## 2 Materials and Test Program
### Nuclear Magnetic Resonance Testing  
#### 2.4.1 Introduction to Nuclear Magnetic Resonance Testing  
In this study, NMR technology was used to investigate the pore characteristics of the compacted expansive soil instead of the more common mercury intrusion porosimetry (MIP). NMR was considered beneficial because the size of the sample used in MIP is small (nearly 1 cm\({}^{3}\)), meaning that the test result is significantly affected by the sample used in the test and that the results was widely dispersed, especially for heterogeneous soil (with cracks). NMR can test large-sized samples of 60 mm \(\times\) \(\Phi\)60 mm and does not damage the soil. It is capable of measuring the same sample multiple times, reflecting continuous changes in the sample's microstructure. Nuclear magnetic resonance refers to a technology in which the nuclear spin in the low-energy state transitions to a high-energy state by absorbing the energy provided by a radio frequency (RF) field, and the energy change of the nucleus in the magnetic field provides information regarding the nucleus. The free decay curve of the nuclear magnetic signal (FID) was measured by considering that a group of protons with a spin moment in a uniform magnetic field deflects and loses balance under the interference of an RF magnetic field; the group of protons recovers from a non-equilibrium state to an equilibrium state  
Figure 1: (a) Soaking process in California Bearing Ratio (CBR) test (b) CBR testing apparatuses. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Moisture** & **Compaction Energy** & **Compaction Degree** & **The Number of Freeze–thaw** \\
**Content (\%)** & **(hits)** & **(\%)** & **Cycles** \\ \hline
16.4 & 98 & 100 & 0,1,2,4,6,8,10,12 \\
19 & 27 & 90 & 0,1,2,4,6,8,10,12 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The samples prepared for CBR tests under different freeze-thaw cycles. when RF interference is stopped. Through Fourier transformation, the \(T_{2}\) time distribution curve of the pore water in the soil samples could be generated. The peak area below the distribution curve represents the nuclear signal corresponding to the \(T_{2}\) range, i.e., moisture content [30,31]. Next, the relaxation rates in soils were simplified as follows [32]:  
\[\frac{1}{T_{2}}=\frac{1}{T_{2s}}=\rho_{2}\big{(}\frac{S}{V}\big{)}_{pore} \tag{1}\]  
where \(T_{2}\) is the lateral relaxation time of the water in the pores; \(T_{2s}\) represents the surface relaxation time; \(\rho_{2}\) is the surface relaxation coefficient which changes with the surface properties of rock and soil particles, especially the paramagnetic ions on the surface of the soil particles. \(S\) is the surface area; and \(V\) is the pore volume. Equation (1) can be written as Equation (2) based on the hypothesis that the pores in soils are cylindrical, based on research by [PERSON] et al. [33]. \[\frac{1}{T_{2}}=\rho_{2}\frac{4}{D} \tag{2}\]  
where, \(D\) (\(\mu\)m) is the diameter of the pore. \(\rho_{2}\) can be calculated with Equation (3) [34]. \[\rho_{2}=\big{(}k_{s}\phi^{4}T_{2 LM}^{2}\big{)}^{1/2} \tag{3}\]  
where \(k_{s}\) (\(\mu\)m\({}^{2}\)) is the permeability of the soil; \(\phi\) denotes the porosity of the soil, and \(T_{2 LM}\)(ms) denotes the weighted geometric mean value of the \(T_{2}\) spectrum. Next, the pore volume \(V_{i}\) with a certain diameter is written as follows [35]:  
\[V_{i}=\frac{A_{i}}{\sum A_{i}}.\frac{m_{w}}{\rho_{w}}=\frac{A_{i}}{\sum A_{i}}.\frac{m_{s}-m_{d}}{\rho_{w}} \tag{4}\]  
where, \(A_{i}\) is the signal intensity at a certain \(T_{2}\), \(m_{w}\) is the mass of water, \(m_{s}\) is the mass of saturated sample, and \(m_{u}\) is the mass of a dry sample. The nuclear magnetic resonance device applied in the present study was composed of a sample tube, a magnet unit, an RF system, a temperature-controlling system and a data acquisition and analysis system. To generate a stable magnetic field, the temperature of the magnet unit was set to 32 \({}^{\circ}\)C, with a variation of \(\pm\) 0.01 \({}^{\circ}\)C [36].