Studying the Characteristics of Chaos and Fractals of Construction Rocks under Different Loading Velocities
Abstract
:Highlights
- Rock materials exhibit obvious strain rate effects at different loading velocities.
- The damage evolution process of rock materials contains chaotic features.
- Logical mapping is used to analyze rock material damage–strain information sequences.
- The fractal dimension of rock sample crack is positively correlated with load velocity.
Abstract
1. Introduction
2. SHPB Test
2.1. Sample Preparation
2.2. Experimental Setup and Test Method
3. Results
3.1. Stress–Strain Curves
3.2. The Sample Debris after Loading
4. Discussion
4.1. The Chaotic Characteristics of Rock Sample Damage Evolution
4.1.1. Rock Damage
4.1.2. Chaotic Characteristics
4.2. Effect of Loading Velocity on Chaotic Characteristics
4.3. The Fractal Characteristics of Rock Sample Damage Evolution
4.3.1. The Damage Fractal Dimension
4.3.2. The Variation of Fractal Dimension
5. Conclusions
- Construction rock exhibits significant strain rate effects under dynamic loading conditions. As the impact pressure increases from 0.05 to 0.23 MPa, the peak stress of the sample increases from 82.19 to 284.16 MPa (an increase of 245.74%), and the increase process is in accordance with the power function law; the average particle size of the sample debris is reduced from 46.57 to 18.34 mm (reduced by 60.62%).
- The damage–strain evolution information of the construction rock shows chaotic characteristics. The increase in the load velocity can delay the evolution of the generalized damage variable into the bifurcation state and the chaotic state.
- The damage–strain evolution law (trend) of the sample from the initial moment of damage to the start of the period of bifurcation at different loading pressures shows similarity, and the slope of the fitted straight line is less than 7%.
- Under dynamic loading conditions, the damage evolution process of the samples has fractal characteristics at the start of the bifurcation and chaotic periods, and the damage cracks have statistical self-similarity. Meanwhile, the increase in load velocity significantly increases the degree of homogenization of crack development in the process of damage.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Sample Number | Impact Pressure | Impact Velocity (m/s) | Peak Strength (MPa) | Stress Values Corresponding to Different Starting Times (MPa) | ||
---|---|---|---|---|---|---|
(MPa) | Damage | Period-Doubling Bifurcation | Chaotic | |||
DT-A-1 | 0.05 | 3.52 | 81.10 | 36.1 | 71.2 | 79.4 |
DT-A-2 | 0.05 | 3.42 | 80.31 | 32.3 | 67.5 | 77.4 |
DT-A-3 | 0.05 | 3.46 | 85.17 | 37.6 | 73.3 | 82.3 |
DT-B-1 | 0.08 | 6.65 | 167.51 | 72.0 | 159.8 | 165.4 |
DT-B-2 | 0.08 | 6.91 | 159.91 | 78.3 | 145.7 | 155.7 |
DT-B-3 | 0.08 | 6.67 | 162.11 | 75.7 | 163.8 | 159.9 |
DT-C-1 | 0.14 | 9.71 | 237.02 | 119.4 | 231.7 | 236.3 |
DT-C-2 | 0.14 | 9.77 | 221.52 | 123.1 | 227.5 | 225.7 |
DT-C-3 | 0.14 | 9.90 | 230.33 | 117.9 | 237.9 | 227.8 |
DT-D-1 | 0.23 | 3.61 | 275.10 | 203.3 | 266.6 | 273.4 |
DT-D-2 | 0.23 | 3.67 | 287.38 | 207.9 | 273.7 | 284.9 |
DT-D-3 | 0.23 | 3.55 | 289.99 | 200.3 | 269.9 | 288.1 |
Sample Number | Impact Pressure (MPa) | mvi/% | m/g | Average Particle Diameter (mm) | ||||
---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | ||||
DT-A-1 | 0.05 | 0.93% | 1.31% | 2.24% | 4.29% | 91.23% | 536 | 46.48 |
DT-A-2 | 0.05 | 1.01% | 1.11% | 2.04% | 4.63% | 91.11% | 540 | 46.45 |
DT-A-3 | 0.05 | 1.29% | 1.10% | 2.39% | 6.99% | 90.99% | 544 | 46.77 |
DT-B-1 | 0.08 | 3.00% | 2.81% | 5.24% | 16.67% | 72.28% | 534 | 39.16 |
DT-B-2 | 0.08 | 3.35% | 2.97% | 5.02% | 15.43% | 73.23% | 538 | 39.45 |
DT-B-3 | 0.08 | 3.54% | 3.54% | 7.08% | 15.27% | 70.58% | 537 | 38.27 |
DT-C-1 | 0.14 | 6.62% | 6.17% | 10.17% | 24.36% | 52.68% | 539 | 31.04 |
DT-C-2 | 0.14 | 7.63% | 5.97% | 11.31% | 25.08% | 50.47% | 543 | 30.13 |
DT-C-3 | 0.14 | 6.31% | 6.77% | 12.32% | 20.61% | 53.99% | 536 | 31.31 |
DT-D-1 | 0.23 | 13.10% | 10.41% | 17.31% | 31.65% | 23.53% | 532 | 18.31 |
DT-D-2 | 0.23 | 13.95% | 10.52% | 20.80% | 31.07% | 23.64% | 535 | 18.55 |
DT-D-3 | 0.23 | 14.10% | 11.81% | 17.71% | 34.04% | 22.34% | 543 | 18.16 |
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Wu, N.; Fu, J.; Xiong, C. Studying the Characteristics of Chaos and Fractals of Construction Rocks under Different Loading Velocities. Materials 2022, 15, 7890. https://doi.org/10.3390/ma15227890
Wu N, Fu J, Xiong C. Studying the Characteristics of Chaos and Fractals of Construction Rocks under Different Loading Velocities. Materials. 2022; 15(22):7890. https://doi.org/10.3390/ma15227890
Chicago/Turabian StyleWu, Nan, Jiyang Fu, and Chao Xiong. 2022. "Studying the Characteristics of Chaos and Fractals of Construction Rocks under Different Loading Velocities" Materials 15, no. 22: 7890. https://doi.org/10.3390/ma15227890
APA StyleWu, N., Fu, J., & Xiong, C. (2022). Studying the Characteristics of Chaos and Fractals of Construction Rocks under Different Loading Velocities. Materials, 15(22), 7890. https://doi.org/10.3390/ma15227890