17. COULOMB'S METHOD
The method is based on estimating a mechanism of failure. The MohrCoulomb failure criterion
is then assumed to be satisfied on the assumed failure planes.
This approach, known as the
limit equilibrium method,
is widely used in geotechnical
engineering.
Experience has shown that it gives solutions that agree reasonably well with
observations of collapse of real soil structures.
The method has advantages over Rankine's method because:
•
It can cope with any geometry
•
It can cope with line loads (In plane problems)
•
Friction between retaining walls and soil can be taken into account
Its main disadvantage is that the common layered soil profile cannot be simply accounted for.
For any point on the failure surface we have
Whenever the soil is at failure a MohrCoulomb locus of this general form can be used,
however, the appropriate values for c and
φ
will depend on the type of analysis.
In a total stress
(undrained) analysis c = c
u
,
φ
=
φ
u
, whereas in an effective stress analysis c = c
′
,
φ
=
φ′
.
We next need to consider the Forces acting on the failure plane
Shear Force
T
=
τ
ds
∫
Normal Force
N =
σ
ds
∫
Cohesive Force
C =
cds
∫
τ
σ
φ
=
c
+
tan
1
direction of soil
movement
Assumed failure plane
Assumed
failure
plane
τ
σ
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View Full DocumentIf the soil properties are constant we can write the failure criterion in terms of Forces as
to facilitate the analysis we split the unknown forces T, N into two forces C, which is generally
known acting parallel to the failure surface, and a resultant R, acting at a known angle
φ
to the
normal to the failure surface.
≡
R
=
N
cos
φ
R
T

C
N
sin
tan
φ
φ
Failure does not always occur within the soil mass.
For the failure of the soil structure a
mechanism is required, and for the case of a retaining wall this means slip must also occur
between the wall and the soil. We assume that the failure conditions can be described by a
MohrCoulomb criterion, that is
τ
σ
φ
c
+
tan
but the parameters c,
φ
become:
c
w
, the adhesion between the wall and the soil
φ
w
, the friction angle between the wall and the soil
This can also be expressed in terms of Forces as
T
C
N
w
w
w
w
=
+
tan
φ
17.1 Total Stress Analysis
As for Rankine's method a total stress analysis is only appropriate if the soil remains undrained,
and in practice this is only true if the stability of clayey soils is being investigated.
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 Three '11
 DAirey
 Force, Stress Analysis, Uuw

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