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3
passive
moment
½
K
d
/
3
=
(
K
p
/K
a
)/(1
+H/d
)
3
0
F =
=
p
(11.6)
active
moment
3
½
K
(
H
d
)
/
3
a
0
is the required safety factor at critical
stability (
F
= 1). The earth-pressure coefficients
K
p
and
K
a
are defined in equation
(7.5).
Here, cohesion is disregarded
and
Figure 11.6 Some failure modes of embedded walls
Following Blum's approach, the contribution under the rotation point
B
is
simplified to a force
P
B
= e
(
K
p
-
K
a
)
H
, acting in the rotation point itself (a safe
assumption), see Fig 11.7a. It does not affect the moments in equation (11.6). From
(11.6) the value of
d
becomes
H
d =
(11.7)
K
/(
FK
)
1
3
p
0
a
After some elaboration, horizontal equilibrium provides, including force
P
B
;
(
;
/
F
)
2
/
3
e/d =
with
;
= K
p
/K
a
(11.8)
0
1
/
3
2
;
1
)(
;
/
F
)
0
The required quality of the wall is determined by the maximum bending
moment. The point
z
, measured from top, where the shear force in the sheet-pile
wall is zero, and the corresponding maximum bending moment
M
max
, become, after
some elaboration
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