Binary-Classification Physical Fractal Models in Different Coal Structures
Abstract
1. Introduction
2. Mathematical Model
2.1. The Binary-Classification Physical Fractal Model of Coal
2.2. Derivation of the Constitutive Equation for the Binary-Classification Physical Fractal Structure of Coal
3. Significance of Model Parameters
3.1. The Influence of the Value of on Dispersion and Attenuation
3.2. The Influence of the Value of on Dispersion and Attenuation
3.3. The Influence of the Value of on Dispersion and Attenuation
4. Experimental Results and Discussion
4.1. Attenuation Experiments Across Frequency Bands for Different Coal Mass Structures
4.2. Fitting Results and Analysis of Partially Saturated Coal Samples Under Variable Confining Pressure Conditions
4.3. Fitting Effects and Analysis of Partially Saturated Coal Samples Under Variable Temperature Conditions
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Models | Component Combination Mode | Complex Modulus | Quality Factor |
---|---|---|---|
Kelvin-Voigt model [23] | |||
Maxwell model [24] | |||
Standard Linear Solid model [25] | |||
Burgers model [26] |
Figure Number | (Dimensionless) | (Dimensionless) | (Dimensionless) | (ms) |
---|---|---|---|---|
Figure 3 and Figure 4 | 0.025~0.055 | 0.2 | 0.3 | 1.667 |
Figure 5 and Figure 6 | 0.03 | 0.1~0.2 | 0.3 | 1.667 |
Figure 7 and Figure 8 | 0.03 | 0.3 | 0.1~0.2 | 1.667 |
Sample | Coal Structure | Length (mm) | Diameter (mm) | Velocity (m/s) | Porosity (%) | Permeability (mD) |
---|---|---|---|---|---|---|
DT-1 | Primary coal | 64.980 | 37.207 | 2394.28 | 7.41 | 0.36 × 10−3 |
DT-4 | Tectonic coal | 65.198 | 36.932 | 2108.13 | 11.23 | 60.7 × 10−3 |
Sample | Confining Pressure (MPa) | (ms) | (Dimensionless) | (Dimensionless) | (Dimensionless) |
---|---|---|---|---|---|
DT-1 | 0.1 | 0.33 | 0.038 | 0.6 | 0.1 |
DT-1 | 7 | 0.19 | 0.036 | 0.6 | 0.1 |
DT-1 | 12 | 0.14 | 0.032 | 0.6 | 0.1 |
DT-4 | 0.1 | 0.55 | 0.065 | 0.2 | 0.8 |
DT-4 | 7 | 0.31 | 0.054 | 0.2 | 0.8 |
DT-4 | 12 | 0.23 | 0.044 | 0.2 | 0.8 |
Sample | Temperature (°C) | (ms) | (Dimensionless) | (Dimensionless) | (Dimensionless) |
---|---|---|---|---|---|
DT-1 | 25 | 0.33 | 0.038 | 0.6 | 0.1 |
DT-1 | 30 | 0.28 | 0.039 | 0.6 | 0.1 |
DT-1 | 42 | 0.22 | 0.040 | 0.6 | 0.1 |
DT-4 | 25 | 0.55 | 0.065 | 0.2 | 0.8 |
DT-4 | 30 | 0.33 | 0.0652 | 0.2 | 0.8 |
DT-4 | 42 | 0.22 | 0.0654 | 0.2 | 0.8 |
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Zou, G.; Che, Y.; Zhao, T.; Yin, Y.; Peng, S.; She, J. Binary-Classification Physical Fractal Models in Different Coal Structures. Fractal Fract. 2025, 9, 450. https://doi.org/10.3390/fractalfract9070450
Zou G, Che Y, Zhao T, Yin Y, Peng S, She J. Binary-Classification Physical Fractal Models in Different Coal Structures. Fractal and Fractional. 2025; 9(7):450. https://doi.org/10.3390/fractalfract9070450
Chicago/Turabian StyleZou, Guangui, Yuyan Che, Tailang Zhao, Yajun Yin, Suping Peng, and Jiasheng She. 2025. "Binary-Classification Physical Fractal Models in Different Coal Structures" Fractal and Fractional 9, no. 7: 450. https://doi.org/10.3390/fractalfract9070450
APA StyleZou, G., Che, Y., Zhao, T., Yin, Y., Peng, S., & She, J. (2025). Binary-Classification Physical Fractal Models in Different Coal Structures. Fractal and Fractional, 9(7), 450. https://doi.org/10.3390/fractalfract9070450