## 2 Material and Method
### Experimental Methods  
The NS (procured commercially) suspended on the surface when the mixed sample was obtained by the ordinary mechanical stirring and mixing method. In order to obtain the uniform soil sample, in addition to the mechanical mixing method, the mixed soil sample passed through a 2.5 mm sieve many times (Figure 2) [26]. The specific operation process was: (1) a certain amount of soil samples and NS were placed in a container and mixed with a mechanical method (Figure 2a); (2) the mixture of soil samples and NS (NS particles  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Soil Type** & **Plastic Limit** & **Liquid Limit** & **Specific Gravity** & **Maximum Dry Density** & **Optimum Water Content** \\  & **(\%)** & **(\%)** & **(g.g\({}^{-1}\))** & **(g.cm\({}^{-3}\))** & **Water Content** \\ \hline Silty clay & 13.4 & 23.8 & 2.71 & 1.98 & 14.3\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical properties of Qinghai-Tibet Plateau silty clay.  
Figure 1: The grain size distribution measured curve of silty clay samples.  
still suspended on the surface of soil samples) was split and placed in a 2.5 mm sieve (Figure 2b); (3) the mixed samples were sieved according to the normal sieving process until no small particles were left in the sieve, and the aggregates were crushed until no white powder was visible (Figure 2c); (4) coarse and fine particles were re-mixed in another container, and the above steps (2) and (3) were repeated until all soil samples were mixed; (5) the mixed soils from step (4) were passed through a 2 mm sieve; (6) steps (2)-(5) were repeated until the white powder was no longer present in the soil sample, and a uniform mixed sample was obtained (Figure 2d). In this study, four NS contents were added to modify Qinghai-Tibet Plateau silty clay, namely 0, 0.25, 1, and 3 percent.  
In order to maintain the pore structure of the modified silty clay samples in the drying process, the natural air-drying method was used instead of the oven drying method. For each of the NS contents, three specimens from the center of samples were selected. Then, we cleaned the particles adhering to the surface, and the specimens were polished with sandpaper. The microscopic features of the NS-modified silty clay were studied using a SEM and MIP (AutoPore IV 9500, Micromerities Instrument Corporation, Norcross, GA, USA). The pore diameter range was 0.003-1000 \(\upmu\)m in the MIP test.  
If we assume that pores in a soil-water system are cylindrical, then mercury will infiltrate the soil-water system when the external force starts. When the external pressure \(P\) (Pa) was applied, the pores with a radius of less than or equal to \(r\) (m) were filled with mercury solution.  
The relationship between pore diameter and external pressure can be described by the Washburn equation [27]:  
\[P=\frac{2T_{s}\cos\alpha}{r} \tag{1}\]  
where \(T_{s}\) is the mercury solution surface tension (N/m), which is 0.483 N/m at 20 \({}^{\circ}\)C, and \(\alpha=135^{\circ}\) is the contact angle between the soil particles and the liquid mercury.  
By Equation (1), the mercury intrusion curve can be obtained by the combination of the total volume of injected mercury and corresponding pressure change during the process of mercury intrusion. The pore diameter distribution can be obtained by differentiating the  
Figure 2: The mixing process of NS-modified silty clay.  
incoming mercury volume function, which depends on the independent variable of pore radius \(r\).  
\[f(r)=\frac{dV(r)}{dr} \tag{2}\]  
where \(V(r)\) is the accumulation of mercury influx (mL/g), and \(f(r)\) is the density function.  
The following relationship can be obtained if \(r\) approaches zero:  
\[\underset{r\to 0}{\lim}V(r)=\frac{e}{G_{s}} \tag{3}\]  
where \(G_{s}\) and \(e\) are the particle-specific gravity and pore ratios, respectively.