## 3 Test Results and Analysis
### Strength Curve  
In order to draw the strength envelope of PCS samples and obtain their strength parameters, the peak of q is used as the failure point, where q = \(\sigma 1-\sigma 3\); taking the normal stress as the abscissa, the shear stress as the ordinate, (\(\sigma 1+\sigma 3\))/2 as the center, and (\(\sigma 1-\sigma 3\))/2 as the radius on the abscissa, the ultimate stress diagram is drawn on the \(\tau\)-\(\sigma\) stress plan graph, as shown in Figure 6; and the envelope of the ultimate stress circle under different confining pressures is drawn as shown in Figure 7; the strength parameters \(c\) and \(\phi\) of the samples are obtained from the strength envelope, as shown in Table 4.  
Figure 6: \(Cont.\)  
Figure 6: _Cont._  
The relationship between the cohesion and the internal friction angle of PCS samples and fiber mass content can be obtained by referring to Figures 6 and 7, and Table 4, as shown in Figures 8 and 9.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fiber Mass Content (\%\(\circ\))** & **Strength Equation** & \(c\) **(kPa)** & \(\phi\) (\({}^{\circ}\))** \\ \hline
0 & \(\tau=0.651\)X + 259.8 & 259.8 & 33.1 \\
2 & \(\tau=0.694\)X + 276.3 & 276.3 & 34.8 \\
4 & \(\tau=0.706\)X + 295.1 & 295.1 & 35.2 \\
6 & \(\tau=0.714\)X + 324.7 & 324.7 & 35.5 \\
10 & \(\tau=0.705\)X + 278.2 & 278.2 & 35.2 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Strength parameters.  
Figure 7: Strength envelope of PCS.  
It can be seen from Table 4, together with Figures 8 and 9 that the cohesion \(c\) and internal friction angle \(\phi\) of 0%\({}_{\infty}\) PCS sample are 259.8 kPa and 33.1\({}^{\circ}\), respectively. Their values for 6%\({}_{\infty}\) PCS sample are 324.7 kPa and 35.5\({}^{\circ}\), respectively. In other words, when the fiber mass content increases from 0%\({}_{\infty}\) to 6%\({}_{\infty}\), the sample's cohesion \(c\) and internal friction angle \(\phi\) increase 25.9% and 7.4%, respectively. However, further increase in fiber mass content lead to a decrease in \(c\) and \(\phi\). When the fiber mass content is 6%\({}_{\infty}\), \(c\) and \(\phi\) reach their maximum values, indicating that the shear strength is enhanced. The existence of an optimal fiber mass content may be justified by considering the effect of fibers in a PCS sample. During the cement hydration process, the fibers were combined with the surrounding matrix (cement-treated soil); as a result, a fiber can offer tensile strength in the sample if the cement slurry can coat each fiber well. This condition can be fulfilled if the fiber content is low. With the increase of fiber content, the cement slurry could be relatively insufficient to combine each fiber with its surrounding matrix; in addition, the overlaps among fibers are even likely to undermine the cement hydration process. As such, the strength parameters of the PCS sample have a decreasing tendency when the fiber content is too large. For instance, the strength parameters decrease when the fiber mass content increases from 6%\({}_{\infty}\) to 10%\({}_{\infty}\). In this study, the optimal fiber mass content was found to be 6%\({}_{\infty}\) as indicated in Figures 8 and 9. A similar phenomenon was reported in reference [32], which examined the strength parameters of cement-tailings with fibers.  
Figure 8: Cohesion of samples under different fiber mass contents.  
Figure 9: Internal friction angle of samples under different fiber mass contents.