3
LAMODEL
The LaModel 3.0 program was selected to simulate the
pillar behavior in this study due to its compatibility with
widely used calibration procedures, such as those in the
Analysis of Coal Pillar Stability (ACPS) program (Mark
and Agioutantis, 2018). Using LAMPRE 3.0, LaModel’s
preprocessor, the coal seam was discretized into 10-ft ele-
ments. A grid size of 1,000 × 1,000 elements (or 10,000
× 10,000 feet) was selected to create a sufficient buffer and
minimize potential edge effects. Openings were modeled
at a nominal 20 ft. even though the combined belt/track
entries are 22 ft. wide as mined. Symmetric boundary con-
ditions were applied on all sides, and the overburden was
modeled as a flat 2,000 ft. for consistency between the lay-
out comparisons.
CALIBRATION OF THE MODEL
Accurate calibration of input parameters is critical to achiev-
ing reliable output in numerical models like LaModel.
Calibration requires using the most reliable data sources,
whether derived from measurements, observations, or
empirical data. This analysis calibrated three parameters:
rock mass stiffness, gob stiffness, and coal strength. These
were calibrated in sequence, as each subsequent parameter’s
calibrated value depended on the previous one (Heasley,
2008).
In LaModel, the stiffness of the rock mass is deter-
mined by the rock mass modulus and lamination thickness
(see Figure 4).
Adjusting these parameters alters the stiffness of the
overburden, which in turn affects the extent of the abut-
ment. For this study, the rock mass modulus was held con-
stant at 3,000,000 psi. Lamination thickness was adjusted
to reflect the empirically suggested abutment extent, where
90% of the load is distributed within a distance of five
times the square root of the depth (H) (Mark, 2010).
The final gob modulus, which defines the stiffness of
the strain-hardening gob material, controls the magnitude
of the abutment load. This was conceptualized using the
abutment angle (see Figure 5). Based on stress measure-
ments from five U.S. mines, an average abutment angle
of 21° was used (Mark, 1992). To match this angle, gob
modulus values of 300,000 psi and 180,000 psi were used
for the 705-ft and 1,000-ft panel layouts, respectively.
The Mark-Bieniawski pillar strength was used to cali-
brate coal strength, assuming an in-situ coal strength of
900 psi and a mining height of 7.5 ft. To match the Mark-
Bieniawski pillar strength, an elastic-plastic material model
was chosen for the coal. This material model was preferred
due to its widespread understanding and ability to match
pillar strength without further calibration of in-situ coal
Figure 4. Overburden layers indicating thickness, modulus,
and Poisson’s ratio
Figure 5. Conceptualization of the abutment angle depicting a supercritical panel (A) and a
subcritical panel (B) (after Mark, 2010)
LAMODEL
The LaModel 3.0 program was selected to simulate the
pillar behavior in this study due to its compatibility with
widely used calibration procedures, such as those in the
Analysis of Coal Pillar Stability (ACPS) program (Mark
and Agioutantis, 2018). Using LAMPRE 3.0, LaModel’s
preprocessor, the coal seam was discretized into 10-ft ele-
ments. A grid size of 1,000 × 1,000 elements (or 10,000
× 10,000 feet) was selected to create a sufficient buffer and
minimize potential edge effects. Openings were modeled
at a nominal 20 ft. even though the combined belt/track
entries are 22 ft. wide as mined. Symmetric boundary con-
ditions were applied on all sides, and the overburden was
modeled as a flat 2,000 ft. for consistency between the lay-
out comparisons.
CALIBRATION OF THE MODEL
Accurate calibration of input parameters is critical to achiev-
ing reliable output in numerical models like LaModel.
Calibration requires using the most reliable data sources,
whether derived from measurements, observations, or
empirical data. This analysis calibrated three parameters:
rock mass stiffness, gob stiffness, and coal strength. These
were calibrated in sequence, as each subsequent parameter’s
calibrated value depended on the previous one (Heasley,
2008).
In LaModel, the stiffness of the rock mass is deter-
mined by the rock mass modulus and lamination thickness
(see Figure 4).
Adjusting these parameters alters the stiffness of the
overburden, which in turn affects the extent of the abut-
ment. For this study, the rock mass modulus was held con-
stant at 3,000,000 psi. Lamination thickness was adjusted
to reflect the empirically suggested abutment extent, where
90% of the load is distributed within a distance of five
times the square root of the depth (H) (Mark, 2010).
The final gob modulus, which defines the stiffness of
the strain-hardening gob material, controls the magnitude
of the abutment load. This was conceptualized using the
abutment angle (see Figure 5). Based on stress measure-
ments from five U.S. mines, an average abutment angle
of 21° was used (Mark, 1992). To match this angle, gob
modulus values of 300,000 psi and 180,000 psi were used
for the 705-ft and 1,000-ft panel layouts, respectively.
The Mark-Bieniawski pillar strength was used to cali-
brate coal strength, assuming an in-situ coal strength of
900 psi and a mining height of 7.5 ft. To match the Mark-
Bieniawski pillar strength, an elastic-plastic material model
was chosen for the coal. This material model was preferred
due to its widespread understanding and ability to match
pillar strength without further calibration of in-situ coal
Figure 4. Overburden layers indicating thickness, modulus,
and Poisson’s ratio
Figure 5. Conceptualization of the abutment angle depicting a supercritical panel (A) and a
subcritical panel (B) (after Mark, 2010)