# Effects of Polypropylene Fiber on the Liquefaction Resistance of Saturated Sand in Ring Shear Tests
## 3 Results
### Stress Paths and the Collapsed Structure of Specimens  
The effective stress paths of tested specimens are presented in Figures 9 and 10. As seen in Figure 9, the trends of the effective stress paths variation of specimens at a density of 1.29 g/cm\({}^{3}\) were similar under the same shear method. For STC tests, soon after the shearing was started, the stress path moved left-upward first, which was due to the formation of pore pressure. After the specimen failed, the path changed by falling downward until it was finally steady because of the quick increase in pore pressure. For CTC tests, the stress path of unreinforced sand shifted obviously to the left within the first three cycles, and finally tended to a very small value. The stress paths shifted leftward markedly within the first five, three and four cycles for the fiber reinforcement of 0.2%, 0.4% and 0.6% respectively, and then had a series of continued cycles around a point.  
Figure 8: The cycle numbers of two group specimens with 1.29 and 1.34 g/cm\({}^{3}\) densities in CTC tests.  
Figure 9: The effective stress paths of specimens with 1.29 g/cm\({}^{3}\) density.  
The effective stress paths of specimens with a density of 1.34 g/cm\({}^{3}\) are presented in Figure 10. As seen, in STC tests, the path of unreinforced sand before the failure was like an \"elbow\" shape with a turning point. Due to the formation of pore pressure, the path first moved left and upward. The turning point was induced by the expansion of the specimen, resulting in a reduction in pore pressure. Therefore, it was a right and upward movement in the effective stress path. After the specimen failed, the sharp increase in pore pressure led to a great shift of the path towards the left and down, until a relative stable value was achieved. Fiber reinforcement significantly affected the effective stress path, in addition to the fluctuation between the peak and steady value, the degree of fluctuation became stronger with an increase in fiber content. For CTC tests, the change trends of effective stress paths of specimens with zero and 0.2% fiber addition were similar and the stress paths shifted leftward with lots of cycles and finally swarmed towards a very small value. The stress path of specimens with a fiber content of 0.4% showed a slow shift to the left with dense cycles and finally decreased rapidly to a very small value. The stress path of specimens with a fiber content of 0.6% had no remarkable shift towards the left and a series of cycles almost kept them around a point. It seems that the presence of fiber had almost no effect on the type of stress path for specimens with the same density.  
Some typical photographs of the specimens after shearing are presented in Figure 11. As shown, the fully liquefied unreinforced specimens with density of 1.29 g/cm\({}^{3}\) show a completely collapsed structure, and the ones with a higher density of 1.34 g/cm\({}^{3}\) collapsed partly. All the fiber-treated specimens maintained structural stability, especially the ones with fiber content of 0.4% and 0.6%. It is speculated that the lateral failure (a phenomenon when the liquefied specimen collapses when the lateral support is removed) of the sand induced by liquefaction can be limited or even prevented by mixing the fibers. This investigation was in agreement with the phenomenon found by [PERSON] et al. in triaxial undrained tests [18]. The fiber variation after performing ring shear tests was also considered, and we found that the fiber showed obvious orientation in dense reinforced sand while that in loose sand still maintained a comparatively random distribution. Also, the surface of some fiber monofilament in dense reinforced specimens was with fine scratches, and light elongation. These results all demonstrated that fiber inclusion significantly improved the liquefaction resistance of reinforced sand, especially dense sand.  
Figure 10: The effective stress paths of specimens with 1.34 g/cm\({}^{3}\) density.