## 4 Results and Discussions
### Microscopic Characteristics of NS-Modified Silty Clay
The four components are approximately arranged according to a certain regularity (the center to outer layers are the soil particles, NS particles, or pore solution, and air, respectively) [32; 33]. However, the sizes, shapes, and mineral components of the soil particles are various due to geological and environmental processes [34]. The surface of soil particles or the voids of soil-water systems are randomly filled with water, NS particles, and air. Therefore, even at the same NS addition, the microstructures of fifty NS-modified Qinghai-Tibet silty clay specimens show significant randomness and variability (Figures 5 and 6). For instance, compared to the minimum median pore diameter of each NS addition, the range abilities for NS contents of 0, 0.25%, 1%, and 3% are 10.05%, 19.14%, 26.17%, and 16.69%, respectively. Similarly, the range abilities of \(V_{D<0.1\ \mu\)m for NS contents of 0, 0.25%, 1%, and 3% are 21.89%, 16.72%, 25.28%, and 14.50%, respectively. Figure 5: Determination of median pore size of soil samples with different NS contents. Figure 6: Determination of \(V_{D<0.1\mu\)m of soil samples with various NS contents. As indicated in Figure 5, the values of median pore size of all NS-modified Qinghai-Tibet silty clay are smaller than that of the plain silty clay. For instance, the median pore diameter of NS-modified Qinghai-Tibet silty clay ranges from 124.72 nm to 157.35 nm when the addition is 1%. The standard deviation and mean value are 10.25 nm and 139.10 nm, respectively. Box plots were used to reflect the variability of the median pore size of NS-modified Qinghai-Tibet silty clay (Figure 5b). Because the micro-pores of a soil-water system are filled by nano-material, the pore filling rate increases with the increase of the NS addition amount, and the median pore diameter decreases. It is very interesting to find that the addition of NS distinctly decreases the median pore diameter; the addition of 0.25%, 1%, and 3% decreases the median pore diameter by 11.20%, 15.29%, and 43.30%, respectively. Therefore, it is essential to study the variability of the median pore size of soil modified by NS. As observed from Figure 6, the addition of NS slightly increases the \(V_{D<0.1\ \upmu\text{m}}\) when the NS addition ranges from 0 to 1%. For example, the incorporation of 0.25% and 1% NS increases the \(V_{D<0.1\ \upmu\text{m}}\) values by 2.32% and 10.63%, respectively, compared to the plain Qinghai-Tibet silty clay. However, the mean \(V_{D<0.1\ \upmu\text{m}}\) has a sharp increase from 36.07% to 52.17% when NS content increases from 1% to 3%. In addition, it is more noticeable that the maximum difference reaches 8.07% in the variability of the \(V_{D<0.1\ \upmu\text{m}}\) with an NS content of 1% while the mean value of \(V_{D<0.1\ \upmu\text{m}}\) is only 36.07%. Meanwhile, the \(V_{D<0.1\ \upmu\text{m}}\) values of NS-modified silty clay with NS contents of 0, 0.25%, and 3% varies distinctly, with values ranging from 29.25% to 35.65%, 31.13% to 36.34%, and 48.81% to 55.89%, respectively. Hence, it cannot be determined precisely by limited specimen tests that the \(V_{D<0.1\ \upmu\text{m}}\) of NS-modified Qinghai-Tibet silty clay.