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Relation between void ratio and contact fabric of granular soils

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Abstract

Void ratio is one of the key engineering properties of granular soils. It reflects how well the grains are packed and hints whether the soil is contractive or dilative upon shearing. On the other hand, fabric tensor has been at the centre of experimental and theoretical granular mechanics research over the past decade for its intimate relation with the material’s anisotropy and critical-state behaviour. This paper tests the hypothesis that the void ratio and the fabric tensor of granular soils are tightly correlated to each other. Through discrete element method, a series of isotropic/anisotropic consolidation tests and monotonic triaxial compression and extension tests are conducted. The obtained void ratio data are found to collapse onto one unique surface, namely the fabric–void ratio surface (FVS), when plotted against the first two invariants of the contact-based fabric tensor. The robustness of this relation is confirmed by testing samples with different initial void ratios under various consolidation and monotonic triaxial stress paths. An additional undrained cyclic triaxial test followed by continuous shearing to critical state is performed to further examine the fabric–void ratio relation under complex loading paths. It is found that the previously identified FVS from monotonic tests still attracts the states of these specimens at critical state, although their fabric–void ratio paths deviate from the FVS during cyclic loading. The newly discovered FVS provides a refreshing perspective to interpret the structural evolution of granular materials during shearing and can serve as an important modelling component for fabric-based constitutive theories for sand.

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Data availability statement

The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.

Abbreviations

a 1, a 2, a 3 :

Parameters in the Gunary equation

A 1, A 2 :

Parameter in the NL-FVS equation

b, b e :

Principal stress ratio and principal strain ratio

\(d,\overline{d }\) :

Particle diameter and average particle diameter

e :

Void ratio

e 0 :

Initial void ratio taken at p = 50 kPa

e c :

Critical-state void ratio

e r :

Reference void ratio

e data :

Void ratio of the DEM data

e FVS :

Corresponding void ratios on the FVS of DEM data

E :

Particle Young’s modulus

E 1, E 2, E 3 :

Major, intermediate, and minor principal values of the second kind fabric tensor

E ij :

Fabric tensor of the second kind

F :

Fabric anisotropy

F c :

Critical-state fabric anisotropy

F data :

Fabric anisotropy from DEM data

F n, F s :

Normal and tangential forces between two particles in contact

F ij :

Fabric tensor of the third kind

G ij :

Fabric tensor of the first kind

h :

Parameter in the O’Hern equation

h r :

Parameter in the NL-FVS equation

I :

Inertia number

k n, k s :

Normal and tangential stiffness of a particle

K n, K s :

Normal and tangential stiffness of a contact

M c, M e :

Critical stress ratio at compression and extension

n, n r :

Porosity and reference porosity

n :

Unit contact normal vector

N :

Number of loading cycles in cyclic triaxial test

N c,:

Number of contacts

N p :

Number of particles in the assembly

p :

Mean effective stress

p a :

Atmosphere pressure

p c :

Mean effective stress at the end of consolidation or the beginning of triaxial shearing

q :

Deviatoric stress

R :

Particle radius

Z :

Coordination number

Z c :

Critical-state coordination number

Z r :

Coordination number at reference porosity

Z data :

Coordination number from DEM data

Z th :

Threshold coordination number that distinguish the liquefied and non-liquefied state

δ n, δ s :

Normal and tangential displacement of a contact

δ ij :

Kronecker delta

Δt cr :

Critical time step

ε 1, ε 2, ε 3 :

Major, intermediate, and minor principal strain

ε a :

Axial strain

\(\dot{\varepsilon }\) :

Strain rate

η, η 0 :

Deviatoric stress ratio and the deviatoric stress ratio during consolidation

θ E :

Fabric lode angle

λ :

Parameter in the equation of e-p normal consolidation line

μ :

Particle friction coefficient after the initial compaction with p > 5 kPa

μ 0 :

Particle friction coefficient during the initial compaction with p ≤ 5 kPa

ξ :

Parameter in the equation of e–p normal consolidation line

ρ :

Directional distribution of contact normals

\({\overline{\rho }}\) :

Directional distribution density of contact normals

ρ g :

Particle density

σ 1, σ 2, σ 3 :

Major, intermediate, and minor principal stress

φ :

Parameter in the O’Hern equation

ζ :

Parameter in the NL-FVS equation

Γ:

Maximum void ratio in the equation of e–p normal consolidation line

Ω:

Solid angle

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Acknowledgements

This research was supported by the U.S. National Science Foundation (NSF) under NSF CMMI Award no. 2113474.

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  1. Department of Civil, Environmental and Architectural Engineering, University of Colorado Boulder, Boulder, CO, USA

    Yuxuan Wen & Yida Zhang

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  1. Yuxuan Wen
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Correspondence to Yida Zhang.

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Wen, Y., Zhang, Y. Relation between void ratio and contact fabric of granular soils. Acta Geotech. 17, 4297–4312 (2022). https://doi.org/10.1007/s11440-022-01507-7

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