Civil Engineering Reference
In-Depth Information
available to calculate the mean and standard devi-
ation. Otherdistributionscanbeusedasapplicable.
Figure 6.14(c) shows the distribution of the
factor of safety generated, using the Monte Carlo
method (see Section 1.4.4(b)), as the result of
10,000 iterations with values randomly selec-
ted from the input parameter distributions. The
histogram shows that the mean, maximum and
minimum factors of safety are 1.36, 2.52 and
0.69 respectively. Also, the factor of safety was
less than 1.0 for 720 iterations, so the probabil-
ity of failure is 7.2%. If the mean values of all the
input parameters are used in the stability analysis,
the calculated deterministic factor of safety is 1.4.
The sensitivity analysis associated with these cal-
culations shows that the factor of safety is most
strongly influenced by the dip of the slide plane,
and least influence by the depth of water in the
tension crack. This analysis was performed using
the computer program ROCPLANE (Rocscience,
2003).
4m
f
=60
°
z
= 4.35 m
T
T
z
w
=3m
p
=35
°
Figure 6.15
Plane failure geometry for Example
Problem 6.1.
Factor of safety calculations
(a)
Calculate the factor of safety of the slope for
the conditions given in Figure 6.15.
(b)
Determine the factor of safety if the tension
crack were completely filled with water due
to run-off collecting on the crest of the slope.
(c)
Determine the factor of safety if the slope
were completely drained.
6.7 Example Problem 6.1: plane
failure—analysis and stabilization
(d)
Determine the factor of safety if the cohesion
were to be reduced to zero due to excessive
vibrations from nearby blasting operations,
assuming that the slope was still completely
drained.
Statement
A 12-m high rock slope has been excavated at a
face angle of 60
◦
. The rock in which this cut has
been made contains persistent bedding planes that
dip at an angle of 35
◦
into the excavation. The
4.35-m deep tension crack is 4 m behind the crest,
and is filled with water to a height of 3 m above
the sliding surface (Figure 6.15). The strength
parameters of the sliding surface are as follows:
(e)
Determine whether the 4.35-m deep tension
crack is the critical depth (use Figure 6.6).
Slope reinforcement using rock bolts
(a)
It is proposed that the drained slope with
zero cohesion be reinforced by installing ten-
sioned rock bolts anchored into sound rock
beneath the sliding plane. If the rock bolts are
installed at right angles to the sliding plane,
that is,
ψ
T
=
Cohesion,
c
=
25 kPa
37
◦
Friction angle,
φ
=
55
◦
, and the total load on the
anchors per lineal meter of slope is 400 kN,
calculate the factor of safety.
The unit weight of the rock is 26 kN
/
m
3
, and the
unit weight of the water is 9.81 kN
/
m
3
.
(b)
Calculate the factor of safety if the bolts are
installed at a flatter angle so that the
ψ
T
is
decreased from 55
◦
to 20
◦
.
Required
Assuming that a plane slope failure is the most
likely type of instability, analyze the following
stability conditions.
(c)
If the working load for each bolt is 250 kN,
suggest a bolt layout, that is, the number of
bolts per vertical row, and the horizontal and
