2
Post-elastic behavior may be strain-hardening, soften-
ing or ideally elastic as seen in the figure (Pariseau 1999).
Effects of joint sets on rock properties are readily included.
Formation properties may be isotropic or anisotropic up to
orthotropy with three axes of material symmetry.
Step 2 begins with a mesh that represents the geom-
etry and geology of the considered ramp route. The mesh
is a numerical model specified by computer files describing
mostly element geometry but also boundary conditions and
material behavior. Several common cross section shapes are
available.
Mesh generation is easy and is done interactively with
the aid of a computer program. First, the name of the rock
properties file is requested, then the ramp type is called for
(switchback or spiral). Grade is also requested and so it
goes. All files needed for a finite element analysis are gen-
erated including a finite element run stream file. A short
file that echoes input data is also generated. A visual mesh
check is made possible by plotting the mesh using a conve-
nient plotting program.
Step 3 is simply execution of the finite element run
stream, perhaps after some simple editing. A tap on the
executable finite element program file is all that is needed.
Design evaluation follows from study of results, especially
results in the form of element safety factor distributions.
EXAMPLE–SWITCHBACK (ZIG-ZAG)
RAMP
This example relates to the former Homestake Mine in
Lead, SD. This gold mine was developed to a depth of
8,000 ft (2,500 m) before closure and subsequent con-
version to an underground research facility, the Sanford
Underground Research Facility (SURF). Level interval at
the mine is 150 ft (47.5 m). Ramps extended from surface
to considerable depth.
Much rock mechanics data have been gathered through
many studies during the operating life of the mine includ-
ing stress measurements and formation properties (Pariseau
1985). The mine is located in Precambrian meta-sediments
that impart distinct directional features to the rock. The
Poorman formation formed the footwall ore was located
in the Homestake formation, and the Ellison formation
formed the hanging wall. Laboratory testing of oriented
drill core down the dip of the foliation, on strike and nor-
mal to the plane of the foliation suggested an orthotropic
material model with three distinct directions abc of anisot-
ropy (Duan 1985). The finite element axes are xyz. The axes
of anisotropy are related to the reference axes by the dip
direction and dip angles, a, d. Depth to a particular for-
mation and formation thickness are also specified in the
material properties file.
Step 1 Preparation of a materials property file Specification
of formation properties includes effects of joint sets (Golder
Associates 2010) illustrated in Figure 2.
The resulting equivalent rock properties are
NLYRS =3
NSEAM =3
(1) Ellison
0.288E+07 0.402E+07 0.389E+07 0.08 0.30 0.19
0.218E+07 0.115E+07 0.890E+06 0.00 0.00 0.00
HARDENING
SOFTENING
IDEALLY PLASTIC
UNLOADING
RELOADING
STRESS
STRAIN
Figure 1. Idealized uniaxial stress-strain plots
Figure 2. Schematic illustration of the two joint sets used in
computing equivalent properties
Post-elastic behavior may be strain-hardening, soften-
ing or ideally elastic as seen in the figure (Pariseau 1999).
Effects of joint sets on rock properties are readily included.
Formation properties may be isotropic or anisotropic up to
orthotropy with three axes of material symmetry.
Step 2 begins with a mesh that represents the geom-
etry and geology of the considered ramp route. The mesh
is a numerical model specified by computer files describing
mostly element geometry but also boundary conditions and
material behavior. Several common cross section shapes are
available.
Mesh generation is easy and is done interactively with
the aid of a computer program. First, the name of the rock
properties file is requested, then the ramp type is called for
(switchback or spiral). Grade is also requested and so it
goes. All files needed for a finite element analysis are gen-
erated including a finite element run stream file. A short
file that echoes input data is also generated. A visual mesh
check is made possible by plotting the mesh using a conve-
nient plotting program.
Step 3 is simply execution of the finite element run
stream, perhaps after some simple editing. A tap on the
executable finite element program file is all that is needed.
Design evaluation follows from study of results, especially
results in the form of element safety factor distributions.
EXAMPLE–SWITCHBACK (ZIG-ZAG)
RAMP
This example relates to the former Homestake Mine in
Lead, SD. This gold mine was developed to a depth of
8,000 ft (2,500 m) before closure and subsequent con-
version to an underground research facility, the Sanford
Underground Research Facility (SURF). Level interval at
the mine is 150 ft (47.5 m). Ramps extended from surface
to considerable depth.
Much rock mechanics data have been gathered through
many studies during the operating life of the mine includ-
ing stress measurements and formation properties (Pariseau
1985). The mine is located in Precambrian meta-sediments
that impart distinct directional features to the rock. The
Poorman formation formed the footwall ore was located
in the Homestake formation, and the Ellison formation
formed the hanging wall. Laboratory testing of oriented
drill core down the dip of the foliation, on strike and nor-
mal to the plane of the foliation suggested an orthotropic
material model with three distinct directions abc of anisot-
ropy (Duan 1985). The finite element axes are xyz. The axes
of anisotropy are related to the reference axes by the dip
direction and dip angles, a, d. Depth to a particular for-
mation and formation thickness are also specified in the
material properties file.
Step 1 Preparation of a materials property file Specification
of formation properties includes effects of joint sets (Golder
Associates 2010) illustrated in Figure 2.
The resulting equivalent rock properties are
NLYRS =3
NSEAM =3
(1) Ellison
0.288E+07 0.402E+07 0.389E+07 0.08 0.30 0.19
0.218E+07 0.115E+07 0.890E+06 0.00 0.00 0.00
HARDENING
SOFTENING
IDEALLY PLASTIC
UNLOADING
RELOADING
STRESS
STRAIN
Figure 1. Idealized uniaxial stress-strain plots
Figure 2. Schematic illustration of the two joint sets used in
computing equivalent properties