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Micro-scale modeling of anisotropy effects on undrained behavior of granular soils

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Abstract

This paper presents a micro-scale modeling of fabric anisotropy effects on the mechanical behavior of granular assembly under undrained conditions using discrete element method. The initial fabrics of the numerical samples engendered from the deposition under gravity are measured, quantified and compared, where the gravitational field can be applied in different directions to generate varying anisotropy orientations. The samples are sheared under undrained biaxial compression, and identical testing conditions are applied, with samples having nearly the same anisotropy intensities, but with different anisotropy directions. The macroscopic behaviors are discussed for the samples, such as the dilatancy characteristics and responses at the critical state. And the associated microstructure changes are further examined, in terms of the variables in the particulate scale, with the focus on the fabric evolution up to a large deformation reaching the critical state. The numerical analysis results compare reasonably well with available experimental data. It is also observed that at critical state, in addition to the requirements by classical critical state theory, a unique fabric structure has also been developed, and might be independent of its initial fabric. This observation is coincided with the recent theoretical achievement of anisotropic critical state theory. Finally, a general framework is introduced for quantifying and modeling the anisotropy effects.

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Abbreviations

\(\alpha \) :

Bedding angle with respect to horizontal axis during gravitational deposition of sample preparation

\(\sigma _{x},\sigma _{y}\) :

Principal stresses along \(x\) and \(y\) directions respectively

\(p,q\) :

Mean normal stress and deviatoric stress respectively

\(CN\) :

Coordination number

\(\varepsilon _{a}\) :

Axial strain along \(y\) direction

\(D\) :

Dilatancy

\({\varvec{\varepsilon }} _v^p ,{\varvec{\varepsilon }} _q^p \) :

Plastic volumetric and deviatoric strains respectively

\(F_{ij}\) :

Fabric tensor

\(F^{{\prime }}_{ij}\) :

Fabric tensor by an orthogonal rotation

\(\vartheta \) :

Orthogonal rotation angle of fabric tensor

\(F_{11}, F_{22},\) :

Components of fabric tensor \(F_{ij}\) in

\(F_{12}\) :

two-dimension

\(F_{1},F_{2}\) :

Principal values of fabric tensor \(F_{ij}\)

\(\Delta ,\varphi \) :

Intensity and principal direction (with respect to horizontal axis) of fabric tensor \(F_{ij}\)

\(\Delta ^{p}, \varphi ^{p}\) :

Intensity and principal direction fabric tensor \(F_{ij}\) in terms of particle orientation

\(\Delta ^{c}, \varphi ^{c}\) :

Intensity and principal direction fabric tensor \(F_{ij}\) in terms of contact unit normal

\(\Delta ^{b},\varphi ^{b}\) :

Intensity and principal direction fabric tensor \(F_{ij}\) in terms of branch vector orientation

\(\mu \) :

Inter-particle friction

\({\varvec{\sigma }}_{ij},{\mathop {{\varvec{\sigma }}}\limits ^\frown }_{ij}\) :

Stress tensor and deviatoric direction of stress tensor respectively

\(A\) :

Anisotropic state parameter

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Acknowledgments

The financial support provided by the Research Grants Council (HKU 7191/05E) is acknowledged. The first author is also grateful for support by Natural Science Foundation of China (Nos. 50808159 and 51178421) and project of Zhejiang Education Department (No. N20110091) and Zhejiang provincial natural science foundation (No. Y1110181).

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Authors and Affiliations

  1. Department of Civil Engineering, Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou, China

    Z. X. Yang & L. Z. Wang

  2. Department of Civil Engineering, The University of Hong Kong, Hong Kong, China

    J. Yang

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Correspondence to Z. X. Yang.

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Yang, Z.X., Yang, J. & Wang, L.Z. Micro-scale modeling of anisotropy effects on undrained behavior of granular soils. Granular Matter 15, 557–572 (2013). https://doi.org/10.1007/s10035-013-0429-5

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