Civil Engineering Reference
In-Depth Information
Limit equilibrium method
20.1 Theory of the limit equilibrium method
The limit equilibriummethod is by far the most commonly used analysis for the stability
of geotechnical structures. The steps in calculating a limit equilibrium solution are as
follows:
1. Draw an arbitrary collapse mechanism of slip surfaces; this may consist of any
combination of straight lines or curves arranged to give a mechanism.
2. Calculate the statical equilibriumof the components of the mechanismby resolving
forces or moments and hence calculate the strength mobilized in the soil or the
external forces (whichever is unknown).
3. Examine the statical equilibrium of other mechanisms and so find the critical
mechanism for which the loading is the limit equilibrium load.
Remember that, as always, we must distinguish between cases of undrained and
drained loading. For undrained loading the ultimate strength of the soil is given by
τ
=
s
u
(20.1)
where
s
u
is the undrained shear strength. For drained loading where pore pressures
can be determined from hydrostatic groundwater conditions or from a steady state
seepage flownet, the strength is given by
τ
=
σ
tan
φ
=
φ
σ
−
(
u
) tan
(20.2)
φ
is a friction angle.
As discussed in Sec. 9.2 soil has a peak strength, a critical state strength and a
residual strength which are mobilized at different strains or displacements. The factors
which determine which strength should be used in stability calculations are discussed
in Chapter 18.
As in the previous chapter on the upper and lower bound methods, the analyses in
this chapter calculate ultimate limit states where the slope, wall or foundation can be
said to have collapsed. For design of safe and serviceable structures factors have to be
applied. The total or partial factors of safety or load factors applied in limit equilib-
rium analyses are the same as those applied in bound analyses. They are discussed in
Chapter 18 and will be discussed in later chapters dealing with different structures.
where
