# Effects of Polypropylene Fiber on the Liquefaction Resistance of Saturated Sand in Ring Shear Tests
## 3 Results
### Cyclic-Torque-Controlled (CTC) Tests  
For CTC tests, the initial shear stresses are kept at 40 kPa and 80 kPa in specimens with higher and lower void ratios, respectively; whereas the applied shear stress amplitudes and the loading frequencies are kept at 60 kPa and 0.5 Hz, respectively. The measured shear strength of a specimen is predicted between \(40\pm 60\) kPa for loose sand and \(80\pm 60\) kPa for dense sand, and the amplitude of the tested data is lower than the maximum of the predetermined value. Before liquefaction, the amplitude of measured shear stress of a specimen is comparatively close to the maximum of the predetermined value. Nevertheless, when there is liquefaction, the amplitude of shear stress reduced rapidly and obviously lower than the maximum of the predetermined value. It is mainly induced by the variation in micro-structure inside the fiber-reinforced sand. The CTC test results are summarized in Table 3. The specimens were made with three different fiber contents and two different densities. The normal stress, pore pressure and shear stress against elapsed time are presented in Figure 7. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Test** & \(\mathbf{P_{f}}\)**(\%)** & \(\mathbf{\rho_{dra}}\) (**g/cm\({}^{3}\))** & \(\mathbf{N^{1}}\) & \(\mathbf{\boldsymbol{L_{cycle}}^{2}}\) (**mm)** & \(\mathbf{\boldsymbol{W_{cycle}}^{3}}\) (**\(\mathbf{\boldsymbol{j/m^{2}}}\))** & \(\mathbf{\boldsymbol{I_{total}}}\) (**mm)** & \(\mathbf{\boldsymbol{W_{total}}}\) (**\(\mathbf{\boldsymbol{j/m^{2}}}\))** \\ \hline CTC-1 & 0.00 & 1.29 & 3.00 & 14.71 & 581.20 & 78.17 & 2176.74 \\ CTC-2 & 0.20 & 1.29 & 50.00 & 280.23 & 11,767.08 & 459.96 & 16,188.95 \\ CTC-3 & 0.40 & 1.29 & 189.00 & 561.72 & 29,386.18 & 1066.55 & 46,866.21 \\ CTC-4 & 0.60 & 1.29 & 300.00\(\dagger\) & / & / & / & / \\ CTC-5 & 0.00 & 1.34 & 54.00 & 128.97 & 12,103.65 & 875.02 & 71,749.19 \\ CTC-6 & 0.20 & 1.34 & 301.00 & 719.56 & 64,148.68 & 1435.22 & 86,517.91 \\ CTC-7 & 0.40 & 1.34 & 558.00 & 890.21 & 87,849.17 & 1674.13 & 105,928.90 \\ CTC-8 & 0.60 & 1.34 & 600.00\(\dagger\) & / & / & / & / \\ \hline \hline \end{tabular}  
\({}^{1}N=\) number of cycles. \({}^{2}\)\(L_{cycle}=\) shear displacement of cycles. \({}^{3}\)\(W_{cycle}=\) shear energy of cycles.  
\end{table} 
Table 3: Results of cyclic-torque-controlled (CTC) tests. Figure 6: The peak shear stress and shear energy of specimens with different densities in STC tests: (**a**) 1.29 g/cm\({}^{3}\); (**b**) 1.34 g/cm\({}^{3}\). Figure 7a indicated that the monitored shear stress of unreinforced sand showed varied amplitudes with application of cyclic loading, due to the shear failure of the sand within the first cycle of applied shear stress. After four cycles, the shear stress decreased continuously and finally reached a very small value. The shear stress of reinforced sand with 0.2% fiber content in Figure 7a shows the same amplitude in shear stress as the applied one in the initial cyclic shearing period. The amplitude in each cycle decreased in the first 10 cycles, underwent a small increase in cycles 11-23 and then decreased until about cycle 50. Subsequently, the shear stress decreased rapidly to a small value. Shear stress amplitude decreased rapidly and then increased to keep a relative steady value in reinforced sand with 0.4% fiber content, as presented in Figure 7a. After 100 cycles, it becomes smaller with some ups and downs until the 189 th cycle where the shear stress reduces markedly to a very small value. The shear stress cyclic amplitude of reinforced sand with 0.6% fiber content is shown in Figure 7a as well; it shows a rapid change with a decrease and increase in shearing in the beginning, then it remains almost the same until the cyclic number becomes larger than 300. From the above results, it can be stated that the cycle number and amplitude increased markedly with the increase in the fiber content in loose specimens. With the increase of fiber content, a large number of reticular structures are formed in the specimen.