## 4 Results and Discussions
### Comparative Analysis of the NMRI and MIP Measurements  
The mercury injection porosimetry (MIP) test, which was widely used in pore distribution analysis of thawed soils, was applied to measure the frequency distribution curve of pore diameter of a cylindersample with its diameter of 20 mm and height of 20 mm after the artificial freezing treatment of -5 \({}^{\circ}\)C. The distributed frequency of pores under a diameter was calculated as Equation (9) and the NMRI-based pore size frequency distributed curve of thawed soils after an artificial freezing treatment of -5 \({}^{\circ}\)C was obtained to compare with the MIP result, as shown in Figure 9. It can be seen that the shape and peak positions of the two curves were in a good consistency. Moreover, the optimal pore diameters by NMRI and MIP were about 5.6 \(\upmu\)m and 5.8 \(\upmu\)m, which werequite close to each other. Thus, it is reasonable to use \(T_{2}\) spectrums from NMRI measurements to analyze pore size distribution characteristics of thawed soils.  
\[f_{i}=\frac{V_{i}}{\sum V_{i}}\times 100\%, \tag{9}\]  
where \(f_{i}\) denotes the distributed frequency of the pore with a certain diameter.  
Theoretically, both NMRI and MIP results reflect pore structures in porous mediums so the pore size distribution curves from these two methods should keep completely consistent [39]. However, the pore size distributions obtained by the two methods have relatively obvious difference in the distribution of pores with diameter over 20 \(\upmu\)m. This is because the method for obtaining pore size distribution by MIP and NMR has a difference of their physical principles. For the MIP test, the pore distributed condition in soils to the maximum mercury inlet pressure can only be measured by mercury injection. However, the connectivity of pores in soils is complicated and it is difficult for the mercury saturation of macro-pores to reach 100% [40]. The response of MIP results to the larger pore structure was limited, resulting in insufficient measurements of the connected macro-pores corresponding to the pore radius of mercury injection. Accordingly, the distributed frequency of large pores was underestimated while the frequency of small pores was relatively overestimated from the MIP measurements. Meanwhile, the NMRI method measured the total volume of pore water in saturated soils. For a fully saturated sample, the volume of pore water was approximately equal to the total pore volume, so the measurement from NMRI was extremely close to the actual pore structure in the tested sample. Besides, the NMRI scan was completely non-destructive to the internal structure of the tested sample while the mercury injection process during MIP measurements caused damage to the internal structure. Through data analysis, it was found that the average relative error of frequencies with different pore diameters between MIP and NMR was 18.16%, approximately. It is therefore concluded that the NMRI was more accurate than MIP measurements, as a new method to quantitatively study pore distribution characteristics of soils.  
Figure 9: The frequency distribution curve of pore diameter.