Information Circular 9448

Proceedings of the Second International Workshop

on Coal Pillar Mechanics and Design

Edited by Christopher Mark, Ph.D., Keith A. Heasley, Ph.D.,

Anthony T. Iannacchione, Ph.D., and Robert J. Tuchman

U.S. DEPARTMENT OF HEALTH AND HUMAN SERVICES

Public Health Service

Centers for Disease Control and Prevention

National Institute for Occupational Safety and Health

Pittsburgh Research Laboratory

Pittsburgh, PA

June 1999
International Standard Serial Number

ISSN 1066-5552
CONTENTS

Page

Abstract ...................................................................................... 1

Introduction ................................................................................... 2

A unique approach to determining the time-dependent in situ strength of coal pillars, by K. Biswas, Ph.D.

(University of Ballarat), Australia, C. Mark, Ph.D. (National Institute for Occupational Safety and Health),

and S. S. Peng, Ph.D. (West Virginia University), U.S.A .............................................. 5

Developments in coal pillar design at Smoky River Coal Ltd., Alberta, Canada, by P. Cain, Ph.D., P.Eng.

(Smoky River Coal Ltd.), Canada ................................................................. 15

Coal pillar design for longwall gate entries, by J. W. Cassie, P. F. R. Altounyan, Ph.D., and P. B. Cartwright

(Rock Mechanics Technology Ltd.), United Kingdom ................................................. 23

Analysis of longwall tailgate serviceability (ALTS): a chain pillar design methodology for Australian conditions,

by M. Colwell (Colwell Geotechnical Services), R. Frith, Ph.D. (Strata Engineering), Australia, and C. Mark,

Ph.D. (National Institute for Occupational Safety and Health), U.S.A. .................................... 33

Experience of field measurement and computer simulation methods for pillar design, by W. J. Gale, Ph.D. (Strata

Control Technology), Australia ................................................................... 49

University of New South Wales coal pillar strength determinations for Australian and South African mining

conditions, by J. M. Galvin, Ph.D., B. K. Hebblewhite, Ph.D. (University of New South Wales), Australia,

and M. D. G. Salamon, Ph.D. (Colorado School of Mines), U.S.A. ....................................... 63

Practical boundary-element modeling for mine planning, by K. A. Heasley, Ph.D., and G. J. Chekan (National

Institute for Occupational Safety and Health), U.S.A .................................................. 73

Experience with the boundary-element method of numerical modeling to resolve complex ground control

problems, by G. J. Karabin, P.E., and M. A. Evanto, P.G. (Mine Safety and Health Administration), U.S.A. ...... 89

The fracture mechanics approach to understanding supports in underground coal mines, by J. M. Kramer, Ph.D.,

G. J. Karabin, P.E., and M. T. Hoch (Mine Safety and Health Administration), U.S.A. ....................... 115

A hybrid statistical-analytical method for assessing violent failure in U.S. coal mines, by H. Maleki, Ph.D.

(Maleki Technologies, Inc.), E. G. Zahl, and J. P. Dunford (National Institute for Occupational Safety and

Health), U.S.A. ............................................................................... 139

Empirical methods for coal pillar design, by C. Mark, Ph.D. (National Institute for Occupational Safety and

Health), U.S.A. ............................................................................... 145

Coal pillar strength and practical coal pillar design considerations, by D. W. H. Su, Ph.D., and G. J. Hasenfus

(CONSOL, Inc.), U.S.A. ........................................................................ 155

New strength formula for coal pillars in South Africa, by J. N. van der Merwe, Ph.D. (Itasca Africa (Pty.) Ltd.),

Republic of South Africa ........................................................................ 163

The role of overburden integrity in pillar failure, by J. N. van der Merwe, Ph.D. (Itasca Africa (Pty.) Ltd.),

Republic of South Africa ........................................................................ 173

Using a postfailure stability criterion in pillar design, by R. K. Zipf, Jr., Ph.D. (University of Missouri-Rolla),

U.S.A ....................................................................................... 181
UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT

ft foot (feet) kPa/m kilopascal per meter

GPa gigapascal m meter

ha hectare mm millimeter

hr hour MN/m meganewton per meter

in inch MN/m3 meganewton per cubic meter

in/in inch per inch MPa megapascal

kg/cm2

kilogram per square centimeter psi pound (force) per square inch

kg/m3

kilogram per cubic meter psi/ft pound (force) per square inch per foot

km kilometer sec second

km2

square kilometer % percent

kN/m3

kilonewton per cubic meter ° degree

The views expressed by non-NIOSH authors in these proceedings are not necessarily those of the National Institute for

Occupational Safety and Health.

Mention of any company name or product does not constitute endorsement by the National Institute for Occupational Safety and

Health.

To receive other information about occupational safety and health problems, call 1-800-35-NIOSH (1-800-356-4674), or visit

the NIOSH Home Page on the World Wide Web at http://www.cdc.gov/niosh
PROCEEDINGS OF THE SECOND INTERNATIONAL WORKSHOP

ON COAL PILLAR MECHANICS AND DESIGN

Edited by Christopher Mark, Ph.D.,1 Keith A. Heasley, Ph.D.,1

Anthony T. Iannacchione, Ph.D.,2 and Robert J. Tuchman3

ABSTRACT

Pillar design is the first line of defense against rock falls—the greatest single safety hazard faced by

underground coal miners in the United States and abroad. To help advance the state of the art in this

fundamental mining science, the National Institute for Occupational Safety and Health organized the Second

International Workshop on Coal Pillar Mechanics and Design. The workshop was held in Vail, CO, on June 6,

1999, in association with the 37th U.S. Rock Mechanics Symposium. The proceedings include 15 papers from

leading ground control specialists in the United States, Canada, Australia, the United Kingdom, and the

Republic of South Africa. The papers address the entire range of issues associated with coal pillars and have

a decidedly practical flavor. Topics include numerical modeling, empirical design formulas based on case

histories, field measurements, and postfailure mechanics.

1

Supervisory physical scientist.

2Deputy director.

3Technical writer-editor. 

Pittsburgh Research Laboratory, National Institute for Occupational Safety and Health, Pittsburgh, PA.
2

INTRODUCTION

By Christopher Mark, Ph.D.1

Pillar design is one of the oldest and most fundamental of the

mining sciences. Without pillars to support the great weight of

the overburden, underground coal mining would be practically

impossible. Coal pillars are employed in a wide variety of mining operations, from shallow room-and-pillar mines to deep

longwall mines. Yet despite more than 100 years of research

and experience, pillar failures continue to occur, placing miners'

lives at risk. Some recent examples are [Mark et al. 1998]:

Massive collapses: In 1992, miners were splitting pillars at

a mine in southern West Virginia when the fenders in a 2.3-ha

area suddenly collapsed. The miners were knocked to floor by

the resulting airblast; 103 ventilation stoppings were destroyed.

At least 12 similar events have occurred in recent years in the

United States and 15 others in Australia, fortuitously without a

fatality.

Pillar squeezes: At a coal mine in Kentucky, pillars were

being extracted in the main entries under 270 m of cover. The

pillars began to crush in response to the vertical load, resulting

in a roof fall that killed two miners. This incident is an extreme

example of hazardous conditions that can be associated with

slow pillar failure. At least 45 recent instances of pillar

squeezes in room-and-pillar mines have been identified.

Longwall tailgate blockages: In 1984, 26 miners at the

Wilberg Mine in Utah could not escape a deadly fire because of

a tailgate roof fall. Similar blockages were common in the

1980s, and 50 cases have been documented.

Pillar bumps: Extracting the initial lift from a standing pillar at

a deep operation in eastern Kentucky resulted in a bump that killed

two miners. However, bumps are not confined to pillars; another

fatal bump occurred at a longwall face in Utah just days later.

Multiple-seam interactions: Some studies indicate that most

remaining coal reserves will experience multiple-seam interactions. At a mine in West Virginia where four seams had been

previously extracted, one fatality occurred when the roof collapsed without warning beneath a remnant barrier pillar.

Abandoned mine subsidence: As suburban development

expands into historic coal mining areas, unplanned subsidence

has become an important issue. In one case, residents above

50-year-old workings were disturbed by seismicity emanating

from collapsing pillars. In the Republic of South Africa, collapsing pillars in the Vaal Basin are creating large sinkholes

that threaten many homes.

To help reduce the safety hazards of pillar failures, this

Second International Workshop on Coal Pillar Mechanics and

1

Supervisory physical scientist, Pittsburgh Research Laboratory, National

Institute for Occupational Safety and Health, Pittsburgh, PA.

Design was organized. (The first workshop was held in Santa

Fe, NM, in 1992.) The proceedings of the second workshop

feature 15 invited papers from leading rock mechanics experts

in the United States, Australia, the Republic of South Africa,

the United Kingdom, and Canada. Mines in these five countries

employ increasingly similar methods, including:

• Retreat longwall mining, usually using large chain pillars;

• Room-and-pillar mining with continuous mining machines;

and

• Roof bolts for primary roof support.

The similarity of mining methods means that it is easier and

more valuable to transfer safety technologies like pillar design

from one country to another. Indeed, one of the striking features of these proceedings is the convergence of research results

across international borders.

Other trends affecting the mining industries of the five

countries are also reflected in these proceedings, some of which

have been less positive. In the 7 years since the first workshop,

underground production has risen in Australia and the Republic

of South Africa, declined in the United Kingdom and Canada,

and remained steady in the United States. However, great

employment losses have occurred in all five countries because

of technological advances and dramatic productivity increases.

One consequence has been a significant decline in institutional support for mining research. Since 1992, the U.S. Bureau of Mines (USBM), the Canada Centre for Mineral and

Energy Technology's (CANMET) Coal Research Laboratory,

British Coal's Headquarters Technical Division, and the South

African Chamber of Mines research department have all closed

their doors. Government funding for mining research is now

indirect and open for competition everywhere, except in the

United States. In the United States, the National Institute for

Occupational Safety and Health (NIOSH) has taken up the

USBM's traditional mine safety research role, although at a

reduced level, and continues to receive direct funding from the

U.S. Congress.

University mining departments have also been under pressure due to fluctuating student enrollments, reduced research

funding, and a shortage of qualified junior faculty. Lower profit margins and a renewed emphasis on the bottom line has

meant that few mining companies now maintain any in-house

research capability. As the traditional sources of mining research have faltered, in many cases private consulting firms

have taken up the challenge. Often staffed by former government researchers and sometimes supported in part by government contracts, consultants are now often on the cutting edge of

research.
3

Figure 1.CEmpirical pillar strength formulas derived from

case histories by Mark (U.S.A.), Galvin (Australia), and van der

Merwe (Republic of South Africa).

In comparing the proceedings of the second workshop with

those of the first [Iannacchione et al. 1992], the most obvious

difference is that the current collection of papers is a slimmer

volume. There are 15 papers in these proceedings, compared

with 23 in 1992. Australia, which in many ways has the

healthiest mining research community, is the only country to

see its representation increase (see table 1). Although the

number of papers from industry, government, and academia all

decreased by at least 50%, the number of papers from private

consultants more than doubled.

Another consequence of the changed research environment

is reflected in the proceedings' pervasive emphasis on practical

problem-solving. Although about one-half of the papers at the

first workshop addressed issues of a more theoretical nature,

nearly every paper in the current collection uses case histories,

field measurements, and/or practical experience to develop

techniques for solving real-world pillar design problems.

The papers divide almost evenly between those that focus

primarily on the application of numerical modeling and those

that discuss empirical formulas derived from statistical analysis

of case histories (table 1). Of the numerical modelers, two used

finite-difference methods (Gale, Cassie et al.), four used

boundary elements (Heasley-Chekan, Maleki et al., Zipf,

Karabin-Evanto), and one used finite elements (Su-Hasenfus).

Field measurements feature prominently in six papers, with

Cassie et al., Colwell et al., and Gale monitoring stress and

deformation, Heasley-Chekan and Karabin-Evanto mapping

underground conditions, and Biswas et al. measuring changes

in rock strength.

In general, however, the similarities between the papers are

more striking than their dissimilarities despite the variety of

countries, author affiliations, and research methods. For

example, new empirical formulas are presented for the Republic

of South Africa (van der Merwe), the United States (Mark), and

Australia (Galvin et al.). Derived independently from different

sets of case histories from around the world, the three formulas

are within 15% of each other (see figure 1).

Five papers (Su-Hasenfus, Gale, Cassie et al., Mark, and

Colwell et al.) explicitly address the design of squat (large

width-to-height (w/h) ratio) pillars, primarily for protection of

longwall gate entries. All agree that the strength of these pillars

can vary widely depending on the roof, floor, and seam parting

characteristics. Moreover, the strength of the roof is often just

as important to the design process as the strength of the pillar

itself. The degree of consensus that has been achieved on this

complex topic is an important advance. At the other end of the

w/h scale, van der Merwe, Zipf, and Mark address slender

pillars and their potential for sudden collapse. Again, all three

reach similar conclusions regarding the importance of pillar

geometry and postfailure pillar stiffness.

The beginnings of a consensus are also evident in one of the

oldest pillar design controversies—the value of compressive

strength tests on coal specimens. Only two papers (KarabinEvanto and Maleki et al.) make use of laboratory tests to

evaluate seam strength. On the other hand, van der Merwe, SuHasenfus, Cassie et al., Galvin et al., Gale, and Mark all

conclude that variations in the uniaxial compressive strength

have little effect on the in situ pillar strength.

With the focus on pillar strength, it is important not to

overlook the other half of the design equation—the load. Gale

and Colwell et al. describe field measurements that shed new

light on the loads that occur during longwall mining. HeasleyChekan and van der Merwe address the effect of overburden

behavior on the pillar loading. Kramer et al. have extended

their fracture mechanics approach for estimating load

distribution to consider the effects of other kinds of supports.

Other special topics that are discussed in these proceedings

include the effect of weathering on long-term pillar strength

(Biswas et al.), the geologic and geotechnical factors that affect

the potential for coal bumps (Maleki et al.), thick-seam roomand-pillar mining (Cain), multiple-seam mine design (HeasleyChekan), and the strength of rectangular pillars (Galvin et al.

and Mark).

One final comparison between the first and second

workshops is perhaps in order. The proceedings of the first

workshop [Iannacchione et al. 1992] included papers from a

number of now retired individuals whose names have been

synonymous with pillar design for nearly 3 decades: Salamon,

Bieniawski, Wagner, Barron, and Carr. In many ways, their

contributions laid the foundation upon which rests much of our

current understanding of coal pillars. Their retirement has left

a large gap that cannot be filled (although it is hoped that they

will continue to contribute to the profession!). To paraphrase

Sir Isaac Newton, it is only by standing on the shoulders of

such giants that we can hope to achieve further progress.
4

Table 1.CSummary of papers for the Second International Workshop

on Coal Pillar Mechanics and Design

Primary author Country Affiliation Method

Biswas ....... Australia .... University ....... Empirical.

Cain ......... Canada ..... Mining company . . Empirical.

Cassie ........ U.K. ........ Consultant ....... Numerical.

Colwell ....... Australia .... Consultant ....... Empirical.

Gale ......... Australia .... Consultant ....... Numerical.

Galvin ........ Australia .... University ....... Empirical.

Heasley ....... U.S.A. ...... Government ..... Numerical.

Karabin ....... U.S.A. ...... Government ..... Numerical.

Kramer ....... U.S.A. ...... Government ..... Numerical.

Maleki ........ U.S.A. ...... Consultant ....... Empirical/numerical.

Mark ......... U.S.A. ...... Government ..... Empirical.

Su ........... U.S.A. ...... Mining company . . Numerical.

van der Merwe . South Africa . Consultant ....... Empirical.

Zipf .......... U.S.A. ...... University ....... Numerical.

REFERENCES

Iannacchione AT, Mark C, Repsher RC, Tuchman RJ, Jones CC, eds.

[1992]. Proceedings of the Workshop on Coal Pillar Mechanics and Design.

Pittsburgh, PA: U.S. Department of the Interior, Bureau of Mines, IC 9315.

Mark C, Su D, Heasley KA [1998]. Recent developments in coal pillar

design in the United States. In: Aziz NI, Indraratna B, eds. Proceedings of the

International Conference on Geomechanics/Ground Control in Mining and

Underground Construction. Wollongong, New South Wales, Australia:

University of Wollongong, Vol. 2, pp. 309-324.
5

A UNIQUE APPROACH TO DETERMINING THE TIME-DEPENDENT

IN SITU STRENGTH OF COAL PILLARS

By Kousick Biswas, Ph.D.,1 Christopher Mark, Ph.D.,2

and Syd S. Peng, Ph.D.3

ABSTRACT

In general, it cannot be assumed that the strength of coal pillars remains constant over long periods of time.

Field observations indicate that a coal seam, especially when it contains a parting layer, deteriorates over time,

reducing the load-bearing capacity of the pillars. This paper discusses a unique approach to determining the

time-dependent strength of coal pillars in the field. Three coal pillars that were developed 5, 15, and 50 years

ago were chosen for the study. Holes were drilled in coal and parting layers in each pillar, and the strength

profiles were determined for each hole using a borehole penetrometer. The strength data were treated

statistically to establish time-dependent strength equations for different layers. The results can be used to help

estimate the loss of pillar capacity over time.

1

Lecturer, School of Engineering, University of Ballarat, Victoria, Australia.

2

Supervisory physical scientist, Pittsburgh Research Laboratory, National Institute for Occupational Safety and Health, Pittsburgh, PA.

3Chairman and Charles T. Holland professor, Department of Mining Engineering, West Virginia University, Morgantown, WV. 
6

Sv'

(H(W%We)(L%We)

(WL)

, (1)

S

p

' S10.64 % 0.36 W

h

, (2)

SF '

Pillar strength

Pillar stress

'

S

p

Sv

. (3)

INTRODUCTION

All manmade structures deteriorate over time; pillars in

underground coal mines are no exception. There are numerous

examples of coal pillars failing many years after they were

developed. Scrutiny of existing pillar design theories indicates

that few make any attempt to consider the effect of time.

Similarly, there is rarely an attempt to consider the

inhomogeneous nature of most coal seams. For example, the

classic pillar design methodology involves the following three

steps:

1. Calculate the vertical stress on the pillar:

where Sv ' vertical stress,

( ' unit weight of the overburden,

H ' depth of the seam,

W ' pillar width (minimum pillar dimension),

L ' pillar length (maximum pillar dimension),

and We ' entry width.

2. Calculate the pillar strength using Bieniawski's formula

[Bieniawski 1992]:

where Sp ' pillar strength,

S1 ' in situ seam strength,

and h ' seam height.

3. Calculate the stability factor (SF) as

The stability factor that is calculated using equations 1-3

assumes that—

• The coal strength is constant and does not deteriorate over

 time; and

• Coal seams are homogenous.

Back-analyses of subsidence above abandoned mines using

the classic methodology have found that pillar failures have

occurred over a broad range of stability factors [Marino and

Bauer 1989; Craft and Crandall 1988]. The implication is that

over time the standard pillar design methodology loses its

ability to accurately predict the strength of coal pillars.

One recent South African study focused on the phenomenon

of pillar scaling over time [van der Merwe 1998]. Twentyseven case histories of pillar failure, occurring as long as

15 years after mining, were included in the database. Three

parameters were found to be statistically significant: coal seam,

pillar height, and time to failure. The study concluded that the

scaling rate decreases exponentially over time and further

hypothesized that "the inner portions of the pillar, being

protected from the atmosphere, would then weather at a lower

rate."

This paper describes a detailed study of the time-dependent

structural deterioration of coal pillars and proposes a means to

estimate the strength reduction of the coal seam in situ by

taking into account the seam heterogeneity.

FIELD OBSERVATIONS

A survey conducted by West Virginia University, Department of Mining Engineering, of room-and-pillar mines in the

eastern Appalachian region found that some of the coal seams

contain one or more mudstone or claystone layers with variable

thicknesses [Tsang et al. 1996]. For example, the Pittsburgh

and Twin Freeport Seams contain parting layers in the coal

seam. During field visits to several coal mines developed in

these seams, the conditions of many pillars in worked-out

districts, some as much as 100 years old, were visually

inspected. Most of the pillars did not show any apparent sign

of instability because of their large size compared to their depth

(stability factors ranged from 2 to 12).

A more detailed inspection revealed several kinds of

weathering actions on the different layers of the coal seam with

varying degrees of severity. The following structural deteriorations were noticed on older pillars:
7

Figure 1.CPeeling of weathered parting in coal seam.

 Figure 2.CConceptualization for strength deterioration for

parting. (Note: time1 < time2 < time3.)

 Figure 3.CConceptualization for strength deterioration for

coal. (Note: time1 < time2 < time3.)

• Conversion of mudstone/claystone layer to clay due to

prolonged exposure to the mine moisture;

• Squeezing of the softer parting layer by the top and bottom

portion of the coal;

• Major peeling of the parting layer;

• Separation of the parting from the host coal along the slick

interfaces (perhaps the result of differential slippage); and

• Minor peeling of the top and bottom portion of the coal.

Figure 1 illustrates this deterioration in the structure of a pillar.

From the field observations, it was concluded that the

structural deteriorations in both coal and parting are dependent

on time. From these observations, aided by some laboratory

studies and finite-element modeling [Biswas 1997], it was

possible to postulate a conceptual model of the time-dependent

strength profiles in the coal and parting layers (figures 2 and 3).

Its assumptions are that—

• The pillars are not affected by any mining activity in their

vicinity; and

• The majority of the yield zones depicted in figures 2 and

3 are the result of the weathering action on the different layers

in the pillar.

IN SITU DETERMINATION OF TIME-DEPENDENT STRENGTH

The goal of this study was to determine one set of timedependent strength profiles under in situ conditions. A detailed

testing program was designed to establish the strength reduction

in various layers of a pillar in situ over time.

THE STUDY SITE

The study was conducted at the Safety Research Coal Mine

at the National Institute for Occupational Safety and Health's

(NIOSH) Pittsburgh Research Laboratory. The Safety Research Coal Mine was selected for the following reasons:

• The overburden depth is very shallow, ranging from 15 to

18 m (50 to 60 ft); thus, any deterioration of the pillars is

attributable to the effect of weathering rather than stress.

• The mine is developed in the Pittsburgh Seam, and it

contains a parting of varying thickness (from 0.15 to 0.3 m (6

to 12 in)).

• The mine has accessible pillars developed as recently as

1991 and as long ago as the 1940s.

• The mine remains more or less inactive in terms of mining

activities.
8

Figure 4.CMine plan indicating three faces chosen for the BPT tests.

Three pillars were chosen in the mine based on their current

conditions and the thickness of the parting. The three pillars

were developed 5, 15, and 50 years ago. Due to other technical

difficulties, more faces could not be chosen for this experiment.

Figure 4 shows the mine plan and the location of the study sites.

THE APPARATUS

A borehole penetrometer (BPT) was used to measure the

strength profiles in the coal and parting layers. The basic

principle followed by the BPT is to fracture the borehole wall

by means of an indenter and record the pressure that initiates

the first fracture [Hladysz 1995]. The recorded failure pressure

is then converted by a formula to determine the uniaxial

compressive strength (UCS) at that location in the borehole.

The BPT's great advantages are that the rock strength is tested

in situ, and multiple tests can be conducted within a single

borehole [Zhang et al. 1996].

The BPT consists of the following components:

• Head

• Hydraulic pump with oil reservoirs and pressure

transducers

• Displacement indicator

• Four-wire electric cable

• High-pressure hydraulic hose with quick couplers

• Set of extension rods
9

Figure 5.CBPT test setup. Figure 6.CTypical raw BPT test data analysis for parting.

The BPT test setup is illustrated in figure 5. To perform the

test, the head of the device is inserted into a standard NX drill

hole with the help of a set of extension rods. When the head is

positioned at the desired depth, the indenter is forced into the

borehole wall using the hydraulic pump. At the critical

pressure, the indenter penetrates the rock rapidly, making a

small crater around the indenter's tip. This event is indicated by

a rapid movement of the needle on the displacement indicator

and by a sudden drop in pressure (figure 6). In hard and brittle

rock, an audible sound is often associated with rock failure.

The critical pressure causing the rock to break is a function of

rock separation resistance (or penetration resistance).

Penetration resistance is proportional to the material properties

of the rock mass and the state of stresses. By repositioning the

head and repeating the test procedures along the entire length of

the hole, a penetration profile (or strength profile) for the tested

section of the rock mass can be determined.

To achieve accuracy, a pressure transducer, a data acquisition module, and a digital readout unit are used. The failure

pressure and ram displacement data recorded at a specified time

interval are stored during an individual test and later transferred

to a computer to determine the failure pressure. A portable

battery-operated recorder unit records the collected data. The

pressure transducer that is connected to the hydraulic pump

generates the pressure signal; the displacement signal comes

from a linear variable differential transformer (LVDT) that is

linked to the indenter. The recorded data are stored in the data

logger unit memory and later played back using a personal

computer driven by application software. The data from a

typical BPT test include the pressure, displacement of ram

or indenter, time and an identification for the hole No., test

depth, test date, etc. More details about the instrument, its

specifications, principles, and testing procedure can be found

elsewhere [Hladysz 1995].

THE EXPERIMENT

For each BPT test, the following steps were conducted:

 1. Connect the hydraulic hoses to the head and to the pump.

 2. Connect the cable to the head and to the data acquisition

displacement input terminals.

 3. Connect the cable to the pressure transducer and to the

data acquisition pressure input terminals.

 4. Set up the recording session parameters in the data

logger unit (e.g. date, ID No., etc.).

 5. Insert the head into the borehole and position the device

at the desired depth.

 6. Close the main valve of the pump.

 7. Initiate a data recording session.

 8. Increase pressure slowly at a constant rate, continuing to

pump until failure occurs.

 9. Open the valve to allow the indenter to retract fully and

stop recording.

10. Reposition the penetrometer head and repeat steps 4

to 9.

Two NX boreholes were drilled in each test pillar, one in

coal and one in the parting. The holes were each 3 m (10 ft)

long. About 15-20 tests were conducted along each borehole.

The testing frequency was higher near the pillar edge; it was

postulated that the rib edge would be more disturbed than the

intact central portion of the pillar. All of the data for each test

were collected in the storage module during the tests and later

transferred to a computer for more detailed analysis. The data

for each test point were manipulated in a spreadsheet program;

finally, a graph was plotted for each test point. The graph

consists of time on the X-axis, failure pressure on the primary

Y-axis, and the relative displacement rate of the indenter on the

secondary Y-axis. Typical graphs for the parting and the coal

are shown in figures 6 and 7, respectively. The failure pressure

in the hard rock, in general, is characterized by a distinct jump

(increase) in the ram displacement.

DATA ANALYSIS

The first step in analyzing the data was to determine the

failure pressures at all test points. Then, the following conversion formula was used to convert the failure pressure to the

UCS:
10

UCS ' (Fs)Pf, (4) y ' a(1.01 & e

&bx) , (5)

Figure 7.CTypical raw BPT test data analysis for coal.

Figure 8.CBest-fit curve for 5-year-old parting.

Figure 9.CBest-fit curve for 15-year-old parting.

Figure 10.CBest-fit curve for 50-year-old parting.

where Fs ' strength factor,

and Pf ' failure pressure from the BPT test.

For coal, the value of the strength factor was 1.25, as suggested

by Zhang et al. [1996]. For the parting, a value of 1.00 was

used based on laboratory studies of the cores of the parting

obtained from the BPT test holes [Biswas 1997].

The scatter plots of the converted strength values were

obtained for each hole in each face. Because these scatter plots

showed considerable variability in the trend of the strength

deterioration, which is a typical characteristic of any experiment

conducted in situ, a curve-fitting program called Curve Expert

was used to fit the best curve with the highest correlation

coefficient. Figures 8-10 illustrate the best-fit curves for the

parting, and figures 11-13 illustrate the best-fit curves for the

coal for all three faces.

The general form of all of the best-fit equations for both coal

and parting is

where a and b are the coefficients,

y is the failure pressure or the strength,

and x is the depth (in this case, the range is from 0.06 to

 3 m (0.2 to 10 ft).

The negative exponential and its negative power give the

best-fit curves their asymptotic form. The correlation

coefficients for the best-fit equations for the parting and coal for

each age group are 0.84, 0.85, 0.89 and 0.96, 0.88, 0.94,

respectively.

For the parting, the gradient in the weathered zone for the

younger face is initially steeper, but the slope flattens as the age

increases. This change in strength gradient before it reaches the

intact or stabilized strength is considerable. The weathered

zone apparently expands from 1 to 3 m (3.2 to 10 ft) over the

50 years. For coal, the strength gradient for all of the age

groups is steeper than that of the parting, and the expansion of
11

Figure 11.CBest-fit curve for 5-year-old coal.

Figure 12.CBest-fit curve for 15-year-old coal.

Figure 13.CBest-fit curve for 50-year-old coal.

Figure 14.CTime-dependent strength deterioration for parting.

Figure 15.CTime-dependent strength deterioration for coal.

the weathered zone is much less (from 0.2 to 1 m (0.7 to

3.2 ft)). These findings fit the conceptual model of the strength

degradation for parting and coal over time described earlier.

Figures 8-13 also indicate that there is some borehole-toborehole variability in the intact strength measured in the

interior of the pillars for both the coal and the parting. This

variability may be attributed to natural variability between the

three different faces. In order to generalize the results, the data

from each borehole were normalized to the measured intact

strength. The normalized strength curves are shown in

figures 14 and 15.

FORMULATION OF TIME-DEPENDENT

STRENGTH DETERIORATION

The BPT data can be used to derive a time-dependent

strength formula for the pillars in the study. Using the best-fit

equations shown in figures 14-15, data sets were generated for

each material for all three ages. The data sets were generated

for the depth ranges from 0.06 to 3 m (0.2 to 10 ft). No data

could be generated right at the ribline because no BPT tests

were conducted there. A nonlinear regression analysis was

conducted on these data sets separately for the coal and for the

parting with two independent variables (time and depth) and

one dependent variable (strength). A freeware software called

NLREG34 was used to perform the nonlinear regression.

Equation 6 is the stress gradient for the parting, and equation 7

is the final equation for coal:
12

Figure 16.CSafety factor reduction over time.

% parting strength ' 100 (1.01 & e&0.5 D) & 0.45t (6)

% coal strength ' 100 (1.01 & e&3.5 D) & 0.13t (7)

where D ' depth into the rib, ft,

and t ' time after mining, years.

In these equations, the strength is defined as a percent of the

original intact compressive strength that is assumed to be

constant in the core of the pillar. Near the rib, the strength is a

function of the distance from the rib (depth) and the time after

mining. The relationship between the strength and the depth is

a negative exponential, but that between strength and time is

linear.

Unfortunately, applying these time-dependent strength

equations to predict the strength of full-scale pillars is not

simple. Three issues are foremost:

1. Effect of parting thickness: If the parting is the pillar's

weakest layer, as in this study, then a thicker parting would be

expected to result in a weaker pillar.

2. Effect of parting on confining stress within the pillar:

Most of the load-bearing capacity of a coal pillar is due to the

development of confining stress within the pillar's core. Studies

have shown that many pillars contain weak layers of clay or

friable coal, but their effect on overall pillar strength is

ambiguous [Mark and Barton 1996].

3. Nonlinear effect of time: In reality, the rate of strength

degradation probably decreases with time, as suggested by van

der Merwe [1998]. Because this study included only three

pillars, it was difficult to quantify the nonlinear relationship

between time and strength. 

Nevertheless, if the limitations of the necessary assumptions

are kept in mind, it is possible to use the strength gradient

equations to shed light on the possible effects of time on coal

pillar stability. The following example illustrates one possible

approach. The key assumption is that at any particular time,

the distance from the actual pillar rib and the depth at which

the strength is 60% of the intact strength will be considered as

the width of the portion of the weathered zone that is not

capable of carrying any load and thus transfers the load on the

intact portion of the pillar. The effect of this assumption is that

the pillar's strength is decreased over time as the width-toheight ratio diminishes, whereas the applied stress increases as

the pillar's load-bearing area is reduced.

To calculate the time-dependent stability factor, the following steps are followed:

1. Calculate the original stability factor using equations 1-3.

2. Determine the strength profile at a specified time using

equation 3 or 4, and determine the depth of weathering (where

the strength is 60% of the intact).

3. Calculate the resultant pillar width by subtracting the

depth of weathering from the original pillar width.

4. Recalculate the applied stress using equation 1 and the

new pillar dimensions.

5. Use equation 2 to determine the new pillar strength and

equation 3 to calculate the reduced stability factor at the

specified time.

6. Repeat this process to determine the approximate lifespan

of the pillar.

For example, assume the following parameters:

• The overburden depth is 244 m (800 ft).

• The pillar is a square pillar with a 15.2-m (50-ft)

dimension.

• The seam height is 1.8 m (6 ft).

• The entry width is 6.1 m (20 ft).

• The in situ seam strength is 6.2 MPa (900 psi).

Because the parting is the weakest layer of the seam in this

case, to be on the conservative side, equation 6 (for the parting)

is used to determine the strength profile and also the width of

yielded zone due to the weathering process. From a statistical

point of view, it is recommended that equations 6 and 7 be used

within the same time range as the original field data used in

their development, i.e., 5 to 50 years [Myers 1990].

Figure 16 illustrates the changes in strength and applied

stress over time. Where the two curves meet, at time '

35 years, the stability factor is 1.0, which means that the pillar

has a 50% chance of failing before that time.
13

CONCLUSIONS

The use of the BPT to measure the in situ time-dependent

strength is the unique feature of this study. It generated a set of

in situ strength data in a relatively simple field-testing program.

The in situ data were used to develop time-dependent strength

equations for coal and parting layers. An example case was

used to demonstrate the use of these equations in predicting the

change of stability factor over the years.

The parting material weathered much more rapidly than the

coal. This implies that much of the observed between-seam

variability in long-term pillar strength may be due to the

presence or absence of partings in the coal. However, this

study only addressed a single type of parting material within a

single coal seam. Much work remains before the effect of time

on coal pillar strength is fully understood.

ACKNOWLEDGMENTS

The authors are grateful for the opportunity to use the Safety

Research Coal Mine at NIOSH's Pittsburgh Research

Laboratory (PRL) for the in-mine studies. The expertise and

assistance of PRL employees David C. Oyler, mechanical

engineer, and Craig S. Compton, engineering technician, were

also invaluable.

REFERENCES

Bieniawski ZT [1992]. A method revisited: coal pillar strength formula

based on field investigations. 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. 158-165.

Biswas K [1997]. Study of weathering actions on partings and their effects

on long-term stability of coal pillar [Dissertation]. Morgantown, WV: West

Virginia University, Department of Mining Engineering.

Craft JL, Crandall TM [1988]. Mine configuration and its relationship to

surface subsidence. Paper in Proceedings, Mine Drainage and Surface Mine

Reclamation, USBM IC 9184, Vol. 3, pp. 373-382.

Hladysz Z [1995]. Borehole rock strength tester manual. Rapid City, SD:

Hladysz Rock Testers and Consulting.

Marino GG, Bauer RA [1989]. Behavior of abandoned room-and-pillar

mines in Illinois. SME preprint 89-3. Littleton, CO: Society for Mining,

Metallurgy, and Exploration, Inc.

Mark C, Barton TM [1996]. The uniaxial compressive strength of coal:

should it be used to design pillars? In: Ozdemir L, Hanna K, Haramy KY,

Peng S, eds. Proceedings of the 15th International Conference on Ground

Control in Mining. Golden, CO: Colorado School of Mines, pp. 61-78.

Myers RH [1990]. Classical and modern regression with applications.

Boston, MA: PWS-KENT Publishing Co., pp. 424-449.

Tsang P, Peng SS, Biswas K [1996]. Current practice of pillar design in

U.S. coal mines. Min Eng 48(12):55-60.

van der Merwe JN [1998]. Practical coal mining strata control.

Johannesburg, Republic of South Africa: Itasca Africa (Pty.) Ltd., 2nd ed.,

appendix B.

Zhang YJ, Unrug KF, Thompson ED [1996]. New approach to determine

the in-situ strength of coal in mine pillars. Min Eng 48(10):49-53.
15

DEVELOPMENTS IN COAL PILLAR DESIGN AT SMOKY RIVER 

COAL LTD., ALBERTA, CANADA

By Peter Cain, Ph.D., P.Eng.1

ABSTRACT

Smoky River Coal Ltd. mines low-volatile metallurgical coal by surface and underground methods in the

foothills of the Rocky Mountains of Alberta, Canada. Current underground operations are confined to the

5B-4 Mine. Development of 5B-4 began in January 1998; production from depillaring sections commenced

in July 1998.

This paper describes the history of underground mining on the Smoky River property in terms of extraction

methods and pillar design. The development of the present pillar design guidelines is discussed in this context.

Recent work to prepare a number of case histories for back-analysis using the Analysis of Retreat Mining Pillar

Stability (ARMPS) method is described, along with the modifications developed for calculating the ARMPS

stability factor for retreat extraction of thick seams. The design criteria are described, as well as the

geotechnical program implemented in order to verify its applicability.

1

Senior ground control engineer, Smoky River Coal Ltd., Grande Cache, Alberta, Canada.
16

Figure 1.—Location of Smoky River Coal Ltd.

Figure 2.—Site layout.

 Figure 3.—Generalized stratigraphic column, Smoky River

Coalfield.

INTRODUCTION

The Smoky River Coalfield is located in west-central Alberta, Canada, within the inner foothills of the Rocky Mountains. The mine is approximately 20 km north of Grande Cache

and 360 km west of Edmonton (figure 1). Most of the property

is contained in a block approximately 29 km long by 19 km

wide. The coal leases cover about 30,000 ha. The general mine

layout is shown in figure 2. Underground mining is currently

located in the 5 Mine area.

The coal seams and surrounding strata are within the Gates

Formation (of the Lower Cretaceous Luscar Group) and outcrop

near the mine. The Gates Formation is divided into three members: Torrens, Grande Cache, and Mountain Park (figure 3). The

Torrens is a distinct marine sandstone and siltstone sequence

about 30 m thick. It is overlain by the Grande Cache Member,

which consists of approximately 158 m of nonmarine siltstones,

sandstones, mudstones, and all of the significant coal seams in the

area. The Grande Cache Member is overlain by the Mountain

Park Member, which consists of 155 to 192 m of nonmarine

sandstones, mudstones, siltstones, and minor coal seams.

The predominant structure of the coalfield strikes northwest

to southeast and comprises thrust sheets containing folded

layers of competent sandstone and siltstone units, incompetent

mudstone, and coal. Dips vary considerably, from horizontal

to overturned. Underground mining by room-and-pillar

methods is restricted to areas where the strata dip less than 16°,

which is the practical limit of continuous miner and shuttle car

operation. The orientation of the underground mine workings

in figure 2 gives a clear indication of the structural

environment; the workings are either faulted or steeply folded

off on the northeast and southwest limits of mining.

The significant coal seams present are numbered from the

lower (older) to the upper (younger) and comprise the 4, 8, 10,

and 11 Seams. 4 Seam has been mined extensively (figure 2)

using conventional room-and-pillar mining techniques. 8 and

11 Seams are not considered economical to mine because of

thickness and low quality. Mining in 10 Seam has been attempted, including two longwall panels above 9G-4 Mine; however, a weak immediate roof comprising two 0.6-m coal seams

in the first 2 m of strata has always presented stability

problems.
17

Figure 4.—Development of mining methods. A, threeentry system, long-life panels; B, five-entry system, short-life

panels.

HISTORICAL MINING METHODS AND PILLAR DESIGN

Underground mining at Smoky River Coal Ltd. (SRCL)

commenced in 1969 in 5-4 and 2-4 Mines. The initial intent

was to develop for longwall extraction; however, two early attempts at longwall mining failed and retreat room-and-pillar

extraction became standard.

The original mining method was to develop three 6-m-wide

entries on 30-m centers from the portal to the limit of mining,

generally along strike, with crosscuts at 30-m centers. Parallel

sets of entries were driven separated by 50-m barrier pillars

(figure 4). On reaching the limit of mining, the road and barrier

pillars were split along strike to form blocks approximately

12 m wide and mined using an open-ended "Christmas tree"

method, taking 6-m passes each side with a conventional continuous miner. This method, described in more detail by

Wright [1973], worked well in 2-4 Mine, but was unsuccessful

in 5-4 Mine due to the weaker roof and pervasive thrust faulting

in and above the coal seam.

In the early 1970s, a major geotechnical investigation program was launched to assist mine staff in planning pillar dimensions and support. Extensive load and deformation monitoring

was conducted [Bielenstein et al. 1977]; concurrent testing by

air injection investigated the development of yield and elastic

zones within coal pillars [Barron et al. 1982].

In the early 1980s, the many disadvantages of the three-entry

system were overcome by adopting a five-entry system (figure 4B) with short-life panels [Robson 1984]. Panels comprising five parallel entries were developed off of main development sections. This mining method depended for its success on

the stability of pillars separating the panels and pillars that protected the main entries from the depillared areas. In fact, five

types of pillars were recognized:

• Barrier pillars between mining panels;

• Entry pillars protecting the main entries;

• Panel pillars formed during the development of mining

panels;

• Split pillars formed by splitting panel pillars prior to

depillaring; and

• Remnant pillars, the diminishing remnants of split pillars

formed during depillaring operations.

Tolerable probabilities of failure were estimated for each

pillar type, and an empirical design criterion was developed that

took into account this probability of failure [Barron et al. 1982].

Favorable trials of the five- entry system in A Mine (figure 2)

resulted in its adoption in 9H and 9G Mines. Further refinement of pillar design methods, relying heavily on practical

experience and a comprehensive review of pillar design methods from around the world, resulted in a design nomogram

[Kulach 1989]. The method was based on the tributary area

method of load calculation (considered to represent the best and

safest estimate of the loads developed on pillars) and

Bieniawski's [1983] method of determining pillar strength.

Mining continued in the late 1980s and 1990s in 9H and

9G Mines using this method of pillar design. The small

resource block exploited by the LB-4 Mine necessitated a

change in method, with entries developed to the farthest extent

and retreated back, but all three mines were successful from a

pillar stability standpoint.

In 1997, plans were developed to exploit a previously

untouched parcel of coal to the north of the old 5-4 Mine. The

shape of the resource block, 370 m wide by 2,500 m long,

bounded by steeply dipping thrusted zones to the northeast and

southwest, largely dictated the mining layout, which is shown

in figure 5.

During the planning stages of the mine, it was soon realized

that conditions would be very different from the more recent

underground operations, which were carried out at shallow to

moderate depths under a competent sandstone roof. The

proposed 5B-4 Mine would operate at depths of up to 550 m

and beneath a roof affected by pervasive thrust faulting. Both

pillar design and roof support requirements necessitated reevaluation for the operation to be successful.

Although the SRCL pillar design criterion had been used

successfully in a number of mines, it had some obvious disadvantages with respect to its application in 5B-4 Mine:

• The nomogram is restricted to 12-m-wide by 3.6-m-high

pillars and 6-m-wide roadways.

• The method is based on a strength calculation for square

pillars and severely underestimates the strength of rectangular

pillars.

• The design criterion is based on U.S. methods that have

undergone substantial modification in the past 10 years.
18

Figure 5.—Layout of 5B-4 Mine. (Elevation in feet.)

Mining plans for 5B-4 included rectangular pillars ranging

from 15 m to 36 m wide and 3.6 m high, standing between

4.9-m-wide roadways, which lay outside the empirical basis of

the design nomogram. Although a nomogram for 5B-4

parameters could have been developed, the availability of more

recently developed design methods that specifically address the

strength of rectangular pillars warranted consideration of a

change in design approach.

ANALYSIS OF RETREAT MINING PILLAR STABILITY (ARMPS)

The most recent development in pillar design in the United

States is the Analysis of Retreat Mining Pillar Stability

(ARMPS). ARMPS was developed by the former U.S. Bureau

of Mines [Mark and Chase 1997] based on extensive case

history data. ARMPS is available as a Windows 95TM software

package and has the following advantages over previous

methods used by SRCL:

• The increased load-bearing capacity of rectangular

pillars over that of square pillars of the same width is taken into

consideration.

• The load-bearing capacity of diamond- or parallelogram-shaped pillars is taken into consideration.

• ARMPS allows for an analysis of the stability of

pillars in the active mining zone (AMZ) during development,

during retreat, and with gobs on one or both sides.

• The effect of depth on abutment loading, based on

angles of caving, is considered.

• The effect of slabbing the interpanel pillar on pillars in

the AMZ is considered.

ARMPS is a very flexible method of analysis. The software allows the user to input all of the major parameters

relating to layout, mining, and pillar dimensions and location of

any worked-out, caved areas. It also allows analysis of changes

in pillar stability as a result of mining progress, from development to the extraction of coal pillars alongside a gob or between

two gobs. Mark and Chase [1997] present a full description of

the methods used to calculate pillar loading and pillar strength

in the ARMPS program. The principal output of the program

is the stability factor (SF), which is the product of the estimated
19

load-bearing capacity of pillars in the AMZ divided by the

estimated load on those pillars.

The concept of the AMZ follows from a hypothesis by Mark

and Chase [1997] that pillars close to the retreat extraction line

behave together as a system, i.e., if an individual pillar is overloaded, load is transferred to adjacent pillars. If these are of adequate size, the system remains stable, otherwise the pillars fail in

turn, resulting in a domino-type transfer of load and pillar failure.

The size of the AMZ is a function of depth, H, based on

measurements of abutment zone widths conducted by Mark

[1990], which showed that 90% of abutment loads fall within

a distance 2.8/H from the gob edge.

U.S. case history data indicate that where the ARMPS SF

is <0.75, nearly all of the designs were unsatisfactory; where

the SF is >1.5, nearly all of the designs were satisfactory. For

the deeper case histories, there was some evidence that stability

factors can be lower and still ensure overall pillar stability. In

addition, case histories with less competent roof rock were

more stable than those with stronger roof strata, as this

promoted pillar squeeze or burst activity.

Despite its utility and comprehensive analytical method,

ARMPS has several drawbacks when applied to SRCL

conditions:

• Case histories were confined to U.S. mines. As with

any empirically based design method, this presents problems in

application outside the case history environment.

• The case history database extends only to depths of

about 1,100 ft, and only a few case histories were obtained at

this depth of cover.

• None of the case histories matched the seam thicknesses mined at SRCL (up to 6 m).

After discussions with the developers of ARMPS [Mark

1998], it was decided that in order to confirm the applicability

of ARMPS to SRCL operations, a series of calibration analyses

based on depillaring operations in the coalfield was required.

BACK-ANALYSIS OF CASE HISTORIES

Mine plans from 9G, 9H, and LB-4 Mines (figure 2) were

reviewed, and relevant mining data were extracted to develop

a series of case histories. Each case history was then analyzed

using the ARMPS method, and safety factors were recorded

and compared to the existing U.S. case history database.

In order to consider the extraction of thick seams as practiced at SRCL, the calculation of the SF was modified.

ARMPS allows input of a single working thickness; in most

SRCL depillaring operations, however, there are two mining

heights. During development, the mining height is 3.7 m;

during depillaring, the mining height is 6.1 m. This variation in

mining height has a marked effect on pillar stability through the

height/width ratio of the pillars. Rationally, load shed to the

AMZ from the 6.1-m-high pillars in the mined-out area is more

effectively controlled by the pillars of 3.7-m height in the AMZ.

In order to take into account this variation in mining height,

ARMPS stability factors and details of pillar loading were

calculated for extraction heights of both 3.7 m and 6.1 m. The

SRCL stability factor was derived as follows:

(a) The pillar load transferred to pillars in the AMZ for a

mining height of 6.1 m was determined using ARMPS.

(b) The load-bearing capacity of pillars in the AMZ for a

mining height of 3.7 m was determined using ARMPS.

A stability factor was calculated as: (b) divided by (a). 

Table 1 presents details of the mining parameters for each

of the case histories considered, as well as the stability factors

obtained. Figure 6 compares the SRCL stability factors with

those obtained from the published U.S. database [Mark and

Chase 1997] and indicates that SRCL stability factors representing satisfactory conditions range from 0.47 to 1.74, with the

majority (66%) in the range of 0.5 to 1.0.

Local mining conditions provided some assurance that the

low SF values were valid. Firstly, the lowest values occurred

at the greatest depth; it has been recognized that acceptable

stability factors appear to be lower at depth, perhaps due to the

influence of horizontal stresses in reducing the pillar loading.

Secondly, the SRCL case histories are characterized by a

strong, competent roof; under such conditions in the United

States, acceptable pillar stability was obtained at lower values

of the calculated SF.
20

Figure 6.—Comparison of U.S. and SRCL stability factors.

Table 1.—Summary of SRCL case histories analyzed using the ARMPS method

Mine District Depth,

ft

ARMPS

SF

(6.1 m)

Load shed

to AMZ,

tons

ARMPS

SF

(3.7 m)

Capacity

 of AMZ,

tons

SRCL

SF

 Load

condition

LB-4 ..... Mine 580 1.35 5.83E+6 1.99 1.16E+7 1.56 2

9H-4 ..... SW2 390 1.23 1.18E+6 1.80 2.05E+6 1.74 3

9H-4 ..... SW3 485 1.35 1.69E+6 0.92 1.63E+6 0.96 3

9H-4 ..... SW4 575 0.73 2.44E+6 1.12 2.49E+6 1.02 3

9H-4 ..... SW5 660 0.56 3.43E+6 0.89 2.69E+6 0.78 3

9H-4 ..... SW6 715 0.49 4.05E+6 0.77 2.77E+6 0.68 3

9H-4 ..... SW7 755 0.61 4.71E+6 1.04 4.14E+6 0.87 3

9H-4 ..... SW8 832 0.50 6.11E+6 0.79 4.35E+6 0.71 3

9H-4 ..... SW9 932 0.35 4.60E+6 0.53 2.30E+6 0.50 3

9G-4 ..... SW2 560 0.85 2.05E+6 1.27 2.46E+6 1.20 3

9G-4 ..... SW3 650 0.58 3.26E+6 0.94 2.65E+6 0.81 3

9G-4 ..... SW4 730 0.49 4.10E+6 0.80 2.83E+6 0.69 3

9G-4 ..... SW5 745 0.51 3.98E+6 0.85 2.83E+6 0.71 3

9G-4 ..... SW6 780 0.51 4.01E+6 0.88 2.90E+6 0.72 3

9G-4 ..... SW7 840 0.41 5.21E+6 0.69 2.97E+6 0.57 3

9G-4 ..... SW8 885 0.37 5.84E+6 0.62 3.05E+6 0.52 3

9G-4 ..... SW9 920 0.34 6.56E+6 0.51 3.11E+6 0.47 3

9G-4 ..... SW10 915 0.34 6.49E+6 0.53 3.10E+6 0.47 3
21

DEVELOPMENT OF A DESIGN CRITERION

After considering the results of the case history analysis,

it was decided to use the ARMPS method to assist in pillar design

at 5B-4 Mine. Appropriate engineering practice in such cases is

to design to the minimum SF that resulted in stable conditions.

Evidence suggests that a pillar design resulting in an ARMPS SF

of $0.5 would be stable in Smoky River Coalfield conditions.

A more conservative SF of 0.7 was established.

A further limitation was imposed after an analysis of the

pillar stresses on the gob corner pillar. This pillar, located adjacent to both the active retreat section gob and the barrier pillar

between the active panel and the old gob, is subjected to the

highest stresses and is therefore more prone to failure. The

primary concern in this case is the threat of coal bumps or pillar

burst, resulting in the transference of loads to adjacent pillars in

the AMZ and possibly massive failure.

ARMPS analyses of SRCL case histories revealed that the

maximum stress experienced on any gob corner pillar was

about 41 MPa. At this stress level, the pillar proved to be

stable.

A third criterion was adopted based on the size of pillars

analyzed from the case histories. The minimum pillar size analyzed was 12 m wide between 6-m roadways. Maintaining this

extraction ratio for the 4.9-m-wide roadways employed at

5B-4 Mine precluded the use of ARMPS for pillars <9.7 m wide.

Based on the ARMPS output from the case history data

compiled from previous pillar retreat mining in the Smoky River

Coalfield, the following design criterion for pillars is suggested:

• The ARMPS SF should be maintained above 0.7.

• The maximum stress on the corner pillar should not

exceed 41 MPa (6,000 psi).

• Pillar widths must not be <9.7 m.

It was realized that the ARMPS-derived design criterion

was also limited in application, specifically to the depths encountered in the case history analysis. With depths of cover

projected to exceed those of the case histories by 50%, there

was an element of uncertainty with respect to the applicability

of the design criterion. This is currently being addressed by a

geotechnical program that includes pillar stress monitoring,

numerical modeling, and continuing assessment of the design

criterion.

Vibrating wire stress cells, electronic convergence meters,

and an I. S. Campbell data logger have already been deployed

at three monitoring sites to collect data on the effects of mining

on pillar stability. Two of the sites monitored stress changes

while the site was being "mined by" during the development

phase. It is hoped that these two sites will provide valuable information on the strength of the coal pillars monitored.

Results are still being evaluated; however, indications are

that the design criterion is applicable. Further sites will be established as mining progresses, and the results will be incorporated into the design criterion.

SUMMARY

Development of pillar design methods at SRCL's underground

operation has proceeded with developments in the mining method.

The extension of mine workings to previously unencountered

depths at the new 5B-4 Mine has resulted in a requirement to develop pillar design methods to match the new mining environment.

Pillar designs are currently being based on the results of

a back-analysis of case histories using the recently developed

ARMPS method. As with any empirical method of design,

prudent engineering practice dictates the collection and analysis

of pillar behavior information for design verification. Monitoring results already obtained are being analyzed to improve

the design criteria. Future sites will collect data from greater

depth and adjacent to more extensive workings.

REFERENCES

Barron K, Wright PL, Smales T [1982]. Guidelines for the design of coal

pillars in the No. 4 seam at McIntyre Mines Ltd., Grande Cache, Alberta.

Paper presented at the First International Conference on Stability in

Underground Mining (Vancouver, British Columbia, Canada).

Bielenstein HU, Wright PL, Mikalson D [1977]. Multi-seam mining at

Smoky River. Paper presented at the Sixth International Strata Control

Conference (Banff, Alberta, Canada).

Bieniawski ZT [1983]. New design approach for room-and-pillar coal

mines in the U.S.A. In: Proceedings of the Fifth ISRM Congress on Rock

Mechanics. Balkema, pp. E27-E36.

Kulach J [1989]. Smoky River Coal Ltd. pillar design criteria. SRCL

internal report, May.

Mark C [1990]. Pillar design methods for longwall mining. Pittsburgh,

PA: U.S. Department of the Interior, Bureau of Mines, IC 9247.

Mark C [1998]. Personal communication between C. Mark, Pittsburgh

Research Laboratory, National Institute for Occupational Safety and Health,

and P. Cain, Smoky River Coal Ltd.

Mark C, Chase FE [1997]. Analysis of retreat mining pillar stability

(ARMPS). In: Proceedings - New Technology for Ground Control in Retreat

Mining. Pittsburgh, PA: U.S. Department of Health and Human Services,

Public Health Service, Centers for Disease Control and Prevention, National

Institute for Occupational Safety and Health, DHHS (NIOSH) Publication

No. 97-122, IC 9446, pp. 17-34.

Robson TA [1984]. The application of improved room-and-pillar

techniques at Smoky River Coal's underground operations. SRCL internal

report, August.

Wright PL [1973]. Layout of continuous mining operations in the Smoky

River Mines. CIM Bulletin, March.
23

COAL PILLAR DESIGN FOR LONGWALL GATE ENTRIES

By John W. Cassie,1 Peter F. R. Altounyan, Ph.D.,2 and Paul B. Cartwright3

ABSTRACT

This paper describes measured data on strata behavior obtained in recent years from sites in the United

Kingdom and the implications for pillar design. The data include results from overcoring stress measurements

adjacent to coal mine roadways and deformation monitoring related to longwall extraction. The stresses

adjacent to mine roadways or entries have been measured at a number of coal mine sites in the United

Kingdom. The results are analyzed with regard to the information they provide on pillar behavior and strength

estimates.

A reduction in stress consistent with yielding of the strata adjacent to the roadways is evident. This is

consistent with the confined core model for pillar behavior. The pillar strength is dependent on the rate at

which vertical stress can increase with distance from the pillar edge and hence the confinement provided to

the yielded material.

The measured data indicate a wide range in pillar strengths. Two groups of results are identified that show

significantly different behavior corresponding to differing effective pillar strengths. Estimates of pillar

strengths derived from the measured data for these two groups are compared with established equations used

for pillar design.

The differing behaviors and strengths are attributed to variations in the amount of yielding and deformation

in roof and floor strata and hence in the amount of confinement they provide to the coal seam. Numerical

modeling is used to provide a comparison with the measured data and to indicate that this provides a feasible

mechanism to account for the measured data.

As the depth of mining increases, pillars tend to become increasingly wide and squat. In such cases, it is

possible for the surrounding roadways to become badly deformed and damaged while the pillars remain stable.

The criteria of comparing pillar strengths and loads to establish pillar stability become less applicable in these

circumstances; rather, considerations of roadway stability may be the limiting factor in determining suitable

pillar dimensions. 

This is the case for pillar dimensions typically employed around longwall panels in the United Kingdom.

Depending on the properties of the site and what are deemed to be satisfactory roadway conditions, this can

lead to wide variations in required pillar dimensions. Measured data for deformations in roadways influenced

by adjoining longwall workings are presented. These show that in some circumstances the influence of

longwall extraction can be transmitted over large distances and confirm the variability in required pillar sizes

depending on site properties.

1

Senior engineer.

2General manager.

3Engineer.

Rock Mechanics Technology Ltd., Burton-on-Trent, United Kingdom.
24

INTRODUCTION

There are many equations and methods for designing coal

pillars; these include back-analyses of failed and successful

case histories, extrapolation from strength tests on small-scale

coal samples to full-size pillars, and analytical consideration of

the limiting stress distribution across the pillar. The latter

approach would nowadays normally involve the use of

numerical modeling. In many instances, a combination of these

approaches is adopted.

The range of methods developed can be accounted for by

the wide range of geological conditions encountered underground and the different functions that coal pillars must fulfill

in different mining methods. It would be remarkable if a single

design equation were applicable to the entire range of coal pillar

types and conditions. The design approach employed should be

relevant to both the geological conditions at the site and the

function of the coal pillar being considered.

Stress measurements provide a tool that can assist in the

study of pillars. Comparison of the results from different sites

shows a wide range of potential strata conditions and resulting

pillar characteristics. For pillars of moderate widths sufficient

to allow the development of confinement within the coal, the

stress measurements can be used to obtain estimates of the

available pillar strengths or load-bearing capacities.

For wider pillars employed in deeper mines and with longwall layouts, characterizing pillars simply by their strength is

less applicable. Such pillars are unlikely to fail in the sense of

collapsing. However, the size of pillar employed can have a

major influence on conditions in the surrounding entries. In

this case, the distribution of stress within the pillars becomes

more relevant, and the performance of pillars can be assessed

by its impact on deformations and support requirements in the

surrounding entries.

STRESS MEASUREMENT DATA

Measurement of stresses provides another tool for studying

pillar behavior. During recent years, the stresses adjacent to

mine roadways or entries have been measured at a number of

coal mine sites in the United Kingdom. The results have been

analyzed, and estimates of pillar strengths derived from them

were compared with established pillar design equations [Cassie

et al., in press]. The data and main points of the analysis are

discussed here.

The general form of the results obtained was consistent

with the confined core concept—the stresses are reduced

immediately adjacent to the ribside and increase deeper into the

strata. They provide a measure of the rate of increase of

vertical stress actually obtained underground and can be studied

with regard to their implications for the potential strength and

behavior of pillars at sites where the confined core concept is

considered valid.

Twenty sites have been included in this analysis where

there were sufficient reliable results to allow the stresses to be

characterized. At these sites, 63 stress measurements were

available; they were carried out by overcoring hollow inclusion

stress cells. Relevant data on the 20 sites are presented in

table 1; individual test results are listed in table 2. Although

only the vertical stress component has been used in this analysis

and listed in the table, the measurement technique employed

provides all six stress components. Knowledge of these can be

invaluable in assessing the reliability of individual tests and

interpreting overall behavior at a site.

The results were collated from several field investigations

that have been previously reported and analyzed on a site-bysite basis [Hendon et al. 1995; ECSC 1997a, 1997b, 1998]. In

several instances, the primary objective of the measurements

was to investigate mine entry, rather than pillar behavior. The

extraction geometries varied widely, including individual

entries unaffected by other mine openings, twin-entry

developments, room-and-pillar panels, and yield pillars.

Working depths at the sites ranged from <200 m to >1,000 m.

Site T was located at Jim Walter Resources, Inc.'s No. 7 Mine

in Alabama; all other sites were in the United Kingdom.
25

Table 1.CMeasurement sites

Site Depth,

m

Seam

height,

m

Roadway

height,

m

Mining geometry Deformation level

A .... 620 7.5 3.5 Single-entry gate road ..... High.

B .... 500 3.0 2.9 20-m pillar .............. High.

C .... 500 3.0 2.9 30-m pillar .............. High.

D .... 480 2.5 2.7 30-m pillar .............. High.

E .... 950 2.2 2.8 20-m pillar .............. High.

F .... 950 2.2 2.8 Single-entry gate road ..... High.

G .... 900 2.2 3.0 Single-entry gate road ..... High.

H .... 800 1.5 3.0 Irregular pillar ........... High.

I ..... 950 2.4 3.0 60-m pillar .............. High.

J .... 840 2.2 2.8 Single-entry gate road ..... Low.

K .... 840 2.2 2.8 Yield pillar trial ........... Low.

L .... 320 2.8 2.9 Single-entry gate road ..... Low.

M .... 400 3.0 3.7 Trunk roadway .......... Low.

N .... 480 2.7 2.6 Single-entry gate road ..... Low.

O .... 560 2.5 2.9 Single-entry gate road ..... Low.

P .... 700 2.0 4.0 Trunk roadway .......... Low.

R .... 1,060 2.6 3.0 Trunk roadway .......... Low.

S .... 1,085 2.6 4.1 40-m pillar .............. Low.

T .... 560 2.5 2.5 Multientry gate road ...... Low.

U .... 180 1.2 1.2 11-m pillar .............. Low.

Table 2.CMeasurement data

Site

Height

above

roof, m

Distance

into

ribside, m

Vertical

stress,

MPa

Site

Height

above

roof, m

Distance

into

ribside, m

Vertical

stress,

MPa

A ... 3.2 4.0 5.9 L .... 1.8 1.7 6.3

A ... 4.5 5.7 8.2 L .... 1.6 3.4 1

7.6

A ... 5.0 9.4 14.1 L .... 2.1 6.4 1

7.8

B ... 4.6 3.9 7.4 L .... 2.0 10.0 1

8.0

B ... 4.6 6.2 10.5 M .... 3.1 1.1 10.0

B ... 4.6 6.4 15.2 M .... 3.2 2.6 14.8

B ... 4.6 8.1 17.5 M .... 3.0 4.3 1

15.5

C ... 4.6 4.2 9.0 M .... 6.6 10.7 1

13.8

C ... 4.6 6.9 8.7 N .... 3.5 1.5 9.0

C ... 4.6 8.6 15.0 N .... 3.5 3.0 16.9

C ... 4.6 11.7 1

15.7 N .... 3.6 7.0 111.4

D ... 1.4 2.5 6.0 N .... 3.6 7.5 1

10.8

D ... 1.2 4.1 10.3 O .... 4.8 2.9 13.3

E ... 4.8 4.6 8.8 O .... 5.0 5.4 1

19.8

E ... 5.2 7.2 10.6 O .... 5.0 7.4 1

15.6

E ... 3.9 9.6 20.0 P .... 3.8 1.9 10.0

F ... 1.5 2.2 4.6 P .... 3.6 3.0 14.7

F ... 2.9 4.2 11.3 P .... 3.3 4.8 19.5

F ... 4.0 5.9 13.7 P .... 6.5 8.1 1

18.5

G ... 5.3 2.8 5.0 R .... 0.6 0.8 2.6

G ... 4.2 3.7 9.5 R .... 1.7 2.4 12.0

G ... 6.3 6.1 15.2 R .... 1.8 3.2 17.1

G ... 6.8 10.9 24.5 R .... 3.5 4.7 21.6

H ... 3.0 3.0 5.5 S .... 1.7 1.1 15.4

H ... 5.9 5.2 8.9 S .... 1.5 3.0 26.7

H ... 4.2 7.3 14.1 S .... 1.5 6.1 30.0

I .... 1.0 1.5 1.1 T .... 1.0 2.5 16.5

I .... 2.2 3.0 8.5 T .... 1.0 5.0 19.4

I .... 3.5 3.9 18.2 T .... 1.0 10.0 1

21.0

J ... 2.2 5.6 26.0 U .... 1.6 1.0 8.4

K ... 2.6 4.1 11.7 U .... 1.8 3.3 22.3

U .... 1.7 5.2 1

23.5

1Postpeak.
26

Figure 1.CTypical measurement site.

Figure 2.CInterpretation of test results.

Figure 3.CMeasured data from high and low deformation sites.

ANALYSES OF DATA

For consistency and ease of interpretation, it would have

been preferable to conduct the tests in the coal seam. However,

because of the need for sufficiently competent strata in which to

conduct the overcore tests, they were conducted above, rather

than within, the coal seam, with the height above the roof dependent on the strength and condition of the roof at the site. At

each site, several tests were conducted at varying distances from

the mine entry (figure 1). Those tests deeper into the strata and

judged to be beyond the sector of increasing stress (i.e., postpeak)

were omitted from the analyses (figure 2). A tendency for the data to form two groups with different rates of stress increase was

evident (figure 3). It was also observed that the sites where the

rate of stress increase was lower were characterized by large and

deep-seated strata deformations. These sites were all at depths

>480 m. The stress gradients measured were lower than for

similar data from sites in the United States [Mark and

Iannacchione 1992].

The lower rate of stress increase observed at sites where the

strata deformations around roadways were large was not unexpected. The rate at which the vertical stress can increase will be related to the degree of confinement that the roof and floor provide

to the coal seam. If the roof and floor provide a high degree of confinement to the coal in the ribside, the stress it can sustain will increase rapidly with distance from the ribside. The frictional properties of the coal and its bounding strata will influence this. The

amount of failed or yielding ground surrounding a roadway will

also have a large influence. If the roof and/or floor are themselves

deforming, the confinement that they can provide to the coal ribside

will reduce, as will the rate at which the vertical stress can increase.

This is consistent with the correspondence observed between the

measured stresses and entry deformations.

The nonzero stresses at the ribside indicated by the results

in figure 3 are worth noting here. They may be a consequence

of the stresses being measured above, rather than within, the

seam. Very low stresses in the immediate yielded coal ribside,

which increase rapidly with distance into the ribside, would be

expected to result in nonzero stresses in the roof immediately

above the coal rib. Measuring the stresses in the roof may

therefore average out the stress variations in the seam.

ESTIMATES OF PILLAR STRENGTHS

Pillar load-bearing capacities were estimated from the

measured stress data with the assumption that the stress is

related linearly to distance from the ribside normalized with

respect to roadway height. Utilizing the measured stress data in

this manner could underestimate pillar strengths. They provide

an estimate of stresses that can be sustained in the ribside, but

not necessarily of the maximum stresses. Given that the stress

distribution in the ribside may be expected to be nonlinear (with

the gradient increasing deeper into the pillar), assuming a linear

distribution will also tend to underestimate pillar strengths when

extrapolated to greater pillar widths. The linear estimates of

pillar strength have been obtained not because it is proposed

that they be adopted as a design equation, but rather to enable

a comparison with the values given by recognized equations.

The formulas used as a basis for comparison were those

presented by Bieniawski [1984], Wilson [1983], and the

Salamon squat pillar equation with the parameters described by

Wagner [1992]. An in situ coal compressive strength of 6 MPa

was used in the Bieniawski formula.

Using results from sites typified by low deformations, the

strengths were similar to those obtained using the Bieniawski

equation and the Salamon squat pillar formulas (figure 4). This
27

Figure 4.CComparison of pillar strength estimates.

was making use of the average or regressed stress distribution.

Estimates obtained for single sites within this group would

imply strengths significantly in excess of or below these values.

The Bieniawski and Salamon formulas were derived from backanalysis of failed and unfailed pillars or from testing of rock

and coal specimens with different sizes and shapes; they have

been widely recognized and applied to room-and-pillar layouts.

In the case of the formulas, the strength at low width-to-height

(w/h) ratios is associated with the in situ coal strength. For the

estimates derived from the stress measurements, it is associated

with the nonzero intercept obtained from linear regressions of

the data. Despite this conceptual difference, the correspondence with the strength estimates for the low deformation sites is

striking.

The pillar strengths implied using results from sites typified

by high deformations were considerably lower. They indicate

that, in these cases, strengths obtained using the same formulas

and parameters could represent an overestimate. Significantly

lower in situ coal strengths would be required to obtain a match

with the measured data. Given that these equations are rooted

in experience and the degree of acceptance that they have

gained, in the mining environments where they are applied the

strata conditions giving rise to the lower pillar strengths cannot

be widely encountered. This could largely be accounted for by

the observation that all of the stress measurement sites categorized as high deformation were at depths of 480 m or more;

room-and-pillar mining operations are mostly at depths less than

this. Not all of the deeper sites fell into the category of high

deformation with weaker pillars. At one of the deepest sites

(>1,000 m), analysis of the measured results and experience

indicated pillar strengths significantly greater than the estimates

provided by the equations used in figure 4. The weaker pillar

strengths are in closer agreement with those estimated using

Wilson's equations.

The measured stress data imply a wide range of possible

pillar strengths depending on whether a site falls into the high

or low deformation categories used here. Using a set of case

histories that includes some of the sites listed here, two types of

behavior were similarly identified by Gale [1996]. He noted

that the identification of two groups is somewhat arbitrary and

it may be expected that the full range of behaviors between

these extremes could be encountered.

It is possible that part of the apparent variation in pillar

strength inferred from the measured stresses was associated

with variations in the in situ uniaxial compressive strength

(UCS) of the coal. However, the form of behavior assumed in

interpreting the measured stress data implies that the coal in the

ribside had already yielded (with a reduction in cohesion) and

that its strength was due to its frictional properties and confinement rather than cohesion. This would suggest that variations in the coal's UCS were unlikely to have a major influence.

A study by Mark and Barton [1996] suggested that variations in

laboratory test values for coal UCS were poorly correlated with

pillar strengths determined by back-analyses of failed and unfailed cases.

It appears that for the sites considered here the degree of

confinement provided to the coal seam was a major factor in

determining the pillar strength. If the roof and/or floor are

themselves yielding and deforming, the confinement that they

can provide to the coal ribside will reduce, as will the rate at

which the vertical stress can increase, thus leading to a weaker

pillar. This is consistent with the marked correlation between

the measured stresses and roadway deformations and is largely

equivalent to the distinction between the cases of rigid or

yielding roof and floor made by Wilson.

COMPARISON WITH NUMERICAL MODELING

Computer modeling has been used to investigate pillar or

entry behavior at the various sites in conjunction with the field

measurements. The model parameters used and results presented here were not intended to represent any individual site;

rather, they illustrate the strata behavior and properties that may

explain the measured data, in particular, the influence of the

strata bounding the coal pillar.
28

Figure 5.CStrong roof and floor strata.

The main parameters are summarized in table 3. Plane

strain was assumed with two-dimensional cross sections of pillars being represented and boundary conditions set to define

vertical axis of symmetry through the center of both the pillar

and adjoining roadway. Initial stresses were applied and the

roadway excavated to form the pillar. The loading on the pillar

was then increased in several stages by displacing the upper and

lower boundaries of the model grid. Results obtained for two

cases are included. In the first, a uniformly strong host rock has

been used; in the second, 3.0 m of weaker strata have been

included above and below the seam. In other respects, the

properties were identical. A cohesion equivalent to an in situ

UCS of 6 MPa was used for the coal.

Table 3.CModeling parameters

Modeling code ...................... FLAC (version 3.3).

Initial stresses, MPa ................. 5 (sxx, syy, and szz).

Dimensions:

 Seam height, m ............................. 2.4

 Roadway height. m .......................... 2.4

 Roadway width, m ........................... 4.8

 Pillar width, m ............................... 20.0

Strata sequence:

 Case 1 ................. Host rock and seam only.

 Case 2 ................. 3.0 m of weak strata in roof

 and floor.

Material properties Coal Host

 rock

 Weak

 strata

Density, kg/m3

............. 1,500 2,500 2,500

Bulk modulus, GPa ......... 1.5 12.0 6.0

Shear modulus, GPa ........ 1.0 7.0 3.5

Cohesion, MPa ............ 1.6 12.0 4.0

Friction angle, ° ............ 35 40 30

Tensile strength, MPa ....... 0.8 6.0 2.0

Residual cohesion, MPa ..... 0.1 0.1 0.1

Residual friction angle, ° ..... 35 40 30

Dilation angle, ° ............ 0 0 0

In the case of the stronger strata, yielding was effectively

confined within the coal seam. The vertical stresses in the ribside increased progressively, and large stresses developed as

loading proceeded (figure 5). Examining the stresses at a horizon 3 m above the seam, the results were compared with the

measured data that were also obtained from above the seam,

although not at a constant horizon. The model results show the

rate of stress buildup increasing as the pillar was loaded. For

average stresses across the pillar corresponding to the range

likely to be encountered in practice, they lay through the measured data from low deformation sites. Given sufficiently strong

roof and floor strata, very high pillar strengths can be

developed.

With weaker strata introduced in the immediate roof and

floor, the behavior was similar for the initial load stages

(figure 6). As the loading was increased, the roof and floor

started to yield and the rate of stress buildup in the ribside

reduced. For the final load stages, yielding of the roof and floor

had fully developed, spread across the width of the pillar being

modeled, and the stresses settled to an approximately constant

residual distribution. For these latter stages, the stress distribution was irregular due to the development of bands of strata that

were actively shearing with the stresses at yield; between these

bands, the stresses are below yield. The trend of model results

matched those of the measured data at high deformation sites.

For the strata properties and loading path used in this

example, the weaker strata model exhibits a postpeak reduction

in strength to a residual value (figure 7). The loss of pillar

strength was associated with the reducing confinement as the

strata bounding the coal seam yielded, rather than a reduction

in coal strength. Should the initial stresses be sufficient to

cause the roof and floor to yield and deform as the entries and

pillar were formed, there would be no apparent loss in pillar

strength by this mechanism and the postpeak strength would be

applicable from the outset. In this way, the initial stresses, in

addition to the strata properties, may influence pillar behavior.

Numerical modeling allows an improved interpretation of

measured data. The influence of more factors can be taken into

account, and it provides a better means of extrapolating to
29

Figure 6.CWeak roof and floor strata.

Figure 7.CModeled pillar loads.

different geometries or loading. In addition, the interaction between pillars and the surrounding entries can be assessed and

taken into account. In many circumstances, particularly with

wider pillars, considerations of entry rather than pillar stability

may be the limiting factor.

WIDE PILLARS

With large w/h ratios, it is widely accepted that the probability of pillar failure and loss of strength decreases. Nevertheless, excessive loading of the pillars may result in damage to

the surrounding mine entries. For deeper mines and those using

longwall mining methods, pillar w/h ratios frequently exceed

those for which the most widely known strength equations were

derived. In these circumstances, it is likely that pillar dimensions will be limited by considerations of the stability of the

surrounding mine entries, rather than that of the pillars.

Design of pillars or pillar systems to maintain acceptable

conditions in the surrounding entries is likely to lead to consideration of the nonuniform stress distribution across pillars,

rather than simply the average stress or total load acting through

a pillar. Although a simplification, one possible approach is to

limit the maximum stress or the stress at a particular location

expected within a pillar. This approach was adopted by Wilson

with his "entry stability" as opposed to "ultimate stability" criteria for pillar strength [Carr and Wilson 1982].

The choice of a suitable limiting value for the stress is

fundamental to this approach. Wilson related the maximum

allowable stress to the triaxial strength of the strata and the

in situ vertical stress. Other estimates are possible, although it

is likely to depend in some degree on the surrounding strata

strength. In some regards, the choice of this value is analogous

to the problem of determining the appropriate value for the

in situ coal strength for use in pillar strength equations such as

Bieniawski's.

The wide range of entry conditions encountered at sites

subject to similar stress levels, but with different strata properties, suggests that appropriate values for the maximum stress

to allow in a pillar may vary widely from site to site. The variation may be greater than that apparent in effective in situ coal

strengths.

An advantage for using numerical modeling in investigating pillar behavior is that it enables consideration of the

interaction between pillars and the surrounding entries. Mine

entry conditions are, of course, influenced by factors other than

surrounding pillars. This should be taken into account if

adopting an approach of using favorable mine entry conditions

as an objective of pillar design.
30

Figure 8.CTypical longwall retreat layout in U.K. coal mines. Figure 9.CPillar widths between retreat longwall panels.

PROTECTION PILLARS BETWEEN LONGWALL PANELS

The pillars left between longwall panels are a particular

case of wide pillars as described above. The method of

longwall retreat typically employed in U.K. coal mines uses a

single gate at each side of the panel, with adjacent panels

separated by wide protection pillars (figure 8). The tailgate for

the next in a sequence of longwall panels is driven during or

subsequent to retreat of the previous panel. As a result, the

tailgate may be driven in a stress regime that is subsequently

altered by extraction of the previous panel, one that has already

been altered, or a combination of these.

Pillar widths that have been adopted for recent layouts of

this type in the United Kingdom are shown in figure 9. They

clearly come into the category of wider pillars (the w/h ratios

range up to 40:1). Coal pillars of these dimensions do not fail

in the normally accepted sense. Despite this, the use of

inadequate pillars may result in difficult mining conditions.

The choice of pillar dimensions may influence—

1. The stress change due to extraction of the previous

panel and hence conditions in the tailgate while or after it is

driven;

2. The concentration of stress and hence conditions at the

tailgate-faceline junction during retreat; and

3. The surface subsidence profile across the sequence of

panels.

The first and second of the above will almost certainly be

considered in determining the pillar size. The third may be

considered if the surface is subject to subsidence limitations.

Wilson's pillar equations were originally developed as a

method for determining dimensions for this kind of pillar. The

method estimates the distribution of stresses transferred onto

the pillar due to extraction of the panels. It effectively limits

the stress at the location of the tailgate with the first panel

extracted and the maximum stress across the pillar with both

panels extracted. Numerical modeling can now be used to

provide a more sophisticated estimate of how the stresses will

be distributed across the pillar. It will, however, be strongly

dependent on the caving behavior of the longwall and the

reconsolidation of the waste that remains subject to

considerable uncertainty. Suitable limits to place on the stress

levels must also be determined for the site, as described earlier.

Roof displacements showing the influence on gate

conditions of stresses distributed over substantial pillars such as

these are shown in figures 10-12. The data are from telltale

devices used to measure roof deformations [Altounyan and Hurt

1998]. Their purpose is to provide a routine assessment of roof

condition, rather than acting as field measurement stations for

research purposes. However, the data obtained can be used to

enable a comparison between different entries and sites.

In figure 10, a histogram compares data from the tailgate

and main gate for a panel at an average depth of 590 m with a

50-m pillar. At this depth, the pillar width is at the lower range

in figure 9. For the main gate, none of the instruments showed
31

Figure 10.CComparison of roof displacements in main gate

and tailgate during development.

Figure 11.CRoof displacements in main gate during retreat.

Figure 12.CRoof displacements in tailgate during retreat.

displacements in excess of 40 mm; in the tailgate, 20%

exceeded this value. There was considerable spread in the roof

deformations along the length of each gate; this can be

expected due to geological variations. The form of the distributions suggests that in zones of weaker geology the increased stress levels experienced by the tailgate resulted in

increased roof displacements. The displacements plotted were

those recorded up to 50 days after drivage of the gate; the

difference between the gates increased with time and during

retreat of the panel.

Increasing roof displacements as the retreating panel

approaches are plotted in figures 11 and 12. For the main gate

(figure 11), its influence only becomes apparent within the final

50 m. The displacements in the tailgate (figure 12) are larger

and start to accelerate at an earlier stage than for the main gate.

In fact, tailgate conditions for this panel were poor with large

amounts of convergence and roof softening. A considerable

amount of extra support had to be installed in the tailgate to

maintain stability up to the junction with the faceline. The

different amount of support employed in the gates needs to be

taken into account in comparing figures 11 and 12.

Variability in conditions such as that evident in figures 10-

12 may provide a guide in determining suitable pillar dimensions. If the difference between main gate and tailgate attributable to increased stress is small compared to the spread due to

geological variability along the length of each gate, there is little

point in increasing pillar widths in order to improve conditions

in subsequent tailgates.

Although pillar dimensions are usually described with

regard to consideration of vertical stresses and their effects,

many other factors can also affect longwall gate conditions and

influence the choice of suitable pillar dimensions. These

include—

• Horizontal stresses and their orientation relative to the

panel;

• Timing of gate drivage relative to the previous panel; and

• Interaction with workings in other seams.
32

If significant interaction is expected, this may be the dominant

consideration in determining the position of the tailgate and

thus the pillar size. These are technical factors and are not the

sole determinants of pillar size. The choice of pillar size will

also be strongly influenced by the priorities of the

mine management or operator. If the priority is to maximize

extraction, smaller pillars are likely to be adopted, with adverse

conditions in the tailgate giving rise to increased repair and

support costs being accepted. If the priority is to minimize

production costs, larger pillars are likely to be adopted.

SUMMARY

Comparison of stress measurement results from different

sites, mostly in U.K. mines, shows a wide range of potential

strata conditions and resulting pillar characteristics. The

range can be accounted for by variations in the degree of

confinement provided to the coal by the roof and floor strata.

The lower pillar strengths inferred from measured stress data

were encountered at deeper sites with weak roof or floor strata

and characterized by large deformations. Such sites are likely

to employ mining methods other than room- and-pillar and

use wide pillars. Although the wider pillars employed

between longwall panels may not fail in the usual sense, their

dimensions can have a critical impact on conditions in the

surrounding entries or gates.

For wide pillars, it is likely that pillar dimensions will be

limited by considerations of the stability of the surrounding

mine entries rather than of the pillars. This requires that factors

other than pillar strengths and load be taken into account.

A possible general approach is to establish stress levels that are

acceptable for a site and dimension pillars so that these stress

levels are not exceeded and to consider the pillar in context

with the stability of the entries.

REFERENCES

Altounyan P, Hurt K [1998]. Advanced rockbolting technology. World

Coal May:30-36.

Bieniawski ZT [1984]. Rock mechanics design in mining and tunnelling.

Rotterdam: A. A. Balkema.

Carr F, Wilson AH [1982]. A new approach to the design of multi-entry

developments for retreat longwall mining. In: Proceedings of the Second Conference on Ground Control in Mining. Morgantown, WV: West Virginia

University, pp. 1-21.

Cassie JW, Cartwright PB, Altounyan PFR [in press]. Coal pillar

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1999).

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reinforcement techniques to difficult mining conditions. Report on ECSC

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for longwall access and trunk roadways. Report on ECSC Research Project

7220-AB/834.

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Report on ECSC Project 720-AF/861.

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Symposium of Geology in Longwall Mining, pp. 185-191.

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entry designs, Welbeck Colliery (UK) and Jim Walter Resources (USA). In:

Proceedings of the 14th International Conference on Ground Control in Mining. Morgantown, WV: West Virginia University, pp. 94-103.

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should it be used to design pillars? In: Ozdemir L, Hanna K, Haramy KY,

Peng S, eds. Proceedings of the 15th International Conference on Ground

Control in Mining. Golden, CO: Colorado School of Mines, pp. 61-78.

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models and field measurements compared. 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. 78-93.

Wagner H [1992]. Pillar design in South African collieries. 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. 283-301.

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rocks of the coal measures. Int J Min Eng 1:91-187.
33

ANALYSIS OF LONGWALL TAILGATE SERVICEABILITY (ALTS): 

A CHAIN PILLAR DESIGN METHODOLOGY

FOR AUSTRALIAN CONDITIONS

By Mark Colwell,1 Russel Frith, Ph.D.,2 and Christopher Mark, Ph.D.3

ABSTRACT

This paper summarizes the results of a research project whose goal was to provide the Australian coal

industry with a chain pillar design methodology readily usable by colliery staff. The project was primarily

funded by the Australian Coal Association Research Program and further supported by several Australian

longwall operations.

The starting point or basis of the project was the Analysis of Longwall Pillar Stability (ALPS) methodology.

ALPS was chosen because of its operational focus; it uses tailgate performance as the determining chain pillar

design criterion rather than simply pillar stability. Furthermore, ALPS recognizes that several geotechnical

and design factors, including (but not limited to) chain pillar stability, affect that performance.

There are some geotechnical and mine layout differences between United States and Australian coalfields

that required investigation and, therefore, calibration before the full benefits offered by the ALPS methodology

could be realized in Australia.

Ultimately, case history data were collected from 19 longwall mines representing approximately 60% of all

Australian longwall operations. In addition, six monitoring sites incorporated an array of hydraulic stress cells

to measure the change in vertical stress throughout the various phases of the longwall extraction cycle. The

sites also incorporated extensometers to monitor roof and rib performance in response to the retreating longwall

face.

The study found strong relationships between the tailgate stability factor, the Coal Mine Roof Rating, and

the installed level of primary support. The final outcome of the project is a chain pillar design methodology

called Analysis of Longwall Tailgate Serviceability (ALTS). Guidelines for using ALTS are provided.

1

Principal, Colwell Geotechnical Services, Caloundra, Queensland, Australia.

2Principal, Strata Engineering, Teralba, New South Wales, Australia.

3Supervisory physical scientist, Pittsburgh Research Laboratory, National Institute for Occupational Safety and Health, Pittsburgh, PA.
34

INTRODUCTION

In many cases, chain pillars in Australia have been designed

solely with regard to pillar stability using a process similar to

that used for pillars within bord-and-pillar operations. The

bord-and-pillar approach is based on analysis of collapsed pillar

cases from Australia and the Republic of South Africa

[Salamon et al. 1996] and applies a factor of safety in relation

to pillar collapse. This approach is inappropriate for a number

of reasons when designing chain pillars.

Australian chain pillars typically have minimum width-toheight (w/h) ratios >8, which is approximately 4.5 standard

deviations away from the mean of the pillar collapse case histories. In addition, the chain pillar loading cycle and active life

are significantly different from those experienced by pillars

within a bord-and-pillar operation. Finally, the goal of maintaining gate road stability is very different from that of avoiding

a pillar collapse.

The need for a design method uniquely developed for Australian longwall chain pillars was clear. The original submission for funding by the Australian Coal Association Research

Program (ACARP) stated that the calibration (to Australian

conditions) of a proven chain pillar design methodology offered

the least risk for a successful and timely outcome. It was assessed that the most comprehensive chain pillar design tool then

available was the Analysis of Longwall Pillar Stability (ALPS)

[Mark 1990; Mark et al. 1994]. The primary consideration in

selecting ALPS is that it uses gate road (i.e., tailgate)

performance as the determining chain pillar design criterion.

Secondly, ALPS is an empirical design tool based on a U.S.

coal mine database; thus, it provided a ready framework for

calibration to Australian conditions.

The aim of the project was to provide the Australian coal industry with a chain pillar design methodology and computer-based

design tool readily usable by colliery staff. A further objective was

to ensure that the methodology developed by the project had the

widest possible application to all Australian coalfields by identifying where local adjustments and limitations may apply.

In formulating the design methodology, the primary goal was

to optimize pillar size (specifically pillar width) so as to—

• Maintain serviceable gate roads such that both safety and

longwall productivity are unaffected;

• Minimize roadway drivage requirements so as to have a

positive impact on continuity between successive longwall

panel extraction; and

• Maximize coal recovery.

In designing chain pillars, specifically with regard to satisfactory gate road performance, the following design criteria

were proposed:

• The chain pillar must provide adequate separation between

the main gate travel road and belt road, such that the travel road

(tailgate of the subsequent longwall panel) will be satisfactorily

protected from the reorientation and intensification of the stress

field caused by the extraction of the first longwall panel.

• The tailgate (with a focus on the tailgate intersection with

the longwall face) will be sufficiently serviceable for ventilation

and any other requirements (setting of secondary support,

second egress, etc).

BACKGROUND

ALPS was originally developed by Mark and Bieniawski

[1986] at The Pennsylvania State University. It was further

refined [Mark 1990, 1992; Mark et al. 1994] under the auspices

of the former U.S. Bureau of Mines (USBM).4 The initial

ALPS research involved field measurements of longwall abutment loads at 16 longwall panels at 5 mines. These measurements were used to calibrate a simple conceptualization of the

side abutment, similar to models proposed by Wilson [1981]

and Whittaker and Frith [1987]. The side abutment (A) equates

to the wedge of overburden defined by the abutment angle ($)

(see figure 1). The tailgate loading condition is considered to

be some percentage of the side abutment, called the tailgate

abutment factor (Ft). The U.S. field measurements found a

range of abutment angles, from $ ' 10.7° to $ ' 25.2°. A value

of $ ' 21° and Ft ' 1.7 was selected for use in design.

4The safety and health research functions of the former U.S. Bureau of

Mines were transferred to the National Institute for Occupational Safety and

Health in October 1996.

Because of the encouraging results obtained from the initial

study, the USBM commissioned further research directed toward quantifying the relative importance of roof and floor

quality and artificial support on gate road performance. The

approach was to analyze actual longwall mining experience.

Case histories from 44 U.S. longwall mines were characterized

using 5 descriptive parameters. Pillar design was described by

the ALPS stability factor (ALPS SF ' pillar strength ÷ pillar

load); roof quality was described by the Coal Mine Roof Rating

(CMRR) [Molinda and Mark 1994; Mark and Molinda 1996].

Other rating scales were developed for primary support,

secondary support, and entry width.

Mark et al. [1994] reported that statistical analyses indicated

that in 84% of the case histories the tailgate performance

(satisfactory or unsatisfactory) could be predicted correctly

using only the ALPS SF and the CMRR. It was further stated

that most of the misclassified cases fell within a very narrow

borderline region. The analyses also confirmed that primary
35

PSUP '

Lb( Nb( Db

Sb( we( 84

, (2)

Figure 1.—Conceptual model of the side abutment load.

roof support and gate entry width are essential elements in successful gate entry design. The relative importance of the floor

and of secondary support installed during extraction could not

be determined from the data.

The following equation (relating the ALPS SF and CMRR)

was presented to assist in chain pillar and gate entry design:

ALPS SFR ' 1.76 & 0.014 CMRR, (1)

where the ALPS SFR is the ALPS SF suggested for design.

The Primary Support Rating (PSUP) used in ALPS was

developed as an estimate of roof bolt density and is calculated

as follows:

where Lb ' length of bolt, m,

Nb ' number of bolts per row,

Db ' diameter of the bolts, mm,

Sb ' spacing between rows of bolts, m,

and we ' entry (or roadway) width, m.

PSUP treats all bolts equally and does not account for load

transfer properties, pretensioning effects, etc.

NEED FOR CALIBRATION

Conventional longwall mines in the United States generally

use a three-heading gate road system; Australian longwall panel

design typically employs a two-heading gate road system with

rectangular chain pillars separating these gate roads. A typical

Australian longwall panel layout is presented in figure 2.

Figure 2 also details the stages of the chain pillar loading cycle:

1. Development loading (calculated using tributary area

concepts);

2. Front abutment loading, which occurs when the first

longwall face is parallel with the pillar;

3. Main gate (side) abutment loading, when the load has

stabilized after the passage of the first face;

4. Tailgate loading, when the second face is parallel with

the pillar; and

5. Double goafing, when the pillar is isolated between two

gobs.

It is during tailgate loading that the chain pillar (or cross

section thereof adjacent to the tailgate intersection) experiences

the greatest vertical loading during its "active life," i.e., the

period where the chain pillar is playing its role in helping to

maintain satisfactory gate road conditions. This project focused

on tailgate performance (at the T-junction) as the design condition. The pillar stability factor in relation to the tailgate loading

condition is designated as the "tailgate stability factor" (TG SF).

The project found that Australian chain pillars have an average

length-to-width ratio of 3.2; crosscut centers on average are

spaced at 100 m. The pronounced rectangular shape of Australian

chain pillars may add strength to the pillar compared to a square

pillar of the same minimum width. Mark et al. [1998b]

reanalyzed the U.S. database using the Mark-Bieniawski rectangular pillar strength formula and found a slightly better

correlation (in relation to the predictive success rate) than using

the Bieniawski equation. In addition to the Bieniawski equation,

this project assessed both the Mark-Bieniawski rectangular pillar

formula [Mark and Chase 1997] and the squat pillar formula

[Madden 1988] in relation to the correlation between the pillar

stability factor and the CMRR.

In Australia, the significant impact of horizontal stress on

coal mine roof stability is well documented [Frith and Thomas

1995; Gale and Matthews 1992]. The in situ horizontal stresses

should not have a significant direct influence on tailgate roof

stability due to the presence of an adjacent goaf. However,

there is an indirect influence in terms of the degree of damage

done to the roof during the initial roadway development and
36

Figure 2.—Stages in the dynamic loading cycle of longwall chain pillars.

then to the main gate travel road and cut-throughs during

longwall retreat. The effect of the in situ horizontal stress field

on gate road serviceability (particularly on roof stability) is not

taken into account directly by the ALPS methodology and was

considered in more detail by the ACARP project.

Finally, the project aimed to verify the applicability of the

ALPS loading parameters to Australian conditions. The ALPS

methodology uses an abutment angle of 21° in all cases, and it

assumes that the tailgate load is 1.7 times the side abutment

load.

MEASUREMENTS OF AUSTRALIAN ABUTMENT LOADS

The project measured changes in vertical stress across (and

within) chain pillars at six collieries to determine whether the

ALPS approximations should be refined. Three sites were located in the Bowen Basin Coalfield in Queensland (Central,

Crinum, and Kenmare Collieries), two were in the Newcastle

Coalfield (Newstan and West Wallsend Collieries), and one was

at West Cliff Colliery in the Southern Coalfield. Each monitoring site included an array of hydraulic stress cells (HSCs)

generally located at midseam height to measure the changes in

vertical stress. Most sites also included extensometers to

monitor roof and rib performance. A general instrumentation

layout is shown in figure 3.

The HSC used in this project is a modification of the

borehole-platened flatjack developed by the former USBM.

The HSC was developed, calibrated, and tested by Mincad

Systems Pty. Ltd. [1997]. The HSC consists of a stainless steel

bladder into which hydraulic fluid is pumped via tubing

extending along the borehole. The bladder is encased between

two steel platens that are forced against the borehole wall as the

bladder is pumped up.

As with every stress measurement instrument, proper calibration is important. Mincad Systems provided two calibration

formulas based on its research with the HSC. The formula used

in this project employs a calibration factor K ' 1.0 for a stress

increase of #5 MPa and K ' 1.3 for that portion of an increase

above 5 MPa. Because ALPS is a comparative chain pillar design tool, it is not critical which calibration method is used

as long as the method is consistent from site to site.

The six sites add considerably to the ALPS abutment load

database. They include a much wider range of cover depths and

width-to-depth ratios than the original U.S. data. There is also

much more variety in the geologic environments. In addition,

because the stress readings could be made remotely, monitoring

was possible subsequent to the passing of the second longwall
37

Figure 3.—Instrumentation layout at a typical stress measurement site.

face. Of the 16 original U.S. panels, there were sufficient data

to characterize the side abutment load in only 6, and only one

panel provided data on the tailgate abutment factor. In contrast,

data on both the side and tailgate loads were obtained from all

six Australian monitoring sites.

At the Australian sites, entry width and height ranged from

4.8 to 5.2 m and 2.5 to 3.6 m, respectively. Pillar width and

length (rib to rib) ranged from 26 to 40 m and 95 to 125 m,

respectively; cover depths varied from 130 to 475 m. Due to

the relatively high length-to-width ratio of Australian chain

pillars (i.e., extracted crosscut coal <5%), a plane strain or twodimensional loading analysis is common in Australia and was

considered appropriate by the Australian researchers. Furthermore, the Australian researchers recognized that the location of

the stress cells within the pillar would in all probability affect

the measured vertical stress changes. In placing the cells near

a cut-through rather than across the longitudinal center of the

chain pillar, the monitoring exercises were viewed as recording

the loading behavior of a thin, two-dimensional slice of the

pillar near a critical location during its "active life."

The ALPS loading parameters account for the extracted coal

within the cut-throughs. Therefore, the abutment angles reported by the ACARP project [Colwell 1998] would be slightly

different if the load had been addressed in the same manner as

the U.S. field measurements in back-calculating the abutment

angles. However, the end effect on the design chain pillar

width is negligible.

Measurements of the main gate side abutment loading are

used to calculate the abutment angle; measurements of the

tailgate abutment (when longwall 2 is parallel with the instruments) are used to calculate the tailgate abutment factors.

Examples of the data obtained from two of the sites are shown

in figure 4. The results from all six monitoring sites are summarized in table 1 and figure 5 (along with the U.S. data).

The measurements of the abutment angle from the three

Queensland mines and from Newstan Colliery clearly fall within the range of the U.S. data. However, the abutment angles

calculated for the two deepest mines, West Wallsend and West

Cliff, are the smallest of any in the database. The overburden

at these two mines (and at Newstan Colliery) also contains the

massive sandstone and sandstone/conglomerate strata commonly associated with the Newcastle and Southern Coalfields.

The low width-to-depth ratio, along with the strong overburden,

may be affecting the caving characteristics of the gob.

Table 1 also shows two sets of tailgate abutment factors.

The first set was obtained by dividing the measured tailgate

loading by the measured main gate (side abutment) loading.

The second set, which is the one used in the U.S. version of

ALPS, is obtained by dividing the measured tailgate load (adjacent to the T-junction) by the calculated side abutment load

using an abutment angle of $' 21°. The one U.S. measurement

found this second tailgate abutment factor to be 1.7. The

Australian data in table 1 show a high variability, with the mean

at 1.3 in relation to an ALPS-style analysis.

Figure 6 plots the development of the change in load during

tailgate loading (as a multiple of the side abutment) against face

position. It clearly indicates that the nature of the loading behavior at Central, Crinum, and Kenmare Collieries closely approximates that proposed by ALPS. However, the tailgate

loading behavior at Newstan Colliery and particularly at West

Wallsend Colliery reveals that the double goaf load is significantly greater than twice the measured main gate side abutment load. It is likely that West Cliff would have behaved in a

manner similar to Newstan if the cabling and/or cells had not

become inoperable with the second longwall face only 5 m past

the instrumentation site.

The field data associated with Newstan, West Wallsend, and

West Cliff Collieries clearly suggest that a much greater portion

of the main gate abutment load is distributed onto the adjacent

unmined longwall panel than calculated on theoretical grounds

(see figure 2).

Although the double goaf loading condition could not be

measured at West Wallsend Colliery, it would seem that the

bulk of the tailgate load manifests itself within that distance

100 m outby of the face. There are distinct increases in the rate

of loading at approximately 70 m and again at 20 m outby of the

face. This correlates well with the observed tailgate condition

and strata behavior.

In contrast to West Wallsend Colliery, the bulk of the tailgate load at Newstan Colliery manifests itself after the passage

of the longwall face. Both Newstan and West Wallsend Collieries have experienced greater difficulties with regard to both

gate road and face control issues when massive sandstone/

conglomerate channels are within 0 to 30 m of the mining horizon. Face width optimization has played a critical role in

alleviating the face control difficulties.
38

Figure 4.—A, Abutment load profiles at different locations of the longwall face (Crinum Colliery)

with highly cleated coal. B, Abutment load profiles at different locations of the longwall face (West

Wallsend Colliery), where the tailgate load is extremely aggressive.

Table 1.—Results of stress measurements
39

Figure 5.—Development of abutment load at the six monitoring

sites.

Figure 6.—Abutment angles determined from stress measurements.

Monitoring site H,

m

w,

m

wp,

m

Pw,

m

$, °

Ft

(Meas

)

Ft

(Calc

)

Central ........ 265 39.9 5.1 230 24.7 1.77 2.05

Crinum ........ 125 30.2 4.8 275 19.1 1.52 1.35

Kenmare ....... 130 24.8 5.2 200 19.2 1.49 1.22

Newstan ....... 180 26.0 5.0 130 15.3 1.48 1.04

West Cliff ...... 475 37.2 4.8 200 5.9 1.81 0.60

West Wallsend . . 240 30.1 4.9 145 8.5 3.79 1.52

NOTE.—$ and Ft (Meas) are based on two-dimensional

analyses (( ' 0.25 MN/m3; Kenmare ( ' 0.23 MN/m3). Ft

(Meas) is based on ALPS loading parameters ($ ' 21° and

( ' 0.255 MN/m3).

A possible explanation for the variation in the manifestation

of the tailgate load (in relation to face position) is that while a

near-seam conglomerate channel exists in relation to the monitoring site at West Wallsend Colliery, it is absent at the

Newstan Colliery site. The anecdotal evidence suggesting the

near-seam channel as a possible cause of this variation in load

manifestation is strong (i.e., secondary support requirements,

seismic monitoring [Frith and Creech 1997]; however, the

mechanics are not yet fully understood.

The stress measurements collected by the project were supplemented by data from similar investigations previously conducted by other collieries, which were gratefully made available

to the project. The supplementary field data were obtained using nearly all of the different types of stress cells that have been

used in Australia (CSIRO HI, IRAD, Geokon, and HSC). The

variety of instruments hinders comparison between studies, yet

some trends emerge.

In general, the supplementary field data support the observations made from the project data. In Bowen Basin collieries,

the loading behavior closely approximates that proposed within

ALPS. In contrast, there are some significant departures in

New South Wales for collieries that have strong, spanning overburden and a low width-to-depth ratio. Table 2 indicates that at

Angus Place, South Bulli, West Cliff, West Wallsend, and

Wyee the measured side abutment angles are significantly less

than 21°.

In summary, it seems that an abutment factor of 1.5, in conjunction with an abutment angle of $ ' 21°, is a reasonable and

generally conservative approximation of the actual tailgate load

for most Australian mines. The exceptions are two collieries

and one locality (containing three collieries) within the Australian database, where there is sufficient evidence to suggest

that site-specific loading parameters are more applicable. These

are the Central and West Wallsend Collieries, and the deepest

collieries within the Southern Coalfield (South Bulli, Tower,

and West Cliff Collieries). For Central Colliery, the appropriate

loading parameters seem to be $ ' 26° and Ft ' 1.6. With

regard to the three Southern Coalfield collieries, the recommended loading parameters are $ ' 10° and Ft ' 1.5, which

also apply to areas associated with West Wallsend Colliery that

are unaffected by the near-seam sandstone/conglomerate

channels. In areas where thickening of the channel occurs, it is

assessed that the abutment angle of $ ' 10° should be

maintained, while Ft should be increased to 3.5.

Two other variables can influence the calculation of pillar

stability factors: in situ coal strength (S1) and the overburden

density ((). A comprehensive study in the United States recently concluded that uniaxial compressive strength tests on small

coal samples do not correlate with in situ pillar strength [Mark

and Barton 1996]. That study and others in Australia and the

Republic of South Africa [Salamon et al. 1996] found that using

a constant seam strength works well for empirical pillar design

methods. Accordingly, the in situ coal strength is taken to be

6.2 MPa, as used in ALPS.

In some Australian mines, there is so much coal in the overburden that the overburden density is significantly reduced below the ( ' 0.25 MN/m3

 that is typical for sedimentary rock.

Dartbrook and Kenmare Collieries have undertaken satisfactory

analyses of their overburden and have determined that

( ' 0.22 MN/m3 and 0.23 MN/m3, respectively.
40

Table 2.—Supplemental stress measurements from other Australian mines

Site details Reference Cell type Cell position Remarks N, ° Ft

(Meas)

Angus Place longwall 12 ...... Clough [1989] .............. CSIRO HI . . In roof ...... Author indicates vertical stress increase small; may be

 affected by clay bands within roof strata.

5.5 —

Central longwalls 301-302 ..... Wardle and Klenowski [1988] . . IRAD ...... In seam ..... Satisfactory results from which to interpret main gate and

 tailgate loading.

26.8 1.48

Cook longwalls 5-6 .......... Gale and Matthews [1992] .... CSIRO HI . . In roof ...... Satisfactory results from which to interpret main gate and

 tailgate loading.

38.0 1.31

Ellalong longwall 1 .......... Wold and Pala [1986] ........ IRAD ...... In seam ..... Satisfactory results from which to interpret main gate

 loading for barrier and adjacent development pillars.

17.2 —

Ellalong longwall 1 .......... Wold and Pala [1986] ........ IRAD ...... In seam ..... Satisfactory results so as to interpret main gate loading

 for chain pillar.

9.8 —

Kenmare longwall 1B1........ Gordon [1998] .............. CSIRO HI . . In roof ...... Satisfactory results from which to interpret main gate

 loading condition.

54.2 —

North Goonyella longwalls 3-4 . . Nemcik and Fabjanczyk [1997] . CSIRO HI . . In roof ...... Only 2 of 4 cells functioned reliably such that a

 subjective assessment of the stress profiles was

 required.

31.5 1.2

South Bulli longwalls 504-505 . . Mincad Systems Pty. Ltd. [1997] IRAD and

 hydraulic.

In seam ..... Satisfactory results from which to interpret main gate and

 tailgate loading.

8.8 1.47

Ulan longwalls A and B ....... Mills [1993] ................ CSIRO HI . . In roof ...... Satisfactory results from which to interpret main gate and

 tailgate loading.

35.3 1.09

West Cliff longwall 1 ......... Skybey [1984] .............. IRAD ...... In seam ..... 3-heading with large/small pillar combination; subjective

 assessment of main gate stress profile was required.

4.9 —

West Cliff longwalls 12-13 ..... Gale and Matthews [1992] .... CSIRO HI . . In roof ...... 3-heading with large/small pillar combination,

 interpretation of main gate and tailgate loading.

0.9 1.52

West Wallsend longwall 12 .... Stewart [1996] .............. Hydraulic ... In seam ..... Satisfactory results from which to interpret main gate

 loading condition.

5.2

Wyee longwall 5 ............ Seedsman and Gordon [1991] . Geokon .... In seam ..... Satisfactory results from which to interpret main gate

 loading condition.

6.2-8.8

1SCT operations stress monitoring exercise with HI Cells located in roof above this project's hydraulic stress cell site.
41

Figure 7.—The angle " used to determine the value of HORST.

INDUSTRY REVIEW

The aim of the industry review was to construct a historical

database of gate road and chain pillar performance. During the

course of the project, 19 longwall mines (a cross section from

the 5 major Australian coalfields) were visited. Underground

inspections were conducted at each that incorporated a subjective assessment of gate road performance while documenting

the relevant details in relation to panel and pillar geometry, roof

and floor geology, artificial support, and in situ stress regime.

Brief summary reports were then forwarded to each mine to

confirm the accuracy of the recorded data. Table 3 summarizes

the Australian case histories.

The U.S. database included the Secondary Support Rating

(SSUP), which is described as a rough measure of the volume

of wood installed per unit length of the tailgate [Mark et al.

1994]. It should be noted that 59 of the 62 cases (i.e., 95%)

within the U.S. database used standing secondary support (predominantly in the form of timber cribbing) along the tailgate.

In the Australian database, less than 50% (9 out of 19) mines

routinely installed standing secondary support along the tailgate.

In the context of this study, standing secondary support refers

to timber cribbing, the Tin Can system, Big Bags, etc., and does

not include tendon support (cable bolts or Flexibolts) installed

within the roof. Because of the variety of secondary supports

used, no Australian SSUP was attempted. Instead, a yes/no

outcome is provided in table 3.

An additional geotechnical parameter included within the

Australian database, but not considered during the development

of ALPS in the United States, is the presence of adverse horizontal stress conditions (HORST) (see table 3). Horizontal

stress can damage roadways when they are first driven, and

stress concentrations associated with longwall retreat can cause

further roof deterioration. The following criteria were used to

categorize the operations visited on a yes/no basis:

• 30° < " < 135° (see figure 7); and

• The magnitude of the major horizontal stress (FH)

is >10 MPa.

Actual stress measurements were available from all except

three mines in the database. The major horizontal stress is characteristically twice the vertical stress within Queensland and

New South Wales coalfields. Therefore, at a depth of cover

equal to 200 m, FH is approximately 10 MPa.

It is recognized that geological structure can result in an

adverse reorientation and/or magnification of the general in situ

stress regime. However, there are insufficient data, within the

context of this study, to include such an assessment within

HORST.

STATISTICAL ANALYSES

The same statistical technique used with the U.S. ALPS

database, that of discriminant analysis, was used with the

Australian data. Discriminant analysis is a regression technique that classifies observations into two (or more) populations. In the case of the ALPS data, the classified populations

are tailgates with satisfactory and unsatisfactory tailgate

conditions.

An initial change that was made with the Australian data was

to include "borderline" tailgates with the unsatisfactory cases.

This modification is consistent with the Australian underground

coal industry's desire to have in place strata management plans

that design against both borderline and unsatisfactory gate

road conditions. It also adds to the otherwise small pool of unsatisfactory cases available for analysis.

In their analysis, Mark et al. [1994] were not able to quantify

the effect of standing secondary support on tailgate conditions.

However, because nearly every U.S. case used some standing

support, SSUP is basically intrinsic to the design equation (see

equation 1). Because less than 50% of Australian mines use secondary support, it seems reasonable to assume that tailgates that

presently incorporate standing secondary support would become

unsatisfactory if it were removed. A major modification was to

include all collieries utilizing standing secondary support in the

modified-unsatisfactory category of tailgate conditions.
42

Table 3.—Australian tailgate performance case history database

Mine Location

 Pillar

 width,

 m

 Pillar

 length,

 m

 Seam

 height,

 m

 Depth,

 m

Panel

width,

m

CMRR TG SF PSUP SSUP,

Yes/No

HORST,

Yes/No

Tailgate

condition

Angus Place ........ Tailgate 21 ................. 40 95.5 3.0 340 256 35 0.84 0.84 Yes No S

Angus Place ........ Tailgate 18 ................. 40 94.5 3.0 280 206 35 1.11 0.84 Yes No B

Angus Place ........ Tailgate 22 ................. 40 95.5 3.0 360 256 35 0.76 0.84 Yes Yes U

Central (200) ........ Tailgate 202 ................ 25 94.9 2.5 165 200 55 1.33 0.27 No No S

Central (200) ........ Tailgate 203 ................ 25 94.9 2.5 190 206 55 1.05 0.27 No No S

Central (200) ........ Tailgate 204 ................ 30 94.9 2.5 210 206 55 1.26 0.27 No No S

Central (200) ........ Tailgate 205 ................ 35 94.9 2.5 225 206 55 1.50 0.27 No No S

Central (200) ........ Tailgate 206 ................ 45 94.9 2.5 240 206 55 2.14 0.27 No Yes S

Central (200) ........ Tailgate 207 ................ 45 94.9 2.5 265 206 55 1.87 0.27 No Yes S

Central (200) ........ Significant jointing ............ 94.9 2.5 48 1.05 0.50 No No S

Central (300) ........ Tailgate 302 ................ 30 94.9 2.8 140 200 50 2.00 0.27 No No S

Central (300) ........ Tailgate 303 ................ 30 94.9 2.8 170 206 50 1.63 0.27 No No S

Central (300) ........ Tailgate 304 ................ 35 94.9 2.8 190 206 50 1.80 0.27 No No S

Central (300) ........ Tailgate 305 ................ 40 94.9 2.8 210 206 50 1.95 0.27 No No S

Central (300) ........ Tailgate 306 ................ 45 94.9 2.8 230 206 50 2.07 0.27 No No S

Central (300) ........ Tailgate 307 - 18 cut-through ... 45 94.9 2.8 285 206 31 1.45 0.50 No No U

Clarence ........... Tailgate 2 .................. 45 54.5 4.1 260 178 59 1.20 0.23 No No S

Clarence ........... Tailgate 3 .................. 43 54.5 4.1 260 200 59 1.10 0.23 No No S

Clarence ........... Tailgate 5 .................. 45 54.5 4.1 260 158 59 1.21 0.23 No No S

Clarence ........... Tailgate 6 .................. 45 39.5 4.1 260 200 59 1.22 0.23 No No S

Crinum ............ Tailgate 2 .................. 35 125.2 3.6 135 275 40 2.57 0.69 Yes No S

Dartbrook .......... Tailgate 2 .................. 35 94.8 3.9 250 200 51 0.86 0.42 No No S

Elouera ............ Tailgate 2 - 4 lower stress ...... 45 12.5 3.3 350 155 40 1.02 0.85 Yes No S

Elouera ............ Tailgate 4 - 19.5 cut-through .... 45 125.0 3.3 350 155 40 1.00 0.85 Yes Yes B

Gordonstone ........ Tailgate 102 ................ 40 94.8 3.2 230 200 30 1.49 0.79 Yes No B

Gordonstone ........ Tailgate 202 ................ 40 94.8 3.2 230 255 35 1.49 0.79 Yes No S

Kenmare ........... Tailgate 2 - 13 cut-through ..... 30 119.8 3.1 172 200 65 1.46 0.53 No No S

Kenmare ........... Tailgate 3 - stronger roof 25 119.8 3.1 160 200 65 1.17 0.28 No No S

Kenmare ........... Tailgate 3 - weaker roof ........ 25 119.8 3.1 130 200 46 1.65 0.42 No No S

Newstan ........... Tailgate 10 ................. 31 97.0 3.3 180 130 39 1.39 0.66 Yes Yes B

North Goonyella ..... Tailgate 4 .................. 30 94.8 3.4 180 255 38 1.26 0.77 No No S

Oaky Creek ......... Tailgate 7 - normal roof ........ 30 94.8 3.2 180 200 57 1.32 0.40 No No S

Oaky Creek ......... Tailgate 7 - weaker roof ........ 30 94.8 3.2 200 48 1.32 0.57 No No S

South Bulli (200) ..... Tailgate 203 ................ 24 84.0 2.7 465 138 57 0.23 0.44 Yes Yes U

South Bulli (200) ..... Tailgate 204 ................ 31 94.0 2.7 470 183 57 0.36 0.44 Yes Yes U

South Bulli (200) ..... Tailgates 205-208, 210 ........ 40 96.0 2.7 460 183 57 0.66 0.44 Yes Yes B

South Bulli (200) ..... Tailgates 209, 211-212 ........ 38 97.0 2.7 460 183 57 0.59 0.44 Yes Yes B

South Bulli (300) ..... Tailgate 303 ................ 40 96.0 2.7 450 138 65 0.68 0.44 Yes No S

South Bulli (300) ..... Tailgates 304-305 ............ 55 74.0 2.7 450 183 65 1.15 0.44 Yes No S

See explanatory notes at end of table.
43

Table 3.—Australian tailgate performance case history database—Continued

Mine Location

 Pillar

 width,

 m

 Pillar

 length,

 m

 Seam

 height,

 m

 Depth,

 m

Panel

width,

m

CMRR TG SF PSUP SSUP,

Yes/No

HORST,

Yes/No

Tailgate

condition

South Bulli (300) ..... Tailgates 308-309 ............ 38 97.0 2.7 410 185 65 0.68 0.44 Yes No S

Southern (600) ...... Tailgate 606 ................ 30 94.8 2.8 170 200 60 1.62 0.26 No No S

Southern (600) ...... Tailgates 607-608 ............ 35 94.8 2.8 190 200 60 1.79 0.26 No No S

Southern (700) ...... Tailgate 702 ................ 30 94.8 2.8 160 250 60 1.79 0.26 No No S

Springvale .......... Tailgate 402 ................ 45 95.2 2.7 325 250 35 1.22 0.63 Yes Yes B

Tower ............. Tailgate 14 ................. 45 66.0 3.2 500 203 40 0.59 1.26 No No S

Ulan .............. Tailgate 11 ................. 30 94.8 3.1 145 255 50 1.65 0.28 No No S

West Cliff .......... Tailgate 22 ................. 42 97.2 2.5 480 200 48 0.69 0.49 Yes No S

West Wallsend ...... Tailgate 13 - 4.5 cut-through .... 35 97.1 2.9 240 145 40 1.24 0.75 Yes Yes U

West Wallsend ...... Tailgate 13 - 7 cut-through ..... 35 97.1 2.9 255 233 40 1.11 0.75 No Yes S

West Wallsend ...... Tailgates 14-16 .............. 32 110.1 2.9 250 145 40 0.99 0.75 Yes Yes U

West Wallsend ...... Tailgate 17 - 6 cut-through ..... 35 110.1 3.2 250 145 40 1.08 0.75 Yes Yes B

Wyee ............. Tailgate 13 ................. 35 102.0 2.8 220 163 45 1.43 0.52 No Yes B

 Mean ........................................ 31.2 94.5 3.0 266 200 49.52 1.27 0.49

 Standard deviation .............................. 7.2 16.9 0.4 106 33 10.04 0.47 0.24

S Satisfactory. B Borderline. U Unsatisfactory.
44

Figure 8.—The final design equation relating the CMRR to the TG SF.

Two cases posed additional complications. Tower Colliery

does not incorporate standing secondary support, yet its

PSUP (1.26) is 3.2 standard deviations above the Australian

mean. Therefore, Tower Colliery was also included within the

modified-unsatisfactory tailgate category. Crinum uses standing

secondary support, but it is a relatively new operation, and it

seems that there has been an understandable, but nonetheless

highly conservative approach to its geotechnical design. To

include Crinum within the modified-unsatisfactory group would

have been overly conservative, so it was excluded from the

database entirely.

Therefore, the final database includes 50 case histories with

29 modified satisfactory and 21 modified-unsatisfactory cases.

Numerous analyses were conducted to determine the best design

equation. Ultimately, the most successful design equation

relates the required TG SF to the CMRR, as shown in figure 8:

TG SF ' 2.67 & 0.029 CMRR (3)

Equation 3 correctly predicted the outcome of all except

seven case histories, for a success rate of 86%. Comparing

equation 3 to the U.S. design equation (equation 1), it may be

seen that the TG SF is generally more conservative than the

ALPS SF for weaker roof, but the TG SF decreases more rapidly than the ALPS SF as the roof becomes stronger.

Another strong relationship that was evident in the case

histories was between the primary support and the roof quality.

Figure 9 plots the PSUP against the CMRR, and the best-fit

regression is of the following form:

PSUP ' 1.35 & 0.0175 CMRR (4a)

It seems that Australian mine operators have intrinsically

adapted their primary support patterns to the roof conditions

and operational requirements. Mark et al. [1994] reached a

similar conclusion for the United States.

Upper- and lower-boundary equations (4b and 4c, respectively) relating CMRR to PSUP have also been proposed and

are illustrated in figure 8:

PSUPU ' 1.45 & 0.0175 CMRR (4b)

PSUPL ' 1.24 & 0.0175 CMRR (4c)

Equation 4c may be applicable, for example, when the mining

layout is not subject to adverse horizontal stress conditions

and/or standing secondary support is planned as part of the

colliery's strata management plan.

Mark et al. [1994] also found a strong correlation between

the CMRR and the entry width. No such correlation was seen

here.

It is interesting to note some similarities and differences between the U.S. and Australian databases. For example, overall

roof quality seems to be reasonably similar in the two countries.

The mean CMRR in the United States is 53.7 with a standard

deviation (SD) of 13.9; this compares with an Australian mean

of 49.5 and SD ' 10.0. However, the mean Australian PSUP

is 0.49 (SD ' 0.23), which is approximately twice that of the

U.S. database.

Studies by Mark [1998] and Mark et al. [1998a] suggest

that the horizontal stress levels in the two countries are comparable. It seems that philosophical differences are more likely

responsible for the different levels of primary support. Most
45

Figure 9.—Design equations for primary support based on the CMRR.

Australian coal mines have an unwritten (sometimes written)

policy of no roof falls; U.S. multientry mining systems seem

more tolerant of roof falls. Also, most Australian coal mines

have an antipathy toward standing secondary support for

reasons associated with a two-entry gate road system. It seems

that the main way in which Australian operations prevent poor

tailgate conditions is to install substantial primary support on

development. Therefore, in Australia one would expect a

strong relationship between the level of primary support and a

reliable roof rating system. This is exactly what transpires,

which adds to the credibility of the CMRR.

Additional statistical analyses tested whether the accuracy

of ALPS could be improved by replacing the original

Bieniawski formula with another pillar strength formula. Two

formulas were trialed—the Mark-Bieniawski formula [Mark

and Chase 1997] and Salamon's squat pillar formula [Madden

1988]. The Mark-Bieniawski formula had virtually no impact

on the classification success rate. However, incorporating the

squat pillar formula resulted in a significant decrease in the

classification success rate. The conclusion was to remain with

the original Bieniawski formula used in the "classic" ALPS.

ANALYSIS OF TAILGATE SERVICEABILITY (ALTS)

The chain pillar design methodology proposed by the

project is referred to as "Analysis of Longwall Tailgate

Serviceability" (ALTS). The design methodology recognizes

the impact of ground support on tailgate serviceability and

incorporates guidelines in relation to the installed level of

primary support and the influence of standing secondary

support on the design process.

A design flowchart (figure 10), Microsoft® Excel

Workbook, and user manual have been developed. The spreadsheet workbook (ALTS Protected.xls) was formulated to

facilitate the computational components of the design

methodology.

The ALTS design process should only be employed in

designing chain pillars that are subject to second-pass longwall

extraction. If the chain pillars under consideration are not to be

subject to second-pass longwall extraction, then an alternative

pillar design method should be employed based on pillar

stability and outer gate road serviceability requirements. The

monitored chain pillar loading behavior (conducted as a part of

the project) will assist in estimating the main gate load for

design purposes.

The recommended chain pillar width (rib to rib) is

contingent upon an appropriate level of primary support. That

level of primary support (i.e., PSUPL to PSUPU) is dependent on

(1) the orientation of longwall retreat in relation to the

magnitude and direction of the major horizontal stress and

(2) the use of standing secondary support along the length of the

gate road.

The database is able to identify situations where it is likely

that standing secondary support may be required. However,

there are insufficient data at this stage to make numerical

recommendations for the SSUP similar to those made for the

TG SF and PSUP. Appropriately qualified personnel should

assess the type, level, and timing of SSUP installation.
46

Figure 10.—Flowchart for using Analysis of Longwall Tailgate Serviceability (ALTS).
47

CONCLUSIONS

The following main goals of the project were achieved:

• To establish a chain pillar design methodology that has

widespread application to Australian longwall operations; and

• To quantify the probable variance in the chain pillar

loading environment between collieries and mining localities

and to incorporate this variance within the design methodology.

In addition, the study has been able to propose definitive

guidelines with regard to the installed level of primary support

and to conduct a subjective analysis regarding the impact of

standing secondary support on the design process. This provides the Australian coal industry with a truly integrated design

methodology with regard to tailgate serviceability that has been

able to address the main factors controlled by the mine operator.

The initial benefit from this project is that mine managers

and strata control engineers will be able to identify where chain

pillars can be reduced in size and where increases may be

necessary. They can make these decisions with the confidence

that a credible Australian database is the foundation for the design methodology.

This project has identified that there is an opportunity for

some mines that do not currently incorporate the routine installation of secondary support along their tailgate to make

significant reductions in chain pillar width. It is an operational

decision whether a reduction in pillar width is more or less

beneficial to production output and costs than the introduction

of secondary support along the length of the tailgate. This

project simply highlighted that the opportunity exists.

The chain pillar monitoring exercises conducted at collieries under deep cover or with strong roof have found that the

abutment load may be overestimated by using a generic

abutment angle of $ ' 21°. However, the aggressive tailgate

loading behavior monitored at West Wallsend Colliery (see

figure 5) provided a warning, which emphasized the need to use

great caution before making any sweeping changes to a proven

chain pillar design tool. Although the way in which the load

manifested itself at West Wallsend was significantly different

from that proposed by ALPS, the resultant tailgate load was

quite similar.

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headgate ground control. Min Eng 50(1):61-68.

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strength from back-calculation. Part of a New South Wales Joint Coal Board

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No. 1336.

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West Cliff Colliery. Australian Coal Association Research Program, published

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LW 12 cut-through 11. Coffey Partners International Pty. Ltd. report

No. Z267/4-AB to Oceanic Coal Australia Ltd., November.

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to longwall mining. Proceedings of the Sixth International Conference on

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pp. 172-182.

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Peng SS, ed. Proceedings of the First International Conference on Ground

Control in Mining. Morgantown, WV: West Virginia University, pp. 1-12.

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Geomechanics, coal mining report No. 65.
EXPERIENCE OF FIELD MEASUREMENT AND COMPUTER

SIMULATION METHODS FOR PILLAR DESIGN

By Winton J. Gale, Ph.D.1

49

ABSTRACT

Coal pillar design has been based on generalized formulas of the strength of the coal in a pillar and

experience in localized situations. Stress measurements above and in coal pillars indicate that the actual

strength and deformation of pillars vary much more than predicted by formulas. This variation is due to failure

of strata surrounding coal. The pillar strength and deformation of the adjacent roadways is a function of failure

in the coal and the strata about the coal. When the pillar is viewed as a system in which failure also occurs in

the strata rather than the coal only, the wide range of pillar strength characteristics found in the United

Kingdom, United States, Republic of South Africa, Australia, People's Republic of China, Japan, and other

countries are simply variations due to different strata-coal combinations, not different coal strengths.

This paper presents the measured range of pillar strength characteristics and explains the reasons. Methods

to design pillar layouts with regard to the potential strength variations due to the strata strength characteristics

surrounding the seam are also presented.

1Managing director, Strata Control Technology, Wollongong East, New South Wales, Australia.
50

INTRODUCTION

The strength characteristics of coal pillars have been

studied by many, and the subject is well discussed in the

literature (Salamon and Munro [1967]; Wilson [1972];

Hustrulid [1976]; Mark and Iannacchione [1992]; Gale [1996]).

In general, a range of strength relationships has been derived

from four main sources:

(1) Laboratory strength measurements on different-sized

coal block specimens;

(2) Empirical relationships from observations of failed and

unfailed pillars;

(3) A theoretical fit of statistical data and observations; and

(4) Theoretical extrapolation of the vertical stress buildup

from the ribside toward the pillar center to define the load

capacity of a pillar.

These relationships provide a relatively wide range of potential

strengths for the same pillar geometry. In practice, it has been

found that various formulas are favored (or modified) by users,

depending on past experience in their application to certain

mining districts or countries.

In general, the application of empirically and statistically

based formulas has been restricted to the mining method and

geological environment for which they were developed, and

they often relate to specific pillar geometries. In general, these

methods were developed for shallow, extensive bord-and-pillar

operations for which the pillar was designed to hold the weight of

overburden. The wider application of longwall mining methods

and increasing depth has required a greater understanding of

factors influencing pillar strength and their role in the control of

ground deformation about the mining operations. The development of stress measurement and detailed rock deformation

recording tools over the last 10-15 years has allowed much more

quantification of actual pillar stresses and deformations. Few data

were available when many of the pillar strength relationships

were originally defined. Similarly, the development of computer

simulation methods has allowed detailed back-analysis of the

mechanics of strata-coal interaction in formed-up pillars.

The author and his colleagues have conducted numerous

monitoring and stress measurement programs to assess roadway

stability and pillar design requirements in Australia, the United

Kingdom, Japan, the United States, Indonesia, and Mexico.

The results of these investigations and others reported in the literature have demonstrated that the mechanical response of the

coal and surrounding strata defines the pillar strength, which

can vary widely depending on geology and stress environment.

The application of a pillar strength formula to assess the

strength of a system that is controlled by the interaction of geology, stress, and associated rock failure is commonly an

oversimplification.

MECHANICS OF THE PILLAR-COAL SYSTEM

The strength of a pillar is determined by the magnitude of

vertical stress that can be sustained within the strata-coal

sequence forming and bounding it. The vertical stress developed

through this sequence can be limited by failure of one or more of

the units that comprise the pillar system. This failure may occur

in the coal, roof, or floor strata forming the system, but usually

involves the coal in some manner. The failure modes include

shear fracture of intact material, lateral shear along bedding or

tectonic structures, and buckling of cleat-bounded ribsides.

In pillar systems with strong roof and floor, the pillar coal

is the limiting factor. In coal seams surrounded by weak beds,

a complex interaction of strata and coal failure will occur; this

will determine the pillar strength. The strength achievable in

various elements largely depends on the confining stresses

developed, as illustrated in figure 1. This indicates that as confinement is developed in a pillar, the axial strength of the material increases significantly, thereby increasing the actual

strength of the pillar well above its unconfined value.

The strength of the coal is enhanced as confining stress

increases toward the pillar center. This increased strength is

often related to the width-to-height (w/h) ratio; the larger the

ratio, the greater the confinement generated within the pillar.

Hence, squat pillars (high w/h) have greater strength potential

than slender ones (low w/h).

The basic concepts related to confinement within coal

pillars were developed by Wilson [1972]; with the growing

availability of measurement data, these general mechanics are

widely accepted. However, confining stress can be reduced by

roadway deformations such as floor heave, bedding plane slip,

and other failure mechanisms. These mechanisms are described

below.

ROADWAY DEVELOPMENT PHASE

Prior to mining, the rock and coal units will have in situ

horizontal and vertical stresses that form a balanced initial

stress state in the ground. As an opening (roadway) is created

in a coal seam, there is a natural tendency for the coal and rock

to move laterally and vertically into the roadway. In this

situation, the horizontal stress acting across the pillar will form

the confining stress within that pillar. If this lateral displacement is resisted by sufficient friction, cohesion, and shear

stiffness of the immediate roof and floor layers, then most of

the lateral confining stress is maintained within the pillar. Consequently, the depth of "failure" (yield) into the pillar ribside is

small. If the coal and rock layers are free to move into the

roadways by slippage along bedding planes or shear deformation of soft bands, this confining stress will be reduced.
51

Figure 1.CEffect of confining stress on compressive

strengths of intact and fractured rocks.

Figure 2.CRapid buildup of vertical stress into the pillar

where high confining stresses are maintained.

Hence, the depth of failure into the pillar ribside may be

significantly greater.

The geometry of failure in the system and the residual

strength properties of the failure planes will therefore determine

the nature of confining stress adjacent to the ribsides and extending across the pillars. This mechanism determines the

depth of failure into the pillar and the extent of ribside displacement during roadway drivage.

PILLAR LOADING BY ABUTMENT STRESSES

Roadways are subjected to an additional phase of loading

during longwall panel extraction, as front and then side abutment pressures are added to the previous (and generally much

smaller) stress changes induced by roadway excavation. These

abutment stresses typically considered are predominantly vertical in orientation, but can generate additional horizontal (confining) stresses (by the Poisson's ratio effect) if there is sufficient lateral restraint from the surrounding roof and floor.

Conversely, if the ground is free to move into the roadway, this

increased horizontal stress is not well developed and increased

rib squeeze is manifest instead.

This concept is presented in figure 2; with strong cohesive

coal-rock interfaces the confining stress in the pillar increases

rapidly inward from the ribsides, allowing high vertical stresses

to be sustained by the pillar. The opposite case of low shear

strength coal-rock contact surfaces is presented in figure 3. In

this situation, confinement cannot be maintained sufficiently;

hence, the allowable vertical stress would be significantly less

than that in figure 2. The diagram shows that the pillar has

failed because of its inability to sustain the imposed vertical

abutment stresses. In addition, lateral movement has caused

floor heave and severe immediate roof shearing.

The implications of this for the strength of an isolated pillar

are presented in figure 4, where the load carried by the pillar is

the mean of the vertical stress across it. If this mean stress is

equal to the average "applied load" to be carried by the pillar,

then the pillar is stable (figure 4A). If the applied load is greater, then the pillar is said to fail (figure 4B) and the deficit stress

must be redistributed onto nearby pillars.

Conceptually, pillar strength behavior should fall between

the two end members of:

(1) Lateral slip occurring totally unresisted, so that pillar

strength is limited to the unconfined value of the coal; and

(2) Lateral slip being resisted by system cohesion and

stiffness, such that pillar strength is significantly above its

unconfined value due to confinement.

A range of potential pillar strengths associated with these

two end members relative to the w/h ratio is presented after

Gale [1996] in figure 5. It is assumed that the rock mass

strength of the coal is 6.5 MPa and that the coal is significantly

involved in the failure process. This range of pillar strengths is

representative of most rock failure combinations, except in rare

cases where small stiff pillars may punch into soft clay-rich

strata at loading levels below the field uniaxial compressive

strength of the coal. In the punching situations, pillar strength

may be lower than that depicted, but the variation would generally be confined to pillars having small w/h ratios.

A comparison of these "end member" situations with a

range of pillar strengths determined from actual measurement

programs conducted in Australia and the United Kingdom by

Strata Control Technology and from the United States [Mark
52

Figure 3.CSlow buildup of vertical stress in the pillar where

slip occurs and confinement is reduced.

Figure 4.CPillar strength cases for strong and weak

geologies. A, strong system; B, weak system.

Figure 5.CRange of potential pillar strengths relative to w/h based on confinement

variation (after Gale [1996]).

et al. 1988] is presented in figure 6. The comparison indicates

that a wide range of pillar strengths have been measured for the

same geometry (in terms of w/h) and that the data appear to

span the full interval between the end members. However, two

groupings can be discerned and are shaded in figure 7:
53

Figure 6.CPillar strength information relative to changes (after Gale [1996]).

Figure 7.CGeneralized groupings of strong/normal and weak geology (after

Gale [1996]).
54

Figure 8.CGeological sections modeled to assess load deformation characteristics. A, coal-claylaminite; B, coal-siltstone-laminite; C, coal-sandstone; D, coal-laminite-sandstone.

(1) The "strong/normal" geologies, where pillar strength

appears to be close to the upper bound.

(2) The structured or weak geologies, where the strength

is closer to the lower bound and it is apparent that the strength

of the system is significantly limited.

It should be noted that these two groupings are arbitrary and are

possibly due to limited data. With more data points, the

grouping may become less obvious.

EFFECT OF GEOLOGY

It is clear that a wide range of pillar strengths is possible

and that these are not only related to coal strength and w/h ratio.

Geological factors have a major impact on the strength achievable under the various pillar geometries.

EFFECT OF GEOLOGY ON PILLAR STRENGTH

The effect of various strata types in the roof-coal-floor

pillar systems has been investigated further by computational

methods. Computer models of four pillar systems were loaded

to determine their strength characteristics (figure 8). These

are—

• Massive sandstone-coal-massive sandstone

• Laminite-coal-sandstone

• Weak siltstone-coal-weak siltstone

• Laminite-clayband-coal-clayband-laminite
55

Figure 9.CStrength and w/h for models.

The results of the pillar strength characteristics relative to

w/h are presented in figure 9. The results closely relate to the

field measurement data and confirm that the strata types

surrounding the coal have a major impact on strength and also

provide insight into the geological factors affecting strength.

The results indicate that—

(1) Strong immediate roof and floor layers and good

coal-to-rock contacts provide a general relationship similar to

the upper bound pillar strength in figure 5.

(2) Weak, clay-rich, and sheared contacts adjacent to the

mining section reduce pillar strength to the lower bound areas.

(3) Soft strata in the immediate roof and floor, which fail

under the mining-induced stresses, will weaken pillars to the

lower bound areas.

(4) Tectonic deformation of coal in disturbed geological

environments will reduce pillar strength, although the extent

depends on geometry and strength of the discontinuities.

Obviously, combinations of these various factors will have

a compounding effect. For example, structurally disturbed,

weak, and wet roof strata may greatly reduce pillar confinement

and, consequently, pillar-bearing capacity.

EFFECT OF GEOLOGY ON POSTPEAK PILLAR

STRENGTH

The postpeak pillar strength characteristics for some of the

pillars modeled are presented in figure 10. The pillar strength

is presented as a stress/strain plot for various width/height

pillars. The results presented in figure 10A show that in strong

sandstone geology, high strengths are achievable in small pillars

(w/h ' 5) and the pillar maintains a high load-carrying

capability. In the example modeled, "short-term" load losses

were noted to occur in association with sudden rib failure.

These instances are present in figure 10A as "rib bumps." In

sections of laminite roof, these pillars may lose strength if the

laminite fails at a very high load above the pillar. For pillars

with a w/h less than 4/5, a loss in strength is expected at a high

load due to failure of the coal.

In pillar systems with weak strata surrounding the coal, the

pillars typically exhibit a strength loss after peak load is

achieved. Large width/height pillars are required to develop a

high load-carrying capacity after failure in the weak pillar

systems modeled. Two examples are presented in figure 10B,

which shows the postpeak strength characteristics of pillars

with weak mudstone or clay surrounding the coal. In these
56

Figure 10.CPostpeak strength of models. A, w/h ' 5;

B, w/h ' 15.

examples, the strength loss is greater in the situation of weak

clay surrounding the coal.

The implications of this are significant for the design of

barrier and chain pillars where high loads are anticipated. If

excessive loads are placed on development pillars in this

environment, pillar creep phenomena are possible due to the

load shedding of failed pillars sequentially overloading adjacent

pillars. The effect of load shedding in chain pillars when

isolated in the goaf is to redistribute load onto the tailgate area

and to potentially display increased subsidence over the pillar

area. The typical result is to have major tailgate deformation,

requiring significant secondary support to maintain access and

ventilation.

AN APPROACH TO PILLAR DESIGN

Field studies suggest that a range of strengths is possible

extending within upper and lower bounds. If we make use of

these relationships as "first-pass estimates" to be reviewed by

more detailed analysis later, then a number of options are available. In known or suspected weak geologies, the initial design

may utilize the lower bound curve of the weak geology band in

figure 7. In good or normal geologies, the Bieniawski or squat

pillar formulas may be suitable for initial estimates. Two

obvious problems with this approach are:

(1) Estimates of pillar size can vary greatly, depending on

the geological environment assumed; and

(2) The pillar size versus strength data set used (figure 6)

is limited.

This is why such formulas or relationships are considered as

first-pass estimates only, to be significantly improved later by

more rigorous site-specific design studies utilizing field measurements and computer simulation.

Design based on measurement requires that the vertical

stress distribution within pillars be determined and the potential

strength for various sized pillars be calculated. It is most useful

to measure the vertical stress rise into the pillar under a high

loading condition or for the expected "working loads." The

stress measurement profiles are used to determine the potential

load distributions in pillars of varying dimension and hence to

develop a pillar strength relationship suitable for that geological

site. An example of stress measurements over a pillar is presented in figure 11; however, the method is limited to determining the potential stress distribution in different pillar widths

under the measured loading condition.

Extrapolation of increased loading is more problematic. In

weak ground, an approach is to extrapolate the vertical stress

buildup from the rib toward the pillar center. This may be possible where the vertical stress buildup approximates a line in the

yield zone. This often provides a low estimate of the peak pillar

strength and should be considered a working estimate only. An

example of this is presented in figure 11B. Experience suggests

that this is more likely in weak ground; however, in stronger

ground the stress buildup is often more exponential and, as

such, difficult to extrapolate.

To assess the potential strength under higher loading conditions, a method to redistribute the stress within the pillar associated with an increased average load, or the ability to monitor

the effect of additional loading, is required.

Monitoring of stress distributions within pillars during mining can provide elevated loading conditions for analysis. An

example is presented in figure 12, whereby small pillars were
57

Figure 11.CStress measurements over ribsides for

strength assessment. A, typical stress measurement locations; B, stress distribution in pillar from measurements.

Figure 12.CExample of small pillar monitoring studies indicating pillar stress history.

instrumented with CSIRO HI Cells and monitored until well

isolated in the goaf after the passage of a longwall panel.

Computer modeling methods have been developed to

simulate the behavior of the strata sections under various stress

fields and mining geometries. For mine design, such simulations must be validated against actual ground behavior and

stress measurements. This provides confidence that sufficient

geological investigation has been undertaken and that the

strength properties and deformation mechanisms are being

simulated accurately. The computer software developed by

Strata Control Technology has been verified in a number of

field investigations where computer predictions of stress

distributions and rock failure zones have been compared. An

example is presented in figure 13, which compares the

measured and modeled stress distribution over a yield pillar and

solid coal in a deep mine. Another example of computer
58

Figure 13.CStress over yield pillar and adjacent to longwall.

Figure 14.CComparison of modeled and measured (A) vertical

and (B) horizontal stress over a longwall side abutment. Stress

measurements were made in a borehole drilled from an adjacent

roadway.

modeling capabilities is presented in figure 14 for weak ground

adjacent to a longwall panel. A series of stress measurements

was conducted to define the abutment geometry and compared

to computer simulations based on the geological section and

goaf geometry. The results indicate a very close correlation and

that rigorous computer simulation methods can provide a good

estimation of the actual stresses and ground failure zones.

One major benefit of computer modeling is that the

behavior of roadways adjacent to the pillars can be simulated.

In this way, the design of a pillar will reflect not only the stress

distribution within it, but also its impact on roadway stability.

An example is presented in figure 15 in which the anticipated

deformation of a roadway adjacent to a longwall panel under

elevated abutment loading was evaluated. The effect of various

reinforcement, support, and mining sections was simulated to

determine the appropriate mining approach.

In mining situations where there are large areas of solid

ground about the working area, the potential for regional

collapse of pillars is typically low. Design in these areas usually relates to optimizing roadway conditions and controlling

ground movements rather than the nominal pillar strength.

Yield pillars and chain pillars are obvious examples of this

application. Design must assess the geometry of other pillars

and virgin coal areas in determining the impact of a particular

stress distribution within a pillar and the ability of the overburden to span over a yielded pillar and safely redistribute the

excess stress to adjacent ground. Figure 13 shows an example

of this process for a failed ("yield") pillar adjacent to solid

ground.

CHAIN PILLAR DESIGN ISSUES

It has become increasingly apparent from field monitoring

and computer simulations of longwall caving that the design of

chain pillars requires a larger scale review of ground behavior

rather than "small-scale" pillar strength criteria. Microseismic

monitoring [Kelly et al. 1998] has demonstrated significant rock

fracture above and below chain pillars. Computer modeling of

caving [Gale 1998] has also demonstrated rock fracture above

and below pillars. Rock failure above and below chain pillars

occurs as a result of gross scale stress changes and fluid pressure redistributions.

The strength and loading conditions of chain pillars can

reflect the larger scale fracture geometries that may develop.

An example of an abutment stress within a pillar at shallow

depth (250 m) is presented in figure 16. In this case, rock failure extends over the ribside and shifts the abutment distribution

within the pillar.

Modification of the vertical abutment stress distribution has

been noted in field monitoring and computer simulations under

conditions of high lateral stress. It has been found that the abutment distribution tends to have a lower peak stress, but it

spreads over a longer lateral extent. An example is presented

in figure 17.

In both of these examples, computer modeling of the

caving process within the geological section closely correlates
59

Figure 15.CSimulation of roadway conditions under abutment stress.

with the measured data. The use of generalized empirical

methods to determine the abutment profile is also presented and

indicates that their application is best utilized as initial estimates

to be reassessed by site-specific investigations for key design

areas.

Rock failure above and below chain pillars does not

necessarily occur at all sites; however, experience suggests that

this is common. The gross scale rock failure about longwall

panels, therefore, requires design for ground control issues

rather than pillar design, as traditionally conceived. Field measurement, computer modeling, and microseismic investigations

play a key role in defining the design criteria. Empirical databases are also useful; however, the user should be aware of the

ground deformation mechanics in order to assess the

applicability of the data being used relative to the site conditions to which it would be applied.
60

Figure 16.CLongwall side abutment profiles for modeled, measured, and empirical approaches.

In this example, rock failure occurred about the pillar, forming a more extensive yield zone.

Figure 17.CLongwall side abutment profiles for modeled, measured, and empirical approaches in a high stress

mining area.

CONCLUSIONS

The strength characteristics of pillars depend on the

strength properties of the strata surrounding the coal.

It is important to consider the postfailure strength of pillars

in design, particularly in areas of weak strata where a postfailure strength loss in moderate to large width/height pillars is

possible.

Computer simulation methods in association with site

measurements are recommended for the design of key layouts

that require an assessment of geological variations, pillar size,

and stress field changes to optimize the mining operation. This

approach also assesses the expected roadway conditions or

pillar response for various mine layouts; these can be monitored

to determine if the ground is behaving as expected.

Design of pillars adjacent to large extraction areas needs to

include the large-scale fracture distributions and, in general,

needs to be based on a ground control criterion rather than on

a pillar strength criterion only.
61

REFERENCES

Gale WJ [1996]. Geological issues relating to coal pillar design. In:

McNally GH, Ward CR, eds. Symposium of Geology in Longwall Mining,

pp. 185-191.

Gale WJ [1998]. Experience in computer simulation of caving, rock

fracture and fluid flow in longwall panels. In: Proceedings of the International

Conference on Geomechanics/Ground Control Mining and Underground Construction, pp. 997-1007.

Hustrulid WA [1976]. A review of coal strength formulas. Rock Mech

8:43-50.

Kelly M, Gale WJ, Luo X, Hatherly P, Balusu R, LeBlanc Smith G

[1998]. Longwall caving process in different geological environments; better

understanding through the combination of modern assessment methods. In:

Proceedings of the International Conference on Geomechanics/Ground Control

Mining and Underground Construction, pp. 573-589.

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.

Mark C, Iannacchione AT [1992]. Coal pillar mechanics: theoretical

models and field measurements compared. 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. 78-93.

Mark C, Listak JM, Bieniawski ZT [1988]. Yielding coal pillars: field

measurements and analysis of design methods. In: Proceedings of the 29th

U.S. Symposium on Rock Mechanics. New York, NY: American Institute of

Mining, Metallurgical, and Petroleum Engineers, pp. 261-270.

Salamon MDG, Munro AH [1967]. A study of the strength of coal

pillars. J S Afr Inst Min Metall, pp. 55-67.

Wilson AH [1972]. An hypothesis concerning pillar stability. Min Eng

(London) 131(141):409-417.
63

UNIVERSITY OF NEW SOUTH WALES COAL PILLAR STRENGTH

DETERMINATIONS FOR AUSTRALIAN AND SOUTH 

AFRICAN MINING CONDITIONS

By Jim M. Galvin, Ph.D.,1 Bruce K. Hebblewhite, Ph.D.,2

and Miklos D. G. Salamon, Ph.D.3

ABSTRACT

A series of mine design accidents in the late 1980s resulted in a major research program at the University

of New South Wales, Australia, aimed at developing pillar and mine design guidelines. A database of both

failed and unfailed Australian underground coal mine pillar case studies was compiled. A procedure was

developed to enable the effective width of rectangular pillars to be taken into account. The database was

analyzed statistically using the maximum likelihood method, both independently and as a combined data set

with the more extensive South African database. Probabilities of failure were correlated to factors of safety.

It was found that there was less than a 4% variance in pillar design extraction ratios resulting from each of

these approaches. There is a remarkable consistency between the design formulas developed from backanalysis of the two separate national pillar databases containing many different coal seams and geological

environments.

1

Professor and Head, School of Mining Engineering, University of New South Wales, Sydney, Australia.

2

Professor, School of Mining Engineering, University of New South Wales, Sydney, Australia.

3Distinguished professor, School of Mining Engineering, Colorado School of Mines, Golden, CO.
64

Fs1 ' K1r % (1&r)

w

h

, (1)

INTRODUCTION

In the 3-year period to 1992, 60 continuous miners were

trapped by falls of strata for more than 7 hr in collieries in New

South Wales, Australia. In the preceding 2 years, eight coal

miners were killed in pillar extraction operations in New South

Wales. In the New South Wales and Queensland coalfields,

at least 15 extensive collapses of bord-and-pillar workings occurred unexpectedly in the 15-year period to 1992. Six of these

collapses occurred in working panels; fortuitously, five occurred during shutdown periods and the sixth occurred while

the continuous miner was being flitted to the surface for repairs.

One contributor to these events was the lack of a comprehensive pillar design procedure. Legislation in New South

Wales at the time simply required coal pillars to have a

minimum width of one-tenth depth or 10 m, whichever was

greater. The influence of pillar height on strength received no

recognition.

This set of circumstances led to funding by the New South

Wales Joint Coal Board of a major research project on pillar design and behavior. The research was undertaken by the School of

Mining Engineering at the University of New South Wales

(UNSW). The primary objectives of the research were to improve

the understanding of coal pillars and associated floor and roof

strata behavior under various loading conditions and to incorporate

these outcomes into the mine design knowledge base.

RESEARCH METHODOLOGY

The approach adopted to pillar design was based on that

developed for square pillars by Salamon and Munro [1966,

1967]. However, the extensive use of rectangular and diamondshaped pillars in Australia required more detailed consideration

of the effective width of parallelepiped pillars and the effect of

this width on pillar strength.

Firstly, an adequate Australian database of failed and

unfailed pillar case histories was established. A relationship

was then developed to factor in the influence of rectangular and

diamond-shaped pillars, which comprised just over 50% of the

database. This database was then subjected to rigorous statistical analysis using a range of techniques in order to quantify

parameters associated with each of two generally accepted

empirical formulas for describing pillar strength. This facilitated

the establishment of correlation, for all strength expressions,

between the probability that a formula would yield a successful

design versus the respective design factor of safety.

The Australian database was also combined with the much

larger and long-established South African database, and the

analysis was repeated to determine if the two population bases

could be considered as one. A close correlation was obtained,

leading to an increased level of confidence in this methodology

and to a number of more universal conclusions concerning pillar

design.

EMPIRICAL COAL PILLAR STRENGTH ESTIMATIONS

The development of computer and numerical technologies

in recent decades has facilitated, at least in principle, the analysis of stresses in pillars and their foundations, i.e., the roof and

floor strata. Unfortunately, physical experimentation has not

advanced equally rapidly. Hence, the understanding of the

intrinsic constitutive laws controlling the behavior of yielding

rocks is still unsatisfactory. More immediate problems include

the significant discrepancies between the physical properties exhibited by rocks in situ and those measured in the laboratory by

testing small specimens. These problems relate to the effects of

size and shape on rock strength.

Many investigators have proposed simple empirical formulas to describe the strength of coal pillars. The most common

feature of most of these empirical relationships is that they define strength ostensively only in terms of the linear dimensions

of the pillars and a multiplying constant, representing the

strength of the unit volume of coal. Investigators over the years

have proposed formulas that belong to one of two types. One

type defines pillar strength simply as a linear function of the

width-to-height (w/h) ratio:

where K1

 is the compressive strength of a cube and r is a dimensionless constant. The quantities of w and h are the width and

height of the pillar, respectively.

If the notation

 R ' w/h (2)
65

Fs2 ' K2

w

w0

"

h

h0

$

, (4)

we' w1w2

, (5)

we' 4

A

p

C

p

, (6)

is introduced, then equation 1 becomes

Fs1 ' K1[r % (1 & r)R]. (3)

According to this formula, geometrically similar pillars have the

same strength regardless of their actual dimensions.

A second commonly used pillar strength formula takes the

form

which is expressed in a dimensionally correct form. " and $ are

dimensionless parameters; w and h are the linear dimensions of

the pillar. Multiplier K2

 is the strength of a reference body of

coal of height h0

 and a square cross section with side length w0.

In most instances, the reference body is taken to be cube of

unit volume for convenience's sake, in which case h0

 and w0 are

both unity and can be omitted from the formula. Expressions

belonging to this family are referred to as power law strength

formulas. In contrast to formulas of the form of equation 1,

these formulas are also volume-sensitive.

EFFECTIVE WIDTH OF PARALLELEPIPED PILLARS

The development of statistically based pillar design formulas rests minimally upon the premise that a fairly large and

tolerably reliable database of unfailed and failed pillar panels

can be compiled. Salamon et al. [1996] have identified a number of strict criteria that must be satisfied before a case can be

included in the database. One of these that must be appreciated

when applying the outcomes of this pillar design research is that

these outcomes apply only to competent roof and floor environments, i.e., the database relates only to failures of the coal

pillar element of the pillar system, not to the roof or floor

elements.

Against this background, an Australian database of

19 failed and 16 unfailed cases was assembled. Rectangular

pillars comprised eight of the failed and nine of the unfailed

cases. Diamond-shaped pillars comprised one failed case. In

order to preserve in these circumstances the availability of the

strength formulas derived for square pillars, many researchers

have proposed the introduction of an effective width.

One of the most basic approaches is to define the effective

width, we

, as

where w1 ' minimum pillar width (measured along 

roadway)

and w2 ' maximum pillar width (measured along 

roadway).

In situations where w2

is not extremely different to w1, this approach has merit. However, when w2

 » w1, the equation produces an unrealistic effective pillar width (table 1).

Table 1.CApplication of various effective

pillar width formulas

(Width and height in meters)

w1 w2 h /w1w2 4Ap

/Cp w1

100 100 3 100.0 100 100

80 100 3 89.4 88.9 88.9

50 100 3 70.7 66.7 66.7

30 100 3 54.7 46.2 46.2

20 100 3 44.7 33.3 33.3

15 100 3 38.7 26.1 21.7

10 100 3 31.6 18.2 10.7

1 100 3 10.0 2.0 1

The most promising recommendation has come from Wagner

[1974, 1980], who, making use of the concept of hydraulic

radius, suggested that the effective width be defined as

where Ap

 and Cp are the cross-sectional area and the circumference of the pillar, respectively.

Application of equation 6 produces effective pillar width

similar to that of equation 5 when w1

 is greater than about 0.5w2

(table 1). At moderate to low values of w1 (0.4w2 # w1 #

0.2w2), equation 6 predicts a smaller effective width, which is

more sensible from a mechanistic viewpoint. However, at very

low values of w1

 (w1 < 0.2w2), the equation is still considered to

overestimate the effective pillar width. This is because when a

pillar is narrow, failure is likely to occur across the narrow dimension before sufficient confinement is generated in the

longitudinal direction to be of benefit.
66

1o'

2w2

w1% w2

. (9)

we' w1

R&Rl

Ru&Rl

o ' w1.

(10)

V ' w

2

h R '

w1sin 2

h

'

w

h

(14)

Figure 1.CDefinition of mining variables associated with a

parallelepiped pillar.

Figure 2.CComparison of the various proposals for calculating

the effective width of a 100-m-long, 3-m-high rectangular pillar.

This leads to the concept that rectangular and irregular

pillars need to be of a critical minimum width before benefit is

gained from confinement generated in the longitudinal direction. This benefit can be expected to ramp up to a plateau level

as the minimum width increases. Furthermore, it is reasonable

to expect that this minimum critical width will be a function of

mining height, increasing with increasing mining height.

The need to nominate a minimum critical pillar width has

been incorporated into the analysis by modifying equation 6 on

the basis that almost all pillars can be regarded as parallelepipeds, i.e., their bases are parallelograms (figure 1). Pillars

therefore have side lengths w1

and w2 (w1# w2) and an internal

angle 2 # 90°. Equation 6 then becomes

we o ' 1ow, (7)

where w is the minimum width of the pillar, i.e.,

w ' w1 sin 2 (8)

and the dimensionless factor 1o is defined by

The range of this factor is 1 # 1o

 < 2, which is encountered as

the aspect ratio moves from unity toward infinity. Experience

indicates that much before the complete failure of a pillar, its

edges are already yielding. Thus, if the w/h ratio in one direction of a rectangular pillar is low, one of the principal

stresses confining its core will remain small, and this stress,

together with the maximum stress, will control failure.

Hence, the extra confinement that may arise from the

aspect ratio will have little or no effect. It is suggested that

such apprehension may be catered for by postulating that the

effective width is the minimum width, i.e., we ' w as long as

R < Rl

, and it becomes we ' weo when R > Ru.

In the intermediate range, i.e., when Rl # R # Ru

, the effective width changes smoothly in accordance with

Here, the choice of the limiting w/h ratios is open to judgment.

It appears reasonable, however, to use the following values:

 Rl ' 3 Ru ' 6 (11)

Table 1 and figure 2 show the effects of the various approaches when applied to calculating the effective width of a

100-m-long, 3-m-high rectangular pillar.

Using the concept of effective width, the power law in

equation 4 can be rewritten for pillars with a general parallelepiped shape:

Fs2 ' K2w

"

h

$ 1"

(12)

An alternative form of this formula expresses the strength as the

function of the pillar volume V and the w/h ratio R:

Fs2 ' K2V

 aR b 1"

, (13)

where the volume refers to a dummy square pillar of width w

and height h, and the w/h ratio is calculated from the minimum

pillar width:
67

a '

1

3

(" % $) b '

1

3

(" & 2$) (15)

Fs2 ' K2V

aR

b

o 1

" b

g

R

Ro

g

&1 %1 , (16)

qm' (H*

(w%b1) (w2% b2/ sin 2)

ww2

(18)

Fs2 ' 7.4

w

0.46

h

0.66

(MPa) (19a)

Fs2 '

19.24

w

0.133 h0.067

0.237 w

5h

2.5

&1 %1 (MPa) (19b)

The new constants a and b can be defined in terms of constants

" and $:

Experience has shown that the original power law formula

(equation 4) tends to underestimate the strength of squat pillars,

i.e., pillars with a w/h ratio in excess of about 5. To cater for

this problem, Salamon and Wagner [1985] suggested an

extension of equation 4 into the range of higher w/h ratios.

This extension, after adaptation to pillars of parallelepiped

shape, is

which is valid if R > Ro

 and where 1 is defined in equation 10.

This particular form was chosen to ensure that there is a smooth

transition between this and equation 13 at R ' Ro

 [Salamon and

Wagner 1985]. Here, Ro

 and g are appropriately chosen constants. The expression is often referred to as the squat pillar

strength formula. Since its inception, it has been applied

widely in the Republic of South Africa using the following pair

of constants:

Ro ' 5 g ' 2.5 (17)

In critical situations, the judgment exercised in deriving the

effective pillar width relationship may be regarded as too speculative. This concern can be addressed by either choosing an

elevated design factor of safety to account for this level of uncertainty or reverting to the use of the minimum pillar width in

pillar strength calculations.

Another aspect to the use of rectangular pillars is the calculation of pillar load. In calculating the tributary load, the true

dimensions need to be employed. Thus, the pillar load assumes

the following form:

In this relationship, * is a modifier. It is unity in all cases where

the pillar burden is the conventional tributary load. If, however,

due to secondary extraction the pillar load is believed to differ

from this value, the load can be adjusted by applying this factor.

Moreover, to remain consistent with earlier calculations, ( is

taken to be: ( ' 1.1 psi/ft ' 24.8827 kN/m3 ' 24.8827 kPa/m.

UNSW INITIAL DESIGN FORMULAS

In 1992, following a number of serious incidents related to

the lack of restriction on pillar height, the Chief Inspector of

Coal Mines in New South Wales required operators to obtain

approval to mine at heights exceeding 4 m. To address the need

for a pillar design methodology, the UNSW research team

undertook in 1995 a preliminary analysis of its database

[Hocking et al. 1995]. At the time, the database comprised

14 collapsed cases and 16 stable cases that satisfied the

selection criteria. The database was analyzed statistically using

the full maximum likelihood method. Galvin and Hebblewhite

[1995] subsequently published the following pillar design

formulas, which find current application in Australia:

and its squat pillar version (R > 5):

A conservative approach was adopted, and the minimum

pillar width was proposed as the effective width. It follows,

therefore, that 1 ' 1 in these expressions. There was little

difference in the pillar strength obtained by allowing all

parameters to float in the statistical analysis as opposed to allowing only the K values to float and fixing the other parameters to

be the same as those used for many years in the Republic of

South Africa. To avoid confusion and to facilitate the introduction of the formulas, therefore, only those formulas derived

by allowing the K values to float were presented to operators.

The formula for strength based on the linear relationship took

the following form:

Fs1 ' 5.36(0.64 % 0.36R) (MPa) (20)
68

Fs2 ' 8.60 (w1)

0.51

h

0.84

(MPa) (21a)

Fs2 '

27.631

0.51

w

0.220 h0.110

0.290 w

5h

2.5

&1 %1 (MPa) (21b)

Fs2 ' 6.88 (w1)

0.42

h

0.60

(MPa) (22a)

Fs2 '

16.361

0.42

w

0.116 h0.058

0.215 w

5h

2.5

&1 %1 (MPa) (22b)

Figure 3.CPillar strength and pillar load relationship for

both the failed (o) and unfailed (+) Australian cases.

UNSW REFINED (RECTANGULAR) FORMULAS

In 1996, a more comprehensive statistical analysis of the

expanded Australian database was completed that incorporated

the effective width of rectangular pillars as defined earlier

[Salamon et al. 1996]. Statistical methods included least

squares, limited maximum likelihood, and full maximum likelihood. Both power law models and linear law models were

evaluated, and all parameters were allowed to float. In all instances, the power law model gave better correlations.

The following strength formulas were found to best

describe the observed behavior of pillars in New South Wales

and Queensland:

The corresponding expression for squat pillars is given by

In these expressions, w ' w1

 sin 2, and the effective width

factor 1 is as defined in equation 10.

The relationship between pillar strength and pillar load

produced by these equations for each point in the database is

shown in figure 3. Design factors of safety associated with the

probability of achieving a stable design are shown in table 2.

Table 2.CProbability of failure

versus factor of safety

Probability of

failure

Factor of

safety 

8 in 10 ........... 0.87

5 in 10 ........... 1.00

1 in 10 ........... 1.22

5 in 100 .......... 1.30

2 in 100 .......... 1.38

1 in 100 .......... 1.44

1 in 1,000 ........ 1.63

1 in 10,000 ....... 1.79

1 in 100,000 ...... 1.95

1 in 1,000,000 ..... 2.11

REANALYSIS OF THE SOUTH AFRICAN DATABASE

The original extensive South African coal pillar database

used by Salamon and Munro in 1966 has since been updated

and supplemented by Madden and Hardman [1992]. This

combined South African database comprises 44 failed and

98 unfailed cases. It has also been reanalyzed using the same

statistical techniques used for the Australian database. Two

failed cases were later omitted from the data set [Salamon et al.

1996].

This analysis has produced the following strength

formulas:

The corresponding expression for squat pillars (R > 5) is given

by

The linear version of the strength estimator is simply

Fs1 ' 5.60(0.69 % 0.31R) (MPa) (23)
69

Fs2 ' 6.88 w1

h

0.7

(MPa) (24a)

Fs2 '

19.05 1

w

0.133 h0.066

0.253 w

5h

2.5

&1 %1 (MPa) (24b)

Figure 4.CComparison between South African power formulas, 1966/82 and 1996. A, h ' 2 m; B, h ' 4 m.

Figure 5.CThe failed (o) and unfailed (+) cases in a pillar

strength versus pillar load plot using the combined AustralianSouth African database.

Figure 4 shows the comparison between the pillar strength

produced by equations 22a and 22b and that predicted by the

original Salamon and Munro formula and its modified squat

pillar form. In the case of a mining height of 2 m, the figure

shows that for a given pillar strength, pillars designed with the

updated formulas may need to be about 2 m wider. For a bord

width of 6 m at a w/h ratio of 10, this results in about 3% less

resource recovery. For similar circumstances in a 4-m mining

height, the increase in pillar size is on the order of 3.2 m.

COMBINED AUSTRALIAN AND SOUTH AFRICAN DATABASES

A further step in the research program was to combine the

South African and Australian databases and to analyze them as

a combined population, then compare and contrast them with

the two independent data populations for each country. This

combined database comprised 177 cases of pillar systems,

including 61 collapsed cases. This produced the following

formulas:

For R > 5, the squat version of this expression takes the

following form:

The corresponding linear formula is simply

Fs1 ' 5.41(0.63 % 0.37R) (MPa) (25)

Figure 5 shows failed and unfailed cases in the load plane.

The figure illustrates a fairly good discrimination between the

two sets of points. Only one unfailed point occurs on the wrong

side of the s ' 1 line, and the median failed cases is 1.039.

Figure 6 shows a comparison between pillar strengths

using power law estimators derived from the Australian, South

African, and combined Australian-South African databases. The

closeness of the predictions is remarkable considering the geographical separation of the Australian and South African

coalfields.
70

Figure 6.CComparison between power law strength formulas derived for the Australian, South African, and combined databases. 

A, h ' 2 m; B, h ' 4 m.

CONCLUSIONS

The statistical analysis of the Australian database indicates

that the method proposed for calculating the effective width of

parallelepiped pillars produced sensible outcomes. However,

it must be remembered that, although of sufficient size to be

statistically significant, the parallelepiped database is small.

The method should therefore be used with caution.

In order to enhance confidence in the pillar design procedure, including the use of the effective pillar width method,

additional research was undertaken. It was noted that the formula derived from the initial Australian database closely resembled the original Salamon-Munro expression. This somewhat surprising resemblance prompted further research and

enlargement of the database. The larger database yielded pillar

strengths that again were similar to those obtained from the

initial UNSW research and by Salamon and Munro. The combination of the Australian and South African databases reinforced the original impression, namely, that the underlying

pillar strengths in these countries resembled each other closely.

The outcome of the investigation lends support to the view

expressed by Mark and Barton [1996]. They suggested that

strength values obtained in the laboratory cannot be utilized in

a meaningful way in pillar design and that the variation in the

strength of pillars of the same size can be disregarded in many

instances. Mark and Barton [1996] emphasize that they do not

claim that the in situ strength of all U.S. coal is the same. Their

study merely showed that a uniform strength is a better approximation than one based on laboratory testing. Although the

UNSW research conclusions are encouraging, complacency is

not justified. The formulas are based on competent roof and

floor conditions. Significantly different pillar strengths may be

associated with abnormal strata behavior mechanisms. Because

pillars with w/h ratios greater than 10 have not been tested to

destruction, it must also be recognized that neither linear nor

power law formulas have been validated at w/h ratios greater

than about 8.

It cannot be overemphasized that, because the design formulas have been developed on a probabilistic basis, they need to

be reviewed periodically as the database expands and the understanding of pillar mechanics advances. A fundamental rule

of empirical research is that the results should be used within the

range of data used in their derivation. Extrapolation with

empirical formulas is always fraught with danger.

REFERENCES

Galvin JM, Hebblewhite BK [1995]. UNSW pillar design methodology.

Sydney, Australia: University of New South Wales, School of Mining Engineering, Research Release No. 1.

Hocking G, Anderson I, Salamon MDG [1995]. Coal pillar strength formulae and stability criteria. Sydney, Australia: University of New South

Wales, School of Mining Engineering, Research Report 1/95.

Madden BJ, Hardman DR [1992]. Long-term stability of bord-and-pillar

workings. In: Proceedings of the Symposium on Construction Over Mined

Areas. Pretoria, Republic of South Africa.

Mark C, Barton TM [1996]. The uniaxial compressive strength of coal:

should it be used to design pillars? In: Ozdemir L, Hanna K, Haramy KY,

Peng S, eds. Proceedings of the 15th International Conference on Ground Control in Mining. Golden, CO: Colorado School of Mines, pp. 61-78.

Salamon MDG, Munro AH [1966]. A study of the strength of coal pillars.

Transvaal and Orange Free State Chamber of Mines, Research Report

No. 71/66.

Salamon MDG, Munro AH [1967]. A study of the strength of coal pillars.

J S Afr Inst Min Metall, pp. 55-67.
71

Salamon MDG, Wagner H [1985]. Practical experiences in the design of

coal pillars. In: Green AR, ed. Proceedings of the 21st International

Conference of Safety in Mines Research Institutes (Sydney, Australia).

Balkema, pp. 3-9.

Salamon MDG, Galvin JM, Hocking G, Anderson I [1996]. Coal pillar

strength from back calculation. Sydney, Australia: University of New South

Wales, School of Mining Engineering, Research Report 1/96.

Wagner H [1974]. Determination of the complete load deformation

characteristics of coal pillars. In: Proceedings of the Third International

Congress on Rock Mechanics. International Society for Rock Mechanics,

pp. 1076-81.

Wagner H [1980]. Pillar design in coal mines. J S Afr Inst Min Metall,

pp. 37-45.
72
73

PRACTICAL BOUNDARY-ELEMENT MODELING FOR MINE PLANNING

By Keith A. Heasley, Ph.D.,1 and Gregory J. Chekan2

ABSTRACT

As part of the initial investigation and validation of a new boundary-element formulation for stress

modeling in coal mines, the underground stresses and displacements at two multiple-seam coal mines with

unique stress problems were modeled and predicted. The new program, LAMODEL, calculates stresses and

displacements at the seam level and at requested locations in the overburden or at the surface. Both linear

elastic and nonlinear seam materials can be used, and surface effects, multiple seams, and multiple mining

steps can be simulated. In order to most efficiently use LAMODEL for accurate stress prediction, the program

is first calibrated to the site-specific geomechanics based on previously observed stress conditions at the mine.

For this calibration process, a previously mined area is "stress mapped" by quantifying the observed pillar and

strata behavior using a numerical rating system. Then, the site-specific mechanical properties in the model

are adjusted to provide the best correlation between the predicted stresses and the observed underground stress

rating. Once calibrated, the model is then used to predict future stress problems ahead of mining. At the two

case study mines, the calibrated models showed good correlation with the observed stresses and also accurately

predicted upcoming high stress areas for preventive action by the mines.

1

Supervisory physical scientist.

2Mining engineer.

Pittsburgh Research Laboratory, National Institute for Occupational Safety and Health, Pittsburgh, PA.
74

INTRODUCTION

Mine planners have a variety of modeling methods, both

empirical and numerical, for analyzing pillar stresses and

determining safe pillar sizes for various mine geometries and

geologic structures. Empirical methods emphasize the

collection and interpretation of case histories of pillar

performance. The Analysis of Longwall Pillar Stability (ALPS)

and Analysis of Retreat Mining Pillar Stability (ARMPS)

programs are two such empirical programs that are derived

from large databases of real-world pillar studies and can be

used for determining pillar sizes for single-seam longwall and

retreat room-and-pillar mining, respectively [Mark 1992; Mark

and Chase 1997]. The Virginia Polytechnic Institute and State

University, Blacksburg, VA, recently developed a comparable

empirical program called Multi-Seam Analysis Package

(MSAP) for sizing pillars for multiple-seam situations

[Kanniganti 1993]. These empirical programs are closely

linked to reality and very user-friendly; for many typical mining

geometries, they work extremely well.

However, it is difficult to apply these empirical programs to

mining situations beyond the scope of the original empirical

database. Therefore, when complicated stress conditions arise

from complex single- or multiple-seam mining geometries,

numerical modeling techniques such as finite-element,

boundary-element, discrete-element, or finite-difference are

usually applied. In general, these numerical, or analytical,

design methods are derived from the fundamental laws of force,

stress, and elasticity. Their primary advantage is that they are

very flexible and can quickly analyze the effect of numerous

geometric and geologic variables on mine design. Their

primary disadvantage is that they require difficult-to-obtain

and/or controversial information about material properties,

failure criteria, and postfailure mechanics. In this paper, the

solid foundation of empirical pillar design and in-mine

observation is combined with the flexibility of numerical

modeling to provide a practical technique for mine planning in

difficult situations.

LAMODEL

In order to analyze the displacements and stresses associated

with the extraction of large tabular deposits such as coal,

potash, and other thin vein-type deposits, the displacementdiscontinuity variation of the boundary-element technique is

frequently the method of choice. In the displacementdiscontinuity approach, the mining horizon is treated

mathematically as a discontinuity in the displacement of the

surrounding media. Using this technique, only the planar area

of the seam needs to be discretized, or gridded, in order to

obtain the stress and displacement solution on the seam. Often,

this limited analysis is sufficient, because in many applications

only the distributions of stress and convergence on the seam

horizon are of interest. Also, by limiting the detailed analysis

to only the seam, the displacement-discontinuity method

provides considerable computational savings over other

techniques that discretize the entire body (such as finiteelement, discrete-element, or finite-difference). It is a direct

result of this computational efficiency that the displacementdiscontinuity method is able to handle large areas of tabular

excavations, which is needed in many practical coal mining

problems.

A displacement-discontinuity program incorporating a

laminated medium was recently developed by the National

Institute for Occupational Safety and Health, Pittsburgh

Research Laboratory; this new program is called LAMODEL.

Traditional displacement-discontinuity programs use a

homogeneous isotropic elastic formulation that simulates the

overburden as one solid material. In contrast, the LAMODEL

program simulates the geologic overburden stratifications as a

stack of layers with frictionless interfaces. Specifically, each

layer is homogeneous isotropic elastic and has the same elastic

modulus, Poisson's ratio, and thickness. This "homogeneous

layering" formulation does not require specifying the material

properties for each individual layer, yet it still provides a

realistic suppleness to the mining overburden that is not

possible with the classic homogeneous isotropic elastic

overburden model. From our experience, this suppleness

provides a more accurate strata response for modeling local

deformations, interseam interactions, and/or surface subsidence.

The LAMODEL program calculates stresses and displacements

at the seam level and at requested locations in the overburden

or at the surface. Both linear elastic and nonlinear seam

materials can be used. The program also has the ability to

analyze (1) the interseam stresses resulting from multiple-seam

mining, (2) the effects of topographic relief on pillar stress and

gob loading, (3) the stress changes during mining through

multiple mining steps, and (4) the surface subsidence.

INITIAL MATERIAL PROPERTY GENERATION

As mentioned earlier, one of the most difficult aspects of

using a numerical model is determining the correct (most

accurate) material properties for input. After developing

numerous displacement-discontinuity models and then

comparing their results with field measurements and

observations, a fairly streamlined, systematic technique for

developing initial material properties was developed. Initially,

the critical material properties (coal, gob, and rock mass) are
75

determined using a combination of laboratory research,

empirical formulas, and experience. Then, in the calibration

process, these initial material properties are systematically

adjusted in subsequent runs of the model until the results

correspond as closely as possible to field observations. This

technique for determining material properties has many

similarities to the procedure used by Karabin and Evanto

[1999].

First, to address the problem of determining the input coal

behavior, the basic coal strengths are derived from the empirical

pillar strength formulas, which are solidly based on observed

pillar behavior. Specifically, the peak strength of a model coal

element is directly determined based on an in situ coal strength

and its distance from the edge of the pillar [Heasley 1998] using

the stress gradient implied by the Bieniawski pillar strength

formula [Mark and Chase 1997]. This peak strength is then

implemented using an elastic, perfectly plastic material model

[Zipf 1992]. For an initial estimate, an in situ coal strength of

6.2 MPa (900 psi) [Mark and Barton 1997] and an elastic

modulus of 2 GPa (300,000 psi) is typically used.

This general procedure for generating the initial coal

properties for elements in LAMODEL fulfills a number of

practical requirements. It provides LAMODEL pillars with

peak strengths that closely follow the empirically proven MarkBieniawski pillar strength formula and with stress profiles that

closely follow the Bieniawski stress profile. As opposed to a

simple elastic material model with no load limit, this procedure

using elastic-plastic material allows the pillars to reach a

maximum load-carrying capacity and then realistically shed

additional load to surrounding areas. Table 1 presents typical

elastic-plastic material input values for 3-m (10-ft) coal

elements in a 1.8-m (6-ft) seam with a 6.2-MPa (900-psi) in situ

coal strength. (Note that the peak stress for the coal elements

decreases from the core to the rib of the pillar, which gives the

pillar the proper stress profile.)

Second, to address the gob loading and compaction

behavior, a combination of laboratory research and modeling

experience is used. In the laboratory, Pappas and Mark [1993]

found that an exponentially strain-hardening material with a

tangent modulus that increases linearly with stress provided a

reasonable representation of simulated gob material. This

material model is implemented in LAMODEL [Heasley 1998]

and is used for the gob modeling. The necessary input for this

material is initial modulus, final modulus, and final vertical

stress. From experience, these three values are initially set at

6.2 MPa (900 psi), 110 MPa (16,000 psi) and 27.6 MPa (4,000

psi), respectively (see table 1).

Table 1.CTypical elastic-plastic coal and

strain-hardening gob parameters

COAL ELEMENTS: UPPER MINE

Element

Peak

stress,

MPa

Peak

strain

A (core) ....... 85.9 0.04152

B ............ 56.1 0.02712

C ............ 38.3 0.01992

D (rib) ........ 11.4 0.00552

GOB ELEMENTS

Initial

modulus,

MPa

Final

modulus,

MPa

Final

stress,

MPa

6.2 110 27.6

The third critical set of material inputs in LAMODEL is for

the overburden and consists of a lamination thickness and an

elastic modulus. In LAMODEL, the lamination thickness has

a major influence on the stress and displacement distribution at

the seam and throughout the overburden. Prior research

[Heasley 1998] comparing LAMODEL results with empirical

relationships and measured field data shows that for large-scale

stress distributions (such as longwall abutments) lamination

thicknesses ranging from 15 to 100 m (50 to 300 ft) provide the

best match to field measurements. However, when small-scale

stress distributions (such as interseam stresses) or overburden

displacements (such as subsidence) are of primary concern,

then lamination thicknesses ranging from 3 to 15 m (10 to 50 ft)

provide the best match to field observations [Karabin and

Evanto 1999; Pappas and Mark 1993]. A lamination thickness

of 15 m (50 ft) was used for case study 1, and a thickness of

5 m (15 ft) was used for case study 2. In both case studies, an

elastic modulus of 20 GPa (3,000,000 psi) was used for the

overburden.

STRESS MAPPING

In order to optimally use LAMODEL for accurate stress

prediction at a given mine, the program should first be

calibrated to the site-specific geomechanics based on previously

observed stress conditions at that mine. One of the simplest and

easiest methods to "quantify" the stress at a particular mine is

to use "stress mapping." The pillar-centric stress mapping

technique used here to quantify the observed stress conditions

is a slight modification of the stress mapping technique

originally developed for mapping areas of high horizontal stress

[Mucho and Mark 1994]. For LAMODEL calibration in these

case studies, the primary interest is the stress in the pillars;

therefore, the primary stress indicator is the pillar rib damage,

although other stress-related features, such as roof cracks or

floor heave, are also noted during the stress mapping process

because they can be useful indicators of stress reactions.

Stress mapping a mine area essentially consists of traveling

the rooms and crosscuts in that area and carefully observing the

conditions of the pillars, roof, and floor. The observed
76

conditions are assigned a numerical rating and indicated on a

map. For the rib damage stress mapping used here, the

following numerical rating criteria were applied:

0: Rib still intact with no sloughed coal, original rock dust

 still in place.

1: Very slight pillar sloughage, some broken coal at base of

 rib.

2: Slight pillar sloughage, broken coal covers one-third of

 rib.

3: Significant pillar sloughage, broken coal piled halfway

 up rib.

4: Severe pillar sloughage, broken coal piled almost to roof.

5: Rib is composed of completely broken coal at the angle

 of repose, pillar may be failed.

MODEL CALIBRATION

In the model calibration process, the initial material

properties are systematically adjusted in subsequent runs of the

model until the results correspond as closely as possible to field

observations and/or empirical formulas. For the coal properties,

the in situ coal strength is adjusted until the pillar stress/failure

in the model matches the observed pillar behavior as

represented by the stress mapping/rib rating. For the gob

properties, the final modulus value is typically adjusted up or

down in LAMODEL to increase or decrease the gob stress until

the model gob stress matches empirical abutment angle

formulas [Mark and Chase 1997] and/or field measurements

and observations. For the overburden properties, the lamination

thickness is typically adjusted up to provide wider abutment

stresses and smaller interseam stresses or adjusted down to

provide narrower abutment stresses and greater interseam

stresses as dictated by the observed stress mapping.

Once the model is reasonably calibrated and realistic pillar

strengths and load distributions have been established, the

mechanics-based overburden behavior in the LAMODEL

program can be effectively used to accurately analyze the

complicated stresses and displacements associated with future

complex mining scenarios. The above technique of combining

empirical pillar strength and abutment load formulas with

in-mine stress mapping and the analytical mechanics of a

displacement-discontinuity model capitalizes on the strengths

of both the empirical and analytical approaches to pillar design.

The empirical formulas and observational calibration base the

model on realistic behavior; the analytical mechanics allow the

model to accurately consider and analyze the effects of

numerous geometric and geologic variables. Using this

technique, a displacement-discontinuity model can be the most

practical approach for stress analysis and pillar design in

complex mining situations such as multiple seams, random

pillar layouts, and/or variable topography.

CASE STUDY 1

The first case study location was a multiple-seam, room-andpillar coal mining situation in eastern Kentucky. At this

location, the lower mine had been adversely affected by mining

in the upper seam (see figure 1). In particular, the lower mine

experienced serious ground control problems when it mined

under a barrier pillar between two upper seam gobs ("Model

Area" shown in figure 1). At this multiple-seam interaction

site, in-mine stress mapping was used to quantify the severity

of the multiseam interactions. This stress mapping was also

used to calibrate a LAMODEL simulation of the area. The

results of this numerical simulation provided predicted stress

levels to avoid in future multiple-seam or high-cover mining.

The geology at this location is fairly typical of the southern

Appalachian coal basin, with various sedimentary layers of

sandstones, siltstones, shales, and numerous coal seams. The

topography is very rugged, with various steep ridges and

valleys that have a topographic relief of over 600 m (2,000 ft)

(see figure 1). The overburden in the study area ranged from

150 to 450 m (500 to 1,500 ft), with an average of about 300 m

(1,000 ft). Because of the highly variable topography at this

mine, it was critical to include the topographic stress effects in

LAMODEL in order to obtain accurate results.

The overlying, or upper, mine operates in the Upper Darby

Seam, which typically averages about 2.0 m (6.0 ft) thick. The

lower mine operates in the Kellioka Seam, which averages

about 1.5 m (4.5 ft) thick in the study area. The interburden

between the two seams averages about 14 m (45 ft) and consists

of interbedded sandstones and shales. The core logs nearest to

the study site indicate about 3.5 to 5 m (10 to 15 ft) of shale

directly over the Kellioka Seam. This is then overlain by 7.5 to

10.5 m (25 to 35 ft) of interbedded sandstones and shales, with

shale primarily forming the floor of the Upper Darby Seam.

Both mines are room-and-pillar drift mines and use continuous

miners for coal extraction. In some production sections,

depending on local mining conditions, the mines remove the

pillars on retreat for full extraction.

In the study area, the lower mine was forced to dogleg

around an abandoned, flooded mine in the upper seam (not

shown in figure 1). This dogleg forced the lower mine to

develop entries under a barrier pillar between two previously

mined, upper seam gobs, as shown in the detail of figure 2.

Mine management anticipated increased multiple-seam stresses

in this area. In an effort to safely control these higher stress

levels, the mine located the critical travelway and belt entries
77

Figure 1.CMine map for case study 1.

Figure 2.CEnlargement of model area for case study 1.

 away from the influence of the barrier pillar and used a double

row of supplemental cable bolts on 0.6-m (2-ft) centers

throughout most of the travel entry under the upper seam

mining. With these precautions, the mine was able to safely

and efficiently mine the entries under the barrier pillar and

surrounding gob. However, throughout the section, the stress

effects of the overlying barrier and gob were abundantly visible,

and on two occasions (in the northeast corner of the section),

the mine was unable to complete crosscuts because of roof

instability and poor pillar conditions.

STRESS MAPPING

In order to quantify the stress effects of the barrier pillar and

gob zones on the lower seam, a detailed stress mapping of a

large portion of overmined area was performed. As previously

described, the amount of rib sloughing was noted on a scale of

0 to 5, and any stress-related features such as roof cracking,

potting, cutting, or floor heave were also noted. The results of

this stress mapping exercise are shown in figure 3A. In this

figure, the observed condition of the pillar ribs is shown in gray

scale by degree of damage; the darker shades signify increased

sloughing (or stress). Also, the observed roof cracking, potting,

cutting, and floor heave are indicated on the map.

Several useful observations can be made from the detailed

stress mapping shown in figure 3A. First, the transfer of the

abutment stresses from the overlying mine to the area under the

barrier pillar and to the area at the ends of the pillared sections

can clearly be inferred in the rib conditions of the lower mine

pillars. Also, as a corollary to the interseam transfer of the

barrier pillar abutment stresses, the lower seam pillars under the

gob areas in the upper seam show considerable stress relief.

The next major observation pertains to the location and

orientation of the roof tension cracks and guttering. Clearly, the

tension cracks in the roof of the northeast corner of the section

are situated directly under the overlying barrier pillar and are

oriented parallel to the axis of this pillar. Also, the observed
78

 Figure 3.CComparison between (A) in-mine stress mapping and (B) LAMODEL

calculated stresses for mine 1.
79

compressional roof cutters are located at the edge of, or

adjacent to, the overlying abutment zones and oriented parallel

to these zones. This location and orientation of the tension and

compression suggest that the lower mine roof is behaving like

a beam that is bending into the relatively soft coal seam under

the load of the barrier pillar in the upper seam. This beam

scenario correctly accounts for the tension directly under the

applied load and the compression adjacent to the applied load.

MODEL DESIGN

For the LAMODEL simulation of this area, the seams were

discretized with 3-m (10-ft) elements in a 150-by-150 grid with

the model boundary, as shown in figure 2. Symmetrical seam

boundary conditions were set on all four sides, and no freesurface effects were included. The interburden was set at 14 m

(45 ft), and the rock mass was simulated with a modulus of

20 GPa (3,000,000 psi) and 15-m (50-ft) thick laminations. An

elastic, perfectly-plastic material was used for the coal in both

seams, and the peak strength of the coal was determined from

the Mark-Bieniawski pillar strength formula, as in appendix C

of Heasley [1998]. Table 2 presents the coal and gob input

values used in LAMODEL for this particular case study.

Also, because of the high topographic relief at the site, the

topography was discretized with 15-m (50-ft) elements for an

area extending 300 m (1,000 ft) beyond the limits of the

displacement-discontinuity grids. The importance of including

the topographic stress effects in the model is evident in figure 4,

which shows the topographic stress at the level of the lower

mine. It is interesting to note in this figure the amount to which

the topographic stress is "smoothed" with depth compared to

the original topography. Also, it is evident that the overburden

stress changes about 3 MPa (450 psi) in traversing from the

southwest to the northeast corner of the pillars in the study area.

This difference in overburden stress could very well account for

the increased mining difficulties at the northeast corner of the

section.

MODEL CALIBRATION AND ANALYSIS

Very little work was required for calibrating the LAMODEL

simulation to the observed stress mapping. In both seams, the

original Mark-Bieniawski pillars strengths and the initial

overburden modulus and lamination thickness provided a good

fit to the observed pillar behavior (see figure 3). The only

parameter that was ultimately manipulated was the modulus of

the gob material (see table 2). This modulus was adjusted to

provide a peak gob stress in the range of 40% to 60% of in situ

stress, a reasonable range for a 90-m (300-ft) wide gob in

300 m (1,000 ft) of cover [Mark and Chase 1997]. A number

of variations in pillar strength, overburden modulus, and

lamination thickness were investigated, and the simulation

results varied a little. However, the initial parameter values

with the adjusted gob modulus provided a reasonably optimum

fit to the observational stress mapping.

Table 2.CCoal and gob parameters

for case study 1

COAL ELEMENTS: UPPER MINE

Element

Peak

stress,

MPa

Peak

strain

A (core) ..... 85.9 0.04152

B .......... 56.1 0.02712

C .......... 38.3 0.01992

D (rib) ...... 11.4 0.00552

COAL ELEMENTS: LOWER MINE

Element

Peak

stress,

MPa

Peak

strain

A (core) ..... 113.2 0.05472

B .......... 73.5 0.03552

C .......... 53.6 0.02592

D (rib) ...... 13.9 0.00672

GOB ELEMENTS

Initial

modulus,

MPa

Final

modulus,

MPa

Final

stress,

MPa

6.2 110 27.6

The calculated pillar stresses from the final calibrated

LAMODEL run are shown in figure 3B. These modeled

stresses correlate extremely well with the stress mapping in

figure 3A. The high stresses under the barrier pillar are evident

in the model results; the area of stress relief under the gob is

also shown. Even the intermediate stress levels under the

overlying pillars and solid coal in the southwest corner of the

model closely match the observed pillar stress mapping. A few

more details of the modeled stress output are shown in figure 5,

where the isolated single-seam stress and just the interseam

stress are displayed. In this figure, the effect of the overlying

barrier pillar can be clearly seen. In particular, the maximum

single-seam stress on the pillars (figure 5A) of around 15 MPa

(2,200 psi) is seen to increase to over 36 MPa (5,200 psi) with

the addition of the barrier pillar stress (figures 5B and 5C).

Also, it is interesting to note the increased abutment stress in

the northeast corner of the section (figure 5C), presumably due

to the increasing overburden and the increasing distance from

the upper panel boundaries. A stress relief of about 7 MPa

(1,000 psi) under the gob areas is also shown in figure 5C.

For the mine management, this stress modeling using

LAMODEL, in conjunction with good in-seam correlations

with stress mapping, provided valuable background information

for future multiple-seam mine planning. In this case study,

a calculated multiseam stress concentration of about 15 MPa

(2,200 psi) with pillar stresses of 35 MPa (5,200 psi) at this site

caused sufficient roof instability to prohibit the mine from

driving two crosscuts. Therefore, it seems that the 15-MPa

stress concentration (35-MPa pillar stress) is close to an upper

limit for successful entry development at this mine. The mine

can use this calculated limit in conjunction with future

modeling in order to lay out future room-and-pillar panels

influenced by overlying workings.
80

Figure 4.CCalculated topographic stress for case study 1.
81

 Figure 5.CThe LAMODEL stress output for case study 1. A, Single-seam stress; B, multiple-seam stress; C, additional stress from

upper seam.
82

CASE STUDY 2

The second study site was a longwall mine located in Greene

County, PA, and operating in the Sewickley Seam. This mine

is underlain by an abandoned room-and-pillar operation in the

Pittsburgh Seam. The primary problem at this site was the

transfer of multiple-seam stress from the lower mine. Yielding

of smaller pillars and the subsequent transfer of their load to

larger pillars in the lower seam apparently caused increases in

vertical stress in the upper seam that were noticed during

development of the headgate entries (see figure 6). Severe

pillar spalling and poor roof conditions were experienced when

mining the headgate over these large pillars in the lower seam

(figure 7). Mine management was concerned that these

underlying abutment pillar stresses would continue to be a

problem farther inby in the headgate and also in the longwall

panel because there were several areas in the lower seam where

similar pillar conditions seemed to exist.

In the study area, the overburden above the Sewickley Seam

ranges from 150 to 280 m (500 to 910 ft) and consists

predominantly of interbedded shales and sandstones. The

interburden between the Sewickley and Pittsburgh Seams

ranges from 27 to 30 m (90 to 100 ft) thick and consists of

interbedded shales and limestones. The average mining heights

of the Sewickley and Pittsburgh Seams are 1.5 m (5 ft) and

1.8 m (6 ft), respectively. The immediate roof of the Sewickley

Seam is composed of a jointed dark sandy shale that ranges

from 3 to 4.5 m (10 to 15 ft) thick and is overlain by a

competent limey shale. The immediate floor of the Sewickley

Seam is composed of a 1.2-m (4-ft) thick dark limey shale

underlain by a competent limestone unit.

STRESS MAPPING

Figure 6 shows the overlay of the lower seam workings on

the upper seam longwall panel and the area of the headgate

where the stress mapping and model calibration were

conducted. As described earlier, the process of calibration

involved the use of stress mapping to assign a rating from 0 to

5 based on the observed pillar rib conditions. The first 600 m

(2,000 ft) of the headgate entries, where problems first occurred

(see figure 6), were traversed and assigned rating numbers

based on the observed conditions. Figure 7A shows the rib

damage rating assigned to each rib in this area of the headgate.

MODEL DESIGN AND CALIBRATION

Once the stress mapping was complete, LAMODEL

calibration was initiated. For calibration purposes, the "Stress

Mapped Area" shown in figure 6 was discretized with 3-m

(10-ft) elements with a 90-by-200 grid. Symmetrical boundary

conditions were set on all four sides, and no free-surface effects

were included. The interburden was set at 27 m (90 ft), and the

rock mass was simulated with a modulus of 20 GPa (3,000,000

psi) and 5-m (15-ft) thick laminations. The overburden above

the lower mine in this area ranged from 180 to 300 m (600 to

1,000 ft). Due to this variable topography, the topographic

stress effects were included in LAMODEL in order to obtain

accurate overburden stress results.

Based on the observed stress mapping, model calibration

was conducted under the assumption that the smaller pillars

(<10.5 m (<35 ft) wide) in the lower mine had essentially

yielded and transferred their load to nearby larger pillars.

Therefore, in the first step of the calibration process, the coal

strength in the lower mine model was adjusted until the pillars

showed this observed behavior. Initially, using the elasticplastic implementation of the Bieniawski formula, as previously

explained, an in situ coal strength of 6.2 MPa (900 psi) was

used to calculated peak stress and strain values for each coal

element, and the initial calibration model was run. In this initial

model, the coal in the lower mine was too strong and did not

show the desired yielding in the smaller pillars. Therefore, in

order to obtain the desired small pillar yielding and subsequent

stress transfer to the larger pillars, the in situ coal strength in the

lower seam was gradually decreased to 4.2 MPa (600 psi).

With the in situ coal strength of 4.2 MPa (600 psi) in the

lower seam and the original coal strength of 6.2 MPa (900 psi)

in the upper seam, the model correlated very well with the rib

damage rating from the stress mapping. The rib damage rating

is in gray scale in figure 7A; the results from the model are in a

comparative gray-scale plot in figure 7B. Clearly, the model

pillars with high rib stress correlate well with the pillars with

high damage ratings. It can be observed in figure 6 that these

high rib stresses occur over the large pillars located in the lower

mine in conjunction with overburden that exceeds 250 m

(870 ft). The final coal and gob properties used in LAMODEL

for the upper and the lower mine are presented in table 3.

Table 3.CCoal and gob parameters

for case study 2

COAL ELEMENTS: UPPER MINE

Element

Peak

stress,

MPa

Peak

strain

A (core) ..... 102.3 0.04944

B .......... 66.5 0.03216

C .......... 48.7 0.02352

D (rib) ...... 12.9 0.00624

COAL ELEMENTS: LOWER MINE

Element

Peak

stress,

MPa

Peak

strain

A (core) ..... 56.8 0.02747

B .......... 36.9 0.01787

C .......... 27.0 0.01307

D (rib) ...... 7.2 0.00347

GOB ELEMENTS

Initial

modulus,

MPa

Final

modulus,

MPa

Final

stress,

MPa

6.2 138 27.6
83

Figure 6.CMine map for case study 2.
84

 Figure 7.CComparison between in-mine stress mapping and LAMODEL calculated stresses. A, rib damage rating; B, stress (MPa). 

STRESS PREDICTION FOR MINE PLANNING

With material properties calibrated from observed stress

conditions in the mine, additional LAMODEL analyzes were

created and run in order to predict areas of potential problems

within the remaining headgate and the future longwall panel.

Figure 8 shows two areas of the headgate and longwall panel

that were modeled using optimized properties from the

calibration process. These gray-scale plots show the interseam

stress, which is the additional stress on the upper mine due to

the lower seam mining. In this figure, zone 1 covers the upper

(inby) part of the headgate panel and the first 365 m (1,200 ft)

of the longwall panel; zone 2 covers the lower part of the

headgate (where the stress problems were first noticed) and the

last (outby) 330 m (1,100 ft) of the longwall panel. In these

two zones, the lower mine pillar conditions and the overburden

depths appeared similar; therefore, the poor pillar conditions

encountered in zone 2 were expected in zone 1.

However, when comparing the interseam stress between

these two zones as shown in figure 8, it is obvious that the

stress in zone 2 is considerably greater than that in zone 1.

Closer investigation reveals two primary reasons for this. First,

the maximum depth over the gate roads and panel in zone 2 is

over 280 m (920 ft); in zone 2, the maximum depth is just over

250 m (870 ft). Second, when examining the model output for

the lower mine, there seems to be less pillar yielding in zone 1

than in zone 2. In figure 6, it can be seen that the smaller pillars

in zone 1 are dispersed among larger pillars and have widths

>12 m (>40 ft), whereas in zone 2, there is a large area of pillars

with widths <10.5 m (<35 ft). The larger, more dispersed small
85

Figure 8.CInterseam stress for zones 1 and 2.
86

pillars in zone 1 suffer less pillar yielding and therefore cause

less load transfer (or interseam stress) on the upper mine (see

figure 8). During headgate development in zone 1, no pillar

problems were encountered. Thus, the calibrated model

successfully predicted the reduced stress conditions in the

headgate of zone 1.

The mine management was also concerned about the

multiple-seam stresses adversely affecting the retreating

longwall panel. In particular, a large, irregularly shaped barrier

pillar in the lower mine is superimposed under the center line

of the initial half of the longwall panel in zone 1 (see figure 8).

However, the interseam stress calculated by the model from this

barrier pillar reaches only about 3 MPa (450 psi). When the

panel was mined, this slightly increased face stress presented

very little problem. Some slight spalling was present on the

face during the extraction, but overall face conditions were

generally good and no severe ground control problems were

evident.

However, in the lower part of the panel near the headgate

location where poor ground conditions were first encountered

(see zone 2, figure 8), an area of interseam stress up to 9 MPa

(1,300 psi) is evident in the panel. Because of the underlying

barrier pillar, the mine anticipated difficult face conditions in

this area. Indeed, when the longwall face reached this area,

ground control problems that included severe face spalling and

poor roof condition in the headgate entries were encountered.

In fact, the stress interaction with the lower seam was severe

enough to stop the longwall face about 15 m (50 ft) short of the

longwall recovery chute and make recovery of the supports

difficult.

When comparing conditions in zone 1 with those of zone 2,

there seems to be a very fine line in the occurrence of ground

control problems in the upper seam depending on the

overburden depth and the pillar size in the lower seam.

Problems were more likely to occur when the depth of cover

over the Sewickley Seam exceeded 250 m (820 ft) and when

large areas of narrow pillars (<10.5 m (<35 ft) wide) in the

lower seam were located adjacent to a larger barrier pillar.

These conditions caused yielding of the narrow pillars and the

shedding of their load to the adjacent larger pillar. This

concentrated abutment stress was then transferred to the upper

mine, resulting in poor ground conditions in areas of the

headgate entry and longwall panel. Throughout this case study,

the calibrated LAMODEL program successfully predicted the

high stress areas in advance of mining.

CONCLUSIONS

The primary purpose of the case studies presented in this

paper was to validate the new LAMODEL boundary-element

program and investigate its utility for stress modeling in mine

planning. Based on the comparisons between the stress

mapping and the model results for the two case studies, it seems

that the LAMODEL program can be calibrated to produce good

correlations with the observed stresses. In addition, once

realistic pillar strengths and load distributions were established

by calibration, the mechanics-based overburden behavior in

LAMODEL effectively analyzed the complicated stresses and

displacements associated with the complex multiple-seam

mining scenarios and successfully predicted upcoming high

stress conditions in advance of mining for preventive action by

mine management. In case study 1, a calculated multiseam

stress concentration of around 15 MPa (2,200 psi) with pillar

stresses of 35 MPa (5,200 psi) seemed to be an upper limit for

successful entry development at this mine. Similarly, in case

study 2, a calculated multiple-seam stress concentration of

9 MPa (1,300 psi) produced severe face spalling and poor roof

conditions in the headgate entries, whereas a 3-MPa (450-psi)

stress concentration was barely noticeable.

A secondary goal was to present a fairly streamlined,

systematic methodology for developing initial material

properties and then calibrating these properties to field

observations. Initially, the critical material properties (coal,

gob, and rock mass) are developed using a combination of

laboratory research, empirical formulas, and experience. Then,

in the calibration process, a previously mined area is "stress

mapped" by quantifying the observed pillar and strata behavior

using a simple numerical rating system. Finally, the initial

material properties are systematically adjusted in subsequent

runs of the model until the results provide the best correlation

between the predicted stresses and the observed underground

stress rating. This methodology of combining empirical pillar

strength and abutment load formulas with in-mine stress

mapping and the analytical mechanics of a displacementdiscontinuity model capitalizes on the strengths of both the

empirical and analytical approaches to pillar design to provide

a practical technique for mine planning in difficult situations.
87

REFERENCES

Heasley KA [1998]. Numerical modeling of coal mines with a laminated

displacement-discontinuity code [Dissertation]. Golden, CO: Colorado School

of Mines, Department of Mining and Earth Systems Engineering.

Kanniganti RS [1993]. Interactive prediction software for underlying

multi-seam design [Thesis]. Blacksburg, VA: Virginia Polytechnic Institute

and State University, Department of Mining and Minerals Engineering.

Karabin GJ, Evanto MA [1999]. Experience with the boundary-element

method of numerical modeling to resolve complex ground control problems.

In: Proceedings of the Second International Workshop on Coal Pillar

Mechanics and Design. Pittsburgh, PA: U.S. Department of Health and Human

Services, Public Health Service, Centers for Disease Control and Prevention,

National Institute for Occupational Safety and Health, DHHS (NIOSH)

Publication No. 99-114, IC 9448.

Mark C [1992]. Analysis of longwall pillar stability (ALPS): an update.

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. 238-249.

Mark C, Barton TM [1997]. Pillar design and coal strength. In:

Proceedings - New Technology for Ground Control in Retreat Mining.

Pittsburgh, PA: U.S. Department of Health and Human Services, Public Health

Service, Centers for Disease Control and Prevention, National Institute for

Occupational Safety and Health, DHHS (NIOSH) Publication No. 97-122,

IC 9446, pp. 49-59.

Mark C, Chase FE [1997]. Analysis of retreat mining pillar stability

(ARMPS). In: Proceedings - New Technology for Ground Control in Retreat

Mining. Pittsburgh, PA: U.S. Department of Health and Human Services,

Public Health Service, Centers for Disease Control and Prevention, National

Institute for Occupational Safety and Health, DHHS (NIOSH) Publication

No. 97-122, IC 9446, pp. 17-34.

Mucho TP, Mark C [1994]. Determining horizontal stress direction using

the stress mapping technique. In: Peng SS, ed. Proceedings of the 13th

International Conference on Ground Control in Mining. Morgantown, WV:

West Virginia University, pp. 277-289.

Pappas DM, Mark C [1993]. Behavior of simulated longwall gob material.

Pittsburgh, PA: U.S. Department of the Interior, Bureau of Mines, RI 9458.

Zipf RK Jr. [1992]. MULSIM/NL theoretical and programmer's manual.

Pittsburgh, PA: U.S. Department of the Interior, Bureau of Mines, IC 9321.
89

EXPERIENCE WITH THE BOUNDARY-ELEMENT METHOD

OF NUMERICAL MODELING TO RESOLVE COMPLEX

GROUND CONTROL PROBLEMS

By George J. Karabin, P.E.,1 and Michael A. Evanto, P.G.2

ABSTRACT

The Mine Safety and Health Administration, Pittsburgh Safety and Health Technology Center, Roof Control

Division, is routinely involved in the evaluation of ground conditions in underground coal mines. Assessing

the stability of mined areas and the compatibility of mining plans with existing conditions is essential to

ensuring a safe working environment for mine workers at a given site. Since 1985, the Roof Control Division

has successfully used the boundary-element method of numerical modeling to aid in the resolution of complex

ground control problems. This paper presents an overview of the modeling methodology and details of

techniques currently used to generate coal seam, rock mass, and gob backfill input data. A summary of coal

and rock properties used in numerous successful evaluations throughout the United States is included, and a

set of deterioration indices that can aid in the quantification of in-mine ground conditions and verification of

model accuracy is introduced. Finally, a case study is detailed that typifies the complexity of mining situations

analyzed and illustrates various techniques that can be used to evaluate prospective design alternatives.

1

Supervisory civil engineer.

2Geologist.

Mine Safety and Health Administration, Pittsburgh Safety and Health Technology Center, Roof Control Division, Pittsburgh, PA.
90

INTRODUCTION

Effective mine design has long been recognized as an

essential element in establishing safe and productive mining

operations. Numerous investigators have developed techniques

to analyze pillar stability and maximize mining efficiency. The

work of Holland and Gaddy [1964], Obert and Duvall [1967],

and Bieniawski [1984], to name a few, served as a staple for

mining engineers for many years. With the advent of longwall

mining, new techniques were developed by Carr and Wilson

[1982], Hsuing and Peng [1985], Choi and McCain [1980], and

Mark [1990] to address design considerations for that

technology. Most recently, the development of the Analysis of

Retreat Mining Pillar Stability (ARMPS) methodology [Mark

and Chase 1997] for the evaluation of retreat mining operations

added an additional tool for engineers to design and evaluate

full pillaring techniques.

Each of these methods can provide a reasonable estimate of

pillar strength and stability under specific conditions and

relatively simple mining geometries. In practice, however,

situations often arise where areas of concern contain a number

of pillar configurations with varying entry and crosscut widths,

spacings, and orientations. Additional factors, such as nonuniform pillar lines, remanent stumps scattered throughout

irregularly shaped gobs, and multiple-seam mining, can further

complicate an analysis. In such instances, application of the

previously mentioned empirical and analytical methods to

accurately evaluate ground stability is difficult, if not totally

impossible.

A primary function of the Roof Control Division, Pittsburgh

Safety and Health Technology Center, is to provide technical

assistance to the Mine Safety and Health Administration

(MSHA) and the mining industry in the resolution of complex

roof control problems. In order to evaluate mining systems not

easily treated by simplified empirical or analytical methods,

boundary-element numerical modeling was initiated in 1984

and expanded in 1987 with acquisition of the BESOL system

from Crouch Research, Inc., St. Paul, MN. The ability of the

three-dimensional (3-D) boundary-element method to model

large mine areas with complex geometries has enabled the Roof

Control Division to successfully simulate conditions and

identify potential solutions to ground control problems in mines

throughout the United States. The technique has been applied

to a variety of mining scenarios, including longwall and roomand-pillar operations using both conventional and yield pillar

configurations. The influence of vertical and horizontal stress

has been modeled to simulate underground conditions ranging

from deteriorating roof and persistent falls to areas of squeezing

ground and complete pillar failure.

In the process of developing numerical models for the

various mining operations analyzed during the last 10 years,

a systematic simulation methodology has evolved. Techniques

to estimate the necessary coal, rock, and gob backfill properties

have been established, and a deterioration index was developed

to quantify in-mine roof, floor, and pillar behavior to assist in

calibrating model parameters and evaluating potential mine

design alternatives. This paper presents a brief description of

the BESOL system, an overview of the simulation process used,

and details of methods used to construct models and estimate

rock mechanics parameters. A discussion of the deterioration

index system and details of a case study typifying an actual

mine simulation and techniques used to evaluate conditions and

proposed mining options is also included.

BESOL SYSTEM DESCRIPTION

BESOL is a system of computer programs for solving rock

mechanics problems based on the boundary-element displacement discontinuity method of analysis. The 3-D MS221

version (yielding and multiple-seam capability) was acquired

from Crouch Research, Inc., and has been used by the Roof

Control Division to evaluate complex mining systems since

1987. The BESOL system is complete with graphic pre- and

postprocessors that greatly simplify model construction and

output data interpretation.

Figure 1 presents a generalized BESOL boundary-element

model that illustrates a tabular seam or ore body surrounded by

a homogenous, isotropic, linearly elastic rock mass. Input data

include elastic rock mass properties and rock strength criteria,

seam properties, and backfill or artificial support characteristics.

A definition of the seam plane(s), detailed geometry of the

excavation, mining depth, seam height, and a complete 3-D

in situ stress state of the model are also required. Output

capabilities include stress, strain, and displacement calculations

within user-selected areas (both on and off the seam plane),

failure index (Mohr-Coulomb or Hoek-Brown roof and floor

safety factors) calculations at variable locations in the rock

mass, and energy release estimates in yielding areas.
91

Figure 1.CGeneralized BESOL boundary-element model.

BESOL was selected by the Roof Control Division because

it offered a number of features considered essential in simulating complex mining situations. These include:

• 3-D capability

• Large fine-mesh grid (180 by 270 elements)

• Yielding seam option (user-defined)

• Multiple-seam capability

• Backfill and artificial support materials

Other features that made the package attractive were:

• PC-based operation

• Off-seam stress/strain capability

• Failure index calculation (Mohr-Coulomb/Hoek-Brown)

• Graphic pre- and postprocessors

• Multiform hard-copy output capability
92

Figure 2.CSimulation process.

SIMULATION PROCESS

Figure 2 presents an eight-step process used by the Roof

Control Division during the simulation of underground mining

systems. Although it is specifically directed to numerical

modeling applications, it can also be used in conjunction with

empirical or analytical methods.

1. Observe Underground Areas: This is an essential first

step in solving ground control problems regardless of the

methodology employed. Mine conditions should be categorized

in a number of areas where differing pillar sizes, panel configurations, and overburden levels are found. The deterioration

index system, which will be discussed later in this paper, can

aid in the description of in-mine ground conditions.

2. Estimate Model Parameters: Coal, rock, and gob properties must be established consistent with the requirements of

a particular numerical method. Ideally, these properties will be

based on coal and rock tests of the specific mine site. In the

absence of these data, published properties of adjacent or same

seam mines can be used. When no site-related data are

available, general coal and mine roof rock properties can be

used. Regardless of the source of data, it cannot be overemphasized that they represent only a first estimate of mine

roof and rock properties that must be validated.

3. Model Observed Areas: The third step of the process

involves modeling each of the areas observed underground.

The properties estimated above are tested under various

geometric and overburden conditions to determine their

usability. Successfully modeling many areas under a variety of

different conditions increases confidence in the properties used.

4. Verify Model Accuracy: This is the most critical step in

the entire simulation process. Each of the areas modeled must

be closely examined to ensure that the results correlate with

observed conditions. If reasonable correlations cannot be made,

the model must be recalibrated (material properties adjusted)

and the process repeated. It should be noted that relating the

output of numerical models (stress, convergence, etc.) to

observed conditions (pillar sloughing and roof or floor

deterioration) is often difficult given the complexities of the

underground environment. The use of regression techniques to

define actual conditions as a function of model output

parameters (using the deterioration index rating system) can

simplify that task.

5. Establish Threshold Limits: Once the accuracy of the

model is verified, threshold limits delineating acceptable and

unacceptable mining conditions must be established in order to

evaluate the effectiveness of proposed design alternatives.

Stress or convergence levels corresponding to deteriorating

ground conditions can be identified. Other factors such as the

extent of pillar yielding or predicted pillar, roof, and floor

conditions from a more comprehensive regression analysis can

also be used.

6. Model New Configurations: Having established an

effective model and a means of evaluating the results of

analyses, new mining techniques can be simulated. Generally,

several alternatives are modeled under the conditions expected

at the mine location where the design will be implemented.

7. Evaluate New Configurations: The various alternatives

can be evaluated relative to the threshold limits established. For

instance, if specific stress and convergence values were found

to correspond to deteriorating ground conditions, an alternative
93

Figure 3.CModel elements and strain-softening locations.

that produces levels lower than those values would be desired.

However, if none of the configurations evaluated meet the

threshold requirement for stable conditions, new alternatives

must be developed and analyzed.

8. Implement Best Alternative: Once the best alternative is

identified (either meeting the threshold criteria or providing the

most favorable conditions), it can be cautiously implemented.

The level of confidence in achieving a successful design is

directly proportional to the breadth of the evaluation and the

degree of correlation noted in the model verification process.

In any event, conditions should be closely monitored as the

design is implemented; any deviations from the expected

behavior warrants recalibration of the model.

MINING GEOMETRY AND INITIAL STRESS

An essential element in the simulation process is creating a

model grid that duplicates the in-mine geometry. The seam

must be broken into elements of a size that allows the entry,

crosscut, and pillar dimensions to be accurately reproduced.

Seam elements must be small enough to model details of the

mine geometry and produce discernable differences in

performance, yet large enough to allow broad areas of the mine

to be included in the simulation.

Generally, setting the element size at 1/2 the entry width

(figure 3) has provided acceptable results in most coal mining

applications. A 10-ft element width (for a 20-ft-wide entry/

crosscut configuration) enables a large area (1,800 by 2,700 ft)

to be modeled, yet provides the stress and convergence detail

needed to effectively evaluate conditions. Both larger (oneentry width) and smaller (1/4-entry width) element sizes have

been used out of necessity in specific applications, but are

limited in application to scenarios where detail (large elements)

or influence area (small elements) are not critical.

A number of other geometric guidelines have been identified

that can aid in creating an effective boundary-element model:
94

• To the extent possible, locate model boundaries over solid

coal or known stable areas to reduce the likelihood of erroneous

loading conditions (resulting from the exclusion of transferred

stress from adjacent yielded areas in the zone of interest).

• Orient the model such that the primary areas of interest are

positioned away from the boundaries to minimize end effects.

• Known or potential yielding pillars should not contain

linear-elastic elements that could erroneously affect the stress

transfer to adjacent areas.

• Known or potential yielding pillars should contain an odd

number of elements across the minimum dimension to ensure

accurate pillar strength and peak core stress calculations.

• Care should be taken when entries or crosscuts are not

oriented at 90° angles (see figure 3) to ensure that the effective

widths and percent extraction match the actual mine geometry.

Initial stress conditions on the rock mass, in the absence of

known high horizontal stress fields, have generally been as

follows:

Szz (vertical) ' 1.1 psi per foot of depth

Sxx (x-horizontal) ' 50% of the vertical stress

Syy (y-horizontal) ' 50% of the vertical stress

These values have resulted in effective simulations of in-mine

conditions in the vast majority of cases modeled, even when the

influence of horizontal stress was suspected. High horizontal

stress was rarely found to actually control mine conditions, and

high horizontal stress values are only used when clear evidence

of their existence and magnitude is available.

ROCK PROPERTIES

The rock mass properties needed for boundary-element

models are minimal because the assumption of a linearly elastic

material is inherent. The BESOL system requires only

estimates of the modulus of elasticity and Poisson's ratio of the

rock mass. Initially, it may seem that treating a complex rock

structure in such a simplistic manner is not appropriate. However, considering that seam stresses are generated through

massive main roof loading (generally remaining in elastic

compression), it is not unreasonable to expect that an effective

representation of pillar loading (the crux of a boundary-element

model) would result.

The Roof Control Division uses a weighted-average

technique to calculate the rock mass modulus of elasticity. As

many borehole logs as possible located over areas to be

modeled are examined, and the percentages of the various rock

types (e.g., shale, sandstone, coal) in each core are identified

(table 1). These values are averaged, multiplied by the modulus

of elasticity of each rock type to calculate composite portions,

then summed to estimate the rock mass modulus of elasticity.

Ideally, individual strata moduli are established by site-specific

tests. If those data are not available, then published data for

local mine roof strata or typical rock properties must be used.

It should be noted that published data for particular rock types

vary widely, and some judgment is needed in selecting

appropriate values. The specific rock moduli listed in table 1

have been used successfully in a number of instances when onsite data were not available.

A similar weighted-average process is recommended for the

calculation of Poisson's ratio. Again, the use of site-specific

data would be ideal, but estimates based on published data are

generally used. Poisson's ratios ranging from 0.20 to 0.25 have

been acceptable in the analyses made to date.

The properties used to define the rock mass can have a

significant effect on the accuracy of a simulation. Overestimating the rock modulus results in lower pillar stresses

within a panel or mined area (gob) and higher loads over the

Table 1.CComposite rock modulus calculation

Rock type

Percent in borehole Rock

modulus, psi

Composite 

portion, psi Hole

No. 1

Hole

No. 2

Hole

No. 3

Hole

No. 4 Average

Dirt .......... 10.84 8.07 11.51 15.64 11.52 50,000 5,750

Coal ......... 1.52 1.60 1.34 0.96 1.36 473,000 6,409

Shale ......... 51.15 26.86 21.79 48.22 37.01 900,000 333,090

Slate ......... 1.18 0.78 2.54 0 1.13 1,250,000 14,125

Sandstone ..... 22.28 28.63 23.70 26.31 25.23 2,200,000 555,060

Limestone ..... 0 0 0 0 0 3,200,000 0

Sandy shale ... 11.47 31.70 36.01 7.78 21.74 1,500,000 326,100

Fireclay ....... 1.57 2.35 3.11 1.08 2.03 900,000 18,270

 TOTAL ............................................................. 1,258,804

_

E ' 1,260,000 psi

adjacent abutments due to the enhanced bridging action (less deformation) of the rock strata. Conversely, underestimating
95

the rock modulus leads to higher panel pillar stress or gob

loading in mined areas and lower stresses on the adjacent

abutments.

As noted previously, the BESOL system contains a failure

index (safety factor) calculation to evaluate the rock strength/

stress ratios using either a Mohr-Coulomb or Hoek-Brown

failure criterion. Essentially, the state of stress of a point in the

rock mass is calculated in terms of 3-D principal stresses, and

the "available strength" of the rock (as influenced by

confinement) is compared to the existing stress level. To date,

only the Mohr-Coulomb technique has been used, which

requires input of cohesion, friction angle, and tensile strength of

the rock (roof or floor) material. Because the analysis of the

rock structure is completely elastic, exact properties (although

desirable) are not required. The failure index analysis is treated

in a relative manner (higher failure indices indicate a more

stable condition), and the following parameters have provided

reasonable results:

Tensile strength - 1,000 psi

Cohesion - 800 psi

Friction angle - 25°

The failure index has been successfully used to indicate high

stress locations and the effect of mining changes to relieve those

stresses. Although they can be calculated anywhere in the rock

mass, failure index calculations made at the immediate roof or

floor lines have been most useful. Coupling them with stress

and convergence data provides a more complete picture of mine

stability that can be correlated to observed or expected

conditions.

COAL PROPERTIES

Establishing representative coal properties for a boundaryelement analysis is the most critical step in model formulation.

The need for yielding seam capability is clear to accurately

simulate the complex underground environment where localized

coal failure results in the redistribution and concentration of

stress in adjacent areas. The strain-softening approach [Crouch

and Fairhurst 1973] has been identified as a reasonable method

of describing coal seam behavior. Although that concept has

been widely discussed, little specific information is available

concerning the actual construction of a strain-softening model.

The Roof Control Division has established a technique to

make a first approximation of the stress and strain values

needed to describe the strain-softening characteristics of a

specific coal seam. As generalized in figure 4, peak and

residual (postpeak) stress and strain levels are required for seam

elements located at various distances from a mined area.

BESOL allows up to six user-defined elements (each characterized by three stress-strain values), and model elements

located farther away from a free face are treated as linearly

elastic (figure 3).

Peak coal strength values are estimated at the center of each

of the six yielding seam elements by the following equation:

Sp

(i) ' S1 ( (0.78 % 1.74 x/h), (1)

where Sp

(i) ' peak strength of element (i), psi,

S1 ' in situ coal strength, psi,

x ' distance from element (i) center to free face, ft,

and h ' seam height, ft.

Equation 1 was based on the derivations of Mark and

Iannacchione [1992] for estimating the stress gradient in the

yield zone of several empirical pillar design formulas and

represents an average of the Bieniawski and Obert-Duvall

methods. The in situ coal strength is usually based on uniaxial

compression tests of samples acquired from the mine, although

published data have also been used when site-specific data were

not available. Strength reduction factors of 1/5 for 2-in cubes

and 1/4 for 3-in cubes have been used to estimate in situ

strength from test data and have generally provided acceptable

results. Figure 5 presents a summary of peak strengths measured (with borehole pressure cells) at various depths into coal

pillars at three mines where pillar yielding was evident. Data

are shown as a ratio of the measured peak stress to that

estimated by equation 1; the majority fall within 10% of the

predicted stress level. Because the seam is considered to behave

elastically until peak stress is reached, the total strain at that

level is simply

ep

(i) ' Sp(i)/E, (2)

where ep

(i) ' strain at peak strength of element (i), in/in,

Sp

(i) ' peak strength of element (i), psi,

and E ' coal seam modulus of elasticity, psi.

Residual (postpeak) seam stress and strain values are approximated by the following relationship:

SR1(i) ' (0.1385 ( ln (x) % 0.413) ( Sp

(i) (3)
96

Figure 4.CGeneral strain-softening element characteristics.

eR1(i) ' 2 ( ep

(i) (4)

SR2(i) ' (0.2254 ( ln (x)) ( Sp

(i) (5)

eR2(i) ' 4 ( ep

(i) (6)

where SR1(I) ' first residual stress level of element (i), psi,

eR1(I) ' strain of element (i) at first residual stress

 level, in/in,

SR2(I) ' second residual stress level of element (i), psi,

eR2(I) ' strain of element (i) at second residual stress

level, in/in,

and x ' distance from element (i) center to free face,

ft.

These relationships were patterned after the load/deflection

response of coal samples under uniaxial testing, yield pillar

stress and entry convergence measurements made at one mine

site, and the assumption that at increasing depth into the pillar

core a higher residual strength would be maintained.
97

Figure 5.CMeasured versus calculated peak coal strength.

Figure 6 presents a summary of residual stress levels

measured at various depths at four mines where pillar yielding

was monitored. The data are illustrated as a percentage of

measured peak stress and compared to levels predicted by the

above equations. The R1 levels represent the initial drop in

stress once the peak has been reached; the R2 values indicate the

final magnitude after substantial convergence. Both are difficult

to identify because deformation plays a significant role in the

unloading process; however, figure 6 represents a best estimate

of those stress levels for the pillars monitored.

Figure 7 illustrates a family of six curves representing a

strain-softening model with an element size of 10 ft, a seam

height of 2.8 ft, an elastic modulus of 500,000 psi, and an in situ

coal strength of 967 psi. Curve No. 1 represents the behavior of

free-face or pillar perimeter elements; the remaining curves

represent the stress-strain relationship of elements located

successively deeper into the pillar core.

The BESOL system also requires estimates of the seam shear

modulus (G) and similar shear stress-strain characteristics for

the six yieldable elements described above. These geotechnical
98

Figure 6.CMeasured versus calculated residual strength.
99

Figure 7.CTypical strain-softening seam behavior.
100

data are rarely available, and estimates (using the previously

described procedure) based on a shear modulus equal to 1/2 to

1/3 of the elastic modulus and shear strengths of 1/2 to 1/3 of

the strain softening values have been used.

It must again be emphasized that, although the methodology

described above has been successfully used to estimate coal

strain-softening properties, the properties generated are only a

first approximation that must be verified for accuracy.

Although in situ measurements have generally validated

properties assigned to near-excavation locations, peak and

residual stress levels deeper than 20 ft into a pillar or solid coal

(where yielding rarely occurs) are largely unverified. Further,

the procedure has been applied only to a limited number of coal

seams, none of which experienced bump problems. The

application of this technique to bump coal is not recommended

because the strength increase due to confinement would likely

exceed that predicted by the peak stress equations.

The suitability of assigned coal properties can be assessed by

comparing the simulation output to observed pillar conditions.

Test models should include underground areas (varying depths

and pillar sizes) where definite observed pillar behavior can be

isolated. For instance, if a model with 8-ft-wide elements

predicts corner yielding, significant sloughing and crushing for

a length of 8 ft from the pillar corner should be obvious. A

similar condition would be expected along the sides of pillars if

perimeter yielding were projected. In general, more observed

pillar deterioration than that projected by the model suggests

that the coal strength has been overestimated; less sloughing

than predicted indicates that it has been underestimated. There

are occasions, however, where the element size itself can

contribute to erroneous interpretations. A model using 10-ft

elements may indicate elevated stress at the pillar corners, but

no yielding. Underground observations of 4-ft crushed zones at

the pillar corners may suggest that the model coal strength has

been overestimated. Remodeling the area using 4-ft elements

(with corresponding recalculation of element properties) may in

fact result in the prediction of corner yielding that would match

the in-mine conditions.

When constructing calibration models to verify coal strength,

it is essential that:

• The element size selected is appropriate to illustrate

phenomena (yielding) observed underground; and

• Element properties are recalculated when element sizes are

changed; smaller elements have lower strength values than

larger ones because of their proximity to the free face.

GOB PROPERTIES

When numerical models contain large mined areas, such as

longwall or pillar line gobs, some mechanism must be employed

to simulate caving and stress relief associated with those areas.

Without it, the full weight of the overburden would be transferred to adjacent areas and result in a significant overestimation

of abutment loads. The stress relief process is complex and

comprises caving, bulking, and subsequent compaction of the

gob material. Although a number of investigators, including

Pappas and Mark [1993], have evaluated the behavior of gob

material, little published data exist regarding the simulation of

caving in 3-D boundary-element numerical models.

The BESOL system provides a fill material that has been

used to absorb a portion of the gob loads and provides a

measure of stress relief associated with caving. The stress-strain

relationship for the fill material is based on the work of

M. D. G. Salamon and is of the form [Crouch Research, Inc.

1988]:

Fn ' a ( en / (b & en), (7)

where Fn ' normal stress on the fill element,

en ' normal strain of the fill element,

b ' limiting value of normal strain (total compaction),

and a ' stress to compress fill 1/2 of b.

For a first approximation, values for the necessary constants

have been estimated as:

a ' 100 psi

b ' 0.50 in/in

Figure 8 illustrates the relatively soft stress-strain response

of backfill using these parameters. That material was tested in

a number of general scenarios; resultant abutment loads were

compared with those predicted by the inverse square decay

function used by Mark [1990] in the Analysis of Longwall Pillar

Stability (ALPS) methodology. As typified by figure 9, a

reasonable agreement in resultant abutment stress distributions

was found. The peak stress of the BESOL model exceeds that

of the inverse square decay function; the average stress over the

first 150 ft of the abutment (usually the zone of concern) is

nearly identical. It appears that the use of a relatively soft

backfill compensates for the tendency of boundary-element

models to distribute abutment loads over a wide area and results

in a reasonable approximation of near-gob stresses. Fill material of this type has been placed in gob areas during the

BESOL simulation of nine mines (starting 20-30 ft from solid

coal to allow an area of hanging roof) that have been successfully evaluated.
101

Figure 8.CBESOL strain-hardening backfill behavior.
102

Figure 9.CBESOL versus inverse square decay function.
103

As with the other material properties discussed in this paper,

the suitability of gob backfill based on the above or any other

parameters must be verified. Obviously, the use of backfill that

is too stiff will result in excessive gob loading and reduced

abutment loads. Conversely, a gob material that is too soft will

generate excessive abutment loads and low-gob stress. The

modulus of elasticity of the rock mass and other geometric

parameters (depth, panel width, etc.) can have a significant

impact on backfill loading and must be considered. Examining

backfill stress in gob areas can indicate the amount of relief

simulated by the model and can be compared to known or

anticipated cave heights associated with those areas.

SUMMARY OF PROPERTIES

In the process of simulating ground conditions at mines

throughout the United States (12 coal seams in 5 States), a host

of coal and rock properties have been generated. Table 2

summarizes the in situ coal strength, coal modulus of elasticity,

and rock moduli of elasticity used in 18 successful evaluations.

The mining depth of each simulation is also shown in the table.

The data are presented for reference purposes and illustrate the

variation in properties that can be expected at different sites.

Table 2.CSuccessfully applied coal and rock properties

State and

coal seam

Mining

depth,

ft

In situ

coal strength,

psi

Coal modulus

of elasticity,

psi

Rock modulus

of elasticity,

psi

PA:

 Lower Freeport ....... 420 1

462 1550,000 21,000,000

 Upper Freeport ....... 700 1

405 1200,000 1590,000

 Upper Freeport ....... 360 1

775 1200,000 1740,000

 Pittsburgh ........... 950 2

790 2350,000 22,100,000

 Pittsburgh ........... 650 2

900 2500,000 23,280,000

 Pittsburgh ........... 575 2

790 2350,000 22,140,000

 Lower Kittanning ...... 375 2

679 2300,000 21,850,000

WV:

 Cedar Grove ......... 900 1

705 2500,000 21,800,000

 Dorothy ............. 150 1

290 1121,000 2910,000

 Eagle ............... 950 1

712 1490,000 1880,000

 Eagle ............... 850 1

850 1500,000 1810,000

 Lower Lewiston ....... 260 1

583 1200,000 22,400,000

 Sewell .............. 470 1

312 1250,000 21,400,000

KY:

 Elkhorn No. 3 ........ 420 1

951 1548,000 21,750,000

 Hazard No. 4 ......... 900 1

967 2500,000 21,260,000

 Hazard No. 4 ......... 950 2

967 2500,000 21,260,000

IL:

 Illinois No. 5 ......... 700 2

620 2330,000 21,000,000

AL:

 Blue Creek .......... 1,200 2

750 2580,000 21,440,000

1Based on site-specific tests.

2Estimated from published data provided by the mine or found in literature reviews.

DETERIORATION INDICES AND ANALYSIS

As mentioned previously, the most critical phase of the simulation process is verifying the accuracy of a model through

correlation with actual underground conditions. To aid in that

exercise, a set of deterioration indices was established to

quantify pillar, roof, and floor behavior. Observed sites are

assigned a numerical rating on a scale of 0 to 5 (0 is the best

condition; 5 is the most severe) in each of the three categories.

The deterioration index levels are reasonably well defined to

minimize subjectivity of observations and promote consistency

in ratings from site to site.

The pillar deterioration index (PDI) establishes observable

sloughing levels that can be directly related to numerical model

projections. A rating of 1 indicates corner crushing for a distance equal to one element width (usually 1/2-entry width) in

the boundary-element model. A rating of 2 indicates some

perimeter sloughing, but to a depth of less than one element

width. This corresponding model would indicate yielding of

some, but not all, of the perimeter seam elements. At the 2.5

level, sloughing is severe enough to cause concern over the

stability of the area. A PDI of 3.5 represents a situation where
104

sloughing caused widening of the entry to a point that supplemental support (cribs or posts) was required to narrow the

roadway. A corresponding model would indicate yielding of all

perimeter elements and elevated pillar core stresses. PDIs of

4 and 5 represent progressively more severe conditions. A

model response equivalent to a level 4 would indicate deeper

pillar yielding and core stresses approaching the maximum

capacity; a level of 5 indicates total pillar yielding and elevated

convergence.

Pillar deterioration index (PDI)

 0 Virtually no sloughing

1.0 Corner sloughing

2.0 Light perimeter sloughing

2.5 Onset of pillar stability concerns

3.0 Significant perimeter sloughing

3.5 Supplemental support required

4.0 Severe perimeter sloughing

5.0 Complete pillar failure

The roof deterioration index (RDI) defines a rating scale to

quantify the condition of the roof strata in observed areas.

Unlike the PDI, however, roof deterioration cannot be directly

correlated to model output. The levels were established to

correspond to progressively more significant observable

phenomena ranging from roof flaking or sloughing (level 1) to

widespread and massive roof falls (level 5). The severity of

each feature can be identified within a one-point band. For

instance, areas with only a hint of roof cutters would be rated at

1.6; those containing many severe cutters (a situation causing

roof stability concerns) would receive a 2.5 rating. A roof

deterioration index of 3.5 corresponds to conditions where

supplemental support was required to maintain stability.

Roof deterioration index (RDI)

 0 Virtually no deterioration

1.0 Flaking or spalling

2.0 Cutter roof

2.5 Onset of roof stability concerns

3.0 Broken roof

3.5 Supplemental support required

4.0 Significant roof falls

5.0 Widespread and massive roof falls

The floor deterioration index (FDI) provides a measure of

mine floor stability relative to fracturing and the level of heave

experienced. Like the RDI, this index cannot be directly

correlated to the model output, and the established levels

represent progressively more serious floor conditions. An FDI

of 2.5 represents the occurrence of heave that causes concern

over floor stability; a level of 3.5 indicates a condition that

impedes passage and requires grading to maintain an active

travelway.

Floor deterioration index (FDI)

 0 Virtually no deterioration

1.0 Sporadic cracks

2.0 Consistent localized cracks

2.5 Onset of floor stability concerns

3.0 Widespread cracks and obvious heave

3.5 Travel impeded; grading required

4.0 Significant floor displacement

5.0 Complete entry closure

The deterioration indices have been effectively used to

describe in-mine ground conditions and to correlate BESOL

output data to those observations. While simulation output such

as stress and convergence can often be directly related to inmine conditions, many instances arise where the combined

influence of a number of factors affects ground behavior. To

better establish those relationships and provide an effective

means of evaluating potential design alternatives, a multiple

linear regression can be used to relate model output to observed

(deterioration index) conditions.

Table 3 presents a partial listing of BESOL output (stress,

convergence, and failure index (FI) at the immediate roof line)

and deterioration indices for a number of areas modeled and

observed during an actual mine analysis. Other BESOL output

(i.e., horizontal stress or displacement) could be included if

applicable to a particular situation, but the three parameters

listed are those routinely used. After model and observation

data for all of the evaluated areas are compiled, multiple linear

regression analyses are performed to define each deterioration

index as a function of model output. In the sample instance in

table 3, the various deterioration indices were related to

maximum stress, maximum convergence, and minimum failure

index at the roof line, and the resultant regression equations and

correlation coefficients are listed.

Once the model accuracy is verified by comparing predicted

to observed pillar yielding, examining the regression correlation

coefficients, and using the regression equations to backcalculate deterioration indices for the observed (modeled) areas,

design alternatives can be modeled and expected conditions

predicted. Table 4 contains projected deterioration indices at a

critical pillar line location for various pillar sizes and depths of
105

cover as predicted by BESOL output and the verified regression

equations. The difference in expected conditions with each

design alternative is clear.

The deterioration index/regression equation technique has

proved to be a viable method of verifying numerical model

accuracy and evaluating the potential of design alternatives

provided that relatively consistent mining conditions exist.

When changing roof, pillar, or floor strengths are encountered,

the usability of the regression technique may be greatly reduced.

Further, the relationships established are based on strata reaction

at a particular mine, and only those observed (which are limited

by current mine design and environment) can be included in the

database. This is a particular concern when the use of yield

pillars as an alternative configuration is considered, but no

complete pillar yielding is evident at the mine.

The Roof Control Division is currently exploring the use of

normalizing parameters in the regression analysis to alleviate

these difficulties. Factors such as in situ coal strength and seam

height (for the PDI), a roof rock rating such as the Coal Mine

Roof Rating (CMRR) [Molinda and Mark 1993] for the RDI,

and a floor characterization number (for the FDI) are being

evaluated to determine their usefulness in the regression

analysis to buffer the variations found within a given mine and

also between mines. If successful, the resultant technique could

enhance individual mine analyses and allow the experience of

many mines to be used.

Table 3.CPartial BESOL/deterioration index listing and regression equations

Location and

entry

BESOL output Deterioration indices

Maximum

stress, psi

Maximum

convergence,

ft

Minimum

failure

index (FI)

Observed Back-calculated

PDI RDI FDI PDI RDI FDI

Face area:

 1 .......... 4,000 0.113 1.04 1.5 1.5 0.0 1.5 1.2 0.2

 2 .......... 6,800 0.195 1.09 2.0 1.8 0.3 2.5 2.4 1.2

 3 .......... 8,100 0.251 0.96 3.5 3.0 1.0 3.0 2.9 1.7

 4 .......... 8,800 0.289 0.89 4.0 4.2 2.5 3.3 3.3 2.0

 5 .......... 8,800 0.307 0.87 4.0 3.5 4.0 3.3 3.4 2.1

1 crosscut outby:

 1 .......... 3,100 0.083 1.11 1.2 1.5 0.0 1.1 0.9 0.0

 2 .......... 5,400 0.161 1.16 1.5 1.5 0.0 2.0 1.9 0.8

 3 .......... 7,000 0.207 1.11 2.0 2.0 0.5 2.6 2.5 1.3

 4 .......... 7,500 0.230 1.02 3.0 3.0 1.0 2.8 2.7 1.5

 5 .......... 7,500 0.223 0.94 3.0 3.0 3.0 2.7 2.6 1.4

3 crosscuts outby:

 1 .......... 2,710 0.063 1.25 1.0 0.5 0.0 1.0 0.7 0.0

 2 .......... 3,900 0.089 0.93 1.5 0.8 0.0 1.3 1.1 0.0

 3 .......... 6,000 0.150 1.16 1.5 1.5 0.2 2.2 2.0 0.9

 4 .......... 7,000 0.182 1.13 2.0 2.0 1.0 2.5 2.4 1.2

 5 .......... 7,300 0.204 1.21 3.0 2.5 2.0 2.7 2.6 1.4

3-Right:

 2 .......... 2,240 0.059 1.53 1.0 0.5 0.0 1.0 0.7 0.0

 4 .......... 2,560 0.070 1.41 1.4 1.0 0.0 1.1 0.8 0.0

 5 .......... 2,820 0.072 1.45 1.5 1.4 0.1 1.2 0.9 0.0

1-Right:

 2 .......... 1,530 0.040 2.13 1.0 0.2 0.0 1.0 0.6 0.0

 4 .......... 1,700 0.047 1.91 1.0 1.0 0.0 1.0 0.6 0.0

 5 .......... 1,780 0.047 2.00 1.0 1.0 0.0 1.0 0.7 0.0

PDI ' 0.000268 ( STR % 3.259622 ( CONV % 0.379665 ( FI & 0.383740 r

2 ' 0.79

RDI ' 0.000263 ( STR % 4.603502 ( CONV % 0.309200 ( FI & 0.643870 r

2 ' 0.80

FDI ' 0.000170 ( STR % 6.094244 ( CONV % 0.600442 ( FI & 1.82412 r

2 ' 0.60
106

Table 4.CFull pillaring BESOL output and predicted deterioration index

Pillar size (ft),

depth, and

location

Maximum

stress, psi

Maximum

convergence,

ft

PDI RDI FDI

50 by 50 (900-ft depth):

 1 ................

1

8,300 10.291 23.0 23.1 31.7

 2 ................

1

8,200 20.247 23.1 23.1 31.9

 3 ................

3

5,900 20.185 32.1 32.0 30.8

 4 ................

3

5,600 30.161 32.2 32.0 31.0

40 by 40 (900-ft depth):

 1 ................

1

9,690 10.385 13.8 14.0 22.7

 2 ................

1

9,690 10.343 13.8 13.9 22.6

 3 ................

1

8,700 20.245 23.0 23.0 31.6

 4 ................

1

8,300 20.230 23.1 23.0 31.7

40 by 40 (800-ft depth):

 1 ................

1

9,690 10.305 13.5 13.6 32.2

 2 ................

1

9,690 10.269 13.6 13.5 32.2

 3 ................

2

6,800 20.198 32.4 32.3 31.0

 4 ................

2

6,600 20.182 22.5 32.4 31.3

40 by 40 (600-ft depth):

 1 ................

2

7,300 20.204 22.6 22.5 31.2

 2 ................

2

7,150 30.171 22.7 22.5 31.4

 3 ................

3

3,500 30.095 31.2 31.0 30.0

 4 ................

3

3,400 30.087 31.3 31.0 30.1

40 by 30 (400-ft depth):

 1 ................

3

4,400 30.116 31.5 31.3 30.2

 2 ................

3

4,200 30.098 31.4 31.2 30.1

 3 ................

3

2,660 30.063 31.0 30.7 30.0

 4 ................

3

2,320 30.060 31.1 30.8 30.0

1Severe conditions.

2Borderline conditions.

3Desirable mining conditions.

CASE STUDY

An investigation was conducted at a coal mine in eastern

Kentucky to determine the cause of a roof fall and deteriorating

ground conditions that were encountered on a full pillaring

section. The mine is located in the Hazard No. 4 Seam and has

a mining height of 32-40 in. Figure 10 presents an illustration

of the 1-Left Mains in the vicinity of the roof fall. These mains

were developed as a five-entry system on 50- by 60-ft centers

with 20-ft-wide entries and crosscuts. Panels were driven to the

right and retreated as the mains were advanced (13 panels total).

Following development of the mains (and panels) to the

property boundary, retreating of those pillars was initiated. As

figure 10 illustrates, a roof fall occurred one crosscut outby the

pillar line as the 18th row of blocks was being extracted. Cover

at the face was about 800 ft, but ranged from 480 ft near the

mouth of the section (about 2,400 ft outby) to over 950 ft

several hundred feet inby and to the right of the fall. The

immediate roof strata were composed of a 15-ft-thick laminated

shale and were overlain by a 20-ft-thick sandstone layer. Roof

support was provided by 4-ft-long fully grouted bolts installed

in a 4- by 4-ft pattern throughout the mains.

Observations were made throughout the 1-Left Mains to

characterize ground conditions under various depths of cover

and degrees of gob influence. Significant deterioration (heavy

pillar sloughing, cutters, and broken roof zones) was noted in

the face area; conditions were most severe in the immediate

vicinity of the roof fall. Outby the face, conditions gradually

improved, although the right side of the mains consistently

showed heavier deterioration than the left side. The most

significant conditions noted in the outby area corresponded to

zones of heavier cover, suggesting that overburden depth and

the adjacent gob areas contributed to the deteriorating conditions. Detailed deterioration index ratings were made

throughout the observed areas to quantify the roof, floor, and

pillar behavior. The data presented in table 3 represent a partial

listing of these ratings in a number of entry locations (crosscut

conditions were also quantified and used in the analysis).

Higher PDI, RDI, and FDI levels correspond to more severe

deterioration, which were observed in the face area and along

the right side of the mains. Cover at the face was about 800 ft

and about 650 ft and 480 ft over the 3-Right and 1-Right outby
107

Figure 10.CCase study: partial mine map of pillaring section - roof fall area.

areas, respectively, where conditions were much improved.

Figure 11 presents a composite deterioration index drawing of

conditions observed at and just outby the face, illustrating the

concentration of deterioration in the vicinity of the roof fall and

along the right side of the section.

A series of three BESOL models was subsequently created

to simulate conditions in the areas observed during the

underground investigation. The first model (covering the area

shown in figure 10) was used to simulate mining at the time of

the roof fall and also at inby and proposed outby face positions
108

Figure 11.CCase study: observations on pillaring section - roof fall area.
109

where cover was approximately 800 ft. Additional models

were constructed of the outby areas (3-Right (650-ft cover) and

1-Right (480-ft cover)) to provide model verification under

significantly differing conditions. Vertical stress applied to the

models equaled 1.1 psi per foot of depth, and a horizontal stress

of 1/2 the vertical stress was assumed in both the x and y

directions. The element size used in the simulations was 10 ft,

or 1/2 the 20-ft-entry width.

A composite rock modulus of 1,260,000 psi was based on

data obtained from four boreholes in the vicinity, as shown in

table 1. The individual rock moduli were estimated from

published data for the specific strata contained in each borehole.

A Poisson's ratio of 0.21 and the default Mohr-Coulomb

properties (cohesion ' 800 psi, friction angle ' 25°, and tensile

strength ' 1,000 psi) were used because no site-specific data

were available.

Coal properties were based on an in situ strength of 967 psi

(site-specific coal strength data were provided by the mine); the

peak and residual strength levels were calculated as outlined

previously in this paper. A seam height of 2.8 ft was used, and

a coal modulus of elasticity of 500,000 psi was assumed. The

stress-strain curves of figure 7 represent the strain-softening

model used in the analysis. Shear stress-strain properties were

based on a shear modulus of 200,000 psi (0.4E).

Gob caving was simulated using the Salamon backfill

discussed earlier with the constants a ' 100 psi and b ' 0.50.

The comparison of abutment loading between BESOL and the

inverse square decay function of figure 9 was based on the rock

mechanics parameters used in this simulation.

Maximum pillar stress, maximum roof/floor convergence,

and minimum failure index values were determined from the

3 models for 37 locations (entries and crosscuts) corresponding

to the observed areas. The stress and convergence data compiled indicate the highest levels found in or adjacent to the 37

locations; the failure index values represent the lowest levels

detected at the roof line in each area. A portion of these data

(entry locations) is listed in table 3. A series of multiple linear

regression analyses was made to relate the deterioration indices

observed to the BESOL data and resulted in the equations also

listed in table 3. The R-squared values for the PDI (0.79) and

the RDI (0.80) were very good, but marginal for the FDI (0.60).

It should be noted that the characterization of floor conditions

was not a primary concern during the investigation, but sketchy

data acquired were used to illustrate the process. The BESOL

output was then inputted into the regression equations to predict

(back-calculate) deterioration indices for the observed locations;

these values describing entry conditions are also listed in table 3. Most of the predicted PDI and RDI levels match the

observed data fairly well, and the trend of higher deterioration

indices in areas of more severe conditions was evident, even

with the FDI.

Figure 12 presents a composite of maximum pillar stress and

convergence levels predicted by the BESOL model of the roof

fall site. Note the correlation of BESOL stress and convergence

with the degree of deterioration observed underground. The

zone of high convergence (>0.25 ft) and stress (>9,500 psi)

encompasses the area of deteriorating conditions at the pillar

line, including the roof fall. Lower stress and convergence

levels also correspond to zones of lesser deterioration, and the

more severe conditions predicted on the right side of the mains

(indicating the influence of the adjacent gob) also match the

conditions observed underground. These correlations, coupled

with the good fit of the regression analysis (deterioration

indices), confirmed the accuracy of the model (and properties

used) to simulate conditions at the mine. Confidence was

further enhanced by an evaluation of the BESOL model with a

face position several crosscuts inby the roof fall. The results

showed significantly lower stress and convergence levels in the

face area that correlated to the better mining conditions actually

encountered.

It was concluded that the roof fall (and deteriorating conditions) resulted from a combination of stresses from the active

and adjacent gobs overriding the pillar line (yielding) and

focusing outby the face. The small pillar size employed (30 by

40 ft) on the mains, the lack of protection provided by the

combination of chain and barrier pillars from the adjacent gob,

and the depth of cover (>800 ft) contributed to the problems

encountered.

A series of additional models was created to evaluate the

performance of various pillar sizes at different mining depths

that would be encountered. Figure 13 illustrates the pillaring

plan to be implemented using a 200-ft barrier between adjacent

panels that would be roomed and retreated along with the panel

being extracted. Stresses and convergences were examined at

four entry locations near the face (during retreat of the second

panel), as illustrated in figure 14. Threshold levels delineating

expected conditions (from the 1-Left models) were established

as follows:

Severe conditions:

Stress > 8,000 psi; convergence > 0.25 ft

PDI $ 3.5; RDI $ 3.5; FDI $ 3.5

Borderline conditions:

Stress ' 6,500 to 8,000 psi; convergence ' 0.18 to 0.25 ft

PDI ' 2.5 to 3.4; RDI ' 2.5 to 3.4; FDI ' 2.5 to 3.4

Desirable mining conditions:

Stress < 6,500 psi; convergence < 0.18 ft

PDI < 2.5; RDI < 2.5; FDI < 2.5

It was predetermined that good (desirable) mining conditions

should exist at locations 3 and 4 since no supplemental supports

(posts) would be installed in those areas. Borderline conditions

could be tolerated at locations 1 and 2 (posts are set in this area),
110

Figure 12.CCase study: BESOL output pillaring section - roof fall area.
111

Figure 13.CCase study: full pillaring plan.
112

Figure 14.CCase study: full pillaring analysis locations.

but the occurrence of severe conditions should be avoided or at

least limited to location 1.

Table 4 presents the BESOL and predicted deterioration

index data for each of the four locations for a number of

scenarios. The analysis indicated that the use of 40- by 30-ft

pillars would result in good conditions through a depth of

400 ft and that 40- by 40-ft pillars would be effective up to 600

ft of cover. Pillars 50- by 50-ft in size would be needed for

deeper cover areas, although severe conditions could be possible

at locations 1 and 2 as the depth approaches 900 ft.

CONCLUSION

Boundary-element modeling has proven to be an effective

tool for mining engineers to resolve complex ground control

problems. The techniques set forth in this paper describing coal,

rock, and gob behavior have been effectively used to evaluate

a variety of mining scenarios. Although they are supported by

a number of in situ measurements and have resulted in near

duplication of underground conditions in many instances, they

provide only a first estimate of parameters that must be validated. Successful numerical simulation requires a substantial 

effort, including the observation of conditions in many areas

and the often repetitive process of calibrating model parameters.

The use of techniques such as the deterioration index/regression

method has greatly facilitated the linking observed and

simulated mine conditions. It cannot be overemphasized, however, that in order to be of any value, a numerical model must be

validated and provide a realistic representation of the underground environment for which it is applied.
113

REFERENCES

Bieniawski ZT [1984]. Rock mechanics design in mining and tunneling.

A. A. Balkema, 272 pp.

Carr F, Wilson AH [1982]. A new approach to the design of multi-entry

developments for retreat longwall mining. In: Proceedings of the Second

Conference on Ground Control in Mining. Morgantown, WV: West Virginia

University, pp. 1-21.

Choi DS, McCain DL [1980]. Design of longwall systems. Trans Soc Min

Eng AIME, Vol. 268, pp. 1761-1764.

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, pp. 23-27.

Crouch Research, Inc. [1988]. The BESOL system: boundary element

solutions for rock mechanics problems: user's guide, version 2.01. St. Paul,

MN: Crouch Research, Inc., pp. 5-19.

Holland CT, Gaddy FL [1964]. The strength of coal in mine pillars. In:

Proceedings of the 6th U.S. Symposium on Rock Mechanics. Rolla, MO:

University of Missouri, pp. 450-466.

Hsuing SM, Peng SS [1985]. Chain pillar design for U.S. longwall panels.

Min Sci and Technol, Vol. 2, pp. 279-305.

Mark C [1990]. Pillar design methods for longwall mining. Pittsburgh, PA:

U.S. Department of the Interior, Bureau of Mines, IC 9247.

Mark C, Chase FE [1997]. Analysis of retreat mining pillar stability

(ARMPS). In: Proceedings - New Technology for Ground Control in Retreat

Mining. Pittsburgh, PA: U.S. Department of Health and Human Services,

Public Health Service, Centers for Disease Control and Prevention, National

Institute for Occupational Safety and Health, DHHS (NIOSH) Publication

No. 97-122, IC 9446, pp. 17-34.

Mark C, Iannacchione AT [1992]. Coal pillar mechanics: theoretical

models and field measurements compared. 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. 78-93.

Molinda GM, Mark C [1993]. The coal mine roof rating (CMRR):

a practical rock mass classification for coal mines. In: Proceedings of the 12th

International Conference on Ground Control in Mining. Morgantown, WV:

West Virginia University, pp. 92-103.

Obert L, Duvall WI [1967]. Rock mechanics and the design of structures

in rock. New York, NY: Wiley, pp. 542-545.

Pappas DM, Mark C [1993]. Load deformation behavior of simulated

longwall gob material. In: Proceedings of the 12th International Conference on

Ground Control in Mining. Morgantown, WV: West Virginia University,

pp. 184-193.
115

THE FRACTURE MECHANICS APPROACH TO UNDERSTANDING 

SUPPORTS IN UNDERGROUND COAL MINES

By James M. Kramer, Ph.D.,1 George J. Karabin, P.E.,2 and M. Terry Hoch3

ABSTRACT

This paper introduces the fracture mechanics approach—a unique way to predict the stability of a coal mine

panel. The technique uses analytic equations to calculate the stress, strain, and yield characteristics of coal

support systems. It uses fracture mechanics to model almost every type of mine support structure. Another

feature is a method that incorporates field-tested knowledge into the analytical analysis. For example, this

technique can model the yield characteristics of a coal seam by combining empirical pillar strength equations

into the analytic analysis. It may be possible to simulate multiple-seam mining by incorporating subsidence

methods into the analysis. The method is simple and quick, which makes it attractive for stress analysis

software. It should be more accessible to those in the mining industry who do not have expertise in rock

mechanics or numerical modeling. Although the purpose of this research is for modeling coal mines, it should

be adaptable to any mine in a tabular deposit.

1Mining engineer.

2

Supervisory civil engineer.

3Chief.

Roof Control Division, Pittsburgh Safety and Health Technology Center, Mine Safety and Health Administration, Pittsburgh, PA.
116

Fy(x) '

Fx

x

2&a2

,

(1)

INTRODUCTION

This paper presents a new way to analyze the mechanical

behavior of underground coal mine supports. Included are

analytic expressions describing the stress, strain, and yielding

characteristics of a coal seam. The fracture mechanics approach

(FMA) provides the capability to model almost every type of

mine structure, including pillars, yield pillars, longwall gob,

chocks, cribs, posts, and hydrostatic loads. In addition, it predicts

pillar stability by combining empirical pillar strength equations

into the analytic analysis. This makes the procedure useful for

understanding how various support structures affect the

mechanical performance of a mine panel.

Although the method is not as sophisticated as numerical

analysis, it offers several advantages. The analytic equation

makes it is as accurate as numerical modeling, but quicker and

easier to use. Because of the few equations involved, it is easy

to incorporate the process into a computer spreadsheet or

programmable calculator. Real-time design analysis is possible

by incorporating the technique into computer code. For example, one can change a design structure (e.g., add a crib) and

see instantly the resultant stress effect. The coal yielding process uses empirical pillar strength equations derived from years

of field measurements. Combining these equations into the

analytic analysis provides insight into pillar stability. The

system presented in this paper offers a unique perspective from

which to study mine panel stability.

DESIGNING SUPPORT STRUCTURES FOR COAL MINES

There are several ways to analyze the stability of a mine

layout. The easiest and, in some cases, most reliable is to use

pillar strength equations. These equations are developed from

extensive knowledge of coal seam behavior [Mark and Iannacchione 1992]. Most are based on physical stress measurements;

however, some come from numerical studies or analytic

equations. All of these methods use the pillar width-to-height

ratio as the controlling factor. These strength equations can be

accurate; however, they assume that the coal pillar is the single

means of support. It is not possible to study the effects of cribs,

posts, longwall gob, chocks, etc. Also, these equations do not

predict the stress distribution through the panel, nor do they

predict the extent of the yield zone in the coal.

There are other, more accurate, ways to analyze stability.

Numerical modeling, if used properly, can be very accurate. It

can predict the stress distribution throughout the entire mine

environment, including the coal seam, surrounding strata, slips,

faults, and all types of supports. However, this method is timeconsuming and requires a certain amount of technical skill. For

example, using finite elements, it would take a skilled engineer

a day or more to analyze the yield zone in a coal pillar based on

data derived from field measurements.

This paper discusses a simple, quick, and accurate solution

for predicting the stress distribution in coal pillars and other

structures. It uses a combination of fracture mechanics and empirically derived techniques to predict the extent of the yield

zone in a coal pillar. It can model nearly every structure used

for mine support. Numerical modeling will validate the accuracy of the technique.

THE FRACTURE MECHANICS APPROACH

Understanding the FMA requires visualizing a coal seam

as an extremely thin layer in the stratum of the Earth. A tunnel

or opening in the coal would appear as a thin crack in an

infinite mass.4

 It should then make sense that it is possible to

use the mechanics of cracks to analyze the stresses surrounding

openings in coal seams.

Visualizing a mine opening as a crack is not new; others

applied it to their research [Barenblatt 1962; Hacket 1959;

Crouch and Fairhurst 1973; Berry 1960, 1963]. However, this

paper describes a way to use the fracture mechanics directly to

predict pillar stress. Combined with a superpositioning

4

In this paper, the term “crack” infers a mine opening and vice versa.

Therefore, crack-tip stress is the same as rib or pillar stress.

technique, it is possible to obtain the complete stress distribution

throughout the mine panel. A yielding technique completes the

analysis by offering realistic characteristics to the coal pillars.

Westergaard's equation is fundamental to fracture mechanics theory and is also the basic equation for the FMA

[Westergaard 1939]. The stress distribution at the crack tip is

identical to the distribution adjacent to a mine opening.

Westergaard describes the stress at the tip of a crack as
117

Figure 1.CCrack of width 2a subjected to a uniform biaxial

stress field.

where Fy(x) ' stress distribution adjacent to a crack tip,

a ' 1/2 the crack width,

F ' in situ stress,

and x ' distance from the center of the crack.

This equation implies that the only parameters needed to

predict elastic rib stress are the entry width and the in situ stress

(figure 1). Westergaard derived equation 1 by assuming that

the stress field acting on the crack is located at an infinite

distance from the crack surface. Another assumption is that the

crack width must align with the planes of this stress field. In

general, these conditions are similar to a mine environment.

The Westergaard equation will accurately predict the stress

distribution into the coal seam provided that the analysis

remains within the elastic range.

NUMERICAL METHODS VALIDATE THE

WESTERGAARD EQUATION FOR MINE ANALYSIS

Westergaard developed his stress function by making the

following assumptions: the crack has a thickness of zero; it is

contained in an infinite, homogeneous plate; and the plate is

subjected to a uniform biaxial stress field. These conditions

match fairly the conditions encountered in a coal mine opening.

There are differences, however. A mine opening has an actual

thickness. The structural properties of the coal differ from

those of the surrounding rock mass. Also, a coal mine's

environment is under the influence of a graduated, nonuniform,

biaxial stress field controlled by gravity. It is necessary to consider all of these factors to validate the FMA. Previous research

demonstrates the accuracy of the FMA by comparing it to

numerical modeling output [Kramer 1996]. It is shown that the

technique matches the numerical modeling predictions with a

high degree of accuracy.

Figures 2 through 7 are plots that compare the stress

prediction of the FMA with that of numerical modeling. The

purpose is to show how well the FMA can predict stress even

in conditions less ideal than those used by Westergaard to

derive equation 1. Such conditions are similar to those encountered in an underground coal mine. All of the evaluations

use FLAC5

 as the numerical modeling software. Spreadsheet

graphs are used to compare the FMA stress prediction with that

determined by FLAC. Each demonstrates that the FMA compares reasonably well with the FLAC model for varying conditions of nonhomogeneity. Initially, the model is homogeneous and simple. The FMA matches extremely well with

the numerical model [Kramer 1996]. Then, in order to

introduce nonhomogeneity into the numerical model, each

5

Fast Langrangian Analysis of Continuum, Itasca Corp., Minneapolis,

MN.

individual structural property is altered independently and the

results are compared with the FMA. Finally, an evaluation is

made between the FMA and a nonhomogeneous numerical

model consisting of strata with properties even more variant

than an actual mine environment.

Figure 2 charts the comparative stress predictions between

the FMA and FLAC for a simple, elastic, and homogeneous

model. Note that the stress distributions are nearly exact. The

only real difference is at the edge of the mine opening. This

difference is due to the approximation technique used in numerical analysis. The model in figure 3 has the same homogeneous properties as those for figure 2; it plots the stress

distribution through various planes in the coal seam. This illustrates that the distribution, at any plane, remains consistent

with the distribution through the center plane of the seam.

Figures 4 and 5 demonstrate that the coal's modulus of elasticity

or Poisson's ratio has little effect on the stress distribution

through the center plane of the coal seam. The next step is to

compare the accuracy of the FMA for predicting the stress of a

nonhomogeneous numerical model. Figures 6 and 7 relate the

results of the simulation.

Figure 6 shows the comparison between FLAC and the FMA

for the stress distribution produced in a graduated, nonuniform,

biaxial stress field similar to that encountered in an underground

mine. For these studies, the horizontal stress is 0.3 times the

vertical stress. The design of the model places the coal seam at

a depth of 381 m. The structural parameters of the coal and rock

are equivalent. This study also compares the Westergaard equation to the stress at various planes in the seam (figure 6).

It can be seen that the nonuniform stress field in the numerical model causes a deviation in stress from the Westergaard

prediction; however, most of the difference is near the edge of

the mine opening. In this portion of the mine rib, the coal is

yielding. Analytical methods do not exist for predicting the

stress distribution in this region. Introduced later in this paperis

a method that uses field measurements to describe the stress

distribution in the yield zone of a coal rib.
118

Figure 2.CStress distribution in a coal seam next to a mine opening: comparison between numerical

analysis and the Westergaard equation. Homogeneous model.

Figure 3.CStress distribution at various levels in the coal seam. Properties similar to the model

in figure 2.
119

Figure 4.CStress profile for coal with different moduli. Four separate FLAC models.

Figure 5.CHow the Poisson ratio affects the stress distribution. Three separate FLAC models.
120

Figure 6.CThe effect of a graduated, nonuniform biaxial stress distribution similar to conditions

underground. Stress profile at various levels in the seam.

Figure 7.CComparison of a model simulation of a real mine environment.
121

KA'

P

Ba

a % x

a & x

(2)

KB'

P

Ba

a & x

a % x

(3)

Figure 8.CCrack with wedge forces at x.

The numerical model described below will validate the

FMA's ability to analyze structural variations found in a real

mine environment. In this model, the strata are nonhomogenous. In addition, the surrounding stress field is variable in

both the vertical and horizontal planes. Such a model has

structural variations greater than those encountered in most coal

mines. The surrounding rock mass has a Young's modulus of

27,580 MPa and a Poisson's ratio of 0.2. The unit weight of

this mass is 0.03 MN/m3

. The coal seam has a Young's

modulus of 3,448 MPa, a Poisson's ratio of 0.3, and a unit

weight of 0.03 MN/m3

. The unit weights are high to enhance

the stress comparisons by increasing the effect of gravity

loading. To show the effect of mining in an area subjected to

a high stress field, the model is initialized with a premining

stress prior to adding the mine opening. Adding a mine

opening to a model with a high biaxial stress field already

in place would alter the stress in the areas adjacent to the mine

opening. Figure 7 compares the Westergaard equation to

FLAC's analysis for different levels in the coal seam. The

distributions vary considerably; however, most of this deviation

is near the mine opening. In this area, the coal will yield.

A technique will be presented in this paper that describes the

stress distribution in the yield zone of the coal.

THE POINT-FORCE METHOD USED TO SIMULATE MINE SUPPORTS

An essential concept of the FMA is the process by which

a point force, acting on the surface of the crack, affects the

stress intensity at the crack tip. In mining, this point force

could be a mine post or hydraulic jack. A continuous series of

point forces can model a yield pillar, longwall gob, the yield

zone of the pillar, or any other type of mining supports [Kramer

1996]. Figure 8 depicts a crack with an internal point force,

P, pushing out against the crack surface. This force P is at a

distance x from the crack center. This force affects the stress

intensity factor K at points A and B. The point force is similar

to the loading from a single-point mine support, such as a post

or hydraulic jack.6

Green functions are used to predict the stress intensity

factors [Paris and Sih 1965]. The factors are:

where KA ' stress intensity at point A,

KB ' stress intensity at point B,

P ' point force,

a ' 1/2 the opening width,

and x ' distance from opening center

6

The stress intensity factor is of utmost importance in the study of

fracture mechanics. It is a measure for the stress singularity at the crack tip.

For the case of uniaxial compression with force P at infinity, K must be proportional to P. KA

 and KB must also be proportional to the square root of a

length. For an infinite object, the only characteristic length is the crack size;

thus, K must take the form: K ' F/(Ba).

YIELD PILLARS

Yield pillars are common in longwall mining; they control

floor heave and/or fine tune roof behavior. As the name

implies, the pillars yield, thus redistributing the load around a

control area in the mine. It is possible to model yield pillars as

a continuous series of point forces. Equations derived from

in situ pillar strength measurements can determine the

intensities of the point forces. However, for the present

discussion, the point forces are considered uniform and equal

to the yield strength of the coal (figure 9).

To illustrate the method, it is necessary to discuss only the

stress effect at a single crack tip (e.g., point A in figure 9).

Either equation 2 or equation 3 can describe the stress intensity

at point A. The correct equation to use depends on the location

of the point forces with respect to the a-origin. In the

discussion below, the location of the point forces (figure 9) is

chosen to provide the most complete example of the technique.

Because the locations of the point forces are equally distributed

on both sides of the origin, solution to the stress effect at

point A requires using a combination of equations 2 and 3. In
122

Kinsitu ' Finsitu Ba . (4)

K%x' KA'

F

ys

Ba

m

d

0

a % x

a & x

dx . (5)

K&x' KA'

F

ys

Ba

m

d

0

a & x

a % x

dx . (6)

K ' F Ba . (9)

adummy '

K

2

total

BF

2

insitu

. (10)

Fmodified (x) '

Finsitu x

x

2 & a

2

dummy

.

(11)

Figure 9.CYielded pillar modeled as a continuous set of point forces.

absence of the yield pillar, the stress intensity at point A is

[Dugdale 1960]:

The yield pillar will act to reduce this intensity. The a-origin

is located in the center of the point forces; thus, the distribution

in the &x side is equal to the distribution in the %x side

(figure 9). The stress intensity factor at point A caused by the

continuous point forces on the %x side of the origin is

The stress intensity factor at point A caused by the continuous

point forces on the &x side of the origin is

The stress intensity factor for the yield pillar becomes

Kyield ' K%x % K&x

. (7)

With the yield pillar in place, the stress intensity factor at

point A becomes

Ktotal ' Kinsitu & Kyield. (8)

The Westergaard equation relates rib stress to the in situ

stress and the width of the opening. Because Ktotal includes not

only the in situ stress but also the effect of the yield pillar, it is

necessary to modify the Westergaard equation to reflect this

effect. It is necessary to modify the Westergaard equation by

substituting a dummy variable in place of a real variable. The

opening half-width variable "a" is the proper choice for the

substitution.7

 Solving for "a" in Ktotal and substituting it into the

Westergaard equation as a dummy variable will provide the

proper stress distribution at point A. The following demonstrates the concept.

The stress intensity factor is defined as

To modify the Westergaard equation, it is necessary to substitute values and solve for the unreal "a", making it a dummy

variable such that

The reduced Westergaard stress distribution at point A then

becomes

7Modifying F would result in the stress distribution leveling to a value

below the in situ stress.
123

K3'

F

ys

Ba

m

18.3

0

a & x

a % x

dx

'

12.4

B61 m

18.3

0

61& x

61% x

dx

' 14.1

K4'

F

ys

Ba

m

18.3

0

a % x

a & x

dx

'

10.3

B61 m

18.3

0

61% x

61& x

dx

' 15.9

LONGWALL GOB

The technique used to model longwall gob is similar to

that for the yield pillar. An assumption can be made that the

center of the gob is in contact with the roof and floor and the

material is compacted completely. Due to symmetry, it is

necessary to model only one-half the gob width to determine

its effect on the stress intensity at the tip of the opening.

Therefore, the opening extends from the gob center to edge of

the gate pillar at point A (figure 10). The residual strength of

this material is a function of the amount of compaction.

Because the center of the gob has the greatest compaction, it

has the greatest residual strength; the outside edge of the gob

has the least. To simulate gob material, the point forces are

high in the center of the gob and low at the edge. Originally,

the following example was formulated using U.S. customary

units of measurement. Conversion to the metric system makes

some values appear awkward.

As usual, the a-origin and x-origin begin at a point

equidistant from point A and the gob center. The point forces to

the right of the origin (i.e., %x side) would use equation 5 to

analyze the effect at point A; the point forces to the &x side of

the origin will use equation 6. "Derive—A Mathematical

Assistant"8

 is used to solve for the integral in each equation.

Included in table 1 are the input variables and resultant stress

intensity factors for the gob depicted in figure 10. The gob

material in the model is divided into six sections, each reflecting

a different yield strength (YS1

 to YS6). The first three sections

are in the &x side (KB

 side) of the origin; the other three are in

the %x side (KA

 side). The location of the section determines

which point-force equation to use. The total effect of the gob is

the summation of the K-values for all six sections:

Kgob ' K1 % K2 % K3 % K4 % K5 % K6

. (12)

This value is subtracted from the Kinsitu value (the stress intensity

for the large opening without the gob material in place) to obtain

the proper stress intensity factor at point A. The relation is

Ktotal ' Kinsitu & Kgob. (13)

EXAMPLE

Below is an example that demonstrates the technique. It

analyzes the effect from two sections of the complete model

shown in figure 10. These particular sections (sections 3 and

4) were chosen to illustrate forces on either side of the axis

origin. The point forces in section 3 align in the &x direction;

those in section 4 are in the %x direction. The stress intensity

factor will be determined using a combination of equations 5

and 6. Table 1 lists the results from the complete analysis.

8Derive—A Mathematical Assistant," Soft Warehouse, Inc., 3660

Waialae Ave., Honolulu, HI.

Input Parameters:

Width of longwall face ' 232 m

1/2 width of longwall face ' 116 m

2a (width of longwall face plus gate entry) ' 122 m

a ' 61 m

Finsitu ' 13.8 MPa

Section 3:

The yield strength for section 3 is Fys3 ' 12.4 MPa. It occupies

the &x portion of the a-axis for the 0- to (&)18.3-m segment.

The effect on the stress intensity at point A due to section 3 of

the gob is

NOTE: Although the point forces are in the -x region, the limits

of the integral are from 0 to (%)18.3 m.

Section 4:

The yield strength for section 4 is Fys4 ' 10.3 MPa. This section

occupies the %x portion of the a-axis for the 0- to (%)18.3-m

segment. The effect on the stress intensity at point A due to

section 4 of the gob is

"Derive—A Mathematical Assistant" solved both of these

integrals. The solutions yield a rather cumbersome equation that

is impractical to include in this paper; however, it can be incorporated into spreadsheet software or computer code. Table 1

includes the K factors for all six sections of the longwall gob.

The effect on the stress intensity factor at point A caused by all

six sections is

Kgob ' K1 % K2 % K3 % K4 % K5 % K6

Kgob ' 13.8 % 10.7 % 14.1 % 15.9 % 18.0 % 25.8

Kgob ' 98.3
124

Kinsitu ' Finsitu Ba

Kinsitu ' 13.8 B61

Kinsitu ' 191.0

adummy '

K

2

total

BF

2

insitu

adummy '

(92.7)

2

B(13.8)

2

adummy ' 14.4 m

Fmodified(x) '

Finsitux

x

2 & a

2

dummy

Fmodified(x) '

13.8x

x

2 & 14.42

Figure 10.CLongwall gob simulated as point forces of different strengths.

Table 1.CInput variables and stress intensity factors for each section of the longwall panel

depicted in figure 10

Section 1 Section 2 Section 3 Section 4 Section 5 Section 6

Fys, MPa .............. 13.8 13.1 12.4 10.3 8.3 6.9

x-range, m ............. 61.0-36.6 36.6-18.3 18.3-0 0-18.3 18.3-36.6 36.6-55.0

Stress intensity at point A

 (%x side) ............. C C C 15.9 18.0 25.8

Stress intensity at point A

 (&x side) ............. 13.8 10.7 14.1 C C C

Kgob .................. 98.3 C C C C C

Input parameters:

Width of longwall face ' 232 m

1/2 width of longwall face ' 116 m

2a (width of longwall face plus gate entry) ' 122 m

a ' 61 m

Finsitu ' 13.8 MPa

Equation 4 determines the stress in absence of the gob (point

forces) as

It is necessary to reduce this intensity to reflect the addition of

the gob material. The stress intensity factor at point A now

becomes

Ktotal ' Kinsitu & Kgob

Ktotal ' 92.7

The dummy variable used to relate this stress reduction to the

Westergaard equation is

The modified Westergaard distribution at point A becomes
125

Figure 11.CCrack opening completely filled with point forces equal to the in situ stress.

Figure 12.CStress distribution at point A is nearly flat and equal to the in situ stress.

This is the general technique used to model longwall gob. Luo

significantly improved the above technique and developed a

computer program to model the stability of longwall chain

pillars [Kramer et al. 1998].

HYDROSTATIC FORCES

It is possible to measure the effect of hydrostatic forces on

the coal seam. A hydrostatic force acts with equal strength in

all three cardinal directions. It is similar to the pressure exerted from water or gas. To simulate a hydrostatic force, it is

necessary to fill the entire mine opening with a continuous

distribution of point forces (figure 11). In order to test the

hydrostatic effect, the point forces are set equal to the in situ

stress (13.8 MPa). This situation should have the effect of

flattening the stress distribution at point A to a level equal to the

in situ stress.

Figure 12 is a plot of the stress distribution. It can be seen

the distribution is almost uniform and equivalent to the in situ

stress. This further demonstrates that the point-force method

accurately describes the effective stress distribution at the mine

rib.
126

K '

P

Ba

m

a

s

a % x

a & x

%

a & x

a % x

dx . (15)

K ' 2P

a

B

cos&1 s

a

. (16)

TECHNIQUE TO COMBINE DIFFERENT

MINE SUPPORTS

It is possible to combine any type of mine supports and

predict the resultant stress distribution in the coal seam.

Figure 13 presents a typical mining environment combining the

following structures: a longwall gob, a yield pillar, and a crib.

Analyzing this arrangement requires a combination of the stress

intensity factors for each support member. This combined

value is used to reduce the total stress intensity at point A. The

procedure for doing this is as follows:

• Calculate Kinsitu for point A

• Calculate Kgob for point A

• Calculate Kyield for point A

• Calculate Kcrib for point A

• Combine the stress intensity factors for each support,

and use this value to reduce the stress intensity associated with

the entire opening width:

Ktotal ' Kinsitu & Kgob & Kyield & Kcrib

EVALUATING PILLAR YIELD

Because coal mines are often located at a great depth

below the surface, the stress levels often exceed the yield

strength of the coal. It is necessary to account for yielding in

the coal pillars to correctly assess structural stability. Fracture

mechanics is useful in predicting the yielding characteristics

of the coal.

The Westergaard equation introduces a singularity at the

pillar edge. This is where the stress distribution approaches

infinity. The pillar edge yields and redistributes the loading

in order to eliminate the singularity. The yielded zone

continues to offer residual support to the roof and floor.

Dugdale provides a way to estimate the length of this

yield zone in the pillar [Dugdale 1960; Broek 1982]. The

following sections describe how to determine the extent of the

yield zone. Also described is a way to predict the stress

distribution in the elastic core of the pillar. First, the basic

technique used by Dugdale to arrive at his yield zone

prediction is reviewed. Later, a technique is introduced that

determines the extent of the yield zone specifically in coal.

THE EFFECT OF POINT LOADING ON THE

STRESS INTENSITY AT THE CRACK TIPS

As mentioned previously, figure 8 depicts a crack with an

internal wedge force P pushing out against the crack surface.

This force P is at a distance x from the crack center. These

wedge forces affect the stress intensity function, K, at points

A and B. It is possible to use equations 2 and 3 to predict

these stress intensity factors, K [Paris and Sih 1965]. A form

of these equations is fundamental in the development of

residual forces supporting the roof and floor in the yielded

portion of the pillar.

DUGDALE'S APPROACH TO CRACK TIP

YIELDING

Although the pillar edge yields, it has a residual strength

that supports the roof and floor of the coal seam. Imagine this

residual support as a continuous distribution of dislocated

point forces (figure 14). Dugdale determined the extent of the

yielded zone by first assuming that the residual strength of each

point force is equal to the yield strength, Fys, of a material (in this

case, coal) [Dugdale 1960; Broek 1982]. Because the yielded

edge is significantly weaker, it would seem as though the mine

opening becomes wider. The mine opening would theoretically

extend into the pillar to the point where yielding stops. At this

point, the singularity disappears because of the canceling effect

of the residual stress in the yield zone. The effective mine width,

aeff ' a % D, represents the distance to the new elastic crack tip,

where D symbolizes the extent of the yielded zone.

The yielded zone, D, exerts a residual stress equal to the yield

stress, Fys. The yield zone, D, depicted as additional opening

width, is not really an opening; the material can still bear the yield

stress. The size of D is chosen so that the stress singularity

disappears: Ktotal approaches zero. This means that the stress

intensity, Kinsitu, due to the uniform in situ stress, F, has to be

compensated by the stress intensity, KD

, due to the residual wedge

forces Fys [Broek 1982]. In other words:

Kinsitu ' &KD

(14)

Satisfying equation 14 leads to the determination of D in the

following manner. Equations 2 and 3 describe how a point load

affects the stress intensity factor, K. If the wedge forces are

distributed from s to the effective crack tip, the stress intensity

becomes

Solution to this integral is
127

D '

B

2F2

a

8F

2

ys

,

(17)

Figure 13.CModeling various support structures using the point-force technique.

Figure 14.CContinuous point forces approximate the residual pillar strength in

yielded zone preceding the elastic crack tip.

Applying this result to the crack in figure 14, the integral

has to be taken from s ' a to a ' a % D. Thus, "a" has to be

substituted for "s" and "a % D" for "a" in equation 16, while

P equals the yield strength, Fys [Broek 1982]. This leads to

the determination of the yield zone as

where D is the extent of the pillar yield zone.

Dugdale's description of the yield zone does not

provide a simple way to predict the stress distribution in the

elastic core adjacent the yielded edge. Irwin presents a

method to predict the stress distribution in the elastic

portion of the pillar [Broek 1982]. Irwin describes a yield

zone that is similar in length to Dugdale's prediction;

however, the crack tip extends only one-half the distance

(figure 15).

The singularity vanishes if area A ' area B. It was possible

to verify this using spreadsheet software. It is particularly

accurate for values of F/Fys less than 0.75. Irwin's description

produces the stress distribution shown in figure 16. This

distribution is not representative with in situ measurements taken

at underground mines [Mark and Iannacchione 1992].

PLAIN STRAIN

Dugdale's method concerns conditions of plane stress.

Pillar analysis requires a plane strain condition. Studies indicate

that for the case of plain strain, the effective yield stress can be

as great as three times that for a similar plain stress analysis.

This is due to confinement, which increases the triaxial yield

strength. Broek suggests modifying the yield stress with the

constraint factor:

p.c.f. ' 1.68Fys (18)
128

Figure 15.CThe Westergaard distribution originates at the beginning of the Irwin zone, but does not take

effect until the beginning of the elastic zone.

Figure 16.CPillar stress distribution as predicted by the Dugdale-Irwin method.

THE DUGDALE-IRWIN METHOD AS IT RELATES TO

A MINE ENVIRONMENT

Previous research indicates that confinement increases the

yield strength of a pillar core [Crouch and Fairhurst 1973;

Karabin and Evanto 1999; Sih 1966; Salamon and Munro

1967]. However, the measured pillar stress distribution does

not resemble the distribution predicted by Dugdale-Irwin shown

in figure 16. Underground measurements show the residual

strength should be low at the wall of the mine opening, but

increase proportionally with the distance into the pillar

core.

The mathematical model predicted by Dugdale-Irwin is

accurate; only the visual perception is misleading. The

residual stress distribution in the yielded area can take on

any shape as long as area A equals area B (figure 17).

A more realistic stress distribution such as that in figure 18

should then be possible.
129

Fv(x) ' S1× 0.78 % 1.74 x

h

, (19)

Figure 17.CYield stress can assume any shape provided that area A equals area B.

Figure 18.CPossible contour of pillar stress using the Dugdale-Irwin method.

COMBINING EMPIRICAL METHODS INTO THE ANALYTIC ANALYSIS

The Westergaard equation introduces a singularity at

the pillar edge; this is where the stress approaches infinity.

To eliminate this singularity, the edge must yield and

redistribute the load. The yielded edge retains a residual

strength that offers confinement to the core.

In situ field measurements demonstrate a nonlinear

residual stress distribution in the yield zone of a coal pillar.

The stress is low at the pillar rib and increases rapidly into

the center of the pillar. This indicates that confinement

makes the pillar strength higher than the unconfined

compressive strength used by Dugdale-Irwin. It is possible

to use the point-force method to model this residual strength

and thus predict the extent of the yield zone. It is a

common numerical technique to study the yielding coal

with a strain-softening model [Crouch and Fairhurst 1973; Wilson 1972]. Figure 19 depicts a model in terms of stress versus

strain in a timeframe denoted by peak and post (residual) stress.

It is possible to use any of the popular pillar strength

equations to predict the strain-softening characteristics of the

coal. The equations of Bieniawski and Holland-Gaddy are the

most accepted of these equations [Mark and Iannacchione 1992].

Mark and Iannacchione developed an equation that represents an

average of these two equations. It predicts the pillar strength as

a function of distance from the opening. This equation is:
130

F

avg

' Fv(1m) ' 3.5 0.78 % 1.74 1

2

' 5.8 MPa

K

ps1,1

'

F

avg

Baeff

m

a

eff

a

aeff % x

aeff & x

%

aeff & x

aeff % x

dx .

Figure 19.CThe stress-strain characteristics in the yield

zone of a coal seam.

Figure 20.CIt is possible to model peak or post stress as

several groups of point forces.

where Fv ' peak stress at distance x, MPa,

S1 ' in situ coal strength, MPa,

x ' distance to the free face, m,

and h ' seam height, m.

It is possible to model the stress distribution in the yield

zone as a series of point forces (figure 20). These

continuous series of point forces has a uniform intensity

within each group. Equation 19 will predict the average

strength assigned to each group. It is necessary to use an

iterative technique to determine the extent of the yield zone.

This iterative technique progressively yields each group

while testing for the disappearance of the singularity. When

KP $ Kinsitu, the yielding stops. Luo has eliminated the need

for an iterative technique by providing the exact solution for

the equation [Kramer et al. 1998].

EXAMPLE: USING STRAIN-SOFTENING TO DETERMINE THE EXTENT

OF THE YIELD ZONE

Originally, this example was formulated using U.S.

customary units of measurement. Conversion to the metric

system makes some values appear awkward.

GROUP 1: 0-2 m INTO THE PILLAR

Input Parameters:

S1 ' 3.5 MPa

Finsitu ' 6.9 MPa

Entry width (2a) ' 6 m

a ' 3 m

Extension of group 1 (e1

) ' 2 m

h ' 2 m

aeff1 ' a % e1 ' 5 m

The first group of point forces simulates the post strength

for group 1, which is the first 2 m into the pillar

(figure 20). These point forces are uniform; therefore, it is

necessary to use equation 19 to determine an average

strength value. This value will be assigned the point forces

in group 1. An estimate of the average point force for

group 1 would be determined from equation 19 for a point

1 m into the pillar.

The stress intensity relating to this average point force is

taken from equation 15 as
131

K

ps1,1

' 2F

avg

aeff

B

cos&1 a

aeff

K

ps1,1

' 2 ( 5.8

5

B

cos&1 3

5

' 13.6

K

pstotal

' K

ps1,1

' 13.6

Kaeff1' 6.9 B(3 % 2)

' 27.3

K

ps2,2

' 2 (11.9

7

B

cos&1 5

7

' 27.5

K

ps1,2

'

5.8

B7

m

5

3

7 % x

7 & x

%

7 & x

7 % x

dx

K

ps1,2

' 6.1

K

pstotal

' K

ps2,2

% K

ps1,2

' 33.6

Kaeff2' 6.9 B(5 % 2)

' 32.3

FIrwin zone'

Finsitux

x

2 & (a % *)2

.

(21)

Equation 16 solves this integral as

The stress intensity for group 1 in absence of the point forces

is

Kps total is less than Kaeff1; therefore, this section is yielded and

the crack extends to the end of the next section (group 2). The

coal continues to yield until the residual pillar stress overcomes

the in situ Westergaard stress.

GROUP 2: 2-4 m INTO THE PILLAR

Input Parameters:

e2 ' 2 m

aeff1 ' 5 m

aeff2 ' aeff1 % e2 ' 7 m

Midpoint of group 2 is 3 m into the pillar

The crack tip is extended 4 m (i.e., e1 % e2

) to the end of

group 2. This makes aeff2, the effective crack tip, equal to 7 m.

Using equation 19, the average stress in this section is

11.9 MPa. This is the post strength determined for a location

3 m into the pillar. The stress intensity caused by the wedge

forces in group 2 is

It is necessary to also consider the stress intensity caused by

the residual point forces in group 1. Because the crack tip

extended into the 2-to 4-m (group 2) section of the yield zone,

it is necessary to recalculate the effect of the 0- to 2-m

(group 1) section of the yield zone:

"Derive—A Mathematical Assistant" determined this value

to be:

The total stress caused by the point forces is

The stress intensity caused by the crack extension to the end

of group 2 in absence of the residual point forces is

This stress factor is less than the stress intensity due to the

residual strength point forces (Kaeff2 < Kps total); thus, the

yielding ceases in group 2. Because the values are nearly

equal, the crack extended almost to the end of group 2 (i.e.,

4 m into the pillar). It is possible to refine this distance, but

it is unnecessary for this example. Equation 19 will predict

the stress distribution in the yield zone; the Westergaard

equation will predict the distribution in the elastic core.

Irwin suggests a way to use the Westergaard equation to

predict the stress distribution in the pillar's elastic core (at the

edge of the yield zone) [Broek 1982]. Irwin agrees with

Dugdale's prediction for the extent of the yield zone, but he

argues that the crack tip extends into this zone one-half the

distance predicted by Dugdale such that

* ' D/2 ' 2 m (in the previous example).

This increases the effective crack width to

aeff ' a % * ' 5 m.

This is the beginning of the Irwin zone—the region from

which the Westergaard equation predicts the stress

distribution into the core of the material (figure 21).

Extending the crack tip to the beginning of the Irwin zone,

the Westergaard equation becomes
132

Figure 21.CThe Westergaard equation begins in the Irwin zone; it takes effect in the elastic

zone.

Figure 22.CStrain softening in the process zone and a Westergaard distribution in the elastic zone.

Although the x-origin in the Westergaard equation

begins in the Irwin zone, the stress distribution does not

take effect until the beginning of the elastic zone. Equation

19 describes the stress distribution throughout the entire yield

zone. Figure 22 shows the stress distribution for the combined

strain-softening and analytic models.
133

Fcomponent '

Finsitux

x

2 & a2

& Finsitu .

(22)

Figure 23.CPillar stress broken down into three components.

SUPERPOSITION

A mine opening affects the stress distribution at each of

its sides. A mine panel is a gridwork of regularly or

irregularly spaced entries and crosscuts.9

 For a complete

stress analysis, it is necessary to consider the stress influences caused by every mine passageway. A superposition

technique makes this possible [Kramer 1996].

The superposition technique requires subdividing the

stress distribution into its constitutive components

(figure 23). Each side of the pillar is subjected to a

9An entry is a tunnel aligned in the main direction of mining.

A crosscut connects individual entries, usually at a right angle. Several

entries and crosscuts comprise a mine panel. A pillar is coal remaining in

place between two entries and crosscuts; it supports the mine roof.

Westergaard stress distribution. Restricting the pillar model to

two dimensions, as in the case of plane strain, limits these

distributions to the left and right sides of the pillar. The basic

components needed in the superposition are the uniform in situ

stress, the stress component from the left opening, and the stress

component from the right opening. The right and left stress

components are each equal to the Westergaard equation with the

in situ stress removed such that
134

Figure 24.CPillar with stress superimposed from both sides.

Figure 25.CWestergaard equation and superpositioning stress over an entire mine panel.

Comparison with numerical model.

The left stress component has the origin of its axis

located to the left of the pillar. The positive direction, relative to this axis, is rightward from the origin into the pillar.

The right component is the mirror image of the left. This

component has the origin of its axis to the right of the pillar.

The variable "a" can have a different value for each side of

the pillar (figure 23). The total stress distribution on the

pillar is equal to the left component plus the uniform

in situ stress plus the right component. As verified by FLAC,

the superposition technique accurately predicts the stress

distribution across a single pillar (figure 24).

A mine opening affects the stress distribution for a substantial

distance. A mine panel consists of a gridwork of entries and

crosscuts. It is necessary to superimpose the stress components

from all mine passageways. FLAC compares the results of the

superposition across an entire mine panel (figure 25).
135

Figure 26.CFracture mechanics predicts the center stress in both directions through the

pillar. An interpolation technique translates the stress along the elliptical trajectories.

POSSIBLE ENHANCEMENTS

It is possible to enhance the modeling capabilities of the

FMA. Adding other techniques would give the ability to

analyze displacements in the strata, creep behavior in mine

supports, and the effects of multiple-seam mining. Because

the FMA is straightforward and easy to use, there is

potential to model many different mining situations.

The following sections discuss some possible additions

to the FMA. Although each technique presented seems reasonable, no comparison has been made with numerical

analysis to qualify accuracy.

VIEW OF STRESS DISTRIBUTION FROM A

PLANAR PERSPECTIVE

Sometimes it is desirable to study the stress distribution

looking down on the coal seam (planar view) instead of into

it (cross-sectional view). In a planar view, coal pillars are

rectangular. The corners of the pillar generate mathematical

singularities that create problems for analysis. One way to

eliminate the singularities is to assume the pillar is an ovaloid

instead of a rectangle [Kramer 1996]. It is possible to segment

the pillar into concentric ovaloid lines of equal distance (figure 26). Fracture mechanics predicts the stress distribution

through the pillar centers, as indicated by the vertical and

horizontal lines in figure 26. An interpolation technique can approximate the stress throughout the pillar by using the concentric

ovaloid arcs as interpolation pathways. For instance, the arc

segment between points A and B in figure 26 would be the interpolation path between the stresses at points A and B. It is

easy to interpolate the stresses along ovaloid paths. The basic

equations for mapping elliptical coordinates to Cartesian

coordinates are:

x ' a cos 2

y ' b sin 2 (23)

An example of the interpolation process follows.
136

90

5

' 18° (24)

1,500 psi & 1,000 psi

5 intervals

' 100 psi per interval (25)

COD ' 2v '

4F

E

a

2 & x2

(27)

CODmax' 2v '

4Fa

E

. (28)

Figure 27.CRelationship between elliptical and rectilinear coordinates.

Figure 28.CStresses distributed along interpolation arc.

Figure 29.CThe crack opening displacement (COD) method

considers the displacement of the entire surface of a crack.

EXAMPLE OF INTERPOLATION

Considering the elliptical path shown in quadrant I of

figure 27, interpolate the stresses along path A-B in the outer

arc of quadrant I. For this example, assign the following

properties:

FA ' 1,000 psi

FB ' 1,500 psi

a ' 20

b ' 10

Divide 2 into five equal angles:

Determine the stress interpolation interval for each 18° arc:

Figure 28 illustrates the stress distribution along this arc.

Equation 24 relates any point on the A and B axis to any point

on the ovaloid (figure 27). Therefore, it is possible to

approximate the stress distribution throughout the entire pillar.

VISCOELASTICITY

Sih [1966] and Paris and Sih [1965] discuss crack behavior

in viscoelastic (time-dependent) material. For viscoelastic

material, the crack-tip stress field is the same, only the stress

intensity factors KI

 are functions of time, such that

KI ' KI

(t) (26)

This function shows promise for future applications using the

FMA. For instance, it could be valuable for studying the behavior of salt.

DISPLACEMENTS

Fracture mechanics may also predict the displacement/

strain in a mine environment. A common method to predict

displacement is referred to as the "crack opening

displacement" (COD) [Broek 1982]. The COD method takes

into account the total displacement of the crack surface

(figure 29). In mining, the COD predicts the combined

displacement of the roof and floor of an opening, such that

and at the center of the opening:
137

MULTIPLE-SEAM MINING

It may be possible to predict the effects on stress distribution caused by mining activity in seams above or below the

area of interest. By using stress influence functions developed

for mine subsidence prediction, it should be possible to predict

multiple-seam influences with a respectable degree of

accuracy

[Luo 1997]. This multiple-seam model could be more

accurate than other numerical methods because most other

methods use influence functions based on the theory of

elasticity, which assumes infinitesimal displacements. Using

influence functions based on mine subsidence profiles takes

into account the well-documented, large-scale displacements

measured at various mine locations.

CONCLUSION

This paper presents the FMA for predicting the stresses in a

mine panel. It can model any combination of mine supports

such as longwall gob, yield pillars, cribs, chocks, posts,

automated temporary roof supports, and hydrostatic loads. The

technique uses an analytic expression; thus, it is fast, simple,

and accurate. It simulates pillar yield by combining the analytic

equation with any empirical pillar strength equations. The procedure incorporates easily into spreadsheets or computer

software. The FMA predicts pillar stress with a high degree of

accuracy; however, it is no match to good numerical modeling

software. Its main function is to be quick and simple in order to encourage nonspecialized personnel to use it as a

guide for studying mine supports.

The FMA works well for coal seams aligned along a

horizontal plane. Additional effort is needed to assess its

accuracy for seams aligning along inclined planes. More

work is also necessary to develop FMA techniques for thickseam mining, multiple-seam mining, and displacement

prediction. Computer software featuring the FMA is

available from the author.

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Eng (London) 131(141):409-417.
139

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. Dunford3

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.
140

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 involved—

(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

the literature. Damage levels were assigned a ranking between

0 and 3. Level 1 signifies interruptions in mining operations;
141

Figure 1.CHistogram frequency diagram for pillar width.

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

Figure 2.—Histogram frequency diagram for the maxiumum

principal stress.

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. of

cases

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
142

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-and-effect 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

1Two-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
143

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.—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.

• Method.—Mining 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.—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;

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 on

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.

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

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

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Productivity and Protection - Proceedings of the 25th Symposium on Rock

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

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

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

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

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

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

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

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Colorado School of Mines, Department of Mining Engineering.

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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.

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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.

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Lakewood, CO: Rocky Mountain Coal Mining Institute, pp. 38-43.
145

EMPIRICAL METHODS FOR COAL PILLAR DESIGN

By Christopher Mark, Ph.D.1

ABSTRACT

Empirical methods involve the scientific interpretation of real-world experience. Many problems in ground

control lend themselves to an empirical approach because the mines provide us with plenty of experience with

full-scale rock structures. During the past 10 years, powerful design techniques have emerged from statistical

analyses of large databases of real-world pillar successes and failures. These include the Analysis of Retreat

Mining Pillar Stability (ARMPS), the Analysis of Longwall Pillar Stability (ALPS), the Mark-Bieniawski

rectangular pillar strength formula, and guidelines for preventing massive pillar collapses. In the process, our

practical understanding of pillar behavior has been greatly enriched.

1

Supervisory physical scientist, Pittsburgh Research Laboratory, National Institute for Occupational Safety and Health, Pittsburgh, PA.
146

Figure 1.CClassification of modeling problems (after Starfield and Cundall [1988]).

INTRODUCTION

“Empirical” is defined by Webster's Dictionary [1988] as

"relying upon or gained from experiment or observation." Until

relatively recently, all pillar design methods used in the United

States were empirical. The earliest, proposed by Bunting

[1911], was based on case histories supplemented by laboratory

testing. Later formulas followed the same basic pattern and

were derived from laboratory tests (the Holland-Gaddy and

Obert-Duvall formulas), large-scale in situ tests (the Bieniawski

formula), or case histories (the Salamon-Munro formula).

Each of these "classic" pillar design formulas consisted of

three steps:

(1) Estimating the pillar load using tributary area theory;

(2) Estimating the pillar strength using a pillar strength

formula; and

(3) Calculating the pillar safety factor.

In each case, the pillar strength was estimated as a function of

two variables—the pillar's width-to-height (w/h) ratio and the

coal seam strength. For many years, these classic formulas performed reasonably well for room-and-pillar mining under

relatively shallow cover. Their key advantages were that they

were closely linked to reality and were easy to use.

The greatest disadvantages of empirical formulas are that

they cannot be easily extended beyond their original database,

and they provide little direct insight into coal pillar mechanics.

The growth of longwall mining exposed these shortcomings.

Full extraction results in large abutment loads, which cannot be

estimated by tributary area. More important is that longwall

mining uses pillars that are much more "squat" (large w/h ratio)

than those for which the classic formulas were developed.

Testing such pillars in situ is prohibitively expensive, and laboratory tests of squat pillars are clearly inappropriate. Moreover, longwall mining raised some new issues even about the

definition of what constitutes pillar "failure." The classic approach assumes that "pillars will fail when the applied load

reaches the compressive strength of the pillars" and that "the

load-bearing capacity of the pillar reduces to zero the moment

the ultimate strength is exceeded" [Bieniawski 1992]. When

large w/h longwall pillars "fail," however, their load-bearing

capacity does not disappear. Rather, the gate roads become unserviceable.

During the 1970s, analytical methods began to emerge as an

alternative to the classic formulas. Wilson [1972, 1983] of the

British National Coal Board was the first to take a radically

different approach to pillar design. He treated pillar design as

a problem in mechanics, rather than one of curve-fitting to

experimental or case history data. A pillar was analyzed as a

complex structure with a nonuniform stress gradient, a buildup

of confinement around a high-stress core, and progressive pillar

failure. Although his mathematics were seriously limited [Mark

1987; Salamon 1992], Wilson's basic concepts are now broadly

accepted.

The advent of powerful computer models gave a further

boost to the analytical approach. The primary advantage of numerical models is that they can test assumptions about pillar

behavior as affected by a variety of geometric and geologic

variables. For example, independent studies reported by Gale

[1992] and Su and Hasenfus [1997] concluded that for pillars

whose w/h > 6, weak host rocks or partings have greater effects

on pillar strength than the uniaxial compressive strength (UCS).

Unfortunately, effective numerical modeling requires numerous

assumptions about material properties, failure criteria, and postfailure mechanics.

In their insightful article, Starfield and Cundall [1988]

introduced a classification of modeling problems (figure 1).

One axis on the graph refers to the quality and/or quantity of the

available data; the other measures the understanding of the

fundamental mechanics of the problem to be solved. In many

branches of mechanics, most problems fall into region 3, where

there is both good understanding and reliable data. This is the

region where numerical models can be built, validated, and used

with conviction. Starfield and Cundall argued that problems in

rock mechanics usually fall into the data-limited categories 2 or

4 and require a more experimental use of models.

In the field of coal mine ground control, however, many

problems may actually fall into Starfield and Cundall's region 1.

Our understanding of the complex mechanical behavior and

properties of rock masses may be limited, but the potential for

data collection is huge. Hundreds of longwall and room-andpillar panels are mined each year, and each one can be considered a full-scale test of a pillar design. As Parker [1974]

noted: "Scattered around the world are millions and millions of
147

pillars—the real thing—under all imaginable conditions; and

tabulating their dimensions, the approximate loads, and whether

they are stable or not would provide most useful guidelines for

pillar design."

Actually, simply tabulating data does not necessarily lead to

useful conclusions. Fortunately, today's data analysis techniques are far more powerful than those that were available to

the pillar design pioneers. In the past 30 years, sciences like

economics, sociology, psychology, anthropology, and epidemiology have all been transformed by quantitative data analysis

using statistics [Encyclopedia Britannica 1989]. Sophisticated

statistical packages enable researchers to efficiently comb large

databases for significant relationships between the variables.

The empirical approach requires that the researcher begin

with a clear hypothesis, often in the form of a simplified model

of the real world that abstracts and isolates the factors that are

deemed to be important. It therefore requires, as Salamon

[1989] indicated, "a reasonably clear understanding of the physical phenomenon in question." Without prudent simplification,

the complexity of the problem will overwhelm the method's

ability to discern relationships between the variables. However,

a key advantage is that critical variables may be included, even

if they are difficult to measure directly, through the use of

"rating scales."

During the past 5 years, modern empirical techniques have

been applied to a variety of problems in coal mine ground

control. They have resulted in some very successful design

techniques, as well as some new insights into pillar and rock

mass behavior. This paper discusses some of them in more

detail.

DESIGN OF LONGWALL GATE ENTRY SYSTEMS

In the 15 years after 1972, the number of U.S. longwall faces

increased from 32 to 118 [Barczak 1992]. The new technology

created a host of operational and safety problems, including the

maintenance of stable travelways on the tailgate side. Researchers initially viewed gate entry ground control primarily

as a pillar design issue. The clear correlation between larger

pillars and improved conditions that had been established by

trial and error at many mines supported this approach.

The most obvious difference between longwall pillars and

traditional coal pillars is the abutment loading. The major

contribution of the original Analysis of Longwall Pillar Stability (ALPS) was a formula for estimating the longwall pillar

load based on numerous underground measurements [Mark

1990]. An evaluation of 100 case histories showed that 88% of

the failed cases had stability factors <1.0; 76% of the successful

cases had stability factors $1.0 [Mark 1992]. It was evident

that ALPS had captured an essential element of the gate entry

design problem.

On the other hand, there was a wide range of stability factors

(approximately 0.5 to 1.2) in which both successful and

unsuccessful designs occurred. Clearly, other variables in

addition to the ALPS stability factor were influencing tailgate

performance. A hypothesis was proposed stating that tailgate

performance is determined by five factors:

• Pillar design and loading;

• Roof quality;

• Entry width;

• Primary support; and

• Supplemental support.

Attacking this extremely complex problem with traditional,

deterministic rock mechanics using analytical or numerical

models would have been extremely difficult. On the other

hand, the problem was ideal for an empirical approach. The

empirical method could make full use of the wealth of full-scale

case history data that had been collected. Moreover, it could

focus directly on the variable of interest—tailgate performance.

It quickly became clear that roof quality was the key.

Studies conducted as early as the 1960s had concluded that

"whether or not the stress [from an extracted longwall panel]

will influence a roadway depends more on the strength of the

rocks which surround the roadway itself than on the width of

the intervening pillar" [Carr and Wilson 1982]. Yet the variety

and complexity of geologic environments had defied effective

measurement.

The Coal Mine Roof Rating (CMRR) overcame this obstacle

by providing a quantitative measure of the structural competence of coal mine roof [Molinda and Mark 1994; Mark and

Molinda 1996]. The CMRR applies many of the principles of

Bieniawski's Rock Mass Rating (RMR), with the following

significant differences:

• The CMRR focuses on the characteristics of bedding

planes, slickensides, and other discontinuities that determine the

structural competence of sedimentary coal measure rocks.

• It is applicable to all U.S. coalfields and allows a meaningful comparison of structural competence, even where lithologies are quite different.

• It treats the bolted interval as a single structure while

considering the contributions of the different lithologic units

that may be present within it.

The CMRR weighs the importance of the geotechnical factors

that determine roof competence and combines these values into

a single rating on a scale from 0 to 100.

Data on tailgate performance were collected from approximately 55% of all U.S. longwall mines; these mines were selected to represent a geographic and geologic cross section of

the U.S. longwall experience. A total of 64 case histories were
148

Figure 2.CU.S. longwall case histories showing the modified

design equation for ALPS (R) with the Mark-Bieniawski pillar

strength formula.

classified as "satisfactory" or "unsatisfactory" based on the

conditions in the tailgate [Mark et al. 1994]. Each case history

was described by the ALPS stability factor (SF), entry width,

and primary support rating, as well as the CMRR.

Multivariate statistical analysis showed that when the roof is

strong, smaller pillars can safely be used. For example, when

the CMRR is 75, an ALPS SF of 0.7 is adequate. When the

CMRR drops to 35, the ALPS SF must be increased to 1.3.

Significant correlations were also found between the CMRR

and both entry width and the level of primary support [Mark

et al. 1994]. A simple design equation related the required

ALPS SF to the CMRR:

ALPS SF ' 1.76 & 0.014 CMRR (1)

THE ALPS database was recently revisited, with several

new variables added. These include:

Rectangular pillar strength formula: All of the SFs were

recalculated with the Mark-Bieniawski formula (see the section

below on "Interactions With Numerical Models") substituted

for the original Bieniawski formula. The new result is

designated as the ALPS (R) SF.

Uniaxial compressive strength: Nearly 4,000 laboratory

tests were compiled from the literature into the Database of

Uniaxial Coal Strength (DUCS) [Mark and Barton 1996].

From these data, typical seam strength values were obtained for

60 U.S. coalbeds.

Width-to-height (w/h) ratio: The w/h of the largest pillar in

the gate entry system was included as an independent variable

to check if the pillar strength formula could be improved.

Depth of cover (H): H was included as an independent variable primarily to check the loading formulation.

The entry width and the primary support were included as

before.

The statistical analysis showed that the ALPS (R) SF and the

CMRR still correctly predicted 85% of the outcome, including

94% of the failures. None of the other new variables would be

included even at the 50% confidence level (a 90% confidence

level would be required for a covariate to be considered statistically significant). Figure 2 shows the distribution of the

case histories and the revised design equation

ALPS (R) SF ' 2.0 & 0.016 CMRR (2)

Since 1987, ALPS has become the most widely used pillar

design method in the United States. The ALPS-CMRR method

directly addresses gate entry performance and makes U.S.

longwall experience available to mine planners in a practical

form. ALPS reduces a multitude of variables (e.g., depth of

cover, pillar widths, seam height, entry width, roof quality) into

a single, meaningful design parameter—the stability factor.

ALPS has been accepted because it easy to use, its essential

concepts are easy to grasp, and it has been thoroughly verified

with case histories. Most importantly, ALPS gives reasonable

answers that make sense in terms of experience. Tailgate

blockages are far less common today than 10 years ago; ALPS

can surely claim some of the credit.

PILLAR DESIGN FOR ROOM-AND-PILLAR MINING

Room-and-pillar mining still accounts for nearly 50% of the

underground coal mined in the United States (even after

excluding longwall development). Most room-and-pillar mines

operate under relatively shallow depth, often working small,

irregular deposits. Approximately 20% of room-and-pillar coal

is won during pillar recovery operations [Mark et al. 1997b].

Room-and-pillar mines still suffer from large-scale pillar

failures, including sudden collapses and the more common

"squeezes." The classical empirical pillar strength formulas

were developed precisely to prevent these types of failures, but

they have never been entirely satisfactory. First, they did not

consider the abutment loads that occur during pillar recovery

operations. Second, laboratory testing to determine coal

strength has remained controversial despite the fact that textbooks have considered it an integral part of pillar design for

30 years. Third, because the empirical formulas were developed from tests on relatively slender specimens, their applicability to squat pillars has been open to question. Finally,

attempts to verify the formulas' accuracy with U.S. case histories have been incomplete and conspicuously lacking in

examples of pillar failure [Holland 1962; Bieniawski 1984].

An intensive research effort to develop an improved design

method culminated in the Analysis of Retreat Mining Pillar
149

Figure 3.CU.S. room-and-pillar case histories.

Stability (ARMPS). ARMPS employs many of the same basic

constructs as ALPS, adapted to more complex and varied retreat

mining geometries [Mark and Chase 1997]. The abutment load

formulas were adapted to three dimensions to account for the

presence of barrier pillars and previously extracted panels.

Because the pillars used in retreat mining are often rectangular,

the Mark-Bieniawski pillar strength formula was developed to

estimate pillar strength. Features such as varied entry spacings,

angled crosscuts, and slab cuts in the barrier can all be modeled.

To verify ARMPS, more than 200 retreat mining case

histories were obtained from field visits throughout the United

States. The case histories come from 10 States and cover an

extensive range of geologic conditions, roof rock caveability,

extraction methods, depths of cover, and pillar geometries.

Ground conditions were characterized in each case as satisfactory or unsatisfactory. Where possible, data were also collected to assess the CMRR. Site-specific data on coal strength

were not generally available for individual case histories, but

DUCS again provided estimates of UCS for most coalbeds.

Finally, the depth of cover and the w/h were also included as

independent variables in the analysis. Details on the individual

case histories have been presented elsewhere [Mark and Chase

1997].

When the entire data set was evaluated, it was found that

77% of the outcomes could be correctly predicted simply by

setting the ARMPS SF to 1.46. Including either the depth or

the w/h increased the correlation coefficient, r2

, slightly without

improving the accuracy (figure 3). The depth and the w/h ratio

were strongly correlated with each other within the data set.

The accuracy improved when the data set was divided into

two parts. One group included only cases where cover was

shallow (H < 200 m (650 ft)) and where the pillars were not

squat (w/h < 8). For this group, when the ARMPS SF ' 1.5,

83% of the outcomes were correctly predicted. However, for

the deep cover/squat pillar group, only 58% of the cases were

correctly predicted at ARMPS SF ' 0.93. No other variables

could be included in either group at the 90% confidence level.

It seems clear that ARMPS works quite well at shallow depth

and moderate w/h ratios, but that other factors must be considered when squat pillars are used at greater depths.

The analysis also found that using laboratory UCS tests did

not improve the accuracy of ARMPS at all. This finding confirms the results of a previously published study [Mark and

Barton 1996], which showed that ARMPS was more reliable

when the in situ coal strength was always assumed to be

6.2 MPa (900 psi). It also showed that the "size effect" varies

dramatically from seam to seam depending on the coal cleat

structure.

Studies in the Republic of South Africa and Australia have

also found that a uniform coal strength worked reasonably well

in pillar design formulas [Salamon 1991; Galvin and Hebblewhite 1995]. It has already been noted that ARMPS is significantly less reliable for squat pillars. It seems likely that while

the strength of the intact coal (which is what is measured in a

laboratory test) is not related to pillar strength, large-scale

geologic features like bedding planes, clay bands, rock partings,

and roof and floor rock may determine the strength of squat

pillars. Such features influence the amount of confinement that

can be generated within the pillar and therefore the load-bearing

capacity of the pillar core. Similar conclusions have been

reached by researchers using numerical models [Su and

Hasenfus 1997; Gale 1992].

Although the CMRR was not found to be significant in the

overall data set, one local study indicated that caveability may

affect pillar design. More than 50 case histories were collected

at a mining complex in southern West Virginia. Analysis

showed that satisfactory conditions were more likely to be

encountered under shale roof (figure 4) than under massive

sandstone roof (figure 5). The implication is that better caving

occurs with shale, resulting in lower pillar loads.
150

Figure 4.CPillar performance under different roof geologies at a mining complex in West VirginiaCshale

roof.

Figure 5.CPillar performance under different roof geologies at a mining complex in West

VirginiaCsandstone roof.
151

Figure 6.CA portion of the room-and-pillar case history database showing examples of pillar collapse.

MASSIVE PILLAR COLLAPSES

Most of the pillar failures included in the ARMPS database

are "squeezes" in which the section converged over hours, days,

or even weeks. There are also 15 massive pillar collapses that

form an important subset [Mark et al. 1997a]. Massive pillar

collapses occur when undersized pillars fail and rapidly shed

their load to adjacent pillars, which in turn fail. The

consequences of such chain-reaction failures typically include

a powerful, destructive, and hazardous airblast.

Data collected at 12 massive collapse sites revealed that the

ARMPS SF was <1.5 in every case and <1.2 in 81% of the

cases (figure 6). What really distinguished the sudden collapses

from the slow squeezes, however, was the pillar's w/h ratio.

Every massive pillar collapse involved slender pillars whose

w/h was <3. The overburden also included strong, bridging

strata in every case.

In this instance, the empirical analysis led to a hypothesis

about the mechanism of the failure. Laboratory tests have

shown that slender coal specimens typically have little residual

strength, which means that they shed almost their entire load

when they fail. As the specimens become more squat, their

residual strength increases, reducing the potential for a rapid

domino-type failure. The mechanism of massive collapses was

replicated in a numerical model [Zipf and Mark 1997], providing further support for the hypothesis.

Three alternative strategies were proposed to prevent massive pillar collapses:

• Prevention: With the prevention approach, the panel

pillars are designed so that collapse is highly unlikely. This can

be accomplished by increasing either the SF of the pillars or

their w/h ratio.

• Containment: In this approach, high extraction is practiced within individual compartments that are separated by

barriers. The small pillars may collapse within a compartment,

but because the compartment size is limited, the consequences

are not great. The barriers may be true barrier pillars, or they

may be rows of development pillars that are not split on retreat.

The containment approach has been likened to the use of

compartments on a submarine.

• High extraction: By removing enough coal during retreat

mining, failure of the overburden may be induced, which would

remove the airblast hazard.

The empirical analysis, using case histories, has allowed the

first two of these approaches to be quantified in terms of the

w/h ratio and the ARMPS SF. The guidelines are now being

implemented in southern West Virginia, where the majority of

these events have occurred.

INTERACTIONS WITH NUMERICAL MODELS

A number of important links have developed between empirical methods and numerical models. Because they were obtained from real-world data, empirical models are a good starting

point for material property input to models. For example, Mark

[1990] analyzed numerous field measurements of abutment stress

and determined that the stress decay over the ribside could be

approximated as an inverse square function. Karabin and Evanto

[1999] adjusted the gob parameters in the BESOL boundaryelement model to obtain a reasonable fit to the inverse square

function. Similarly, Heasley and Salamon [1996a,b] used the

same stress decay function to calibrate the LAMODEL program.

Empirical formulas have also helped provide coal properties

for some models. Although empirical formulas do not explicitly consider the effect of internal pillar mechanics, it is

apparent that they imply a nonuniform stress distribution because of the w/h effect. A derivation of the implied stress

gradients was published by Mark and Iannacchione [1992]. For

example, the Bieniawski formula

Sp ' S1

 (0.64 % 0.36 w/h) (3)
152

Figure 7.CConceptual depiction of the Mark-Bieniawski pillar strength formula.

implies a stress gradient within the pillar at ultimate load of

Sv ' S1

 (0.64 % 2.16 x/h), (4)

where Sp ' pillar strength,

S1 ' in situ coal strength,

Sv ' vertical pillar stress,

and x ' distance from pillar rib.

The stress gradient defines the vertical stress within the pillar at

maximum load as a function of the distance from the nearest

rib.

These empirical stress gradients have been widely used to

estimate coal properties for use in boundary-element models

that use strain-softening pillar elements. In the models, the

peak stress increases the further the element is from the rib.

The empirical stress gradients help ensure that the initial

strength estimates are reasonable.

The same empirical stress gradient was used to extend a

classic pillar strength formula to rectangular pillars. The

original Bieniawski formula was derived for square pillars and

underestimates the strength of rectangular pillars that contain

proportionately more core area. By integrating equation 4 over

the load-bearing area of a rectangular pillar, the MarkBieniawski pillar strength formula is obtained:

Sp ' S1

 (0.64 % 0.54 w/h & 0.18 (w2/Lh), (5)

where L ' pillar length.

The approach is illustrated in figure 7 and described in more

detail by Mark and Chase [1997].

Other sections of this paper have indicated areas where

numerical models and empirical methods have reached similar

conclusions about important aspects of pillar mechanics. In

light of these insights, old concepts of pillar "failure" have

given way to a new paradigm that identifies three broad

categories of pillar behavior:

• Slender pillars (w/h < 3), which have little residual

strength and are prone to massive collapse when used over a

large area;

• Intermediate pillars (4 < w/h < 8), where "squeezes" are

the dominant failure mode in room-and-pillar mining and where

empirical pillar strength formulas seem to be reasonably

accurate; and

• Squat pillars (w/h > 10), which can carry very large loads

and are strain-hardening, and which are dominated by entry

failure (roof, rib, and floor) and by coal bumps.
153

CONCLUSIONS

Empirical methods rely on the scientific interpretation of

actual mining experience. Because they are so firmly linked to

reality, they are particularly well suited to practical problems

like pillar design. Empirical methods like ALPS and ARMPS

have met the mining community's need for reliable design

techniques that can be used and understood by the

nonspecialist.

Successful empirical research has three central elements:

• A hypothesis or model that simplifies the real world, yet

incorporates its most significant features;

• A large database of case histories, developed using

consistent and thorough in-mine data collection techniques; and

• Quantitative analysis using appropriate statistical

techniques.

Empirical techniques are not, of course, the only tool in the

ground control specialist's kit. Indeed, one of the most satisfying developments in recent years is the synergy that has

developed between empirical techniques and numerical modeling. The two approaches seem to have converged on a number

of important conclusions, including:

• Laboratory testing of small coal samples, particularly

UCS tests, are not useful for predicting pillar strength;

• The strength becomes more difficult to predict as the pillar

becomes more squat;

• The w/h ratio is important for predicting not only the pillar

strength, but also the mode of failure; and

• Many ground control problems must be considered from

the standpoint of entry stability, where pillar behavior is just

one component.

Certainly, more work remains before the age-old questions of

pillar design are finally solved. In particular, much remains to be

learned about the mechanics of squat pillars and roof-pillar-floor

interactions. Currently, there is no accepted way to determine the

frictional characteristics of the contacts, bedding planes, and

partings that are so crucial to pillar strength. It is similarly difficult

to characterize the bearing capacity of the floor. Simple, meaningful field techniques for estimating these properties will be

necessary for further progress with either numerical or empirical

techniques. Indeed, the cross-pollination between the numerical

and empirical methods that has characterized the recent past can be

expected to bear further fruit in the future.

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155

COAL PILLAR STRENGTH AND PRACTICAL COAL 

PILLAR DESIGN CONSIDERATIONS

By Daniel W. H. Su, Ph.D.,1 and Gregory J. Hasenfus2

ABSTRACT

This paper demonstrates that finite-element modeling can be used to predict in situ coal pillar strength,

especially under nonideal conditions where interface friction and roof and floor deformation are the primary

controlling factors. Despite their differences in approach, empirical, analytical, and numerical pillar design

methods have apparently converged on fundamentally similar concepts of coal pillar mechanics. The finiteelement model results, however, are not intended to suggest a new pillar design criterion. Rather, they

illustrate the site-specific and complex nature of coal pillar design and the value of using modeling procedures

to account for such complex site-specific conditions. Because of the site-specific nature of coal pillar design,

no single pillar design formula or model can apply in all instances. Understanding and accounting for the sitespecific parameters are very important for successful coal pillar design. More work remains before the

century-old problems related to pillar design are finally solved. Future research should focus on the crosslinkage of empirical, analytical, and numerical pillar design methods.

1

Senior research scientist.

2Group leader.

CONSOL, Inc., Research & Development, Library, PA.
156

INTRODUCTION

The strength of coal and coal pillars has been the subject of

considerable research during the past 40 years. Coal strengths

determined in the laboratory typically increase with increasing

specimen width-to-height (w/h) ratio and decrease with

increasing height and size. Based on the shape and size effect

derived from testing of cubical specimens, a number of

empirical pillar strength formulas [Gaddy 1956; Holland 1964;

Obert and Duvall 1967; Salamon and Munro 1967; Bieniawski

1968] and closed-form analytical solutions for pillar strength

[Wilson 1972; Barron 1984] were proposed during the past

4 decades and used by coal operators and regulatory authorities

with varying degrees of success. However, empirical formulas

may not be extrapolated with confidence beyond the data range

from which they were derived, typically from pillars with w/h

ratios of #5 [Mark and Iannacchione 1992], and these formulas

inherently ignore roof and floor end constraint and subsequent

interactions.

The importance of friction and end constraint on laboratory

coal strength has been demonstrated by many researchers,

including Khair [1968], Brady and Blake [1968], Bieniawski

[1981], Salamon and Wagner [1985], Babcock [1990, 1994],

and Panek [1994]. Practitioners and researchers alike,

including Mark and Bieniawski [1986], Hasenfus and Su

[1992], Maleki [1992], and Parker [1993], have noted the

significance of roof and floor interactions on in situ pillar

strength.

The importance of incorporating fundamental principles of

rock material response and failure mechanics into a pillar

strength model using a finite-element modeling (FEM)

technique has been demonstrated by Su and Hasenfus [1996,

1997]. To accurately assess pillar strength, a model should

account not only for the characteristics of the coal, but also for

those of the surrounding strata. The frictional end-constraint

interaction between the pillar and the surrounding roof and floor

has been demonstrated to be one of the most significant factors

in the strength of very wide pillars. This paper summarizes the

results of a series of FEM cases designed to evaluate the effect

on pillar strength of end constraint or confinement over a wide

range of pillar w/h ratios, as well as the effects of seam

strength, rock partings, and weak floor. The interdependence

among pillar design, entry stability, and ventilation efficiency

in longwall mining is briefly discussed. Finally, the sitespecific nature of coal pillar design is emphasized, and a

direction of future research is suggested.

USE OF FINITE-ELEMENT MODELING IN PILLAR DESIGN

In recent years, FEM has been used to predict in situ coal

pillar strength, especially under nonideal conditions in which

interface friction and roof and floor deformation are the primary

controlling factors. Practical coal pillar design considerations

that incorporated the results of FEM and field measurements

were presented by Su and Hasenfus [1996]. Nonlinear pillar

strength curves were first presented to relate pillar strength to

w/h ratio under simulated strong mine roof and floor conditions

(figure 1). Confinement generated by the frictional effect at

coal-rock interfaces was demonstrated to accelerate pillar

strength increase beginning at a w/h ratio of about 3. Thereafter, frictional constraint limitations and coal plasticity

decelerate pillar strength increases beginning at a w/h of

about 6. The simulated pillar strength curve under strong roof

and floor compared favorably with measured peak strengths of

four failed pillars in two coal mines in southwestern Virginia

(figure 2) and is in general agreement with many existing coal

pillar design formulas at w/h < 5.

FEM has also been used to evaluate the effect of in-seam and

near-seam conditions, such as seam strength, rock partings, and

weak floor rock, on pillar strength [Su and Hasenfus 1997]. On

a percentage basis, seam strength was found to have a

negligible effect on the peak strength for pillars at high w/h

ratios (figure 3). For practical coal pillar design, exact

determination of intact coal strength thus becomes unnecessary;

for wide pillars, an average seam strength of 6.2 to 6.6 MPa

may suffice for most U.S. bituminous coal seams. Rock

partings within the coal seam, however, were found to have a

variable effect on pillar strength, depending on the parting

strength. A competent shale parting within the coal seam

reduces the effective pillar height, thus increasing the ultimate

pillar strength (figure 4). Conversely, a weak claystone parting

slightly decreases pillar strength. In addition, weak floor rocks

may decrease the ultimate pillar strength by as much as 50%

compared to strong floor rock (figure 5). Field observations

confirm pillar strength reduction in the presence of weak floor

rocks.

Similar to CONSOL's studies, an earlier numerical study by

the former U.S. Bureau of Mines employing a finite difference

modeling technique concluded that pillar strength was highly

dependent on the frictional characteristics of the coal-roof and

coal-floor interfaces [Iannacchione 1990].
157

 Figure 1.CPillar strength comparison of FEM model results versus existing empirical

formula.

 Figure 2.CComparison of FEM modeled versus field pillar strength data (strong roof and

strong floor conditions).
158

Figure 3.CEffect of seam strength on FEM model results.

Figure 4.CEffect of claystone and shale parting on FEM model results.
159

Figure 5.CEffect of weak claystone (soft) floor on pillar strength.

FUTURE PILLAR DESIGN CONSIDERATIONS RELATED

TO SITE-SPECIFIC CONDITIONS

Because many coal pillar design formulas are empirical

relationships that were developed under limited conditions,

application of these formulas may be inappropriate when other

factors not specifically addressed in these relationships are

encountered. As demonstrated, pillar strength and therefore

entry stability are extremely sensitive to the in situ characteristics of not only the coal, but also the adjacent and inclusive

rock that comprise the coal pillar system. Unfortunately, a

single site-specific empirical formula cannot accurately account

for the variations of features that may significantly affect pillar

and entry stability within a single coalfield or even a single

mine. In addition, it is neither practical nor efficient to develop

site-specific empirical formulas for all variations of roof, floor,

and pillar characteristics that may occur within a mine.

Over the past decade, the Analysis of Longwall Pillar

Stability (ALPS) approach to longwall pillar design has gained

wide acceptance for longwall pillar design analysis in U.S.

coalfields [Mark and Chase 1993]. Although it has proven to

be applicable for use in many mines and mining regions, ALPS,

which relies solely on the Bieniawski formula for pillar strength

calculation, does not always accurately represent pillar strength

at high w/h ratios. For example, for the prevailing strong roof

and floor conditions in the Virginia Pocahontas No. 3 Coalfield,

ALPS significantly underestimates pillar strength (figure 6).

Conversely, under very weak, "soft" conditions, ALPS may

significantly overestimate pillar strength (figure 7). Although

recent versions of ALPS provide a Coal Mine Roof Rating

(CMRR) routine that modifies the safety factor requirement and

better accommodates hard roof conditions, this routine does not

correct the inherent error in pillar strength calculation, which

may be important not only for entry stability and safety, but

also for subsidence planning and design.
160

Figure 6.CFEM model and Bieniawski formula comparison with strong roof and floor data.

Figure 7.CEmpirical pillar strength formula comparison with soft floor field data.
161

FUTURE PILLAR DESIGN CONSIDERATIONS RELATED TO ENTRY 

STABILITY AND VENTILATION EFFICIENCY

The ultimate goal of a successful pillar design is to achieve

entry stability with optimum support. The classical pillar

design approach focuses on determining safety factors from

estimates of pillar strength and pillar load. This works well in

room-and-pillar operations without second mining and in main

entries not subject to abutment pressures. A successful

longwall gate road design, on the other hand, requires stable

headgate and tailgate entries under the influence of longwall

abutment pressures. Headgate or tailgate entry failures, such as

a roof fall, severe floor heave, or severe pillar spalling, may

pose serious safety hazards and may stop longwall mining for

days or weeks. Traditionally, headgate and tailgate stabilities

have been correlated with pillar sizes, and many ground control

researchers have focused on the design of longwall chain pillars

for improving gate road stability. However, gate entry

performance is influenced by a number of geotechnical and

design factors, including pillar size, pillar loading, roof quality,

floor quality, horizontal stresses, entry width, and primary and

secondary supports [Mark and Chase 1993]. It suffices to say

that pillar size is not the only factor affecting longwall headgate

and tailgate stability. Therefore, strength of roof and floor

rocks, state of in situ horizontal stresses, entry width, and

support methodology are other important factors that should be

included in any practical longwall chain pillar design

methodology.

In the early 1990s, Mark and Chase [1993] used a backcalculation approach to suggest an ALPS stability factor for

longwall pillars and gate entries based on a CMRR. The

importance of floor stability and secondary support could not be

determined from the data and were not included in the backcalculation. Nevertheless, their effort pioneered pillar design

research that included roof rock strength and integrated pillar

and entry roof stability. Although the floor strength, roof

support, horizontal stresses, and entry width can theoretically be

included in a numerical pillar design model, other issues, such

as gob formation, load transfer, material properties, and

geological variations, may make model formulation difficult.

It seems that a hybrid method of the back-calculation and

numerical approaches may provide a more effective and

versatile pillar design method in the future.

A more rigorous, yet practical pillar design methodology

could be developed by incorporating a site-specific pillar

strength formula obtained from numerical models or alternative

field observations into the ALPS stability factor approach. As

an example, for strong roof and floor, the FEM-based pillar

strength curve, which incorporates site-specific roof and floor

strength, predicts a strength for an 80-ft-wide pillar that closely

emulates field results, but is nearly 40% higher than that

predicted by the Bieniawski formula (figure 6). In addition,

under very weak floor conditions, the Holland-Gaddy formula

may better represent pillar strength than the Bieniawski formula

(figure 7).

If such a combined approach is adopted, it could be done

either on an independent basis or perhaps even as a

modification to the overall ALPS design approach.

Nevertheless, it is apparent that pillar design methodology

could still benefit from a combination of empirical, analytical,

and numerical methods to formulate practical pillar design

based on site-specific roof, floor, and seam conditions.

An aspect of longwall gate road design that is often

overlooked is its impact on ventilation. Specifically, for eastern

U.S. coal mines that employ only three or four gate road entries,

the ability to provide an effective internal bleeder system in the

tailgate behind the face can be quite important. Obviously,

effective ventilation area in the tailgate between two gobs is

influenced by roof and floor geology, entry width and height,

pillar load and pillar strength, and primary and secondary

support. Where longwall chain pillar designs must provide an

effective internal bleeder system, ground control engineers must

account for the aforementioned factors in addition to pillar load

and pillar strength.

CONCLUSIONS

With the capability of modeling interface friction and

various boundary conditions, a finite-element code can be an

effective tool for site-specific evaluation of in situ coal pillar

strength that considers the complex failure mechanisms of

in situ coal pillars. The modeling technique can be most useful

for conditions where interface friction and roof and floor

deformation are the primary controlling factors. Nonlinear

pillar strength curves relate the increase of pillar strength to the

w/h ratio. Confinement generated by frictional effects at the

coal-rock interface is shown to increase the pillar strength more

rapidly at w/h ratios of about 3. The finite-element modeled

in situ pillar strength curve for strong roof and floor conditions

compares favorably with the measured peak strengths of five

failed pillars in two southwestern Virginia coal mines and is in

general agreement with many existing coal pillar design

formulas at w/h ratios of <5. However, for wide pillars,

modeling predicts a higher in situ coal pillar strength than most

accepted formulas. Consequently, use of more conservative

empirical formulas may lead to the employment of unnecessarily wide pillars or a lower estimated safety factor.
162

However, to accurately assess pillar strength, a model or

formula should account not only for the characteristics of the

coal, but also for those of the surrounding strata. Although

seam strength is observed to have some effect on pillar strength,

its significance is often overrated. In fact, for coal pillars with

large w/h ratios, ultimate pillar strength is more dependent on

end constraints than on seam strength. This reduces the

significance of laboratory coal compressive strength determination for such conditions. For practical purposes, a uniform

seam strength averaging about 6.2 to 6.6 MPa is adequate for

most U.S. bituminous coal seams when employing finiteelement models to simulate pillars with high w/h ratios.

The finite-element model results presented are not intended

to suggest new pillar design relationships with w/h ratios. The

primary objective of this paper is to emphasize the site-specific

nature of coal pillar design and the value of using modeling

procedures to account for such site-specific conditions.

Understanding the site-specific parameters is an important

ingredient for successful coal pillar design. Due to the

variability of in situ properties, no currently available empirical,

analytical, or numerical pillar design formula is applicable in all

cases. Utilization or imposition of pillar design formulas that

do not, or cannot, account for site-specific variations in roof,

floor, and parting conditions may lead to incorrect assessments

of pillar strength, whether high or low, and incorrect estimates

of pillar design safety factors. Empirical, analytical, or

numerical design procedures should be validated by sitespecific measurements or observational field studies whenever

possible.

For longwall mining, pillar design is not the only factor

affecting headgate and tailgate stability and ventilation

efficiency. Strength of roof and floor rocks, state of in situ

stresses, entry width, and support methodology are other

important factors affecting longwall gate road stability and

should be considered in practical longwall chain pillar design.

Certainly, more work remains before the century-old problems

related to pillar design are finally solved. Future pillar design

methodology could benefit from a cross-linkage of empirical,

analytical, and numerical pillar design methods.

REFERENCES

Babcock CO [1990]. True uniaxial compressive strengths of rock or coal

specimens are independent of diameter-to-length ratios. Denver, CO: U.S.

Department of the Interior, Bureau of Mines, RI 9316.

Babcock CO [1994]. Critique of pillar design equations from 1833 to

1990. Denver, CO: U.S. Department of the Interior, Bureau of Mines, IC 9398.

Barron K [1984]. An analytical approach to the design of coal pillars.

CIM Bulletin 77(868):37-44.

Bieniawski ZT [1968]. The effects of specimen size on the compressive

strength of coal. Int J Rock Mech Min Sci 5:325-335.

Bieniawski ZT [1981]. Improved design of coal pillars for U.S. mining

conditions. In: First Annual Conference on Ground Control in Coal.

Morgantown, WV: West Virginia University, pp. 13-22.

Brady BT, Blake W [1968]. An elastic solution of the laterally constrained

circular cylinder under uniaxial loading. In: 10th U.S. Symposium on Rock

Mechanics, pp. 199-214.

Gaddy FL [1956]. A study of the ultimate strength of coal as related to the

absolute size of the cubical specimens tested. Blacksburg, VA: Virginia

Polytechnic Institute and State University, Bulletin VPI 49(10), tables 6-10.

Hasenfus GJ, Su DWH [1992]. A comprehensive integrated approach for

longwall development design. 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. 225-237.

Holland CT [1964]. The strength of coal in mine pillars. In: Proceedings

of the Sixth Symposium on Rock Mechanics. Rolla, MO: University of

Missouri, pp. 450-456.

Iannacchione AT [1990]. The effect of roof and floor interface slip on coal

pillar behavior. In: Proceedings of the 31st U.S. Symposium on Rock

Mechanics, pp. 156-160.

Khair AW [1968]. The effects of coefficient of friction on strength of

model coal pillar [Thesis]. Morgantown, WV: West Virginia University,

Department of Mining Engineering.

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.

Mark C, Bieniawski ZT [1986]. Field measurements of chain pillar

response to longwall abutment loads. In: Proceedings of the Fifth Conference

on Ground Control in Mining, pp. 114-122.

Mark C, Chase FE [1993]. Gate entry design for longwall using the coal

mine roof rating. In: Proceedings of the 12th International Conference on

Ground Control in Mining. Morgantown, WV: West Virginia University,

pp. 76-83.

Mark C, Iannacchione AT [1992]. Coal pillar mechanics: theoretical

models and field measurements compared. 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. 78-93.

Obert L, Duvall WI [1967]. Rock mechanics and the design of structures

in rock. New York, NY: John Wiley and Sons, pp. 542-545.

Panek L [1994]. Sealing mine pillar size and slope with the R function.

SME preprint 94-52. Littleton, CO: Society for Mining, Metallurgy, and

Exploration, Inc.

Parker J [1993]. Mine pillar design in 1993: computers have become the

opiate of mining engineering, parts I and II. Min Eng July:714-717 and

Aug:1047-1050.

Salamon MDG, Munro AH [1967]. A study of the strength of coal pillars.

J S Afr Inst Min Metall 68:55-67.

Salamon MDG, Wagner H [1985]. Practical experiences in the design of

coal pillars. In: Green AR, ed. Proceedings of the 21st International

Conference of Safety in Mines Research Institutes (Sydney, Australia).

Balkema, pp. 3-9.

Su DWH, Hasenfus GJ [1996]. Practical coal pillar design considerations

based on numerical modeling. Handout at the 15th International Conference

on Ground Control in Mining (Golden, CO).

Su DWH, Hasenfus GJ [1997]. Effects of in-seam and near-seam

conditions on coal pillar strength. Handout at the 16th International

Conference on Ground Control in Mining (Morgantown, WV).

Wilson AH [1972]. An hypothesis concerning pillar stability. Min Eng

(London) 131(141):409-417.
163

NEW STRENGTH FORMULA FOR COAL PILLARS IN SOUTH AFRICA

By J. Nielen van der Merwe, Ph.D.1

ABSTRACT

For the last 3 decades, coal pillars in the Republic of South Africa have been designed using the well-known

strength formula of Salamon and Munro that was empirically derived after the Coalbrook disaster. The

database was recently updated with the addition of failures that occurred after the initial analysis and the

omission of failures that occurred in a known anomalous area. An alternative method of analysis was used

to refine the constants in the formula. The outcome was a new formula that shows that the larger width-toheight ratio coal pillars are significantly stronger than previously believed, even though the material itself is

represented by a reduced constant in the new formula. The formula predicts lower strength for the smaller

pillars, explaining the failure of small pillars that were previously believed to have had high safety factors. 

Application of the new formula will result in improved coal reserve utilization for deeper workings and

enhanced stability of shallow workings.

1Managing director, Itasca Africa (Pty.) Ltd., Johannesburg, Republic of South Africa.
164

 Figure 1.CConcept of the measure of success of a safety factor formula. A, The overlap area between the failed and stable cases

should be a minimum. B, At a safety factor of 1.0, one-half of the pillars should have failed.

INTRODUCTION

The Coalbrook disaster in January 1960, in which more than

400 men lost their lives when the mine's pillars collapsed, led

to a concerted research effort that eventually resulted in the

creation of two formulas for the prediction of coal pillar

strength: the power formula of Salamon and Munro [1967] and

the linear equation of Bieniawski [1968]. The Bieniawski

formula was based on in situ tests of large coal specimens; the

Salamon-Munro formula, on a statistical analysis of failed and

stable pillar cases. The South African mining industry adopted

the Salamon-Munro formula, even though the differences

between the two formulas were not significant for the range of

pillar sizes that were mined at the time.

It is characteristic of the Salamon-Munro formula that the

strength increases at a lower rate as the width-to-height (w/h)

ratios of the pillars increase. Later, this was rectified by the socalled squat pillar formula refined by Madden [1991]. This

formula is valid for w/h ratios >5 and is characterized by an

accelerating strength increase with increasing w/h ratios.

An intriguing aspect of the Salamon-Munro formula is the

relatively high value of the constant in the formula that

represents the strength of the coal material—7.2 MPa. This

compares with the 4.3 MPa used in the Bieniawski formula.

The question has always been why the statistical back-analysis

yielded a higher value than the direct underground tests. An

attempt by van der Merwe [1993] to explain the significantly

higher rate of pillar collapse in the Vaal Basin yielded a

constant for that area of 4.5 MPa, more similar to Bieniawski

than to Salamon and Munro, but not directly comparable

because it was valid for a defined geological district only.

In the process of analyzing coal pillar failures for other

purposes, an alternative method of analysis was used that

resulted in a formula that is 12.5% more effective in

distinguishing between failed and stable pillars in the database.

This paper describes the method of analysis and the results

obtained.

REQUIREMENTS OF A SAFETY FACTOR FORMULA

A safety factor formula should satisfy two main requirements: (1) it should successfully distinguish between failed and

stable pillars and (2) it should provide the means whereby

relative stability can be judged. The third requirement,

simplicity, has become less important with the widespread use

of computers, but is still desirable.

These fundamental requirements are conceptually illustrated

in figure 1. Figure 1A shows the frequency distributions of

safety factors of the populations of failed and stable pillars,

respectively. The area of overlap between the populations can

be seen as a measure of the success of the formula; the perfect

formula will result in complete separation of the two

populations. Figure 1B is a normalized cumulative frequency

distribution of the safety factors of the failed cases plotted

against safety factors. At a safety factor of 1.0, one-half of the

pillars should have failed, or the midpoint of the distribution of

failed pillars should coincide with a safety factor of 1.0.
165

F ' k

R

b

0

V

a

b

g

R

R0

g

&1 %1 , (3)

F '

0.0786

V

0.0667

R

2.5 % 181.6 (4)

F ' 0.0786 w

2.366

h

2.5667

% 9 . (5)

EXISTING FORMULAS IN SOUTH AFRICA

The safety factor is a ratio between pillar strength and pillar

load. In its simplest form, the load is assumed to be the weight

of the rock column overlying the pillar and the road around the

pillar, i.e., the tributary area theory is normally used. This is

widely held to be a conservative, and thus safe, assumption.

However, it has at least one complication when this load is used

to derive a safety factor empirically: if the load used to

determine pillar strength is greater than the actual load, then the

strength derived will also be greater than the actual pillar

strength. If an alternative method is then used later to calculate

pillar load, such as numerical modeling, and the strength is not

modified, then the calculated safety factor will be greater than

the real safety factor.

For purposes of this paper, the tributary area loading theory

is used, and the restriction must then be added that the derived

strength is only valid for situations where the tributary area load

is used. This is not a unique restriction; even if not explicitly

stated, it is also valid for any other empirical safety factor

formula for which the tributary area loading assumption was

used, such as the Salamon-Munro formula.

It then remains to determine a satisfactory formula for the

calculation of pillar strength. The strength of a pillar is a

function of the pillar dimensions, namely, width and height for

a square pillar, and a constant that is related to the strength of

the pillar material. According to Salamon and Munro [1967],

the strength is

F ' kw"h

$

, (1)

where h ' pillar height,

w ' pillar width,

and k ' constant related to material strength.

The parameters k, ", and $ are interdependent. Salamon and

Munro [1967] used the established greatest likelihood method

to determine their values simultaneously and found:

k ' 7.2 MPa,

" ' 0.46,

and $ ' &0.66.

The linear formula of Bieniawski [1968] is

F ' 4.3(0.64 % 0.36 w/h). (2)

With the addition of new data on failures after 1966 to the

Salamon and Munro database, Madden and Hardman [1992]

found:

k ' 5.24 MPa,

" ' 0.63,

and $ ' &0.78.

These new values, however, did not result in sufficiently

significant changes to safety factors to warrant changing the old

formula, and they were not used by the industry. Note,

however, the increases in values of " and $ and reduction of k.

According to Madden [1991], the squat pillar formula, valid

only for pillars with a w/h > 5, is

where R ' pillar w/h ratio,

R0 ' pillar w/h ratio at which formula begins to be

 valid ' 5.0,

and V ' pillar volume.

Substituting k ' 7.2 MPa, a ' 0.0667, b ' 0.5933, R0 ' 5.0,

and g ' 2.5 results in a somewhat simplified form of the

formula that is sometimes used:

For quick calculations, equation 4 can be approximated with

negligible error by
166

S '

Strength

Load

. (6)

Load '

DgH(w % B)

2

w

2

, (7)

Strength ' 7.2

w

"

h

$

, (8)

f '

Ms& Mf

S

2

s % S

2

f

,

(9)

R ' 0.5 &

1

f

(2B)

&0.5

exp

&f

2

2

(10)

I '

As& An

As

, (12)

ALTERNATIVE METHOD OF ANALYSIS

Although ", $, and k are interdependent, they can be

separated for purposes of analysis. It was found that changing

" and $ affected the overlap area of the populations of failed

and stable pillars. Modifying k does not affect this relationship;

it causes an equal shift toward higher or lower safety factors in

both populations. Therefore, " and $ can be modified

independently to minimize the overlap area between the two

populations; once that is done, k can be adjusted to shift the

midpoint of the population of failed pillars to a safety factor

of 1.0.

DETERMINATION OF " AND $

The data bank for failed pillars for the analysis described

here was that quoted by Madden and Hardman [1992], which

was the original Salamon and Munro data. The post-1966

failures were added to the data, and the three Vaal Basin

failures were removed because the Vaal Basin should be treated

as a separate group (see van der Merwe [1993]). (Note that a

subsequent back-analysis indicated that the changes to the data

bank did not meaningfully affect the outcome.)

For the first round of analysis, " and $ were both varied

between 0.3 and 1.2 with increments of 0.1. Safety factors

were calculated for each case of failed and stable pillars. For

each of the 100 sets of results, the area of overlap between the

populations of failed and stable pillar populations was

calculated. A standard procedure was used for this, taken from

Harr [1987]. This involved the simplifying assumption that the

distributions were both normal, but because it was only used for

comparative purposes, the assumption is valid. Using the same

procedure, the overlap area for the Salamon-Munro formula

was also calculated. This was used as the basis from which an

improvement factor was calculated for each of the new data

sets.

The safety factor, S, was

The tributary area theory was used to calculate the load:

where H ' mining depth,

w ' pillar width,

and B ' bord width.

Then, the strength was varied, as follows:

where w ' pillar width,

h ' pillar height,

" ' 0.3 to 1.2 with 0.1 increments,

and $ ' 0.3 to 1.2 with 0.1 increments.

Equations 6 through 9 were applied to each of the cases of

failed and stable populations, thus creating 100 sets of

populations of safety factors of failed and stable cases. For

each set, a comparative improvement factor was calculated.

The first step was to calculate "f" for each of the 100 sets:

where Ms ' mean safety factor of the population of stable

 pillars,

Mf ' mean safety factor of the population of failed

 pillars,

Ss ' standard deviation of the safety factors of the

 stable pillars,

and Sf ' standard deviation of the safety factors of the

 failed pillars.

Then,

and the overlap area between the two populations is

A ' 0.5 & R. (11)

Finally, the improvement factor, I, for each set is
167

Strength ' 4

w

0.81

h

0.76 (8)

 Figure 2.CContour plot of percentage improvement in efficiency of formula to separate failed

and stable pillar cases for variations of " between 0.3 and 1.2 and for $ between 0.3 and 1.2. The

Salamon and Munro [1967] combination is shown by the dotted lines.

where As ' overlap area with the original Salamon-Munro

 formula,

and An ' overlap area with the new formula.

It was then possible to construct contours of the

improvement factors for variations of " and $ (figure 2).

Figure 2 shows that the greatest improvement was for "

between 0.7 and 0.8 and for $ between 0.75 and 0.85. Fine

tuning was then done by repeating the procedure with

increments of 0.01 for " from 0.7 to 0.8 and for $ between 0.75

and 0.85. The resulting contours are shown in figure 3.

On the basis of the contours of improvement factors in

figure 3, it was concluded that for " ' 0.81 and $ ' 0.76, the

improvement in efficiency of the formula to distinguish

between failed and stable pillar cases is 12.5%.

DETERMINATION OF "k"

The last step was to determine k for the new exponents of "

and $. This was done by adjusting k so that the midpoint of the

population of failed pillars coincided with a safety factor of 1.0.

It was found that a value of k ' 4.0 MPa satisfied this

condition; this is shown in figure 4.

FINAL NEW FORMULA

The full new formula for pillar strength in the Republic of

South Africa is then as follows:
168

 Figure 3.CContour plot of percentage improvement in efficiency of formula to separate failed and

stable pillar cases for variations of " between 0.77 and 0.86 and for $ between 0.72 and 0.81.

 Figure 4.CPlot of cumulative normalized frequency against safety

factors calculated with the Salamon-Munro formula (solid line) and

the new formula (broken line). For the new formula, k = 4 MPa, " =

0.81, and $ = 0.76.
169

COMPARISON OF THE DIFFERENT FORMULAS

Again using the accepted Salamon-Munro formula as a

basis, the formulas of Bieniawski [1968] and Madden and

Hardman [1992] were also compared for relative changes in the

overlap area of failed and stable pillar populations. The method

used was the one described in the previous section. The

relevant strength formulas were used in turn for the calculation

of safety factors, and the overlap areas were calculated and

compared with the original Salamon-Munro formula. The

results are summarized below.

The table shows that the Bieniawski [1968] formula was

only slightly less efficient than the Salamon-Munro formula;

Madden and Hardman [1992] was slightly more efficient,

although the decision not to implement the latter was probably

correct because the improvement is small. The formula derived

in this paper, referred to in the table above as the "new

formula," is, however, 12.5% more efficient, which is

considered significant.

Strength formula Improvement

factor, %

Bieniawski [1968] ........... &1.5

Madden and Hardman [1992] . . % 2.3

New formula ............... %12.5

DISCUSSION AND IMPLICATIONS FOR THE INDUSTRY

The new formula yields higher values of safety factors for

most pillars than either of the formulas proposed previously for

South African coals. The exceptions are the small pillars,

such as those typically found at shallow depth. The new

formula is more successful in explaining the "anomalous" pillar

collapses of small pillars at shallow depth.

Figure 5 compares pillar strengths obtained with the various

formulas for different w/h ratios of the pillars. Note that due to

the different exponents of width and height, the relationships

are ambiguous (except for the linear formula of Bieniawski

[1968] and the Mark-Bieniawski formula described by Mark

and Chase [1997]). For purposes of this comparison, the pillar

heights were fixed at 3 m and the widths adjusted to obtain the

different ratios.

An important feature of the comparison is the close

correlation between the Mark-Bieniawski formula and the new

formula. They were derived independently using different

databases in different countries. Both predict stronger pillars

for the same dimensions as the other formulas. The new

formula only deviates meaningfully from Mark-Bieniawski in

the lower range of the w/h ratio, where it predicts weaker

pillars. This is in accordance with observations where the

failure of small pillars was previously regarded as anomalous.

The major implication for the coal mining industry is that

higher coal extraction can be obtained without sacrificing

stability. In effect, this is nothing more than a correction of the

overdesign that has been implemented over the past decades.

Figure 6 shows examples of the benefits with regard to the

percentage extraction. The greater the depth and the higher the

required safety factor, the greater the benefit.

As the new formula deals with underground pillar stability,

it is inherently linked to the safety of underground mine

personnel. In particular, it will enhance the stability of shallow

workings, which has hitherto been a shortcoming of the

Salamon-Munro formula. For deeper workings and for cases

where surface structures are undermined, the new formula will

enable mines to extract more coal without sacrificing stability.
170

 Figure 5.CComparison of the strength increase with increasing width to height of pillars.

The new formula results in higher strength values for most of the pillar sizes. This

comparison is included for demonstration purposes only, because the relationship between

width to height and pillar strength is ambiguous for all cases where the exponents of width

and height are not equal. Note the similarity between the new formula and the MarkBieniawski formula.

 Figure 6.CIllustration of the benefit obtained by using the new formula. As the safety factors

and depth of mining increase, more extraction can be obtained without sacrificing stability. For

purposes of this comparison, the mining height was 3 m and the road width was 6.6 m.
171

ACKNOWLEDGMENTS

This work is part of a larger research project sponsored by Sasol Mining (Pty.) Ltd., whose support is gratefully acknowledged.

REFERENCES

Bieniawski ZT [1968]. In situ strength and deformation characteristics of

coal. Eng Geol, Vol. 2, pp. 325-340.

Harr ME [1987]. Reliability-based design in civil engineering. McGrawHill Book Co., pp. 130-134.

Madden BJ [1991]. A re-assessment of coal pillar design. J S Afr Inst Min

Metall 91(1):27-37.

Madden BJ, Hardman DR [1992]. Long-term stability of bord-and-pillar

workings. In: Proceedings of the Symposium on Construction Over Mined

Areas (Pretoria, Republic of South Africa, May 1992). Yeoville, Republic of

South Africa: South African Institution of Civil Engineers.

Mark C, Chase FE [1997]. Analysis of retreat mining pillar stability

(ARMPS). In: Proceedings - New Technology for Ground Control in Retreat

Mining. Pittsburgh, PA: U.S. Department of Health and Human Services,

Public Health Service, Centers for Disease Control and Prevention, National

Institute for Occupational Safety and Health, DHHS (NIOSH) Publication

No. 97-122, IC 9446, pp. 17-34.

Salamon MDG, Munro AH [1967]. A study of the strength of coal pillars.

J S Afr Inst Min Metall Sep:55-67.

Van der Merwe JN [1993]. Revised strength factor for coal in the Vaal

Basin. J S Afr Inst Min Metall 93(3):71-77.
172
173

THE ROLE OF OVERBURDEN INTEGRITY IN PILLAR FAILURE

By J. Nielen van der Merwe, Ph.D.1

ABSTRACT

The move toward partial pillar extraction versus full pillar extraction has necessitated a new approach to

underground section stability. When pillars are mined too small to support the weight of the overburden, they

will, in some cases, remain stable for a considerable period; in other cases, they will collapse unexpectedly and

violently. There is no discernable difference between the pillar safety factors of the failed and stable cases.

The explanation lies in the characteristics of the overburden layers.

A method is proposed that recognizes the overburden characteristics in the evaluation of stability. Two

stability factors are calculated: one for the pillars, the other for the overburden. Using this method, it is

possible to make use of the bridging capabilities of overburden layers to prevent pillar collapse. It is possible

to scientifically design partial pillar extraction layouts that will be safe. Using energy considerations, it is also

possible to prevent violent failure of pillars.

1Managing director, Itasca Africa (Pty.) Ltd., Johannesburg, Republic of South Africa.
174

INTRODUCTION

In order for underground coal pillars to fail completely, two

requirements must be met: (1) the pillars themselves must be

loaded to beyond their load-bearing capacity, and (2) the

overburden must deflect sufficiently to totally deform the pillars. In the consideration of pillar failure, the first requirement

historically has received almost all of the attention; only scant

mention is sometimes made of the role of the overburden.

Until recently, this has not been necessary. South African

mining methods, longwalling apart, were either bord-and-pillar

or pillar extraction methods with a number of variations. For

bord-and-pillar, the pillars are sufficiently large to support the

full weight of the overburden and the stiffness of the overburden is a bonus, merely decreasing the load on the pillars. In

pillar extraction, the overburden usually fails completely, although there are situations where it is prone to be self-supporting for large enough distances to result in overloaded pillars

and the well-known and understood negative consequences

thereof.

Lately, however, there has been a move toward partial pillar

extraction with a number of different names attached to the

methods, like pillar robbing, pillar splitting, checkerboard

extraction, etc. These methods all have in common the partial

extraction of pillars, leaving self-supporting snooks (stubs) in

the back area. They are usually larger than the ones left in normal stooping operations. These snooks are often stable for long

periods of time, even though their strengths are less than that

required to support the full overburden. This in turn creates the

impression that the pillars are much stronger than the prediction

made with the strength formula.

There have also been occasions where the snooks failed after

a period of time. The author has been involved in investigations into two of these. In both instances, the lack of serious

accidents can only be ascribed to luck, both having occurred in

the off-shift. In one case, ventilation stoppings were destroyed

for a distance of several kilometers; in the other, the collapse

overran unmined pillars and resulted in severe roof falls up to

six lines of pillars beyond the end of the split pillars.

The difference between the cases that failed and those that

remained stable is not to be found in the strengths of the pillars.

The range of safety factors was from 0.5 to 0.7, and the stable

ones were not the ones with the higher safety factors. The pillar

safety factor alone does not explain stability in these marginal

cases. There were, however, significant differences in the overburden composition and stability. The investigation indicated

that in the stable cases, the overburden was strong enough to

bridge the panels; in the failed cases, the overburdens failed.

This resulted in the development of a concept that takes into

account the overburden stability as well as pillar stability. This

concept will be explained in this paper.

EFFECTS OF MINING ON THE OVERBURDEN

Mining results in increased loads on the unmined pillars.

This causes the pillars to compress; the amount of compression

is a function of the additional load on the pillars and the pillar's

modulus of elasticity. The pillar compression is translated into

deflection for the overburden. The higher the pillar loads, the

greater the compression and the more the overburden will deflect. In the most simplistic view, coal mine overburdens can

be regarded as a series of plates that can be conveniently simplified further to a series of beams in the general case where the

panel lengths are several times greater than the panel widths.

The beam deflection results in induced tensile stress in the

upper beam edges and the bottom center of the beam. The most

simplistic view, adopted here as the starting point for the development of a more accurate model, is that the beam will fail

when the induced tension exceeds the sum of the virgin horizontal stress and the tensile strength of the beam material.

However, it is well known that the overburden, consisting predominantly of sedimentary rock types often supplemented by a

dolerite sill, is vertically jointed and therefore the tensile

strength of the material can be ignored. Failure will thus occur

when the induced tensile stress exceeds the virgin horizontal

compressive stress.

The amount of deflection of any individual beam in the

overburden is enhanced by the weight of the material on top of

it and restricted by the resistance of the pillars underneath.

There are no major differences in the moduli of the overburden

rocks, dolerite sills apart, and the differential amounts of

bending become a function of the thicknesses of the beams. In

considering overburden stability, the identification of thick

lithological units therefore is more important than the ratio of

mining depth to panel width.
175

)h '

)F

Ec

h ,

(1)

Ecf '

0.562w

h

& 2.293 . (2)

)F

p

' (H

1

1 & e

& 1 , (3)

0 '

(rL

4

32Ert

3

, (4)

Ft'

(rL

2

2t

2

. (5)

Ft'

16t)hEr

L

2

(6)

MATHEMATICAL RELATIONSHIP BETWEEN PILLAR LOAD

AND OVERBURDEN DEFLECTION

The link between overburden deflection and pillar load is the

pillar compression. The pillar cannot compress by a greater

amount than the overburden deflection and vice versa. The

maximum pillar deflection, )h, is

where h ' pillar height,

)F ' load increase caused by mining,

and Ec ' modulus of elasticity of coal.

The above is valid for the situation where the overburden is

sufficiently soft not to restrict the compression of the pillars.

There is general consensus that the modulus of elasticity of coal

is around 4 GPa. However, the postfailure modulus is a

function of the pillar shape. According to data supplied by van

Heerden [1975], the postfailure modulus, Ecf, appears to be2

Assuming tributary area loading conditions, the load increase on the pillars due to mining is

where H ' mining depth,

e ' areal extraction ratio,

and ( ' Dg.

RELATIONSHIP BETWEEN PILLAR DEFLECTION AND INDUCED TENSION

IN OVERBURDEN BEAM

The generic equation for beam deflection is

where L ' panel width,

Er ' modulus of elasticity of the rock layer,

t ' thickness of the rock layer,

and (r ' unit load on the rock layer.

The generic expression for the maximum generated tensile

stress is

By substituting 0 by )h, the tension induced by bending can

also be expressed in terms of the deflection, as follows:

This is the tensile stress that will be generated in the

overburden beam if the restriction to deflection is the resistance

offered by the pillars underneath. It is also the upper limit of

the generated tension because the resistance offered by the pillars will not allow further deflection. However, the overburden

has inherent stiffness that will also restrict deflection. The

maximum deflection that an unsupported beam will undergo is

indicated by equation 4.

If 0 from equation 4 is greater than )h from equation 1, it

means that the overburden is dependent on the pillars to restrict

deflection and that the tensile stress generated in the beam is

that found with equation 6. If )h is greater than 0, it means

that the beam is sufficiently stiff to control its own deflection

and that the tension generated in the beam is that found with

equation 5.

2Author's own linear fit to van Heerden's data.
176

OSR '

Fh

Ft

. (9)

PSF '

Strength

Load (10)

Load '

DgH

1&e

, (11)

Strength ' 4

w

0.81

h

0.76

. (12)

Figure 1.CPlot of OSR and PSF. Values of <1.0

for either indicate imminent instability.

OVERBURDEN FAILURE

The overburden beams will fail if the induced tension

exceeds the virgin horizontal compression; this is conveniently expressed in terms of the vertical stress as

Fh ' kFv, (7)

or

Fh ' k(HN, (8)

where HN is the depth at which the rock layer under consideration is located, not the depth of mining.

Next, define the overburden stability ratio (OSR) as

PILLAR STABILITY

Pillar stability is evaluated by comparing pillar strength to

pillar load; thus:

The pillar load is conservatively estimated from the tributary

area loading assumption as follows:

and the strength for South African pillars is [van der Merwe

1999]:

OVERALL STABILITY EVALUATION

To evaluate the overall stability of a coal mine panel, it is

necessary to consider both the overburden and the pillar

stability. This can be done by viewing the two stability

parameters—the pillar safety factor (PSF) and the overburden

stability ratio (OSR)—separately, or better, by plotting the two

onto a plane. The concept is illustrated in figure 1.

The quadrants in figure 1 have different meanings for the stability evaluation. In quadrant I, both the overburden and the pillars are stable. This is the ideal situation for main development.

In quadrant II, the overburden is stable, although the pillars

are unable to support the full weight of the overburden. This is

potentially the most dangerous situation because there could be

a false impression of stability when the OSR is not much greater than 1.0. The pillars will be stable for as long as the overburden remains intact; however, the moment that the overburden fails, the pillars will also fail. This may occur because

of time-related strength decay of the stressed overburden or

when mining progresses into an area with an unfavorably

oriented unseen joint set in the overburden. The closer the OSR

is to 1.0, the more dangerous the situation.

Quadrant III indicates a situation where both the pillars and

the overburden will fail. This is again the ideal situation for the

snooks in pillar extraction. One wants both to fail in this

situation.

Quadrant IV indicates that the pillars are able to support the

overburden, even though the overburden may fail. This is also

a safe situation, although gradual failure may occur over a long

period as the pillars lose strength.
177

I

v

' 1 &

Ecf

4

(13)

Figure 2.COSR/PSF plot of the different options

discussed in the example.

PRACTICAL EXAMPLE

The following practical example is provided to indicate how

the OSR/PSF procedure is applied in practice.

The mining depth is 143 m. The overburden consists of

alternating layers of sandstones and shales. From the surface

down, their thicknesses are as follows: 10, 5, 10, 20, 10, 50, 10,

10, 5, and 10 m. The mining height is 3 m; pillars are initially

18 m wide, and the roads are 6 m wide. The k-ratio is 2.0. The

PSF is then 2.7, shown as point A in figure 2.

Pillars are then split by a 6-m-wide cut through the center,

leaving remnants of 18 by 6 m, with an equivalent width (see

Wagner [1980]) of 8 m. One line of pillars is left intact on

either side of the panel, resulting in a width over which the

pillars are split of 102 m. The PSF now decreases to 0.8. The

OSR is calculated for each of the strata layers individually (see

results in table 1).

It is seen from table 1 that because the pillars are beyond

their failure limit, the overburden behavior is governed by the

beam characteristics. Except for unit 6, all of the units will fail.

Unit 6, however, is close to not failing and will probably be

self-supporting for a short while. This combination of OSR and

PSF is indicated by point B in figure 2.

During the time when they have not yet failed, it is probable

that the pillars will have a stable visual appearance. Load

cannot be seen. One's perception of pillar load is determined by

the observed effects that accompany pillar compression, like

slabbing. In this case, the pillar compression will be the greater

of the deflection of unit 6 or the compression caused by the

weight of the rock layers underneath unit 6. The deflection of

unit 6 is 4 mm, and the compression of the pillars due to the

weight of the strata underneath unit 6 is less than 2 mm. With

the 4-mm compression of the pillars, the strain is 0.0013, which

corresponds to a pillar load of 5.3 MPa. The strength of the

snook is 8.4 MPa; the apparent safety factor is 1.6, and it will

have the visual appearance of a stable pillar. However, the

situation will change dramatically as soon as the overburden

fails. At that moment, the pillars will be loaded by the full

overburden weight. The safety factor will immediately decrease to 0.8.

Table 1.COSR for the different strata layers

with split pillars, panel width of 102 m

Unit No. Thickness, m 0 )h OSR

1 ......... 10 0.028 31.5 0.038

2 ......... 5 0.564 31.5 0.01

3 ......... 10 0.113 31.5 0.038

4 ......... 20 0.025 31.5 0.154

5 ......... 10 0.282 31.5 0.038

6 ......... 50 0.004 31.5 0.961

7 ......... 10 0.62 31.5 0.038

8 ......... 10 0.677 31.5 0.038

9 ......... 5 5.75 31.5 0.01

10 ........ 10 0.761 31.5 0.038

MODE OF FAILURE

Energy considerations indicate that failure will be violent

if the stiffness of the pillars is less than that of the loading

mechanism, which is the overburden. When the overburden

fails, it loses continuity and, consequently, all stiffness as well.

The stiffness of the loading mechanism is then 0. Therefore,

the only way in which failure can be nonviolent in the situation

where the overburden fails is where the pillars have a positive

postfailure modulus. According to equation 2, this happens

when the width-to-height (w/h) ratio of the pillars exceeds 4.08.

The w/h ratio of the pillars in this case is only 2.3;

consequently, the failure will be violent, similar to what has

been experienced on more than one occasion. This is similar to

a conclusion reached by Chase et al. [1994], who analyzed

pillar failures in the United States and found that massive

collapses occurred where the w/h ratios of the pillars were less

than 3. They also concluded that those collapses occurred

where the overburden was able to bridge the excavation for a

considerable distance before failure occurred.

The postfailure stiffness of coal with increasing w/h ratio of

the pillars increases approximately linearly. There is thus no

sudden distinction between what could be termed "violent" and

"nonviolent" failure; rather, the relative degree of violence

decreases with increasing w/h. It is suggested that the degree

of violence be indicated by an index based on the magnitude of

the postfailure stiffness of the coal, Ecf. It could be defined as

follows:
178

With the limited information at hand, mainly that of Chase

et al. [1994], it appears that if Iv

 > 1.15, the failure may result

in a dangerous situation. This obviously also depends on the

area involved.

By substituting equation 2 into equation 13, the relative

degree of violence may be expressed in terms of the w/h ratio

as follows:

Iv ' 1.57 & 0.14 w/h (14)

CONTROL MEASURES

There are a number of ways in which pillar splitting

situations can be controlled using the OSR/PSF. One is to limit

the width over which the pillars are split. For instance, if the

width in the example is limited to 78 m (i.e., by splitting only

three lines of pillars), the OSR of unit 6 increases to 1.6 and

there is a much higher probability that the unit will remain to be

self-supporting, if only for a longer time. Note that when this

is done, the PSF is not affected; it remains at a value of 0.8.

This situation is indicated by point C in figure 2. This

corresponds to other situations that have been observed, i.e.,

where split pillars with low apparent safety factors remain

stable for considerable periods of time.

A second alternative is to do full extraction of every second

pillar on a checkerboard pattern, leaving the alternating pillars

intact. When this is done, the PSF decreases to 0.7. The OSR

of the strongest unit, No. 6, is 0.3, indicating failure of the overburden. This is shown as point D in figure 2. However, the

w/h ratio of the pillars is 6.0, which means that the pillars will

not fail violently. The attraction of this option is that 50% of all

of the coal contained in pillars is extracted, as opposed to 17%

using the method in the previous paragraph.

INFLUENCE OF GEOLOGY

A cautionary note must be expressed at this point. The

process of pillar failure for low safety factor pillars is driven by

the overburden characteristics. It is thus very important to have

detailed knowledge of the overburden composition. For instance,

if the thickness of unit 6 in the example is 40 m instead of 50 m,

then the control measure to restrict the number of pillars to be

split to 78 m will not be effective; the OSR in that case will be

1.0, which places it back into the category with the highest

uncertainty. The example in the previous section is nothing more

than an example to illustrate the application of the method: it is

not to be viewed as a guideline for panel widths, etc.

The full application of the method will require the establishment of guidelines for limit values of OSR and PSF. It

seems reasonable to assume that there will be an area in the

center of the plot shown in figure 1 that is to be avoided—the

area of highest uncertainty, where the values of OSR and PSF

are close to 1.0. Those limits need to be established; the best

way of doing that will probably be through back-analysis in

areas where there are examples of failed and stable cases for

different periods of time.

CONCLUSIONS

• For underground workings to collapse, both the pillars and

the overburden must fail. The model described here, simplified

as it is, offers a method to evaluate the stability of pillar

workings with low pillar safety factors by adding an evaluation

of overburden stability to the evaluation of pillar stability.

• Even if the pillars are not strong enough to support the

overburden, it is possible to prevent collapse by limiting the

panel width, thereby allowing the overburden to be selfsupporting.

• Refinement of the model will enable the scientific design

of alternatives to full pillar extraction, avoiding the situation

where apparent stability caused by temporary bridging of the

overburden leads to a false sense of security, only to be

followed by catastrophic collapse.

• Quantification of the energy considerations can be done,

leading to a design that will result in nonviolent failure of

pillars.

• These conclusions are broadly similar to those reached by

Chase et al. [1994]. The main difference is that this work offers

a simple method of classifying the likelihood of failure

occurring and the mode of failure should it occur.

ACKNOWLEDGMENTS

This work is part of a larger research project sponsored by Sasol Mining (Pty.) Ltd., whose support is gratefully acknowledged.
179

REFERENCES

Chase FE, Zipf RK Jr., Mark C [1994]. The massive collapse of coal

pillars: case histories from the United States. In: Peng SS, ed. Proceedings of

the 13th International Conference on Ground Control in Mining. Morgantown,

WV: West Virginia University, pp. 69-80.

Van der Merwe JN [1999]. New strength formula for coal pillars in South

Africa. In: Proceedings of the Second International Workshop on Coal Pillar

Mechanics and Design. Pittsburgh, PA: U.S. Department of Health and

Human Services, Public Health Service, Centers for Disease Control and

Prevention, National Institute for Occupational Safety and Health, DHHS

(NIOSH) Publication No. 99-114, IC 9448.

Van Heerden WL [1975]. In situ determination of complete stress-strain

characteristics of large coal specimens. J S Afr Inst Min Metall 75(8):207-217.

Wagner H [1980]. Pillar design in coal mines. J S Afr Inst Min Metall

80:37-45.
181

USING A POSTFAILURE STABILITY CRITERION IN PILLAR DESIGN

By R. Karl Zipf, Jr., Ph.D.1

ABSTRACT

Use of Salamon's stability criterion in underground mine design can prevent the occurrence of catastrophic domino-type pillar

failure. Evaluating the criterion requires computation of the local mine stiffness and knowledge of the postfailure behavior of

pillars. This paper summarizes the status of the practical use of this important criterion and suggests important research to

improve our capabilities.

Analytical and numerical methods are used to compute the local mine stiffness. Work to date in computing local mine

stiffness relies mainly on elastic continuum models. Further work might investigate local mine stiffness in a discontinuous rock

mass using alternative numerical methods.

Existing postfailure data for coal pillars are summarized, and a simple relationship for determining the postfailure modulus

and stiffness of coal pillars is proposed. Little actual postfailure data for noncoal pillars are available; however, numerical models

can provide an estimate of postfailure stiffness. Important factors controlling postfailure stiffness of rock pillars include the

postfailure modulus of the material, end conditions, and width-to-height ratio.

Studies show that the nature of the failure process after strength is exceeded can be predicted with numerical models using

Salamon's stability criterion; therefore, a method exists to decrease the risk of this type of catastrophic failure. However, the

general lack of good data on the postfailure behavior of actual mine pillars is a major obstacle. Additional back-analyses of failed

and stable case histories in conjunction with laboratory testing and numerical modeling are essential to improve our ability to

apply the stability criterion.

1Assistant professor, Department of Mining Engineering, University of Missouri-Rolla.
182

INTRODUCTION

As first noted by Cook and Hojem [1966], whether a test

specimen in the laboratory explodes violently or crushes

benignly depends on the stiffness of the testing system relative

to the postfailure stiffness of the specimen. Full-scale pillars in

mines behave similarly. Salamon [1970] developed the local

mine stiffness stability criterion, which formalizes matheatically laboratory and field observations of pillar behavior in

the postfailure condition. Although we understand the

principles well, little is known by direct observation or backcalculation about the postfailure behavior of actual mine pillars.

The local mine stiffness stability criterion governs the

mechanics of cascading pillar failure (CPF) [Swanson and

Boler 1995], also known as progressive pillar failure, massive

roof collapse, domino-type pillar failure, or pillar run. In this

type of failure, when one pillar collapses, the load it carries

transfers rapidly to its neighbors, causing them to fail and so

forth. This failure mechanism can lead to the rapid collapse of

very large mine areas. In mild cases, only a few tens of pillars

fail; in extreme cases, hundreds, even thousands of pillars can

fail.

Recent work by Chase et al. [1994] and by Zipf and Mark

[1997] document 13 case histories of this failure mechanism in

coal mines and 6 case histories in metal/nonmetal mines within

the United States. Further work by Zipf [in press] has analyzed

additional examples of this failure mechanism in the

catastrophic collapse of web pillars in highwall mining

operations. Reports by Swanson and Boler [1995], Ferriter

et al. [1996], and Zipf and Swanson [in press] document the

events and present analyses of the partial collapse at a trona

mine in southwestern Wyoming, where one of the largest

examples of this failure mechanism occurred.

Numerous instances of CPF have occurred in other parts of

the world. The most infamous case is the Coalbrook disaster in

the Republic of South Africa in which 437 miners perished

when 2 km2

 of the mine collapsed within a few minutes on

January 21, 1960 [Bryan et al. 1966]. Other instances occurred

recently at a coal mine in Russia and a large potash mine in

Germany.

These collapses draw public interest for two reasons. First

and foremost, a collapse presents an extreme safety hazard to

miners. Obviously, the collapse area itself is the greatest

hazard, but the collapse usually induces a devastating airblast

due to displacement of air from the collapse area. An airblast

can totally disrupt a mine's ventilation system by destroying

ventilation stoppings, seals, and fan housings. Flying debris

can seriously injure or kill mining personnel. The failure

usually fractures a large volume of rock in the pillars and

immediate roof and floor. In coal and certain other mines, this

sudden rock fragmentation can release a substantial quantity of

methane into the mine atmosphere that could result in an

explosion.

Secondly, large mine collapses emit substantial seismic

energy indicative of an implosional failure mechanism. For

example, the seismic event associated with the collapse in

southwestern Wyoming had a local magnitude of 5.3 [Swanson

and Boler 1995]. Strong seismic signals of this type receive

scrutiny from the international community because of U.S.

obligations under the Comprehensive Test Ban Treaty (CTBT).

Large collapses may initiate questions from the Federal

Government and could result in further questions from other

nations participating in the CTBT [Casey 1998; Heuze 1996].

The pillar failure mechanism considered in this paper (CPF

or domino-type pillar failure) should not be confused with coal

mine bumps and rock bursts, although both failure types are

frequently associated with large seismic energy releases.

Although the damage can seem similar, the underlying

mechanics are completely different. The mechanism of pillar

collapse largely depends on vertical stress and the postfailure

properties of pillars. The mechanism for coal mine bumps and

rock bursts is more complex. In these events, larger failures

(seismic events) in the surrounding rock mass induce severe

damage in susceptible mine workings.

LOCAL MINE STIFFNESS STABILITY CRITERION

When the applied stress on a pillar equals its strength, then

the "safety factor" defined as the ratio strength over stress

equals 1. Beyond peak strength when the strength criterion is

exceeded, the pillar enters the postfailure regime, and the failure

process is either stable or unstable. In this paper, stability refers

to the nature of the failure process after pillar strength is

exceeded. Based on the analogy between laboratory test

specimens and mine pillars, Salamon [1970] developed a

criterion to predict stable or unstable failure of mine pillars.

Figure 1 illustrates this well-known criterion.
183

 Figure 1.CUnstable, violent failure versus stable, nonviolent failure. Loading machine stiffness or local mine

stiffness is represented by the downward sloping line intersecting the pillar load convergence (stress-strain) curve.

A, Loading machine stiffness less than postfailure stiffness in a "soft" loading system. B, Loading machine stiffness

greater than postfailure stiffness in a "stiff" loading system.

 Figure 2.CBoth cases violate the local mine stiffness stability criterion, i.e., *KLMS * < *Kp*. A, Slow squeeze

results when *KLMS * < *Kp

*. B, Rapid CPF results when *KLMS * « *Kp*. 

Stable, nonviolent failure occurs when

|KLMS| > |KP

|

and unstable, violent failure occurs when

|KLMS| < |KP

|,

where |KLMS| is the absolute value of the local mine stiffness and

|KP

| is the absolute value of the postfailure stiffness at any point

along the load convergence curve for a pillar. As long as this

criterion is satisfied, CPF (domino-type pillar failure) cannot

occur; however, when the criterion is violated, then unstable

failure is possible.

Salamon's local mine stiffness stability criterion does not

include the time variable and thus does not predict the rapidity

of an unstable failure should it occur. CPF resides at the far end

of the unstable pillar failure spectrum. At the other end are

slow "squeezes" that develop over days or weeks. Workers and

machinery have ample time to get out of the way of the failure.

In a CPF, the failure is so rapid that workers and machinery

cannot evacuate in time. Both CPF and squeezes violate a

strength criterion and, somewhat later, the stability criterion;

thus, unstable pillar failure can proceed. The rapidity of a

failure may depend on the degree to which the local mine

stiffness stability criterion is violated, i.e., the magnitude of the

difference between KLMS and KP

, as shown in figure 2.
184

KLMS '

)P

)D

'

(Su& S

p

)A

Du& D

p

,

COMPUTING LOCAL MINE STIFFNESS

The local mine stiffness KLMS relates deformation in the rock

mass to changes in force on the rock mass. Force changes

occur as stresses in the mined-out rock go from in situ values to

zero as a result of mining. Deformations then occur in the rock

mass. If a given amount of mining (and force change) results

in small deformations, the system is "stiff"; if the resulting

deformations are large, the system is "soft." The magnitude of

the local mine stiffness depends in part on the modulus of the

rock mass and in part on the geometry of the mining

excavations. In general, the more rock that is mined out, the

softer the system. Obtaining direct measurements of the local

mine stiffness is generally not possible, since it is more of a

mathematical entity than a measurable quantity for a rock mass.

Numerical or analytical methods are employed to evaluate it for

use in the stability criterion.

Figure 3 illustrates the behavior of the local mine stiffness

for different mine layouts. This hypothetical example consists

of an array of long narrow openings separated by similar pillars.

An opening width to pillar width of 3 is assumed, implying

75% extraction. As the number of pillars increases from 3 to

15, stress concentration on the central pillar approaches its

theoretical maximum of 4, and the local mine stiffness

decreases as the panel widens. Local mine stiffness decreases

as the extraction ratio increases. At sufficient panel width and

high enough extraction, local mine stiffness decreases to zero,

which is the worst possible condition for failure stability since

it corresponds to pure dead-weight loading. If failure occurs,

its nature is unstable and possibly violent.

An expression for local mine stiffness is

where )P ' change in force,

)D ' change in displacement,

Su ' unperturbed stress,

Sp ' perturbed stress,

Du ' unperturbed displacements,

Dp ' perturbed displacements,

and A ' element area.

This expression is easily implemented into boundaryelement programs such as MULSIM/NL [Zipf 1992a,b; 1996],

LAMODEL [Heasley 1997, 1998], and similar programs.

Changes in stress and displacement are noted between adjacent

mining steps, i.e., the "unperturbed" and "perturbed" state. By

way of example, to compute the local mine stiffness associated

with a pillar, first stresses and displacements are calculated at

each element in the model in the usual way, giving the so-called

unperturbed stresses and displacements. The pillar is then

removed and all of the stresses and displacements are

recomputed, giving the so-called perturbed stresses and

displacements. In this case, Sp

 is identically zero. Local mine

stiffness KLMS is then calculated with the expression above.

Other numerical models can also be used to calculate KLMS.

Recent studies of web pillar collapses in highwall mining

systems [Zipf, in press] used FLAC2

 to calculate local mine

stiffness. Two-dimensional models of the web pillar geometry

were used for the initial stress and displacement calculations.

All elements comprising one pillar were removed, and stresses

and displacements were recomputed. Sp

 is identically zero at

the mined-out pillar. Local mine stiffness for the pillar is then

evaluated for the pillar. When using FLAC, a simple FISH

function can be constructed to facilitate the numerical

computations.

2

Fast Langrangian Analysis of Continuum, Itasca Corp., Minneapolis, MN.
185

 Figure 3.CStress concentration factor versus number of panel pillars showing behavior of local mine stiffness

as panel width increases.

POSTFAILURE STIFFNESS OF COAL PILLARS

In addition to the local mine stiffness parameter, Salamon's

stability criterion also depends on the postfailure pillar stiffness,

KP

, which is the tangent to the downward sloping portion of the

complete load-deformation curves shown in figure 1. Jaeger

and Cook [1979] discuss the many variables that affect the

shape of the load convergence curve for a laboratory specimen,

such as confining pressure, temperature, and loading rate. For

many mining engineering problems of practical interest, the

width-to-height (w/h) ratio of the test specimen is of primary

interest. Figure 4 from Das [1986] shows how the magnitude

of peak strength, slope of the postfailure portion of the stressstrain curve, and magnitude of the residual strength changes as

w/h increases for tests on Indian coal specimens. Seedsman

and Hornby [1991] obtained similar results for Australian coal

specimens. Peak strength increases with w/h, and various wellknown empirical coal strength formulas reflect this behavior

[Mark and Iannacchione 1992]. At low w/h, the postfailure

portion of the stress-strain curve slopes downward, and the

specimen exhibits strain-softening behavior. Postfailure

modulus increases with w/h; at a ratio of about 8, it is zero,

which means that the specimen exhibits elastic-plastic behavior.

Beyond a w/h of about 8, the postfailure modulus is positive

and the specimen exhibits strain-hardening behavior.

Full-scale coal pillars behave similarly to laboratory test

specimens; however, few studies have actually measured the

complete stress-strain curve for pillars over a wide range of

w/h. Wagner [1974], Bieniawski and Vogler [1970], and van

Heerden [1975] conducted tests in the Republic of South

Africa. Skelly et al. [1977] and more recently Maleki [1992]

provide limited data for U.S. coal. Figure 5 summarizes the

measurements of postfailure modulus for the full-scale coal

pillars discussed above. The laboratory data shown in figure 4
186

 Figure 4.CComplete stress-strain curves for Indian coal

specimens showing increasing residual strength and postfailure

modulus with increasing w/h (after Das [1986]).

 Figure 5.CSummary of postfailure modulus data for full-scale coal pillars and laboratory specimens. Also shown is

proposed approximate equation for Ep

.

and the field data exhibit an upward trend as w/h increases,

although the laboratory data show better definition. The

laboratory postfailure modulus becomes positive at a w/h ratio

of about 8, whereas the pillar data become positive at about 4.

Based on these field data, an approximate relationship for

postfailure modulus of full-scale coal pillars is proposed as

EP

 (MPa) ' &1,750 (w/h)&1 % 437.

Assuming a unit width for the pillar, the postfailure stiffness is

related to the postfailure modulus as

KP ' EP

 (w/h)

or

KP ' (MN/m) ' &1,750 % 437 (w/h).

As shown in figure 5, the simple relation for EP

 decreases

monotonically and becomes positive at a w/h of 4. The

proposed relationship is not based on rigorous regression

analysis. It is a simple, easy-to-remember equation that fits the

general trend of the data.
187

Figure 6.CFLAC models of pillar-floor system for increasing pillar width and w/h.

POSTFAILURE STIFFNESS OF METAL/NONMETAL PILLARS

In comparison to coal, very little data exist for the postfailure

behavior of pillars in various metal/nonmetal mines. Direct

measurements of the complete stress-strain behavior of actual

pillars are difficult, very expensive to conduct, and often simply

not practical. Laboratory tests on specimens with various w/h

can provide many useful insights similar to the coal data shown

previously. Numerical methods seem to be the only recourse to

estimate the complete load-deformation behavior of full-scale

pillars where real data are still lacking. Work by Iannacchione

[1990] in coal pillars and Ferriter et al. [1996] in trona pillars

provides examples of numerical approaches to estimating KP

.

Ferriter et al. [1996] used FLAC to calculate the complete

load-deformation behavior of the pillar-floor system in a trona

mine. The objective for this modeling effort was to estimate

postfailure stiffness of the pillar-floor system for a variety of

pillar w/h ratios. Figure 6 shows the basic models considered.

Each contained the same sequence of strong shale, trona, oil

shale, and weak mudstone. A strain-softening material model

was employed for these layers.

Figure 7 shows the computed rock movement after considerable deformation has occurred. The computed failure

involving the pillar resembles a classic circular arc. The

computed deformations agree qualitatively with observations;

however, the model deformations are much smaller than those

observed in the field. The difference may arise because FLAC

uses a continuum formulation to model a failure process that

gradually becomes more and more discontinuous. Recognizing

this limitation, the model results only apply up to the onset of

failure and with caution a little beyond. Failure stability

assessment is therefore possible in the initial computed

postfailure regime.

The computations provide an estimate of the complete

stress-strain behavior of the overall pillar-floor system. Using

the "history" function within FLAC, the model recorded

average stress across the middle layer of the pillar and the

relative displacement between the top and bottom of the pillar

from which strain was computed. Figure 8 shows the effective

stress-strain curves determined for the pillar-floor system from

these four models. The initial postfailure portion of these

curves is an estimate of KP

 for use in ascertaining the failure

process nature, either stable or unstable, on the basis of the local

mine stiffness stability criterion.
188

Figure 7.CCalculated deformation of pillar-floor system.

Figure 8.CStress-strain behavior of pillar-floor for increasing pillar width and w/h.
189

 Figure 9.CUnstable case: (A), stress before pillar weakening, (B), convergence before pillar weakening, (C), stress after pillar

weakening, (D), convergence after pillar weakening. Light to dark gray indicates increasing magnitude of calculated vertical stress

and convergence.

USEFULNESS OF THE LOCAL MINE STIFFNESS STABILITY CRITERION

In practical mining engineering, we frequently want failure

to occur. Failure usually means that we are extracting as much

of a resource as practical. However, we want failure to occur

in a controlled manner so that no danger is presented to mining

personnel or equipment. The local mine stiffness stability

criterion governs the nature of the failure process—stable and

controlled or unstable and possibly violent. Field data in

conjunction with numerical modeling enable calculation of

local mine stiffness (KLMS), estimation of postfailure stiffness

(KP

), and thus evaluation of the local mine stiffness stability

criterion.

The stability criterion was implemented into the boundaryelement program MULSIM/NL and used to evaluate the nature

of the failure process [Zipf 1996; Chase et al. 1994]. The

following example shows results from two contrasting

numerical models. Depending on whether the criterion is

satisfied or violated, the stress and displacement calculations

with MULSIM/NL behave in vastly different manners.

Figure 9 shows an unstable case, which violates the local

mine stiffness stability criterion. In the initial model,

calculations for an array of pillars show that stresses are close

to peak strength and roof-to-floor convergence is still low. In
190

 Figure 10.CStable case: (A), stress before pillar weakening, (B), convergence before pillar weakening, (C), stress after pillar

weakening, (D), convergence after pillar weakening. Light to dark gray indicates increasing magnitude of calculated vertical

stress and convergence.

the next modeling step, several pillars are removed to simulate

mining or else initial pillar failure. This small change triggers

dramatic events in the model. Convergence throughout the

model increases dramatically, indicating that widespread failure

has occurred. A small disturbance or increment of mining

results in a much, much larger increment of failure in the

model.

Figure 10 shows a stable case, which satisfies the stability

criterion. As before, pillar stresses in the initial model are

everywhere near failure and convergence is low. In the next

step, additional pillars are removed, as before. However, in the

stable model, this significant change does not trigger

widespread failure. An increment of mining results in a more

or less equal increment of additional failure in the model.

The local mine stiffness stability criterion inspires three

different design approaches to control CPF in mines:

(1) containment, (2) prevention, and (3) full-extraction mining

[Zipf and Mark 1997]. In the containment approach, panel
191

pillars must satisfy a strength-type design criterion, but they

violate the stability criterion. Substantial barrier pillars

"contain" the spread of potential CPF that could start. In the

prevention approach, pillars must satisfy two design criteria—

one based on strength, the other based on stability. This more

demanding approach ensures that should pillar failure

commence, its nature is inherently stable. Finally, the fullextraction approach avoids the possibility of CPF altogether by

ensuring total closure of the opening (and surface subsidence)

upon completion of retreat mining.

SUMMARY AND RECOMMENDATIONS

Practical work to date with the local mine stiffness stability

criterion reveals both the promises and shortcomings of the

criterion in the effort to prevent catastrophic failures in mines.

Back-analysis of case histories in various mines demonstrates

the possibilities of using the criterion in predictive design to

decrease the risk of catastrophic collapse [Swanson and Boler

1995; Zipf 1996; Chase et al. 1994; Zipf, in press]. The tool

could have wide application in metal, nonmetal, and coal roomand-pillar mines, as well as other mining systems. However,

a larger database of properly back-analyzed case histories of

collapse-type failure is required. In addition to collapse-type

failures, the criterion could evaluate the nature of shear-type

failure and have applications in rock burst and coal mine bump

mitigation.

Practical calculations of the local mine stiffness (KLMS) term

in the stability criterion have been done using analytical

methods [Salamon 1970; 1989a,b] and, more recently,

numerical methods [Zipf, in press]. Major factors affecting

KLMS are rock mass modulus; mine geometry, including panel

and barrier pillar width; and the percentage extraction, i.e., the

overall amount of mining. Analytical and numerical KLMS

calculations done to date assume an elastic continuum and

neglect the presence of major discontinuities. The effect of

these discontinuities is certain to decrease KLMS; however, the

magnitude of these effects requires further numerical study. 

Other numerical approaches, such as discrete-element or

discontinuous deformation analysis, may provide useful insight

into the KLMS for practical mine design.

Better understanding of the postfailure behavior of mine

pillars requires additional effort. Experiments on full-scale

pillars are generally not practical; however, careful laboratory

and numerical studies could provide justifiable estimates of KP

for mine pillars. Tests in the laboratory should examine the

complete stress-strain behavior of various roof-pillar-floor

composites at a variety of w/h ratios. Other variables to

consider include the effect of horizontal discontinuities and

water in the rock mass. Laboratory experiments can provide the

necessary benchmark data for numerical studies that extrapolate

to the field.

This paper summarizes the status of practical evaluation of

the local mine stiffness stability criterion for prevention of

certain types of catastrophic ground failures in mines. Backanalyses of collapse case histories show that the stability

criterion can predict the possibility of these catastrophic

failures. Evaluating the criterion depends on numerical

computation of KLMS and limited knowledge of the postfailure

behavior of pillars. Further laboratory and numerical studies of

the input parameters KLMS and KP

 should increase our

confidence in predicting failure nature with the local mine

stiffness stability criterion.

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DHHS (NIOSH) Publication No. 99-114

June 1998

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