6
less than what is empirically suggested using the lamination
thickness wizard.
The calibration of the gob stiffness, which is based on
borehole pressure cell (BPC) measurements, necessitated
the identification of an appropriate calibration technique
for the BPC data. Over the years, numerous attempts
have been made to correlate measured BPC data with the
actual stress in the rock mass. These attempts have been
documented by various researchers (Sellers, 1970 Bauer et
al.,1985 Babcock, 1986 Heasley, 1989 Su and Hasenfus,
1990). Two significant factors that influence the response of
BPCs are the setting pressure and the stiffness of the mate-
rial in which the BPC is installed. Given that the BPCs
used in this study had varying setting pressures and most
were installed in the rock parting, it was deemed crucial to
employ a calibration procedure that was suitable for this
specific context.
To address this challenge, the BPC data was calibrated
using a secondary, empirical data source. This calibration
method, which is a variant of the work conducted by Tulu
and Heasley (2012), makes the assumption that the peak
stress in the pillar at the location of the yielded BPC aligns
with what is expected based on the Bieniawski pillar stress
gradient (Mark and Chase, 1997). The percentage increase
of the measured value versus the expected value can then be
used as a calibration factor for the remaining BPCs that did
not yield (see Tables 1 and 2). This BPC calibration tech-
nique was selected so that the BPC measurements could be
directly related to the results from either ACPS or LaModel.
As can be seen from Table 2, the expected abutment
loading for the side abutments is 3.1 times the development
load. For the back bleeders, an average of 2.6 times the
development load over the instrumented area is expected.
These values can now be used to calibrate the LaModel pro-
gram based on the expected abutment loading compared to
what was measured in the field.
The final gob modulus defines the stiffness of the strain-
hardening gob material and controls the magnitude of the
abutment load. This is typically conceptualized using the
abutment angle (see Figure 12), where stress measurements
from five mines suggested an average of 21° in U.S. mines
(Mark, 1992). The final gob modulus that best matched the
calibrated BPC measurements of the abutment loads was
found to be 460,000 psi. This is equivalent to an abutment
angle of approximately 29–30°. While this is significantly
higher than the average, it falls within the range of mea-
sured cases, particularly at shallow cover depths of less than
600 ft.
The coal strength calibrated for the initial model
assumed the pillars were 9-ft. high, as measured at Sites 2
and 3. The Mark-Bieniawski pillar strength, assuming a
900-psi in-situ coal strength, was used to simulate the coal
material using an elastic-plastic material model. This model
was chosen due to its widespread understanding compared
to the calibration process involving strain-softening materi-
als. It matches the Mark-Bieniawski pillar strength without
calibrating the in-situ coal strength, which is a function of
pillar size for strain-softening materials.
THE VIRTUAL MINING HEIGHT
Based on the results of the initial calibrated model, it
was determined that the half-yield block reached its peak
strength when the pillar line was 170 ft. outby the instru-
mentation site. However, measurements obtained clearly
indicate that the pillar reaches this point in reality when the
pillar line is 290 ft. outby. Therefore, the strength of the pil-
lar required an adjustment to align with the measurements
taken in the field.
Figure 12. Conceptualization of the abutment angle
depicting a supercritical panel (A) and a subcritical panel (B)
(after Mark, 2010).
Table 2. Measured and expected stress for the three BPC
locations where sufficient data was recorded in the abutment
pillars at Sites 2 and 3 labeled S1, S2, and S3 and the average
for all BPC data collected from Site 1 labeled Bld.
Table 1. Measured and expected stress for the four BPCs
that reached their peak pressure in the half leave pillars
indicating an average BPC calibration factor of 1.6.
less than what is empirically suggested using the lamination
thickness wizard.
The calibration of the gob stiffness, which is based on
borehole pressure cell (BPC) measurements, necessitated
the identification of an appropriate calibration technique
for the BPC data. Over the years, numerous attempts
have been made to correlate measured BPC data with the
actual stress in the rock mass. These attempts have been
documented by various researchers (Sellers, 1970 Bauer et
al.,1985 Babcock, 1986 Heasley, 1989 Su and Hasenfus,
1990). Two significant factors that influence the response of
BPCs are the setting pressure and the stiffness of the mate-
rial in which the BPC is installed. Given that the BPCs
used in this study had varying setting pressures and most
were installed in the rock parting, it was deemed crucial to
employ a calibration procedure that was suitable for this
specific context.
To address this challenge, the BPC data was calibrated
using a secondary, empirical data source. This calibration
method, which is a variant of the work conducted by Tulu
and Heasley (2012), makes the assumption that the peak
stress in the pillar at the location of the yielded BPC aligns
with what is expected based on the Bieniawski pillar stress
gradient (Mark and Chase, 1997). The percentage increase
of the measured value versus the expected value can then be
used as a calibration factor for the remaining BPCs that did
not yield (see Tables 1 and 2). This BPC calibration tech-
nique was selected so that the BPC measurements could be
directly related to the results from either ACPS or LaModel.
As can be seen from Table 2, the expected abutment
loading for the side abutments is 3.1 times the development
load. For the back bleeders, an average of 2.6 times the
development load over the instrumented area is expected.
These values can now be used to calibrate the LaModel pro-
gram based on the expected abutment loading compared to
what was measured in the field.
The final gob modulus defines the stiffness of the strain-
hardening gob material and controls the magnitude of the
abutment load. This is typically conceptualized using the
abutment angle (see Figure 12), where stress measurements
from five mines suggested an average of 21° in U.S. mines
(Mark, 1992). The final gob modulus that best matched the
calibrated BPC measurements of the abutment loads was
found to be 460,000 psi. This is equivalent to an abutment
angle of approximately 29–30°. While this is significantly
higher than the average, it falls within the range of mea-
sured cases, particularly at shallow cover depths of less than
600 ft.
The coal strength calibrated for the initial model
assumed the pillars were 9-ft. high, as measured at Sites 2
and 3. The Mark-Bieniawski pillar strength, assuming a
900-psi in-situ coal strength, was used to simulate the coal
material using an elastic-plastic material model. This model
was chosen due to its widespread understanding compared
to the calibration process involving strain-softening materi-
als. It matches the Mark-Bieniawski pillar strength without
calibrating the in-situ coal strength, which is a function of
pillar size for strain-softening materials.
THE VIRTUAL MINING HEIGHT
Based on the results of the initial calibrated model, it
was determined that the half-yield block reached its peak
strength when the pillar line was 170 ft. outby the instru-
mentation site. However, measurements obtained clearly
indicate that the pillar reaches this point in reality when the
pillar line is 290 ft. outby. Therefore, the strength of the pil-
lar required an adjustment to align with the measurements
taken in the field.
Figure 12. Conceptualization of the abutment angle
depicting a supercritical panel (A) and a subcritical panel (B)
(after Mark, 2010).
Table 2. Measured and expected stress for the three BPC
locations where sufficient data was recorded in the abutment
pillars at Sites 2 and 3 labeled S1, S2, and S3 and the average
for all BPC data collected from Site 1 labeled Bld.
Table 1. Measured and expected stress for the four BPCs
that reached their peak pressure in the half leave pillars
indicating an average BPC calibration factor of 1.6.