16. EARTH PRESSURES (Rankine’s Method)
16.1 Modes of failure
F
Some force is required to support the soil. This force may be provided by
•
friction at the base (gravity retaining walls)
•
founding the wall into the ground (sheet retaining walls)
•
anchors and struts
•
external loads
If the force is too small the soil behind the wall will reach a state of failure with the wall
moving away from the soil (active failure). If the force is too large the soil will reach another
state of failure with the wall moving into the soil (passive failure).
Rankine’s theory allows the limiting pressures on retaining walls to be determined.
16.2 Rankine’s theory
In Rankine’s method it is assumed that the wall is frictionless. The normal stress acting on
the wall will therefore be a principal stress. If the wall is vertical and the soil surface
horizontal, the vertical and horizontal stresses throughout the retained soil mass will be
principal stresses. In this situation the vertical stress at any depth can be simply determined,
as follows:
1
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d
1
d
2
γ
1
γ
2
z
The horizontal stress can then be calculated from the MohrCoulomb failure criterion. If short
term stability is being considered this can be achieved using undrained (total stress) parameters
while if long term stability is being considered drained (effective stress) parameters must be
used.
From MohrCoulomb failure criterion we can write for soil at failure
1
3
=
N
+
2 c
N
σ
σ
φ
φ
The implications of this expression are most easily investigated by considering the response of
soil adjacent to a frictionless retaining wall.
Then we can identify two limiting conditions:
16.2.1 Active failure
There is insufficient force to support the soil.
Assuming that the vertical stress is given simply
by the weight of the overlying soil and does not change during deformation, the minimum
horizontal stress may be determined from
hmin
v
=

2 c
N
N
σ
σ
φ
φ
16.2.2 Passive failure
The force on the wall is greater than the resistance provided by the soil.
The horizontal stress
reaches a maximum value given by
hmax
v
=
N
+
2 c
N
σ
σ
φ
φ
In the Rankine method a stress state is found that is in equilibrium with the applied loads and
has the soil at failure. In plasticity theory this approach is referred to as a lower bound
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 Three '11
 DAirey
 Geotechnical Engineering, total stress, active failure

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