Civil Engineering Reference
In-Depth Information
Area (m
2
)
Slice
Weight (kN)
Normal, N (kN)
Tangential, T (kN)
1
3.7
71
71
−
7
2
8.7
168
163
42
3
11.6
224
191
116
4
7.7
148
104
106
Σ
529
Σ
257
The N values are not actually required in this example as we are assessing stability in
the undrained state, but are included to demonstrate how these are established for use
in a drained analysis.
c R
u
θ
= ×
70 10 7 76 180
.
×
/
× =
π
993
kN
c R
T
θ
u
F
=
Σ
993
257
3 9
=
=
.
13.2.4 Pore pressure ratio, r
u
As mentioned in the previous section, if the long-term factor of safety of a slope is required, an analysis
must be carried out in terms of effective stress. Such an analysis can be used in fact for any intermediate
value of pore pressure between undrained and drained.
Before looking at the effective stress methods of analysis, let us consider the determination of the pore
pressure ratio, r
u
.
There are two main types of problem in considering pore pressures in a slope: those in which the value
of the pore water pressure depends upon the magnitude of the applied stresses (e.g. during the rapid
construction of an embankment), and those where the value of the pore water pressure depends upon
either the groundwater level within the embankment or the seepage pattern of water impounded by it.
Rapid construction of an embankment
The pore pressure at any point in a soil mass is given by the expression:
=
0
∆
u
u
u
Where
u
0
=
initial value of pore pressure before any stress change
Δ
u
=
change in pore pressure due to change in stress.
From Chapter
4:
∆
u B
=
[
∆
σ
+
A
(
∆
σ
−
∆
σ
)]
3
1
3
