## 3 Direct Shear Test
### Test Results and Analysis  
According to the test data, the relationship between shear force (\(F\)) and shear displacement (\(s\)) of polypropylene-fiber-reinforced iron tailings powder can be plotted, as shown in Figure 6. In Figure 6, (a)-(e) correspond to the \(F\)-\(s\) curve of the sample under the normal stresses of 100, 200, 300, and 400 kPa when the polypropylene fiber dosage is 0%-1%.  
Figure 6: _Cont._According to the F-s curve, the shear force corresponding to the 4 mm shear displacement is the peak force \(F_{\text{max}}\)[34]. The peak shear strength \(\tau_{\text{max}}\) is calculated according to Equation (1). According to the Mohr-Coulomb principle (Equation (2)), the cohesive force c and the internal friction angle \(\varphi\) of the reinforced iron tailings powder with different polypropylene fiber dosages can be calculated and plotted in Figure 7.  
\[\tau_{\text{max}}=\frac{F_{\text{max}}}{A} \tag{1}\]  
\[\tau=c+\sigma\tan\varphi \tag{2}\]  
It can be seen from Figure 7 that with the addition of polypropylene fibers, the cohesive force firstly increases and then gradually decreases. When the dosage was increased from 0% to 0.25%, the cohesive force increased from 12.3 to 31.9 kPa. When the dosage was increased from 0.25% to 1%, the cohesive force gradually decreased from 31.9 to 9 kPa, which was lower than that of iron tailings powder with no fiber dosage. When the fiber dosage was increased from 0% to 0.25%, a small amount of fiber filled the pores between the iron tailings powder, taking advantage of the spatial constraint effect, so as to increase the cohesive force of fiber-reinforced iron tailings powder. When the fiber dosage was increased from 0% to 0.25%, the agglomeration effect of fiber was increased due to the increase of fiber. The cohesive force of fiber-reinforced iron tailings powder was decreased on account of the spatial constraint effect finding it hard to proceed.  
With the increase of fiber dosage, the internal friction angle of polypropylene-fiber-reinforced iron tailings powder firstly decreases and then increases. When the fiber dosage was increased from 0% to 0.25%, the internal friction angle was reduced from 31.7 to 29.3\({}^{\circ}\). When the fiber dosage was increased  
Figure 6: \(F\)-\(s\) curve with different polypropylene fiber dosages. (**a**) 0% polypropylene fiber dosage [33] (**b**) 0.25% polypropylene fiber dosage; (**c**) 0.5% polypropylene fiber dosage; (**d**) 0.75% polypropylene fiber dosage; (**e**) 1% polypropylene fiber dosage.  
from 0.25% to 1%, the internal friction angle increased from 29.3 to 35.3\({}^{\circ}\). When the fiber dosage was increased from 0% to 0.25%, the fiber was dispersed among the iron tailings powder. A small amount of fiber cannot produce an obvious friction effect, and the internal friction angle of iron tailings was decreased due to the particle spacing of iron tailings being increased. When the fiber dosage was increased from 0.25% to 1%, the combination form between fiber and iron tailings was diversified due to the fiber density in the same volume being increased, and the angle of internal friction was large due to the strengthening of the friction effect.  
It can be concluded from the direct shear test results that when the fiber dosage is between 0% and 0.25%, the cohesive force increases, the internal friction angle decreases; when the fiber dosage is between 0.25% and 1%, the cohesive force decreases, and the internal friction angle increases. Therefore, it is difficult to analyze the reinforcement effect of polypropylene fiber on iron tailings powder using the variation law of cohesive force and internal friction angle. Other parameters are needed to describe the reinforcement effect of polypropylene fiber.