Civil Engineering Reference
In-Depth Information
z
σ
1
=
γ
z
σ
3
= K
o
γ
z
Fig. 7.1
Vertical and lateral stresses.
h
σ
1
=
γ
h
σ
3
= K
a
γ
h
d
σ
1
=
γ
d
σ
3
= K
p
γ
d
slight movement (yielding)
Fig. 7.2
Active and passive states.
G
D
φ
'
O
A
C
B
F
E
Active earth
pressure
K
a
γ
h
Vertical stress,
γ
h
Passive earth pressure, K
p
γ
h
Fig. 7.3
Active and passive earth pressures.
Behind the wall (active),
σ
3
=
K
a
γ
h
In front of the wall (passive),
σ
3
=
K
p
γ
d
The active earth pressure is the minimum value of lateral pressure (
σ
3
) the soil can withstand. The passive
earth pressure is the maximum value.
Consider now a single element of soil at depth, h below the ground surface. The vertical stress (
σ
1
) at
this depth is equal to
γ
h. Referring to the previous paragraph, the two extreme values of
σ
3
can be
obtained from the Mohr circle diagram for the soil, as shown in Fig.
7.3.
From Fig.
7.3
it is seen that the lateral pressure can reduce to a minimum value at which the stress circle
is tangential to the strength envelope of the soil. This minimum value is the active earth pressure and
equals K
a
γ
h. The lateral pressure can rise to a maximum value (with the stress circle again tangential to
the strength envelope) known as the passive earth pressure, which equals K
p
γ
h. From the figure, it is clear
that when considering active pressure, the vertical pressure due to the soil weight,
γ
h, is a major principal
