Determining Soil-Water Characteristic Curves from Mercury Intrusion Porosimeter Test Data Using Fractal Theory
Abstract
:1. Introduction
2. MIP Theory
3. SWCC Fractal Model
4. Parameter Determination from MIP Test Results
4.1. Fractal Dimension
4.2. Air-Entry Value
4.2.1. Sample Scale Effect
4.2.2. Determining the Air-Entry Value Ψa by Considering the Sample Scale Effect
5. Materials and Tests
5.1. MIP Tests
5.2. SWCC Tests
6. Results and Discussion
6.1. Critical Pore Size and Fractal Dimension
6.2. Air-Entry Value
6.3. Validation with SWCC Data
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Dry Density (g/cm3) | Expression of Fitting Line | Correlation Coefficient R2 | Fractal Dimension D |
---|---|---|---|
1.30 | y = 0.050x − 0.299 | 0.985 | 2.950 |
1.35 | y = 0.050x − 0.276 | 0.989 | 2.950 |
1.40 | y = 0.050x − 0.265 | 0.991 | 2.950 |
1.45 | y = 0.049x − 0.251 | 0.994 | 2.951 |
1.50 | y = 0.047x − 0.237 | 0.994 | 2.953 |
1.60 | y = 0.046x − 0.225 | 0.995 | 2.954 |
1.71 | y = 0.041x − 0.187 | 0.994 | 2.959 |
Dry Density (g/cm3) | Expression of Fitting Line | Correlation Coefficient R2 | Fractal Dimension D |
---|---|---|---|
1.30 | y = 0.041x − 0.316 | 0.998 | 2.959 |
1.35 | y = 0.041x − 0.293 | 0.998 | 2.959 |
1.40 | y = 0.044x − 0.279 | 0.992 | 2.956 |
1.45 | y = 0.043x − 0.263 | 0.998 | 2.957 |
1.50 | y = 0.043x − 0.247 | 0.998 | 2.957 |
1.60 | y = 0.043x − 0.232 | 1 | 2.957 |
1.71 | y = 0.041x − 0.189 | 0.996 | 2.959 |
Dry Density (g/cm3) | φ | dmax/(μm) | Ψa/(kPa) |
---|---|---|---|
1.30 | 0.53 | 172,73 | 0.17 |
1.35 | 0.51 | 6880 | 0.44 |
1.40 | 0.49 | 922 | 3.25 |
1.45 | 0.47 | 583 | 5.15 |
1.50 | 0.45 | 265 | 11.33 |
1.60 | 0.42 | 59 | 50.82 |
1.71 | 0.38 | 23 | 129.56 |
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Tao, G.; Chen, Y.; Xiao, H.; Chen, Q.; Wan, J. Determining Soil-Water Characteristic Curves from Mercury Intrusion Porosimeter Test Data Using Fractal Theory. Energies 2019, 12, 752. https://doi.org/10.3390/en12040752
Tao G, Chen Y, Xiao H, Chen Q, Wan J. Determining Soil-Water Characteristic Curves from Mercury Intrusion Porosimeter Test Data Using Fractal Theory. Energies. 2019; 12(4):752. https://doi.org/10.3390/en12040752
Chicago/Turabian StyleTao, Gaoliang, Yin Chen, Henglin Xiao, Qingsheng Chen, and Juan Wan. 2019. "Determining Soil-Water Characteristic Curves from Mercury Intrusion Porosimeter Test Data Using Fractal Theory" Energies 12, no. 4: 752. https://doi.org/10.3390/en12040752