Anisotropic Mechanical Properties and Fracture Mechanism of Transversely Isotropic Rocks under Uniaxial Cyclic Loading
Abstract
:1. Introduction
2. Materials and Methods
2.1. Specimen Preparation
2.2. Test Equipment and Methods
3. Results and Discussion
3.1. Mechanical Properties
3.1.1. Peak Strength
3.1.2. Elastic Modulus
3.2. Damage Evolution
3.2.1. Deformation Evolution Process
3.2.2. Energy Evolution Process
3.2.3. Damage Variable
3.3. Acoustic Emission Characterization
3.3.1. AE Characteristics under Monotonic Loading
3.3.2. AE Characteristics under Cyclic Loading
3.4. Fracture Mechanism
3.4.1. Macroscopic-Fracture Characteristics
3.4.2. Microscopic-Fracture Characteristics
4. Conclusions
- (1)
- The peak strength of specimens varies with the loading–foliation angle under cyclic loading, exhibiting a U-shaped trend similar to that observed under monotonic loading. The strength of the specimens at the same loading–foliation angle is close under both loading paths. The variation in elastic modulus of the specimens under uniaxial cyclic loading confirms the transversely isotropic model.
- (2)
- The secant moduli at different positions of the stress–strain curve exhibit unique variation characteristics under cyclic loading. These moduli can reflect the damage evolution process of the specimen with respect to various aspects. Eu and E20 reflect the influence of compaction and the damage effects on the specimen during cyclic loading and unloading. Es mainly reflects the damage of the specimen caused by the loading–unloading cycles, with Es− being more effective in characterizing this feature than Es+.
- (3)
- The input of the total energy density of the specimen is mainly dependent on the loading–foliation angle at the same stress level. The elastic-energy density and the dissipated-energy density are affected by the loading–foliation angle, cyclic stress step and number of cycles. When the degree of damage in the rock is low, increasing the stress level of the cyclic load or increasing the number of cycles can reduce the proportion of dissipated energy. The damage variable is influenced by both the loading–foliation angle and the cyclic stress step.
- (4)
- The AE characteristics of the specimen are closely related to the loading condition and the loading–foliation angle, presenting an obvious anisotropy. Under cyclic loading, regardless of cyclic stress step, the AE counts of specimens at β = 0° are concentrated near the peak region, consistent with the Kaiser effect, whereas those of specimens at the other loading–foliation angles are mainly distributed in the early stage of each cyclic-loading process, exhibiting an obvious Felicity effect.
- (5)
- The failure mechanism of slate specimens is jointly determined by the loading–foliation angle, loading condition, and cyclic stress step. The fracture modes are classified into four categories: the tensile fracture along the foliation plane (β = 0°, 90°), the tensile fracture through the foliation plane (β = 30°, 90°), the shear fracture along the foliation plane (β = 30°, 45°) and the shear fracture through the foliation plane (β = 45°, 90°). The SEM images of corresponding fracture surfaces show different characteristics, with more rock debris formed in the fracture surface of the specimen subjected to cyclic loading than to monotonic loading.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Loading Path | Specimen Name | β (°) | Cyclic Stress Step (MPa) | Number of Cycles (Force Control + Displacement Control) |
---|---|---|---|---|
Monotonic loading | U-0 | 0 | \ | \ |
U-30 | 30 | \ | \ | |
U-45 | 45 | \ | \ | |
U-90 | 90 | \ | \ | |
Cyclic loading and unloading | C-0-20 | 0 | 20 | 6 + 2 |
C-0-40 | 0 | 40 | 3 + 1 | |
C-30-20 | 30 | 20 | 3 + 3 | |
C-30-40 | 30 | 40 | 2 + 2 | |
C-45-20 | 45 | 20 | 3 + 1 | |
C-90-20 | 90 | 20 | 4 + 4 | |
C-90-40 | 90 | 40 | 3 + 4 |
β (°) | 0 | 30 | 45 | 90 |
E (GPa) | 20.39 | 16.15 | 15.49 | 13.57 |
Specimen Name | Quadratic Coefficient | Primary Term Coefficient | Number of Fit Points | Correlation Coefficient |
---|---|---|---|---|
C-0-20 | 0.022 | 0.399 | 8 | 0.9998 |
C-0-40 | 0.020 | 0.624 | 4 | 0.9999 |
C-30-20 | 0.025 | 0.553 | 6 | 0.9998 |
C-30-40 | 0.023 | 0.701 | 4 | 1.0000 |
C-45-20 | 0.027 | 0.741 | 4 | 0.9999 |
C-90-20 | 0.030 | 0.536 | 8 | 0.9998 |
C-90-40 | 0.032 | 0.409 | 7 | 0.9981 |
Specimen Name | uN (kJ/m3) | ue,N (kJ/m3) | ud,N (kJ/m3) |
---|---|---|---|
C-0-20 | 382.58 | 306.05 | 76.53 |
C-0-40 | 453.46 | 255.23 | 198.23 |
C-30-20 | 359.82 | 292.96 | 66.85 |
C-30-40 | 247.14 | 215.93 | 31.21 |
C-45-20 | 147.91 | 115.80 | 32.11 |
C-90-20 | 482.01 | 331.05 | 150.97 |
C-90-40 | 512.15 | 396.38 | 115.77 |
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Li, K.; Du, G.; Li, J.; Han, D.; Wang, Y. Anisotropic Mechanical Properties and Fracture Mechanism of Transversely Isotropic Rocks under Uniaxial Cyclic Loading. Appl. Sci. 2024, 14, 4988. https://doi.org/10.3390/app14124988
Li K, Du G, Li J, Han D, Wang Y. Anisotropic Mechanical Properties and Fracture Mechanism of Transversely Isotropic Rocks under Uniaxial Cyclic Loading. Applied Sciences. 2024; 14(12):4988. https://doi.org/10.3390/app14124988
Chicago/Turabian StyleLi, Kaihui, Guangzhen Du, Jiangteng Li, Dongya Han, and Yan Wang. 2024. "Anisotropic Mechanical Properties and Fracture Mechanism of Transversely Isotropic Rocks under Uniaxial Cyclic Loading" Applied Sciences 14, no. 12: 4988. https://doi.org/10.3390/app14124988
APA StyleLi, K., Du, G., Li, J., Han, D., & Wang, Y. (2024). Anisotropic Mechanical Properties and Fracture Mechanism of Transversely Isotropic Rocks under Uniaxial Cyclic Loading. Applied Sciences, 14(12), 4988. https://doi.org/10.3390/app14124988