# Study on Pore Structure Evolution Characteristics of Weakly Cemented Sandstone under Freeze–Thaw Based on NMR

^{1}

^{2}

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## Abstract

**:**

_{2}fractal theory and spectral peak analysis. The results show that the evolution of the pore structure of weakly cemented sandstone can be divided into three stages during the freeze–thaw cycle. In stage 1, the rock skeleton can still significantly restrict frost heave, and the effect of rock pore expansion occurs only on the primary pore scale, primarily in the transformation between adjacent scales. In stage 2, as the restraint effect of the skeleton on frost heave decreases, small-scale secondary pores are gradually produced, pore expansion occurs step by step, and its connectivity is gradually enhanced. In stage 3, as rock pore connectivity improves, the effect of pore internal pressure growth in the freezing process caused by water migration is weakened, making it impossible to break through the skeleton constraint. Thus, it becomes difficult for freezing and thawing to have an obvious expansion effect on the rock pore structure. The strength of the freeze–thaw cycle degradation effect is determined by the effect of the rock skeleton strength under the freeze–thaw cycles and the connectivity of small-scale pores in the rock. The lower the strength of the rock skeleton, the worse the connectivity of pores, and the more obvious the freeze–thaw degradation effect, and vice versa.

## 1. Introduction

_{2}fractal theory, combined with the peak analysis method of the spectrogram, in order to provide a solid test basis for establishing its freezing and thawing damage model.

## 2. Test Materials and Methods

^{3}, and 12.97%~13.41%, respectively. Table 1 shows the basic physical parameters of the selected test objects (Table 1).

_{2}spectrum was collected after each drying by combining it with NMR, and T

_{2}cut-off values were calculated. To avoid the loss of bound water caused by too high a test temperature and too long a drying time, the sample was dried for 10 min at 85 °C. Figure 2 depicts the test path and the test results. Figure 2 shows that the moisture content and drying times changed exponentially, with the moisture content nearly reaching a minimum in the last two drying tests.

## 3. Analysis of Pore Structure of Rock under Freeze–Thaw Cycles

#### 3.1. Variation Rule of Pores at Different Scales

_{2}spectrum of the initial state and the T

_{2}spectrum after each cycle, as shown in Figure 4. The proportions of micropores, fine pores, macropores, and free water before and after the freezing and thawing cycles are shown in Figure 5.

#### 3.2. Change Rule of Bound and Free Pores

_{2}cut-off value was calculated using the T

_{2}distribution curve of NMR at the time of complete saturation of the sandstone and the first drying. To obtain the accumulation curve, the nuclear magnetic signals in the two states were accumulated, and a horizontal line was drawn from the maximum value of the first drying accumulation so that this horizontal line intersected with the accumulation curve in a fully saturated state. The abscissa value of the intersection point is the T

_{2}cut-off value, which was calculated to be 5.264 ms, as shown in Figure 6 below.

## 4. Fractal Characteristics of T_{2} under Freeze–Thaw Cycles

#### 4.1. T_{2} Fractal Theory of NMR

_{2}) + (D − 3) Lg(T

_{2max})

_{2}in total pore volume; D is the fractal dimension; and T

_{2}max is the transverse relaxation time corresponding to the maximum diameter.

_{2}NMR spectrum yields Equation (2), and the slope a of the fitting formula can obtain the fractal dimension; b is the intercept.

_{2}) + b

_{2}spectrum is:

#### 4.2. Analysis of Pore Fractal Characteristics

_{2}cut-off value of 5.264 ms obtained above as the boundary, and the fractal dimension was calculated. Simultaneously, the fractal characteristics were examined, and the fitting degree was 0.728~0.837. Figure 8 depicts the results using the initial state as an example, as well as the fractal dimension changes of the two types of pores at different cycles.

## 5. Characteristics of T_{2} Peak Splitting under Freeze–Thaw Cycles

#### 5.1. NMR Pore Size Division and Processing Method

#### 5.1.1. NMR Pore Size Division

_{2}analysis that pores of the same size only show a fixed value in the T

_{2}spectrum, and that the T

_{2}spectrum can be obtained by accumulating this fixed value of pores of all sizes in the sample. However, according to the NMR testing principle, the decay rate of the hydrogen nucleus is related to the degree of binding on the fluid, and the further the water inside the pore is from the pore surface, the lower the binding degree, implying that the actual test result of a single pore should be in the wave crest area (Figure 9).

_{2}peak splitting method can be used to narrow the pore division range and then obtain the pore evolution characteristics of different scales, in order to further analyze the transformation rule between different scales of pores during freezing–thawing cycles and to reveal the evolution mechanism of meso freezing–thawing damage in more depth.

_{2}spectrum measured in this experiment had a bimodal distribution, and the peak fitting results had multiple solutions. As a result, while ensuring a high degree of fitting, it is necessary to consider the practical significance of the fitting results. Therefore, it was necessary to choose the smallest number of peak splittings.

#### 5.1.2. Processing Method of Peak Splitting

_{2}spectrum were first converted using a log function, and then fitted using the least square method. Equation (4) depicts the Gaussian function.

_{0}is the baseline, its value is 0 in T

_{2}curve; x

_{c}is the selected peak center; A is the peak area; and w is the selected half-peak width.

#### 5.2. Peak Splitting Analysis of Pore

_{2}spectrum in its initial state, and Table 3 depicts the peak height parameters of the T

_{2}spectrum in each experimental state, as well as the fitting degree of the corresponding fitting curve.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Lai, J.; Wang, G.; Wang, Z.; Chen, J.; Pang, X.; Wang, S.; Fan, X. A review on pore structure characterization in tight sandstones. Earth-Sci. Rev.
**2018**, 177, 436–457. [Google Scholar] [CrossRef] - Lai, J.; Wang, G.; Cao, J.; Xiao, C.; Wang, S.; Pang, X.; Qin, Z. Investigation of pore structure and petrophysical property in tight sandstones. Mar. Pet. Geol.
**2018**, 91, 179–189. [Google Scholar] [CrossRef] - Xin, Y.; Wang, G.; Liu, B.; Ai, Y.; Cai, D.; Yang, S.; Chen, K. Pore structure evaluation in ultra-deep tight sandstones using NMR measurements and fractal analysis. J. Pet. Sci. Eng.
**2022**, 211, 110180. [Google Scholar] [CrossRef] - Behroozmand, A.A.; Keating, K.; Auken, E. A Review of the Principles and Applications of the NMR Technique for Near-Surface Characterization. Surv. Geophys.
**2015**, 36, 27–85. [Google Scholar] [CrossRef] - Meyer, M.; Buchmann, C.; Schaumann, G.E. Determination of quantitative pore-size distribution of soils with
^{1}H NMR relaxometry. Eur. J. Soil Sci.**2018**, 69, 393–406. [Google Scholar] [CrossRef] - Benson, P.; Meredith, P.; Platzman, E.; White, R. Pore fabric shape anisotropy in porous sandstones and its relation to elastic wave velocity and permeability anisotropy under hydrostatic pressure. Int. J. Rock Mech. Min. Sci.
**2005**, 42, 890–899. [Google Scholar] [CrossRef] - Ye, D.; Liu, G.; Luo, N.; Gao, F.; Zhu, X.; Yue, F. Quantitative Analysis of the Topological Structure of Rock Pore Network. Geofluids
**2021**, 2021, 3554563. [Google Scholar] [CrossRef] - Dou, W.; Liu, L.; Jia, L.; Xu, Z.; Wang, M.; Du, C. Pore structure, fractal characteristics and permeability prediction of tight sandstones: A case study from Yanchang Formation, Ordos Basin, China. Mar. Pet. Geol.
**2021**, 123, 104737. [Google Scholar] [CrossRef] - Yang, H.; Cheng, W.; Liu, Z.; Wang, Y.; Zhao, D.; Wang, W. Fractal characteristics of effective seepage channel structure of water infusion coal based on NMR experiment. Rock Soil Mech.
**2020**, 41, 1279–1286. (In Chinese) [Google Scholar] - Ding, Z.W.; Li, X.F.; Tang, Q.B.; Jia, J.D. Study on correlation between fractal characteristics of pore distribution and strength of sandstone particles. Chin. J. Rock Mech. Eng.
**2020**, 39, 1787–1796. (In Chinese) [Google Scholar] - Jia, P.; Mao, S.; Qian, Y.; Wang, Q.; Lu, J. The Dynamic Compressive Properties and Energy Dissipation Law of Sandstone Subjected to Freeze–Thaw Damage. Water
**2022**, 14, 3632. [Google Scholar] [CrossRef] - Huang, S.; Yu, S.; Ye, Y.; Ye, Z.; Cheng, A. Pore structure change and physico-mechanical properties deterioration of sandstone suffering freeze-thaw actions. Constr. Build. Mater.
**2022**, 330, 127200. [Google Scholar] [CrossRef] - Niu, C.; Zhu, Z.; Zhou, L.; Li, X.; Ying, P.; Dong, Y.; Deng, S. Study on the microscopic damage evolution and dynamic fracture properties of sandstone under freeze-thaw cycles. Cold Reg. Sci. Technol.
**2021**, 191, 103328. [Google Scholar] [CrossRef] - Wang, P.; Xu, J.Y.; Liu, S.; Wang, H.Y.; Liu, S.H. Static and dynamic mechanical properties of sedimentary rock after freeze-thaw or thermal shock weathering. Eng. Geol.
**2016**, 210, 148–157. [Google Scholar] [CrossRef][Green Version] - Liu, H.; Yang, G.; Yun, Y.; Lin, J.; Ye, W.; Zhang, H.; Zhang, Y. Investigation of Sandstone Mesostructure Damage Caused by Freeze-Thaw Cycles via CT Image Enhancement Technology. Adv. Civ.Eng.
**2020**, 2020, 8875814. [Google Scholar] [CrossRef] - Zhou, Y.; Wu, S.; Li, Z.; Zhu, R.; Xie, S.; Jing, C.; Lei, L. Multifractal study of three-dimensional pore structure of sand-conglomerate reservoir based on CT images. Energy Fuels
**2018**, 32, 4797–4807. [Google Scholar] [CrossRef] - Zhao, S.; Li, Y.; Wang, Y.; Ma, Z.; Huang, X. Quantitative study on coal and shale pore structure and surface roughness based on atomic force microscopy and image processing. Fuel
**2019**, 244, 78–90. [Google Scholar] [CrossRef] - Zhao, S.; Li, Y.; Wang, Y.; Ma, Z.; Huang, X. Characterization of multi-type pore structure and fractal characteristics of the Dalong Formation marine shale in northern Sichuan Basin. Energy Sources Part A Recovery Util. Environ. Eff.
**2020**, 42, 2764–2777. [Google Scholar] - Liu, S.; Xu, J.; Liu, S.; Wang, P. Fractal study on the dynamic fracture of red sandstone after F-T cycles. Environ. Earth Sci.
**2022**, 81, 152. [Google Scholar] [CrossRef] - Abdolghanizadeh, K.; Hosseini, M.; Saghafiyazdi, M. Effect of freezing temperature and number of freeze–thaw cycles on mode I and mode II fracture toughness of sandstone. Theor. Appl. Fract. Mech.
**2019**, 105, 102428. [Google Scholar] [CrossRef] - Sun, Y.; Guo, S. Qualitative and quantitative characterization of shale microscopic pore characteristics based on image analysis technology. Adv. Earth Sci.
**2016**, 31, 751–763. (In Chinese) [Google Scholar] - Sun, Y.; Guo, S. Characteristics of microscopic pores of shale from Upper Sinian Doushantuo Formation in the western of Hunan and Hubei, China and the main controlling factors. J. Earth Sci.Environ.
**2017**, 39, 114–125. [Google Scholar] - Jia, H.; Ding, S.; Zi, F.; Dong, Y.; Shen, Y. Evolution in sandstone pore structures with freeze-thaw cycling and interpretation of damage mechanisms in saturated porous rocks. Catena
**2020**, 195, 104915. [Google Scholar] [CrossRef] - Li, J.; Kaunda, R.B.; Zhou, K. Experimental investigations on the effects of ambient freeze-thaw cycling on dynamic properties and rock pore structure deterioration of sandstone. Cold Reg. Sci. Technol.
**2018**, 154, 133–141. [Google Scholar] [CrossRef] - Liu, T.; Zhang, C.; Cao, P.; Zhou, K. Freeze–thaw damage evolution of fractured rock mass using nuclear magnetic resonance technology. Cold Reg. Sci. Technol.
**2020**, 170, 102951. [Google Scholar] [CrossRef] - Hou, C.; Jin, X.; He, J. Investigation on the Microscopic Deterioration Characteristics of Anhydrite Rock Exposed to Freeze-Thaw Cycles. Int. J. Geomech.
**2022**, 22, 04022013. [Google Scholar] [CrossRef] - Yuan, J.; Wang, Y.; Chen, X. Study on the Evolution of Pore Structure of Anthracite Coal under Liquid-Nitrogen Freeze-Thaw Cycles. ACS Omega
**2022**, 7, 4648–4654. [Google Scholar] [CrossRef] [PubMed] - Park, C.J.; Synn, H.; Shin, D.S. Experimental study on the thermal characteristics of rock at low temperatures. Int. J. Rock Mech. Min. Sci.
**2004**, 4, 81–86. [Google Scholar] [CrossRef] - Jia, H.L.; Liu, Q.B.; Xiang, W.; Zhang, W.; Lang, L. Damage evolution model of saturated sandstone under freeze-thaw cycles. Chin. J. Rock Mech. Eng.
**2013**, 32, 3049–3055. (In Chinese) [Google Scholar] - Jia, H.L.; Xiang, W.; Tan, L.; Zhang, W.L.; Zeng, W.; Cao, S.; Cheng, C.J. Theoretical analysis and experimental verification of freeze-thaw damage mechanism of sandstone. Chin. J. Rock Mech. Eng.
**2016**, 35, 879–895. (In Chinese) [Google Scholar] - Jia, H.; Xiang, W. Direct observation of the pore structure of sandstone after repeated frost action. Electron. Geotech. Eng.
**2015**, 20, 11. [Google Scholar] - Jia, H.; Xiang, W.; Krautblatter, M. Quantifying Rock Fatigue and Decreasing Compressive and Tensile Strength after Repeated Freeze-Thaw Cycles. Permafr. Periglac. Process.
**2015**, 26, 368–377. [Google Scholar] [CrossRef] - Jia, H.; Ding, S.; Wang, Y.; Zi, F.; Sun, Q.; Yang, G. An NMR-based investigation of pore water freezing process in sandstone. Cold Reg. Sci. Technol.
**2019**, 168, 102893. [Google Scholar] [CrossRef] - Liu, Y.; Zhang, T.; Ma, Y.; Yang, K.; Tang, M. Dynamic Response and Fractal Characteristics of a Pore-Fracture System in Ultralow Permeability Sandstone Based on Low-Field NMR. Energy Fuels
**2020**, 35, 397–407. [Google Scholar] [CrossRef] - Chen, S.; Tang, D.; Tao, S.; Ji, X.; Xu, H. Fractal analysis of the dynamic variation in pore-fracture systems under the action of stress using a low-field NMR relaxation method: An experimental study of coals from western Guizhou in China. J. Pet. Sci. Eng.
**2019**, 173, 617–629. [Google Scholar] [CrossRef]

**Figure 5.**Evolution of the proportion of micro-, fine, and large pores, as well as free water, before and after freeze–thaw cycles.

**Figure 8.**(

**a**) Fractal dimension of initial state; (

**b**) fractal dimension variation curves of various holes before and after freeze–thaw cycles.

**Figure 9.**(

**a**) Analysis mode of NMR T

_{2}under ideal conditions; (

**b**) analysis mode of NMR T

_{2}in its actual state.

Wave Velocity (m/s) | Saturation Density (g/cm^{3}) | Dry Density (g/cm^{3}) | Saturated Volume Water Content (%) |
---|---|---|---|

736.9 | 2.23 | 2.13 | 13.35 |

Peak | Peak Center (ms) | Half-Peak Width (ms) |
---|---|---|

1 | 0.488 | 0.384 |

2 | 1.589 | 1.244 |

3 | 15.703 | 12.522 |

4 | 54.789 | 44.436 |

Number of Cycles | A Crest | B Crest | C Crest | D Crest | Degree of Fit (%) | |
---|---|---|---|---|---|---|

Peak height | 0 | 90.784 | 101.479 | 103.548 | 141.959 | 99.765 |

1 | 92.749 | 108.714 | 90.065 | 167.824 | 99.670 | |

2 | 88.429 | 105.401 | 84.361 | 168.092 | 99.685 | |

3 | 92.971 | 72.600 | 96.993 | 138.538 | 99.929 | |

4 | 93.125 | 78.784 | 93.756 | 147.266 | 99.902 | |

5 | 88.665 | 98.723 | 85.167 | 162.382 | 99.720 | |

6 | 89.577 | 98.239 | 85.081 | 161.522 | 99.703 |

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**MDPI and ACS Style**

Lin, J.; Yang, Y.; Yin, J.; Liu, Y.; Li, X. Study on Pore Structure Evolution Characteristics of Weakly Cemented Sandstone under Freeze–Thaw Based on NMR. *Water* **2023**, *15*, 281.
https://doi.org/10.3390/w15020281

**AMA Style**

Lin J, Yang Y, Yin J, Liu Y, Li X. Study on Pore Structure Evolution Characteristics of Weakly Cemented Sandstone under Freeze–Thaw Based on NMR. *Water*. 2023; 15(2):281.
https://doi.org/10.3390/w15020281

**Chicago/Turabian Style**

Lin, Jian, Yi Yang, Jianchao Yin, Yang Liu, and Xiangwei Li. 2023. "Study on Pore Structure Evolution Characteristics of Weakly Cemented Sandstone under Freeze–Thaw Based on NMR" *Water* 15, no. 2: 281.
https://doi.org/10.3390/w15020281