Civil Engineering Reference
In-Depth Information
will fail if the depth exceeds the critical height
H
c
; this is given by Eq. (21.15) where
s
u
can be found from an unconfined compression test carried out on a sand-castle at the
same density and water content. The vertical cut cannot be continued below the water
table C where the pore pressures are zero. (The cut often fails just above the water
table where the sand is saturated and the negative pore pressures are small.) Notice
that pore pressures behind the cut BC are negative so the face should look dry.
You know that it is very difficult to dig the hole below the water table. If you
excavate slowly there will be steady state seepage so the angle of the slope CD will
be about
φ
c
but, if you can excavate below water the angle of the slope DE will be
smaller. In practice seepage into the excavation along CD usually causes erosion and
you cannot dig much below the water table.
When you do this experiment remember that the factor of safety of the vertical cut
BC is probably reducing with time and you must be very careful that it does not collapse
on you. You should also observe what happens to your hole as the tide comes in or as
the sun shines on to the face BC.
1
2
21.11 Summary
1. Slopes fail as soil moves on slip surfaces and there are several possible mechanisms
depending on the ground and groundwater conditions.
2. Immediately after excavation or filling pore pressures are reduced and, as time
passes, pore pressures rise, effective stresses reduce and the safety of a slope
deteriorates.
3. For slope stability calculations the factor of safety accounts for uncertainties in
the determination of the soil parameters and the analyses. For routine analyses
the critical state strength will give safe designs with factors of safety accounting
for uncertainties in the pore pressures. If previous landsliding has occurred the
strength may have reduced to the residual before construction starts.
4.
Slope stability calculations can be done using the upper and lower bound methods
or the limit equilibrium method; preliminary designs can be carried out making
use of routine stability numbers.
Worked examples
Example 21.1: Undrained slope stability
Figure 21.21 shows the geometry of a simple
slope. From Eq. (21.42) and replacing
s
u
with
s
u
/
F
s
,
N
s
s
u
γ
F
s
=
H
20
◦
and
n
d
=∞
From Fig. 21.18 for
i
=
we have
N
s
=
5.5 and
5.5
×
40
F
s
=
=
2.2
20
×
5
Notice that this is rather less than the result
F
s
2.98 obtained for Example 20.3,
indicating that the slip circle in Fig. 20.18 was not the critical one.
=
