## 3 Results and Discussion
### Microscopic Observations
#### 3.2.5 Fiber Tensile Force  
Fibers perform their mechanical reinforcement function by working as tension-carrying members that transfer the shear stresses in the sand matrix into tensile resistance via the interface friction along their surface. Thanks to the bond that develops between the particles, the parallel-bond contact model allows for the development of tensile forces. The tensile force along the fibers was calculated by the total tensile force at parallel-bonded contacts. Figure 14 displays the variation of the tensile force computed for all bond contacts in the fibers within the FRS samples. Figure 14 clearly shows that the mobilization of tensile force inside the reinforcing fibers is strongly influenced by shear displacement. A gradual increase of the tensile force in the fibers was recorded as the shear displacement increases up to 6 mm, which indicates the contribution of fibers progressively mobilized during the process. However, above a shear displacement of 6 mm, the tensile force is relatively stable and stays high. These results further support the idea that mobilization of the fiber reinforcement generally requires a certain horizontal displacement in the shear stress-displacement curve of the FRS.  
The modeling results also clearly show that significant differences of fiber tensile force exist in FRS with different fiber orientations. Obviously, the highest tensile force was mobilized when fibers were placed at an angle of 60\({}^{\circ}\), with successively lower mobilization at 90\({}^{\circ}\), 30\({}^{\circ}\), and lastly 0\({}^{\circ}\). Interestingly, the tensile force in the specimen with horizontal fibers is nearly zero, which suggests that horizontal fibers have no effect on reinforcement. The change laws of mobilized tensile force following the change  
Figure 14: Evolution of fiber tensile force.  
Figure 13: Evolution of coordination number for sand–fiber contact.  
of fiber orientation is in accordance with laws of stresses and displacements in the FRS composite. This could confirm that fiber reinforcement was actually influenced by the fiber tensioning process.  
Contribution of fibers to the shear strength is effective when FRS are subjected to tension, although the fibers play no role in compression as they may buckle or kink [44]. Figure 15 shows the spatial distributions of the contact force in fibers for different shear displacements. The figure shows that fibers may be subject to tension (yellow) or pressure (blue) in FRS with different fiber orientations and horizontal displacements. To analyze the difference quantitatively, Figure 16 shows the proportion of numbers of tensile contacts to the total number of contacts in fibers. Obviously, most of the fibers in different samples are subjected to tension at the initial state, although the value is very small. The number of tensile contacts in fibers with fiber orientations of 0\({}^{\circ}\) and 30\({}^{\circ}\) first decreased and then increased to a stable value. However, the number of tensile contacts in FRS with fiber orientations of 90\({}^{\circ}\) and 60\({}^{\circ}\) always stayed high during the whole progression. The FRS with fiber orientation of 60\({}^{\circ}\) had the highest numbers of tensile contacts, which contributes to the understanding that the fiber initial orientations of 60\({}^{\circ}\) mobilized the largest tensile force.  
Figure 15: Spatial distributions of force in fibers (blue: compression; yellow: tension).