The Marshall County Coal Company et al v. Oliver et al

Filing 14

MEMORANDUM in Opposition to Plaintiff's 21 Motion for a Temporary Restraining Order by Home Box Office, Inc., Partially Important Productions, LLC, Time Warner, Inc. . (Attachments: # 1 Exhibit A, # 2 Exhibit B, # 3 Exhibit C, # 4 Exhibit D, # 5 Exhibit E, # 6 Exhibit E (con'd), # 7 Exhibit F, # 8 Exhibit G)(Fitzsimmons, Robert) Modified on 7/28/2017 to link to Motion (kac).

Appendix G - AAI August 9, 2006, Report
GENWAL Main West Retreat Analysis--Preliminary Results

G-1

G-2

G-3

G-4

G-5

G-6

G-7

G-8

G-9

G-10

G-11

G-12

G-13

G-14

G-15

G-16

G-17

G-18

G-19

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G-21

G-22

G-23

G-24

G-25

G-26

G-27

G-28

G-29

G-30

G-31

G-32

Appendix H - AAI December 8, 2006, Report
Crandall Canyon Mine Ground Condition Review for Mining in the Main West North Barrier

H-1

H-2

H-3

H-4

H-5

H-6

Appendix I - AAI April 18, 2007, Report
GENWAL Crandall Canyon Mine Main West South Barrier Mining Evaluation

I-1

I-2

I-3

I-4

I-5

I-6

I-7

I-8

I-9

I-10

Appendix J - Roof Control Plan for Recovering South Barrier Section

J-1

J-2

J-3

J-4

J-5

Appendix K - Massive Pillar Collapse

The accident that occurred on August 6 at Crandall Canyon Mine was a rapid, catastrophic
failure of coal pillars. In a very short time period, failure was manifested as pillar bursting that
propagated over a broad area of the mine. Failure of coal pillars in “domino” fashion is referred
to using a variety of terms such as massive pillar collapse, cascading pillar failure, or pillar run.
At Crandall Canyon Mine the failure involved the violent expulsion of coal; however, other
events characterized using the same terms (e.g., massive pillar collapse) may not.
Bureau of Mines investigations in the 1990’s 19, documented more than a dozen massive pillar
collapse events that occurred in U.S. coal mines. A detailed examination of these events
revealed the following common characteristics:
• slender pillars (width-to-height ratio less than 3.0),
• low StF (less than 1.5),
• competent roof strata,
• collapsed area greater than 4 acres, and
• minimum dimension of the collapsed areas greater than 350 ft.
Based on these findings, Mark et al. recommended several strategies to reduce the likelihood of
such catastrophic failures. However, the strategies pertain only to collapses involving small or
slender pillars under relatively shallow overburden (i.e., the types of failure they had evaluated).
Although these failures are sudden (often involving substantial air blasts), they are distinctly
different from coal bursts. Mark et al. noted this distinction as follows:

Finally, it is important to note that the massive pillar collapses discussed in this
paper are not to be confused with coal bumps or rock bursts. Although the
outcomes may appear similar, the underlying mechanics are entirely different.
Bumps [bursts] are sudden, violent failures that occur near coal mine entries and
expel large amounts of coal and rock into the excavation (Maleki 20). They occur
at great depth, affect pillars (and longwall panels) with large w/h ratios, and are
often associated with mining-induced seismicity. The design recommendations
discussed here for massive pillar collapses do not apply to coal bump control.
Pillars in the Main West and adjacent North and South Barrier sections were at low risk for the
type of slender pillar collapse that Mark et al. studied. However, they were at significant risk for
bursting.
The basic condition for a massive pillar collapse is a large area of pillars loaded almost to failure.
Since all of the pillars are near failure, when one instability occurs, the transfer of load from that
pillar to its neighbors causes them to fail and so on. In a large area of similarly sized pillars near
failure, this process can continue unabated. Larger or more stable pillars (or barriers) that may
stop the progression of failure are absent. Such was the case in the Main West area of Crandall
Canyon Mine.

K-1

Furthermore, the pillars at Crandall Canyon Mine were not slender * and were capable of storing
substantial amounts of energy that was released as a burst. Pillars with width-to-height (w/h)
ratios between 5 and 10 21 are considered to be bump prone. Pillar w/h ratios at Crandall Canyon
Mine ranged from 7 ½ to 8 ¾ in the collapse area.

Slender pillars are those that are relatively narrow with respect to their height (e.g., width is less than 5
time the height).
*

K-2

Appendix L - Subsidence Data
Information was obtained from the U. S. Geological Survey (USGS) that defined the extent of
surface deformation above the accident site. USGS scientists use radar satellite images
(interferometric synthetic aperture radar or InSAR) to measure small movements on the earth’s
surface for their research on volcanoes, earthquakes, subsidence from groundwater pumping, and
other ground disturbances from natural and man-made causes. The technique has been used in
Europe to study mining subsidence since 1996, but its use has been limited in the U.S. coal
mining industry. USGS applied this technology in the vicinity of the Crandall Canyon Mine and
were able to identify an extensive subsidence region associated with the August 2007 accident.
Neva Ridge Technologies (Neva Ridge) was contracted to verify the USGS study. The Neva
Ridge report is provided in Appendix M in its entirety.
InSAR Surface Deformation
The InSAR deformation measurement technology relies on bouncing radar signals off the earth
from satellites orbiting over the same area at different time periods. By studying the differences
in the images, InSAR can detect small changes in the distance to the ground surface relative to
the satellite. InSAR detects very small movements that can not be visually noticed. InSAR
shows patterns of deformation as color bands with each band representing a few centimeters
(cm) of movement. The following figures from the USGS publication “Monitoring Ground
Deformation from Space” illustrate the use of the InSAR technology. Figure 96 depicts the
orbiting satellites scanning the surface of the earth with transmitted radar waves bouncing back
to the satellite.

Figure 96 - How Satellites and Radar Interferometry Detect Surface Movement
from USGS Fact Sheet 2005-3025

L-1

Figure 97 – Example of Interferogram Color Banding from USGS Fact Sheet 2005-3025

The radar images are processed to determine deformation. Figure 97 is an example from
California showing the interferogram color banding generated from an InSAR analysis that
depicts regional subsidence and localized uplift. Included in Figure 97 is the topographic detail
of the subsidence and uplift for the study area with the vertical scale exaggerated.
Crandall Canyon Mine InSAR Surface Deformation.
There are only a limited number of InSAR images over the Crandall Canyon Mine area. The
USGS identified a Japanese ALOS PALSAR satellite scan for June 8, 2007 (before the accident)
that covered the Crandall Canyon Mine reserve area and another satellite scan on September 8,
2007 (after the accident). InSAR analysis of the radar imagery between the June and September
time periods generated the InSAR deformation image shown in Figure 98. The image identifies
a region of subsidence centered on the west flank of East Mountain in the vicinity of the Crandall
Canyon August 2007 accident sites. Figure 98 shows the terrain surrounding the mine area, with
nearby valleys identified for geographic reference. The Line-of-Sight (LOS) deformation in
Figure 98 represents subsidence movement measured in a non vertical direction from the
satellite. In the USGS analysis, the deformation is measured along a LOS of 39.7º from vertical.
The InSAR images were processed and provided by a staff scientist of the Radar Project of Land
Sciences at the USGS Earth Resources Observation and Science Center.

L-2

Figure 98 - USGS InSAR Image of Subsidence above the Accident Site.
The surface deformation depicted occurred between June 8, 2007, and September 8, 2007.

The InSAR image furnished by USGS was referenced by latitude and longitude, allowing
conversion into state plane coordinates. The accident investigation team translated and rotated
the InSAR image onto the Crandall Canyon Mine coordinate system using known state plane and
corresponding mine local survey points. The InSAR deformation image with 5 cm color banding
was contoured by the accident investigation team with some guidance from USGS to delineate
the ground surface subsidence (see Figure 99).
The displacement contour values are Line-of-Sight (LOS) from the satellite. In Figure 99,
maximum LOS subsidence contour is 20 cm (approximately 8 inches LOS). Each repetition of
the color band (i.e., sequence of rainbow colors) represents 5 cm of LOS deformation with the
repetitive color banding indicating successive 5 cm increments of movement. Mining
subsidence is typically vertical; therefore, LOS subsidence values are multiplied by 1.29 (1/cos
39.7º) to determine vertical deformation. Consequently, the 20 cm LOS deformation contour
converts to approximately 25 cm (approximately 10 inches) vertical surface subsidence. The
movement is significant but, at a magnitude that cannot be detected visually on the mountainside.

L-3

Figure 99 - Surface Deformation from USGS InSAR
Color banding contoured to delineate Line-of-Sight successive 5 cm subsidence movement. Maximum LOS
movement of 20 cm (~8 inches) contoured.

The analysis performed by Neva Ridge included a contoured map of 5 cm vertical subsidence
contours. The contoured map is included as Figure 100 below.

Figure 100 - InSAR Vertical Subsidence Contours (cm) from Neva Ridge

L-4

The contours on the USGS results were converted to vertical values and overlain on the Neva
Ridge results for comparison. All measurements less than 2 cm were considered noise by Neva
Ridge and removed from the map. The comparison of the two results is shown in Figure 101.
The results are very similar except for the south-west portion of the depression. Tracing the
contours of the USGS image was very difficult in this area due to the rapid rate of change,
making it challenging to follow the color banding in Figure 99. The uncertainty in this area was
a factor in retaining an independent analysis. The Neva Ridge contours developed by experts in
InSAR analysis were therefore used throughout this report. The Neva Ridge InSAR surface
subsidence contours were overlain onto the mine workings and identify a wide spread subsidence
basin with the 25 cm (10-inch) vertical subsidence contour centered within the South Barrier
section, roughly between crosscuts 133 and 139 (see Figure 31).

Figure 101 - Comparison of Vertical Subsidence from Interpreted USGS and Neva Ridge InSAR Results

The geometry of the InSAR surface subsidence depression indicates that the Main West and
North and South Barrier sections have undergone extensive pillar failure. The knowledge that
surface deformations radiate around collapse regions was used to extrapolate the extent of
damage into adjoining regions that could not be traveled or investigated. Subsidence principles
suggest that the extent of the collapse at seam level would be less laterally but greater vertically
than the surface expression implies. The development of bed separations and other openings
within the overburden can cause surface subsidence to be less than the full height of closure at
mine level. Conversely, the collapse at mine level will draw the overburden downward with
subsidence deformations radiating outward and laterally over an area greater that the collapsed
area. Although subsidence research has primarily focused on full extraction mining, it is
reasonable to expect that strata will respond similarly to a pillar collapse.
InSAR analyses were performed using satellite images from December 2006 and June 2007
specifically to determine if surface subsidence had been associated with pillar recovery in the
L-5

North Barrier section. No subsidence was detected. However, it is possible that subsidence
occurred but the deformation was too small to measure or it was masked by ground surface
conditions. December radar scans would be affected by snow cover and June’s radar scans
would not. Snow cover tends to generate data scatter (noise) that interferes with InSAR
analyses.
InSAR Validation with Longwall Subsidence Monitoring Data
In 1999, a subsidence monitoring line was established on the north-to-south trending ridge of
East Mountain. The survey line over a portion of Main West and Panels 13 to 17 was monitored
from September 2000 to July 2004 by Ware Surveying, LLC (surveying contractor) using GPS
survey technology. Surveys were performed using a Trimble GPS Total Station 4700 and Real
Time Kinematics processing. The vertical accuracy of these surveys was reported to be ± 0.2foot (roughly ± 6 cm). The survey monuments were 5/8-inch rebar driven into the ground.

Surface monuments were resurveyed on August 17, 2007, along the portion of the line from the
center of Panel 14 to just north of Panel 13. These GPS subsidence measurements are the only
reliable information available for comparison with the InSAR analyses. On August 17, six of 16
survey stations had been destroyed in the area of interest. However, some of the remaining
monuments lie within the deformation crater identified using InSAR. The northern end of the
survey line terminates along the 20 cm (8-inch vertical) deformation contour. The southern
portion of the line lies outside of the 2 cm vertical subsidence contour (see Figure 102).

Figure 102 - InSAR Vertical Subsidence Contours & GPS Subsidence Line Data

Three stations near the southern end of the survey line showed no movement since 2004; this
observation is consistent with the InSAR analysis in this area (see Figure 102). Two survey
stations which showed approximately 10 cm of vertical movement (since 2004) were located
within the 2 to 5 cm InSAR vertical deformation contours. Five stations at the northern end of
the survey line showed 30 cm of vertical movement (since 2004) although they were located
along the 20 cm InSAR vertical deformation contour.

L-6

InSAR provides a more reliable characterization of surface subsidence associated with pillar
recovery in the South Barrier section since it only captures movement that occurred between
June and September 2007. GPS survey data incorporates deformations that occurred over a
longer time period between 2004 and August 17, 2007. For example, the five northern stations
of the survey line showed remarkably similar displacements between 2004 and 2007 (i.e., 29 to
33 cm). These stations are situated near the edge of Panel 13 and the original unmined South
Barrier. The data suggest that this area subsided gradually over the years between 2000 and
2004. It is possible that some amount of residual longwall subsidence and variations due to
surveying precision (±6 cm) account for the 10 cm difference between the InSAR and GPS
survey data.
Longwall Mining Subsidence History
Main West and adjoining barrier pillars near the accident area are bounded to the north and also
to the south by six extracted longwall panels. To establish if unanticipated or unusual subsidence
from the longwall extraction affected the region, the Panels 13 to 17 subsidence information was
compared to information from handbooks and references. The data suggests that the Crandall
Canyon Mine subsidence is similar to that published for deep longwall districts.

Data from the subsidence surveys show the development of the subsidence trough with the
extraction of successive longwall panels. As illustrated in Figure 103 surface profiles do not
begin to show the formation of a critical subsidence basin 22 (i.e., when subsidence reaches the
maximum possible value) until 2001 when the third successive panel (Panel 15) was extracted.
This delayed subsidence behavior is typical of the Wasatch Plateau where strong, thick strata in
the overburden control caving characteristics. Similarly, these strong units can resist caving and
form cantilevers at panel boundaries (as indicated by the absence of subsidence over more than
half the width of Panel 13). Subsidence data collected elsewhere in the region indicates that the
amount or extent of cantilevered strata at panel boundaries varies. These strata can be
responsible for high abutment stresses and long abutment stress transfer distances.

Figure 103 - Longwall Panels 13 to 15 GPS Surveyed Subsidence Profiles

L-7

Early measurements (2000 to 2002) show a surface elevation increase above the baseline from
about the middle of Panel 13 to the barrier south of Main West. Cantilevered strata may be
responsible for this movement. The data also suggest that the strata gradually subsided in this
area over time.
Subsidence values derived from the surveyed profiles over Panels 13 to 17 are summarized in
Table 14. The Panel 13 to 17 profile is supercritical in character where maximum subsidence
(Smax) is achieved. Also, listed in Table 14 is the horizontal distance (d) from the excavation
edge to the inflection point (point dividing the concave and convex portions of the subsidence
profile). The supercritical width (W) for these Crandall Canyon Mine longwall panels is
comparable to other Wasatch Plateau longwall panels. Also, the subsidence factor (Smax/m)
shown in the table is typical for longwall mining.
The distance to the inflection point (d) was calculated from subsidence references using Panel 13
to 17 factors as shown in the lower portion of Table 14. This distance for the Panel 13 to 17
profile survey is roughly 500 feet. This value is similar to the values calculated from references.
This information suggests that the Crandall Canyon subsidence and associated overburden
bridging over extracted panels is comparable to other deep full extraction mining.
Table 14 - Crandall Canyon Longwall Subsidence Parameters, Values, and Comparisons

Parameter
Longwall
Subsidence Data
Source
Crandall Canyon
Mine Panels 13-17
Surface Subsidence
Engineering
Handbook22
Average Estimate
from SDPS Chart 23

Values

Approx.
Depth
(h), ft.

Mined
Height
(m), ft.

Approx.
Maximum
Subsidence
(Smax), ft.

Approx.
Supercritical
Width (W), ft.

Smax/m

Approx.
Distance to
Inflection
Point (d), ft.

2,150

7.9

5.0

2,300

0.63

500

2,300
used in chart
Fig 2.4
2,300
used in Fig
3.2.1

0.63
used in
Fig 2.4

495

2,150
used in
Fig 2.4
2,150
used in
Fig 3.2.1

L-8

505

Appendix M - Neva Ridge Technologies Report

M-1

Final Report
MSHA Contract DOLB08MR20605
April 18, 2008

Prepared by Neva Ridge Technologies

Contact:

David Cohen, Ph.D.
Neva Ridge Technologies
4750 Walnut Street
Suite 205
Boulder, Colorado 80301
[phone]
[e-mail]

Neva Ridge Technologies, 4750 Walnut St., Suite 205 Boulder CO, 80301, [phone]

1

Introduction

1.1 Data Description
Data from the ALOS/PALSAR sensor were obtained from the AADN (Americas ALOS Data
Node, http://www.asf.alaska.edu/alos), located at the Alaska Satellite Facility in Fairbanks,
Alaska. The dates of the acquisitions and the unique data designation numbers are shown in the
table below.
Date
June 8, 2007
September 8, 2007

Designation
HH-ALPSRP072960780
HH-ALPSRP086380780

The ALOS satellite maintains a sun-synchronous, near polar orbit; this is a retrograde orbit that
precesses in a plane that is at an inclination of 98.16 degrees. For the geographic location of this
data collection, the following figure shows the geometry. Note that for these particular data
acquisitions, the satellite was in the ascending portion of its orbit; the satellite looks to the right
(starboard) side during data collection. Locally, then, the line-of-site is 38.7 degrees from the
local vertical and 10.0 degrees above the local East direction.

Sa
tell
i

te
Sii
-S

te O

f
-o
e-

rbi
t

L in

E

38.7°

-N

-10.0°

Figure 1. Diagram showing the geometry of the data acquisition at the site of
interest.

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2

1.2 Processing Description
Data were processed to complex SAR imagery using tools from Gamma Software. This is
standardized processing software that ingests data from most civil SAR sensors. (Neva Ridge is a
US distributor for this software.) The interferometry is performed with a combination of
additional Gamma Software tools and internal Neva Ridge tools. Complex images are
coregistered and the modeled phase due to topography is subtracted using the USGS 3 arcsecond
elevation product. Following an iteration to remove errors in the estimated baseline, the
interferogram is smoothed using a Goldstein filter1 with a filter exponent of .6. The converted
unwrapped results naturally represent the motion along the radar line-of-site (see previous figure)
but can be converted to vertical motion with some assumptions. In particular, under the
assumption that the ground motion is purely in the vertical direction, we can back-project the
measured motion along the vertical direction. However, if we assume that the actual ground
motion has a combination of horizontal and vertical components, there is no way to uniquely
attach the measured line-of-site displacement to a unique set of horizontal and vertical
displacements.
For display and some data manipulation, reprojection, and minor post-processing of the results,
we use a combination of PCI Geomatics, Gamma display utilities, and internal tools.

2

Results

In the following sections, we include plan view diagrams (those specified in the SOW)
representing the results of the interferometric processing. Each of the plan view figures below
represent a region approximately centered on the coordinate NAD27 39°28’01.6”N,
111°13’16.2”W, with spatial extent of 3514 meters on a side.
In addition, in each of the plan view figures, reference points (shown as crosshairs) are included.
The coordinates of these are:
Point
1.
2.
3.

WGS 84
111°14’04.9”W, 39°27’12.2”N
111°13’13.3”W, 39°27’43.0”N
111°13’09.1”W, 39°28’04.8”N

2.1 Line-of-Site InSAR Color Contours
In this representation, line-of-site displacements are presented as color-coded contours. In order
to enhance the visual dynamic range of the image, the color scale wraps at a specified interval,
which is shown on the adjacent color bar. For context, the color contours in Figure 2 are
superimposed on the corresponding SAR image. As the interpretation of the SAR image is not
necessarily intuitive, we have also annotated the physical regions represented by the SAR image
shades/textures. The peak line-of-site subsidence measured in this data is 24 cm. Figure 3 shows
the same information without the SAR image background layer.

1

R.M. Goldstein, C.L. Werner, “Radar Interferogram Filtering for Geophysical Applications,” Geophys. Res.
Letters, V25, No21, 1998

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3

Each color cycle means
10 cm of displacement

0 cm

-10 cm
Valley Floor

West Face

Treeless Region

Figure 2. Color contours superimposed on the corresponding SAR image. A peak
displacement of 24 cm (along the line-of-site, away from the radar) is measured.
Each color cycle means
10 cm of displacement

0 cm

-10 cm

Figure 3. Color contour with no SAR image background layer. A peak
displacement of 24 cm (along the line-of-site, away from the radar) is measured.

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4

2.2 Line-of-Site Deformation Contours
The line-of-site deformation contours are produced at 5 cm intervals and are shown in Figure 4.
It is not uncommon in InSAR measurements to contain atmospheric effects that are on the order
of 1-2 cm. These are produced by moisture (dielectric) variations in the atmosphere that produce
noise due to variable phase delays of the radar signal. Using an initial contour of 5 cm mitigates
visual interference due to this low-level noise.
LOS Contours
∆=5 cm

5
10
15
20

Figure 4. Line-of-site deformation contours with intervals of 5 cm. Motion is
away from the radar.
2.3 Vertical Deformation Contours
Vertical deformation measurements may be derived from the line-of-site measurements under
the assumption that motion is purely vertical. Based on the diagram in Figure 1, the relationship
between the line-of-site measurement and vertical measurements is:

δ vert =

δ LOS
cos(38.7)

The result of this transformation is shown in Figure 5.

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5

Vertical Contours
∆=5 cm

5
10
15
20
25

Figure 5. Vertical contours. A peak displacement of 30 cm (vertical, downward)
is measured.

Vertical Contours
∆=5 cm

5

2

10
15
20
25

Figure 6. Vertical contours are combined with a color scale. For visual clarity,
measurements outside the main feature, with values of 2 cm or less, have been
removed.
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6

2.4 Google Earth View
Figure 7 shows a Google Earth composite with the InSAR vertical displacements. The InSAR
data have been filtered so as to remove measurements outside the main feature, with
displacements of less than 2 cm. This results in a better visual representation of the data.

Figure 7. Google Earth composite image.

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7

Appendix N - Seismic Analysis
University of Utah Seismograph Stations
Continuous earthquake monitoring has been conducted at the University of Utah since 1907.
The University of Utah Seismograph Stations (UUSS) is an entity within the Department of
Geology and Geophysics. The mission of the UUSS is primarily academic research while also
providing earthquake information to the general public and public officials. The UUSS is also a
participant in the Advanced National Seismograph System (ANSS). The mission of the ANSS is
to provide accurate and timely data for seismic events.

The UUSS maintains a regional/urban seismic network of over two hundred stations. An
average of one thousand seismic events is detected in Utah each year. The number of events
depends on the magnitude threshold of reporting. The number of recorded events includes those
from natural sources (tectonic earthquakes) as well as those related to mining activity. In the
Wasatch Plateau and Book Cliffs mining areas, at least 97% of the events have been identified as
being related to mining activity. These events are termed mining-induced seismicity. Both
tectonic and mining-induced seismic events can be referred to as earthquakes.
The majority of coal mining in Utah occurs in the Wasatch Plateau and Book Cliffs area. The
coal fields form the shape of an inverted “U” in Carbon and Emery counties. In the coal mining
region, nearly all the seismic events are mining-induced. Again, the number of events depends
on the magnitude threshold. Special studies have recorded several thousand such events in a
single year. Figure 104 is a plot of mining-induced seismicity from 1978 to 2007. Over 19,000
events are included. Mining-induced seismicity occurs regularly from normal mining activity in
the Utah coal fields.

Figure 104 - Mining-Induced Seismicity in Utah
(from W. Arabasz presentation to Utah Mining Commission, November 2007)

N-1

The regional seismograph network includes several stations situated in the mining region. The
location of these stations is shown in Figure 105. The stations are connected by telemetry to the
UUSS central recording laboratory.

Figure 105 - Locations of UUSS Seismographs in the Wasatch Plateau
In the Book Cliffs Mining Area 24

Seismic Event Locations and Magnitudes
The magnitude of earthquakes is often reported in terms of the local magnitude (ML). The local
magnitude scale is a logarithmic scale developed by Charles Richter to measure the relative sizes
of earthquakes in California. The scale was based on the amplitude recorded on a WoodAnderson seismograph. The scale has been adapted for use around the world and is also known
as the Richter scale.

Many additional scales have been used to measure earthquakes. Most scales are designed to
report magnitudes similar to the local magnitude. The coda magnitude (MC) is based on the
length of the seismic signal. The coda magnitude scale used by the UUSS was calibrated to
N-2

provide similar results on average with the local magnitude scale for naturally occurring
earthquakes. The UUSS has observed that mining related seismic events are shallow compared
to most naturally occurring earthquakes and the duration or coda tends to be longer. This results
in a slightly higher coda magnitude than local magnitude for mining-induced events.
It was not possible for the UUSS to calculate the local magnitude for all events. The coda
magnitude was available for all reported events. While the local magnitude or ML was the
preferred scale, to maintain consistency, the coda magnitude or MC was used in this report except
where noted. The coda magnitude for the 3.9 ML event on August 6, 2007, was 4.5.
Following the August 6, 2007, event, a location was automatically calculated and posted on the
UUSS and USGS websites. The plotted location was not over the Crandall Canyon Mine and
contributed to speculation that the event was not mining-related.
The location of a seismic event is determined by the travel times to each seismograph station and
the velocity of the seismic wave through the earth. The velocity varies with depth. To calculate
locations, a model of the velocity at different depths needs to be created. Any difference
between the velocity model and actual velocities or lateral non-homogeneity in actual velocities
can result in errors in the location.
Depths of the events were difficult to determine due to the distance to the nearest recording
station and the shallow depths involved. According to UUSS seismologists, in order to
accurately determine the depth of a seismic event, a seismograph station is generally needed at a
distance less than or equal to the depth of the event. Because the depth of the August 6, 2007,
accident was approximately 2000 feet, and the nearest station was approximately 11 miles away,
the initial calculated depths were uncertain.
The UUSS deployed five additional portable units to the site to improve their ability to locate
seismic events. Installation of the portable units began on August 7 and was completed on
August 9, 2007.
A review of the seismic data revealed that several seismic events could be correlated to coal
bursts that were observed underground. Known locations could be used to reduce the effect of
errors in the velocity model, thus improving the accuracy for locating other events. Therefore,
MSHA provided Dr. Pechmann of the UUSS with the known location of the August 16, 2007,
accident to use as a fixed point to improve the locations for the other events. Two different
methods were used by UUSS to improve the locations.
The first method was the calibrated master event method. In this method, corrections were made
to the arrival times to fit the August 16 event to the known location. For each other event, the
corrections were applied and new locations calculated. These corrections were applied to 189
recorded events going back approximately two years to August 2, 2005. This method relocated
the August 6, 2007, event to the North barrier section at approximately crosscut 149.
The second method used by UUSS was the double difference method. This method determines
the relative location between multiple events by minimizing differences between observed and
theoretical travel times for pairs of events at each station. 25 Only 150 of the 189 events could be
located using this method. Figure 106 shows the progressively refined locations for four selected
events together with their known locations and the calculated locations for the August 6, 2007,
accident. Shown on the figure are the initial standard locations, the locations as revised by the
N-3

master event method, and the locations as revised by the double difference method. As shown
on the figure, the double difference locations match the known locations most closely. The
location for the August 6 accident is given at the No. 3 entry of the South Barrier section
between crosscuts 143 and 144. The August 6 accident was known to extend over a wide area.
Because locations of seismic events are determined by the first arrival of the seismic waves, only
the location of the initiation of the August 6 accident can be calculated. Therefore, the location
shown indicates where the event began, not the center of the event.

Figure 106 – Locations of Selected Events showing Progressive Refinements Using Three Methods

A review of mine records and records from the rescue and recovery operations revealed that ten
events were both noted underground and recorded by the UUSS. Figure 107 shows the high
degree of correlation with the underground locations and the double difference locations
calculated by the UUSS. This provides some measure of the accuracy of the locations. Only the
location of the August 16, 2007, accident had been provided to the UUSS. Excluding the
August 16 accident event that was used for calibration, the mean distance between the reported
locations and calculated locations was 450 feet. The median distance was 421 feet.

N-4

Figure 107 - Observed and Calculated Locations for Events

N-5

Figure 108 - Calculated Double Difference Locations and the Location of Mining Color Coded by Month

N-6

Figure 108 shows all of the calculated double difference locations and the location of mining
activity color coded by month. The symbols are sized according to the coda magnitude of the
events. The double difference locations show a high degree of correlation with pillar recovery
mining in South Mains and the Main West barriers.
Figure 109 shows the seismic location of the August 6, 2007, accident in red. The events
occurring after the accident on August 6 and 7 are shown in tan. Events occurring on August 8
to 27 inclusive are shown in blue. The locations of seismic events occurring on August 6 and 7
are notably clustered along a north to south line near crosscut 120 of the South Barrier section.
The location corresponds with the outby extent of the collapse in the South Barrier section as
determined by underground observation in the South Barrier section entries and Main West inby
the breached seal. The seismic events extend from the South Barrier to the North Barrier. The
initiation point for the collapse is located at the western boundary of the area. The collapse
would have progressed to the east. The continuing events may have been the result of residual
stress at the edge of the collapsed area. The events colored in blue occurred later and may
represent settling at the west end of the collapse area.

Figure 109 – Seismic Location of the August 6 Accident and Following Events

Analysis of the Seismic Event
The ground motions produced by the August 6, 2007, event were recorded on the UUSS
seismographs. Earthquakes produce body and surface waves. Body waves travel through the
interior of the earth. P-waves or primary waves and S-waves or secondary waves are types of
body waves. P-waves are also known as compressional waves and consist of particle motion in

N-7

the direction of travel. P-waves travel faster than any other type of seismic wave and are the first
to arrive at a seismograph station after an event.
A typical tectonic earthquake produced by a slip on a fault will result in part of the earth being
placed in compression and part in dilation. This type of movement will typically generate Pwaves with the initial or first motion on a vertical component seismograph in an upward
direction or in compression at some locations and P-waves with a downward first motion or
dilatation at other locations.
An analysis of the seismograph recordings from the August 6, 2007, event indicated that the
initial or first motion recorded on a vertical component seismograph was downward in all cases
(Pechmann 2008)2. This is characteristic of a collapse or implosion. Coal mining-related events
are commonly collapse type events where caving or a coal burst has sudden roof-to-floor
convergence. The lack of compressional or upward first motions is highly suggestive of a
collapse but not conclusive. It may be possible that some upward first motions may have been
missed. Figure 110 is a simplified diagram illustrating the types of motions expected for mine
collapse and normal-faulting earthquakes.

Figure 110 - P-Wave First Motion Analysis Examples
(from W. Arabasz presentation to Utah Mining Commission, November 2007)

N-8

Figure 111 shows the seismograph stations in place around the mining district as well as seismic
waveforms of the vertical component from selected stations for the August 6, 2007, event. The
waveforms are not shown to scale and are intended only to illustrate examples of first motions.

Figure 111 - Vertical Component Waveform Data for August 6, 2007 Event

The source mechanism of a mine collapse involves a change in volume at the source and is
unusual compared to fault slip sources where the primary movement is slipping with no change
in volume. These unusual mine collapse occurrences are of particular interest to persons
engaged in monitoring to ensure compliance with the nuclear Comprehensive Test Ban Treaty.
Considerable effort has been expended to distinguish man-made events from naturally occurring
tectonic earthquakes.
As early as August 9, 2007, scientists at the University of California at Berkley Seismological
Laboratory and the Lawrence Livermore National Laboratories studied the data and prepared a
report titled “Seismic Moment Tensor Report for the 06 Aug 2007, M3.9 Seismic event in central
Utah” that was made available on the UUSS website. A paper based on this analysis titled
“Source Characterization of the August 6, 2007 Crandall Canyon Mine Seismic Event in Central
Utah” also has been prepared3. The techniques employed in this analysis are beyond the scope
of this report. However, the results can be summarized by Figure 112, reproduced from their
paper, which shows seismic events plotted according to their source mechanism. The term DC
refers to a double couple of forces or opposing forces which create shear or slip type movement
resulting in natural earthquakes with no change in volume. The data for the August 6, 2007
event is shown as the red star. Its location characterizes it as an anti-crack or closing crack. This
N-9

would be consistent with an underground collapse. Natural or tectonic earthquakes plot near the
center of this diagram. The orange star represents a natural tectonic earthquake of similar size
that occurred on September 1, 2007 near Tremonton, Utah. The August 6 event is clearly
outside this area. The explosion plotted in the figure was a nuclear test explosion. The three
other collapses plotted were two trona mine collapses in Wyoming and a collapse of an
explosion test cavity.

Figure 112 - Source Type Plot from Ford et al. (2008).

An analysis of the source depth for the August 6 event was conducted by Ford et al. (2008)
Different depths for the event were assumed and the source type and variance reduction were
calculated. Variance reduction is a measure of fit; the greater the reduction, the better the fit.
Figure 113 shows the variance reduction results from the analyses in the inset box and the source
type for the different assumed depths. As indicated, the shallowest depths (shown in red) result
in the best fit. Even at depths up to 5 km, the source type remains as a closing crack and does
not indicate the double-couple mechanism typical of natural tectonic earthquakes.

N-10

Figure 113 – Depth Analysis of August 6, 2007 event from Ford et al 2008.

Ford et al. (2008)3 noted that while the primary and dominant source mechanism was a closing
crack, the seismic record could not be explained by a pure vertical crack closure alone. Love
waves that have motion horizontal to the direction of travel were present and can not be
produced by the vertical closure. Possible explanations offered included that the collapse was
uneven or that there was sympathetic shear on a roof fault adding a shear component to the
collapse.
Pechmann et al. (2008)2 similarly noted that while the event was dominantly implosional, there
was a shear component. The most likely explanation offered was slip on a steeply dipping crack
in the mine roof with a strike of approximately 150 degrees and motion downward on the east
side.
Given that the event initiated at the west edge of the collapse area and seismic events occurred in
the following 37 hours at the east edge of the collapse area (see Figure 109), the most likely
explanation is that the event began at the western edge of the area and progressed eastward. The
eastern edge, where the collapsed stopped, would have resulted in residual stress at the
cantilevered edge and continued seismic activity.
Additionally, careful examination of the seismic waveforms by the UUSS did not reveal any
indication of an event immediately preceding the main August 6, 2007 event. There was no
evidence that the collapse was caused by an immediately preceding natural occurring event.
N-11

Duration of Seismic Events
It was initially reported in the media and by others that the August 6, 2007, event lasted four
minutes. According to UUSS seismologists, the recorded length of vibratory motion of a
seismograph will be orders of magnitude longer than the actual duration of the seismic source
event. This is due to the arrival of seismic waves from many different and indirect paths. For
example, the August 16 event generated one seismic record 63 seconds long2 when the actual
event was nearly instantaneous.

It is not straight forward to estimate the duration of a source event from the seismic record. The
duration of the August 6 accident can be estimated by eye witness reports. One witness stated
that the mine office building shook for several seconds and the shaking subsided quickly. None
of the smaller events was reported to have any significant duration by underground witnesses.
The building shaking may represent the collapse event and residual vibrations. The best estimate
for the duration of the August 6, 2007, event is a few seconds.

N-12

Appendix O - Images of March 10, 2007, Coal Outburst Accident

North Barrier Section after March 2007 Coal Outburst Accident

The following images were taken on March 16, 2007, during an investigation of the March 10,
2007, coal burst by Michael Hardy and Leo Gilbride of AAI and Laine Adair and Gary Peacock
of GRI. A location diagram was inserted into each photo by the accident investigation team.
The green arrow indicates the camera view point as determined from AAI’s notes.

O-1

O-2

O-3

O-4

O-5

O-6

O-7

O-8

O-9

O-10

O-11

O-12

Appendix P- ARMPS Method Using Barrier Width Modified Based
on Bearing Capacity

To account for the bleeder pillar being used as part of the barrier system, the bleeder pillar load
bearing capacity is added to the load bearing capacity of the barrier to approximate the total load
bearing capacity of the barrier system. This analysis method modifies the barrier width so that
the load bearing capacity is adjusted to include a bleeder pillar. This process addresses those
cases where the section pillar remains alongside the barrier pillar separating Active Gob and 1st
Side Gob. The process involves mathematically modifying the barrier pillar system as outlined
below:
1. Establish input parameters for mining geometry (i.e. overburden, pillar size, mining
height, etc.).
2. Determine conventional stability factors by modeling the section as if all pillars are
extracted. Note the PStF, BPStF, and remnant BPStF.
3. Note the load bearing capacity of the actual barrier width at the AMZ.
4. Note the load bearing capacity of the pillar that will be left alongside the barrier pillar.
5. Determine the equivalent load bearing capacity of a modified barrier system with the
following:

Equivalent Barrier
Capacity (tons )

=

Original Barrier
Capacity (tons)

+

Pillar Capacity (tons ) x AMZ Breath
Pillar Crosscut Center

6. Model the section with an Active Gob as retreating without the unmined section pillar
(pillar line and section reduced by one pillar).
7. Modify the barrier width using the input screen, recalculate, and check the resultant
barrier Capacity at the AMZ. Continue modifying the barrier width using this iterative
process until the Equivalent Barrier Capacity is achieved.
8. Assign the resultant PStF for the AMZ, BPStF, and remnant BPStF as the values for the
section pillars and the modified barrier pillar system stability values.

P-1

Appendix Q - Finite Element Analysis of Barrier Pillar Mining
at Crandall Canyon Mine

by
William G. Pariseau
University of Utah

Q-1

FINITE ELEMENT ANALYSIS OF BARRIER
PILLAR MINING AT CRANDALL CANYON

Prepared for the Mine Safety and Health Administration
Arlington, Virginia

by
William G. Pariseau
University of Utah
Salt Lake City, Utah

May 26, 2008

CONTENTS
INTRODUCTION

1

FORMULATION of the PROBLEM

2

Mine Geology
Mine Geometry
Premining Stress
Rock Properties
Mining Sequence
Boundary Conditions

3
5
7
7
10
10

FINITE ELEMENT ANALYSIS
Main Entry Mining
Longwall Panel Mining
Node Displacements and Subsidence
Element Safety Factor Distributions
Barrier Pillar Entry Mining
North Barrier Pillar Mining
South Barrier Pillar Mining

11
12
16

23

DISCUSSION

30

CONCLUSION

34

REFERENCES

35

INTRODUCTION
This report discusses finite element analysis of mining in barrier pillars at the Crandall
Canyon Mine in central Utah. Analyses are two-dimensional and represent vertical crosssections from surface to about 1,000 ft (300m) below the mining horizon, the Hiawatha seam.
The finite element program is UT2. This computer code has been in service for many years and
well validated through numerous bench-mark comparisons with known problem solutions. UT2
has been used in many rock mechanics studies through the years, most recently in the study of
inter-panel barrier pillars used in some Utah coal mines.

The study objective is to develop a better understanding of the strata mechanics
associated with recent events (August, 2007) at the Crandall Canyon Mine. This mine is in the
Wasatch coal field in central Utah, west of Price, Utah. There are three coal seams of interest in
the stratigraphic column of the Wasatch Plateau, namely the Hiawatha seam and the overlying
Cottonwood and Blind Canyon seams. Mining is not always feasible in every seam.

The Crandall Canyon property is developed from outcrop, as are almost all coal mines in
Utah. Relief is high in the topography of the Wasatch Plateau region; depth of overburden
increases rapidly with distance into a mine. Depth to the Hiawatha seam at Crandall Canyon
varies with surface topography and ranges roughly between 1,500 and 2,000 ft (450 to 600 m).
Thickness is also variable and of the order of 8 ft (2.4 m). Development consists of five
nominally 20-ft (6-m) wide main entries separated by 70-ft (21-m) wide pillars driven in an eastwest direction. Length of these main entries is about 17,700 ft (4,210 m). Six longwall panels
were mined on either side of the main entries from entry ends near a major fault (Joe’s Valley

1

fault) that strikes in a north-south direction. These panels were roughly 780 ft (234 m) wide by
4,700 ft (1,140 m) long on the north side of the main entries and 810 ft (243 m) wide by 7,040 ft
(2,112 m) long on the south side. Panels were parallel to the main entries.

FORMULATION OF THE PROBLEM
Finite element analysis is a mature subject and a popular method for solving boundary
value problems in the mechanics of solids and other fields as well [e.g., Zienkiewicz, 1977;
Bathe, 1982; Oden, 1972; Desai and Abel, 1972; Cook, 1974]. In stress analysis, equations of
equilibrium, strain-displacement relationships, and stress-strain laws are requirements met under
the constraints of tractions and displacements specified at the boundaries of a region of interest.
The method is popular, especially in engineering, because of a relative ease of implementation
compared with traditional finite difference methods. The method has important advantages in
coping with non-linearity and complex geometry.

Finite element analysis of mining involves computation of stress, strain, and displacement
fields induced by excavation. Rock response to an initial application of load is considered
elastic. Indeed the elastic material model is perhaps the de facto standard model in solid
mechanics. However, the range of a purely elastic response is limited by material strength.
Beyond the elastic limit, flow and fracture occur, collectively, plastic deformation, i.e.,
“yielding”. Although strictly speaking inelastic deformation is elastic-plastic deformation,
“plastic” is used for brevity. Plastic deformation may be time-dependent and various
combinations of elastic and plastic deformation are possible, e.g., elastic-viscoplastic
deformation allows for time-dependent plasticity beyond the elastic limit.

2

Generally, excavation takes place in initially stressed ground, so changes in stress are
computed. When stress changes are added to the initial stresses, post-excavation stresses are
obtained. These stresses may then be used to determine a local factor of safety, the ratio of
strength to stress in an element. A safety factor greater than 1.0 indicates a stress state in the
range of a purely elastic response to load. A computed safety factor less than 1.0 indicates stress
beyond the elastic limit, while a safety factor of 1.0 is at the elastic limit where further loading
would cause yielding. Unloading from the elastic limit induces an elastic diminution of stress.
Safety factors less than 1.0 are physically impossible because yielding prevents stress from
exceeding the elastic limit. However, in a purely elastic analysis, computed safety factors may be
less than 1.0.

Elastic analyses offer the important advantages of speed and simplicity. Although safety
factor distributions based on elastic analysis may differ from elastic-plastic analyses, the
differences are not considered important especially in consideration of questions that may arise
about the plastic portion of an elastic-plastic material model. Generally, the effect of yielding is
to “spread the load” by reducing peak stresses that would otherwise arise while increasing the
region of elevated stress.

Mine Geology
A drill hole log of hole DH-7 was used to define the stratigraphic column at Crandall
Canyon. This hole is centrally located in the area of interest. Figure 1 shows a color plot of the
stratigraphic column used in subsequent analyses. The Hiawatha seam is the thin gray line at the
1,601 ft (480 m) depth. A thickness of 8 ft (3 m) is indicated. Roof and floor are sandstone.

3

Figure 1. Stratigraphic column, formation names, depths in feet, seam names, and thicknesses
(in parentheses in feet). There are 11 layers in the column.

4

Mine Geometry
The overall region used for analysis is shown in Figure 2 where the colors correspond to
the same colors and rock types shown in the stratigraphic column (Figure 1). Details of the main
entry geometry are shown in Figure 3. Elements in the mesh shown in Figures 2 and 3 are
approximately 10 ft wide and 10 ft high (3.0x3.0 m), except at seam level where element height
is 8 ft (2.4 m). Element size is a compromise between interest in detail at seam level and a larger
view of panel and barrier pillar mining beyond the main entry development.

Figure 2. Overall finite element mesh geometry. There are 172,368 elements and 173,283 nodes
in the mesh.

The mine geometry changes with development of the main entries and subsequent mining
of longwall panels parallel to the mains and on both sides. Barrier pillars 450 ft (135 m) wide are
left on both sides of the main entries as shown near seam level in Figure 4. Only 100 ft (30 m) of
the future longwall panels are shown in Figure 4. Panels in the analyses are eventually mined
2,600 ft (780 m) on the north and south sides of the main entries. Panels, barrier pillars, main
entries and entry pillars account for the 6,480 ft (1,944 m) wide mesh. Cross-cuts are not
included in two-dimensional analyses.
5

Figure 3. Geometry of the main entries. Coal seam elements are 10x8 ft (3.0x2.4 m).

Figure 4. Expanded view at seam level showing main entries, adjacent barrier pillars, and 100 ft
(30 m) of future longwall panel excavation.

6

Premining Stress
The premining stress field is associated with gravity loading only. This simple stress
field assumes that the vertical stress before mining is the product of average specific weight of
material times depth, or to a reasonable approximation, 1 psi per foot of depth (23 kPa/m of
depth). Horizontal stresses are equal in all directions and are computed as one-fourth of the
vertical premining stress. Thus, at the top of the Hiawatha seam, the vertical premining stress is
1,601 psi (11.04 MPa) and the horizontal stresses are 400 psi (2.76 MPa). Shear stresses relative
to compass coordinates (x=east, y=north, z=up) are nil. Water and gas are considered absent, so
these stresses are also the effective stresses before mining. When the depth of cover changes, the
premining stresses also change in accordance with the assumed vertical stress gradient and ratio
of horizontal to vertical premining stress.

Rock Properties
Rock properties of importance to the present study are the elastic moduli and strengths.
The various strata in the geologic column are assumed to be homogeneous and isotropic, so only
two independent elastic properties are required, and also only two independent strengths for each
material. Young’s modulus (E) and Poisson’s ratio (<) are the primary elastic properties and
most easily measured. These properties are shown in Table 1 and were adapted from Jones
(1994), Rao (1974), and from laboratory tests on core from holes near coal mines in the Book
Cliffs field in central Utah. Unconfined compressive and tensile strengths, Co and To,
respectively, are the basic strength properties and are also shown in Table 1. Other properties
such as shear modulus and shear strength may be computed from the properties given in Table 1
on the basis of isotropy.

7

Table 1. Rock Properties.
E
(10 psi)

<

Co
(103 psi)

To
(102 psi)

1. North Horn Formation

2.6

0.26

11.80

7.0

2. Price River Formation

3.2

0.26

9.98

3.8

3. Castle Gate Sandstone

3.0

0.22

9.59

4.3

4. Sand+Siltstone

3.1

0.24

13.50

11.9

5. Blind Canyon Coal

0.43

0.12

4.13

2.8

6. Roof/Floor Siltstone

2.8

0.23

12.18

12.9

7. Cottonwood Coal

0.43

0.12

4.13

2.8

8. Roof Sandstone

3.4

0.26

14.50

10.9

9. Hiawatha Coal

0.43

0.12

4.13

2.8

10. Floor Sandstone

3.4

0.26

11.72

11.7

11. Masuk Shale

2.2

0.35

10.30

0.60

Property

6

Material

Compressive strength of rock is generally dependent on confining pressure as shown in
laboratory tests. The well-known Mohr-Coulomb strength criterion is one way of expressing
confining pressure dependency. This criterion may be expressed in terms of the major and minor
principal stress at failure in the form
(1)

where

are the major principal stress, minor principal stress, cohesion and angle

of internal friction, respectively, and compression is positive. The left side of (1) is the
maximum shear stress, while the sum of the principal stresses on the right side is a mean normal
stress in the plane of the major and minor principal stresses. Cohesion and angle of internal
friction may be expressed in terms of the unconfined compressive and tensile strengths. Thus,
8

(2)

An alternative form of (1) that shows the direct dependency of compressive strength on confining
pressure is

(3)

where Cp and p are compressive strength under confining pressure and confining pressure,
respectively. Equation (3) has applicability to pillar strength because often a pillar is much wider
than it is high and has a core confined by horizontal stress. The ratio of unconfined compressive
strength to tensile strength in (3) is often 10 or greater and thus multiplies the confining pressure
effect by an order of magnitude or more.

Often the increase of compressive strength with confining pressure is non-linear and
moreover the intermediate principal stress may influence strength. A criterion that handles both
possibilities is a non-linear form of the well-known Drucker-Prager criterion that may be
expressed as
(4)

where compression is positive and

are second invariant of deviatoric stress,

first invariant of stress, an exponent, and material properties, respectively. The variable %J2 is a
measure of shear stress intensity, while I1 is a measure of the mean normal stress that includes the
three principal stresses. The last two, A and B, may be expressed in terms of the unconfined
compressive and tensile strengths, while the exponent (N) is decided upon by test data. A value
9

of 1 reduces (4) to the original Drucker-Prager criterion. A value of 2 allows for non-linearity
and more realistic fits to test data. A value N = 2 is used in this study. The maximum value of
J21/2 for the given mean normal stress (I1 / 3) can be extracted from (4). The ratio of this
maximum value to the actual value is a factor of safety for the considered point. Thus, an
element factor of safety fs = J21/2 (strength) / J21/2 (stress). This ratio has an analogy to the ratio of
shear strength to shear stress. Uniaxial compression and tension are special cases included in this
definition of element safety factor. Other definitions are certainly possible, but the one described
here is embedded in UT2 and serves the important purpose of indicating the possibility of stress
exceeding strength and thus the possibility of yielding.

Mining Sequence
The mining sequence involves several stages: (1) excavation of the main entries, (2)
excavation of panels on either side of the main entries, (3) entry excavation in the north barrier
pillar, (4) entry excavation in the south barrier pillar. Main entries are excavated in strata
initially stressed under gravity loading alone. Stress changes induced by mining entries are
added to the initial stresses to obtain the final stresses at the end of main entry excavation. These
final stresses are the initial stresses for the next stage of excavation (panel mining) and so on.

Boundary Conditions
Displacements normal to the sides and bottom of the mesh shown in Figure 2 are not
allowed, that is, they are fixed at zero. The top surface of the mesh is free to move as mining
dictates. Initial conditions are boundary conditions in time. These are the stresses at the start of
each excavation stage.

10

There is a possibility that computed seam closure, the relative displacement between roof
and floor, may exceed mining height. This event is physically impossible and thus must be
prohibited by appropriate boundary conditions. Because the bottom of the mesh is fixed in the
vertical direction, floor heave is somewhat restricted relative to a mesh of greater vertical extent.
Roof sag is not restricted, so specification of roof sag in an amount that prevents overlap of floor
heave is a reasonable physical constraint to impose as an internal boundary condition. Where
overlap of roof and floor does not occur, no constraint is necessary.

FINITE ELEMENT ANALYSIS
The main results of an analysis are stress, strain and displacements induced by mining.
Visualization of information derived from these basic results assists in understanding strata
mechanics associated with mining and in assessment of overall safety of a particular mining plan.
Color contours of element safety factors are especially helpful. In two-dimensional analyses,
variables such as widths of entries, pillars, panels and barriers may be changed at will as may
other input data including stratigraphy and rock properties. The list of parameters is long; a
design parameter study on the computer could be lengthy, indeed. However, in a case study, the
input is fixed and thus computation time is greatly reduced. When the stratigraphic column
extends to the surface, subsidence may be extracted from displacement output. If the actual
subsidence profile is known, a match between finite element model output and mine
measurements may be used to constrain the model in a reasonable manner.

11

Main Entry Mining
Figure 5 shows before and after views of main entry mining. The “before” view is just
the mesh shown in Figure 3, but to the same scale as the “after” view that shows the distribution
of the element safety factors according to the color scale in the figure. The three yellow bands
are coal seams and show almost a uniform safety factor of 2.7 away from the main entries.
Pillars between the entries and ribs of the outside entries show a slightly lower safety factor of
2.2. Roofs and floors show much higher safety factors (greater than 4.5) because of the greater
strength of roof and floor strata. Pillar safety factors are with respect to compressive stress as
inspection of the stress output file shows. A safety factor of 2 to 4 in compression is suggested in
the literature [Obert and Duvall 1967], so the main entry system is considered safe.

Stress concentration in great detail is not obtained in this analysis stage because of the
relatively coarse mesh that uses 10x8 ft (3.0x2.4m) coal seam elements about an entry 20 ft (6 m)
wide by 8 ft (2.4 m) high. In fact, element stresses are average stresses over the area enclosed by
an element. Stresses in a pillar rib element are average stresses over the 10 ft (3 m) distance into
the rib and over the full mining height of 8 ft (2.4 m). A highly refined mesh would reveal
details about an entry and perhaps compressive stress concentrations enough to cause yielding at
entry ribs and tensile stress concentrations possibly high enough to cause roof and floor failure.
Such effects would necessarily be localized within about a half-element thickness (5 ft, 1.5 m)
because no failure in ribs, roof, and floor is indicated in elements adjacent to the main entries in
Figure 5. Figure 6 shows the distribution of vertical and horizontal stress across the main entries
and pillars. The U-shape pattern is typical of vertical stress after mining. The horizontal stress
increases from zero at the ribs with distance into the rib rather rapidly because of element size.

12

Figure 5. Element safety factor distribution. (a) before mining main entries, (b) after mining.

13

Figure 6. Stress distribution across the main entries and pillars after excavation. Sv=vertical
stress, Sh=horizontal stress. Dashed lines are premining values.

The average vertical stress in each pillar in Figure 6 is shown by the horizontal lines
labeled P1, P2, P3, and P4. These values are obtained from the finite element analysis and have
an overall average of 2,021 psi (13.9 MPa). A tributary area or extraction ratio calculation gives
a slightly higher average of 2,057 psi (14.2 MPa) because of the assumption of an infinitely long
row of entries and pillars. The average vertical pillar stress is well below the unconfined
compressive strength of coal. In fact, the ratio of strength to average vertical stress is a safety
factor of sorts with a value of 2.0. Because the vertical stress varies across a pillar and horizontal
stress increases confinement with distance into a pillar, the local element safety factor varies

14

through a pillar. This variation is shown in Figure 7 where data are from finite element results
and the local factor of safety (fs) is based on the formulation used in UT2. Also shown in Figure
7 is a normalized vertical stress obtained by dividing the post-mining vertical stress (Sv) by the
premining vertical stress (So), in essence, a stress concentration factor for vertical stress. The
local safety factor is least at the pillar ribs where confinement is nil and vertical stress is high and
greatest at the core of the pillar where confinement is high and vertical stress is less concentrated
than at the rib. The close agreement between the tributary area calculation of vertical pillar stress
after mining and the finite element results provides a check on the finite element analysis.

Figure 7. Pillar safety factor distribution from UT2 data and normalized vertical stress across the
main entries and pillars.

15

Longwall Panel Mining
Six longwall panels were mined on the north and south sides of the main entries that were
excavated in an east-west direction. For the most part, two panel entries were used for
development. The chain pillars of the panel entries undoubtedly are lost as a panel is mined and
are not considered in analysis of panel excavation effects on the main entries. Six panels
approximately 780 ft to 810 ft (234 m to 243 m) wide were excavated on each side of the main
entries. Barrier pillars approximately 450 ft (135 m) wide separate the nearest of these panels
from the main entries. In the second stage of finite element analysis, panel mining extends 2,600
ft (780 m) on each side of the barrier pillars. The geometry of this stage of analysis is shown in
Figures 2, 3, and 4.

Node Displacements and Subsidence. The first analysis of panel mining was only partially
successful. While the solution process proceeded monotonically and convergence was excellent,
roof and floor displacements over the central portions of the excavated panels indicated seam
closure greater than seam thickness, a physical impossibility. A correction was applied in the
second analysis that prevented excess seam closure. In this analysis, seam closure was set in a
way that allowed maximum surface subsidence over the panel centers to approximate observed
surface subsidence while preventing roof-floor overlap. Thus, seam level roof sag was restricted
over the horizontal length of 1,300 ft (390 m) from panel centers (mesh sides). No restrictions
on floor heave were imposed. Subsidence profiles across panels 13 through 17 on the south side
of the main entries that were plotted for the years 1999 through 2002 indicated formation of a flat
subsidence trough with about 5 ft (1.5 m) of surface subsidence.

16

Figure 8a shows displacements in the form of a deformed mesh after a second attempt at
panel mining. The displacement scale is exaggerated relative to the distance scale in order to
visualize the overall displacement pattern. Maximum displacement of 63 inches or about 5 ft
(160 cm or about 1.5 m) occurs at the mesh sides, that is, over the centers of panel mining.
Interestingly, 18 inches (46 cm) of subsidence occurs over the center of the main entries. Floor
heave (upward displacement) is also maximum at the mesh sides but diminishes with distance to
the main entries. At 130 ft (39 m) from the outside barrier pillar ribs, floor heave diminishes to
zero. With further distance from the mesh sides towards the mesh center and center of the main
entries, floor displacement is downwards indicating that the barrier pillars and entry pillars
depress the floor under the weight transferred from panel mining. Figure 8b is a close up view of
the deformed mesh about the main entries and only hints at entry roof sag and floor rise. The
rough agreement between maximum subsidence obtained from finite element analysis and that
observed in actual subsidence profiles, although indirectly imposed through seam closure,
suggests the finite element model of panel mining is reasonable.

17

Figure 8. Displacements after panel and entry mining. (a) overall, (b) entries.

18

Element Safety Factor Distributions. Element safety factor distributions reveal at a glance areas
that have reached the elastic limit and are therefore subject to yielding and areas well below the
elastic limit and of much less concern. Safety and stability of an entry surrounded by an
extensive zone of yielding would surely be threatened. A pillar with all elements stressed beyond
the elastic limit would also be of great concern. Absence of extensive zones of yielding would
be reassuring.

Figure 9 shows the overall distribution of element safety factors in two ways, one without
contours that supplement the color coding and one with contours. The seemingly faded color is a
result of the plot density that brings white element borders into close proximity and allows only a
tiny area for coloring. The jumps in contours occur across strata interfaces where discontinuities
in material properties occur. Disruption of contours occurs at seam level across portions of the
seam that have been excavated (panels and entries). Symmetry of the contour pattern is apparent
and as the pattern should be. The dark (black) regions of yielding are extensive. Near the
surface above the main entries strata flexure leads to tensile failure. Much of the roof and floor
yield is also tensile.

An expanded half-mesh view is shown in Figure 10 where the yield zones are more
clearly seen. Strata flexure in tension and failure is indicated near seam level in the roof outside
the barrier pillar rib. Floor failure below is also evident in Figure 10. Interestingly, yielding is
small in the immediate sandstone floor, but is extensive in the Masuk shale below.

19

Figure 9. Whole mesh element safety factor distributions. (a) without line contours, (b) with.

20

Figure 10. A half-mesh view of element safety factors showing dark (black) zones of yielding
mainly in horizontal tension associated with strata flexure.

Yielding under high compressive stress penetrates the barrier pillar from the panel side a
distance of 110 ft (33 m). Thus, about 25% of the barrier yields after panel excavation. This
penetration is accompanied graphically by large horizontal excursions of the safety factor contour
lines in Figure 11 which shows details of the element safety factor distribution in the vicinity of a
barrier pillar. Half of the main entries are included in Figure 11. The remainder of the barrier
pillar while not yielding is highly stressed with element safety factors no greater than 1.34.
Yielding in the two overlying coal seams is evident in a region above the barrier pillar.

21

Figure 11. Element safety factors about a barrier pillar after panel mining.

Details of the element safety factor distribution about the main entries is shown in Figure
12. The pink and red zones indicate relatively low safety factors. The highest safety factor in the
main entry pillars is 1.34, the same peak value in the barrier pillars on either side of the main
entries. Thus, all pillar element safety factors are less than the minimum of 2 recommended by
Obert and Duvall (1967). Roof and floor safety factors are in the 4 to 5 range. Although mesh
refinement would lead to lower safety factors at the roof and floor of an entry, there appears to be
no significant threat to roof and floor safety at this stage of mining.

22

Figure 12. Distribution of element safety factors about the main entries after panel mining.

Barrier Pillar Entry Mining
Barrier pillar entry mining in the analysis consists of four entries 20 ft (6 m) wide
separated by pillars 60 ft (18 m) wide. Two sets of such entries were mined, one on the north
side and one on the south side of the original main entries. The north side barrier pillar entries
were separated from the north side longwall panels by a pillar 140 ft (42 m) wide and from the
main entries by a pillar 50 ft (15 m) wide. The south side barrier pillar entries were separated
from the south side longwall panels by a 120 ft (36 m) wide pillar and from the original main
entries by a 70 ft (21 m) pillar. These dimensions were estimated using the distance function in a
drawing of the mine geometry. Without doubt, the as-mined dimensions differ from these

23

nominal dimensions. Provided such dimensional differences are small, finite element results
should differ only slightly as well and not affect inferences from analysis results concerning
overall safety of the mining plan.

North Barrier Pillar Mining. The third stage of analysis follows the first and second stages of
main entry development and panel mining. This stage involves further entry and pillar
development in the north barrier pillar. Mining geometry is illustrated in Figure 13 and shows
four additional entries and associated pillars. Only 100 ft (30 m) of the 2,600 ft (780 m) of prior
panel mining is shown in Figure 13. Mining height is 8 ft (2.4 m) as before.

Figure 13. North barrier pillar entry geometry.

The distribution of element safety factors after entry development in the north barrier
pillar is shown in Figure 14. Most elements in the north side barrier pillar are now at yield. Rib
elements in pillars adjacent to the original main entries are also at yield. The outside entry of the
original main entries shows ribs yielding in the pillar between it and the new north side barrier
pillar entry. The south outside entry ribs shows yielding extending 10 ft (3 m) into the ribs. The
highest safety factor in any pillar element in Figure 14 is 1.2.

24

Figure 14. Element safety distribution after entry development in the north barrier pillar.

South Barrier Pillar Mining. The fourth and last stage of analysis is entry development in the
south barrier pillar and follows entry development in the north barrier pillar. Mining geometry is
illustrated in Figure 15 and shows four additional entries and associated pillars in the south
barrier pillar. Only 100 ft (30 m) of prior panel mining is shown in Figure 15. Mining height is
8 ft (2.4 m). Entry and pillar widths in the south barrier pillar development are 20 ft (6 m) and 60
ft (18 m), respectively. Four additional entries are developed in the south barrier pillar.

Figure 15. South barrier pillar mining geometry.
25

The distribution of element safety factors after entry development in the south barrier
pillar is shown in Figure 16. Almost all elements in the south side barrier pillar are now at yield.
Indeed all pillar elements across the mining horizon are close to yield. Peak vertical stress in the
barrier pillars exceeds 38,400 psi (264.8 MPa), over 9 times the unconfined compressive strength
of the coal. Horizontal stress exceeds 7,300 psi (50.3 MPa). Even so this high confining
pressure is insufficient to prevent yielding. The lowest vertical pillar stress is about 6,000 psi
(41.4 MPa), almost half again greater than the unconfined compressive strength of the coal; the
lowest horizontal pillar stress is about 1,500 psi (10.3 MPa). Any release of horizontal
confinement would likely result in rapid destruction of pillars. Additionally, entries nearest to
the mined panels are showing reduced roof and floor safety factors. Yield zones extend to depth
in the floor. Overlying coal seams are also yielding or are very close to yielding over portions of
the barrier pillars, as seen in Figure 16.

Figure 16. Element safety distribution after entry development in the south barrier pillar.

26

Figure 17 shows the distribution of element safety factors about the original main entries
after entry mining in the north and south barrier pillars. Roof and floor element safety factors
have decreased significantly from the original values obtained during development prior to
longwall panel mining and range between 2 and 4, as seen in the color code. Roof and floor
element safety factors about the new entries mined in the barrier pillars are lower, roughly in the
range of 2 to 4 in Figure 17.

Figure 17. Distribution of element safety factors about the original main entries after
development in the north and south barrier pillars.

The distribution of horizontal and vertical element stresses after main entry development,
panel mining, and entry development in the north and south barrier pillars is shown in Figure 18
where gaps are entry elements. The very high vertical stresses on the ribs of the barrier pillars
27

adjacent to the panels mined north and south of the barrier pillars is striking. Although these
extreme peaks in vertical stress diminish rapidly across the pillars, they remain well above the
unconfined compressive strength of the coal, also shown in Figure 18. Recall the analysis is
elastic. If yielding were allowed as in an elastic-plastic analysis, these peaks would diminish and
the extent of yielding would likely spread across regions of the pillars that have not yielded
according to the elastic results. Horizontal confinement in rib elements at the ribs of the barrier
pillars, where the vertical stress is high, is because of averaging over the width of rib elements.
The actual horizontal stress at the rib must be zero. The high analysis value is associated with
mesh refinement and the use of a 10 ft (3 m) wide element. A lower horizontal stress would
enhance the spread of pillar yielding. Again, purely elastic behavior leads to an underestimate of
the extent of yielding that is indicated by elements with a safety factor less than one.

A tributary area calculation of the average pillar stress across the entire seam is also
shown in Figure 18 as is the finite element analysis result. These two values agree within one
percent and lend credence to the analysis. In essence, the calculation shows that the requirement
for equilibrium of stress in the vertical direction is satisfied in the course of four stages of
mining. Any analysis result, regardless of method, should meet this requirement.

Figure 19 shows the distribution of element safety factors at seam level. Safety factors
less than one are a consequence of a purely elastic calculation. Safety factors less than one
indicate a potential for shedding stress to adjacent elements.

28

Figure 18. Post-excavation pillar stress distribution. Sv=premining vertical stress. Sp=average
pillar stress, fem=finite element method, trib=tributary area, Co=unconfined compressive
strength.

Figure 19. Post-excavation element safety factor distribution.

29

DISCUSSION
Several questions that often arise about finite element analysis involve input data, twodimensional analysis, and interpretation of output results. A brief discussion of these questions
may not alleviate concerns, but does allow for some explanation and expression of opinion.

The first issue here is the proverbial one about quality of input data and consequences for
output results. In fact, this question is present in all engineering analysis and is not unique to the
finite element method or other computer-based models for stress analysis or for the analysis of
business plans and so forth. Generally, the problem of mine excavation using UT2 is a wellposed mathematical problem in solid mechanics, so small variations in input data lead to only
small variations in output. However, if there are errors in input, then the output will also be
erroneous. For this reason, checks on results are important when available. An extraction ratio
calculation after main entry excavation indicates reliable output at this stage of analysis.
Subsidence results in agreement with mine observations, although indirectly imposed, also
indicate reliable output.

Another question is the use of two-dimensional analyses in a three-dimensional world of
underground coal mining. Here the long drive of main entries, over three miles, and the
extensive mining on both sides of the main entries suggests a tunnel-like geometry amenable to
two-dimensional analysis in a vertical cross-section. Depth varies over the main entries because
of topography and certainly influences analysis results because greater depth is associated with
higher premining stress. Depths ranged to 2,000 ft (600 m) or more. A depth of 1,601 ft (480 m)
used in the analyses here is therefore relatively shallow. For this reason, any adverse results

30

would be of even more concern at greater depth. Thus, an optimistic view is taken using a
relatively shallow depth.

Another question concerns the role of cross-cuts that are not seen in a vertical section
across the mains and through the pillars between entries. The effect is to produce an optimistic
or lower stress in pillars because the additional load transferred to pillars from cross-cuts is not
taken into account. An adjustment can be made to increase pillar load (Pariseau, 1981) but this
was not done for the sake of analysis clarity. Cross-cuts also lead to greater roof spans at entry
intersections with cross-cuts and thus more complex strata flexure in roof and floor, but again
this complication was avoided with error on the side of optimism. A threat to roof or floor safety
in two-dimensional analysis would indicate a greater threat in a three-dimensional analysis.

Mesh refinement is always a question of interest in any numerical analysis of stress.
Large elements average out stress and may mask yielding that would be observed with smaller
elements. Large is relative to excavation size. Tabular excavations are very wide compared to
height and thus represent a challenge for numerical analysis. A compromise is always necessary
between desire for detail and problem size and run time limitations. In any case, a coarse mesh
results in optimistic output, lower element stresses and also lower displacements. For example, a
roof element 10x10 ft (3.0x3.0 m) over a 20-ft (6 m) wide entry would certainly mask stress
concentration in the roof compared with roof elements 1x1 ft (0.3x0.3 m). However, 100 more
small elements per large element would be required. If this requirement were extended over the
mesh used, more than 17 million elements would be needed, an impractical number for
engineering applications.

31

A more subtle question that arises in “stress analysis” concerns material behavior. A
closely related question concerns relationships between laboratory and mine scale rock
properties. These questions are of much interest in rock mechanics research for which there is no
general consensus and that are well-beyond the scope of this report. An elastic material model
was used here as were laboratory rock properties. Strengths were used to compute the limit to a
purely elastic response and element safety factors. Generally, rock masses contain discontinuities
such as joints and cleats that are absent in laboratory-scale test specimens. Consequently, rock
masses tend to be weaker and more compliant than laboratory test results would indicate. The
result is an optimistic analysis of stress because the higher laboratory moduli and strengths used
lead to smaller displacements and less yielding. If an adverse result is observed using rock
properties from laboratory tests, results for the mine would likely be worse.

Inelastic behavior of rock under low confinement is likely to be “brittle” with inelasticity
appearing in the form of cracking or “damage”. A falling compressive stress-strain curve is often
observed in the laboratory in tests under displacement control past the peak of the curve.
Without displacement control, fast, violent failure of the test specimen is likely. While a rising
stress-strain curve beyond the elastic limit is strain-hardening, a falling curve indicates “strainsoftening”. The first is intrinsically stable, while the latter is unstable. Introduction of strainsoftening is likely to make a potentially adverse situation, say, with respect to pillar stress, a
catastrophic case. Again, a purely elastic model is optimistic because of the avoidance of
complex inelastic behavior that may lead to catastrophic failures.

32

A potentially important inelastic effect absent in elastic analyses is “caving”. Caving
over longwall panels is considered to relieve load on shield supports at the face and on chain
pillars in panel entries because the length of a cantilever roof beam immediately above the
supports is shortened by tensile failure and thus reduces “weight” on the supports. Caving
certainly occurs over longwall panels. How high into the remote roof caving propagates is an
open question that is sometimes addressed by rules of thumb or experience in a particular mining
district. Strata flexure still occurs above the caved zone and transfers load to pillars remaining.
Thick, massive sandstones in roof and floor may transfer load over large spans and if failure
ensues, large scale collapse is possible. However, reliable caving models, those that initiate and
propagate caving from first principals, are not available, and thus, the question of caving effects
is left open.

CONCLUSION
Finite element analysis of barrier pillar mining at Crandall Canyon indicates a decidedly
unsafe, unstable situation in the making. This conclusion is based on a two-dimensional elastic
analysis of a vertical section transverse to the main entries and parallel longwall panels outside of
barrier pillars adjacent to the main entries. Elasticity is the de facto standard model for
engineering design of bridges, skyscrapers, concrete dams and similar structures throughout the
world. Approximations in the analyses here are generally on the optimistic side, so that an
adverse situation evident in output data is likely to be worse. For example, complications such as
damage in pillar ribs from locally high stress concentration is ignored. Another example is the
neglect of load transfer to pillars from cross-cut excavation that would be in addition to load
transfer associated with entry excavation. A relatively shallow depth of 1,601 ft (480 m) was

33

used; actual depth ranges to 2,000 ft (600 m). No pillar extraction was considered after entry
development in the barrier pillars. Transfer of load to the remaining pillars during pillar mining
in the barrier pillars would increase stress about the entries and remaining pillars as would
consideration of greater depth. Both increase outby the considered analysis section.

Elastic behavior is optimistic because stress may exceed strength in a purely elastic
analysis. Thus, if an unsafe condition is inferred from results of an elastic analysis, then caution
is certainly indicated. In an elastic-plastic analysis, stresses above strength are relieved by
fracture and flow of ground (“yielding”). Reduction of peak stress by yielding is likely to cause
the zone of fracture and flow (yield zone) to spread to adjacent ground. Yielding by fracture is
accompanied by a sudden loss of strength and is associated with fast failure. Glass breakage is
an example of fast failure. Yielding by flow may also be accompanied by reduction in strength
(“strain softening”) which is also unstable and may to lead to fast failure.

However, yielding by flow may also be slow as loss of strength occurs in time.
Unfortunately, time effects in strata mechanics are not well understood. Creep, that is, timedependent flow, to failure may occur in a matter of minutes, hours, or years. Elasticity may also
be delayed, that is, strain may not occur instantaneously with stress. In this regard, there are
many mathematical models of time-dependent (rheological) material behavior available for
analysis, but reliable calculations for engineering design are problematic. Successful forecasts of
time to failure in rock mechanics are rare, if they exist at all. In any event, long-term strength is
less than short term strength (determined by laboratory tests) used in elastic analysis here. Again,
elastic analysis is optimistic because of the use of higher strength.

34

A multi-stage mining sequence was followed in the analysis here. Main entries were
mined first. A tributary area check on pillar stress confirmed finite element results. Entry roofs,
pillars, and floors were well within the elastic limit; no yielding was indicated.

Panel mining on both sides of the main entries was done next. During this stage,
displacements were constrained in the finite element model to prevent physically impossible
overlap of roof and floor strata at seam level during the panel mining stage. This constraint
assisted in achieving reasonable agreement between measured subsidence and finite element
results. Results indicated 25% of the barrier pillars yielded, while the remaining portions were
near yield. Entry pillar safety factors decreased significantly to 1.3; roof and floor safety factors
also decreased but remained in the elastic domain.

Entry mining in the north barrier pillar led to yielding of the remaining portion of this
pillar and a significant penetration of yielding into the south barrier pillar. The highest safety
factor in any pillar, including main entry pillars was 1.2; the lowest was 0.4. Subsequent entry
development in the south barrier caused further yielding. The greatest vertical stress in a rib
element was more than nine times the unconfined compressive strength of coal. Extensive zones
of strata flexure and tensile yielding were observed in roof and floor. A tributary area
calculation of average vertical stress at the conclusion of the last mining stage showed close
agreement with finite element results.

The large excess of vertical rib stress over strength indicates a potential for rapid
destruction of the rib with expulsion of the broken coal into the adjacent entry. The presence of

35

thick, strong sandstone in roof and floor strata would reinforce this expectation. The broken coal
could fill the entry and perhaps restore some horizontal confinement. If a bulking porosity of
0.25 is assumed, then rib failure would extend 60 ft (18 m) into a rib. The extent of failure into a
single rib would be less, if both entry ribs failed. Photographs show entries partially filled with
broken coal under intact roof. If bottom coal were left, then floor heave could occur, and
similarly, if top coal were left. Failure of either top or bottom coal is a release mechanism of
horizontal confinement. Another expectation of large, horizontal motion of rib coal into entries
would be evidence of shear slip at contacts between roof and floor sandstones, perhaps in the
form of “fault” gouge, that is, finely pulverized coal.

In the opinion of the writer, were these finite element model results available in advance,
mining in barrier pillars at Crandall Canyon would not be justified.

REFERENCES

Bathe, K.-L., (1982) Finite Element Procedures in Engineering Analysis. Englewood Cliffs, N.
J., Prentice-Hall, pp 735.
Desai, C. S., and J. F. Abel (1972) Introduction to the Finite Element Method for Engineering
Analysis. Van Nostrand Reinhold Co., N. Y., pp 477.
Cook, R. D. (1972) Concepts and Applications of Finite Element Analysis. John Wiley & Sons,
Inc., N. Y., pp 402.
Jones, R. E. (1994) Investigation of Sandstone Escarpment Stability in the Vicinity of Longwall
Mining Operations. M. S. Thesis, Department of Mining Engineering, University of Utah.
Obert, L. and W. I. Duvall (1967) Rock Mechanics and the Design of Structures in Rock. John
Wiley & Sons, Inc., N. Y., pg 490.
Oden, J. T. (1972) Finite Elements of Nonlinear Continua. N.Y., McGraw-Hill, pp 432.

36

Pariseau, W. G. (1981) Inexpensive but Technically Sound Mine Pillar Design Analysis. Intl. J.
for Numerical and Analytical Methods in Geomechanics. Vol. 5, No. 4, pg 429-447.
Pariseau, W. G. (2007) Finite Element Analysis of Inter-Panel Barrier Pillar Width at the
Aberdeen (Tower) Mine. Department of Mining Engineering, University of Utah and Bureau of
Land Management, Salt Lake City, Utah.
Rao, T. V. (1974) Two Dimensional Stability Evaluation of a Single Entry Longwall Mining
System. M. S. Thesis, Department of Mining Engineering, University of Utah.
Zienkiewicz, O. C. (1977) The Finite Element Method (3rd ed). N. Y., McGraw-Hill, pp 787.

37

Appendix R - Description of BEM Numerical Models
AAI developed numerical models for Crandall Canyon Mine as early as 1995. Between 1995
and 2004, AAI performed several design/modeling projects using a program called EXPAREA.
According to AAI:
“This program was developed at the University of Minnesota by Dr. S. Crouch and
Dr. Starfield (Starfield and Crouch (1973), St. John (1978)). It was initially used
for Project Salt Vault in the early days of the Nuclear Waste program. It uses the
displacement discontinuity method. The development of the program and later
variations such as MULSIM were further developed at the University of Minnesota
under funding from the USBM [US Bureau of Mines]. AAI has used the program
since 1979 for design of underground thin-seam mines, particularly for coal
mines.”
However, in 2006, AAI elected to use another program, LaModel5, to model ground behavior at
the mine. According to NIOSH26:
“LAMODEL is software that uses boundary-elements for calculating the stresses
and displacements in coal mines or other thin, tabular seams or veins. It can be
used to investigate and optimize pillar sizes and layout in relation to pillar stress,
multiseam stress, or bump potential (energy release). LAMODEL simulates the
overburden as a stack of homogeneous isotropic layers with frictionless interfaces,
and with each layer having the identical elastic modulus, Poisson's Ratio, and
thickness. This "homogeneous stratification" formulation does not require specific
material properties for each individual layer, and yet it still provides a realistic
suppleness to the overburden that is not possible with the classic, homogeneous
isotropic elastic overburden used in previous boundary element formulations such
as MULSIM or BESOL. LAMODEL consists of three separate programs LAMPRE, LAMODEL, and LAMPLT. You must install all three programs to use
LAMODEL:
LAMPRE is the pre-processor that facilitates creating the input file for LAMODEL.
LAMPRE accepts all of the numerical parameters input for LAMODEL and allows
graphical input of the material codes for the seam grids. Also, a "Material Wizard"
helps generate reasonable coal properties and appropriate yield zones on coal
pillars.
LAMODEL calculates the stresses and displacements at the seam level from the
user’s input file. Model runs can take several minutes to several days depending on
the computer speed and model complexity. The output from LAMODEL is stored
for subsequent analysis by LAMPLT, the post-processing program.
LAMPLT is the post-processor that allows the user to plot and analyze the output
from LAMODEL.”

R-1

Appendix S - Back-Analysis of the Crandall Canyon Mine Using
the LaModel Program

by
Keith A. Heasley, Ph.D., P.E.
West Virginia University

S-1

Back Analysis of the
Crandall Canyon Mine
Using the LaModel Program

By
Keith A. Heasley, Ph.D., P.E.
June 20, 2008

Executive Summary
On August 6th , 2007, the Crandall Canyon Mine in Utah collapsed entrapping six miners. It
appeared that a large area of pillars in the Main West and South Barrier sections of the mine had
bumped in a brief time period, filling the mine entries with coal from the failed pillars and
entrapping the six miners working in the South Barrier section. Ten days later, during the heroic
rescue effort, another bump occurred thereby killing three of the rescue workers, including one
federal inspector, and injuring six other rescue workers. A few days after the August 16th
incident, a panel of ground control experts determined that the Main West area was structurally
un-stable and underground rescue attempts halted. Subsequently the mine was abandoned and
sealed.
The objective of this investigation is to utilize the LaModel boundary-element program along
with the best available information to back-analyze the August 6th , 2007 collapse at the Crandall
Canyon Mine in order to better understand the geometric and geo- mechanical factors which
contributed to that collapse. Ultimately, it is hoped that this back-analysis will help determine
improvements in mine design that can be made in the future to eliminate similar type events.
In order to determine the optimum parameter values for matching the observed mine
behavior, to assess the sensitivity of the model results to the input values, and to investigate
various triggering mechanisms, an extensive parametric analysis was performed. This analysis
examined: different overburden properties, gob properties, coal behavior and triggering
mechanisms. In all, over 230 different models were run to perform the parameter optimization,
sensitivity analysis and trigger investigation.
Based on this extensive back analysis of the Crandall Canyon Mine using the LaModel
program and with the benefit of hindsight from the March bump and August collapse, a number
of conclusions can be made concerning the mine design and August 6th collapse:
1) Overall, the Main West and adjacent North and South Barrier sections were primed for a
massive pillar collapse because of the large area of equal size pillars and the near unity safety
factors. This large area of undersized pillars was the fundamental cause of the collapse.
a. The pillars and inter-panel barriers in this portion of the Crandall Canyon Mine
essentially constitute a large area of similar size pillars, one of the essential ingredients
for a massive pillar collapse.
b. The high overburden (2200 ft) was causing considerable development stress on the pillars
in this area, and bringing pillar development safety factors below 1.4.
c. Considerable longwall abutment stress was overriding the barrier pillars between the
active sections and the old longwall gobs.
2) The abutment stress from the active North Barrier retreat section was key to the March 10th
bump occurrence and the modeling indicated that the North Barrier abutment stress
contributed to the August 6th pillar collapse.
3) From the modeling, it is not clear exactly what triggered the August collapse. A number of
factors or combination of factors could have been the final perturbation that initiated the
collapse of the undersized pillars in the Main West area.
4) LaModel analysis demonstrated that the active pillar recovery mining in the South Barrier
section could certainly have been the trigger that initiated the August collapse; however, the
modeling by itself does not indicate if the active mining was the most likely trigger.

ii

Table of Contents

Page

Executive Summary .....................................................................................................ii
List of Figures.................................................................................................................v
1. Objective ....................................................................................................................1
2. Background ...............................................................................................................1
2.1
2.2

The Crandall Canyon Mine...................................................................................1
The LaModel Program..........................................................................................1
2.2.1 Calibrating LaModel.................................................................................2
2.2.1.1 Rock Mass Stiffness...................................................................3
2.2.1.2 Gob Stiffness..............................................................................4
2.2.1.3 Coal Strength..............................................................................8
2.2.1.4 Post-Failure Coal Behavior ........................................................9
2.2.2 LaModel and Bumps ...............................................................................10
2.2.3 LaModel and Massive Pillar Collapses...................................................11
2.2.4 LaModel and Time and Homogeneity....................................................11
2.2.5 Pillar Safety Factors in LaModel ............................................................12

3. The LaModel Analysis ........................................................................................15
3.1
3.2

3.3
3.4

3.5

Approach………….. ...........................................................................................15
Basic Calibration Points......................................................................................15
3.2.1 Main West...............................................................................................15
3.2.2 North Barrier...........................................................................................15
3.2.3 South Barrier...........................................................................................18
3.2.4 Results of the August 6th Collapse ..........................................................18
The LaModel Grid ..............................................................................................18
Calibrating the Critical Parameters.....................................................................19
3.4.1 Determining the Rock Mass Lamination Thickness ...............................19
3.4.2 Determining the Gob Stiffness................................................................21
3.4.3 Determining the Coal Strength ...............................................................22
3.4.3.1 Back Analysis of the North Barrier Bump...............................23
Analyzing the August 6th Collapse .....................................................................26
3.5.1 Primary Results.......................................................................................26
3.5.2 Triggering the Collapse of the South Barrier Section.............................30
3.5.2.1 Reduced Coal Strength.............................................................31

iii

Page

3.6
3.7

3.5.2.2 Joint Slip ..................................................................................31
3.5.2.3 Softer Southern Gob.................................................................36
Parametric Analysis ............................................................................................36
Final Back Analysis Model.................................................................................38

4. Summary…………….. ............................................................................................42
5. Conclusions …………….. .......................................................................................43
References ………………..............................................................................................45

iv

List of Figures

Page
2.1

Conceptualization of the abutment angle....................................................................6

2.2

Suggested stability factors for the ARMPS deep-cover database...............................7

2.3

Stress-strain and safety factor curves for the North Barrier 60 X 70 pillar ..............14

3.1

Map of the Main West area.......................................................................................16

3.2

Rib and pillar failure in the North Barrier section as of March 16th 2007................17

3.3

Overburden stress as calculated by LaModel ...........................................................20

3.4

Average gob stress as a function of lamination thickness and final gob modulus ...22

3.5

Analysis of North Barrier bump ...............................................................................24

3.6

Plot of pillar and element safety factors for step 3 ...................................................27

3.7

Plot of pillar and element safety factors for step 5 ...................................................28

3.8

Plot of pillar safety factors with coal strength adjusted in Main West .....................29

3.9

Plot of pillar and element safety factors for step 6 with 4 pillars removed ..............32

3.10 Plot of pillar safety factors for weakened coal in the Main West.............................33
3.11 Plot of pillar safety factors for the model with a joint at crosscut 137 .....................34
3.12 Plot of pillar safety factors for softer gob in the southern panels .............................35
3.13 Final model of Crandall Canyon Mine – steps 3 & 5 ...............................................40
3.14 Final model of Crandall Canyon Mine – step 9 ........................................................41

v

1. Objective
The objective of this investigation is to utilize the LaModel boundary-element program
along with the best available information to back-analyze the August 6th , 2007 collapse at the
Crandall Canyon Mine in order to better understand the geometric and geo- mechanical
factors which contributed to that collapse. A secondary objective of this work is to perform a
parametric analysis of the pertinent input parameters to assess the sensitivity of the model
results to the input values. Ultimately, it is hoped that this back-analysis will help determine
improvements in mine design that can be made in the future to eliminate similar type events.

2. Background
2.1 The Crandall Canyon Mine
On August 6th , 2007, the Crandall Canyon Mine in Utah collapsed entrapping six miners.
It appeared that a large area of pillars in the Main West and South Barrier sections of the
mine had bumped in a brief time period, filling the mine entries with coal from the failed
pillars and entrapping the six miners working in the South Barrier section. The seismic event
associated with the initial accident registered 3.9 on the Richter scale. Ten days later during
the heroic rescue effort, another bump occurred thereby killing three of the rescue workers,
including one federal inspector, and injuring six other rescue workers. A few days after the
August 16th incident, a panel of ground control experts determined that the Main West area
was structurally unstable and posed a significant risk to anyone entering the area. At this
point, underground rescue attempts halted and subsequently the mine was abandoned and
sealed.

2.2 The LaModel Program
The LaModel program is used to model the stresses and displacements on thin tabular
deposits such as coal seams. It use the displacement-discontinuity (DD) variation of the
boundary-element method, and because of this formulation, it is able to analyze large areas of
single or multiple-seam coal mines (Heasley, 1998). LaModel is unique among boundary
element codes because the overburden material includes laminations which give the model a
very realistic flexibility for stratified sedimentary geologies and multiple-seam mines. Using
LaModel, the total vertical stresses and displacements in the coal seam are calculated, and
also, the individual effects of multiple-seam stress interactions and topographic relief can be
separated and analyzed individually.
Since LaModel’s original introduction in 1996, it has continually been upgraded (based
on user requests) and modernized as operating systems and programming languages have
changed. The present program is written in Microsoft Visual C++ and runs in the windows
operating system. It can be used to calculate convergence, vertical stress, overburden stress,
element safety factors, pillar safety factors, intra-seam subsidence, etc. on single and multiple
seams with complex geometries and variable topography. Presently, the program can
analyze a 1000 x 1000 grid with 6 different material models and 26 different individual in-

-1-

seam materials. It uses a forms-based system for inputting model parameters and a graphical
interface for creating the mine grid. Also, it includes a utility referred to as a “Wizard” for
automatically calculating coal pillars with a Mark-Bienawski pillar strength and another
utility to assist with the development of “standard” gob properties. Recently, the LaModel
program was interfaced with AutoCAD to allow mine plans and overburden contours to be
automatically imported into the corresponding seam and overburden grids. Also, the output
from LaModel can be downloaded into AutoCAD and overlain on the mine map for
enhanced analysis and graphical display.
2.2.1 Calibrating LaModel:
The accuracy of a LaModel analysis depends entirely on the accuracy of the input
parameters. Therefore, the input parameters need to be calibrated with the best available
information, either: measured, observed, or empirically or numerically derived. However, in
calibrating the model, the user also needs to consider that the mathematics in LaModel are
only a simplified approximation of the true mechanical response of the overburden and
because of the mathematical simplifications built into the program, the input parameters may
need to be appropriately adjusted to reconcile the program limitations.
In particular, after many years of experience with the program, it is clear that in many
situations the overburden model in LaModel is not as flexible as the true overburden. The
laminated overburden model in LaModel is inherently more flexible than a homogeneous
elastic overburden as used in previous displacement-discontinuity codes and it is more
flexible than a stratified elastic model without bedding plane slip as used in many finiteelement programs. However, using reasonable values of input parameters, the LaModel
program still does not produce the level of seam convergence and/or surface subsidence as
measured in the field. It is believed that this displacement limitation in the model may be
due to the lack of any consideration for vertical joint movement in the program. The
laminated model makes a good attempt at simulating bedding plane slip in the overburden,
but it does not consider any overburden movement due to vertical/sub- vertical joint slip,
thereby limiting the amount of calculated displacements.
Knowing the inherent limitations of LaModel, the user can either calibrate for realistic
stress output or for realistic displacement output. In general, it is not possible to accurately
model both with the same set of material parameters. If the user calibrates the model to
produce realistic stress values, then the input parameters are optimized to match as closely as
possible the observed/measured stress levels from the field, and it is likely that the calculated
displacement values will be low. On the other hand, if the user optimizes the input
parameters to produce realistic displacement /subsidence values, then generally, the
calculated stress values will be inaccurate. Historically, the vast majority of LaModel users
have been interested in calculating realistic stresses and loads, and in this back-analysis of
the pillar stability at the Crandall Canyon Mine realistic stress and load calculations are also
the primary objective.
When actually building a model, the geometry of the mining in the seams and the
topography are fairly well known and fairly accurately discretized into LaModel grids. The
most critical input parameters with regard to accurately calculating stresses and loads, and,
therefore, pillar stability and safety factors, are then:

-2-

•
•
•

The Rock Mass Stiffness
The Gob Stiffness
The Coal Strength

These three parameters are always fundamentally important to accurate modeling with
LaModel and particularly so in simulations analyzing abutment stress transfer (from gob
areas) and pillar stability as in the Crandall Canyon Mine situation. During model
calibration, it is critical to note that these parameters are strongly interrelated, and because of
the model geo-mechanics, the parameters need to be calibrated in the order shown above.
With this sequence of parameter calibration, the calibrated value of the subsequent
parameters is determined by the chosen value of the previous parameters, and changing the
value of any of the preceding parameters will require re-calibration of the subsequent
parameters. The model calibration process as it relates to each of these parameters is
discussed in more detail below.
2.2.1.1 Rock Mass Stiffness: The stiffness of the rock mass in LaModel is primarily
determined by two parameters, the rock mass modulus and the rock mass lamination
thickness. Increasing the modulus or increasing the lamination thickness of the rock mass
will increase the stiffness of the overburden. With a stiffer overburden: 1) the extent of the
abutment stresses will increase, 2) the convergence over the gob areas will decrease and 3)
the multiple seam stress concentrations will be smoothed over a larger area. When
calibrating for realistic stress output, the rock mass stiffness should be calibrated to produce a
realistic extent of abutment zone at the edge of the critical gob areas. Since changes in either
the modulus or lamination thickness cause a similar response in the model, it is most efficient
to keep one parameter constant and only adjust the other. When calibrating the rock mass
stiffness, it has been found to be most efficient to initially select a rock mass modulus and
then solely adjust the lamination thickness for the model calibration.
In calibrating the lamination thickness for a model based on the extent of the abutment
zone, it would be best to use specific field measurements of the abutment zone from the
mine. However, often these field measurements are not available. In this case, visual
observations of the extent of the abutment zone can often be used. Most operations
personnel in a mine have a fairly good idea of how far the stress effects can be seen from an
adjacent gob.
Without any field measurements or observations, general historical field measurements
can be used. For instance, historical field measurements would indicate that, on average, the
extent of the abutment zone (D) at depth (H) (with both terms expressed in units of ft) should
be (Mark and Chase, 1997; Mark, 1992):

D = 9.3 H

(2.1)

or that 90% of the abutment load should be within:

D =5 H

(2.2)

Once the extent of the abutment zone (D) at a given site is determined, an equation
recently derived from the fundamental laminated overburden model can be used to determine
-3-

the lamination thickness (t) required to match that abutment extent based on the value of
some of the other site parameters:

2E 12(1 − v 2 )  D - d 

t= s
×
 ln(1 - Lg ) 
E×M



2

(2.3)

Where:
E = The elastic modulus of the overburden
v = The Poisson’s Ratio of the overburden
Es = The elastic modulus of the seam
M = The seam thickness
d = The extent of the coal yielding at the edge of the gob
Lg = The fraction of gob load within distance D
As mentioned previously, there is a practical trade-off between getting a realistic stress
distribution and getting realistic convergence. Equation 2.3 provides an optimum lamination
thickness to use for matching the desired abutment stress extent; it should not be used for
determining the optimum lamination thickness for accurately calculating displacement and/or
subsidence values. Furthermore, when using equation 2.3, the user is fairly accurately
matching the “global” stress transfer in the field with the global stress transfer in the model.
In many practical mining situations, the more “local” stress transfer between adjacent pillars
or between adjacent multiple seams is probably determined by the local flexing of the thinner
strata laminations in the immediate roof or interburden. To optimally match these more local
effects or to compromise between matching global and local stress transfer, a thinner
lamination thickness than determined by equation 2.3 may be appropriate.
2.2.1.2 Gob Stiffness: In a LaModel analysis with gob areas, an accurate input stiffness for
the gob (in relation to the stiffness of the rock mass) is critical to accurately calculating pillar
stresses and safety factors. The relative stiffness of the gob determines how much
overburden weight is carried by the gob; and therefore, not transferred to the surrounding
pillars as an abutment stress. This means that a stiffer gob carries more load and the
surrounding pillars carry less, while a softer gob carries less load and the surrounding pillars
carry more. In LaModel, three models are available to simulate gob behavior: 1) linearelastic, 2) bilinear and 3) strain-hardening. The gob wizard available in LamPre is designed
to assist the user in developing strain- hardening input parameters.
In the strain hardening model, the stiffness of the gob is primarily determined by
adjusting the “Final Modulus” (Heasley, 1998; Pappas and Mark, 1993; Zipf, 1992). A
higher final modulus gives a stiffer gob and a lower modulus value produces a softer gob
material. Given that the behavior of the gob is so critical in determining the pillar stresses
and safety factors, it is a sad fact that our knowledge of insit u gob properties and stresses is
very poor.
For a calibrated LaModel analysis, it is imperative that the gob stiffness be calibrated
with the best available information on the amount of abutment load (or gob load) experienced
at that mine. Once again, it would be best to use specific field measurements of the abutment
load or gob load from the mine in order to determine realistic gob stiffness. However, these

-4-

types of field measurements are quite rare (and sometimes of questionable accuracy). Also,
visual observations are not very useful for estimating abutment loads or gob loads; and
therefore, general empirical information is quite often the only available data.
In order to calibrate the gob stiffness for a practical situation, it is best to consider a
number of general guiding factors. For a first approximation, a comparison of the present
gob width and the critical gob width for the given depth can provide some insight. For a
critical (or supercritical) panel width (where the maximum amount of subsidence has been
achieved), it would be expected that the peak gob load in the middle of the panel would
approach the insitu overburden load. As the depth increases from the critical situation and
the gob width becomes more subcritical, a laminated overburden analysis with a linear gob
material would suggest that the peak gob load would increase linearly with depth from the
load level in the critical case (Chase et al., 2002; Heasley, 2000).
The critical depth (Hc) for a given gob width (P) and abutment angle (ß) can be
calculated as:
P
Hc =
(2.4)
2 × tan( ß )
Where:
P = Panel Width (ft)
β = Abutment Angle
and then the expected average gob stress (s gob-lam-av) at the actual seam depth (H) can be
calculated as:
 H  H c × δ   H × δ 
s gob-lam −av = 
 H  2 ×144  =  288 

 

 c 

(2.5)

Where:
H = Seam Depth (ft)
δ = Overburden Density (lbs/cu ft)
Equation 2.5, which is based on a laminated overburden and a linear elastic gob, implies that
the average gob stress for a subcritical panel is solely a function of the depth and equal to
half of the insitu stress. (In reality, gob material is generally considered to be strainhardening and therefore, equation 2.5 may underestimate the actual gob loading. )
Another factor to consider in estimating the gob stiffness and the abutment loading is the
abutment angle concept utilized in ALPS and ARMPS. In both these programs, an average
abutment angle of 21º was determined from a large empirical database and is used to
calculate the abutment loading. Using the abutment angle concept and the geometry shown
in Figure 2.1, the average gob stress (s gob-sup-av) for a supercritical panel can be calculated as:
 H × δ  P − (H × tanß ) 
s gob-sup−av = 


P
 144 


Where:
H = Seam Depth (ft)
δ = Overburden Density (lbs/cu ft)
-5-

(2.6)

P = Panel Width (ft)
β = Abutment Angle
Similarly, the average gob stress (s gob-sub-av) for a subcritical panel can be calculated from the
geometry in Figure 2.1 as:
s gob-sub− av =

P  1  δ 



4  tanß  144 



(2.7)

Equation 2.7, which is based on the abutment angle concept of gob loading, implies that the
average gob stress for a subcritical panel (with an assumed abutment angle) is solely a
function of the panel width.

H tan β

P/2

LS - Side Abutment Load

LSS

H

β- Abutment Angle
Mined out panel

β
P

Supercritical

Subcritical

Figure 2.1 Conceptualization of the abutment angle.
Recent work has noted that the concept of a constant abutment angle as used in ALPS
and ARMPS appears to breakdown under deeper cover (see Figure 2.2)(Chase et al., 2002;
Heasley, 2000). In particular, for room-and-pillar retreat panels deeper than 1250 ft, it was
found that a stability factor of 0.8 (for strong roof) could be successfully used in ARMPS, as
opposed to a required stability factor of 1.5 for panels less than 650 ft deep. One of the more
likely explanations for this reduction in allowable stability factor is that the actual pillar
abutment loading may be less than predicted by using the constant abutment angle concept
(Chase et al., 2002). Colwell found a similar situation with deep longwall panels in Australia
where the measured abutment stresses were much less than predicted with a 21º abutment
angle (Colwell et al., 1999).

-6-

ARMPS Stability Factor

2

Successful Case
Unsuccessful Case

1.5

1

Design Line

0.5

0
650

850

1050

1250

1450

1650

1850

Depth of Cover (ft)

Figure 2.2 Suggested stability factors for the ARMPS deep-cover database.
The degree to which a constant abutment angle might overestimate the abutment loading
can be investigated by comparing the recommended NIOSH stability factors for shallow and
deep cover. Below 650 ft, a stability factor greater than 1.5 is recommended but, at depths
greater than 1250 ft, 0.8 is acceptable. Since higher coal strengths have not been correlated
with greater depth, it is most likely that the lower stability factor recommendation is due to
an overestimate of applied stress or load. Based on the NIOSH recommendations, it appears
that the abutment loading based on the constant abutment angle of 21B could be as much as
1.875 (1.5/0.8) times higher than actual loading experienced in the field. Implementing this
adjustment produces the following equation for an adjusted average gob load for a subcritical
panel based on the abutment angle concept (given without derivation):

  0.8   (4H ∗ tanß ) − P   H ∗ δ 
 ∗ 
s gob-adj−av = 1 − 
 ∗



  1.5   4H ∗ tanß   144 

(2.8)

Where:
H = Seam Depth (ft)
δ = Overburden Density (lbs/cu ft)
P = Panel Width (ft)
β = Abutment Angle
The preceding discussion on gob stiffness and loading has produced several competing
concepts/equations. Equation 2.5, which is based on a laminated overburden model and a
linear elastic gob, implies that the average gob stress for a subcritical panel is solely a
function of the depth. Equation 2.7, which is based on the abutment angle concept of gob
loading, implies that the average gob stress for a subcritical panel is solely a function of the
panel width. Equation 2.8 modifies the abutment angle concept in an attempt to produce
more realistic results for panels deeper than 1250 ft.

-7-

It is not entirely clear which concept or equation provides the most realistic estimates of
gob stress. From recent exp erience, Equation 2.7 appears to provide a lower bound for
realistic gob stresses and Equation 2.8 appears to provide an upper bound. Equation 2.5 is
between the bounds set by equations 2.7 & 2.8 and may provide a reasonable starting point
for further calibration. Regardless of which equation is chosen as a starting point, it is clear
that a realistic gob/abutment loading is critical to a realistic model result and that the gob
stiffness should be carefully analyzed and calibrated in a realistic model.
If the user desires to calibrate the abutment and/or gob loading in the model based on a
laminated approximation or a specific abutment angle, then either equation 2.5, 2.7 or 2.8,
depending on the situation, could be used to determine the average gob loading. Each of
these equations provides an estimate of average gob stress. After choosing among them, the
user would need to run several models with various gob stiffnesses (in LaModel or LaM2D),
measure the average gob loading in the model, and then choose the final gob modulus which
best fits the estimated gob stress.
2.2.1.3 Coal Strength: Accurate insitu coal strength is another value which is very difficult
to obtain and yet is critical to determining accurate pillar safety factors. It is difficult to get a
representative laboratory test value for the coal strength and scaling the laboratory values to
accurate insitu coal pillar values is not very straightforward or precise (Mark and Barton,
1997). For the default coal strength in LaModel, 900 psi (Si) is used in conjunction with the
Mark-Bieniawski pillar strength formula (Mark, 1999):

 w 2 
w
Sp = Si  0.64 + 0.54  − 0.18
 lh 

h




(2.9)

Where:
Sp = Pillar Strength (psi)
Si = Insitu Coal Strength (psi)
w = Pillar Width
l = Pillar Length
h = Pillar Height
This formula also implies a stress gradient from the pillar rib that can be calculated as:

 x 
s p (x) = Si  0.64 +2.16   

 h 


Where:
s p(x)
x
Si
h

(2.10)

= Peak Coal Stress (psi)
= Distance into Pillar
= Insitu Coal Strength (psi)
= Pillar Height

The best technique to determine appropriate coal strength for LaModel is to back analyze
a previous mining situation (similar to the situation in question) where the coal was close to,

-8-

or past, failure. Back-analysis is an iterative process in which coal strength is increased or
decreased to determine a value that provides model results consistent with the actual
observed failure. This back analysis should, of course, use the previously determined
optimum values of the lamination thickness and gob stiffness. If there are no situations
available where the coal was close to failure, then the back-analysis can at least determine a
minimum insitu coal strength with some thought of how much stronger the coal may be, or
the default average of 900 psi can be used.
The 900 psi insitu coal strength that is the default in LaModel comes from the databases
used to create the ALPS and ARMPS program and is supported by considerable empirical
data. It is the author’s opinion that insitu coal strengths calculated from laboratory tests are
not more valid than the default 900 psi, due to the inaccuracies inherent to the testing and
scaling process for coal strength. If the LaModel user chooses to deviate very much from the
default 900 psi, they should have a very strong justification, preferably a suitable back
analysis as described above.
2.2.1.4 Post-Failure Coal Behavior: The present understanding of the post failure behavior
of coal pillars is very limited, and most of this understanding comes from the analysis of coal
specimens tested in the laboratory, not pillars in the field (Barron, 1992; Das, 1986). It is
generally understood that a slender coal specimen tested past its ultimate strength will
initially reach maximum peak strength at the point of “failure” and then, with further strain,
the specimen will “soften” (carry increasingly less load as it continues to be deformed) until
the broken coal reaches a final “residual” strength. In general, as the specimen width-toheight ratio increases or the confining pressure on the specimen increases, the peak strength
will increase, the residual strength will increase, and the softening modulus will flatten. At a
particular width-to-height ratio (Das found this to be approximately 8:1) or confining stress,
the specimen will no longer soften after elastic failure, but will become essentially “elasticplastic”. At higher width-to-height ratios or confining pressure, the coal specimens actually
become “strain- hardening”, where they carry increasing load with increasing deformation
after elastic failure. There is also some information that indicates that coal in the field may
actually become pseudo-ductile at very high confining stresses (Barron, 1992; Heasley and
Barron, 1988).
When the post- failure behavior of coal pillars needs to be accurately simulated (as is the
case with this back-analysis of Crandall Canyon Mine), “residual strength” and “residual
strain” must be determined accurately. These parameters essentially define the pillar postfailure behavior. Some insights to residual strength and residual strain have been provided
by laboratory tests where the peak and residual strength are seen to increase with increased
confining pressure (or distance into the pillar) while the softening modulus decreases with
increased confinement. These trends are also seen/assumed to be valid in the field.
Some pioneering work in trying to accurately quantify the strain softening behavior of
coal pillars for boundary-element modeling was done by Karabin and Evanto (1999). In this
work, they developed an equation from field measurements which estimated an ultimate
residual stress level (s r):

s r (x) = (0.2254 × ln (x )) s p (x)
Where:

-9-

(2.11)

s r(x) = Residual Stress (psi)
s p(x) = Peak Stress (psi)
x
= Distance into Pillar
and the strain level (er) for the final residual stress:

e r (x) = 4 × e p (x)
Where:
er(x)
ep (x)
x

(2.12)

= Residual Strain (psi)
= Peak Strain (psi)
= Distance into Pillar

These post- failure stress-strain relationships are consistent with trends in the
load/deflection response of coal samples as described above; however, Karabin and Evanto
certainly note that these properties are only “first approximations” and must be verified for
accuracy. For use in LaModel or any boundary element model, these are some of the only
post-failure coal properties calculations available. Certainly, this is an area for additional
research. (It should be noted in equation 2.11 that the value, “0.2254” essentially determines
the global magnitude of the residual stress in this strain-softening coal model and that the
value of “4” in equation 2.12 essentially determines the global magnitude of the residual
strain value in this strain-softening model. For LaModel calibration purposes, these single
values can be adjusted in order to vary the residual strength or strain of the coal model.)
2.2.2 LaModel and Bumps:
The term “bump” is used in this report to describe the sudden violent failure of a coal
pillar or rib which ejects coal into the adjacent openings. At the present time, the exact
mechanics of coal bumps are not completely understood. However, a lot of research has
been done to understand the bump phenomenon, and a lot of progress has been made.
Bumps are known to be associated with deep cover, competent strata and retreat mining
which concentrates overburden stress. Also, it is known that bump behavior can be triggered
in laboratory specimens by using a “soft” loading system or by suddenly releasing confining
stresses. The past bump research has produced many significant improvements in
minimizing or eliminating coal bumps (in some situations ) through better mine designs and
cut sequencing. However, in general, it is still not possible to precisely predict whether a
particular pillar or mine plan will bump, nor is it generally possible to predict the exact
timing of a bump event. Bump prediction can be readily compared to earthquake prediction.
The general area and nature of certain earthquakes (bumps) are well understood, but
predicting the exact timing, location and magnitude of the next earthquake (bump) is still
beyond the present scientific capability.
In LaModel, a bump is simply simulated as a pillar (or coal) failure. LaModel does not
calcula te any of the details of the coal or overburden failure mechanics; the program does not
consider whether a bump occurs from simply overloading the coal or whether there is some
external loading mechanism or sudden loss of confinement. However, coal that bumps has to
be at, or very near, its ultimate failure strength at the time of the bump; therefore, it is
reasonable to associate the point of coal failure in LaModel simulations with potential coal

- 10 -

bumps. Since LaModel does not have any dynamic capabilities, it cannot distinguish
between a gentle controlled pillar failure and a violent pillar bump. However, that distinction
can generally be determined from the geology and /or history of the mine. In some mines, the
pillars fail gently while in other mines, with “bump-prone” conditions, pillar failure is likely
to occur as a bump. Therefore, in a bump-prone mine or in bump-prone conditions, it can be
assumed that any pillar failure could be a potential bump.
2.2.3 LaModel and Massive Pillar Collapses:
The term massive pillar collapse (also called “cascading pillar failures”, “domino-type
failures” or “pillar runs”) refers to the situation in a room-and-pillar mine where a large area
of undersized pillars dynamically fails. In a massive pillar collapse, it is generally assumed
that one pillar fails (for some reason), it sheds its load to the adjacent pillars, causing them to
fail, and so forth (Mark et al,, 1997). This phenomenon has occurred a dozen or so times in
the U.S, and has been fairly well documented and analyzed (Mark et al., 1997; Zipf, 1996).
The basic condition for a massive pillar collapse is a large area of pillars loaded almost to
failure. Generally, the roof and floor must be fairly competent or they would yield and
relieve the pressure on the pillars. Also, the pillars have to be strain-softening in order for
them to shed load and propagate the collapse. (On initial inspection, the Crandall Canyon
Mine failure certainly appears to be consistent with a massive pillar collapse; however, the
depth of the mine workings, the size of the collapse area and the bump-type failure set this
failure outside of the previous database of massive pillar collapses.)
In LaModel, a massive pillar collapse is simulated when a “small” change in the mining
condition results in a “large” number of pillars failing over a “large” area. The small change
in mining condition can be any one (or combination) of a number of items: an additional cut
or two, the pulling of another pillar, a small drop in coal strength (e.g. deterioration over
time), the sudden movement on a fault or joint, etc. Of course, in LaModel, as in reality, to
accurately simulate the massive pillar collapse, a large area of pillars must be close to failure
and they must be strain-softening.
2.2.4 LaModel and Time and Homogeneity:
A complete discussion of LaModel calibration must also address time and homogeneity.
In a LaModel analysis, the solutions are static. The model converges on a static solution of
stresses and displacements based on the given geometry and material properties. In reality,
we know that geologic materials change over time without necessarily any outside stress or
displacement influence. Coal pillars can slough, weaken and fail, roof rock can crack, soften
and fall, and floors can heave, etc. In fact, the geo- mechanical environment in a mine is very
dynamic. Not only is the geometry constantly changing due to the active mining, but the
pillars, roof and floor are continuously adjusting to the stresses through time. Generally, the
geo- mechanical adjustment to new stresses initially occurs quickly and then slows
exponentially as time advances.
In a LaModel analysis, geologic materials are assumed to be perfectly homogeneous.
The material behavior is identical at different locations in the model and the stresses and
displacements are continuous and smooth from one location to another and from one step to
the next. In reality, we know that geologic material is not homogeneous. The rock and coal
have bedding planes, joints and other discontinuities, and the intrinsic material properties can
change dramatically (10-20% or more) in very short distances. Similarly, failure in a mine is

- 11 -

not typically continuous and smooth. The roof and floor can appear essentially stable and
then suddenly fail, pillars can suddenly slough or fail and certainly large cave/gob areas are
known to advance in a stepwise fashion.
Since LaModel does not inherently account for the effects of time or inhomogeneity, the
user needs to consider these factors in the analysis and interpretation of any results. For
instance, in a given cut sequence, LaModel may indicate that a certain pillar has just barely
failed. In reality, considering time, it may take a little while for the pillar to ultimately fail,
or considering homogeneity, the pillar may be a little weaker or stronger than modeled and
may fail a little sooner or later in the cut sequence. The static and homogenous nature of
LaModel actually resists sudden changes in stability. The classic example is the analysis of a
large area of equal size (strain-softening) pillars. A LaModel analysis may show that all of
these “equal” pillars have exactly the same stability factor that is a bit greater than one; and
therefore, the area is stable. In reality, the pillars have some statistical distribution of
strength, and the stability factor of each individual pillar is slightly different. So, even if the
average stability factor of the section is greater than one, once the weakest pillar fails and
sheds it load, this can overload the adjacent pillars and the whole section can collapse.
To account for the assumptions regarding time and homogeneity inherent in LaModel,
users must use some intuition to properly assess the realistic stability of the modeled mine
plan. For example, the user needs to consider how the result might change if the material
weakens over time, or if there is some variation in material properties. In an analysis of a
massive pillar collapse with LaModel, small changes in material properties and/or geometry
can cause large changes in pillar stability. Time dependent behavior or a local
inhomogeneity in the material properties can have a large effect on the real stability of the
situation and greatly affect the correspondence between the model and reality. Therefore, it
is very difficult to “exactly” model unstable mining situations with LaModel; however, the
general instability can easily be modeled.
2.2.5 Pillar Safety Factors in LaModel:
Recently, the capability of calculating safety factors was added to the LaModel program
(Hardy and Heasley, 1996). For the strain-softening and elastic-plastic material models, the
safety factor is calculated as the ratio between the peak strain defined for that particular
element and the applied strain:
SF =

ep
ea

(2.13)

Where:
SF = Safety Factor
ep = Peak Strain
ea = Applied strain
For the linear elastic model, which has no pre-defined peak stress or strain, the strain safety
factor is set to a default value of 10 (in order to adjust the scaling).
Conventionally, safety factors are calculated on a stress basis, rather than a strain basis.
However, stress based calculations can be problematic when determining safety factors in the
post-failure range in LaModel as inappropriate values result for the elastic-plastic and strainsoftening material models. The strain-based safety factor calculation detailed above yields
values equivalent to the stress-based calculation in the pre-failure range but also gives

- 12 -

appropriate values in the post- failure range for all the materials. Safety factors below 1.0
indicate that an element has failed. Values lower than 1.0 provide a measure of the amount
of strain that has occurred beyond failure. For instance, an element which has compressed to
twice the peak strain will generate a safety factor of 0.5. Therefore, the strain-based safety
factor as shown in Equation 2.13 above is used throughout LaModel.
In LaModel, the safety factor is initially calculated for each individual element and this
value can be displayed in the output. However, most users desire to know the safety factor
for the entire pillar. In order to provide a pillar safety factor, safety factors from each
individual element comprising a pillar are averaged. This algorithm is easy to implement,
but does not necessarily give a pillar safety factor which equates to the safety factor that
would be determined from a traditional analysis of the full stress-strain curve for the pillar.
The safety factor calculation is accurate for the stress-strain curve of the individual elements,
but when the element safety factors are averaged over the pillar, the average does not give a
traditional safety factor result.
With strain-softening elements, the peak stress and peak strain are determined from the
insitu coal strength, the coal modulus, and the distance of the element into the pillar (see
equation 2.10). For the weaker elements at the edge of the pillar, the peak stress is reached at
much lower levels of strain than the elements in the confined core of the pillar. After the
edge elements reach peak stress, they soften as pillar strain continues and the interior
elements move towards failure. At the point of peak pillar strength (the “traditional” point of
failure and a unity safety factor) only a few elements in the core of the pillar are still in the
elastic range and have safety factors greater than one. Thus, the overall safety factor for the
pillar calculated from an average of the elements will be much lower than one. The exact
magnitude of this reduced safety factor is determined by: the size and shape of the pillar, the
amount of strain-softening in the elements, and the flexibility of the rock mass. Since the
pillar elements do not reach peak stress at the same time, the ultimate strength of the pillar is
not the sum of the ultimate strengths of the elements. In particular, the pillar peak stress is
affected by the degree of strain softening input to the elements. (For a pillar made of elasticperfectly plastic materials as generated by the LaModel coal wizard, the peak strength of the
pillar will be the weighted sum of the peak strength of the elements.)
For an individual pillar, a comparison between the pillar stress-strain curve and the
averaged pillar safety factor calculated in LaModel can be observed by plotting these values
on the same graph (see Figure 2.3). The exact values for these plots are determined by
calculating the stress value and safety factor for each pillar element at various strain values.
Next, at each strain level, the stress values and safety factors are weighted by the number of
each type of element in the pillar and then finally, the total weighted stress and safety factor
values are averaged by the total number of elements in the pillar. The plot in Figure 2.3
show the values for a 60 X 70 foot pillar as used in the North Barrier Section of the Crandall
Canyon Mine. With the amount of strain-softening in the elements of this pillar and the
dimensions of the pillar, the peak stress in the pillar corresponds to a safety factor of 0.55,
quite a bit below 1.0. (In the following analysis of the Crandall Canyon Mine, the pillar
safety factors whe re adjusted so that the point of peak stress corresponded to a pillar safety
factor of 1.0. As an example, for this pillar, the pillar safety factor calculated by LaModel
would be divided by 0.55 to get the adjusted safety factor.)

- 13 -

4000

1.8

Pillar Stress-Strain Curve

1.6

3500

Average Element Safety Factor

Stress (psi)

1.2

2500

1.0

Peak Stress, 3343
Safety Factor, 0.55

2000

0.8

1500
0.6

1000

Pillar Safety Factor

1.4

3000

0.4

500

0.2

0

0.0

0.0000

0.0200

0.0400

0.0600

0.0800

0.1000

Strain

Figure 2.3. Stress-strain and safety factor curves for the North Barrier 60 X 70 ft pillar.

- 14 -

3. The LaModel Analysis
3.1 Approach
The major effort in this back-analysis was directed toward calibrating the critical rock
mass, gob and coal properties to provide the best LaModel simulation of what we know
happened at Crandall Canyon Mine. Initially, the mine and overburden geometries of the
Main West area of the mine were developed into LaModel mine and overburden grids. Then,
the rock mass stiffness was calibrated against the expected abutment load distribution (i.e.,
extent) consistent with empirical averages and local experience. Next, the gob behavior was
calibrated to provide reasonable abutment and gob loading magnitudes. For the coal
properties, the peak strength was primarily determined from back analyzing a March 10th
bump in the Main West North Barrier section, and the strain-softening behavior was
optimized from the back-analysis of the August 6, 2007, event. Throughout the backanalysis, a wide range of reasonable input parameter values were investigated to optimize the
agreement between the model and the observed reality. Also, a number of different events
that could have triggered the August 6th collapse were investigated with the basic model.

3.2 Basic Calibration Points
Knowledge of the actual mining conditions and the scenarios in which they occurred
served as the basis for calibrating the LaModel model to the reality of the mining situation at
Crandall Canyon Mine. A number of particular locations, situations and conditions were
used as distinct calibration points.
3.2.1 Main West:
During the initial mining of the Main West section, the pillars were assumed to be stable,
although some difficulties were encountered in this area and the safety factor under the
deepest cover was probably not very high (see Figure 3.1). When longwall Panel 12 to the
north and Panel 13 to the South were being mined, the abutment stress effects were seen in
the outside entries of Main West and additional support was installed. When the Main West
section was eventually sealed, some of the intersections had fallen and the pillars were in
poor shape.
3.2.2 North Barrier:
When the North Barrier Section was initially developed, the section was fairly stable.
Under the lower cover at the western end of the section, the pillar retreat was fairly
successful. As the retreat line moved under the deeper cover to the east, pillar line stresses
increased and became untenable in the 137-138 crosscut area where a couple of pillar rows
were then skipped. After mining a couple of pillars between crosscuts 134 and 135, a bump
(pillar failure) occurred that effected: the two rows of pillars inby, a number of pillar ribs and
the barriers along the bleeder entry, and one to two rows of pillars outby crosscut 134 (see
Figure 3.2). At this point, the section was abandoned and sealed shortly after that.

- 15 -

1200

00
12

Figure 3.1 Map of the Main West area.

1200

1600
16
00

00
16

- 16 -

00
20

Model Grid Boundary

00
20

0

200

400

600

16
00

00
20

1600

20
00

2000

- 17 -

Figure 3.2 Rib and pillar failure in the North Barrier section as of March 16th , 2007.

3.2.3 South Barrier:
When the South Barrier section was developed, the section was fairly stable. Also, as the
section retreated to crosscut 142, the conditions were mostly manageable. There were some
signs of high stress and some bumping noted in the section before the August 6th , 2007
collapse.
3.2.4 Results of The August 6th Collapse:
Immediately after the August 6th , 2007, collapse, it appeared that the pillars in the South
Barrier Section inby crosscut 120 had bumped and filled the entries with coal. Stress effects
from the collapse were visibly evident in the pillar ribs as far outby as crosscut 116 in the
South Barrier and Main West Sections. On the inby end of the South Barrier, video from the
drillholes revealed that there was still several feet of open entry at the intersections of cross
cuts 137-138 and entry #2, but that the entries and crosscuts were bumped full of coal.
Further inby the South Barrier section in the bleeder area at crosscut 142, the entry was half
filled with bumped coal, and at the end of the bleeder at crosscut 147, the entry was wide
open. Observations made during the rescue operation indicated that the remaining south
barrier had certainly bumped on the north rib and subsequent analysis indicates that it may
have completely failed under the deepest cover.
A Richter 3.9 seismic event was associated with the collapse. Subsequent analysis of the
initial part of this event locates it over the barrier pillar between the Main West and South
Barrier sections at about crosscut 143. After the collapse, seismic activity was located along
a North-South line through the whole Main West area around crosscut 120 and around
crosscut s 141 to 146.

3.3 The LaModel Grid
The LaModel simulation of the Main West area encompassed the entire Main West,
North Barrier and South Barrier Sections so that all of the areas of interest could be included
within one grid. Thus, the west and east boundaries of the model were set as shown in Figure
3.1. The north and south boundaries were established to include the full abutment loading
from both the northern and southern longwall mining districts for at least a couple of panels.
So, anticipating a symmetric boundary condition, model boundaries were set in the middle of
the longwall panels, 1-1/2 panels from the north and south barriers (see Figure 3.1).
For determining an optimum element size, a number of factors were considered. First,
the desired model area shown in Figure 3.1 is approximately 6000 X 4000 ft. Presently,
LaModel is limited to a maximum grid size of 1000 X 1000 elements; therefore, the required
element size must be greater than 6 ft. Second, the pillar sizes were examined. The pillars
are 80 X 92 ft on centers in the North Barrier section, 90 X 92 ft on centers in the Main West
section, and 80 X 130 ft on centers in the South Barrier section. Also, in this deep cover,
high stress situation, it was desired to have a pillar yield zone that would extend completely
through the 120 ft wide barriers to the north and south of the room-and-pillar sections. So,
considering all of these factors, a 10 ft wide element was chosen. This width fits most of the
pillar dimensions fairly well and can easily span the 6000 ft grid width. Also, with a 10 ft
wide element, the 120 ft wide barrier will only require 12 yield zone elements to reach to the
middle of the pillar (two element codes are required to define each yield zone in models
developed for this report).

18

Five and 6 ft wide elements were also considered. However, in the case of the 5 ft
element, a 5000 ft wide grid would not span the desired model area, it does not fit the pillar
dimensions any better than the 10 ft element, and it would take 24 yield elements to represent
the larger barrier pillars. In the case of the 6 ft element, a 6000 ft grid just barely spans the
desired model area, it does not fit the pillar dimensions any better than the 10 ft element, and
it would take 20 yield elements to cover the larger barrier pillars.
In the final grid, 10 ft elements were used and overall dimensions were set at 570
elements in the east-west direction and 390 elements in the north-south direction with a grid
boundary as shown in Figure 3.1. The actual mine grid was automatically generated from the
AutoCAD mine map of the Main West area with some manual editing to enforce 2 element
entry widths and rectangular pillars.
For inputting the overburden information to the model, an overburden grid was developed
that was 1500 ft wider on all 4 sides than the model grid and used 100 ft wide elements on an
87 X 69 element grid. This overburden grid was then automatically generated from the
AutoCAD topographic lines as shown in Figure 3.1. The result of the overburden grid
generation process is the calculated overburden stress on the coal seam as shown in Figure
3.3. In the plotted overburden stress, it can be seen how the laminated model softens the
effects of the ridges and valleys in the topography. Also, a couple other points should be
noted in this plot. First, the north-south trending ridge centered over crosscuts 130 in both
the North and South Barrier sections dominates the overburden stress. From the center part
of this ridge, the overburden stresses drop quickly to both the east and west, or both the inby
and outby ends of the North Barrier, Main West and South Barrier Sections. Also, the
slightly higher overburden stress above longwall Panel 12 should be noted. This higher
stress is probably carried to some extent by the abutment onto the North Barrier section.

3.4 Calibrating the Critical Parameters
3.4.1 Determining the Rock Mass Lamination Thickness:
Equation 2.3 was used to determine an appropriate lamination thickness to give a realistic
extent of the abutment zone in this model. In this equation, the rock mass was assumed to
have an elastic modulus of 3,000,000 psi and a Poisson’s ratio of 0.25. The coal seam was
assumed to have an elastic modulus of 300,000 psi and to average 8 ft thick. A “high
average” overburden depth of 2000 ft was used resulting in a full abutment extent (Equation
2.1) of 416 ft and 90% of the abutment load (Equation 2.2) within 224 ft. Using a yield zone
depth of 40 ft (consistent with the extent of yielding actually observed in the model), the
required lamination thickness was calculated as 533 ft. As part of the parametric analysis
discussed later, lamination thicknesses of 300, 500 and 600 ft were investigated. Ultimately,
the 500 ft value appeared to match the observed conditions best and was subsequently used
in the optimum model.
For Crandall Canyon Mine, Equations 2.1 and 2.3 appear to be fairly appropriate. The
mine noted the effects of increasing stresses in the Main West section when the adjacent
longwalls were retreating and these longwalls are some 430 ft away. Also, the Wasatch
Plateau area and the Crandall Canyon Mine are known for stiff massive sandstones in the
overburden which would help bridge and transfer the abutment stresses for considerable
distances and, therefore, help justify thicker model lamination.

19

1200

00
12

00
16

00
20

20

Model Grid Boundary

2000

Figure 3.3. Overburden stress as calculated by LaModel.

1200

1600
16
00

00
20

0

200

400

160
0

600

0
200

1600

200
0

(psi)

1200

1320

1440

1560

1680

1800

1920

2040

2160

2280

2400

Overburden
Stress

3.4.2 Determining the Gob Stiffness:
A number of factors were examined to optimize gob loading and gob stiffness in the
model. First, Equation 2.4 was used with an 800 ft wide panel at 2000 ft of cover and an
abutment angle of 21º to calculate a critical seam depth of 1042 ft. Then, using Equation 2.5,
the laminated overburden model would suggest that an average gob loading of 1125 psi
would be appropriate. Next, the gob loading as used in ALPS and ARMPS was calculated
using Equation 2.7 with an abutment angle of 21º and an overburden density of 162 lbs/cu ft.
This results in an average gob stress of 586 psi and a corresponding abutment load of 1659
psi. However, with the 2000+ feet of overburden the “correction” factor of 1.875 was
applied to the abutment load resulting in a suggested average gob loading (Equation 2.8) of
1362 psi.
From these vario us calculations of gob loading, the average gob stress value of 586 psi,
(73% abutment load) as determined by the abutment angle concept, is considered a very
lower bound. The average gob loading of 1362 psi, (38% abutment load) as determined by
adjusting the abutment loading by the 1.875 “deep-cover” factor, is considered an upper
bound. The actual gob loading is probably somewhere in between, but choosing the exact
value is very difficult. In this mining situation at the very deepest part of the ARMPS deepcover database, the tendency might be to start on the high end of gob loading range,
something in the 1000-1300 psi range, but with the stiff competent overburden at the mine,
the gob loading would tend to be less.
To investigate the appropriate final gob modulus to use in the model, a simple grid was
built of the Crandall Canyon Mine without any barrier mining in the Main West area. The
depth was set at 2000 ft and then various combinations of lamination thickness and final gob
modulus were input and the resultant average gob stress adjacent to the Main West area was
determined. The results of this parametric analysis are shown in Table 1 and Figure 3.4. In
these results, it is easy to see that, for a given lamination thickness, increasing the final gob
modulus increases the average stress on the gob. Also, it is clear that for a given final gob
modulus, increasing the lamination thickness reduces the average stress on the gob.
In the parametric analysis discussed later, average gob stresses of 800 – 1400 psi were
evaluated. Ultimately, gob stress around 900 psi (60% abutment loading) was determined to
be best for matching the observed results. With the 500 ft lamination thickness this gob
stress translates to a final gob modulus of 250,000 psi (see Table 1 and Figure 3.4).

- 21 -

Table 3.1 Average Gob Stress as a function of lamination
thickness and final gob modulus.
Final
Modulus
(psi)
100,000
200,000
300,000
400,000
500,000
600,000
700,000

Average Gob Stress (psi)
Lamination Thickness
300 ft
500 ft
600 ft
680
435
365
1066
763
662
1305
1012
903
1467
1198
1094
1581
1340
1242
1668
1449
1359
1735
1538
1455

1800

Average Gob Stress (psi)

1600
1400
1200
1000
800
600
300 ft Laminations
500 ft Laminations
600 ft Laminations

400
200
0
0

100,000

200,000

300,000 400,000 500,000

600,000

700,000 800,000

Final Gob Modulus (psi)

Figure 3.4 Average gob stress as a function of lamination thickness and final gob modulus.

3.4.3 Determining the Coal Strength:
In determining appropriate coal strength, a couple of simple analyses provided significant
insight. The pillars in the Main West Section were certainly stable when they were mined,
and the overburden stress plot (Figure 3.3) shows some 2200 psi of insitu stress. With 90 X
92 ft centers and 20 ft wide openings, the extraction ratio would be 39.1% and the assumed
tributary area stress on these pillars would be 3614 psi. Using the Mark-Bieniawski pillar

- 22 -

strength formula, this implies that the insitu coal strength must be at least 943 psi. Similarly,
evaluating the 80 X 92 ft pillars in the North Barrier section and the 80 X 130 ft pillars in the
South Barrier section (with 18 ft wide entries), implies a minimum coal strength of 965 psi
and 813 psi, respectively. This analysis assumes tributary area loading, but with the narrow
panels and competent overburden, this may not be the case causing the true pillar loading to
be somewhat less. From underground observations, these pillars did not appear to be too
close to failure on development; and therefore, the insitu coal strength could be higher than
the calculated minimum. However, considering that the Main West was showing
considerable weakness when it was eventually sealed, the safety factors on development
were certainly not excessive.
Another simple analysis which can provide some insight is to compare the pillar design in
the North Barrier section to the design in the South Barrier section. Based on the above
analysis, and comparing the 965 psi minimum strength in the North Barrier to the 813 psi
minimum strength in the South Barrier implies that the larger pillars in the South Barrier
section provide a 16% stronger design than the pillars in the North Barrier section.
3.4.3.1 Back Analysis of North Barrier Bump: Ultimately, the best information for
computing the insitu coal strength at Crandall Canyon Mine is the pillar bump that occurred
on March 10th , 2007, in the North Barrier Section (see Figure 3.2). A back-analysis of this
event can provide reasonably reliable insitu coal strength to use in the further analysis of the
subsequent collapse. To develop a back-analysis of the North Barrier Section bump, a six
step LaModel run was developed to represent the cut sequence leading up to the bump. This
model starts when the pillar retreat line is at crosscut 141, and retreats the pillar line one
crosscut per step until the point when the bump occurred (i.e., after the pillars were pulled at
crosscut 134 (see Figure 3.5)). For this back-analysis, Figure 3.2 was used as the primary
calibration objective. This figure indicates that 2 rows of pillars inby crosscut 135 failed and
bumped and that 1 to 2 rows of pillars outby crosscut 134 failed and bumped, also, the
failures appear to be more prevalent towards the north. To calibrate the model, the coal
strength was adjusted until the calculated conditions matched the observed conditions as
closely as possible. Figure 3.5 shows the results of this calibration process. (Note: the safety
factors in Figure 3.5 were adjusted so that the peak pillar strength in the North Barrier pillars
corresponds to a safety factor of 1.0. This same adjustment was made to all pillar safety
factors plots in this report.)
In the back-analysis of the North Barrier bump shown in Figure 3.5, the lamination
thickness was set at 500 ft, the final modulus of the gob was set at 300,000 psi, and the coal
strength was calibrated to an input value of 1325 psi (in the strain softening equations of 2.11
and 2.12). For the strain softening coal behavior, the residual stress was calculated using
equation 2.11 with a factor of 0.188 (essentially a 30% reduction from the peak stress), and
the residual strain was calculated with equation 2.12 using a peak stress multiplication factor
of 2. The resultant pillar strength correlates to a Mark-Bieniawski pillar strength with an
insitu coal strength of 927 psi.

- 23 -

A. Retreat Line at XC 141

B. Retreat Line at XC 140

C. Retreat Line at XC 139

D. Retreat Line at XC 138

E. Retreat Line at XC 138.5

F. Retreat Line at XC 134

Figure 3.5 Analysis of North Barrier bump.

- 24 -

The model results illustrated in Figure 3.5 agree reasonably well with the observed
behavior. When the retreat line is at crosscut 141 (see Figure 3.5A), the model shows that
two pillars on the retreat line have safety factors slightly less than one. This is a pretty
typical response of a room-and-pillar retreat section. These pillars on the retreat line
(although the model shows failure) may not fail in the short amount of time that they are
under this stress condition, and often can be safely extracted. (However, if the section is
allowed to sit idle for a length of time, these pillars may indeed fail.) As the North Barrier
Section continues to retreat under deeper cover (the deepest cover is essentially crosscuts
131-132, see Figure 3.1), safety factors on the retreat line decrease. When the retreat line is
at crosscut 138 (see Figure 3.5D & E), the model now shows that two full rows of pillars on
the retreat line have safety factors less than one. It was at this point that deteriorating ground
conditions prompted mine personnel to stop recovering pillars, move the section a couple
rows outby, and continue retreating. The mine then extracted two pillars between crosscut
134 and 135 and the bump occurred. In the calibrated model, the extraction of the two pillars
between crosscut 134 and 135 caused 4 pillars to fail outby, 2 pillars to fail to the north and
the 4 pillars inby to fail more, or soften considerably. These calibrated pillar conditions
appear to match the observed conditions in Figure 3.2 fairly well. Also, this response in the
model, where a small mining step causes a large amount of failure, is certainly indicative of a
dynamic event, such as the bump in this case.
It should also be noted in Figure 3.5, that as the North Barrier Section is retreated,
considerable failure also occurs in the Main West Section. This response was seen in all of
the calibrated models indicating that if the coal strength is adjusted to fail at the pillar
geometry of the bump, then pillars in the Main West will also fail. This reaction seems
entirely reasonable considering that: 1) the pillars in the Main West are only about 2%
stronger than the pillars in the North Barrier Section, 2) the overburden stress is a little
greater over the Main West than either the North or South Barrier sections, and 3) the
abutme nt loading from the North Barrier gob can easily transfer over the intervening 50 ft
wide barrier just as it transfers further inby in the North Barrier section. It is not believed
that this amount of failure in the Main West section actually occurred at this time. Some
adjustments to the model to correct this apparent inconsistency in the sequence of observed
failure are discussed later in section 3.5.1.
In performing this back-analysis of the North Barrier Section with various sets of
parameter properties (see the parametric analysis section), a couple of important points
become evident. First, once the coal strength is reduced in the calibration process to a
development safety factor under the deepest cover of 1.4 or less, retreating the pillar line into
the high stress, deep cover area will cause significant pillar failure at the retreat line (at some
point) due to the combination of the high development stress from the deep cover and the
abutment stress from the retreat line. The exact location of the significant pillar failure will
move further west under the shallower cover if the coal is weaker or the failure point will
move further east under the deeper cover if the coal is stronger. Second, it is apparent from
the occurrence of the bump, and the model definitely indicates, that moving the face two
rows of pillars outby the old retreat line was not sufficient to isolate it from the previous
retreat line abutment stresses in the given conditions.

- 25 -

3.5 Analyzing the August 6 th Collapse
Once the optimum lamination thickness and gob modulus were developed (within the
given resolution) and the coal strength was calibrated from the North Barrier bump, the
parameters were set to use LaModel to back-analyze the August 6th , 2007, collapse at the
Crandall Canyon Mine. For this collapse analysis, a six step model was developed:
1.
2.
3.
4.
5.
6.

Development of the Main West Section
Development of the North Barrier Section
Final retreat of the North Barrier Section
Development of the South Barrier Section
Final retreat of the South Barrier Section
Final retreat of the South Barrier Section, with bump triggers.

When performing this back-analysis, a number of critical calibration conditions needed to
be met. For step 1, the Main West Section should be stable on development. Similarly, for
step 2, the North Barrier Section should be stable on development. For step 3, the pillar
failure in the North Barrier Section should be consistent with Figure 3.2. For step 4, the
South Barrier Section sho uld be stable on development. Finally, for Step 6, after the bump
event, pillar failure should cover the middle portion of the South barrier Section and extend
outby to crosscut 122 to 124. Also, pillar failure (and pillar bumps) should extend into the
face area at least to crosscut 138 with some moderate pillar bumping at crosscut 142 (as
indicated by the drillholes).
3.5.1 Primary Results:
The primary results of the initial back-analysis model for the Crandall Canyon Mine are
shown in Figures 3.6-3.8. Figure 3.6 show the average pillar and individual element safety
factors for step 3 which is the March 2007 bump geometry. Figure 3.6a is identical to Figure
3.5f and pillar failure in this plot was discussed above. Figure 3.6b shows the individual
element safety factors calculated in the model for the bump geometry (step 3). By examining
the element safety factors, it can be seen that the 50 ft wide barrier between the Main West
and the North Barrier sections is indicating substantial failure between crosscut 137 and
crosscut 144. Figure 3.6 also clearly shows the effect of the depth of cover on the pillar
safety factors which increase rapidly as the cover drops below 2000 ft west of crosscut 145
and east of crosscut 125. Similarly, under the deepest cover between crosscuts 129 and 134,
many pillars have not yet failed but they have very low safety factors and are close to failure.
Finally, this figure indicates that the abutment stress from the active retreat gob is one of the
primary factors driving the bump and the pillar failure; and therefore, the pillar failure
radiates out from the active gob area. In addition, the deep cover stress is seen as a
significant factor in propagating the pillar failure to the east.
Figure 3.7 shows the average pillar and individual element safety factors calculated by
the model after the South Barrier section was developed and retreated to its final
configuration. Several important observations can be made from this figure. First, on
development and partial retreat, the pillars in the central portion of the South Barrier section
(crosscuts 120–138) are shown to be fairly stable with the lowest safety factors.

- 26 -

- 27 -

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Figure 3.6 Plot of pillar and eleme nt safety factors for step 3.

1600

Safety Factor

B. Element Safety Factors

00
20

A. Pillar Safety Factors

00
20

1600
1600

1600
160
0

160
0

- 28 -

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Figure 3.7 Plot of pillar and element safety factors for step 5.

1600

Pillar Safety Factor

B. Element Safety Factors

00
20

A. Pillar Safety Factors

00
20

1600
1600

1600
160
0

160
0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

- 29 -

Figure 3.8 Plot of pillar safety factors with coal strength adjusted in Main West.

1600

Pillar Safety Factor

B. 5.7% Stronger Coal in Main West

00
20

A. 3.8% Stronger Coal in Main West

00
20

1600
1600

1600
16
00

160
0

around 1.2-1.4. As previously noted, these pillars are about 16% stronger than the pillars in
the Main West or North Barrier sections, and this stability is undoubtedly a result of this
higher strength. Next, it can be seen by examining the pillar safety factors from crosscut
139-145 in the South Barrier section that the stresses from the active retreat line/working
section are fairly isolated from the potentially unstable pillars under the deeper cover to the
east. The retreat line is under relatively shallow cover and there are five rows of fairly stable
pillars (safety factors up to 1.8) between the active mining and the 2000 ft cover line.
Finally, it can be seen by comparing Figure 3.7 with the previous Figure 3.6 that the
small increase in stress from the development of the South Barrier section has caused
considerable additional pillar failure in the Main West and North Barrier sections. Fourteen
additional pillars have failed in the North Barrier section and 46 additional pillars have failed
in the Main West section. There is no evidence to support whether this degree of failure
actually did or did not occur. It does not seem reasonable that a failure of this magnitude
could have gone unnoticed during development of the South Barrier section. However, the
failure may have been very gradual. More likely, the difference in Main West pillar failure
between Figure 3.6 and 3.7 was part of the collapse on August 6th . Regardless, this model
response certainly indicates how sensitive the Main West and North Barrier geometries are to
any slight change in loading condition.
To maintain general stability in the Main West through the final retreat position of the
South Barrier does not take much of a change in the model. A 50 psi (3.8%) increase in coal
strength in just the Main West reduces the number of failed pillars in the Main West from 76
to 33 (see Figure 3.8a), and a 75 psi (5.7%) increase in coal strength reduces the pillar failure
in the Main West to 12 pillars (see Figure 3.8b). However, either of these increases in coal
strength in the Main West adversely affects the degree of fit to the March 2007 bump, but not
too much (see Figure 3.8). The only strong justification for increasing the strength of the
coal in the Main West in the model above the calibrated strength is to postpone the pillar
failure until the August collapse. There is not much physical evidence that the Main West
coal is any different than the coal in the North and South Barrier sections. On one hand, the
coal in the Main West might be expected to be weaker than in the surrounding sections
because it had been standing for 10+ years. However, there are a variety of possible
explanations for pillars in this area not to exhibit lower strength. For example, the floor may
have yielded enough over time to allow some overburden stress to bridge the section and
functionally reduce the pillar load or roof falls and/or gobbed crosscuts may functionally
provide additional confinement to the pillars. Any number of small changes in the loading
condition of the Main West section could account for the pillars not failing at exactly the
point indicated by the model. This is one point where the back-analysis model does not
easily/smoothly match the perceived reality of the Crandall Canyon Mine; ho wever, certainly
a 4-6% increase in the stability of the Main West pillars (for any number of possible reasons)
would be easily conceivable considering the natural variability of the geologic and mining
systems.
3.5.2 Triggering the Collapse of the South Barrier Section:
It can be seen in Figure 3.7a, that when the pillars in the Main West do start to fail, there
is reluctance for the failure to propagate south past the barrier pillar and into the South
Barrier Section. However, we know that this failure did occur on August 6th . To investigate
what possible conditions may have triggered the collapse, or what conditions or parameter

- 30 -

changes are necessary to replicate the observed South Barrier failure in the model, a number
of different trigger scenarios were investigated.
A classic boundary-element technique used to check the stability of a potentially unstable
mining plan is to simulate the extraction of a few pillars in the model (i.e., cause a small
stress increase) and observe the magnitude of the resultant changes. In the optimized
Crandall Canyon Mine model, four pillars (with a safety factor around 1) were removed
between crosscut 128 and 132 on the south side of the Main West. The results of this
perturbation are shown in Figure 3.9; it can be observed that the removal of the pillars has
indeed caused 25 pillars to fail in the South Barrier section between crosscuts 125 and 134.
Comparing this figure with Figure 3.7, it can also be observed that additional pillars in the
Main West have failed between crosscut 124 and 129, and that the stability of the barrier
between the sections has greatly decreased. The final pillar failure results shown in the South
Barrier section of Figure 3.9 are not quite as extensive as observed in the field, but it does
demonstrate that a relatively small change in the model conditions can cause the pillar failure
to continue into the South Barrier section.
3.5.2.1 Reduced Coal Strength: The next triggering technique was to reduce the coal
strength in the Main West by 50 psi or 3.8%. The results of this investigation are shown in
Figure 3.10. Figure 3.10a shows that the small strength reduction has caused 37 pillars to fail
in the South Barrier section between crosscuts 124 and 137, also many more pillars have
failed in the Main West section. Figure 3.10b includes the removal of four pillars in the
Main West and shows that the failure in the South Barrier section has encompassed the face
area (crosscuts 137 to 139) and several pillars in the bleeder area (crosscuts 141 to 143). If
Figures 3.8a and 3.10a are compared, it can be seen that a 7.7% reduction in the coal strength
of the Main West pillars will cause 37 pillars to fail in the South Barrier section and 94
additional pillars to fail in the Main West. This large number of pillar failures in the model
due to a relatively small decrease in coal strength effectively simulates the observed August
6th collapse. Seeing these model results, it certainly seems reasonable and plausible that the
strength of the Main West pillars may have degraded from the effects of time and the
northern abutment stresses, and a massive pillar collapse initiated which swept through the
Main West pillars and down through the South Barrier section.
3.5.2.2 Joint Slip: The seismic eve nt that accompanied the August 6th collapse was
analyzed by personnel at the University of Utah Seismological Stations. The seismic signal
was consistent with a collapse event but there was a small component of shear. Thus, it
seems plausible that movement along one of the pervasive vertical joint surfaces known to
exist on the mine property may have initiated the collapse (or certainly have contributed to
the collapse). In order to simulate this possibility, a simple joint model was added to a
special version of LaModel as part of this investigation. This joint model simulates a
frictionless vertical plane in the LaModel grid, such that the plane does not allow any transfer
of shearing or bending stresses across the joint. Basically, the plane is inserted between two
rows or columns of the LaModel grid, and the program calculates the modified seam stresses
and displacements that result from the addition of the joint.

- 31 -

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

- 32 -

Figure 3.9 Plot of pillar and element safety factors for step 6 with 4 pillars removed.

1600

Pillar Safety Factor

B. Element Safety Factors

00
20

A. Pillar Safety Factors

00
20

1600
1600

1600
160
0

160
0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

- 33 -

Figure 3.10 Plot of pillar safety factors for weakened coal in the Main West.

1600

Pillar Safety Factor

B. Step 6 - 4 Pillars Removed in Main West

00
20

A. Step 5 - South Barrier Retreated

00
20

1600
1600

1600
160
0

160
0

1600

- 34 -

Figure 3.11 Plot of pillar safety factors for the model with a joint at crosscut 137.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pillar Safety Factor

B. Step 6 - 2 Pillars Removed in Main West with a Fault

00
20

A. Step 5 - South Barrier Retreated with a Fault

00
20

1600
1600

1600
16
00

160
0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

- 35 -

Figure 3.12 Plot of pillar safety factors for softer gob in the southern panels.

1600

Pillar Safety Factor

B. Step 7 - 4 Pillars Removed in Main West

00
20

A. Step 6 - 2 Pillars Removed in Main West

00
20

1600
1600

1600
16
00

160
0

For the analysis of a possible fault trigger, the joint was placed at crosscut 137 of the
South Barrier section and oriented in a north-south direction between the columns of the
LaModel grid. The results of this joint analysis are shown in Figure 3.11. Figure 3.11a
indicates that the addition of the joint by itself does not cause any failure in the South Barrier
section, but the joint with a couple pillars removed in the Main West causes 35 pillars to fail
in the South Barrier section. This analysis indicates that a sudden change in stresses due to
slip along a joint in the roof certainly could have been a factor in triggering the collapse seen
on August 6th .
3.5.2.3 Softer Southern Gob: Given that pillars in the South Barrier section are 16%
stronger than the pillars in the North Barrier section and 14% stronger than the pillars in the
Main West section, and that overburden loading in the south appears a little less than in the
Main West, one would anticipate that pillars in the Main West would have failed before the
South Barrier pillars, as seen in the previous models. This actually may have occurred and
gone unnoticed, but it is also possible that failure in both areas occurred simultaneously. To
account for this simultaneous failure, it seems reasonable to hypothesize that the abutment
loading from the southern longwall panels may have been higher than the abutment loading
from the northern longwall panels. In the north, longwall panel 12 (see Figure 3.1) was the
last longwall in the northern district, whereas longwall panel 13 to the south of the South
Barrier section was the first longwall panel in the southern district. This configuration may
have resulted in a higher abutment load from the southern longwalls, or the southern geology
may have been a little stiffer or more massive causing additional abutment load.
To simulate additional abutment load from the southern longwall, the gob modulus in the
south was reduced from 300,000 psi to 250,000 psi. Nominally, this reduces the average gob
loading from 1013 psi to 888 psi, and increases the abutment load from 1187 psi to 1312 psi
(10.5%). The results of this loading condition are shown in Figure 3.12 where it can be
clearly seen that the increased southern abutment loading certainly increases the amount of
failure in the Southern Barrier section. By comparing Figure 3.12b with 3.8a, it can be seen
that the softer southern gob has caused an additional 23 pillars to fail and caused the failure
to encompass the face area in the South Barrier section. Also, the softer southern gob has
made the South Barrier section more likely to fail as a “natural” extension of failure in the
Main West (see Figure 3.12a)

3.6 Parametric Analysis
In order to assess the sensitivity of the model results to the input values and to determine
the optimum parameter values for matching the observed mine behavior, an extensive
parametric analysis was performed. This analysis examined: 3 different lamination
thicknesses (300 ft, 500ft and 600 ft); final gob moduli ranging from 100,000 psi to 700,000
psi; strain-softening coal strengths ranging from 1150 psi to 1450 psi (corresponding to a
Mark-Bieniawski insitu coal strengths of 835 psi to 1115 psi); post-failure residual coal
strength reductions of 20%, 30% and 40%, and several different mechanisms for triggering
the collapse. In all, over 230 models were evaluated.
In a back-analysis, suc h as this investigation of the Crandall Canyon Mine collapse, there
are an infinite number of parameter combinations that might be analyzed. The resolution of
each optimized parameter (and therefore the accuracy of the back-analysis) can always be

- 36 -

further improved. Obviously, there is a practical time constraint and also, it is only
reasonable to refine the parameters to within the overall accuracy of the general input values.
In this case, with a geo-mechanical model, an accuracy of 10-20% seems more than
sufficient. In this back-analysis, the smallest resolution of the critical parameters was:
•
•
•
•

Lamination Thickness
Final Gob Modulus
Coal Strength
Residual Strength Reduction

100 ft
50,000 psi
25 psi
10%

To investigate the optimum lamination thickness, 300 ft, 500 ft and 600 ft thicknesses
were examined (with a fixed rock mass modulus of 3,000,000 psi). The 300 ft lamination
thickness has an abutment extent of around 180 ft and, in general, it showed a relatively local
influence of the abutment stresses from the gob areas. The longwall abutment stresses did
not appropriately influence the North and South Barrier sections and the North Barrier
section gob did not project sufficient abutment stress into the bump area. On the other hand,
the 600 ft lamination thickness had an effective (90% of abutment load) abutment extent of
around 235 ft; however, this thickness had a tendency to over-extend the abutment zones and
cause the coal failures to travel further than observed. Of the three lamination thicknesses
investigated, the 500 ft thickness appeared to be most realistic. If the lamination thickness
were to be further refined, the next selection would be in the 300 to 500 ft range.
A fairly wide range of final gob moduli and the resultant abutment loads were
investigated. When the abutment loads reached 65-75% of the overburden load, it was found
that the North and South Barrier sections were beginning to fail on development. Also, this
high abutment loading produced stresses in the barrier sections that were very biased towards
the gob, much more than was actually experienced. On the other end of the spectrum, when
the abutment loading was reduced to 30-40% of the overburden load, the low abutment stress
ceased to be much of a factor in the modeled failure. At this point, the pillar failures were
primarily driven by just the tributary overburden load. In this scenario, very low coal
strengths were required to recreate a wide spread failure in the model. However these low
strength pillars were close to failure on development and this behavior was not observed.
The abutment loading was ultimately found to be most realistic in the 55-65% range (highest
in the south) resulting in a final gob modulus between 200,000 and 300,000 psi (with the 500
ft lamination thickness).
The coal strengths in the model were readily calibrated using the North Barrier bump
geometry once a lamination thickness and abutment loading was determined. The calibrated
coal strength essentially correlated with the modeled abutment loading. Increasing the
abutment load required a corresponding increase in coal strength to calibrate the model.
Conversely, decreasing the abutment load required a decrease in the coal strength for a
realistic calibration. The final optimized strain-softening coal strength was in the 1300-1400
psi range corresponding to Mark-Bieniawski formula insitu coal strengths of 910-980 psi.
The final critical parameter that was investigated in the parametric analysis was the post
failure coal behavior. In this investigation, coal strength reductions of 20%, 30% and 40%
after pillar failure were examined. Essentially, the magnitude of strength reduction
determines the tendency for the pillar failures to propagate (or run) and generate a massive
pillar collapse. With the 20% reduction, it was difficult for the model to produce the pillar

- 37 -

run that was observed. The pillars failed, but did not run across large areas of the sections.
On the other hand, with the 40% reduction in coal strength, the pillar failures ran too far, out
to around crosscut 115. Of the post-failure coal strength reductions examined, the 30% level
produced the best results. If this value were to be further refined, it would be increased in
order to get the pillar failures to spread further outby crosscut 124 in the South Barrier
section as was observed.
The magnitude of the post failure reduction in coal strength in this model necessary to
simulate the observed pillar behavior is somewhat surprising. The classic laboratory tests by
Das (1986) would indicate that a 60 ft wide pillar in an 8 ft seam (w/h=7.5) would be close to
elastic, perfectly-plastic behavior and would not have much strain-softening behavior.
Obviously, there was a massive pillar collapse; and therefore, the pillars had to exhibit
significant strain-softening behavior. It is not clear whether this magnitude of strainsoftening behavior is: typical for a pillar with a width-to-height of 7.5, a behavior unique to
the seam at this mine, an effect of the bump-type pillar failure, a manifestation of the
veracity/dynamics of the pillar collapse or has some other explanation.

3.7 Final Back Analysis Model
In the initial model analyzed in section 3.5 above, all of the coal and gob at different
locations have identical properties. However, it was shown that this assumption causes the
pillars in the Main West section to fail too soon and the pillars in the South Barrier to be
difficult to fail. It was also shown that a small (<8%) change in the coal strength or loading
condition in the Main West pillars would make their behavior correlate well with observed
conditions and that a small change (10.5%) in the southern abutment loading brings the
South Barrier pillars’ behavior closer to observations. So, by combining all of these
adjustments into one model, a final back-analysis model of the Crandall Canyon Mine can be
developed that:
•
•
•

Accurately simulates the March 10th , 2007 bump,
Accurately simulates the South Barrier section development, and
Accurately simulates the final August 6th collapse.

In this model, the lamination thickness was set at 500 ft, the final modulus of the north
gob was set at 250,000 psi, and the final modulus of the southern gob was set at 200,000 psi.
The coal strength in the North and South Barrier sections was set at 1300 psi and coal
strength in the Main West was set at 1400 psi. For the strain softening coal behavior, the
residual stress was set with a 30% reduction from the peak stress.
The results from this final back analysis model are shown in Figure 3.13 and 3.14. In
Figure 3.13a, the March 2007 bump is simulated with fairly good correlation to the observed
results in Figure 3.2. In this final model, only one pillar has failed in the Main West at the
time of the bump. Figure 3.13b shows the development and retreat of the South Barrier
section. In this final model, the pillars in the South Barrier section have fairly good stability,
although some 42 pillars have failed in the Main West. Then, in Figure 3.14 after perturbing
the model by removing 6 pillars, the August 6th collapse is simulated. The removal of the six
trigger pillars has caused 106 additional pillars to fail in the Main West and 59 pillars to fail
in the South Barrier section. The failure runs from crosscut 123 in the Sout h Barrier section

- 38 -

in to crosscut 146 in the bleeder area. This final model does a fairly good job of simulating
most of the critical observation of the geo- mechanical behavior at the Crandall Canyon Mine.

- 39 -

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

- 40 -

Figure 3.13 Final model of Crandall Canyon Mine – steps 3 & 5.

1600

Pillar Safety Factor

B. Step 5 - South Barrier Retreated

00
20

A. Step 3 - North Barrier Bump

00
20

1600
1600

1600
16
00

160
0

- 41 -

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Figure 3.14 Final model of Crandall Canyon Mine - step 9.

1600

Safety Factor

B. Step 9 - Element Safety Factors

00
20

A. Step 9 - Pillar Safety Factors

00
20

1600
1600

1600
16
00

16
00

4. Summary
In this back analysis of the Crandall Canyon Mine, a six step base model of the mining in
the Main West area was initially developed. The mine grid for the model was sized to cover
the entire area of interest with a 10 ft element size that sufficiently fit the pillar sizes and
entry widths. An appropriate overburden grid was also developed. This base model included
a step for each of the critical stages in the mining of this area: development of the Main West
Section, development of the North Barrier Section, final retreat of the North Barrier Section,
development of the South Barrier Section, and final retreat of the South Barrier Section.
Next, calibrated values for the critical input parameters: rock mass stiffness, gob stiffness
and coal strength, were developed. The rock mass stiffness was calibrated against the
expected abutment load distribution (i.e., extent) consistent with empirical averages and local
experience. The gob behavior was calibrated to provide reasonable abutment and gob
loading magnitudes. The peak strength of the coal was primarily determined from back
analyzing the March 10th bump in the Main West North Barrier section, and the strainsoftening behavior was optimized from back-analysis of the August 6th , 2007, event.
Throughout this calibration process, a number of particular locations, situations, and
conditions were used as distinct calibration points.
As part of calibrating the critical input parameters, a wide range of reasonable sets of
input parameter values were investigated (a parametric study) to optimize agreement between
the model and the observed reality, and to assess the sensitivity of the model results to
changes in the critical input parameters. Also, a number of different events that could have
triggered the August 6th collapse were investigated with the basic model. In total, over 230
different sets of input parameters were evaluated, and from this extensive analysis a broad
understanding of the factors that affected ground conditions at Crandall Canyon Mine was
developed. Also, a pretty clear picture of the range of reasonable input values for the critical
parameters was developed: lamination thickness, 300-600 ft; gob load, 25-60% of insitu load;
coal strength, 1250-1450 psi - 20-40% strain softening.
In all of these models (with different sets of lamination thicknesses and gob loadings),
once the coal strength was calibrated to the North Barrier bump, LaModel naturally showed
that the pillars in the Main West were also close to failure. Once the South Barrier was
subsequently developed, the model showed that it was very likely for the entire Main West
and South Barrier sections to collapse upon the South Barrier development, or just a small
perturbation was needed to initiate the collapse. Different sets of lamination thickness and
coal strength primarily just determined the exact timing and extent of the collapse. With the
initial base model where all of the coal and gob in different areas are maintained at the same
strength, the critical input parameters which best matched the known collapse conditions at
the Crandall Canyon Mine were: a lamination thickness = 500 ft, a gob load = 40% of insitu
load, and a coal strength = 1325 psi with 30% strain softening (see Figures 3.5-3.12).
In the initial optimized base model were all of the coal and gob have identical properties,
it was noted that the pillars in the Main West section seemed to fail a little too soon (or too
easy) while the pillars in the South Barrier seemed to resist failure. Relaxing the condition
that all of the coal and gob have the same properties, a final model was developed that fits
the known conditions a bit better than the optimized base model (See Figures 3.13 and 3.14).
In this final model, the Main West coal strength was raised to 1400 psi while the rest of the
coal strength was lowered slightly to 1300 psi, Also, the south gob load was decreased to

- 42 -

36% of insitu load. With these two changes, the final model accurately simulates the March
10th , 2007 bump and minimizes the pillar failure in the Main West at that time. Also, the
final model now more accurately simulates the final August 6th collapse with the
simultaneous failure of 106 pillars in the Main West and 59 pillars in the South Barrier
section. The collapse runs from crosscut 123 in the South Barrier section completely through
the active section to crosscut 146 in the Sout h Barrier bleeder area (see Figure 3.14).

5. Conclusions
Based on the extensive back analysis of the Crandall Canyon Mine using the LaModel
program describe above, and with the benefit of hindsight from the March bump and August
collapse, a number of conclusions can be made concerning the mine design and the August
6th collapse.
1) Overall, the Main West and adjacent North and South Barrier sections were primed for a
massive pillar collapse because of the large area of equal size pillars with near unity
safety factors. This large area of undersized pillars was the fundamental cause of the
collapse.
a. The pillars and inter-panel barriers in this portion of the Crandall Canyon Mine
essentially constitute a large area of similar size pillars. The pillars in the North
Barrier and Main West section are essentially the same size and strength. Also, the
inter-panel barrier pillars between the Main West section and the North and South
Barrier sections have a comparable strength (+15%) to the pillars in the sections. The
pillars in the South Barrier section are stronger than the pillars in the North Barrier
and Main West sections, but only by about 16%. Therefore, the South Barrier section
pillars might also be included as part of the large area of equal size pillars. This large
area of similar size pillars is one of the essential ingredients for a massive pillar
collapse (Mark et al., 1997; Zipf and Mark, 1996).
b. The high overburden (2200 ft) was causing considerable development stress on the
pillars in this area and bringing pillar development safety factors below 1.4.
c. Considerable longwall abutment stress was overriding the barrier pillars between the
active sections and the old longwall gobs. In the north, the abutment stress from
Panel 12 was overriding the North Barrier section and in the south the abutment stress
from Panel 13 was overriding the South Barrier Section.
2) The abutment stress from the active North Barrier retreat section was key to the March
10th bump occurrence and the modeling indicated that the North Barrier abutment stress
contributed to the August 6th pillar collapse.
3) From the modeling, it was not clear exactly what triggered the August collapse. A
number of factors or combination of factors could have been the perturbation that
initiated the collapse. Likely candidates include: the active retreat mining in the South

- 43 -

Barrier section, random pillar failure, a joint slip in the overburden, a gradual weakening
of the coal over time, a change in the abutment loading, etc. The boundary element
modeling identified a number of possible triggers, but by itself could not distinguish the
most likely trigger.
4) LaModel analysis demonstrated that the active pillar recovery mining in the South Barrier
section could certainly have been the trigger that initiated the August collapse; however,
the modeling by itself does not indicate if the active mining was the most likely trigger.
Certainly removing more coal in the South Barrier section contributed to the ultimate
collapse by applying additional load to the outby area that was primed to collapse. In
fact, if the active mining was not the specific trigger on August 6th , then it is fairly certain
that as the South Barrier section had retreated further under the deeper cover, it would
have eventually triggered the collapse of the undersized pillars in the Main West area.

- 44 -

References
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Pillar Mechanics and Design, BuMines IC 9315, p. 144-157.
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Coalfields,” Proceedings of the 21st International Conference on Ground Control in Mining,
Morgantown, WV, Aug. 6-8, p. 68-80.
Das, M. N., 1986, “Influence of Width/Height ratio on Postfailure Behavior of Coal,”
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Hardy, R. and K. A. Heasley, 2006, “Enhancements to the LaModel Stress Analysis
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Heasley, K. A, 2000, “The Forgotten Denominator, Pillar Loading”, Proceedings of the 4th
North American Rock Mechanics Symposium, Seattle, WA, July 31-Aug. 3, p. 457-464.
Heasley, K. A., 1998, "Numerical Modeling of Coal Mines with a Laminated DisplacementDiscontinuity Code", Ph.D. Dissertation, Colorado School of Mines, May, 187 pp.
Heasley, K. A. and K. Barron, 1988, “A Case Study of gate Pillar Response to Longwall
Mining in Bump-Prone Strata,” Proceedings of the 3rd Annual Longwall USA Exhibition and
Conference, Chicago, MacLean-Hunter, p. 92-105
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Second International Workshop on Coal Pillar Mechanics and Design, NIOSH IC 9448, p.
89-113.
Mark, C., 1999, “Empirical Methods for Coal Pillar Design,” Proceedings of the Second
International Workshop on Coal Pillar Mechanics and Design, NIOSH IC 9448, p. 145-154.
Mark, C. and F. E. Chase, 1997, “Analysis of Retreat Mining Pillar Stability (ARMPS),”
Proceedings of New Technology for Ground Control in Retreat Mining, NIOSH IC 9446, p.
17-34.
Mark, C. and T. M. Barton, 1997, “Pillar Design and Coal Strength, ” Proceedings of New
Technology for Ground Control in Retreat Mining, NIOSH IC 9446, p. 49-59.
Mark, C., F.E. Chase and R. K. Zipf, 1997, “Preventing Massive Pillar Collapses in Coal
Mines,” Proceedings of New Technology for Ground Control in Retreat Mining, NIOSH IC
9446, p. 35-48.

- 45 -

Mark, C., 1992, “Analysis of Longwall Pillar Stability (ALPS); an update,” Proceedings of
the Workshop on Coal Pillar Mechanics and Design, BuMines IC 9315, p. 238-249.
Mark, C., 1990, “Pillar Design Methods for Longwall Mining, BuMines IC 9247.
Pappas, D. M. and C. Mark, 1993, “Behavior of Simulated Longwall Gob Material,”
BuMines RI 9458.
Zipf, R. K. and C. Mark, 1996, “Design Methods to Control Violent Pillar Failures in Roomand-Pillar Mines,” Proceedings of the 15th International Conference on Ground Control in
Mining, Golden, CO, Colorado School of Mines, p. 225-264.
Zipf, R. K., 1992, “MULSIM/NL Theoretical and Programmer’s Manual,” BuMines IC
9321.

- 46 -

Appendix T - Abutment Load Transfer

The magnitude of abutment load transferred to mine workings adjacent to a gob area depends on
the mechanical characteristics of the gob, the mechanical characteristics of the strata, and the
extraction geometry (e.g. width, height, and overburden depth). Unfortunately, the mechanics of
caving strata is not well established in the mining literature. Predictions of abutment loads and
load distribution often rely on empirical relationships derived from field data or rules of thumb
based on experience or theory. For example, one rule of thumb suggests that abutment loads
would be anticipated at distance up to about one panel width away regardless of depth. Another
relates the distance to overburden depth:
Ws = 9.3 h
where Ws = width of the side abutment (or influenced zone), feet
h = overburden depth, feet
Experience has shown that these approaches provide useful insight. However, predictions of
magnitude and distribution become much more reliable when they are based on mine-specific
measurements and observations.
Between June 1995 and January 1996, Neil & Associates (NAA) conducted field studies in the
6th Right yield-abutment gateroad system at Crandall Canyon Mine. This study provided data on
ground behavior including information relative to abutment stress transfer. Measurements
indicated that stress changes due to abutment loading could be detected at a distance of more
than 280 feet ahead of the advancing longwall face. Similarly, changes were measured adjacent
to the extracted panel (side abutment loads) more than 170 feet away. These measurements were
made at a location beneath 1,100 feet of overburden.

T-1

Appendix U - Coal Properties Input

Agapito Associates Inc. (AAI) assigned calculated coal properties using a “method of slices”
approach to approximate the load bearing capacity of pillars in LaModel. The method assumes
that the strength of a pillar element is a function of its distance from the nearest rib. AAI
modeled the Crandall Canyon Mine workings using 5-foot elements. As illustrated in Table 15,
eight sets of peak and residual strength values were calculated to correspond to depths up to 37.5
feet from a pillar rib. These parameters were determined using the following relationships:
x
σ v = S i [0.71 + 1.74( )]
(Equation 1)
h
where σv = Confined coal strength
Si = In situ coal unconfined strength
x = Distance from the nearest rib
h = Pillar height

εv = σv / E

(Equation 2)

where εv = Peak strain
σv = Confined coal strength
E = Coal elastic modulus

σ r = 0.2254 × ln( x) × σ v

(Equation 3)

where σr = Residual stress
x = Distance from the nearest rib, and
σv = Confined coal strength

εr = 4×εv

(Equation 4)

where εr = Residual strain
εv = Peak strain.
Table 15 - LaModel Confined Coal Strength

These relationships are very similar to those that Karabin and Evanto14 proposed to be used as a
first approximation of stress and strain values for a strain softening coal model. AAI used a
constant of 0.71 in the confined coal strength formula whereas Karabin and Evanto used 0.78.
Also, Karabin and Evanto used two points to define the post-peak slope of the stress-strain curve
whereas AAI used only one. As illustrated in Figure 114, the slope of the post-peak curve that
U-1

AAI used departs somewhat from that proposed by Karabin and Evanto. However, this approach
is reasonable given the assumptions inherent in using strain softening properties. Karabin and
Evanto acknowledged that information was lacking at the time that they wrote their paper:

“The strain-softening approach has been identified as a reasonable method of
describing coal seam behavior. While that concept has been widely discussed,
little specific information is available concerning the actual construction of a
strain-softening model.”
Unfortunately, little research has been done to improve our understanding of strain-softening
behavior in coal since this was written.
Elastic
Stress-Strain
Relationship

Strain-Softening
Model

Peak Strength - σv

AAI Unloading Path (i.e. from peak values
directly to second residual values of σ and ε)
Peak
Strain
εp

First Residual Strength - σr1

Stress (psi)

First
Residual
Strain
εr1

Second Residual Strength - σr2
Second
Residual
Strain
εr2

Strain
Figure 114 - General Strain-Softening Element Characteristics

Traditionally, strain softening properties have been deployed in a displacement-discontinuity
pillar model as a series of concentric rings with the weakest material on the perimeter and
progressively stronger materials approaching the center (see Figure 115)14. In reality, pillar
corners experience less confinement and, therefore, have lower peak strengths. However, this
simplification (i.e., not considering corner effects) has proven to be generally acceptable. At
least one BEM program, BESOL, assigned yielding properties in this manner when the user
elected to use the program’s “automatic yield allocation” feature.
U-2

I

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H H H H H H H H H H H H H

I

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H G G G G G G G G G G G H

I

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H G F F F F F F F

F F G H

I

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H G F E E E E E E E F G H

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H G F E D D D D D E F G H

I

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H G F E D C C C D E F G H

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H G F E D C B C D E F G H

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H G F E D C C C D E F G H

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H G F E D D D D D E F G H

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H G F E E E E E E E F G H

I

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H G F F F F F F F

F F G H

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H G G G G G G G G G G G H

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H H H H H H H H H H H H H

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Figure 115 - Traditional Strain-Softening Element Distribution

The LaModel preprocessor, LamPre, has an automatic yield property allocation feature.
However, the “apply yield zone” utility in LaModel distributes properties in the manner
illustrated in Figure 116. This distribution provides a separate element designation (i.e., letter
code) for corners so that modeled pillar strengths can be more consistent with empirically
derived pillar strength formulas and the assumed stress gradient.
LaModel provides up to 26 different material property inputs. These properties can be deployed
manually in any manner deemed appropriate by the user. However, LamPre’s automatic
yielding property allocation utility limits the depth of yielding to 4 elements. Although the
utility utilizes nine material properties, the depth of the yield zone is still limited to four elements
deep. One of the nine codes represents linear elastic behavior, four represent yielding ribs, and
four are slightly lower strength yielding elements used to more accurately represent reduced
corner confinement.
Models constructed by AAI utilized eight strain-softening material properties (as shown in Table
1 of AAI’s July 2006 report). These properties are consistent with equations 2 through 5 using in
situ coal strength (Si) of 1640 psi and element depths (from the ribline) from 2.5 to 37.5 feet.
However, the properties actually were deployed in AAI’s models as illustrated in Figure 116.
One result of this element configuration is to limit the maximum depth of pillar yielding to 20
feet when 5-foot elements are used. Another is to substantially increase the modeled pillar
strength beyond the value that traditional pillar strength formulae (such as those used to
determine Equation 2) would predict.

U-3

I

H H H H H H H H H H H H H H

I

H G F F F F F F F F F F F F G H
H F E D D D D D D D D D D E F H
H F D C B B B B B B B B C D F H
H F D B A A A A A A A A B D F H
H F D B A A A A A A A A B D F H
H F D B A A A A A A A A B D F H
H F D B A A A A A A A A B D F H
H F D B A A A A A A A A B D F H
H F D B A A A A A A A A B D F H
H F D B A A A A A A A A B D F H
H F D B A A A A A A A A B D F H
H F D C B B B B B B B B C D F H
H F E D D D D D D D D D D E F H
H G F F F F F F F F F F F H G H
I

H H H H H H H H H H H H H H

I

Figure 116 - Strain-Softening Element Distribution to Account for Corner Effects (as Deployed by AAI)

If eight elements (“B” through “I”) are assigned yielding (e.g., strain-softening properties), as
distributed and shown in Figure 115, any pillar 16 elements wide or less would be comprised of
“yieldable” elements. If 5-foot wide elements are employed, pillars up to 80 feet would be
capable of yielding and transferring load to adjacent pillars once the peak strengths of the
elements within the pillar were exceeded. In contrast, the same properties distributed as shown
in Figure 116 will provide full yielding only for pillars up to 8 elements wide, which is 40 feet in
width (8 elements x 5 feet/element). The group of elements labeled “A” in Figure 116
corresponds to linear elastic elements that have no peak strength and cannot transfer load to
adjacent structures. In effect, any pillar over 40 feet in width will be represented in the model
with a linearly elastic core that will not fail.

U-4

Appendix V - Rock Mass Properties

AAI indicated in a written response to the investigation team that the rock mass modulus was
modified from 1x106 psi used in their calibrated EXPAREA model to 2x106 psi to account for
the reduced stiffness introduced by the laminated rock mass used in LaModel. However, the
engineer who conducted the work subsequently indicated that he had used the default elastic
modulus in LamPre (i.e. 3x106 psi) and evaluated the response of their model to lamination
thicknesses of 25 and 50 feet. He noted no difference between the two thickness values and
opted to use 25 feet thereafter.
In his dissertation, Heasley5 provides equations that represent the relationship between
convergence in the laminated overburden used in LaModel and homogeneous elastic rock masses
used in other boundary element models. First, he notes that the seam convergence across a twodimensional slot for the laminated model (sl) as a function of the distance from the panel
centerline (x) can be determined as:

sl ( x) =

12(1 − ν 2) q 2
(L − x2 )
t
E

Equation 1

where: s = seam convergence,
x = distance from the panel centerline,
υ = rock mass Poisson’s ratio,
t = layer or lamination thickness,
q = overburden stress,
E = rock mass elastic modulus, and
L = half width of longwall panel.
A comparable equation for convergence in a homogeneous, isotropic, elastic overburden (sh) is
provided by Jaeger and Cook 27:
q
sh ( x) = 4(1 − ν 2 )
( L2 − x 2 )
Equation 2
E
Heasley equates these relationships and solves for the lamination thickness (t) corresponding to
the convergence at the center of the panel (x=0):
12(1 − ν 2) q 2
q
sl (0) =
L = 4(1 − ν 2 ) L = sh (0)
Equation 3
t
E
E
Assuming that the elastic modulus in both cases is constant, the result is:
3
L
t=
Equation 4
4 1 −ν 2
However, in the present case, AAI increased the modulus threefold. To account for dissimilar
moduli, equations 1 and 2 can be solved in a similar manner to yield the following relationship:
3 E HOMOGENEOUS
L
Equation 5
t=
4 E LAMINATED
1 −ν 2
Equation 5 indicates that the required thickness is reduced by a factor of three as a result of
increasing the rock mass modulus for the laminated model. However, if we assume a panel halfwidth of 117 meters (385 feet or half the width of an average 770-foot wide longwall panel), the
estimated lamination thickness is 35 meters (115 feet) which is more than four times greater than
the 25-foot thickness that AAI used. The effect of thin laminations is that stress will be
concentrated more at the edges of openings rather than be distributed farther away.
V-1

Appendix W - MSHA Main West 2006 ARMPS

As part of a plan review involving the AAI August 2006 analysis for pillar recovery in the Main
West North and South Barriers inby crosscut 107, MSHA District 9 conducted an independent
ARMPS study. Based on the 9 Left – 1st North pillar recovery panel, MSHA established that a
minimum ARMPS PStF should be 0.42. To assess the North Barrier section pillar recovery, a
model was constructed where the sealed portion of the Main West entries and the North Barrier
section entries were combined to form the 9-entry geometry shown in Figure 117. The projected
South Barrier section pillar recovery was also studied. In a manner similar to the North Barrier
section, the South Barrier section pillar recovery was modeled as the 9-entry geometry shown in
Figure 118 where Main West and South Barrier section pillars are combined.
In the North Barrier section analysis, the pillar extraction row included all nine entries as if pillar
recovery included extracting pillars from Main West and the barrier separating Main West and
the North Barrier section. In the South Barrier section analysis, the pillar extraction row also
included all nine entries with the barrier separating Main West and the South Barrier section
modeled as an extracted section pillar. This layout generates low pillar stability values in order
to model a worse case scenario, considering that only two pillars per row were to be recovered in
the North and South Barrier sections, and not eight pillars per row as modeled by MSHA. The
MSHA Main West 2006 analysis did not address barrier pillar stability factors.
At 2,000 feet of overburden, the MSHA Main West 2006 ARMPS pillar stability values are
under the 0.42 MSHA derived minimum criteria for the pillar stability values. The MSHA
analysis led to further discussion between Owens and GRI concerning the AAI study. After
discussing MSHA’s concerns with GRI, Owens agreed with AAI’s analysis.
At the time of the MSHA 2006 study, 80 x 92-foot center pillars were proposed for the South
Barrier section. MSHA District 9 did not run ARMPS studies for the as-mined South Barrier
section pillar design having 80 x 130-foot center pillars and a 40-foot barrier slab cut.

W-1

Figure 117 - North Barrier MSHA 2006 ARMPS Model

W-2

Figure 118 - South Barrier MSHA 2006 ARMPS Model

W-3

Appendix X - Mine Ventilation Plan

The mine ventilation plan in effect at the time of the accident was submitted January 5, 2006,
and approved on July 27, 2006. The plan superseded all previously approved ventilation plans
with exception of amendments for pillar recovery in South Mains, sealing of 1st South Mains and
South Mains, and the ventilation map accepted on July 6, 2007. At the time of the accident,
pillar recovery in South Mains had been completed. The approved plan to seal 1st South Mains
and South Mains had not been implemented.
The plans to develop and recover pillars in the Main West barrier pillars consisted of five
separate plan amendments. Separate plans were submitted for the development and recovery of
each barrier and a site specific plan for the drilling of drainage boreholes into an adjacent sealed
area. An amendment to permanently seal the North Barrier section was also submitted. A
description of each amendment follows.
The amendment to the ventilation plan for the development of the North Barrier section dated
November 10, 2006, was received by MSHA on November 15, 2006, and was approved on
November 21, 2006. The plan states that a separate roof control plan amendment would be
submitted. Four entries were projected into the North Barrier. Entries were numbered from left
to right with Nos. 1 and 2 entries projected to be intake air courses, No. 3 entry was projected as
the isolated section belt, and No. 4 entry was projected as the return air course. The intake air
split ventilated the Main West seals prior to ventilating the working section. The seals were to
be examined in accordance with 30 CFR 75.360(b)(5).
The ventilation plan amendment to recover pillars in the North Barrier section was dated and
received by MSHA on February 3, 2007, and was approved February 9, 2007. The plan required
a measurement point location (MPL) to be established at the deepest point of penetration or at
the edge of accumulated (roofed) water. The mine map provided after the accident indicated that
mining was stopped short of the location shown on the approved plan. Pillar recovery was
initiated approximately 92 feet inby crosscut 158. Measurements indicating the quantity, quality,
and direction of air at the MPL were not recorded in the weekly examination record book as
required by 30 CFR 75.364.
A ventilation plan amendment to drill boreholes between the North Barrier section and the sealed
portion of Main West dated February 8, 2007, was approved February 14, 2007. The stated
intent of the boreholes was to drain any water that may accumulate in the North Barrier section
into the sealed portion of Main West.
The ventilation plan amendment to seal the North Barrier section dated March 14, 2007, was
received by MSHA on March 15, 2007, and provisionally approved on March 16, 2007. The
plan specifies that cementitious foam alternative seals would be installed in the four entries of
the North Barrier section between crosscuts 118 and 119. The stoppings in crosscut 118 were
removed to establish ventilation across the seal line.
The ventilation plan amendment to develop entries in the Main West South Barrier was received
by MSHA on March 22, 2007, and approved on March 23, 2007. Four entries were projected
into the Main West South Barrier. The No. 1 entry was projected to be an intake air course,
Nos. 2 and 3 entries were projected as the section belt and common entries, and No. 4 entry was
projected as the return air course.
X-1

The ventilation plan amendment to recover pillars in the South Barrier section dated May 16,
2007, was received by MSHA on May 21, 2007, and approved on June 1, 2007. The plan
allowed pillar recovery between the Nos. 1 and 3 entries, and slabbing of the barrier south of the
No. 1 entry (except between crosscuts 139 and 142). The ventilation plan depicted pillar
recovery between the No. 1 and No. 2 entries and slabbing of the barrier to the south between
crosscuts 139 to 142. However, the approved roof control plan was revised to afford additional
protection to the bleeder system by not permitting any pillar recovery between crosscuts 139 and
142, including slab cuts from the barrier (refer to South Barrier Section - Pillar Recovery Plan).
The plan amendment approved June 1, 2007, shows an MPL location at the inby end of the
bleeder entry as well as an alternate MPL location if water was allowed to accumulate. A copy
of this amendment is included at the end of this appendix. The alternate location was to be at
“the edge of accumulated (roofed) water.” The plan also states that “Entries will be maintained
to keep the entries free of standing water in excessive depths which would prevent safe travel.”
Mining was conducted approximately 40 feet inby crosscut 149.
Mining conducted inby the last crosscut did not provide for an MPL to be established at the
deepest point of penetration as required in the approved plan. The bleeder entry did not extend
to the deepest point of penetration. Measurements indicating the quantity, quality and direction
of the MPL were not recorded in the weekly examination record book as required by
30 CFR 75.364.
A revised ventilation map dated June 2007 was received by MSHA on July 2, 2007. Mining
development was shown to crosscut 141 of the South Barrier section. The map depicted the
section as being ventilated with 51,546 cubic feet per minute (cfm) of intake air at crosscut 121.
The section regulator between crosscuts 107 to 108 is shown with an air quantity of 60,687 cfm.
The return air includes 11,980 cfm of belt air being dumped through a regulator adjacent to the
number 6 belt drive. The intake and return quantities on the map are also recorded in the weekly
examination book for the week ending June 23, 2007 under the location “Main West #139-#39.”

X-2

X-3

X-4

X-5

X-6

X-7

X-8

Appendix Y - Glossary of Mining Terms as used in this Report
Abutment - In coal mining, (1) the weight of the rocks above a narrow roadway is transferred to
the solid coal along the sides, which act as abutments of the arch of strata spanning the roadway;
and (2) the weight of the rocks over a longwall face is transferred to the front abutment, that is,
the solid coal ahead of the face and the back abutment, that is, the settled packs behind the face.
Act - The Federal Mine Safety and Health Act of 1977.
Active workings - Any place in a coal mine where miners are normally required to work or
travel.
Advance - Mining in the same direction, or order of sequence; first mining as distinguished from
retreat.
Agent – Any person charged with responsibility for the operation of all or a part of a coal or
other mine or the supervision of the miners in a coal or other mine.
Air split - The division of a current of air into two or more parts.
Air course - An entry or a set of entries separated from other entries by stoppings, overcasts,
other ventilation control devices, or by solid blocks of coal or rock so that any mixing of air
currents between each is limited to leakage. Also known as an airway.
AMS Operator - The person(s) designated by the mine operator, who is located on the surface
of the mine and monitors the malfunction, alert, and alarm signals of the AMS and notifies
appropriate personnel of these signals.
Angle of dip - The angle at which strata or mineral deposits are inclined to the horizontal plane.
Angle of draw - In coal mine subsidence, this angle is assumed to bisect the angle between the
vertical and the angle of repose of the material and is 20° for flat seams. For dipping seams, the
angle of break increases, being 35.8° from the vertical for a 40° dip. The main break occurs over
the seam at an angle from the vertical equal to half the dip.
Angle of repose - The maximum angle from horizontal at which a given material will rest on a
given surface without sliding or rolling.
Arching - Fracture processes around a mine opening, leading to stabilization by an arching
effect.
Atmospheric Monitoring System (AMS) - A network consisting of hardware and software
meeting the requirements of 30 CFR 75.351 and 75.1103–2 and capable of: measuring
atmospheric parameters; transmitting the measurements to a designated surface location;
providing alert and alarm signals; processing and cataloging atmospheric data; and, providing
reports. Frequently used for early-warning fire detection and to monitor the operational status of
mining equipment.

Y-1

Azimuth - A surveying term that references the angle measured clockwise from any meridian
(the established line of reference). The bearing is used to designate direction. The bearing of a
line is the acute horizontal angle between the meridian and the line.
Back-Analysis - A process in which known failures or successes are evaluated to determine the
relationship of engineering parameters to outcomes.
Barricading - Enclosing part of a mine to prevent inflow of noxious gasses from a mine fire or
an explosion. If men are unable to escape, they retreat as far as possible, select some working
place with plenty of space, short-circuit the air from this place, build a barricade, and remain
behind it until rescued.
Barrier - Barrier pillars are solid blocks of coal left between two mines or sections of a mine to
prevent accidents due to inrushes of water, gas, or from explosions or a mine fire; also used for a
pillar left to protect active workings from a squeeze.
Beam - A bar or straight girder used to support a span of roof between two support props or
walls.
Beam building - The creation of a strong, inflexible beam by bolting or otherwise fastening
together several weaker layers. In coal mining this is the intended basis for roof bolting.
Bearing plate - A plate used to distribute a given load; in roof bolting, the plate used between
the bolt head and the roof.
Bed - A stratum of coal or other sedimentary deposit.
Belt air course - The entry in which a belt is located and any adjacent entry(ies) not separated
from the belt entry by permanent ventilation controls, including any entries in series with the belt
entry, terminating at a return regulator, a section loading point, or the surface.
Belt conveyor - A looped belt on which coal or other materials can be carried and which is
generally constructed of flame-resistant material or of reinforced rubber or rubber-like substance.
Bit - The hardened and strengthened device at the end of a drill rod that transmits the energy of
breakage to the rock. The size of the bit determines the size of the hole. A bit may be either
detachable from or integral with its supporting drill rod.
Bituminous coal – A middle rank coal (between sub-bituminous and anthracite) formed by
additional pressure and heat on lignite. Usually has a high Btu value and may be referred to as
"soft coal."
Bleeder entries - Special entries developed and maintained as part of the bleeder system and
designed to continuously move air from pillared areas into a return air course or to the surface of
the mine.
Bleeder system - a ventilation network used to ventilate pillared areas in underground coal
mines and designed to continuously dilute and move air-methane mixtures and other gases,

Y-2

dusts, and fumes from the worked-out area away from active workings and into a return air
course or to the surface of the mine.
Borehole - Any deep or long drill-hole, usually associated with a diamond drill.
Bottom - Floor or underlying surface of an underground excavation.
Boss - Any member of the managerial ranks who is directly in charge of miners (e.g., “shiftboss,” “face-boss,” “fire-boss,” etc.).
Brattice or brattice cloth - Fire-resistant fabric or plastic partition used in a mine passage to
confine the air and force it into the working place; also termed “curtain,” “rag,” “line brattice,”
“line canvas,” or “line curtain.”
Bounce - A heavy sudden often noisy blow or thump; sudden spalling off of the sides of ribs and
pillars due to the excessive pressure; any dull, hollow, or thumping sound produced by
movement or fracturing of strata as a result of mining operations; also known as a bump.
Bump – see definition for “Bounce.”
Bump Prone Ground 28 – Strong, stiff roof and floor strata not prone to failing or heaving when
subjected to high stress (e.g., deep overburden); also can refer to locations where bumps or bursts
have historically occurred.
Burst - An explosive breaking of coal or rock in a mine due to pressure; the sudden and violent
failure of overstressed rock resulting in the instantaneous release of large amounts of
accumulated energy where coal or rock is suddenly expelled from failed pillars. In coal mines
they may or may not be accompanied by a copious discharge of methane, carbon dioxide, or coal
dust; also called outburst; bounce; bump; rock burst.
Can – A brand name type of floor-to-roof support constructed of prefabricated steel sheet metal
cylinders filled with light-weight concrete.
Cap - A miner's safety helmet.
Certified - Describes a person who has passed an examination to do a required job.
Cleat - The vertical cleavage of coal seams. The main set of joints along which coal breaks
when mined.
Coal - A solid, brittle, more or less distinctly stratified combustible carbonaceous rock, formed
by partial to complete decomposition of vegetation; varies in color from dark brown to black; not
fusible without decomposition and very insoluble.
Coal reserves - Measured tonnages of coal that have been calculated to occur in a coal seam
within a particular property.

Y-3

Coda Magnitude – The coda magnitude (MC) is based on the length of the seismic signal and
calibrated to provide similar results with the local magnitude (ML) or Richter scale for naturally
occurring earthquakes.
Competent rock - Rock which, because of its physical and geological characteristics, is capable
of sustaining openings without any structural support except pillars and walls left during mining
(stalls, light props, and roof bolts are not considered structural support).
Contact - The place or surface where two different kinds of rocks meet. Applies to sedimentary
rocks, as the contact between a limestone and a sandstone, for example, and to metamorphic
rocks; and it is especially applicable between igneous intrusions and their walls.
Continuous mining machine - A machine that removes coal from the face and loads that coal
into cars without the use of cutting machines, drills, or explosives.
Contour - An imaginary line that connects all points on a surface having the same elevation.
Convergence – Reduction of entry height; closure between the mine floor and the mine roof.
Core sample – A cylinder sample generally 1-5" in diameter drilled out of an area to determine
the geologic and chemical analysis of the overburden and coal.
Cover - The overburden of any deposit.
Crib - A roof support of prop timbers or ties, laid in alternate cross-layers, log-cabin style.
Cribbing - The construction of cribs or timbers laid at right angles to each other, sometimes
filled with earth, as a roof support or as a support for machinery.
Crosscut - A passageway driven between parallel entries or air courses for ventilation purposes.
Curtain – see definition for “Brattice.”
Cycle mining - A system of mining in more than one working place at a time, that is, a
continuous mining machine takes a lift from the face and moves to another face while permanent
roof support is established in the previous working face.
Depth - The word alone generally denotes vertical depth below the surface. In the case of
boreholes it may mean the distance reached from the beginning of the hole, the borehole depth,
or the inclined depth.
Detectors - Specialized chemical or electronic instruments used to detect mine gases.
Development mining - Work undertaken to open up coal reserves prior to pillar recovery.
Dilute - To lower the concentration of a mixture; in this case the concentration of any hazardous
gas in mine air by addition of fresh intake air.

Y-4

Dip - The inclination of a geologic structure (bed, vein, fault, etc.) from the horizontal; dip is
always measured downwards at right angles to the strike.
Double Difference Method – A technique to improve the precision of the location of seismic
events by determining the relative location between multiple events. When combined with a
known location, it can improve the accuracy of the locations.
Drainage - The process of removing surplus ground or surface water either by artificial means or
by gravity flow.
Drift - A horizontal passage underground. A drift follows the vein, as distinguished from a
crosscut that intersects it, or a level or gallery, which may do either.
Drift mine – An underground coal mine in which the entry or access is above water level and
generally on the slope of a hill, driven horizontally into a coal seam.
Dump - To unload; specifically, a load of coal or waste; the mechanism for unloading, e.g. a car
dump (sometimes called tipple); or, the pile created by such unloading, e.g. a waste dump (also
called heap, pile, tip, spoil pike, etc.).
Entry - An underground horizontal or near-horizontal passage used for haulage, ventilation, or
as a mainway; a coal heading; a working place where the coal is extracted from the seam in the
initial mining; same as "gate" and "roadway," both British terms.
Extraction - The process of mining and removal of cal or ore from a mine.
Face – The exposed area of a coal bed from which coal is being extracted.
Face cleat - The principal cleavage plane or joint at right angles to the stratification of the coal
seam.
Fall - A mass of roof rock or coal which has fallen in any part of a mine.
Fan signal - Automation device designed to give alarm if the main fan slows down or stops.
Fault - A slip-surface between two portions of the earth's surface that have moved relative to
each other. A fault is a failure surface and is evidence of severe earth stresses.
Fault zone - A fault, instead of being a single clean fracture, may be a zone hundreds or
thousands of feet wide. The fault zone consists of numerous interlacing small faults or a
confused zone of gouge, breccia, or mylonite.
Feeder - A machine that feeds coal onto a conveyor belt evenly.
Floor - That part of any underground working upon which a person walks or upon which
haulage equipment travels; simply the bottom or underlying surface of an underground
excavation.

Y-5

Formation – Any assemblage of rocks which have some character in common, whether of
origin, age, or composition. Often, the word is loosely used to indicate anything that has been
formed or brought into its present shape.
Fracture - A general term to include any kind of discontinuity in a body of rock if produced by
mechanical failure, whether by shear stress or tensile stress. Fractures include faults, shears,
joints, and planes of fracture cleavage.
Fresh Air Base – Mine rescue teams establish a fresh air base (FAB) under controlled
ventilation at the entrance to unexplored areas. The FAB includes a hardwired communications
system running to the surface command center. The FAB serves as a safe retreat and as a
communication hub between the exploring teams and the command center.
Gob - The term applied to that part of the mine from which the coal pillars have been recovered
and the rock that falls into the void; also called goaf. Also, refers to loose waste in a mine.
Grading - Digging up the bottom to give more headroom in roadways.
Ground control - Measures taken to prevent roof falls or coal bursts.
Ground pressure - The pressure to which a rock formation is subjected by the weight of the
superimposed rock and rock material or by diastrophic forces created by movements in the rocks
forming the earth's crust. Such pressures may be great enough to cause rocks having a low
compressional strength to deform and be squeezed into and close a borehole or other
underground opening not adequately strengthened by an artificial support, such as casing or
timber.
Haulage - The horizontal transport of ore, coal, supplies, and waste.
Haulageway - Any underground entry or passageway that is designed for transport of mined
material, personnel, or equipment, usually by the installation of track or belt conveyor.
Heaving - Applied to the rising of the bottom after removal of the coal.
Horizon - In geology, any given definite position or interval in the stratigraphic column or the
scheme of stratigraphic classification; generally used in a relative sense.
Hydraulic - Of or pertaining to fluids in motion. Hydraulic cement has a composition which
permits it to set quickly under water. Hydraulic jacks lift through the force transmitted to the
movable part of the jack by a liquid. Hydraulic control refers to the mechanical control of
various parts of machines, such as coal cutters, loaders, etc., through the operation or action of
hydraulic cylinders.
Immediate roof - The roof strata immediately above the coalbed, requiring support during the
excavation of coal.
Inby – Into the mine; in the direction of the working face.

Y-6

In situ - In the natural or original position. Applied to a rock, soil, or fossil when occurring in the
situation in which it was originally formed or deposited.
Intake air - Air that has not yet ventilated the last working place on any split of any working
section, or any worked-out area, whether pillared or nonpillared.
Isopach - A line, on a map, drawn through points of equal thickness of a designated unit.
Jackpot - A cap-shaped unit designed for pre-stressing prop-type supports developed by New
Concept Mining.
Joint - A divisional plane or surface that divides a rock and along which there has been no
visible movement parallel to the plane or surface.
Lamp - The electric cap lamp worn for visibility.
Layout - The design or pattern of the main roadways and workings. The proper layout of mine
workings is the responsibility of the manager aided by the planning department.
Lift - The amount of coal obtained from a continuous mining machine in one mining cycle.
Line Curtain - Fire-resistant fabric or plastic partition used in a mine passage to confine the air
and force it into the working place; also termed “line brattice” or “line canvas.”
Lithology - The character of a rock described in terms of its structure, color, mineral
composition, grain size, and arrangement of its component parts; all those visible features that in
the aggregate impart individuality of the rock. Lithology is the basis of correlation in coal mines
and commonly is reliable over a distance of a few miles.
Loading point – The point where coal or ore is loaded onto conveyors.
Local Magnitude – The local magnitude (ML) or Richter scale is a logarithmic scale originally
devised by Charles Richter to quantify the intensity of California earthquakes and has been
adopted for use around the world.
Longwall mining – One of three major underground coal mining methods currently in use.
Employs a steal plow, or rotation drum, which is pulled mechanically back and forth across a
face of coal that is usually several hundred feet long. The loosened coal falls onto a conveyor for
removal from the mine.
Loose coal - Coal fragments larger in size than coal dust.
Main entry - A main haulage road. Where the coal has cleats, main entries are driven at right
angles to the face cleats.
Main fan - A mechanical ventilator installed at the surface; operates by either exhausting or
blowing to induce airflow through the mine.
Man trip - A carrier of mine personnel, by rail or rubber tire, to and from the work area.

Y-7

Methane – A potentially explosive gas formed naturally from the decay of vegetative matter,
similar to that which formed coal. Methane, which is the principal component of natural gas, is
frequently encountered in underground coal mining operations and is kept within safe limits
through the use of extensive mine ventilation systems.
Methane monitor - An electronic instrument often mounted on a piece of mining equipment that
detects and measures the methane content of mine air.
Miner – Any individual working in a coal or other mine.
Mobile bridge continuous haulage system - A system of movable conveyors that carry coal
from a continuous mining machine to the section belt allowing the machine to advance over
short distances without interrupting the mining and loading operation.
Mobile Command Center Vehicle – Class A motor home equipped with communication
equipment, conference facility, and office equipment maintained by MSHA’s Mine Emergency
Operations unit.
MSHA - Mine Safety and Health Administration; the federal agency which regulates coal mine
safety and health.
Operator - Any owner, lessee, or other person who operates, controls, or supervises a coal or
other mine or any independent contractor performing services or construction at such mine.
Outburst Accident - coal or rock outburst that cause withdrawal of miners or which disrupts
regular mining activity for more than one hour (even if no miners are injured).
Outby - Nearer to or toward the mine entrance, and hence farther from the working face; the
opposite of inby.
Overburden – Layers of soil and rock covering a coal seam; also referred to as “depth of cover.”
Overcast - Enclosed airway which permits one air current to pass over another without
interruption.
Pager Phone – A telephone system approved for use in coal mines and capable of broadcasting
voice messages over a loud speaker.
Panel - A coal mining block that generally comprises one operating unit.
Parting - (1) A small joint in coal or rock; (2) a layer of rock in a coal seam; (3) a side track or
turnout in a haulage road.
Percentage extraction - The proportion of a coal seam which is removed from the mine. The
remainder may represent coal in pillars or coal which is too thin or inferior to mine or lost in
mining. Shallow coal mines working under townships, reservoirs, etc., may extract 50%, or less,
of the entire seam, the remainder being left as pillars to protect the surface. Under favorable
conditions, longwall mining may extract from 80 to 95% of the entire seam. With pillar methods
of working, the extraction ranges from 50 to 90% depending on local conditions.

Y-8

Permissible - That which is allowable or permitted. It is most widely applied to mine equipment
and explosives of all kinds which are similar in all respects to samples that have passed certain
tests of the MSHA and can be used with safety in accordance with specified conditions where
hazards from explosive gas or coal dust exist.
Permit – As it pertains to mining, a document issued by a regulatory agency that gives approval
for mining operations to take place.
Pillar - An area of coal left to support the overlying strata in a mine; sometimes left permanently
to support surface structures.
Pillared area - Describes that part of a mine from which the pillars have been removed; also
known as robbed out area.
Pillar line - The line that roughly follows the rear edges of coal pillars that are being recovered
during retreat mining; the line along which the roof of a coal mine is expected to break.
Pillar recovery - Any reduction in pillar size during retreat mining. Refers to the systematic
removal of the coal pillars between rooms or chambers to regulate the subsidence of the roof;
also termed “pillar robbing,” “bridging back” the pillar, “drawing” the pillar, or “pulling” the
pillar.
Portal - The surface entrance to a mine.
Post - The vertical member of a timber set.
Prop - Coal mining term for any single post used as roof support. Props may be timber or steel;
if steel--screwed, yieldable, or hydraulic.
Qualified Person - (1) An individual deemed qualified by MSHA and designated by the
operator to make tests and examinations required by this 30 CFR part 75; and (2) An individual
deemed, in accordance with minimum requirements established by MSHA, qualified by training,
education, and experience, to perform electrical work, to maintain electrical equipment, and to
conduct examinations and tests of all electrical equipment.
Rag – see definition for “Brattice.”
Recovery - The proportion or percentage of coal or ore mined from the original seam or deposit.
Regulator - Device (wall, door) used to control the volume of air in an air split.
Reserve – That portion of the identified coal resource that can be economically mined at the time
of determination. The reserve is derived by applying a recovery factor to that component of the
identified coal resource designated as the reserve base.
Resin bolting - A method of permanent roof support in which steel rods are grouted with resin.
Resources – Concentrations of coal in such forms that economic extraction is currently or may
become feasible. Coal resources broken down by identified and undiscovered resources.

Y-9

Identified coal resources are classified as demonstrated and inferred. Demonstrated resources
are further broken down as measured and indicated. Undiscovered resources are broken down as
hypothetical and speculative.
Retreat mining - A system of robbing pillars in which the robbing line, or line through the faces
of the pillars being extracted, retreats from the boundary toward the shaft or mine mouth.
Return air - Air that has ventilated (or mixed with air that has ventilated) the last working place
on any split of any working section, or any worked-out area, whether pillared or nonpillared.
Rib - The side of a pillar or the wall of an entry; the solid coal on the side of any underground
passage.
Rider - A thin seam of coal overlying a thicker one.
Rob - To extract pillars of coal previously left for support.
Rock Dust - Pulverized limestone, dolomite, gypsum, anhydrite, shale, adobe, or other inert
material, preferably light colored. Rock dust is applied to underground areas of coal mines to
increase the incombustible content of mine dust so that it will not propagate an explosion.
RocProp - A type of hydraulically wedged standing roof support, registered trademark of Mine
Support Products.
Roof - The stratum of rock or other material above a coal seam; the overhead surface of a coal
working place; same as “back” or “top.”
Roof bolt - A long steel bolt driven into the roof of underground excavations to support the roof,
preventing and limiting the extent of roof falls. The unit consists of the bolt (up to 4 feet long),
steel plate, expansion shell, and pal nut. The use of roof bolts eliminates the need for timbering
by fastening together, or “laminating,” several weaker layers of roof strata to build a “beam.”
Roof Coal – A layer of coal immediately above the mine opening as a result of leaving the upper
horizon of the coalbed unmined, usually to protect weak shale in the immediate roof from
weathering; also known as “head coal” or “top coal.”
Roof fall - A coal mine cave-in, especially in active areas such as entries.
Roof jack - A screw- or pump-type hydraulic extension post made of steel and used as
temporary roof support.
Roof sag - The sinking, bending, or curving of the roof, especially in the middle, from weight or
pressure.
Roof stress - Unbalanced internal forces in the roof or sides, created when coal is extracted.
Roof support – Posts, jacks, roof bolts and beams used to support the rock overlying a coal
seam in an underground mine. A good roof support plan is part of mine safety and coal
extraction.

Y-10

Room and pillar mining – A method of underground mining in which approximately half of the
coal is left in place to support the roof of the active mining area. Large "pillars" are left while
"rooms" of coal are extracted.
Safety factor - The ratio of the ultimate breaking strength of the material to the force exerted
against it.
Sandstone - A sedimentary rock consisting of quartz sand united by some cementing material,
such as iron oxide or calcium carbonate.
Scaling - Removal of loose rock from the roof or walls. This work is dangerous and a long bar
(called a scaling bar) is often used.
Scoop - A rubber tired-, battery- or diesel-powered piece of equipment designed for cleaning
roadways and hauling supplies.
Seam - A stratum or bed of coal.
Section - A portion of the working area of a mine.
Self-contained breathing apparatus - A self-contained supply of oxygen used during rescue
work from coal mine fires and explosions.
Self-contained self-rescuer (SCSR) – A type of closed-circuit, self-contained breathing
apparatus approved by MSHA and NIOSH under 42 CFR part 84 for escape only from
underground mines. The device is capable of sustaining life in atmospheres containing deficient
oxygen.
Self-rescuer – A small filtering device carried by a coal miner underground, either on his belt or
in his pocket, to provide him with immediate protection against carbon monoxide and smoke in
case of a mine fire or explosion. It is a small canister with a mouthpiece directly attached to it.
The wearer breathes through the mouth, the nose being closed by a clip. The canister contains a
layer of fused calcium chloride that absorbs water vapor from the mine air. The device is used
for escape purposes only and does not sustain life in atmospheres containing deficient oxygen.
Filter self-rescuers approved by MSHA and NIOSH under 42 CFR part 84 provide at least one
hour of protection against carbon monoxide.
Shaft - A primary vertical or non-vertical opening through mine strata used for ventilation or
drainage and/or for hoisting of personnel or materials; connects the surface with underground
workings.
Shale - A rock formed by consolidation of clay, mud, or silt, having a laminated structure and
composed of minerals essentially unaltered since deposition.
Shift - The number of hours or the part of any day worked.
Shuttle car – A self-discharging vehicle, generally with rubber tires, used for receiving coal
from the loading or mining machine and transferring it to an underground loading point, mine
railway, or belt conveyor system.

Y-11

Slabbing – A method of mining pillars in which successive lifts are cut from one side of the
pillar.
Sloughing - The slow crumbling and falling away of material from roof, rib, and face.
Spad – A spad is a flat spike hammered into the mine ceiling from which is threaded a plumbline
to serve as an underground survey station. A sight spad, is a station that allows a mine foreman
to visually align entries or breaks from the main spad.
Span - The horizontal distance between the side supports or solid abutments.
Split - Any division or branch of the ventilating current or the workings ventilated by one
branch. Also, to divide a pillar by driving one or more roads through it.
Squeeze - The settling, without breaking, of the roof and the gradual upheaval of the floor of a
mine due to the weight of the overlying strata.
Step-Up Foreman – A crewmember who acts in a supervisory role during a foreman’s absence.
Strike - The direction of the line of intersection of a bed or vein with the horizontal plane. The
strike of a bed is the direction of a straight line that connects two points of equal elevation on the
bed.
Stump - Any small pillar.
Stopping – A permanent wall built across unused crosscuts or entries to separate air courses and
prevent the air from short circuiting.
Subsidence – The gradual sinking, or sometimes abrupt collapse, of the rock and soil layers into
an underground mine.
Sump - A place in a mine that is used as a collecting point for drainage water.
Support - The all-important function of keeping the mine workings open. As a verb, it refers to
this function; as a noun it refers to all the equipment and materials--timber, roof bolts, concrete,
steel, etc.--that are used to carry out this function.
Tailgate - A subsidiary gate road to a conveyor face as opposed to a main gate. The tailgate
commonly acts as the return airway and supplies road to the face.
Tailpiece - Also known as foot section pulley. The pulley or roller in the tail or foot section of a
belt conveyor around which the belt runs.
Timber - A collective term for underground wooden supports.
Time of Useful Consciousness – Also known as “Effective Performance Time.” These
interchangeable terms describe the period of time between the interruption of the oxygen supply
or exposure to an oxygen-poor environment and the time when a person is unable to perform
duties effectively, such as putting on oxygen equipment or taking corrective action.

Y-12

Ton – A short or net ton is equal to 2,000 pounds.
Top - A mine roof; same as “back.”
Tractor - A piece of self-propelled equipment that pulls trailers, skids, or personnel carriers.
Also used for supplies.
Tram - Used in connection with moving self-propelled mining equipment (i.e., to tram or move
a machine).
Transfer point - Location in the materials handling system, either haulage or hoisting, where
bulk material is transferred between conveyances.
Underground mine – Also known as a "deep" mine. Usually located several hundred feet
below the earth's surface, an underground mine's coal is removed mechanically and transferred
by shuttle car or conveyor to the surface.
Velocity - Rate of airflow in lineal feet per minute.
Ventilation - The provision of a directed flow of fresh and return air along all underground
roadways, traveling roads, workings, and service parts.
Violation - The breaking of any state or federal mining law.
Water Gauge (standard U-tube) - Instrument that measures differential pressures in inches of
water.
Wedge - A piece of wood tapering to a thin edge and used for tightening in conventional
timbering.
Weight - Fracturing and lowering of the roof strata at the face as a result of mining operations,
as in “taking weight.”
Worked out area - An area where mining has been completed, whether pillared or nonpillared,
excluding developing entries, return air courses, and intake air courses.
Working - When a coal seam is being squeezed by pressure from roof and floor, it emits
creaking noises and is said to be “working.” This often serves as a warning to the miners that
additional support is needed.
Working face - Any place in a coal mine in which work of extracting coal from its natural
deposit in the earth is performed during the mining cycle.
Working place - The area of a coal mine inby the last open crosscut.
Workings - The entire system of openings in a mine for the purpose of exploitation.
Working section - All areas of the coal mine from the loading point of the section to and
including the working faces.

Y-13

Appendix Z - References

1

USBM dictionary 1996.

2

Pechmann, J.C., Arabasz, W.J., Pankow, K.L., and Burlacu, R.L., 2008, Seismological report
on the August 6, 2007 Crandall Canyon Mine Collapse in Utah, submitted to Seismological
Research Letters.

3

Ford, S.R., Dreger, D.S., and Walter, W.R., 2008, Source characterization of the August 6,
2007 Crandall Canyon Mine seismic event in central Utah, submitted to Seismological Research
Letters.
4

Pariseau, W.G., 1978, Interpretation of Rock Mechanics Data (Vol. II), (A Guide to Using
UTAH2), USBM OFR 47-80, June 1978, 41pp.
5

Heasley, K.A., 1998, Numerical Modeling of Coal Mines with a Laminated DisplacementDiscontinuity Code, Ph.D. Thesis, Colorado School of Mines

6

Mark, C., ARMPS v.5.1.18 Help file, Stability Factors.

7

Chase, F.E., Mark, C., and Heasley, K.A., 2002, Deep Cover Pillar Extraction in the U.S.
Coalfields, Proceedings of the 21st International Conference on Ground Control in Mining,
Morgantown, WV, West Virginia University.

8

Koehler, J.R., and Tadolini, S.C., 1995, Practical Design Methods for Barrier Pillars, USBM
Information Circular 9427, 19 pp.

9

Goodrich, R.R., Agapito, J.F.T., Pollastro, C., LaFrentz, L., and Fleck, K., 1999, Long load
transfer distances at the Deer Creek Mine, Rock Mechanics for Industry, 37th U.S. Rock
Mechanics Symposium, Vail, CO, June 6-9, 1999, p. 517-523.
10

Abel Jr., J.F., 1988, Soft Rock Pillars, International Journal of Mining and Geological
Engineering, Vo. 6, pp. 215-248.
11

Barrientos, G., and Parker, J., 1974, Use of the Pressure Arch in Mine Design at White Pine,
Trans. SME of AIME, Vol. 255, pp. 75-82.

12

Gilbride, L.J., and Hardy, M.P., 2004, Interpanel Barriers for Deep Western U.S. Longwall
Mining, Proceedings of the 23rd International Conference on Ground Control in Mining, August
2004, 7 pp.
13

Karabin, G.J., and Evanto, M.A., 1999, Experience with the Boundary-Element Method of
Numerical Modeling to Resolve Complex Ground Control Problems, Proceedings of the Second
International Workshop on Coal Pillar Mechanics and Design, NIOSH IC 9448, pp. 89-113.

14

Karabin, G.J. and Evanto, M.A., 1994 Experience with the Boundary Element Method of
Numerical Modeling as a Tool to Resolve Complex Ground Control Problems, Proceedings of
the 13th International Conference on Ground Control in Mining, Morgantown, WV, pp. 201-213.
15

Chase, F. and C. Mark, 1997, Analysis of Retreat Mining Pillar Stability (ARMPS),
Proceedings: New Technology for Ground Control in Retreat Mining, eds. C. Mark and R.
Tuchman, NIOSH IC 9446, March 1997, p. 17-34.

Z-1

16

Miller, T.M., and Mazur, P.O. (Fermilab), 1983, Oxygen Deficiency Hazards Associated with
Liquefied Gas Systems Development of a Program of Controls, FERMILAB-TM-1163, Jan
1983, 30pp.

17

http://www.cdc.gov/niosh/mining/statistics/disall.htm

18

Lexan (LEXAN) is a registered trademark for General Electric's (now SABIC Innovative
Plastics) brand of highly durable polycarbonate resin thermoplastic intended to replace glass
where the need for strength justifies its higher cost.

19

Chase, F.E., R.K. Zipf, and C. Mark (1994) “The Massive Collapse of Coal Pillars- Case
Histories in the U.S.,” Proceedings of the 13th International Conference on Ground Control in
Mining. West Virginia University, Morgantown, WV, pp. 69-80.
20

Maleki, H. (1995) “An Analysis of Violent Failure in U.S. Coal Mines – Case Studies,”
Proceedings: Mechanics and Mitigation of Violent Failure in Coal and Hard-Rock Mines,
Bureau of Mines, SP 01-95, pp. 5-25.

21

NSA Engineering, Inc., 2000, “Final Report – Review of Current Yielding Gate Road Design
Approaches and Applications in U.S. Longwall Operations,” January 7, 2000, 77 pp. (included
as Appendix 11 in UNSW/SCT Collaborative ACARP Project C9018, “Systems approach to
pillar design: Module 1 – Pillar design procedures,” January 2005).
22

Peng, S.S., 1992, Surface Subsidence Engineering, Society for Mining, Metallurgy, and
Exploration, Inc., Littleton, CO, 161 pp.
23

Agioutantis, Z., and Karmis, M., 2003, Surface Deformation Prediction System (SDPS),
Virginia Polytechnic Institute and State University, Blacksburg, VA, p. 42.
24

Arabasz W.J., 2007, Presentation to Utah Mining Commission, November 2007

25

Waldhauser, F., and Ellsworth, W.L., 2000, A double difference earthquake location
algorithm: Method and application to the northern Hayward fault, Bulletin of the Seismological
Society of America 90, 1353-1368.

26

http://www.cdc.gov/niosh/mining/products/product54.htm

27

Jaeger, J.C., and Cook, N.G.W., 1979, Fundamental of Rock Mechanics, London: Chapman
and Hall.

28

Iannacchione, A.T., and Zelanko, J.C., 1995, Occurrence and Remediation of Coal Mine
Bumps: A Historical Review, Proceedings: Mechanics and Mitigation of Violent Failure in Coal
and Hard-Rock Mines, USBM, May 1995.

Z-2