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On the Micromechanics of True Triaxial Test, Insights from 3D DEM Study

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Iranian Journal of Science and Technology, Transactions of Civil Engineering Aims and scope Submit manuscript

Abstract

In this paper, three dimensional discrete element method simulations of true triaxial test are presented. During simulations, the major, the intermediate and the minor principal strains are monitored to maintain the b-value constant. The effect of intermediate principal stress on the frictional parameters of granular materials is studied. Furthermore, the micromechanics of samples using the Stress–Force–Fabric (SFF) relationship is investigated. The SFF relationship is comprised of anisotropy tensors of fabric, contact normal and tangential forces. Results show that, the mobilized friction angles in simulations with different b-values have very good agreements with results of the so-called general stress tensors, which are made of force and position vectors at contact points. It is observed that the evolution of anisotropy in the sample is at the origin of different responses of granular materials in macro scale. The frictional properties of granular materials is observed sensitive to the intermediate principal stress both at macro and grain scale. Our observations highlight the important role of intermediate principal stress, and are consistent with experimental studies of true triaxial tests on granular materials.

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Abbreviations

\( a_{d}^{n} \) :

Deviatoric coefficient of normal contact force anisotropy

\( a_{ij}^{n} \) :

Normal contact force anisotropy tensor

\( a_{d}^{r} \) :

Deviatoric coefficient of fabric anisotropy

\( a_{i}^{r} \) :

Principal coefficients of fabric anisotropy

\( a_{ij}^{r} \) :

Fabric anisotropy tensor

\( a_{d}^{t} \) :

Deviatoric coefficient of tangential contact force anisotropy

\( a_{ij}^{t} \) :

Tangential contact force anisotropy tensor

c :

Contact point for two particles

\( {\text{d}}\varOmega ,\Delta \varOmega \) :

Orientation interval

\( E\left( \varOmega \right) \) :

Distribution function of contact normal

\( \bar{f}_{0} \) :

Average normal contact force

\( f_{i}^{c} \) :

Force vector

\( \bar{f}^{n} \left( \varOmega \right) \) :

Distribution function of average normal contact force

\( F_{ij}^{n} \) :

Normal contact force tensor

\( F_{ij}^{{{\prime }n}} \) :

Deviator normal contact force tensor

\( \bar{f}_{i}^{t} \left( \varOmega \right) \) :

Distribution function of tangential contact forces

\( \bar{f}^{t} \left( \varOmega \right) \) :

Tangential contact forces magnitude

\( F_{ij}^{t} \) :

Tangential contact force tensor

\( F_{ij}^{{{\prime }t}} \) :

Deviator tangential contact force tensor

\( \bar{l}_{0} \) :

The averaged contact length for all contacts

\( l_{j}^{c} \) :

Position vector

\( m_{V} \) :

Assembly contact density

\( n_{i} \) :

Contact normal component

\( R_{ij} \) :

Fabric tensor

\( R_{ij}^{{\prime }} \) :

Deviator fabric tensor

V :

Volume of assembly

\( \alpha \) :

Horizontal angle in spherical coordination system

\( \beta \) :

Vertical angle in spherical coordination system

\( \gamma \) :

Coordination number

\( \delta_{ij} \) :

Unit matrix

\( \varepsilon_{\text{a}} \) :

Axial strain

\( \varepsilon_{\text{V}} \) :

Volumetric strain

\( \sigma_{1} \) :

Major principal stress

\( \sigma_{2} \) :

Intermediate principal stress

\( \sigma_{3} \) :

Minor principal stress

\( \sigma_{ij} \) :

Stress tensor

\( \sigma_{\text{v}} \) :

Vertical stress on cubic cell

\( \sigma_{h}^{a} \) :

First horizontal stress on cubic cell

\( \sigma_{h}^{b} \) :

Second horizontal stress on cubic cell

\( \varphi^{^\circ } \) :

Residual friction angle

\( \varphi_{\hbox{max} }^{^\circ } \) :

Maximum of friction angle

\( \phi_{\text{mobilized}} \) :

Mobilized friction angle

\( \varOmega \) :

Small fraction on spherical coordinate system surface

\( \varOmega^{\text{g}} \) :

Partitioned group of unit sphere

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Authors and Affiliations

  1. School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Omid Dorostkar & Ali Asghar Mirghasemi

  2. Swiss Federal Institute of Technology Zurich (ETH Zurich), Zurich, Switzerland

    Omid Dorostkar

  3. Swiss Federal Laboratories for Materials Science and Technology (Empa), Dubendorf, Switzerland

    Omid Dorostkar

Authors
  1. Omid Dorostkar
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  2. Ali Asghar Mirghasemi
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Correspondence to Ali Asghar Mirghasemi.

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Dorostkar, O., Mirghasemi, A.A. On the Micromechanics of True Triaxial Test, Insights from 3D DEM Study. Iran J Sci Technol Trans Civ Eng 42, 259–273 (2018). https://doi.org/10.1007/s40996-018-0102-7

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  • DOI: https://doi.org/10.1007/s40996-018-0102-7

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