Civil Engineering Reference
In-Depth Information
20.4 Simple slip circle analyses for undrained loading
A mechanism in which the slip surface is a circular arc - or a slip circle - as shown in
Fig. 20.2, is very commonly used in routine limit equilibrium analyses in geotechni-
cal engineering. The methods of solution are different for drained and for undrained
loading and we will consider each separately.
Figure 20.8 shows a section of a slope with a foundation at the top and water in a
river or lake at the toe. There is a mechanism consisting of a single circular arc with
centre at O. The forces on the mechanism are due to the foundation load
V
, the weight
of the soil
W
, the free water
P
w
and the shear stresses in the soil
T
s
u
AB where AB
is the length of the arc AB; these forces have lever arms
x
and
R
as shown. Taking
moments about O, the foundation and slope are just stable when
=
s
u
AB
R
Wx
w
+
Vx
f
−
P
w
x
u
=
(20.15)
The limit equilibrium solution must be found by searching for the critical slip circle by
varying the radius and the position of the centre. Notice in Fig. 20.8 that the normal
stresses on the slip circle are radial and pass through the origin, so they have no moment
about O. Calculation of values for
Wx
w
and
s
u
AB
R
can be simplified by dividing the
mechanism into a number of vertical slices and tabulating the results as in Fig. 20.18
in Example 20.3.
20.5 Slip circle method for drained loading - the
method of slices
Figure 20.9(a) shows a slope with part of a steady state seepage flownet to a drain at the
toe of the slope. The broken line in Fig. 20.9(a) is the slip circle shown in Fig. 20.9(b)
and there is a standpipe with its tip on the slip circle and on an equipotential. The height
Figure 20.8
Slip circle method for undrained loading.
