Mechanical properties of granular materials: A variational approach to grain‐scale simulations

Holtzman, Ran; Silin, Dmitriy; Patzek, Tadeusz W

doi:10.1002/nag.725

Cited by 26 publications

(46 citation statements)

References 37 publications

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“…The abundance of related applications and their large socioeconomic impact have motivated intensive research in the field of granular mechanics (see the references within [1,2]). Technical difficulties associated with grain-scale measurements, together with the shortcomings of continuum macroscopic models, make micromechanical simulations a prominent tool.…”

Section: Introductionmentioning

confidence: 99%

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Frictional granular mechanics: A variational approach

Holtzman¹,

Silin²,

Patzek³

2009

Numerical Meth Engineering

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SUMMARYThe mechanical properties of a cohesionless granular material are evaluated from grain-scale simulations. Intergranular interactions, including friction and sliding, are modeled by a set of contact rules based on the theories of Hertz, Mindlin, and Deresiewicz. A computer generated, three-dimensional, irregular pack of spherical grains is loaded by incremental displacement of its boundaries. Deformation is described by a sequence of static equilibrium configurations of the pack. A variational approach is employed to find the equilibrium configurations by minimizing the total work against the intergranular loads. Effective elastic moduli are evaluated from the intergranular forces and the deformation of the pack. Good agreement between the computed and measured moduli, achieved with no adjustment of material parameters, establishes the physical soundness of the proposed model.

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Section: Introductionmentioning

confidence: 99%

“…A computational technique to simulate deformation of a granular material and evaluate its mechanical properties, denoted hereafter as Quasi-Static Granular Model (QuSGM), has been presented in [1]. In QuSGM, a three-dimensional (3D) irregular pack of spherical grains is loaded by incremental displacement of its boundaries.…”

Section: Introductionmentioning

confidence: 99%

Frictional granular mechanics: A variational approach

Holtzman¹,

Silin²,

Patzek³

2009

Numerical Meth Engineering

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“…so that the function v 0 does not depend on x and satisfies the boundary conditions (31). Then, Equations (33)-(34) take on the form…”

Section: 32mentioning

confidence: 99%

“…First, the coordinates of future grain centers have to be generated. We utilize the centers of a pack of spherical grains computed by simulation of compaction [31]. Second, the initial grain structures are generated by Voronoi tesselation [3,74].…”

Section: Evaluation Of the Permeability Tensor By Subsamplingmentioning

confidence: 99%

Digital Rock Studies of Tight Porous Media

Silin¹

2012

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Abstract. This technical report summarizes some recently developed approaches to studies of rock properties at a pore scale. Digital rock approach is complementary to laboratory and field studies. It can be especially helpful in situations where experimental data are uncertain, or are difficult or impossible to obtain. Digitized binary images of the pore geometries of natural rocks obtained by different imaging techniques are the input data. Computer-generated models of natural rocks can be used instead of images in a case where microtomography data are unavailable, or the resolution of the tools is insufficient to adequately characterize the features of interest. Simulations of creeping viscous flow in pores produce estimates of Darcy permeability. Maximal Inscribed Spheres calculations estimate two-phase fluid distribution in capillary equilibrium. A combination of both produce relative permeability curves. Computer-generated rock models were employed to study two-phase properties of fractured rocks, or tight sands with slit-like pores, too narrow to be characterized with micro-tomography. Various scenarios can simulate different fluid displacement mechanisms, from piston-like drainage to liquid dropout at the dew point.A finite differences discretization of Stokes equation is developed to simulate flow in the pore space of natural rocks. The numerical schemes are capable to handle both no-slip and slippage flows. An upscaling procedure estimates the permeability by subsampling a large data set. Capillary equilibrium and capillary pressure curves are efficiently estimated with the method of maximal inscribed spheres both an arbitrary contact angle. The algorithms can handle gigobytes of data on a desktop workstation. Customized QuickHull algorithms model natural rocks. Capillary pressure curves evaluated from computer-generated images mimic those obtained for microtomography data.

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“…The fractured medium for this study was computer-generated using QHull codes [3]. Holtzman et al [10] simulated compaction of a pack of spherical grains. The grain centers produced by this simulation were used to compute a Voronoi tessellation.…”

Section: Digital Datamentioning

confidence: 99%

Pore-Scale Study of the Impact of Fracture and Wettability on Two-Phase Flow Properties of Rock

Silin

Ajo‐Franklin

Helland

et al. 2012

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Abstract. Fractures and wettability are among other factors that can strongly affect the twophase flow properties of porous media. Maximal-inscribed spheres (MIS) and finite-difference flow simulations on computer-generated structures mimicking micro-CT images of fractured rock suggest the character of the capillary pressure and relative permeability curves modification by natural or induced fracture and wettability alteration.

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Mechanical properties of granular materials: A variational approach to grain‐scale simulations

Cited by 26 publications

References 37 publications

Frictional granular mechanics: A variational approach

Frictional granular mechanics: A variational approach

Digital Rock Studies of Tight Porous Media

Pore-Scale Study of the Impact of Fracture and Wettability on Two-Phase Flow Properties of Rock

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