Civil Engineering Reference
In-Depth Information
•
recognizes the existence of contacts or
interfaces between discrete bodies, such as
slabs of rocks formed by discontinuities dip-
ping steeply into the slope face;
failure is described by Davies and Smith (1993).
The toppling occurred in siltstones in which the
beds were very closely spaced and dipped at
between 90
◦
and 70
◦
into the face. Excavation
for a bridge abutment resulted in a series of ten-
sion cracks along the crest, and stabilization of the
slope required the installation of tensioned rock
bolts and excavation to reduce the slope angle.
•
calculates the motion along contacts by
assigning a finite normal stiffness along the
discontinuities that separate the columns of
rock. The normal stiffness of a discontinuity
is defined as the normal closure that occurs
on the application of a normal stress and
can be measured from a direct shear test (see
Figure 4.17);
9.6 Example Problem 9.1: toppling
failure analysis
•
assumes
deformable
blocks
that
undergo
Statement
bending and tensile failure;
Consider a 6 m high slope with an overhanging
face at an angle of 75
◦
There is a fault, dipping
at an angle of 15
◦
out of the face, at the toe of
the slope that is weathering and undercutting the
face. A tension crack, which is wider at the top
than at the bottom, has developed 1.8 m behind
the crest of the slope indicating that the face is
marginally stable (Figure 9.13). The friction angle
φ
of the fault is 20
◦
and the cohesion
c
is 25 kPa.
The slope is dry.
•
allows finite displacements and rotations
of the toppling blocks, including complete
detachment, and recognizes new contacts
automatically as the calculation progresses;
•
uses an explicit “time”-marching scheme to
solve the equation of motion directly. This
allows modeling of progressive failure, or the
amount of creep exhibited by a series of top-
pling blocks for a chosen slope condition,
such as excavation at the toe of the slope.
Note that the time step in the analysis is not
actual time but a simulation of progressive
movement; and
Required
(a)
Calculate the factor of safety of the block
against sliding if the density of the rock is
23.5 kN
/
m
3
.
•
allows the user to investigate different
stabilization measures, such as installing rock
bolts or installing drain holes, to determine
which scenario has the most effect on block
movements.
(b)
Is the block stable against toppling as defined
by the relation:
x/y >
tan
ψ
p
—stable?
Because of the large number of input paramet-
ers that are used in UDEC and the power of the
analysis, the most reliable results are obtained if
the model can be calibrated against an existing
toppling failure in similar geological conditions
to those in the design slope. The ideal situation
is in mining operations where the development
of the topple can be simulated by UDEC as the
pit is deepened and movement is monitored. This
allows the model to be progressively updated
with new data. Chapter 10 discusses numerical
modeling of slopes in more detail.
The application of kinematic stability tests
and reinforcement design for a flexural toppling
Y
=6m
=15
°
x
= 1.8 m
∆
Figure 9.13
Toppling block illustrating Example
Problem 9.1.
