenergy Science and Engineering 229 (October 2023): 212104. http://dx.doi.org/10.1016/j.geoen.2023.212104.

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14

Kellers, Benjamin, Martin P. Lautenschlaeger, Nireas Rigos, Julius Weinmiller, Timo Danner, and Arnulf Latz. "Systematic Workflow for Efficient Identification of Local Representative Elementary Volumes Demonstrated with Lithium-Ion Battery Cathode Microstructures." Batteries 9, no. 7 (July 22, 2023): 390. http://dx.doi.org/10.3390/batteries9070390.

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The concept of a representative elementary volume (REV) is key for connecting results of pore-scale simulations with continuum properties of microstructures. Current approaches define REVs only based on their size as the smallest volume in a heterogeneous material independent of its location and under certain aspects representing the same material at the continuum scale. However, the determination of such REVs is computationally expensive and time-consuming, as many costly simulations are often needed. Therefore, presented here is an efficient, systematic, and predictive workflow for the identification of REVs. The main differences from former studies are: (1) An REV is reinterpreted as one specificsub-volume of minimal size at a certain location that reproduces the relevant continuum properties of the full microstructure. It is therefore called a local REV (lREV) here. (2) Besides comparably cheap geometrical and statistical analyses, no further simulations are needed. The minimum size of the sub-volume is estimated using the simple statistical properties of the full microstructure. Then, the location of the REV is identified solely by evaluating the structural properties of all possible candidates in a very fast, efficient, and systematic manner using a penalty function. The feasibility and correct functioning of the workflow were successfully tested and validated by simulating diffusive transport, advection, and electrochemical properties for an lREV. It is shown that the lREVs identified using this workflow can be significantly smaller than typical REVs. This can lead to significant speed-ups for any pore-scale simulations. The workflow can be applied to any type of heterogeneous material, even though it is showcased here using a lithium-ion battery cathode.

15

Perré, Patrick, and Ian Turner. "Determination of the Material Property Variations Across the Growth Ring of Softwood for Use in a Heterogeneous Drying Model. Part 2. Use of Homogenisation to Predict Bound Liquid Diffusivity and Thermal Conductivity." Holzforschung 55, no. 4 (June 21, 2001): 417–25. http://dx.doi.org/10.1515/hf.2001.069.

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Summary In this work, the extensive knowledge of wood gained at the Ecole Nationale du Génie Rural des Eaux et Forêts by using a combination of microscopic observation and experimental work is being used to postulate material property correlations for a macroscopic heterogeneous “Cerne” growth ring model of softwood. In this second part, the method of homogenisation is used to capture the contrast of property between the gaseous phase and the solid phase. Homogenisation problems are computed using a Control Volume formulation. The tracheid model developed in Part 1 has been used to define several elementary representative volumes. Consequently, bound water diffusivity and thermal conductivity can be predicted for each material direction as a function of local wood density. For practical applications, analytical models fitted from the computed values allow these property variations to be easily and accurately determined.

16

Loyola, Ana Carolina, Jean-Michel Pereira, and Manoel Porfírio Cordão Neto. "General Statistics-Based Methodology for the Determination of the Geometrical and Mechanical Representative Elementary Volumes of Fractured Media." Rock Mechanics and Rock Engineering 54, no. 4 (February 3, 2021): 1841–61. http://dx.doi.org/10.1007/s00603-021-02374-6.

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17

Charon, Willy, Marie-Christine Iltchev, and Jean-François Blachot. "Mechanical simulation of a Proton Exchange Membrane Fuel Cell stack using representative elementary volumes of stamped metallic bipolar plates." International Journal of Hydrogen Energy 39, no. 25 (August 2014): 13195–205. http://dx.doi.org/10.1016/j.ijhydene.2014.06.125.

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18

Guévelou, Simon, Benoit Rousseau, Gilberto Domingues, Jérôme Vicente, and Cyril Caliot. "Representative elementary volumes required to characterize the normal spectral emittance of silicon carbide foams used as volumetric solar absorbers." International Journal of Heat and Mass Transfer 93 (February 2016): 118–29. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.09.069.

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19

Schmidt, Selma, Max Wiebicke, and Ivo Herle. "Characterisation of the heterogeneity of a sand specimen in triaxial compression using x-ray CT and representative elementary volumes." E3S Web of Conferences 544 (2024): 04003. http://dx.doi.org/10.1051/e3sconf/202454404003.

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Standard laboratory tests, such as the triaxial test, are often considered to be element tests. But, when observing such a test, it becomes obvious that this assumption of homogeneity is far from accurate. The localisation of strain is often visible to the naked eye and becomes even more obvious when observed on the grain scale. Other variables, such as those describing the soil fabric, are expected to localise as well. In this work, two sand samples are analysed at different loading states regarding the heterogeneity of three soil variables: void ratio, coordination number and contact orientation anisotropy. For this purpose, the size of a Representative Elementary Volume (REV) is determined using three criteria: the convergence of the mean and variance of the variables with increasing element size as well as a χ2-test. The size of the REV is varying depending on the chosen variable but almost the same for the two specimens when related to the mean grain diameter d50. The REV is placed in a regular grid throughout the specimen and the three variables are determined for each REV. The stochastic as well as spatial heterogeneity is identified for each specimen. As one of the samples is analysed for different loading states throughout a triaxial test, the evolution of the soil heterogeneity is identified. A localisation of all three variables can be observed at the end of the triaxial test as well as a strong initial heterogeneity for both sand samples.

20

Liu, Haifeng, Chenghao Ma, and Changqi Zhu. "X-ray Micro CT Based Characterization of Pore-Throat Network for Marine Carbonates from South China Sea." Applied Sciences 12, no. 5 (March 3, 2022): 2611. http://dx.doi.org/10.3390/app12052611.

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The pore-throat network of rock exerts a vital influence on the permeability and mechanical properties of the rock. Resorting to X-ray micro-CT scanning, the present work investigates the pore-throat structure of marine biogenic carbonate samples from the South China Sea and compares them to terrigenous sedimentary sandstone. With the help of the maximum ball (MB) algorithm, the pore-throat networks inside representative elementary volumes of rock samples are revealed by stick-and-ball diagrams, which enables quantitative analyses afterwards. Higher and more deviant cross sectional porosity was observed for the carbonate samples compared to the sandstone sample, indicating relatively heterogeneous pores in the carbonate. Over 85% of pores in the carbonate samples were classified as mesopores. Irregular triangular cross sections can be inferred for the pores and throats of the carbonate. The type of rock and the porosity seem to have little effect on the shapes of the pores and throats. In the studied carbonate, the average volume of the throat was approximately one order of magnitude smaller than the average volume of a pore. The distribution of throat radius differed significantly between the studied carbonate samples. The average coordination number of the carbonate was measured to be 1.

21

Fraccica, Alessandro, Enrique Romero, and Thierry Fourcaud. "Large cell triaxial tests of a partially saturated soil with vegetation." E3S Web of Conferences 382 (2023): 05005. http://dx.doi.org/10.1051/e3sconf/202338205005.

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The use of vegetation roots as a nature-based solution against landslides and erosion requires the definition of sample preparation protocols and adoption of equipment that allows testing representative elementary volumes of the whole soil-root system. For this purpose, large cell triaxial compression tests were carried out on fallow and vegetated samples at different degrees of saturation. Samples were prepared by static compaction of a silty sand and seeded with Cynodon dactylon. The hydraulic state during plants growth was controlled and reproduced on bare soil samples. After isotropic compressions, the shearing phase was carried out at very low confining stresses (i.e., below 50 kPa). Tests were deemed to be comparable by assessing the normalised volume of roots with respect to soil, after shearing. For a given confining stress, soil samples with higher matric suction exhibited higher shear strength, furtherly increased by roots. The stress-strain behaviour observed in the vegetated soil systematically changed, when comparing tests at low and high matric suction values, due to the different mechanisms of vegetation reinforcement depending on the hydraulic state at the soil-root interface. The results were successfully interpreted within a failure criterion and skeleton stress framework for partially saturated soils, considering soil suction, degree of saturation, soil microstructure and the normalised volume of roots.

22

Sow, Libasse, Fabrice Bernard, Siham Kamali-Bernard, and Cheikh Mouhamed Fadel Kébé. "Experiment-based modelling of the mechanical behaviour of non-hazardous waste incineration bottom ashes treated by hydraulic binder." MATEC Web of Conferences 149 (2018): 01038. http://dx.doi.org/10.1051/matecconf/201814901038.

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Instrumented indentation tests have been carried out on an isolated 25 mm diameter particle of Non-Hazardous Waste Incineration bottom ash. These tests have enabled one to assess the intrinsic mean reduced modulus of elasticity “Er” of the particles. This result is used as input data for a 3D numerical model of Representative Elementary Volumes (REV) of a road gravel made with this kind of by-products. This numerical model is based on a multi-scale hierarchical modelling strategy. The aggregates treated with cement have been decomposed into two REV at the sub-mesoscopic and mesoscopic scales. The numerical simulations campaign (“virtual laboratory”) lead to the following results. At the sub-mesoscopic scale, we determined the input parameters for the Concrete Damaged Plasticity Model (CDPM) used at the mesoscopic scale. At the mesoscopic scale, the mechanical characteristics of the road aggregates usually determined through experiments have been found. The non-hazardous waste incineration bottom ashes treated by hydraulic binder was classified into mechanical classe 3.

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Sow, Libasse, Fabrice Bernard, and Siham Kamali-Bernard. "Mechanical Behaviour of Cement-Bound Gravels by Experiment-Based 3D Multi-Scale Modelling: Application to Non-Hazardous Waste Incineration Bottom Ashes Aggregates for Use in Road Engineering." International Journal of Engineering Research in Africa 54 (June 2021): 71–85. http://dx.doi.org/10.4028/www.scientific.net/jera.54.71.

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This paper presents a hierarchical multi-scale modelling approach devoted to investigating the mechanical behaviour of cement-bound gravels. Material studied is based on Non-Hazardous Waste Incineration (NHWI) bottom ashes. The elastic moduli of NHWI particles have been previously determined by an original indentation campaign never conducted so far on these types of aggregates. The results of the experimental campaign serve as input data to the developed numerical strategy. The modelling is based on the definition of Representative Elementary Volumes (REV) considering all the heterogeneities of the material. The "virtual laboratory" set up made it possible to determine the mechanical parameters characterizing the gravel treated with 3% of cement. The high value obtained of the internal friction angle (76 °) gives the material a good bearing capacity. The classification in mechanical classes 3 and 4 when the Young's modulus of the NHWI particles varies from 20 to 80 GPa proves the feasibility of the reuse of this type of industrial by-products in this sector of activity. The present modelling approach is validated by means of comparisons with experimental results of the literature.

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Yang, Sung Soo, and Yeon June Kang. "Effect of fiber cross-section on the transport and acoustic properties of fibrous materials." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, no. 5 (August 1, 2021): 1239–42. http://dx.doi.org/10.3397/in-2021-1785.

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Fibrous materials can efficiently dissipate acoustic energy, and their intrinsic properties are determined by fiber geometries (microscale). In this study, the effect of cross-sections of fibers on the transport and acoustic properties of fibrous materials was investigated. First, fibers of various cross-sections were modeled by adjusting their open porosity. The representative elementary volumes of fiber structures were generated to describe the periodic unit-cell structures. Next, the transport properties (such as static airflow resistivity, high-frequency limit of the dynamic tortuosity, viscous characteristic length, thermal characteristic length, and static thermal permeability) of fibrous materials were calculated by solving numerical problems using the finite element method. These properties of fibrous materials with complex cross-sections were compared with those with circular cross-sections. Finally, the sound absorption coefficients were predicted using the Johnson-Champoux-Allard-Lafarge (JCAL) model and rigid frame approximation, and the differences in sound-absorbing behavior were analyzed. This study can provide insights into the design of lightweight fibrous materials while maintaining optimal sound absorption performance.

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Kulatilake, Pinnaduwa H. S. W., Hasan Ucpirti, and Ove Stephansson. "Effects of finite-size joints on the deformability of jointed rock at the two-dimensional level." Canadian Geotechnical Journal 31, no. 3 (June 1, 1994): 364–74. http://dx.doi.org/10.1139/t94-044.

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A numerical decomposition technique, which has resulted from a linking between joint-geometry modeling and generation schemes, and a distinct element code (UDEC), is used to study the effect of joint-geometry parameters of finite-size joints on the deformability properties of jointed rock at the two-dimensional (2D) level. The influence of joint-geometry parameters such as joint density, ratio of joint size to block size, and joint orientation on the deformability of jointed rock is shown. Relations are established between deformability properties of jointed rock and fracture-tensor parameters. An incrementally linear elastic, anisotropic constitutive model is developed to represent the prefailure mechanical behaviour of jointed rock at the 2D level. This constitutive model has captured the anisotropic, scale-dependent behaviour of jointed rock. In this model, the effect of the joint-geometry network in the rock mass is incorporated in terms of fracture-tensor components. Some insight is given related to estimation of representative elementary volumes for deformability properties of jointed rock. Key words : rock masses, deformability, distinct element method, fracture tensor, anisotropy, scale effects.

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Zielinski, Tomasz G., Nicolas Dauchez, Thomas Boutin, Mikel Leturia, Alexandre Wilkinson, Fabien Chevillotte, François-Xavier Bécot, and Rodolfo Venegas. "3D printed sound-absorbing materials with double porosity." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 3 (February 1, 2023): 4100–4109. http://dx.doi.org/10.3397/in_2022_0586.

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The paper shows that acoustic materials with double porosity can be 3D printed with the appropriate design of the main pore network and the contrasted micro-porous skeleton. The microporous structure is obtained through the use of appropriate additive manufacturing (AM) technology, raw material, and process parameters. The essential properties of the microporous material obtained in this way are investigated experimentally. Two AM technologies are used to 3D print acoustic samples with the same periodic network of main pores: one provides a microporous skeleton leading to double porosity, while the other provides single-porosity material. The sound absorption for each acoustic material is determined both experimentally using impedance tube measurements and numerically using a multiscale model. The model combines finite element calculations (on periodic representative elementary volumes) with scaling functions and analytical expressions resulting from homogenization. The obtained double-porosity material is shown to exhibit a strong permeability contrast resulting in a pressure diffusion effect, which fundamentally changes the nature of the sound absorption compared to its single-porosity counterpart with an impermeable skelton. This work opens up interesting perspectives for the use of popular, low-cost AM technologies to produce efficient sound absorbing materials.

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Steinbrecher, Ivo, Alexander Popp, and Christoph Meier. "Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes." Computational Mechanics 69, no. 3 (November 28, 2021): 701–32. http://dx.doi.org/10.1007/s00466-021-02111-4.

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AbstractThe present article proposes a mortar-type finite element formulation for consistently embedding curved, slender beams into 3D solid volumes. Following the fundamental kinematic assumption of undeformable cross-section s, the beams are identified as 1D Cosserat continua with pointwise six (translational and rotational) degrees of freedom describing the cross-section (centroid) position and orientation. A consistent 1D-3D coupling scheme for this problem type is proposed, requiring to enforce both positional and rotational constraints. Since Boltzmann continua exhibit no inherent rotational degrees of freedom, suitable definitions of orthonormal triads are investigated that are representative for the orientation of material directions within the 3D solid. While the rotation tensor defined by the polar decomposition of the deformation gradient appears as a natural choice and will even be demonstrated to represent these material directions in a $$L_2$$ L 2 -optimal manner, several alternative triad definitions are investigated. Such alternatives potentially allow for a more efficient numerical evaluation. Moreover, objective (i.e. frame-invariant) rotational coupling constraints between beam and solid orientations are formulated and enforced in a variationally consistent manner based on either a penalty potential or a Lagrange multiplier potential. Eventually, finite element discretization of the solid domain, the embedded beams, which are modeled on basis of the geometrically exact beam theory, and the Lagrange multiplier field associated with the coupling constraints results in an embedded mortar-type formulation for rotational and translational constraint enforcement denoted as full beam-to-solid volume coupling (BTS-FULL) scheme. Based on elementary numerical test cases, it is demonstrated that a consistent spatial convergence behavior can be achieved and potential locking effects can be avoided, if the proposed BTS-FULL scheme is combined with a suitable solid triad definition. Eventually, real-life engineering applications are considered to illustrate the importance of consistently coupling both translational and rotational degrees of freedom as well as the upscaling potential of the proposed formulation. This allows the investigation of complex mechanical systems such as fiber-reinforced composite materials, containing a large number of curved, slender fibers with arbitrary orientation embedded in a matrix material.

28

Claes, Steven, Fadi H. Nader, and Souhail Youssef. "Coupled experimental/numerical workflow for assessing quantitative diagenesis and dynamic porosity/permeability evolution in calcite-cemented sandstone reservoir rocks." Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 73 (2018): 36. http://dx.doi.org/10.2516/ogst/2018027.

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Some of the world best hydrocarbon reservoirs (carbonates and siliciclastics) are also believed to be valuable for subsurface storage of CO2 and other fluids. Yet, these reservoirs are heterogeneous in terms of their mineralogy and flow properties, at varying spatial-temporal scales. Therefore, predicting the porosity and permeability (flow properties) evolution of carbonates and sandstones remains a tedious task. Diagenesis refers to the alteration of sedimentary rocks through geologic time, mainly due to rock-fluid interactions. It affects primarily the flow properties (porosity and permeability) of already heterogeneous reservoir rocks. In this project a new approach is proposed to calculate/quantify the influence of diagenetic phases (e.g. dissolution, cement plugging) on flow properties of typical sandstone reservoir rocks (Early Jurassic Luxembourg Formation). A series of laboratory experiments are performed in which diagenetic phases (e.g. pore blocking calcite cement in sandstone) are selectively leached from pre-studied samples, with the quantification of the petrophysical characteristics with and without cement to especially infer permeability evolution. Poorly and heavily calcite-cemented sandstone samples, as well as some intermediate cemented samples were used. The results show a distinctive dissolution pattern for different cementation grades and varying Representative Elementary Volumes (REVs). These conclusions have important consequences for upscaling diagenesis effects on reservoirs, and the interpretation of geochemical modelling results of diagenetic processes. The same approach can be applied on other type of cements and host-rocks, and could be improved by integrating other petrophysical analyses (e.g. petroacoustic, NMR).

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Cazaurang, Simon, Manuel Marcoux, Oleg S. Pokrovsky, Sergey V. Loiko, Artem G. Lim, Stéphane Audry, Liudmila S. Shirokova, and Laurent Orgogozo. "Numerical assessment of morphological and hydraulic properties of moss, lichen and peat from a permafrost peatland." Hydrology and Earth System Sciences 27, no. 2 (January 19, 2023): 431–51. http://dx.doi.org/10.5194/hess-27-431-2023.

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Abstract. Due to its insulating and draining role, assessing ground vegetation cover properties is important for high-resolution hydrological modeling of permafrost regions. In this study, morphological and effective hydraulic properties of Western Siberian Lowland ground vegetation samples (lichens, Sphagnum mosses, peat) are numerically studied based on tomography scans. Porosity is estimated through a void voxels counting algorithm, showing the existence of representative elementary volumes (REVs) of porosity for most samples. Then, two methods are used to estimate hydraulic conductivity depending on the sample's homogeneity. For homogeneous samples, direct numerical simulations of a single-phase flow are performed, leading to a definition of hydraulic conductivity related to a REV, which is larger than those obtained for porosity. For heterogeneous samples, no adequate REV may be defined. To bypass this issue, a pore network representation is created from computerized scans. Morphological and hydraulic properties are then estimated through this simplified representation. Both methods converged on similar results for porosity. Some discrepancies are observed for a specific surface area. Hydraulic conductivity fluctuates by 2 orders of magnitude, depending on the method used. Porosity values are in line with previous values found in the literature, showing that arctic cryptogamic cover can be considered an open and well-connected porous medium (over 99 % of overall porosity is open porosity). Meanwhile, digitally estimated hydraulic conductivity is higher compared to previously obtained results based on field and laboratory experiments. However, the uncertainty is less than in experimental studies available in the literature. Therefore, biological and sampling artifacts are predominant over numerical biases. This could be related to compressibility effects occurring during field or laboratory measurements. These numerical methods lay a solid foundation for interpreting the homogeneity of any type of sample and processing some quantitative properties' assessment, either with image processing or with a pore network model. The main observed limitation is the input data quality (e.g., the tomographic scans' resolution) and its pre-processing scheme. Thus, some supplementary studies are compulsory for assessing syn-sampling and syn-measurement perturbations in experimentally estimated, effective hydraulic properties of such a biological porous medium.

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Kolegov, Grigoriy A., and Aleksey Yu Krainov. "Simulation of the coal mine ventilation with account for gob areas." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 79 (2022): 78–88. http://dx.doi.org/10.17223/19988621/79/7.

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Mine ventilation network models are widely used in underground coal mining in Russia. The models cover a variety of practical problems ranging from simple air distribution in active mine workings to changes in the static air pressure gradient associated with complex technological or hazardous processes occurring in mines. Isolated gob areas are integral parts of ventilation networks in coal mines. The most commonly used underground coal extraction technology in Russia is the longwall mining. A gob forms when a coal seam is extracted, and the upper layers of the rock cave in. Gobs are isolated from active mine entries with seals, but there is always air leakages from active faces inducing the air circulation in isolated areas. Gobs join different coal seams and often become the sources of underground fires. Therefore, the inclusion of gobs in mine ventilation network models would help contain accidents and eliminate the caused damage. The study uses the method of representative elementary volumes to incorporate a porous medium into mine ventilation network models. Quadratic resistances are assigned to the edges of the model, where Kirchhoffs laws are valid. The aerodynamic resistances of the gob edges are calculated using the Ergun equation. The proposed method has been used to evaluate pressure gradients in the gob area of the Raspadskaya mine. Several scenarios of the aerodynamic resistance variation in the active mine workings surrounding the gob area, such as partial flooding and drilling of boreholes from the surface, have been simulated, and the corresponding changes in pressure gradients have been analyzed.

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Zhang, Jing, Richeng Liu, Liyuan Yu, Shuchen Li, Xiaolin Wang, and Ding Liu. "An Equivalent Pipe Network Modeling Approach for Characterizing Fluid Flow through Three-Dimensional Fracture Networks: Verification and Applications." Water 14, no. 10 (May 16, 2022): 1582. http://dx.doi.org/10.3390/w14101582.

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The equivalent pipe network (EPN) model is an effective way to model fluid flow in large-scale fractured rock masses with a complex fracture network due to its straightforwardness and computational efficiency. This study presents the EPN model for characterizing fluid flow through three-dimensional fracture networks using the Monte-Carlo method. The EPN model is extracted from an original three-dimensional discrete fracture network (DFN) model and is used to simulate the fluid flow processes. The validity of the proposed EPN modeling approach is verified via the comparisons of permeability (k) with analytical solutions and simulation results reported in the literature. The results show that the numerically calculated k using EPN models agrees well with the analytical values of simplified DFN models and the simulation results of complex DFN models. The k increases following an exponential function with the increment of mean length of exponentially distributed fractures (u), which is strongly correlated with fracture density (P32) and average intersection length (Li). The P32 increases in an exponential way with the increment of u. The Li increases as u increases, following a power-law function. The increment of u leads to the increment of a number of long fractures in three-dimensional DFN models. A larger u results in a denser fracture network and a stronger conductivity when the number and length distribution range of fractures remain the same. The representative elementary volumes (REVs) of three-dimensional DFN models with u = 9 m and P32 = 0.4 m2/m3 are determined as 2.36 × 104 m3, 9.16 × 103 m3, and 1.26 × 104 m3 in 3 flow directions, respectively.

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de Araújo, O. M. O., K. V. Sharma, A. S. Machado, T. M. P. Santos, C. G. Ferreira, R. Straka, F. W. Tavares, and R. T. Lopes. "Representative elementary volume in limestone sample." Journal of Instrumentation 13, no. 10 (October 25, 2018): C10003. http://dx.doi.org/10.1088/1748-0221/13/10/c10003.

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Zhang, M. Z., G. Ye, and K. Van Breugel. "Un método numérico-estadístico para determinar el volumen elemental representativo (VER) de la pasta de cemento en la medición de la difusividad." Materiales de Construcción 60, no. 300 (December 15, 2010): 7–20. http://dx.doi.org/10.3989/mc.2010.60810.

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Trotsuk, I. V., and M. V. Subbotina. "‘Core’ and ‘periphery’ of the concepts ‘happiness’ and ‘justice’: Unfinished sentences technique as a means of validation." RUDN Journal of Sociology 22, no. 4 (December 30, 2022): 782–801. http://dx.doi.org/10.22363/2313-2272-2022-22-4-782-801.

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The article continues a series of publications based on the results of a long-term research project of the Sociology Chair of the RUDN University, which combines research and methodological study of the self-identification of Russian students in terms of happiness. At the current stage, two new ‘dimensions’ were added to the project: first, the contextualization of questions about happiness by the concept and elements of social justice (as its ‘external determinant’); second, ‘measuring’ the images of a happy/unhappy person with the projective technique (unfinished sentences) and taking into account social ideas about justice/injustice. Being limited by the size of the article, the authors focus on the second ‘dimension’ - identify the possibilities and limitations of the unfinished-sentences technique as a means for validating the results of the project rather than a means for starting it. The structure of the article contributes to the solution of this task: in the first, introductory part, the author set the research problem as determined by the self-diagnostic mania of the contemporary society (in terms of the level of happiness) and the attempts to classify the factors of happiness; the second part presents the main stages of the project and its conclusions based on the results of the surveys (on the sample of the RUDN University students and on the all-Russian representative online panel); the third, main part presents the results of the unfinished-sentences technique application, which were obtained with the simplest content-analytical coding of the elementary endings. The authors reconstructed a single-type structure of images of a happy/unhappy person (in the context of factors determining such ‘statuses’) and of justice/injustice (taking into account their characteristics) - the core, the near periphery and the far periphery, which differ in their semantic ‘volumes’ and evaluation trends.

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EDWARDS, MARK S., and PETER GRINDROD. "A CHANNEL NETWORK MODEL FOR CHEMICAL MIGRATION IN SUBSURFACE MEDIA." Mathematical Models and Methods in Applied Sciences 05, no. 05 (August 1995): 641–57. http://dx.doi.org/10.1142/s0218202595000371.

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We consider the migration of chemical species through saturated heterogeneous media, where the scale of the flow path geometry is large enough to invalidate a Fickian based, representative elementary volumes, approach to dispersal. Channel network models combine the effects of channeling over small spatial scales with network mixing which gives rise to an equivalent dispersion effect over large spatial scales. We extend equations and solutions given previously for ideal nonabsorbing tracers, to include the retardation of chemically active species. The primary aim is to derive explicit solutions for future calibration purposes, and illustrate scale dependent dispersive behavior with and without chemical absorption processes. In this paper we develop a twin channel model allowing for various specification of the retardation process. This allows the retardation to be either positively or negatively correlated with pathway apertures (which are in turn related directly to flow rates of the respective channels). We show that if absorption is controlled by specific surface area, then a scaling argument infers that highly transmissive paths are also less retarding. We illustrate the model’s applicability to such cases. We shall discuss the scale dependence of calculated (observed) equivalent dispersivities obtained by analyzing the moments of breakthrough curves at various distances. For a range of parameter values we exhibit scaling behavior similar to that observed in the field and laboratory. This does not necessarily imply any validity to the approach: it is a direct consequence of deferring the network — mixing effect to large length scales. An important point of consideration is that wherever conceptual model choices must be made, in modeling natural processes such as chemical migration, there is a possibility of biasing calculations by sole reliance on a particular approach. Channel network models marry channeling models and classical Fickian models. Thus in calibrating a model such as the Twin Channel model from given experimental behavior, we can immediately estimate over which scales channeling or Fickian dispersive effects are likely to be dominant.

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Zhang, Ting Ting, E. Chuan Yan, Xian Ming Hu, and Yang Bing Cao. "Fractal Description of Rock Mass Structure Representative Elementary Volume." Advanced Materials Research 594-597 (November 2012): 439–45. http://dx.doi.org/10.4028/www.scientific.net/amr.594-597.439.

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The mechanical parameters of the rock masses are scale dependent because of the existence of the discontinuities. The self-similarity of the discontinuities makes the application of fractal theory in the description of the rock mass structure possible. The novel point in this study is that the structure representative elementary volume (SREV) of rock mass is proposed. Rock mass structures were obtained through the two-dimensional discontinuity network simulation results, from which ten pieces of square rock mass specimens were chosen. The side lengths of the specimens were increased in turn from 1m to 10m. And the fractal dimension of each specimen with different sizes was calculated by the box-counting principal of the fractal geometry. The fractal dimensions of the rack mass structures became larger with their side lengths increasing, and finally stable. And the SREV of the rock mass was determined based on the variation rule of the fractal dimensions. Further, the relation between the structure representative elementary volume (SREV) and mechanical parameter representative elementary volume (REV) was qualitatively analyzed from the strength differences between the discontinuities and intact rock. And the conclusion was inferred that the size of the SREV was the upper limit of mechanical parameter REV. Meanwhile, the conclusion was verified by the results of the finite element method. This study can provided a referring value for the estimation of the mechanical parameter REV in future.

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Puyguiraud, Alexandre, Philippe Gouze, and Marco Dentz. "Is There a Representative Elementary Volume for Anomalous Dispersion?" Transport in Porous Media 131, no. 2 (November 16, 2019): 767–78. http://dx.doi.org/10.1007/s11242-019-01366-z.

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Xue, Yufang, Zhongxian Cai, Heng Zhang, Qingbing Liu, Lanpu Chen, Jiyuan Gao, and Fangjie Hu. "Insights into Heterogeneity and Representative Elementary Volume of Vuggy Dolostones." Energies 15, no. 16 (August 10, 2022): 5817. http://dx.doi.org/10.3390/en15165817.

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Carbonate reservoirs commonly have significant heterogeneity and complex pore systems due to the multi-scale characteristic. Therefore, it is quite challenging to predict the petrophysical properties of such reservoirs based on restricted experimental data. In order to study the heterogeneity and size of the representative elementary volume (REV) of vuggy dolostones, a total of 26 samples with pore sizes ranging from micrometers to centimeters were collected from the Cambrian Xiaoerbulake Formation at the Kalping uplift in the Tarim Basin of northwestern China. In terms of the distribution of pore size and contribution of pores to porosity obtained by medical computed tomography testing, four types of pore systems (Types I–IV) were identified. The heterogeneity of carbonate reservoirs was further quantitatively evaluated by calculating the parameters of pore structure, heterogeneity, and porosity cyclicity. The results indicate that different pore systems yield variable porosities, pore structures, and heterogeneity. The porosity is relatively higher in Type-II and Type-IV samples compared to those of Type-I and Type-III. It is caused by well-developed large vugs in the former two types of samples, which increase porosity and reduce heterogeneity. Furthermore, the REV was calculated by deriving the coefficient of variation. Nine of the twenty-six samples reach the REV within the volume of traditional core plugs, which indicates that the REV sizes of vuggy dolostones are commonly much larger than the volume of traditional core plugs. Finally, this study indicates that REV sizes are affected by diverse factors. It can be effectively predicted by a new model established based on the relationship between REV sizes and quantitative parameters. The correlated coefficient of this model reaches 0.9320. The results of this study give more insights into accurately evaluating the petrophysical properties of vuggy carbonate reservoirs.

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Rong, Guan, Jun Peng, Xiaojiang Wang, Guang Liu, and Di Hou. "Permeability tensor and representative elementary volume of fractured rock masses." Hydrogeology Journal 21, no. 7 (September 7, 2013): 1655–71. http://dx.doi.org/10.1007/s10040-013-1040-x.

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Li, J. H., L. M. Zhang, Y. Wang, and D. G. Fredlund. "Permeability tensor and representative elementary volume of saturated cracked soil." Canadian Geotechnical Journal 46, no. 8 (August 2009): 928–42. http://dx.doi.org/10.1139/t09-037.

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Cracks are prevalent in near-ground-surface soils and provide preferential pathways for fluid flow. Cracks increase water infiltration or contaminant solute transport into soils. This paper studies the development of a permeability tensor and a representative elementary volume (REV) for saturated cracked soils. First, a method of generating random crack networks based on the statistical parameters of the crack geometry is presented. Then, the permeability tensor and REV for a crack network are studied by modeling water flow through the generated random crack networks. Finally, the permeability tensor for a cracked soil is obtained by combining the crack network and the soil matrix, and the properties of the permeability tensor and the REV for the cracked soils are investigated. Results show that the permeability tensor can be used to represent the permeability anisotropy of a cracked soil. An REV can be readily established when the crack network is relatively dense. An REV can be defined and the contribution of the crack network to permeability is small when a crack network exists in homogeneous sands. An REV is harder to establish and the hydraulic conductivity is dominated by the random crack network when a sparse crack network exists in clays.

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Wang, Da Yong, Hu Shan Xu, and Xiao Jing Ma. "Computed Tomography Analysis of Representative Elementary Volume (REV) of Porous Medium." Advanced Materials Research 868 (December 2013): 234–37. http://dx.doi.org/10.4028/www.scientific.net/amr.868.234.

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Representative Elementary Volume (REV) is not only a necessary measure for studying heterogeneous pore structure of reservoir rocks but also an important parameter for core-scale numerical modeling. In this paper, we accordingly analyze the REV for different porous media with different grain sizes based on computed tomography (CT) measurement. Our results show that that CT measurement is a relible method for REV analysis and that there is an appropriate linear relationship between grain size and REV.

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Sedaghat, Mohammad H., and Siroos Azizmohammadi. "Representative-Elementary-Volume Analysis of Two-Phase Flow in Layered Rocks." SPE Reservoir Evaluation & Engineering 22, no. 03 (August 1, 2019): 1075–83. http://dx.doi.org/10.2118/194014-pa.

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Sutopo, Norio ARIHARA, Kozo SATO, and Maghsood ABBASZADEH. "Representative Elementary Volume of Naturally Fractured Reservoirs Evaluated by Flow Simulation." Journal of the Japan Petroleum Institute 45, no. 3 (2002): 156–68. http://dx.doi.org/10.1627/jpi.45.156.

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Razavi, MR, B. Muhunthan, and O. Al Hattamleh. "Representative Elementary Volume Analysis of Sands Using X-Ray Computed Tomography." Geotechnical Testing Journal 30, no. 3 (2007): 100164. http://dx.doi.org/10.1520/gtj100164.

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45

Muaaz-Us-Salam, Syed, Peter John Cleall, and Michael John Harbottle. "The case for examining fluid flow in municipal solid waste at the pore-scale – A review." Waste Management & Research: The Journal for a Sustainable Circular Economy 37, no. 4 (February 21, 2019): 315–32. http://dx.doi.org/10.1177/0734242x19828120.

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In this paper, we discuss recent efforts from the last 20 years to describe transport in municipal solid waste (MSW). We first discuss emerging themes in the field to draw the reader’s attention to a series of significant challenges. We then examine contributions regarding the modelling of leachate flow to study transport via mechanistic and stochastic approaches, at a variety of scales. Since MSW is a multiphase, biogeochemically active porous medium, and with the aim of providing a picture of transport phenomena in a wider context, we then discuss a selection of studies on leachate flow incorporating some of the complex landfill processes (e.g. biodegradation and settlement). It is clear from the literature survey that our understanding of transport phenomena exhibited by landfilled waste is far from complete. Attempts to model transport have largely consisted of applying representative elementary-scale models (the smallest volume which can be considered representative of the entire waste mass). Due to our limited understanding of fluid flow through landfilled waste, and the influence of simultaneously occurring biogeomechanical processes within the waste mass, elementary-scale models have been unable to fully describe the flow behaviour of MSW. Pore-scale modelling and experimental studies have proven to be a promising approach to study fluid flow through complex porous media. Here, we suggest that pore-scale modelling and experimental work may provide valuable insights into transport phenomena exhibited by MSW, which could then be used to revise elementary-scale models for improved representation of field-scale problems.

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Gasmi, H., M. Touahmia, A. Torchani, E. Hamdi, and A. Boudjemline. "Determination of Fractured Rock’s Representative Elementary Volume by a Numerical Simulation Method." Engineering, Technology & Applied Science Research 9, no. 4 (August 10, 2019): 4448–51. http://dx.doi.org/10.48084/etasr.2854.

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The present study aims at developing a numerical program called DISSIM which can analyze the homogenization of rock massifs using a new subroutine which calculates Representative Elementary Volume (REV). The DISSIM methodology consists of two steps. The first step involves the modeling of the fractured network in order to provide a surface simulation that represents the real fracture of the examined front. The second step is to numerically model the wave propagation through the simulated fracture network while characterizing the attenuation of vibrations due to the effect of discontinuities. This part allows us to determine in particular the wave propagation velocity through the fractured mass, from which we can determine the homogenized Young's modulus. However, after extensive bibliographic research, it was realized that a third step appeared to be necessary. In fact, it is necessary to look for a representative elementary volume on which we apply the proposed homogenization method. Two types of the representative elementary volume are proposed in this article, the geometric REV and the mechanical REV. The presentation of these two types of REV and the DISSIM methodology are detailed in this paper. Then, this methodology was applied to the study of a real case. The present research provides a method allowing the calculation of both types of REV for fissured rocks. The case study yielded comparable results between the mechanical REV and the geometric REV, which is compatible with previous research studies.

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Fenaux, Michiel, Encarnacion Reyes, Jaime C. Gálvez, Amparo Moragues, and Jesús Bernal. "On the Tortuosity-Connectivity of Cement-Based Porous Materials." Applied Sciences 11, no. 13 (June 23, 2021): 5812. http://dx.doi.org/10.3390/app11135812.

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In this work, the transport equations of ionic species in concrete are studied. First, the equations at the porescale are considered, which are then averaged over a representative elementary volume. The so obtained transport equations at the macroscopic scale are thoroughly examined and each term is interpreted. Furthermore, it is shown that the tortuosity-connectivity does not slow the average speed of the ionic species down. The transport equations in the representative elementary volume are then compared with the equations obtained in an equivalent pore. Lastly, comparing Darcy’s law and the Hagen–Poiseuille equation in a cylindrical equivalent pore, the tortuosity-connectivity parameter is obtained for four different concretes. The proposed model provides very good results when compared with the experimentally obtained chloride profiles for two additional concretes.

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Silva, William Godoy de Azevedo Lopes de, Edmilson Helton Rios, Fernanda Oliveira Hoerlle, Elizabeth May Braga Dulley Pontedeiro, Leonardo Fonseca Borghi de Almeida, José Luis Drummond Alves, and Paulo Couto. "REPRESENTATIVE ELEMENTARY VOLUME OF A REGION OF INTEREST OF A HETEROGENEOUS CARBONATE ROCK USING X-RAY COMPUTED MICROTOMOGRAPHY AND NUMERICAL SIMULATION." Revista Brasileira de Geofísica 36, no. 4 (December 21, 2018): 1. http://dx.doi.org/10.22564/rbgf.v36i4.1975.

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ABSTRACT. Characterization of carbonate rocks presents several challenges regarding the acquisition of petrophysical parameters and the understanding of fluid-flow dynamics in their pore system. To face these challenges, techniques such as X-ray microtomography, three-dimensional digital model reconstruction and fluid-flow numerical simulations have been continuously developed and improved. This study analyzes the representative elementary volume (REV) of a region of interest (ROI) of a highly heterogeneous stromatolite sample. Porosity and permeability are estimated for different subvolumes of the sample based on digital petrophysics. All necessary steps for reconstruction and segmentation of the complex pore system of the sample, as well as numerical simulations of fluid flow, are presented and discussed. The workflow is promising for reservoir evaluation because it can be applied to any type of carbonate rock.Keywords: Stromatolite, mCT, segmentation, REV, digital petrophysicsRESUMO. A caracterização de rochas carbonáticas apresenta diversos desafios quanto à determinação de seus parâmetros petrofísicos e o entendimento da dinâmica de escoamento de fluidos em seus sistemas porosos. Técnicas como a microtomografia de raios X, a modelagem digital tridimensional e a simulação numérica do escoamento de fluidos têm sido continuamente desenvolvidas e aprimoradas para superar esses desafios. Este estudo analisa o volume elementar representativo (REV) em uma região de interesse (ROI) de uma amostra de estromatólito altamente heterogênea. A porosidade e a permeabilidade são estimadas em diferentes subvolumes da amostra através da petrofísica digital. São apresentadas e discutidas todas as etapas necessárias para a reconstrução e segmentação do sistema poroso e a simulação numérica do escoamento de fluidos. A metodologia é promissora para avalição de reservatórios visto que o fluxo de trabalho pode ser aplicado a qualquer tipo de rocha carbonática.Palavras-chave: Estromatólitos, mCT, segmentação, REV, petrofísica digital

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Brown, G. O., H. T. Hsieh, and D. A. Lucero. "Evaluation of laboratory dolomite core sample size using representative elementary volume concepts." Water Resources Research 36, no. 5 (May 2000): 1199–207. http://dx.doi.org/10.1029/2000wr900017.

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Wiącek, Joanna, and Marek Molenda. "Representative elementary volume analysis of polydisperse granular packings using discrete element method." Particuology 27 (August 2016): 88–94. http://dx.doi.org/10.1016/j.partic.2015.08.004.

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