Discrete Element Modelling of the Mechanical Behavior of Sand–Rubber Mixtures under True Triaxial Tests
Abstract
:1. Introduction
2. Modelling Using the Discrete Element Method
2.1. Rolling Resistance Contact Model
2.2. Model Generation and Loading Paths
2.3. Calibration Procedure
3. Results
3.1. Macroscopic Behavior
3.1.1. Deviatoric Stress and Volumetric Strain Against the Axial Strain
3.1.2. Effect of Rubber Content and Intermediate Principal Stress Ratio on the Stress Ratio in the Peak State
3.2. Micromechanical Response
3.2.1. Coordination Number
3.2.2. Proportion of Strong Contact in Different Types of Contacts
3.2.3. Fabric Tensor and Anisotropy
3.2.4. Normal Contact Force and the Probability Density Function of Normal Contact Force
4. Conclusions
- The peak strengths of samples under conventional triaxial tests first decrease with 10% rubber particles added, and then increase when the proportion of rubber particles rises up to 30%, but the peak strengths sand–rubber mixtures with either 10% or 30% rubber particles are lower than those of pure sand. This trend is in agreement with previous experimental results and numerical simulations on sand–rubber mixtures with large rubber particles, which confirms the feasibility of the simulations conducted in this study. The same trend can also be observed in the peak friction angles for the samples at each intermediate principal stress ratio.
- For sand–rubber mixtures, the relationship between the peak friction angle and the intermediate principal stress ratio is quite different from that for pure sand, which means adding rubber particles can change the failure behavior of sand under complex loading conditions. A suggested explanation of this phenomenon is that the added large rubber particles mainly affect the inherent stability of the strong network. This study can provide a reference for the constitutive model development of sand–rubber mixtures.
- The investigation on the strong contact ratio of different types of contacts show that nearly all of the rubber–rubber contacts of sand–rubber mixtures are strong contacts, no matter what the rubber contents and the values of intermediate principal stress ratio are. While the strong contact ratio of rubber–sand contacts is higher than that of overall contacts for specimens with 10% of rubber particles, and becomes nearly equal to that of the overall contacts when rubber content rises up to 30%. It can be concluded that rubber content can significantly influence the micro structure and the force transmission in the contact network. This finding also confirms the explanation in the Conclusion 2.
- For samples with the same rubber content, the strong contact ratio of rubber–sand contacts decrease with the principal stress ratio b, while the coordinate number of rubber–sand contacts increase with b. It means that with an increase of b, the force transmitted through the rubber particles increases, and more rubber–sand contacts are needed to support the force chain.
- The analysis of the fabric anisotropy shows that the deviatoric fabric of strong contacts demonstrates a decline by adding large rubber particles, and the deviatoric fabric of strong contacts also decreases with b, which is in line with the previous numerical simulations.
Author Contributions
Funding
Conflicts of Interest
Nomenclature
RSM | Sand–rubber mixtures |
DEM | Discrete element method |
PSD | Particle size distribution |
RC | Rubber content |
Probability density function | |
The normal stiffness | |
The shear stiffness | |
The friction coefficient | |
The rolling resistance moment | |
The rolling resistance stiffness | |
The rolling friction coefficient | |
The major principal stress | |
The intermediate principal stress | |
The minor principal stress | |
The major principle strain | |
The deviatoric stress | |
The mean stress | |
The Intermediate principal stress ratio | |
The peak friction angle | |
The mobilized friction angle | |
The mechanical coordination number | |
The coordination number of sand–sand contacts | |
The coordination number of rubber–sand contacts | |
The coordination numbers of rubber–rubber contacts | |
Major principal fabric of strong contacts | |
Intermediate principal fabric of strong contacts | |
Minor principal fabric of strong contacts | |
Strong deviatoric fabric |
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Set Test ID | b Values | Rubber Content (%) | Sand Particles | Rubber Particles |
---|---|---|---|---|
CS-100-b | 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 | 0 | 43,693 | 0 |
CS-200-b | 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 | 0 | 43,693 | 0 |
RS-10-100-b | 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 | 10 | 34,909 | 299 |
RS-10-200-b | 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 | 10 | 34,909 | 299 |
RS-30-100-b | 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 | 30 | 18,995 | 631 |
RS-30-200-b | 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 | 30 | 18,995 | 631 |
Parameters | Values | |||
---|---|---|---|---|
Rubber–Rubber Contact | Sand–Sand Contact | Rubber–Sand Contact | Wall-Particle Contact | |
Effective modules | 3.5 × 104 | 1.0 × 108 | 8.0 × 106 | 1.0 × 108 |
Normal to shear stiffness ratio | 1.0 | 1.0 | 1.0 | 1.0 |
Inter-particle friction coefficient | 1.5 | 0.335 | 0.5 | 0.0 |
Rolling friction coefficient | 1.0 | 0.35 | 0.5 | N/A |
Damping coefficient | 0.7 | 0.7 | 0.7 | N/A |
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Liu, Y.; Liao, X.; Li, L.; Mao, H. Discrete Element Modelling of the Mechanical Behavior of Sand–Rubber Mixtures under True Triaxial Tests. Materials 2020, 13, 5716. https://doi.org/10.3390/ma13245716
Liu Y, Liao X, Li L, Mao H. Discrete Element Modelling of the Mechanical Behavior of Sand–Rubber Mixtures under True Triaxial Tests. Materials. 2020; 13(24):5716. https://doi.org/10.3390/ma13245716
Chicago/Turabian StyleLiu, Yiming, Xinchao Liao, Lihua Li, and Haijun Mao. 2020. "Discrete Element Modelling of the Mechanical Behavior of Sand–Rubber Mixtures under True Triaxial Tests" Materials 13, no. 24: 5716. https://doi.org/10.3390/ma13245716