Pore Structure and Fractal Characteristics of Coal Rocks Under Variable Moisture Content Increment Cycles Using LF-NMR Techniques

Abstract

The spatiotemporal heterogeneity of moisture distribution causes the coal pillar dams in underground water reservoirs to undergo long-term dry–wet cycles (DWCs) under varying moisture content increments (MCIs). Accurately measuring the pore damage and fractal dimensions (D_f) of coal rock by different MCIs under DWCs is a prerequisite for in-depth disclosure of the strength deterioration mechanism of underground reservoir coal pillar dams. This study employed low-field nuclear magnetic resonance (LF-NMR) to quantitatively characterize the pore structural evolution and fractal dimension with different MCI variations (Δw = 4%, 6%, 8%) after one to five DWCs. The results indicate that increasing MCIs at constant DWC numbers (N_DWC) induces significant increases in pore spectrum area, adsorption pore area, and seepage pore area. MRI visualization demonstrates a progressive migration of NMR signals from sample peripheries to internal regions, reflecting enhanced moisture infiltration with higher MCIs. Total porosity increases monotonically with MCIs across all tested cycles. Permeability, T₂ cutoff (T_2C), and D_f of free pores exhibit distinct response patterns. A porosity-based damage model further reveals that the promoting effect of cycle numbers on pore development and expansion outweighs that of MCIs at N_DWC = 5. This pore-scale analysis provides essential insights into the strength degradation mechanisms of coal pillar dams under hydro-mechanical coupling conditions.

1. Introduction

Water shortage and high-intensity coal mining have always been the biggest constraints on the green and sustainable development of mining areas in western China [1]. Shendong Mining Area has implemented coal mine underground reservoir technology (CM-UWRT); that is, the goaf is closed by connecting coal pillars with concrete to form a water storage space [2,3]. Coal pillar dams are exposed to a complex water environment for long-term conditions [4]. As shown in Figure 1, the water level in the reservoir changes dynamically due to fissure water recharge and artificial drainage activities, and the moisture content of the coal pillar dam presents a complex non-uniform distribution state, resulting in significant mechanical differences in time-space dimensions of the water-soaked coal pillar [5,6]. However, the macroscopic mechanical damage of coal pillars is inevitably linked to the evolution of microscopic pore structure [7]. Therefore, it is significant to explore the pore damage effect of different moisture content increments (MCIs) under dry–wet cycles (DWCs) for revealing the strength weakening mechanism and seepage characteristics of coal rock with complex water distribution.

The engineering characteristics of coal pillar dams distinguish them from other rock mass engineering subject to DWCs, such as slopes, tunnels, and reservoir dam foundations [8,9,10]. Firstly, coal mass is prone to rapid water infiltration with its intricate pore and fracture system, which is challenging to expel due to water retention through microporous adsorption. Numerous studies indicate that the saturated moisture content of coal typically exceeds that of coal measure sandstone by approximately 7% to 9% [11,12]. Secondly, being the main load-bearing structure, the coal pillar dam is subject to various mining-induced disturbances. The coupled hydro-mechanical impacts lead to increased complexity in the fractures, stress, and water distribution within the coal mass [13]. Thirdly, the strength weakening effect of coal under DWCs is more pronounced. Following five DWCs, the uniaxial compressive strength (UCS) of coal samples typically decreases by 30% to 50% more than that of sandstone [14,15]. By summarizing the mechanical behavior of various coal or rock types under DWCs, common characteristics in the mechanical damage mechanisms of different coal rock masses can be identified. Under increasing DWCs, the mechanical parameters of the specimens, such as crack stress threshold, elastic modulus, and cohesion, demonstrated an exponential decline. Concurrently, acoustic emission (AE) monitoring detected a rise in high-frequency, low-amplitude microcracks and high-energy events, accompanied by increased energy reflectivity and fractal dimension [16,17,18]. Considerable advancements have been achieved in investigating the degradation of mechanical properties in coal rock masses subjected to DWCs. Nevertheless, prevailing studies commonly define saturated and dry conditions as the extremes of DWCs. Coal pillar dams display intricate water distribution and moisture content characteristics, with their realistic conditions more closely mirroring DWCs shaped by variable MCIs. Existing research has not adequately addressed the distinct impacts of moisture content gradients on the strength-weakening of coal rock masses.

The intrinsic mechanisms of mechanical parameter degradation in engineering rock masses can be understood by examining the distinct mechanical behavior of coal rock specimens using microstructural characterization techniques. These methods commonly include low-field nuclear magnetic resonance (LF-NMR), high-pressure mercury intrusion, scanning electron microscopy (SEM), and X-ray diffraction (XRD) [19,20,21,22,23]. LF-NMR has emerged as a fundamental method for analyzing pore structures in porous materials like coal rock due to its rapid, lossless, and high-precision capabilities [24]. Recently, LF-NMR has seen significant advancements in geotechnical and mining engineering, particularly in quantitatively characterizing pore structures, fractal patterns, and predicting seepage behaviors [25,26,27,28]. The transverse relaxation time T₂ serves as a crucial parameter for accurately assessing NMR pore structures. By transforming relationships, various structural characteristics such as pore size distribution, porosity, and pore connectivity can be determined [29]. Zheng et al. conducted the inaugural measurement of the surface relaxation rate of coal bodies, laying the groundwork for establishing coal sample pore size distributions and field logging applications [30]. Yu et al. elucidated the dynamic evolution mechanism of coal rock pore structure from the perspective of pore compression and effective stress [31]. Furthermore, multi-fractal characteristics are commonly observed in coal rock masses. Applying multi-fractal theory enables the derivation of correlations between pore structure parameters, mineral composition, and fractal dimensions. The findings demonstrate that pore structure complexity and heterogeneity increase with rising pore ratio and pore size [32,33]. Additionally, nuclear magnetic resonance (NMR) pore parameters can be utilized to accurately predict coal permeability, with the Schlumberger–Doll Research (SDR) model being the most widely recognized. However, as research subjects and conditions diversify, the predictive accuracy of existing models has progressively declined. To address this limitation, scholars have proposed alternative models, such as the Warren–Root and FCP models, which improve permeability predictions for ultrasonically fractured coal bodies and deep coal reservoirs [34,35]. Previous research has advanced the understanding of coal and gas prevention, freeze–thaw damage, coal pyrolysis, and fracturing. However, the evolution of pore structure in coal pillar dams within complex water-bearing environments remains unclear. Precise measurement of DWCs under varying MCIs is crucial for understanding pore damage and fractal characteristics of coal. This investigation is essential for elucidating the strength degradation mechanisms of coal pillar dams in complex aqueous environments.

In summary, the current DWC studies mainly focus on the number of DWCs and seldom consider the MCI effect. Accurate measurement of DWCs under different MCIs is essential for analyzing the pore damage and strength-weakening mechanism of coal pillar dams under complex water conditions. The study investigated the pore structure and fractal characteristics of three samples with varying MCIs following 1–5 DWCs using NMR and self-developed rock non-destructive water-soaking equipment. The research procedures and ideas are shown in Figure 2. The coal rock subjected to DWCs was meticulously assessed and quantitatively characterized through various approaches, including T₂ spectrum analysis, magnetic resonance imaging (MRI), pore size distribution (PSD), porosity, permeability, and fractal dimension. The study delved into the variations in pore structure and fractal dimension resulting from changes in MCIs and N_DWC. A pore damage model was devised based on porosity, and the study analyzed the progression of pore damage concerning MCI and DWC occurrences. Furthermore, the relationship between pore structure parameters and pore damage mechanisms in coal bodies under varying MCIs and DWCs was explored. This research offers insights into understanding the mechanisms behind the weakening of coal pillar dams at the microscale level.

2. Materials and Methods

2.1. Specimen Selection

The sampling site, as depicted in Figure 3a,b, was situated at Lingxin Coal Mine in Ningxia, China (38.12° N, 106.58° E). The mine area covers approximately 28 km², with a coal reserve of about 226.48 million metric tonnes. Based on the geological data provided by the mine, the coal seam at the study sampling site exhibits a simple structure. The thickness of the coal seam is about 3.18 m, with a hardness f = 2~2.5 and laminated structure. The coal seams occur in an environment characterized by significant regional variability, and the coal itself is highly heterogeneous. Consequently, the information presented above is specific to the study area and cannot be generalized. The mine was selected as study area because it serves as a typical demonstration site for CM-UWRT. Six storage areas have been developed there, and complex hydrological conditions pose challenges to reservoir safety. Samples were promptly wrapped in cling film on-site and transported to the laboratory for analysis. In accordance with the guidelines of the International Society for Rock Mechanics (ISRM), standard specimens measuring φ50 × 100 mm were extracted from the vertical stratification to ensure the end face’s parallelism within ±0.05 mm and axial deviation within ±0.25° (Figure 3c) [36]. To minimize errors caused by coal sample heterogeneity, wave velocity tests were conducted (Figure 3d). The average wave velocity of the specimens was 1245.44 m/s, with a standard deviation of 15.13, indicating high homogeneity.

2.2. Test Equipment and Specimen Pretreatment

The experiment utilized a self-developed rock non-destructive water immersion device to saturate the samples with water, while maintaining a constant temperature of 26 °C in the humidification chamber. The device employs atomized water to achieve non-destructive saturation, effectively preserving the integrity of the samples. A forced-air drying oven was used for drying treatment, with the temperature set at 60 °C to prevent radiation damage to the coal matrix caused by high temperatures [37].

The specimen’s average moisture content was determined using Equation (1) and correlated with water absorption (drying) time, as illustrated in Figure 4. The average saturated moisture content of the specimen was 11.45%. The water absorption and drying curves exhibited contrasting trends; however, both the average moisture content and time conformed to an exponential function relationship [15]. The water absorption process can be segmented into three stages based on the rate of increase in average moisture content: rapid absorption (0–5.1 h), slow absorption (5.1–10.1 h), and saturation (10.1–43.1 h). Similarly, the drying process can be classified into rapid evaporation (0–5.2 h), slow evaporation (5.2–16.2 h), and near-dryness (16.2–26 h). The formula for calculating moisture content is as follows:

$$w_i={\displaystyle \frac{m_{si}-m_{di}}{m_{di}}}\times 100\%$$

(1)

where w_i, m_si, and m_di represent the moisture content, the water absorption mass, and dry mass of the ith specimen, respectively.

The spatial and temporal heterogeneity of water distribution within coal pillars is attributed to the dynamic fluctuations in moisture content, which leads to variations in pore structures and deformation characteristics across different locations [6]. To examine the impact of MCIs (Δw) on the evolution of pore structure and the assessment of damage in coal under DWC conditions, the fitted equations for the water absorption and drying processes, as illustrated in Figure 4, demonstrate that the specimens exhibit specific moisture states at various time intervals throughout these processes. Experimental observations and theoretical analyses indicate that extreme drying and saturation treatments induce crack propagation on coal specimen end faces. This damage results from coupled mechanisms of clay mineral dehydration shrinkage and pore water pressure expansion, significantly increasing experimental uncertainty [38]. As evidenced in Figure 4, achieving absolute dryness or complete saturation requires prohibitively long durations (>40 h). Consequently, implementing moisture content boundaries of 2% (lower limit) and 10% (upper limit) during wet–dry cycling achieves dual objectives: mitigating structural anomaly risks and enhancing experimental efficiency. Consequently, three specimens with varying MCIs (Δw = 4%, 6%, and 8%) were prepared. The duration required for the specimens to achieve the designated moisture states is detailed in

Table 1. The mass of the specimen at various time intervals required to achieve a specific level of moisture content.

Δw 1 (%)	Ta 2 (min)	Td 3 (min)
1.95	50.02	494.39
4.17	107.81	298.09
5.94	183.77	183.26
8.30	294.88	101.79
10.03	505.51	38.59

Note: ¹ Δw is the MCIs; ² T_a is the absorbing duration; ³ T_d is the drying duration.

. To reduce measurement errors, mass was recorded at one-minute intervals as the specimens approached the target moisture content, ensuring that the moisture content deviation was maintained within 0.5% [39]. Owing to experimental uncertainties, the measured moisture content increments (Δw) deviate from integer values. For systematic data comparison and pattern analysis, these values will be mathematically rounded in subsequent processing.

Figure 5 presents a schematic representation of the variations in DWCs corresponding to different MCIs. Initially, the specimens were placed in a saturated state and subsequently underwent drying treatments for varying durations, as outlined in Table 1. Upon achieving the target moisture content, the specimens were subjected to saturation treatments for differing durations to attain the desired moisture levels, followed by appropriate drying treatments. The culmination of this entire sequence was defined as one complete wet–dry cycle. The repetition of these procedures resulted in specimens that experienced 3 and 5 DWCs, respectively.

The microstructural properties of the samples were examined utilizing a MacroMR12-150H-I low-temperature and high-pressure nuclear magnetic resonance (NMR) experimental system (Suzhou Niumag Analytical Instrument Corporation, Suzhou, China). This system operates within a magnetic field intensity range of 0.3 ± 0.05 T, with a waiting time of 3500 ms, an echo time of 0.16 ms, and a sampling frequency of 200 kHz, while maintaining an operating temperature of 32 °C. The samples were prepared through centrifugation using a TD5A-WS core centrifuge, from which the T₂ spectrum data under centrifugal conditions were subsequently obtained. Given the low inherent strength of water-saturated coal rock, the centrifugal speed was calibrated to 500 r/min for a duration of 1 h to preserve the overall integrity of the samples [15].

2.3. NMR Principles and Procedure

Low-frequency nuclear magnetic resonance (LF-NMR) technology offers a swift and non-destructive approach for the quantitative characterization of the intricate pore structures present in various materials. When subjected to a low radiofrequency magnetic field, hydrogen nuclei resonate, allowing for the determination of the transverse relaxation time (T₂) through a series of radiofrequency pulse excitations, specifically utilizing the Carr–Purcell–Meiboom–Gill (CPMG) sequence. The T₂ relaxation time, along with signal intensity, constitutes essential parameters for the analysis and characterization of pore structures within materials. In coal rock, the pore fluids (H₂O) exhibit three distinct relaxation mechanisms, free relaxation, surface relaxation, and diffusion relaxation, which satisfy the following relationship [40]:

$${\displaystyle \frac{1}{T_2}}={\displaystyle \frac{1}{T_{2s}}}+{\displaystyle \frac{1}{T_{2B}}}+{\displaystyle \frac{1}{T_{2D}}}$$

(2)

where T_2B is the free relaxation time, unit ms. T_2S is the surface relaxation time, unit ms. T_2D is the diffusion relaxation time, unit ms.

The free relaxation time of coal rock materials is smaller than that of surface relaxation time and can be ignored. Diffusion relaxation can be ignored when the magnetic field gradient is small and the echo interval is short. At this time, T₂ can be expressed as [41]

$${\displaystyle \frac{1}{T_2}}\approx \rho {({\displaystyle \frac{S}{V}})}_{pore}={\displaystyle \frac{\rho F_p}{R_p}}$$

(3)

where ρ represents the transverse surface relativity. (S/V) _pore denotes the specific surface area of pores with different scales in the sample matrix. R_p stands for the pore radius of coal rock, with the unit of μm. F_p is the pore shape factor, where F_p equals 2 for cylindrical pores and 3 for spherical pores. It can be observed that R_p is directly proportional to T₂, and a larger T₂ value indicates a larger pore size. This forms the basis for characterizing the pore structure of coal rock using the NMR T₂ spectrum.

The LF-NMR experiments include specimen pretreatment and LF-NMR testing procedures (Figure 6).

(1) Specimens with different MCIs during DWCs were prepared using non-destructive water immersion equipment and electric heating drying ovens. The saturation and drying durations were determined according to Table 1, with the moisture content error consistently controlled within 0.5% throughout the process.

(2) The specimens were immersed in distilled water and subjected to vacuum saturation treatment, sealed, and maintained at 0.1 MPa for 12 h. This process aims to expel air from the pores and achieve specimen saturation.

(3) After wiping the surface moisture of the test sample, it was placed on the testing platform and MRI and saturated T₂ spectrum measurements were perform sequentially. Then the sample was centrifuged to obtain the centrifugal T₂ spectrum data. Subsequently, the DWC treatment on the sample was repeated for 3 and 5 cycles, respectively, followed by nuclear magnetic resonance tests.

To analyze the effect of DWCs on the cumulative damage of specimens, the same specimen was repeatedly subjected to DWCs for the same MCIs to ensure the accuracy of experimental results.

2.4. Fractal Dimension Theory

Coal rock is a medium with complex pore structures, and its pore system includes macroscopic fractures formed by coal seam faults and bedding planes, as well as pores formed during sedimentary and metamorphic processes [42]. The NMR pore fractal model is of great significance for accurately characterizing the complexity of internal pore structures in coal rocks. Compared to optical methods and mercury intrusion porosimetry, NMR technology can measure both connected and unconnected pores without damaging the material structure, demonstrating its significant technical advantages.

According to the Hausdorff theory, if an object is divided into several parts of similar size and shape, there exists a mathematical relationship between the scale r of each part and the probability P(r). The Hausdorff dimension D is defined as [43]

$$D={\displaystyle \frac{\ln P(r)}{\ln (1/r)}}$$

(4)

The pore system of coal rock is regarded as a collection of spherical pores and capillary pores, with the cumulative porosity percentage S_v defined as [44]

$$S_v={({\displaystyle \frac{r}{r_{\max }}})}^{3-D}$$

(5)

where r_max and r_min are the maximum and minimum of pore radii.

According to the theory of porous media, the capillary pressure is inversely proportional to the pore radius [45].

$$P_c=2{\sigma }_p{\displaystyle \frac{\cos \theta }{r}}$$

(6)

where P_c represents the capillary pressure in MPa, and σ_p and θ denote the surface tension and contact angle, respectively.

Combining Equation (5) and Equation (6) yields

$$S_v={({\displaystyle \frac{P_c}{P_{c\min }}})}^{D-3}$$

(7)

The capillary pressure P_c and the relaxation time T₂ satisfy the following mathematical relationship [46]:

$$\begin{array}{l}{P}_c=Y/T_2\\ Y={\displaystyle \frac{2{\sigma }_p\cos \theta }{F_p\rho }}\end{array}$$

(8)

where Y is a constant coefficient. By substituting Equation (8) into Equation (7), S_v can be expressed as

$$S_v={({\displaystyle \frac{T_{2\max }}{T_2}})}^{D-3}$$

(9)

Taking the natural logarithm of both sides of the above equation yields

$$\ln (S_v)=(3-D)\ln (T_2)+(D-3)\ln (T_{2\max })$$

(10)

where T_2max represents the maximum transverse relaxation time, which is 10,000 ms. The parameter of (3-D) is the slope of the straight-line fitting the curve of ln(S_v) versus ln(T₂). A larger value of D indicates a more significant difference in the geometry of pore systems in coal [47].

3. Results and Analyses

3.1. T₂ Spectral and Magnetic Resonance Imaging Evolution

The T₂ relaxation time is commonly used as a criterion for classifying pore types in coal rocks: T₂ < 10 ms corresponds to micropores, 10 ms < T₂ < 100 ms corresponds to mesopores, and T₂ > 100 ms corresponds to macropores. The T₂ spectra of samples under saturated and centrifuged states, influenced by different MCIs under DWC conditions, are shown in Figure 7. The saturated and centrifuged T₂ spectra of the samples, affected by MCIs and N_DWC, primarily exhibit a single peak (micropores), indicating that the quantity and development of micropores in the coal are superior to those of mesopores and macropores. As for the MCIs from the initial 4% to 8%, the T₂ spectra generally shift to the right, with negligible changes in the peak height and width of the first peak, showing only a slight increase. However, the peak characteristics of the T₂ spectra provide limited insight into the influence of MCIs on pore structure. Therefore, a detailed quantitative analysis of T₂ spectral parameters was conducted based on the T₂ distribution.

The T₂ spectrum area is a crucial parameter for quantitatively characterizing the evolution of coal pore structure, obtained by summing the amplitudes within different T₂ relaxation time ranges. In the T₂ spectrum, the total pore spectrum area (S_t) is derived from the cumulative amplitudes corresponding to all T₂ relaxation times; the adsorption pore area (S_a) is obtained by summing the amplitudes within the T₂ < 10 ms range; and the seepage pore area (S_s) is calculated by accumulating the amplitudes in the T₂ > 10 ms range, as shown in

Table 2. NMR T₂ spectral area for specimens with different MCIs under DWCs.

NDWC	Δw (%)	St	Sa	Ss
1	4	125,198.17	119,325.57	5872.6
	6	127,715.23	120,579.18	7136.05
	8	130,473.68	123,912.76	6560.92
3	4	127,043.92	121,104.09	5939.83
	6	131,143.32	122,311.08	8832.24
	8	134,679.37	127,566.52	7112.85
5	4	136,434.08	127,634.07	8800.01
	6	136,744.85	125,778.45	10,966.4
	8	138,469.96	128,965.45	9504.51

[15]. Based on Table 2, the evolution characteristics of coal pore areas and MCIs under DWCs are illustrated in Figure 8. For comparative analysis, the initial values of various pore spectrum areas are defined as $S_k^0$, and the variation rates of pore spectrum areas are denoted as δS_k. The variation rates of pore spectrum areas under different MCIs during DWCs can be calculated using the following equation:

$$\delta S_k={\displaystyle \frac{\Delta S_k^x}{S_k^0}}={\displaystyle \frac{S_k^x-S_k^0}{S_k^0}}\times 100 \%$$

(11)

where k represents t, a, and s, respectively. $∆S_k^x$ denotes the pore spectrum area of the xth group, and $S_k^0$ represents the pore spectrum areas of the specimen in its initial state.

Figure 8 illustrates the variation characteristics of the pore spectrum area under different MCIs during DWCs. The analysis revealed that with a constant number of DWCs, the pore spectrum area, adsorption pore area, and seepage pore area all exhibited varying degrees of increase as the moisture content increased. This phenomenon occurs because higher MCIs lead to greater dissolution of hydrophilic clay minerals in water during each DWC, which intensifies the damage propagation of pores with different diameters within the coal matrix. Consequently, this resulted in a general increase in the pore spectrum area.

Additionally, when N_DWC = 5, as the MCIs increased from 4% to 6%, the δS_t, δS_a, and δS_s values were 0.23%, −1.45%, and 24.62%, respectively. Similarly, when the MCIs increased from 4% to 8%, the δS_t, δS_a, and δS_s values increased by 1.26%, 1.04%, and 8.01%, respectively. This indicates that under DWCs, as MCI per cycle increases, the total pore area change rate and seepage pore area change rate of coal rock gradually increase, whereas the adsorption pore area change rate initially decreases and then increases. This phenomenon occurs because a higher MCI represents more water infiltrating the coal matrix during each cycle, leading to an increased dissolution of clay mineral particles. This promotes the formation of micropores within the coal matrix, thereby enhancing the pore spectrum area growth rate. The influence of high MCI cycling on the seepage pore area is more pronounced than that on the adsorption pore area. This is attributed to pore structure transformation under high MCIs; specifically, DWC action with high MCIs facilitates the conversion of adsorption pores into seepage pores in coal. Consequently, the adsorption pore area decreased, whereas the seepage pore area increased.

Magnetic resonance imaging (MRI) reflects the distribution characteristics of internal fluids in coal and can be used to analyze pore distribution and the development of initial damage within the coal matrix. In MRI images, the color depth represents the magnitude of the nuclear magnetic signal or fluid content, with the color scale ranging from blue to red, indicating a gradual increase in fluid content and larger pore volumes. Because the DWC effect on coal pores is a result of cumulative damage, to highlight the final state of pore development, the MRI features after five DWCs under different MCIs are presented (Figure 9). Median filtering was applied to reduce the influence of noise in the MRI images.

Horizontal magnetic resonance scanning results indicate that the nuclear magnetic signal intensity of the coal exhibits a banded distribution along the coal bedding plane. As the MCI continues to increase, the color intensity in the central region of the sample gradually deepens, accompanied by an increase in band thickness and enhanced connectivity between adjacent bands. This suggests that a higher MCI promotes the development and expansion of coal pores, while improving pore connectivity and enhancing coal permeability. This phenomenon occurs because the sample was processed from field coal blocks perpendicular to the bedding plane, where the inherent bedding provides natural pathways for water migration and pore development under DWCs. A higher MCI signifies greater water intrusion and loss, thereby increasing the probability of water erosion in deep coal matrices. The DWC process enlarges the pore size and connectivity, facilitating the formation of additional seepage channels.

The lateral magnetic resonance scanning results indicated that as the MCI increases, the distribution of nuclear magnetic signals gradually extended from the sample edges toward the interior. This suggests that during the DWC process, a low MCI primarily affects the surface pores of the coal, whereas with increasing moisture content, water gradually migrates deeper into the coal, thereby enhancing pore expansion in the interior. These findings provide valuable insights into the stability monitoring of coal pillar dams in the field. Given the differential effects of DWCs on various regions of coal, special attention should be paid to the surface of coal pillars under high moisture content conditions to prevent potential failure due to pore expansion or connectivity.

3.2. Pore Size Distribution Measured by NMR

According to the NMR principle, the T₂ spectrum reflects the pore size distribution (PSD) of the coal rock. A smaller T₂ value indicates a smaller pore size in the coal rock and vice versa [48,49]. Therefore, to accurately characterize the pore size distribution features of coal rock, the study converted the T₂ distribution into PSD using Equation (3).

As shown in Equation (3), the key to solving aperture R_p lies in determining ρ and F_p. The ρ values for low-, medium-, and high-rank coals were 15.1, 11.8, and 5.1 nm/ms, respectively. Because the samples used in this study were low-rank coal, ρ was 15.1 nm/ms [50]. The internal pores of coal can be regarded as cylindrical; therefore, the F_p value is 2. Substituting ρ and F_p into Equation (3) yields the aperture T₂ corresponding to F_p, thereby providing the abscissa values of the PSD. The ordinate of the PSD represents the porosity corresponding to each aperture, necessitating the conversion of the original T₂ spectrum to obtain the PSD. LF-NMR characterizes porosity using either the spectral area method or the peak point method; this study employs the spectral area method for conversion [51]. Calibration experiments indicate that the porosity and the unit volume T₂ spectral area exhibit a linear relationship, as follows:

$$\mu =391.42+27.43\phi$$

(12)

where μ represents the unit volume T₂ spectral area; φ denotes porosity. The fitting correlation coefficient R² between the two parameters is 0.96, meeting the error requirements for LF-NMR calibration.

The T₂ spectrum area of the specimen was directly obtained using the LF-NMR system software (V1.0). Because all test samples were standard cylinders (φ50 × 100 mm), the specimen volume was 196.25 cm³. The T₂ spectrum area per unit volume for the initial state and specimens with different MCIs under DWCs is listed in

Table 3. NMR T₂ spectral area per unit volume for specimens with different MCIs under DWCs *.

NDWC	Δw (%)	U	μ	φ (%)
0	4	125,508.06	639.53	9.05
	6	127,246.37	648.39	9.37
	8	125,630.72	640.16	9.07
1	4	125,198.17	637.95	8.99
	6	127,715.23	650.78	9.46
	8	130,473.68	664.83	9.97
3	4	127,043.92	647.35	9.33
	6	131,143.32	668.24	10.09
	8	134,679.37	686.26	10.75
5	4	136,434.08	695.21	11.04
	6	136,744.85	696.79	11.13
	8	138,469.96	705.58	11.45

Notes: * N_DWC = 0 represents the pore parameter in the initial state of the specimens, U is T₂ spectral area, μ is T₂ spectral area per unit volume, and φ is porosity.

. The relationship between the signal intensity (vertical coordinate) corresponding to each T₂ value in the T₂ spectrum and the proportion of each pore size (vertical coordinate) in the PSD satisfies Equation (13) as follows:

$${\phi }_i=\phi \times {\displaystyle \frac{{\gamma }_i}{\gamma }}$$

(13)

where φ_i represents the porosity ratio (%) corresponding to each pore size, φ denotes the total porosity (%) of the sample, γ_i indicates the signal intensity corresponding to each T₂ value, and γ stands for the total signal intensity.

Therefore, based on Equations (3), (12), and (13), the abscissa and ordinate of the T₂ spectrum of the samples can be converted into the pore size and the corresponding proportion in the PSD, respectively.

The evolution patterns of the PSD in samples with different MCIs under DWCs are illustrated in Figure 10. As shown in Figure 10a–c, the PSD of the samples exhibits a unimodal characteristic, predominantly concentrated in pores with 10 < R_p < 100 nm, followed by R_p < 10 nm and 100 < R_p < 1000 nm. The proportion of pores with R_p > 1000 nm is negligible. Unlike previous studies in which the pore size distribution was characterized by multiple sets of peaks, the pore sizes of the specimens in this study were mainly concentrated at R_p < 100 nm [25,52]. This indicates that the wet–dry cycling effect of water most significantly promotes the expansion of pores with 10 < R_p < 100 nm in coal, while its influence on pores with R_p > 1000 nm is relatively weak. With increasing MCIs, the proportion of pores with 10 < R_p < 100 nm in the PSD generally increased, as reflected by the enhanced peak intensity and width. Therefore, during the operation of underground reservoirs, special attention should be paid to the expansion and interconnection of small pores within coal pillars owing to their well-developed pore structure, to prevent hydraulic seepage and damage-induced failure.

Figure 10d–f present the specific distribution characteristics for pores of different size ranges. Considering that the DWC effect on coal rock pore structure is a cumulative process, and pores with 10 < R_p < 100 nm are significantly affected by DWCs, the analysis here focuses on N_DWC = 5. For N_DWC = 5, when the MCI increases from 4% to 8%, the proportion of pores with R_p < 10 nm decreases from 2.13% to 1.99%, while the proportion of pores with 10 < R_p < 100 nm increases from 6.81% to 7.18%. The proportion of pores with 100 < R_p < 1000 nm rises from 1.92% to 2.03%, and that of pores with R_p > 1000 nm increases from 0.18% to 0.25%. These results indicate that under DWC, a higher MCI promotes the expansion and interconnection of pores with R_p < 10 nm, leading to their predominant transformation into pores with 10 < R_p < 100 nm.

3.3. Quantitative Characterization of Pore Structure Parameters

The LF-NMR technique for measuring coal rock porosity offers the advantages of being non-destructive, convenient, and relatively accurate, leading to its extensive research and application in recent years. Based on the quantitative relationship between porosity and unit volume spectral area presented in Section 3.2, as well as the saturation–centrifugation combined measurement method, the evolution patterns of total porosity, effective porosity, and residual porosity can be determined. The porosity under saturated conditions is regarded as the total porosity φ_t, while the porosity under centrifuged conditions is considered the residual porosity φ_r. The difference between these two values represents the effective porosity φ_e. φ_e reflects the pore space and seepage capacity within the coal matrix, playing a crucial role in evaluating the development of fractures and the strength stability of coal rock masses. φ_r denotes the porosity associated with irreducible water in the coal body.

Figure 11a illustrates a positive correlation between the total porosity of the specimen and the increase in MCIs across varying N_DWC. Specifically, For N_DWC = 1, the total porosities corresponding to MCIs of 4%, 6%, and 8% are 8.99%, 9.46%, and 9.97%, respectively. Meanwhile, for N_DWC = 5, the total porosities for Δw = 4%, 6%, and 8% are 11.04%, 11.13%, and 11.45%, respectively. Notably, with each 2% rise in Δw, the total porosity increases by 0.09% and 0.32%, respectively. This observation suggests that augmenting the MCIs during DWCs facilitates an overall increase in porosity. This phenomenon stems from the fact that a higher MCI enables enhanced dissolution of clay mineral particles during each DWC, resulting in varying degrees of pore expansion and consequently a rise in total porosity [53].

Figure 11b depicts the correlation between effective porosity and MCIs. Initially, effective porosity decreases as MCI increases, followed by an increase, resulting in an overall upward trend. The inflection point is primarily attributed to water absorption, swelling, and the diffusive adhesion of clay mineral particles, leading to a reduction in pore diameters and subsequently limiting water flow space. Effective porosity is indicative of pore volume and water seepage capacity within the coal matrix. For N_DWC values of 1, 3, and 5, effective porosity increases by 0.86%, 0.55%, and 0.19%, respectively, as MCI rises from 4% to 8%. Consequently, elevating MCIs can boost the dissolution efficiency of clay minerals and enhance the effective porosity of coal samples.

As depicted in Figure 11c, residual porosity initially rises and then declines as MCI increases. For N_DWC = 5, residual porosity values of specimens are 3.12%, 3.78%, and 3.34% with different MCIs (Δw = 4%, 6%, and 8%), indicating a sequential 0.66% increase followed by a 0.44% decrease. This behavior stems from the dissolution of mineral particles in coal upon water absorption, coupled with intricate swelling and diffusion–adsorption processes akin to those observed in montmorillonite and illite. Subsequent to centrifugation, these particles adhere to partial pores, thereby diminishing residual porosity.

The correlation between porosity and MCIs suggests that elevated moisture content during DWCs contributes to increased porosity. The pores in coal serve as pathways for moisture movement, thereby indicating that alterations in porosity have a direct impact on seepage properties. Permeability, a key parameter delineating fluid flow within the coal structure, signifies the flow capacity and connectivity of water in the coal matrix. Hence, this research delves into the developmental patterns of coal permeability under heightened MCIs during DWCs using NMR T₂ spectra.

Several models are commonly used to estimate coal sample permeability from NMR T₂ spectra. These models include the Schlumberger–Doll Research (SDR) model, the modified SDR model, the Timur–Coates (T–C) model, the modified T–C model, and the Producible Porosity (PP) model. The Timur–Coates (T–C) model and the Producible Porosity (PP) model demonstrate reduced accuracy in predicting permeability for low-permeability coal samples, with their performance being contingent on the volume of data available [24,54]. Following a thorough evaluation of model performance, the study ultimately selects the modified SDR model for its superior matching capabilities, expressed as

$$k_{{SDR}^{\prime }}=0.0224\times {(T_{2gm}^s)}^{1.534}\times {(T_{2gm}^c)}^{0.182}$$

(14)

where k_SDR′ represents permeability, and $T_{2gm}^s$ and $T_{2gm}^c$ denote the geometric mean of T₂ under saturated and centrifugal states, respectively, which is related to the average pore size of the material.

$$T_{2gm}=\exp \left[{\displaystyle \sum _{T_{2s}}^{T_{2\max }}\frac{A_i}{A_T}}\ln (T_{2i})\right]$$

(15)

where T_2max = 10,000 ms; T_2s is the initial relaxation value of the T₂ spectrum (ms); A_i is the amplitude corresponding to T_2i; A_T is the total amplitude of the NMR T₂ spectrum; and T_2i represents the independent T₂ value (ms).

The permeability of coal rock under DWCs with different MCIs was calculated according to Equations (14) and (15), as shown in

Table 4. Permeability of coal rocks with different MCIs under DWCs.

NDWC	Δw (%)	${\mathit{T}}_{2\mathit{g}\mathit{m}}^{\mathit{s}}$ (ms)	${\mathit{T}}_{2\mathit{g}\mathit{m}}^{\mathit{c}}$ (ms)	kSDR′ (mD)
1	4	1.174	0.786	0.0274
	6	1.126	0.760	0.0256
	8	1.132	0.617	0.0248
3	4	1.109	0.572	0.0237
	6	1.133	0.609	0.0242
	8	1.172	0.564	0.0257
5	4	1.071	0.604	0.0227
	6	1.087	0.575	0.0230
	8	1.190	0.777	0.0279

.

Based on the data presented in Table 4, a relationship between MCIs and permeability during DWCs was established (Figure 12). For N_DWC = 1, Δw increased from 4% to 8%, leading to a decrease in permeability from 0.0274 mD to 0.0248 mD, indicating an inverse correlation between permeability and MCIs. This phenomenon can be attributed to the relatively low number of DWCs at this stage, where the higher MCIs facilitated clay mineral swelling around the pores upon water absorption. This swelling resulted in clay minerals adhering to pore surfaces, thereby reducing space for water migration and impeding water seepage capacity. With an increase of the N_DWC (N_DWC = 3, N_DWC = 5), permeability demonstrated a linear increase alongside the rise in MCIs; this shows some similarity to previous studies [15,25,55]. Specifically, as the MCIs escalated from 4% to 8%, the permeability for N_DWC = 3 and N_DWC = 5 rose by 0.002 mD and 0.0052 mD, respectively. Consequently, a higher MCI can enhance coal permeability under DWC conditions. This enhancement can be attributed to the repetitive DWCs weakening the adhesion of clay mineral particles surrounding coal matrix pores. Consequently, these particles continuously dissolve in water, enlarging pore size and connectivity, thereby improving coal sample permeability.

Furthermore, the anisotropy inherent in coal’s pore structure and mechanical response profoundly governs its seepage and damage behaviors. Existing studies establish that anisotropic seepage primarily arises from fracture network characteristics, wherein mineral-filling particles dictate fracture surface heterogeneity [56,57]. This microstructural feature drives stress-dependent anisotropic compression and damage evolution within fracture systems [58]. However, coal, as a complex porous media material, has an internally existing pore system that undergoes heterogeneous changes in response to external factors (e.g., stress, temperature, water), which in turn leads to alterations in the fracture system [59]. This interdependence demonstrates that coal’s stress state, pore architecture, fracture system, and seepage behavior exhibit coupled anisotropy through mutual feedback mechanisms. Regarding the permeability (k) statistically derived from NMR T₂ spectra in this study, while effectively characterizing macroscopic flow through connected pore channels, its capacity to resolve directional permeability anisotropy remains constrained. Future studies could investigate the influence of coal’s microporous structure on anisotropic seepage using fluid infiltration experiments, digital rock reconstruction, and pore-scale hydrodynamic simulations.

3.4. T₂ Cutoff Value and Fractal Dimension Features

The T₂ cutoff value (T_2C) is a crucial parameter that differentiates between movable fluids and bound fluids, serving as an indirect indicator of pore connectivity within the material. A lower T_2C signifies a greater movable space and enhanced pore connectivity in coal, whereas a higher T_2C indicates reduced pore connectivity. By comparing the positions of T_2C and T₂, the segment where T₂ < T_2C is categorized as bound water, while the rest is identified as free water.

The determination methods of T_2C include the centrifugal method, T₂ spectrum form method, and T_2GM method. The centrifugal method is currently recognized as the standard approach for determining T_2C in reservoir rocks. The T₂ spectrum form method exhibits high applicability only for sandstones with typical bimodal T₂ distributions but has limited effectiveness for coal with complex pore structures. The T_2GM method is unsuitable for measuring T_2C in coal, as it tends to amplify T_2GM, leading to inaccurate results [15,30]. Therefore, the study employed the centrifugal method to measure the T_2C of coal rock after DWCs. The determination of T_2C via the centrifugal method is illustrated in Figure 12. First, the T₂ distributions under saturated and centrifuged states were converted into cumulative porosity curves. A horizontal tangent was drawn from the maximum point of the cumulative porosity curve under the centrifuged state toward the vertical axis. The intersection of this tangent with the saturated cumulative porosity curve was identified, and a perpendicular line was dropped from this intersection to the horizontal axis. The foot of this perpendicular represents the T_2C.

Based on the T_2C obtained from Figure 13, the evolution characteristics of T_2C in coal rock under different MCIs during DWCs were plotted (Figure 14). It can be clearly observed that as the N_DWC increases, the T_2C under varying MCIs exhibits similar trends, showing a gradual decrease with increasing cycle numbers. This indicates that DWCs significantly promote the expansion of mobile spaces within the coal matrix, thereby enhancing the connectivity of internal pores. Furthermore, with N_DWC = 1, an increase in MCIs from 4% to 8% resulted in a decrease in T_2C from 1.438 to 1.237. This decrease is linked to a reduction in the frequency of DWCs, with the MCIs notably impacting the dissolution efficiency of clay minerals in the coal matrix. Consequently, there was a gradual rise in effective pore volume, facilitating the interconnection of pores of varying sizes.

When N_DWC =3 and N_DWC =5, the MCI increases, while T_2C initially rises and then declines, with minimal overall variation. Consequently, as the N_DWC continues to increase, the effect of MCIs on the T_2C of coal rock is relatively weak, and the N_DWC exerts a more significant influence on the pore connectivity of coal than the MCIs. The internal pore connectivity of coal gradually stabilizes under multiple DWCs, leading to an overall insignificant change in T_2C under the MCIs at this stage.

Based on T_2C, the internal pore structure of coal rock subjected to DWCs can be classified into bound pores (T₂ < T_2C) and free pores (T₂ > T_2C). Under the DWCs, both the MCIs and the N_DWC induce varying degrees of mineral particle expansion, adhesion, and dissolution reactions within the coal matrix, leading to differences in the fractal dimension of the pore structure. Equation (10) presents the NMR pore fractal theoretical model, and the bilogarithmic relationship between S_v and T₂ is illustrated in Figure 15. Accordingly, the pore fractal dimensions of coal rock under the DWCs at different MCIs were fitted separately for bound pores and free pores.

Based on the multifractal characteristics of coal rock, the effective pore fractal dimension ranges from 2 to 3 [60]. Fitting data indicates that bound pores do not exhibit significant fractal characteristics, whereas the fractal dimension of free pores is predominantly distributed between 2.9 and 3, with high data fitting accuracy, consistent with numerous studies [61,62]. Therefore, this study focuses on investigating the evolution characteristics of free pore fractal dimension in coal rock under the influence of MCIs during DWCs.

Figure 16 illustrates the evolution of the fractal dimension of free pores in coal rock under the influence of DWCs and MCIs. For different MCIs, increasing the N_DWC significantly reduces the fractal dimension of free pores. This occurs because repeated DWCs causes the T_2C to continuously shift leftward and decrease, while the slope of the fitted line between ln(S_v) and ln(T₂) progressively increases, thereby leading to a continuous reduction in the fractal dimension of free pores. When N_DWC = 1, comparing MCIs from 4% to 8%, the fractal dimension of free pores decreases. This indicates that the mineral particles within the coal rock undergo expansion and dissolution upon water absorption, reducing the geometric heterogeneity of free pores and smoothing the pore surface. As the N_DWC gradually increases to 3 and 5, the relationship between the fractal dimension of free pores and MCIs initially increases and then decreases, ultimately showing that higher MCIs correspond to higher fractal dimensions. This suggests that the geometric heterogeneity of free pores gradually increases under multiple DWCs, and higher MCIs moderately enhance the complexity of pore structures within the coal rock.

3.5. Pore Damage of Dry–Wet Cycling

During the DWCs with varying MCIs, complex changes such as particle dissolution, pore expansion and interconnection, and water absorption-induced swelling of clay particles occur within coal due to coal–water interactions. Since coal pillar dams are exposed to complex aqueous environments, the damage and deterioration of coal pore structures constitute a critical factor that cannot be overlooked in underground reservoir engineering. To quantitatively analyze the extent of pore damage in coal, the damage to coal pore structure caused by DWCs is defined as the pore damage variable (D_p). Based on the porosity of specimens measured by NMR, this study investigates the evolution characteristics of pore damage in coal under the influence of MCIs and N_DWC.

The total volume of the specimens can be considered as consisting of internal pores and solid particles, with the effective loading area borne by the solid particles. Therefore, the pore damage variable D_p is defined as

$$D_p=1-{\displaystyle \frac{V^{\prime }}{V_0}}$$

(16)

where D_p is the pore damage variable, V′ is the volume of solid particles in the specimen after different MCIs under DWCs, and V₀ is the initial particle volume of the specimens. During the DWC process, the total volume of the specimens undergoes only minor changes; thus, it is assumed that the total volume V₀ remains constant throughout the DWCs. The volume of solid particles in the specimens can be expressed as

$$\left\{\begin{array}{l}{V}^{\prime }=V(1-{\phi }^{\prime })\\ V_0=V(1-{\phi }^0)\end{array}\right.$$

(17)

where ${\phi }^{\prime }$ is the porosity of the specimens after DWC treatment, and ${\phi }^0$ is the porosity of the specimens in the initial state.

Combining Equation (16) and Equation (17), the expression for the pore damage variable of the specimens after DWCs treatment is obtained as

$$D_p=1-{\displaystyle \frac{1-{\phi }^{\prime }}{1-{\phi }^0}}$$

(18)

According to Equation (18), the evolution of pore damage variables in specimens under different MCIs during DWCs was calculated (Figure 17). The analysis indicates that both N_DWC and MCIs can increase the degree of pore damage in coal rock. However, different N_DWC exhibit distinct evolutionary patterns between pore damage degree and MCIs. When N_DWC = 1 and N_DWC = 3, the pore damage variable follows an exponential trend with increasing MCIs. A higher MCI leads to a greater rate of pore damage variation, with the development of pore damage primarily controlled by N_DWC and MCIs. This suggests that when the N_DWC is low, a high MCI can accelerate pore damage in coal. This occurs because a higher MCI increases the dissolution of soluble mineral particles upon water exposure, thereby promoting faster development in both the number and size of pores.

When N_DWC = 5, the pore damage variable and MCIs approximately exhibit a linear relationship. As N_DWC increases, the influence of MCIs on the rate of pore damage variation gradually diminishes. In other words, compared to the MCIs, the N_DWC plays a more significant role in promoting pore development and expansion. This indicates that both the N_DWC and MCIs can enhance the degree of pore damage in coal. This phenomenon results from complex processes such as dissolution, expansion, and migration of mineral particles within the coal during DWCs. Moreover, the N_DWC gradually becomes the dominant factor in increasing the dissolution of soluble mineral particles in coal.

4. Discussion

4.1. Correlative Analysis of Porosity and Pore Structure

The interaction of MCIs and DWCs affects the NMR pore spectrum area, T_2C, and fractal dimension of coal samples, collectively influencing porosity evolution. To further analyze the evolution characteristics of coal porosity under DWCs, this section aims to investigate the relationships among NMR pore spectrum area, T_2C, fractal dimension, and porosity under the influence of MCIs and DWCs to analyze the evolution of coal porosity.

Figure 18a,b depict the interrelationships among NMR adsorption pore area, seepage pore area, and porosity across all specimens subjected to DWC conditions. The analysis demonstrates a direct linear correlation ($R_1^2=0.9413$, $R_2^2=0.8840$) between specimen porosity and both adsorption and seepage pore areas, suggesting a proportional increase in porosity with the enlargement of these pore areas. This observation indicates that throughout DWC, there is a rise in the proportion of adsorption and seepage pores in coal, thereby facilitating the expansion and transformation of the overall pore structure.

Figure 18c,d depict the relationship between T_2C, D_p, and porosity in specimens. Although the correlation among these parameters is relatively weak, an overall negative trend is observed; as T_2C and D_p increase, porosity gradually decreases. Section 3.4 and Section 3.5 analyze the impact of varying MCIs and N_DWC on the T_2C and D_p of coal rock. The evolution patterns of T_2C and D_p, as observed through NMR, indicate the pore connectivity and complexity of coal rock. The increase in porosity corresponds to enhanced pore connectivity and complexity of coal, consistent with previous studies. The analysis attributes these findings to coal being a porous medium containing soluble minerals like illite and montmorillonite. During coal–water interactions, these minerals undergo water absorption, expansion, and dissolution, leading to increased porosity and improved pore connectivity [63,64]. The distribution characteristics of soluble mineral particles within the coal matrix influence their expansion and dissolution, resulting in non-uniform pore distribution and heightened geometric heterogeneity. This process is intricate, irregular, and random, contributing to the complexity of coal pore structure.

4.2. Damage Mechanisms of Dry–Wet Cycling on Coal Pores

The evolution of coal rock pore structure parameters under DWCs and MCIs reveals distinct influences of these two factors. As demonstrated in Section 3.3, at low DWC numbers (N_DWC = 1), increasing MCIs restricts fluid seepage capacity within pores, thereby reducing permeability. However, as N_DWC increases, permeability exhibits an approximately linear rise with MCIs. These findings indicate that coal rock pore structure is jointly governed by DWC frequency and MCIs, with coal–water interaction mechanisms varying across different parameter conditions.

Figure 19 presents the pore evolution mechanisms in coal subjected to DWCs. Extensive research has elucidated the intricate processes governing coal–water interactions. Coal, characterized by a variety of pore structures, undergoes complex physicochemical transformations upon water ingress, including swelling, migration, and dissolution, primarily driven by the presence of hydrophilic mineral particles [6,15,62]. This study systematically examines how N_DWC and MCIs influence coal pore structure. Nuclear magnetic resonance (NMR) experimental results (Section 3) reveal that initial water exposure triggers non-uniform swelling of hydrophilic mineral particles, reducing overall porosity and permeability while decreasing pore geometric heterogeneity. Simultaneously, inter-pore cementation weakens. As MCIs and DWCs increase, weakened cementation facilitates partial mineral particle migration and dissolution, ultimately enhancing porosity and permeability. Concurrently, pore structure complexity intensifies progressively.

The pore fractal dimension serves as a representative example. When the N_DWC is low, the dominant factor influencing pore structure is the MCI. As the MCI increases, the fractal dimension decreases, indicating that a higher MCI reduces the complexity of pore distribution and enhances overall pore uniformity. Consequently, this improved pore uniformity increases the lubrication effect between the pore matrix and water, thereby reducing cohesion. This mechanism provides a theoretical basis for understanding the evolution of coal’s mechanical parameters following water erosion [12,14]. As N_DWC increases, the pore fractal dimension initially rises and then declines with further MCIs. However, the final value remains higher than the initial state, suggesting that repeated DWCs dissolve mineral particles attached to pore surfaces. This process increases pore complexity and enhances pore heterogeneity.

4.3. Research Limitations and Prospects

This study preliminarily investigated the effects of varying MCIs and DWC numbers on coal pore structure using NMR. However, experimental and analytical limitations necessitate further research in the following several areas:

(1) The limitations of samples and experimental conditions. Despite sampling from the same mining area and implementing screening procedures, inherent coal heterogeneity introduced unavoidable sample-related uncertainties. Additionally, the exclusive use of samples from underground reservoir coal seams limits the generalizability of findings due to their site-specific nature. Experimentally, while moisture content was controlled during dry–wet cycling, imprecise duration control introduced uncertainty. Future work should utilize more homogeneous rock materials and improve precision in moisture control during cyclic treatments. This would reduce experimental uncertainty and enhance the generalizability of results.

(2) Insufficiency of experimental analysis means. The alteration of coal’s internal pore structure under cyclic wet–dry conditions arises from mineral particle swelling, dissolution, and migration. While this study quantified the evolution of pore structure parameters, it did not address the underlying changes in mineral composition and quantity. Future work should, therefore, employ microscopic characterization techniques (e.g., SEM, MIP, XRD) to comprehensively investigate fluid–rock interactions. Concurrently, pore structure evolution governs macroscopic mechanical properties. Although DWC effects on coal mechanics are well-studied, this work lacks micro-to-macro mechanical linkage. Future research should implement coupled hydro-mechanical testing under engineering-relevant conditions to elucidate damage mechanisms in cyclically saturated coal.

This study establishes the evolution characteristics of coal’s microporous structure under DWC conditions with varying MCIs using NMR technology. These findings provide critical insights into coal strength degradation mechanisms. The engineering significance of the results manifests in two primary aspects:

(1) Direct application to coal pillar dam design

Evolution equations quantifying porosity and permeability as functions of DWCs and MCIs enable derivation of material deterioration depth models. These models inform minimum width specifications for coal pillar dams, ensuring sufficient structural compensation for cyclic water-induced damage, which is a fundamental requirement for long-term stability of underground reservoirs.

(2) Foundation for stability assessment frameworks

Microscopically quantified parameters (e.g., permeability k, pore damage factor D) provide essential inputs for numerical simulations. Embedding these relationships into coupled hydromechanical-fracture models enables predictive analysis of dam integrity under field conditions, establishing a physics-based stability evaluation system.

5. Conclusions

This study systematically examines the pore structure and fractal characteristics of coal rock subjected to 1–5 DWCs with three distinct MCIs. This investigation utilized low-field nuclear magnetic resonance (NMR) and a self-developed rock water immersion device. By conducting detailed measurements and quantitative assessments encompassing T₂ spectra, magnetic resonance imaging (MRI), pore size distribution, porosity, permeability, fractal dimension, and pore damage, the study scrutinized the distinct variations in pore structure and fractal dimension in response to different MCIs and DWC frequencies. Key findings include the following:

(1) After cyclic treatment with varying moisture content increments, the T₂ spectrum area and magnetic resonance imaging (MRI) results of the samples showed significant variations. Maintaining a consistent number of DWCs, the pore spectrum area, adsorption pore area, and percolation pore area showed incremental increases with higher MCIs. MRI analysis demonstrated that the overall NMR signal intensity displayed a banded distribution along the coal rock bedding. As the MCIs increased, the signal intensity in the central region intensified, adjacent bands became interconnected, and the NMR signal distribution expanded progressively from the sample edges toward deeper regions.

(2) The DWCs had a significant impact on the expansion of pores ranging from 10 to 100 nm in the specimens. The pore size distribution exhibited a unimodal pattern, with pores between 10 and 100 nm being the most prevalent, followed by pores smaller than 10 nm and between 100 and 100 nm, while pores larger than 100 nm were present in minimal amounts. When the MCIs increased from 4% to 8% for N_DWC = 5, the proportion of pores smaller than 10 nm decreased from 2.13% to 1.99%, whereas the proportion of pores between 10 and 100 nm increased from 6.81% to 7.18%. Higher MCIs during DWCs facilitated the transformation and enlargement of pores smaller than 100 nm.

(3) The porosity and permeability of the specimens exhibit distinct variation characteristics influenced by the N_DWC and MCIs. As MCI increases during DWCs, the total porosity of the specimens rises. Specifically, for every 2% increase in MCI, the total porosity increases by 0.09% and 0.32%, respectively. Meanwhile, effective porosity initially decreases before increasing, displaying an overall upward trend. Permeability evolution, modeled using the improved SDR method, correlates with the N_DWC. For N_DWC = 1, an increase in MCI from 4% to 8% results in a decrease in permeability by 0.0026 mD. Conversely, for N_DWC = 3 and N_DWC = 5, the permeability increases by 0.002 mD and 0.0052 mD, respectively, indicating a positive correlation between permeability and MCI.

(4) The evolution processes of T_2C and the fractal dimension exhibited distinct patterns under the combined influence of DWCs and MCIs. For N_DWC = 1, as the MCI increases from 4% to 8%, T_2C decreases by 0.201, and the free pore fractal dimension diminishes. However, for N_DWC = 3 and N_DWC = 5, both T_2C and free pore fractal dimension initially increased and then decreased with increasing MCIs, ultimately demonstrating higher fractal dimensions under larger MCIs.

(5) Both the N_DWC and the MCIs can increase the degree of pore damage in coal rock, but the relationship between pore damage and MCIs follows different evolution patterns under varying N_DWC. For N_DWC = 1 and N_DWC = 3, the pore damage variable exhibited an exponential trend with increasing MCIs; the higher the MCIs, the greater the rate of pore damage change. For N_DWC = 5, the N_DWC exerted a more pronounced promoting effect on pore development and expansion.