## 3 Results and Discussions
### Peak Strength  
The peak strength of sand is the maximum shear stress reached during the shearing process, which is an important feature to measure its mechanical performance. To reflect the influences of fiber strips on the peak strength of sand, the peak strength ratios, defined as the ratio of peak shear stress of reinforced sand to that of unreinforced sand [13], were calculated and are listed in Table 2. According to its definition, a peak strength ratio larger  
Figure 3: Shear stress–displacement responses of sand specimens in direct shear tests under normal pressure of 100 kPa initially oriented at (**a**) 60\({}^{\circ}\), (**c**) 90\({}^{\circ}\), and (**e**) 120\({}^{\circ}\) and under normal pressure of 400 kPa initially oriented at (**b**) 60\({}^{\circ}\), (**d**) 90\({}^{\circ}\), and (**f**) 120\({}^{\circ}\). than 1.0 meant that the fiber strips provided an enhancement effect on the peak strength of sand, whereby a larger peak strength ratio led to a larger enhancement effect of fiber strips. As can be observed from Table 2, for the specimens sheared at the same normal pressure and fiber content, the peak strength ratios decreased with the initial orientation angle. For most specimens, the fiber strips initially orientated at 60\({}^{\circ}\) and 90\({}^{\circ}\) increased the peak strength of sand, as indicated by the peak strength ratios greater than 1.0. The effects of fibers initially orientated at 60\({}^{\circ}\) were more significant. In contrast, the fiber strips initially orientated at 120\({}^{\circ}\) did not improve and, in some cases, even weakened the sand, as indicated by the peak strength ratios smaller than or equal to 1.0. Similar results were also obtained by [12,14]. As mentioned in Section 1, the influence of initial orientation angle of fiber on sand strength may be explained by the stress mobilization in fibers. As measured by [15], the direction of the principle tensile strains in a dense sand specimen was close to 60\({}^{\circ}\) relative to the shear direction. Therefore, the tensile stress in fiber strips initially orientated at 60\({}^{\circ}\) in this study could be mobilized most effectively; and the most obvious reinforcement effects were observed. For the fibers initially oriented at 90\({}^{\circ}\), because the normal strain in the oblique plane vertical to the fibers was still in the tensile direction, they still provided a reinforcement effect. However, when the fibers were rotated to an angle such that the compressive strain was more dominant on the corresponding oblique plane, such as in the case of the 120\({}^{\circ}\) initial orientation, they had a negative effective reinforcement effect because they were in compression. In this situation, the fibers could even reduce the peak strength of sand because the compressed fibers could reduce the density of nearby sand. For the sand specimens with fiber strips of same initial orientation angle, their peak strength ratios increased with the increase in fiber content. This is consistent with the common perception. When the fiber content and initial orientation angle were the same, the peak strength ratios decreased with the increase in normal pressure. According to the Mohr-Coulomb strength criteria of granular materials, the strength of pure sand increases proportionally with the increase in normal pressure. However, the decrease in peak strength ratios indicated that the strength increments induced by the fiber strips did not increase proportionately with normal pressure. This phenomenon is further discussed below by considering the shear strength envelopes of sand specimens obtained from peak strength data. As shown in Figure 4, with the exception of sand specimens with a fiber content of 0.04% and fiber initially orientated at 120\({}^{\circ}\), the strength envelopes of other specimens were all lifted by introducing fiber strips.