Civil Engineering Reference
In-Depth Information
Fig. 13.26
Determination of average r
u
value.
The average r
u
for whole cross-section
A r
+
A r
+
A r
+
a ua
b ub
c uc
=
A
+
A
+
A
+
a
b
c
where A
a
=
area of the slice a, and r
ua
=
average r
u
value in slice a.
Example 13.8:
Bishop and Morgenstern's charts (i)
A proposed embankment will have a slope of 1 vertical to 2 horizontal. The properties
of the soil are c
′
=
9 kPa and
φ
′
=
20°, and the unit weight of the compacted fill will be
γ
=
18 kN/m
3
. The height of the embankment will be 10 m and the average pore pres-
sure ratio is anticipated to be 0.2.
Using Bishop and Morgenstern's charts, determine the factor of safety for the slope.
Solution:
A series of dotted lines labelled r
ue
are plotted on the charts of n values. If the relevant
r
ue
value is less than the actual design r
u
then the set of charts with the next highest
depth factor should be used. The procedure therefore becomes as follows.
Calculate c
′
/
γ
H and, using the chart with D
=
1.0, check that r
u
is less than r
ue
. If it is,
then this is the correct chart to use: if r
u
is not less than r
ue
select the next chart
(D
=
1.25). In the case of c
′
/
γ
H
=
0.05, r
ue
should again be checked and if r
u
is greater
than this value then the chart for D
=
1.5 should be used.
′
=
c
γ
9
18 10
=
0 05
.
×
Select the chart with D
=
1.0
r
=
0 64
.
⇒
this chart is acceptable since r
(
>
r
)
ue
ue
u
m
=
1 39
.
n
=
1 07
.
⇒ =
F
1 39
.
−
(
0 2 1 07
.
×
.
)
=
1 18
.
