Civil Engineering Reference
In-Depth Information
Numerical analysis
Dr Loren Lorig and Pedro Varona
1
10.1 Introduction
The previous four chapters discussed limit equi-
librium methods of slope stability analysis for
rock bounded by specified slide planes. In con-
trast, this chapter discusses numerical analysis
methods to calculate the factor of safety without
pre-defining slide planes. These methods are more
recent developments than limit equilibrium meth-
ods and, at present (2003), are used predomin-
ately in open pit mining and landslides studies,
where interest often focuses on slope displace-
ments rather than on the relative magnitude of
resisting and displacing forces.
Numerical models are computer programs that
attempt to represent the mechanical response of a
rock mass subjected to a set of initial conditions
such as
in situ
stresses and water levels, bound-
ary conditions and induced changes such as slope
excavation. The result of a numerical model sim-
ulation typically is either equilibrium or collapse.
If an equilibrium result is obtained, the resultant
stresses and displacements at any point in the rock
mass can be compared with measured values. If a
collapse result is obtained, the predicted mode of
failure is demonstrated.
Numerical models divide the rock mass into
zones. Each zone is assigned a material model
and properties. The material models are idealized
stress/strain relations that describe how the
material behaves. The simplest model is a linear
elastic model, which uses the elastic properties
(Young's modulus and Poisson's ratio) of the
material. Elastic-plastic models use strength
parameters to limit the shear stress that a zone
may sustain.
2
The zones may be connected together, termed a
continuum model, or separated by discontinuities,
termed a discontinuum model. Discontinuum
models allow slip and separation at explicitly
located surfaces within the model.
Numerical models tend to be general purpose in
nature—that is, they are capable of solving a wide
variety of problems. While it is often desirable to
have a general-purpose tool available, it requires
that each problem be constructed individually.
The zones must be arranged by the user to fit the
limits of the geomechanical units and/or the slope
geometry. Hence, numerical models often require
more time to set up and run than special-purpose
tools such as limit equilibrium methods.
There are several reasons why numerical
models are used for slope stability studies.
•
Numerical models can be extrapolated confid-
ently outside their databases in comparison to
empirical methods in which the failure mode
is explicitly defined.
•
Numerical analysis can incorporate key geo-
logic features such as faults and ground water
providing more realistic approximations of
behavior of real slopes than analytic models.
2 In numerical analysis the terms “elements” and “zones” are
used interchangeably. However, the term element is used
more commonly in finite element analysis, and the term
zone in finite difference analysis.
1 Itasca Consulting Group, Inc., Minneapolis, Minnesota
55401 USA.
