## 4 Results and Discussion  
### A Site  
Point A is located in Huwei Town, Yunlin County, with a sampling depth of 5.0-5.75 m and a groundwater level of 2.3 m. The soil sample A-2 belongs to poorly graded sandy soil, and it is classified as SP according to the USCS method. The soil unit weight is 2.02 t/m\({}^{3}\), the water content is 16.09%, and the specific gravity is 2.76. Figure 10a shows the soils liquefied at 15 cyclic times. Figure 10b indicates soil grain size distribution, from which most local soils are sandy soils, but the curve shows most soil particles contain a little fine. The shrinkage of the sample during cyclic loadings is not apparent for the A-2 specimen in Figure 10c, and we can find that the initial liquefaction occurred in the 10 th cyclic number from the excess pore water ratio developed curve in Figure 10d. Figure 10e displays the double strain of the specimen with respective cyclic axial strain. Figure 10f is the stress-strain diagram of the first five cycles for A-2. Only the first five cycles are used because they are easier to analyze, and the analysis results are more accurate. The shear modulus of the first five cycles can be obtained, and click on each to get the shear modulus curve. The spring coefficient k of A-2 can be obtained as k = 244e\({}^{-0.1\text{t}}\) kgf/cm. Due to liquefaction, the cyclic number of times is 15. The damping coefficient (c) of A-2 directly uses the damping ratio curve trend as the basis for the damping coefficient, and the damping ratio curve is obtained from the previous five cycles in Figure 10f. The damping coefficient c of A-2 can be c = 0.739e\({}^{-0.257}\) kgf-s/cm since the number of liquefaction times is 11.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Mass (m)** & **Spring Coefficient (k)** & **Damping Coefficient (c)** & **External Force (Q\({}_{0}\))** \\ \hline The degree of influence & medium & high & low & high \\ \hline \hline \end{tabular}
\end{table}
Table 9: Influence degree of each parameter of a mass-spring-damping system.  
The mass m, damping coefficient c, spring coefficient k, and external force Q\({}_{0}\) of point A are brought into the mass-spring-damping system calculation and compared with the liquefaction repeated triaxial test results, as shown in Figure 11. The strain of the first four cycles simulated by the mass-spring-damping system at point A has a relatively irregular amplitude, and the strain peak will have an upward trend as the number of cycles increases. The strain was obtained through repeated liquefaction triaxial tests. The peak value is flat, with no upward trend. After the eleventh cycle, there will be a more noticeable difference between the two. This may be related to the cumbersome simulation process and soil properties such as acceptable material content and ratio. The stress-strain diagram of this specimen is similar to taking the upper end of the block circle as the vertex and rotating clockwise from the lower left to the upper left; it is different from the stress-strain diagrams of the other three specimens.  
Figure 10: The results of the cyclic liquefaction triaxial test for the sample at site A.