Evolution of Pore Structure and Fractal Characteristics in Red Sandstone under Cyclic Impact Loading
Abstract
1. Introduction
2. Methods
2.1. Materials and Experimental Procedures
- (1)
- Saturation treatment: prior to conducting NMR tests, the samples were subjected to a 48 h moisture saturation using a vacuum saturation device at a pressure of 0.1 MPa to ensure complete saturation of the pores.
- (2)
- NMR testing: Each specimen underwent NMR tests utilizing the AiniMR-150 NMR system manufactured by Suzhou Newmarket Analytical Instruments Co., Ltd. [3,31]. The CPMG sequence was applied with specific parameters: a 0.256 ms echo time (TE = 0.256 ms), 4096 echoes (NECH = 4096), a 6000 ms waiting time (TW = 6000 ms), and 32 scans. The porosity, T2 distribution, and MRIs were obtained.
- (3)
- Centrifugation and drying: After saturation and the NMR test, the samples were centrifuged at 4000 rpm for 90 min, followed by NMR testing. Subsequently, the specimens were placed in an oven and dried at 60 °C for 12 h before undergoing further NMR testing.
- (4)
- SHPB cyclic impact loading experiments: The SHPB equipment is mainly composed of a cylinder that generates power, a cone-shaped striker, an incident bar, a transmission bar, an absorption bar, and a data receiving and collecting system [4,8]. The pressure in the high-pressure gas chamber was set to 0.3 MPa, and the release pressure was released to drive the striker out at a speed of (3.27 ± 0.18) m/s.
2.2. Multi-Exponential Decay Principle of NMR
3. Results
3.1. Evolution of Pore Structure
3.1.1. T2 Spectrum Distribution Measured According to Pore Connectivity
3.1.2. Quantitative Analysis of Pore Evolution Based on Pore Size
3.1.3. Pore Evolution Analysis Based on MRI
3.2. Fractal Characteristics of Pore Structure
4. Discussion
4.1. Correlation of Porosity and Fractal Dimension
4.2. Variation Correlation between Porosity and Fractal Dimension
5. Conclusions
- (1)
- The pore structure of red sandstone develops gradually under cyclic equal–amplitude impact loading, and the porosity increment increases with the accumulation of impacts. This increase is mainly observed in mesopores (0.1–1 μm) and macropores (>1 μm). After six impacts, macropores increased by 96.56%. The most probable developed pores are those with a pore size of about 1 μm.
- (2)
- The double T2 cutoff (T2c) value effectively evaluates pore connectivity. The T2c2 value distinguishes between the MF pores and the non–MF pores (CBF pores and CAF pores). Under cyclic impact, both T2c2 and T2c1 decrease, while the porosity of the MF pores increases by 37.8%, thereby enhancing the pore connectivity of the sandstone.
- (3)
- MRI visualizes the development of pores. The most probable gray value increases during cyclic impact. There is an increase in the number of macropores, which expand, forming pore clusters and even macro fissures.
- (4)
- Based on pore size and pore connectivity, the pores were analyzed, and their fractal dimension was calculated. The fractal dimension of various types of pores gradually decreased under cyclic impact. Additionally, the porosity of mesopores and macropores showed a non–linear correlation with their fractal dimension using the F–ps method. On the other hand, the porosity of the CAF and MF pores exhibited a linear correlation with their fractal dimension using the F–T2c method. Notably, micropores with small size or CBF pores with weak connectivity lack fractal features when analyzed from a surface geometry perspective.
- (5)
- Taking into account the magnitude of changes in the pore structure of rocks during equal–amplitude cyclic impact loading, a correlation model between ΦI and DI was established. Mesopores, macropores, and all pores exhibit a nonlinear power function relationship between ΦI and DI. In contrast, the CAF pores and MF pores show a linear correlation between ΦI and DI.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
T2 | Transverse relaxation time |
r | Pore radius |
0 | Initial porosity |
i | Porosity after ith impacts |
Φcb | Porosity of CBF pores |
Φca | Porosity of CAF pores |
Φm | Porosity of MF pores |
D | Fractal dimension |
Dcb | Fractal dimension of CBF pores |
Dca | Fractal dimension of CAF pores |
Dm | Fractal dimension of MF pores |
T2c | T2 cutoff |
MRI | Magnetic resonance imaging |
SHPB | Split Hopkinson pressure bar |
NMR | Nuclear magnetic resonance |
PSD | Pore size distribution |
CBF | Clay–bound fluid |
CAF | Capillary–bound fluid |
MF | Movable fluid |
F–T2c | Calculation of D value based on T2 cutoff |
F–ps | Calculation of D value based on pore size |
ΦI | The percent increase in porosity |
DI | The percent increase in fractal dimension |
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Total Pores | Micropores | Mesopores | Macropores | |||||
---|---|---|---|---|---|---|---|---|
Number of Impacts | D (rmin < r < rmax) | Standard Deviation | Ds1 (rmin < r < 0.1 μm) | Standard Deviation | Ds2 (0.1 μm < r < 1 μm) | Standard Deviation | Ds3 (1 μm < r < rmax) | Standard Deviation |
0 | 2.642 | 0.039 | 1.775 | 0.158 | 2.825 | 0.022 | 2.979 | 0.018 |
1 | 2.638 | 0.071 | 1.815 | 0.123 | 2.802 | 0.042 | 2.978 | 0.013 |
2 | 2.612 | 0.099 | 1.769 | 0.134 | 2.795 | 0.028 | 2.976 | 0.014 |
3 | 2.607 | 0.079 | 1.783 | 0.132 | 2.805 | 0.040 | 2.975 | 0.018 |
4 | 2.596 | 0.031 | 1.811 | 0.090 | 2.782 | 0.047 | 2.968 | 0.011 |
5 | 2.561 | 0.017 | 1.778 | 0.078 | 2.710 | 0.045 | 2.963 | 0.028 |
6 | 2.516 | 0.121 | 1.770 | 0.143 | 2.666 | 0.044 | 2.944 | 0.017 |
CBF Pores | CAF Pores | MF Pores | ||||
---|---|---|---|---|---|---|
Number of Impacts | Dcb (rmin < r < rc1) | Standard Deviation | Dca (rc1 < r < rc2) | Standard Deviation | Dm (rc1 < r < rmax) | Standard Deviation |
0 | 0.570 | 0.020 | 2.603 | 0.010 | 2.881 | 0.002 |
1 | 0.569 | 0.040 | 2.583 | 0.014 | 2.878 | 0.001 |
2 | 0.400 | 0.064 | 2.527 | 0.026 | 2.874 | 0.005 |
3 | 0.540 | 0.058 | 2.476 | 0.013 | 2.863 | 0.001 |
4 | 0.365 | 0.033 | 2.404 | 0.013 | 2.856 | 0.001 |
5 | 0.460 | 0.102 | 2.354 | 0.042 | 2.847 | 0.003 |
6 | 0.364 | 0.047 | 2.306 | 0.067 | 2.836 | 0.007 |
Fitting Equation | R2 | p | |
---|---|---|---|
F–ps method | D = 2.632–8.4 × 10−4 × x2.761 | 0.981 | 0.002 |
Ds1 = 1.797–0.002 × x | 0.163 | 0.625 > 0.05 | |
Ds2 = 2.803–2.3 × 10−4 × x3.596 | 0.955 | 0.0003 | |
Ds3 = 2.978–8.6 × 10−5 × x3.318 | 0.990 | 0.007 | |
F–T2c method | Dcb = 0.571–0.040 × x | 0.806 | 0.010 |
Dca = 2.614–0.049 × x | 0.978 | 0.007 | |
Dm = 2.885–0.007 × x | 0.988 | 0.004 |
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Qiao, H.; Wang, P.; Jiang, Z.; Liu, Y.; Tian, G.; Zhao, B. Evolution of Pore Structure and Fractal Characteristics in Red Sandstone under Cyclic Impact Loading. Fractal Fract. 2024, 8, 437. https://doi.org/10.3390/fractalfract8080437
Qiao H, Wang P, Jiang Z, Liu Y, Tian G, Zhao B. Evolution of Pore Structure and Fractal Characteristics in Red Sandstone under Cyclic Impact Loading. Fractal and Fractional. 2024; 8(8):437. https://doi.org/10.3390/fractalfract8080437
Chicago/Turabian StyleQiao, Huanhuan, Peng Wang, Zhen Jiang, Yao Liu, Guanglin Tian, and Bokun Zhao. 2024. "Evolution of Pore Structure and Fractal Characteristics in Red Sandstone under Cyclic Impact Loading" Fractal and Fractional 8, no. 8: 437. https://doi.org/10.3390/fractalfract8080437
APA StyleQiao, H., Wang, P., Jiang, Z., Liu, Y., Tian, G., & Zhao, B. (2024). Evolution of Pore Structure and Fractal Characteristics in Red Sandstone under Cyclic Impact Loading. Fractal and Fractional, 8(8), 437. https://doi.org/10.3390/fractalfract8080437