Table 4.—Bivariate correlation coefficients between damage and selected other variables

Significant variables" Coefficient Insignificant variables Coefficient
Damage ...........-..-.- 1 Pillar width 01
ee 0.65 Ratio of P to Q o4
Gradyield . -0.57 Young's modulus of roof to coal 0.07
Jointrf ... . 0.52
Pillar factor of safety........ -0.44
Uniaxial strength of roof to coal 0.36
Face factor of safety ....... 0.33
No. interacting seams ...... 0.33
Panel width todepth ....... -0.31
Mining method .... 0.26

* Two-tailed tests

Gradyield Ratio of roof and floor yield characteristics to stress
gradient.

Panelwd Ratio of panel width to depth.
Youngre Ratio of Young's modulus of the roof to the seam.

Table 4 presents the bivariate correlation coefficients between
the damage variable and selected geologic and geometric
variables. Energy (M,), face factor of safety, stress gradient,
pillar factor of safety, joint spacing, and uniaxial compressive
strength of roof to coal were the most significant. Other variables
were poorly correlated with damage, including the ratio of P to Q,
pillar width, and Young’s modulus of roof to coal.

Multiple Linear Regression Analysis

There are two methods used by engineers and researchers as
tools to help predict conditions in the future: statistical and com-
putational. Starfield and Cundall (16) identify rock mechanics
problems as “data-limited,” that is, one seldom knows enough
about a rock mass to use computational models unambiguously.
Statistical methods, on the other hand, are uniquely capable of
being applied where there are good data but a limited
understanding of certain natural phenomena, such as coal bumps.

In this study, the authors combined the strength of both
methods to identify important variables and to develop predictive
capabilities. Computational methods have been used to assess the
influence of a combination of geometric variables into single
variables, such as pillar factor of safety and released energy. This
was very useful for increasing goodness-of-fit and enhancing
multiple regression coefficients. Statistical methods were used to
identify significant variables, to build confidence intervals, and so
forth.

In the final step in the analysis, a multilinear regression
procedure was used, which involved entering the independent
variables one at a time (table 4) into an equation using a forward

selection methodology (/5). In this method, the variable having
the largest correlation with the dependant variable is entered into
the equation. If a variable fails to meet entry requirements, it is
not included in the equation. If it does meet the criteria, the
second variable with the highest partial correlation will be
selected and tested for entering into the equation. This procedure
is very desirable when there is a cause-and-effect structure among
the variables. An example of the cause-and-effect relationship is
shown when a greater depth reduces pillar factor of safety,
contributes to an accumulation of energy, and ultimately results
in greater damage. Using the above procedures, any hidden
relationship between depth and pillar factor of safety, energy, and
damage is evaluated and taken into account during each step of
the analysis.

Several geomechanical variables (table 3) were initially used
as dependent variables. The multiple correlation coefficient (R),
which is a measure of goodness-of-fit, for the last step was 0.87

The assumptions of linear regression analysis were tested and
found to be valid by an analysis of variance, F-statistics, and a
plot of standardized residuals (figure 6) (15). Residual plots dia
not indicate the need for inclusion of nonlinear terms because
there was no special pattern in the residuals.

20 i
15 4
10F . 4
ost . 74
ok 4
05 fw . 74
OF +

a5 E . 4

L L L

STANDARDIZED PREDICTED

20

2 a ° 1 2
REGRESSION STANDARDIZED RESIDUAL

Figure 6.—Standardized scatterplot for dependent
variable, “damage”


Table 1.—Statistical summary of geologic variables.

Variable Mean Standard deviation __ Range No. of cases

Joint sets. 1.4 06 13 25
Cleat sets . 1.8 04 1-2 25
Inseam partings . 1 09 0-3 24
Joint spacing, m . 67 55 15-15 24
Rock Quality Designation 18 50-100 15

134 275-820 25
Roof beam thickness, m_. 3.3 15-122 25
Young's modulus, coal, MPa........... 3310 830 2410-4620 25
Young's modulus, roof and floor, MPa... 20,700 6900 6900-33,000 25
Uniaxial strength, MPa 52 13.8-32 25
Uniaxial strength, root and floor, MPa 238 55-150 25
Max. horizontal stress, MPa 78 0.7-26 25
Interacting seams 04 1-3 25
Local yield characteristics .........---- 02 25

Table 2.—Statistical summary of geometric variables.

Variable Mean Standard deviation Range No. of cases
Pillar width, Mo... eee 19 oO 9-42 23
Pillar height, m 25 03 1.7-3 25
Entry span, m 5.8 03 55-6 25
Barrier pillar width, m 50 27 15-73 6
Face width, m 40 61-244 25
Mining method . 04 1-2 25
Stress gradient ...........- 0.6 0-2 25
Table 3.—Statistical summary of geomechanical variables

Variable Mean Standard deviation Range No. of cases
Pillar factor of safety........... 08 03 0.5-1.4 23
Face factor of safety .......... 0.9 02 0.6-1.5 22
Energy (M,) - 3 05 24 22
Damage ... 1.4 1 03 25

Bivariate Correlations and Data Reduction

In the next step of the analysis, “damage” was denoted as the
dependent variable against which all other variables were tested
to determine which of these variables were effective in deducing
bump potential.

Based on preliminary bivariate correlations among all
geologic, geometric, and geomechanical variables, the number of
variables was reduced by combining some variables into new
ones and eliminating those that were intrinsically interrelated. In
addition, the cause-and-effect (/5) structure in the data was

identified, helping to tailor the procedures for multiple regression
analysis using forward stepwise inclusion of variables. The new
variables were as follows:

Pgratio Ratio of maximum principal horizontal stress (P) to
minimum stress (Q).

Strenrc Ratio of uniaxial compressive strength of the roof to
the coal.

Jointrf Joint spacing times roof beam thickness divided by
mining height.


Table 5.—Standardized regression coefficients and statistical

significance
Variable Standardized coefficient T-significance
ENGGY vececeeee cere 0.28 0.049
Pillar factor of safety . -0.34 0.011
Mining method . . . 0.26 0.064
Gradyield 0... -0.55 0.0004
Constant .........--- ++ NA 0.234
NA Not applicable.
Important Variables Contributing to Bump-Prone Conditions assessing bump-prone conditions, which in turn will result in

safer designs for coal mines

Based on an examination of standardized regression

coefficients (table 5), the following variables best explain
variations in damage and thus statistically have the most
significant influence on coal bump potential.

Energy. This variable includes the effects of the mechanical
properties of the roof and coal, depth, stress field, and joint
density, and thus directly relates to damage.

Mining method. Mining method has a bearing on coal bump
potential. The room-and-pillar method is associated with a
higher degree of damage than is longwall mining.

Pillar factor of safety. Gate pillar geometry contributes
directly to the severity of damage.

Stress gradient and yield characteristics. Mining toward
areas of high stress creates a potential for coal bumps, while
localized yielding roof and floor conditions encourage gradual
failure, which reduces the amount of damage.

CONCLUSIONS

‘A statistical-analytical approach was used to identify the most

significant factors contributing to coal bumps. Twenty-five
variables were initially considered (mechanical properties of
strata, stress fields, face and pillar factors of safety, joint spacings,
mining methods, and stress gradients, among others). Pillar and
face factors of safety were calculated using displacement-

discontinuity methods for specific geometries.

The most

important variables contributing to coal bumps were identified as

(J) energy as calculated using the mechanical properties of the
strata, depth of overburden, and joint density, (2) mining method,
(3) pillar factor of safety, and (4) stress gradient and yield
characteristics.

By combining the strength of both computational and

statistical methods, the authors are making significant progress in
predicting coal bump potential and for building confidence
intervals. Since the method relies on an extensive amount of
geotechnical data from 25 case studies in U.S. coal mines, it will
be helpful to mine planners in selecting relevant variables for

REFERENCES

Crouch, S. L., and C, Fairhurst. The Mechanics of Coal
Mine Bumps and the Interaction Between Coal Pillars,
Mine Roof, and Floor. U.S. Bur. Mines contract
0101778, Feb. 1973, pp. 25-26.

Babcock, C. O., and D. L. Bickel. Constraint—The
Missing Variable in the Coal Burst Problem. Paper in Rock
Mechanics in Productivity and Protection, Proceedings,
25th Symposium on Rock Mechanics, ed. by C. H. Dowding
and M. M. Singh (Northwestern Univ., Evanston, IL, June
25-27, 1984). Soc. Min. Eng., 1984, pp. 639-647.
Tannachione, T., and J. C. Zelanko. Pillar Mechanics of
Coal Mine Bursts: A Control Strategy. Paper in
Proceedings of the 16th World Mining Congress (Sofia,
Bulgaria, Sept. 12-16, 1994). Bulgarian Nat. Organ.
Comm, v. 5, 1994, pp. 15-23.

Maleki, H. An Analysis of Violent Failure in U.S. Coal
Mines: Case Studies. Paper in Proceedings: Mechanics
‘and Mitigation of Violent Failure in Coal and Hard-Rock
Mines, ed. by H. Maleki, P. F. Wopat, R. C. Repshar, and R.
J. Tuchman, U.S. Bur. Mines Spec. Publ. 01-95, 1995, pp-
5-25.

‘Arabasz, W. J., S. J. Nava, and W. T. Phelps. Mining
Seismicity in the Wasatch Plateau and Book Cliffs Coal
Mining District, Utah, USA: Overview and Update.
Presented at [5th International Conference on Ground
Control in Mining,Golden, CO, Aug. 13-15, 1996.
McGarr, A. Some Applications of Seismic Source
Mechanism Studies to Assessing Underground Hazard.
Paper in Rockbursts and Seismicity in Mines, ed. by N.C.
Gay and E. H. Wainwright (Proc. of Symp. on Seismicity in
Mines, Johannesburg, S. Afr., 1982). S. Afr. Inst, Min,
Metall., Symp. Series 6, 1984, pp. 199-208

National Mining Association. Facts About Coal, 1996, p.
23.

Cullen, E. B. Accident Data Analysis: A Users Guide.
Spokane Research Center, U.S. Bur. Mines, 1988, 97 pp.


Development of a Statis

ical-Analytical Approach for Assessing Coal

Bump Potential

Hamid Maleki, President
Maleki Technologies, Inc.
Spokane, WA

Eric Zahl, Civil Engineer
John Dunford, Mining Engineer
National Institute for Occupational Safety and Health
Spokane Research Center
Spokane, WA

ABSTRACT

Coal bumps are defined as sudden failures of rock and coal
near entries that are of such a magnitude that they expel large
amounts of material into a mine opening. Coal bumps are
influenced by geologic conditions, the geometric design of coal
mine excavations, and the sequence and rate of extraction.
Researchers from private industry and the National Institute for
Occupational Safety and Health have studied mechanisms of
violent failure and have identified individual factors that
contribute to coal bumps. In an attempt to develop tools for
assessing coal bump potential, the authors initiated a
comprehensive study using information from 25 case studies
undertaken in U.S. mines. Multiple linear regression and
numerical modeling analyses were used to identify the most
significant variables contributing to coal bumps (excluding bumps
related to fault-slip).

Twenty-five geological, geometrical, and geomechanical
variables were considered initially, The most important of these
variables were then identified as (1) energy as calculated using the
mechanical properties of the strata, depth of overburden, and joint
density, (2) mining method, (3) pillar factor of safety, and (4)
stress gradient and yield characteristics.

INTRODUCTION

Coal bumps are not only a safety concern in U.S. coal mines,
but have also affected safety and resource recovery in other
countries, including Germany, England, Poland, France, Mexico,
China, India and South Africa, Gradual or progressive failure,
which is commonly experienced in coal mines, has less effect on
mining continuity and safety and is generally controlled by timely
scaling, cleaning, and bolting.

Researchers from private industry, government, and academia
have studied the mechanisms of coal bumps (/-4) and mine seis-
micity (5-6) and have identified individual factors that contribute

to coal bump occurrence, including rapid changes in stress over
a short distance or time, stiffness and strength of near-seam strata,
and dynamic effects associated with failure of surrounding rocks.
In an attempt to identify the most significant variables contribut-
ing to coal bumps, the authors analyzed information from 25
sites in mines in Colorado, Utah, Virginia, and Kentucky.

RESEARCH RATIONALE

The need for an analytical methodology for assessing coal
bumps has been indicated in conference proceedings (4) and by
accident statistics gathered by the Mine Safety and Health Admin-
istration (MSHA).

Underground coal mines have a higher incidence of accidents
relative to surface coal mines (figure 1). Of particular concern is
‘the potential for an increased number of bumps in mines using the
longwall mining method, especially because trends indicate more
extensive use of this method. Energy Information Administration
data show that longwall production has risen from 20% in 1983
to 45% in 1995 as a percentage of all underground coal
production (7). Although room-and-pillar operations are more
prone to bumps, it is anticipated that as easily recovered reserves
are mined, the trend will be toward deeper mines and those in less
stable geologic settings. Both conditions are known to increase
bump potential. In addition, new advances in longwall mining
technology, such as longer panel length (up to 5,500 m ina mine
in Colorado), are creating the need to better understand bump
potential so that the problem may be addressed in new mine
designs.

MSHA statistics for 1978 through 1995 were analyzed by
National Institute for Occupational Safety and Health (NIOSH)
personnel using the U.S. Bureau of Mines’ Accident Data Anal
ysis (ADA) program (8). No field in the MSHA database specili-
cally indicates injuries resulting from coal bumps, so ADA code
categories designated as “fall of roof,” “fall of rib-side-Laci
“falling material,” or “entrapment” were compared to the remaiin-



Maleki, H. In Situ Pillar Strength and Failure Mechanisms
for U.S. Coal Seams. Paper in Proceedings of the
Workshop on Coal Pillar Mechanics and Design, comp. by
A. T. lannacchione, C. Mark, R. C. Repsher, R. J. Tuchman,
and C. C. Jones (Santa Fe, NM, June 7, 1992), U.S. Bur.
Mines Inform. Cir. 9315, 1992, pp. 73-77.

Bickel, D. Rock Stress Determinations from Overcoring:
An Overview. U.S. Bur, Mines Bull. 694, 1993, 146 pp.
Maleki, H. Development of Modeling Procedures for Coal
Mine Stability Evaluation. Paper in Rock Mechanics
Contributions and Challenges: Proceedings of the 31st
U.S. Symposiwn, ed. by W. A. Hustrulid and G. A. Johnson.
(CO School of Mines, Golden, CO, June 18-20, 1990).
Balkema, 1990, pp. 85-92.

Crouch, S. L. Analysis of Stresses and Displacements
Around Underground Excavations: An Application of
Displacement Discontinuity Method. Univ. MN
Geomechan. Rep., 1976.

Zipf, R. K., Jr. Stress Analysis in Coal Mines with
MULSIMINL. Paper in Proceedings of the 89th Meeting of
the Rocky Mountain Coal Mining Institute (Beaver Creek,
CO, 1993). Rocky Mt. Coal Min, Instit., Lakewood, CO,
1993, pp. 38-43.

Wu, X., and M. G, Karfakis. An Analysis of Strain Energy
Accumulation Around Long- wall Panels Under Strong
Roofs. Paper in Proceedings, Sth Conference on Ground
Control for Midwestern U.S. Coal Mines, ed. by Y. P.
Chugh and G. A. Beasley (Collinsville, IL, June 1994).

Dept. of Min. Eng., S. IL Univ., 1994, pp. 230-253.

SPSS. Statistical Packages for the Social Sciences,
Chicago, IL, 1995.

Starfield, A. M., and P. A. Cundall, Toward a Methodology
for Rock Mechanics Modeling. Inter. J. Rock Mech. Min.

Sci. & Geomech. Abst., v. 25, no. 3, 1988, pp. 99-106.


INJURIES PER 200,000 man-hr

4978 1980 1982 1984 1986 1988 1990 1992 1994

Figure 1.—Accident incident rates in underground and surface coal mines in the United States, 1978-1994

100%

80%

28588
B88 88

Figure 2.—Accidents in U.S. longwall mines by category, 1985-1995

8

1991

ing accident injury categories (figure 2). “Materials handling”
appeared as the largest contributor to accidents, but the great
diversity of causes of these accidents would require a significantly
larger research effort than would addressing the second largest
contributor, “falls of roof and rib.”

Coal bumps are of primary concer to miner safety in relation
to falls of roof and rib. These categories do not specifically
identify coal bumps, but provide a basis for understanding the
level of problems associated with ground control that may be
resolved with methods described in this paper.

FACTORS INFLUENCING COAL BUMPS

In an attempt to identify the most significant factors that
contribute to coal bumps, the authors analyzed geologic, geotech-
nical, and in-mine monitoring data from 25 sites in 6 room-and-
pillar coal mines and 19 longwall mines in Colorado, Utah, Vir-

1992

Handing materials
Fall rootitace

Slip or fall
Machinery

Hand tools

Powered haulage

Seeeeod

Other

ginia, and Kentucky. Both computational and statistical tech-
niques were used in the analyses. The first step involved the
identification of 25 geologic, geometric, and geomechanical
variables that might have had the potential to contribute to coal
bump occurrence (tables 1, 2, and 3). Typical frequency
histograms are presented in figures 3, 4, and 5 and show the range
of coverage provided by the selected variables.

In situ strength was estimated in 12 coal seams where uniaxial
compressive strength exceeded 14 MPa. Allowances were made
for favorable local yielding characteristics of mine roof and floor
in reducing damage severity. Pillar and face factors of safety
were calculated using displacement-discontinuity methods for
specific geometries.

Some of the variables used in the first step of the analysis are
described below.

+ Mechanical property values. Mechanical property values for


roof, floor, and coal seams were originally obtained through
laboratory tests of samples of near-seam strata, The in situ
strength of coal seams was estimated using procedures
suggested by Maleki (9).

Horizontal stresses. Maximum and minimum secondary
horizontal stresses were originally obtained using overcoring
stress measurements from one to three boreholes (10).

Pillar and face factors of safety. Pillar and face factors of
safety were obtained in individual case studies using both
two- and  three-dimensional, displacement-discontinuity
techniques (11-13). Results were compared with field data
when such data were available.

Energy release. Energy release from a potential seismic event
was calculated using both boundary-element modeling and
analytical formulations as suggested by Wu and Karafakis
(/4) to estimate energy accumulation in both roof and coal,
and energy release (6) in terms of Richter magnitude (M,,
using the following formula:

1.5M, =A x log (E) - 11.8,
where E = total accumulated energy in roof and seam, ergs,
and A = coefficient depending on joint density,

Damage rating. A damage rating to assess the severity of
coal bumps was developed by and based on the authors?
observations of physical damage to face equipment and/or
injury to personnel, as well as observations by other
researchers as cited in the literature. Damage levels were
assigned a ranking between 0 and 3. Level 1 signifies
interruptions in mining operations while level 3 signifies
damage to both face equipment and injuries to mine
personnel.

Roof beam thickness. Roof beam thicknesses varied between
1.5 and 12 m. The thickness chosen for evaluation was the
strongest beam of the near-seam strata located between | and
4 times the total seam thickness in the immediate mine roof.
Although there is some evidence that massive upper strata
have contributed to coal bumps in some mines (4), their
influence was not directly evaluated in this study because of
the lack of geological and mechanical property data.

Local yield characteristics. Local yield characteristics of
immediate roof and floor strata influence coal pillar failure
and the severity of coal bumps. This factor varied from 0 to
2, where 0 indicates insignificant yielding in the roof and
floor and 2 indicates favorable, gradual yielding.

Stress gradients. Stress gradients varied from 0 to 2,
depending on whether or not mining proceeded toward an
area of high stress (resulting either from previous mining or
rapid changes in topography) and/or abnormal geologic
conditions such as occasionally found near faults or grabens.

T T T T T T
Standard deviation=134

to |. Mean=600
N=25

FREQUENCY
>

4

2

0)

200 300 400 500 600 700 800 909
DEPTH, m

Figure 3.—Frequency diagram for depth

TT T T T fT
‘Standard deviation=0.5
Mean=3

FREQUENCY

°
1.75 2.00 2.28 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25
RICHTER MAGNITUDE, M4

Figure 4.—Frequency diagram for released energy

12 Lr
Standard deviation=10
Mean=19
N=23

FREQUENCY

6 12 18 24 30 36 42 48
PILLAR WIDTH, m

Figure 5.—Frequency diagram for pillar width