# Effects of Polypropylene Fiber on the Liquefaction Resistance of Saturated Sand in Ring Shear Tests
## 2 Materials and Methods
### Test Procedure
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Test** & \(\mathbf{P_{\text{f}}}\) **(\%)** & \(\mathbf{e_{0}^{1}}\) & \(\mathbf{P_{\text{dra}}^{2}}\) & \(\mathbf{D_{\text{r}}^{3}}\) & \(\mathbf{B_{\text{D}}^{4}}\) & \(\mathbf{\sigma_{\text{con}}^{5}}\) & \(\mathbf{\tau_{\text{static}}}^{6}\) & \(\mathbf{\tau_{\text{cyclic}}}^{7}\) & \(\mathbf{f}^{8}\) & **Shear** \\  & & & **(g/cm\({}^{3}\))** & **(\%)** & **(kPa)** & **(kPa)** & **(kPa)** & **(kPa)** & **(kPa)** & **(Hz)** & **Method** \\ \hline T1 & 0 & 1.05 & 1.29 & 14.85 & 0.98 & 200 & 40 & / & / & STC-1 \\ T2 & 0.2 & 1.05 & 1.29 & 14.85 & 0.98 & 200 & 40 & / & / & STC-2 \\ T3 & 0.4 & 1.05 & 1.29 & 14.85 & 0.97 & 200 & 40 & / & / & STC-3 \\ T4 & 0.6 & 1.05 & 1.29 & 14.85 & 0.96 & 200 & 40 & / & / & STC-4 \\ T5 & 0 & 0.97 & 1.34 & 32.16 & 0.97 & 200 & 80 & / & / & STC-5 \\ T6 & 0.2 & 0.97 & 1.34 & 32.16 & 0.98 & 200 & 80 & / & / & STC-6 \\ T7 & 0.4 & 0.97 & 1.34 & 32.16 & 0.97 & 200 & 80 & / & / & STC-7 \\ T8 & 0.6 & 0.97 & 1.34 & 32.16 & 0.96 & 200 & 80 & / & / & STC-8 \\ T9 & 0 & 1.05 & 1.29 & 14.85 & 0.98 & 200 & 40 & 60 & 0.5 & CTC-1 \\ T10 & 0.2 & 1.05 & 1.29 & 14.85 & 0.98 & 200 & 40 & 60 & 0.5 & CTC-2 \\ T11 & 0.4 & 1.05 & 1.29 & 14.85 & 0.97 & 200 & 40 & 60 & 0.5 & CTC-3 \\ T12 & 0.6 & 1.05 & 1.29 & 14.85 & 0.96 & 200 & 40 & 60 & 0.5 & CTC-4 \\ T13 & 0 & 0.97 & 1.34 & 32.16 & 0.97 & 200 & 80 & 60 & 0.5 & CTC-5 \\ T14 & 0.2 & 0.97 & 1.34 & 32.16 & 0.98 & 200 & 80 & 60 & 0.5 & CTC-6 \\ T15 & 0.4 & 0.97 & 1.34 & 32.16 & 0.97 & 200 & 80 & 60 & 0.5 & CTC-7 \\ T16 & 0.6 & 0.97 & 1.34 & 32.16 & 0.96 & 200 & 80 & 60 & 0.5 & CTC-8 \\ \hline \hline \end{tabular}  
* \(\epsilon_{0}\) = void ratio after consolidation. \({}^{2}\)\(\rho_{\text{dra}}\) = dry density after consolidation. \({}^{3}\)\(D_{\text{r}}\) = relative density. \({}^{4}\)\(B_{0}\) = pore-water pressure coefficient. \({}^{5}\)\(\sigma_{\text{con}}\) = normal stress during consolidation. \({}^{6}\)\(\tau_{\text{static}}\) = initial shear stress. \({}^{7}\)\(\tau_{\text{cyclic}}\) = amplitude of the shear stress. \({}^{8}\)\(f\) = loading frequency.  
\end{table} 
Table 1: The primary information of performing tests used in this study. were considered in this study. The STC test indicates the properties of sand under successive ring shearing, while the CTC demonstrates sand anti-liquefaction behavior under successive rotations in both clockwise and anticlockwise directions. The designed test parameters of each test are summarized in Table 1. Thereafter, the drainage valve was closed to ensure an undrained state for the ring shear tests. During shearing in all tests, normal stress of 200 kPa was kept, which was loaded until liquefaction occurred or the steady value was reached. The static shear stress in STC was carried out with monotonic loading of a constant shear stress rate 1 kPa/s. The dynamic shear stress in CTC was performed with an amplitude of 60 kPa for the shear stress and a cyclic loading frequency of 0.5 Hz. In this study, the failure refers to the state after reaching the peak shear strength of specimens. The liquefaction refers to the phenomenon that sand suddenly changes from a solid state to liquid state. The normal stress, shear stress, excess pore pressure, shear displacement, vertical displacement and other parameters were measured continuously.