# Effects of Polypropylene Fiber on the Liquefaction Resistance of Saturated Sand in Ring Shear Tests
## 3 Results
### Shear-Torque-Controlled (STC) Tests
0.7, the shear energy elevated from approximately 1440 to 1995 J/m\({}^{2}\), 1881 to 2602 J/m\({}^{2}\) and 3398 to 4465 J/m\({}^{2}\), with an increment of 555 J/m\({}^{2}\), 721 J/m\({}^{2}\) and 1067 J/m\({}^{2}\), respectively. With the increase of fiber content, a large number of reticular structures formed in the specimen. The existence of a mesh structure restricts the movement of sand particles, which enables more energy to be used to overcome the resistance between sand particles. As seen in Figure 5b, the pore pressure ratio of unreinforced sand with a density of 1.34 g/cm\({}^{3}\) increased gradually within the shear displacement range approximately 0-0.3 mm, decreased during the shear displacement approximately 0.3-1.3 mm, and then again increased gradually in the shear displacement range of approximately 1.3-99.6 mm, finally reaching a steady value of approximately \(r_{\rm u}\) being 0.5. When the shear deformation of specimens increased from 8.9 to 99.6 mm, pore pressure increased from approximately 0.1 to 0.5, and shear energy enhanced from about 954 to 5618 J/m\({}^{2}\). Therefore, it is concluded that sand requires a large amount of energy from destruction to liquefaction during the shearing process. For the fiber-reinforced specimens in Figure 5b, the pore pressure ratio showed a variation in shape, increasing then decreasing at the beginning, like the unreinforced sand. After that, a fluctuating increment in pore pressure ratio was observed approximately from 0.05 to 0.5, 0 to 0.63 and 0 to 0.85, respectively, until they changed to a comparatively constant value. These fluctuations turned to be more violent with an increment in fiber addition amount, which was related to the interfacial interactions in the specimen. The interfacial interactions between sand and fibers are greatly affected by fiber content. As fiber content increased, the fiber formed a large number of mesh structures in the specimen, which improved interfacial interactions. The roughness of the fiber surface plays a vital role in fiber sliding resistance [39]. Thus, the shear stress of reinforced sand increased with the increase in fiber content and more energy was spent to overcome the resistance. The shear energy elevated approximately from 2087 to 17,757 J/m\({}^{2}\), 57,977 to 253,479 J/m\({}^{2}\) and 68,227 to 325,217 J/m\({}^{2}\), with an increment of 15,670 J/m\({}^{2}\), 195,502 J/m\({}^{2}\) and 256,990 J/m\({}^{2}\), respectively. The peak shear stress and shear energy of tested specimens are given in Figure 6. As shown in Figure 6a, the peak shear stress of loose sand is not affected much by fiber reinforcement, and the shear energy until peak shear stress (\(W_{\rm peak}\)) and total shear energy until liquefaction (\(W_{\rm total}\)) increases with the fiber content. It is seen from Figure 6a and Table 2 that the shear energy in unreinforced specimens mainly dissipates before shear strength attains the peak value; however, in the case of all fiber-reinforced specimens the shear energy dissipated after reaching the peak value. The total shear energy \(W_{\rm total}\) in reinforced specimens with fiber contents of 0.2%, 0.4% and 0.6% was approximately 1995 J/m\({}^{2}\), 2602 J/m\({}^{2}\) and 4465 J/m\({}^{2}\), which was 1.9, 2.5 and 4.3 times that of the unreinforced specimens, respectively. The fiber made it difficult for specimens to engage in liquefaction. The specimens need to consume more energy to liquefy after reaching the peak shear resistance. As shown in Figure 6b, the peak shear stress of specimens with a higher density increased with the increase of fiber contents for denser specimens and were more strongly affected by the fiber content than the looser specimens as shown in Figure 6; they were 129.8 kPa, 137.3 kPa, 186.6 kPa and 187.67 kPa for the fiber contents of 0%, 0.2%, 0.4% and 0.6%, respectively. The interfacial interactions between sand and fibers are greatly affected by sand dry density.