Numerical Study of a Binary Mixture of Similar Ellipsoids of Various Particle Shapes and Fines Contents
Publication: International Journal of Geomechanics
Volume 22, Issue 4
Abstract
This paper presents a numerical study of the mechanical properties of a binary mixture of similar prolate ellipsoids of various particle shapes and fines’ contents using the discrete element method. The ratio of the major axis of a small ellipsoid to that of a large ellipsoid is 0.2. Because all particles have the same shape, the particle shape of the binary mixture is defined unambiguously. The effect of fines content is examined with samples of the same particle shape. The effect of particle shape is examined by comparing the samples of different particle shapes. Very dense samples are generated and sheared under drained and constant volume conditions. The macroscopic and microscopic behaviors of these samples are studied at both peak and critical states. The mechanical behavior can be grouped into two or three regions for our binary mixture depending on the fines content. Although the critical state line varies with fines content, a unified critical state line is identified using the intergranular void ratio, which is a function of fines content and a parameter. The parameter is a constant for the samples of the same particle shape. This constant is different for the samples of different particle shapes. The finding explains why some studies defined the parameter as a function of fines. The intergranular void ratio does not relate well to the peak friction angle. The microscopic behavior is examined through contact normal, particle orientation, and stress partition. Although some microscopic parameters can identify the region where the sample belongs, we do not find any dominant microscopic parameter that relates to the macroscopic behavior of a binary mixture of various fines contents.
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Acknowledgments
This work was partially supported by the National Natural Science Foundation of China (No. U1865204).
Notation
The following symbols are used in this paper:
- e
- void ratio;
- ecs
- critical state void ratio;
- eg
- equivalent void ratio;
- fc
- fines content, the ratio between the weight of the small ellipsoids and the total weight of ellipsoids;
- fth
- threshold fines content (transitional fines content) at which small particles fill the available void formed by large particles completely;
- pcs
- the mean stress in a critical state;
- r
- particle size ratio (the ratio of the major axis of a small ellipsoid to that of a large ellipsoid);
- ɛp
- the major strain at maximum deviator stress;
- ϕcs
- the critical state friction angle;
- ϕp
- the peak friction angle;
- σ
- confining pressure;
- σLL
- the ratio of the mean stress from the contact forces of two large particles to the initial mean stress of a sample;
- σLS
- the ratio of the mean stress from the contact forces of a large particle and a small particle to the initial mean stress of a sample;
- σSS
- the ratio of the mean stress from the contact forces of two small particles to the initial mean stress of a sample;
- the ratio of the octahedral shear stress from the contact forces of two large particles to the initial mean stress of a sample;
- the ratio of the octahedral shear stress from the contact forces of a large particle and a small particle to the initial mean stress of a sample; and
- the ratio of the octahedral shear stress from the contact forces of two small particles to the initial mean stress of a sample.
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International Journal of Geomechanics
Volume 22 • Issue 4 • April 2022
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© 2022 American Society of Civil Engineers.
History
Received: Mar 30, 2021
Accepted: Nov 20, 2021
Published online: Feb 2, 2022
Published in print: Apr 1, 2022
Discussion open until: Jul 2, 2022
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- Ehsan Yazdani, Amy Nguyen, T. Matthew Evans, Shear-Induced Instability of Sand Containing Fines: Using the Equivalent Intergranular Void Ratio as a State Variable, International Journal of Geomechanics, 10.1061/(ASCE)GM.1943-5622.0002486, 22, 8, (2022).