Geoscience Reference
In-Depth Information
When cohesion is involved, it can be shown that (11.1) becomes
K
i
H
2
Q =
½
4
2
cH
K
i
(11.2)
Here,
K
i
= K
p
refers to the passive state, and
K
i
= K
a
to the active state, similar to
equations (7.5). It should be noted that the horizontal thrust on an earth-retaining
wall for an active state is only obtained when the wall allows the soil to lean on by
its own. If this is not possible (not permitted because of restrictions on
deformation), the thrust will be larger, which has to be considered in the design.
For rough walls Coulomb's theory of straight slip lines does not apply. The same
counts for Rankine's theory (see Fig 7.4). For a plastic zone of soil, in which
everywhere the limit state occurs, i.e. in every point the stress state is such that the
corresponding Mohr circle touches the failure line:
47
, equilibrium
conditions can be elaborated along the direction of slip lines, the
s-r
system (see
Fig 11.4a and Fig 11.4b). A new variable is introduced
= c +
tan
0
=
+ c/
tan
and
=
0
tan
(11.3)
B
s
B
0
+
,s
ds
+
,s
ds
+
,s
ds
ds
A
0
+
0,s
ds
D
+
,s
ds
E
D
0
F
dr
,s
dsdr
E
D
F
+
,r
dr
0
+
0,r
dr
,r
drds
E
C
D
r
+
,r
dr
+
,r
dr
E
/2+
+
,s
ds + +
,r
dr 2
+
,r
dr
C
Figure 11.4a Curved slip lines or characteristic lines
47
Note, that the formula refers to effective stresses; the dash has been omitted for
convenience.
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