Civil Engineering Reference
In-Depth Information
fails to resolve the problem, the analysis should
be abandoned.
Figure 8.17 gives a correction factor
f
0
, which
is used in calculating the factor of safety by
means of the Janbu method. This factor allows
for inter-slice forces resulting from the shape of
the slide surface assumed in the Janbu analysis.
The equation for
f
0
given in Figure 8.17 has been
derived by Hoek and Bray (1981) from the curves
published in Janbu (1954).
this procedure until the difference between
successive factors of safety is less than 0.001.
Generally, about ten iterations will be required
to achieve the required accuracy in the calculated
factor of safety.
8.6.3 Example of Bishop's and Janbu's
methods of analysis
A slope is to be excavated in blocky sandstone
with very closely spaced and persistent discon-
tinuities. The slope will consist of three, 15-m
high benches with two 8-m wide berms, the
primary function of which are to collect surface
runoff and control erosion (Figure 8.19). The
bench faces will be at 75
◦
to the horizontal, and
the slope above the crest of the cut will be at
an angle of 45
◦
. The assumed position of the
water table is shown on the figure. It is required
to find the factor of safety of the overall slope,
assuming that a circular type stability analysis is
appropriate for these conditions.
The shear strength of the jointed rock mass is
based on the Hoek-Brown strength criterion, as
discussed in Section 4.5, which defines the strength
as a curved envelope. The cohesion and friction
angle for this criterion are calculated using the pro-
gram ROCLAB 1.004 (RocScience, 2002a), for
which the input parameters are as follows:
8.6.2 Use of non-linear failure criterion
in Bishop stability analysis
When the material in which the slope is cut obeys
the Hoek-Brown non-linear failure criterion dis-
cussed in Section 4.5, the Bishop's simplified
method of slices as outlined in Figure 8.18 can
be used to calculate the factor of safety. The
following procedure is used, once the slice para-
meters have been defined as described earlier for
the Bishop and Janbu analyses:
Calculate the effective normal stress
σ
act-
ing on the base of each slice by means of
the Fellenius equation (equation (8.17) on
Figure 8.18).
1
Using these values of
σ
, calculate tan
φ
and
c
for each slice from equations (4.24)
and (4.25).
2
3
Substitute these values of tan
φ
and
c
into the
factor of safety equation in order to obtain the
first estimate of the factor of safety.
•
Very poor quality rock mass, GSI
=
20;
•
Uniaxial compressive strength of intact rock
(from point load testing)
≈
150 MPa;
4
Use this estimate of FS to calculate a new value
of
σ
on the base of each slice, using the Bishop
equation (equation (8.18) on Figure 8.18).
•
Rock material constant,
m
i
=
15;
0.025 MN
/
m
3
;
•
Unit weight of rock mass,
γ
r
=
0.00981 MN
/
m
3
;
•
Unit weight of water,
γ
w
=
On the basis of these new values of
σ
, calcu-
late new values for tan
φ
and
c
.
5
•
For careful blasting used in excavation, dis-
turbance factor
D
=
0.7; and
6
Check that conditions defined by equa-
tions (8.8) and (8.9) on Figure 8.16 are sat-
isfied for each slice.
•
Average
24 m (this height
together with the rock mass unit weight
defines the average vertical stress on the sliding
surface).
slice
height
=
7
Calculate a new factor of safety for the new
values of tan
φ
and
c
.
8
If the difference between the first and second
factors of safety is greater than 0.001, return
to step 4 and repeat the analysis, using
the second factor of safety as input. Repeat
Using these parameters, ROCLAB calculates, at
the appropriate vertical stress level, a best fit line
to the curved strength envelope to define a friction
angle of 43
◦
and a cohesion of 0.145 MPa. This is
