*6.3.1 Koerner's design method*

*Slope Engineering*

**Figure 9.**

**Table 3.**

Ordinary or Fellenius

Morgenstern – Price

Sarma – vertical

slices

**Table 4.**

*Design charts for ru = 0.25 and 0.5 after Jewell [14].*

*Equations of statics satisfied (after Krahn [50]).*

*Interslice forces and relationships (after Krahn [50]).*

**Normal (E)**

Bishop's Simplified Yes No Horizontal Janbu's Simplified Yes No Horizontal Spencer Yes Yes Constant

**Method Interslice** 

**Method Moment Equilibrium Force Equilibrium**

**Interslice Shear (X)** **Inclination of X/E Resultant, and X-E** 

**Relationship**

No No No interslice forces considered

Yes Yes Variable; user function

Janbu Generalized Yes Yes Applied line of thrust and moment equilibrium

Yes Yes X = C + E tan

of slice

φ

Ordinary or Fellenius Yes No Bishop's Simplified Yes No Janbu's Simplified No Yes Spencer Yes Yes Morgenstern-Price Yes Yes Janbu Generalized Yes (by slice) Yes Sarma – vertical slices Yes Yes

**22**

Koerner [51] proposed a method of slices for analysis of geosynthetic reinforced homogeneous slope neglecting interslice forces. Assuming circular arc failure surfaces minimum FS is found by varying the radius and coordinates of the origin of the circle. For slope reinforced with horizontal layers (**Figure 10**) of geosynthetics, FS, is

$$FS = \frac{\sum\_{i=1}^{i=n} (Ni \tan \phi + c\Delta li)R + \sum\_{j=1}^{j-n} TjYj}{\sum\_{i=1}^{i=n} (wi \sin \theta i)R} \tag{2}$$

where Wi = weight of ith slice, θi = angle made by tangent to the failure arc at the center of ith slice with the horizontal, Ni = Wi cos , θ*i* ∆li = arc length of ith slice, R = radius of circular curve, c and φ- strength parameters, Tj = allowable tensile strength of geosynthetic at jth layer, yj = moment arm for jth layer, m = number of geosynthetic layers, n = number of slices. For fine grained soil, the equation for FS simplifies to

$$FS = \frac{cL\_{ave}R + \sum\_{i=1}^{m} T\_i iY\_i}{WX} \tag{3}$$

where W = weight of circular slice and X is the horizontal distance of CG of soil mass from the center of the critical slip circle.
