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A HYBRID STATISTICAL-ANALYTICAL METHOD FOR ASSESSING VIOLENT

FAILURE IN U.S. COAL MINES

By Hamid Maleki, Ph.D., 1 Eric G. Zahl, 2 and John P. Dunford 3

ABSTRACT

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 government agencies around the

world have studied mechanisms of violent failure and have identified individual factors that contribute to coal

bumps. To develop predictive 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 of geological and mining conditions were used to identify the most significant

factors contributing to stress bumps in coal mines.

Twenty-five factors were considered initially, including mechanical properties of strata, stress fields, face

and pillar factors of safety, joint spacings, mining methods, and stress gradients. In situ strength was

estimated in 12 coal seams where uniaxial compressive strength exceeded 2,000 psi. 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.

This work identified the most important variables contributing to coal bumps. These are (1) mechanical

properties of strata, including local yield characteristics of a mine roof and floor, (2) gate pillar factors of

safety, (3) roof beam thickness, joint spacing, and stiffness characteristics, which influence released energy,

(4) stress gradients associated with the approach of mining to areas of higher stress concentrations, and

(5) the mining method. By combining the strength of both analytical and statistical methods, new capabilities

were developed for predicting coal bump potential and for building confidence intervals on expected damage.

1

Principal, Maleki Technologies, Inc., Spokane, WA.

2Civil engineer, Spokane Research Laboratory, National Institute for Occupational Safety and Health, Spokane, WA.

3Mining engineer, Spokane Research Laboratory, National Institute for Occupational Safety and Health, Spokane, WA.
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INTRODUCTION

Coal bumps are sudden failures near mine entries that are

of such a magnitude that they expel large amounts of coal and

rock into the face area. These destructive events have resulted

in fatalities and injuries to underground mine workers in the

United States. Coal bumps are not only a safety concern in

U.S. coal mines, but also have affected safety and resource recovery in other countries, including Germany, the United

Kingdom, Poland, France, Mexico, the People's Republic of

China, India, and the Republic of 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 [Crouch and

Fairhurst 1973; Salamon 1984; Babcock and Bickel 1984;

Iannacchione and Zelanko 1994; Maleki et al. 1995] and mine

seismicity [Arabasz et al. 1997; McGarr 1984]. Seismic events

are generated as mining activities change the stress field; they

often result in either crushing of coal measure rocks (strain bump)

or shearing of asperities along geological discontinuities (faultslip). Sudden collapse of overburden rocks [Maleki 1981, 1995;

Pechmann et al. 1995] has also been associated with large seismic

events, triggering coal bumps in marginally stable pillars.

To differentiate between stable and violent failure of

rocks, Crouch and Fairhurst [1973] and Salamon [1984]

proposed a

comparison of postpeak stiffness of a coal seam and the

loading system (mine roof and floor). Linkov [1992] proposed

an energy criterion emphasizing that violent failure results

when kinetic energy is liberated above that consumed during

fracturing of the coal. In practice, it is difficult to estimate

postpeak stiffness of coal for any geometry [Maleki 1995] or

to calculate fracture energies. This led some practitioners to

use either stored elastic strain energy or changes in energy

release [Cook et al. 1966] to evaluate the likelihood of violent

failure.

In view of limitations for unambiguous calculations of

postpeak stiffness, many researchers have attempted to identify

individual factors influencing coal bumps using the data from

single-field measurement programs. Using such data analyses

and in the absence of rigorous statistical treatment of all case

studies, it is very difficult to identify geotechnical factors that

influence coal bumps, to assign confidence intervals, and to

develop predictive capabilities.

To identify the most significant factors contributing to

coal bumps, the authors analyzed geometric and geologic data

using both computational and statistical analysis techniques.

The data included information on both violent and nonviolent

failures from 25 mine sites in Colorado, Utah, Virginia, and

Kentucky, where detailed geotechnical and in-mine monitoring

results were available.

DATA ANALYSIS

The first step in developing a statistical model was to

create suitable numerical values that express geologic,

geometric, and geomechanical conditions. The second step

was to reduce the number of independent variables by

combining some existing variables into new categories and

identify highly correlated independent variables. Reducing the

number of variables is needed when there are too many

variables to relate to the number of data points. The presence

of highly correlatable variables influences which procedures

are selected for multiple regression analyses. The third step

was to develop a multivariate regression model and identify

significant factors that contribute to coal bumps.

Some geologic variables were readily available in numerical format; other geomechanical factors had to be calculated using numerical and analytical techniques. These

activities involvedC

(1) Obtaining mechanical property values for roof, floor,

and coal seams through laboratory tests of samples of nearseam strata. In situ strength of coal seams was estimated using

the procedures suggested by Maleki [1992].

(2) Calculating both maximum and minimum secondary

horizontal stresses using overcoring stress measurements from

one to three boreholes [Bickel 1993].

(3) Calculating pillar and face factors of safety for individual case studies using both two- and three-dimensional

boundary-element techniques [Maleki 1990; Crouch 1976; Zipf

1993]. Results were compared with field data when such data

were available.

(4) Calculating energy release from a potential seismic

event using boundary-element modeling and analytical formulations suggested by Wu and Karfakis [1994] for estimating

energy accumulation in both roof and coal and energy release

[McGarr 1984] in terms of Richter magnitude (M1

) using the

following formula:

1.5 M1 = a × log (E) & 11.8, (1)

where E 'total accumulated energy in roof and seam, erg,

and a 'coefficient depending on joint density.

(5) Assessing the severity of coal bumps using a damage

rating developed by and based on the authors' observations of

physical damage to face equipment and/or injury to mine personnel, as well as observations by other researchers as cited in
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Figure 1.CHistogram frequency diagram for pillar width.

Figure 3.CHistogram frequency diagram for the uniaxial compressive strength of roof.

Figure 2.CHistogram frequency diagram for the maxiumum

principal stress.

the literature. Damage levels were assigned a ranking between

0 and 3. Level 1 signifies interruptions in mining operations;

level 3 signifies damages to both face equipment and injuries

to mine personnel.

The first step of the analyses involved the identification of

25 geologic, geometric, and geomechanical variables that had

the potential to contribute to coal bump occurrence. Both

violent (bump-prone) and nonviolent conditions in 6 room-andpillar mines and 19 longwall mines were studied. Tables 1-3

summarize these data and include averages, ranges, and standard deviations. Typical frequency histograms are presented in

figures 1-3 and indicate that these case studies provided good

coverage of the variables.

Table 1.CStatistical summary of geologic variables

Variable Mean Standard

deviation Range No. ofcases

Joint sets ............................... 1.4 0.6 1-3 25

Cleat sets............................... 1.8 0.4 1-2 25

In-seam partings.......................... 1 0.9 0-3 21

Joint spacing, ft.......................... 22 18 5-50 24

Rock Quality Designation (RQD) ............. 77 18 50-100 15

Depth, ft................................ 1,640 440 900-2,700 25

Roof beam thickness, ft.................... 14 11 5-40 25

Young's modulus, million psi ................ 0.4-8 0.12 0.35-0.67 25

Young's modulus of roof and floor, million psi ... 3 1 1-4.8 25

Uniaxial strength, psi...................... 3,240 750 2,000-4,600 25

Uniaxial strength of roof and floor, psi ......... 14,700 3,460 8,000-22,000 25

Maximum horizontal stress, psi .............. 1,920 1,100 100-3,800 25

Interacting seams......................... 1.2 0.4 1-3 25

Local yield characteristics.................. 0.8 0-2 25

Table 2.CStatistical summary of geometric variables

Variable Mean Standard

 deviation Range No. ofcases

Pillar width, ft...... 63 34 30-140 23

Pillar height, ft....... 8.3 1 5.5-10 25

Entry span, ft....... 19 1 18-20 25

Barrier pillar width, ft. . 165 90 50-240 6

Face width, ft....... 550 130 200-800 25

Mining method...... 1.2 0.4 1-2 25

Stress gradient...... 0.9 0.6 0-2 25

Table 3.CStatistical summary of geomechanical variables

Variable Mean Standard

deviation Range No. ofcases

Pillar factor of safety... 0.8 0.3 0.5-1.4 23

Face factor of safety... 0.9 0.2 0.6-1.5 22

Energy (M1) ......... 3 0.5 2-4 22

Damage............ 1.4 1 0-3 25
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Roof beam thickness ranged from 5 to 40 ft. The beam chosen

for the evaluation was the strongest beam of the near-seam strata

located between one and four times the seam thickness in the mine

roof. Although there is some evidence that massive upper strata

have contributed to coal bumps in some mines [Maleki 1995], their

influence was not directly evaluated in this study because of the

lack of geological and mechanical property data.

Local yield characteristics of the 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 in both roof and floor.

Stress gradients varied from 0 to 2, depending on whether

mining proceeded toward an area of high stress (resulting from previous mining) and/or abnormal geologic

conditions, such as those occasionally found near faults or

grabens.

BIVARIATE CORRELATIONS AND DATA REDUCTION

The second step in the analyses involved correlations and

variable reductions. 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. In addition, the cause-andeffect structure in the data was identified, helping to tailor the

procedures for multiple regression analysis using forward

stepwise inclusion of dependent variables, as described later in

this paper. The new variables were as follows:

Pqratio Ratio of maximum principal horizontal stress

(P) to minimum stress (Q)

Strenrc The ratio of uniaxial compressive strength of

the roof to the coal

Jointrf Joint spacing × roof beam thickness ÷ mining 

 height

Gradyield Ratio of roof and floor yield characteristics to 

 stress gradient

Panelwd Ratio of panel width to depth

Youngrc Ratio of Young's modulus of the roof to the 

 seam

Table 4 presents the bivariate correlation coefficients between the variable "damage" and selected geologic and

geometric variables. Energy (M1), 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.

Table 4.CBivariate correlation coefficients

between damage and selected variables

Variable Coefficient

Significant variables: 1

 Damage...................... 1

 Energy....................... 0.65

 Gradyield..................... &0.57

 Jointrf........................ 0.52

 Pillar factor of safety............ &0.44

 Uniaxial strength of roof to coal .... 0.36

 Face factor of safety ............ &0.33

 No. of interacting seams......... 0.33

 Panel width to depth............ &0.31

 Mining method................. 0.26

Insignificant variables:

 Pillar width.................... 0.1

 Ratio of P to Q................. 0.1

 Young's modulus roof to coal ..... 0.07

1

Two-tailed tests.

MULTIPLE LINEAR REGRESSION ANALYSIS

The last step in developing predictive capabilities was to

complete multiple regression analyses using the numerical

values obtained through measurements and numerical modeling. This is a hybrid approach where the strengths of both

statistical and computational methods are combined. 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, build confidence intervals, etc.

The multilinear regression procedure consisted of entering

the independent variables one at a time into the equation using

a forward selection methodology. 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 meets the

criteria, the second variable with the highest partial correlation

is 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-andeffect relationship is shown when a greater depth reduces pillar
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Figure 4.CStandardized scatterplot for the dependent variable

"damage."

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 damage variable, however,

resulted in the highest multiple regression coefficient. 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 4). Residual plot

did not indicate the need to include nonlinear terms because

there was no special pattern in the residuals.

IMPORTANT VARIABLES CONTRIBUTING TO BUMP-PRONE CONDITIONS

Based on an examination of standardized regression coefficients (table 5), the following variables best explain the

variations in damage and thus statistically have the most

significant influence on coal bump potential:

$ Energy release.CThis 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.

$ Method.CMining method has a bearing on coal bump

potential. The room-and-pillar method is associated with a

higher degree of damage than longwall mining.

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

$ Stress gradient and yield characteristics.CMining toward areas of high stress creates a potential for coal bumps;

localized yielding roof and floor conditions encourage gradual

failure, reducing the severity of damage.

Table 5.CStandardized regression coefficients and

statistical significance

Variable Standardized

coefficient T-significance

Energy .............. 0.28 0.049

Pillar factor of safety.... &0.34 0.011

Method.............. 0.26 0.064

Gradyield............ &0.55 0.0004

Constant............. NAp 0.234

NAp Not applicable.

CONCLUSIONS

A hybrid statistical-analytical approach was developed to

identify the most significant factors contributing to coal

bumps. By combining the strength of both analytical and

statistical methods, the authors achieved new capabilities for

predicting coal bump potential and for building confidence

intervals o n

expected damage. Because the method relies on an extensive

amount of geotechnical data from 25 case studies in U.S. coal

mines, it should be helpful to mine planners in identifying

bump-prone conditions. This in turn will result in safer designs

for coal mines.

REFERENCES

Arabasz WJ, Nava SJ, Phelps WT [1997]. Mining seismicity in the

Wasatch Plateau and Book Cliffs coal mining districts, Utah, U.S.A. In:

Gibowicz SJ, Lasocki S, eds. Proceedings of the Fourth International Symposium on Rockbursts and Seismicity in Mines. Balkema, pp. 111-116.

Babcock CO, Bickel DL [1984]. ConstraintCthe missing variable in the

coal burst problem. In: Dowding CH, Singh MM, eds. Rock Mechanics in Productivity and Protection - Proceedings of the 25th Symposium on Rock

Mechanics. Littleton, CO: Society for Mining, Metallurgy, and Exploration,

Inc., pp. 639-647.

Bickel DL [1993]. Rock stress determinations from overcoring: an

overview. Denver, CO: U.S. Department of the Interior, Bureau of Mines,

Bulletin 694.

Cook NGW, Hook E, Petorius JPG, Ortlepp WD, Salamon MDG [1966].

Rock mechanics applied to the study of rock bursts. Int J S Afr Inst Min Metall,

pp. 435-528.

Crouch SL [1976]. Analysis of stresses and displacements around underground excavations: an application of displacement discontinuity method.

University of Minnesota Geomechanics Report.
144

Crouch SL, Fairhurst C [1973]. The mechanics of coal mine bumps and

the interaction between coal pillars, mine roof, and floor. U.S. Department of

the Interior, Bureau of Mines, OFR 53-73.

Iannacchione AT, Zelanko JC [1994]. Pillar mechanics of coal mine

bursts: a control strategy. In: Proceedings of the 16th World Mining Congress,

The Mining Industry on the Threshold of XXI Century (Sofia, Bulgaria). Vol. 5,

pp. 15-23.

Linkov AM [1992]. Dynamic phenomena in mines and the problem of

stability. University of Minnesota/MTS Systems Corp., lecture notes.

Maleki H [1981]. Coal mine ground control [Dissertation]. Golden, CO:

Colorado School of Mines, Department of Mining Engineering.

Maleki H [1990]. Development of modeling procedures for coal mine

stability evaluation. In: Hustrulid WA, Johnson GA, eds. Rock Mechanics

Contributions and Challenges: Proceedings of the 31st U.S. Symposium.

Balkema, pp. 85-92.

Maleki H [1992]. In situ pillar strength and failure mechanisms for U.S.

coal seams. In: Proceedings of the Workshop on Coal Pillar Mechanics and

Design. Pittsburgh, PA: U.S. Department of the Interior, Bureau of Mines,

IC 9315, pp. 73-77.

Maleki H [1995]. An analysis of violent failure in U.S. coal mines: case

studies. In: Proceedings - Mechanics and Mitigation of Violent Failure in Coal

and Hard-Rock Mines. Spokane, WA: U.S. Department of the Interior, Bureau

of Mines, SP 01-95, pp. 5-25.

Maleki H, Wopat PF, Repsher RC, Tuchman RJ, eds. [1995]. Proceedings -

Mechanics and Mitigation of Violent Failure in Coal and Hard-Rock Mines.

Spokane, WA: U.S. Department of the Interior, Bureau of Mines, SP 01-95.

McGarr A [1984]. Some applications of seismic source mechanism studies

to assessing underground hazard. In: Gay NC, Wainwright EH, eds. Rockbursts

and Seismicity in Mines - Proceedings of the Symposium on Seismicity in Mines,

Johannesburg, Republic of South Africa, 1982. South African Institute of

Mining and Metallurgy, Symposium Series 6, pp. 199-208.

Pechmann JC, Walter WR, Arabasz W, Nava S [1995]. The February 3,

1995, M 5.1 seismic event in the trona mining district of southwestern Wyoming.

Seismol Res Letter, Vol. 66, pp. 25-34.

Salamon MDG [1984]. Energy considerations in rock mechanics:

fundamental results. Int J S Afr Inst Min Metall, pp. 237-246.

Wu X, Karfakis MG [1994]. An analysis of strain energy accumulation

around longwall panels under strong roofs. In: Chugh YP, Beasley GA, eds. Proceedings of the Fifth Conference on Ground Control for Midwestern U.S. Coal

Mines. Southern Illinois University, Department of Mining Engineering,

pp. 230-253.

Zipf RK Jr. [1993]. Stress analysis in coal mines with MULSIM/NL. In:

Proceedings of the 89th Meeting of the Rocky Mountain Coal Mining Institute.

Lakewood, CO: Rocky Mountain Coal Mining Institute, pp. 38-43.