# Effects of Polypropylene Fiber on the Liquefaction Resistance of Saturated Sand in Ring Shear Tests
## 3 Results
### Shear-Torque-Controlled (STC) Tests
After the peak shear strength was reached, the specimen failed and the shear stress then decreased slowly, and finally dropped to approximately 24.5 kPa. Due to the constant shear and the stable normal stress, the pore pressure increased gradually with shear displacement. When the shear stress tends to be stable, the pore pressure also tends to be stable. The fiber-reinforced specimens showed similar change trends as the unreinforced sand before reaching peak shear strength. Thereafter, the reinforced specimens, unlike the unreinforced sand, showed a fluctuating decrease in shear stress for some time after shear failure, until they finally dropped to a relative steady value, that is, the variation amplitude of shear strength was comparatively lower than before (see in Figure 4b). The fluctuations were stronger with increasing fiber contents, which was related to the interfacial interactions in the specimen. The interfacial interactions between sand and  
Figure 4: The normal stress, pore pressure and shear stress against elapsed time for specimens with different densities in STC tests: (**a**) 1.29 g/cm\({}^{3}\); (**b**) 1.34 g/cm\({}^{3}\). fibers are greatly affected by fiber content. As fiber content increases, the fiber formed a large number of mesh structures in the specimen, which improved interfacial interactions. The pore pressure ratio (\(r_{\text{u}}\)) and dissipated energy against with elapsed time are presented in Figure 5.  
As seen in Figure 5a, the pore pressure ratio of unreinforced sand increased quickly within the shear displacement ranging from approximately 2 mm to 6 mm, and then increased slowly to the comparatively constant value with \(r_{\text{u}}\) being approximately 0.80. Figure 5a also shows that there was no liquefaction before the shear deformation of 36.5 mm. It took about 292 and 1041 kJ/m\({}^{3}\) to induce deformation of 6 and 36.5 mm, respectively. Despite such variation in shear deformation (i.e., 6 mm to 36.5 mm), the pore pressure ratio change was less than 0.15. During the shearing process, the consumption of external shear energy can be classified as two categories, one part was consumed by generating plastic deformation, including particles rearrangement, bonding distortion, and grain crushing, and another was consumed by sand grains as internal energy in the form of heat, kinetic, or surface energy of sand grains. It was hence predicted that when the shear deformation exceeded 6 mm, in addition to the pore pressure generation, the frictional heat and others also contributed to the consumption of external shear energy. For the fiber-reinforced loose specimens in Figure 5a, the pore pressure ratios had an obvious increment in the shear displacement range of specimens approximately 25 to 40 mm, 33 to 53 mm and 57 to 80 mm with fiber contents of 0.2%, 0.4% and 0.6%, respectively. After that, the pore pressure ratios of all three fiber-reinforced specimens moved immediately to a relatively constant value with \(r_{\text{u}}\) being approximately 0.7. It is different from the unreinforced specimen in the sense that the shear energy in specimens reinforced with fiber contents of 0.2%, 0.4% and 0.6% mainly dissipated during the beginning period within the deformation range of about 0-25 mm, 0-33 mm and 0-57 mm, respectively, while the pore pressure ratio increased by approximately 0.3 and the shear strength reached the peak value. In this initial shearing period, the shear energy elevated approximately to 1440 J/m\({}^{2}\), 1881 J/m\({}^{2}\) and 3398 J/m\({}^{2}\) for specimens reinforced with fiber contents of 0.2%, 0.4% and 0.6%, respectively. Yet in the pore pressure ratio range from 0.3 to  
Figure 5: The pore pressure ratio \(r_{\text{u}}\) and dissipated energy against with elapsed time for specimens with different densities in STC tests: (**a**) 1.29 g/cm\({}^{3}\); (**b**) 1.34 g/cm\({}^{3}\).