Civil Engineering Reference
In-Depth Information
not account for external forces such as water
pressures or reinforcement comprising tensioned
rock bolts, which can have a significant effect on
stability. The usual design procedure is to use
kinematic analysis to identify potentially unstable
blocks, followed by detailed stability analysis of
these blocks using the procedures described in
Chapters 6-9.
An example of kinematic analysis is shown in
Figure 2.18 where a rock slope contains three sets
of discontinuities. The potential for these discon-
tinuities to result in slope failures depends on their
dip and dip direction relative to the face; stabil-
ity conditions can be studied on the stereonet as
described in the next section.
2.6.2 Plane failure
In Figure 2.18(a), a potentially unstable planar
block is formed by plane AA, which dips at a flat-
ter angle than the face (
ψ
A
<ψ
f
) and is said
to “daylight” on the face. However, sliding is
not possible on plane BB which dips steeper than
the face (
ψ
B
>ψ
f
) and does not daylight. Simil-
arly, discontinuity set CC dips into the face and
sliding cannot occur on these planes, although
toppling is possible. The poles of the slope face
and the discontinuity sets (symbol
P
) are plotted
on the stereonet in Figure 2.18(b), assuming that
all the discontinuities strike parallel to the face.
The position of these poles in relation to the slope
face shows that the poles of all planes that day-
light and are potentially unstable, lie inside the
pole of the slope face. This area is termed the
day-
light envelope
and can be used to identify quickly
potentially unstable blocks.
The dip direction of the discontinuity sets will
also influence stability. Plane sliding is not pos-
sible if the dip direction of the discontinuity
differs from the dip direction of the face by more
than about 20
◦
. That is, the block will be stable
if
(a)
A
A
<
f
: sliding possible
A
B
A
Toppling set
B
>
f
: stable
C
C
B
f
C
B
>
20
◦
, because under these condi-
tions there will be an increasing thickness of intact
rock at one end of the block which will have suf-
ficient strength to resist failure. On the stereonet
this restriction on the dip direction of the planes
is shown by two lines defining dip directions of
(
α
f
+
|
α
A
−
α
f
|
(b)
Great circle of
face, dip
N
f
20
◦
). These two lines desig-
nate the lateral limits of the daylight envelope on
Figure 2.18(b).
20
◦
) and (
α
f
−
20
(90
°
-
°
P
AA
j
10
°
P
CC
P
BB
P
f
f
)
f
10
°
20
°
2.6.3 Wedge failure
Kinematic analysis of wedge failures (Figure
2.16(b)) can be carried out in a similar manner
to that of plane failures. In this case the pole of
the line of intersection of the two discontinuities
is plotted on the stereonet and sliding is possible
if the pole daylights on the face, that is (
ψ
i
<ψ
f
).
The direction of sliding of kinematically permiss-
ible wedges is less restrictive than that of plane
failures because there are two planes to form
release surfaces. A daylighting envelope for the
Legend
Daylight envelope for wedges
Daylight envelope for planar failures
Toppling envelope
Figure 2.18
Kinematic analysis of blocks of rock in
slope: (a) discontinuity sets in slope; and (b) daylight
envelopes on equal area stereonet.
