2
anisotropic and, indeed, often exhibit directional proper-
ties, especially in the presence of joints.
PROBLEM APPROACH
Approach to the problem is done in three steps: (1) prepa-
ration of a rock properties file including elastic moduli and
strengths, specific weight, depth, thickness and orientation
of each stratigraphic unit in the geological column, (2) gen-
eration of a finite element mesh that represents the shaft
and adjacent geological column, and (3) analysis –execu-
tion of the finite element program.
Post-analysis is essentially an engineering judgment
concerning shaft safety. Most mine excavations are stress-
limited, so the distribution of element safety factors pro-
vides useful guidance to overall shaft safety. In squeezing
ground, displacement limits may occur, but this is not the
case for the shaft considered here.
THE #5 VENTILATION SHAFT
A long history of rock mechanics studies in the trona
patch of southwestern Wyoming has led to an accumula-
tion of useful data including laboratory test data and mine
observations that provide useful background to the current
study. These data make the compilation of strata properties
in Step 1 easily done including the important effects of
joint sets on strata moduli and strengths, mainly a reduc-
tion in magnitude of elastic moduli and strengths, but also
the introduction of directional properties -anisotropy.
Step 1 Preparation of a materials property file
(stratigraphic column)
Trona occurs in the Green River formation as illustrated
in Figure 4. There are numerous trona beds in the strati-
graphic column, not all of which are of mineable thickness.
In this regard, mining methods are room and pillar and
longwall. The latter is now the most favored. Some solution
mining of former room and pillar sections is ongoing. Oil
shale roof and floor strata are common as seen in the figure.
Figure 5 shows the actual stratigraphic column used in
the analysis. There are 12 formations in the column that
includes two trona beds. Depth to the first mining horizon
is 1500 ft or about 457 m. This trona bed is 10 ft (3 m)
thick in the analysis.
Figure 6 shows five joint sets determined by mapping
(Agapito et al 1978) underground. These joint sets were
used in the computation of equivalent strata properties,
elastic moduli and strengths (Pariseau 1999) Results are
given in Table 1, layer by layer with additional information
pertaining to depth, thickness and layer orientation.
Figure 2. Cutter head used to excavate the #5 shaft (https://mineconnect.comarticlecement
ationamericas.)
HARDENING
SOFTENING
IDEALLY PLASTIC
UNLOADING
RELOADING
STRESS
STRAIN
Figure 3. Idealized uniaxial stress-strain plots
anisotropic and, indeed, often exhibit directional proper-
ties, especially in the presence of joints.
PROBLEM APPROACH
Approach to the problem is done in three steps: (1) prepa-
ration of a rock properties file including elastic moduli and
strengths, specific weight, depth, thickness and orientation
of each stratigraphic unit in the geological column, (2) gen-
eration of a finite element mesh that represents the shaft
and adjacent geological column, and (3) analysis –execu-
tion of the finite element program.
Post-analysis is essentially an engineering judgment
concerning shaft safety. Most mine excavations are stress-
limited, so the distribution of element safety factors pro-
vides useful guidance to overall shaft safety. In squeezing
ground, displacement limits may occur, but this is not the
case for the shaft considered here.
THE #5 VENTILATION SHAFT
A long history of rock mechanics studies in the trona
patch of southwestern Wyoming has led to an accumula-
tion of useful data including laboratory test data and mine
observations that provide useful background to the current
study. These data make the compilation of strata properties
in Step 1 easily done including the important effects of
joint sets on strata moduli and strengths, mainly a reduc-
tion in magnitude of elastic moduli and strengths, but also
the introduction of directional properties -anisotropy.
Step 1 Preparation of a materials property file
(stratigraphic column)
Trona occurs in the Green River formation as illustrated
in Figure 4. There are numerous trona beds in the strati-
graphic column, not all of which are of mineable thickness.
In this regard, mining methods are room and pillar and
longwall. The latter is now the most favored. Some solution
mining of former room and pillar sections is ongoing. Oil
shale roof and floor strata are common as seen in the figure.
Figure 5 shows the actual stratigraphic column used in
the analysis. There are 12 formations in the column that
includes two trona beds. Depth to the first mining horizon
is 1500 ft or about 457 m. This trona bed is 10 ft (3 m)
thick in the analysis.
Figure 6 shows five joint sets determined by mapping
(Agapito et al 1978) underground. These joint sets were
used in the computation of equivalent strata properties,
elastic moduli and strengths (Pariseau 1999) Results are
given in Table 1, layer by layer with additional information
pertaining to depth, thickness and layer orientation.
Figure 2. Cutter head used to excavate the #5 shaft (https://mineconnect.comarticlecement
ationamericas.)
HARDENING
SOFTENING
IDEALLY PLASTIC
UNLOADING
RELOADING
STRESS
STRAIN
Figure 3. Idealized uniaxial stress-strain plots