**6.3 Limit equilibrium (LE) method of stability analysis**

Various LE Methods such as Bishop's Simplified, Janbu's Simplified, Spencer, Morgenstern-Price, Janbu Generalized, Sarma, etc., have been developed for slope stability analysis. The problem is considered in two dimension i.e. plane strain case. The primary difference among all these methods lies in the equations of statics considered, which interslice normal and shear forces are included, and the assumed relationship between the interslice forces. **Tables 3** and **4** summarize the conditions for some of the common methods of stability analysis.

**Figure 8.** *Design chart for ru = 0 after Jewell [14].*

#### **Figure 9.**

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


#### **Table 3.**

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


**23**

**Figure 10.**

*Geoysynthetic Reinforced Embankment Slopes DOI: http://dx.doi.org/10.5772/intechopen.95106*

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

( )

φ

*i*

φ

=

A generalized limit equilibrium (GLE) formulation was developed by Fredlundand and Krahn [52] and Fredlund et al. [53]. This method encompasses the key elements of all the methodslistedin **Table 2**. The interslice shear forces

> *X E fx* = λ

*FS*

*Circular arc slope stability analysis for geosynthetic reinforced c-* φ *soil (after [44]).*

∑

tan

1

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

*i j i n*

= = = =

1 1

where Wi = weight of ith slice, θi = angle made by tangent to the failure arc at the

∑ ∑

*i n j m*

= =

( )

sin

*wi i R*

= +

*WX*

where W = weight of circular slice and X is the horizontal distance of CG of soil

∑1

*m arc i i i cL R T iY*

θ

θ

*i* ∆li = arc length of ith slice,

( ) (4)


(2)

(3)

*Ni c li R TjYj*

+∆ +

of the circle. For slope reinforced with horizontal layers (**Figure 10**) of

*FS*

center of ith slice with the horizontal, Ni = Wi cos ,

mass from the center of the critical slip circle.

*6.3.2 Generalized limit equilibrium method*

(Morgenstern and Price [49]) are

R = radius of circular curve, c and

=

*6.3.1 Koerner's design method*

geosynthetics, FS, is

simplifies to

#### **Table 4.**

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