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The kinematics is presented in Fig 9.10. It is essential to fit the visco-plastic
subzones (wedges and rigid zones) perfectly, like a jigsaw puzzle. The motion is
divided in three zones: A, B and C. Zone A and C are supposed to undergo a rigid
motion of
,
t
along their circular slip surface, according to a rotation speed in centre
M
1
or M
2
. Zone B is considered as a square block with height
h
. The movement of
zone A causes block B to move with speed
?
,t
to the right. In Case I, the
corresponding friction over the underground leads to a dissipation work of
?
?
,t
hk'
. In
order to fit the side of zone A the left side of zone B has to deform over ¼
,t
. This
is achieved by assuming a plastic wedge, and the corresponding dissipation work,
according to equation (9.39) with ¼
?
,t
kh
.
Here,
k = k'
because the material of zone A and B are equal. The right hand side of
block B fits rigid zone C by assuming another plastic wedge and here
?
,t
=
,t
h
, becomes (
k
+½
k'
)¼
?
,t
h
=
3
/
8
?
?
,t
=
,t
h
,
which leads to a dissipation work of (
k
+½
k'
)
?
,t
h
=
3
/
2
?
,t
kh
. The total dissipation
work becomes for Case I
W
,t
= W
A,t
+ W
C,t
+ W
B,t
with
W
B,t
=
?
,t
kh
(
k'/k
+
3
/
8
+
3
/
2
) =
?
,t
kh
(
k'/k +
1.875)
(9.44)
Here,
k
is the apparent dynamic cohesion in the Holocene layer and
k'
at the
interface in the uplift zone;
k'
could be taken zero because of local high excess pore
pressures.
B
6
B
5
?
,t
2?
,t
/h
2
?
,t
?
,t
B
10
B
9
A
h
B
7
B
8
B
5
B
6
C
clay
B
4
B
3
B
2
B
1
sand
dowel
Figure 9.11 Kinematics of uplift zone B with a dowel that rotates
?
,t
/2h
In Case II, the dike stability is improved by applying a buried short sheet pile, a
dowel, penetrating in the Pleistocene layer. The kinematics shown in Fig 9.11
consists of zone A and zone C, similar to the previous situation. Zone B has now
10 elementary subzones to accommodate the induced rotation of the dowel. In
addition, the two wedges of Case I are superimposed to accommodate the rotations
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