# Effects of Polypropylene Fiber on the Liquefaction Resistance of Saturated Sand in Ring Shear Tests
## 3 Results
### Cyclic-Torque-Controlled (CTC) Tests
These reticular structures could effectively resist the effects of external forces, allowing the specimen to withstand more shear cycles compared with specimens with low fiber content. At the same time, a large number of fibers raised the interfacial interactions between sand and fibers, which prevented specimens from deforming under small shear stress. The change curves of pore pressure in Figure 7a showed that after cyclic loading, the pore pressure built up quickly, especially for specimens with a higher fiber content. The shear contraction phenomenon occurred in specimens during several shear cycles, which lead to an increase in pore pressure. The unreinforced sand underwent a slow increase and reached a steady and large value (see Figure 7a). The specimens with fiber content of 0.2%  
Figure 7: The normal stress, pore pressure and shear stress against elapsed time for specimens with different densities in CTC tests: (**a**) 1.29 g/cm\({}^{3}\); (**b**) 1.34 g/cm\({}^{3}\). and 0.4% kept almost the same value and then had a second increase, whereas the specimen with 0.6% fiber content showed a small amplitude around a value approximately equal to 65% of normal stress. For specimens with a higher density of 1.34 g/cm\({}^{3}\), the shear stress of unreinforced sand (Figure 7b) showed that the amplitude occurred after the cyclic shearing, but the amplitude became weaker markedly. After 56 cycles, the shear stress dropped rapidly to a very small value while liquefaction was triggered. The shear stress of the reinforced specimen with fiber content of 0.2% (Figure 7b) showed full amplitude (60 kPa) at the start of shearing, and then decreased to about one-third of the full amplitude. Afterwards the shear stress changed about 200 cycles with this amplitude and 50 cycles with very little amplitude and subsequently, the shear stress decreased rapidly to a very small value. Figure 7b also shows that the shear stress of specimens with a fiber content of 0.4% showed a fluctuating amplitude; the largest amplitude of 40 kPa was two-thirds of the full amplitude and the lowest amplitude occurred four times during the cyclic shearing. Finally, the shear stress dropped rapidly to a very small value. The shear stress of specimens with a fiber content of 0.6% (Figure 7b) showed a different change trend in that the shear stress kept almost half of the full amplitude and then its amplitude increased slowly to the full amplitude. Subsequently, it kept almost the same until the cyclic number reached larger than 600. Comparing these results, it can be stated that the cycle number and main amplitude increased with the increase in the fiber content of dense specimens. With the increase of fiber content, a large number of reticular structures are formed in the specimen. These reticular structures could effectively resist the effects of external forces, allowing the specimen to withstand more shear cycles compared with specimens with a low fiber content. At the same time, a large number of fibers raised the interfacial interactions between sand and fibers, which prevented the specimens from deforming under small shear stress. As shown in Figure 7b, the pore pressure of all the unreinforced and fiber-reinforced specimens had some cycles with a small amplitude at the initial cyclic shearing period. It had a second increase quickly to a very high value for the specimens with fiber contents of 0%, 0.2% and 0.4%, but kept almost the same in the whole shearing period with 600 cycles for the reinforced specimens with a fiber content of 0.6% (Figure 7b). In this study, we also used the cycle number to evaluate the resistance to liquefaction of the sand-fiber matrix. A cycle is defined as when a specimen changes from the balance position and undergoes a rotation cycle in both clockwise and anticlockwise directions to the balance position again. The greater the cycle number, the better the liquefaction resistance of the specimen.