## 4 Results and Discussions
### Analysis of Pore Size Distributions  
In this present section, the distribution curves of relaxation times \(T_{2}\) were analyzed, and the peak areas were determined. The \(T_{2}\) spectrum curves that exhibit two different peaks were plotted in Figure 4. It is clear that the major peak was significantly higher than the secondary peak in each \(T_{2}\) spectrum curve. As the freezing temperature dropped, the maximum value of the major and secondary peak increased noticeably. The values of peak area that were calculated from \(T_{2}\) spectrum curves indicate the pore water volumes in the tested sample. With the freezing temperature drops from \(-5\) to \(-30\)\({}^{\circ}\)C, the maximum value of the major peak increased from 525 to 633, and the secondary peak increased from 12 to 45, approximately. As illustrated in Figure 5, the relation between freezing temperatures and peak areas was studied by linear regression analysis since the value of peak area increased linearly with the drop in the freezing temperature. Besides, the linear function presented in Figure 5 could approximately express the correlation between temperatures and peak areas because the square of correlation coefficients \(R^{2}\) was 0.8724. In the \(T_{2}\) spectrum curves, the X-coordinate (\(T_{2}\)) and the Y-coordinate (NMR signal amplitude) reflect the pore volume and the distribution frequency of pores with a corresponding volume, respectively. On that basis, the pore size distribution of the thawed soils could be further analyzed. From the investigations on properties presented in Table 1, it shows that the permeability was 0.9012 \(\upmu\)m\({}^{2}\) and the porosity was 0.3098. Besides, the weighted mean geometric value \(T_{2 LM}\) of its \(T_{2}\) spectrum curve was 1.072 ms. Based on Equation (5), the coefficient \(\rho_{2}\) of granite residual soils was calculated as 0.3098 \(\upmu\)m/ms. Therefore, according to Equations (7) and (8), the volume distributions  
Figure 3: The photo of the NMRI equipment and the sample after freezing and thawing treatments. of pores with different diameters were obtained from \(T_{2}\) spectrum curves, as presented in Figure 6. Besides, according to the pore volume distribution curves, the accumulative pore volume distribution curves were plotted, also presented in Figure 6. In the pore volume distribution curves, the major peaks representing small pores were mainly distributed from 1 to 20 \(\upmu\)m, while the secondary peaks representing large pores were distributed from 30 to 200 \(\upmu\)m. From the accumulative pore volume distribution curves, the total pore volume of the sample under different freezing temperatures was 30.85 cm\({}^{3}\), 32.26 cm\({}^{3}\), 35.51 cm\({}^{3}\) and 38.38 cm\({}^{3}\), respectively. Besides, the volume of the major peaks and secondary peaks both increased with the drops of freezing temperatures. It is suggested that the pore volume contents of the residual soils significantly varied under the effect of artificial freezing process. Figure 4: The \(T_{2}\) spectrum curves of thawed soils under different freezing temperatures. Figure 5: The curve of relation between freezing temperature and peak area of thawed soils. Based on the pore volume distributions from NMRI measurements, the pores in thawed soils can be divided into three different grades by diameters: macro-pores (\(<\)5 \(\upmu\)m), meso-pores (5-10 \(\upmu\)m) and macro-pores (\(>\)10 \(\upmu\)m). The corresponding result of the pore classification is demonstrated in Figure 7. It can be observed that the volumes of pores with the full range of diameters increased when the freezing temperature decreased. The increasing rate of the micro-pore, meso-pore and macro-pore from temperature \(-\)5 to \(-\)30 \({}^{\circ}\)C was 16.82%, 22.23% and 45.19% approximately. Thus, the volume of macro-pores (diameter \(>\)10 \(\upmu\)m) showed the most significant increases as the freezing temperature dropped.