Civil Engineering Reference
In-Depth Information
UDEC (Version 3.10)
500
Legend
Cycle 487840
400
Block plot
Velocity vectors
Maximum = 0.043
300
0
0.2
200
100
0
-100
Horizontal axis (m)
0
100
200
300
400
500
600
700
Figure 10.7
Plane failure mode with rigid blocks determined with UDEC.
If a tension crack does form, then the factor
of safety is slightly reduced. Deformable blocks
with elastic-plastic behavior are required to form
tension cracks within the UDEC analysis. When
deformable zones are used, the resultant safety
factor is 1.27, similar to the value of 1.3 given by
the analytic solution. The difference may be that
the analytic solution assumes a vertical tension
crack, whereas the UDEC analysis indicates that
the tension crack curves where it meets the sliding
plane (see Figure 10.8).
Similar analyses can be performed for non-
daylighting failure planes. In this case, failure
involves sliding on discontinuities and shearing
through the rock mass at the toe of the slope, as
shown in Figure 10.9. Here, the cohesionless slid-
ing planes dip at 70
◦
and are spaced 20 m apart.
The resultant safety factor is about 1.5.
analyses must be performed in three dimensions.
As with plane failure, sliding analysis of day-
lighting rigid blocks is best solved using analytic
methods, as described in Chapter 7. Analyses
involving formation of tension cracks and/or non-
daylighting wedges require numerical analysis.
Candidate codes include FLAC3D and 3DEC.
The plasticity formulation in FLAC3D uses a
mixed discretization technique and presently
provides a better solution than 3DEC in cases
where rock mass failure dominates. On the other
hand, setting up problems involving more than
one sliding plane in FLAC3D is more difficult and
time consuming than similar problems in 3DEC.
10.4.4 Toppling failure—block and flexural
Toppling failure modes involve rotation and thus
usually are difficult to solve using limit equilib-
rium methods. As the name implies, block top-
pling involves free rotation of individual blocks
(Figure 9.3(a)), whereas flexural toppling involves
bending of rock columns or plates (Figure 9.3(b)).
10.4.3 Wedge failure—daylighting and
non-daylighting
Analyses involving wedge failures are similar to
those involving plane failures, except that the
