Effect of Loading Conditions on the Shear Behaviors of Rock-like Materials Containing Circular Holes, with the CZM Method
Abstract
:1. Introduction
2. Materials and Methods
2.1. Traction Separation Criterion
2.2. The Inserting Process of Zero-Thickness Cohesive Elements
3. Model Establishment
3.1. Determination of Parameters
3.2. Establishment of the Direct Shear Test Model
4. Results of Numerical Simulation
4.1. Mechanical Properties
4.2. Normal Displacement Characteristics
4.3. Description of Cracking Behavior
4.3.1. Effect of Loading Rate
4.3.2. Effect of Normal Stress
5. Conclusions
- (1)
- The results exhibit that the shear process in this research could be determined and identified as the elastic, strengthening, plastic, and residual stress stages, respectively. The cracks’ initiation at the beginning of the crack strengthening stage gradually gathered and penetrated, mainly at the rock bridge.
- (2)
- It was observed that the crack initiation stress and the peak shear strength were significantly affected by the shearing rate and normal stress. The shear rate and normal stress were positively related to the peak shear strength. When the shear rate was 0.02 mm/s and the normal stress was 2 MPa, the crack initiation stress was the smallest, and it was easier than it was in the other conditions to bring about the crack initiation. This point should be considered in engineering practice.
- (3)
- The shear rate and normal stress significantly influenced rock masses’ cracking behavior and the mechanical properties of those with holes. Specifically, the maximum shear dilatancy was positively related to the shear rate, but negatively related to normal stress. The rock bridge played a reinforcing role in the load transfer process, as the vertical displacement near the load end was larger than that far from the load side. Hence, the displacement field of the specimen was non-centrosymmetric.
- (4)
- In this paper, a detailed analysis of the crack initiation, propagation, and coalescence behavior was carried out, and it was found that the shear rate and normal stress have significant effects on crack initiation, propagation, and coalescence. Under the load, the cohesive element at the end of the artificial crack in the edge-notched cracks were more likely to reach the damage evolution stage. The crack always started from the edge-notched, artificial crack tip, near the shear load end, and the stress concentration was more pronounced at the tip of the crack.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Materials | Parameters | Value |
---|---|---|
Solid element | Density/kg·m−3 | 2500 |
Young’s modulus/GPa | 15 | |
Poisson’s ratio | 0.3 | |
Cohesive element | Initial tensile stiffness/GPa·m−1 | 15 |
Initial shear stiffness/GPa·m−1 | 5.28 | |
Normal traction force/MPa | 6 | |
Tangential traction force/MPa | 22 | |
Model-I fracture energy/N·mm−1 | 0.06 | |
Model-II fracture energy/N·mm−1 | 0.165 | |
Plate | Density/kg·m−3 | 7800 |
Young’s modulus/GPa | 210 | |
Poisson’s ratio | 0.3 |
Numerical Number | Shear Rate (mm/s) | Normal Stress (MPa) |
---|---|---|
AI | 0.01 | 1 |
AII | 0.02 | 1 |
AIII | 0.04 | 1 |
BI | 0.02 | 1 |
BII | 0.02 | 2 |
BIII | 0.02 | 4 |
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Zhu, Y.; Chen, H.; Li, A.; Wu, Y.; Zhang, X. Effect of Loading Conditions on the Shear Behaviors of Rock-like Materials Containing Circular Holes, with the CZM Method. Appl. Sci. 2022, 12, 4708. https://doi.org/10.3390/app12094708
Zhu Y, Chen H, Li A, Wu Y, Zhang X. Effect of Loading Conditions on the Shear Behaviors of Rock-like Materials Containing Circular Holes, with the CZM Method. Applied Sciences. 2022; 12(9):4708. https://doi.org/10.3390/app12094708
Chicago/Turabian StyleZhu, Yinge, Huiyuan Chen, Anqi Li, Yue Wu, and Xiaoli Zhang. 2022. "Effect of Loading Conditions on the Shear Behaviors of Rock-like Materials Containing Circular Holes, with the CZM Method" Applied Sciences 12, no. 9: 4708. https://doi.org/10.3390/app12094708
APA StyleZhu, Y., Chen, H., Li, A., Wu, Y., & Zhang, X. (2022). Effect of Loading Conditions on the Shear Behaviors of Rock-like Materials Containing Circular Holes, with the CZM Method. Applied Sciences, 12(9), 4708. https://doi.org/10.3390/app12094708