Wasatch Formation

Ohio Creek Member

Barren Member

Mancos Shale

Rollins Sandstone

Bowie Interbedded 

Shale and Sandstone

Paonia Interbedded Shale 

Sandstone and Siltstone

Interbedded Shale 

and Sandstone

Ground Stress in Mining (Part 2): 

Calibrating and Verifying Longwall Stress Models

NIOSH Mining Program Report of Investigations RI 9703
Report of Investigations 9703

Ground Stress in Mining (Part 2): Calibrating and Verifying Longwall Stress 

Models

Mark K. Larson, Douglas R. Tesarik, Jeffrey C. Johnson

DEPARTMENT OF HEALTH AND HUMAN SERVICES

Centers for Disease Control and Prevention

National Institute for Occupational Safety and Health

Office of Mine Safety and Health Research

Pittsburgh, PA • Spokane, WA

January 2020
This document is in the public domain and may be freely 

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Suggested Citation

NIOSH [2020]. Ground stress in mining (part 2): calibrating and verifying longwall stress models. By 

Larson MK, Tesarik DR, Johnson JC. WA: U.S. Department of Health and Human Services, Centers for 

Disease Control and Prevention, National Institute for Occupational Safety and Health, DHHS (NIOSH) 

Publication No. 2020-104. https://doi.org/10.26616/NIOSHPUB2020104.

DOI: https://doi.org/10.26616/NIOSHPUB2020104.

DHHS (NIOSH) Publication No. 2020-104

January 2020
Table of Contents

ABSTRACT...............................................................................................................1

INTRODUCTION......................................................................................................3

LITERATURE SURVEY ON MODEL CALIBRATION........................................7

CALIBRATION USING SCALE FACTORS.................................................................... 7

CALIBRATION TO EMPIRICAL RESULTS .................................................................. 8

CALIBRATION TO BOTH EMPIRICAL AND EXPERIMENTAL RESULTS ............. 9

CALIBRATION TO OTHER MEASUREMENTS AND OBSERVATIONS.................. 9

GENERAL PROCEDURE OF CALIBRATION OF MODELS ..................................... 10

CALIBRATION TO POST-PEAK STRENGTH BEHAVIOR....................................... 12

SUMMARY...................................................................................................................... 14

CASE STUDIES DESCRIPTION.......................................................................... 15

SITES................................................................................................................................ 15

OBSERVATIONS AND MEASUREMENTS................................................................. 24

CONVERTING THE MEASUREMENT OF DISTANCE TO FIRST

ARRIVAL OF ABUTMENT STRESS TO EQUIVALENT

LOAD TRANSFER DISTANCE ........................................................................... 25

MINE A ............................................................................................................................ 25

MINE B............................................................................................................................. 34

SUMMARY...................................................................................................................... 38

MODELING TOOLS.............................................................................................. 39

EMPIRICAL METHOD................................................................................................... 39

THE LAMODEL CODE .................................................................................................. 41

MULSIMNL/LARGE....................................................................................................... 42

THE FINITE DIFFERENCE CODE FLAC3D................................................................. 43

INTERCHANGING TOOLS FOR VARIOUS MODELING STEPS ............................. 52

CALIBRATION PROCEDURES........................................................................... 52

EMPIRICAL METHOD CALIBRATION....................................................................... 54

LAMODEL CALIBRATION........................................................................................... 55

MULSIMNL/LARGE CALIBRATION........................................................................... 58

FLAC3D METHOD CALIBRATION ............................................................................... 67

MULSIMNL/LARGE WITH COAL AND FLOOR PROPERTIES FROM

FLAC3D PILLAR MODEL CALIBRATION................................................................... 83

SUMMARY OF CALIBRATION........................................................................ 110

CONCLUSIONS AND RECOMMENDATIONS ............................................... 111
ACKNOWLEDGMENTS..................................................................................... 113

REFERENCES...................................................................................................... 114

APPENDIX A: MULSIMNL/LARGE FILE FORMAT AND

VERIFICATION PROBLEMS............................................................................. 125

SUMMARY.................................................................................................................... 125

BACKGROUND ............................................................................................................ 125

CHANGES IN FEATURES ........................................................................................... 126

POSSIBLE FUTURE CAPABILITIES.......................................................................... 127

INPUT FILE FORMAT.................................................................................................. 127

VERIFICATION PROBLEMS ...................................................................................... 130

CONCLUSION............................................................................................................... 142

REFERENCES FOR APPENDIX A.............................................................................. 143

LISTING OF VERIFICATION PROBLEM INPUT FILE CONTENTS...................... 144

APPENDIX B: VISUAL BASIC MACROS FOR MICROSOFT EXCEL

TO CONVERT FINE ELEMENT MATERIAL CODES TO BLOCK

MATERIAL CODES............................................................................................ 157

SUMMARY.................................................................................................................... 157

BACKGROUND ............................................................................................................ 157

CONSTRUCTION OF MATERIAL CODES FOR LAMODEL .................................. 157

CONSTRUCTION OF MATERIAL CODES FOR MULSIMNL/LARGE .................. 158

LISTING OF THE EXCEL MACROS .......................................................................... 161

REFERENCES FOR APPENDIX B .............................................................................. 167

APPENDIX C: DISTRIBUTED MODELING OF LONGWALL PANELS: 

EXPANDING OPTION........................................................................................ 169

SUMMARY.................................................................................................................... 169

BACKGROUND ............................................................................................................ 169

STRATEGY.................................................................................................................... 170

PILLARS AND PANELS .............................................................................................. 171

APPLICATION OF OVERBURDEN STRESS............................................................. 181

PROGRAM MODIFICATIONS—LAMODEL............................................................. 182

PROGRAM MODIFICATIONS—FLAC3D................................................................... 184

PROGRAM MODIFICATIONS—LONGWALL MODELING ENVIRONMENT..... 191

CONCLUSIONS............................................................................................................. 192

REFERENCES FOR APPENDIX C .............................................................................. 193

APPENDIX D: PILLAR STRENGTH EQUATIONS......................................... 197

SUMMARY.................................................................................................................... 197
BACKGROUND ............................................................................................................ 197

MODELS ........................................................................................................................ 198

ASSUMPTIONS............................................................................................................. 203

NUMERICAL IMPLEMENTATION............................................................................ 204

CONCLUSIONS AND RECOMMENDATIONS ......................................................... 208

REFERENCES FOR APPENDIX D.............................................................................. 209

APPENDIX E: GROUND CONDITION RATINGS VERSUS

MODEL OUTPUT................................................................................................ 211

SUMMARY.................................................................................................................... 211

BACKGROUND ............................................................................................................ 211

DESCRIPTION............................................................................................................... 211

CONCLUSION............................................................................................................... 219

REFERENCES FOR APPENDIX E .............................................................................. 220

APPENDIX F: BOREHOLE PRESSURE CELL CALIBRATION ISSUES...... 221

SUMMARY.................................................................................................................... 221

BACKGROUND ............................................................................................................ 221

LU METHOD ................................................................................................................. 224

BABCOCK METHOD ................................................................................................... 225

APPLICATION OF CALIBRATION METHODS TO BPC DATA AT MINE A ....... 226

MODELED STRESS TRANSFER WITH AND WITHOUT GOB.............................. 227

ADJUSTMENTS............................................................................................................ 230

CONCLUSIONS............................................................................................................. 234

RECOMMENDATIONS................................................................................................ 234

REFERENCES FOR APPENDIX F............................................................................... 235

APPENDIX G: FIVE-POINT STRESS-STRAIN MATERIAL MODEL 

IMPLEMENTED IN MULSIMNL/LARGE........................................................ 237

SUMMARY.................................................................................................................... 237

BACKGROUND—NEED FOR FIVE-POINT MATERIAL MODEL......................... 237

VERIFICATION PROBLEMS ...................................................................................... 239

ELASTIC PROBLEM .................................................................................................... 240

MARK-BIENIAWSKI SOFTENING PROBLEM ........................................................ 242

CONCLUSION............................................................................................................... 243

REFERENCES FOR APPENDIX G.............................................................................. 244

INPUT FILES CONTENTS LISTING FOR VERIFICATION PROBLEMS............... 245
Figures

Figure 1. Engineering wheel of design that illustrates the relationship between

each step of the design process and the implementation and reevaluation that

must take place after each step ................................................................................................4

Figure 2. Diagram of the model input and calibration process as described by 

Wiles.............................................................................................................................................10

Figure 3. Plots of experimental results of stress versus strain on coal according

to various width-to-height ratios...........................................................................................13

Figure 4. Complete axial stress-strain curves obtained in triaxial compression

tests on Tennessee Marble at various confining pressures.............................................13

Figure 5. Class I and class II post-peak strength behavior of rock illustrated in 

general plot of stress with strain............................................................................................14

Figure 6. A map of Mine A with overlain mapped and projected faulting ................17

Figure 7. Lithology of the area around Mine A and Mine B .........................................19

Figure 8. Idealized stratigraphic column adapted from Robeck and used for 

modeling in this report.............................................................................................................20

Figure 9. Mine B gate roads in the vicinity of the study site .........................................23

Figure 10. Loading profile in a vertical section at mid-panel of a conceptual

model of loading as a result of longwall mining...............................................................26

Figure 11. LaModel contours of stress increase resulting from panel mining ..........28

Figure 12. Conversion factors determined from LaModel’s calculated result ..........29

Figure 13. A Mulsim elastic model with reduced coal modulus near rib...................30

Figure 14. Piecewise linear conversion factor functions derived from the

Mulsim model for determining equivalent LTD at Mine A...........................................31

Figure 15. Contours of stress increase resulting from mining the B-13 Panel..........35

Figure 16. Piecewise linear conversion factor functions derived from Mulsim 

model for determining equivalent LTD at Mine B...........................................................36

Figure 17. Conceptualizations of the side abutment load, patterned after

King and Whittaker ..................................................................................................................39

Figure 18. FLAC3D model showing topography. ..............................................................44

Figure 19. Conceptual model of caving ..............................................................................48

Figure 20. Conceptual model of caving in longwall mining..........................................49

Figure 21. Example of a detailed model of half of a pillar showing strata as 

FLAC3D groups..........................................................................................................................51
Figure 22. Standard empirical stress profile for Mine A headgate geometry and 

empirical stress profile calibrated to measured load transfer distance ........................55

Figure 23. Contours of stress increase over prepanel-mining stress for case

of calibrated to the empirical standard..........................................................................57

Figure 24. Contours of stress increase over prepanel-mining stress for the

case of calibrated to LTD.................................................................................................58

Figure 25. Stress increase contour graph for MulsimNL/Large model of

Panel 1 of Mine A using Mark-Bieniawski 6.21-MPa (900-psi) strength model.....60

Figure 26. Pillar strengths versus pillar width-to-height ratio.......................................61

Figure 27. Strength by distance from the rib in a coal pillar for various pillar 

strength criteria shown in Figure 26.....................................................................................61

Figure 28. Stress increase contour graph for MulsimNL/Large model of Panel 1

of Mine A using Mark-Bieniawski 9.65-MPa (1,400-psi) strength model. ...............62

Figure 29. Stress increase contour graph for MulsimNL/Large model using

elastic seam material with the elastic modulus in the first and second rings of 

elements reduced to 60% and 80% of the full amount to simulate the effect of

some yielding near the ribs.....................................................................................................63

Figure 30. Measured and synthetic load transfer distance by borehole

pressure cell location................................................................................................................64

Figure 31. Contours of stress increase with respect to prepanel mining stress

of the B-12-Panel at Mine B. .................................................................................................66

Figure 32. Plan view of 1 North pillars and barrier pillar at outby site with 

locations of borehole pressure cells......................................................................................68

Figure 33. Plan view of 2 North pillars and barrier pillar at outby site with 

locations of borehole pressure cells......................................................................................68

Figure 34. Plan view of 1 North detailed pillar model with monitored

section “A” used in FLAC3D panel model equivalent element. ....................................71

Figure 35. Plan view of 2 North detailed pillar model with monitored

sections “A” and “B” used in FLAC3D panel model equivalent element. ..................71

Figure 36. Stress-versus-strain for a quarter section “A” of a 1 North coal

pillar model and calculated BPCs labeled NP1-3.............................................................73

Figure 37. Vertical stress calculated from measurements and models for BPC 

locations at the 1 North outby site, barrier pillar...............................................................74

Figure 38. Vertical stress calculated from measurements and models for BPCs in 2 

North, south pillar, north pillar, and next panel ................................................................78
Figure 39. Calculated vertical stress with FLAC3D versus measured vertical

stress (reduced with Babcock method) for 1 North pillars and barrier pillar ............82

Figure 40. Calculated vertical stress with FLAC3D versus measured vertical

stress (reduced with Babcock method) for 2 North pillars and Panel 2......................82

Figure 41. Experimental, re-referenced, and model curves showing average

pillar stress versus strain for width-to-height of 2.78 ......................................................84

Figure 42. FLAC3D zones for mine floor, coal seam, and mine roof...........................85

Figure 43. Average pillar strengths from numerical pillar model compared to 

Bieniawski’s pillar strength equation...................................................................................86

Figure 44. Mine floor property set domain based on floor heave observations........87

Figure 45. Average pillar strengths from FLAC3D pillar models and 

Holland-Gaddy equation.........................................................................................................89

Figure 46. Measured and Mulsim-calculated vertical stress in 1 North section .......91

Figure 47. Measured and Mulsim-calculated vertical stress in 2 North section .......94

Figure 48. Average laboratory properties for sandstone, mudstone, and shale

are shown with reference to the region of properties, producing observed

heave or no heave of the floor, along with scaled values to be used in

detailed pillar models.............................................................................................................101

Figure 49. Horizontal cross section of FLAC3D model at seam midheight

showing how finite difference zones are grouped into “Mulsim cells” ....................103

Figure 50. Stress versus strain extracted from cells representing

Rings 1, 2, 3, and 4 of the 2 North detailed pillar model..............................................104

Figure 51. Five-point strength versus strain curves used to represent such

curves extracted from detailed pillar model of 1 North pillars....................................106

Figure 52. Five-point strength versus strain curves used to represent such

curves extracted from detailed pillar model of 2 North pillars....................................107

Figure 53. Five-point strength-versus-strain curves for three rings representing

1 North pillar behavior shown for comparison with Mark-Bieniawski curves

for a 6.21 MPa (900 psi) coal...............................................................................................108

Figure 54. Contours of stress increase with respect to prepanel state with 

MulsimNL/Large model using FLAC3D-extracted cell curves....................................109

Figure 55. Vertical seam stress profile calculated at midpanel of Panel 1 from

gob at headgate, through the next panel to be mined, and passing through the

next headgate and beyond.....................................................................................................110

Figure A1. Example of five-point strength law...............................................................127
Figure A2. Contours of vertical stress and closure of results calculated with 

MulsimNL/Large for longwall example from Zipf........................................................131

Figure A3. Longwall example—results of vertical stresses and closure 

displacements around headgate during mining step 2 ...................................................132

Figure A4. Cross-sectional profiles of stresses and closures calculated with 

MulsimNL/Large for longwall example from Zipf........................................................133

Figure A5. Longwall example—normal stresses along cross section just

ahead of face during mining step 2. Stresses are in psi.................................................134

Figure A6. Longwall example—normal closures along cross section just

behind face during mining step 2........................................................................................135

Figure A7. Contours of normal stresses as calculated by MulsimNL/Large for 

multiple-seam example in Zipf............................................................................................136

Figure A8. Multiple-seam mining example—normal stresses....................................137

Figure A9. Contours of normal closures as calculated by MulsimNL/Large for 

multiple-seam example in Zipf............................................................................................138

Figure A10. Multiple-seam mining example—normal closures.................................139

Figure A11. Contours of normal stress and normal closure as calculated by 

MulsimNL/Large for the random pillar example in Zipf..............................................140

Figure A12. Random room-and-pillar mining example—normal stresses and 

normal closures during mining step 2................................................................................141

Figure B1. Portion of spreadsheet where conversion to average coarse material 

code was calculated................................................................................................................160

Figure C1. Diagram showing relationship between tools, categories of their

use and their scales. ................................................................................................................170

Figure C2. Plan view of LaModel pillar showing cells.................................................171

Figure C3. Typical load deformation curve defined for a pillar cell in LaModel ..172

Figure C4. Type of element by location in plan view....................................................174

Figure C5. Average pillar strength according to the Bieniawski and Vesić 

formulas, showing how both might be used together to limit pillar strength ..........175

Figure C6. Diagram illustrating linkages between the pillar model and

the panel model........................................................................................................................176

Figure C7. Example showing how synthetic borehole pressure cell measurements 

generated by a model might be compared to actual measurements ...........................179

Figure C8. Example of synthetic borehole pressure cell measurements with

average pillar strain as extracted from a FLAC3D detailed model of a pillar..........180 
Figure C9. Example showing synthetic borehole pressure cell measurements 

generated from LaModel calculations ...............................................................................181

Figure C10. Input files and general content list of each for the topographic

mesh generator.........................................................................................................................185

Figure C11. FLAC3D model of area around a western U.S. coal mine as 

generated by the authors' topographic mesh generator..................................................186

Figure C12. Vertical section of equivalent column horizon, extracted from

part of detailed column model .............................................................................................187

Figure C13. Typical relative curves needed for determination of a detailed 

response that inputs to an equivalent element..................................................................188

Figure C14. Graph showing the example relative curves obtained in the 

progression of the determination of cohesion vs. seam-lumped column

plastic strain..............................................................................................................................189

Figure D1. Normalized pillar strength versus pillar width-to-height ratio, 

augmented by Tesarik et al...................................................................................................198

Figure D2. Pillar average vertical failure stress at failure load for

constant formulation...............................................................................................................199

Figure D3. Strength variation over the pillar...................................................................200

Figure D4. Strength variation over the pillar for the Holland-Gaddy

pillar equation ..........................................................................................................................201

Figure D5. Strength variation over pillar for Maleki confinement equation ...........202

Figure D6. Plan view of the failure stress distribution of a square coal pillar 

subdivided into eight pieces.................................................................................................203

Figure D7. Bieniawski variable strength as a function of distance from the rib.....205

Figure D8. Variable strength as a function of distance from the rib for an

example using the Holland-Gaddy pillar strength equation.........................................207

Figure D9. Maleki variable strength as a function of distance from the rib

with confined control strength plotted as circles and structure control

strength plotted as boxes.......................................................................................................208

Figure E1. Ground condition ratings vs. closure calculated by LaModel using 

default parameters for rock mass stiffness and gob stiffness with coal having a 

uniaxial compressive strength of 6.21 MPa (900 psi) and a distributed strength 

according to the Mark-Bieniawski criterion.....................................................................213

Figure E2. Ground condition ratings versus closure calculated by LaModel using 

rock mass stiffness calibrated for measured LTD and default gob stiffness with 
coal having a uniaxial compressive strength of 6.21 MPa (900 psi) and a 

distributed strength according to the Mark-Bieniawski criterion ...............................214

Figure E3. Ground condition ratings versus closure calculated by Mulsim using 

best-guess parameters for rock mass stiffness and default gob stiffness as 

calculated by LamPre assuming coal having a uniaxial compressive strength

of 6.21 MPa (900 psi) and a distributed strength according to the

Mark-Bieniawski criterion....................................................................................................215

Figure E4. Largest ground condition rating of floor, rib, or roof vs. closure 

calculated by Mulsim using best-guess parameters for rock mass stiffness and 

default gob stiffness as calculated by LamPre assuming coal having a uniaxial 

compressive strength of 6.21 MPa (900 psi) and a distributed strength

according to the Mark-Bieniawski criterion.....................................................................216

Figure E5. Ground condition ratings versus closure calculated by Mulsim

using best-guess parameters for rock mass stiffness and default gob stiffness

as calculated by LamPre assuming empirical conditions..............................................217

Figure E6. Ground condition ratings versus closure calculated by Mulsim

using best-guess parameters for rock mass stiffness and default gob stiffness

as calculated by LamPre assuming empirical conditions..............................................218

Figure E7. Ground condition ratings versus closure calculated by Mulsim

using best-guess parameters for rock mass stiffness and default gob stiffness

as calculated by LamPre assuming empirical conditions..............................................219

Figure F1. The borehole pressure cell (BPC) K-factor determined with a finite 

element model of a coal having Young's modulus of 1.103 GPa (160,000 psi).....223

Figure F2. BPC stress change measurements compared to MulsimNL/Large

stress change calculations at the 1 North outby site when face was inby the 

instrument line by several approximate distances ..........................................................228

Figure F3. BPC stress change measurements compared to MulsimNL/Large

stress change calculations at the 2 North outby site when face was inby the 

instrument line by several approximate distances ..........................................................229

Figure F4. Target and fitted curve for deterioration of Young's modulus of coal

to simulate the effect of coal deterioration on the response of the instrument........231

Figure F5. Recalculated BPC stress change measurements (by modifying a 

nonlinearity constant, and by Young’s modulus softening) compared to 

MulsimNL/Large stress change calculations at the 1 North outby site when

face was inby the instrument line by several approximate distances.........................232

Figure F6. Recalculated BPC stress change measurements (by modifying a 

nonlinearity constant, and by Young’s modulus softening) compared to 
MulsimNL/Large stress change calculations at the 2 North outby site when

face was inby the instrument line by several approximate distances.........................233

Figure G1. LTD determined from BPC pressure histories (measured) and

from interpolation of model results....................................................................................238

Figure G2. Example of five-point material strength model .........................................239

Figure G3. Material codes for mining step 1 of example model. ...............................240

Figure G4. Material codes for mining step 2 of example model ................................240

Figure G5. Differences in stress at mining step 1 for elastic problem ......................241

Figure G6. Differences in stress at mining step 2 for elastic problem ......................242
Tables

Table 1. Gate road geometry at Mine A.................................................................. 17

Table 2. Panel geometry at Mine A ........................................................................ 18

Table 3. Strata members of idealized stratigraphic column with thickness,

density, and elastic properties................................................................................. 21

Table 4. Strata members of idealized stratigraphic column with

strength properties................................................................................................... 22

Table 5. Groups of strata that were combined in FLAC3D models because a 

member or members had thickness that was too small for modeling purposes...... 22

Table 6. Gate road geometry at Mine B.................................................................. 24

Table 7. Panel geometry at Mine B......................................................................... 24

Table 8. BPC data from the 1 north outby site ....................................................... 32

Table 9. BPC data from the 2 north outby site ....................................................... 32

Table 10. List of equivalent LTDs determined from BPCs for 1 north and

2 north outby sites and the average LTD for both sites.......................................... 32

Table 11. Support Can data from the 2 north outby site......................................... 33

Table 12. Closure instrument data from entry 3 of 2 north of Mine A................... 33

Table 13. Data from instrument sites where ground condition surveys

were conducted........................................................................................................ 34

Table 14. Summary of LTD and relative sensitivity factors by method ................ 34

Table 15. Overburden depth at each instrument site............................................... 36

Table 16. List of BPCs at Mine B from which measurements of distance

could be determined from the gob at first arrival of abutment stress..................... 37

Table 17. List of results from the H21 outby instrumented support Can with 

determined equivalent LTD .................................................................................... 38

Table 18. List of results from the T34 closure data with determined

equivalent LTD ....................................................................................................... 38

Table 19. Elastic properties and Hoek-Brown constitutive equation

parameters for all coal used in detailed pillar models............................................. 69

Table 20. Material properties used in FLAC3D detailed pillar and panel models ... 69

Table 21. Subiquitous joint properties.................................................................... 69

Table 22. Elastic properties and Hoek-Brown constitutive equation

parameters used in models...................................................................................... 86
Table 23. Strata type and thickness for 1 north, listed in order of

strata member from top to bottom........................................................................... 98

Table 24. Strata type and thickness for 2 north, listed in order of

strata member from top to bottom........................................................................... 99

Table 25. Laboratory-scale material properties...................................................... 99

Table 26. Field-scale material properties for each major rock type ..................... 100

Table 27. Interface properties for 1 north pillar model......................................... 101

Table 28. Interface properties for 2 north pillar model......................................... 102

Table A1. Records, variables, and formats for MulsimNL/Large input files....... 128

Table A2. Material model parameters and material properties for array

EPROP in record 4 ................................................................................................ 129

Table A3. Material model parameters and material properties for

parameters 7 to 12 for model 7 for array EPROP in record 4 .............................. 129

Table C1. Average pillar maximum stress for a pillar with width-to-height

of 8, calculated by various methods...................................................................... 172

Table C2. Strength capacity in pillar by location ................................................. 174

Table C3. Various linkages between pillar and panel models.............................. 176

Table C4. Contents and format of the .tpo file or overburden stress file

that serves as input to LaModel ............................................................................ 182
ACRONYMS AND ABBREVIATIONS

ALPS Analysis of Longwall Pillar Stability

ARMPS Analysis of Retreat Mining Pillar Stability

BPC borehole pressure cell

CMRR Coal Mine Roof Rating

CPC cylindrical pressure cell

CWFS cohesion weakening, friction strengthening

FISH FLACish

FLAC Fast Lagrangian Analysis of Continua

FLAC3D Fast Lagrangian Analysis of Continua in Three Dimensions

LTD load transfer distance

MSHA Mine Safety and Health Administration

MMT Mass Mining Technology

NIOSH National Institute for Occupational Safety and Health

PIB Program Information Bulletin

Sh shale

Siltst siltstone

SS sandstone

SSMC strain-softening Mohr Coulomb

UCS unconfined compressive strength

UDEC Universal Distinct Element Code
UNIT OF MEASURE ABBREVIATIONS

cm centimeter or centimeters

° degree or degrees

ft foot or feet

GPa gigapascal or gigapascals

in inch or inches

kg kilogram or kilograms

kg/m3kilograms per meter cubed

km kilometer or kilometers

kPa kilopascal or kilopascals

ksi kilopounds per square inch

lb pound force

lb/ft3pound force per cubic foot

m meter or meters

mm millimeter or millimeters

MPa megapascal or megapascals

Pa pascal or pascals

psi pound per square inch or pounds per square inch

s second or seconds
1

Ground Stress in Mining: (Part 2): Calibrating and Verifying 

Longwall Stress Models

Mark K. Larson1, Douglas R. Tesarik2, Jeffrey C. Johnson3

1 Mining Engineer, Spokane Mining Research Division, NIOSH, Spokane, Washington.

2 Mechanical Engineer, Spokane Mining Research Division, NIOSH, Spokane, Washington (retired).

3 Mining Engineer, Spokane Mining Research Division, NIOSH, Spokane, Washington (retired).

Abstract

Researchers from the National Institute for Occupational Safety and Health (NIOSH) have 

been conducting ground control research with the goal of improving the stability of mine 

excavations to ensure the safety of mine workers. Numerical models are used to evaluate mine 

layout design to establish better procedures for predicting ground stress in mining to identify safe 

and unsafe working areas and escapeways. Current published guidance by the Mine Safety and 

Health Administration (MSHA) recommends an approach to calibrating models to observations, 

but it does not include recommendations for using in situ measurements to calibrate such models. 

A specific goal of this research is to explore and demonstrate procedures for calibrating 

numerical models to both observations and measurements.

In cooperation with two mining companies in the western United States, NIOSH researchers 

compiled large data sets of measurements and observations during mining. The purpose of these 

case studies was to determine ways to calibrate and verify models constructed with various 

modeling tools to measurements and observations, evaluate pillar strength formulas for 

applicability, identify deficiencies in the model calibration process, and recommend procedures 

for calibrating models so that longwall gate road design is improved and the margin between safe 

and unsafe designs is more clear. The data sets from these two mines were described in Part 1, 

Larson et al. [NIOSH 2020] (herein referred to as Ground Stress in Mining Part 1), of this twopart series of reports. Also in Part 1, a procedure was recommended to detect first arrival of 

mining-induced abutment stress ahead of the face with various instruments and with an 

observational survey of ground conditions. Taking such measurements is critical in the model 

calibration process.

In this report (Part 2), observations of floor heave and no floor heave were used to determine 

the general range of strength properties of the floors of the mine’s gate roads. Measurements of 

first arrival of mining-induced abutment stress were converted to equivalent side load transfer 

distances for use in calibrating models. Load transfer distance at Mine A was four times the 

result calculated with the empirical Peng and Chiang equation. The load transfer distance at 

Mine B could not be determined with the same precision, but its probable range is consistent 

with the load transfer distance measured at Mine A.

Calibration of rock mass stiffness or of stratigraphic moduli of elasticity was possible in 

these case studies using equivalent load transfer distance. However, for the boundary element 

code LaModel, a displacement-discontinuity program used in this analysis, the rock mass 

stiffness was so great that it was impossible to calibrate final gob stiffness and achieve 

reasonable gob loading. 

 
2

The boundary element code MULSIM/NL was modified to accommodate a larger number of 

elements in the mesh, and a stress-versus-strain material model defined by a piecewise linear 

function, called the five-point material model, was added and verified. This updated version of 

MULSIM/NL is named MulsimNL/Large. MulsimNL/Large and FLAC3D, the latter using an 

unverified and uncalibrated caving model, calculated gob loading that was in a reasonable range. 

However, better estimates of gob loading are necessary to proceed further with full model 

calibration.

Detailed pillar models using FLAC3D suggested that alternatives to the Mark-Bieniawski 

pillar strength model should be considered, especially for pillars with a width-to-height ratio 

greater than eight. A Holland-Gaddy equation fit to data from FLAC3D models consisting of 

average pillar strength versus pillar width-to-height ratio showed better ability to describe model 

results than did the Mark-Bieniawski strength equation. Experience with the detailed pillar 

models also suggests that stratigraphy should be modeled, wherever possible.

Borehole pressure cell (BPC) trends and comparison of model-calculated load transfer 

distance with equivalent load transfer distance determined from measurements of first arrival of 

mining-induced abutment stress strongly suggest that commonly used yield models were 

inadequate to describe seam material behavior near the ribs at Mine A. A MulsimNL/Large 

elastic model with the coal modulus reduced in the outer two rings to 60% and 80% of full value, 

respectively, provided the best match of “measured” versus model-calculated load transfer 

distance derived from stress increase at each BPC site. In considering appropriate strength 

models that might sufficiently simulate this behavior, measurements indicate that ribs are 

sometimes able to take much more stress than that calculated using most common yield strengths 

models, suggesting that strain-hardening might be an important part of the coal pillar behavior 

near pillar ribs.

Observations in these two case studies (Mines A and B) suggest that geologic structure 

changes, not represented in the models, were important for predicting stress and instability of 

ground. Observations suggest that prior knowledge of structure change and individual structure 

properties would be necessary to adequately simulate its effect on stresses and failures with a 

particular mining layout.
3

Introduction

In any design task, engineers usually follow a process that helps to determine and implement 

an optimized solution that meets the design objective. Mine layout design is no exception. Peck 

[1969, Figure 3a] discussed the observational method used by Terzaghi [1961] in soil mechanics 

and stated that, although it has pitfalls and limitations, it has great advantages in savings of time 

and money without sacrificing safety. However, he was clear that this method should not be used 

unless the designer has a plan of action for every unfavorable situation that is discovered. 

McMahon [1988] estimated a 36% risk of encountering serious geotechnical problems in 

construction or mining projects. He said that roughly two-thirds of these problems are the result 

of inadequate recognition of uncertainty in the geotechnical design analyses and around one-third 

are due to unknown geological conditions, use of the wrong geotechnical criteria, postinvestigation design changes, or human errors.

Bieniawski [1992] outlined design principles for rock mechanics and illustrated those 

principles with a flow chart. Stacey [2009] took Bieniawski’s flow chart of principles and 

illustrated them as a “wheel of design,” shown here as Figure 1. Besides illustrating the 

progression of steps in the design process, the relationship between each step and the last step of 

“implementation” is emphasized. These relationships mean that the process of design is very 

dynamic, with the necessity of rethinking each step as problems arise.

Defining the problem, determining requirements and constraints, minimizing the unknowns, 

and determining a conceptual model are very important. Solving the wrong problem, having 

inadequate requirements, not considering necessary constraints, or exerting insufficient effort to 

determine unknowns can result in a poor conceptual model. Models play an important part of this 

process, playing roles in steps 4 through 7 of Stacey’s wheel of design. Various modeling tools 

are based on different conceptual models, and the availability of specific modeling tools may 

also affect the choice of conceptual model.

Models may be used to evaluate designs, but only if the model adequately represents 

important mechanics and if the model is calibrated. Models not properly calibrated are useless in 

the design evaluation process.
4

Figure 1. Engineering wheel of design that illustrates the relationship

between each step of the design process and the implementation

and reevaluation that must take place after each step. After Stacey [2009].

In the aftermath of the Crandall Canyon Mine Disaster [MSHA 2008], MSHA issued 

Program Information Bulletin (PIB) 09–03 [MSHA 2009] to provide guidance on how to 

calibrate models used to evaluate underground mine layout designs when analysis beyond simple 

empirical and analytical methods is warranted or desired. The steps outlined in the PIB were 

based on earlier work of Karabin and Evanto [1994]. The short descriptions of these steps are:

1. Observe underground areas.

2. Estimate model parameters.

3. Model observed areas.
5

4. Verify model accuracy.

5. Establish threshold limits.

6. Model new configurations.

7. Evaluate new configurations.

8. Implement best alternative.

In the first of these steps, the modeler categorizes deterioration indexes with differing pillar 

sizes, panel configurations, and overburden heights to establish patterns. In the second step, 

model parameters are estimated from laboratory measurements and appropriately scaled. In the 

absence of measurements and site-specific information, general coal and rock properties 

(meaning published values from the literature or other reliable sources) may be used. In the third 

step, these estimated parameters are input to a model and results obtained. The fourth step is, 

perhaps, the most critical. Skiles and Stricklin [MSHA 2009] state that “each of the areas 

modeled must be closely examined to ensure that the results correlate with observed conditions.” 

While this statement is good counsel, the PIB does not mention correlation of model results with 

measurements of stress, load, displacement, or other possible quantities that shed light on the 

mechanics involved. Measurements and observations together better tell the story of important 

mechanisms and improve the calibration and verification of numerical models. Interestingly, in 

six and a half years since this PIB was published, not one mine layout plan has been submitted to 

MSHA where these steps were followed to calibrate and verify a numerical model that justifies 

the proposed design [Mark 2015].

The purpose of this report is to describe the research findings of a project entitled, 

“Calibration and Verification of Longwall Stress Models,” conducted over a 3.5-year period that 

outlines procedures to calibrate and verify numerical models to not only observations, but to 

selected kinds of measurements, principally stress or load change measurements that provide 

estimates of load transfer distance (LTD). The LTD is the distance to the side of the mined panel 

at which load increase resulting from mining is first detected. More information on LTD and its 

meaning is found later in this report. The results of this report and its companion report, 

including consequential guidelines, are intended to be applicable, at minimum, to calibrating 

models used to evaluate mine layout in any tabular deposit.

Although the calibration procedure of numerical models is extremely important, another 

important step precedes the use of a numerical model. The user needs to evaluate the mechanics 

of a site and decide which are important and then choose the appropriate tool that is capable of 

simulating those important mechanisms. For example, although finite element methods or finite 

difference methods might be more time-consuming, they might be capable of following an 

important failure mechanism in the roof or floor of a mine that cannot be captured by an elastic 

representation of the rock mass found in boundary element methods. Joints and faults may play 

such an important role that they cannot be well represented by a scaled continuum but must be 

more appropriately modeled directly. Such evaluation of important mechanics must take place 

before calibration proceeds. It has been shown that choice of modeling tool can limit the solution 

space available [Larson and Whyatt 2009b; 2010]. While all numerical models are simplified 

simulations of reality, critical mistakes can be made by not selecting the appropriate tool with 

important mechanisms. For example, Heasley found in his back analysis of the Crandall Canyon 

collapse with LaModel that one of the likely triggers of the seismic event was slip along a 

vertical fault soon after pillars started to be mined in retreat [Heasley 2008a, 2009a].

In Part 1 of this two-part report, measurements and observations were reported of maximum 

distance from the face at which first arrival of mining-induced stress increase is detected at two 
6

mine sites in the western United States. These data were obtained with various instruments and 

techniques, and subsequently, were analyzed. However, the distance from the face or gob to 

where first arrival of mining stress was detected is almost always in a direction outby the face 

and does not meet the definition of LTD by Peng and Chiang [1984]—i.e., the distance to the 

side of an excavated panel to the location where mining-induced stress is first detected. This 

definition also assumes that the measurement location is far from both the face and the start-up 

room. Therefore, these distances of first arrival reported in Part 1 still needed to be converted to 

an equivalent side-of-panel LTD.

In this report (Part 2), these distances at first arrival of abutment stress were converted to 

equivalent LTD at the side of the panels. The LTDs then were used to calibrate several models as 

much as was possible. A full calibration was not possible because of the lack of measurements 

on distribution of overpanel weight between the gob and the unmined coal. The results of several 

numerical modeling tools are compared, and these results are, in turn, compared to results from 

the empirical approach. Reference to the design process as illustrated in Figure 1 is repeated in 

this report as the results of the Mine A and Mine B case studies are presented. Because of 

lacking measured material properties that match observations of ground behavior, two alternative 

methods for calibrating numerical models are demonstrated. Research needed to facilitate or 

improve calibrations is recommended in the Conclusions and Recommendations section.

The subject of coal bumps or mining-induced seismic events and how to design and evaluate 

the risk of such events is an exhaustive subject in itself. Although such mining-induced events 

did occur at the mines studied, ranging from very small events to damaging events such that they 

are very much of concern, calibration of models that evaluate such risk depend on better 

understanding of post-peak-strength behavior. Such behavior was not measured and making such 

measurements was beyond the scope of this study. Instead, this study concentrates on general 

calibration of models that include elastic parameters, yielding, and peak strength. Proper 

evaluation of mining-induced seismic risk would require much more specific properties study, 

identification of probable mechanisms, and calibration of post-peak-strength behavior. Although 

some work has been done in determining likely mechanisms of mining-induced seismic events, 

such as mining-induced fault slip [Mark et al. 2012], the authors of this report have not dismissed 

other mechanisms as possible candidates. Such subject matter deserves careful and extensive 

treatment elsewhere.

In mine layout design, the engineer should start simply, with approaches such as using 

empirical methods. When such methods have historically indicated designs that have had 

success, these methods should be sufficient, except in cases where conditions significantly depart 

from standard conditions. If conditions warrant more investigation, modeling tools can assist 

with evaluation of conditions and mechanisms. Empirical tools are quick and provide a statistical 

approach with comparison against an extensive database. In cases where local conditions are 

highly variable or where they depart from assumptions of the empirical method, using techniques 

that more closely simulate the effects of stratigraphy or specific failure mechanisms are likely 

necessary to improve understanding to increase the chance of success and minimize risk. One 

example might be the work on pillar strength and design by Wilson [1972] and Wilson and 

Ashwin [1972] in which they describe the mechanics of pillars, including the concept of an inner 

core and confining failed material.

Before proceeding with the details of this study, a review of the literature on the calibration 

of numerical models is appropriate. Such a review will provide the reader with an understanding 

of successful numerical modeling calibration practices over the last 35 years.
7

Literature Survey on Model Calibration

Various modeling methods and modeling software might be used to evaluate mine layout 

design. For various reasons, boundary element methods, finite element methods, finite difference 

methods, discrete element methods, particle methods, or displacement discontinuity analysis 

methods might be used. Each method has its limitations, including the mechanisms that each can 

simulate. Moreover, each has limitations or ranges of solution space that can be accessed [Larson 

and Whyatt 2009a, 2009b; Larson and Whyatt 2010]. If an appropriate model is used for a 

specific case, the input parameters, such as the elastic and strength properties, need to be 

calibrated so that the model calculations output have relevance.

Models might be calibrated in several ways, including scaling properties between laboratory 

and field, scaling model calculations to empirical results, and scaling to experimental results or 

observations among others. The following sections detail the different methods.

Calibration Using Scale Factors

The material properties used for initial numerical models can be based on measured 

laboratory values of elastic parameters and strengths. However, these values need to be scaled to 

reflect the larger-scale behavior of the rock mass, which may have several joints, flaws, or other 

imperfections that weaken the rock mass [Heuze 1980]. Heuze stated that the majority of cases 

have a ratio between field and laboratory scale for modulus from 0.20 to 0.60.

One well-founded method is used and described by Pariseau et al. [1984], Pariseau et al. 

[1986], and by Pariseau et al. [USBM 1992d]. These authors describe using measurements with 

extensometers over a large scale, which are monitored as mining progresses. By comparing 

relative displacements between anchor locations as calculated by the model with those measured 

displacements, an average slope, determined by regression analysis, represents a reduction factor 

needed to adjust from laboratory-scale moduli to rock mass scale moduli and is represented by 

the equation: 

slope or strength reduction factor = rock mass moduli

laboratory moduli

(1)

assuming only small variation in conditions that affect scaling. As long as the anchor positions 

are in ground that remains linear or only slightly nonlinear, then this slope represents an average 

reduction factor for the elastic moduli in the model. In their case, Pariseau et al. [USBM 1992d]

reported an elastic reduction factor of 14% to 17%. The correlation coefficient, r2, in the 

reduction of elastic properties in this case was 0.75, which the authors deemed satisfactory. 

By preference, strength should be reduced independently of the elastic moduli. Pariseau et al. 

[USBM 1992d] stated that this should be done by determining extent of yield zones through 

measurement and observation and comparing with yield zones calculated by the model. They 

stated that “the usual indication of yielding is a relatively large increase in measured 

displacements compared with previous displacement changes and earlier stope cuts.” They also 

noted that some yielding may take the form of violent rock bursts. Models having strengths that 

are too high will not be able to produce the displacements that are associated with yielding.

However, these authors reported that none of the extensometers in their case were placed in a 

way to define the yield zones. Yielding took place elsewhere. Instead, they outlined two 
8

empirical rules or approaches that allow the user to estimate the strength reduction factor 

compared to the elastic moduli reduction factor:

First, the strain to failure is maintained constant under uniaxial compression. Then

εf = (

C0

E

) (2)

is a constant, where εf = strain at failure, C0 = unconfined compressive strength, and E = 

Young’s modulus. Thus, the strength scaling factor is equal to the elastic modulus scaling factor.

Second, the strain energy is constant at failure under uniaxial compression. According to this 

rule,

Ustrain = 

(C0

)

2

2E

(3)

is a constant, where Ustrain = strain energy density at failure. In their case, Pariseau et al. 

[USBM 1992d] selected an elastic scaling factor range of 0.14 to 0.17 but found that using the 

same reduction factor for strength and modulus provided too much yielding. Therefore, they 

used the second rule, so that if the elastic modulus reduction factor were 0.16, the strength 

reduction factor would be 0.40 (= √0.16). Thus, the range of the strength reduction factor was 

0.37 to 0.41.

Using the same rule in a later study, Pariseau et al. [USBM 1996] adjusted the elastic 

modulus and strength reduction factors to 0.25 and 0.50, respectively. They also justified this 

strength factor because of the amount of yielding inferred from a calibrated two-dimensional 

model done by Pariseau et al. [USBM 1995] and a simple analytical relationship between twoand three-dimensional back analyses of long cylindrical and spherical excavations. Later, 

Pariseau et al. [2012] maintained these reduction factor amounts for a study associated with the 

Deep Underground Science and Engineering Laboratory (DUSEL) project.

Zipf [2006] started with laboratory point-load tests for strength, then reduced to rock-mass 

scale for model by applying a 0.56 fraction, per Gale and Tarrant [1997]. He made major, but 

reasonable assumptions for input parameters for the strain-softening model in FLAC.

Gale et al. [2004] used laboratory tests, scaled by 0.58. This scaling factor was obtained by 

extrapolating to a 1-m diameter specimen using an equation fitted to compiled data by Hoek and 

Brown [1980] for relating strength of specimens having diameters between 10 mm and 200 mm 

[Gale 2016]. The 1-m size was considered representative of the rock mass scale. Esterhuizen et 

al. [2010b] justified using the 0.58 scaling factor in the same way. Gale et al. [2004] inferred 

modulus from stress measurement strains obtained by Dolinar [2003]. The focus of Gale et al. 

[2004] was the study of interaction between roof rock and bolts on a small scale, as opposed to a 

mine-wide scale.

Calibration to Empirical Results

Esterhuizen et al. [2010b] used FLAC3D. They took pillar stress measurements from field 

studies in the U.S., with peak stress about 5 m into the pillar. They numerically tested the 

sensitivity of interface properties and considered the experience of other researchers with 

interface properties. They calibrated Hoek-Brown strength parameters to match the Bieniawski 

strength equation. The results for cases with pillar width-to-height ratios between 3 and 8 fit 

reasonably with the final input parameter set. They represented gob using [Salamon's1990]

equation for caved material:
9

σ = 

a ε

b− ε

, (4)

where σ = vertical stress on the gob,

ε = vertical strain, and 

a and b are empirically derived parameters.

This equation was fit to tests of Pappas and Mark [USBM 1993] on scaled gob material of 

shale, weak sandstone, and strong sandstone.

In modeling 670 cases of the influence of support, Esterhuizen and Tulu [2015] calibrated 

their models against the results of empirically based Analysis of Roof Bolt Stability (ARBS) 

[Mark et al. 2001], which is based on cases in 37 mines in the eastern U.S.

Calibration to Both Empirical and Experimental Results

Ozbay and Badr [2010] used strain softening to predict the behavior of chain pillars in a 

longwall gate road with a FLAC3D model. They calibrated a model of a pillar loaded against 

empirical assumptions. They adjusted parameters to fit their model to three in-situ pillardeformation tests by Wagner [1974], including fitting to post-peak behavior. Afterward, they 

applied these results to a deep, two-entry longwall mine using yielding chain pillars. In 

examining verification of their model, they compared model results with BPC measurements in 

the pillars. Stress relief in the pillars as indicated with the BPCs was much earlier than that 

predicted by the model; however, the longwall face position at the onset of maximum stress was 

within a few meters of that predicted by the model. Although rates of stress reduction compared 

well, amounts of stress reduction differed, which fact is not surprising, given the experience at 

Mine A by NIOSH. Ozbay and Badr [2010] recommended further studies, such as looking at 

dynamic failures with discrete element models to analyze failure mechanisms. In other words, 

their present model might be useful in predicting risk, but more detailed models that can simulate 

bump mechanisms are needed.

Calibration to Other Measurements and Observations

Wiles [2007] advocated model calibration by using back analysis of consistent mine behavior 

and correlating model results with mine results. Figure 2 (Wiles’ Figure 6) illustrates the process 

of considering inputs to the model and comparing the model’s predictions with consistent 

observations and measurements in the mine and then using coefficient of variation for estimating 

the reliability of the model to predict observed behavior. In this process Wiles gave specific 

examples of using pillar failure, microseismicity, and structurally controlled overbreak to 

calibrate and refine models.
10

Figure 2. Diagram of the model input and calibration

process as described by Wiles. After Wiles [2007].

Andrieux et al. [2008] advocated using microseismicity to calibrate strength of materials in a 

model, especially the post-peak softening part of a strength-strain curve. In their approach, they 

advocated: (1) carefully selecting seismic events that are the result of stress increase from mining 

to be part of a comparison database, (2) including relevant geologic horizons in the model, and 

(3) identifying mining steps that have caused the largest and clearest seismic reactions. When 

this was performed in their case study, they compared extent of zone yielding with location of 

these seismic events. After several iterations, they were able to determine the strength curve, 

including the softening portion of the curve so that extent of yielding matched location of 

seismic events.

Crockford et al. [2015] determined depth of yielding from a seismic array, drilling cores, and 

observations from site visits. They tested several models: Hoek-Brown, strong strain-softening 

Mohr Coulomb (SSMC), and cohesion weakening, friction strengthening (CWFS). The SSMC 

model fit results the best. In order to optimize the parameter fit, three more models were run: A 

stronger SSMC model, a strong brittle SSMC model, and a CWFS model with a higher initial 

friction. The stronger SSMC model provided the best fit to the field data.

General Procedure of Calibration of Models

Displacement discontinuity codes require a different procedure for calibration because of 

their simpler framework. However, the same fundamental procedure can be used to calibrate 
11

codes based on other modeling methods, such as finite element method, finite difference method, 

or even discrete element method. Referring to his code, LaModel [Heasley 2007; 2010 for later

version], Heasley [2008b] identified that the following items are interrelated and need to be 

calibrated in the following order:

1. Rock mass stiffness

2. Gob stiffness

3. Coal strength

Heasley noted that the interrelationship between these items usually requires that multiple 

iterations of these steps be performed before the model is adequately calibrated. In the absence of 

measurements and observations, Heasley [2008b] recommended calibrating to the empirical 

database criterion established by Mark [1987; USBM 1990; Mark 1992] for the Analysis for 

Longwall Pillar Stability (ALPS) program, and later, the Analysis for Retreat Mining Pillar 

Stability (ARMPS) program [Mark and Chase 1997]. The empirical criterion relies on the 

equation for the distance from the mined panel that the load is transferred to the abutment as 

determined by Peng and Chiang [1984], based on cases in the eastern United States:

D1.0 = 9.3√H (5)

where D1.0 = distance from the gob in ft within which is found 100% of the portion of the 

overpanel weight that is transferred to the abutment as a result of mining, and

H = height in ft of the overburden.

Calibrating to D1.0 is impossible for this class of codes because the load transferred in the 

model solution is approaching zero but is theoretically still nonzero at an infinite distance from 

the gob. Heasley recommended calibrating to D0.9, which is the distance from the gob within 

which 90% of the transferred overpanel weight is located. Using Mark’s abutment loading 

inverse function [USBM 1990], D0.9 is approximately:

D0.9 = 5√H (6)

The procedure for calibrating gob stiffness is less straightforward due, in part, to there being 

few cases where actual gob loading has been measured or can be accurately estimated. In 

LaModel’s input software LamPre [Heasley 2010], the final gob stiffness is determined in an 

iterative two-dimensional scheme based on the empirically assumed amount of gob loading. To 

the knowledge of the authors of this report, only Maleki et al. [1984] have successively measured 

gob pressures in one case, which was accomplished with Gloetzl cells and is described later in 

this report. Others’ attempts to measure gob loading are discounted for reasons given later. 

Measuring gob load is very difficult in today’s longwall panels. However, opportunities to 

measure gob load arise if cross-panel entries are developed well in advance of the longwall face 

[Seymour et al. 1998]. A possible alternative would require expensive drilling in the floor across 

the panel and installation of an instrument in these boreholes. Currently, the authors of this report 

are not aware of a proven set of instruments that could be inserted in such long boreholes. 

Coal strength calibration is an area of study with much room for advancement. The empirical 

method of ALPS and ARMPS assumes a uniaxial compressive strength for coal of 6.21 MPa 

(900 psi). Strength increases with depth into the pillar because of confinement, depending on the 

pillar strength formula used—the Mark-Bieniawski formula in the case of ALPS and ARMPS 

[Mark 1999]. Improvement upon this assumption of coal strength might be made by 
12

measurements, observations, and using some of the techniques of authors previously mentioned 

[USBM 1992d; Wiles 2007; Andrieux et al. 2008].

Calibration to Post-peak Strength Behavior

It is beyond the scope of this paper to address calibration of post-peak behavior. Even so, 

such calibration is very important to predicting risk of mining-induced seismic events and, 

therefore, the literature is reviewed here. Such calibration can only happen indirectly—such as 

by comparing model results of deformation or yielding obtained with a set of post-peak 

parameters to measurements or observations of deformation or yielding—or by measuring such 

behavior in the laboratory and making assumptions about post-peak strength behavior on a larger 

scale. There have been many attempts to simulate it in the laboratory, but the attempts to 

calibrate models of field sites involving post-peak behavior are not extensive. Instead, here is 

only a very small sampling of papers about post-peak behavior and calibrating to it.

Several factors affect post-peak-strength behavior. Width-to-height ratio of samples has been 

shown to drastically affect residual strength levels, probably even more so than it affects peak 

strength (see Figure 3) [Das 1986] [Özbay 1989]. At low ratios of 0.5 or 1.0, a rock sample may 

be extremely brittle, losing all strength immediately. With increasing width-to-height ratio, the 

stress-strain curves of uniaxial tests begin to show residual strength, followed by ductile and 

strain hardening behavior. The degree of hardening may increase with increasing width-to-height 

ratio [Das 1986]. Özbay [1989] showed with several rock types that post-peak modulus is 

dependent on width-to-height ratio, also. Esterhuizen et al. [2010a] conducted numerical 

experiments on pillars calibrated to the Bieniawski pillar strength formula. The pillars began to 

strain harden if their width-to-height ratios were above 8.0. Small width-to-height pillar ratio has 

been associated with several massive pillar collapses that occurred in the U.S. [Chase et al. 

1994].

Confining pressure also has a similar effect in changing a rock sample’s behavior that might 

be brittle with no lateral confinement to ductile [Cook 1965; Wawersik and Fairhurst 1970; Price 

1979; Hakami 1988; Kumar et al. 2010] or even strain hardening [Bawden 2010] (see Figure 4). 

Class II behavior can be present for brittle material with unconfined testing [Wawersik and 

Fairhurst 1970] (see Figure 5). Confining pressure changes class II to class I behavior. Zhao 

[1994] conducted tests on Carmenellis granite with a geothermal testing system. The triaxial tests 

showed typical variation of post-peak behavior with confining pressure—that is, the elastic 

modulus remained constant, but the peak stress and associated strain increased with confining 

pressure as did the residual strength. They found that peak strength was decreased significantly 

by increased temperature. Mishra and Nie [2013] conducted unconfined testing using lateral 

strains as feedback for a closed-loop servo-hydraulic system. With such a system, they were able 

to follow class II behavior with no confinement. Coal samples from the Hiawatha seam showed 

class II behavior with no confinement and exhibited class I behavior with confinement. When 

confinement was 1,000 psi, this coal showed strain-hardening behavior. Tesarik et al. [2003]

measured stress change and dilation of pillars confined by backfill, with pillars mined 

sequentially. They calibrated a UTAH3 model to extensometer readings using the elasticperfectly plastic Drucker-Prager constitutive material model. The calibrated model showed postpeak hardening if there was confinement.
13

Figure 3. Plots of experimental results of stress versus strain on coal

according to various width-to-height ratios. After Das [1986, Figure 3a].

Lan et al. [2010] performed numerical tests with Universal Distinct Element Code (UDEC) 

[Itasca Consulting Group 2012] on simulated samples with grain-line structure. This type of 

model was used to simulate the microheterogeneity caused by elastic variation and contact 

stiffness anisotropy. The results showed that the compressive stress required to initiate the 

formation of macroscale dilation and strain localization is controlled by crack density.

Figure 4. Complete axial stress-strain curves obtained in triaxial compression tests

on Tennessee Marble at various confining pressures. After Wawersik and Fairhurst [1970].
14

Figure 5. Class I and class II post-peak strength behavior of rock illustrated in

general plot of stress with strain. After Wawersik and Fairhurst [1970].

Zhang et al. [2015] conducted numerical experiments on a synthetic rock mass specimen of 

particles. Various characteristics of joint sets were inserted into the specimen. Peak strength was 

dependent on orientation of the joints, with highest strength at orientations of 0° and 90°, and 

minimum strength at 45°. The peak strength also decreased with increasing joint size. Brittle 

post-peak behavior was observed in specimens having low persistence of joints. The post-peak 

behavior became more ductile when the joint sets were inclined or more persistent.

As mentioned earlier, Andrieux et al. [2008] were able to determine the strength curve, 

including the softening portion of the curve so that extent of yielding in the rock mass matched 

location of seismic events.

Jaiswal and Shrivastva [2009] developed a model for coal pillars, based on deterioration of 

some Hoek-Brown parameters and the dilatancy model of Alejano and Alonso [2005]. They 

calibrated their model to fit several cases of coal pillars in Indian mines, determining initial and 

residual values of the Hoek-Brown parameters among other material constants.

Li and Heasley [2015] used the concept of local mine stiffness [Salamon 1970] to calibrate 

post-peak behavior of coal that caused extensive bump damage in the Crandall Canyon Mine 

disaster [MSHA 2008].

Summary

Calibration of models can best be accomplished by adjusting key model inputs so that model 

calculations match measurements and observed behavior as much as possible. Laboratory 

measurements of elastic modulus and strength properties are a good start, with appropriate 
15

scaling applied. However, measurements and observations provide justification for further 

refinement of elastic properties, strength properties, gob properties, and possibly can be used to 

infer post-peak-strength behavior. In the cases with measurements described in Part 1 of this 

series of reports, these principles of calibration, with particular reference to the steps outlined by 

Heasley [2008b], will be followed to determine possible ways forward to calibrate numerical 

models.

Case Studies Description

Sites

Both case studies (Mines A and B) were conducted in western U.S. coal mines located close 

to each other and in an area of dramatic variability in topographic relief. They had similar 

geology, but were in different seams, and the range of overburden thickness for each mine was 

significantly different. For Mine A, the cover depth ranged from 405 m to 735 m (1,330 ft to 

2,410 ft) in the study area. For Mine B, the overburden ranged from 204 m to 354 m (670 ft to 

1,160 ft) in the area where the study was conducted. At Mine A, the 1 North outby 

instrumentation site had an average overburden of about 682.3 m (2,239 ft), while the 2 North 

outby instrumentation site averaged about 691.4 m (2,268 ft). The average overburden between 

these sites was 686.9 m (2,253.5 ft). At Mine B, the instrumentation sites had overburden 

ranging from 229 m (750 ft) to 337 m (1,105 ft). 

Ground Stress in Mining Part 1 described the geology of both Mine A and Mine B that will 

not be repeated here. However, a description of the geometry of the gate roads is important to 

this discussion. Figure 6 shows a map of the area of Mine A where the study was conducted, 

including the mining of Panel 1 and Panel 2. Panel 1 is the longwall panel between the 1 North 

and 2 North gate roads. Panel 2 is the panel between the 2 North and 3 North gate roads. The red 

boxes indicate the location of most of the installed instruments. The sites in each set of gate 

roads were differentiated with the names inby and outby. Thus, the instrumented sites were 

named the 1 North inby, 1 North outby, 2 North inby, and 2 North outby. The 3 North gate roads 

were under development during early mining of Panel 1. The 4 North gate roads and 5 North 

gate roads had not been developed at the time of this study.

Faulting intersected the gate roads in several locations, as shown in Figure 6. The location of 

these faults influenced the selection of the test sites, although the 2 North outby site was placed 

close to the fault intersecting the south pillar for practical reasons.

Table 1 lists geometric information of the pillars and entries in the 1 North and 2 North gate 

roads. Table 2 lists the dimensions of Panels 1 and 2. The width of the 2 North pillars was 

increased as a result of the development of a local, deep-cover Analysis of Longwall Pillar 

Stability [Mark 1987] database, determining a critical stability factor for the mine. Subsequent 

negotiations with MSHA resulted in approval of a pillar width about 14% larger than that 

required by the locally determined critical stability factor.

In fact, this increased pillar size did not prevent a mining-induced seismic event of 

magnitude 3.1 on the Richter scale that occurred on February 17, 2011, at 17:47 local time in the 

2 North gate roads. The location was somewhere between crosscuts 11 and 15.

Subsequently, the Panel 2 longwall face was advanced a short distance to approximately 

crosscut 15, and a new startup room was developed at crosscut 10. The longwall mining 
16

equipment was moved between March 25, 2011, and April 6, 2011, when longwall mining

resumed and continued until Panel 2 was completed.

For modeling purposes, the description of stratigraphy by Robeck [2005], whose graphical 

column is reproduced here as Figure 7, was adapted and idealized to that shown in Figure 8. 

Material properties from laboratory tests of core samples taken from the area were not available 

for these stratigraphic members. Therefore, best estimates of material properties listed in Tables 

3 and 4 were chosen on the following basis:

• Experience modeling generic cases that represent a typical Utah coal field 

stratigraphic column [Larson and Whyatt 2009b].

• General knowledge that the strata of western Colorado was less stiff and not as strong 

as the Utah strata.

• Experience of a contractor drilling in various seams in these mines that suggested the 

DU Seam, where Panels 1 and 2 were located, was weaker and slightly less stiff than 

the other seams.

• The values chosen were within the wide range of values suggested in the literature for 

the basic member types [Farmer 1968; Pariseau 2012; Goodman 1989; Blyth and de 

Freitas 1984; Sheorey 1997; Maleki et al. 2007; Vutukuri et al. 1974; Lama and 

Vutukuri 1978c, 1978b, 1978a].

No scaling of these initial estimates was performed to more closely represent rock mass scale 

other than to include ubiquitous joints in the FLAC3D [Itasca Consulting Group 2009] model. It 

was assumed that field scale was, at least in part, built in to these estimated amounts.
17

.

Figure 6. A map of Mine A with overlain mapped and projected faulting.

After Larson et al. [NIOSH 2019]. Blue lines indicate both mapped and

projected faults. Red boxes indicate location of main instrument sites in this study.

Table 1. Gate road geometry at Mine A

Item 1 North, m 1 North, ft 2 North, m*

2 North, ft*

Entry width 6.1 20 6.1 20

Crosscut width 6.1 20 6.1 20

Pillar width 22.3 73 51.8 170

Pillar length 54.9 180 54.9 180

Mining height used for 

models 3.4 11 3.4 11

*3 North geometry is the same as 2 North geometry.
18

Table 2. Panel geometry at Mine A

Item Panel 1, m Panel 1, ft Panel 2, m Panel 2, ft

Width* 245.4 805 257.7 845.6

Length* 2,128 6,980 2,225 7,300

*Panel width and length include half of adjacent entries.

The conceptual model of the stratigraphic column was developed for the code FLAC3D

because the idealized stratigraphy could be preserved. The idealized column was further 

simplified to optimize the FLAC3D model in the discussion that follows. The initial properties for 

the boundary element codes were determined from the column developed for FLAC3D.

Several strata members had thicknesses that were too small to model efficiently in a volumeelement code like FLAC3D. For that reason, these thin members were combined with adjacent 

thicker strata. Table 5 lists five groups of strata that were combined. All of these groups included 

thin coal seams that were lumped with thicker strata members. Material properties for the 

equivalent strata member were determined by thickness-weighted averaging. No interfaces were 

placed between or within strata members in FLAC3D models of this scale.

Initial Young’s modulus and Poisson’s ratio of the rock mass at Mine A for boundary 

element tools, described later, were determined by thickness-weighted averaging of Young’s 

moduli and Poisson’s ratios of the strata above the DU Seam using the average thickness of the 

overburden at the outby instrumentation sites. These same values were used as a starting point at 

Mine B because the weighted average of elastic parameters at that mine above the B Seam is not 

significantly different from that determined for Mine A.
19

Figure 7. Lithology of the area around Mine A and Mine B. Adapted from Robeck [2005].
20

Figure 8. Idealized stratigraphic column adapted from Robeck [2005]

(full lithology shown in Figure 7) and used for modeling in this report.
21

Table 3. Strata members of idealized stratigraphic column with thickness, density, and 

elastic properties

Strata Thickness, 

m

Thickness, 

ft

Young’s 

modulus, 

GPa

Young’s 

modulus, 

103 psi

Poisson’s 

ratio

Density, 

kg/m3

Density, 

lb/ft3

Wasatch Formation 152 500 16.2 2.350 0.291 2,595 162

Ohio Creek Member 122 400 16.2 2.350 0.291 2,595 162

Barren Member 366 1,200 16.9 2.450 0.277 2,595 162

F Seam 0.610 2 2.76 0.400 0.330 1,362 85

Upper Interbedded 

Sh*, SS†

24.4 80 13.8 2.000 0.326 2,595 162

E Seam 1.22 4 2.76 0.400 0.330 1,362 85

Paonia Interbedded 

Sh, SS, Siltst‡ 61.0 200 13.1 1.900 0.323 2,595 162

DU Seam 3.35 11 2.55 0.370 0.350 1,362 85

Paonia Interbedded 

SS, Sh, Siltst 24.4 80 20.2 2.930 0.293 2,595 162

DL Seam 1.22 4 2.55 0.370 0.350 1,362 85

Bowie Upper SS 12.2 40 27.6 4.000 0.230 2,595 162

Bowie Siltst 3.05 10 13.8 2.000 0.250 2,595 162

Bowie Middle SS 9.14 30 27.6 4.000 0.230 2,595 162

CU Seam 0.610 2 2.76 0.400 0.330 1,362 85

Upper Bowie Shale 3.05 10 10.3 1.500 0.350 2,595 162

Bowie Lower SS 15.2 50 27.6 4.000 0.230 2,595 162

CL_Seam 1.83 6 2.76 0.400 0.330 1,362 85

Bowie Interbedded 

Siltst, SS, Sh 7.62 25 14.9 2.160 0.269 2,595 162

BU Seam 6.10 20 2.76 0.400 0.330 1,362 85

Lower Bowie Shale 9.14 30 10.3 1.500 0.350 2,595 162

BL Seam 3.66 12 2.76 0.400 0.330 1,362 85

Bowie Interbedded 

Sh, SS 27.4 90 12.8 1.850 0.333 2,595 162

A Seam 1.22 4 2.76 0.400 0.330 1,362 85

Rollins Sandstone 42.7 140 27.6 4.000 0.230 2,595 162

Mancos Shale 1,370 4,500 10.3 1.500 0.350 2,595 162

*Sh = shale

†SS = sandstone

‡Siltst = siltstone
22

Table 4. Strata members of idealized stratigraphic column with strength properties

Strata UCS*

, MPa UCS, psi

Friction 

angle, °

Tensile 

strength, 

MPa

Tensile 

strength, 

psi

Wasatch Formation 1.42 9,800 32.5 0.142 980

Ohio Creek Member 1.42 9,800 32.5 0.142 980

Barren Member 1.48 10,200 32.5 0.148 1,020

F Seam 0.174 1,200 35 0.0174 120

Upper Interbedded Sh, SS 1.16 8,000 32 0.116 800

E Seam 0.174 1,200 35 0.0174 120

Paonia Interbedded Sh, SS, Siltst 1.07 7,400 31.5 0.107 740

DU Seam 0.131 900 35 0.0131 90.0

Paonia Interbedded SS†, Sh‡, 

Siltst§ 1.13 7,800 26 0.113 780

DL Seam 0.131 900 35 0.0131 90.0

Bowie Upper SS 2.03 14,000 35 0.203 1,400

Bowie Siltst 1.16 8,000 30 0.116 800

Bowie Middle SS 2.03 14,000 35 0.203 1,400

CU Seam 0.174 1,200 35 0.0174 120

Upper Bowie Shale 0.580 4,000 30 0.0580 400

Bowie Lower SS 2.03 14,000 35 0.203 1,400

CL Seam 0.174 1,200 35 0.0174 120

Bowie Interbedded Siltst, SS, Sh 1.29 8,900 31.25 0.129 890

BU Seam 0.174 1,200 35 0.0174 120

Lower Bowie Shale 0.580 4,000 30 0.0580 400

BL Seam 0.174 1,200 35 0.0174 120

Bowie Interbedded Sh, SS 1.02 7,000 31.5 0.102 700

A Seam 0.174 1,200 35 0.0174 120

Rollins Sandstone 2.03 14,000 35 0.203 1,400

Mancos Shale 0.580 4,000 30 0.0580 400

*UCS = Unconfined compressive strength

†Sandstone

‡Shale

§Siltstone

Table 5. Groups of strata that were combined in FLAC3D models because a member or 

members had thickness that was too small for modeling purposes 

Group 1 strata Group 2 strata Group 3 strata Group 4 strata Group 5 strata

1. F Seam

1. Paonia

Interbedded SS,

Sh, Siltst

1. CU Seam 1. Bowie Lower SS 1. Bowie

Interbedded Sh, SS

2. Upper

Interbedded Sh, SS 2. DL Seam

2. Upper Bowie

Shale 2. CL Seam 2. A Seam

3. E Seam - - - -

The name of the dominating stratigraphic member that was used as a name for the group in a modified stratigraphic 

column is bolded.
23

Figure 9 shows a plan view of the gate roads at Mine B in the vicinity of the instrumentation 

sites. In Ground Stress in Mining Part 1, Larson et al. [NIOSH 2020] described the instruments 

installed and measurements at the locations indicated. In most cases, the gate roads consisted of 

two yield pillars (between entries 1 and 2) alongside an abutment pillar (between entries 2 and 

3). Table 6 lists the dimensions of the pillars and gate roads in the area. Table 7 lists the panel 

block widths and lengths, without any entry space in the dimensions.

Figure 9. Mine B gate roads in the vicinity of the study site.

Numbers along gate roads identify crosscuts.
24

Table 6. Gate road geometry at Mine B

Item

B10 

TG*, 

m

B10 

TG, ft

B10 

HG†, 

m

B10 

HG, ft

B11 

HG, 

m

B11 

HG, ft

B12 

HG, 

m

B12 

HG, ft

B13 

HG, 

m

B13 

HG, ft

Entry width 5.5 18 5.5 18 5.5 18 5.5 18 5.5 18

Crosscut width 5.5 18 5.5 18 5.5 18 5.5 18 5.5 18

Pillar width‡

20.4 

and 

20.4

67 

and 

67

14.6 

and 

31.1

48 

and 

102

14.6 

and 

28.0

48 

and 

92

14.6 

and 

34.1

48 

and 

112

14.6 

and 

38.7

48 

and 

127

Pillar length‡

40.2 

and 

40.2

132 

and 

132

25.0 

and 

55.5

82 

and 

182

25.0 

and 

55.5

82 

and 

182

25.0 

and 

55.5

82 

and 

182

25.0 

and 

55.5

82 

and 

182

Mining height used 

for models 2.7 9 2.7 9 2.7 9 2.7 9 2.7 9

*TG = Tailgate

†HG = Headgate

‡For pillar width and length, the first number is the dimension of the pillar between entries 1 and 2, and the second 

number is the dimension of the pillar between entries 2 and 3.

Table 7. Panel geometry at Mine B

Item

B10 

Panel, 

m

B10 

Panel, ft

B11

Panel, 

m

B11

Panel, ft

B12 

Panel, 

m

B12 

Panel, ft

B13 

Panel, 

m

B13 

Panel, ft

Width* 263 862 263 862 266 872 266 872

Length 941.8 3,090 989.1 3,245 1,530 5,020 1,457 4,780

*Panel width only includes the panel block and is not center-to-center of entries.

Observations and Measurements

In Ground Stress in Mining Part 1, Larson et al. [NIOSH 2020] described observations and 

measurements made at Mine A and Mine B. Important points concerning calibration and 

verification of numerical models are as follows:

• Floor heave was present in 2 North as the longwall face approached. Floor heave in 1 

North was insignificant, except for minor heave in anomalous areas associated with 

faults. Not all locations where faults intersected the gate roads in 1 North experienced 

floor heave. Calibrated models should have properties and/or structure features with 

properties that explain this phenomenon.

• Borehole pressure cells (BPCs), instrumented support Cans, ground condition 

surveys, and floor-to-roof closures, particularly when not right next to a support Can,

gave some measure of first arrival of abutment stress resulting from mining. The 

distance from gob to first arrival of abutment stress was much higher than that 

calculated by the empirical equation [see Equation 5], even before conversion to an 

equivalent side load transfer distance (LTD). The LTD is very important for 

calibrating material properties of the strata. BPCs had the most sensitivity to first 

arrival of abutment stress. Instrumented support Cans that measure load on the Can 

were almost as sensitive as BPCs in detecting first arrival. Ground condition surveys 

and entry closure were significantly less sensitive and may be approximately the same 

insensitivity.
25

• Measurements of BPC cell pressure indicate that the coal behavior varied 

significantly. Trends indicate a variable capacity to take load near the ribs (cells at 2.3 

m (7.5 ft) of depth). Usually peak stress was reached at these BPCs during mining of 

the panel, but peak stresses varied greatly. Many BPCs became damaged or a steady, 

lower stress after passage of the face was not often reached; therefore, residual load 

usually was not possible to determine, assuming the cell pressure to be indicative of 

rock stress. The largest stress was located deeper into the pillar; for example, the 

highest measured cell pressures were located at 5.33 m (17.5 ft) from the rib. The 

center of the pillar carried less stress than cells located at 5.33 m (17.5 ft) from the 

rib. These trends in the pillar profile are useful when considering the coal strength 

model that might be most suitable.

• Because BPCs were not installed in the panel being mined, it is impossible to 

accurately estimate the front abutment stress profile and, in turn, estimate the side 

abutment stress profile. Such estimation, if made, would infer the proportion of 

overpanel weight transferred through the gob. Therefore, it is not possible to calibrate 

gob stiffness with measurements made in these case studies. It is only possible to 

assess whether or not the gob loading indicated by a model output is reasonable.

Converting the Measurement of Distance to First Arrival of Abutment 

Stress to Equivalent Load Transfer Distance

Several reported load transfer distances are reported in the literature [Larson et al. 2015], but 

such reported data were measured in various ways and most were detected ahead of the face. 

Such a reported location does not adhere to load transfer distance as defined by Peng and Chiang 

[1984].

Larson et al. [NIOSH 2019] reported on measuring of the distance to the first arrival of 

abutment stress by several instrument types and methods. Comparing these first arrivals of 

mining-induced abutment stress with the empirically calculated load transfer distance (LTD) is 

only possible if the measured distances to first arrival are converted to an equivalent side 

distance, or LTD. Recall that LTD was defined by Peng and Chiang [1984] to be at the side of a 

panel at about midlength, as illustrated in Figure 10. This is possible through use of an 

appropriate model that compares ratios of the distances from gob to a contour line of stress 

increase—i.e., the distance from the corner of the gob to the contour line in the direction of the 

instrument at first arrival of abutment stress compared to the distance from the side of the gob at 

mid-panel to the same contour line in the direction perpendicular to the side edge of the panel. 

This ratio varies because the instruments are located to the sides of the panel in the pillar, barrier 

pillar, or next panel. The ratio has to be determined for a given angle from the panel where the 

instrument is located at the first arrival of abutment stress, detected by a stress increase 

equivalent to that represented by the contour line.

Mine A

Larson and Whyatt [2012] used the model calculations from a LaModel simulation of panel 

mining at Mine A to determine conversion or equivalency factors from these ratios (see Figure 
26

11). Lines at various angles from the panel were drawn and marked for determining ratios of 

distance to contour line in a particular direction with respect to that on the side at midpanel. The 

model’s rock mass stiffness was calibrated, but it was great enough that the influence of the gate 

roads on the contours was negligible. Also, the ratios were determined from the 69-kPa (10-psi) 

contour line instead of the 138-kPa (20-psi) line, in which the increase served as the threshold 

indicating arrival of abutment stress. Presumably, the ratios determined from any contour line 

near the 69-kPa (10-psi) contour should be at least nearly equal. The ratios were determined at 5° 

intervals, and a fifth-order polynomial equation was fitted to the ratios for interpolating between 

sampled ratios. In this case, fitted parameters for polynomial equations for higher than second 

order were not significant. However, the fitted fifth-order polynomial produced the least 

maximum error and the highest r-squared statistic, it was only slightly higher than that of the 

lower-order fitted polynomial equations. Fitting such a function to equivalency ratios at this 

interval was justifiable because of the negligible influence of the gate roads. Figure 12 shows the 

sample ratios and fitted equations for both headgate and tailgate. Larson and Whyatt [2012] used 

these equivalency factors to determine equivalent side LTD by subtracting an assumed yield 

distance of 9.1 m (30 ft) from the net distance to gob and dividing that quantity by the 

equivalency factor for the particular direction to the instrument at detection of first arrival of 

abutment stress. The 9.1-m (30-ft) distance of assumed yield was an estimated result from the 

LaModel pre-processor.

Figure 10. Loading profile in a vertical section at mid-panel of a conceptual model

of loading as a result of longwall mining. Load transfer distance is shown.

σ0= premining stress, or stress on the seam before mining of the panel.

However, Larson et al. [NIOSH 2019] reported a technical audit of face positions with shift 

reports, which caused adjustment of some face positions with time. This adjustment affected the 

detection of distance to first arrival of abutment stress and net distance compared to those 

distances reported previously by Larson and Whyatt [2012]. Moreover, Larson and Whyatt 

[2013] found that MulsimNL/Large (also referred to as Mulsim in this report) was a better 

alternative to LaModel for the stratigraphy around these mines because the rock mass stiffness in 

the LaModel simulation had to be increased to unrealistic values to achieve measured LTD. The 

high rock mass stiffness prevented almost all loading of the gob in LaModel, and calibration of 

gob stiffness became impossible. In addition, as explained later in this report, the best model for 

matching first arrival of abutment stress as calculated by Mulsim was the model with coal 

represented as an elastic material. However, yielding was represented in the model by reducing 

the coal modulus in the outer ring of 3.0-m (10-ft) wide elements in pillars and panels to 60% of 

the full value and reducing it in the second ring of elements to 80% of the full value. The gate 

roads were present in this model (see Figure 13). The conversion ratios were determined for a 

smaller range of angles (0° to 30°), with ratio samples taken at 1° intervals or smaller as needed 
27

to capture changing trends in the contour line. In addition, all ratios were calculated with respect 

to the side distance on the right of the panel because of the interference of workings to the left of 

the panel. No continuous function could adequately describe the trends. Therefore, interpolation 

for converting first arrival distance to equivalent LTD was done on a piecewise linear basis, 

based on the result shown in Figure 14. The presence of the gate roads caused minimal 

disturbance in the trend of the contours, but they did cause some contours to form complete rings 

inside the pillars of the headgate, tailgate, and West Mains.

In the absence of measurements or observations indicating LTD, Heasley [2008b, 2009b]

recommended calibrating to the empirical representation (Equation 6) of the distance at which 

90% of the abutment load is transferred to each of the abutments. The abutment load is 

determined from the overpanel weight using the abutment angle, β. The empirical curve does not 

have a yield zone naturally incorporated into its stress profile. In Heasley’s [2010] preprocessor 

to the LaModel program, LamPre, the abutment load within the estimated yield zone depth is 

neglected, and the amount of load within distance D0.9 of the extent of the laminated yield zone 

is matched to the empirical abutment load that occurs within distance D0.9 of the rib. 

Accordingly, before converting to equivalent LTD, the yield distance assumed in this model (two 

rings of elements) of 6.1 m (20 ft) was assumed to have negligible stress and, therefore, was 

subtracted from the net distance from gob determined by Larson et al. [NIOSH 2020] (Ground 

Stress in Mining Part 1) at which abutment stress was first detected.
28

Figure 11. LaModel contours of stress increase resulting from panel mining. Coordinate

system was chosen for convenience in modeling. Also shown are lines at various angles

from the gate roads. These lines were used to help in determining equivalency factors.

-1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

4.0

4.4 50403020 10 0

 Y-COORDINATE, 10

3 ft

X-COORDINATE, 103 ft Stress increase

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200 0

 10 20 304050

 0

0.069

0.138

0.207

0.276

0.345

0.414

0.483

0.551

0.621

0.689

0.758

0.827

0.896

0.965

1.034

1.103

1.172

1.241

1.310

1.379

 MPa psi

-4 -3 -2 -1 0 1 2 3 4 5 6 7 8

0

1

2

3

4

5

6

7

8

9

10

11

12

13 Y-COORDINATE, 10

2 m

X-COORDINATE, 102 m
29

Figure 12. Conversion factors determined from LaModel’s calculated result.
30

Figure 13. A Mulsim elastic model with reduced coal modulus near rib. This model

was used to determine conversion factors for equivalent LTD on the side of the panel.

-2 -1 0 1 2 3 4 5

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

11

12

30° 25°20° 15° 5° 10° 0° 30° 25° 20° 15° 10° 5° Y-COORDINATE, 10

3 ft

X-COORDINATE, 103 ft 0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

Excavation step 057 (Single runs) with respect to step 003 Stress increase MPa psi

0°

 0

0.138

0.276

0.414

0.552

0.689

0.827

0.965

1.103

1.241

1.379

1.517

1.655

1.793

1.931

2.068

2.206

2.344

2.482

2.620

2.758

-0.5 0.0 0.5 1.0 1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5 Y-COORDINATE, 10

3 m

X-COORDINATE, 103 m
31

Figure 14. Piecewise linear conversion factor functions derived from

the Mulsim model for determining equivalent LTD at Mine A.

Table 8 lists the net distance to first arrival of mining-induced stress for BPCs at the 1 North 

outby instrument site, as reported by Larson et al. [NIOSH 2020] in Ground Stress in Mining 

Part 1, along with the angle from the panel, corresponding conversion factor from Figure 14, and 

equivalent LTD. Table 9 presents the same data for BPCs at the 2 North outby station. The 

standard deviation of the average site LTD at both of these sites was surprisingly low—8.4% and 

4.4% for the 1 North outby and 2 North outby sites, respectively. Table 10 summarizes the 

average distances for each site and lists the average for the two sites. This average LTD is 3.98 

times that calculated with the empirical Peng and Chiang Equation 5, using an average depth of 

686.9 m (2,253.5 ft).
32

Table 8. BPC data from the 1 North outby site

Instrument

Net distance 

from gob 

minus yield 

distance, m

Net distance 

from gob 

minus yield 

distance, ft

Angle from 

entry along 

panel when 

threshold 

reached, °

Conversion 

factor

Equivalent 

LTD, m

Equivalent 

LTD, ft

BP2 445.5 1,461.5 11.13 0.7640 583.1 1,913.0

BP3 511.5 1,678.3 12.96 0.7537 678.7 2,226.7

SP1 436.4 1,431.8 3.97 0.8951 487.6 1,599.6

SP2 462.4 1,517.0 4.12 0.8907 519.1 1,703.1

SP3 464.8 1,525.0 4.81 0.8661 536.7 1,760.9

SP4 500.6 1,642.4 5.12 0.8581 583.4 1,914.0

SP5 481.3 1,579.1 5.69 0.8533 564.1 1,850.6

NP1 476.0 1,561.8 2.37 0.8678 548.5 1,799.7

NP2 489.5 1,605.9 1.95 0.8517 574.7 1,885.5

NP3 467.0 1,532.2 1.35 0.8588 543.8 1,784.1

NP4 465.8 1,528.1 0.65 0.8731 533.4 1,750.1

NP5 479.9 1,574.6 0.27 0.8842 542.8 1,780.8

Average - - - - 558.0 1,830.7

St. Dev. - - - - 46.9 153.9

Table 9. BPC data from the 2 North outby site

Instrument

Net distance 

from gob 

minus yield 

distance, m

Net distance 

from gob 

minus yield 

distance, ft

Angle from 

entry along 

panel when 

threshold 

reached, °

Conversion 

factor

Equivalent 

LTD, m

Equivalent 

LTD, ft

NP3 457.6 1501.4 8.60 0.8437 542.4 1779.7

NP4 425.4 1395.8 11.20 0.8418 505.4 1658.1

NP5 412.2 1352.5 13.59 0.8476 486.4 1595.8

NP6 448.3 1470.9 13.28 0.8476 529.0 1735.4

NP7 423.0 1387.9 14.50 0.8473 499.3 1638.1

Average - - - - 512.5 1681.4

St. Dev. - - - - 22.8 74.7

Table 10. List of equivalent LTDs determined from BPCs for 1 North and 2 North outby 

sites and the average LTD for both sites

Location Average equivalent 

LTD, m

Average equivalent 

LTD, ft

St. dev. of 

equivalent LTD, m

St. dev. of 

equivalent LTD, ft

1 North outby 558.0 1,830.7 46.9 153.9

2 North outby 512.5 1,681.4 22.8 74.7

Average 535.2 1,756 - -

The conversion factors were applied to the net distances at first detection of abutment stress 

determined from instrumented support Cans, as reported by Larson et al. [NIOSH 2020] in 

Ground Stress in Mining Part 1. The net distances minus assumed yield distance, angle from 

along the gate roads, conversion factors, and equivalent LTD for the 2 North outby site are listed 

in Table 11 for those instrumented Cans whose trends to determine first arrival of abutment 

stress met a quality criteria (set forth in Ground Stress in Mining Part 1). The average equivalent 

LTD was 502.0 m (1,647 ft), which is 3.73 times the empirical LTD. This LTD is 6.2% less than 

that indicated by the BPCs.
33

Table 11. Support Can data from the 2 North outby site

Support Can

Net distance 

from gob 

minus yield 

distance, m

Net distance 

from gob 

minus yield 

distance, ft

Angle from 

entry along 

panel when 

threshold 

reached, °

Conversion 

factor

Equivalent 

LTD, m

Equivalent 

LTD, ft

A 384.5 1,345.4 15.43 0.8254 504.2 1,654.3

C 405.6 1,330.7 15.60 0.8167 504.1 1,653.9

F 410.1 1,261.5 16.85 0.7849 497.6 1,632.6

Average - - - - 502.0 1,647.0

St. Dev. - - - - 3.78 12.40

Table 12 lists similar data determined from closure measurements with string 

potentiometers located in the entries near support Cans and mounted on a support Can. In 

Ground Stress in Mining Part 1, Larson et al. [NIOSH 2020] found entry closure measurements 

to have greater success in detecting first arrival of abutment stress than those measurements from 

sensors mounted on a Can assembly. The average equivalent LTD was 381.1 m (1250 ft), which 

is 2.83 times the empirical LTD, or 28.8% lower than that determined with the BPCs.

Table 12. Closure instrument data from entry 3 of 2 North of Mine A

Instrument

Net distance 

to gob 

minus yield 

distance, m

Net distance 

to gob 

minus yield 

distance, ft

Angle from 

entry along 

panel when 

threshold 

reached, °

Conversion 

factor

Equivalent 

LTD, m

Equivalent 

LTD, ft

Int-RF9 234.5 769.3 27.33 0.7008 334.6 1,097.7

Int-RF10 2,551.2 824.3 26.13 0.7047 356.5 1,169.6

Can A 275.7 904.6 23.13 0.7076 389.7 1,278.4

MP-RF7 285.9 938.0 22.77 0.7110 402.2 1,319.4

MP-RF8 318.2 1044.1 20.36 0.7265 438.0 1,437.1

MP-RF10 257.2 843.9 25.40 0.7034 365.7 1,199.7

Average - - - - 381.1 1,250.3

St. Dev.*

- - - - 36.8 120.7

*St. Dev. = Standard Deviation

Table 13 lists ranges of net distances from the yield extent around the gob, angle from along 

the gate roads when the first arrival threshold was met, conversion factors, and equivalent LTD 

ranges. Because the ground condition surveys were not conducted with more frequency, the 

ranges are large. Even so, it appears that sensitivity of ground condition surveys to determining 

LTD may be close to and probably slightly less than that of the closure measurements.

If the average LTD of each method is used as an indicator of sensitivity of the determining 

method, and the BPC method is used as the standards, the relative sentivities as a fraction of the 

BPC-determined LTD are calculated. These distances and ratios are found in Table 14.
34

Table 13. Data from instrument sites where ground condition surveys were conducted

Site

Net distance 

to gob 

minus yield 

distance, m

Net distance 

to gob 

minus yield 

distance, ft

Angle from 

entry along 

panel when 

threshold 

reached, °

Conversion 

factor

Equivalent 

LTD, m

Equivalent 

LTD, ft

1 North outby 286.1 to 

515.1

938.6 to 

1,690.0 4.97 and 2.78 0.8603 and 0.8860

332.5 to 

581.4

1,091.0 to 

1907.4

2 North outby 61.2 to 261.1 200.9 to 

856.7

54.58 and 

11.85

0.6259 and 

0.8430 97.8 to 309.7 320.9 to 1016.2

*Average of 

1 North 

minimum 

and 2 North 

maximum

- - - - 321.1 1053.6

*This average provided for approximate determination of relative sensitivity factor between methods.

Table 14. Summary of LTD and relative sensitivity factors by method

Method LTD, m LTD, ft Sensitivity ratio

BPCs 535.2 1756 1

Instrumented Cans 502.0 1647 0.938

Closures 381.1 1250.3 0.712

Ground condition surveys 321.1 1053.6 0.6

Mine B

The process used to determine the conversion factors for the equivalent load transfer distance 

(LTD) at Mine A was also applied at Mine B. Figure 15 shows stress increase contours of the B13 Panel at approximately the location when BPCs at the H22 site detected first arrival of 

mining-induced abutment load. As at Mine A, the coal within a distance of 6.1 m (20 ft) from the 

gob was assumed to have yielded. The shortest distance from this yield perimeter to the threshold 

contour was determined at regular angular intervals from the direction of the gate roads. In 

addition, such distances were determined at angles between these intervals where directional 

changes in the threshold contour line warranted the additional data. The distance from the 

headgate gob to the same contour at midpanel was also determined, so that ratios representing 

conversion factors could be established between the various directions and the side direction at 

midpanel. A similar contour plot was made for the B-12 Panel and conversion factors determined 

in the same manner. Figure 16 shows the piecewise linear conversion factors determined for each 

gate road of the two panels mined. Differences between panels are mostly the result of changes 

in gate road geometry, although previous mining of the B-11 Panel may have played a role. 

Mining of the B-10 Panel was assumed to have a negligible effect and is not represented in this 

model.
35

Figure 15. Contours of stress increase resulting from mining the B-13 Panel.

Lines at various angles from the gob corners are superimposed.
36

Figure 16. Piecewise linear conversion factor functions derived from

Mulsim model for determining equivalent LTD at Mine B.

For ease of comparing results to empirical LTD, Table 15 lists the overburden depth at each 

site.

Table 15. Overburden depth at each instrument site

Site

Overburden 

depth, m

Overburden 

depth, ft

T5 228.6 750

T6 231.6 760

T15 297.2 975

T16 304.8 1,000

T39 263.7 865

T34 254.5 835

T33 253 830

T21 277.4 910

T20 286.5 940

H43 323.1 1,060

H42 329.2 1,080

H22 335.3 1,100

H21 336.8 1,105
37

Larson et al. [NIOSH 2019] analyzed measurements taken with various instruments at Mine 

B. None of these measurements passed the quality tests used at Mine A to continue as candidates 

for determining LTD. Larson et al. described the causes of the quality deterioration, which are 

not enumerated here. In spite of the quality of the measurements, they characterized cell pressure 

trends and were used to determine ranges of distance from the face at which the cell pressure 

trends departed from pre-abutment stress trends, indicating first arrival of mining-induced 

abutment stress. In the case of closure measurements, better precision of the Midas datalogger 

permitted consideration of a much smaller threshold to indicate arrival of abutment stress. In this 

case, the two thresholds were used as the lower and upper bounds of a range of distance to the 

gob at first arrival. In either case, ranges were generally reported (Ground Stress in Mining Part 

1). The bounds of these ranges were also converted to equivalent LTD.

Table 16 lists data used to determine equivalent LTD for BPCs at sites H22 in the B-12 

headgate and T21 in the B-12 tailgate. The range of confidence in the determinations varies, as 

does the range equivalent LTD. The large upper bound reported, 748.5 m (2,456 ft), seems 

extremely high, and therefore, it is considered to be an outlier and discounted. The remaining 

range of equivalent LTD ranges from 227.8 m to 472.6 m (747.2 ft to 1,551 ft), which 

corresponds to a range of ratios with respect to the empirical LTD of 2.66 to 5.53.

Table 16. List of BPCs at Mine B from which measurements of distance could be 

determined from the gob at first arrival of abutment stress

BPC

Net distance 

to gob 

minus yield 

distance, m

Net 

distance to 

gob minus 

yield 

distance, ft

Confidence in 

measurement

Angle from 

entry along 

panel when 

threshold 

reached, °

Conversion 

factor

Equivalent 

LTD, m

Equivalent 

LTD, ft

Ratio to 

empirical 

LTD

T21-

P46 187.9* 616.5* Low 4.14 0.8250 227.8 747.2 2.66

T21-

P12

272.5 to 

393.0

894.0 to 

1289

Fair to good 

for range

0.752 to 

0.525

0.7524 to 

0.7624

362.2 to 

748.5

1,188 to 

2456†

4.24 to 

8.75†

T21-

L12

254.5 to 

360.7

835.0 to 

1,183

Fair to good 

for range

-1.41 to -

1.00

0.7605 to 

0.7632

334.7 to 

472.6

1,098 to 

1551

3.91 to 

5.53

H22-

P48 177.4 581.9 Good 12.47 0.6942 255.5 838.2 2.72

H22-

P12

177.8 to 

298.1

583.2 to 

977.9 Low 15.97 to 9.58

0.6572 to 

0.7476

270.5 to 

398.7

887.4 to 

1,308

2.88 to 

4.24

*

In Ground Stress in Mining Part 1, Larson et al. [2020] argued that this net distance could have ranged as high as 

253 m (830 ft) by different selection of initial points to characterize the trend before first arrival.

† Upper range is considered to be too high and an outlier.

Table 17 lists results from one Can that was used to determine equivalent LTD. The data was 

very noisy, but the departure from initial trend was very pronounced. Therefore, it is difficult to 

assume this LTD is an outlier. To justify the result, we might look to local variation in the 

geology that might have caused additional closure at this site, but such information is not 

available.
38

Table 17. List of results from the H21 outby instrumented support Can with determined 

equivalent LTD

Support 

Can

Net 

distance to 

gob minus 

yield 

distance, m

Net 

distance 

to gob 

minus 

yield 

distance, 

ft

Angle 

from entry 

along 

panel 

when 

threshold 

reached, °

Conversion 

factor

Equivalent 

LTD, m

Equivalent 

LTD, ft

Ratio to 

empirical 

LTD

H21-

outby 523.9 1,719 6.17 0.7518 696.9 2,286 7.41

Table 18 lists results from two closure-measurement histories from the T34 site. The 

equivalent LTD ranges are reasonable. 

Table 18. List of results from the T34 closure data with determined equivalent LTD

Instrument

Net 

distance 

to gob 

minus 

yield 

distance, 

m

Net 

distance 

to gob 

minus 

yield 

distance, 

ft

Angle 

from 

entry 

along 

panel 

when 

threshold 

reached, °

Conversion 

factor

Equivalent 

LTD, m

Equivalent 

LTD, ft

Ratio to 

empirical 

LTD

T34 inby 

entry

203.8 to 

283.7

668.7 to 

930.7

0.374 to 

0.271

0.7906 to 

0.7878

257.8 to 

360.1

845.8 to 

1181

3.15 to 

4.40

T34 inby 

Can

201.2 to 

281.0

660.0 to 

922.0

0.379 to 

0.274

0.7908 to 

0.7879

254.4 to 

356.7

834.6 to 

1,170

3.11 to 

4.35

Summary

The equivalent LTD for Mine A was derived from measurement trends that provide more 

confidence in the results, as compared to Mine B. Therefore, they give some measure of 

sensitivity between the methods. Given similar stratigraphy, the difference in overburden depth 

would suggest that the equivalent LTD at Mine B would be less than that at Mine A. The range 

of ratio of measured-equivalent-to-empirical LTD at Mine B (2.7 to 5.5) does not permit 

confirmation of this expectation. However, the best quality determinations (derived from the 

BPC at H22-P48 and the two closure measurements at T34) may indicate such ratios of 2.7 and 

approximately 3.1 to 4.4. The finer threshold associated with these upper bounds may have been 

smaller than the accuracy of the sensor hardware, suggesting that the lower portion of these 

ranges is more realistic. Therefore, the more likely ratio of measured-equivalent-to-empirical 

LTD is likely in the range of 2.7 and 3.8. This range would be consistent with measured LTD at 

Mine A. The results of measurements at Mine B do not support that LTD at that mine is 

comparable to the empirical LTD.
39

Later in this report, the best loading model at Mine A is shown to be an elastic model in 

Mulsim with the outer two rings of elements having elastic modulus reduced to 60% and 80% of 

the full amount. If the same rock mass stiffness is used as the value calibrated for LTD at Mine 

A, then this model suggests that Mine B has an LTD of 326 m (1,068 ft) when the overburden 

depth is 335 m (1,100 ft) and a ratio of measured-equivalent-to-empirical LTD of 3.5 at Mine B.

Modeling Tools

Several modeling tools are commonly used to evaluate coal mine layout design. These are 

the empirical method (ALPS), displacement discontinuity codes such as LaModel and 

MulsimNL/Large, and FLAC3D. Each has advantages and disadvantages when used for 

evaluation of coal mine layout. In this section, each tool is described in order to inform the 

reader of their backgrounds and capabilities. Also, some of the challenging issues in using 

FLAC3Dare described. 

Empirical Method

The empirical approach forms the basis of two research publications that describe mine 

layout software tools: Analysis of Longwall Pillar Stability [Mark 1987, 1992] and Analysis of 

Retreat Mining Pillar Stability [Mark and Chase 1997]. The empirical method uses three 

equations as its basis to describe stress distribution resulting from mining. The first equation is 

used to determine overpanel weight transferred to the abutment. Mark [1987] used the 

conceptual loading model suggested by King and Whittaker [1970], shown here as Figure 17. 

For his empirical database, Mark noted field measurements from which he calculated β ranging 

from 10.7° to 25.2° and concluded that β = 21° was sufficiently conservative for longwall pillar 

design.

Figure 17. Conceptualizations of the side abutment load,

patterned after King and Whittaker [1970]. 

The weight per unit length of gate road is represented in Figure 17 as Ls and Lss for 

supercritical and subcritical cases, respectively. They are calculated as
40

Ls = H2

(tan β) (

γ

2

), and (7)

Lss = [HP

2

− 

P

2

8 tan β] γ, (8)

where Ls = weight per unit length of gate road, shown in the shaded region in the left part of 

Figure 17, that is transferred to the abutment for the case of a critical or 

supercritical panel;

Lss = weight per unit length of gate road, also shown as a shaded region on the right in 

Figure 17, that is transferred to the abutment for the case of a subcritical panel;

H = height of the overburden;

P = width of the panel;

β = the angle that defines the portion of the overpanel volume whose weight is 

transferred to the abutment; and 

γ = density of the overburden.

If P ≥ 2H tan β, then Equation 7 is used; otherwise, Equation 8 is used. Also, Ls(or Lss for the 

subcritical case) is that area under the abutment stress curve in Figure 10.

The second equation, proposed by Peng and Chiang [1984], defines load transfer distance 

(LTD) as a function of overburden depth (H) based on a small number of observations. This 

equation was mentioned earlier as Equation 5 and shown graphically in Figure 10. It is repeated 

here, using LTD instead of D1.0 to emphasize that it is load transfer distance,

LTD = 9.3√H. (9)

Equation 10 describes the decay of mining-induced stress, σ, as a function of distance from 

the abutment rib, x, until x = LTD. This rule, proposed by Mark [USBM 1990], is based on a 

curve fit of a small group of pressure measurements. The magnitude of mining-induced stress 

transferred to the abutment, L, depends on the angle, β, which represents partitioning of 

undermined overburden loading between abutments and gob. (See Figure 17, where L is 

represented by Ls or Lss.)

σ = 

3L(β)

(LTD)

3

[(LTD) − x]

2

, (10)

where σ = stress transferred to the coal seam from mining the panel,

L(β) = Ls or Lss, and

x = distance from the edge of the gob.

Loading of pillars is based on tributary load under this curve for a specific pillar, as shown by 

Mark [USBM 1990]. The load divided by the total strength capacity of the pillar determines the 

stability factor. The Analysis of Longwall Pillar Stability uses the Mark-Bieniawski pillar 

equation [Mark 1999] for that purpose:
41

Sp = S1 (0.64 + 0.54 w

h

− 0.18 w2

lh ), (11)

where Sp = pillar strength,

S1 = in situ coal strength,

w = pillar width,

h = pillar height, and

l = pillar length.

Mark et al. [1994] found that Coal Mine Roof Rating (CMRR), developed by Molinda and 

Mark [USBM 1994], could be used to determine a critical stability factor that discriminated 

correctly between successful and unsuccessful gate road pillar designs in 84% of case histories 

that they compiled by using the equation

ALPS SFR = 1.76 − 0.014 CMRR, (12)

where ALPS SFR = ALPS stability factor suggested for design, and

CMRR = Coal Mine Roof Rating.

Advantages of this method are that it is simple to execute and is founded in the results of 

many case histories. However, it does not account for local variability caused by geology and 

structure. For example, Lawson et al. [2013] found significant sensitivity of loading factors to β

and measured LTD, instead of that calculated with Equation 9. In reality, structure and properties 

of the overburden can vary the amount of overpanel weight that transfers through the gob versus 

that transferred to the abutment. Measurements described by Larson and Whyatt [2012], which 

were updated earlier in this report, attest to large departures from the empirical LTD in some 

mines, particularly those in the western United States having massive, strong strata above or 

below the seam being mined.

The LaModel Code

Based on work of Salamon [1963], Crouch and Fairhurst [1973] developed a code for 

representing a tabular deposit in an elastic medium with a series of squares, each having a 

closure and stress centered at its midpoint. This was a displacement-discontinuity-type boundary 

element code. Others have developed versions of this type of code, but one code has been used 

prevalently in evaluating coal mining layouts for the last 16 or 17 years.

Heasley [1998] developed a displacement discontinuity modeling code, LaModel, that is 

based on the solution described by Salamon [1991] of a crack in a continuous medium consisting 

of a series of frictionless laminated plates, based on thin plate theory. Heasley [2010] developed 

this software into a very convenient tool, with pre- and post-processors (LamPre and LamPlt, 

respectively). LamPre is equipped with tools (called wizards) for determining lamination 

thickness, coal properties, and gob properties that approximately calibrate to the empirical 

solution (for example, calibrating rock mass stiffness so that 90% of the load falls with the 

calculated result of Equation 6). With a laminated rock mass, the LaModel software can 

reasonably simulate subsidence [Heasley and Barton 1998; Heasley and Barton 1999].

Some of the capabilities of the current version (3.0) of LaModel are:

• 2,000 by 2,000 seam grid;

• Simulation of topography by adding compression and tensile stresses at a datum 

above the coal seam;
42

• Grid determination from an AutoCAD map;

• Three coal models: elastic, Mark-Bieniawski coal with post-peak modulus (usually 

zero for elastic-perfectly-plastic material), and strain-softening to a residual stress;

• Three gob models, including linear, bilinear, and linearly increasing tangent modulus;

• Ability to calculate stress and displacement on an off-seam plane;

• Ability to define an off-seam fault plane;

• Ability to do energy calculations;

• Ability to calculate safety factors;

• Ability to calculate roof bending stresses; and

• Ability to accommodate 200 mining steps, although LamPre is hardwired to allow a 

maximum of only 20.

One of the tremendous advantages of LaModel is the speed of calculations. Because it only 

calculates vertical stress and vertical displacements (closure of the seam and off-seam 

displacements), calculation time is usually much less than using other numerical modeling tools. 

This advantage allows the user to complete calculations of over 100 mining steps overnight or in 

just a few hours.

A caution is appropriate for using the topographic feature. Whyatt et al. [2011] found that 

highly variable terrain can introduce some errors in the propagation of stresses onto the seam, but 

generally, reasonable results are obtained by using a datum representing the average height of the 

overburden above the coal seam over the entire model.

The main disadvantage of LaModel or any boundary element code is that the rock mass is 

represented as an elastic medium. Therefore, no roof or floor failure mechanics can be simulated.

Grids for the current problem were not constructed directly from AutoCAD because the stage 

represented in existing drawings did not coincide with the gate road workings. Instead, a grid 

was superimposed on the AutoCAD map having the closest gate road state to what was needed 

for representing development in the model. A grid was set up in an Excel spreadsheet, and gate 

roads were constructed by assigning the character “1” if the greatest area of an element were 

mined and “A” if the greatest area of an element were unmined. Subsequent mining steps such as 

longwall mining were accomplished on other pages of the spreadsheet with the copy and paste 

function, with only minor changes made to represent the mining for that step. Yield elements 

were determined by copying the grid into an input file for one cut and letting LamPre assign the 

yield materials. This grid was then copied to a text file, and tab characters were deleted. Final 

input files were then constructed using DOS copy functions to combine initial inputs and 

subsequent mining step material codes. In this fashion, for example, a 185-step model was 

constructed to simulate mining of Panel 1 and Panel 2 at Mine A.

MulsimNL/Large

Mulsim is another displacement-discontinuity code that was developed to model tabular 

deposits. Sinha [1979] developed the original version to analyze multiple, parallel coal seams. 

He included the ability to subdivide coarse blocks into finer mesh so that the scheme was 

computationally more efficient. Beckett and Madrid [1986]; [USBM 1988] developed additional 

features for Mulsim (their version was called MULSIM/BM), such as additional seam materials 

like gob, pack walls, and cribs; graphical development of grids; and an increase in the number of 

coarse blocks and the number of blocks that could be subdivided into finer mesh. Donato 

[USBM 1992c] converted MULSIM/BM to a PC environment. Itasca Consulting Group added 
43

the ability to consider multiple mining steps [USBM 1992b]. Zipf [USBM 1992b, 1992a] added 

nonlinear seam materials such as strain-softening, elastic-plastic, bilinear hardening gob, and 

strain-hardening—the same materials mentioned for LaModel. Zipf’s version, called 

MULSIM/NL, ran from DOS. Its use has decreased over the years because LaModel was better 

supported, faster, and easier to use.

Mulsim differs from LaModel in that the rock mass is represented by an elastic medium with 

no laminations. As such, it does not simulate surface subsidence very well. Mulsim handles four 

seams, the same as LaModel, but these seams only have to be parallel, and not horizontal. The 

version of Mulsim in the public domain does not handle topography yet, but energy equations are 

part of the analysis. The code divides the seam into course blocks. The user designates a 

rectangular area of interior blocks that are divided into five-by-five fine elements. The outside 

boundary of the coarse blocks is not allowed to displace, whereas the outside boundaries of a 

LaModel grid can be rigid like Mulsim boundaries or they can be symmetrical.

Larson and Whyatt [2013] took Zipf’s MULSIM/NL and expanded it to examine problems 

described in this report and called it MulsimNL/Large. The current version runs in DOS and has 

not been released by NIOSH. Appendix A describes the format of this updated version. The 

code’s input precision and output precision were increased to allow better comparison with 

results from other modeling tools. Additionally, Zipf’s three example problems [USBM 1992a]

were run with MulsimNL/Large (see Appendix A) for purposes of verification. Results compare 

very well.

Construction of the input file for modeling Mine A, particularly the fine and coarse codes, 

was a daunting task, with room for many potential mistakes, if done manually. Most of this 

difficulty was the result of the decision to convert a certain perimeter of LaModel fine element 

codes into the closest equivalent coarse code to reduce the size of the MulsimNL/Large model. 

This was necessary because of the significantly increased time required to run a Mulsim 

problem. This process was automated with a Visual Basic macro. The steps required to construct 

both LaModel and Mulsim grids are described in Appendix B. This appendix also lists the Visual 

Basic functions used to accomplish this task. The macros can be adjusted easily to be used on 

any size grid, with an interior grid that contains fine-element blocks converted to zeroes, as 

needed by the Mulsim coarse grid input.

The Finite Difference Code FLAC3D

If failure mechanics of the roof or floor are important, or more thorough mechanics of the 

coal seam is important, then a volume-element type of modeling code is necessary. Possible code 

types might include finite element, finite difference, or distinct element codes. In this study, the 

finite difference code FLAC3D, both versions 4.0 and 5.0, was used to model Mine A only. Such 

models may not be used extensively by most engineers who perform analysis and modeling of 

mining layout because of the time, cost, and detail required. Volume element codes require many 

more inputs than boundary element codes, including determination of appropriate constitutive 

laws and material parameters, determining geometry for purposes of construction of a model 

grid, and including irregularities that might be important, such as nonplanar stratigraphy and 

variable topography.

For purposes of this study, the idealized stratigraphy shown in Figure 8 was used along with 

properties listed in Tables 3 and 4 for basic rock types, as described earlier. Thin coal seams 

were combined with the thickest member for those groups listed in Table 5. Presence of faults 
44

was ignored, but elevations of the top of seam and surface were obtained using the AutoCAD 

Civil 3D for the purposes of constructing a model. The model was built with FISH (short for 

FLACish, a computer language embedded in Itasca Consulting Group codes) functions, using 

elevations of the top of the DU Seam and all other stratigraphy having constant thickness and 

being parallel with that seam. The lowest member, the Mancos Shale, had a constant elevation at 

the bottom of the model. The FISH functions built the model one plan-view section at a time. 

Section division was necessary to accommodate geometries of the panels and graduation of zone 

sizes. Within each section, the zones were constructed one strata member at a time, with columns 

of zones with the x and y coordinates being constant for a column of grid points. No interfaces 

were used between strata. A view of the constructed model grid is shown in Figure 18.

Overcoring stress measurements taken in the area showed variable results, but generally were not 

much different from that induced by gravity loading.4

4 Measurements from private communication with mine operator. Statement is the judgment of the 

authors.

For that reason, bottom and side 

boundaries were fixed for normal displacement and loading was by gravity before any 

excavations were introduced to the model.

Figure 18. FLAC3D model showing topography.

Each color represents a different member of the strata.

 
45

To use FLAC3D to model longwall mining, there are two significant challenges. These are:

• Simulation of caving or gob loading; and

• Simulation of local effects, particularly of the coal seam—simulating such effects 

would require building a model with such fine zones that the model would be too 

large for available workstation memory and also require long computational times to 

complete the task, even if such memory were available.

Gob Simulation

The problem of how to reasonably and accurately model gob loading has never been solved 

well. In longwall coal mining, it is not currently possible to measure loading of the gob. Maleki 

et al. [1984] measured pressure at the floor of gob at various points in a retreat pillar section that 

was mined in similar fashion to a longwall panel. That is, a longwall-like panel was mined by 

developing two rows of pillars at the face end of the panel. One row of pillars closest to the gob 

was mined, leaving one row of pillars. The next row of pillars was then developed, and the cycle 

repeated. This sequence allowed placement of Gloetzl cells (a brand of earth pressure cells) on 

the floor of the cross-panel entries. The cells were buried in 0.3 m (1 ft) of gravel and covered 

with a conveyer belt for protection. The hydraulic lines led to the gate roads, and these were 

protected with slotted wooden 2 by 4 pieces, overlapped and fastened together around the lines. 

These measurements showed that initial panel mining resulted in almost all load being 

transferred to the abutments and gate roads. Caving was largely controlled by the presence of 

periodic faults (that is, when a fault was undermined). Others have installed instrumentation to 

measure gob loading, but either critical details of the instrument and installation were missing to 

permit critical review [Ramírez Oyanguren 1972; Wade and Conroy 1980] or the nonlinear 

behavior resulting from the absence of full contact between the rigid cylinder and the borehole 

wall does not inspire full confidence in the results [Wade and Conroy 1980].

Point measurements, even over time, do not create a full picture of gob loading, but gob 

loading should vary according to stratigraphy and structural features. Thus, the empirical 

standard of β = 21° is not likely to hold true for cases having massive, strong strata in the 

overburden.

This report describes three approaches to modeling gob loading. In using any of the three 

approaches, the model still must be calibrated and verified.

Gob Stiffness Increases Linearly with Increasing Stress

Modeling the nonlinear nature of gob loading took a significant step when Zipf [USBM 

1992a, 1992b] included a gob hardening material in Mulsim/NL. Previously, the gob had been 

represented as an inserted linear-elastic material that could be adjusted because of changing cave 

heights [Beckett and Madrid 1986; USBM 1988, 1992c]. The basic equation for the gob modulus 

was
46

Egob = (

EF − EI

n σF

) σ + EI

n

, (13)

where Egob = gob modulus,

σF = final or ultimate gob stress,

EI = initial gob modulus,

EF = final or ultimate gob modulus (the modulus at σF),

σ = gob vertical stress, and

n = gob height factor—the ratio of gob height to seam height. This factor is needed to 

reduce the gob stiffness if the gob height is larger than the seam height.

As Zipf [USBM 1992b] showed, an expression for gob stress as a function of strain or 

closure can be obtained by solving the differential relation between stress and strain,

dσ = Egob dε, (14)

where ε = seam closure strain.

The solution produces

σ = 

EI

n

(

n σF

EF− EI

) {e[(EF− EI

n σF

)(D

h

)] − 1}, (15)

where D = seam closure, and

h = seam height.

Heasley [1998] implemented this same equation in LaModel. In LamPre, the gob wizard 

assumes an initial modulus of 0.689 MPa (100 psi) and an ultimate stress of 27.58 MPa (4,000 

psi) [Heasley 2010]. It uses a built-in version of the LaM2D (two-dimensional LaModel 

program) to solve for the final modulus so that gob loading matches that suggested by the 

empirical method.

The Pappas and Mark Gob

Pappas and Mark [USBM 1993] conducted several tests on three materials to determine how 

to characterize gob stiffness for numerical models. From photographs of gob material, they 

developed a method to determine three-dimensional particle-size distribution from twodimensional photographs and to scale these distributions down to laboratory size. Three 

materials were then used to construct 20 samples total of shale, weak sandstone, and strong 

sandstone. The specimens were tested in a chamber with an inner diameter of 36.36 cm (14.314 

in) and a height of 30.48 cm (12 in). The samples were filled to about 2.54 cm (1 in) of the top, 

and a top platen was used to apply load. Initial weight with initial volume was used to determine 

initial void ratio.

Results showed nonlinear stiffness for each material. Salamon’s equation for compressive 

behavior of backfill [1990] was fitted to the experimental data very well. His equation is
47

σ = 

E0 ε

1− ε

εm

, (16)

where σ = gob stress

E0 = initial secant modulus,

ε = strain, and

εm = maximum strain.

This equation can be differentiated (dσ

dε ⁄ ) to determine the current tangent modulus, 

Et = E0 = 

2σ

εm

+ σ

2

εm

2

 E0

, (17)

where Et = tangent modulus. 

Parameters were fitted for each of the three materials. For shale, weak sandstone, and strong 

sandstone, the fitted equations are (with stress in units of psi), respectively,

σ = 

1110 ε

1− ε

(

1

2.26 ⁄ )

, (18)

σ = 

1340 ε

1− ε

(

1

2.49 ⁄ )

, and (19)

σ = 

1890 ε

1− ε

(

1

2.34 ⁄ )

. (20)

These equations might be used easily in numerical models to calculate stresses in gob material 

following excavation of a cut in a panel or mining a pillar in a retreat section.

Alternatively, Pierce [2010a] fit a general equation for the instantaneous gob modulus that 

conforms to the Pappas and Mark results [USBM 1993]. That equation is described further in the 

next section.

Longwall Caving Model

Itasca Consulting Group developed a model for block caving for two mining-industry-funded 

projects, the International Caving Study (ICS) and the Mass Mining Technology Project (MMT). 

The conceptual model, shown in Figure 19, shows a mobilized or caved volume or zone, below a 

volume of yielded material that has developed much fracturing, but has not displaced much. An 

air gap is usually between these zones. Above the yielded zone, microseismic events have 

occurred as a result of joint slip and fracture extension in the seismogenic zone. Elastic material 

is, of course, above the seismogenic zone.
48

Figure 19. Conceptual model of caving. After Pierce and Board [2010a],

who adapted this figure from Duplancic and Brady [1999].

The model uses the strain-softening ubiquitous joint model to represent cohesion weakening, 

tensile strength weakening, friction strengthening, and dilation in zones having a continuum 

matrix and embedded ubiquitous joints. Clark [2006] first developed the ubiquitous joint rock 

mass model for FLAC, but it was later adapted to use with FLAC3D [Sainsbury et al. 2008; 

Board and Pierce 2009]. 

During caving, the rock mass increases in volume because of dilation under shear or 

volumetric expansion under tension. This increase in volume decreases the stiffness of the caving 

material. 

Pierce and Board [2010a] adapted this model for sedimentary deposits. This adaptation is 

described here and briefly in Appendix C. Their conceptual model for sedimentary deposits is 

shown in Figure 20. In this case, the mobilized zone is the same as the indicated cave zone, and 

the fractured zone is the same as the yielded zone. However, the equivalent of the seismogenic 

zone is absent from the figure. Pierce and Board [2010a] state that this model “is likely to be more 

complex in longwalling, involving slip and tensile failure on large-scale persistent bedding planes 

and brittle failure of massive, thick, brittle units (e.g. sandstone) as well as slip on open joints, 

opening of new fractures in tension and slip on major faults.”

Poeck et al. [2008] conducted a study using the Universal Distinct Element Code (UDEC) 

and compared caving with random blocks formed by Voronoi tessellation, a method derived 
49

from the work of Voronoi [1908], with blocks characteristic of stratified ground. The results 

showed that stratified ground exhibits less bulking and more surface subsidence, suggesting that 

a lower dilation angle and lower maximum porosity are appropriate in stratified ground 

compared to porphyries, where the block caving mining method is used.

Figure 20. Conceptual model of caving in longwall mining. After

Pierce and Board [2010a]. Modified from Singh and Kendorski [1981].

In their tests on scaled gob materials, Pappas and Mark [USBM 1993] reported equations 

relating tangent modulus of the material with unconfined compressive strength (UCS) of the 

material and the average shape factor (thickness to width ratio) of the materials. The equations 

took the form:

Et = a (UCS) + b (shape factor) − c, (21)

where a, b, and c are constants that vary with bulking factor. Pierce [2010b] fit an equation to 

each of these constants, because they were related to bulking factor. By using volumetric strain 

(εvsi) (bulking factor = 1 + εvsi) as the dependent variable, he fitted the following equations to 

represent the constants:

a = 0.1316(εvsi)

−2.145

, (22)

b = 1110.5(εvsi)

−2.574, and (23)

c = 981.14(εvsi)

−2.318

, (24)

where a is dimensionless, and b and c have units of psi. 

Pierce [2010b] noted that these equations were valid only in the volumetric strain range of 

0.25 to 0.50. The upper limit of bulking is manually set to be within this range. For caving 

material having a value of εvsi between 0 and 0.25, the tangent elastic modulus is interpolated 

linearly between the intact modulus and that calculated by Equation 21 with εvsi = 0.25.
50

In the original caving algorithm, much of the microseismicity occurred before peak strength. 

In the case of longwall mining, there can be massive failure of units or slip along faults, both of 

which can cause release of very large amounts of energy. Because of the potential for massive 

amounts of energy release, energy tracking was set up to keep track of dissipated and stored 

elastic energy of each zone. The tracking also included separating the volumetric and deviatoric 

components of both dissipated and stored elastic energy, along with the totals of both [Pierce and 

Board 2010a].

The original Longwall Modeling Environment [Pierce and Board 2010b] had FISH 

(FISHish) functions that read strata information and properties from a text file. These functions 

set up a uniform and horizontal grid for each stratum, with a radially constructed surrounding 

grid that extends to some far-field boundary. A driver file called the functions to execute 

construction of the grid, assignment of properties, setting up of panel mining, and panel mining. 

The authors modified these functions to exclude the radial zones out to a far-field boundary. 

Instead, the area of interest formed its own boundary, and sides and bottom boundaries were 

fixed in the normal direction. The topographic model generator described earlier was 

incorporated.

Detailed Pillar Models and Equivalent Element Method

The size of a panel-scale model would require more zones than is possible or practical for 

either Mine A or Mine B panels. However, coarse elements do not allow for direct simulation of 

gate roads and the complexities of pillar loading in the gate roads of a longwall panel. Board and 

Damjanac [2003] (see also [Board et al. 2007]) developed a method to capture the detailed pillar 

and rib behavior to include in a panel scale model with coarser zones. This is done by 

constructing and loading fine-zoned pillar models that include detailed strata and structural 

features of and near the seam that are representative of actual geometry, material behavior, and 

conditions. An example for a half pillar is shown in Figure 21. A different model is required for 

each pillar (or half- or quarter-pillar), barrier, and solid-coal geometry in the panel model. A 

detailed model is loaded by applying a small, downward, even, constant velocity at the top 

boundary of the model such that the model maintains quasi-equilibrium. Two models of each 

case, one with plasticity and one that is purely elastic, are required so that macro-seam plastic 

behavior can be separated from elastic behavior.

Esterhuizen and Mark [2009] developed a procedure for implementing the Board and 

Damjanac approach to capture the detailed pillar behavior as a one-dimensional equivalent 

element that could be implemented into the panel model. The equivalent element has for 

dimensions the height of the seam and the width and length of the outer boundaries of the 

detailed model. The equivalent element addresses are set up in a memory chain in a FISH 

function. This allows the program to set all stress components except the vertical stress to zero at 

each calculation step, thus keeping the equivalent element one-dimensional.

The strain determination in this report differs from the one implemented Esterhuizen and 

Mark. Esterhuizen and Mark used strain at one set of grid points at the center of the pillar. Here 

the authors, instead, computed a strain that was averaged over the entire plan view of the detailed 

pillar model. An average stress was calculated from those zones whose centroids were within 

one zone height of the midpillar plane. Arrays of these grid points were established before 

loading the model.

The objective of modeling the detailed pillar was to obtain a cohesion-versus-strain curve 

that represented the nonlinear plastic behavior of the pillar, floor, and roof near the pillar, 
51

combined and represented as if all such plastic behavior is in the horizon of the excavation height 

(height of the pillar). The details of determining this curve for a particular equivalent element are 

found in the section Equivalent Elements and Detailed Pillar Models of Appendix C.

In the case of Mine A, for which a large multipanel model was constructed, the entire DU 

Seam was replaced with equivalent elements, with each set of equivalent elements having the

same dimensions. Upon converting to equivalent elements after establishing equilibrium of the 

unmined panel model, the stress of each equivalent element having entry excavations was 

adjusted according to the extraction ratio.

Figure 21. Example of a detailed model of half of a pillar showing strata as FLAC3D groups.
52

After the model was executed to simulate mining the longwall panels, the displacement 

history of the elements representing locations of instrument sites was obtained. This information 

was used to determine stress state at instrument sites (for example BPC locations) within the 

detailed pillar model, most often by interpolation between saved states. These calculated stresses 

at instrument locations might be referred to as synthetic instrument stresses.

This method had the disadvantage that, while the detailed pillar model was loaded evenly, the 

equivalent element was loaded unevenly, especially near the mined panel. This caused 

nonuniform closure across the equivalent elements. Therefore, the synthetic instrument stresses 

were just estimates, and with some error, particularly when the face was near the equivalent 

element. The authors’ arsenal of detailed pillar model script functions has the capability of 

adding a tilt in the loading surface with initial linear variation in velocity of the top boundary. 

However, that capability was never used because the “tilt” of an equivalent element changes with 

the progress of mining, making it nearly impossible to load the detailed model in the same way 

for every single equivalent element. Instead, presence of error is acknowledged, but the user can 

estimate location of the largest errors in the detailed pillar models, as panel mining effects on 

instruments are estimated.

Interchanging Tools for Various Modeling Steps

In the process of modeling tool testing and analysis, the advantages and disadvantages of 

each tool came to light. The various scales necessary for modeling the problem accurately caused 

examination of which tool might be optimum for a particular part of the problem, and whether an 

interface between results and inputs might be possible. Appendix C describes the different parts 

of a modeling problem—in situ stress distribution, pillar-scale modeling, and panel-scale 

modeling—and how they might optimally be accomplished with more than one tool, with the 

output of one tool used as input to another tool. For example, for highly variable topography, 

FLAC3D might provide the most accurate result of topographic loading. Such results, if grids 

match that of LaModel, for example, can be input directly to LaModel, thanks to a slight 

modification made by Heasley, mentioned briefly by Whyatt et al. [2011], and described more 

fully in Appendix C.

The same can be said of other tools. Simple spreadsheet calculations of pillar behavior, 

including calculations of synthetic instrument readings, according to various pillar models can be 

compared to actual measurements to infer the best pillar model. The best pillar model might then 

be optimally used in a boundary element code.

Complicated failure mechanisms involving floor and/or roof require investigations with 

detailed pillar models using a volume-element tool, such as FLAC3D. An analysis of important 

mechanisms is required in evaluating the optimum tool for any phase of modeling.

Calibration Procedures

The two sites were not conducive to installation of many extensometers, which would be 

required to do the kind of calibrations suggested by Pariseau et al. [1984], Pariseau et al. [1986], 

and Pariseau et al. [USBM 1992d]. Microseismic activity is troublesome in sedimentary deposits 

because elevation of events cannot be located accurately unless a good vertical velocity model is 

determined. Therefore, the methods of Andrieux et al. [2008] to calibrate strength and post-peak 
53

behavior cannot be used in this study. The principles of the approach of [Wiles 2007] can be 

used for these two sites, but the three focuses or steps in the approach of [Heasley 2008b] seems 

appropriate for all evaluation tools, and not just displacement discontinuity codes. Those steps 

will be restated later in this section. Model calibration procedures are part of the evaluation 

process of design.

Although the mine layout designs at both Mines A and B were determined before this study, 

it is useful to discuss the process of mine layout design with reference to Stacey’s engineering 

wheel of design (Figure 1). Probably the original problem statement used by mine engineers was 

to determine the size of gate road pillars to maintain safe openings and reduce the risk of mininginduced seismic events. Likely requirements and constraints were that: (1) pillars needed to 

safely bear the load transferred from the overpanel weight—i.e., the weight of the overburden 

over the mined panel; and (2) other hazards should not be introduced or increased. In the design 

wheel process, efforts were made to determine several unknowns, but that information was not 

significantly used in the initial gate road design process.

For example, as previously mentioned, at Mine A the empirical method, Analysis of 

Longwall Pillar Stability, was used. Because ALPS does not have a critical stability factor 

associated with depth of cover, Mine A developed its own local ALPS database for deep cover. 

A local critical stability factor was determined, but MSHA agreed to a critical stability factor that 

was 14% larger, resulting in the large pillar size for two rows of chain pillars. In effect, efforts in 

step 3 of the wheel of design process were put into developing the local ALPS database and 

developing a critical stability factor. The conceptual model was decided upon, and then pertinent 

unknowns were gathered. The result raised other concerns, such as ventilation. A similar story at 

Mine B resulted in a gate road system of yield pillars alongside larger pillars.

In what follows, attempts were made to improve upon the results by using modeling tools 

and applying the MSHA [2009] PIB09–03, which outlines steps to calibrate models to 

observations. However, an attempt at improvement to this process was also made, so that a 

working modification was made to the PIB steps. The modified list would be, with additions 

italicized:

1. Observe and make measurements in underground areas,

2. Evaluate which modeling tool is appropriate,

3. Estimate model parameters,

4. Model observed and measured areas,

5. Verify model accuracy,

6. Establish threshold limits,

7. Model new configurations,

8. Evaluate new configurations, and

9. Implement best alternative.

The challenge is in making good measurements with accurate and reliable instruments. What 

should be measured and with what? Some of those questions have been answered by Larson et 

al. [NIOSH 2019] and work presented earlier in this report. The most sensitive instrument was 

the borehole pressure cell (BPC), with which the load transfer distance (LTD) was measured to 

be 535 m (1,756 ft) at Mine A and probably between 256 m and 354 m (840 ft and 1160 ft) at 

Mine B for 335 m (1,100 ft) of overburden depth.

But more attention is needed to lacking information. Heasley [2008b] summarized it 

concisely in the steps he recommended for calibrating a model with LaModel. Those steps were 

to calibrate, in this order:
54

1. Rock mass stiffness,

2. Gob stiffness, and

3. Coal strength.

The process is slightly more complicated than this simplistic list, but it captures the essence 

of the process. First, the stiffness of the overburden in any tool has to be calibrated to distribute 

the overpanel load over the abutment accurately. Heasley [2008b] recommended, in the absence 

of measurements and observations, to calibrate to the empirical standard. For rock mass stiffness, 

he calibrated to distance from the gob within which 90% of the distributed overpanel weight was 

transferred. This was necessary instead of using LTD because the LaModel solution theoretically 

never goes to zero, except for approximating it at an infinite distance from the mined panel. 

This is a data-limited problem [Starfield and Cundall 1988], in that nothing is known about 

loading of the gob—i.e., how much of the overpanel weight is transferred through the gob. In the 

cases described in this report, no measurements of gob loading were made, nor could the amount 

of gob loading be inferred by approximating the abutment loading curve. If gob loading could be 

estimated reasonably, then gob stiffness (presumed nonlinear) must be adjusted to meet that gob 

loading target. That adjustment in turn affects LTD so that rock mass stiffness must be adjusted 

again. This iterative process is necessary until both rock mass stiffness and gob stiffness are 

calibrated. 

Floor and roof strata properties can be calibrated and verified by observations and 

measurements. For example, at Mine A significant floor heave was encountered in the 2 North 

gate roads, but almost no floor heave was found in the 1 North gate roads. This difference might 

be caused by the larger pillar, but differences in strata column and properties might also need to 

be considered.

Finally, pillar strength and behavior are unknowns. Perhaps a more accurate description is 

needed for the coal strength model. This term emphasizes that selection of an appropriate coal 

strength model is required, in addition to calibrating strength amounts within that model. Perhaps 

the best way to evaluate a pillar strength model is to compare synthetic instrument readings 

calculated from various models to actual measurements at various locations in a pillar. Once a 

reasonable pillar model is selected and calibrated, it may be necessary to make slight adjustments 

to the rock mass stiffness and gob stiffness, followed by calibration adjustments to the coal 

model until all three parts of Heasley’s recommended calibration process are satisfied.

In the case of Mine A and Mine B, no measurement or reasonable estimate of gob loading 

was available. The best scenario possible was to estimate gob stiffness and to see if it provided 

gob loading in a reasonable range.

Empirical Method Calibration

The empirical method fixes the loading, stress profile, and coal strength according to the 

overburden height and panel width for all three calibration steps outlined by Heasley [2008b]. 

However, this loading profile does not reflect the long LTDs measured at Mine A and Mine B. 

The stress profile could be adjusted to a measured LTD of 535.2 m (1,756 ft), adjusted simply in 

Equation 10.

Figure 22 shows the empirical stress profile using standard equations and the stress profile 

calibrated to measured LTD. Locations of gob, headgate pillars, and the next panel of coal are 

shown to give an indication of the contrast in pillar loading in each case. Larson and Whyatt 

[2013] found the area under the calibrated empirical curve to be low compared to a Mulsim 
55

profile and adjusted the calibrated curve proportionally to have equal area compared to the 

Mulsim profile. Even so, the pillar loading next to the mined panel was low compared to the 

loading calculated with the Mulsim model. 

Using such a calibrated empirical approach is not recommended, because it deviates from the

standard approach. Another conceptual model is necessary.

Figure 22. Standard empirical stress profile for Mine A headgate geometry and

empirical stress profile calibrated to measured load transfer distance (LTD).

LaModel Calibration 

LaModel is based on another conceptual model—a nonlinear material model for the seam 

surrounded above and below by a series of plates having no friction or cohesion between them—

and deserves consideration in calibration toward design analysis because of its widespread use. 

Calibration of a model using LaModel could only be accomplished for the rock mass stiffness, 

given that no measurements were taken that could be used to reasonably estimate gob loading.

As a starting point, elastic modulus of the rock mass was calculated as a thickness-weighted 

average of the elastic moduli of the overburden listed in Table 3. Lamination thickness was then 

calculated with the LamPre numerical modeling wizard, using Equation 25:
56

t = 2 Es √12 (1− ν2)

E h (

5 √H − d

ln(0.1)

)

2

, (25)

where E = elastic modulus of overburden,

ν = Poisson’s Ratio of overburden,

Es = elastic modulus of the seam,

h = seam thickness,

d = extent of coal yielding at the edge of the gob, and

H = seam depth.

Values from Table 3 were used as much as possible, but the default coal strength of 6.21 

MPa (900 psi) was used to conform to the empirical standard. The gob wizard in LamPre was 

used to determine final gob modulus associated with 27.58 MPa (4,000 psi)—the default 

ultimate stress.

In calibrating LaModel when there are no measurements or observations to indicate LTD, 

Heasley [2008b] recommends calibrating to the empirical standard. This is done by requiring that 

the distance from the gob at which 90% of the abutment loading be the same for LaModel as it is 

for the empirical method. From this equivalency, Heasley derived this equation by rearranging 

Equation 25:

Et = 

2 Es √12 (1− ν2)

h

(

5 √H − d

ln(0.1)

)

2

. (26)

Recall that the term 5 √H is the empirical distance within which 90% of the abutment load is 

found. The single seam solution is invariant with the product, Et, making it the actual rock mass 

stiffness property. 

It is not clear how to identify the D0.9 boundary in a mine. However, the LTD has been

demonstrated as measurable by Peng and Chiang [1984] and shown again recently by Larson and 

Whyatt [2012] (see also NIOSH [2020] and earlier in this report). As reported by Larson and 

Whyatt [2012], the procedure to calibrate to LTD with LaModel is to reorder Equation 5 to find 

an effective H corresponding to the LTD, and substituting the effective H into Equation 26.

Figure 23 shows contours of stress increase with respect to prepanel conditions at one 

longwall face position with the face approaching the 2 North outby station. The locations of 

instruments along the entries when first arrival of mining-induced stress increase was detected 

are superimposed for this face position. The 138-kPa (20-psi) contour in the model results is far 

from the locations of the instruments when a 20-psi increase in the cells was detected. The figure 

highlights the need for calibration of rock mass stiffness to better approximate LTD.

The calibration procedure outlined above, using effective H in Equation 26 was carried out. 

Figure 24 shows contours of model-calculated stress increase with respect to prepanel mining 

conditions, but with calibrated Et. The locations of the instruments when they detected first 

arrival of mining-induced stress increase was detected are superimposed for this face position—

the average position when the BPCs detected that stress increase. The 138-kPa (20-psi) stressincrease contour is much closer to where the BPCs detected a 138-kPa (20-psi) change. 

However, Larson and Whyatt [2013] found that the rock mass was so stiff that only 0.28% of the 

overpanel weight was transferred through the gob. By comparison, the empirical method and 

LaModel, calibrated to the empirical standard, transferred 23% and 47%, respectively, of the 

overpanel weight through the gob. The total overpanel weight is different for LaModel than for 

the empirical method because LaModel accounts for topography. Even so, the small amount of 
57

gob loading with calibrated Et strongly suggests that a laminated model is inappropriate for this 

stratigraphy.

Because of this result, no attempts were made to model the Mine B mine layout with 

LaModel. Instead, another conceptual model—a nonlinear material model for the seam in an 

elastic continuum—and its associated modeling tool (MulsimNL/Large) was considered.

Figure 23. Contours of stress increase over prepanel-mining stress

for case of Et calibrated to the empirical standard.
58

Figure 24. Contours of stress increase over prepanel-mining 

stress for the case of Et calibrated to LTD. 

MulsimNL/Large Calibration 

Calibration steps for MulsimNL/Large are the same as outlined by Heasley [2008b]—that is, 

in order, rock mass stiffness, gob stiffness, and coal strength. As with LaModel, we cannot 

determine gob stiffness with measurement with the current data set. Therefore, the authors 

proceeded with the same initial rock mass elastic modulus determined for LaModel from values 

listed in Table 3. Final gob stiffness was determined with the LamPre utility of the LaModel 

software using appropriate geometry, the coal modulus from Table 3, and a coal strength of 6.21 

MPa (900 psi)—the standard for the empirical method. This combination of rock mass stiffness 

and gob stiffness was the starting point for models that were investigated for purposes of 

calibration. 

Mulsim has elastic, elastic-perfectly plastic (or elastic followed by hardening), and elasticsoftening models, as does LaModel. These calibration exercises began with elastic, perfectlyplastic yield models because it is the most common strength model in use. However, several 

possible strength models might be implemented. For example, the Mark-Bieniawski formula 

[Mark and Chase 1997], Holland-Gaddy formula [Holland 1964], the Maleki confinement 

formula, and the Maleki structural formula [1992] all calculate various pillar strengths according 

to various criteria (for example, pillar width-to-height ratio). Appendix D contains a discussion 
59

of pillar formulas by one of the authors of this report, Dr. Jeffrey C. Johnson. He shows how 

these formulas can be integrated to provide mathematical representation of yield strength by 

location in the pillar. Such representations permit calculation of strengths necessary for 

MulsimNL/Large input files.

Yield Models

Larson and Whyatt [2012] previously demonstrated that rock mass stiffness could be 

calibrated using LaModel with a Mark-Bieniawski material yield model to measured LTD at 

Mine A. However, they found that the rock mass had to be excessively stiff so that it was 

impossible to determine a gob stiffness that would provide reasonable distribution of overpanel 

weight between the gob and the abutment [Larson and Whyatt 2013] for such large LTD with 

respect to the empirical LTD. For that reason, LaModel was not used in further analysis in this 

study.

LaModel’s LamPre has material wizards that calculate Mark-Bieniawski strength for various 

element locations. The coal material wizard’s default uniaxial strength is 6.21 MPa (900 psi). 

Other input parameters such as lamination interval and final gob stiffness are also calibrated with 

wizards to the empirical assumptions. The case of 6.21-MPa (900-psi) coal with default wizarddetermined final gob stiffness was the first case that was modeled with MulsimNL/Large. Figure 

25 shows contours of stress increase over the prepanel stress state when the face was 

approximately at the location when BPCs detected the threshold increase in cell pressure. The 

location of the line of BPCs in the headgate is indicated. The figure also shows that contours are 

affected by yielding of coal near the ribs—this effect bends the contour significantly outby as it 

nears the gate roads. This bending aside, the base trend of the contour appears to have overshot 

the instrument line slightly.

Figure 26 shows pillar strength calculated with various common pillar strength formulas with 

width-to-height ratio. For the Bieniawski and Holland-Gaddy strength models, the coal strength 

was 6.21 MPa (900 psi). The width-to-height ratios of 1 North and 2 North pillars were 6.64 and 

15.45, respectively. Figure 27 shows how these same formulas, integrated to show strength by 

distance from the rib, vary from one another with distance from the rib for a seam height of 3.4 

m (11 ft). Post-yield softening would only cause greater bending of the threshold contour outby 

as it approaches the gate roads. Examination of other pillar strength equations compared to the 

Bieniawski formula reveals less capacity to load near ribs, even for large pillars such as those 

found in 2 North. The Bieniawski formula (and by extension, the Mark-Bieniawski equation) 

seems to be the upper limit of strength for those big pillars. Therefore, the Mark-Bieniawski 

strength equations were used for another MulsimNL/Large model, but with a 9.65-MPa (1,400-

psi) strength coal. It was thought that this value was beyond the upper bound of coal strength 

possible at Mine A.

Figure 28 shows contours of stress increase with respect to the prepanel stress state when the 

face was approximately at the location when the BPCs first detected mining-induced abutment 

stress. As with the lower strength Mark-Bieniawski model, the contours curve outby as they 

approach the gate roads, which is inconsistent with measurements. However, the trend of the 

threshold contour line when it is not close to the gate roads suggests that rock mass stiffness 

would be calibrated for this strength model aside from the effect of yielding at and near the gate 

roads. This result says something about the coal strength model, suggesting that hardening must 

be involved in the seam material behavior, even near the ribs. The yield models, with elasticperfectly-plastic behavior are inadequate to model the stress distribution accurately.
60

Figure 25. Stress increase contour graph for MulsimNL/Large model of Panel 1 of

Mine A using Mark-Bieniawski [Mark and Chase 1997] 6.21-MPa (900-psi) strength model.
61

Figure 26. Pillar strengths versus pillar width-to-height ratio.

Coal strength is set at 6.21 MPa (900 psi) where applicable.

Figure 27. Strength by distance from the rib in a coal pillar

for various pillar strength criteria shown in Figure 26.
62

Figure 28. Stress increase contour graph for MulsimNL/Large model of Panel 1 of Mine A

using Mark-Bieniawski 9.65-MPa (1,400-psi) strength model [Mark and Chase 1997].

Elastic Models

Because common yield models were inadequate, an elastic model was applied. However, 

loading of the ribs was too high. To compensate for some minor yielding of the rib, the elastic 

modulus of the first and second rings of “yield” elements were reduced to 60% and 80% of the 

full amount. Figure 29 shows contours of stress increase over the prepanel state when the face 

was approximately located when the BPCs detected a 138-kPa (20-psi) increase in cell pressure. 

In the figure, the contours are only perturbed slightly near the gate roads. Moreover, the 

threshold contour appears to run very close to the instrument line. Surprisingly, the rock mass 

elastic properties for this model were determined by thickness-weighted averaging of the 

properties chosen for each member above the DU Seam in the idealized stratigraphic column. 

Figure 29 shows that the initial set of elastic properties was close enough to achieve initial 

calibration to LTD. 

The result says something more about the seam material model. The behavior at the ribs is 

softened compared to that of the interior of the pillar. However, if a strength material model is to 

be used, then the secant stiffness of the combined elastic and hardening portions of the strengthstrain model must show similar reduction compared to the full amount of elastic modulus.
63

Figure 29. Stress increase contour graph for MulsimNL/Large model using elastic

seam material with the elastic modulus in the first and second rings of elements reduced

to 60% and 80% of the full amount to simulate the effect of some yielding near the ribs.

Another way of illustrating the necessity of this softening effect is to compare measured LTD 

with “synthetic” LTD—that is, LTD as calculated from various models. Figure 30 shows 

measured LTD by BPC location along with LTD calculated at these locations from various 

models. Also shown is the average LTD of the two sites. The models having yielded coal near 

the ribs could not calculate a load transfer distance. For synthetic LTDs calculated by 

interpolation from two elements, one having yielded, the results were low, causing the synthetic 

LTDs at more interior locations to be too high compared to the measured LTDs. Only the elastic 

model with less stiff outer rings of elements provided a reasonable match between synthetic and 

measured LTDs.
64

Figure 30. Measured and synthetic load transfer distance by borehole pressure cell location.
65

At Mine B, the measured LTD was not definitive. However, for modeling calibration, LTD is 

necessary information. For the purpose of testing model calibration, site H22 was selected as the 

reference point from which to locate a longwall face in the model that should produce the 

threshold stress increase resulting from mining of the panel at the H22 site. The longwall face 

location was determined by averaging data from Table 16. For ranges of distance, the midpoint 

of each range was used as a site measurement. Weights were assigned: 1 for low confidence, 2 

for fair to good confidence of being within the range, and 10 for good confidence. The resulting 

average distance to the face along the entry was 219.4 m (719.8 ft). Using MulsimNL/Large, a 

model was constructed in which a face position was 217.9 m (715 ft) inby the H22 instrument 

site.

Figure 31 shows contours of stress increase calculated by MulsimNL/Large at a face location 

when the B-12 Panel was being mined. The stress increase is with respect to the stress state just 

before that panel was mined. The seam material was elastic with the moduli of the outer two 

rings of elements reduced, as described before. The rock mass material properties used are the 

same as those used at Mine A. The 138-kPa (20-psi) contour line appears to run approximately 

through the H22 instrument line, thus indicating that the best-guess properties that calibrated to 

LTD at Mine A appear to calibrate to LTD at Mine B as well. The uncertainty of the Mine B 

LTD makes this a weak conclusion, but the result appears to be consistent with that at Mine A.

Because gob stiffness could not be calibrated, two other final gob stiffnesses were used to 

examine the effect on calibration. The final gob stiffnesses used were 3.134 GPa (454,500 psi), 

5.114 GPa (741,700 psi), and 8.343 GPa (1,210,000 psi), and labeled soft gob, default gob, and 

stiff gob. These stiffnesses are significantly different from each other. Choice of final gob 

stiffness caused a change in the load transfer distance. However, it was found that rock mass 

stiffness could be easily recalibrated by adjusting it linearly according to the ratio of the distance 

from the yield depth around the corner of the gob to the instrument line over the distance along 

the same path to the threshold contour line.

At this point in the design process, MulsimNL/Large, with the elastic rock mass, appears to 

provide the closest match to measured LTD, but an elastic seam does not permit calculation of 

safety factors, and therefore, a simple evaluation of safety or adequacy of the design. The results 

suggest the need for a material model having strain hardening. This issue is discussed later in this 

report.
66

Figure 31. Contours of stress increase with respect to

prepanel mining stress of the B-12-Panel at Mine B.

Correlation of Model Results with Ground Condition Survey Data

Results of LaModel and MulsimNL/Large model calculations of entry closure versus ground 

condition ratings are described and shown in Appendix E. Ground condition ratings had no 

correlation to model-calculated closures. The difference in ground condition ratings is likely the 

result of variation in local structure and conditions that could not be represented in the numerical 

models.

BPC Calibration Issues Identified with MulsimNL/Large Model

Data from borehole pressure cells (BPCs) have been reduced under specific assumptions of 

horizontal to vertical loading by one of two methods: the Lu method [1984] or the Babcock 

method [1986]. Appendix F describes these methods. Because the Babcock method is nonlinear, 

it was preferred in this report for representing stress from BPCs. However, as detailed in 

Appendix F, neither calibration method provides reasonable stress values, at least at higher cell 

pressure. This is likely the result of the coal not behaving elastically. The BPC appears to act as a 

hard inclusion, so that stresses determined from raw BPC data were higher than were possible as 

estimated with the MulsimNL/Large elastic model with the modulus reduced in the outer two 

rings to simulate some yielding effect near the ribs. 
67

Therefore, the reader must be aware that the amount of stress calculated from raw BPC data 

is not accurate, particularly at higher stress. Even so, trends of BPC curves still provide 

information about the seam material behavior and are useful in evaluating potential strength 

models for coal.

The results of this study indicate that it would be useful to develop a softer inclusion 

instrument having the stable characteristics of the BPC. Such an instrument must be rugged, but 

not depend on elastic behavior of host material to be accurate.

FLAC3D Method Calibration

Larson et al. [NIOSH 2020] described various caving conditions in Panel 1 at Mine A 

ranging from immediate initial caving with gradual caving behind the longwall shields to intact 

roof sagging until it contacted the floor. In addition, they reported different roof, rib, and floor 

conditions in the gate roads; most notably, significant floor heave was observed in the headgate 

of Panel 1, but no significant floor heave was observed in that panel’s tailgate. For these reasons, 

another conceptual model that allowed failure in the roof and floor was desired. FLAC3D was 

used because it is capable of following the mechanics of failure in the roof, floor, and coal, and it 

was thought that the elastic rock mass of the displacement discontinuity codes may not be 

sufficient to follow significant failure mechanisms. Moreover, the authors of this report wanted 

to try a new caving simulation capability that was available in FLAC3D and was described 

earlier, even though caving calibration had not yet been investigated and was not performed in 

this study.

Calibration of a FLAC3D Panel Model using Stress and Strain from a FLAC3D Pillar Model

A FLAC3D pillar model, using half symmetry, comprised of the mine roof, coal seam, and 

mine floor with 6.1-m (20-ft) entries and crosscuts, was used to produce average stress-versusstrain relationships for sections of the pillar. These relationships, and those for locations in the 

pillar at which BPCs were located, as shown in Figures 32 and 33, were used to calibrate a 

FLAC3D panel model. Mine strata were included in the model for thicknesses as small as one 

foot, and for this reason, it was called a “detailed pillar model.”
68

Figure 32. Plan view of 1 North pillars and barrier pillar at

outby site with locations of borehole pressure cells.

0 30 m

NP5 NP3

NP4 NP2 NP1

SP1 SP2

SP3 SP4 SP5

BP3 BP2 BP1

distance

to line of

instruments

Inby direction

1 North outby instrumentation site

0 100 ft

Scale

face

Figure 33. Plan view of 2 North pillars and barrier pillar at

outby site with locations of borehole pressure cells.

0 30 m

SP7

SP5

SP4

SP6

SP3

SP2

SP1 NP1

NP2

NP3

NP4

NP5

NP6

NP7

BP3

BP2 BP1

distance

to line of

instruments

Inby direction

2 North outby instrumentation site

0 100 ft Scale face

Hoek-Brown parameters used for the DU Coal Seam and the other remaining coal seams are 

listed in Table 19. These properties were determined by [Esterhuizen et al. 2010b]. Rock 

properties used in the models, listed in Table 20, were based on modeling experience of Utah 

stratigraphy, and a small reduction of those properties was estimated as appropriate for western 

Colorado. A survey of material properties in the literature [Farmer 1968; Pariseau 2012; 

Goodman 1989; Blyth and de Freitas 1984; Sheorey 1997; Maleki et al. 2007] found these 
69

properties within reasonable range, even if high for field scale. Cohesion, tension, and dilation 

angle were strain softened over a plastic shear strain of 0.04. Residual cohesion for each rock 

type was 10% of its initial value. The initial and residual dilation angles for the three rock types 

were 5° and 0°, respectively.

Table 19. Elastic properties and Hoek-Brown constitutive equation parameters for all coal 

used in detailed pillar models

Parameter Amount

UCS (laboratory scale) 20.00 MPa (2901 psi)

Young’s modulus 3.00 GPa (435 ksi)

Poisson’s ratio 0.25

a 0.65

m 1.47

m, residual 1.00

s 0.07

s, residual 0.001

Peak-to-residual strain 0.04

Strain-softening ubiquitous joints (subiquitous joints is the abbreviated term used by Itasca 

Consulting Group, Inc. to refer to this strength model), with their properties listed in Table 21, 

were used to reduce rock properties from laboratory-scale to field-scale. Peak-to-residual plastic 

shear strain was 0.005 for those properties that were softened. Interfaces between strata were not 

applied. 

Table 20. Material properties used in FLAC3D detailed pillar and panel models 

Material

Young’s 

Modulus,

GPa (ksi)

Poisson’s 

ratio

Angle of 

internal 

friction,°

Cohesion,

MPa (psi)

Unconfined 

compressive 

strength,

MPa (psi)

Tensile 

strength,

MPa (psi)

Specific 

density,

kg/m3( lb/ft

3

)

Sandstone 34.47 (5,000) 0.2 40 13.05 (1,893) 56.0 (8,120) 5.6 (812) 2,595 (162)

Mudstone 27.6 (4,000) 0.25 30 16.26 (2,344) 56.0 (8,120) 5.6 (812) 2,595 (162)

Shale 20.68 (3,000) 0.35 20 19.6 (2,843) 56.0 (8,120) 5.6 (812) 2,595 (162)

Table 21. Subiquitous joint properties

Rock type Cohesion,

MPa (psi)

Residual 

cohesion,

MPa

Angle of 

internal 

friction, °

Residual 

angle of 

internal 

friction, °

Tension,

MPa (psi)

Residual 

tension,

MPa

Dilation 

angle,°

Residual 

dilation 

angle,°

Sandstone 13.05 (1,893) 0 35 35 5.6 (812) 0 5 0

Mudstone 0.16 (23.4) 0 25 25 0 0 5 0

Shale 0.07 (10.0) 0 15 15 0 0 5 0

The mine roof was meshed with 0.3 m (1-ft) thick cubes to a height of 9.8 m (32 ft) above the 

seam and 10.4 m (34 ft) below the seam. For zones located greater than 9.8 m (32 ft) above the 

seam, the vertical dimension of each successive zone increased by a ratio of 1.9. Zones located 

greater than 10.4 m (34 ft) below the seam increased in the vertical dimension by a ratio of 1.9.
70

The zone side-length in the horizontal direction was 0.3 m (1 ft) for all zones. Load was applied 

with a constant boundary velocity at the top of the mesh of 2.54 × 10-6 m/s (0.0001 in/s), where 

the time unit is not actual, but used in the static calculation process toward equilibrium.

The average vertical stress-versus-strain relationship produced from the detailed pillar model 

was used to describe the stress-versus-strain relationship for selected zones that comprised pillars 

in a FLAC3D panel model, called “equivalent elements.” Stress in the DU Seam of the pillar 

model was monitored at midheight, and strain was measured from 7.6 m (26 ft) below the seam 

to 7.9 m (25 ft) above the seam. Substituting the stress-versus-strain relationship of the 

multistrata pillar model into equivalent elements in the panel model provided a means of 

incorporating the effect of complex stratigraphy in a coarsely discretized panel model.

Figure 34 illustrates the use of this method for a 1 North pillar. In this case, a FLAC3D zone 

that represents one pillar and one-half of the adjacent entries in the panel model is indicated by 

the outer red perimeter line. This pillar is subdivided into four equivalent elements. The stressversus-strain relationship produced from section A of the detailed pillar model is used to describe 

the pillar behavior for the four detailed cases as shown in Figure 34. For the larger 2 North 

pillars, two stress-versus-strain relationships are developed from the detailed pillar model, 

indicated by “A” and “B” in Figure 35.

When the panel model is executed, corner node displacements of each equivalent element are 

monitored. These displacements for adjacent equivalent elements that represent half of a pillar, 

including half of a crosscut, are used to determine strain for half of a pillar (e.g., equivalent 

elements “A” on the upper side of the equivalent element in Figure 34). This strain can be related 

to calculated strain of the underlying detailed pillar model. Average stress is calculated by 

averaging the stress of the equivalent elements that compose the same half-pillar. This stress can 

be related also to the stress calculated by the underlying detailed pillar model. The resulting 

stress-versus-strain relationship is then used to extract stresses from the detailed pillar model for 

borehole pressure cells (BPCs) as described in the next section.
71

Figure 34. Plan view of 1 North detailed pillar model with monitored

section “A” used in FLAC3D panel model equivalent element.

Figure 35. Plan view of 2 North detailed pillar model with monitored

sections “A” and “B” used in FLAC3D panel model equivalent element.
72

Procedure for Comparing Modeled-to-Measured Stress Changes

Stress changes from the FLAC3D panel model with equivalent elements were compared to 

measured stress changes by implementing the steps listed below. The term “face distance” refers 

to the distance between an instrument location and longwall face along the entry adjacent to the 

panel. “Prepanel mining vertical stress” in a pillar refers to average vertical stress in a pillar at a 

face distance large enough such that mining-induced stress has not yet occurred. For example, 

1,790 m (5,900 ft) was a sufficient distance for the 1 North panel model. The steps for 

comparison are:

1. A FLAC3D detailed pillar model was run. The average vertical stress for section “A” 

and vertical stress for BPC locations (interpolated from adjacent zones) were plotted as 

a function of the average closure strain of section “A” as shown in Figure 36.

2. A FLAC3D panel model containing equivalent elements was run, and the resulting 

average vertical stresses and strains for equivalent elements that contained BPCs were 

paired in a spreadsheet with face distance.

3. The prepanel-mining vertical stress on an equivalent element containing instruments 

was used to calculate average pillar force on this pillar, and in turn, this force was used 

to calculate average vertical stress when applied to the detailed pillar. The resulting 

stress on the detailed pillar was larger than that of the equivalent element because of the 

smaller horizontal cross-sectional area of the detailed pillar. 

4. The closure strain corresponding to the premining detailed pillar stress was located on 

the stress-versus-strain plot as shown in Figure 36. For this example, the average 

vertical stress is 21.1 MPa (2,909 psi), and the corresponding closure strain is 0.009.

5. The vertical BPC strain changes corresponding to longwall face advance as recorded in 

the spreadsheet were located along the BPC curves in Figure 36, and the associated 

stresses were obtained for each BPC. For example, the strain change from prepanel 

mining, i.e., a face distance of -1790 m (-5900 ft), to a face distance of -30.5 m (-100 ft) 

is 0.007. The corresponding stress at this strain increment for the BPC labeled NP1 is 

6.89 MPa (1,000 psi).

6. Step 5 was repeated for various face distances, and the resulting stresses were plotted 

along with measured stresses as a function of face distance as illustrated in Figure 37, 

and with results of several other models. The comparison between measured and 

numerically calculated stresses served as a guideline for altering the parameters in the 

Hoek-Brown failure equation and improving the match between calculated and 

measured BPC stresses.
73

Figure 36. Stress-versus-strain for a quarter section “A” of a

1 North coal pillar model and calculated BPCs labeled NP1-3.
74

Figure 37. Vertical stress calculated from measurements and models for BPC locations

at the 1 North outby site, barrier pillar. A, Instrument BP3; B, BP2; and C, BP1.

-1500 -1000 -500 0

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A STRESS, psi

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70 STRESS, MPa DISTANCE FROM FACE, m

B STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--BP2

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70 STRESS, MPa DISTANCE FROM FACE, m

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0

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20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m

C STRESS, psi

DISTANCE FROM FACE, ft

 Measured

 LaModel (calibrated to ALPS)

 LaModel (rock mass stiffness calibrated)

 Mulsim (Mark-Bieniawski 900-psi coal)

 Mulsim (Mark-Bieniawski 1200-psi coal)

 Mulsim (elastic coal)

 Mulsim (elastic coal with 60% & 80%

 elastic softening)

 FLAC3D LME w/ equiv. elements

 Measured (YM softening)

 Mulsim (Holland-Gaddy k=11750 coal)

1 North Outby, Panel 1--BP1
75

Figure 37 (continued). Vertical stress calculated from measurements

and models for BPC locations at the 1 North outby site, south pillar.

D, Instrument SP5; E, SP4; F, SP3; G, SP2; and H, SP1.

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H

F G

D E

 Measured

 LaModel (calibrated to ALPS)

 LaModel (rock mass stiffness calibrated)

 Mulsim (Mark-Bieniawski 900-psi coal)

 Mulsim (Mark-Bieniawski 1200-psi coal)

 Mulsim (elastic coal)

 Mulsim (elastic coal with 60% & 80%

 elastic softening)

 FLAC3D LME w/ equiv. elements

 Measured (YM softening)

 Mulsim (Holland-Gaddy k=11750 coal)

-400 -300 -200 -100 0

0

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20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m

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30

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60

70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--SP5

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0

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20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m

-400 -300 -200 -100 0

0

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20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m

-400 -300 -200 -100 0

0

10

20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--SP1 STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--SP4 STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--SP3 STRESS, psiDISTANCE FROM FACE, ft 1 North Outby, Panel 1--SP2
76

Figure 37 (continued). Vertical stress calculated from measurements

and models for BPC locations at the 1 North outby site, north pillar.

I, Instrument NP1; J, NP2; K, NP3; L, NP4; and M, NP5.

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70 STRESS, MPa DISTANCE FROM FACE, m

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0

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70 STRESS, MPa DISTANCE FROM FACE, m

-400 -300 -200 -100 0

0

10

20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m M

K L

I J

 Measured

 LaModel (calibrated to ALPS)

 LaModel (rock mass stiffness calibrated)

 Mulsim (Mark-Bieniawski 900-psi coal)

 Mulsim (Mark-Bieniawski 1200-psi coal)

 Mulsim (elastic coal)

 Mulsim (elastic coal with 60% and 80%

 elastic softening)

 FLAC3D LME w/ equiv. elements

 Measured (YM softening)

 Mulsim (Holland-Gaddy k=11750 coal) STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--NP1

-400 -300 -200 -100 0

0

10

20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--NP4 STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--NP2 STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--NP5 STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--NP3
77

A comparison between trend lines of measured and numerically calculated stresses in 1 

North pillars and the barrier pillar follows.

Instruments located in the barrier pillar (BP1):

• Plots of measured and numerically calculated stresses for BP1 are nearly identical. 

(Stress and strain were not monitored in the detailed model for BP2 and BP3.)

Instruments located 2.3 m (7.5 ft) from the pillar rib (SP1, SP5, NP1, and NP5):

• Stresses measured by SP5, NP1, and NP5 peaked near the instrument line.

Numerically calculated stresses were at their post-failure values at -457.2 m (-1,500 

ft) from the instrument line and decreased near the instrument line.

• Both measured and numerically calculated stresses for SP1 were at their post-failure 

values at a face distance of -457.2 m (-1500 ft), and their trend lines have similar 

shapes.

Instruments located 5.3 m (17.5 ft) from the pillar rib (SP2, SP4, NP2, and NP4):

• Numerically calculated peak stresses occur before measured peak stresses with 

respect to face distance. 

Instrument location near the pillar center (SP3 and NP3):

• Plots of measured and numerically calculated stresses for SP3 have similar shapes.

Numerically calculated stresses peak before measured stresses.

• Measured peak stress for NP3 is about 60% of the stress measured by SP3, which 

suggests that NP3 did not function correctly, or there is an anomalous weak zone in 

the pillar at this location.

The same procedure that was used to compare measured to numerically calculated stress 

changes for pillars in 1 North pillars was used to compare these stresses in 2 North pillars.

Vertical stresses at BPC locations in the 2 North detailed pillar model shown in Figure 33 and

average vertical stresses for sections “A” and “B” pictured in Figure 35 were calculated. 

Numerically calculated and measured stress changes are plotted as a function of face distance in 

Figure 38, along with results of several other models.
78

Figure 38. Vertical stress calculated from measurements and models for BPCs in 2 North,

south pillar, north pillar, and next panel. A, Instrument SP7; B, SP5; C, SP4; D, SP6; and E, SP3.

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B STRESS, psi

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C D

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70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--SP5

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50

60

70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--SP4

-400 -300 -200 -100 0

0

10

20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--SP6

-400 -300 -200 -100 0

0

10

20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--SP3

-400 -300 -200 -100 0

0

10

20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m

 Measured

 LaModel (calibrated to ALPS)

 LaModel (rock mass stiffness calibrated)

 Mulsim (Mark-Bieniawski 900-psi coal)

 Mulsim (Mark-Bieniawski 1200-psi coal)

 Mulsim (elastic coal)

 Mulsim (elastic coal with 60% & 80%

 elastic softening)

 FLAC3D LME w/ equiv. elements

 Measured (YM softening)

 Mulsim (Holland-Gaddy k=11750 coal)
79

Figure 38 (continued). Vertical stress calculated from measurements

and models for BPCs in 2 North, south pillar, north pillar, and

next panel. F, Instrument SP2; G, SP1; H, NP1; I, NP2; J, NP3; and K, NP4.

-1500 -1000 -500 0

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G STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--SP2 F

H I

J K

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0

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70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--SP1

-400 -300 -200 -100 0

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70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--NP1

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0

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DISTANCE FROM FACE, ft 2 North Outby, Panel 1--NP2

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70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--NP3

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0

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40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--NP4

-400 -300 -200 -100 0

0

10

20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m
80

Figure 38 (continued). Vertical stress calculated from measurements

and models for BPCs in 2 North, south pillar, north pillar, and

next panel. L, Instrument NP5; M, NP6; N, NP7; O, BP3; P, BP2; and Q, BP1.

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DISTANCE FROM FACE, ft 2 North Outby, Panel 1--NP5 L

N O

P Q

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0

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70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--NP6

-400 -300 -200 -100 0

0

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40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--NP7

-400 -300 -200 -100 0

0

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30

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50

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70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--BP3

-400 -300 -200 -100 0

0

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20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--BP2

-400 -300 -200 -100 0

0

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20

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40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--BP1

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0

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30

40

50

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70 STRESS, MPa DISTANCE FROM FACE, m
81

A comparison between measured and model-calculated stresses in 2 North pillars and Panel 2

follows.

Instruments located in Panel 2 (BP3):

• Plots of measured and numerically calculated stresses for BP3 are similar in shape. 

(Stress and strain were not monitored in the detailed model for BP2 and BP1.)

Instruments located 2.3 m (7.5 ft) from the pillar rib (SP1, SP7, NP1, and NP7):

• Both measured and numerically calculated stresses for SP1, SP7, and NP1 were at 

their post-failure values at a face distance of -457.2 m (-1,500 ft).

• Measured stresses remain relatively unchanged for NP7, up to a face distance of 

-274.4 m (-900 ft), and then increase, whereas numerically calculated stresses were at 

their post-failure values at a face distance of -457.2 m (-1,500 ft) and decrease at a 

face distance of about -91.4m (-300 ft).

Instruments located 4.6 to 11.4 m (15 to 37.5 ft) from the pillar rib (SP2, SP3, SP6, NP2, 

NP3, NP5, and NP6):

• The low magnitude of instrument readings from SP2, SP, and SP6 at a face distance 

of -457.2 m (-1,500 ft) indicates these instruments probably malfunctioned.

• Measured stresses for NP2 and NP3 increased more rapidly than numerically

calculated stresses at face distances near the instrument line.

• Plots of measured and numerically calculated stresses from NP5 are nearly identical.

Instrument locations near the pillar center (SP4, SP5, and NP4):

• Plots of measured and numerically calculated stresses are similar in shape.

The most prominent difference between modeled and in situ pillar behavior indicated by 

comparing plots of measured and numerically calculated vertical stresses is that modeled pillar 

ribs fail before in situ pillar ribs as the longwall approaches the instrument line. An increase in 

pillar strength achieved by increasing σc in the initial Hoek-Brown yield envelope could possibly 

address this discrepancy.

A comparison between measured and numerically calculated stress changes was made to 

determine if a modification of the elastic modulus of the coal pillar could improve the match 

between modeled and in situ pillar behavior. Calculated-versus-measured vertical stress changes 

at instrument locations were plotted as shown in Figures 39 and 40. Only prefailure stress 

changes, as indicated by the instrument readings, were used. The small r2values of 0.54 and 0.32 

for 1 North and 2 North, respectively, indicate that measured and numerically calculated stress 

changes are not well correlated and, thus, the slope of the regression line cannot be used to 

provide a factor to modify the elastic modulus of the coal pillar.
82

Figure 39. Calculated vertical stress with FLAC3D versus measured vertical stress

(reduced with Babcock method) for 1 North pillars and barrier pillar.

Figure 40. Calculated vertical stress with FLAC3D versus measured vertical stress

(reduced with Babcock method) for 2 North pillars and Panel 2.
83

MulsimNL/Large with Coal and Floor Properties from FLAC3D Pillar Model Calibration

Calibration of Hoek-Brown Properties for Coal

The first step in the calibration of the MulsimNL/Large panel model was to determine the 

parameters for the Hoek-Brown equation [Hoek et al. 2002] for coal. This equation was selected 

as the strength criterion because it has been used to successfully model the in situ behavior of 

coal pillars [Duncan Fama et al. 1995; Esterhuizen et al. 2010b; Jaiswal and Shrivastva 2009, 

2012], and is written as follows:

σ1 = σ3 + σc (m

σ3

σc

+ s) ,

a

(27)

where σ1 = maximum principal strength,

σ3 = least confining stress,

σc = uniaxial compressive strength of intact rock, and

m, s, and a = empirically derived parameters.

Hoek-Brown parameters were first calibrated to a scaled stress-versus-strain curve from one 

of Bieniawski’s in situ unconfined compression tests of a pillar with a width-to-height ratio of 

2.78 [Bieniawski and Van Heerden 1975] by using FLAC3D. Experimental stresses and strains

were halved to adjust to the U.S. empirical coal strength of 6.2 MPa (900 psi) [Mark and Barton 

1996] as shown in Figure 41. The 20.6 MPa (2,985 psi) capacity of Bieniawski’s in situ pillar 

was reduced to 10.2 MPa (1475 psi) for the target curve and is consistent with Bieniawski’s 

equation, represented by Equation 28, when 6.2 MPa (900 psi) is used for strength. The specific 

weight of the coal was 1,281 kg/m3(80 lb/ft3).
84

Figure 41. Experimental, re-referenced, and model curves showing

average pillar stress versus strain for width-to-height of 2.78.

Bieniawski’s pillar equation is

σP = UCScube (0.64 + 0.36 w

h

), (28)

where σP = average pillar capacity,

UCScube = unconfined compressive strength of a coal cube with side length = 1.5 m (5 ft),

w = width of a square pillar, and 

h = height of a square pillar

A FLAC3D model was constructed of the mine roof, coal pillar, and mine floor at Mine A 

using quarter symmetry, as shown in Figure 42. The model did not include detail of stratigraphy 

but simulated one average material for the roof and another for the floor. It was then exercised to 

calibrate the Hoek-Brown parameters. The strata above the seam was constructed of mesh layers 

having thicknesses, from bottom to top, of 3, 3.7, 14.6, and 26.8 m (10, 12, 48, and 88 ft) and

side lengths of 0.3, 0.6, 1.2, and 2.4 m (1, 2, 4, and 8 ft), respectively. The mine floor was 

symmetrical with respect to the roof, except that the thickness of the 2.4-m (8-ft) zone layer was 

increased to 78 m (256 ft) to decrease the influence of boundary conditions. Load was applied by 

a constant velocity boundary condition at the top of the mesh of 2.54 × 10-6 m/s (0.0001 in/s).
85

Figure 42. FLAC3D zones for mine floor, coal seam, and mine roof.

The roof and floor in the numerical model were kept elastic with typical sandstone properties 

of 20.68 GPa (3x106psi) for the modulus [Pariseau 2012], 2,595 kg/m3(162 lb/ft3) for specific 

density, and 0.25 for Poisson’s ratio. Initial Hoek-Brown parameters developed by Esterhuizen et 

al. [2010b], who used parameter softening, were adjusted in the FLAC3D model until a stressversus-strain plot for the coal pillar produced by FLAC3D matched Bieniawski’s experimental 

curve as shown in Figure 41 [Tesarik et al. 2013].

These calibrated parameters, listed in Table 22, were then used in FLAC3D pillar models with 

various width-to-height ratios to ensure that modeled strengths were acceptably close to pillar 

strengths produced by Bieniawski’s empirical strength equation. The match between the two sets 

of strength data was acceptable up to a width-to-height ratio of 8 as shown in Figure 43. The 

maximum pillar width-to-height ratio used in Bieniawski’s tests was 3.4, which indicates that the 

use of these calibrated Hoek-Brown parameters in FLAC3D produce realistic pillar behavior.
86

Table 22. Elastic properties and Hoek-Brown constitutive equation parameters used in 

models

Parameter Amount

UCS (laboratory scale) 20.3 MPa (2950 psi)

Young’s modulus 3.79 GPa (550 ksi)

Poisson’s ratio 0.25

a 0.65

m 1.47

m, residual 0.36

s 0.07

s, residual 0.001

Peak-to-residual strain 0.051

Figure 43. Average pillar strengths from numerical pillar model

compared to Bieniawski’s pillar strength equation.
87

Calibration of Floor Properties

The next step in the calibration of the FLAC3D model of the mine floor, coal seam, and mine 

roof was to calibrate the mine floor to underground observations at Mine A. It was observed that 

the floor heaved near 51.8-m (170-ft) wide pillars and was absent around 22.3-m (73-ft) wide 

pillars. Modeled pillar widths of 52.4 m (172 ft) and 23 m (76 ft) were used to simplify mesh 

construction. These dimensions were considered close enough for purposes of this exercise.

The elastic modulus of the mine roof in the numerical model was reduced to 9.79 GPa (1.42 

× 106psi), which is in the lower range of modulus values for shale [Farmer 1968]. Specific 

density in the mine roof was 2,195 kg/m3(137 lb/ft3) and Poisson’s ratio was 0.25. 

The floor stratigraphy was represented as a continuum using the Mohr-Coulomb failure 

criterion [Jaeger and Cook 1976]. This assumption implies that there were no structures in the 

floor that dominated its response to load. It was also assumed that the stratigraphy of the floor 

beneath the two pillar sizes was the same. Young’s modulus, specific density, and Poisson’s ratio 

for the floor were the same as that of the roof.

Floor strength parameters were varied systematically in a number of models [Tesarik et al. 

2013]. The goal was to define a floor strength parameter region that would replicate floor 

deformation observations for both the 52.4-m (172-ft) wide and 23-m (76-ft) wide pillars. Floor 

heave was defined as a distortion of the floor where vertical displacement at one point exceeded 

another by 3.8 cm (1.5 in). Any model whose calculations continued until the pillar at the rib had 

shortened to 0.9 m (3 ft) (roughly 30% strain) and the relative floor displacement did not exceed 

3.8 cm (1.5 in) was designated as having no floor heave. Boundary lines that separate floor heave 

from no floor heave are plotted in Figure 44 for the two pillar sizes. The property set that results 

in no floor heave for the 23-m (76-ft) wide pillars is above the red line in the figure and the 

property set that results in floor heave for the 52.4-m (172-ft) wide pillars is below the blue line. 

The property set between the two lines produces numerical model results that satisfy observed 

underground heave or no-heave conditions of the floor for both pillar sizes.

Figure 44. Mine floor property set domain based on floor heave observations.
88

A lower, horizontal boundary of 8° was added to the material property set based on FLAC3D

results and the observed location of floor heave. It was observed that floor heave occurred at the 

center of the entry and was produced at this location by FLAC3D when the angle of internal 

friction was greater than 8°.

Application of Floor Properties in a Boundary Element Panel Model

A method of calculating the strength distribution in a pillar as a function of distance from the 

pillar’s rib was developed by Johnson et al. [2014]. They assumed that pillar strength as a 

function of distance from the pillar’s rib has the same shape as average pillar strength expressed 

as a function of pillar width-to-height ratio. This method was used to establish strength 

distributions for pillars in a panel-scale boundary element model of a section of Mine A.

The function used in this study that relates average pillar strength to pillar width-to-height 

ratio was developed using the FLAC3D model as described above. A point near the center of the 

property set domain in Figure 44, having a cohesion of 3.4 MPa (500 psi) and an angle of 

internal friction of 15°, was selected for floor properties in the pillar model. The FLAC3D model 

was run for various width-to-height ratios, and average pillar strength was plotted against pillar 

width-to-height ratio, as shown in Figure 45. The empirical Holland-Gaddy equation [Holland 

1964] was then fit to these data by setting parameter k to 9,700 lb/in3/2in Equation 29. 

Parameters in the Holland-Gaddy equation are expressed in English units for comparison with 

other values reported in the literature [Holland 1964; Lawall and Holland 1937]. The HollandGaddy equation and their material parameter k are:

σP = 

k √w

h

, (29)

where k = Gaddy constant [Gaddy 1956] (lb/in3/2) defined in Equation 30

w = pillar width (in),

h = pillar height (in),

σP = pillar strength (lb/in2), and

k = Sc √d, (30)

where Sc = coal specimen strength, (lb/in2), and

d = side length of specimen cube (in).
89

Figure 45. Average pillar strengths from FLAC3D pillar models and Holland-Gaddy equation. 

Equation 29 served as the basis for defining the vertical strength distribution as a function of 

distance from a pillar’s rib, using the method developed by Johnson et al. [2014]. This strength 

distribution, in turn, was used to assign strengths to “cells” or pillar subdivisions in the numerical 

model MulsimNL/Large [Larson and Whyatt 2013], which is an enlarged version of Zipf’s 

Mulsim/NL [USBM 1992a, 1992b]. Post-yield strength for each cell in the model was assigned 

the value of yield stress of that cell, and remained constant as a function of strain, i.e. the stressversus-strain functions for the cells were elastic, perfectly plastic. MulsimNL/Large, herein 

referred to as just Mulsim, was then used to simulate mining of the longwall panels at Mine A. 

The comparison of measured (reduced using the Babcock method [1986]) and numerically 

calculated vertical stresses for 1 North, shown in Figure 46, indicates that: 

• In general, calculated vertical stresses peak before measured stresses with respect to face

distance. The term “face distance” refers to the distance along the entry between the

location of the line of instruments and the longwall face.

• In most cases, calculated vertical stresses peaked when the longwall face was greater than

457 m (1,500 ft) inby the instruments’ locations. This is indicated by the horizontal lines

on the graphs, such as is shown in Figure 46, graph D. The line is the residual section of

the elastic, perfectly plastic, stress-versus-strain function for the Mulsim cell at an

instrument’s location.

• The trends of the measured and calculated vertical stress-versus-distance plots for

instruments located in the 1 North longwall gate roads were similar, but calculated

vertical stresses exceeded measured vertical stresses as shown in Figure 46, graphs A-C.
90

Comparison of measured (reduced using the Babcock method [1986]) and numerically

calculated vertical stresses for 2 North shown in Figure 46 indicates that:

• Calculated vertical stresses peaked before measured vertical stresses at locations near pillar 

ribs.

• The trends of vertical stress versus face distance were similar in shape for those instruments 

located near the center of pillars such as instruments SP5, SP4, and NP4 as shown in Figure 

47.

Based on the above results, an increase in pillar strength as a function of distance from the rib 

was needed in the Mulsim model in order to achieve a closer match between calculated and 

measured vertical stress trend lines. The value of “k” in the Holland-Gaddy equation was 

increased to 11,750 lb/ft3/2 as a first step, then the vertical stress distribution as a function of 

distance from the rib was calculated using the method developed by Johnson et al. [2014], and 

the panel-wide model was run again using Mulsim.

In general, increasing k in the Holland-Gaddy equation to 11,750 lb/ft3/2 did not significantly 

improve the match between measured and numerically calculated vertical stress trend lines. 

Numerically calculated peak stresses still occurred before measured peak stresses with regard to 

the longwall panel face location. Exceptions to this generality are instrument BP1, located in 1 

North as shown in Figure 46, and instruments SP4 and SP5, located in 2 North near the middle of 

the south pillar as shown in Figure 47. These results emphasize again the need for a material 

model having strain hardening.

To summarize this candidate procedure, detailed pillar models were calibrated to determine 

the range of material properties which produced observed floor behavior. A pillar equation was 

matched to the results. This pillar equation was integrated (see Appendix D for the details of the 

integration) to determine equations for calculating Mulsim cell strength parameters. Although 

this method did not work as well as hoped because of the element yielding near the ribs, it might 

well work for conditions of shallower cover, where strain hardening may not be required. Safety 

factors could then be determined, and the mine layout design evaluated. Calculation of safety 

factors is not currently incorporated into MulsimNL/Large but could be easily added.
91

Figure 46. Measured and Mulsim-calculated vertical stress in 1 North section.

A, Instrument BP3; B, BP2; C, BP1; D, SP5; and E, SP4.

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70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--BP2

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70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft

 Measured

 Mulsim (Holland-Gaddy k=11,750 lb/in3/2)

 Mulsim (Holland-Gaddy k=9,700 lb/in3/2)

1 North Outby, Panel 1--BP1

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DISTANCE FROM FACE, ft 1 North Outby, Panel 1--SP5

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DISTANCE FROM FACE, ft 1 North Outby, Panel 1--SP4

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92

Figure 46 (continued). Measured and Mulsim-calculated vertical stress in

1 North section. F, Instrument SP3; G, SP2; H, SP1; I, NP1; and J, NP2.

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DISTANCE FROM FACE, ft 1 North Outby, Panel 1--SP3 F

I J

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70 STRESS, MPa DISTANCE FROM FACE, m

 Measured

 Mulsim (Holland-Gaddy k=11,750 lb/in3/2)

 Mulsim (Holland-Gaddy k=9,700 lb/in3/2) STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--SP2

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0

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70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--SP1

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70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--NP1

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70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--NP2

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93

Figure 46 (continued). Measured and Mulsim-calculated vertical stress in

1 North section. K, Instrument NP3; L, NP4; and M, NP5.

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DISTANCE FROM FACE, ft 1 North Outby, Panel 1--NP3 K

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70 STRESS, MPa DISTANCE FROM FACE, m

 Measured

 Mulsim (Holland-Gaddy k=11,750 lb/in3/2)

 Mulsim (Holland-Gaddy k=9,700 lb/in3/2) STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--NP4

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0

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30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 1 North Outby, Panel 1--NP5

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70 STRESS, MPa DISTANCE FROM FACE, m
94

Figure 47. Measured and Mulsim-calculated vertical stress in 2 North section.

A, Instrument SP7; B,SP5; C, SP4; D, SP6; and E, SP3.

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DISTANCE FROM FACE, ft 2 North Outby, Panel 1--SP7 A

D E

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70 STRESS, MPa DISTANCE FROM FACE, m

 Measured

 Mulsim (Holland-Gaddy k=11,750 lb/in3/2)

 Mulsim (Holland-Gaddy k=9,700 lb/in3/2) STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--SP5

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0

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70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--SP4

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70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--SP6

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70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--SP3

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70 STRESS, MPa DISTANCE FROM FACE, m
95

Figure 47 (continued). Measured and Mulsim-calculated vertical stress in

2 North section. F, Instrument SP2; G, SP1; H, NP1; I, NP2; and J, NP3.

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G H STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--SP2 F

-400 -300 -200 -100 0

0

10

20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m

 Measured

 Mulsim (Holland-Gaddy k=11,750 lb/in3/2)

 Mulsim (Holland-Gaddy k=9,700 lb/in3/2) STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--SP1

-400 -300 -200 -100 0

0

10

20

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DISTANCE FROM FACE, ft 2 North Outby, Panel 1--NP1

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70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--NP2

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50

60

70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--NP3

-400 -300 -200 -100 0

0

10

20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m
96

Figure 47 (continued). Measured and Mulsim-calculated vertical stress in

2 North section. K, Instrument NP4; L, NP5; M, NP6; and N, NP7.

-1500 -1000 -500 0

0

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L M STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--NP4 K

-400 -300 -200 -100 0

0

10

20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m

 Measured

 Mulsim (Holland-Gaddy k=11,750 lb/in3/2)

 Mulsim (Holland-Gaddy k=9,700 lb/in3/2) STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--NP5

-400 -300 -200 -100 0

0

10

20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--NP6

-400 -300 -200 -100 0

0

10

20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--NP7

-400 -300 -200 -100 0

0

10

20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m
97

Figure 47 (continued). Measured and Mulsim-calculated vertical stress in

2 North section. O, Instrument BP3; P, BP2; and Q, BP1.

-1500 -1000 -500 0

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

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11000

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0

1000

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DISTANCE FROM FACE, ft 2 North Outby, Panel 1--BP3 O

-400 -300 -200 -100 0

0

10

20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m

 Measured

 Mulsim (Holland-Gaddy k=11,750 lb/in3/2)

 Mulsim (Holland-Gaddy k=9,700 lb/in3/2) STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--BP2

-400 -300 -200 -100 0

0

10

20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m STRESS, psi

DISTANCE FROM FACE, ft 2 North Outby, Panel 1--BP1

-400 -300 -200 -100 0

0

10

20

30

40

50

60

70 STRESS, MPa DISTANCE FROM FACE, m

Calibration Using Scaled Stratigraphy

The method just described did not use all information available about stratigraphy. Nearseam stratigraphy was determined from drilling reports. Cores were drilled in the roof and floor 

near both outby instrumentation sites by a contractor. For example, cores were taken from the 

roof to a depth of 9.3 m (31.5 ft) and from the floor to a depth of 9.3 m (30.5 ft) in crosscut 11 of 

2 North. In 1 North, cores were taken from the roof to a depth of 9.8 m (32 ft) at crosscut 5. A 

hole was cored in the floor to a depth of 8.7 m (28.4 ft) in entry #2 of 1 North, but its location 

along that entry is unknown.

Mine stratigraphy was used in the detailed FLAC3D pillar model in a second calibration of the 

coal strength for MulsimNL/Large. Strata type and thickness are shown in Tables 23 and 24. 

Laboratory-scale material properties for sandstone and shale were selected from published values 

as listed in Table 25 [Farmer 1968; Pariseau 2012; Goodman 1989; Blyth and de Freitas 1984; 

Sheorey 1997; Maleki et al. 2007] because measured values from core were not available. A 

value of 0.25 was assumed for Poisson’s ratio for sandstone, shale, and mudstone. Tensile 
98

strength was assumed to be 10% of the unconfined compressive strength (UCS). Strength values 

were chosen for mudstone with the assumption that the failure envelope for mudstone was 

between shale and sandstone. Laboratory properties were then reduced as shown in Tables 25 

and 26, as described below.

Table 23. Strata type and thickness for 1 North, listed in order of strata member from top 

to bottom

Material Thickness, m (ft)

Sandstone 51.2 (168)

Mudstone 0.61 (2)

Coal 0.61 (2)

Mudstone 3.66 (12)

Coal 0.30 (1)

Mudstone 2.74 (9)

Coal 0.30 (1)

Mudstone 1.52 (5)

DU seam 3.35 (11)

Mudstone 1.52 (5)

Coal 1.52 (5)

Mudstone 0.61 (2)

Sandstone 0.30 (1)

Mudstone 1.52 (5)

Sandstone 0.30 (1)

Mudstone 1.22 (4)

Sandstone 53.95 (177)
99

Table 24. Strata type and thickness for 2 North, listed in order of strata member from top 

to bottom

Material Thickness, m (ft)

Sandstone 51.21 (168)

Coal 1.22 (4)

Sandstone 0.91 (3)

Mudstone 0.91 (3)

Sandstone 3.04 (10)

Mudstone 3.66 (12)

DU seam 3.35 (11)

Mudstone 1.22 (4)

Sandstone 0.3 (1)

Mudstone 0.61 (2)

Sandstone 0.91 (3)

Mudstone 0.91 (3)

Sandstone 1.52(5)

Coal 0.61 (2)

Shale 0.91 (3)

Coal 0.91 (3)

Shale 0.61 (2)

Sandstone 0.61 (2)

Sandstone 53.34 (175)

Table 25. Laboratory-scale material properties

Material

Young’s 

Modulus,

GPa (ksi)

Poisson’s 

ratio, m/m 

(in/in)

Angle of 

internal 

friction, °

Cohesion,

MPa (psi)

Unconfined 

compressive 

strength,

MPa (psi)

Tensile 

strength,

MPa (psi)

Specific 

density,

kg/m3(lb/ft3)

Sandstone 34.47 (5,000)

a,b 0.25 34c,d 15.33 

(2,224)c,d 57.67 (8,365)a,b 5.77 (837) 2,307 (144)

a

Mudstone 27.6 (4,000) 0.25 30 16.26 (2,344) 56.0 (8,120) 5.6 (812) 2,275 (142)

Shale 20.68 (3,000)a,b 0.25 23c,d,e 15.15 

(2,197)c,d,e 45.78 (6,640)a,b,f 4.58 (664) 2,275 (142)a

a

[Farmer 1968]

b

[Pariseau 2012]

c

[Goodman 1989]

d

[Blyth and de Freitas 1984]

e

[Sheorey 1997]

f

[Maleki et al. 2007]

The target elastic modulus for the composite mine floor was 9.65 GPa (1.4 × 106psi). This 

was the floor modulus used in the FLAC3D models that satisfied field observations for floor 

heave. The reduction factor for 1 North was calculated by dividing 9.65 GPa (1.4 × 106psi) by 

the thickness-weighted laboratory modulus, yielding 0.42. The reduction factor for 2 North was 

obtained by the same method, which yielded 0.39. The average reduction factor of 0.4 was then 

used to multiply the laboratory value of Young’s modulus of each stratigraphic rock layer in 1 
100

North and 2 North to obtain field-scale moduli. This value is midrange of moduli reduction 

factors produced from a collection of test data [Heuze 1980].

The laboratory-scale strength properties for the angle of internal friction and UCS were 

reduced using the same method used to reduce Young’s moduli and are listed in Table 26. The 

cohesion was calculated from the reduced angle of internal friction and reduced UCS. The 

average laboratory material properties for each major rock type are shown in Figure 48. The 

scaled properties, also shown in the figure, are all found in the region that produces the observed 

heave or no heave condition. 

An interface was introduced between the mined coal seam and each of the adjacent layers

above and below it. Each interface was given a relatively large friction angle and tensile strength 

to provide confinement near the pillar’s rib and to help prevent heave at its location. Another 

interface was inserted between the two strata below and adjacent to the coal seam being mined.

Weak properties were assigned to this interface in the 2 North pillar model to allow horizontal 

movement and induce floor heave near the center of the floor. Cohesion and angle of internal 

friction for this interface in the 1 North model were assigned larger values than those in the 2 

North model to help prevent floor heave. This difference in interface properties was necessary 

because, if stratigraphy was included in the model, the heave/no-heave observation was not 

simulated. The interface properties are listed in Tables 27 and 28.

Table 26. Field-scale material properties for each major rock type

Material

Young’s 

Modulus,

GPa (ksi)

Poisson’s 

ratio, m/m 

(in/in)

Angle of 

internal 

friction, °

Cohesion,

MPa (psi)

Unconfined 

compressive 

strength,

MPa (psi)

Tensile 

strength,

MPa (psi)

Specific 

density,

kg/m3( lb/ft3)

Sandstone 13.79 (2,000) 0.25 18 4.15 (602) 11.41 (1,655) 1.14 (166) 2,307 (144)

Mudstone 11.03 (1,600) 0.25 16 4.19 (608) 11.07 (1,606) 1.11 (161) 2,275 (142)

Shale 8.27 (1,200) 0.25 12 3.66 (531) 9.06 (1,314) 0.90 (131) 2,275 (142)
101

Figure 48. Average laboratory properties for sandstone, mudstone, and shale

are shown with reference to the region of properties, producing observed heave

or no heave of the floor, along with scaled values to be used in detailed pillar models.

Table 27. Interface properties for 1 North pillar model

Interface Normal stiffness,

MPa/m (psi/in)

Shear stiffness,

MPa/m (psi/in)

Cohesion,

kPa (psi)

Friction angle,

°

Tensile strength,

MPa (psi)

1

* 7,329,072 

(27,000,000)

7,329,072 

(27,000,000) 103 (15) 25 150

2

† 7,329,072 

(27,000,000)

7,329,072 

(27,000,000) 103 (15) 25 150

3

‡c 7,329,072 

(27,000,000)

7,329,072 

(27,000,000) 103 (15) 5 0

*

Interface between coal seam and roof

†

Interface between coal seam and floor

‡

Interface between the two strata beneath and adjacent to coal seam
102

Table 28. Interface properties for 2 North pillar model

Interface Normal stiffness,

MPa/m (psi/in)

Shear stiffness,

MPa/m (psi/in)

Cohesion,

kPa (psi)

Friction angle,

°

Tensile strength,

MPa (psi)

1

a 7,329,072 

(27,000,000)

7,329,072 

(27,000,000) 103 (15) 25 150

2

b 7,329,072 

(27,000,000)

7,329,072 

(27,000,000) 103 (15) 25 150

3

c 7,329,072 

(27,000,000)

7,329,072 

(27,000,000) 34 (5) 2 0

a

Interface between coal seam and roof

b

Interface between coal seam and floor

c

Interface between two strata beneath and adjacent to coal seam

Using the properties listed in Tables 27 and 28 produced about 22.9 cm (9 in) of heave in the 

center of the floor next to the 2 North pillar and limited heave to less than 2.5 cm (1 in) in the 

floor next to the 1 North pillar, which was not considered visually perceptible in the field 

[Tesarik et al. 2013]. These results confirmed that this material property set satisfied visual 

observations. Vertical stress-versus-strain relationships from 3 m x 3 m (10 ft × 10 ft) sections of 

the FLAC3D pillar model were then used as input to the Mulsim panel-scale model. These 

sections are shown graphically in Figure 49.

Figure 50 shows stress-versus-strain curves extracted from various cells of the 2 North 

detailed pillar model. Because of symmetry, only one quarter of the pillar was considered. 

Similar results were obtained from the 1 North detailed pillar model that was 24 m (80 ft) in 

width. The curves for the 1 North detailed pillar model that was 21 m (70 ft) in width were very 

close to those of the 24-m (80-ft) wide pillar model, such that fitting of 5-point approximation 

curves was based solely on the 24-m (80-ft) wide pillar model. In LaModel and Mulsim, each 

yield ring normally has two types of strengths, the corner cell and the side cell. From these 

results, it was determined that the cells immediately adjacent to the corner cells were 

significantly different from the other side cells, so that a different material model was warranted. 

Therefore, three types of cells per yield ring were determined—corner, adjacent to side, and side. 

There was some degree of variational trend from the corner cell to the middle side cell in any 

given ring. However, aside from the cells adjacent to the corner cell, the rest of the side cells 

were not significantly different from each other, so that they were considered together for the 

purposes of fitting a five-point, piecewise linear model to the extracted strength-versus-strain 

curves. Figure 50 shows graphs by those distinctions (i.e., corner, adjacent to corner, and rest of 

side) for each ring of elements. Included in these graphs of curves extracted from the FLAC3D

models are the five-point, piecewise linear models that were fitted visually.

Figure 51 shows the fitted five-point models from the 1-North pillar model, and Figure 52 

shows the same from the 2 North pillar model. All detailed model calculations were stopped 

where the curves end because a zone had deformed excessively and triggered FLAC3D’s “illegal 

geometry” error that stops the calculations. Because of those stoppages, no evidence of yielding 

was present in ring 4. Therefore, for purposes of implementation in MulsimNL/Large, ring 4 was 

considered elastic, and only three yield rings were used.
103

Figure 49. Horizontal cross section of FLAC3D model at seam midheight showing

how finite difference zones are grouped into “Mulsim cells.” Strength versus

strain is then extracted for each cell. The numbers represent the “yield ring” number.

Figure 53 shows the fitted five-point model for the three types of elements of each of the 

three yield rings for 1 North. For comparison, the equivalent elastic-plastic yield rings for MarkBieniawski strength models for the 1 North case are shown. The first ring models compare very 

well. The second and third rings show notable differences in the amount of final strength. The 

FLAC3D-extracted second ring models show significantly higher ultimate elastic-plastic strength 

than do the Mark-Bieniawski models. The FLAC3D-extracted third ring elastic-plastic strengths 

are higher than the Mark-Bieniawski strengths, but the differences are not as high as in the 

second ring. 

The FLAC3D-extracted material models were organized as input to a MulsimNL/Large model 

of the two panels in Mine A. As a comparison to earlier stress increase contour graphs, Figure 54 

shows stress increase with respect to the stress state before mining Panel 1 at the average face 

location when 2 North instruments detected the threshold stress increase of 138 kPa (20-psi). As 

with the other strength models, this model also shows a bending of the model-calculated 

threshold contour as it approaches and encounters the gate roads, which is incompatible with 

measurements.
104

Figure 50. Stress versus strain extracted from cells representing Rings 1, 2, 3, and 4 of the

2 North detailed pillar model. Also shown is the approximation of the curve or curves

with a five-point representation that can be input as a model in MulsimNL/Large.

A, Ring 1 corner cell; B, Ring 1 cells adjacent to corner; C, Ring 1 remaining side cells;

D, Ring 2 corner cell; E, Ring 2 cells adjacent to corner; F, Ring 2 remaining side cells.
105

Figure 50 (continued). Stress versus strain extracted from cells representing Rings

1, 2, 3, and 4 of the 2 North detailed pillar model. Also shown is the approximation of the

curve or curves with a five-point representation that can be input as a model in

MulsimNL/Large. G, Ring 3 corner cell; H, Ring 3 cells adjacent to corner; I, Ring 3 remaining

side cells; J, Ring 4 corner cell; K, Ring 4 cells adjacent to corner; L, Ring 4 remaining side cells.
106

Figure 51. Five-point strength versus strain curves used to represent

such curves extracted from detailed pillar model of 1 North pillars.

Comparison of contours in Figure 54 with the contours of the elastic model with reduced 

modulus in the outer rings (Figure 31)—the model that best matches model-calculated LTD with 

measured LTD at the BPC sites—suggests that the FLAC3D model needs improvement. The 

comparison of side stress profiles at midpanel shown in Figure 55 demonstrates that the 

FLAC3D-extracted material models cause the peak stress to be higher and further into the pillar 

than the Mark-Bieniawski 6.21-MPa (900-psi) material model, which may be an improvement. 

However, in this case, the Hoek-Brown coal model needs to reflect higher strength. When 

compared with a higher-strength Mark-Bieniawski model (Figure 28), higher strength alone 

seems insufficient, making strain-hardening near the ribs necessary. Therefore, the Hoek-Brown 

model may not be adequate to simulate the coal behavior measured at Mine A.

Even though the MulsimNL/Large model results using FLAC3D-extracted curves did not 

produce a good enough result to simulate coal behavior, particularly near the ribs, the method of 

using FLAC3D-extracted curves is demonstrated. This tool can be used with better FLAC3D

models to produce material curves that more closely match measured behavior.
107

Figure 52. Five-point strength versus strain curves used to represent

such curves extracted from detailed pillar model of 2 North pillars.
108

Figure 53. Five-point strength-versus-strain curves for three rings representing 1 North pillar

behavior shown for comparison with Mark-Bieniawski curves for a 6.21 MPa (900 psi) coal.
109

Figure 54. Contours of stress increase with respect to prepanel state with

MulsimNL/Large model using FLAC3D-extracted cell curves.
110

Figure 55. Vertical seam stress profile calculated at midpanel of Panel 1 from gob at

headgate, through the next panel to be mined, and passing through the next headgate

and beyond. Mining of Panel 1 is complete, and Panel 2 remains unmined.

For comparison, the stress profile for a 6.21-MPa (900-psi) coal is also shown.

Summary of Calibration

The model calibration procedures demonstrated in this report provide multiple ways to 

determine a reasonable model. There are various ways to measure LTD, each with varying 

sensitivities. The BPCs do not provide accurate measurements of stress change when cell 

pressures are in their upper range, presumably because the elastic condition upon which 

calibration equations are based is violated. But the BPC cell pressure histories are still very 

useful in evaluating material strength models and providing the best measure of first arrival of 

mining-induced abutment stress and LTD.

Larson et al. [NIOSH 2020] demonstrated that the entry closure and support-Can closure did 

not produce enough high-quality measurements to make determinations of LTD; however, with 

recommended adjustments in procedure, measured support Can loads might be used to determine 

a more consistent LTD that is nearly as sensitive as LTD measured with BPCs. Ground condition 

surveys, though less sensitive than BPCs, can provide useful information about changes in LTD 

and possible changes in structure along gate roads.
111

The Mulsim/NL model has been revived as MulsimNL/Large, and a five-point seam material 

model has been successfully added. Using alternative material models and extracting such 

material models from a FLAC3D detailed pillar model have been demonstrated. MulsimNL/Large 

demonstrated the ability to show reasonable behavior for a large range of final gob stiffness 

while maintaining calibration to LTD. With LaModel, the final gob stiffness could not be 

adjusted to provide reasonable gob loading while maintaining measured LTD.

In the calibration sequence, the ways to make measurements or estimations of gob-versusabutment loading by overpanel weight are lacking. Measurement methods for longwall situations 

are either not developed or not proven. Gob-loading estimation methods need to be developed 

for the purpose of calibration of gob simulation models. One way to estimate the gob loading 

fraction might be by using a calibrated caving model [Pierce and Board 2010a, 2010b], but the 

model still needs verification, and calibration procedures still need to be developed. 

In Ground Stress in Mining Part 1, Larson et al. [NIOSH 2020] reported that ground 

condition surveys reveal that conditions were variable along the gate roads, and that differences 

in caving indicate that structure significantly affects behavior. This behavior deviates from 

calibrated model predictions, which are based on constant geology. Implementation of the 

guidance provided by MSHA for calibration of models would be improved by the addition of 

measurements to observations and ground condition mapping in calibrating and verifying a 

model.

In the progress toward predicting risk of seismic events with models, it is important to have a 

well calibrated model, but it is also important to simulate the geologic features that might 

contribute to risk of seismic events. Models used might better be used to study indicators of 

seismic risk if better information about geologic structure, gob loading, and material properties 

were available. Inclusion of these features in models, along with better information on coal and 

other strata peak strength and post-peak strength properties, must be implemented because 

multiple mechanisms are known to cause seismic events (see papers from the 1958 Coal Bump 

Symposium [Brown 1958; Campbell 1958; Holland 1958; Mauck 1958; Peperakis 1958; Talman 

and Schroder 1958; Thomas 1958] and [Newman 2008; Iannacchione and Tadolini 2016; Maleki 

2017].

Referring to the wheel of design in Figure 1, the ability of the numerical models as calibrated 

in this report to indicate elevated seismic hazard was not evaluated. In fact, various pillar sizes 

were used throughout the mine (see Figure 6), and none of them prevented mining-induced 

seismic events. Pillar sizing is not the only factor to consider when designing a safe mine layout. 

Although the calibration process outlined here must be completed, other unknown factors that 

might increase the risk of such events need to be evaluated and understood.

Conclusions and Recommendations

The following conclusions can be drawn from this research:

• The 138-kPa (20-psi) cell pressure increase with BPCs served well as a way to 

determine load transfer distance and calibrate rock mass stiffness or stiffnesses. The 

cells must, however, be installed in clean boreholes and fully encapsulated in grout if 

not pre-encapsulated.

• Load transfer distance at Mine A was determined to be about four times that 

calculated by the Peng and Chiang empirical equation. The range of load transfer 
112

distance determined at Mine B was large compared to that calculated with the 

empirical equation.

• In addition to instrument data, observations of ground behavior were found to be very 

important in determining appropriate material properties and possibly material 

models. For example, drilling observations provided the basis for making the seam 

being mined less stiff and slightly weaker than other seams in the model.

• Calibration of LaModel rock mass stiffness to large load transfer distance was 

possible, but such calibrated rock mass stiffness did not allow any significant gob 

loading and, as a result, final gob stiffness could not be calibrated.

• MulsimNL/Large easily calibrated to large load transfer distance, and a wide range of 

final gob stiffness was possible for calibrating overpanel weight distribution between 

abutment and gob.

• The added MulsimNL/Large five-point material model provided additional capability 

to model strain-hardening seam behavior. This piecewise linear function is also 

capable of characterizing softening.

• Borehole pressure cell data reduction procedures in the literature do not hold true in 

the case of Mine A at higher cell pressures.

• Local variability in conditions and structure made it difficult to incorporate these 

variations in a panel-scale numerical model, which made it difficult to match 

observations to model outputs, as suggested by Skiles and Stricklin [MSHA 2009]. In 

such case, a recommendation follows. 

• Observations of caving and ground condition surveys suggest that knowledge of 

geologic structure is very important to be able to calibrate models. Prediction of 

hazards cannot be accomplished unless significant structure is known, along with its 

significant characteristics, and then represented in a calibrated model.

As a result of this study, the following recommendations are offered:

• In case of much local variation in conditions, multiple local models or even panel 

scale models with properties representing various local behavior is recommended to 

assess the effect of local variation of conditions on the mine layout design.

• The calibration of BPCs should be re-examined with careful laboratory testing in 

blocks of coal to determine how the cells behave at high cell pressure when the state 

of the coal has surpassed elasticity.

• A soft-inclusion pressure cell should be developed to minimize the effect of 

instruments acting as hard inclusions.

• More studies should be conducted on coal strength behavior, especially with regard to 

appropriate material models that describe the full stress-strain curve.

• Procedures for calibration of the longwall caving model should be developed.

• Procedures for calibration of material models using microseismic data, particularly 

peak and post-peak strength behavior, should be developed and tested.

• Research should be conducted in characterizing peak and post-peak strength behavior 

of various coal-measure rocks found in regions prone to mining-induced seismic 

events. Modeling studies should be conducted to determine conditions likely to 

produce such events (e.g., location with respect to the mined seam and thickness of 

brittle strata). 
113

• Mine design evaluation should include characterization of the full stress-versus-strain 

curve for near-seam strata and characterization of structure that might cause the risk 

of unstable failure in gate road systems to increase significantly.

Acknowledgments

The authors are greatly indebted to the mining companies that operate Mine A and Mine B 

for allowing NIOSH personnel to come on site and install instruments. Engineers and personnel 

at these mines participated in installation of the instruments and subsequent monitoring. They 

made this project possible. Agapito and Associates installed the BPCs at Mine A. Their drilling 

expertise, careful notes, and subsequent discussion of measurements and providing information 

are very much appreciated. NIOSH Mining co-workers, Brad Seymour, Craig Compton, David 

Oyler, Tristan Jones, and Dennis Dolinar participated in various parts of the field installations. 

Their efforts are very much appreciated. Co-worker Eric Zahl was on site at the mines numerous 

times to lead installation efforts, troubleshoot problems, make equipment moves, and extract 

datalogger readings. His efforts and dedication made possible the results of this project.

Helpful discussions with Dr. R. Karl Zipf (retired, NIOSH) about the Fortran source code for 

MULSIM/NL are gratefully acknowledged. Dr. Marc Loken (former Senior Research Fellow, 

NIOSH) assisted by examining the source code and changing Fortran compilers to successfully 

compile an early version of MulsimNL/Large.

Dr. Matthew Pierce, of Itasca Consulting Group, contributed to Appendix C by adding to the 

description of the Longwall Modeling Environment. The authors gratefully acknowledge his help 

and wonderful cooperation. The authors also thank Dr. Jeffrey K. Whyatt (retired, NIOSH), for 

his useful ideas on content, technical issues, and structure of that appendix.

Finally, the help, discussions, and encouragement of Dr. Jeffrey K. Whyatt over the life of

this research project and writing of both reports, Part 1 and Part 2, have been invaluable.
114

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125

Appendix A: MulsimNL/Large File Format and Verification Problems

Summary

Because of difficulties encountered in calibrating a panel-scale model using LaModel 

[Heasley 2010] to a large load transfer distance (LTD) and finding final gob stiffness that 

produced reasonable gob loading, the Zipf version of MULSIM/NL [USBM 1992b, 1992a] was 

enlarged, and other enhancements were added for ease of use. This appendix describes the 

changes that were made and the format needed for the input file for this enlarged and enhanced 

version, called MulsimNL/Large. Three example problems from the work of R. K. Zipf, Jr. 

[USBM 1992a] were run, and the results verified that MulsimNL/Large is working properly. 

Additionally, a five-point constitutive law was added to MulsimNL/Large. This addition is 

described in Appendix G but is mentioned here for the purpose of providing information on the 

input file format. 

Background

The last public version of Mulsim was developed by Zipf [USBM 1992b, 1992a]. Zipf’s 

version of Mulsim has largely been supplanted by LaModel [Heasley 2010] as a tool for 

evaluating coal mine design, largely because of the further development of LaModel and the 

shorter time to complete model calculations. However, Larson and Whyatt [2013] recently 

demonstrated that it is difficult to calibrate LaModel to a large LTD and maintain reasonable gob 

loading. The authors of this report took Zipf’s copy of the source code and enlarged the arrays so 

that it handles problems of a size comparable to that of LaModel. This was necessary because the 

maximum number of coarse blocks in both x- and y-directions in the original source code was 

70—too small to handle today’s panel-scale models. The maximum number of coarse blocks in 

the x or y-direction that could be converted to 5 × 5 fine elements was 50, making the maximum 

fine mesh size 250 × 250. In addition, the maximum number of material codes was 26, which 

was insufficient to handle the number of yield rings around larger pillars for the case study 

examined by Larson and Whyatt [2012, 2013]. The number of material codes was increased to 

52, all of which were identified by using both capital and small letters of the alphabet.

As upgrades to the code began, other needed improvements became apparent. Output files 

from any problem were given the same name, necessitating first that problems be run in separate 

folders, and second that filename changes be made so that results from different models were not 

mixed inadvertently after completion. Filename maintenance became cumbersome, even with the 

use of DOS batch files to effect the name changes.

In addition, some Fortran syntax was out of date and needed correction. Initially, a LaheyFujitsu compiler [Lahey Computer Systems 2011] was used in an attempt to compile the code

but was abandoned without success. Intel Visual Fortran Studio XE for Windows with Microsoft 

Visual Studio provided a successful development environment.5

 

5 Mention of specific products does not imply endorsement by the National Institute for Occupational 

Safety and Health.
126

Changes in Features

The current compiled version of MulsimNL/Large is version 1.2. The following features 

were changed from the Zipf version:

• The number of coarse block elements was increased from 70 by 70 to 450 by 450.

• The number of these coarse block elements that could convert to 5 by 5 fine elements 

was increased to 400 by 400 from 50 by 50, thus making it possible to have 2,000 by 

2,000 fine elements instead of only 250 by 250 fine elements.

• The number of material codes was increased to 52 (denoted by letters A through Z 

and a through z) from 26 material codes (A through Z).

• The number of significant digits of variables in all output files was increased. Stresses 

output in the Zipf version of the code were rounded to the nearest 10 units (usually 

psi). Although such rounding may be practical, it did not lend itself to code 

verification nor to close comparison to outputs from LaModel. In the current version, 

both stresses and closure displacements are output with seven decimal places. The 

responsibility belongs to the user to report specific results that are rounded 

appropriately.

• The program asks for keyboard input of the variable “rootname.” This string forms 

the first part of all input and output filenames. For example, if the root filename is 

entered as “Model1”, then the input file must be named Model1.inp, the output files 

will be named Model1_for11.dat, Model1_for21.dat, Model1_for31.dat, and 

Model1_for41.dat, and the log file will be named Model1_log.dat. In addition, two 

files are created at the start and end of a model and are named, for example, 

Model1_start.txt and Model1_end.txt. These two files only contain a date and time 

stamp so that the user can determine the time duration of the model calculations.

• A five-point strength law (constitutive model #7) was added. The last point represents 

a residual strain that remains constant for strains greater than that at the fifth point. 

Figure A1 shows an example of such a law. Details of this constitutive law and its 

verification are found in Appendix G.

• Energy calculations were updated to be in accordance with the equations described by 

Sears [2009].
127

Figure A1. Example of five-point strength law.

Possible Future Capabilities

Two capabilities found in LaModel have not yet been implemented in the MulsimNL/Large

software, but are future possibilities:

• Border symmetry (currently, only fixed borders are possible).

• Topography, implemented the same as by Heasley [1998], with forces applied and 

propagated from a datum at average depth above the seam.

In addition, it might be advantageous, as Heasley [2010] has done, to implement pre- and 

post-processing capabilities.

Input File Format

The input file variables and formats are listed in Table A1. Table A2 lists the parameters 

needed for each constitutive model. Table A3 lists additional varaibles needed for constitutive 

model 7, the five-point strength law.
128

Table A1. Records, variables, and formats for MulsimNL/Large input files

Record Variables Description Format

1 Title Descriptive title of model 20a4

2 v, e, nseam

Poisson’s ratio and Young’s modulus of 

rock mass, number of parallel seams at 

depth

f8.6, e12.5, i8

3 Nmats Number of in-seam materials (up to 52) i8

4 (eprop(n,i), i=1,12)* Properties for nth material (need nmats 

lines for this record)†

f8.0, 11e16.7

5

a11, b11, a12, b12, a13, 

b13, a22, b22, a23, b23, 

a33, b33

Primitive stress parameters (σxx, ∆σxx, 

τxy, ∆τxy, τxz, ∆τxz, σyy, ∆σyy, τyz, ∆τyz, 

σzz, ∆σzz

6(f12.5, f12.8)

6

bw, nbxx, nbyy, nosp, ifxs, 

ifxe, ifys, ifye

Block width, number of blocks in xdirection, number of blocks in y-direction, 

number of off-seam planes, fine-mesh 

starting block in x-direction, fine-mesh 

ending block in x-direction, fine-mesh 

starting block in y-direction, fine-mesh 

ending block in y-direction

f8.2, 2i8, 8x, 5i8

7

(xo(n), yo(n), zo(n), 

sthick(n), n = 1, nseam)

Global coordinates, xo, yo, & zo of the 

centroid of the lower, left block of seam n, 

thickness of seam n

4f8.1

8 ((en(i,j),i = 1, 3),j = 1, 3) Direction cosines of local coordinate 

system axes 9f8.6

9

orf, sigacc, itmax, nstep, 

mxstep

Over-relaxation factor, stress convergence 

criterion, maximum number of iterations, 

beginning mining step number, number of 

new mining steps

f8.6,f12.10,i8,24x,2i8

10 (fmptmp(ltmp,k),k=1,nexx) Fine material property codes for seam 1 for 

first mining step 2000a1

0 (fmptmp(ltmp,k),k=1,nexx) Fine material property codes for seam 2†

for first mining step 2000a1

0 (fmptmp(ltmp,k),k=1,nexx) Fine material property codes for seam 3†

for first mining step 2000a1

0 (fmptmp(ltmp,k),k=1,nexx) Fine material property codes for seam 4†

for first mining step 2000a1

11 (mtsblc(jb,ib,ns),ib=1,nbxx) Coarse material property codes for seam 1 

for first mining step 2000a1

1 (mtsblc(jb,ib,ns),ib=1,nbxx) Coarse material property codes for seam 

2

†

for first mining step 2000a1

1 (mtsblc(jb,ib,ns),ib=1,nbxx) Coarse material property codes for seam 

3

†

for first mining step 2000a1

1 (mtsblc(jb,ib,ns),ib=1,nbxx) Coarse material property codes for seam 

4

†

for first mining step 2000a1

12 (fmptmp(ltmp,k),k=1,nexx) Fine material property codes for seam 1 for 

second mining step§ 2000a1

2 (fmptmp(ltmp,k),k=1,nexx) Fine material property codes for seam 2†

for second mining step§ 2000a1

2 (fmptmp(ltmp,k),k=1,nexx) Fine material property codes for seam 3†

for second mining step§ 2000a1

2 (fmptmp(ltmp,k),k=1,nexx) Fine material property codes for seam 4†

for second mining step§ 2000a1
129

Record Variables Description Format

13 (mtsblc(jb,ib,ns),ib=1,nbxx) Coarse material property codes for seam 1 

for second mining step§ 2000a1

3 (mtsblc(jb,ib,ns),ib=1,nbxx) Coarse material property codes for seam 

2

†

for second mining step§ 2000a1

3 (mtsblc(jb,ib,ns),ib=1,nbxx) Coarse material property codes for seam 

3

†

for second mining step§ 2000a1

3 (mtsblc(jb,ib,ns),ib=1,nbxx) Coarse material property codes for seam 

4

†

for second mining step§ 2000a1

Repeat 

records 12 

and 13 for 

additional 

mining steps

- - -

*Not all fields are used, depending on the material type selected. See Table A2 and Table A3 for the list of material 

types and inputs needed.

†Material code inputs for seams 2 through 4 are only if those seams exist in the model.

‡For gravitational stresses, one would enter the absolute stresses as zero, and the changes in stress per unit of depth 

as nonzero. Changes in shear stresses per unit of depth are zero if the initial principal stresses line up with the model 

axes.

§Material code inputs for mining steps greater than the first mining step are only if those mining steps are designated 

by variable mxstep in record 9.

Table A2. Material model parameters and material properties for array EPROP in record 4 

(after Zipf [USBM 1992a], except model 7)

Model Parameter 1 Parameter 2 Parameter 3 Parameter 4 Parameter 5 Paramater 6

1

Linear elastic 

coal (1)

Young’s 

modulus

Shear 

modulus NA* NA NA

2

Strainsoftening coal 

(2)

Peak stress Peak strain Residual 

stress Residual strain Poisson’s ratio

3

Elastic-plastic 

coal (3) Peak stress Peak strain Plastic modulus Poisson’s ratio NA

4

Bilinearhardening gob 

(4)

Offset stress Offset strain Hardening 

modulus Poisson’s ratio Gob height factor

5

Strainhardening gob 

(5)

Initial modulus Final modulus Final stress Gob height 

factor Poisson’s ratio

6

Linear elastic 

gob (6)

Young’s 

modulus

Shear 

modulus

Gob height 

factor NA NA

7

Five-point 

stress-strain 

coal (7)

Stress 1 Strain 1 Stress 2 Strain 2 Stress 3

*NA = Not applicable

Table A3. Material model parameters and material properties for parameters 7 to 12 for 

model 7 for array EPROP in record 4

Model Parameter 7 Parameter 8 Parameter 9 Parameter 10 Parameter 11 Parameter 12

7 Strain 3 Stress 4 Strain 4 Residual 

stress Residual strain Poisson’s ratio
130

Verification Problems

Zipf [USBM 1992a] listed three verification problems: (1) longwall example, (2) multipleseam example, and (3) random pillar example. The contents of the input files are located at the 

end of this appendix, but the font is reduced in size to minimize the number of lines that are 

continued as multiple lines. These problems, whose inputs are listed in the format presently 

required, were run with version 1.2 of MulsimNL/Large. As the post-processing code that Zipf 

used for Mulsim was not available, the authors used OriginPro v. 9.0 to generate contour plots 

for comparison with those shown by Zipf.

The longwall example simulates the progression of a longwall retreat from mining step 1 to 

mining step 2. The area of mesh refinement includes part of the gob and one of the gate roads. 

Figure A2 shows plots of stress and seam closure calculated by MulsimNL/Large at mining step 

2. It is difficult to discern the location of grayscale contours in Zipf’s plots, but this figure seems 

to correspond well to Zipf’s Figure 24, shown here as Figure A3. A more detailed comparison is 

possible by comparing the same stress and closure profiles calculated with those provided by 

Zipf [USBM 1992a]. The corresponding profiles calculated by MulsimNL/Large are shown here 

in Figure A4. Zipf’s comparable figures are shown here as Figures A5 and A6. It should be noted 

that Zipf’s results were calculated with much less precision than does MulsimNL/Large. For 

example, his stress output was rounded to the nearest 10 stress units (for example, psi) in the 

version received by the authors. Therefore, slight differences in output are inevitable, and may be 

evident in the output plots. Even so, it appears that the profiles of Figure A4 and the contours of 

Figue A2 reasonably match those corresponding contours and profiles in the figures of Zipf 

[USBM 1992a]. 

The multiple-seam example includes an upper seam with room and pillar mining and a lower 

seam with longwall development. The metric system is used, with the two seams at 560 m and 

600 m from the surface. Only one mining step is calculated. Three material property types are 

used: (1) linear elastic with no extraction of material, (2) linear elastic with 50% extraction, and 

(3) linear elastic gob. The simulated extraction of the second material was done by using half of 

the elastic modulus used in the first material. Contours of vertical stress of each seam as 

calculated with MulsimNL/Large are shown in Figure A7. Zipf’s matching Figure 32 is shown 

here as Figure A8. Contours of closure of each seam are shown in Figure A9. Zipf’s matching 

Figure 33 is shown here as Figure A10. Again, these results seem to correspond very well to 

those of Zipf [USBM 1992a].

The random pillar example is a seam at a 20° dip. Four linear-elastic materials are used, with 

properties representing extraction ratios of 0%, 75%, 50%, and 25%, named A, B, C, and D, 

respectively. A high vertical stress gradient is used to simulate the effect of a hillside. Although 

this problem had three mining steps, only the first two steps were simulated for verification 

purposes, because Zipf [USBM 1992a] only showed contours of stress and closure for mining 

step 2. Figure A11 shows contours of stress and closure calculated with MulsimNL/Large for 

mining step 2. These contours also seem to correspond well to those shown by Zipf in his Figure 

41, shown here as Figure A12.
131

Figure A2. Contours of vertical stress (upper) and closure (lower) of results

calculated with MulsimNL/Large for longwall example from Zipf [USBM 1992a].
132

Figure A3. Longwall example—results of vertical stresses (top) and closure

displacements (bottom) around headgate during mining step 2. Stresses are in

units of psi, and displacements are in units of inches. After Zipf [USBM 1992a], Figure 24.
133

Figure A4. Cross-sectional profiles of stresses (upper) and closures (lower)

calculated with MulsimNL/Large for longwall example from Zipf [USBM 1992a].
134

Figure A5. Longwall example—normal stresses along cross section just ahead of face

during mining step 2. Stresses are in psi. After Zipf [USBM 1992a, Figure 25].
135

Figure A6. Longwall example—normal closures along cross section just behind face

during mining step 2. Displacements are in inches. After Zipf [USBM 1992a, Figure 26].
136

Figure A7. Contours of normal stresses as calculated by MulsimNL/Large

for multiple-seam example in Zipf [USBM 1992a].
137

Figure A8. Multiple-seam mining example—normal stresses. Top, Upper seam;

bottom, lower seam. Stresses are in MPa. After Zipf [USBM 1992a, Figure 32].
138

Figure A9. Contours of normal closures as calculated by MulsimNL/Large

for multiple-seam example in Zipf [USBM 1992a].
139

Figure A10. Multiple-seam mining example—normal closures. Top, Upper seam;

bottom, lower seam. Displacements are in meters. After Zipf [USBM 1992a, Figure 33].
140

Figure A11. Contours of normal stress (upper) and normal closure as calculated

by MulsimNL/Large for the random pillar example in Zipf [USBM 1992a].

7 8 9 10 11 12 13 14 15 16 17 18

7

8

9

10

11

12

13

14

15

16

17

18 Y-COORDINATE, 10

3 in

X-COORDINATE, 103 in

-518

-271

-24

222

469

716

963

1210

1456

1703

1950

Mining step 2 Vertical stress, psi

7 8 9 10 11 12 13 14 15 16 17 18

7

8

9

10

11

12

13

14

15

16

17

18 Y-COORDINATE, 10

3 in

X-COORDINATE, 103 in

-0.086

-0.039

0.007

0.054

0.101

0.148

0.194

0.241

0.288

0.334

0.381

Mining step 2 Vertical closure, in
141

Figure A12. Random room-and-pillar mining example—normal stresses (top) and normal

closures (bottom) during mining step 2. Stresses are in psi. After Zipf [USBM 1992a, Figure 41].
142

Conclusion

MulsimNL/Large version 1.2 has been verified by running the example problems provided 

by Zipf [USBM 1992a] and showing similar results. Any slight differences can be attributed to 

the greater precision used in MulsimNL/Large and slight differences between Zipf’s post 

processor and OriginPro v. 9.0 in calculating contour placement.
143

References for Appendix A

Heasley KA [1998]. Numerical modeling of coal mines with a laminated displacementdiscontinuity code. Ph.D. Dissertation. Golden, Colorado: Colorado School of Mines, 205 pp.

Heasley KA [2010]. LaModel, ver. 3.0, Morgantown, WV: West Virginia University.

Lahey Computer Systems I [2011]. Lahey/Fujitsu Fortran, ver. 7.3.

Larson MK, Whyatt JK [2012]. Load transfer distance calibration of a coal panel scale model: A 

case study. In: Barczak T et al. eds. Proceedings of the 31st International Conference on Ground 

Control in Mining. (Morgantown, WV: July 31–August 2, 2012) Morgantown, WV: West 

Virginia University, pp. 195–205.

Larson MK, Whyatt JK [2013]. Panel-scale modeling of a deep longwall panel: The MULSIM

alternative. In: Barczak T et al. eds. Proceedings: 32nd International Conference on Ground 

Control in Mining. (Morgantown, WV: July 30–August 1, 2013) Morgantown, WV: West 

Virginia University, pp. 181–188.

Sears MM [2009]. Implementing energy release rate calculations into the LaModel program. 

M.S. thesis. Morgantown, WV: West Virginia University, 95 pp.

USBM [1992a]. MULSIM/NL application and practitioner's manual. By Zipf RK, Jr. 

Information Circular 9322, Pittsburgh, PA: U.S. Department of the Interior, Bureau of Mines 

(USBM), 44 pp.

USBM [1992b]. MULSIM/NL theoretical and programmer's manual. By Zipf, RK, Jr. 

Information Circular 9321, Pittsburgh, PA: U.S. Department of the Interior, Bureau of Mines 

(USBM), 52 pp.
144

Listing of Verification Problem Input File Contents

In this appendix, the demonstration problems used by Zipf verified that the present version of 

Mulsim produces output that is equivalent to that obtained by Dr. Zipf. However, because the 

format of the input has since changed to permit more precision, the input files are listed here by 

problem. For example, the input file listings are found under subheadings that identify the test 

problem—longwall example, multiple-seam example, and random room-and-pillar example.
145

Longwall Example

LONGWALL EXAMPLE

0.150000 9.00000E+05 1

 8

 1. 5.0000000E+005 2.1700000E+005 0.0000000E+000 0.0000000E+000 0.0000000E+000

 6. 5.0000000E+003 1.7900000E+003 1.0000000E+000 0.0000000E+000 0.0000000E+000

 1. 2.7500000E+005 1.1900000E+005 0.0000000E+000 0.0000000E+000 0.0000000E+000

 3. 5.0000000E+002 0.2500000E-002 0.0000000E+000 0.3000000E+000 0.0000000E+000

 1. 4.0000000E+005 1.7400000E+005 0.0000000E+000 0.0000000E+000 0.0000000E+000

 1. 3.0000000E+005 1.3000000E+005 0.0000000E+000 0.0000000E+000 0.0000000E+000

 1. 2.0000000E+005 8.7000000E+004 0.0000000E+000 0.0000000E+000 0.0000000E+000

 1. 1.0000000E+005 4.3000000E+004 0.0000000E+000 0.0000000E+000 0.0000000E+000

 0.00000 0.04580000 0.00000 0.00000000 0.00000 0.00000000 0.00000 0.04580000 0.00000 

0.00000000 0.00000 0.09170000 //This line is a continuation of the previous line.

 300.00 50 32 0 30 45 9 24

 0.0 0.0 -6000.0 72.0

1.000000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000

1.350000 50.00000000 100 1 2

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD1111DAAD1111DAAAAAAAAAAD1111DAAAAAAAAAAAAAAAAAAA

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD1111DAAD1111DAAAAAAAAAAD1111DAAAAAAAAAAAAAAAAAAA

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD1111DAAD1111DAAAAAAAAAAD1111DAAAAAAAAAAAAAAAAAAA

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD1111DAAD1111DAAAAAAAAAAD1111DAAAAAAAAAAAAAAAAAAA

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD1111111111111111111111111111DAAAAAAAAAAAAAAAAAAA

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD1111111111111111111111111111DAAAAAAAAAAAAAAAAAAA

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD1111111111111111111111111111DAAAAAAAAAAAAAAAAAAA

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD1111111111111111111111111111DAAAAAAAAAAAAAAAAAAA

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD1111DDDD1111DDDDDDDDDDDD1111DAAAAAAAAAAAAAAAAAAA

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AAAAAAAAAAAAAAAADBCDCBDAABAAAAAAAAAAAAAA

AAAAAAAAAAAAAAACCBCCADCBCDAAAAAAAAAAAAAA

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157

Appendix B: Visual Basic Macros for Microsoft Excel to Convert Fine 

Element Material Codes to Block Material Codes

Summary

An automated process via Visual Basic macros in Microsoft Excel is described to convert 

some of the fine element material codes from a grid for LaModel to equivalent coarse block 

material codes for MulsimNL/Large. The macros used are listed.

Background

None of the Mulsim codes, including MulsimNL/Large, has had symmetrical boundary 

conditions. They are fixed—meaning that no closure is allowed in the seam at the outer x- and yboundaries of the model. To minimize boundary effects in the area of mining, boundaries must 

be far away. Placing the boundaries far away increases the size of the model substantially. 

However, the structure of a Mulsim grid is a rectangular array of even, square, coarse blocks. In 

the area of interest, the coarse blocks are further subdivided into five by five fine elements. In 

this way, the size of the problem may be kept to a minimum by minimizing the rectangular area 

of coarse blocks that is converted to fine elements.

A grid in LaModel is comprised of only fine elements. However, if symmetry is designated 

on the boundaries, then the necessity of locating outer boundaries far from the area of interest is 

minimized. In this study, an LaModel grid with a series of excavations was constructed before 

any Mulsim grid. Mulsim models of comparable size take much longer to run than do those in 

LaModel. For that reason it is desirable, when converting a grid from LaModel to Mulsim, to 

further reduce the size of the inner grid of fine elements by converting several five-by-five fine 

elements to equivalent coarse blocks. This process is done on and near the boundary of the inner 

grid of fine elements that is initially formed by the LaModel grid. The choice to convert fine 

elements to coarse blocks is made judiciously where the elements are still a reasonable distance 

from the area of mining interest. Equivalency is approximate by choosing a coarse block material 

code that best represents the average behavior of the composite of fine elements that it replaces. 

This appendix reviews the procedure used in constructing LaModel grids in this study and 

the conversion of these grids to be appropriate for MulsimNL/Large. The conversion process was 

tedious and prone to mistakes, if done manually. The need was great for the process to be 

automated.

Construction of Material Codes for LaModel

In preparing material codes for LaModel [Heasley 2010], an AutoCad map was available, but 

it was not the size of the model grid planned, and the map did not show the exact excavation 

state. Therefore, LaModel’s interface [Heasley et al. 2003; Wang and Heasley 2005] for 

AutoCad was not used to assign material property codes to cells. Instead, a grid was 

superimposed on the map and codes were chosen, fine element by fine element, and placed in a 

spreadsheet. The panel excavations and progression of panel mining were then easy to add to the 

initial gate roads model. These initial codes were comprised only of the characters, “A”, “1”, 

“Z”, and “a”, which represented the elastic material, excavated cell, Panel 1 gob and previous 
158

gob, and Panel 2 gob, respectively. However, Heasley’s [2010] pre-processing tool in LamPre 

3.0 was used for preparing input for LaModel 3.0 [Heasley 2010]. This tool was used to 

individually assign yield codes for each mining step. These codes were then assembled into one 

input file for the 185 excavations used in the model.

Each mining step was placed on a different sheet, with first row and column having index 

numbers and the next row and column being blank or having x- or y-coordinates. The sheet with 

the gate roads was then copied to the next sheet, and panel mining was able to proceed with easy 

copy and paste exercises. Thus, all 185 mining cuts were easily constructed after the initial gate 

road layout was completed.

Construction of Material Codes for MulsimNL/Large

When converting the same mining steps for use with MulsimNL/Large, the size of the fine 

mesh in LaModel was too large for efficient running of Mulsim models. It was decided to narrow 

down the dimensions of the fine-element area by converting some of the 5-by-5 fine element 

codes outside of that narrowed fine-element area to average block codes. Therefore, the 640 

columns by 1,370 rows of fine-element material codes used with LaModel were modified to 

convert some of the fine-element material codes to average block material codes. Material codes 

found in the block defined by columns 66 to 475 and rows 170 to 1,150 (counting from bottom 

to top) were kept the same. However, 5-by-5 fine-element material codes outside that area were 

converted to block material codes by averaging the peak strengths of the fine-element material 

codes within that block and selecting a block code whose peak strength was closest to that 

average value. To that end, the Mark-Bieniawski strengths [Mark and Iannacchione 1992]

calculated for 10-ft elements and 12 yield rings were used in that determination because that 

system is linear. To the outside of these converted block codes in each sheet of the spreadsheet, 

20 block rows and columns were added to form additional border distance. Thus, the left coarseblock border consisted of 20 added columns plus 13 converted columns, and the right coarseblock border consisted of 33 converted columns and 20 added columns. The bottom coarse-block 

border consisted of 20 added rows plus 34 converted rows, and the top coarse-block border 

consisted of 44 converted rows and 20 added rows. These added rows and columns served to 

distance the area of interest from the rigid boundaries of the model because MulsimNL/Large 

does not yet have implemented symmetrical boundary conditions.

A procedure was developed for automating the conversion of 5-by-5 fine-element material 

codes to an average code for block elements. The procedure was completed using Excel 

functions. Figure B1 shows an area of the spreadsheet, where column XT, in this case, is two 

columns to the right of the last column where the LaModel material codes were located on each 

sheet. In the area with the light green background, the material codes are listed along with their 

corresponding strength (in this case, 900-psi Mark-Bieniawski coal [Mark and Barton 1996]). 

For an excavated cell, zero strength is given. For the two gob materials, “Z” and “a”, some 

strength was needed that was higher than zero. The authors elected to use the first yield ring side 

element strength as the strength for both gobs for the purposes of average block strength 

estimation. 

The procedure was to copy a 5-by-5 set of fine codes from the spreadsheet, corresponding to 

a coarse block, and paste them in the area with light blue background, beginning at row 3, as 

shown in Figure B1. Rows 9 through 13 below that, in the light orange, contain the 

corresponding peak strengths obtained with Excel’s VLOOKUP function on columns XT and 
159

XU. Cell XX15, with cyan background, has the result of the average of the strengths listed in the 

light orange cells. Column XV, with light red background, contains the absolute value of the 

difference between the code strength in column XU and the average block strength (in cyan). 

The yellow highlighted area shows the minimum from column XV, the row number where that 

minimum appears (via the MATCH function), and the corresponding material code (via the 

INDIRECT function). That letter code is then copied and pasted to the centroid cell of the block 

being converted from fine-element material codes to an equivalent block code.

Even with the use of Excel functions, the risk of error is very high. Therefore, the authors 

wrote Visual Basic macros to automate this process after first copying the contents of the cells 

shown in Figure B1 to the same cells in all sheets. These macros are found later in this appendix. 

The first macro, AllSheetsToCoarse(), loops through the sheets. The second macro, 

MakeCoarseElements(), performs the automatic looping through the various sets of 5-by-5 fine

elements that correspond to a block, copies it to the cells XX3:YB7 and replaces the fine 

elements with blanks in all cells of the block except the center cell, where it places the average 

coarse block material code determined in cell XX19. The macro puts “0” in the center cell of 

blocks that will retain the fine-element codes. A copy of the original spreadsheet with fine 

element codes was retained so that a record was maintained of the fine-element codes.

After the code conversion macros were executed, the coarse-block material codes of each 

mining step were copied to an ASCII text file editor, such as Notepad. Tab codes were removed 

by the Search and Replace utility, and then saved with a name reflecting that the file has coarse 

material codes and the number of the mining step. The fine element codes were copied from the 

fine-element area to another text file, the tab codes removed, and the file saved, with the name 

reflecting that the file contains fine-element material codes and the number of the mining step.

The control block of the series of mining steps was constructed in another ASCII text file. 

This control block includes the first few lines of the input file that define the model parameters 

but does not include the material codes. The authors chose to run each mining step in parallel 

instead of in series in order to save time. Running each mining step in parallel means that the 

solution is arrived at from the premining state instead of from the previous mining step. The 

question arose on how this shortcut might affect the final output of each step; however, it was 

determined that the only likely problem was an increase in seam closure with each sequential 

mining step and that the differences would be minimal. Therefore, a model was run with 10 

successive mining steps. The same mining steps were run individually from the premining state. 

Results from the parallel and series models were compared and found to produce very small 

differences. Therefore, all subsequent models with several mining steps were run in parallel. An 

input file for each mining step was produced by using a Disk Operating System (DOS) batch file 

to combine three files into one input file for each mining step: a control file, a fine-element 

material codes file, and a block material codes file.
160

Figure B1. Portion of spreadsheet where conversion

to average coarse material code was calculated.
161

Listing of the Excel Macros

――――――――――――――――――――――――――――――――――――――

Sub AllSheetsToCoarse()

 Dim k As Integer

 k = 1

 Do While k < 36 ' 36 represents the number of sheets, each sheet representing a mining step with fine material codes before 

' execution of this macro. This subroutine loops down the sheets. The 185 mining steps of this model had to be broken up into multiple

' spreadsheet files to reduce the size of the file.

 Sheets(k).Select

 Range("C3").Select

 MakeCoarseElements

 Range("C3").Select

 k = k + 1

 Loop

End Sub

――――――――――――――――――――――――――――――――――――――

Sub MakeCoarseElements()

'

' MakeCoarseElements Macro

'

'

 Dim i As Integer, j As Integer, NumZ As Integer, NumA As Integer

 Dim fineilower As Integer, fineiupper As Integer

 Dim finejlower As Integer, finejupper As Integer

 Dim MyRef1 As String, MyRef2 As String, MyRef As String, Cont1 As String

 Dim CC11 As String, CC12 As String, CC13 As String, CC14 As String, CC15 As String

 Dim CC21 As String, CC22 As String, CC23 As String, CC24 As String, CC25 As String

 Dim CC31 As String, CC32 As String, CC33 As String, CC34 As String, CC35 As String

 Dim CC41 As String, CC42 As String, CC43 As String, CC44 As String, CC45 As String

 Dim CC51 As String, CC52 As String, CC53 As String, CC54 As String, CC55 As String

 Application.Goto Reference:="R3C3"

 i = 3 ' 3 means row 3 of the spreadsheet, or the first row of codes, since the codes begin on row 3 

' of the spreadsheet.

 finejlower = 66 + 2 ' 66 is the beginning column of fine-element material codes that will not be converted to 

' coarse-block material codes.

 finejupper = 475 + 2 ' 475 is the last column of fine-element material codes that will not be converted to coarse-

' block material codes.

 fineilower = 1370 - 1150 + 3 ' 1370 is the last row of fine-element material codes; 1150 is the last row, counting backward 

' from the last row, where fine element codes will not be converted to coarse-block material codes.

 fineiupper = 1370 - 171 + 3 ' 171 is the first row, counting backward from the last row, where fine-element material 

' codes will not be converted to coarse-block material codes.

 Do While i < 1372 ' 1372 is 2 greater than the number of rows in the material codes of the model; in the 

' spreadsheet, the 1370-row-by-640-column material codes are placed in spreadsheet rows 3 to 1372 and columns 3 to 642.

 j = 3 ' 3 means column 3 of the spreadsheet, or the first column of codes, since the codes begin on 

' column 3 of the spreadsheet.

 Do While j < 642 ' 642 is 2 greater than the number of columns in the material codes of the model; in the 
162

'spreadsheet, the 1370-row-by-640-column material codes are place in spreadsheet rows 3 to 1372 and columns 3 to 642.

 MyRef1 = "R" & i

 MyRef2 = "C" & j

 MyRef = MyRef1 & MyRef2

 Application.Goto Reference:=MyRef

 If i >= fineilower Then 'Test if within fine mesh area

 If i <= fineiupper Then

 If j >= finejlower Then

 If j <= finejupper Then

 CC11 = ActiveCell.Range("A1").Value

 If CC11 = "" Then

 GoTo Line1

 End If

 PutInZero 'Within fine mesh area; Put in zero

 GoTo Line1

 End If

 End If

 End If

 End If

 NumZ = 0

 NumA = 0

 ActiveCell.Range("A1").Select

 CC11 = ActiveCell.Range("A1").Value

 If CC11 = "" Then

 GoTo Line1

 End If

'

 If CC11 = "Z" Then NumZ = NumZ + 1

 If CC11 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC12 = ActiveCell.Range("A1").Value

 If CC12 = "Z" Then NumZ = NumZ + 1

 If CC12 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC13 = ActiveCell.Range("A1").Value

 If CC13 = "Z" Then NumZ = NumZ + 1

 If CC13 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC14 = ActiveCell.Range("A1").Value

 If CC14 = "Z" Then NumZ = NumZ + 1

 If CC14 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC15 = ActiveCell.Range("A1").Value

 If CC15 = "Z" Then NumZ = NumZ + 1

 If CC15 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(1, -4).Range("A1").Select
163

 CC21 = ActiveCell.Range("A1").Value

 If CC21 = "Z" Then NumZ = NumZ + 1

 If CC21 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC22 = ActiveCell.Range("A1").Value

 If CC22 = "Z" Then NumZ = NumZ + 1

 If CC22 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC23 = ActiveCell.Range("A1").Value

 If CC23 = "Z" Then NumZ = NumZ + 1

 If CC23 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC24 = ActiveCell.Range("A1").Value

 If CC24 = "Z" Then NumZ = NumZ + 1

 If CC24 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC25 = ActiveCell.Range("A1").Value

 If CC25 = "Z" Then NumZ = NumZ + 1

 If CC25 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(1, -4).Range("A1").Select

 CC31 = ActiveCell.Range("A1").Value

 If CC31 = "Z" Then NumZ = NumZ + 1

 If CC31 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC32 = ActiveCell.Range("A1").Value

 If CC32 = "Z" Then NumZ = NumZ + 1

 If CC32 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC33 = ActiveCell.Range("A1").Value

 If CC33 = "Z" Then NumZ = NumZ + 1

 If CC33 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC34 = ActiveCell.Range("A1").Value

 If CC34 = "Z" Then NumZ = NumZ + 1

 If CC34 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC35 = ActiveCell.Range("A1").Value

 If CC35 = "Z" Then NumZ = NumZ + 1

 If CC35 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(1, -4).Range("A1").Select

 CC41 = ActiveCell.Range("A1").Value

 If CC41 = "Z" Then NumZ = NumZ + 1

 If CC41 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC42 = ActiveCell.Range("A1").Value

 If CC42 = "Z" Then NumZ = NumZ + 1
164

 If CC42 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC43 = ActiveCell.Range("A1").Value

 If CC43 = "Z" Then NumZ = NumZ + 1

 If CC43 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC44 = ActiveCell.Range("A1").Value

 If CC44 = "Z" Then NumZ = NumZ + 1

 If CC44 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC45 = ActiveCell.Range("A1").Value

 If CC45 = "Z" Then NumZ = NumZ + 1

 If CC45 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(1, -4).Range("A1").Select

 CC51 = ActiveCell.Range("A1").Value

 If CC51 = "Z" Then NumZ = NumZ + 1

 If CC51 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC52 = ActiveCell.Range("A1").Value

 If CC52 = "Z" Then NumZ = NumZ + 1

 If CC52 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC53 = ActiveCell.Range("A1").Value

 If CC53 = "Z" Then NumZ = NumZ + 1

 If CC53 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC54 = ActiveCell.Range("A1").Value

 If CC54 = "Z" Then NumZ = NumZ + 1

 If CC54 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(0, 1).Range("A1").Select

 CC55 = ActiveCell.Range("A1").Value

 If CC55 = "Z" Then NumZ = NumZ + 1

 If CC55 = "A" Then NumA = NumA + 1

 ActiveCell.Offset(-4, -4).Range("A1").Select

 If NumZ >= 13 Then

 PutInZ

 GoTo Line1

 End If

 If NumA = 25 Then

 PutInA

 GoTo Line1

 End If

 

' Determine replacement letter and copy into appropriate cell

 ActiveCell.Range("A1:E5").Select

 Selection.Copy
165

 Application.Goto Reference:="R3C648" ' This is the location of where the 5 by 5 fine-element codes belong to a 

' block are copied for analysis of average strength. The 3 and the 648 are absolute spreadsheet row and column.

 ActiveSheet.Paste

 Application.Goto Reference:=MyRef

 ActiveCell.Range("A1:E5").Select

 Selection.ClearContents

 Application.Goto Reference:="R19C648" ' This cell in the spreadsheet provides, via the match function, the row 

' number where the closest matching strength is located. R20C648 is the cell providing the corresponding code which will be copied to the 

'middle cell of the 5-by-5 fine-element cells as the average coarse-block material code. All other cells in the 5-by-5 cells will be made blank.

 Application.CutCopyMode = False

 Selection.Copy

 Application.Goto Reference:=MyRef

 ActiveCell.Offset(2, 2).Range("A1").Select

 Selection.PasteSpecial Paste:=xlPasteValues, Operation:=xlNone, SkipBlanks _

 :=False, Transpose:=False

 ActiveCell.Offset(-2, -2).Range("A1").Select

 

Line1:

 j = j + 5 ' Go to next row of 5-by-5 fine-element material codes.

 Loop

 i = i + 5 ' Go to the next column of 5-by-5 fine-element material codes.

 Loop

End Sub

――――――――――――――――――――――――――――――――――――――

Sub PutInZero()

'

' PutInZero Macro

'

'

 ActiveCell.Range("A1:E5").Select

 Selection.ClearContents

 ActiveCell.Offset(2, 2).Range("A1").Select

 ActiveCell.Range("A1").Value = "0"

 ActiveCell.Offset(-2, -2).Range("A1").Select

End Sub

――――――――――――――――――――――――――――――――――――――

Sub PutInZ()

'

' PutInZ Macro

'

'

 ActiveCell.Range("A1:E5").Select

 Selection.ClearContents

 ActiveCell.Offset(2, 2).Range("A1").Select

 ActiveCell.Range("A1").Value = "Z"

 ActiveCell.Offset(-2, -2).Range("A1").Select
166

End Sub

――――――――――――――――――――――――――――――――――――――

Sub PutInA()

'

' PutInA Macro

'

'

 ActiveCell.Range("A1:E5").Select

 Selection.ClearContents

 ActiveCell.Offset(2, 2).Range("A1").Select

 ActiveCell.Range("A1").Value = "A"

 ActiveCell.Offset(-2, -2).Range("A1").Select

End Sub

――――――――――――――――――――――――――――――――――――――
167

References for Appendix B

Heasley KA [2010]. LaModel, ver. 3.0, Morgantown, WV: West Virginia University.

Heasley KA, Agioutantis Z, Wang Q [2003]. Automatic grid generation allows faster analysis of 

coal mines. Trans. Soc. Min. Metall. Explor. Inc., Vol. 314, pp. 75–80.

Mark C, Barton T [1996]. The uniaxial compressive strength of coal: Should it be used to design 

pillars? In: Ozdemir L et al. eds. Proceedings: 15th International Conference on Ground Control 

in Mining. (Golden, CO: August 13-15, 1996) Golden, CO: Colorado School of Mines, pp. 61–

78.

Mark C, Iannacchione AT [1992]. Coal pillar mechanics: Theoretical models and field 

measurements compared. In: Iannacchione AT et al. eds. Bureau of Mines Information Circular 

9135, Proceedings of the Workshop on Coal Pillar Mechanics and Design. Washington, DC: 

U.S. Department of the Interior, pp. 78–93.

Wang Q, Heasley K [2005]. Stability mapping system. In: Peng SS et al. eds. Proceedings: 24th 

International Conference on Ground Control in Mining. (Morgantown, WV: August 2–4, 2005) 

Morgantown, WV: West Virginia University, pp. 243–249.

169

Appendix C: Distributed Modeling of

Longwall Panels: Expanding Option6

6 This appendix was coauthored by Mark K. Larson, author of this RI, and Jeffrey K. Whyatt, formerly 

Acting Director, NIOSH Spokane Mining Research Division, Spokane, WA.

Summary

Modeling the ground response to mining of deep coal panels has long been complicated by 

the wide range of scales pertinent to design. These scales range from man-sized structures 

(entries and pillars) to individual panels to mine-wide structures (topography and barrier pillars). 

While models are readily constructed at each of these scales with a variety of modeling 

programs, comprehensive modeling has been problematic. In part, this is because different 

modeling programs often are well suited for modeling only particular parts of the problem. Some 

modeling programs also have difficulties with large contrasts in element or block sizes. In 

addition, the large computational requirements of comprehensive modeling can be prohibitive. 

However, recent progress in constructing links between modeling methods and scales promises 

to expand options available to modelers. These links allow separation of analyses into pieces that 

are both appropriate, and most efficient. That is, modeling is “distributed” into smaller, more 

optimal parts. This appendix describes a distributed approach to modeling longwall panels in a 

deep coal mine. It describes software that has been created for linking various pillar- and panelscale models. These models range in sophistication from spreadsheet calculations to LaModel 

and FLAC3D panel-scale models. In this case, these links allow division of the problem into three 

parts—in situ stress estimation, pillar behavior, and panel behavior. These capabilities are 

demonstrated by modeling gate road pillar response to mining of a longwall panel in a deep coal 

mine. 

Background

This appendix grew out of an effort to verify and calibrate a stress model of deep longwall 

coal panels under mountainous topography. The project was designed to implement recent 

MSHA guidance on verification of numerical stress models to ground condition observations 

[MSHA 2009], and then expand this process to incorporate a variety of other observations and 

measurements. The project draws from a field investigation that included rating of ground 

deterioration with face advance [Lawson et al. 2012] in accord with this guidance. The field 

investigation also included observation of ground deformation mechanisms, instrumentation of 

gate roads and pillars, and deployment of a seismic monitoring system. Further complications 

were provided by mountainous overburden and geologic structures, including a set of shear 

zones striking at low angles to the gate roads. This appendix presents a strategy for developing a 

stress model of this site. The strategy is based on decoupling of modeling into a number of steps 

and scales and tackling each with the most appropriate (and efficient) modeling tools. While this 

approach is not entirely novel, it is one of the most extensive efforts aimed at modeling of a deep 

coal panel. As such, it required modification of mainstream modeling tools, and a number of new 

software tools and utilities.

 
170

Strategy

The essential strategy for this modeling effort revolved around breaking the problem into 

coordinated parts that could be optimized for particular objectives, while retaining links to other 

portions of the model. These parts were organized on three basic scales. The largest scale was 

essentially the mountain overlying the mine, and the distribution of previous mining in several 

coal seams. The intermediate scale incorporated mining of the first two panels of a new district. 

Fortunately, the seam mined in this district was the first to be mined. The smallest scale was a 

number of pillar and gate road sections where observations of ground conditions and ground 

deformation mechanisms, as well as point measurements of closure and pillar stress, were 

modeled. The resulting scheme, illustrated in Figure C1, revolved around establishing 

appropriate links in boundary conditions and load response curves to effectively link models at 

these various scales.

For example, LaModel, a displacement-discontinuity boundary-element code, might 

adequately estimate initial stress if the relief is not highly variable. Otherwise, a volume-element 

code, such as FLAC3D might be required to more accurately determine the effect of high 

topographical relief on seam-level initial stress. Initial stresses may be imported from other tools, 

as long as the format of the information matches that of the receiving tool. Seam-level stresses 

from LaModel may be imposed at the same horizon in FLAC3D, but some assumptions may then 

be necessary to determine stresses throughout the rest of the body. The Itasca Longwall 

Modeling Environment is an additional capability in FLAC3D that allows for mechanistic 

simulation of longwall caving. At the pillar scale, the Mark-Bieniawski formula is a common 

formula used in displacement discontinuity codes, but other material models might be substituted 

in the input file of such codes. FLAC3D has multiple constitutive laws that might be necessary if 

pillar failure is largely dependent on confinement or structural failure in the floor or the roof.

The scheme is similar to sub-modeling efforts employed in a number of programs, most 

notably for this application, the pre-defined response of pillars typically found in boundary 

element programs [Crouch 1976; Sinha 1979; Karabin and Evanto 1999]. The scheme also uses 

the typical boundary element approach of defining an initial stress field as a starting point for 

mining-induced stress calculations, although some further equilibrating may be required when 

volume element methods are used to model panel scale stresses with this approach.

Figure C1. Diagram showing relationship between tools, categories of their use and their scales.
171

Pillars and Panels

Wizard and Spreadsheet Pillar Models

LaModel [Heasley 1998, 2010c], like many boundary element programs, abstracts pillar 

behavior as a one-dimensional response to loading that may include hardening or softening after 

an elastic limit is reached. This response can be based on a more detailed model but is most 

commonly generated by a simple program or spreadsheet using simplifying assumptions. 

LaModel, for instance, includes a wizard application for defining these curves consistent with the 

Mark-Bieniawski pillar capacity formula [Mark and Chase 1997; Mark and Iannacchione 1992]. 

Typically, the program is used to generate an elastic-perfectly-plastic curve for cells making up 

various portions of a pillar, as shown in Figure C2.

Figure C2. Plan view of LaModel pillar showing cells.

The wizard can also generate softening curves, based on the work by Karabin and Evanto 

[1999]. One such cell curve—the LamPre 3.0 default for softening—is shown in Figure C3. 

Heasley proposed more severe softening curves in his Crandall Canyon analysis. One important 

result of softening is that it causes pillar capacity to undershoot the Mark-Bieniawski capacity as 

various parts of the pillar fail at different stages in the pillar deformation process. A simple 

spreadsheet routine, assuming a rigid roof and floor, was used to produce the capacities for a 

pillar having a width-to-height ratio of 8:1 for various softening assumptions in Table C1. The 

formulae are vastly different, as can be seen by the results in the table. For example, the Wilson 

equation [1972, 1981; 1982] evaluates certain loading conditions of a pillar, whereas the 

Bieniawski, Mark-Bieniawski, and Maleki formulae give general strength capacities.
172

Table C1. Average pillar maximum stress for a pillar with width-to-height of 8, calculated 

by various methods. PIllar parameters are listed below the table

Method Pillar capacity, MPa Pillar capacity, psi

Bieniawski 21.84 3168

Mark-Bieniawski 21.84 3168

Maleki (structurally 

controlled) 23.15 3357

Maleki (confining 

controlled) 30.27 4390

Gaddy-Holland 17.55 2546

Wilson 18.63 2702

Vesić 21.59 3131

Parameters used:

Pillar width/height = 8.

Pillar length = pillar width = 24.4 m (80 ft)

Bieniawski:

Coal unconfined comp. strength = 6.20 MPa (900 psi)

Wilson:

φ = 30°

γ = 25.4 kN/m3(162 pcf)

H = 609.6 m (2000 ft)

In situ coal strength = 6.20 MPa (900 psi)

Uniaxial strength of fractured coal = 96.5 kPa (14 psi)

Vesić:

cohesion = 3.52 MPa (510 psi)

Nc = 5.142

Nq/Nc = 0.194

Coal was saturated

Figure C3. Typical load deformation curve defined for a pillar cell in LaModel.
173

LaModel can also import any similar three-segment curves defined by the user, allowing for 

further modification of both pillar capacity and deformation. This is important, because while the 

LaModel wizard employs Mark-Bieniawski’s formula to estimate the peak load in each cell, 

assignment of the curve shape—its initial modulus, softening modulus and post-peak capacity is 

independent of this criterion. The wizard defaults to the Karabin and Evanto [1999] criterion—a 

log function fitting residual stress to distance from the pillar rib. However, this function has two 

flaws. First, the stress goes to negative infinity at the pillar rib (i.e. depth of zero), and it is 

unbounded for large pillars—meaning that there is a pillar size where softening becomes 

hardening, or strengthening, of the pillar.

Fortunately, it is rather simple to construct spreadsheets that employ alternative rules for 

generating pillar response curves and simple to introduce these curves into LaModel. Empirical 

capacity rules can be manipulated to provide stress gradients which can, in turn, be integrated 

into cell peak capacities. The process is even more straightforward for analytical criteria, as they 

provide a stress function directly. A number of spreadsheets were generated, including four 

additional empirical criteria [Bieniawski and Van Heerden 1975; Mark and Chase 1997; Maleki 

1992] and two analytical criteria [Wilson 1972; Vesić 1975] (Table C2). In addition, alternative 

softening schemes were implemented—including a modified log function and a constant strength 

loss—and these schemes provide a wide variety of options for adapting the model to a specific 

site. They also provide a means for examining competing failure criteria. For example, the 

Bieniawski pillar and Vesić floor strength equations might both apply to the pillar and floor at a 

site – one of which will limit capacity of a particular pillar size. Use of both of these 

formulations might be used to limit the strength of a pillar, as illustrated in Figure C5.
174

Table C2. Strength capacity in pillar by location

Method Equations for strength by location in the pillar

Bieniawski

See Figure C4

A core element exists 

only when the centroid 

of an element coincides 

with the pillar centroid.

For side elements: σv = S1 (0.64 + 2.16 x

h

)

For corner elements: σv = S1 (0.64 + 2.16

(x−

w

6

)

h

)

For core elements: σv = S1 (0.64 + 2.16

(x−

w

3

)

h

)

Mark-Bieniawski

See Figure C4

For side elements: σv = S1 (0.64 + 2.16 x

h

)

For corner elements: σv = S1 (0.64 + 2.16

(x−

w

6

)

h

)

For core elements: σv = S1 (0.64 + 2.16

(x−

w

3

)

h

)

Maleki (structural 

control strength) σv = 3836 [1 − e

−2(0.260)x

h {1 −

4(0.260)

h

x +

2(0.260)

2

h

2

x

2}]

Maleki (confinement 

control strength) σv = 4700 [1 − e

−2(0.339)x

h {1 −

4(0.339)

h

x +

2(0.339)

2

h

2

x

2}]

Wilson σv = k p

′ (

2x

h

+ 1)

k−1

Vesić σv = c Nc (1 +

Nq

Nc

) for saturated condition

Variable definitions:

σv = Average vertical strength of coal pillar

x = distance from rib

h = extraction height of coal pillar

S1 = unconfined compressive strength of ≥ 1.5-m sided cube of coal

k = triaxial stress factor = [

1+sin φ

1−sin φ], where φ= 30° to 37°

p

′ = unconfined compressive strength of failed coal at pillar edge (14 psi)

c = cohesion

Nq and Nc = foundation factors = 0.9975 and 5.142, respectively, for saturated condition (φ = 0°)

Figure C4. Type of element by location in plan view.
175

Figure C5. Average pillar strength according to the Bieniawski and Vesić

formulas, showing how both might be used together to limit pillar strength.

For the Vesić formula, internal friction angle = 0° and cohesion = 510 psi.

FLAC3D Pillar Models

Abstracting of pillar response to loading also can be based on more detailed models. These 

can be used as a basis for cell curves introduced to LaModel runs. Alternatively, they can be 

linked to volume element models of panel-scale behavior in FLAC3D. Board and Damjanac 

[2003; Board et al. 2007] developed a method to capture the local behavior effects of pillar 

loading and represent that behavior as “equivalent zones” or “equivalent elements” in a panelscale FLAC3D model of a room-and-pillar trona operation. Esterhuizen and Mark [2009] used 

this approach when modeling a room-and-pillar coal panel using a softening Hoek-Brown 

strength criteria for coal that was calibrated to Bieniawski’s empirical pillar strength equation. 

Esterhuizen, Mark, and Murphy [2010] showed that the “equivalent-element” approach 

compared very well with detailed models. Models constructed for typical lithology of Western 

and Eastern U.S. coal performed well, and were compared to loading at various stages of mining 

predicted by NIOSH’s ARMPS (Analysis of Retreat Mining Pillar Systems) program [Mark and 

Chase 1997]. Their comparison showed that stress models can depart significantly from ARMPS 

estimates, especially for stiffer overburden, as is often found in western U.S. coal mines.

Models can be used to approximate and expand on other pillar capacity equations, most 

notably the Wilson approach to incorporating the effect of weak partings and the Vesić equation 

for estimating pillar foundation strength. Generation of yielding in multiple regions—floor, 

pillar, and parting planes, for instance—allows for a more complete model of pillar behavior that 
176

may depart from a “weakest link” criterion based on individual capacity equations [Lawson et al. 

2012]. It also provides a physical basis for the deformations and residual stresses that are largely 

based on simple assumptions in the spreadsheet approach.

Pillar and Panel Linkage—One Step Further

In our application, we need to take this linkage one step further, by developing expected or 

synthetic readings for instruments placed in the gate roads. That is, our linkages need to go both 

ways so that pillar deformations at the panel scale can be translated into synthetic readings of 

instruments at particular points (Figure C6). A pillar model is used to generate stress-strain 

curves that are used in cells or elements in the panel model. These elements are much coarser 

than cells or elements in the pillar model. The panel model outputs displacements and/or closure 

strains, which are used as linkages to state(s) in the pillar model, which is used to generate 

synthetic instrument readings (e.g., borehole pressure cells), which can be compared directly to 

actual measurements with installed instruments. Table C3 distinguishes between the types of 

linkages between pillar and panel models. Those linkage types are described separately.

Figure C6. Diagram illustrating linkages between the pillar model and the panel model.

Table C3. Various linkages between pillar and panel models

- - Panel model tool Panel model tool Panel model tool

- - LaModel FLAC3D

FLAC3D with 

Longwall Modeling 

Environment

Pillar model tool Spreadsheet Linkage type 1 Linkage type 3 Linkage type 5

Pillar model tool FLAC3D Linkage type 2 Linkage type 4 Linkage type 6
177

Linkage type 1—Spreadsheet Pillar Model and LaModel Panel Model 

This linkage is very trivial. A spreadsheet-type pillar model is imposed on cells in LaModel, 

assuming that the spreadsheet model is simple enough to be represented by three stress-strain 

line segments, the last being at constant stress. For example, Heasley [2010c] has a coal 

softening wizard in LamPre version 3.0 that generates such curves based on the integrated MarkBieniawski pillar formula [Mark and Chase 1997; Mark and Iannacchione 1992] and the Karabin 

and Evanto [1999] residual stress. Such linkage could easily be established for LaModel 3.0 with 

other models that can be described in three such line segments. 

Linkage type 2—FLAC3D Pillar Model and LaModel Panel Model 

In this case, a detailed pillar model generated with FLAC3D is used to average stress-strain 

calculation results for various sections, which correspond to the various grid cells of the pillar in 

LaModel. The stress-strain behavior is approximated with three line segments for each cell. Such 

material behavior is input to LaModel and a panel model is run. The closure strain in cells that 

encompass instrument sites are extracted, and these strains form a link to the FLAC3D pillar 

model. Synthetic instrument readings are generated at corresponding specific locations in the 

FLAC3D pillar model by linking cell closure strains output from LaModel to the same average 

section closure strain in the pillar model. 

Linkage type 3—Spreadsheet Pillar Model and FLAC3D Panel Model 

By using equivalent elements as developed and used by Board and Damjanac [2003] and 

Esterhuizen and Mark [2009], various spreadsheet models can define a pillar or barrier pillar 

stress-strain response that can be input to FLAC3D panel models. The closure strain of equivalent 

elements in the panel model is used to indicate the approximate stresses in the spreadsheet pillar 

model at locations of instruments. Here, care must be taken, because constant closure across 

many cells of a spreadsheet model may not be a good assumption. In such cases, the linkage to 

generate synthetic measurements can only be obtained by imposing a reasonable model of the 

distribution of closure strain across the pillar. The average of these closure strains must equal the 

strain output from the FLAC3D panel model. 

Linkage type 4—FLAC3D Pillar Model and FLAC3D Panel Model 

Using this linkage, a more complicated stress-strain curve might be developed for equivalent 

elements used in the panel model. Assuming that the pillar model has several saved states along 

the process of its loading, the closure strain of an equivalent element from the panel model can 

be used as a link to the closure strain of an equivalent horizon in the detailed pillar model. The 

seam-lumped strain (plastic displacement of the roof and floor are included as seam strain) of the 

equivalent element must be modified to reflect equivalent-horizon strain. This strain can then be 

used to match or interpolate column strain of the equivalent horizon from a couple of saved 

states in the detailed pillar model. Synthetic instrument readings can then be extracted from the 

detailed pillar models. 
178

Linkage types 5 and 6—Various Pillar Models with Longwall Modeling Environment

If linkage types 3 and 4 are established, then linkage types 5 and 6 can be established. Using 

the Longwall Modeling Environment [Pierce and Board 2010] for the panel model is no more 

complicated than using the FLAC3D with standard features for the panel model.

Calibration Using Specific Measurements vs. Synthetic Measurements

Whatever modeling tool is used for the panel scale, synthetic measurements at the same 

coordinates as real instruments can be extracted from the model. By comparing real 

measurements with synthetic measurements, fine-tuning of models can proceed. Figure C7 

shows an example how real borehole pressure cell measurements might be compared to synthetic 

borehole pressure cell measurements. The important comparison here is the difference in stress 

resulting from mining. These cells were spaced from the left rib of a pillar in order (BPC1, 

BPC2, BPC3, and BPC4) until BPC 4 was in the center of the pillar, as shown in the figure. BPC 

5 was placed near the right rib, which was next to the panel being mined, at the same distance 

from the rib as BPC1 was from the left rib. A model was built and run with LaModel and 

synthetic BPC measurements were extracted from the results. The in-seam model was an elasticperfectly plastic coal. The actual measurements indicate a yielding of the pillar near the right rib, 

and highest load change at BPC2. In this case, the instruments indicate that a softening model 

should be used for in-seam material before further calibration.
179

Figure C7. Example showing how synthetic borehole pressure cell

measurements generated by a model might be compared to actual

measurements. Layout of the instruments within the pillar is also shown.
180

Synthetic Measurements

Synthetic measurements at instrument sites can also be generated from FLAC3D models, but 

with an additional step. For a given longwall face position in the panel model, the closure strain 

of the equivalent element containing the measuring instrument is extracted. The two saved states 

of the detailed pillar model having seam-lumped closure strain above and below that amount are 

examined. The seam stresses in a pillar at instrumentation sites can be retrieved from save states 

and interpolated according to the seam-lumped nonlinear closure strain. Closure strain in an 

entry can be determined in the same way. Synthetic measurements of stress for instruments 

located between zone centroids can be determined through a second interpolation.

From these measurements, it is possible to display synthetic measurements for a detailed 

pillar (Figure C8), for a profile along an instrumentation line, or for an instrument with respect to 

face position, as in Figure C9. These can be compared to actual measurements made with 

instruments for the purposes of fine-tuning the calibration of the panel and detailed pillar models.

Figure C8. Example of synthetic borehole pressure cell measurements with 

average pillar strain as extracted from a FLAC3D detailed model of a pillar. 
181

Figure C9. Example showing synthetic borehole pressure

cell measurements generated from LaModel calculations.

Application of Overburden Stress

The first step in a large- (panel-) scale model is determining the in situ stress state. For 

FLAC3D, that means determining the stress state in every zone at equilibrium before any 

excavations. For LaModel, it means determining the premining stress on each element of inseam material. In the case of high-relief topographic terrain, Heasley’s routine [1997] to account 

for topographic effects may have some limitations [Whyatt et al. 2011]. In such cases, the user 

may desire to take advantage of a link to overburden stresses on the seam determined from 

another source, such as FLAC3D. 

To create such a linkage between premining FLAC3D results and LaModel overburden stress 

input, the user only need arrange the vertical stresses calculated with FLAC3D, which correspond 

to the exact locations of the LaModel seam grid centroids and arrange them one per line in a text 

file of the same name as the name of the LaModel run with the .tpo extension. The order of the 

stresses, where i and j represent the x and y indices, starting in the lower left-hand corner of the 

grid, σ1,1, σ1,2, ..., σ1,n, σ2,1, σ2,2, ..., σ2,n, ..., σm,1, σm,2, ..., σm,n. Here, m and n are the 

maximum indices in the x and y directions, respectively. The first three lines of the .tpo text file 

are filled with information listed in Table C4, with each item delimited by a comma. A linkage 

between another source and LaModel can be established in the same manner.
182

Table C4. Contents and format of the .tpo file or overburden stress file that serves as 

input to LaModel

Line Item 1 Item 2 Item 3 Item 4 Item 5 Item 6 Item 7

1 1

Number of 

grid cells

Distance 

between 

cells (in)

Number of 

grid cells in 

x direction

Number of 

grid cells in 

y direction

X 

coordinate 

of origin 

(in)

Y 

coordinate 

of origin 

(in)

1 format I3 I8 F13 I4 I4 F13 F13

2 1

Overburden 

stress NU NU NU NU NU

2 format I3 S17 - - - - -

3 1 Units (psi) NU NU NU NU NU

3 format I3 S17 - - - - -

4 and 

after Stress NU NU NU NU NU NU

4 and 

after 

format

F13 - - - - - -

NU = Not used

Format key:

I = Integer (I3 = Integer of 3 characters)

F = Floating point number or scientific notation (F13 = Floating point number of 13 characters)

S = String (S17 = string of 17 characters)

Another linkage is to provide initial stress for each zone in a FLAC3D model by some other 

calculation. This might be done in one of two ways: 

1. Calculating stress for each zone with some other tool, be it a modeling tool, or a 

spreadsheet calculation of some initial stress model. Save such calculations an initial stress file in 

text format. With the aid of a FISH function, read in the initial stress file and assign stresses by 

matching coordinates.

2. Implement the initial stress model calculations in a FISH function. Calculate the initial 

stress and assign the stress state for each zone in FLAC3D.

Program Modifications—LaModel

LaModel is one of the most used modeling tools for evaluation of coal and trona mine 

design. Its advantage is the speed at which a model may be completed, including preprocessing, 

model calculations, and post-processing. However, it has some limitations that may cause the 

modeler to choose to use another code. Some of these limitations have been overcome by recent 

modifications of LaModel.

Decoupling of Initial Stress Routine

Most modeling procedures use an assumed initial stress field or they use the same modeling 

program to generate an initial stress field. In the case of highly variable topography, volumeelement codes, such as FLAC [Itasca Consulting Group 2011], FLAC3D [Itasca Consulting 

Group 2009], or any finite-element code, might impose an initial tectonic stress field and let 

mass density of the elements and the gravitational field further load the model. Boundary 

element codes generate their own initial stress field. In his code LaModel [Heasley 2010c], a 
183

displacement discontinuity code that uses frictionless, cohesionless interfaces in the host elastic 

rock mass, Heasley [1997], since the code’s inception, has accounted for topographic loading by 

imposing forces at a datum which is usually located above the coal seam at the average depth of 

the overburden. At the request of his co-authors, Dr. Heasley introduced a capability into the 

code to decouple the overburden stress from the mining-induced stress calculations [Whyatt et al. 

2011]. To do this, the overburden stress is input from a file which is previously calculated by 

LaModel or some other model. 

The capability of introducing initial, or overburden, stress through a file has the advantage of 

speeding the completion of parameter studies because initial stresses do not have to be calculated 

for each problem. However, this capability also provides the choice to use initial stress calculated 

from an external source that may not be subject to limitations of the LaModel topographic 

routine or those of an elastic continuum [Whyatt et al. 2011]. For example, an external model 

might have the advantage of simulating the influence of major faults on the initial stress.

Increasing Yield Rings and Number of Materials

Heasley [2010a] increased the maximum number of in-seam materials that can be used in a 

model to 52 for version 3.0 of LaModel. Because of the large loads that may be applied to large 

abutment pillars in the western U.S., it is often necessary to use enough yield rings so that there 

is no elastic core. Otherwise, artificially high and incorrect peak stresses may result. The 

maximum number of materials of different strengths makes it possible, for example, that a large 

abutment pillar, such as one of dimensions 51.8 m by 54.9 m (170 ft by 180 ft) might now be 

modeled with 1.5-m (5-ft) elements instead of 3.0-m (10-ft) elements. This would require 35 

materials (one elastic and 34 nonlinear) for 17 yield rings. However, LamPre 3.0 has not been 

updated to accommodate this many yield rings; it is limited to a maximum of 12. Even so, the 

input file can be modified with a text editor to include the number of materials required and their 

properties. When more yield rings are desired than 12, the user must manually input the

materials in the grid editor.

Increasing Number of Mining Steps

For panel-scale models, it may be desirable to include more than the past traditional limit of 

20 mining steps. In a recent release of LaModel 3.0, Dr. Heasley increased that limit to 200 

[2010b]. Such increased limit allows the user to model panel-scale models with small mining 

steps, which is needed especially as the mining face nears instrumentation sites. Smaller mining 

increments permit more accurate comparison with measurements of stress and displacement for 

purposes of model calibration.

Synthetic Measurements of Stress and Closure

For fine-tuning calibrations, the authors found it desirable to compare actual measurements, 

such as those from closure meters and borehole pressure cells with measurements predicted by 

LaModel. Such a tool for extracting specific measurements at each mining step is not within the 

capabilities of LamPlt 3.0 at present. The authors use LabTalk script in the software, OriginPro 

version 8.5 [OriginLab 2011] to conveniently extract and plot such “synthetic measurements” for 

comparison with actual measurements. Figure C9 shows an example of “synthetic readings” 
184

output from LaModel at locations where actual borehole pressure cell (BPC) measurements were 

taken. 

Program Modifications—FLAC3D

If storage space, calculation time, and complexity of three-dimensional models were not 

limitations, modeling codes such as FLAC3D would be used more frequently for panel-scale 

models because of its ability to simulate failure mechanisms in any part of the model and 

calculate the full stress tensor in each zone or element. However, recent developments have 

made it possible to capture localized behavior in panel-scale model with coarse zones using 

linkages to more detailed submodels [Board and Damjanac 2003; Esterhuizen and Mark 2009]. 

In addition, several FISH functions have been developed for generating a mesh representing 

high-relief topography where the idealized stratigraphy may not be planar. More FISH functions 

have been developed that easily implement gob models, and Itasca has recently developed a 

Longwall Modeling Environment that follows caving logic. Such capabilities make use of 

FLAC3D desirable and, at least, worth consideration.

Topographic Mesh Generator

For complicated three-dimensional geometries, mesh generation is a complex task. Itasca 

Consulting Group, Inc. recommends using KUBRIX [2010] along with the CAD software, 

Rhino3D, to generate such grids. However, the authors chose to develop their own mesh 

generator for FLAC3D [Itasca Consulting Group 2009] that forms a three-dimensional grid to the 

topographic surface. Mesh generation is accomplished with FISH functions and is based on the 

assumption of a geologic column comprised of members having uniform thickness, but that are 

not necessarily planar. The elevations of the top and bottom of each stratigraphic member are 

expressed relative to the elevations of the top of the strata member of interest—in this case, the 

coal seam being mined. Thus, the coal seam does not have to be planar, and input includes 

elevations of the top of coal seam and elevations of surface topography in a regular plan-view 

grid. Elevations are input as tab-delineated text files with grid points at regular x- and ycoordinate intervals. The bottom member is generated from a bottom, horizontal plane up to 

some offset distance from the top of the coal seam. The zones are generated by section, 

stratigraphic member by stratigraphic member from bottom to top, one zone column at a time. 

Therefore, grid generation proceeds slowly. Each member is generated from bottom to top, 

unless the topographic surface is below the top of the member. In such case, the top surface of 

the top zone of that column is forced to conform to the topographic surface. Each section can 

have a different x- and y-interval spacing to allow for different mining geometries. However, 

care must be taken so that grid points on the boundaries of adjacent sections coincide or so that 

the intervals between them are multiples of each other. Once each section is built, the “attach” 

command is used to attach adjacent sections together. Any interfaces are constructed after the 

sections are attached. 

Input files for the topographic mesh generator are shown and general contents listed in Figure 

C10. Each section requires a section file and an Elevs-section file. For example, a mesh with 20 

sections will require 20 section files, 20 Elevs-section files, one strata file, and one driver file, all 

of which are text files. Section and Elevs-section files are data files that can be generated from a 

spreadsheet that is saved as a text file. However, care must be taken to delete all blank lines after 

the last line of data—the last line of the file must be the last line of data.
185

Figure C10. Input files and general content list of each for the topographic mesh generator.

This routine was tested with the case of a high-relief area around a western U.S. coal mine. 

Elevations of seam and topographic surface were extracted from AutoCAD contours of the seam 

elevation and contours of topography using AutoCAD Civil 3D [2011]. Thirty-two sections of 

these elevations were extracted at 15.2-m (50-ft) intervals for an area that was approximately 6.3 

km (3.9 miles) in length along the y axis, and 5.8 km (3.6 miles) in length along the x-axis. The 

FISH routine has the option of skipping a pattern of grid points so that you may chose a coarser 

grid interval than what was extracted from the elevation contours. Figure C11 shows the 

resultant grid, where each stratigraphic member is shown in a different color.
186

Figure C11. FLAC3D model of area around a western U.S. coal mine 

as generated by the authors' topographic mesh generator. 

Equivalent Elements and Detailed Pillar Models 

Esterhuizen and Mark [2009] developed FISH functions to implement the Board-Damjanac 

method [Board and Damjanac 2003] of equivalent elements to model a pillar or barrier in a 

detailed way and representing that behavior as a one-dimensional equivalent element. In this 

method, both sets of authors constructed a detailed model of a pillar or barrier, whose outside 

dimensions in plan view are the same as those of the equivalent element that will represent the 

detailed pillar model behavior in the panel-scale model. 

The authors took what Esterhuizen and Mark accomplished and made some modifications. 

First, the Esterhuizen-Mark method of loading a detailed pillar model was based on a servo 

mechanism controlling applied velocity on the top surface of the model. In the authors’ 

experience, the sudden changes in velocity propagated compression waves through the model, 

causing premature failure of many zones. To minimize this effect, the authors held the velocity 

of the top boundary constant. Second, Esterhuizen and Mark calculated the equivalent column 

strain and the seam strain at the center point of the pillar, only. The authors choose to base these 

calculated strains of the seam and column on the average of vertical pairs of grid points at the 
187

top and bottom of these horizons from throughout plan-view area of the detailed model. In 

calculating these strains by section (for example, if the pillar is divided into two or four 

sections), then only relative displacements of grid point pairs belonging to a particular section 

were included in the calculation of column and seam strains for that section. For seam stress, we 

choose average seam stress near the horizontal midplane of the seam, and for column stress, we 

averaged stress at the bottom row of elements in the equivalent-column horizon, as did 

Esterhuizen and Mark [2009]. Third, the authors recognized that panel models can load 

equivalent elements in a nonuniform manner. To account for such response, the detailed pillar 

model can be loaded nonuniformly in the first few hundred or thousand steps of loading the 

detailed pillar model. In subsequent steps, the imposed, nonuniform displacement step is kept 

constant—i.e., all grid points on the top surface of the model are given the same velocity in the 

vertical direction. Multiple rounds of pillar and panel models must be run until there is little 

difference between the tilting in the panel model’s equivalent elements and that of the detailed 

pillar model. 

In the panel-scale model where the equivalent elements are used, all stresses other than 

vertical stresses are set to zero at each calculation step—thus preserving the one-dimensional 

nature of the equivalent element. 

From the detailed model, a curve of column stress versus column plastic strain is extracted, 

but since we only mine the seam, the nonlinear response of the entire column horizon must be 

lumped into an equivalent element the height of the seam. The equivalent element is forced to 

follow this strength curve by setting the internal friction angle to 0° and representing the 

strength curve with a piecewise linear cohesion curve, where cohesion is half of the current 

uniaxial strength (from the stress-versus-plastic strain curve).

To determine this curve of stress versus plastic (or nonlinear) strain, we need to define some 

variables, with reference to Figure C12, which represents the equivalent horizon from which we 

extract the nonlinear response. The variables are as follows:

Figure C12. Vertical section of equivalent column horizon,

extracted from part of detailed column model.
188

δr

e

, δr

p

, δr = elastic, plastic, and total closure displacement (closure displacement is the 

change in the height of the member) of the roof in the column, respectively. 

δs

e

, δs

p

, δs = elastic, plastic, and total closure displacement of the seam in the column, 

respectively.

δf

e

, δf

p

, δf = elastic, plastic, and total closure displacement of the floor in the column, 

respectively.

εcol, εcol

e = total strain of the column and elastic strain of the column (the column refers to 

the floor, seam, and roof whose responses are considered for the equivalent element), 

respectively.

hr, hs, hf = heights of roof, seam, and floor, respectively, in the column.

Ecol, Es = elastic modulus of column and seam, respectively. Also,

δcol = δr

e + δse + δf

e + δr

p + δsp + δfp

. (C1)

The required data for determination of the column stress-vs.-plastic strain curve (and 

subsequently, the column cohesion-vs.-plastic strain curve) are the column stress-vs.-total 

column strain curve from a model that permits element failure, and the stress-vs.-strain curve 

from a model of the same grid and elastic properties, but with no failure permitted. The latter 

was accomplished by raising all strength parameters to very high amounts. An example of the 

relative relationship of such curves is shown in Figure C13.

Figure C13. Typical relative curves needed for determination of a detailed response that inputs

to an equivalent element. These curves come from two models of the same grid and elastic

properties: (1) where zones are permitted to fail, and (2) where zones are not permitted to fail.
189

Figure C14 shows the same total response curve. That same curve is also shown modified so 

that the strain is multiplied by the ratio of the column and seam heights. This manipulates the 

strain so that all of the displacement occurs within the height of the seam.

Figure C14. Graph showing the example relative curves obtained in the progression

of the determination of cohesion vs. seam-lumped column plastic strain. First, column

stress vs. column total strain is extracted, then the total column deformation is lumped

into the seam height to obtain seam-lumped column total strain. Next, the seam-lumped

plastic strain is extracted. Finally, the curve is expressed as having no friction so that

cohesion is half of the total column stress in the final curve for a one-dimensional model.

The elastic strain response of the column is subtracted from the total strain response to obtain 

the curve of stress vs. plastic strain. Because the command “set large” is used in the FLAC3D

models, the plan area of the pillar increases, especially when there is plastic flow. This actually 

causes a nonlinear elastic response when calculating stress in the seam. However, the purely 

elastic model does not see much nonlinear elastic behavior because there was no plastic strain. 

Therefore, the nonlinear-elastic response is actually lumped in with the calculated plastic 

response.

Finally, the stress is divided by 2 to obtain the cohesion vs. seam-lumped column plastic 

strain response curve, shown in Figure C14. This can be done because the internal friction of the 

equivalent element is set to 0°.
190

To make this approach more clear, the procedure is done in terms of closure displacements, 

instead of strains. In this approach, we determine plastic column displacements by

δcol

p = δcol

total − δcole

, (C2)

where

δcol

total = δr + δs + δf (C3)

and

δcol

e = δr

e + δse + δf

e

. (C4)

The procedure is as follows:

1. From the detailed model with imposed strengths, extract the strain-stress curve of the 

detailed column (εcol vs. σcol).

2. From the elastic model, extract the strain-stress curves of the detailed column and of 

the seam alone (εcol

e

vs. σcol

e

and εs

e vs. σse

).

3. Determine Ecol and Esfrom elastic model. Do this by fitting a line by linear 

regression to determine slopes (Young’s moduli) and intercepts (bcol

e

, bs

e

).

4. From the stress-strain curve extracted in step 1, convert the strains to displacements 

and subtract the elastic displacements given the stress, as determined from the elastic 

model. Ultimately, we want to determine 

δcol

p

hs

or 

(δr

p

+ δs

p

+ δf

p

)

hs at any stress level of the 

model in step 1. This lumps all of the plastic strain in the seam horizon. Here are the 

details:

5. From step 1,

δr + δs + δf = εcol(hr + hs + hf). (C5)

From step 2, 

(δr

e + δse + δf

e

) = (hr + hs + hf)εcol

e = (hr + hs + hf)

σcol

e

Ecol

e

. (C6)

Also, Equation C2 is written in more detail as

(δr

p + δsp + δfp

) = (δr + δs + δf) − (δr

e + δse + δf

e

). (C7)

then

δcol

p

hs

= 

(δr

p+ δs

p+ δfp

)

hs

= 

[εcol(hr+ hs+ hf) − (hr+ hs+ hf)

σcol

e

Ecol

e ]

hs

. (C8)

The plastic strain, as indicated on the left side of Equation C8 is matched to a stress that 

indicates strength. The cohesion for a one-dimensional problem is half the stress at failure. Thus

the curve of cohesion vs. plastic strain is determined. This curve, as a piecewise linear curve is 

input as the strength envelope for that equivalent element in a panel-scale model.

The FISH functions for using equivalent elements are found in an equivalent element 

fishtank that may be called in the panel-scale model to convert certain zones to equivalent 

elements. Cohesion-versus-plastic strain curves are input as text files.
191

Gob Models

Two commonly-used constitutive models for gob are the linearly-varying elastic modulus, 

such as that used in Mulsim/NL [USBM 1992] and LaModel [Heasley 1998], and models based 

on the testing of Pappas and Mark [1993]. For the latter, presently only the equation fit to Pappas 

and Mark’s shale gob have been included in the gob fishtank, but the weak sandstone gob, the 

strong sandstone gob, or a set of equations that Pierce [2010] fit to all of the Pappas and Mark 

results could easily be inserted. These equations are

Ecurrent(psi) = a(UCS) + b(shape factor) + c, (C9)

where UCS = unconfined compressive strength of the material (psi),

shape factor = the average ratio of maximum and minimum dimensions of the gob 

particles (a good value in the absence of definitive information is 0.5), and

a, b, c = variable quantities that depend on the volumetric strain (εvol).

If εvol>= 0.25, then

a = 0.1315(εvol)

−2.145

, (C10)

b = 1110.5(εvol)

−2.574

, and (C11)

c = 981.14(εvol)

−2.3158

. (C12)

If εvol < 0.25, then the modulus is interpolated between the in situ modulus (i.e. at εvol = 0) 

and the modulus that would be estimated with the following coefficients when εvol = 0.25.:

a = 0.1316(0.25)

−2.145

, (C13)

b = 1110.5(0.25)

−2.574

, and (C14) 

c = 981.14(0.25)

−2.318

. (C15)

Input values for each stratigraphic layer are assembled as a tab-delimited text file. For these 

gob files, it is necessary to provide a distance above the coal seam within which all zones whose 

centroids fall are converted to gob. This procedure is done only above portions of the seam that 

are converted to gob and is necessary to maintain appropriate gravitational forces (the gob in the 

coal seam elements cannot have zero density). The density of all gob zones is then adjusted to 

reflect that the mass of the coal seam was extracted.

Program Modifications—Longwall Modeling Environment

Board and Pierce [2009] described logic that they used to simulate the mechanics of block 

caving. In said logic, bulking is not imposed, but results from either dilation during shear or 

volumetric expansion under tensile failure. Such logic seems promising as a way to simulate the 

caving over a longwall panel. Pierce and Board [2010] modified the caving logic to simulate the 

caving above a longwall panel. However, longwall caving has some differences compared to 

block caving of rock masses exhibiting more random jointing. Some of the considerations 

accommodated by Pierce and Board were:

Because of the persistent, weak, and planar nature of bedding planes, strata are often capable 

of accommodating shear and tension with less bulking than more randomly jointed rock. As a 
192

result, dilation angle and maximum porosity are likely to be less in stratified ground than in more 

randomly jointed rock masses.

The associated flow rule for tension tends to over predict bulking in the case of sedimentary 

rock. The solution by Pierce and Board was to model joints as interfaces or use the ubiquitous 

joint model or both.

The Longwall Modeling Environment in FLAC3D also tracks volumetric and shear energy, 

both plastic dissipated energy and elastic stored energy, zone by zone. The model must be run in 

a quasi-static state because it does not model dynamic events. However, the energy tracking can 

infer potential for dynamic events or the likelihood of dynamic occurring from one mining step 

to the next.

The Longwall Modeling Environment capability is compiled in FLAC3D as version 4.01, but 

implemented fully in version 5.0. However, FISH functions included in a fishtank file are needed 

to set up the additional calculations. In the initial version of the fishtank, only horizontal strata 

with a level topography were considered, along with automatic generation of far-field zones 

away from the panel area. For our purposes, we did away with the far-field mesh generation and 

incorporated our topographic mesh generator into the Longwall Modeling Environment fishtank. 

Although the mesh generation is slow, it is a step toward the recommendation of Pierce and 

Board that the next version of the fishtank include topography [2010].

Conclusions

Each of the modeling tools has advantages and disadvantages, strengths and weaknesses. By 

understanding these items and the linkages between the tools, the user can effectively break the 

problem into parts and take advantage of the optimum tool for each task of the modeling 

exercise. The optimum tool is very problem-dependent, so that there is not a tool that optimally 

fits all problems.
193

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and pillar mines. In: Stephansson O ed., Proceedings of the 2003 Swedish Rock Mechanics Day 

Conference.2003) Stockholm: SvebeFo, pp. 1–22 pp.

Board M, Damjanac B, Pierce M [2007]. Development of a methodology for analysis of 

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Board M, Pierce ME [2009]. A review of recent experience in modeling of caving. In: 

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June 28, 2009) Pittsburgh, PA: U.S. Department of Health and Human Services, pp. 19–28.

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pillars, gob and overburden response. In: Barczak T et al. eds. Proceedings: 29th International 

Conference on Ground Control in Mining. (Morgantown, WV: July 27–29, 2010) Morgantown, 

WV: West Virginia University, pp. 46–57.

Esterhuizen GS, Mark C [2009]. Three-dimensional modeling of large arrays of pillars for coal 

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(Asheville, NC: June 28, 2009) Pittsburgh, PA: U.S. Department of Health and Human Services, 

pp. 37–46.

Heasley KA [1997]. A new laminated overburden model for coal mine design. In: Mark C, 

Tuchman RJe eds. NIOSH Information Circular 9446, Proceedings: New Technology for 

Ground Control in Retreat Mining. Pittsburgh, PA: U.S. Department of Health and Human 

Services, pp. 60–73.

Heasley KA [1998]. Numerical modeling of coal mines with a laminated displacementdiscontinuity code. Ph.D. Dissertation. Golden, Colorado: Colorado School of Mines, 205 pp.

Heasley KA [2010a]. E-mail from Dr. Heasley, WVU, to, Personal communication to Larson 

MK, September 12, 1 pp.

Heasley KA [2010b]. E-mail from Dr. Heasley, WVU, to, Personal communication to Larson 

MK, September 19, 2 pp.

Heasley KA [2010c]. LaModel, ver. 3.0, Morgantown, WV: West Virginia University.
194

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dimensions—user's guide (version 4.0). 274 pp.

Itasca Consulting Group [2010]. Kubrix/Rhino users' manual—using KUBRIX and Rhino3D to 

create grids for FLAC3D, 3DEC, PFC3D & other computer-aided engineering tools. 

Minneapolis, MN, 124 pp pp.

Itasca Consulting Group [2011]. FLAC: Fast Lagrangian analysis of continua—user's guide 

(version 7.0), 384 pp.

Karabin GJ, Evanto MA [1999]. Experience with the boundary-element method of numerical 

modeling to resolve complex ground control problems. In: Mark C et al. eds. NIOSH 

Information Circular 9448, Proceedings of the Second International Workshop on Coal Pillar 

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

National Institute for Occupational Safety and Health, pp. 89–113.

Lawson H, Zahl E, Whyatt J [2012]. Ground condition mapping: A case study. In: 2012 SME 

Annual Meeting, "Mine to Market: Now It's Global" Preprint 12–122, (Seattle, WA: Feb 19–22, 

2012) Englewood, CO: Society for Mining, Metallurgy, and Exploration, Inc., 7 pp.

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

Iannacchione AT et al. eds. Bureau of Mines Information Circular 9315, Proceedings of the 

Workshop on Coal Pillar Mechanics and Design. (Santa Fe, NM: June 7, 1992) U.S. Department 

of the Interior, pp. 73–77.

Mark C, Chase FE [1997]. Analysis of Retreat Mining Pillar Stability (ARMPS). In: Mark C, 

Tuchman RJ eds. Proceedings: New Technology for Ground Control in Retreat Mining, DHHS 

(NIOSH) Publication No. 97-133, IC 9446. Pittsburgh, PA: National Institute for Occupational 

Safety and Health (NIOSH), pp. 17–34.

Mark C, Iannacchione AT [1992]. Coal pillar mechanics: Theoretical models and field 

measurements compared. In: Iannacchione AT et al. eds. Bureau of Mines Information Circular 

9135, Proceedings of the Workshop on Coal Pillar Mechanics and Design. Washington, DC: 

U.S. Department of the Interior, pp. 78–93.

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aspects of proposed coal mining plans. By Skiles ME, and Stricklin KG. Program Information 

Bulletin No. P09-03, March 16, 2009, Arlington, VA: U.S. Department of Labor, Mine Safety 

and Health Administration (MSHA), 7 pp.

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OriginLab, [Accessed November 7].

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environment for caving and stress analysis of longwall mining. Report 2552-05, Prepared for 

NIOSH, Spokane Research Laboratory, August 31, 2010, Minneapolis, MN, Itasca Consulting 

Group, Inc., 43 pp.

Pierce ME [2010]. Equations in FISH function of LME for influence of UCS and shape factor. 

Verbal, Personal communication to Larson MK, September 15.

Sinha KP [1979]. Displacement discontinuity technique for analyzing stress and displacements 

due to mining in seam deposits. Ph.D. Thesis. University of Minnesota, 325 pp.
195

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Circular 9322, Pittsburgh, PA: U.S. Department of the Interior, Bureau of Mines (USBM), 44 pp.

USBM [1993]. Behavior of simulated longwall gob material. By Pappas DM, and Mark C. 

Report of Investigations 9458, Pittsburgh, PA: U.S. Department of the Interior, Bureau of Mines 

(USBM), 42 pp.

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handbook, 1st ed., ed. by Winterkorn HF, Fang H-Y, New York: Van Nostrand Reinhold 

Company, pp. 121–147.

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A sensitivity study. In: Barczak T et al. eds. Proceedings: 30th International Conference on 

Ground Control in Mining. (Morgantown, WV: July 26–28, 2011) Morgantown, WV: West 

Virginia University, pp. 58–66.

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determination of pillar size. The Mining Engineer, Vol. 131, Part 9, 1972, pp. 409–417.

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Morgantown, WV: West Virginia University, pp. 1–8.

Wilson AH [1982]. Pillar stability in longwall mining, In: State-of-the-art of ground control in 

longwall mining and mining subsidence, New York: AIME, pp. 85–95.

197

Appendix D: Pillar Strength Equations

Summary

In this appendix, a mathematical method is given that can be used to calculate pillar strength 

as a function of distance within a pillar [Johnson et al. 2014]. A description of this method is 

repeated in this appendix because the equations derived by using this method are used in 

boundary element programs in this report to model the failure of mine pillars. The method uses a 

one-dimensional analysis of strength as a function of distance where distance is measured from 

the rib toward the center of the pillar and is based on a few general principles and assumptions.

Background

Pillar stress yield functions have been investigated by several researchers and their findings 

are summarized in a seminal paper by Hustrulid [1976]. Mark [2006] normalized many of these

equations to have equal strengths for a pillar with a width-to-height (w h⁄ ) ratio of 5:1, a shape 

well-represented in empirical studies, and then compared them. The w h⁄ ratio is an important 

geometrical property of the pillar that controls its strength and influences failure mechanisms 

[Mark 1999]. This normalization, which forms the base for Figure D1, illustrates the divergence 

of different pillar strength estimates for larger pillars with greater w h⁄ ratios.

This divergence is becoming increasingly important, given recent trends towards using larger 

gate road pillars and similar sized inter-panel barrier pillars. Pillar strength curves published by 

[Maleki 1992] and Tesarik et al. [2013] have been added to Figure D1 for comparison [after 

Tesarik et al. 2013]. These curves were of particular interest for studying ground response to 

mining at a deep western underground coal mine with (roughly) 16:1 w h⁄ gate road pillars.

Johnson et al. [2014] described derivation of the general method of finding the implied pillar 

stress gradient, given an empirical pillar strength formula. They then described application of 

this method to estimating pillar cell strengths for boundary element models. This method is 

demonstrated in the following sections for four types of models.
198

Figure D1. Normalized pillar strength versus pillar width-to-height

ratio ([Mark 2006], augmented by Tesarik et al. [2013]).

Models

These pillar yield stress functions include several spatial formulations: (1) constant 

[Bieniawski 1968], (2) linear [Mark and Iannacchione 1992], (3) square root [Holland and 

Gaddy 1957], and (4) exponential [Maleki 1992]. The development of these four spatial model 

types is discussed below.
199

Constant

Figure D2 shows a square mine pillar at failure at maximum average vertical stress σV . This 

failure stress σV is a constant value over the entire pillar. It is calculated from an average pillar 

strength equation of which the pillar’s width, height, and in situ compressive strength are its 

arguments. The most common of these equations is the Bieniawski equation,

σp = σc (0.64 + 0.36 w

h

), (D1)

where σp = average pillar strength,

σc = strength of a cubical specimen tested,

w = width of the pillar, and

h = height of the pillar.

When the average failure stress is integrated over the entire pillar, it is equivalent to the

failure force F of the pillar that is equal and opposite to the load capacity R of the pillar.

Figure D2. Pillar average vertical failure stress at failure load for constant formulation.

In practice, the vertical stress is not constant but varies throughout the pillar. A practical 

variation of stress is zero at the edge of the rib that increases toward the core of the pillar. The 

variation of stress can be obtained from the load capacity of the pillar.
200

Linear

Mark and Iannacchione [1992] give the variable strength equation for the Bieniawski [1968]

average strength equation. The Bieniawski solution gives a linear variation in strength as a 

function of distance from the pillar rib as shown by the pyramid shape of stress in Figure D3. 

The Bieniawski solution, as well as a few other equations, were found by a trial-and-error 

method. These few solutions were used to validate a general mathematical method that has been 

developed for one-dimensional analyses.

A similar approach may be used for the Obert-Duvall strength equation [Obert and Duvall 

1967],

σp = σc (0.778 + 0.222 w

h

), (D2)

which has the same form as the Bieniawski equation, but different constants.

Figure D3. Strength variation over the pillar [Mark and Iannacchione 1992].

Square Root

This class of equations in the literature includes the Holland-Gaddy formula [Holland and 

Gaddy 1957] (which was based on tests by Gaddy [1956] on large coal specimens). These 

empirical equations, introduced later in this appendix, also use pillar width and height and 

unconfined compressive strength (UCS) of the coal to calculate the strength of a mine pillar. 

These are nonlinear formulations that may be more appropriate for pillars having width-to-height 

ratios greater than 8. This is of interest because several mines have such ratios approaching 20.
201

One of the simplest nonlinear average pillar strength equations is the square root model 

variant of the Holland-Gaddy formula proposed by Holland and Gaddy [1957]; [Holland 1964],

σp = σc √

w

h

, (D3)

which will be examined later in this appendix. An example shape of that function over a pillar is 

shown in Figure D4.

Figure D4. Strength variation over the pillar for the Holland-Gaddy pillar equation.

Exponential

Maleki [1992] proposed two equations of this form for designing coal pillars in western U.S. 

mines. The equations form an upper limit of coal pillar strength and were based on 

measurements and observations taken at several western coal mines that showed these coal 

pillars can sustain maximum average stresses from 26.4 to 32.4 MPa (3,836 to 4,700 psi) 

depending on the pillars’ structure and confinement. Beyond this maximum stress level, the 
202

entire pillar system may incur stability problems. These stability problems can result in failures 

in the roof, seam, and floor. Two pillar strength equations are given. The first equation describes 

the failure strength when confinement alone controls the strength. The second equation gives the 

failure strength when structural flaws decrease the strength of the pillar. The confinement and 

structural controlled strength equations are, respectively,

σpC = 4,700 (1 − e

−0.339 w

h ) and (D4)

σpS = 3,836 (1 − e

−0.260 w

h ). (D5)

Both equations give the pillar strength in units of psi where distances are measured in feet. The 

two Maleki equations can be generalized into a single equation:

σp = c1 (1 − e

c2w

h ), (D6)

where c1 = leading coefficient, and

c2 = exponential decay constant.

The shape of the confinement equation is shown in Figure D5.

Figure D5. Strength variation over pillar for Maleki [1992] confinement equation.

When the pillar is large enough, the strength decreases over the

center portion of the pillar from a peak that is closer to the rib.
203

Assumptions

Given the variety of average pillar strength equations, a generalized method was sought to 

obtain the corresponding variable strength equations. A few assumptions were necessary in 

developing a general method to compute a variable from an average pillar strength equation. 

These assumptions are:

1. The method is for square pillars as most empirical equations were first developed for 

square pillars.

2. Pillar material is elastic-plastic. This means that all portions of the pillar are at maximum 

strength at failure.

3. Variation of strength within the pillar is a function of distance from the closest rib. Any 

other variables such as cleat or structure are ignored.

The square pillar is divided into eight symmetric pieces in order to simplify development of 

integral equations. These equations link the stress function σV

(x) to failure force of the pillar. 

The failure force is also a function of its width F(W). Here the stress function is unknown, but 

the answer F(W) = R (total capacity) is known. This method is illustrated in Figure D6. The 

integrators defined for the symmetry piece are illustrated on the right side of Figure D6.

Figure D6. Plan view of the failure stress distribution

of a square coal pillar subdivided into eight pieces.

Variables in or associated with Figure D6 are defined as follows:

W = pillar half-width,

w = 2W = pillar width,

F = total vertical force applied to pillar,

R = pillar load capacity,

x = horizontal location within pillar

y = direction perpendicular to x, and
204

σV

(x) = local strength. 

For clarity, the pillar rib is at x = 0, and the pillar centerline is at x = W.

Numerical Implementation

The total vertical force F is calculated in terms of the vertical pillar stress σV where the 

vertical force is a function of the pillar geometry F(W). Because of symmetry the integration is:

F(W) = 8 ∫ ∫ σV

(x)

y

0

W

0

 dx dy = 8 ∫ I(y) dy W

0

, (D7)

where I(y) = ∫ σV

(x)

y

0

dx, (D8)

and dy and dx are shown in Figure D6. The w2factor in the figure cancels on each side of the 

equation.

Leibnitz’s Rule from elementary calculus is used:

d

dx

(∫ f(t)

x

0

dt) = f(x). (D9)

This rule is applied twice to the above integral. The variable vertical pillar stress equations are:

dF

dW

= 8I(W) = 8 ∫ σV

(x) dx W

0

, and (D10)

d

2F

dW2 = 8 σV

(W). (D11)

The implementation of this procedure in each of the four spatial models is discussed below.

Constant

The one-dimension method is demonstrated using the Bieniawski average pillar strength 

equation using a constant variation. Applying the formulas above, the result is linear making it 

one of the simpler equations. For a square pillar of dimension w , the pillar capacity is

F = σpw2 = σc (0.64 + 0.36 w

h

) w2, (D12)

where, for ease of implementation, w = 2W.

Applying the one-dimension method produces the result that is identical to that reported by 

Mark and Iannacchione [1992]:

d

2F

8 dx2 = σV

(x) = σc (0.64 + 2.16 x

h

). (D13)

Linear

Using a linear variation in the pillar yield stress function, Mark and Iannacchione [1992]

conclude that the variable strength equation has the same “shape” as the average pillar strength 

when average strength is expressed in the pillar’s width-to-height ratio. A graph of the linear 

increase of strength with distance into the pillar is shown in Figure D7. A pillar height of 3.0 m 

(10 ft) and a UCS of 6.21 MPa (900 psi) from Mark [1992] were assumed.
205

Figure D7. Bieniawski variable strength as a function of distance from the rib.

Square Root

The one-dimension method is applied to the Holland-Gaddy (square root spatial variation) 

average pillar strength equation. This equation is one of the simpler nonlinear equations where 

the pillar strength is a square root function of the pillar’s width-to-height ratio. Gaddy [1956]

found from unconfined compression tests that the UCS of cubical coal specimens from a given 

coal seam and the side-length of the cubes are related by the following equation.

σc =

k

√d

, (D14)

where σc = UCS of the cubical specimen,

d = side-length of cubical specimen, and

k= constant determined by plotting σc versus d and is representative of the physical 

characteristics of the coal bed from which the specimens were obtained [MN/m3/2 ( lb/in3/2)].

Holland and Gaddy [1957] developed the following formula for pillar strength that includes 

both pillar width and height:

σp =

k √w

h

, (D15)

where σp = UCS of the pillar (usually given in psi),

w = pillar width, (usually given as in),

h = pillar height, (usually given as in), and

k = constant determined by plotting σc versus h (usually given as lb/in3/2).
206

Solving for k in Gaddy’s equation, assuming that d and h are equivalent, and substituting the 

result into Holland-Gaddy’s Equation D15 yields another form of the Holland-Gaddy [Holland 

and Gaddy 1957] equation:

σp = σc √

w

h

. (D16)

The pillar capacity is

F = σpw2 = σc √

w

h

 w2. (D17)

Differentiating the above equation twice with respect to x = w

2

⁄ the result is

d

2F

8 dx2 = σV

(x) = 2.652 σc√

x

h

. (D18)

The result using the one-dimension method (Equation D18) is the same variable strength 

equation as that reported by Mark and Iannacchione [1992], where the shape of this strength 

variation is graphed in Figure D8. In this figure, the initial pillar strength for a 1-ft cube of coal 

of 3.037 MPa (440.5 psi) was used. This value was obtained using Gaddy’s equation that relates 

σcto k and h (Equation D14) where k is equal to 4,825 lb/in3/2 as reported by Holland [1964] for 

the Clintwood Seam. Assuming a 3.048 m (120-in) seam height gives 3.037 MPa (440.5 psi) for 

the in situ coal strength.

The form of this equation is such that the pillar strength is zero (with infinite slope) along the 

rib face and increases to σc at the pillar center. Because of the symmetric nature of the assumed 

variation of the pillar strength, the square root equation is not smooth (differentiable) along the 

diagonals of the pillar nor at the pillar center.
207

Figure D8. Variable strength as a function of distance from the rib

for an example using the Holland-Gaddy pillar strength equation.

Exponential

Taking Equation D6 and applying the one-dimensional method outlined in Equations D7 to 

D11 results in local pillar strength as

σV = c1

{1 − e

ax[1 + 2ax + 0.5a2x2

]}, (D19)

where a =

2c2

h

. This result is graphed for both of Maleki’s equations in Figure D9.

The form of this equation is such that the pillar strength is zero (with finite slope) at the rib 

face and increases to a maximum at the pillar center. Because of the symmetric nature of the 

assumed variation of the pillar strength, the exponential model is not smooth (differentiable) 

along the diagonals of the pillar nor at the pillar center, but it can be made to approximate the 

Bieniawski (constant) model when c2 = ∞, and the Mark-Bieniawski (linear) model when c2 =

0.
208

Figure D9. Maleki variable strength as a function of distance from the rib with confined control

strength plotted as circles and structure control strength plotted as boxes [Johnson et al. 2014].

Conclusions and Recommendations

This appendix demonstrates a new generalized mathematical method that can be used to 

calculate the maximum pillar variation of vertical stress or variable strength equation from any

average pillar strength equation that is a function of a pillars’ width-to-height ratio. The method 

is demonstrated with formulas in the following classes: constant, linear, square root, and 

exponential. Once the variable strength equation has been determined, it can then be used to 

obtain pillar cell strength or load capacity equations that are used to model mine pillars in 

boundary element programs. The variable strength equation is then used to obtain three pillar cell 

strength equations that are used to model the mine pillar: the rib, corner, and the core. The core 

cell is a newly developed addition to the previous pillar cell equations. The results, using the new 

generalized mathematical method, have been verified with the currently used pillar cell equations 

as reported in the literature. A benefit of this research to the mining industry is that now the bestsuited pillar strength equations, including those developed at any coal field or mine site (based 

on the width-to-height ratio of the pillar), can be incorporated into boundary element programs. 

This advance removes a barrier to mining engineers incorporating their full knowledge of local 

coal and ground characteristics into mine design models.
209

References for Appendix D

Bieniawski ZT [1968]. The effect of specimen size on compressive strength of coal. Int. J. Rock 

Mech. Min. Sci., Vol. 5, No. 4, pp. 325–335.

Gaddy FL [1956]. A study of the ultimate strength of coal as related to the absolute size of the 

cubical specimens tested. Bulletin of the Virginia Polytechnic Institute, Engineering Experiment 

Station Series No. 112. Vol. 49, No. 10, Blacksburg, VA: Virginia Polytechnic Institute, 27 pp.

Holland CT [1964]. The strength of coal in mine pillars. In: Spokes EM, Christiansen CR eds. 

Proceedings of the Sixth Symposium on Rock Mechanics. (Rolla, MO: October 1964) Rolla, 

MO: University of Missouri at Rolla, pp. 450–466.

Holland CT, Gaddy FL [1957]. Some aspects of permanent support of overburden on coal beds. 

In: 1957 Proceedings of the West Virginia Coal Mining Institute. (Huntington, WV, and White 

Sulphur Springs, WV: June 22–23, 1956 and November 2–3, 1956), pp. 43–65.

Hustrulid WA [1976]. A review of coal pillar strength formulas. Rock Mech., Vol. 8, No. 2, pp. 

115–145.

Johnson JC, Whyatt JK, Loken MC [2014]. A generalized method for calculating pillar cell 

capacities for boundary element modeling of coal mines. In: 2014 SME Annual Meeting. 

Preprint 14-162, (Salt Lake City, Utah: February 23–26, 2014) Englewood, CO: Society for 

Mining, Metallurgy, and Exploration, Inc., 15 pp.

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

Iannacchione AT et al. eds. Bureau of Mines Information Circular 9315, Proceedings of the 

Workshop on Coal Pillar Mechanics and Design. (Santa Fe, NM: June 7, 1992) U.S. Department 

of the Interior, pp. 73–77.

Mark C [1992]. Analysis of Longwall Pillar Stability (ALPS): An update. In: Iannacchione AT et 

al. eds. Proceedings of the Workshop on Coal Pillar Mechanics and Design. Pittsburgh, PA: U.S. 

Department of the Interior, Bureau of Mines Information Circular 9315, pp. 238–249.

Mark C [1999]. Empirical methods for coal pillar design. In: Christopher M et al. eds. 

Information Circular 9448, Proceedings of the Second International Workshop on Coal Pillar 

Mechanics and Design. Pittsburgh, PA: U.S. Department of Health and Human Services, Centers 

for Disease Control and Prevention, National Institute for Occupational Safety and Health, 

DHHS (NIOSH), pp. 145–154.

Mark C [2006]. The evolution of intelligent coal pillar design: 1981–2006. In: Peng SS et al. eds. 

Proceedings: 25th International Conference on Ground Control in Mining. (Morgantown, WV: 

August 1–3, 2006) Morgantown, WV: West Virginia University, pp. 325–334.

Mark C, Iannacchione AT [1992]. Coal pillar mechanics: Theoretical models and field 

measurements compared. In: Iannacchione AT et al. eds. Bureau of Mines Information Circular 

9135, Proceedings of the Workshop on Coal Pillar Mechanics and Design. Washington, DC: 

U.S. Department of the Interior, pp. 78–93.

Obert L, Duvall WI [1967]. Rock mechanics and the design of structures in rock, New York: 

John Wiley & Sons, 650 pp.
210

Tesarik DR, Whyatt JK, Larson MK [2013]. Inferring mine floor properties from pillar size and 

floor heave. In: Pyrak-Nolte LJ et al. eds. Proceedings of the 47th U.S. Rock 

Mechanics/Geomechanics Symposium. (San Francisco, CA: June 23–26, 2013) Alexandria, VA: 

American Rock Mechanics Association, pp. 438–450.
211

Appendix E: Ground Condition Ratings versus Model Output

Summary

Ground condition ratings showed no significant correlation with closure calculated with 

MulsimNL/Large. This lack of correlation suggests that variation in geology over the area of the 

survey was more significant than correlation of ground conditions with increased stress and 

closure that result from mining.

Background

Lawson et al. [2012] developed a rating scale for ground conditions of the roof, ribs, and 

floor of a coal mine. It may require modification for application at any given mine. The specific 

description for the sites in this study were described by Larson et al. [NIOSH 2020]. 

The purpose of this appendix is to explore any correlation between ground condition ratings 

and numerical model output. MulsimNL/Large was used to provide output over the large area of 

the surveys at Mine A.

Description

Displacement discontinuity codes such as LaModel [Heasley 1998, 2010] and Mulsim 

[USBM 1992a, 1992b; Larson and Whyatt 2013; Larson 2015] have an advantage of being able 

to model the mining of a large area in a reasonable amount of time. For calibration and 

verification purposes, it is useful to explore if some parameter in these codes corresponds well 

with ground condition ratings. For such a task, because surveys are done in the entries, the 

logical parameter to compare with ground condition survey data to test correspondence is the 

entry closure.

To carry out this investigation of correlation, the closure used for comparison was at 

midpillar, except where the surveys stated the closure was at the intersections. To calculate entry 

closure, the average of closure of the two elements at the same latitude in an entry was 

calculated.

Because use of empirical tools is widespread, the first comparison is with ground condition 

ratings compared to closure as calculated by LaModel, where LaModel has default parameters; 

that is, parameters that enable calibration criterion to empirical assumptions to be met, as 

outlined by Heasley [2008]. As seen from Figure E1, there appears to be no correlation between 

any ground condition rating and model closure.

Because measured load transfer distance (LTD) determined from LaModel was significantly 

different from that predicted by the Peng and Chiang equation, the comparison was done 

between ground control ratings and closure output from LaModel when the rock mass stiffness 

was calibrated to measured LTD. Figure E2 shows that there is no correlation between ground 

condition rating and calculated closure of the model.

The best Mulsim model for predicting measured LTD was obtained by using a fully elastic 

seam model, with cells near the rib reduced in modulus to simulate the effect of softer material 

near ribs that result from yielding or release of gas. Figure E3 shows ground condition ratings 

versus closure at all sites surveyed at the proper states of mining. Interpolation was necessary 
212

when a survey was done with the face located between face location increments in the model. 

Again, correlation between any rating and entry closure was poor. 

Correlation between the maximum ground condition rating and model-calculated closure was 

also investigated. However, Figure E4 exhibits extensive data scatter with no discernible 

correlation.

Examination of results by gate road shows varied results. In 1 North, only one site was 

sampled, at the outby instrumentation site. Figure E5 shows correlation between rib ratings and 

model closure and between roof ratings and model closure. However, the number of surveys 

conducted does not make this correlation certain. Still, Lawson et al. [2012], found ratings at one 

location over time to be indicative of changing ground conditions. Moreover, Larson and Whyatt 

found single site ratings useful as an indication of arrival of abutment stress [2012]. Larson et al. 

[NIOSH 2020] confirmed that use.

In the 2 North gate roads, many more surveys were conducted. However, because areas were 

identified as being anomalous and nonanomalous in their ground condition, it was necessary to 

separate these survey results by anomalous and nonanomalous zones for investigating 

correlation. Figure E6 shows ground condition ratings from nonanomalous zones versus model 

closure—that is, ground condition ratings were from the zones showing typical behavior for 2 

North. The scatter of results appears random. The same result is obtained by examining 

anomalous zone ground condition ratings versus model closure, shown in Figure E7.
213

Figure E1. Ground condition ratings vs. closure calculated by LaModel

using default parameters for rock mass stiffness and gob stiffness with coal

having a uniaxial compressive strength of 6.21 MPa (900 psi) and a distributed

strength according to the Mark-Bieniawski criterion [Mark and Chase 1997].
214

Figure E2. Ground condition ratings versus closure calculated by LaModel using

rock mass stiffness calibrated for measured LTD and default gob stiffness with coal

having a uniaxial compressive strength of 6.21 MPa (900 psi) and a distributed

strength according to the Mark-Bieniawski criterion [Mark and Chase 1997].
215

Figure E3. Ground condition ratings versus closure calculated by Mulsim using

best-guess parameters for rock mass stiffness and default gob stiffness as calculated by

LamPre assuming coal having a uniaxial compressive strength of 6.21 MPa (900 psi) and

a distributed strength according to the Mark-Bieniawski criterion [Mark and Chase 1997].

Shown are all ratings for all locations surveyed in both 1 North and 2 North gate roads. Coal was

elastic, with modulus of outer two rings reduced to 60% and 80%, respectively, of its full amount.
216

Figure E4. Largest ground condition rating of floor, rib, or roof vs. closure calculated by Mulsim

using best-guess parameters for rock mass stiffness and default gob stiffness as calculated by

LamPre assuming coal having a uniaxial compressive strength of 6.21 MPa (900 psi) and a

distributed strength according to the Mark-Bieniawski criterion [Mark and Chase 1997]. Shown

are data from surveys taken at all locations in both 1 North and 2 North gate roads. Coal was

elastic, with modulus of outer two rings reduced to 60% and 80%, respectively, of its full amount.
217

Figure E5. Ground condition ratings versus closure calculated by

Mulsim using best-guess parameters for rock mass stiffness

and default gob stiffness as calculated by LamPre assuming

empirical conditions. Shown are all ratings for one location surveyed

in the 1 North gate roads. Coal was elastic, with modulus of outer

two rings reduced to 60% and 80%, respectively, of its full amount.
218

Figure E6. Ground condition ratings versus closure calculated by Mulsim using

best-guess parameters for rock mass stiffness and default gob stiffness as

calculated by LamPre assuming empirical conditions. Shown are all ratings

from all nonanomalous zones surveyed in the 2 North gate roads. Coal was elastic,

with modulus of outer two rings reduced to 60% and 80%, respectively, of its full amount.
219

Figure E7. Ground condition ratings versus closure calculated by Mulsim

using best-guess parameters for rock mass stiffness and default gob stiffness

as calculated by LamPre assuming empirical conditions. Shown are all ratings from

all anomalous zones surveyed in the 2 North gate roads. Coal was elastic, with the

modulus of outer two rings reduced to 60% and 80%, respectively, of its full amount.

Conclusion

Although ground condition ratings have been found to be useful at a given site to provide 

some indication of arrival of the abutment stress, no correlation with entry closure as calculated 

with various models was obtained. The scatter shown in the figures of this appendix are likely 

indicative of the great variability of ground conditions and possibly stratigraphic variability 

along the gate roads, particularly in 2 North.
220

References for Appendix E

Heasley KA [1998]. Numerical modeling of coal mines with a laminated displacementdiscontinuity code. Ph.D. Dissertation. Golden, Colorado: Colorado School of Mines, 205 pp.

Heasley KA [2008]. Some thoughts on calibrating LaModel. In: Peng SS et al. eds. Proceedings: 

27th International Conference on Ground Control in Mining. (Morgantown, WV: July 29–31, 

2008) Morgantown, WV: West Virginia University, pp. 7–13.

Heasley KA [2010]. LaModel, ver. 3.0, Morgantown, WV: West Virginia University.

Larson MK [2015]. MulsimNL/Large: Reviving a USBM tool for modeling coal mines. In: 

Preprints: 2015 SME Annual Conference & Expo, CMA 117th National Western Mining 

Conference. Preprint 15-039, (Denver, CO: February 15–18, 2015) Englewood, CO: Society for 

Mining Metallurgy, and Exploration, Inc., 11 pp.

Larson MK, Whyatt JK [2012]. Load transfer distance calibration of a coal panel scale model: A 

case study. In: Barczak T et al. eds. Proceedings of the 31st International Conference on Ground 

Control in Mining. (Morgantown, WV: July 31–August 2, 2012) Morgantown, WV: West 

Virginia University, pp. 195–205.

Larson MK, Whyatt JK [2013]. Panel-scale modeling of a deep longwall panel: The MULSIM

alternative. In: Barczak T et al. eds. Proceedings: 32nd International Conference on Ground 

Control in Mining. (Morgantown, WV: July 30–August 1, 2013) Morgantown, WV: West 

Virginia University, pp. 181–188.

Lawson H, Zahl E, Whyatt J [2012]. Ground condition mapping: A case study. In: 2012 SME 

Annual Meeting, "Mine to Market: Now It's Global" Preprint 12–122, (Seattle, WA: Feb 19–22, 

2012) Englewood, CO: Society for Mining, Metallurgy, and Exploration, Inc., 7 pp.

Mark C, Chase FE [1997]. Analysis of Retreat Mining Pillar Stability (ARMPS). In: Mark C, 

Tuchman RJ eds. Proceedings: New Technology for Ground Control in Retreat Mining, DHHS 

(NIOSH) Publication No. 97-133, IC 9446. Pittsburgh, PA: National Institute for Occupational 

Safety and Health (NIOSH), pp. 17–34.

NIOSH [2020]. Ground stress in mining (part 1): Measurements and observations at two western 

U.S. longwall mines. By Larson MK, Lawson HE, Zahl EG, Jones TH. U.S. Department of 

Health and Human Services, Centers for Disease Control and Prevention, National Institute for 

Occupational Safety and Health, DHHS (NIOSH) Publication No. 2019-175, RI 9702.

USBM [1992a]. MULSIM/NL application and practitioner's manual. By Zipf RK, Jr. 

Information Circular 9322, Pittsburgh, PA: U.S. Department of the Interior, Bureau of Mines 

(USBM), 44 pp.

USBM [1992b]. MULSIM/NL theoretical and programmer's manual. By Zipf, RK, Jr. 

Information Circular 9321, Pittsburgh, PA: U.S. Department of the Interior, Bureau of Mines 

(USBM), 52 pp.

 
221

Appendix F: Borehole Pressure Cell Calibration Issues

Summary

Installed in coal, Borehole pressure cell (BPC) internal pressure is shown to depart from the 

data reduction methods of Lu and Babcock for indicating stress change in the coal. The probable 

reason is that the instrument becomes a hard inclusion in a nonlinear medium. Small pressure 

change at close to setting pressure is likely indicative of stress change, and therefore, the 

instrument is effective for sensing the first arrival of mining-induced abutment stress.

Background

Borehole pressure cells (BPCs) have been used in many coal mines to measure change of 

stress resulting from mining. It is not always clear how successful or accurate those 

measurements have been in reflecting change of stress in the coal at the point of installation.

Panek and Stock [1964b] did some experimental work in a limestone mine, developing a 

technique to measure absolute stress and stress change at the rib with BPCs, large flatjacks, and 

sensors. In the technique, they set the pressure in a pair of BPCs, and then relieved vertical stress 

by cutting a slot above the BPCs. The large flatjacks were encapsulated in cement in these slots 

and pressurized until the fluid pressures in the BPCs were returned to their pre-stress-relief 

values. The pressure in the large flatjack was then considered to be the earth pressure in the 

direction perpendicular to the large flatjack. 

About the same time, encapsulated BPCs were tested by Miller and Sporcic [1964a] in coal. 

However, the response of the instruments was not clear, although the instruments did seem to 

respond in some fashion to mining-induced stress increase, bumps, roof events, and rib falls.

Wright et al. [1979] advocated using response tests to determine the relationship between 

rock (or coal) pressure and the cell pressure. However, they noted that when the cells were 

pressurized well over the in situ stress, that fractures formed in line with the cell bladder. Thus, 

as stress increased, the cell pressure increased substantially more than the stress increase in the 

surrounding rock because of the area it was supporting. This lesson was learned by the authors 

and expressed by others in personal communications. As a result, the standard practice of setting 

installation pressure only slightly above in situ stress—often about 10% above—in the direction 

perpendicular to the bladder was used. This practice allows the cell to bleed off slightly as 

seating occurs so that the cell pressure becomes close to the in situ amount of stress.

Several calibration methods have been developed for BPCs and a similar instrument, called 

the Borehole Platened Flatjack (BPF) [Sellers 1970; Bauer et al. 1985; Heasley 1989], but these 

methods have relied on linear-elastic theory of the host medium, and it is doubtful that coal 

behaves linearly.

Two methods of calibration were developed in the 1980s that deserve further consideration, 

even though neither method considers the possibility of coal loading outside its elastic range. Lu 

[1984] developed a way to determine absolute stress and stress change using three cells: (1) a 

cylindrical pressure cell (CPC) placed in a hole of 38.0-mm (1.50-in) diameter (EX hole), which 

is drilled at the end of a BX hole [60-mm (2.36-in) diameter]; (2) a flat bladder [borehole 

pressure cell (BPC) made of 1.52-mm (0.060-in) steel that is 20.3 cm (7.99 in) in length, 5.08 cm 

(2.00 in) wide, and 8.9 mm (0.35 in) high, and encapsulated in a cylinder of Portland cement that 

is 59.3 mm (2.33 in) in diameter] that is oriented in the BX borehole so that the plane of the 
222

bladder is perpendicular to the vertical direction; and (3) another BPC placed in the BX borehole 

near the other two instruments and oriented such that its plane is perpendicular to the horizontal 

direction. This calibration method, which will be described later in this appendix in more detail, 

relies on a linear relationship between the cell pressure and changes in rock stress, and is, 

therefore, dependent on linear-elastic behavior of the host coal. Equilibrium pressures of the 

three gauges at various points in mining history are used to determine absolute stress in the 

directions perpendicular to the two BPC bladders.

The second method, developed by Babcock [1986] is a nonlinear method that depends on 

setting pressure and changes relative to that setting pressure. The sensitivity of change in cell 

pressure to host material stress change is dependent on host material elastic properties, but this 

sensitivity varies according to setting pressure and subsequent amounts of cell pressure, such that 

cell pressure changes at higher absolute pressure indicate lower host material pressure changes 

than does the equivalent cell pressure change at lower absolute pressure. This method is also 

outlined in more detail later in this appendix. In a laboratory setting, Babcock tested the cell in 

several elastic materials, covering a wide range of elastic moduli. However, coal was not one of 

the materials tested, and all tests were conducted at pressures that did not exceed the elastic limit 

of the host material. Even so, Babcock’s tests appear to capture nonlinear behaviors such as that 

resulting from changing contact area as pressure changes. Caution must be exercised because, 

again, coal may not behave linearly in its elastic range because of various discontinuities (e.g., 

cleats and joints) that close with increasing stress. Moreover, the calibration method does not 

hold if the coal is loaded beyond its elastic range.

Knowing that coal often behaves in a nonlinear fashion and that interaction between the cell, 

cement, and host material was nonlinear, Su and Hasenfus [1990] conducted a laboratory study 

and a numerical modeling (finite element) study of what they termed the K-factor—i.e., the ratio 

of cell pressure change to external pressure change. First, they conducted laboratory experiments 

with the cell in a nylon block. With a numerical model using gap elements, they were able to 

reproduce the measured response of the cell versus the loading and unloading of the block very 

well. In their model, they used elasto-plastic, strain-hardening, plane-stress elements for steel and 

concrete. A Mohr-Coulomb yield criterion [Jaeger and Cook 1976] was used for the concrete and 

a von Mises yield criterion [Fung 1965] was used for the steel. After simulating the laboratory 

experiments, these researchers conducted numerical experiments with their model for coal 

having a modulus of 1.103 GPa (160,000 psi) and having elastic-perfectly plastic behavior with a 

Drucker-Prager yield criterion [Drucker and Prager 1952]. Su and Hasenfus [1990] reported the 

changing contact area between the cement and the borehole wall with increasing stress, adding to 

the nonlinearity of the K-factor. Figure F1 shows how the K-factor, calculated with model 

results, varied nonlinearly with setting pressure and increasing external stress. The results of Su 

and Hasenfus [1990] confirm the nonlinear nature of the geometry, which is also captured in 

some measure by the Babcock method. However, the representation of elastic coal behavior by 

Su and Hasenfus [1990] still needs to be confirmed. Moreover, even if their representation is 

accurate for a particular coal type, more experiments are needed on a wide variety of coal types 

to develop equations to represent a wider range of response. Validation of post-yield behavior of 

the coal and its effect on the BPC must also be confirmed and validated.
223

Figure F1. The borehole pressure cell (BPC) K-factor determined with a finite element model

of a coal having Young's modulus of 1.103 GPa (160,000 psi). After Su and Hasefus [1990].

Δσh/Δσv is the ratio of externally applied change in horizontal stress to change in vertical

stress. The successive positions of θa, θb, and θc, show the effect of reducing the horizontal

confinement where setting pressure and applied vertical stress change remain constant.

Examples of BPC use in studies by the Bureau of Mines are DeMarco et al. [1988], Barron 

[1990], Barron et al. [1994], Barron and DeMarco [1995], and Koehler et al. [1996]. However, in 

these studies, the raw, relative cell pressure data was used to characterize the timing of loading 

and relative loads by location [DeMarco 2013]—no data reduction method was used.

Because the Lu and Babcock methods are comprehensive in nature, the theory of each is 

described in this appendix.
224

Lu Method

Lu [1984] derived equations for BPC calibration based on elastic theory of plates and thickwalled cylinders, in addition to application of the elastic and viscoelastic correspondence 

principle. These equations are

NH + NV =

Pe−CPC

1− ν

, and (F1)

NH

NV

=

(

Pe−BH

Pe−BV

⁄ −S)

[1− (

Pe−BH

Pe−BV

⁄ ) S]

, (F2)

where NH = horizontal ground pressure,

NV = vertical ground pressure,

Pe−CPC = pressure of the CPC at equilibrium,

ν = Poisson’s ratio of the rock mass (or coal),

Pe−BH = horizontally oriented (i.e., the normal to its plane is horizontal) BPC pressure at 

equilibrium,

Pe−BV = vertically oriented BPC pressure at equilibrium, and

S = transverse sensitivity of the BPC, which is 0.185, as calculated from the geometry of 

the BPC that the U.S. Bureau of Mines developed. Transverse sensitivity is a measure of the 

effect of an increase in stress in the direction perpendicular to the normal direction of the flatjack 

bladder on the increase in cell pressure.

Changes in pressure are obtained by calculating absolute pressures from the cell readings 

both before and after mining-induced loading and noting the differences. For each set of cell 

pressures, the equilibrium must be established during periods when active mining is far enough 

away so that its effect on load changes of the cells is insignificant. 

Other researchers [Vandergrift and Conover 2010], in order to use only vertically oriented 

BPCs so that more vertical stress measurements can be made (three cells per borehole is the 

maximum for pre-encapsulated flatjacks), have assumed a relationship between the horizontal 

and vertical ground stresses. They assumed that 

NH

NV

=

ν

1 − ν

. (F3)

By rearranging Equation F2, 

PV = (

PH

NH+S NV

) (NV + S NH) or (F4)

PV = w(NV + S NH), (F5)

where w =

PH

NH + S NV

, (F6)

and w is called the response factor, which Vandergrift and Conover [2010] stated is 1.095 for 

coal. At Poisson’s ratio of 0.38 that Vandergrift and Conover used, the ratio of horizontal cell 

pressure to horizontal ground stress had to be constant at 1.426. Vandergrift and Conover do not 

cite the source of the response factor that they used. Even so, if their value for w is valid, then 

the assumption of Equation F3 can be applied so that
225

PV = w [1 +

ν

1 + ν

] NV. (F7)

Using the Poisson’s ratio of Vandergrift and Conover, the cell pressure would be converted 

to ground pressure by multiplying it by 0.820, which is 1

w

. In the case of Mine A (the same site), 

the authors used a Poisson’s ratio of 0.33, and the constant for conversion to ground pressure was 

0.837.

Although it is advantageous to orient all cells in the vertical direction for stress change 

profiling, the assumption of Equation F3 must be evaluated in each case. The assumption may 

not be valid, and therefore introduce error into the stress change calculation. The validity of this 

assumption may even vary by cell location. For example, confinement near a rib would be 

different from that in the middle of a pillar.

Babcock Method

Babcock performed laboratory work with BPCs in several materials with wide ranging elastic 

properties. His experiments showed the transverse sensitivity (NH

NV

⁄ ), to be an average of -

0.333, which differs from the finding of Sellers [1970] (-0.06) and those of Lu [1984] (-0.185). 

In his tests of Plexiglas, oil shale, potash, concrete, limestone, sandstone, and granite, Babcock 

noted the fraction of pressure change of the instrument compared to change of radially applied 

rock pressure (ΔσBPC

ΔNR

⁄ ) and plotted that ratio with setting pressure of the BPC (σBPC

∗

). He fit 

a linear equation to the results for each material: 

ΔσBPC

ΔNR

= m σBPC

∗ + b. (F8)

The slope, m, was also calculated with the intercept, b, set to 0. 

Hanna et al. [1991] fit a nonlinear equation to estimate m with dependent variables being 

Young’s modulus and Poisson’s ratio. Their equation is

m = 4.238 [

1− ν

2

E

]

(

2

3

⁄ )

, (F9)

where E = Young’s modulus of the host material, and

ν = Poisson’s ratio of the host material. 

Vandergrift and Conover [2010] appear to misstate the constant in this equation as 4.348, but 

both constants give reasonably close approximations to Babcock’s data. The authors of this 

report used the constant listed by Vandergrift and Conover [2010].

Babcock’s results fit the equations

ΔNV −

ΔNH

3

=

1

m

ln [

PV

PV

∗

], and (F10)

ΔNH −

ΔNH

3

=

1

m

ln [

PH

PH

∗

], (F11)

where PV

∗ = setting pressure of the vertically oriented cell, and

PH

∗ = setting pressure of the horizontally oriented cell.

From these equations, we can determine
226

ΔNV =

3

8m

ln {[

PV

PV

∗

]

3

[

PH

PH

∗

]}. (F12)

Equation F12 differs in the constants on the right side of the equation from those in the 

corresponding Equation 6 of Babcock [1986] and with corresponding equations outlined by 

Hanna et al. [1991] in their Appendix C. The authors’ Equation F12 is confirmed by Vandergrift 

and Conover [2010].

Using the assumption of Equation F37, it follows that the cell pressure ratios would change 

proportionally in the same way as the rock stresses—that is

PH

PV

=

PH

∗

PV

∗ =

ν

1− ν

(F13)

7 Recall the earlier discussion about validity of this assumption and the need to evaluate whether it holds 

in any particular case and cell location. The same concerns apply here.

Then Equation F12 can be written as

ΔNV =

3

8m

ln {[

PV

PV

∗

]

4

}. (F14)

This equation can then be used to indicate change in vertical stress. In this study, when the 

Babcock method was used for analysis, the initial stress at a cell location was estimated to be the 

initial cell pressure—not necessarily the precise setting pressure, but the first logged 

measurement, which was then treated like a setting pressure for purposes of analysis. 

Admittedly, the absolute measured stresses calculated in this manner are unlikely to be correct, 

but this procedure provides reasonable estimation of absolute stress for the purpose of graphical 

display versus advance of the panel face. Such curves can easily be plotted alongside stress 

calculated with numerical models at BPC locations as the face advances. However, the objective 

is to compare changes in stress and not absolute amounts of stress with face advance.

Application of Calibration Methods to BPC Data at Mine A

The earlier survey of the literature in this study underlines the lack of thorough investigation 

of BPC calibration in various coals. The authors of this report prefer the Babcock method 

because of its nonlinear nature, but they concede that it has no validity beyond the elastic range 

of coal and that there is some question about its validity in coal, since it is based entirely on 

testing other materials only in their elastic range. Results like those of Su and Hasenfus [1990]

would likely be preferable, but their study was not comprehensive enough to develop general 

calibration equations.

For these reasons, Equation F14 was applied as described above to BPC raw pressure 

measurements. These measurements were correlated to distance from the line of instruments to 

the face, that distance being negative when the face was inby the instruments and plotted versus 

face distance. These measurement data are described in detail by Larson et al. [NIOSH 2020]. In 

this appendix, we also show results of applying the Lu calibration method to the BPC raw 

pressure measurements for comparison.

 
227

Modeled Stress Transfer With and Without Gob

Earlier in the main body of this report, plots show the BPC measurements (reduced by the 

Babcock method) compared to stress histories at BPC locations interpolated from output stresses 

of various models. In most cases, unless the instrument failed or the coal yielded, the measured 

stresses became much higher than what the models predicted as the face approached and passed 

the line of instruments. 

As detailed in the main body of this report, the best Mulsim model for predicting stress 

appeared to be the elastic case with coal modulus reduced to 60% and 80% of the full amount in 

the outer first and second rings of elements, respectively. For that reason, this model was used to 

evaluate the validity of the amounts of stress changes measured with BPCs at Mine A.

The elastic model with reduced moduli in the outer two rings was modified so that no gob 

was present. In other words, all weight of overburden over the mined panel was transferred to the 

abutments. This model was used to calculate upper bounds for stress changes at instrument 

locations resulting from mining of Panel 1. These upper bounds, calculated for various face 

positions with respect to the instrument lines, were compared with measurements reduced by the 

Lu and Babcock methods. 

Figures F2 and F3 show what stress changes had taken place at the 1 North outby and 2 

North outby sites, respectively, when the face was at various distances inby each site’s 

instrument line. Measurements of stress change as determined by Lu [1984] and Babcock [1986]

are shown along with the Mulsim results using the reduced coal modulus near the ribs, both with 

and without gob. The green (or olive) results—without gob—show what should be upper bounds 

to the BPC measurements. The BPC results, especially as the face approaches each site’s 

instrument line, were well above what is estimated to be physically possible.

Obviously, neither the Lu nor the Babcock calibration methods hold up at higher stress. The 

trends of stress increase and where those increases occur are not suspect, but the calibration 

methods of Lu [1984] and Babcock [1986], based on linear-elasticity for the host medium, do not 

appear to be valid in this case.
228

Figure F2. BPC stress change measurements compared to MulsimNL/Large stress

change calculations at the 1 North outby site when face was inby the instrument line

by several approximate distances: A, 381 m (1250 ft); B, 305 m (1000 ft); C, 229 m (750 ft);

D, 152 m (500 ft); and E, 76 m (250 ft). Only those instruments that met the criteria to be

used for LTD measurements [Larson and Whyatt 2012] are shown.
229

Figure F3. BPC stress change measurements compared to MulsimNL/Large

stress change calculations at the 2 North outby site when face was inby the

instrument line by several approximate distances: A, 381 m (1,250 ft); B, 305 m (1,000 ft);

C, 229 m (750 ft); D, 152 m (500 ft); and E, 76 m (250 ft). Only those instruments that met

the criteria to be used for LTD measurements [Larson and Whyatt 2012] are shown.
230

Adjustments

Presumably, as stress increases near a BPC, the instrument acts increasingly as a hard 

inclusion. Rising load, then, increasingly seeks the path of most resistance. Two causes of this 

phenomenon could be: (1) the failure and deterioration of the coal near the instrument affecting 

the calibration and (2) the nonlinear-elastic nature of some or most coals.

For the first cause, simulation of coal deterioration might be represented roughly by a 

decrease in Young’s modulus with increasing cell pressure and implemented in Equation F9. For 

the second cause, the increased nonlinearity might be approximated in some fashion by 

increasing the constant in Equation F9. These two methods are not good mechanistic 

representations, but they allow exploration of these concepts and help quantify, in some sense, 

the degree of change in calibration necessary to account for the effect.

Young’s Modulus Adjustment and Results

Figures F2 and F3 show that generally, the nonlinearity of BPC response increases with 

proximity to the rib and decreases in the center of the pillars. Such response correlates 

approximately with the degree of confinement and strongly suggests that post-peak strength 

deterioration of the coal plays a significant role in the increase of nonlinear response.

Trial and error was used to develop a target deterioration of Young’s modulus with 

increasing BPC pressure. The target modulus-versus-BPC-pressure response and a curve from a 

fitted continuous equation used to represent that response are shown in Figure F4. There is little 

expectation that Equation F9 holds under such conditions. However, it is used as a vehicle to 

explore a sense of the yielding involved, as represented by the deterioration of Young’s modulus.

Figures F5 and F6 also show the ground stress response recalculated from softening of 

Young’s modulus. In both 1 North and 2 North, these curves were below the curve of upper 

range of possible responses and were reasonably near the Mulsim result with gob.

The stress-changes determined from the raw cell pressures with these modified Lu and 

Babcock equations were not only below the upper limits determined with the no-gob model, but 

they were near the results of the Mulsim model with gob. However, the amount of deterioration 

in modulus required to bring about these calculated results was, in the opinion of the authors, 

more than is reasonable, suggesting that more than just coal yielding is responsible for the degree 

of nonlinearities.
231

Figure F4. Target and fitted curve for deterioration of Young's modulus of coal

to simulate the effect of coal deterioration on the response of the instrument.
232

Figure F5. Recalculated BPC stress change measurements (by modifying a nonlinearity constant,

and by Young’s modulus softening) compared to MulsimNL/Large stress change calculations at

the 1 North outby site when face was inby the instrument line by several approximate distances:

A, 381 m (1,250 ft); B, 305 m (1,000 ft); C, 229 m (750 ft); D, 152 m (500 ft); and E, 76 m (250 ft).
233

Figure F6. Recalculated BPC stress change measurements (by modifying a nonlinearity constant,

and by Young’s modulus softening) compared to MulsimNL/Large stress change calculations at

the 2 North outby site when face was inby the instrument line by several approximate distances:

A, 381 m (1,250 ft); B, 305 m (1,000 ft); C, 229 m (750 ft); D, 152 m (500 ft); and E, 76 m (250 ft).
234

Calibration Constant Adjustment and Results

The constant in Equation F9 was changed to 7.538, representing an increase of over 73% 

above the constant previously used. This increased the calculated nonlinear response 

considerably. Figures F5 and F6 compare the recalculated ground stress response (labeled 

“Babcock, modified constant”) to the best Mulsim model and the Mulsim model with no gob (the 

latter representing an upper limit of range of BPC response). The recalculated measured stress 

was mostly brought within the curve of upper range of possible responses, as calculated by 

Mulsim, at the 1 North site, but it was still outside that upper range in 2 North. This fact supports 

drilling observations that coal in 2 North might be weaker than in 1 North.

Conclusions

The Lu [1984] and Babcock [1986] BPC calibration methods, modified for the use of 

vertically oriented BPCs only, were inadequate for reasonable calculation of stress change in 

coal at Mine A in this study. The calculated stress changes were higher than was possible, 

determined by comparing to stress change calculated with a model having no overpanel weight 

transmitted through the gob, thus representing an upper limit of stress change possible. This 

comparison was done when the face was at various distances inby the line of BPCs. Among 

probable causes for the calibrations being inadequate are the nonlinear nature of coal in its elastic 

range and deterioration of the coal resulting from yielding and post-yield behavior. The cell 

appeared to act as a hard inclusion in a softening host material such that increased load was 

concentrated through the instrument. These effects appeared to increase with higher mininginduced stress. 

Recommendations

The authors recommend further research to determine the nature of the behavior of various 

coals, both in the elastic and post-yield ranges. Without that information, calibrations can only be 

based on assumptions of coal behavior.

Moreover, the authors recommend that the borehole pressure cell and other comparable 

instruments (e.g., the biaxial stressmeter), be tested under various conditions in both the 

laboratory and the field. In parallel, the numerical experimental work of Su and Hasenfus [1999]

should be expanded to include a wide range of coal behaviors, particularly as more is learned 

about the behavior of various coals. Improved calibration methods should result from such 

studies. Subsequently, these methods should be applied and be subject to further evaluation.
235

References for Appendix F

Babcock CO [1986]. Equations for the analysis of borehole pressure cell data. In: Hartman HL 

ed., Rock Mechanics: Key to Energy Production, Proceedings of the 27th U.S. Symposium on 

Rock Mechanics. (Tuscaloosa, AL: June 23–25, 1986) Littleton, CO: Society of Mining 

Engineers, pp. 233–240.

Barron L, R. [1990]. Longwall stability analysis of a deep, bump-prone western coal mine—case 

study. In: Peng SS ed., Proceedings: 9th International Conference on Ground Control in Mining. 

(Morgantown, WV: June 4–6, 1990) Morgantown, WV: University of West Virginia, pp. 142–

149 pp.

Bauer ER, Ghekan GJ, Hill JC [1985]. A borehole instrument for measuring mining-induced 

pressure changes in underground coal mines. In: Ashworth E ed., 2, Research & Engineering 

Applications in Rock Masses: Proceedings of the 26th U.S. Symposium on Rock Mechanics. 

(Rapid City, SD: June 26–28, 1985) Rotterdam: A. A. Balkema, pp. 1075–1084.

DeMarco MJ [2013]. BPC data reduction. E-mail, Personal communication to Larson MK, May 

25, 2 pp.

DeMarco MJ, Koehler JR, Lu PH [1988]. Characterization of chain pillar stability in a deep 

western coal mine—a case study. Mining Eng., Vol. 40, No. 12, pp. 1115–1119.

Drucker DC, Prager W [1952]. Soil mechanics and plastic analysis for limit design. Q Appl. 

Math., Vol. 10, No. 2, pp. 157–165.

Fung YC [1965]. Foundations in solid mechanics, Englewood Cliffs, NJ: Prentice-Hall, Inc., 549 

pp.

Heasley KA [1989]. Understanding the hydraulic pressure cell. In: Khair AW ed., Rock 

Mechanics as a Guide for Efficient Utilization of Natural Resources: Proceedings of the 30th 

U.S. Symposium. (Morgantown, WV: June 19–22, 1989) Rotterdam: A. A. Balkema, pp. 485–

492 pp.

Jaeger JC, Cook NGW [1976]. Fundamentals of rock mechanics. 2nd ed., New York: John 

Wiley & Sons, Inc., 604 pp.

Koehler JR, DeMarco MJ, Marshall RJ, Fielder J [1996]. Performance evaluation of a cable 

bolted yield-abutment gate road system at the Crandall Canyon No. 1 Mine, Genwal Resources, 

Inc., Huntington, Utah. In: Ozdemir L et al. eds. Proceedings: 15th International Conference on 

Ground Control in Mining. (Golden, Colorado: August 13–15, 1996) Golden, Colorado: 

Colorado School of Mines, pp. 477–495 pp.

Larson MK, Whyatt JK [2012]. Load transfer distance calibration of a coal panel scale model: A 

case study. In: Barczak T et al. eds. Proceedings of the 31st International Conference on Ground 

Control in Mining. (Morgantown, WV: July 31–August 2, 2012) Morgantown, WV: West 

Virginia University, pp. 195–205.

Lu PH [1984]. Mining-induced stress measurement with hydraulic borehole pressure cells. In: 

Dowding CH, Singh MM eds. Rock Mechanics in Productivity and Protection, Proceedings: 

Twenty-Fifth Symposium on Rock Mechanics. (Evanston, IL: June 25–27, 1984) New York, 

NY: Society of Mining Engineers, pp. 204–211.
236

NIOSH [2020]. Ground stress in mining (part 1): Measurements and observations at two western 

U.S. longwall mines. By Larson MK, Lawson HE, Zahl EG, Jones TH. U.S. Department of 

Health and Human Services, Centers for Disease Control and Prevention, National Institute for 

Occupational Safety and Health, DHHS (NIOSH) Publication No. 2019-175, RI 9702.

Sellers JB [1970]. The measurement of rock stress changes using hydraulic borehole gages. Int. 

J. Rock Mech. Min. Sci., Vol. 7, No. 4, pp. 423–435.

Su D, Hasenfus GJ [1990]. Intrinsic response of borehole pressure cells laboratory calibrations 

and nonlinear fem simulation. In: Peng SS ed., Proceedings: Ninth International Conference on 

Ground Control in Mining. (Morgantown, WV: June 4–6, 1990) West Virginia University, pp. 

260–271.

Su DWH, Hasenfus GJ [1999]. Coal pillar strength and practical coal pillar design 

considerations. In: Mark C et al. eds. Proceedings of the Second International Workshop on Coal 

Pillar Mechanics and Design. (Vail, CO: June 6, 1999) Pittsburgh, PA: U.S. Department of 

Health and Human Services, pp. 155–162.

USBM [1964a]. Development of a hydraulic device for measuring relative pressure changes in 

coal during mining: A progress report. By Miller TC and Sporcic R. Report of Investigations 

6571, Pittsburgh, PA: U.S. Department of the Interior, Bureau of Mines (USBM), 16 pp.

USBM [1964b]. Development of a rock stress monitoring station based on the flat slot method of 

measuring existing rock stress. By Panek LA and Stock JA. Report of Investigations 6537, 

Pittsburgh, PA: U.S. Department of the Interior, Bureau of Mines (USBM), 66 pp.

USBM [1991]. Coal mine entry intersection behavior study. By Hanna K, Conover D, Haramy 

KY. Report of Investigations 9337, Pittsburgh, PA: U.S. Department of the Interior, Bureau of 

Mines (USBM), 84 pp.

USBM [1994]. Longwall gate road stability in four deep western U.S. coal mines. By Barron LR, 

DeMarco MJ, Kneisley RO. Information Circular 9406, Pittsburgh, PA: U.S. Department of the 

Interior, Bureau of Mines (USBM), 94 pp.

USBM [1995]. Longwall gate road stability in a steeply pitching thick coal seam with a weak 

roof. By Barron LR, DeMarco MJ. Report of Investigations 9580, Pittsburgh, PA: U.S. 

Department of the Interior, Bureau of Mines (USBM), 37 pp.

Vandergrift T, Conover D [2010]. Assessment of gate road loading under deep western U.S. 

conditions. In: Mark C et al. eds. Proceedings: 3rd International Conference on Coal Pillar 

Mechanics and Design. (Morgantown, WV: July 26, 2010) Morgantown, WV: West Virginia 

University, pp. 38–46.

Wright FD, Howell RC, Dearinger JA [1979]. Rock mechanics study of shortwall mining. 

Contract No. U.S. D.O.E. ET-73-C-01-9010 (formerly U.S.B.M. H0133039), April 30, 1979, 

Lexington, KY, University of Kentucky, 288 pp.
237

Appendix G: Five-Point Stress-Strain Material Model Implemented in 

MulsimNL/Large

Summary

Borehole pressure cell (BPC) measurement histories, determinations of load transfer distance 

(LTD), and observations of relative strength during drilling of different seams in the geologic 

column at Mine A suggested that a more complicated law than was currently available in LaModel 

or MULSIM/NL was needed. Specifically, it appeared that strain hardening beyond a yield point 

followed by softening was required to produce the majority of the BPC pressure histories and the 

LTDs near each rib. As a result, a material strength model with multiple segments defined by five 

points of stress and strain was implemented in MulsimNL/Large. A verification problem with two 

mining steps in which a pillar is excavated was run using two existing material models: (1) the 

elastic coal model with the outer, and next-to-outer, rings of elements having the elastic modulus 

reduced to 60% and 80%, respectively, of the full elastic modulus; and (2) a Mark-Bieniawski 6.2-

MPa (900-psi) coal [Mark and Chase 1997] with softening to a residual stress after the peak stress 

has been reached. The five-point material model was then used in each case to replicate the 

original material model. Any differences between the models were very small. Thus, the five-point 

material model was verified against existing implemented material models.

Background—Need for Five-Point Material Model

Larson and Whyatt [2012] measured LTD with borehole pressure cells (BPCs) at Mine A 

using, as a threshold for that distance detection, a 0.138-MPa (20-psi) increase in raw pressure of 

the cell. The measurements showed a fairly tight cluster of LTD distances from the face, even in 

the cases of BPCs located 2.3 m (7.5 ft) from the rib. Material strength models that implement 

linear elasticity to a peak, followed by elastic-plastic behavior, could not match this tight cluster of 

measured distances because the ribs were already yielded during development, so that further 

increase in stress was not possible. This is illustrated in Figure 30 of this report and is reproduced 

here as Figure G1 of this appendix. Moreover, some of the BPC histories shown elsewhere in this 

report suggested eventual softening near the ribs in some cases, but this behavior was not 

consistent, probably because of the variable nature of the coal. These results, along with drilling 

observations that this coal was relatively weaker than B-Seam coal, suggested that if yielding were 

implemented then there must also be significant strain hardening, which would likely be followed 

by strain softening to a residual stress. Such a strength curve might be implemented most simply 

with more linear segments on the strength-strain curve of a new constitutive model.

A five-point material strength model (model #7) was added to MulsimNL/Large. It is assumed 

that the first line segment begins at zero stress and zero closure strain. The last (fifth) point 

represents a residual stress and strain. For any additional closure strain, the strength remains at the 

residual stress. Figure G2 shows an example of such a material model. Table A2 and Table A3 in 

Appendix A indicate the format of input of these five stresses and strains, along with Poisson’s 

ratio.
238

Figure G1. LTD determined from BPC pressure histories (measured)

and from interpolation of model results.
239

Figure G2. Example of five-point material strength model.

Verification Problems

Two verification problems were run to test the five-point material model against another 

model. Material models replicated with the five-point material model were the elastic model and 

the softening model, which has two points.

Figure G3 and Figure G4 show material codes for mining steps 1 and 2, respectively, of the 

example problem. The fine mesh is seen in the very center of the mesh, with no elastic codes 

(A). In the first mining step, three pillars are mined, although the upper and lower pillars are 

partial pillars in that crosscuts are not driven on the upper and lower sides of the fine mesh. 

Moreover, the lengths of these two partial pillars are shorter than the center pillar. In the second 

mining step, the center pillar is excavated and converted to gob.
240

Figure G3. Material codes for mining step 1 of example model.

A, Entire model; B, zoomed in to fine grid.

Figure G4. Material codes for mining step 2 of example model.

A, Entire model; B, zoomed in to fine grid.

Elastic Problem

Success was achieved in modeling Mine A by reducing the elastic modulus in the outer ring 

of elements to 60% of full modulus and to 80% of full modulus in the next-to-outer ring of 

elements. Accordingly, a model was constructed for a small example, using elastic material for 

one model and replicating that law with the multipoint material having all five points along the 

linear-elastic curve for another model. Figures G5 and G6 illustrate the differences in stress 

output from these models for mining steps 1 and 2, respectively. The maximum difference was 

±7 Pa (±0.001 psi), all located within the fine mesh of the models as seen in the legend of the 

figures. Such difference could be lessened by using a smaller stress tolerance to determine 

equilibrium. The small differences shown indicate that the five-point material model did, indeed, 

replicate the elastic model very well.
241

Figure G5. Differences in stress at mining step 1 for elastic problem.
242

Figure G6. Differences in stress at mining step 2 for elastic problem.

Mark-Bieniawski Softening Problem

The same example as above was modeled, but the Mark-Bieniawski [Mark and Iannacchione 

1992] stress-versus-strain formulation with softening and a coal strength of 6.2 MPa (900 psi) 

was used. Residual stresses were determined by the method of Karabin and Evanto [1994]. 

Residual strain (strain when residual stress is first reached) was set to twice the peak elastic 

strain for each yielding material. The five-point model replicated the two-point softening model 

by placing the third through fifth points further down the residual line. That is, these points had 

the same residual stress as the last point of the two-point softening model, but increased strain 

(0.2, 0.3, and 0.4). In mining step 2, the outer corner elements of the partial pillars had closure 

between points 2 and 3—well past the beginning of residual strain. Output showed no difference 

in results between the models in both mining steps for both stress and closure to the precision 

output by the code. For example, maximum closure error was ±1.23 × 10-8 mm (±4.85 × 10-10

in). It appears that the five-point material model replicates the strain-softening model very well.
243

Conclusion

Numerical model results produced using the five-point stress-strain material strength model 

for coal were compared to results using an elastic coal model and a Mark-Bieniawski coal model 

with softening. The small differences might be reduced further with tighter equilibrium 

tolerance, but they indicate that the five-point material model is functioning properly.
244

References for Appendix G

Karabin G, J., Evanto MA [1994]. Experience with the boundary element method of numerical 

modeling as a tool to resolve complex ground control problems. In: Peng SS ed., Proceedings of 

13th International Conference on Ground Control in Mining. (Morgantown, WV: August 2–4, 

1994) Morgantown, WV: West Virginia University, pp. 201–213.

Larson MK, Whyatt JK [2012]. Load transfer distance calibration of a coal panel scale model: A 

case study. In: Barczak T et al. eds. Proceedings of the 31st International Conference on Ground 

Control in Mining. (Morgantown, WV: July 31–August 2, 2012) Morgantown, WV: West 

Virginia University, pp. 195–205.

Mark C, Chase FE [1997]. Analysis of Retreat Mining Pillar Stability (ARMPS). In: Mark C, 

Tuchman RJ eds. Proceedings: New Technology for Ground Control in Retreat Mining, DHHS 

(NIOSH) Publication No. 97-133, IC 9446. Pittsburgh, PA: National Institute for Occupational 

Safety and Health (NIOSH), pp. 17–34.

Mark C, Iannacchione AT [1992]. Coal pillar mechanics: Theoretical models and field 

measurements compared. In: Iannacchione AT et al. eds. Bureau of Mines Information Circular 

9135, Proceedings of the Workshop on Coal Pillar Mechanics and Design. Washington, DC: 

U.S. Department of the Interior, pp. 78–93.
245

Input Files Contents Listing for Verification Problems

In this appendix, the two problems were used to verify that the multipoint law resulted in the 

same output as the elastic or softening law already built in. The input files of each of the two 

verification problems are listed here in two forms. The first form uses the existing elastic or 

softening law already in Mulsim. The second lists the implementation of the same using the 

multipoint law. Thus, there are two input files for each problem in the input file listings that 

follow.
246

Elastic Problem Using Elastic Model

Filename: test_elastic6080_2step.inp

Test Problem, elastic 60%-80% case, 2 step

0.287913 2.34594e+06 1

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BDFHJLNPRTVX11YXXXXXXXXXXY11XVTRPNLJHFDB

BDFHJLNPRTVX11XWVVVVVVVVWX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVUTTTTTTUVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTSRRRRSTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRQPPQRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPOOPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

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247

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BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPOOPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRQPPQRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTSRRRRSTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVUTTTTTTUVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XWVVVVVVVVWX11XVTRPNLJHFDB

BDFHJLNPRTVX11YXXXXXXXXXXY11XVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVX11YXXXXXXXXXXY11XVTRPNLJHFDB

BDFHJLNPRTVX11XWVVVVVVVVWX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVUTTTTTTUVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTSRRRRSTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRQPPQRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPOOPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

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249

Elastic Problem Using MultiPoint Law

Filename: test_mpel6080_2step.inp 

Note that the material code lines beginning with “7.” are longer than the line space, and 

therefore, are continued on the next line. Each of those lines ends with “3.3000000E-001.”

Test Problem, multipoint elastic 60%-80% case

0.287913 2.34594e+06 1

 27

 1. 0.3700000E+006 1.3909800E+005 0.0000000E+000 0.0000000E+000 0.0000000E+000

 7. 2.0899636E+004 5.6485503E-002 3.1349454E+004 8.4728254E-002 4.1799272E+004 1.1297101E-001 6.2698908E+004 1.6945651E-001 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 2.0605091E+004 5.5689435E-002 3.0907637E+004 8.3534153E-002 4.1210182E+004 1.1137887E-001 6.1815273E+004 1.6706831E-001 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 1.9132364E+004 5.1709092E-002 2.8698546E+004 7.7563638E-002 3.8264728E+004 1.0341818E-001 5.7397092E+004 1.5512728E-001 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 1.8837818E+004 5.0913022E-002 2.8256727E+004 7.6369532E-002 3.7675636E+004 1.0182604E-001 5.6513454E+004 1.5273906E-001 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 1.7365091E+004 4.6932678E-002 2.6047637E+004 7.0399018E-002 3.4730182E+004 9.3865357E-002 5.2095273E+004 1.4079804E-001 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 1.7070545E+004 4.6136608E-002 2.5605818E+004 6.9204912E-002 3.4141090E+004 9.2273216E-002 5.1211635E+004 1.3840982E-001 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 1.5597818E+004 4.2156265E-002 2.3396727E+004 6.3234397E-002 3.1195636E+004 8.4312530E-002 4.6793454E+004 1.2646879E-001 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 1.5303273E+004 4.1360197E-002 2.2954910E+004 6.2040296E-002 3.0606546E+004 8.2720395E-002 4.5909819E+004 1.2408059E-001 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 1.3830545E+004 3.7379851E-002 2.0745818E+004 5.6069777E-002 2.7661090E+004 7.4759703E-002 4.1491635E+004 1.1213955E-001 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 1.3536000E+004 3.6583784E-002 2.0304000E+004 5.4875676E-002 2.7072000E+004 7.3167568E-002 4.0608000E+004 1.0975135E-001 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 1.2063273E+004 3.2603441E-002 1.8094910E+004 4.8905161E-002 2.4126546E+004 6.5206881E-002 3.6189819E+004 9.7810322E-002 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 1.1768727E+004 3.1807370E-002 1.7653091E+004 4.7711055E-002 2.3537454E+004 6.3614741E-002 3.5306181E+004 9.5422111E-002 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 1.0296000E+004 2.7827027E-002 1.5444000E+004 4.1740541E-002 2.0592000E+004 5.5654054E-002 3.0888000E+004 8.3481081E-002 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 1.0001455E+004 2.7030959E-002 1.5002183E+004 4.0546439E-002 2.0002910E+004 5.4061919E-002 3.0004365E+004 8.1092878E-002 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 8.5287273E+003 2.3050614E-002 1.2793091E+004 3.4575921E-002 1.7057455E+004 4.6101229E-002 2.5586182E+004 6.9151843E-002 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 1.0001455E+004 2.7030959E-002 1.5002183E+004 4.0546439E-002 2.0002910E+004 5.4061919E-002 3.0004365E+004 8.1092878E-002 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 6.7614545E+003 1.8274201E-002 1.0142182E+004 2.7411302E-002 1.3522909E+004 3.6548403E-002 2.0284364E+004 5.4822604E-002 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 6.4669091E+003 1.7478133E-002 9.7003637E+003 2.6217199E-002 1.2933818E+004 3.4956265E-002 1.9400727E+004 5.2434398E-002 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 4.9941818E+003 1.3497789E-002 7.4912727E+003 2.0246683E-002 9.9883636E+003 2.6995577E-002 1.4982545E+004 4.0493366E-002 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 4.6996364E+003 1.2701720E-002 7.0494546E+003 1.9052580E-002 9.3992728E+003 2.5403440E-002 1.4098909E+004 3.8105160E-002 

3.7000000E+005 1.0000000E+000 3.3000000E-001

 7. 3.2269091E+003 1.0901720E-002 4.8403637E+003 1.6352580E-002 6.4538182E+003 2.1803440E-002 9.6807273E+003 3.2705160E-002 

2.9600000E+005 1.0000000E+000 3.3000000E-001

 7. 2.9323636E+003 9.9066338E-003 4.3985454E+003 1.4859951E-002 5.8647272E+003 1.9813268E-002 8.7970908E+003 2.9719901E-002 

2.9600000E+005 1.0000000E+000 3.3000000E-001

 7. 1.4596364E+003 6.5749387E-003 2.1894546E+003 9.8624081E-003 2.9192728E+003 1.3149877E-002 4.3789092E+003 1.9724816E-002 

2.2200000E+005 1.0000000E+000 3.3000000E-001

 7. 1.1650909E+003 5.2481572E-003 1.7476364E+003 7.8722358E-003 2.3301818E+003 1.0496314E-002 3.4952727E+003 1.5744472E-002 

2.2200000E+005 1.0000000E+000 3.3000000E-001

 5. 0.1000000E+003 0.2302920E+006 0.4000000E+004 0.1000000E+001 0.3300000E+000

 5. 0.1000000E+003 0.2158980E+006 0.4000000E+004 0.1000000E+001 0.3300000E+000

 0.00000 0.03786010 0.00000 0.00000000 0.00000 0.00000000 0.00000 0.03786010 0.00000 0.00000000 0.00000 

0.09363830

 600.00 48 48 0 21 28 21 28

 0.0 0.0 -27042. 132.0

1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000

1.350000 1.000000000 3000 1 2

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPOOPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRQPPQRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTSRRRRSTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVUTTTTTTUVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XWVVVVVVVVWX11XVTRPNLJHFDB

BDFHJLNPRTVX11YXXXXXXXXXXY11XVTRPNLJHFDB

BDFHJLNPRTVX1111111111111111XVTRPNLJHFDB

BDFHJLNPRTVX1111111111111111XVTRPNLJHFDB

BDFHJLNPRTVX11YXXXXXXXXXXY11XVTRPNLJHFDB

BDFHJLNPRTVX11XWVVVVVVVVWX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVUTTTTTTUVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTSRRRRSTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRQPPQRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPOOPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPOOPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRQPPQRTVX11XVTRPNLJHFDB
250

BDFHJLNPRTVX11XVTSRRRRSTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVUTTTTTTUVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XWVVVVVVVVWX11XVTRPNLJHFDB

BDFHJLNPRTVX11YXXXXXXXXXXY11XVTRPNLJHFDB

BDFHJLNPRTVX1111111111111111XVTRPNLJHFDB

BDFHJLNPRTVX1111111111111111XVTRPNLJHFDB

BDFHJLNPRTVX11YXXXXXXXXXXY11XVTRPNLJHFDB

BDFHJLNPRTVX11XWVVVVVVVVWX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVUTTTTTTUVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTSRRRRSTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRQPPQRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPOOPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

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BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPOOPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRQPPQRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTSRRRRSTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVUTTTTTTUVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XWVVVVVVVVWX11XVTRPNLJHFDB

BDFHJLNPRTVX11YXXXXXXXXXXY11XVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB
251

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVXZZZZZZZZZZZZZZZZXVTRPNLJHFDB

BDFHJLNPRTVX11YXXXXXXXXXXY11XVTRPNLJHFDB

BDFHJLNPRTVX11XWVVVVVVVVWX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVUTTTTTTUVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTSRRRRSTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRQPPQRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPOOPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

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252

Mark-Bieniawski Softening Problem Using Softening Law

Filename: test_MB900sftn_2step.inp

Test Problem, Mark-Bieniawski 900-psi coal, 2 mining steps

0.287913 2.34594e+06 1

 27

 1. 0.3700000E+006 1.3909800E+005 0.0000000E+000 0.0000000E+000 0.0000000E+000

 2. 2.0899636E+004 5.6485504E-002 2.2352322E+004 1.1297101E-001 3.3000000E-001

 2. 2.0605091E+004 5.5689435E-002 2.2037303E+004 1.1137887E-001 3.3000000E-001

 2. 1.9132364E+004 5.1709091E-002 2.0069900E+004 1.0341818E-001 3.3000000E-001

 2. 1.8837818E+004 5.0913022E-002 1.9760921E+004 1.0182604E-001 3.3000000E-001

 2. 1.7365091E+004 4.6932678E-002 1.7824291E+004 9.3865356E-002 3.3000000E-001

 2. 1.7070545E+004 4.6136609E-002 1.7521956E+004 9.2273219E-002 3.3000000E-001

 2. 1.5597818E+004 4.2156265E-002 1.5619243E+004 8.4312531E-002 3.3000000E-001

 2. 1.5303273E+004 4.1360197E-002 1.5324293E+004 8.2720393E-002 3.3000000E-001

 2. 1.3830545E+004 3.7379853E-002 1.3459359E+004 7.4759705E-002 3.3000000E-001

 2. 1.3536000E+004 3.6583784E-002 1.3172718E+004 7.3167568E-002 3.3000000E-001

 2. 1.2063273E+004 3.2603440E-002 1.1350416E+004 6.5206880E-002 3.3000000E-001

 2. 1.1768727E+004 3.1807371E-002 1.1073277E+004 6.3614742E-002 3.3000000E-001

 2. 1.0296000E+004 2.7827027E-002 9.2998919E+003 5.5654054E-002 3.3000000E-001

 2. 1.0001455E+004 2.7030958E-002 9.0338428E+003 5.4061916E-002 3.3000000E-001

 2. 8.5287273E+003 2.3050614E-002 7.3178333E+003 4.6101229E-002 3.3000000E-001

 2. 8.2341818E+003 2.2254545E-002 7.0651069E+003 4.4509091E-002 3.3000000E-001

 2. 6.7614545E+003 1.8274201E-002 5.4184637E+003 3.6548403E-002 3.3000000E-001

 2. 6.4669091E+003 1.7478133E-002 5.1824222E+003 3.4956265E-002 3.3000000E-001

 2. 4.9941818E+003 1.3497789E-002 3.6234518E+003 2.6995577E-002 3.3000000E-001

 2. 4.6996364E+003 1.2701720E-002 3.4097488E+003 2.5403440E-002 3.3000000E-001

 2. 3.2269091E+003 8.7213759E-003 1.9696876E+003 1.7442752E-002 3.3000000E-001

 2. 2.9323636E+003 7.9253071E-003 1.7898987E+003 1.5850614E-002 3.3000000E-001

 2. 1.4596364E+003 3.9449631E-003 5.2950835E+002 7.8899263E-003 3.3000000E-001

 2. 1.1650909E+003 3.1488943E-003 4.2265689E+002 6.2977887E-003 3.3000000E-001

 5. 0.1000000E+003 0.2302920E+006 0.4000000E+004 0.1000000E+001 0.3300000E+000

 5. 0.1000000E+003 0.2158980E+006 0.4000000E+004 0.1000000E+001 0.3300000E+000

 0.00000 0.03786010 0.00000 0.00000000 0.00000 0.00000000 0.00000 0.03786010 0.00000 0.00000000 0.00000 

0.09363830

 600.00 48 48 0 21 28 21 28

 0.0 0.0 -27042. 132.0

1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000

1.350000 1.000000000 3000 1 2

BDFHJLNPRTVX11XVTRPNNPRTVX11XVTRPNLJHFDB

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255

Mark-Bieniawski Softening Problem Using Five-Point Law

Filename: test_mpMB900sftn_2step.inp

Note that the material code lines beginning with “7.” are longer than the line space, and 

therefore, are continued on the next line. Each of those lines ends with “3.3000000E-001.”

Test Problem, multipoint Mark-Bieniawski with softening case

0.287913 2.34594e+06 1

 27

 1. 0.3700000E+006 1.3909800E+005 0.0000000E+000 0.0000000E+000 0.0000000E+000

 7. 2.0899636E+004 5.6485504E-002 2.2352322E+004 1.1297101E-001 2.2352322E+004 2.0000000E-001 2.2352322E+004 3.0000000E-001 

2.2352322E+004 4.0000000E-001 3.3000000E-001

 7. 2.0605091E+004 5.5689435E-002 2.2037303E+004 1.1137887E-001 2.2037303E+004 2.0000000E-001 2.2037303E+004 3.0000000E-001 

2.2037303E+004 4.0000000E-001 3.3000000E-001

 7. 1.9132364E+004 5.1709091E-002 2.0069900E+004 1.0341818E-001 2.0069900E+004 2.0000000E-001 2.0069900E+004 3.0000000E-001 

2.0069900E+004 4.0000000E-001 3.3000000E-001

 7. 1.8837818E+004 5.0913022E-002 1.9760921E+004 1.0182604E-001 1.9760921E+004 2.0000000E-001 1.9760921E+004 3.0000000E-001 

1.9760921E+004 4.0000000E-001 3.3000000E-001

 7. 1.7365091E+004 4.6932678E-002 1.7824291E+004 9.3865356E-002 1.7824291E+004 2.0000000E-001 1.7824291E+004 3.0000000E-001 

1.7824291E+004 4.0000000E-001 3.3000000E-001

 7. 1.7070545E+004 4.6136609E-002 1.7521956E+004 9.2273219E-002 1.7521956E+004 2.0000000E-001 1.7521956E+004 3.0000000E-001 

1.7521956E+004 4.0000000E-001 3.3000000E-001

 7. 1.5597818E+004 4.2156265E-002 1.5619243E+004 8.4312531E-002 1.5619243E+004 2.0000000E-001 1.5619243E+004 3.0000000E-001 

1.5619243E+004 4.0000000E-001 3.3000000E-001

 7. 1.5303273E+004 4.1360197E-002 1.5324293E+004 8.2720393E-002 1.5324293E+004 2.0000000E-001 1.5324293E+004 3.0000000E-001 

1.5324293E+004 4.0000000E-001 3.3000000E-001

 7. 1.3830545E+004 3.7379853E-002 1.3459359E+004 7.4759705E-002 1.3459359E+004 2.0000000E-001 1.3459359E+004 3.0000000E-001 

1.3459359E+004 4.0000000E-001 3.3000000E-001

 7. 1.3536000E+004 3.6583784E-002 1.3172718E+004 7.3167568E-002 1.3172718E+004 2.0000000E-001 1.3172718E+004 3.0000000E-001 

1.3172718E+004 4.0000000E-001 3.3000000E-001

 7. 1.2063273E+004 3.2603440E-002 1.1350416E+004 6.5206880E-002 1.1350416E+004 2.0000000E-001 1.1350416E+004 3.0000000E-001 

1.1350416E+004 4.0000000E-001 3.3000000E-001

 7. 1.1768727E+004 3.1807371E-002 1.1073277E+004 6.3614742E-002 1.1073277E+004 2.0000000E-001 1.1073277E+004 3.0000000E-001 

1.1073277E+004 4.0000000E-001 3.3000000E-001

 7. 1.0296000E+004 2.7827027E-002 9.2998919E+003 5.5654054E-002 9.2998919E+003 2.0000000E-001 9.2998919E+003 3.0000000E-001 

9.2998919E+003 4.0000000E-001 3.3000000E-001

 7. 1.0001455E+004 2.7030958E-002 9.0338428E+003 5.4061916E-002 9.0338428E+003 2.0000000E-001 9.0338428E+003 3.0000000E-001 

9.0338428E+003 4.0000000E-001 3.3000000E-001

 7. 8.5287273E+003 2.3050614E-002 7.3178333E+003 4.6101229E-002 7.3178333E+003 2.0000000E-001 7.3178333E+003 3.0000000E-001 

7.3178333E+003 4.0000000E-001 3.3000000E-001

 7. 8.2341818E+003 2.2254545E-002 7.0651069E+003 4.4509091E-002 7.0651069E+003 2.0000000E-001 7.0651069E+003 3.0000000E-001 

7.0651069E+003 4.0000000E-001 3.3000000E-001

 7. 6.7614545E+003 1.8274201E-002 5.4184637E+003 3.6548403E-002 5.4184637E+003 2.0000000E-001 5.4184637E+003 3.0000000E-001 

5.4184637E+003 4.0000000E-001 3.3000000E-001

 7. 6.4669091E+003 1.7478133E-002 5.1824222E+003 3.4956265E-002 5.1824222E+003 2.0000000E-001 5.1824222E+003 3.0000000E-001 

5.1824222E+003 4.0000000E-001 3.3000000E-001

 7. 4.9941818E+003 1.3497789E-002 3.6234518E+003 2.6995577E-002 3.6234518E+003 2.0000000E-001 3.6234518E+003 3.0000000E-001 

3.6234518E+003 4.0000000E-001 3.3000000E-001

 7. 4.6996364E+003 1.2701720E-002 3.4097488E+003 2.5403440E-002 3.4097488E+003 2.0000000E-001 3.4097488E+003 3.0000000E-001 

3.4097488E+003 4.0000000E-001 3.3000000E-001

 7. 3.2269091E+003 8.7213759E-003 1.9696876E+003 1.7442752E-002 1.9696876E+003 2.0000000E-001 1.9696876E+003 3.0000000E-001 

1.9696876E+003 4.0000000E-001 3.3000000E-001

 7. 2.9323636E+003 7.9253071E-003 1.7898987E+003 1.5850614E-002 1.7898987E+003 2.0000000E-001 1.7898987E+003 3.0000000E-001 

1.7898987E+003 4.0000000E-001 3.3000000E-001

 7. 1.4596364E+003 3.9449631E-003 5.2950835E+002 7.8899263E-003 5.2950835E+002 2.0000000E-001 5.2950835E+002 3.0000000E-001 

5.2950835E+002 4.0000000E-001 3.3000000E-001

 7. 1.1650909E+003 3.1488943E-003 4.2265689E+002 6.2977887E-003 4.2265689E+002 2.0000000E-001 4.2265689E+002 3.0000000E-001 

4.2265689E+002 4.0000000E-001 3.3000000E-001

 5. 0.1000000E+003 0.2302920E+006 0.4000000E+004 0.1000000E+001 0.3300000E+000

 5. 0.1000000E+003 0.2158980E+006 0.4000000E+004 0.1000000E+001 0.3300000E+000

 0.00000 0.03786010 0.00000 0.00000000 0.00000 0.00000000 0.00000 0.03786010 0.00000 0.00000000 0.00000 

0.09363830

 600.00 48 48 0 21 28 21 28

 0.0 0.0 -27042. 132.0

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Promoting productive workplaces through 

safety and health research

DHHS (NIOSH) Publication No. 2020-104

DOI: https://doi.org/10.26616/NIOSHPUB2020104