## 3 Materials and Methods
### NMR Technique  
#### 3.2.1 Principle of NMR Spectrometry  
The low-field NMR, MesoMR23-060H-I (provided by Newmag Company) was employed to investigate the PSD of soft clay. The soft clay sample was composed of soft clay aggregates and water. Additionally, the water distribution reflects pore distribution in the saturated soft clay (Figure 4), the brown particles in the picture represent aggregate, and the blue particles in the pictures represent water in the soil.  
NMR operates on the principle of nuclear spin in a magnetic field. A nucleus spins around its own axis generating a magnetic field when the number of protons is odd, and the number of neutrons is even simultaneously. Therefore, hydrogen, which has an odd number of protons and an even number of neutrons, can be used to calculate liquid water content. There is no magnetization vector detected from a water molecule, unless it is exposed to a magnetic field, wherein it produces a macroscopic longitudinal magnetization vector because of the magnetic field. After a 90\({}^{\circ}\) pulse, the magnetic resonance detects the rotating transverse magnetization vector, then the magnetization vector gradually decreases to zero. The CMPG sequence, which can ensure accurate results and repeatability,  
Figure 4: Pore distribution schematic diagram. Blue areas represent the water-filled pores.  
Figure 3: Uniformity of soft clay sample before freezing: (**a**) shows the data for the freezing duration tests and (**b**) shows the data for the gap time tests.  
is used to identify the saturated soft clay specimens [41]. The parameter \(T_{2}\) is introduced to represent the time required for the transverse magnetization vector decaying to 37% of its maximum value.  
Assume the shape of a pore is cylindrical, and the diffusion time is negligible [35]. The \(T_{2}\) distribution has been correlated with the PSD curve [22], allowing the pore throat radii to be estimated with high accuracy by using the Laplace inverse transform and multiregression analysis [42]. The relationship of pore radius \(r\) (Figure 5) and \(T_{2}\) is given by Equation (2), in which \(\rho_{2}\) is the surface relativity, \(S\) represents surface area of the pore, and V represents the volume of the water.  
\[\frac{1}{T_{2}}\approx\rho_{2}\left(\frac{S}{V}\right)_{\mathit{ pore}}=\rho_{2}\frac{2}{r} \tag{2}\]  
The soft clay sample was scanned before and after the freezing action. The previously prepared saturated soft clay samples were divided into two equal fractions to expose them to the 60 mm \(\times\) 60 mm uniform magnetic field of the NMR equipment. The H elements in water can be detected by the magnetic field accurately, then the water distribution in soft clay is obtained. For the saturated soft clay samples, the distribution of water is the distribution of pores. Different pore size gives different signal intensity, then the pore size distribution is calculated. The small pores mainly come from the voids between soft clay particles, and the medium pores mainly come from the voids between aggregates (Figure 6).  
Figure 5: Pores size schematic diagram. The diagram shows a schematic pore throat indicating the pore throat radius.  
Figure 6: Soft clay structure diagram. In the diagram, blue spaces represent the water-filled pore space in the particle and aggregate material.  
To easily describe the test result in this paper, we defined the main peak as small pores, and the subpeak as medium pores in the soft clay (Figure 7). The freezing action has different influences on the water at different pore sizes. The first, second, and third peak identify the small, medium and large pores separately with the increasing of the radius.