## 3 Results and Discussion
### Quantification of Coal Porosity with NMR Measurements  
Figure 5 shows the initial \(T_{2}\) distribution curves of the four groups of coal samples and the final \(T_{2}\) distribution curves after different discontinuous cyclic loads. According to the NMR relaxation mechanism, the width of the peak of the \(T_{2}\) distribution curve reflects the sorting of certain pore types, and the number of peaks reflects the continuity of pores at various levels [28; 29]. A continuous bimodal distribution is usually observed in the \(T_{2}\) curve of the test coal. This distribution indicates that the pore structure of coal is complex. Pores and cracks of various sizes in coal are pre-existing, and the connectivity between different pores is better. The first peak on the left of the \(T_{2}\) distribution accounts for a large proportion of total pores, which indicates that many micropores exist in the coal sample. An increase in holding time in the discontinuous cycle load increases the amplitude of the \(T_{2}\) distribution curve of all coal samples gradually. When the holding time was 0 min, the average maximum amplitude of the first peak of the \(T_{2}\) distribution was 215. When the holding time increased to 15 min, the average maximum amplitude of the first peak was 320, which is an increase of 48.5%. Therefore, as the holding time increased, the degree of damage inside the specimen increased gradually. These results are similar to the results of [PERSON] [30]. The changes in size and number of pores in the rock can be reflected by the \(T_{2}\) distribution area, where the area is correlated positively with the size and number of the corresponding pores [31]. Figure 6 shows the spectral area changes before and after all samples were destroyed. As the holding time increased, the spectral area increased gradually. When the holding time was 0 min, the average spectral area was 5770. When the holding time was 15 min, the average spectral area increased to 11,000, and the growth rate was 90.9%. As the holding time increased, the size, number, and porosity of the internal pores in the coal sample increased gradually. [PERSON] [32] showed that different relaxation time ranges of \(T_{2}\) distribution curves represent different pore sizes of rock masses. For coal masses, \(T_{2}\) < 10 ms corresponds to micropores; \(T_{2}\) from 10 to 100 ms corresponds to mesopores and \(T_{2}\) > 100 ms corresponds to macropores (cracks), as shown in Figure 7.  
According to the above pore classification method, changes in the proportion of pores of different sizes in the sample under different discontinuous cyclic loads are shown in Table 3. The averages of the pore proportions of coal samples before and after the experiment for different holding times reflect the change in absolute ratio of different pore sizes in the sample with holding time, as shown in Figure 8a-c. As the holding time  
Figure 5: Distribution curve of coal samples under different holding time: (**a**) 0 min; (**b**) 5 min; (**c**) 10 min; (**d**) 15 min. increased, the absolute ratio of micropores decreased from 76.2% (0 min) to 69.5% (15 min), the absolute ratio of mesopores increased from 17.1% (0 min) to 24.2% (15 min), and the absolute ratio of large holes increased from 4.78% (0 min) to 6.28% (15 min). As the holding time increased, the distribution of micropores, mesopores, and macropores (cracks) within the sample changed. The absolute proportion of micropores decreased constantly, whereas the absolute proportion of mesopores and macropores (cracks) increased constantly. Figure 6: Changes in the area of the \(T_{2}\) distribution curve of coal samples. Figure 7: Relationship between \(T_{2}\) and pore size. The difference between the average pore proportion of the coal sample before and after the force is loaded can reflect the increase and decrease in relative pore proportion for different holding times, as shown in Figure 8d.