Relationship between void- and contact normal-based fabric tensors for 2D idealized granular materials

Fu, Pengcheng; Dafalias, Yannis F.

doi:10.1016/j.ijsolstr.2015.02.041

Cited by 70 publications

(42 citation statements)

References 41 publications

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“…Examples include void ratio, coordination number, and various fabric tensors that reflect the directional properties of the material, including particle orientation-, contact normal-, and voidbased fabric tensors, etc., [13,22,24]. However, other fabric features yet to be developed and fully appreciated could also be highly relevant to sand behavior under certain circumstances.…”

Section: Calculation Of Stress Strain and Fabric Quantitiesmentioning

confidence: 99%

“…In the simulations conducted in this paper, the off-diagonal values of the fabric tensor are observed to be well less than 1 % of those in the x and y directions. Particle orientation-based fabric tensors are not applicable to the study of circular particles, and fabric tensors based on void shapes have been found to be strongly correlated with those based on inter-particle contact normal directions [13].…”

Section: Calculation Of Stress Strain and Fabric Quantitiesmentioning

confidence: 99%

“…20-120 loading cycles are performed for each simulation until the saturation of c 0 at liquefaction and each loading cycle consists of at least 40,000 time steps, ensuring sufficient temporal coverage and resolution. Drained biaxial compression and stress rotation simulations results for the same virtual material are available in Fu and Dafalias [13]. * Test ID consists of the prescribed void ratio, deviatoric stress amplitude, and initial consolidation stress.…”

Section: Introductionmentioning

confidence: 99%

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DEM study of fabric features governing undrained post-liquefaction shear deformation of sand

et al. 2016

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In an effort to study undrained post-liquefaction shear deformation of sand, the discrete element method (DEM) is adopted to conduct undrained cyclic biaxial compression simulations on granular assemblies consisting of 2D circular particles. The simulations are able to successfully reproduce the generation and eventual saturation of shear strain through the series of liquefaction states that the material experiences during cyclic loading after the initial liquefaction. DEM simulations with different deviatoric stress amplitudes and initial mean effective stresses on samples with different void ratios and loading histories are carried out to investigate the relationship between various mechanics-or fabric-related variables and postliquefaction shear strain development. It is found that wellknown metrics such as deviatoric stress amplitude, initial mean effective stress, void ratio, contact normal fabric anisotropy intensity, and coordination number, are not adequately correlated to the observed shear strain development and, therefore, could not possibly be used for its prediction. A new fabric entity, namely the Mean Neighboring Particle Distance (MNPD), is introduced to reflect the space arrangement of particles. It is found that the MNPD has an extremely strong and definitive relationship with the post-liquefaction shear strain development, showing MNPD's potential role as a parameter governing post-liquefaction behavior of sand.

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Section: Calculation Of Stress Strain and Fabric Quantitiesmentioning

confidence: 99%

Section: Calculation Of Stress Strain and Fabric Quantitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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DEM study of fabric features governing undrained post-liquefaction shear deformation of sand

et al. 2016

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“…As shown in Equation , contact normal‐based fabric tensors are used in this study to quantify the internal structure of granular materials, although other fabric descriptors such as the particle orientation fabric tensor or void vector fabric tensor have been recently proposed for better describing the micromechanical structure . This is because the contact normal fabric tensor is more suitable for continuum modeling than the other fabric tensors and a strong correlation with the void vector fabric tensor is identified for non‐elongated particles . The strain space multiple mechanism model takes into account the fabric due to touching particles as well as that due to non‐touching particles through the concept of Dirichlet tessellation and Delaunay network .…”

Section: Integrated Form Of the Strain Space Multiple Mechanism Modelmentioning

confidence: 99%

Constitutive modeling of inherent anisotropy in a strain space multiple mechanism model for granular materials

Ueda

Iai

2018

Num Anal Meth Geomechanics

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Summary Consideration of fabric anisotropy is crucial to gaining an improved understanding of the behavior of granular materials. This paper presents a constitutive model to describe the sand behavior associated with fabric anisotropy within a framework of a strain space multiple mechanism model. In the proposed model, a second‐order fabric tensor is extended by incorporating a new function that represents the effect of inherent (or initial fabric) anisotropy, along with three additional parameters: two of them, a1 and a2, control the degree of anisotropy, and the second mode of inherent anisotropy can be expressed by introducing the parameter a2 as well as the first mode by the parameter a1. The third parameter, θ0, expresses the principal direction of inherent anisotropy (eg, the normal vector direction of bedding planes relative to horizontal axis). The formulation of the dilative component of dilatancy (ie, positive dilatancy) is also extended to consider the effect of inherent anisotropy based on the interlocking mechanism. Experimental data on the complex anisotropic responses of Fraser River sand and Toyoura sand under monotonic loading is used to validate this model. The proposed model is shown to successfully capture anisotropic responses, which become contractive or dilative depending on different principal‐stress directions, with a single set of anisotropy parameters; thus, the model is considered to possess the capability to simulate the anisotropic behaviors of granular materials. In addition to different loadings on the same fabric, the effects of different fabric anisotropies upon the sand behavior under the same loadings are also investigated.

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“…Discrete element method allows for direct quantification of the inherent fabric anisotropy of granular materials. Various forms of contact normal‐based and void vector‐based fabric quantities have been proposed and applied in studying the anisotropic behavior of granular materials (e.g., ). The contact normal fabric tensor F c that characterizes the spatial distribution features of inter‐particle contact normal directions is defined in this paper after Satake to be

F_{c} = \frac{1}{2 N_{c}} \sum_{k = 1}^{2 N_{c}} n_{c}^{k} \otimes n_{c}^{k}

where N c is the number of contacting points in the granular assembly,

n_{c}^{k}

is the unit vector representing the normal direction of the k th inter‐particle contact, and ‘⊗’ denotes the tensor product.…”

Section: Simulation Setupmentioning

confidence: 99%

Strength anisotropy of granular material consisting of perfectly round particles

Wang

Tong

et al. 2017

Num Anal Meth Geomechanics

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The strength anisotropy of granular materials deposited under gravity has mostly been attributed to elongated particles' tendency to align long axes along the bedding plane direction. However, recent experiments on near‐spherical glass beads, for which preferred particle alignment is inapplicable, have exhibited surprisingly strong strength anisotropy. This study tests the hypothesis that certain amount of fabric anisotropy caused by the anisotropic stress during deposition under gravity can be locked in a circular‐particle deposit. Such locked‐in fabric anisotropy can withstand isotropic consolidation and leads to significant strength anisotropy. 2D discrete element method simulations of direct shear tests on circular‐particle deposits are conducted in this study, allowing for the monitoring of both stress and fabric. Simulations on both monodispersed and polydispersed circular‐particle samples generated under downward gravitational acceleration exhibit clear anisotropy in shear strength, thereby proving the hypothesis. When using contact normal‐based and void‐based fabric tensors to quantify fabric anisotropy in the material, we find that the intensity of anisotropy is discernible but low prior to shearing and is dependent on the consolidation process and the dispersity of the sample. The fact that samples with very low anisotropy intensity measurements still exhibit fairly strong strength anisotropy suggests that current typical contact normal‐based and void‐based second‐order fabric tensor formulations may not be very effective in reflecting the anisotropic peak shear strength of granular materials. Copyright © 2017 John Wiley & Sons, Ltd.

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Relationship between void- and contact normal-based fabric tensors for 2D idealized granular materials

Cited by 70 publications

References 41 publications

DEM study of fabric features governing undrained post-liquefaction shear deformation of sand

DEM study of fabric features governing undrained post-liquefaction shear deformation of sand

Constitutive modeling of inherent anisotropy in a strain space multiple mechanism model for granular materials

Strength anisotropy of granular material consisting of perfectly round particles

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