Instability of Soil Masses - Environmental Geomechanics - page 84

calculating in a decoupled way a field of pore-water pressure for which the non-
saturated zone corresponds to a negative value of u w , accepting a relative interstitial
air pressure of zero ( u a = 0) and using Fredlund's formulation (equation [3.9]) to
determine the strength.

Calculations of stability through this approach have been presented by Gueye
[GUE 93], by simplifying the suction profiles.

Calculations by the method of finite elements allow a better approach; in the
simplest case, a “traditional” two-phase formulation will be used. This formulation,
which allows the use of finite element method software developed for saturated
media, remains valid for conditions close to complete saturation, i.e. for suction
values less than the air-entry value. Three modifications must occur, however, that
concern the expression of the effective stress, soil permeability, and plasticity
criterion:

- first, the expression of effective stress is modified to take into account suction
by Bishop's expression:

( ) (

ij

)

σσδ =− + − u χ u u δ

[3.10] ij a ij a w ij

and by simplification accepting a relative pore-air pressure of zero ( u a = 0) and a
coefficient of Bishop χ equal to the degree of saturation S r . As in the two-phase
approach, S r is not a state variable; it will be evaluated on the basis of a
phenomenological relationship drawn from the suction curves, i.e.

%

S=S(s) , which

r r

%

is reduced in this case to S=S(u ) if u a = 0. Seker proposed such a relation in the

r r w

form [SEK 83]:

1

S =

r

⎛ ⎞ +

1 100 s

g

[3.11]

Ψ

log 1

⎜ ⎝ ⎠

1

Ψρ

0 w

in which ψ and ψ are material constants. Figure 3.11 gives a graphic
representation for this;