Goddard rattler-jamming mechanism for quantifying pressure dependence of elastic moduli of grain packs

Pride, Steven R.; Berryman, James G.

doi:10.1007/s00707-009-0164-5

Cited by 15 publications

(10 citation statements)

References 23 publications

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“…One class of porous materials that have drained moduli that vary considerably over 0–30 MPa are unconsolidated materials (uncemented grain packs). The reader is referred to Pride () or Pride and Berryman () for analytical models capable of explaining laboratory measurements on grain packs.…”

Section: Models For How the Drained Moduli Change With Stresssupporting

confidence: 88%

Changes in geophysical properties caused by fluid injection into porous rocks: analytical models

Pride

Berryman

Commer

et al. 2016

Geophysical Prospecting

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A B S T R A C TAnalytical models are provided that describe how the elastic compliance, electrical conductivity, and fluid-flow permeability of rocks depend on stress and fluid pressure. In order to explain published laboratory data on how seismic velocities and electrical conductivity vary in sandstones and granites, the models require a population of cracks to be present in a possibly porous host phase. The central objective is to obtain a consistent mean-field analytical model that shows how each modeled rock property depends on the nature of the crack population. The crack populations are described by a crack density, a probability distribution for the crack apertures and radii, and the averaged orientation of the cracks. The possibly anisotropic nature of the elasticity, conductivity, and permeability tensors is allowed for; however, only the isotropic limit is used when comparing to laboratory data. For the transport properties of conductivity and permeability, the percolation effect of the crack population linking up to form a connected path across a sample is modeled. However, this effect is important only in crystalline rock where the host phase has very small conductivity and permeability. In general, the importance of the crack population to the transport properties increases as the host phase becomes less conductive and less permeable.

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Section: Models For How the Drained Moduli Change With Stresssupporting

confidence: 88%

Changes in geophysical properties caused by fluid injection into porous rocks: analytical models

Pride

Berryman

Commer

et al. 2016

Geophysical Prospecting

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“…The Hertz-Mindlin theory can itself predict the stress dependency of unconsolidated sandstones. The predictions of Pride and Berryman (2009) and Agnolin and Roux (2007) based on an HM model show very good agreement with laboratory data for stress-dependency of elasticity of bead packs. However, these theories cannot be applied to the real morphology of sandstones, especially for samples with porosity lower than a sphere packing, where the grain and pore shape can have a significant effect on the elastic response of the sample.…”

Section: Grain Contacts and Micromechanicssupporting

confidence: 56%

A modified coherent potential approximation: Grain-contact moduli and coordination-number effect

Madadi

Christy

2012

GEOPHYSICS

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We modified the self-consistent coherent potential approximation (CPA) for modeling properties of granular composite materials so that it takes into consideration the grain coordination number and distinctive elastic moduli for graincontact zones. The original CPA was reasonably accurate for low-porosity consolidated sandstones but used only inclusion (pore or grain) shape and did not take into account morphological parameters such as coordination number and contact area or contact moduli. In our modified model, the grain inclusion was represented as a "grain with contact area"; therefore, scattering of elastic waves by contacts was incorporated. The modified CPA has been used to calculate data for 3D digital models of sintered quartz bead samples and Fontainebleau sandstones. Reduction of local elastic moduli for contact zones of specified area and thickness reduced effective overall moduli of the bulk sample. The modified theory predicted this weakening accurately, as compared to finite-element simulations.

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“…In addition, laboratory measurements display pressure trends that differ from those predicted by the HM model. Consequently, several authors proposed modifications of the HM model for the dynamic moduli to account for variation of coordination number and relaxation phenomena (Jenkins et al, 2005;Pride & Berryman, 2009;Sajeva, Scarpellini, et al, 2018;Saul et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Including Plastic Strain Into the Discrete Preisach‐Mayergoyz Space: Application to Granular Media

Sajeva

Capaccioli

2019

JGR Solid Earth

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The Preisach-Mayergoyz (PM) model describes hysteretic behavior in several fields. For fractured rocks, a discretized version of the PM model successfully models nonlinear hysteretic elasticity under multiple loading cycles. In addition to hysteresis, granular media are subjected to large irreversible (plastic) deformation. To account for plastic deformation, we propose a modification of the PM density matrix, in which we include negative opening pressure. We associate negative opening pressure with rearrangements of the contact network. We apply the model to three sand samples undergoing multiple isotropic loading cycles. Calibrating the model parameters from quasi-static measurements of volumetric deformation, we estimate the quality of prediction of the dynamic bulk modulus. When this elastoplastic PM model is compared to the classic PM model, strong improvements are found both in matching the strain path and in the estimation of the dynamic bulk modulus.Plain Language Summary Hysteresis in the elasticity of a rock is when its elastic properties depend on its history. A classical model of hysteresis is the Preisach-Mayergoyz model. According to this model, after a compression-decompression cycle, the system comes back to its original state. However, granular media are subject not only to hysteresis but also to irreversible deformation. To model it, we propose a modification of the Preisach-Mayergoyz model. In brief, we assume that some units in the rock remain shrunk after decompression. Mathematically, we obtain this result by imposing that these units have negative opening pressure. From a physical point of view, these units represent rearrangements in the grain network. We apply this model to laboratory measurements on beach samples, and we show that this model, given a small number of parameters, describes sufficiently well the volumetric deformation of the samples and the response of the sample to wave propagation. This is important because this modified model improves the classic hysteresis model, including plasticity in the same mathematical framework. Both the static and dynamic behavior of granular media, as well as the strain path, are better explained.

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Goddard rattler-jamming mechanism for quantifying pressure dependence of elastic moduli of grain packs

Cited by 15 publications

References 23 publications

Changes in geophysical properties caused by fluid injection into porous rocks: analytical models

Changes in geophysical properties caused by fluid injection into porous rocks: analytical models

A modified coherent potential approximation: Grain-contact moduli and coordination-number effect

Including Plastic Strain Into the Discrete Preisach‐Mayergoyz Space: Application to Granular Media

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