Civil Engineering Reference
In-Depth Information
Figure 19.14
Slips fans and corresponding displacement diagrams.
and so the radius of the fan and the increment of displacement remain constant through
a slip fan for undrained loading. From the geometry of Fig. 19.14(b),
r
b
=
r
a
exp(
θ
f
tan
ψ
)
(19.30)
δ
w
b
=
δ
θ
f
tan
ψ
w
a
exp(
)
(19.31)
where
θ
f
is the fan angle; thus the outer arcs of the slip fan and the displacement
diagram are both logarithmic spirals.
For a slip fan like that shown in Fig. 19.14(a), it is necessary to evaluate the
work done on the circular slip surface and on all the radial slip surfaces. From
Fig. 19.15, summing for the elements of the circular arc and for the radial slip surfaces,
