Civil Engineering Reference
In-Depth Information
contracts until it is equal to the minimum allowed
by the grid, that is a fixed number of zone widths.
Thus, the strain in the band is
strength reduction process, these zones should be
considered as a new material with lower strength,
but no further softening should be allowed due
to the plastic strains associated to the gradual
reduction of strength.
Increases in pore pressure with time are not
common in rock slopes for mines. More com-
monly, the pore pressures reduce due to deepen-
ing of the pit and/or drainage. However, there are
cases in which the pore pressures do increase with
time. In such cases, the slope may appear to fail
progressively.
Creep, which is time-dependent deformation of
material under constant load, is not commonly
considered in the context of slope stability. It
is much more common in underground excav-
ations. Several material models are available to
study creep behavior in rock slopes. These include
classical viscoelastic models, power law models,
and the Burger-creep viscoplastic model. Applic-
ation of a creep model to the study of slope beha-
vior at Chuquicamata mine in Chile is discussed
later in this chapter (see Section 10.5.2).
ε
=
u/nz
(10.3)
where
n
is a fixed number,
u
is the displacement
jump, and
z
is the zone width.
If the softening slope is linear, the change in a
property value
p
is proportional to strain, the
change in property value with displacement is:
p
u
=
s
(10.4)
·
n
z
where
s
is the softening slope.
In order to obtain mesh-independent results, a
scaled softening slope
s
can be input, such that
s
z
s
=
(10.5)
where
s
is constant.
In this case,
(p/u)
is independent of
z
.If
the softening slope is defined by the critical strain,
ε
crit
, then
10.3 Modeling issues
Modeling requires that the real problem be ideal-
ized, or simplified, in order to fit the constraints
imposed by factors such as available material
models and computer capacity. Analysis of rock
mass response involves different scales. It is
impossible—and undesirable—to include all fea-
tures, and details of rock mass response mechan-
isms, into one model. In addition, many of the
details of rock mass behavior are unknown and
unknowable; therefore, the approach to model-
ing is not as straightforward as it is, say, in other
branches of mechanics. This section discusses the
basic issues that must be resolved when setting up
a numerical model.
1
z
ε
crit
∝
(10.6)
For example, if the zone size is doubled, the
critical strain must be halved for comparable
results.
Strain-softening models for discontinuities are
much more common than similar relations for
rock masses. Strain-softening relations for dis-
continuities are built into UDEC and 3DEC, and
can be incorporated into interfaces in FLAC and
FLAC3D via a built-in programming language
such as FISH functions. Strain-softening models
require special attention when computing safety
factors. If a strain-softening constitutive model
is used, the softening logic should be turned off
during the shear strength reduction process or the
factor of safety will be underestimated. When
the slope is excavated, some zones will have
exceeded their peak strength, and some amount
of softening will have taken place. During the
10.3.1 Two-dimensional analysis versus
three-dimensional analysis
The
first
step
in
creating
a
model
is
to
decide
whether
to
perform
two-dimensional
or three-dimensional analyses.
Prior to 2003,
