Geoscience Reference
In-Depth Information
a =
(
h
y
)/cos
and
b
,t
/
sin
and
c = y
,t
/
tan
(9.40)
Here,
b
and
c
represent the relative inner and border displacement over
dy
of the
wedge, while reshaping from OAB to OA'B. When assuming a constant maximum
shear stress
k
along the
-inclined slip lines within the volume OAB, the work rate
is determined by
y
A
B
P
A'
P”
a
cdy
P
dy
h
P'
P'
bdy
k
,t
/2-
>t
x
O
Figure 9.8 The Rankine wedge
h
a|b|dy = k
0
h
2(
h
,t
| h
2
/sin(2
W
.t
= k
0
y
)
|
,t
| /
sin(2
)
dy = k|
)
(9.41)
,t
h
2
. The additional work rate along
the border line OA is added, taking into account an interface shear stress
k'
which attains a minimum at
=
/4:
W
.t
= k
h
y|
W
.t
= k'
OA
|
c| dy = k'
0
,t
/
tan
| dy
h
ydy = k'|
| h
2
= k'|
,t
/
tan
|
0
,t
/
2tan
(9.42)
Hence, the total work rate for the Rankine wedge becomes
,t
| h
2
W
.t
W
.t
=
(
k/
sin[2
]
½
k'/
tan
)
|
(9.43)
For the active Rankine state:
=
/
4
/
2 holds and for the passive Rankine
state
=
0) the total
work rate becomes similar to the work rate for the plastic wedge, expression (9.39).
The effect of gravity (soil weight) has been disregarded.
=
/
4
/
2, with
the soil friction angle. For
=
/
4 (and
Dike doweling
In West-Netherlands a soft Holocene top layer commonly occurs on top of a
relatively rigid and permeable Pleistocene sand layer. Through the sand layer high
water levels in adjacent rivers may generate high pore pressures under a dike.
Consequently, effective contact stresses at the layer interface decrease, eventually
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