5.7 General Method of slices

Fredlung and Krahn (1977) have shown that the equations of equilibrium can be formulated

quite generally. The formulation is the same for circular and non-circular slip surfaces (Figure 8).

Soil properties: c', ф',γ

Total normal stress:σ

Shear stress: τ

Pore water pressure: u

Failure criterion:  s=c'+(σ-u)tanф'

Mobilized shear strength: τ=s/FOS

P=σl; T=τl

T=(1/FOS)[c'l+(P-ul)tanф']

Figure 8: General method of slice

Resolving the forces vertically:

Pcos

Rearranging ande substituting for T gives:

P

Where

Resolving the forces horizontally:

Tcos

Rearranging and substituting for T gives:

Overall moment of equilibrium about O yields:

Rearranging and substituting for T gives:

FOS

For Circular slip surfaces f

FOS

Overall force equilibrium:

In order to solve for  and  P must be evaluated. To di this following assumptionms are made:

Bishop (1955)

(X/E) Constant   Spencer (1967)

(X/E)   Morgenstern and Price (1965)

In general   and Bishop (1955) showed that  is much less sensitive to the assumption about interslice forces than