**8.2 Length optimization from face end**

The length, Lf = (Lr - Le) is much larger than Le, the effective length of reinforcement contributing to increase in the stabilizing moment/force. The required pullout force in the reinforcement in the stable zone should equal to that mobilized by the corresponding length of the reinforcement in the unstable zone for equilibrium. It would serve no useful purpose if the length of the reinforcement in the unstable

**Figure 21.** *Critical slip circle for Z0 = 3.0 m, FSmin = 1.51, Lr = 7.27 m.*

zone is more than that required for generating the required stabilizing force. Hence minimizing Lf = (Lr - Le) by moving point P inside the soil mass and away from the slope face by curtailing length of reinforcement but still maintaining FSmin above 1.50 can lead to economy. Accordingly, for reinforced slope of **Figure 21**. Lr has been curtailed from the face end of the slope. As point P is moved inside gradually by reducing Lr, the critical circle continues to be DEF or close to it (**Figure 22**), i.e., practically with no shift of the critical circle.

The minimum length, Lr which provides FSmin = 1.51 is obtained as 5.08 m (**Figure 22**). Thus about 30% reduction in length of reinforcement is achieved without sacrificing the stability of the embankment slope as FSmin is still the required value of 1.5. Hence length optimization from face end leads to saving of reinforcement length. The circle, ABC, is not the critical for the reinforced slope and thus not acceptable as the critical circle with consideration of reinforcement is different from that of unreinforced case.
