## 5 Conclusions  
This study investigated the effect of artificial freezing treatments on pore structure characteristics of thawed residual soils in frozen-wall by conducting NMRI scans. On the basis of analysis, the following conclusions were drawn:  
1. After conducting artificial freezing at different temperatures, which were \(-5\), \(-10\), \(-20\) and \(-30\)\({}^{\circ}\)C, the \(T_{2}\) spectrums which exhibit a bimodal distribution from NMRI measurements on thawed residual soils have a significant variation. With the freezing temperature dropped from \(-5\) to \(-30\)\({}^{\circ}\)C, the maximum value of the major peak in the \(T_{2}\) spectrum increases from 525 to 633, and the secondary peak increased from 12 to 45, approximately. Besides, the peak areas of \(T_{2}\) spectrums increase linearly with the freezing temperatures.
2. The \(T_{2}\) spectrums from NMRI tests could be used for the assessment of pore volume distributions of thawed residual soils by introducing the surface relaxation coefficient (\(\rho_{2}\)). From the obtained pore volume distributions, pores in thawed soils could be divided into three different grades by diameters, which are micro-pores, meso-pores and macro-pores. The volume of pores with the full range of diameters all increased as the freezing temperature decreases.
3. The NMRI test provided a visual result of pore structures in residual soils after freezing and thawing. According to the pore structures observed from \(T_{2}\)-weighted images, the microstructural damage of thawed soils evolved from the surface to the interior of soils as the freezing temperature continuously drops.
4. By comparing the pore size distribution curves obtained from the NMRI and MIP method respectively, the shape and peak positions of two curves were proved to have good consistency. However, the volume of macro-pores measured by MIP was significantly less than the result of NMRI, as a result of insufficient measurements of the macro-pores corresponding to the pore radius of mercury injection. Therefore, the NMRI scan was more accurate than the MIP measurement, as a new method to quantitatively study pore distribution characteristics of soils.  
The paper was written by [PERSON] under the guidance of [PERSON]. The formal analysis and pre-literature research were carried out by [PERSON] and [PERSON]. The laboratory tests were carried out by [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding  
This research was funded by the financial support of the National Natural Science Foundation of China (Grant No. 11692320 and 41372314).  
The authors declare that they have no conflicts of interest.  
List of Symbols  
\(A_{i}\) amplitude of NMR signal  
\(C\) square of relaxation coefficient  
\(D\) (\(\upmu\)m)diameter of pores  
\(f_{i}\) (\(\%\))distributed frequency of pores with a certain diameter  
\(I_{P}\) plasticity index  
\(K_{S}\) (\(\upmu\)m\({}^{2}\)) permeability  
\(m_{d}\) (g) mass of thoroughly dried soil sample  
\(m_{s}\) (g) total mass of saturated sample  
\(m_{w}\) (g) mass of pore water in the tested sample  
\(S\) (\(\upmu\)m\({}^{2}\)) surface area  
\(T_{2}\) (ms) relaxation time  
\(T_{2B}\) (ms) bulk fluid relaxation time  
\(T_{2D}\) (ms) diffusion relaxation time  
\(T_{2 LM}\) (ms) geometric mean value of \(T_{2}\) spectrum\(T_{25}\) (ms) surface relaxation time \(V\) (\(\mu\)m\({}^{3}\)) pore volume \(V_{i}\) (\(\mu\)m\({}^{3}\)) pore volume \(w\) (%) moisture content \(W_{L}\) (%) liquid limit \(W_{P}\) (%) plastic limit \(\rho_{2}\) (\(\mu\)m/ms) relaxation coefficient \(\rho_{w}\) (g/cm\({}^{3}\))density of water \(\phi\) (%)porosity