Civil Engineering Reference
In-Depth Information
the value of the apparent cohesion reduces. This illustrates that, as a clay wets up and its cohesive inter-
cept reduces from c
u
to c
′
, any tensile cracks within it tend to close.
If there is a uniform surcharge acting on the surface of the retained soil such that its
equivalent height
is h
e
(see Section
7.8.1
) then the depth of the tension zone becomes equal to z
0
where z
0
=
h
c
−
h
e
. If,
of course, the surcharge value is such that h
e
is greater than h
c
then no tension zone will exist.
7.5.4 Effect of cohesion on passive pressure
Rankine's theory was developed by Bell (
1915)
for the case of a frictional/cohesive soil. His solution for a
soil with a horizontal surface is:
φ
′
φ
′
+
′
=
+
′
p
=
γ
h
tan
2
45
°+
2
c
tan
45
°+
K h
γ
2c K
p
p
p
2
2
7.6 Coulomb's wedge theory: active earth pressure
Instead of considering the equilibrium of an element in a stressed mass, Coulomb's theory considers the
soil as a whole.
7.6.1 Granular soils
If a wall supporting a cohesionless acting soil is suddenly removed the soil will slump down to its angle
of shearing resistance,
φ
′
, on the plane BC in Fig.
7.14a
. It is therefore reasonable to assume that if the
wall only moved forward slightly, a rupture plane BD would develop somewhere between AB and BC: the
wedge of soil ABD would then move down the back of the wall AB and along the rupture plane BD. These
wedges do in fact exist and have failure surfaces approximating to planes.
Coulomb analysed this problem analytically in 1776 on the assumption that the surface of the retained
soil was a plane. He derived this expression for K
a
:
2
cosec
sin(
−
′
)
ψ
ψ φ
K
a
=
sin(
φ
′ +
δ
) sin(
φ
′ −
β
)
sin(
ψ δ
+ +
)
sin(
ψ β
−
)
where
ψ
=
angle of back of wall to the horizontal
δ
=
angle of wall friction
Fig. 7.14
Wedge theory for cohesionless soils.
