Civil Engineering Reference
In-Depth Information
UDEC (Version 3.20)
500
Legend
Cycle 1153501
Time 1.451E + 03 sec
400
Y displacement contours
Contour interval = 3.0
300
(zero contour line omitted)
-12
-8
-6
-4
-2
0
200
-10
100
Block plot
0
-100
Horizontal axis (m)
0
100
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Figure 10.10
Forward block toppling failure mode determined with UDEC.
Block toppling occurs where narrow slabs
are formed by joints dipping steeply into the
face, combined with flatter cross-joints (see
Section 9.4). The cross-joints provide release
surfaces for rotation of the blocks. In the most
common form of block toppling, the blocks,
driven by self-weight, rotate forward out of
the slope. However, backward or reverse top-
pling can also occur when joints parallel to the
slope face and flatter cross-joints are particularly
weak. In cases of both forward and backward
toppling, stability depends on the location of
the center of gravity of the blocks relative to
their base.
Figure 10.10 shows the results of an analysis
involving forward block toppling. The steep joint
set dips at 70
◦
with a spacing of 20 m. The cross-
joints are perpendicular and are spaced at 30 m.
The resultant safety factor is 1.13. Figure 10.11
shows the result of an analysis involving back-
ward block toppling. In this case, the face-parallel
joints are spaced at 10 m, and the horizontal joints
are spaced at 40 m. The factor of safety for this
failure mode is 1.7.
Flexural toppling occurs when there is one
dominant, closely spaced, set of joints dip-
ping steeply into the face, with insufficient
cross-jointing to permit free rotation of blocks.
The columns bend out of the slope like cantilever
beams. Figure 10.12 shows the results of analysis
with joints spaced at 20 m. The factor of safety
is 1.3, with the safety factor being reduced as
the joint spacing decreases. Problems involving
flexural toppling require finer zoning than prob-
lems involving block toppling. Because flexural
toppling involves high stress gradients across any
rock column, it is necessary to provide sufficient
zones to represent accurately the stress gradients
due to bending. In the modeling of centrifuge
tests reported by Adhikary and Guo (2000),
UDEC modeling required four zones across each
column, resulting in a model with nearly 20,000
three-noded triangular zones. In contrast, a finite
element model with Cosserat plasticity elements
required only about 1200, eight-noded isopara-
metric quadrilateral elements. Both models pro-
duced good agreement with the laboratory results
(see also Section 9.5).
