Civil Engineering Reference
In-Depth Information
and the general expressions for earth pressure, as developed by Rankine, may be
expressed as
P
a
=
c
γ
−
−
K
ac
.
active earth pressure
K
a
(
z
u
)
P
p
=
c
passive earth pressure
K
p
(
γ
z
−
u
)
+
K
pc
.
where
is the soil bulk density,
z
is the depth below surface in a uniform soil and
u
is
the pore water pressure. While the Rankine method displays the principles involved,
the method cannot readily be extended into particular cases where wall friction exists
on the faces contacting the plastic zones. Coulomb adopted a different and more
versatile approach to the same problem; analyzing the stability of a non-plastic active
soil wedge at the point of failure, as shown in Figure 6.6 for a smooth wall and for the
level retained ground case, he obtained a solution identical to that of Rankine. Happily
the form of the active and passive pressure equations may be retained for cases where
inclined surfaces and wall friction are both taken into account.
The equations developed from the Coulomb approach and due to Mueller-Breslau
show that the active earth pressure coefficient for horizontal pressures,
K
a
,is
γ
sin
2
(
cos
δ
a
·
α
−
φ
)
α
+
δ
a
)
1
sin(
2
δ
a
+
φ
)
φ
−
β
·
sin(
)
sin
2
α
·
sin(
+
sin(
α
+
δ
a
) sin(
α
−
β
)
and the passive earth coefficient for horizontal pressure and level ground on the passive
side,
K
p
,is
sin
2
(
α
−
φ
)
)
cos
δ
p
·
α
+
δ
p
)
1
sin(
2
δ
p
+
φ
)
φ
)
·
sin(
sin
2
α
·
sin(
+
sin(
α
+
δ
p
)
·
sin
α
φ
where
=
angle of the internal friction.
inclination of the wall to horizontal (frequently 90
◦
).
α
=
δ
a
=
angle of wall friction on the active side of the wall (soil down drag).
δ
p
=
angle of wall friction on the passive side of the wall (soil rising).
β
=
angle of retained soil surface to horizontal.
Figure 6.6
Forces acting on Coulomb active wedge at failure.
