## 4 Experimental Results and Discussion  
### T\({}_{2}\) Spectrum Distribution Curves  
(1) Change in the T\({}_{2}\) spectrum distribution curves  
According to the principle of NMR technology, the characteristics of mesoscopic structures in rocks can be characterized by the T\({}_{2}\) distribution curve. The T\({}_{2}\) value reflects the size of the pores, and the amplitude of the T\({}_{2}\) spectrum demonstrates the number of pores inside the rock. The T\({}_{2}\) spectrum distribution curves of the samples are shown in Figure 3.  
Figure 3: T\({}_{2}\) spectrum distribution of sandstone. Figure 2: Configuration of NMR test equipment. The T\({}_{2}\) spectrum curves for all the six groups of the specimen consist of three spectral peaks. From left to right, the peaks correspond to the micropores, mesopores, and macropores. However, generally, the amount of change in the T\({}_{2}\) spectrum curves is quite different. For micropores, the peak and area under the peak of the micropore spectrum are the largest, indicating that the rock specimen is relatively dense, and most of the internal pores are micropores. The mesopore and macropore peaks increase with an increase in the external load. The T\({}_{2}\) spectrum distribution curves gradually change from two independent peaks to steadily expanding their volumes until the two peaks overlap. Overall, the T\({}_{2}\) value and spectral peak area increase, especially when the external load is greater than 80% UCS. (2) Analysis of T\({}_{2}\) spectral area  
The T\({}_{2}\) spectral area is positively related to the number of pores and the porosity. The T\({}_{2}\) spectral area is the area enclosed by the T\({}_{2}\) spectral curve and the coordinate axis. Therefore, we can obtain the area of each spectral peak via integration. The spectral area of the three aperture pores and the proportion are shown in Table 1 and Figures 4 and 5. Figure 4: The peak area variation in the T\({}_{2}\) spectrum. A specimen is mainly composed of micropores, especially when the preloading stress is less than 80% UCS, accounting for up to 90% of the total pore area, while macropores account for less than 3%. When the preloading stress increases to greater than 80% UCS, macropores increase their overall volume and account for 15%. When the loading ratio increases from 60% to 70%, the total area of the T\({}_{2}\) spectra distribution actually decreases, indicating that the number of pores in the rock decreases during this process, as shown in Figure 6a. This is because the internal pores of the rock are compacted under external loads, and the rock has not reached the point of mechanical failure. With a continued increase in the external load, the proportion of micropores in the rock decreases, while the percentage of mesopores and macropores increases. This indicates that under the action of an increasing external load, the expansion of internal pores in the rock leads to an increase in the number and size of the pores, which eventually leads to the destruction of the pore structure within the rock. In order to quantitatively analyze the change in the pores in the samples, the variation rate of pore proportions in the samples was established, as shown in Formula (4). We define the ratio of axial compression when the internal damage of a rock suddenly changes as the critical value of damage. \[\Delta\text{Pr}=\frac{|\text{Pr}_{2}-\text{Pr}_{1}|}{\text{Pr}_{1}} \tag{4}\]  
where \(\Delta\text{Pr}\) is the variation rate of pore volume proportions in rocks, %; \(\text{Pr}_{1}\) is the proportion of pore volume in the first stage, %; \(\text{Pr}_{2}\) is the proportion of pore volume in the second stage, %.