Shock Properties of One Unsaturated Clay and Its Equation of State Up to 30 GPa
Abstract
:1. Introduction
2. Experimental Measurement of the Hugoniot Parameters
2.1. Subsection
2.2. Experimental Method
2.3. Data Processing Method
2.4. Experimental Results and Analysis
3. Equation of State of Unsaturated Clay
3.1. p-alpha Compaction Model
3.2. p-alpha Compaction Model
4. Discussion
- (1)
- For the unsaturated clay, the EOS could be separated into low-pressure range and high-pressure range by the compacted pressure pc. The p-alpha compacted model could be used in the low-pressure range and the solid-water two-constituent mixed EOS could be applied for the high-pressure range.
- (2)
- With the original clay extracted from the southern suburbs of Luoyang city in China, three unsaturated clays with moisture content 0%, 8%, and 15%, respectively, were remolded. The Hugoniot parameters of three unsaturated clays were determined by means of the plate impact experiment on a one-stage and two-stage light gas gun. The results were: when the moisture content is 0%, ρ0 = 1.70 g/cm3, c0 = 1.08 ± 0.30 km/s, s = 1.62 ± 0.17; when the moisture content is 8%, ρ0 = 1.84 g/cm3, c0 = 1.29 ± 0.24 km/s, s = 1.72 ± 0.14; when the moisture content is 15%, ρ0 = 1.96 g/cm3, c0 = 1.91 ± 0.18 km/s, s = 1.71 ± 0.10.
- (3)
- With the Hugoniot parameters and the model of two-stage EOS presented here, the high-pressure EOS up to 30 GPa was developed for the unsaturated clays of three moisture contents and was consistent with the experimental results.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Components | Quartz | Calcite | Chlorite | Montmorillonite | Illite | Feldspar | Kaolinite | Amphibole | Hematite |
---|---|---|---|---|---|---|---|---|---|
Mass (%) | 25 | 7 | 15 | 10 | 15 | 18 | 5 | 3 | 2 |
Sample Number | 1 | 2 | 3 |
---|---|---|---|
initial dry density ρd0 (g/cm3) | 1.70 | 1.70 | 1.70 |
initial wet density ρ0 (g/cm3) | 1.70 | 1.84 | 1.96 |
sample weight m (g) | 1.03 | 1.11 | 1.18 |
initial moisture content w (%) | 0 | 8 | 15 |
initial saturation Sr0 (%) | 0 | 35.8 | 67.4 |
Material | ρ0 (g/cm3) | c0 (km/s) | s |
---|---|---|---|
2024 aluminum alloy | 2.785 | 5.328 | 1.338 |
copper | 8.93 | 3.94 | 1.489 |
tantalum | 16.656 | 3.437 | 1.19 |
Clay Samples | No. | Flyer Materials | Flyer Velocity (km/s) | Shock Wave Arrival Time (ns) | Sample Thickness (mm) | Particle Velocity (km/s) | Shock Wave Velocity (km/s) | Pressure (GPa) |
---|---|---|---|---|---|---|---|---|
Dry Clay | 1 | Aluminum | 0.561 | 1868 | 2.98 | 0.48 | 1.60 | 1.29 |
2 | Copper | 1.042 | 1054 | 2.96 | 0.92 | 2.81 | 4.40 | |
3 | Copper | 2.340 | 658 | 2.94 | 1.97 | 4.47 | 14.95 | |
4 | Tantalum | 3.180 | 556 | 3.02 | 2.79 | 5.43 | 25.71 | |
Wet clay (moisture content: 8%) | 5 | Aluminum | 0.563 | 1564 | 2.94 | 0.46 | 1.88 | 1.58 |
6 | Copper | 1.101 | 956 | 2.98 | 0.95 | 3.12 | 5.46 | |
7 | Copper | 2.290 | 640 | 3.00 | 1.89 | 4.69 | 16.26 | |
8 | Tantalum | 3.190 | 500 | 2.94 | 2.74 | 5.88 | 29.60 | |
Wet clay (moisture content: 15%) | 9 | Aluminum | 0.495 | 1192 | 3.00 | 0.37 | 2.52 | 1.84 |
10 | Copper | 1.142 | 848 | 2.98 | 0.97 | 3.51 | 6.63 | |
11 | Copper | 2.370 | 538 | 2.88 | 1.89 | 5.35 | 19.81 | |
12 | Tantalum | 3.130 | 478 | 3.01 | 2.64 | 6.30 | 32.54 |
EOS | Parameters | Dry Clay | 8% Clay | 15% Clay |
---|---|---|---|---|
p-alpha model | Elastic yield strength, pe (GPa) | 0 | 0 | 0 |
Plastic yield strength, ps (GPa) | 4.97 | 2.15 | 1.38 | |
Empirical fitting parameter, N | 2 | 2 | 2 | |
Solid–liquid two-phase model | Fully compacted density, ρc (g/cm3) | 2.73 | 2.42 | 2.23 |
Water proportion under pc, βwc | 0 | 0.18 | 0.29 | |
Solid proportion under pc, βsc | 1 | 0.82 | 0.71 | |
Water phase | ρw0 = 1.0 g/cm3, cw0 = 1500 m/s, kw = 7 | |||
Solid particle phase | ρs0 = 2.73 g/cm3, cs0 = 4500 m/s, ks = 3 |
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Ran, X.; Zou, X.; Zhou, J.; Tang, W. Shock Properties of One Unsaturated Clay and Its Equation of State Up to 30 GPa. Crystals 2022, 12, 119. https://doi.org/10.3390/cryst12010119
Ran X, Zou X, Zhou J, Tang W. Shock Properties of One Unsaturated Clay and Its Equation of State Up to 30 GPa. Crystals. 2022; 12(1):119. https://doi.org/10.3390/cryst12010119
Chicago/Turabian StyleRan, Xianwen, Xuan Zou, Jingyuan Zhou, and Wenhui Tang. 2022. "Shock Properties of One Unsaturated Clay and Its Equation of State Up to 30 GPa" Crystals 12, no. 1: 119. https://doi.org/10.3390/cryst12010119
APA StyleRan, X., Zou, X., Zhou, J., & Tang, W. (2022). Shock Properties of One Unsaturated Clay and Its Equation of State Up to 30 GPa. Crystals, 12(1), 119. https://doi.org/10.3390/cryst12010119