Civil Engineering Reference
In-Depth Information
Figure 19.17
Change of stress across a stress fan for undrained loading.
θ
f
is equal to the rotation
of the direction of the major principal stress across
the fan. Figure 19.17(a) shows a stress fan for undrained loading and Fig. 19.17(b)
shows the Mohr circles of total stress for the outermost discontinuities; within the fan
there are a great many radial discontinuities and there are equally a great many Mohr
circles between those shown. Note that the outermost limits of the fan are defined by
θ
θ
45
◦
. From Eq. (19.19), as
=
θ
b
=
δθ
→
0,
a
d
s
d
θ
=
2
s
u
(19.35)
and integrating through the fan from region A to region B,
s
=
2
s
u
θ
=
2
s
u
θ
f
(19.36)
