## 2 Safety Factor of a Slope Reinforced by Prestressed Anchor Cables
### Changes of Safety Factor of the Slope under Different Cable Prestresses  
Figure 6 shows the relationship between the displacement of slope foot and the strength reduction factor of rock mass in the slope without and with prestressed anchor cables (under different prestresses).  
It can be seen that the displacement of the slope foot without prestressed anchor cables was significantly larger than that with prestressed anchor cables. In particular when the strength reduction factor was larger than 2.0, the displacement of slope foot without prestressed anchor cables was much greater than that with prestressed anchor cables. This indicated that prestressed anchor cables showed a major restriction effect on the displacement of the slope. It was particularly noteworthy that, when applying cables in the slope while having no prestress, with an increasing strength reduction factor, cables still significantly restricted the displacement of the slope, even though there was no prestress on the cables.  
Additionally, by comparing the slope reinforced by cables under different prestresses, it can be seen that with increasing prestress, the displacement of the slope foot was reduced. Correspondingly, the strength reduction factor increased and the growth of prestress exerted greater control over the displacement, that is, the increase of prestress led to a larger safety factor of the slope. However,  
Figure 5: The relationship between the displacement of slope foot strengthened by prestressed anchor cables and the strength reduction factor (obtained by the convergence method).  
Figure 6: The relationship between the displacement of the slope foot and the strength reduction factor.  
with increasing cable prestress, the reduction in displacement at the slope foot was abated. For example, when the strength reduction factor in the figure was 7.8, the displacement of slope foot decreased. However, the reduction in displacement constantly decreased. When the cable prestresses were 500 and 600 kN, there was an insignificant difference in displacement at the slope foot. This implied that, after the prestress reached a certain value, further increases were not beneficial.  
According to inflection point method, the safety factor of the slope can be determined, in which the inflection point of the relationship between the displacement of slope foot and the strength reduction factor was considered as the safety factor of the slope. As shown in Figure 6, the inflection points occurred in all curves when the displacement of slope foot was 1 mm. Therefore, the strength reduction factor corresponding to the displacement of slope foot of 1 mm was regarded as the safety factor of the slope.  
Figure 7 displays the relationship between the cable prestress and the safety factor of the slope. In the figure, the cable prestress was not linearly correlated with the safety factor. After cable prestress reached a certain value, the growth in safety factor slowed down. Further increases in cable prestress showed no significant influence on improving the safety of the slope. Additionally, it should be noticed that the high prestress may cause local failure at the slop surface. Therefore, before applying high prestress on the anchor cable, calculations should be conducted in order to ensure that the rock mass can bear that force. Otherwise, engineering measures should be applied to reduce the concentrated force on the slope surface.