*7.3.2 Required reinforcement*

*Slope Engineering*

For LID case local reinforcement strength, K, is

maximum crack depth to be adopted [59] is

K 2K H y / H = − <sup>t</sup> ( ) (13)

(14)

 <sup>+</sup>

ð ö 3.83c tan 4 2 <sup>h</sup>

y

where y - the vertical coordinate from the slope toe. Maximum depth of crack is limited from the requirement that remaining slope remains stable. Upper bound

*Design charts for intact slopes not subject to crack formation (t = 1), intact slopes subject to crack formation (limited tensile strength of t =0.5, t = 0.2 & t = 0) and cracked slopes. (a) & (b) are for c/*γ*H = 0.05 while (c)* 

max =

**30**

**Figure 17.**

*& (d) are for c/*γ*H = 0.1. (after Abd and Utili [33]).*

Design charts (**Figure 17**) provide the reinforcement strength and embedment length for uniform and linearly increasing reinforcement distributions for different slope angles β and ϕ for specified value of c/γH.

In **Figure 17**, 't' is dimensionless coefficient representing soil tensile strength and is defined as ratio of ground tensile strength to be measured experimentally over maximum unconfined tensile strength consistent with Mohr-Coulomb criteria. Considering the case of intact slopes, it can be observed that for relatively low values of cohesion, c/ϒH = 0.05, the tensile strength, t, has negligible effect on the required reinforcement force. But for higher values of cohesion (c/ϒH = 0.1), t becomes important. Above charts are for fully drained slopes.

Using **Figure 17**, Kt/γH can be determined for given slope angle, β, and angle of shearing resistance, φ , of soil. Tensile strength of reinforcement is calculated using Eq. 10 for given number of layers. Influence of porewater pressure on required amount of reinforcement is analyzed using ru method [60]. A uniform value of ru is assumed throughout the slope and effective stress analysis carried out. **Figure 18** provides Kt/γH for slope inclinations of 400 to 90°, ru = 0, 0.25 and 0.5 for UD and LID cases.

Gray and black lines in **Figure 17** indicate respectively active and inactive constraint of maximum crack depth. The mark + signals the boundary between the two.

Gray and black lines in **Figure 18** indicate respectively active and inactive constraint of maximum crack depth. The mark + signals the boundary between the two (after Abd and Utili [33]).

A combined failure mode consisting of pullout in some layers and rupture (tensile failure) in others, also needs to be considered to calculate the minimum length of the reinforcement layers. **Figure 19** provides Lr/H as a function of slope angle, β for φ of 200 for this case.

#### **Figure 18.**

*Design charts for the required reinforcement for intact and cracked slopes (with* φ *= 20° and c/*γ*H =0.1) (a) UD of reinforcement; and (b) LID.*

**Figure 19.** *Length of reinforcement for a slope with* φ *= 20°, c/*γ*H = 0.05 and ru = 0.*
