# Effects of Polypropylene Fiber on the Liquefaction Resistance of Saturated Sand in Ring Shear Tests
## 3 Results  
### Shear-Torque-Controlled (STC) Tests  
For STC tests, the initial shear stress is 40 kPa in specimens with a higher void ratio and 80 kPa in specimens with a lower void ratio; the shear stress loading rate is 0.8 kPa/sec. The STC tests results are summarized in Table 2. Three different fiber contents and two different densities were considered in the experimental tests. The normal stress, pore pressure and shear stress against elapsed time are presented in Figure 4. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Test** & \begin{tabular}{c} **P\({}_{\text{f}}\)** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **\(\rho_{\text{dra}}\)** \\ **(g/cm\({}^{3}\))** \\ \end{tabular} & \begin{tabular}{c} **\(\tau_{\text{peak}}\)1** \\ **(kpa)** \\ \end{tabular} & \begin{tabular}{c} **\({}_{\text{peak}}\)2** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **\({}_{\text{peak}}\)3** \\ **(J/m\({}^{2}\))** \\ \end{tabular} & \begin{tabular}{c} **\({}_{\text{peak}}\)4** \\ **(J/m\({}^{2}\))** \\ \end{tabular} & \begin{tabular}{c} **\({}_{\text{peak}}\)5** \\ **(J/m\({}^{2}\))** \\ \end{tabular} & \
\begin{tabular}{c} **\({}_{\text{total}}\)6** \\ **(J/m\({}^{2}\))** \\ \end{tabular} &
\begin{tabular}{c} **\({}_{\text{Wtotal}}\)7** \\ **(J/m\({}^{2}\))** \\ \end{tabular} \\ \hline STC-1 & 0.00 & 1.29 & 63.23 & 0.19 & 2.08 & 117.46 & 0.81 & 36.45 & 1040.89 \\ STC-2 & 0.20 & 1.29 & 70.40 & 0.22 & 25.36 & 1440.19 & 0.72 & 39.75 & 1995.13 \\ STC-3 & 0.40 & 1.29 & 71.20 & 0.29 & 32.83 & 1881.33 & 0.71 & 52.53 & 2601.52 \\ STC-4 & 0.60 & 1.29 & 71.45 & 0.27 & 56.62 & 3397.90 & 0.67 & 79.98 & 4465.08 \\ STC-5 & 0.00 & 1.34 & 129.78 & 0.12 & 8.92 & 954.45 & 0.51 & 99.63 & 5618.07 \\ STC-6 & 0.20 & 1.34 & 137.28 & 0.05 & 16.69 & 2087.41 & 0.50 & 315.41 & 17,756.63 \\ STC-7 & 0.40 & 1.34 & 186.57 & \(-\)0.27 & 358.54 & 57,977.46 & 0.85 & 3920.68 & 253,479.20 \\ STC-8 & 0.60 & 1.34 & 187.57 & \(-\)0.07 & 563.70 & 68,227.40 & 0.85 & 4705.94 & 325,217.30 \\ \hline \hline \end{tabular}  
* \(\tau_{\text{peak}}\) = peak shear stress. 2 \({}_{\text{r}_{\text{tot,peak}}}\) = pore pressure ratio until peak shear resistance. 3 \({}_{\text{total}}\) = shear displacement until peak shear resistance. 4 \(W_{\text{post}}\) = shear energy until peak shear resistance. 5 \({}_{\text{r}_{\text{tot,up}}}\) = the highest pore pressure ratio until shearing. 6 \({}_{\text{total}}\) = total shear displacement until liquefaction. 7 \(W_{\text{total}}\) = total shear energy until liquefaction.  
\end{table} 
Table 2: Results of shear-torque-controlled (STC) tests. As seen in Figure 4a, the pore pressure and shear stress of unreinforced and reinforced loose specimens have a similar change trend. At the beginning, the pore pressure and shear stress were in increased proportion to an increment of shearing elapsed time. After the peak shear strength was reached, the specimen failed, the shear stress showed a quick reduction and then decreased slowly until it reached a steady value, meaning that the reduction rate of shear strength trended towards zero. At the same time, the pore pressure grew sharply first and then increased slowly till reaching a relative constant value. Figure 4a also shows that the fiber inclusion and fiber content played a light effect on the pattern of the plots. As shown in Figure 4b, fiber addition and fiber content both significantly influenced the variation of pore pressure and shear stress. Furthermore, the effects induced by fiber reinforcement on dense sand were more obvious than that on loose specimens, as shown in Figure 4a. For the unreinforced specimens (Figure 4b), at the beginning of undrained shearing, the pore pressure displayed an increased trend with an increase in shearing displacement. When the shear displacement reached a certain value, the specimen expanded due to the continuous increase of shear displacement, which leads to a decrease in pore pressure.