Civil Engineering Reference
In-Depth Information
intersection is about 50-55
◦
, while the friction
angle of these joints is in the range of 35-40
◦
.
That is, the line of intersection dips steeper than
the friction angle. These conditions meet the kin-
ematic requirements for failure of the wedge.
Figure 7.1 also illustrates how a slight change in
the site conditions would result in a stable slope.
For example, if the line of intersection had been
slightly behind the face, or just one of the joints
had been discontinuous, then no failure would
have occurred.
The wedge in Figure 7.2 is formed by bedding
on the left and a conjugate joint set on the right.
As in Figure 7.1, the line of intersection daylights
in the slope face and failure occurred. However,
in this wedge, sliding occurred almost entirely on
the bedding with the joint acting as a release sur-
face. Therefore, the shear strength of the joint has
little effect on stability.
The geometry of the wedge for analyzing the
basic mechanics of sliding is defined in Figure 7.3.
Based on this geometry, the general conditions for
wedge failure are as follows:
In addition, equations are presented that can be
used to calculate the factor of safety of wedges
where the shear strength on the two slide planes
is defined by cohesion and friction angle, and
each plane can have different shear strengths. The
analysis can also incorporate water pressure.
The presence of a tension crack, and the influ-
ence of external forces due to water pressures,
tensioned anchors, seismic accelerations or bridge
foundations results in a significant increase in
the complexity of the equations. Appendix III
presents the complete solution for the wedge
analysis.
7.2 Definition of wedge geometry
Typical wedge failures illustrated in Figures 7.1
and 7.2 show the conditions that are normally
assumed for the analytical treatment of wedges.
Figure 7.1 shows a cut slope where a wedge is
formed by two continuous, planar discontinu-
ities and the line of intersection of these two
planes daylights just at the toe of the rock face.
That is, the trend of the line of intersection and
the dip direction of the face are approximately
equal. Furthermore, the plunge of the line of
1
Two planes will always intersect in a line
(Figure 7.3(a)). On the stereonet, the line of
Figure 7.2
Wedge formed by
bedding (left) and a conjugate
joint set (right); sliding
occurred on bedding with
joints acting as a release
surface (bedded shale, near
Helena, Montana).
