Civil Engineering Reference
In-Depth Information
4
32
Average dip
56-60
Average
i
angles for second-
order asperities
°
3
34
14
25
10
Average dip
43.5
°
17
26
15
39
46
13
15
Average
i
angles
for first-order asperities
1m
Average dip
31
°
0 25 50 cm
Approximate scale
1m
Figure 4.11
Measurement of roughness angles
i
for
first- and second-order asperities on rough rock
surfaces (Patton, 1966).
Figure 4.10
Patton's observations of bedding plane
traces in unstable limestone slopes (Patton, 1966).
unstable bedding planes shown in Figure 4.10 and
the (
φ
i
) values, it was necessary to measure only
the first-order asperities.
Later studies by Barton (1973) showed that
Patton's results were related to the normal stress
acting across the bedding planes in the slopes
that he observed. At low normal stresses, the
second-order projections come into play and Bar-
ton quotes (
φ
+
the friction angle of the rock
φ
found from labor-
atory tests on planar surfaces, and the average
roughness
i
angle.
4.2.4 Surface roughness
i
) values in the range of 69-80
◦
for tests conducted at low normal stresses ranging
from 20 to 670 kPa (Goodman, 1970; Paulding,
1970; Rengers, 1971). Assuming a friction angle
for the rock of 30
◦
, these results show that the
effective roughness angle
i
varies between 40 and
50
◦
for these low normal stress levels.
The actual shear performance of discontinuity
surfaces in rock slopes depends on the combined
effects of the surface roughness, the rock strength
at the surface, the applied normal stress and the
amount of shear displacement. This is illustrated
in Figure 4.12 where the asperities are sheared off,
with a consequent reduction in the friction angle
with increasing normal stress. That is, there is a
transition from dilation to shearing of the rock.
The degree to which the asperities are sheared
will depend on both the magnitude of the normal
force in relation to the compressive strength of the
rock on the fracture surface, and the displacement
All natural discontinuity surfaces exhibit some
degree of roughness, varying from polished
and slickensided sheared surfaces with very low
roughness, to rough and irregular tension joints
with considerable roughness. These surface irreg-
ularities are given the general term
asperities
, and
because they can have a significant effect on the
stability of a slope, they should be accounted
for appropriately in design as discussed in this
section.
The discussion in Section 4.2.3 has been sim-
plified because Patton found that asperities can
be divided into two classes: first- and second-
order asperities as shown in Figure 4.11. The
first-order asperities are those that correspond
to the major undulations on the bedding sur-
faces, while the second-order asperities are small
bumps and ripples on the surface and have higher
i
values. In order to obtain reasonable agreement
between field observations of the dip of the
+
