## 3 Results and Discussion
### Experimental Results and Analysis  
#### 3.2.1 Results of Cyclic Triaxial Tests  
To assess the feasibility of applying the aforementioned results from the literature in practical settings, a series of tests were performed on the specimens of sandy soil containing fines with three different PI values (i.e., Liugui fines from Kaohsiung, mudstone, and kaolinite). The fines were added at 15% and 30% by weight to replace the same weights of the original soils. The liquefaction resistance and PWP curves of the non-plastic, low-plasticity, and high-plasticity soils were obtained from the experimental results. In the experiment, kaolinite (PI = 32), mudstone (PI = 12.4), and Liugui fines (PI = 5.7) were added to the Kaohsiung Liugui sandy soils at 15% and 30% by weight to replace the same weights of the original soils. Reconstituted specimens were produced through wet tamping and with a fixed dry soil unit weight (\(\gamma_{\rm d}\)) of 16.57 kN/m\({}^{3}\). The repeated triaxial tests were conducted under the same effective confining pressure (100 kPa). Initial liquefaction was reached when the PWP ratio (Ru) reached 1.0. Table 4 lists the results of the experiments performed using different specimens. Sand-0x is used to denote clean sand specimens, and S, M, and K are used to denote specimens containing Liugui fines, mudstone, and Kaolin, respectively. FC15 and FC30 are used to denote weight percentages of 15% and 30%, respectively. The cyclic numbers (No.) corresponding to each excess PWP ratio (Ru) are also listed in Table 4. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Specimen** & **FC (\%)** & **CSR** & **No. (Ru = 0.2)** & **No. (Ru = 0.5)** & **No. (Ru = 0.7)** & **No. (Ru = 0.9)** & **No. (Ru = 1.0)** \\ \hline Sand-01 & & 0.14 & 7 & 52 & 78 & 85 & 92 \\ Sand-02 & 0 & 0.18 & 2 & 26 & 46 & 51 & 55 \\ Sand-03 & & 0.22 & 1 & 8 & 12 & 15 & 16 \\ \hline S-FC15-01 & & 0.17 & 2 & 10 & 19 & 33 & 60 \\ S-FC15-02 & 15 & 0.21 & 3 & 7 & 10 & 26 & 45 \\ S-FC15-03 & & 0.26 & 2 & 5 & 8 & 16 & 32 \\ \hline S-FC30-01 & & 0.19 & 1 & 2 & 8 & 23 & 139 \\ S-FC30-02 & 30 & 0.23 & 2 & 5 & 12 & 23 & 69 \\ S-FC30-03 & & 0.27 & 1 & 3 & 8 & 15 & 48 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: List of the results of the experiments performed using different specimens. Figure 9: The \(\beta\) value in the model developed by [PERSON] et al. [42] should be between 20 and 250 with comparison with experimental data between red and blue solid lines. Figure 10 plots the CSRs against the cyclic numbers from Table 3 (Ru = 1.0). As indicated in the figure, regardless of the types of fines in the specimens, when the added fines were all plastic fines, the curves of the specimens with FCs of 30% were above those of the specimens with FCs of 15%. This suggests that increasing the plastic FC of soil can strengthen its liquefaction resistance. Among the specimens with FCs of 15%, specimens containing mudstone and Liugui fines had corresponding cyclic resistance curves similar to the curves of the clean sand specimens. By contrast, the curves of the specimens containing kaolinite fines shifted significantly upward. Therefore, when the fines had low PI values and the FCs of the specimens were low, the fines in the specimens did not effectively increase the liquefaction resistance of the specimens. However, when the fines had high PI values, they increased the liquefaction resistance of the specimens. As seen in the figure, the curves of the specimens shifted upward as the PI values of the fines increased. Under the same cyclic number, the pure sandy soils and kaolinite required the lowest and highest cyclic shear ratios, respectively, to reach initial liquefaction. This suggests that the liquefaction resistance is proportional to the PI value of soils. The liquefaction resistance of the specimens varied widely, and the differences in the viscosity of the specimens could be easily noticed during the reconstitution process.