Civil Engineering Reference
In-Depth Information
slightly lower, residual shear stress. The sample
was initially undisplaced, so exhibited a differ-
ence between peak and residual strengths (see
Figure 4.8). The normal stresses at the peak and
residual shear stress values are calculated from
the applied normal load and the contact area.
When calculating the contact area, an allowance
is made for the decrease in area as shear displace-
ment takes place. For diamond drill core in an
inclined hole, the fracture surface is in the shape
of an ellipse, and the formula for calculating the
contact area is as follows (Hencher and Richards,
1989):
As shown in Figure 4.17, it is usual to test
each sample at a minimum of three normal stress
levels, with the sample being reset to its original
position between tests. When the tests are run
at progressively higher normal stress levels, the
total friction angle of the surface will diminish
with each test if the asperities are progressively
sheared. This produces a concave upwards nor-
mal stress-shear stress plot as shown in the upper
left plot of Figure 4.17. The degree to which the
asperities are sheared off will depend on the level
of the normal stress in comparison to the rock
strength, that is, the ratio JCS
/σ
in equation (4.7).
The maximum normal stress that is used in the
test is usually the maximum stress level that is
likely to develop in the slope.
It is also possible to measure the normal stiff-
ness of the discontinuity infilling during the direct
shear test as shown in the lower left plot in
Figure 4.17. Normal stiffness
k
n
is the ratio of
the normal stress
σ
to normal displacement
δ
n
,or
δ
s
b(
4
a
2
1
/
2
δ
s
)
−
A
=
πab
−
2
a
2
ab
sin
−
1
δ
s
2
a
−
(4.10)
where A is the gross area of contact, 2
a
is the
major axis of ellipse, 2
b
is the minor axis of ellipse
and
δ
s
is the relative shear displacement.
The increase in the normal stress with displace-
ment for a constant normal load is shown in the
upper left diagram of Figure 4.17 where the nor-
mal stress for the residual shear stress is greater
than that for the peak shear stress.
The measured friction angle is the sum of the
friction angle of the rock
(φ
r
)
, and the roughness
of the surface
(i)
. The roughness of the surface
is calculated from the plots of shear and normal
displacement
(δ
s
and
δ
n
, respectively, on the lower
right side of Figure 4.17) as follows:
σ
δ
n
k
n
=
(4.12)
The plot of
σ
against
δ
n
is highly non-linear and
the value of
k
n
is the slope of the initial portion of
the curve. The normal stiffness of a fracture is not
usually an issue in rock slope design, and is more
often used in the estimation of the deformation
modulus of a rock mass (Wyllie, 1999), and in
numerical analysis (see Chapter 10).
It can be difficult to measure the cohesion of a
surface with the direct shear test because, if the
cohesion is very low, it may not be possible to
obtain an undisturbed sample. If the cohesion is
high and the sample is intact, the material hold-
ing the sample in the test equipment will have to
be stronger than the infilling if the sample is to
shear. Where it is important that the cohesion of
a weak infilling be measured, an
in situ
test of the
undisturbed material may be required.
tan
−
1
δ
n
δ
s
i
=
(4.11)
This value of
i
is then subtracted from the friction
angle calculated from the plot of shear and nor-
mal stresses at failure to obtain the friction angle
of the rock. While the shear test can be conducted
on a sawed sample on which there is no roughness
component, the saw may polish the surface result-
ing in a low value of the friction angle compared
to a natural surface.
4.4 Shear strength of rock masses by
back analysis of slope failures
For the geological conditions shown in Figure 4.3
where a cut has been made in fractured rock,
