Environmental Engineering Reference
In-Depth Information
ρ
'
tg
ϕ
'
F
=
[3.8]
ρ
tg
α
sat
Thus, for example, for a sandy gravel characterized by ϕ
'
= 35° andρ
'/
ρ
sat
=
0.5,
the
equilibrium limit (
F = 1
) is achieved for a critical slope with angle
α
c
= 19°. This
slope is significantly less than that obtained for the case without water or without
flow, for which the well-known result is
α
c
= φ
, i.e. in this example
α
c
= 35°. This
also explains the fact that unstable slopes are often observed between 10° and 20°,
as indicated earlier in this chapter.
3.3.3.
Methods of slices
To analyze more complex cases (heterogenous mass, complex hydrodynamic
conditions, any geometry and various loads), the mass is divided into slices whose
equilibrium is analyzed by accepting an overall safety factor for the entire slope that
is uniform over the whole potential failure surface. This has given rise to the well-
known “methods of slices”, which are distinguished by the geometry of the failure
surface considered and by the simplified hypotheses introduced to make the system
isostatic (see [CHO 82]). The first and simplest is that of Fellenius, but more
complete methods will be preferred whose application is made possible by using
computer programs: Bishop's method for circular surfaces, Janbu's method for
elongated surfaces (methods that remain rather imprecise) or the Morgenstern and
Price method, which is more rigorous and valid for any failure surface geometry
[MOR 65]. An example of the calculation is given in Figure 3.8.
Figure 3.8.
Example of a stability calculation by the methods of slices
(using the Geo-Slope program)
