EVALUATION OF THE TRANSVERSE LOAD CAPACITY OF BLOCK 

STOPPINGS FOR MINE VENTILATION CONTROL 

Thomas M. Barczak 

Dissertation submitted to the 

College of Engineering and Mineral Resources 

at West Virginia University 

in partial fulfillment of the requirements of 

Doctor of Philosophy 

in 

Mining Engineering 

Syd S. Peng, Ph.D., Chair 

Keith A. Heasley, Ph.D. 

Yi Luo, Ph.D. 

Stephen C. Tadolini, Ph.D. 

Yunqing Zhang, Ph.D. 

Department of Mining Engineering 

Morgantown, West Virginia 

2005 

Keywords: Stoppings, Transverse Load, Ventilation 

Copyright 2005 Thomas M. Barczak 
Evaluation of the Transverse Load Capacity of Block Stoppings 

for Mine Ventilation Control 

Thomas M. Barczak

ABSTRACT 

 The transverse loading requirement for stoppings as specified in the current Code of 

Federal Regulations is 39 psf. This measure is based on physical testing of a freestanding 

wall in accordance with ASTM E 72 specifications, where the dominant parameter is the 

tensile strength of the sealant. A new protocol based on arching has been developed to 

determine the true transverse load capacity of stoppings. Arching is achieved by the restraint 

of the stopping against the mine roof and floor, whereby compressive forces are developed 

within the wall. A laboratory procedure using the NIOSH Mine Roof Simulator (MRS) to 

simulate rigid-arching of stoppings was developed and verified through full-scale in-mine 

tests. Using this protocol, a systematic study of the design parameters that affect arching 

capability in block stoppings was conducted. The study included a theoretical assessment of 

arching and development of design formulations that can accurately define the transverse 

load capacity of various stopping constructions under various loading conditions. This 

approach should lead to a safer mine environment by matching the transverse load 

capabilities of the stopping design to the requirements in the mine to ensure proper 

ventilation control is maintained. 
iii

DEDICATION 

 I dedicate this dissertation to my God Father, John Waddella, who realized the value 

of an education and encouraged me during my high school years to go on to college. He was 

and always will be my “best buddy”. 
iv

ACKNOWLEDGEMENTS 

 The author wishes to thank those who have contributed to the preparation and 

completion of this dissertation. A debt of gratitude is owed to Dr. Syd S. Peng for 

encouraging me to continue my education and guidance in my studies at West Virginia 

University. Special appreciation is also given to the members of my advisory and 

examination committee: Dr. Keith Heasley, Dr. Yi Luo, Dr. Stephen Tadolini, and Dr. 

Yunqing Zhang for their guidance and supervision. 

 The author also wishes to extend his deepest gratitude to Mr. David F. Gearhart and 

Mr. Timothy J. Batchler. Dave has been a colleague for the past 20 years and we have 

worked together on numerous projects during that time. Dave has been instrumental in 

conducting tests in both the Mine Roof Simulator and Experimental Coal Mine in support of 

this dissertation. I also thank Dave for imparting his overall experience in testing of largescale structures and insights into the procedures developed for this study. Tim also 

contributed to this effort by operating the Mine Roof Simulator and processing raw data for 

many of the experiments that were done in support of this dissertation. I would also like to 

acknowledge Lisa Burke, a colleague at NIOSH who recently completed her Masters Thesis 

at Virginia Tech on numerical modeling of stopping walls for axial loading induced by roofto-floor closure of the mine opening. Lisa and I shared many discussions regarding the 

mechanics of the loading behavior of a stopping wall, which helped me tremendously in 

pursuing my goals in this dissertation. 

 I must also express my gratitude to Dr. Gerald L. Finfinger, an old friend and long time 

colleague, who after twenty years of prodding finally convinced me to do this. 

 I would also like to thank my fellow students, who accepted me as one of them even 

though I was nearly 30 years older than most of them. I must also give my sincerest thanks 

to Karen Centofanti, who was a tremendous help to this “non traditional” student, who was 

lost most of the time in knowing where to go, who to see, and what to do in the 

administrative requirements of my schooling. 

 Finally, I express my deepest appreciation to my family, my wife Peggy and daughters 

Sarah and Nora, for putting up with me while I was studying at home in the evenings and on 

weekends and for their overall support in allowing me to achieve this goal at their expense. 
v

TABLE OF CONTENTS 

Page

Abstract ................................................................................................................................. ii 

Dedication ............................................................................................................................. iii 

Acknowledgements............................................................................................................... iv 

Table of contents................................................................................................................... v 

List of Figures ....................................................................................................................... xii 

List of Tables..................................................................................................................... xxxviii 

List of Abbreviations ............................................................................................................ xl 

CHAPTER 1 – INTRODUCTION ...................................................................................... 1 

CHAPTER 2 – REVIEW OF LITERATURE................................................................. 3 

CHAPTER 3 – CURRENT CFR CRITERIA FOR STOPPINGS .................................. 7 

 3.1 ASTM E 72 Test Specifications ...................................................................... 7 

 3.2 Inadequacies of Current CFR Specifications.................................................... 10 

CHAPTER 4 – ARCH LOADING MECHANISM......................................................... 12 

 4.1 Physical Description of Arching ..................................................................... 12 

 4.2 Simulating Arching Through Biaxial Loading in the Mine Roof Simulator.. 14 

 4.2.1 Description of the Mine Roof Simulator ........................................... 15 

 4.2.2 Test Protocol for Simulating Arching................................................ 17 

 4.2.3 Transverse Load Determinations from MRS Half-Wall Testing....... 21 

 4.3 Validation of Experimental Design Methodology and Arching Behavior..... 27 

 4.3.1 NIOSH PRL Experimental Coal Mine Tests..................................... 27 

 4.3.2 NIOSH Lake Lynn Laboratory Tests ................................................ 34 

CHAPTER 5 – DEVELOPMENT OF GENERAL TRANSVERSE LOAD DESIGN 

EQUATION FROM ARCHING MECHANICS................................... 36 

CHAPTER 6 – THEORETICAL ASSESSMENT OF FACTORS THAT AFFECT THE 

TRANSVERSE PRESSURE ................................................................. 40 

 6.1 Wall Height .................................................................................................... 40 

 6.2 Wall Thickness ............................................................................................... 41 

 6.3 Wall Width .................................................................................................... 42 
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 6.4 Arch Thrust .................................................................................................... 42 

 6.5 Lateral Displacement...................................................................................... 48 

 6.6 Compressive Strength and Material Modulus ................................................ 50 

 6.7 Other Factors that Impact the Transverse Load Capacity of a Stopping........ 53 

 6.7.1 Impact of Abutment Stiffness............................................................. 53 

 6.7.2 Impact of Strain Softening of Walls to Absorb Ground 

 Deformation........................................................................................ 57 

 6.7.3 Impact of Ground Pressures from Roof to Floor Convergence.......... 64 

CHAPTER 7 – DEVELOPMENT OF PREDICTIVE TRANSVERSE PRESSURE 

 MODELS ................................................................................................ 75 

 7.1 Predicting the Transverse Pressure from the Lateral Wall Displacement...... 75 

 7.1.1 Example using Rigid Boundary Conditions....................................... 76 

 7.1.2 Example using Non-Rigid Boundary Conditions............................... 82 

 7.1.3 Example Considering Preloading of the Wall from Ground 

 Pressures............................................................................................. 84 

 7.2 Predicting the Transverse Pressure from the Thrust Force ............................ 92 

 7.2.1 Example using Rigid Boundary Conditions....................................... 92 

 7.2.2 Example using Non-Rigid Boundary Conditions............................... 95 

 7.2.3 Example Considering Preloading of the Wall from Ground 

 Pressures............................................................................................. 96 

 7.3 Summary of Predictive Models for Computing Transverse Load Capacity of 

 Mine Ventilation Stoppings............................................................................ 99 

CHAPTER 8 – SUMMARY AND ANALYSIS OF EXPERIMENTAL TEST 

 DATA ..................................................................................................... 101 

 8.1 Klondike Solid Block ..................................................................................... 102 

 8.1.1 Overview of the Test Program ........................................................... 103 

 8.1.2 Parametric Relationships and Trends ................................................. 106 

 8.1.3 Evaluation of the Predictive Models .................................................. 111 

 8.1.4 Theoretical Impact of Boundary Stiffness.......................................... 114 
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 8.2 Peerless Backsaver ......................................................................................... 117 

 8.2.1 Overview of the Test Program ........................................................... 117 

 8.2.2 Parametric Relationships and Trends ................................................. 119 

 8.2.3 Evaluation of the Predictive Models .................................................. 124 

 8.2.4 Theoretical Impact of Boundary Stiffness.......................................... 127 

 8.3 Klondike Hollow Core Block......................................................................... 130 

 8.3.1 Overview of the Test Program ........................................................... 131 

 8.3.2 Parametric Relationships and Trends ................................................. 132 

 8.3.3 Evaluation of the Predictive Models .................................................. 138 

 8.3.4 Theoretical Impact of Boundary Stiffness.......................................... 142 

 8.4 ACCOA Autoclaved Aerated Concrete Block ............................................... 145 

 8.4.1 Overview of the Test Program ........................................................... 146 

 8.4.2 Parametric Relationships and Trends ................................................. 147 

 8.4.3 Evaluation of the Predictive Models .................................................. 151 

 8.4.4 Theoretical Impact of Boundary Stiffness.......................................... 155 

 8.5 Ytong Block.................................................................................................... 157 

 8.5.1 Overview of the Test Program ........................................................... 158 

 8.5.2 Parametric Relationships and Trends ................................................. 159 

 8.5.3 Evaluation of the Predictive Models .................................................. 163 

 8.5.4 Theoretical Impact of Boundary Stiffness.......................................... 166 

 8.6 Kingsway Block ............................................................................................. 169 

 8.6.1 Overview of the Test Program ........................................................... 169 

 8.6.2 Parametric Relationships and Trends ................................................. 170 

 8.6.3 Evaluation of the Predictive Models .................................................. 173 

 8.6.4 Theoretical Impact of Boundary Stiffness.......................................... 175 

 8.7 Omega Block.................................................................................................. 177 

 8.7.1 Overview of the Test Program ........................................................... 177 

 8.7.2 Parametric Relationships and Trends ................................................. 178 

 
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 8.7.3 Evaluation of the Predictive Models .................................................. 183 

 8.7.4 Theoretical Impact of Boundary Stiffness.......................................... 186 

 8.8 Peerless Super Block ...................................................................................... 189 

 8.8.1 Overview of the Test Program ........................................................... 189 

 8.8.2 Parametric Relationships and Trends. ................................................ 201 

 8.8.3 Evaluation of the Predictive Models .................................................. 196 

 8.8.4 Theoretical Impact of Boundary Stiffness.......................................... 199 

CHAPTER 9 – UNIVERSAL DESIGN EQUATIONS FOR STOPPING BLOCK 

 WALLS .................................................................................................. 200 

 9.1 Specific Block Design .................................................................................... 207 

 9.1.1 Klondike Solid Block ......................................................................... 207 

 9.1.1.1 Full Empirical Model........................................................... 207 

 9.1.1.2 Hybrid Theoretical Models.................................................. 209 

 9.1.1.2.1 Hybrid Thrust Model.......................................... 209 

 9.1.1.2.2 Hybrid Lateral Displacement Model .................. 212 

 9.1.1.2.3 Hybrid Combination Model ............................... 214 

 9.1.1.3 Summary of Design Equations for Klondike Solid Block... 216 

 9.1.2 Peerless Backsaver Block................................................................... 217 

 9.1.2.1 Full Empirical Model........................................................... 217 

 9.1.2.2 Hybrid Theoretical Models.................................................. 220 

 9.1.2.2.1 Hybrid Thrust Model.......................................... 220 

 9.1.2.2.2 Hybrid Lateral Displacement Model .................. 222 

 9.1.2.2.3 Hybrid Combination Model ............................... 224 

 9.1.2.3 Summary of Design Equations for Peerless Backsaver 

 Block .................................................................................... 226 

 9.1.3 ACCOA Autoclaved Aerated Concrete Block ................................... 228 

 9.1.3.1 Full Empirical Model........................................................... 228 

 9.1.3.2 Hybrid Theoretical Models.................................................. 230 

 9.1.3.3 Summary of Design Equations for ACCOA Block ............. 230 
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 9.1.4 Ytong Block........................................................................................ 231 

 9.1.4.1 Full Empirical Model........................................................... 231 

 9.1.4.2 Hybrid Theoretical Models.................................................. 233 

 9.1.4.2.1 Hybrid Thrust Model.......................................... 233 

 9.1.4.2.2 Hybrid Lateral Displacement Model .................. 236 

 9.1.4.2.3 Hybrid Combination Model ............................... 238 

 9.1.4.3 Summary of Design Equations for Ytong Block ................. 240 

 9.1.5 Kingsway Block ................................................................................. 242 

 9.1.5.1 Full Empirical Model........................................................... 242 

 9.1.5.2 Hybrid Theoretical Models.................................................. 244 

 9.1.5.2.1 Hybrid Thrust Model.......................................... 244 

 9.1.5.2.2 Hybrid Lateral Displacement Model .................. 247 

 9.1.5.2.3 Hybrid Combination Model ............................... 249 

 9.1.5.3 Summary of Design Equations for Kingsway Block........... 251 

 9.1.6 Omega Block...................................................................................... 253 

 9.1.6.1 Full Empirical Model........................................................... 253 

 9.1.6.2 Hybrid Theoretical Models.................................................. 255 

 9.1.6.2.1 Hybrid Thrust Model.......................................... 255 

 9.1.6.2.2 Hybrid Lateral Displacement Model .................. 258 

 9.1.6.2.3 Hybrid Combination Model ............................... 260 

 9.1.6.3 Summary of Design Equations for Omega Block................ 262 

 9.1.7 Peerless Super Block .......................................................................... 264 

 9.1.7.1 Full Empirical Model........................................................... 264 

 9.1.7.2 Hybrid Theoretical Models.................................................. 266 

 9.1.7.2.1 Hybrid Thrust Model.......................................... 266 

 9.1.7.2.2 Hybrid Lateral Displacement Model .................. 269 

 9.1.7.2.3 Hybrid Combination Model ............................... 271 

 9.1.7.3 Summary of Design Equations for Peerless Super Block.... 273 

 9.1.8 Klondike Hollow Core Block............................................................. 275 
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 9.1.8.1 Full Empirical Model........................................................... 275 

 9.1.8.2 Hybrid Theoretical Models.................................................. 277 

 9.1.8.2.1 Hybrid Thrust Model.......................................... 277 

 9.1.8.2.2 Hybrid Lateral Displacement Model .................. 280 

 9.1.8.2.3 Hybrid Combination Model ............................... 282 

 9.1.8.3 Summary of Design Equations for Klondike Hollow 

 Core Block ........................................................................... 284 

 9.2 Generic Block Models.................................................................................... 286 

 9.2.1 Standard CMU Block ......................................................................... 286 

 9.2.1.1 Generic Empirical ................................................................ 286 

 9.2.1.2 Generic Hybrid Theoretical Models .................................... 287 

 9.2.1.2.1 Generic Hybrid Thrust Model ............................ 288 

 9.2.1.2.2 Generic Hybrid Lateral Displacement Model .... 289 

 9.2.1.2.3 Generic Hybrid Combination Thrust and Lateral 

 Displacement Model........................................... 290 

 9.2.2 Cellular Concrete Block Materials ..................................................... 291 

 9.2.2.1 Generic Empirical Model..................................................... 291 

 9.2.2.2 Generic Hybrid Theoretical Models .................................... 292 

 9.2.2.2.1 Generic Hybrid Thrust Model ............................ 293 

 9.2.2.2.2 Generic Hybrid Lateral Displacement Model .... 294 

 9.2.2.2.3 Generic Hybrid Combination Thrust and Lateral 

 Displacement Model........................................... 295 

 9.2.3 Low Strength Block Materials............................................................ 296 

 9.2.3.1 Generic Empirical Model..................................................... 296 

 9.2.3.2 Generic Hybrid Theoretical Models .................................... 297 

 9.2.3.2.1 Generic Hybrid Thrust Model ............................ 298 

 9.2.3.2.2 Generic Hybrid Lateral Displacement Model .... 299 

 9.2.3.2.3 Generic Hybrid Combination Thrust and Lateral 

 Displacement Model........................................... 300 
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CHAPTER 10 – RECOMMENDED DESIGN FORMULATIONS FOR STOPPING 

 BLOCK WALLS .................................................................................. 302 

 10.1 Specific Block Design Formulations.............................................................. 302 

 10.1.1 Klondike Solid Block Constructions.................................................. 303 

 10.1.2 Peerless Backsaver Block Constructions............................................ 304 

 10.1.3 Klondike Hollow Block Constructions .............................................. 306 

 10.1.4 ACCOA Block Constructions ............................................................ 308 

 10.1.5 Ytong Block Constructions ................................................................ 310 

 10.1.6 Kingsway Block Constructions .......................................................... 312 

 10.1.7 Omega Block Constructions............................................................... 313 

 10.1.8 Peerless Super Block Constructions................................................... 315 

 10.2 Generic Block Design Formulations .............................................................. 316 

SUMMARY AND CONCLUSIONS .............................................................................. 320 

FUTURE RESEARCH RECOMMENDATIONS .......................................................... 330 

BIBLIOGRAPHY............................................................................................................ 332 

APPENDIX A.................................................................................................................. 334 

APPENDIX B .................................................................................................................. 337 

APPENDIX C .................................................................................................................. 395 
xii

LIST OF FIGURES 

 Page

Figure 3-1 Diagram of test apparatus for transverse pressure testing 

stoppings in accordance with ASTM E 72 specifications ....................... 8 

Figure 3-2 A 4 x 8 ft section of wall being placed into reaction frame for 

ASTM E 72 testing. ................................................................................. 9 

Figure 3-3a A 4 x 8 ft section of wall positioned in the reaction frame for 

ASTM E 72 transverse pressure testing................................................... 9 

Figure 3-3b Close up view of sections of pipe used as reaction roller to avoid 

rotational restraint as the wall deflects from the application of 

transverse pressure................................................................................... 9 

Figure 3-4 The wall is not restrained vertically in this free-standing test condition.. 10 

Figure 4-1 Illustration of rigid arching of a wall structure. ....................................... 13 

Figure 4-2 NIOSH Mine Roof Simulator load frame................................................ 16 

Figure 4-3 Full-scale mine ventilation stopping wall being tested in the NIOSH 

Mine Roof Simulator ............................................................................... 16 

Figure 4-4 Diagram illustrating the simulation of rigid arching on a half-wall 

section of a stopping by biaxial testing in the NIOSH Mine Roof 

Simulator.................................................................................................. 17 

Figure 4-5 Apparatus used to conduct half-wall arching tests of stopping walls 

in the NIOSH Mine Roof Simulator ........................................................ 19 

Figure 4-6 Block column rests on rolling platform to allow load cells to measure 

horizontal loading .................................................................................... 20 

Figure 4-7 Load cells used to accurately measure horizontal loading....................... 20 

Figure 4-8 Illustration of how block dimensional tolerances can cause localized 

loading on a three-block-wide wall (not to scale).................................... 21 

Figure 4-9a Test of a half-wall made from lightweight block (546-psi compressive 

strength) ................................................................................................... 22 

Figure 4-9b Test of a half-wall made from conventional concrete block (1,330-psi 

compressive strength) .............................................................................. 22 
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Figure 4-9c Close up view of Kingsway, autoclaved, concrete block shows air 

pockets in the block structure .................................................................. 23 

Figure 4-10 Compressive strength test data for Kingsway block................................ 23 

Figure 4-11 Compressive strength test data for conventional concrete block............. 24 

Figure 4-12 Half-wall rigid-arching tests conducted in the Mine Roof Simulator 

 on the Kingsway lightweight block ......................................................... 25 

Figure 4-13 Half-wall rigid-arching tests conducted in the Mine Roof Simulator 

on conventional concrete block ............................................................... 26 

Figure 4-14 Comparison of half-wall rigid-arch test in the MRS to the full-scale 

stopping wall test in the NIOSH Experimental Coal Mine for the 

Kingsway block ....................................................................................... 28 

Figure 4-15 Comparison of full-scale mine test of Kingsway block with the MRS 

half-wall regression trend line and suite of MRS tests ............................ 29 

Figure 4-16 Photo after the wall was destroyed from the transverse loading. 

Researcher is standing next to the displacement transducers used to 

measure the wall deflection ..................................................................... 30 

Figure 4-17 Arch height shown to occur between top and bottom layer of block 

that were grouted (cemented) in place in this particular test ................... 31 

Figure 4-18 Comparison of half-wall rigid-arch test in the Mine Roof Simulator to 

the full-scale stopping wall test in the NIOSH Experimental Coal mine 

for the Klondike block stopping .............................................................. 32 

Figure 4-19 Comparison of full-scale mine test of Klondike conventional block 

with the MRS half-wall regression trend line and suite of MRS tests..... 32 

Figure 4-20 Photo showing conventional (Klondike) wall after full-scale test in 

the Experimental Coal Mine noting the arch length between the 

top and bottom course of block................................................................ 33 

Figure 4-21 Close up view of the base of the conventional (Klondike) block wall 

showing the rotation of the wall and formation of the bottom hinge 

 of the arch ................................................................................................ 33 
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Figure 4-22 Comparison of Lake Lynn full-scale stopping tests with the MRS 

rigid-arching tests..................................................................................... 35 

Figure 5-1 Half-wall statics showing the width of the arching thrust varies as a 

function of the wall displacement............................................................ 36 

Figure 5-2 Repositioning of the horizontal force to equate to the resultant force acting 

against a full-scale stopping wall............................................................. 37 

Figure 5-3 Displaying transverse pressure acting on half-wall ................................. 38 

Figure 6-1 Impact of wall height on transverse load capacity................................... 40 

Figure 6-2 Impact of wall thickness on transverse load capacity.............................. 41 

Figure 6-3 Diagram of wall geometry as a function of the lateral displacement ...... 45 

Figure 6-4 Impact of wall stiffness on transverse load capacity ............................... 47 

Figure 6-5 Diagram showing that lateral displacement of the stopping reduces the 

 arch width................................................................................................. 48 

Figure 6-6 Hypothetical example of the impact of lateral displacement on the 

 transverse load capacity of stoppings of various half-wall heights ......... 49 

Figure 6-7 The transverse load capacity of a stopping is directly related to the 

 material modulus of the block from which the stopping is constructed .. 51 

Figure 6-8 Chart shows transverse load capacity if all block has the same 

 compressive strength................................................................................ 51 

Figure 6-9 Dashed lines show the required block strength to provide the same 

 transverse load capacity for all three walls.............................................. 52 

Figure 6-10 Impact of reduced abutment stiffness expressed as deformation of the 

abutment due to arch thrust on the lateral displacement of the stopping 

wall........................................................................................................... 54 

Figure 6-11 Test configuration using drywall to soften the abutment stiffness .......... 55 

Figure 6-12 Comparison of transverse pressure determined from half-wall testing in the 

 MRS with rigid abutment (red curve) and softened abutment from 

 drywall roof contact ................................................................................. 56 

Figure 6-13 Close up view of the deformation of the drywall caused by the arching 

 thrust force ............................................................................................... 56 
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Figure 6-14 Comparison of theoretically predicted transverse pressure using the assumed 

 26,000 psi system modulus for the drywall abutment test and the 

 measured transverse pressure................................................................... 57 

Figure 6-15 Damage of a stopping caused by roof-to-floor convergence of a mine 

 entry ......................................................................................................... 58 

Figure 6-16 Two-inch-thick foam plank used to reduce the stiffness and extend the 

 life of a block stopping by allowing the wall to absorb some deforma- 

 tion prior to failure. Only vertical loading is applied in this test ............ 59 

Figure 6-17 Comparison of a block stopping wall’s response to vertical loading 

 with and without a strain softening foam layer........................................ 59 

Figure 6-18 Half-wall test in the MRS with 2-inch-thick foam plank placed between 

 the top two blocks .................................................................................... 60 

Figure 6-19 Comparison of transverse pressure development from half-wall testing in the 

MRS on a block wall with and without a strain-softening foam layer .... 61 

Figure 6-20 Stress-strain relationship for ESP Squeeze Block foam plank commonly 

used in stoppings to reduce the stiffness of the wall................................ 62 

Figure 6-21 Half-walls with foam between the top two blocks shown with 3 inches 

 of lateral displacement (left) and 7 inches of lateral displacement (right). 63 

Figure 6-22 Combining arching with axial loading caused by ground pressures moves 

the resultant arch thrust force more towards the centerline of the wall... 65 

Figure 6-23 Peak transverse pressure occurs at less lateral displacement when 

preload is applied to the wall ................................................................... 67 

Figure 6-24 Boussinesq diagram shows that 90 pct of the stress is relieved within the 

 first 12 inches of ground for a 6-in-thick stopping .................................. 68 

Figure 6-25 Wedges driven into stopping high pressure side allow gap to occur at 

 tension side of stopping which completely destroys arching capability.. 70 

Figure 6-26 Comparison of direction of wedging on top of block stopping relative 

 to impact on transverse load capacity ...................................................... 70 

Figure 6-27 Transverse load capacity is preserved when wedges are driven from the 

 low pressure side of the stopping............................................................. 71 
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Figure 6-28 Arching thrust can also be preserved if wedging is done properly.......... 71 

Figure 6-29 Installation of seal with preloading grout bags used to seal around the 

 perimeter of the block wall ...................................................................... 72 

Figure 6-30 Grout bag increased the amount of displacement that can occur before 

 the block wall fails................................................................................... 73 

Figure 6-31 Testing of a half-wall with grout bag in the Mine Roof Simulator ......... 73 

Figure 6-32 Comparison of laboratory tests with and without the grout bags ............ 74 

Figure 6-33 Closure absorbed by the grout bag during prestressing........................... 74 

Figure 7-1 Flowchart for predicting the transverse pressure capacity of 

 stoppings from the lateral wall displacement........................................... 75 

Figure 7-2 MRS test of a 6-course-high half-wall showing the measured lateral 

 and thrust load development as a function of the applied lateral 

 displacement ............................................................................................ 76 

Figure 7-3 Half-wall test with theoretical calculated thrust shown by the blue line . 78 

Figure 7-4 Comparison of the measured transverse pressure and the calculated 

 transverse pressure................................................................................... 79 

Figure 7-5 Four-course (30 in) high half-wall test result including comparison 

 of the measured and theoretically calculated thrust load......................... 80 

Figure 7-6 Comparison of the measured transverse pressure with that calculated 

 theoretically from the lateral displacement.............................................. 81 

Figure 7-7 The thrust load is limited to 30,858 lbs based on the observed axial 

 load at the measured peak transverse pressure from the MRS test.......... 81 

Figure 7-8 Limiting the thrust load improves the post-peak theoretical prediction of 

 the transverse pressure in this half-wall MRS test................................... 82 

Figure 7-9 Comparison of theoretically predicted transverse pressure using the 

 26,000 psi system modulus for the drywall abutment test and the 

 measured transverse pressure................................................................... 83 

Figure 7-10 Flowchart for predicting the transverse pressure capacity of 

 stoppings from the lateral displacement with preload 

 applied from ground pressures................................................................. 84 
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Figure 7-11 MRS test of 45.75-in-high half wall with 373 psi of preload .................. 85 

Figure 7-12 Laboratory test to determine stiffness of block column. Example 

 shows single block column constructed from six courses of Klondike 

 block......................................................................................................... 86 

Figure 7-13 Plot of the change in the thrust adjustment factor as a function of lateral 

displacement of a half wall test conducted in the MRS........................... 88 

Figure 7-14 Prediction of transverse pressure for test #74 when the d factor is 

 calculated for the full loading cycle......................................................... 88 

Figure 7-15 Regression trend line developed for the thrust adjustment factor for 

 45-in half-wall tests conducted in the MRS............................................. 90 

Figure 7-16 Correlation between calculated transverse pressure and the preload 

 acting on the wall..................................................................................... 91 

Figure 7-17 Correlation between the measured peak transverse pressure and the 

 calculated transverse pressure from the lateral wall displacement .......... 91 

Figure 7-18 Flowchart for predicting the transverse pressure capacity of stoppings if 

 the thrust load is known ........................................................................... 92 

Figure 7-19 Comparison of predicted transverse pressure from the thrust force to the 

laboratory measured transverse pressure for a 45-inch-high half wall test 94 

Figure 7-20 Demonstration of thrust load model with non-rigid boundary conditions. 95 

Figure 7-21 Flowchart for predicting the transverse pressure capacity of stoppings if the 

 thrust load is known................................................................................. 96 

Figure 7-22 Comparison of predicted transverse pressure for full loading using the 

 thrust prediction model compared to the measured transverse pressure 

 from the MRS test.................................................................................... 97 

Figure 7-23 Comparison of calculated peak transverse pressure to the measured peak 

transverse pressure for all 45-in-high tests of this block type ................. 98 

Figure 7-24 Comparison of calculated peak transverse pressure to measured peak 

transverse pressure for 45-in-high tests less than 1,500 psf..................... 99 

Figure 7-25 Comparison of the two predicted models and the measured transverse 

 pressure. ................................................................................................... 99 
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Figure 8-1 Comparison of compressive strength measured from unit block loading 

 of various block materials examined in this research .............................. 101 

Figure 8-2 Comparison of material modulus of various block materials examined 

 in this research for stopping construction ................................................ 102 

Figure 8-3 Klondike conventional Portland cement and aggregate block................. 103 

Figure 8-4 Transverse pressure as measured from MRS laboratory testing as a 

 function of preload for three different half-wall heights. ........................ 107 

Figure 8-5 Lateral displacement at which peak transverse pressure occurs also 

 reaches an asymptotic minimum as the preload exceeds 600 psi ............ 107 

Figure 8-6 Comparison of narrow and wide wall thickness for Klondike block 

 as a function of preload............................................................................ 108 

Figure 8-7 Transverse pressure is directly related to the lateral load acting on the 

 half wall in the MRS laboratory test........................................................ 109 

Figure 8-8 Lateral force is also directly related to the thrust force ........................... 109 

Figure 8-9 Relationship between the transverse pressure and the arch thrust for 

 MRS laboratory tests conducted at three different half-wall heights ...... 110 

Figure 8-10 Correlation of factors involving the material modulus (E), wall 

 thickness (t), and wall height (L) to the transverse pressure capacity of 

 a stopping................................................................................................. 111 

Figure 8-11 Resultant thrust force location for three wall heights as a function of 

 the total arch thrust (Klondike solid block) ............................................. 112 

Figure 8-12 Prediction of transverse pressure when both the lateral load and arch 

 thrust are known. Blue curves predicts transverse pressure when 

 resultant thrust force location is also known and red squares show 

 predicted transverse pressure when resultant thrust force location is 

 calculated from empirical data................................................................. 112 

Figure 8-13 Prediction of transverse pressure from known thrust and lateral loads ... 113 
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Figure 8-14 Impact of reducing the boundary stiffness on transverse pressure capacity 

 of stopping. Data shows individual test at different wall heights with 

 no preload................................................................................................. 115 

Figure 8-15 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 30-in-high half-walls ................. 115 

Figure 8-16 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 46-inch-high half-wall 

 constructions ............................................................................................ 116 

Figure 8-17 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 60-inch-high half-wall 

 constructions ............................................................................................ 116 

Figure 8-18 Peerless Backsaver block......................................................................... 117 

Figure 8-19 Transverse pressure as measured from MRS laboratory testing as a 

 function of preload for three different half-wall heights (Peerless 

 Backsaver block)...................................................................................... 120 

Figure 8-20 Decrease in lateral load development with partially cured Peerless 

 Backsaver block....................................................................................... 120 

Figure 8-21 Lateral displacement at which peak transverse pressure occurs also 

 reaches an asymptotic minimum as the preload exceeds 250 psi ............ 121 

Figure 8-22 Transverse pressure is directly related to the lateral load acting on the 

 half wall in the MRS laboratory test (Peerless Backsaver block)............ 122 

Figure 8-23 Lateral force is also directly related to the thrust force (Peerless 

 Backsaver block)...................................................................................... 122 

Figure 8-24 Relationship between the transverse pressure and the arch thrust for 

 MRS laboratory tests conducted at three different half-wall heights 

 (Peerless Backsaver block) ...................................................................... 123 

Figure 8-25 Correlation of factors involving the material modulus (E), wall 

 thickness (t), and wall height (L) to the transverse load capacity of a 

 stopping (Peerless Backsaver block) ....................................................... 124 
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Figure 8-26 Resultant thrust force location for three wall heights as a function of 

 the total arch thrust (Peerless Backsaver block) ...................................... 125 

Figure 8-27 Prediction of transverse pressure when both the lateral load and arch 

 thrust are known. Blue curves predicts transverse pressure when 

resultant thrust force location is also known and red squares show predicted 

transverse pressure when resultant thrust force location is calculated from 

empirical data........................................................................................... 125 

Figure 8-28 Prediction of transverse pressure from two methods (Peerless 

 Backsaver block)...................................................................................... 126 

Figure 8-29 Impact of reducing the boundary stiffness on transverse pressure 

 capacity of stopping (Peerless Backsaver block)..................................... 128 

Figure 8-30 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 30-inch-high half-wall 

 constructions (Peerless Backsaver block)................................................ 128 

Figure 8-31 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 46-inch-high half-wall 

 constructions (Peerless Backsaver block)................................................ 129 

Figure 8-32 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 60-inch-high half-wall 

 constructions (Peerless Backsaver block)................................................ 129 

Figure 8-33 Hollow core concrete block (manufactured by Klondike)....................... 130 

Figure 8-34 Comparison of the compressive strength of solid and hollow core 

 Block........................................................................................................ 130 

Figure 8-35 Transverse pressure as measured from MRS laboratory testing as a 

 function of preload for three different half-wall heights 

 (Klondike hollow core block) .................................................................. 132 

Figure 8-36 Example of 30-in-high half wall test where the wall was not able to 

 sustain the arch thrust load during localized failure of the block 

 during transverse pressure resulting in lateral load shedding twice 

 during the loading cycle........................................................................... 133 
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Figure 8-37 Another example where the arch thrust force was not sustained 

 during the full loading cycle .................................................................... 134 

Figure 8-38 Lateral displacement at which peak transverse pressure occurs 

approaches asymptotic minimum as preload exceeds 200 psi 

(Klondike hollow core block) .................................................................. 134 

Figure 8-39 Transverse pressure is directly related to the lateral load acting on the half 

 wall in the MRS laboratory test (Klondike hollow core block)............... 135 

Figure 8-40 Lateral force is also directly related to the thrust force (Klondike 

 hollow core block) ................................................................................... 136 

Figure 8-41 Relationship between the transverse pressure and the arch thrust for MRS 

laboratory tests conducted at three different half-wall heights 

 (Klondike hollow core block) .................................................................. 136 

Figure 8-42 Correlation of factors involving the material modulus (E), wall 

 thickness (t), and wall height (L) to the transverse pressure capacity of a 

 stopping (Klondike hollow core block) ................................................... 137 

Figure 8-43 Resultant thrust force location for three wall heights as a function of 

 the total arch thrust (Klondike hollow core block) .................................. 138 

Figure 8-44 Prediction of transverse pressure when both the lateral load and arch thrust 

 are known. Blue curves predicts transverse pressure when resultant thrust 

 force location is also known and red squares show predicted transverse 

 pressure when resultant thrust force location is calculated empirically. . 139 

Figure 8-45 Prediction of transverse pressure from known thrust and lateral loads with 

 a constant material modulus for all tests.................................................. 140 

Figure 8-46 Prediction of transverse pressure from known thrust and lateral loads 

 where the material modulus for the 30-in-high half-walls was reduced 

 by 50 pct................................................................................................... 141 

Figure 8-47 Impact of reducing the boundary stiffness on transverse pressure capacity 

 of stopping. Data shows individual test at different wall heights with 

 no preload................................................................................................. 142 
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Figure 8-48 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 30-inch-high half-wall 

 constructions (Klondike hollow core block)............................................ 143 

Figure 8-49 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 45-inch-high half-wall 

 constructions (Klondike hollow core block)............................................ 144 

Figure 8-50 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 60-inch-high half-wall 

 constructions (Klondike hollow core block)............................................ 144 

Figure 8-51 AAC block manufactured by Aerated Concrete Corporation of 

 America.................................................................................................... 145 

Figure 8-52 Fire resistance capability of aerated concrete block is shown by this 

house which survived devastating fire in California................................ 145 

Figure 8-53 Transverse pressure as measured from MRS laboratory testing as a 

 function of preload for 48-inch-high half-walls (AAC Block from 

 Florida)..................................................................................................... 147 

Figure 8-54 Lateral displacement at which peak transverse pressure occurs also 

 reaches an asymptotic minimum as the preload approaches 150 psi 

 (AAC Block from Florida)....................................................................... 148 

Figure 8-55 Transverse pressure is directly related to the lateral load acting in the 

 48-inch-high half-wall MRS laboratory tests (AAC Block from 

 Florida)..................................................................................................... 149 

Figure 8-56 Relationship between the lateral load and the arch thrust for MRS 

 laboratory tests for the 48-inch half-wall height (AAC Block from 

 Florida)..................................................................................................... 149 

Figure 8-57 Relationship between the transverse pressure and the arch thrust for 

 MRS laboratory tests conducted at 48-inch half-wall height 

 (AAC Block from Florida)....................................................................... 150 
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Figure 8-58 Correlation of factors involving the material modulus (E), wall 

 thickness (t), and wall height (L) to the transverse pressure capacity 

 of a stopping (AAC Block from Florida)................................................. 151 

Figure 8-59 Resultant thrust force location for two block thicknesses as a function 

 of the total arch thrust (AAC block from Florida)................................... 152 

Figure 8-60 Prediction of transverse pressure when both the lateral load and arch 

 thrust are known. Blue curves predicts transverse pressure when 

 resultant thrust force location is also known and red squares show 

 predicted transverse pressure when resultant thrust force location is 

 calculated from empirical data (AAC block from Florida) ..................... 152 

Figure 8-61 Prediction of transverse pressure from known thrust and lateral loads 

 (AAC block from Florida) ....................................................................... 153 

Figure 8-62 Example of test with high preload showing how the thrust force 

 decreases immediately after the preload is applied and continues to 

 decrease through the full loading cycle ................................................... 154 

Figure 8-63 Prediction of transverse pressure from known thrust and lateral loads 

 with premature failures removed (AAC block from Florida).................. 154 

Figure 8-64 Impact of reducing the boundary stiffness on transverse pressure 

 capacity of stopping. Data shows individual test at different wall 

 heights with no preload (AAC block from Florida)................................. 156 

Figure 8-65 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 6-inch-thick half-wall 

 constructions (AAC block from Florida)................................................. 156 

Figure 8-66 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 8-inch-thick half-wall 

 constructions (AAC block from Florida)................................................. 157 

Figure 8-67 Ytong autoclaved aerated concrete block ................................................ 157 

Figure 8-68 Transverse pressure as measured from MRS laboratory testing as a function 

 of preload for three different half-wall heights (Ytong AAC block)....... 159 
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Figure 8-69 Lateral displacement at which peak transverse pressure occurs 

 also reaches an asymptotic minimum as the preload approaches 

 130 psi (Ytong AAC block)..................................................................... 160 

Figure 8-70 Transverse pressure is directly related to the lateral load acting on the 

 half-wall in the MRS laboratory tests (Ytong AAC block) ..................... 161 

Figure 8-71 Relationship between the lateral load and the arch thrust for MRS 

 laboratory tests for three different wall heights (Ytong AAC block) ...... 161 

Figure 8-72 Relationship between the transverse pressure and the arch thrust for MRS 

laboratory tests conducted at three different wall heights (Ytong 

 AAC block).............................................................................................. 162 

Figure 8-73 Correlation of factors involving the material modulus (E), wall 

 thickness (t), and wall height (L) to the transverse pressure capacity of a 

 stopping (AAC Block from Florida)........................................................ 163 

Figure 8-74 Resultant thrust force location for three wall heights as a function of 

 the total arch thrust (AAC block from Florida) ....................................... 164 

Figure 8-75 Prediction of transverse pressure when both the lateral load and arch thrust 

 are known. Blue curves predicts transverse pressure when resultant thrust 

 force location is also known and red squares show predicted transverse 

 pressure when resultant thrust force location is calculated from empirical 

 data (Ytong AAC block).......................................................................... 164 

Figure 8-76 Prediction of transverse load from known thrust and lateral loads with 

premature failures removed (Ytong AAC block) .................................... 165 

Figure 8-77 Impact of reducing the boundary stiffness on transverse pressure capacity 

 of stopping. Data shows individual test at different wall heights with 

 no preload (Ytong AAC block)................................................................ 167 

Figure 8-78 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 31.5-in-high half-wall 

 constructions (Ytong AAC block) ........................................................... 167 
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Figure 8-79 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 47.25-in-high half-wall 

 constructions (Ytong AAC block) ........................................................... 168 

Figure 8-80 Impact of boundary stiffness reductions compared to rigid 

arching conditions as a function of preload for 63-in-high half-wall 

constructions (Ytong AAC block) ........................................................... 168 

Figure 8-81 Kingsway AAC block including close up of highlighted section 

 showing air pockets within concrete structure......................................... 169 

Figure 8-82 Transverse pressure is directly related to the lateral load acting on the 

 half-wall in the MRS laboratory tests (Kingsway AAC block)............... 171 

Figure 8-83 Relationship between the lateral load and the arch thrust for MRS 

 laboratory tests for different wall heights (Kingsway AAC block)......... 171 

Figure 8-84 Relationship between the transverse pressure and the arch thrust for 

 MRS laboratory tests conducted at different wall heights (Kingsway 

 AAC block).............................................................................................. 172 

Figure 8-85 Correlation of factors involving the material modulus (E), wall 

 thickness (t),and wall height (L) to the transverse pressure capacity of a 

 stopping (Kingsway AAC Block)............................................................ 173 

Figure 8-86 Resultant thrust force location for three wall heights as a function of 

 the total arch thrust (Kingsway AAC block) ........................................... 174 

Figure 8-87 Prediction of transverse pressure when both the lateral load and arch thrust 

 are known. Blue curves predicts transverse pressure when resultant thrust 

 force location is also known and red squares show predicted transverse 

 pressure when resultant thrust force location is calculated from empirical 

 data (Kingsway AAC block).................................................................... 174 

Figure 8-88 Prediction of transverse pressure from known thrust and lateral loads with 

premature failures removed (Kingsway AAC block) .............................. 175 

Figure 8-89 Impact of reducing the boundary stiffness on transverse pressure capacity 

 of stopping. Data shows individual test at different wall heights with 

 no preload (Kingsway AAC block) ......................................................... 176 
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Figure 8-90 Omega block manufactured by Burrell Mining Products Inc.................. 177 

Figure 8-91 Transverse pressure as measured from MRS laboratory testing as a 

 function of preload for three half wall heights (Omega block) ............... 179 

Figure 8-92 Lateral displacement at which peak transverse pressure occurs also 

 reaches an asymptotic minimum as the preload approaches 

 150 psi (Omega Block) ............................................................................ 179 

Figure 8-93 Relationship between the lateral load and the arch thrust for MRS 

 laboratory tests for three half-wall heights (Omega Block)..................... 180 

Figure 8-94 Relationship between the lateral load and the arch thrust for MRS 

 laboratory tests for three half-wall heights (Omega Block)..................... 181 

Figure 8-95 Relationship between the transverse pressure and the arch thrust for 

 MRS laboratory tests conducted at three half-wall heights 

 (Omega Block)......................................................................................... 181 

Figure 8-96 Correlation of factors involving the material modulus (E), wall 

 thickness (t), and wall height (L) to the transverse pressure capacity of a 

 stopping (Omega Block).......................................................................... 182 

Figure 8-97 Resultant thrust force location for three wall heights as a function of 

 the total arch thrust (Omega block) ......................................................... 183 

Figure 8-98 Prediction of transverse pressure when both the lateral load and arch 

 thrust are known. Blue curves predicts transverse pressure when 

 resultant thrust force location is also known and red squares show 

 predicted transverse pressure when resultant thrust force location is 

 calculated from empirical data (Omega block)........................................ 184 

Figure 8-99 Prediction of transverse pressure from known thrust and lateral loads 

 (Omega block) ......................................................................................... 185 

Figure 8-100 Impact of reducing the boundary stiffness on transverse pressure 

 capacity of stopping. Data shows individual test at different wall 

 heights with no preload (Omega block)................................................... 187 
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Figure 8-101 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 32-inch-high half-wall 

 constructions (Omega block) ................................................................... 187 

Figure 8-102 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 48-inch-high half-wall 

 constructions (Omega block) ................................................................... 188 

Figure 8-103 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 64-inch-high half-wall 

 constructions (Omega block) ................................................................... 188 

Figure 8-104 Peerless Super Block test set up (showing two blocks stacked on top 

 of one another. ......................................................................................... 189 

Figure 8-105 Transverse pressure as measured from MRS laboratory testing as a 

 function of preload for three half-wall heights (Peerless Super 

 Block)....................................................................................................... 191 

Figure 8-106 Lateral displacement at which peak transverse pressure occurs also 

 reaches an asymptotic minimum as the preload approaches 70-80 psi 

 (Peerless Super Block)............................................................................. 192 

Figure 8-107 Relationship between the lateral load and the arch thrust for MRS 

 laboratory tests for three half-wall heights (Peerless Super Block)......... 193 

Figure 8-108 Relationship between the lateral load and the arch thrust for MRS 

 laboratory tests for three half-wall heights (Peerless Super Block)......... 193 

Figure 8-109 Relationship between the transverse pressure and the arch thrust for 

 MRS laboratory tests conducted at three half-wall heights 

 (Peerless Super Block)........................................................................ .... 194 

Figure 8-110 Separation of weak block from thrust empirical prediction equation 

 provides more accurate model predictive capability for Peerless 

 Super Block......................................................................................... .... 195 

Figure 8-111 Two tests on 32-in-high half-walls show very similar thrust load 

 development except at the initial preloading and significantly 

 different transverse loading (Peerless Super Block)................................ 195 
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Figure 8-112 Photo of Peerless Super Block with close-up showing Styrofoam 

 pellets (small white objects in photo) imbedded in concrete mix............ 196 

Figure 8-113 Resultant thrust force location for three wall heights as a function of 

 the total arch thrust (Peerless Super Block)............................................. 197 

Figure 8-114 Prediction of transverse pressure when both the lateral load and arch thrust 

 are known. (Peerless Super Block) ......................................................... 197 

Figure 8-115 Prediction of transverse pressure from known thrust and lateral loads 

 (Peerless Super Block)............................................................................. 198 

Figure 8-116 Impact of boundary stiffness reductions compared to rigid arching 

 conditions as a function of preload for 46-inch-high half-wall 

 constructions (Peerless Super Block)....................................................... 199 

Figure 9-1 Test conducted in MRS on 6-course-high half wall to determine 

 apparent elastic modulus for the block material ...................................... 201 

Figure 9-2 Flowchart for predicting the transverse load capacity of stoppings 

 (Hybrid Theoretical Thrust Model) ......................................................... 204 

Figure 9-3 Flowchart for predicting the transverse load capacity of stoppings 

 (Hybrid Theoretical Lateral Displacement Model).................................. 205 

Figure 9-4 Flowchart for predicting the transverse load capacity of stoppings 

 (Combined Hybrid Theoretical Thrust and Lateral Displacement 

 Model)...................................................................................................... 206 

Figure 9-5 Comparison of design equation predictions with measured transverse 

 load from laboratory testing (full empirical model – Klondike block).... 208 

Figure 9-6 Transverse load capacity predictions for 6-in-thick walls constructed 

 from Klondike solid block for walls heights ranging from 5 to 10 ft 

 (Full Empirical Model) ............................................................................ 209 

Figure 9-7 Comparison of transverse load capacities from design equations to 

 the measured transverse load from laboratory tests (Hybrid Theoretical 

 Thrust Model) .......................................................................................... 211 
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Page

Figure 9-8 Transverse load capacity predictions for 6-in-thick walls constructed 

 from Klondike solid block for walls heights ranging from 5 to 10 ft 

 (Hybrid Theoretical Thrust Model) ......................................................... 212 

Figure 9-9 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical 

 Thrust Model) .......................................................................................... 213 

Figure 9-10 Transverse load capacity predictions for 6-in-thick walls constructed 

 from Klondike solid block for walls heights ranging from 5 to 10 ft 

 (Hybrid Theoretical Lateral Displacement Model).................................. 214 

Figure 9-11 Comparison of transverse load capacities from design equations to 

 the measured transverse load from laboratory tests (Hybrid 

 Theoretical Combination Model)............................................................. 215 

Figure 9-12 Transverse load capacity predictions for 6-in-thick walls constructed 

 from Klondike solid block for walls heights ranging from 5 to 10 ft 

 (Hybrid Theoretical Combination Model)............................................... 215 

Figure 9-13 Comparison of predicted transverse load capacities compared to the 

 measured capacities for the MRS laboratory tests (Full Empirical 

 Model)...................................................................................................... 216 

Figure 9-14 Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Hybrid Theoretical 

 Models) .................................................................................................... 217 

Figure 9-15 Comparison of design equation predictions with measured transverse 

 load from laboratory testing (Full Empirical Model – Peerless 

 Backsaver block)...................................................................................... 219 

Figure 9-16 Transverse load capacity predictions for 6-in-thick walls constructed 

 from Peerless Backsaver block for walls heights ranging from 5 to 

 10 ft (Full Empirical Model).................................................................... 219 

Figure 9-17 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical 

 Thrust Model) .......................................................................................... 221 
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Figure 9-18 Transverse load capacity predictions for 6-in-thick walls constructed 

from Peerless Backsaver block for walls heights ranging from 5 to 

10 ft (Hybrid Theoretical Thrust Model .................................................. 222 

Figure 9-19 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical 

 Lateral Displacement Model) .................................................................. 223 

Figure 9-20 Transverse load capacity predictions for 6-in-thick walls constructed 

 from Peerless Backsaver block for walls heights ranging from 5 to 

 10 ft (Hybrid Theoretical Lateral Displacement Model) ......................... 224 

Figure 9-21 Comparison of transverse load capacities from design equations 

 to the measured transverse load from laboratory tests (Hybrid 

 Theoretical Combination Model)............................................................. 225 

Figure 9-22 Transverse load capacity predictions for 6-in-thick walls constructed 

from Peerless Backsaver block for walls heights ranging from 5 to 10 ft 

(Hybrid Theoretical Combination Model)............................................... 225 

Figure 9-23 Comparison of predicted transverse load capacities compared to the 

 measured capacities for the MRS laboratory tests (Full Empirical 

 Model)...................................................................................................... 227 

Figure 9-24 Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Hybrid Theoretical 

Models) .................................................................................................... 227 

Figure 9-25 Comparison of design equation predictions with measured transverse 

 load from laboratory testing (Full Empirical Model – ACCOA block)... 229 

Figure 9-26 Transverse load capacity predictions for 6-in-thick walls constructed 

 from ACCOA block for walls heights ranging from 5 to 10 ft (Full 

 Empirical Model)..................................................................................... 230 

Figure 9-27 Comparison of predicted transverse load capacities compared to the 

 measured capacities for the MRS laboratory tests (Full Empirical 

 Model)...................................................................................................... 231 
xxxi

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Figure 9-28 Comparison of design equation predictions with measured transverse 

 load from laboratory testing (Full Empirical Model – Ytong block)....... 232 

Figure 9-29 Transverse load capacity predictions for 6-in-thick walls constructed 

 from Ytong block for walls heights ranging from 5 to 10 ft (Full 

 Empirical Model)..................................................................................... 233 

Figure 9-30 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical 

 Thrust Model) .......................................................................................... 235 

Figure 9-31 Transverse load capacity predictions for 6-in-thick walls constructed 

from Ytong block for walls heights ranging from 5 to 10 ft (Hybrid 

Theoretical Thrust Model) ....................................................................... 236 

Figure 9-32 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical 

 Lateral Displacement Model) .................................................................. 237 

Figure 9-33 Transverse load capacity predictions for 6-in-thick walls constructed 

from Ytong block for walls heights ranging from 5 to 10 ft (Hybrid 

Theoretical Lateral Displacement Model) ............................................... 238 

Figure 9-34 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical 

Combination Model)................................................................................ 239 

Figure 9-35 Transverse load capacity predictions for 6-in-thick walls constructed 

from Ytong block for walls heights ranging from 5 to 10 ft 

(Hybrid Theoretical Combination Model)............................................... 239 

Figure 9-36 Comparison of predicted transverse load capacities compared to the 

 measured capacities for the MRS laboratory tests (Full Empirical 

 Model)...................................................................................................... 241 

Figure 9-37 Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Hybrid Theoretical 

Models) .................................................................................................... 241 
xxxii

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Figure 9-38 Comparison of design equation predictions with measured transverse 

 load from laboratory testing (Full Empirical Model – Kingsway block). 243 

Figure 9-39 Transverse load capacity predictions for walls constructed from 

 Kingsway solid block for walls heights ranging from 5 to 10 ft (Full 

 Empirical Model)..................................................................................... 244 

Figure 9-40 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical ..... 246 

Figure 9-41 Transverse load capacity predictions for 6-in-thick walls constructed 

 from Kingsway solid block for walls heights ranging from 5 to 10 ft 

 (Hybrid Theoretical Thrust Model) ......................................................... 247 

Figure 9-42 Comparison of transverse load capacities from design equations to 

 the measured transverse load from laboratory tests (Hybrid 

 Theoretical Displacement Model)............................................................ 248 

Figure 9-43 Transverse load capacity predictions for walls constructed from 

 Kingsway block for heights ranging from 5 to 10 ft (Hybrid 

 Theoretical Lateral Displacement Model) ............................................... 249 

Figure 9-44 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical 

Combination Model)................................................................................ 250 

Figure 9-45 Transverse load capacity predictions for walls constructed from 

 Kingsway block for walls heights ranging from 5 to 10 ft 

 (Hybrid Theoretical Combination Model)............................................... 250 

Figure 9-46 Comparison of predicted transverse load capacities compared to the 

 measured capacities for the MRS laboratory tests (Full Empirical 

 Model)...................................................................................................... 252 

Figure 9-47 Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Hybrid Theoretical 

Models) .................................................................................................... 252 

Figure 9-48 Comparison of design equation predictions with measured transverse 

 load from laboratory testing (Full Empirical Model – Omega block)..... 254 
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Figure 9-49 Transverse load capacity predictions for 8-in-thick walls constructed 

 from Omega block for walls heights ranging from 5 to 10 ft 

 (Full Empirical Model). ........................................................................... 255 

Figure 9-50 Comparison of transverse load capacities from design equations to the 

 measured transverse load from laboratory tests 

 (Hybrid Theoretical Thrust Model) ......................................................... 257 

Figure 9-51 Transverse load capacity predictions for 8-in-thick walls constructed 

from Omega block for walls heights ranging from 5 to 10 ft (Hybrid 

Theoretical Thrust Model) ....................................................................... 258 

Figure 9-52 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical 

Displacement Model)............................................................................... 259 

Figure 9-53 Transverse load capacity predictions for 8-in-thick walls constructed 

from Omega block for walls heights ranging from 5 to 10 ft (Hybrid 

Theoretical Lateral Displacement Model) ............................................... 260 

Figure 9-54 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical 

Combination Model)................................................................................ 261 

Figure 9-55 Transverse load capacity predictions for 8-in-thick walls constructed 

from Omega block for walls heights ranging from 5 to 10 ft (Hybrid 

Theoretical Combination Model)............................................................. 261 

Figure 9-56 Comparison of predicted transverse load capacities compared to the 

 measured capacities for the MRS laboratory tests (Full Empirical 

 Model)...................................................................................................... 263 

Figure 9-57 Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Hybrid Theoretical 

Models) .................................................................................................... 263 

Figure 9-58 Comparison of design equation predictions with measured transverse 

 load from laboratory testing (Full Empirical Model – Peerless Super 

 Block)....................................................................................................... 265 
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Figure 9-59 Transverse load capacity predictions for 6-in-thick walls constructed 

 from Peerless Super Block for walls heights ranging from 5 to 10 ft 

 (Full Empirical Model) ............................................................................ 266 

Figure 9-60 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical 

 Thrust Model) .......................................................................................... 268 

Figure 9-61 Transverse load capacity predictions for 6-in-thick walls constructed 

 from Peerless Super Block for walls heights ranging from 5 to 10 ft 

 (Hybrid Theoretical Thrust Model) ......................................................... 269 

Figure 9-62 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical 

Displacement Model)............................................................................... 270 

Figure 9-63 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical 

Displacement Model)............................................................................... 271 

Figure 9-64 Comparison of transverse load capacities from design equations 

 to the measured transverse load from laboratory tests (Hybrid 

 Theoretical Combination Model)............................................................. 272 

Figure 9-65 Transverse load capacity predictions for 6-in-thick walls constructed 

 from Klondike hollow core block for walls heights ranging from 5 to 

 10 ft (Hybrid Theoretical Combination Model)....................................... 272 

Figure 9-66 Comparison of predicted transverse load capacities compared to the 

 measured capacities for the MRS laboratory tests (Full Empirical 

 Model)...................................................................................................... 274 

Figure 9-67 Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Hybrid Theoretical 

Models) .................................................................................................... 274 

Figure 9-68 Comparison of design equation predictions with measured transverse 

 load from laboratory testing (full empirical model – Klondike hollow 

 core block) ............................................................................................... 276 
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Figure 9-69 Transverse load capacity predictions for 6-in-thick walls constructed 

 from Peerless Super solid block for walls heights ranging from 5 to 

 10 ft (Full Empirical Model).................................................................... 277 

Figure 9-70 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical 

 Thrust Model) .......................................................................................... 279 

Figure 9-71 Transverse load capacity predictions for 6-in-thick walls constructed 

 from Klondike hollow core block for walls heights ranging from 

 5 to 10 ft (Hybrid Theoretical Thrust Model).......................................... 280 

Figure 9-72 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical 

Displacement Model)............................................................................... 281 

Figure 9-73 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical 

Displacement Model)............................................................................... 282 

Figure 9-74 Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical 

Combination Model)................................................................................ 283 

Figure 9-75 Transverse load capacity predictions for 6-in-thick walls constructed 

from Kingsway block for walls heights ranging from 5 to 10 ft (Hybrid 

Theoretical Combination Model)............................................................. 283 

Figure 9-76 Comparison of predicted transverse load capacities compared to the 

 measured capacities for the MRS laboratory tests (Full Empirical 

 Model)...................................................................................................... 285 

Figure 9-77 Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Hybrid Theoretical 

Models) .................................................................................................... 285 

Figure 9-78 Comparison of predicted transverse pressure capacities compared to 

measured capacities for the MRS laboratory tests for the Klondike block 

(Generic Empirical Model)...................................................................... 287 
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Figure 9-79 Comparison of predicted transverse pressure capacities compared to 

 measured capacities for the MRS laboratory tests for the Klondike block 

(Generic Thrust Model) ........................................................................... 289 

Figure 9-80 Comparison of predicted transverse pressure capacities compared to 

 measured capacities for the MRS laboratory tests for the Klondike block 

(Generic Lateral Displacement Model) ................................................... 290 

Figure 9-81 Comparison of predicted transverse pressure capacities compared to 

 measured capacities for the MRS laboratory tests for the Klondike 

 block (Generic Combination Model)...................................................... 291 

Figure 9-82 Comparison of predicted transverse load capacities compared to 

 measured capacities for the MRS laboratory tests for the Ytong block 

(Generic Empirical Model)...................................................................... 292 

Figure 9-83 Comparison of predicted transverse load capacities compared to 

 measured capacities for the MRS laboratory tests for the Ytong block 

(Generic Thrust Model) ........................................................................... 294 

Figure 9-84 Comparison of predicted transverse load capacities compared to 

 measured capacities for the MRS laboratory tests for the Ytong block 

(Generic Lateral Displacement Model) ................................................... 295 

Figure 9-85 Comparison of predicted transverse load capacities compared to 

 measured capacities for the MRS laboratory tests for the Ytong block 

(Generic Combination Model)................................................................. 296 

Figure 9-86 Comparison of predicted transverse load capacities compared to 

 measured capacities for the MRS laboratory tests for the 

 Omega block (Generic Empirical Model)................................................ 297 

Figure 9-87 Comparison of predicted transverse load capacities compared to measured 

capacities for the MRS laboratory tests for the Omega block (Generic 

 Thrust Model) .......................................................................................... 299 

Figure 9-88 Comparison of predicted transverse load capacities compared to 

 measured capacities for the MRS laboratory tests for the Omega block 

(Generic Lateral Displacement Model) ................................................... 300 
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Figure 9-89 Comparison of predicted transverse load capacities compared to 

 measured capacities for the MRS laboratory tests for the Omega block 

(Generic Combination Model)................................................................. 301 

Figure 10-1 Design chart for Klondike solid block showing transverse load as a 

function of preload for wall heights ranging from 5-10 ft (Hybrid 

Combination Model)................................................................................ 303 

Figure 10-2 Design chart for Peerless Backsaver Block showing transverse load as a 

function of preload for wall heights ranging from 5-10 ft (Hybrid Thrust 

Model)...................................................................................................... 305 

Figure 10-3 Design chart for Klondike Hollow Core block showing transverse load as a 

function of preload for wall heights ranging from 5-10 ft (Hybrid 

Combination Model)................................................................................ 307 

Figure 10-4 Design chart for ACCOA block showing transverse load as a function 

 of preload for wall heights ranging from 5-10 ft (Hybrid Combination 

 Model)...................................................................................................... 309 

Figure 10-5 Design chart for Ytong Block showing transverse load as a function of 

 preload for wall heights ranging from 5-10 ft (Hybrid Combination 

 Model)...................................................................................................... 311 

Figure 10-6 Design chart for Kingsway Block showing transverse load as a 

 function of preload for wall heights ranging from 5-10 ft (Hybrid 

 Combination Model)................................................................................ 312 

Figure 10-7 Design chart for Omega Block showing transverse load as a function 

 of preload for wall heights ranging from 5-10 ft (Hybrid Combination 

 Model)...................................................................................................... 314 

Figure 10-8 Design chart for Peerless Super Block showing transverse load as a 

function of preload for wall heights ranging from 5-10 ft (Hybrid 

Combination Model)................................................................................ 315 

Figure 10-9 Flowchart for Standard CMU model ....................................................... 317 

Figure 10-10 Flowchart for Cellular Concrete model ................................................... 318 

Figure 10-11 Flowchart for the Low Strength Specialty Block model ......................... 319 
xxxviii

LIST OF TABLES 

 Page

Table 7-1 MRS Half-wall tests on conventional concrete block with preload 

 applied...................................................................................................... 89 

Table 8-1 Summary of Klondike 1330 block tests with narrow block thickness..... 104 

Table 8-2 Summary of Klondike 1330 block wide orientation for wall thickness 105 

Table 8-3 Summary of Klondike 1,727 and 1,780 block ......................................... 105 

Table 8-4 Summary of normal strength Peerless Backsaver block tests.................. 118 

Table 8-5 Summary of low strength Peerless Backsaver block tests....................... 119 

Table 8-6 Summary of Klondike, hollow-core block, half-wall tests in the MRS... 131 

Table 8-7 Summary of ACC block tests .................................................................. 146 

Table 8-8 Summary of Ytong block tests................................................................. 158 

Table 8-9 Summary of test configurations and results for the Kingsway block ...... 170 

Table 8-10 Summary of Omega block tests ............................................................... 178 

Table 8-11 Summary of Peerless Super Block Testing.............................................. 190 

Table 9-1 Profile characteristics for various block materials examined in this 

 study......................................................................................................... 203 

Table 9-2 Regression analysis for determining transverse load from modulus and 

 wall geometry parameters........................................................................ 207 

Table 9-3 Multivariable regression analysis for determining arching thrust ........... 210 

Table 9-4 Multivariable regression analysis for determining resultant thrust 

 position factor .......................................................................................... 210 

Table 9-5 Multivariable regression analysis for determining lateral displacement . 213 

Table 9-6 Multivariable regression analysis for determining transverse load from 

 modulus and wall geometric parameters.................................................. 218 

Table 9-7 Multivariable regression analysis for determining arching thrust ........... 220 

Table 9-8 Multivariable regression analysis for determining resultant thrust 

 position..................................................................................................... 221 

Table 9-9 Multivariable regression for determining lateral displacement ............... 223 
xxxix

 Page

Table 9-10 Multivariable regression analysis for determining transverse load from 

 modulus and wall geometric parameters.................................................. 228 

Table 9-11 Multivariable regression analysis for determining transverse load from 

 modulus and wall geometric parameters.................................................. 232 

Table 9-12 Multivariable regression analysis for determining arching thrust ........... 234 

Table 9-13 Multivariable regression analysis for determining resultant thrust position 

 factor ........................................................................................................ 234 

Table 9-14 Multivariable regression for determining lateral displacement ............... 237 

Table 9-15 Multivariable regression analysis for determining transverse load from 

 modulus and wall geometric parameters.................................................. 242 

Table 9-16 Multivariable regression analysis for determining arching thrust ........... 245 

Table 9-17 Multivariable regression analysis for determining resultant thrust 

 position factor .......................................................................................... 245 

Table 9-18 Multivariable regression analysis for determining lateral displacement . 248 

Table 9-19 Multivariable regression analysis for determining transverse load from 

 modulus and wall geometric parameters.................................................. 253 

Table 9-20 Multivariable regression analysis for determining arching thrust ........... 256 

Table 9-21 Multivariable regression analysis for determining resultant thrust 

 position factor .......................................................................................... 256 

Table 9-22 Multivariable regression analysis for determining lateral displacement . 259 

Table 9-23 Multivariable regression analysis for determining transverse load from 

 modulus and wall geometric parameters.................................................. 264 

Table 9-25 Multivariable regression analysis for determining arching thrust ........... 266 

Table 9-26 Multivariable regression analysis for determining resultant thrust position 

 factor ........................................................................................................ 267 

Table 9-27 Multivariable regression analysis for determining lateral displacement . 270 

Table 9-28 Multivariable regression analysis for determining transverse load from 

 modulus and wall geometric parameters.................................................. 275 

Table 9-29 Multivariable regression analysis for determining arching thrust ........... 278 
xl

 Page

Table 9-30 Multivariable regression analysis for determining resultant thrust 

 position factor.................................................................................................. 278

Table 9-31 Multivariable regression analysis for determining lateral displacement . 281 
xli

ABBREVIATIONS OF UNITS 

psf – pounds per square foot 

psi – pounds per square inch 

lbs – pounds 

kips – measure of force equating to 1,000 pounds 

in – inch 

ft – feet 

mils – thousandths of an inch 

pct – percent 

sq ft – square feet 

cu ft – cubic feet 

in2 – square inches 

ft2 – square feet 

water gage, in – inches of water gage where 1 psi equals 27.5 inches of water gage 
1

CHAPTER 1: INTRODUCTION 

An effective ventilation system requires a ventilation plan that is not only sound in 

design, but also well implemented during both mine development and subsequent production 

stages. Ventilation stoppings control ventilation throughout an underground mine and are an 

integral part of the ventilation system. Operating longwalls in the United States (U.S.) alone 

require an estimated 21,600 new stoppings each year, and mines using room-and-pillar 

mining methods will require another 66,000 stoppings (Tien, 1996). With an average cost of 

$600 - $800 per stopping, total costs could easily exceed $90 million per year for the coal 

industry (Tien, 1996). 

 Stoppings are designed primarily to withstand air pressure differentials generated by the 

mine fan that exert transverse loading against the high-pressure side or face of the stopping. 

These pressures, typically measured in inches of water gage, are generally less than 7 inches 

of water in the working sections of the mine, equating to approximately 0.25 psi. The 

pressure increases as the proximity to the mine fan increases. Near the mouth of a bleeder 

fan, the pressure can exceed 1 psi, which exerts considerable force against the stopping. Air 

blasts from roof falls can generate localized areas of higher pressure that can destroy 

stoppings. Seals, with a minimum transverse load capacity of 20 psi, are designed to contain 

explosions, but stoppings also play a role in maintaining ventilation during an explosion. 

Australia, for example, requires a 5 psi transverse load capacity for permanent stoppings used 

in main roadways and near sealed areas (Gillies et al., 2001). This is done, in part, to prevent 

widespread damage to the ventilation system in the event that an explosion does occur. 

 Unlike seals, which are required to pass full-scale testing to ensure their transverse load 

capacity, there are no full-scale tests required for stoppings to determine their load capacity. 

The current Code of Federal Regulations (CFR) requirement is to test 4x8-ft sections of 

freestanding walls (CFR Part 75.333 Ventilation Controls, 1996). This test inadequately 

determines the transverse load capacity of stopping constructions since in the mine the walls 

are restrained by the mine roof and floor, and pillar ribs. This restraint allows for 

significantly greater transverse loading capability by taking advantage of the compressive 

forces that are generated as the wall arches between the mine roof and floor. As a result, the 

true transverse load capacities of mine ventilation stoppings are not known. 
2

 Recently, a new generation of lightweight blocks has been developed for mine 

ventilation stopping constructions. While stoppings utilizing these blocks have all passed the 

current CFR criteria, it is believed that their true transverse load capacity varies considerably. 

This is because the material strength of the block types vary by as much of an order of 

magnitude, and the material strength of the blocks correlates to the arching capability of the 

restrained wall in the mine during transverse loading. Without such knowledge, the design of 

mine ventilation systems using these lighter-weight, but lower-capacity, alternative 

constructions can be misleading, potentially exposing the mine to inadequate ventilation 

control under some circumstances. 

 The objective of this dissertation is to develop a new protocol to examine the transverse 

load capacity of block stopping constructions and use this protocol to evaluate transverse 

load capacities of various stopping constructions under arching conditions. Using the unique 

biaxial loading capabilities of the National Institute for Occupational Safety and Health’s 

(NIOSH) Mine Roof Simulator (MRS), arching conditions for stoppings are simulated in the 

laboratory, using a single or multiple column of block to predict the transverse load capacity 

of an entire stopping. Verification of the procedure has been done through full-scale testing 

of stoppings in a pressure chamber in the NIOSH Experimental Coal Mine and in the 

underground Longwall Gallery at the NIOSH Lake Lynn facility. A complete systematic 

study of the various design parameters that affect the capability of a stopping to develop 

transverse loading under arching conditions was conducted. From this study, predictive 

models were developed and compared against laboratory testing results. The outcome of the 

dissertation is a complete set of design formulations for eight different block material 

constructions and generic design formulations that provide transverse load capacity 

approximations for standard concrete, cellular concrete, and low strength concrete block 

materials. 

CHAPTER 2: REVIEW OF LITERATURE 

Masonry structures have been utilized dating back to building of pyramids and other 

structures 10,000 years ago. Modern masonry type structures using cementitious materials 

date back over a 100 years. As a result of this long history, considerable research has been 
3

1

F

f

F

f

b

b

a

a + =

conducted on masonry structures. Masonry as a general term involves clay brick or concrete 

block structures where the unit blocks are mortared together at the joints to form a more 

continuous structure. Most mine ventilation stoppings are walls constructed from concrete 

blocks and therefore fit this classification, except that stoppings in recent times are drystacked as opposed to having mortared joints. In this regard, the research to support this 

dissertation is considered an extension of what has previously been done in this general area. 

 A comprehensive assessment of masonry design is found in a book authored by 

Drysdale, et al. (1994) entitled “Masonry Structures: Behavior and Design”. Transverse 

loading due to wind pressure has been analyzed for walls spanning vertically between lateral 

supports along the top and bottom edges of the wall face. In two dimensions, this condition 

equates to a simply supported beam. The flexural strength of such walls is determined by the 

tensile strength of the mortared joints, generally at the mid span of the wall. The current U.S. 

CFR requirements for transverse loading of stoppings (CFR Part 75.333 Ventilation 

Controls, 1996) are an extension of this flexural analysis, except the CFR assumes drystacked block construction for mine ventilation stoppings, which therefore have no tensile 

strength. The CFR requires testing of freestanding walls with sealant applied to the lowpressure face of the wall to provide the tensile strength necessary to resist the moment 

induced by the transverse pressure. 

 Drysdale also addresses the impact of axial loading on the wall. For a dry-stacked wall, 

axial loading can significantly increase the transverse load capacity by resisting the bending 

moment induced by the transverse load. In this sense, the axial load can take the place of the 

lack of tensile strength in these dry-stacked configurations. This is why ground pressures 

acting on a stopping wall will greatly increase their transverse load capacity. Drysdale also 

describes a unity equation for combined axial and transverse loading of walls. The unity 

equation 2.1 is present in some masonry codes and requires that the combined compressive 

stresses from axial loading and bending must be limited to the material strength to achieve 

proper design under these conditions. 

 (2.1) 
4

Where fa, fb = compressive stresses due to applied axial load and bending, 

respectively, and

 Fa, Fb = allowable axial and bending compressive stresses, respectively. 

 The loading mechanism being addressed in this dissertation involves arching of the 

wall structure. Drysdale also devotes a section of the book to the arching of walls. 

Generally, arching can be described as bridging between two rigid abutments as opposed to 

unrestrained end conditions. Studies into the arching behavior of masonry date back to 1951. 

The Armour Research Foundation, in conjunction with work sponsored by the U.S. Air Force 

and technically monitored by the Special Studies Office of the Installation Division, Air 

Material Command, first reported on an investigation of the arching theory. At this time, 

arching was a radical departure from conventional beam deflection theory that was typically 

used to evaluate the resistance of masonry walls to wind-generated or some other form of 

lateral loading. 

 McDowell has reported on this work in a paper published in the Proceedings of the 

American Society for Civil Engineers (McDowell et al., 1956). This was the first 

comprehensive paper published in a trade journal on this subject. McDowell showed that 

arching can be used to explain the significantly higher lateral loads that brick beams are 

capable of withstanding than conventional bending analysis would allow. In conventional 

bending analysis, beams strengths relative to lateral loading are controlled by the tensile 

properties of the material. This works well for steel beams since steel has a high tensile 

strength. Conversely, the tensile strength of concrete is generally about one tenth of its 

compressive strength, so masonry structures cannot depend solely on the tensile strength of 

the construction material to resist bending or provide for large lateral loading of wall 

structures. 

 McDowell proposed that a three-hinge arch is formed and that the resistance of the wall 

to lateral loading is due entirely to the tendency of the masonry to crush at the mid span and 

end supports due to the arching action. The masonry material is assumed to be unable to 

withstand tensile stress. McDowell describes the transverse loading of a wall as follows. 

Immediately upon loading, cracks develop on the tension side at the ends and center of the 

span. Initially, these cracks extend to the centerline of the beam (wall). During subsequent 

motion, it is assumed that each half of the wall remains rigid and rotates about an end and 
5

where the two half walls meet at the center of the wall. The resistance to this motion comes 

about through a force couple set up at the ends and center due to crushing of the masonry at 

these positions. The rotation continues until the resisting couple vanishes (i.e., the material 

fails) or the load is removed. 

 McDowell also reported on a series of tests conducted at the Massachusetts Institute of 

Technology where 17 brick beams were tested under fixed-end conditions (Massachusetts 

Institute of Technology, 1954). These tests were consistent with the arching theory. The 

ultimate lateral strength of the beams was shown to correlate to the compressive strength of 

the material. The transverse load capacity was six times greater than what a simply 

supported beam analysis predicts. 

 Anderson (1984) examined the theory of arching in more detail by comparing the 

behavior of masonry walls during the initial loading prior to cracking of the wall and postcracking behavior of the wall. He concluded that the load required to cause cracking of a 

wall with rigid abutments can be three times greater than a wall without arching restraint. He 

also concluded that the ultimate (post-cracking) transverse load capacity of a wall with 

abutments was three to nine times more than the pre-cracking load. Anderson showed the 

significance of the stiffness of the abutments in a theoretical analysis of arching and 

concluded that reducing the stiffness of the abutments will allow greater wall deflections to 

occur; and a theoretical limit of stability exists where the deflection is too large to generate 

an arching thrust. Anderson developed an equation relating the arching thrust to the 

transverse load. This relationship is used in this dissertation with modified coefficients to 

account for the physical characteristics of mine ventilation stoppings. 

 (2.2) 

Where qlat = design lateral strength per unit area of wall, psi, 

 fk = characteristic compressive strength of the masonry, psi, 

 m γ = material safety factor, 

 t = wall thickness, in, and 

 L = span of the wall, in. 

2

⎟

⎠

⎞ ⎜

⎝

⎛ = ×

L

f t

q

m

k

lat

γ
6

 Through these and related efforts, arching has been recognized as a valid loading 

mechanism and design consideration for walls bridging rigid abutments. The British Codes 

of Practice (British Standards Institution, 1978) first recognized arching as a design 

mechanism in 1978. Curiously, arching is not recognized in the U.S. Masonry Designers 

Guide (Masonry Designer’s Guide: Based on Building Code Requirements for Masonry 

Structures (ACI 530-92/ASCE, 5-92/TMS 402-92) and Specifications for Masonry Structures 

(ACI 530.1-92/ASCE 6-93/TMS 602-92)). The design formula specified for arching in the 

British Codes of Practice is of the same form as that developed by Anderson (equation 2.2). 

Close contact between the wall and the end abutments must be maintained for these criteria 

to be applicable in the British code. For vertical spanning walls, such as a wall spanning 

between a floor and roof, the design code requires that the dead weight vertical load be 

sufficient to sustain the arching. This work forms the basis for the rigid-arching assessment 

of stopping walls pursued in this dissertation. 

 The U.S. Bureau of Mines also conducted research on stopping behavior dating back to 

the 1960’s (Kawenski and Mitchell, 1966). The emphasis of this work was primarily on the 

leakage of stoppings as a result of structural damage from either transverse loading or by 

ground movements. Fundamental construction techniques were examined and although fullscale tests of transverse loading were conducted, a study into the loading mechanics was not 

done during this period. 

 Recently, the concept of arching has also been applied to seal behavior (Sapko, et al., 

2003). Tests conducted on seals in a hydrostatic chamber indicated that arching is occurring 

across the width of the seal, in this case the restraint provided by the pillar ribs. Initial tests 

showed good agreement of the ultimate transverse loading pressure of the seal to the arching 

mechanics described in equation 2.2. Research continues in this area to develop scaling 

factors for various materials and seal thicknesses. 
7

CHAPTER 3: CURRENT CFR CRITERIA FOR STOPPINGS 

 Part 75.333 Ventilation Controls of the CFR requires that permanent ventilation control 

structures and mine stoppings for underground coal mines be constructed in a traditionally 

accepted method. Materials that have been tested and shown to have greater or equal 

strength than traditionally accepted in-mine control structures must be used. While this is 

somewhat vague, the statute goes on to specify that alternative stopping technologies be 

tested in accordance with ASTM E 72-80, “Standard Methods of Conducting Strength Tests 

of Panels for Building Construction”, Section 12 – Transverse Loading – Specimen Vertical 

(ASTM Designation E 72-80, 1981). 

3.1 ASTM E 72 TEST SPECIFICATIONS 

 The procedure requires testing of a nominal 4-ft-wide section of wall of a height equal 

to the mining height where the stopping will be used. Hence, for an 8-ft mining height, a 

4x8-ft section of wall would be tested. The wall is to be constructed in the manner it will be 

used in the mine, including the application of sealant when specified. The test apparatus is 

shown in the diagram illustrated in figure 3-1. Figure 3-2 shows a wall section being placed 

into the reaction frame for ASTM E 72 testing at a commercial laboratory (Professional 

Services Industries) in Pittsburgh, PA. As seen from these figures, the freestanding wall is 

tested in a vertical orientation. The wall is placed on a steel channel which rests on a 

cylindrical roller (figure 3-3a) to prevent restrained end conditions. The axis of the roller is 

parallel to the face of the wall, allowing rotation to occur without restraint, as the wall is 

deformed from the application of transverse pressure. Two reaction rollers and contact plates 

positioned at the top and bottom of the wall allow the wall to deflect under the application of 

transverse pressure from the opposite face (figure 3-3b). Again, rollers are utilized to prevent 

longitudinal restraint as the wall deflects. Transverse pressure is applied across the width of 

the wall through a steel contact plate at quarter-height points of the wall. Rollers in the form 

of a steel pipe are again used to transfer load from a central I-beam through the contact 

plates, again to prevent any rotational restraint from occurring. As the load is applied, it is 

required that the load be recorded as a function of the displacement at the mid-span of the 

wall height. The maximum load normalized to the square foot area of the wall is then 
8

defined as the transverse pressure capacity for the wall. It is also required that three separate 

walls be tested. The average transverse pressure capacity from these three tests must exceed 

39 psf to comply with the CFR statute. 

Figure 3-1. Diagram of test apparatus for transverse pressure testing of 

stoppings in accordance with ASTM E 72 specifications. 

TRANSVERSE PRESSURE 

SUPPORT ROLLER 

AND PLATE SPONGE 

RUBBER 

LOADING ROLLER AND PLATE 

ROLLER

REACTION 

FRAME 

SPONGE 

RUBBER 

LOADING ROLLER 

AND PLATE 

ROLLER 

ROLLER 
9

Figure 3-3b. Close up view of sections of pipe used as reaction roller to avoid 

rotational restraint as the wall deflects from application of transverse pressure. 

Transverse pressure

application rollers

Reaction 

roller 

Bottom half of 

4 x 8 ft wall 

Figure 3-2. A 4 x 8 ft section of wall 

being placed into reaction frame for 

ASTM E 72 testing. 

Figure 3-3a. A 4 x 8 ft section of wall 

positioned in the reaction frame for 

ASTM E 72 transverse pressure testing.

Top reaction roller

Transverse pressure 

application rollers 

Bottom 

Base roller reaction roller 

4 x 8 ft 

wall section
10

3.2 INADEQUACIES OF CURRENT CFR SPECIFICATIONS 

Examination of the mechanics of the wall response to transverse pressure reveals the 

inadequacies of the CFR test procedure. First, it is seen that great care is taken to ensure that 

there is no longitudinal restraint provided to the wall as the load is applied. Essentially, the 

wall is considered freestanding and unrestrained from vertical movement as it bends from the 

application of transverse pressure (figure 3-4). The objective of the test is to evaluate the 

flexural strength of the wall. Any structure that is subject to bending produces tensile 

stresses on one side of the structure and compressive stresses on the opposite side of the 

structure (figure 3-4). Typically, the tensile strength of the material, being weaker than the 

compressive strength, controls the capability of the structure to withstand loads that produce 

bending. Concrete has relatively little tensile strength, but a dry-stacked block stopping has 

no effective tensile strength since the joints are not bonded. Theoretically, the transverse 

pressure capacity of a freestanding, dry-stacked stopping would be provided only from the 

weight of the block, which acts to provide a superimposed vertical load on the structure. 

Even the heaviest blocks would not provide enough axial loading to meet the 39-psf criteria 

in the CFR. 

Figure 3-4. The wall is not restrained vertically in this free-standing test condition. 

Tension Compression
11

 The tensile strength is actually provided by the application of sealant to the face of the 

wall. This brings up a few more points of discussion. First, this is obviously not the primary 

function of the sealant. As such, there was little information available about the tensile 

strengths of sealants prior to this research, and in fact, evaluating or knowing the strength of 

the sealant is not part of CFR test requirement. Since the sealant under these conditions is 

providing the major contribution to the transverse pressure capacity of the dry-stacked block 

stopping, the placement of the sealant is also critical to the test results. In order for the 

sealant to be effective in controlling the transverse pressure, it must be applied to the face 

opposite the load application, i.e., the low-pressure side of the stopping in the mine 

environment. If the ventilation could be reversed either intentionally or unintentionally, then 

the sealant should be applied to both sides of the stopping under these criteria. Since several 

sealants are available each with different material properties, then the stopping should only 

be certified with a specific sealant as used in the test. Furthermore, for a given sealant, the 

thickness of the sealant contributes significantly to the effective tensile strength and resulting 

transverse pressure capacity of the wall. How thick the sealant is applied in the test program 

compared to the thickness normally applied to such stoppings in the mine is another issue of 

concern. The test program should exclude abnormally thick sealant applications. 

 In conclusion, the current CFR requirements using ASTM E 72 specifications for 

evaluating stopping walls is nothing more than a test of the sealant tensile strength. 

Observations made in this research, and those reported by MSHA in the approval and 

certification of stoppings, indicate that inconsistent results can be achieved with these 

sealant-related test procedures. As described above, the test procedure is predicated on a 

freestanding wall arrangement, which for dry-stacked stopping constructions requires the 

sealant to control the transverse pressure. The only other factor influencing the transverse 

pressure capability is the height of the wall, and this factor is frequently ignored, as an 8-ft 

test height is a standard height used in ASTM E 72 testing. The physical and material 

properties of the block are irrelevant in this test procedure. This process will allow any block 

type to be used providing the sealant can sufficiently adhere to the block to provide the 

required tensile strength across the block joints. 
12

CHAPTER 4: ARCH LOADING MECHANISM 

In the mine, stopping walls are not freestanding structures as assumed in the 

ASTM E 72 test standard used to define the current CFR criteria. Stoppings, as constructed 

in the mine, bridge the distance between the mine floor and the mine roof and are typically 

wedged in place at the roof interface to provide a tight fit during installation. They also span 

the full entry width, butted against the pillars on both sides. Hence, if the mine stoppings are 

restrained by the mine roof and floor and pillars, this restraint allows for a completely 

different loading mechanism to occur, namely arching. 

4.1 PHYSICAL DESCRIPTION OF ARCHING 

 Arching is the mechanism that occurs when the elongation of the tension face of the 

stopping due to the rotation of the wall as it bends under the application of transverse 

pressure is prevented by the contact abutments of the mine roof and floor. This arching of 

the wall produces a thrust that acts at the mine roof and floor interface, and produces 

compressive forces within the wall that can dramatically increase the transverse pressure 

capacity of the wall compared to a freestanding condition. An examination of the wall as it 

bends from the transverse pressure further explains how arching works. Initially, the ends of 

the wall are in full contact with the mine roof and floor and the individual horizontal joints 

between the courses of block are in full contact with each other. As the transverse pressure 

increases, the wall will begin to bend. Associated with the bending will be the opening of the 

joint along the mid-height span of the wall (location of the maximum positive moment), and 

opening of the joints between the top and bottom block at the roof and floor interface 

(location of the maximum negative moment). A three-hinged arch is formed where the 

external moment caused by the transverse pressure (ρ x L2

/8) is resisted by the internal force 

couple (P x r), where r is defined as the width of the arch and P is the thrust generated by the 

arching. This condition is illustrated in the diagram in figure 4-1, and expressed 

mathematically by equations 4.1 and 4.2. As shown in the figure, crush zones occur at the 

three hinge points. 
13

Figure 4-1. Illustration of rigid arching of a wall structure. 

RIGID 

SUPPORT 

RIGID 

SUPPORT 

L

P 

P

T

R

A

N

S

V

E

R

S

E 

P

R

E

S

S

U

R

E

L/2 

CL 

C

R

U

S

H

I 

N

G

P 

CRUSHING 

CRUSHING 

r 

t/2 t/2 

Ө
14

(4.1) 

(4.2) 

Where ρ = transverse pressure, psi, 

 L = height of the wall, in, 

 P = resultant thrust force at the hinge points, lbs per in of wall width, and 

 r = width of the arch, in. 

 In this analysis, the compressive forces will control the transverse pressure capacity. 

Hence, the compressive strength of the block material becomes the dominant control 

parameter in defining the transverse pressure capacity. Lower strength blocks will have less 

transverse pressure capacity than higher strength blocks. This is a significant departure from 

the dominance of the sealant in controlling the transverse pressure capacity in the current 

CFR testing requirement. Under arching conditions, the contribution of the sealant to the 

transverse pressure capacity would be insignificant for all but the very weakest block 

materials used for stopping construction. 

4.2 SIMULATING ARCHING THROUGH BIAXIAL LOADING 

IN THE MINE ROOF SIMULATOR 

 It is apparent from the preceding analysis that an assessment of the true transverse 

pressure capacity of a mine ventilation stopping cannot be attained by a freestanding wall 

evaluation. Arching has been shown to be an accepted loading mechanism for masonry 

design for walls that are restrained by high stiffness abutments. A ventilation stopping 

bridging between the mine roof and floor satisfies this condition. However, full-scale testing 

of mine ventilation stoppings in an actual underground mine is difficult and time consuming 

to conduct. In order to determine the transverse pressure capacity of a stopping underground, 

2L

8 P r

ρ

× × =

P r

8

2 ρ L = ×

×
15

either a hydrostatic pressure chamber is required to develop the controlled loading or an 

explosive charge is needed to create the loading much like seals are currently tested. 

 Likewise, there are only a few facilities where full-scale laboratory tests of such large 

structures can be conducted. Laboratory testing of partial masonry beams by other 

researchers have been successfully conducted, although these too have been relatively limited 

in scope, requiring specialized reaction frames and fixtures to accomplish rudimentary tests. 

As the theory indicates, the thrust forces involved in rigid arching of wall structures can be 

substantial (over 100 tons of abutment loading for a 4-ft wide wall). This requires robust 

fixtures to preserve the low yielding or rigid abutment conditions. NIOSH has a unique load 

frame that is designed to simulate the behavior of rock masses for underground mining 

operations. It is called the Mine Roof Simulator (MRS). This unique facility provides an 

ideal framework in which to conduct rigid-arch testing of stopping walls. 

4.2.1 Description of the Mine Roof Simulator 

 A photograph of this unique machine is shown in figure 4-2. A detailed description of 

the load frame is provided in Appendix A. The platen size measures 20 x 20 ft, and with a 

maximum vertical opening of 16 ft, the MRS can accommodate full-scale stopping 

constructions, as shown in figure 4-3, where a compressive load is being applied to a 

stopping wall to measure its capacity relative to roof loading. The MRS is capable of 

providing controlled biaxial loading in the vertical and one horizontal axis. Up to 3 million 

lbs of vertical force can be applied through a 24-in stroke of the lower platen and 1.6 million 

lbs of horizontal force through a 16-in stroke of the lower platen. The loads or displacements 

in these two axes can be applied individually or simultaneously if desired. The biaxial 

capabilities of the load frame are used to simulate transverse loading of stoppings. A test 

protocol using half-wall sections of the stopping to evaluate its transverse loading behavior is 

described in the next section. 
16

Figure 4-2. NIOSH Mine Roof Simulator load frame. 

Figure 4-3. Full-scale mine ventilation stopping wall being tested in the NIOSH 

Mine Roof Simulator. 
17

4.2.2 Test Protocol For Simulating Arching 

 In order to simulate arching, a half-height section of a stopping wall is placed in the 

load frame in a typical vertical orientation, as it would be in the mine. The upper platen 

position is adjusted to the height of the block column and is hydraulically clamped to 

maintain its position. The vertical position of the lower platen is commanded to remain 

constant. Hence, the fixed vertical positions of the upper and lower platen allow them to act 

as rigid restraints. The lower platen is then moved horizontally at a constant velocity of 0.5 

inches/minute, causing the wall to rotate (figure 4-4). As the base of the wall is forced to 

move horizontally, hinge points and deformation zones are created at the ends of the wall on 

opposite sides, consistent with the arch loading mechanism. The horizontal force applied by 

the MRS to the base of the half-wall is measured. This force is equivalent to the transverse 

load acting on a stopping wall. The transverse pressure is computed by normalizing the 

resultant of this force over the area of the wall to determine the transverse pressure capacity 

for comparison to the current CFR requirements. 

 

Figure 4-4. Diagram illustrating the simulation of rigid arching on a half-wall 

section of a stopping by biaxial testing in the NIOSH Mine Roof Simulator. 

zone

Crush

Zone Ө

Crush

MRS UPPER PLATEN
18

In order to measure the applied horizontal loading more accurately than the capabilities 

of the MRS which use the large actuator pressures to measure the loading, an arrangement 

using load cells was employed which can independently record the horizontal load at a higher 

resolution. Figure 4-5 illustrates the testing apparatus. A single or triple column of block, 

equal in height to half the full-scale installation height is constructed on the rolling platform. 

The rolling platform is a two-in-thick steel plate that is secured to four 32-ton-capacity 

crawler units (figure 4-6). A load measuring reaction fixture is located adjacent to the 

crawler assembly. Two bolts are secured into the lower platen, which has inserts on a 20 x 

20-in grid to accommodate bolt placements. The bolts serve as the rigid horizontal restraint 

against which transverse pressure of the block column is generated. A two-in-thick metal 

plate is then used to bridge the gap between the two bolts. Two, 20-kip load cells are then 

placed in front of the reaction plate to accurately measure the horizontal load (figure 4-7). 

These have a calibration accuracy of 0.1 pct, meaning they can measure the transverse load 

to an accuracy of 20 lbs. The load cells laid horizontally on the platen have a threaded bar 

extending from them to provide contact with the stopping block’s rolling platform. Two 

machined nuts at the end of the threaded bar provide some minor adjustments to ensure that 

proper contact is established with the block platform before the test commences. 

 Although the apparatus was designed to test a column up to three blocks wide, it was 

concluded from shakedown testing that a single column of block would provide the most 

consistent results for standard masonry block materials. Block dimensional tolerances can 

cause variations in the height of the wall across a three-block arrangement (figure 4-8) for 

dry-stacked block constructions that are being evaluated in this study. Since the MRS is 

acting as a rigid restraint, any differential in the height of the wall will produce non-uniform 

loading of the wall from block-to-block across the width of the wall. By using a single 

column of block, a uniform height can be more easily achieved to provide uniform loading 

and results that are more consistent. Three block wide half-walls were utilized for the lower 

modulus block materials where the block tolerances were not as critical. 
19

Figure 4-5. Apparatus used to conduct half-wall rigid-arching tests of 

stopping walls in the NIOSH Mine Roof Simulator. 

 

Metal Plate 

Rolling 

Tray

Adjusting 

Nuts 20 Kip Load Cell 

Single 

Column 

Concrete Wall 

Platen 

Bolt 

Lower Platen

Upper Platen

Column 

Lower Platen

Upper Platen

Metal Plate 

Nuts 20 Kip Load Cell

Single 

Platen 

Bolt 

PLAN VIEW

Rolling 

Tray 

Column 

Concrete Wall

SIDE VIEW 
20

Figure 4-6. Block column rests on rolling platform to allow load cells to 

measure lateral loading. 

Figure 4-7. Load cells used to accurately measure horizontal loading. 
21

4.2.3 Transverse Pressure Determinations From MRS Half-Wall Testing 

 Two examples of transverse pressure tests conducted on two different types of concrete 

block are shown in figures 4-9a and 4-9b. Both tests consisted of a single column of block, 

stacked four blocks high with the narrow side contact between blocks. The first test (4-9a) is 

a half wall constructed from a lightweight block manufactured by Kingsway Technology 

from autoclaved concrete. Air pockets introduced into the concrete mix (figure 4-9c) result 

in the low material density. This block measures 5.875 x 8.375 x 17.250 inches with a 

density of 42.5 lbs/cu ft resulting in a unit block weight of approximately 21 lbs. Tests 

conducted on an individual block indicated that the compressive strength was 546 psi (figure 

4-10). This type of block is being used by some mines because of its lighter weight to reduce 

material handling injuries associated with stopping construction. The second wall was 

constructed from block made by Klondike Block and Masonry Supplies, Inc., from 

conventional Portland cement, sand, and aggregate material. This block measured 5.625 x 

7.500 x 15.625 inches with a material density of 109.7 lbs/cu ft and a unit weight of 

Figure 4-8. Illustration of how block dimensional tolerances can cause 

localized loading on a three-block-wide wall (not to scale).

Upper Platen

Lower Platen
22

approximately 45 lbs. This block has a compressive strength of 1,330 psi as shown in figure 

4-11. 

Figure 4-9a. Test of a half-wall 

made from lightweight block (546-

psi compressive strength). 

Figure 4-9b. Test of a half-wall made 

from conventional concrete block 

(1,330-psi compressive strength). 
23

Figure 4-10. Compressive strength test data for Kingsway block. 

0

10

20

30

40

50

60

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

DISPLACEMENT, inches

LOAD, kips

0

100

200

300

400

500

600

STRESS, psi

Figure 4-9c. Close up view of Kingsway, autoclaved, concrete block shows air 

pockets in the block structure. 
24

Figure 4-12 documents the half-wall rigid arching test results for the lightweight 

(Kingsway) block. The graph plots the applied lateral load provided by the load frame to 

produce the controlled lateral displacement of the wall. The graph shows that the lateral load 

increases with increasing lateral displacement up to the peak load, which in this test was 

approximately 1,675 lbs occurring at 0.74 inches of lateral displacement. It is also seen from 

figure 4-12 that the thrust reaction load measured by the load frame, since the vertical 

opening of the platens is held constant, also increases as the lateral loading increases. This is 

consistent with arching theory. The measured vertical force is equivalent to the arching force 

or thrust (P).

 The applied lateral load can then be normalized to the area of the wall to provide a 

transverse pressure capacity measured in pounds per square foot or psf. The arching 

mechanics require that the force acting at the based of wall be doubled to properly distribute 

this load as a uniform force over the entire wall. For the example shown in figure 4-12, the 

four-course, single-block column was 17.25 inches wide by 33.50 inches high providing an 

area of 577.88 in2

 or 4.01 ft2. Multiplying the lateral load from the test (1,675 lbs) by 2 and 

dividing this force by the area provides a transverse pressure capacity of 834 psf. This is an 

order of magnitude higher than the 39 psf required by the current CFR criteria based on a 

freestanding wall analysis. 

Figure 4-11. Compressive strength test data for conventional concrete block. 

0

20

40

60

80

100

120

140

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

DISPLACEMENT, inches

LOAD, kips

0

229

457

686

914

1,143

1,371

1,600

STRESS, psi
25

Figure 4-13 shows the test results from the second example using conventional concrete 

block, or conventional masonry units (CMU) as they are sometimes called. This block has a 

compressive strength of 1,330 psi or about 2.5 times that of the autoclaved block tested in the 

first example. As seen in figure 4-13, the peak lateral load acting on this wall was 3,855 lbs 

occurring at a lateral displacement of 1.02 in. This equates to a transverse pressure of 2,134 

psf or 2.56 times that of the autoclaved block used in the previous test. It is noted that the 

difference in lateral load capacity between the lightweight and the conventional block is 

consistent with the difference in material strength. This provides additional validation for the 

application of arching theory to stopping wall behavior. Again, it is noted that this transverse 

pressure is two orders of magnitude higher than current 39-psf allowance under the CFR. 

Figure 4-12. Half-wall rigid-arching tests conducted in the Mine Roof Simulator on the 

Kingsway lightweight block. 

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs ..

0

2

4

6

8

10

12

14

16

18

AXIAL LOAD, kips .

MRS Test #148 -- Lateral Load -- Kingsway Block -- 4 courses high -- 5.875 in thick

MRS Test #148 -- Axial Load -- Kingsway Block -- 4 courses high -- 5.875 in thick

THRUST LOAD, kips 

Thrust Load
26

4.3 VALIDATION OF EXPERIMENTAL DESIGN METHODOLOGY AND 

ARCHING BEHAVIOR 

In order to confirm that arching was the proper loading mechanism controlling the 

transverse pressure capacity of mine ventilation stoppings and to verify the MRS half-wall 

rigid-arching testing protocol, a few full-scale tests of stopping walls were also conducted. 

These tests were conducted in the NIOSH Experimental Coal Mine at the Pittsburgh 

Research Laboratory. Test data was also analyzed from explosion testing of full-scale 

stoppings at the NIOSH Lake Lynn Laboratory. 

4.3.1 NIOSH PRL Experimental Coal Mine Tests 

 The Experimental Coal Mine is an abandoned coal mine that has been used as an 

underground laboratory for conducting various research experiments by NIOSH researchers. 

The mine has been part of the Bureau of Mines since 1910 and is now owned by NIOSH. It 

is located on site at the Pittsburgh Research Laboratory near Bruceton, PA. 

Figure 4-13. Half-wall rigid-arching tests conducted in the Mine Roof Simulator 

on conventional concrete block. 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

5

10

15

20

25

30

35

40

AXIAL LOAD, kips .

MRS Test #102 -- Lateral Load -- Klondike Block -- 4 courses high -- 5.625 in thick 

MRS Test #102 -- Axial Load -- Klondike Block -- 4 courses high -- 5.625 in thick Thrust Load

THRUST LOAD, kips 
27

An air pressure chamber was constructed in one of the crosscuts in the mine to provide 

a facility for static loading of mine ventilation stoppings. The crosscut measures 

approximately 16 ft in width with about an 80-in height. A barrier wall was constructed from 

mortared high strength solid concrete blocks. The barrier is 16 in thick. An access door, air 

intake port, and data acquisition lead wire ports were installed during construction of the 

barrier. A stopping wall is then constructed approximately 3-ft from the barrier wall. A 

concrete pad was formed on the floor of the crosscut to provide a flat foundation for 

constructing the stopping wall. The pillar ribs were also squared up, again to facilitate the 

stopping wall construction in order to minimize air leakage that might occur along this 

interface. 

 Two full-scale wall tests were conducted in the NIOSH Experimental Coal Mine. The 

first test utilized the lightweight autoclaved blocks that were used in the first example 

presented for the MRS rigid-arching tests. The second test was a wall constructed from the 

conventional solid concrete aggregate block that was utilized in the second MRS rigidarching test. This was done so that a direct comparison to these tests could be made. 

 Photos of the remains of the stopping after the full-scale mine test of the lightweight 

block stopping are shown in figures 4-14 and 4-15. It is seen in these figures that the bottom 

and top course of block stayed in place after the wall was blown out. This is most likely 

because the bottom course was grouted in place to provide a level and secure foundation to 

build the wall. Likewise, cement grout was squeezed into the voids on top of the wall 

between and around the wooden wedges to stop air leaks, and this secured the top block to 

the shotcreted roof in the Experimental Coal Mine. This suggests that the functional wall 

height relative to the arching length may have been the eight courses of block between the 

top and bottom layer as denoted in figure 4-14. 

 
28

Figure 4-15. Arch height shown to occur between top and bottom layer of 

block that were grouted (cemented) in place in this particular test. 

Arch length

Figure 4-14. Photo after the wall was destroyed from the transverse 

loading. Researcher is standing next to the displacement transducers 

used to measure the wall deflection. 
29

 The results of the lightweight autoclaved block MRS tests in comparison to the fullscale mine test are shown in figure 4-16. As seen in the figure, the 5-course-high, singlecolumn, half-wall rigid-arching test conducted in the MRS more closely predicted the fullscale wall behavior in the mine than the 4-course-high, half-wall test. The peak transverse 

pressure was 834 psf for the 4-course-high, half-wall and 462 psf for the 5-course-high, halfwall MRS test compared to 400 psf for the full-scale mine test. If it is assumed that the 

arching length did occur over the 8-course height, this suggests that the wall failed 

prematurely in the full-scale mine test compared to the laboratory test, perhaps from a lower 

block strength than was achieved in the laboratory test or due to differences in the boundary 

conditions. 

 Figure 4-17 compares the full-scale mine test with all the MRS half-wall tests 

correlating the term fc x (t/L)2

, where fc is the compressive strength of the concrete block, t is 

the wall thickness, and L is the full wall height. The underlying assumption in this analysis 

is that the arch thrust is limited by the compressive strength of the material. The MRS 

laboratory tests are based on the unit block compressive strength of 546 psi. Two cases are 

presented for the full-scale mine test, one where the compressive strength is derived from 

testing a single block (546 psi unit block compressive strength) using the full construction 

height of 10 courses, and the other where the strength is derived from a column of 4 to 6 

blocks (342 psi column compressive strength) and using the apparent 8-course arching 

height. As seen in this figure, both these measures place the full-scale mine test for the fc x 

(t/L)2 correlation close to the MRS laboratory tests data, but the lower strength (column 

measure) provides the best correlation of the full-scale mine test to the half-wall MRS tests. 
30

Figure 4-16. Comparison of half-wall rigid-arch test in the MRS to the full-scale 

stopping wall test in the NIOSH Experimental Coal Mine for the Kingsway block. 

Figure 4-17. Comparison of full-scale mine test with Kingsway block with the MRS 

half-wall tests. 

0

100

200

300

400

500

600

700

800

900

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE PRESSURE, psf .

Expermental Mine Full-Scale Test (Kingsway)

MRS Half-Wall Test -- 4 course high (Kingsway)

MRS Half-Wall Test -- 5 course high (Kingsway)

y = 229.43x - 179

R2

 = 0.98

0

100

200

300

400

500

600

700

800

900

1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50

fc*(t/L)2

TRANSVERSE PRESSURE, psf .

MRS Half-Wall Test Data (Kingsway)

Experimental Mine Full-Scale Test -- 5 course (Kingsway) -- Unit block strength

Experimental Mine Full-Scale Test -- 4 course (Kingsway) -- Column strength
31

 Photos of the remains of the full-scale stopping test with the conventional Klondike 

block are shown in figures 4-18 and 4-19. The wall was constructed with 10 courses of 

block. Figure 4-18 shows the arching length occurred between the mine roof and bottom 

course of block, equating to 9 courses of block in this case. Figure 4-19 shows a close up 

view of the base of the wall illustrating the rotation of the wall and formation of the bottom 

hinge of the arch. This is proof of the arching mechanism. 

 The comparisons of the MRS half-wall rigid-arching test to the full-scale mine test for 

the walls constructed from the conventional Portland cement, sand, and aggregate block 

manufactured by Klondike are shown in figure 4-20. The graph shown both a 4-course-high 

and a 6-course-high half-wall test in the MRS as well as a projected 5-course-high result in 

comparison to the measured full-scale mine test. Since the wall appeared to arch over a 9-

course height, there is not a direct comparison to a MRS laboratory test, but the projected 5-

course-high half-wall test fits the mine response reasonably well with a peak transverse 

pressure of 1,200 psf compared to the 975 psf for the full-scale mine test. If the lateral 

displacement is considered, the full-scale mine test at failure falls nicely in between the four 

and six course high MRS half-wall response. 

 A comparison of the full-scale mine test to the regression trend line developed from the 

suite of MRS tests showing the correlation of the transverse pressure to the fc x (t/L)2 term is 

shown in figure 4-21. As with the lightweight block test presented in the previous example, 

here again it is seen that the full-scale test was very close to the MRS trend line and is 

slightly better when the column strength is considered with the shorter wall height compared 

to the unit block strength with the higher wall height. 
32

Figure 4-18. Photo showing conventional (Klondike) wall after full-scale 

test in the Experimental Coal Mine noting the arch length between the top 

and bottom course of block. 

Figure 4-19. Close up view of the base 

of the conventional (Klondike) block 

wall showing the rotation of the wall 

and formation of the bottom hinge of 

the arch. 
33

Figure 4-21. Comparison of full-scale mine test of Klondike conventional block 

with the MRS half-wall regression trend line and suite of MRS tests. 

0

400

800

1,200

1,600

2,000

2,400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE PRESSURE, psf .

Experimental Mine Full-Scale Test -- 10 course high (Klondike 1,330 psi)

MRS Half-Wall Test -- 4 course high (Klondike 1,330 psi)

MRS Half-Wall Test -- 6 course high (Klondike 1,330 psi)

Theoretical Prediction -- 5 courses high (Klondike 1,330 psi)

y = 233.41x - 680.64

R2

 = 0.99

0

500

1,000

1,500

2,000

2,500

3,000

0 2 4 6 8 10 12 14 16

fcx(t/L)2

TRANSVERSE PRESSURE, psf .

MRS Half-Wall Test Data (Klondike 1,330 psi)

MRS Half-Wall Test Data (Klondike 1,727 psi)

Experimental Mine Full-Scale Test -- 5 course -- Unit Block strength - 1,330 psi)

Experimental Mine Full-Scale Test -- 4 course -- Column strength - 832 psi)

Figure 4-20. Comparison of half-wall rigid-arch test in the MRS to the full-scale 

stopping wall test in the NIOSH Experimental Coal Mine for the Klondike block.
34

4.3.2 NIOSH Lake Lynn Laboratory Tests 

A series of tests were conducted at the NIOSH Lake Lynn Laboratory at the request of 

the Mine Safety and Health Administration (MSHA) to evaluate the effects of explosions on 

mine ventilation stoppings as part of NIOSH’s research on the prevention and mitigation of 

gas/dust explosions. These tests also provided additional data to validate the transverse 

pressure capacity of stoppings 

The test protocol consisted of constructing stoppings in the crosscuts between the C and 

B-drifts of the Lake Lynn Longwall Gallery, and progressively increasing the intensity of 

gas/dust explosions to induce sufficient air pressures to cause transverse pressure failures of 

the stoppings. Both hollow-core and solid concrete block stoppings were evaluated in this 

study. The hollow-core block had an average material compressive strength of 1,456 psi and 

the solid block an average compressive strength of 1,900 psi. The stopping walls constructed 

in the crosscuts were 12 courses high (7.5 ft), 6-inches thick, and approximately 20 ft in 

length. Pressure transducers were used to measure both the static and dynamic pressure at 

the stoppings resulting from the explosive charge. 

The results of the explosion tests at the Lake Lynn Laboratory indicated that the 

transverse pressure capacity of the dry-stacked, hollow core stopping was 490 psf and 821 

psf for the solid, dry-stacked concrete block stopping. Since neither of these particular 

blocks was available for testing at the MRS, a direct comparison to MRS half-wall tests 

could not be made. However, by computing the term fc X (t/L)2

, a comparison can be made to 

overall MRS test results. Two cases are considered: (1) arching over the full wall height (12 

courses) and (2) arching over 10 courses. For a nominal block height of 8 inches, this 

produces arch heights (L) equal to 96 and 80 inches, respectively. These results are depicted 

in figure 4-22. Here again, there is good agreement between the MRS laboratory tests and 

the full-scale mine tests, and the correlations are more accurate when the lower (column) 

strength is used in the analysis. 
35

y = 233.41x - 680.64

R2

 = 0.99

0

500

1,000

1,500

2,000

2,500

3,000

0 2 4 6 8 10 12 14 16

fcx(t/L)2

TRANSVERSE PRESSURE, psf .

MRS Half-Wall Test Data (Klondike 1,330 psi)

MRS Half-Wall Test Data (Klondike 1,727 psi)

Lake Lynn Full-Scale Test (Conventional Solid Block 1,900 psi)

Lake Lynn Full-Scale Test (Modified Block Strength 1,500 psi)

Lake Lynn Full-Scale Test (Hollow Core Block ) -- 12 courses -- Unit block strength 1,456 psi)

Lake Lynn Full-Scale Test (Hollow Core Block ) -- 10 courses -- Column block strength 903 psi)

Figure 4-22. Comparison of Lake Lynn full-scale stopping tests with the MRS 

rigid arching tests.
36

P (0.8 t δ ) HF L/2 × × − h = ×

CHAPTER 5: DEVELOPMENT OF GENERAL TRANSVERSE LOAD DESIGN 

EQUATION FROM ARCHING MECHANICS 

 Figure 5-1 is used to re-examine the 

half-wall mechanics. Here the arching thrust 

(P) is shown to act on two ends of the wall at a 

distance of one-tenth the wall thickness from 

the end of the wall. The lateral force (HF) is 

shown to act at the ends of wall in accordance 

with the MRS laboratory protocol for 

conducting half-wall test using the biaxial 

capabilities of the simulator. This force will 

be used to compute the transverse load 

capacity of the stopping. Equation 5-1 is 

formed by summing moments about the top 

left corner of the wall as illustrated in figure 

5-1.

 (5.1) 

Where P = arching thrust, lbs, 

 t = thickness of the wall, in, 

 δh = lateral displacement of wall at the mid span, in, 

 HF = horizontal force measured at based of half-wall, lbs, and 

 L/2 = half-wall height, in. 

This equation is then solved for the horizontal force, which is a measured parameter in the 

MRS laboratory testing and is used to verify the test data with the arching mechanics theory. 

 

 (5.2) ( )

L/2

P 0.8 t δ HF × × − h =

L/2 h 0.8×t −δ

P

P

HF

HF

L/2 h 0.8×t −δ

P

P

HF

HF

Figure 5-1. Half-wall statics showing 

the width of the arching thrust varies 

as a function of the wall displacement.
37

 In order to transform the 

measured horizontal force into 

transverse pressure that would be acting 

on a full-scale stopping, the resultant 

horizontal force must be repositioned to 

the middle of wall to represent the 

resultant transverse load of a uniform 

load acting against the face of a 

stopping. This transposition to the 

middle of wall requires the force be 

increased by a factor of two to satisfy 

moment equilibrium requirements as 

expressed in equation 5.1 (see figure 

5-2). 

The transverse load per unit area is computed by dividing the horizontal force acting on 

the half-wall by the area of the wall (equation 5.3). 

 (5.3)

 

Where ρ = transverse load, psf, 

 HF = horizontal force measured at base of wall in laboratory half-wall tests, lbs, 

 w = width of the wall, in, and 

 L/2 = half-wall height, in. 

Substituting the horizontal force (HF) from equation 5.2 into equation 5.3 yields an 

expression for the transverse load as a function of the lateral displacement of the wall. 

 (5.4) 

Figure 5-2. Repositioning of the 

horizontal force to equate to the 

resultant force acting against a fullscale stopping wall. 

h 0.8×t −δ

P

P

HF

h 0.8×t −δ

P

P

HF

2 x HF L/2

144

w L/2

2 HF

ρ ×

×

× =

( )

( ) 144

w L/2

2 P (0.8 t δ ) 144

w L/2

L/2

P 0.8 t δ 2

ρ 2

h

h

×

×

× × × − × = ×

× × − ×

=
38

×ρ

×

× ×ρ× = × ×ρ = ∫ 8

w L

2

y w y dy w

L/ 2 2

0

2 L/ 2

0

Where ρ = transverse load, psf, 

P = arching thrust, lbs, 

 δh = lateral displacement of wall at the mid span, in, 

 w = width of the wall, in, and 

 L/2 = half-wall height, in. 

 A more generalized approach to 

finding a solution to computing the 

transverse pressure can be found by 

integrating the transverse load over the area 

of the wall as illustrated in figure 5-3 to 

equate the maximum bending moment from 

the transverse pressure to the moment 

produced by the arch thrust. The maximum 

bending moment assuming a uniformly 

distributed load produced by the transverse 

pressure can be found from equation 5.5. 

The moment equilibrium requirements 

expressed in equation 5.1 can then be 

expressed as equation 5.6. 

 (5.5) 

 (5.6) 

Equation 5.6 can then be solved for the transverse pressure (ρ) as shown in equation 5.7, 

providing the same solution derived in equation 5.4. 

 (5.7) 

Figure 5-3. Displaying transverse 

pressure acting on half-wall. 

h 0.8×t −δ

P

P

HF

L/2 h 0.8×t −δ

P

P

HF

ρ

( ) ×ρ

×

× × − δ = 8

w L P 0.8 t

2

h

2

h

2

h

w (L / 2)

2 P (0.8 t )

w L

8 P (0.8 t )

×

× × × − δ = ×× × × − δ

ρ =

y
39

Taking moments about the bottom right corner of the half-wall (see figure 5-3), reveals the 

relationship expressed in equation 5.8, which can be solved for the horizontal force (HF) as 

shown in equation 5.9 as a function of the wall width (w), wall height (L), and the transverse 

pressure (ρ). 

 (5.8) 

 (5.9) 

×ρ

×

× = 8

w L HF (L / 2)

2

×ρ

× = 4

w L HF
40

CHAPTER 6: THEORETICAL ASSESSMENT OF FACTORS THAT AFFECT THE 

TRANSVERSE PRESSURE 

 As seen in the previous theoretical analysis of the arching mechanics, several 

parameters affect the transverse pressure of mine ventilation stoppings under arch loading 

conditions. An assessment of these parameters is made to further understand their 

significance. 

6.1 WALL HEIGHT 

 An increase in wall height causes a reduction in the transverse load capacity of a mine 

ventilation stopping. The physical description of arching described in section 4.1 of Chapter 

4 shows that wall height is a critical parameter in controlling the transverse load capacity of a 

stopping. The moment equilibrium equation 5.1 shows that the horizontal force moment arm 

is much larger than the thrust moment arm due to the wall height. Equation 5.4 shows that 

the transverse pressure varies inversely with the square of the half-wall height because of the 

moment equilibrium requirements. Hence, wall height will have a big impact on the 

transverse load capacity. 

 

0

500

1,000

1,500

2,000

2,500

60 70 80 90 100 110 120 130 140

FULL-WALL HEIGHT (L), in

CALCULATED TRANSVERSE PRESSURE (

ρ),psf ..

Constant Lateral Displacement; δh = 1.0 inches

Constant Lateral Displacement: δh = 2.0 inches

Constant Lateral Displacement: δh = 3.0 inches

Thrust Force (P) = 31,500 lbs

Wall Width (w) = 16 inches

Wall Thickness (t) = 5.875 

i h

Figure 6-1. Impact of wall height on transverse load capacity.

144

w (L/2)

2 P (0.8 t δ ) ρ 2

h ×

×

× × − × =
41

0

500

1,000

1,500

2,000

2,500

6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0

WALL THICKNESS (t), in

TRANSVERSE PRESSURE (

ρ), psf .

Constant Lateral Displacement: δh = 1 inches Constant Lateral Displacement; δh = 2 inches

Constant Lateral Displacement; δh = 3 inches

Thrust Force; P = 31,500 lbs

Wall Width; w = 16 inches

Wall Height; L = 90 inches

 Figure 6-1 depicts the transverse pressure as a function of wall height for lateral wall 

displacements of 1, 2, and 3 inches. The wall thickness in this example is a 5.875 inches and 

a constant arching thrust force of 31,500 lbs was acting on a single block column measuring 

16 inches in width. As seen in this figure, the impact of wall height will be greater for 

shorter wall heights and becomes less of a factor as the wall height increases. For example, 

increasing the wall height from 60 to 96 inches decreases the transverse pressure by 61%; 

whereas, increasing the wall height from 96 to 120 inches reduces the transverse load 

capacity by 36%. 

6.2 WALL THICKNESS 

 Equation 5.4 shows that the transverse load capacity is directly related to the 

thickness of the wall. Ultimately, the thickness of the wall determines the arch thrust 

moment arm, which is the distance between the resultant thrust hinge points as shown in 

figure 5-1 and represented by the factor (0.8 x t - δh). The impact of wall thickness on a 90-

inch wall height is shown in figure 6-2 for lateral wall displacements of 1, 2, and 3 inches. 

Increasing the wall thickness from six to 8 inches, representative of a common block 

geometry, increases the transverse load capacity from 784 to 1,232 psf at a lateral 

displacement of 2 inches, an increase of 57%. 

Figure 6-2. Impact of wall thickness on transverse load capacity. 

144

w (L/2)

2 P (0.8 t δ ) ρ 2

h ×

×

× × − × =
42

6.3 WALL WIDTH 

 Equation 5.4 implies that the transverse pressure acting on a wall is also inversely 

related to the width of the wall, the width being analogous to the entry width. However, the 

arching thrust as shown here is the total thrust acting on the full width of the wall. The width 

factor is included only to normalize the thrust to a unit width, which is necessary to calculate 

the transverse pressure acting on the wall. In other words, the arching thrust cannot be 

considered a constant unless the wall width is also a constant. Hence, the wall width does 

not affect the transverse pressure capability of the stopping. 

 Physically, the reason why the width of the wall is not important is that the blocks are 

dry-stacked. If the joints of the block courses were mortared or laterally confined, then the 

arch may form along the width of the wall since this is typically the long axis in comparison 

to the height of the wall. However, since the blocks are dry-stacked, the joints have no 

tensile strength, and the arch is formed from the mine floor to the mine roof instead of from 

coal pillar to coal pillar, as is generally the case in seal behavior. 

6.4 ARCH THRUST 

 Examination of equation 5.4 shows that the transverse capacity of a stopping wall is 

directly related to the arching thrust (P). The higher the arch thrust, the larger the transverse 

load capacity will be. If the arch thrust doubles, the transverse load capacity of the stopping 

will also double. Therefore, the compressive arch thrust force is the key to the how much 

transverse capacity a stopping of a given geometry can develop. The development of the 

arching thrust depends on several factors, including the geometry of the wall (i.e. height and 

thickness). But it is primarily determined by the material properties of the block and 

boundary stiffness of the roof and floor, both of which control how much lateral 

displacement of the wall will occur as the transverse pressure is applied to the face of the 

stopping. Understanding the development and role of the arching thrust requires a 

reexamination of the arching mechanics. 

 Transverse pressure applied to the face of the stopping will cause a three-hinge arch to 

form and lateral displacement of the middle hinge point with respect to the roof or floor 

hinge point. The lateral displacement causes an extension of the tension face of the stopping, 

which is resisted by the mine roof and floor and hinge point at the center section of the wall 
43

(see figure 4-1). These reactions produce the thrust forces. How much thrust force is 

developed depends primarily on the stiffness of the wall structure and the mine roof and 

floor. The stiffness of the half-wall can be expressed as a function of the elastic modulus of 

the wall (see equation 6.1). 

 (6.1) 

 

Where k = stiffness, lbs/in, 

 A = axial loading area of the wall, in2

, 

 E = elastic modulus, psi, and 

 L/2 = half-wall height, in. 

Axial (vertical) loading is produced by the arching thrust. The deformation in the hinge 

zones is a function of the thrust force. Hence, the stiffness of the wall can be expressed as a 

function of the arching thrust and the deformation in the hinge zones (equation 6.2). 

 (6.2)

 

Where k = stiffness, lbs/in, 

 P = thrust force, lbs, and 

 y = deformation in each of the two hinge zones on the half-wall section, in. 

Combining equation 6.1 and 6.2 yields the following expression. 

 (6.3) 

Where A = axial loading area of the wall, in2

, 

 E = elastic modulus, psi, 

 L/2 = half-wall height, in, 

 P = thrust force, lbs, and 

 y = deformation in each of two hinge zones on half-wall section, in. 

L/2

A E k × =

2y

P k =

2y

P

L/2

A E = ×
44

L/2

2 A E y P × × × =

This equation can them be solved for the arching thrust. 

 (6.4) 

Where P = thrust force, lbs, 

 A = axial loading area of the wall, in2

, 

 E = elastic modulus, psi, 

y = deformation in each of two hinge zones on half-wall section, in, and 

 L = full wall height, in. 

 The area, modulus, and height of the wall are all known parameters, but the 

deformation of the hinge areas needs to be calculated. An examination of the arching 

mechanics and formation of the three-hinge arch shows that the deformation of the hinge 

areas is geometrically related to the lateral displacement. The diagram shown in figure 4-1 

shows the three-hinge arch formed from the application of transverse pressure. As seen in 

the diagram, the shaded red areas at the hinge zones represent sections of the wall that must 

deform in order for the lateral displacement to occur. An expression that relates the hinge 

zone deformation (y) to the lateral displacement (δh) can be determined by analyzing the 

geometry of the wall configuration shown in figure 6-3. The distance between the rigid roof 

and floor abutments represents the construction height of the stopping (L). The half-wall 

height is represented as L/2, which as shown in the diagram is half the construction height 

and is the distance between the two hinge zone planes formed at end of the wall and the mid 

span. The hinge zone deformation (y) is shown as the extension of the wall beyond the 

abutment that would occur if the abutment was not there. Although it is illustrated in this 

manner, the “y” distance actually represents the shortening of the tension side of the wall due 

to the deformation of the hinge zone by the arching thrust that is acting against the rigid 

abutment. 
45

 First, examine triangle ABC (beige-shaded triangle) that is formed by the lateral 

displacement of the wall. The lateral displacement is equal to the side AB in this triangle. 

By similarity, examining triangle A ́, B ́, C ́ (green-shaded triangle), it is seen that A ́B ́ also 

equals the lateral displacement of the wall. Now consider the purple-shaded triangle labeled 

BDE. Examining the geometry shows that the side BD is equal to the wall thickness (t) 

minus the lateral displacement (δh). The length of side DE is equal to the half-wall length 

(L/2). Using the rule that the length of the hypotenuse squared is equal to the sum of the 

squared lengths of the other two sides of a triangle, the following relationship can be 

developed. 

Figure 6-3. Diagram of wall geometry as a function of the lateral displacement.

y

A

B

C

E F

A’ B’

C’

D

L/2

L/2-y

t

y

L/2

t - h δ

δ h

L/2

t- hδ

t

D L/2-2y
46

2 2

2

2y t BE

2

L ⎟ + = ⎠

⎞ ⎜

⎝

⎛ −

 (6.5) 

Next, examine the blue-shaded triangle BEF that shares the same hypotenuse as the purpleshaded triangle BDE. The length FE is equal to the thickness (t) of the wall. Examining the 

geometry of the wall shows that BF is equal to the half-wall length (L/2) minus the 

deformation of each crush zone (y). Using the same rule as applied above, the following 

relationship is developed for triangle BEF. 

 

 (6.6)

Equations 6.5 and 6.6 can be combined to form equation 6.7. 

 (6.7)

 

Equation 6.7 can then be solved for the hinge area deformation using the quadratic equation 

(y = ax2

 + bx + c), once the terms are computed and simplified as shown in equation 6.9. 

Equation 6.10 is the solution used to determine the hinge area deformation (y) if the lateral 

displacement (δh) is known for a particular wall thickness (t) and wall height (L). 

 

 (6.8) 

 (6.9) 

 (6.10) 

( ) 2 2

h

2

t δ BE

2

L ⎟ + − = ⎠

⎞ ⎜

⎝

⎛

( ) 2

2

2

h

2

2y t

2

L

t δ

2

L ⎟ + ⎠

⎞ ⎜

⎝

⎛ ⎟ + − = − ⎠⎞ ⎜

⎝

⎛

δ 2 t δ 2 L y 4 y 0 2

h

2

h − × × + × × − × =

8

2 L 4 L 32 t δ 16 δ

y

2

h h

2 × ± × − × × + × =

4 ( ) y 2 L (y) [2 t ] 0 2

h h

2

× − × × + × × δ − δ =

2 a

b b 4 a c Quadratic equation solultion

2

×

− ± − × × y =

( )2 2

2

2

h h

2

2

2y 2y t

2

L 2

2

L

t 2 t δ δ

2

L ⎟ − × × + + ⎠

⎞ ⎜

⎝

⎛ ⎟ + − × × + = ⎠

⎞ ⎜

⎝

⎛
47

 Figure 6-4 shows the thrust force developed as a function of lateral displacement for 

wall stiffness of 80, 120, and 160 kips/in based on an elastic modulus of 40,000, 60,000 and 

80,000 psi, respectfully. As seen from this theoretical analysis, the arch thrust increases 

proportionally with increasing material modulus. From this, it can be deduced that the 

resulting transverse pressure will also increase proportionally with the arching thrust. The 

chart shows that the arching thrust will continue to increase with lateral displacement since 

there is no limit on the material strength in this example. If the arch thrust is limited to the 

compressive strength of the material, the arch thrust will not continue to increase, and as 

such, will limit the transverse load capacity of the stopping. 

Figure 6-4. Impact of wall stiffness on transverse load capacity. 

0

20

40

60

80

100

120

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, in

ARCHING THRUST, kips .

40,000 psi modulus 60,000 psi modulus 80,000 psi modulus
48

6.5 LATERAL DISPLACEMENT 

 The lateral displacement also plays a big role in determining the transverse capacity of 

a block stopping. The diagram in figure 6-5 illustrates the change in wall geometry due to 

lateral displacement. As seen in figure 6-5, the width of the arch, represented by the distance 

between the resultant thrust forces and mathematically expressed as 0.8 x t - δh, will decrease 

as the lateral deflection of the wall increases. The decrease in the width of the arch will 

cause a proportional decrease in the transverse load capacity of the wall, since the force 

couple produced by the arch thrust will decrease. 

 Figure 6-6 illustrates a hypothetical example of the impact of the lateral displacement 

of the wall on the transverse load capacity. In this example, a constant arching thrust of 

31,500 lbs, representative of the thrust acting per unit block width, is considered. The wall 

thickness is 6 inches. Half-wall heights (L/2) of 30, 45, and 60 inches are considered. The 

theoretical transverse pressure is calculated from equation 5.4. 

Figure 6-5. Diagram showing that lateral displacement of the stopping reduces the arch 

width. 

Thrust moment arm

Lateral 

Displacement 
49

 As shown in this figure, the transverse pressure decreases with increasing lateral 

displacement of the wall. The decreasing slope of the curves as the half-wall height increases 

indicates that the lateral displacement will have a greater magnitude in reducing the 

transverse pressure for shorter walls than it will for taller walls. For example, an increase in 

the lateral displacement from 1 to 2 inches, theoretically will cause a decrease in the 

transverse pressure on a 30-in half-wall height from 2,400 psf to 1,750 psf, a decrease 650 

psf. However, for a 60-in half-wall height, the transverse pressure would decrease from 

approximately 600 psf to 440 psf, a decrease of 160 psf. Expressed as a percentage, the 

transverse pressure is decreased by approximately 27 pct for all three wall heights when the 

lateral displacement is increased from 1 to 2 inches. 

 

 Further examination of the chart in figure 6-6 indicates that the transverse pressure will 

continue to decrease until the arch width is reduced to zero. For the 6-inch wall thickness 

used in the example considered in figure 6-6, this will occur at lateral displacement of 4.8 

inches, given the initial assumption that the resulting thrust force is acting at distance onetenth of wall thickness from the end of the block. This maximum lateral displacement can be 

Figure 6-6. Hypothetical example of the impact of lateral displacement on the 

transverse load capacity of stoppings of various half-wall heights. 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

LATERAL DISPLACEMENT (δh), inches

CALCULATED TRANSVERS

E

PRESSURE(

ρ), psf

Length 30 inches Length 45 inches Length 60 inches
50

considered as a limit of stability, beyond which the wall cannot sustain an arching thrust. 

This concept was illustrated graphically in figure 6-5, which showed how the arch width 

decreased as the lateral displacement increased. 

6.6 COMPRESSIVE STRENGTH AND MATERIAL MODULUS 

 The compressive strength and the elastic modulus of the block play important roles in 

defining the transverse load capacity of a mine ventilation stopping. In order to understand 

the impact of these parameters, the arching mechanics need to be fully understood. As 

previously indicated, the arching thrust limits the capability of the wall to sustain transverse 

pressure. The transverse load capacity of a stopping wall is limited even if the material 

strength has not been exceeded, because the rotation of the wall impacts the development of 

the arching thrust and moment equilibrium requires that the force couple developed with the 

arching thrust and the transverse pressure must balance. As was shown in figure 6-4, the 

arch thrust as a function of the lateral wall displacement will be larger for higher modulus 

materials than it will be for lower modulus materials. As a result, the transverse load 

capacity will be greater for higher modulus materials for a wall of a given geometry 

(thickness and height). 

 A theoretical example is shown in figure 6-7. In this example, three modulus values 

are considered: (1) 40,000 psi, (2) 60,000 psi, and (3) 80,000 psi. The peak transverse 

pressure occurs at 2 inches of lateral displacement for all three walls, since this is determined 

by the wall thickness and height. However, the peak transverse pressure for the 80,000-psi 

modulus material is twice that of the 40,000-psi modulus wall construction, since the 

transverse pressure is directly related to the material modulus. Is this example, the 

compressive strength of the block does not affect the transverse load capacity, only the 

mechanics of the arch formation is considered. Figure 6-8 shows what the outcome would be 

if it assumed that the 40,000-psi modulus wall reached the full strength of the block at the 

peak transverse pressure, and this same block strength was assumed for the other two wall 

constructions with the 60,000 and 80,000-psi modulus materials. It is seen that although the 

block strength limits the transverse load capacity of the 60,000 and 80,000-psi modulus 

walls, the transverse load capacity continues to be greater for the higher modulus walls. 
51

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE PRESSURE, psf ..

40,000 psi modulus 60,000 psi modulus 80,000 psi modulus

Figure 6-7. The transverse load capacity of a stopping is directly related to the material 

modulus of the block from which the stopping is constructed. 

0

500

1,000

1,500

2,000

2,500

3,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE PRESSURE, psf ..

40,000 psi modulus 60,000 psi modulus 80,000 psi modulus

Block strength equal for all 

three walls, set equal to the 

40,000 psi modulus wall.

Figure 6-8. Chart shows transverse load capacity if all block had the same 

compressive strength. 
52

Figure 6-9 illustrates the required the block strength if the peak transverse pressure 

were equal for all three walls. As seen in the chart in this theoretical example, the block 

strength would be equal to a 2,066 psi for the lowest modulus block (40,000 psi), 1,396 psi 

for the 60,000-psi modulus block, and 1,310 psi for the 80,000-psi modulus block. 

Following this analysis, it can be seen that there is an optimum block strength that is needed 

to ensure that the full transverse pressure potential is realized. However, it is also seen that 

this optimum strength increases with increasing material modulus. For this theoretical 

example, the optimum strength would be approximately 2,000 psi for the low modulus 

(40,000 psi) material, but it would double to 4,000 psi for the high modulus (80,000 psi) 

material. Beyond this, the transverse pressure will be controlled by the arching mechanics 

and the benefit of the higher block strength will not be realized in the transverse pressure 

development of the stopping. Following this logic, it can also be seen that it is theoretically 

possible for a lower strength block to provide more transverse load capacity than a higher 

strength block, if the modulus of the higher strength block is sufficiently lower than that of 

the lower strength block. While this is unlikely for block of similar materials, it may occur 

for blocks fabricated from dissimilar materials. 

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE PRESSURE, psf ..

0

250

500

750

1,000

1,250

1,500

1,750

2,000

2,250

2,500

HINGE CONTACT STRESS, psi ..

Transverse load -- 40,000 psi modulus Transverse load -- 60,000 psi modulus Transverse load -- 80,000 psi modulus Hinge contact stress -- 40,000 psi modulus Hinge contact stress -- 60,000 psi modulus Hinge contact stress -- 80,000 psi modulus

Figure 6-9. Dashed lines show the required block strength to provide the same 

transverse load capacity for all three walls. 
53

6.7 OTHER FACTORS THAT IMPACT THE TRANSVERSE LOAD 

CAPACITY OF A STOPPING 

Other factors that may impact the transverse load capacity of a stopping include: 

(1) stiffness of the abutments, (2) use of strain softening materials within the wall to absorb 

ground deformation, (3) compressive loading of the wall from ground pressures, (4) use of 

wedges to tighten the wall against the mine roof during construction, and (5) use of 

prestressing devices such as grout bags to seal the perimeter around the stopping. 

6.7.1 Impact of Abutment Stiffness 

 Up to this point, the analysis has assumed a rigid arching condition whereby the 

abutments are assumed not to deform. Under rigid arching conditions, as shown in the 

previous analysis, the lateral displacement of the wall is controlled by the stiffness and elastic 

response of the block wall. It was shown that the transverse load capacity will decreases as 

the block modulus decreases since more lateral displacement will occur. The increase in 

lateral displacement reduces the force couple provided by the arching thrust and this causes a 

decrease in the transverse load capacity of the stopping. If the abutments are not rigid, then 

the lateral displacement will increase further, resulting in a further reduction in the transverse 

load capacity of the stopping. 

 The problem can be analyzed in terms of the stiffness of the system. The system 

consists of both the wall and the abutments. Since the wall and the abutments act in series 

with one another, the system stiffness can be expressed by equation 6.11. 

 (6.11) 

Where Ksystem = system stiffness, lbs/in, 

 Kwall = wall stiffness, lbs/in, and 

 Kabutment = abutment stiffness, lbs/in. 

 If the stiffness of the abutment is infinity (perfectly rigid abutment), then the wall 

stiffness will control the lateral displacement associated with the arching thrust through the 

deformation of the block as described in the previous section. However, examining equation 

wall abutment

wall abutment

System K K

K K K

+

× =
54

6.11 shows that if the abutment stiffness was equal to wall stiffness, the system stiffness 

would be reduced by 50 pct. Therefore, a small change in the abutment stiffness can cause 

significant changes in the arching capacity and transverse load capacity of a stopping. 

 Figure 6-10 shows that a nonlinear relationship exists between the extension into the 

abutment zone and the resulting lateral displacement of the wall. As the deformation of the 

abutment increases due to the arching thrust, the lateral displacement increases more quickly. 

It is also seen that the increase in lateral displacement as a function of increased deformation 

of the abutment is greater for taller walls than for shorter walls. 

 An experiment to show the significance of the abutment stiffness was conducted. A 

45-in-high half-wall made from Portland cement block with a compressive strength of 1,727 

psi was constructed for testing in the MRS, and a piece of 1⁄2-inch-thick drywall was placed 

on top of the wall (see figure 6-11). The impact of the drywall is shown in figure 6-12, 

which compares the transverse pressure from an identical wall without the drywall. As seen 

in figure 6-12, the transverse pressure was reduced from 888 psf to 178 psf. The lateral 

displacement at which the peak transverse pressure occurred increased from 1.35 inches to 

0

1

2

3

4

5

6

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

DEFORMATION OF THE ABUTMENT DUE TO ARCH THRUST, in

LATERAL DISPLACEMENT, in .

Half-wall height 30 inches Half-wall height 45 inches Half-wall height 60 inches

Figure 6-10. Impact of reduced abutment stiffness expressed as deformation of the 

abutment due to arch thrust on the lateral displacement of the stopping wall. 
55

1.98 inches. Therefore, a 47 pct increase in lateral displacement of 0.63 inches, caused the 

transverse pressure to decrease by 710 psf or 80 pct. 

Figure 6-11. Test configuration using drywall to soften the abutment stiffness. 
56

 Figure 6-13 shows a close up view of the 

deformation of the drywall after the completion of the 

test documented in figure 6-12. An indentation of 

approximately 1/10 of an inch occurred at the edge 

where the concrete block was imbedded into the 

drywall. Following the analysis presented in section 

6.7.1, it is determined that a system modulus of 

26,000 psi representing the combined effect of the 

block wall and drywall roof contact, would produce a 

reasonable approximation of the transverse pressure 

for this configuration as shown in figure 6-14. With 

a system modulus of 26,000 psi and a block 

modulus of 80,000 psi for this particular block, the 

modulus of drywall would be about 400 psi as determined from equation 6.11. 

Figure 6-12. Comparison of transverse pressure determined from half-wall testing in the 

MRS with rigid abutment (red curve) and softened abutment from drywall roof contact. 

Figure 6-13. Close up view of the 

deformation of the drywall caused 

by the arching thrust force. 

0

100

200

300

400

500

600

700

800

900

1000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE PRESSURE, psf .

Test #161 -- Lateral Load -- Klondike (1727) -- 67 psi preload

Test # 179 -- Lateral Load -- Klondike (1727) -- 5.625 in thick -- 56 psi Preload -- Dry Wall
57

 In summary, the abutment stiffness can have a major impact on the transverse load 

capacity of a stopping. A relatively small abutment deformation of approximately 1/10 of an 

inch was shown to reduce the transverse pressure by 80 pct in one example. It was shown 

that the transverse pressure could be accurately predicted by considering the system stiffness 

of the block wall and the abutment if the lateral displacement is known. 

6.7.2 Impact of Strain Softening of Walls to Absorb Ground Deformation 

Although concrete block stoppings have considerable load resistance compared to 

most standing roof support systems, they often cannot fully control the ground movement, 

and therefore are still subject to the closure of the mine entry. Since they are very stiff 

structures, they can absorb relatively little deformation, less than 1 pct strain, prior to 

compression loading failures that destroy the integrity of the structure to function effectively 

Figure 6-14. Comparison of theoretically predicted transverse pressure using the 

assumed 26,000-psi system modulus for the drywall abutment test and the measured 

transverse pressure. 

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, in

TRANSVERSE PRESSURE, psf .

MRS Half-Wall Test # 179 -- Klondike (1727) Block -- Measured Transverse Load

Calculated transverse load from measured lateral displacement -- 26,000 psi elastic modulus
58

for ventilation control (Burke, 2004 and Kawenski, 1966). Figure 6-15 shows a photo of a 

section of a stopping wall damaged from closure of the mine opening. 

 In such conditions, some sort of strain softening material is typically incorporated into 

the construction to extend the life of a block stopping by allowing the wall to absorb some 

deformation without developing excessive compressive stresses that lead to premature 

failure. Currently, the most commonly used material is expanded polystyrene foam formed 

into squeeze blocks or planks that are sandwiched between one or more courses of a block 

stopping. Figure 6-16 shows a 4-ft-wide section of a stopping wall with a 2-in-thick foam 

plank placed between the top two courses of block, showing the wall before and after failure 

during a laboratory test. Figure 6-17 compares the response of the wall for vertical loading. 

As seen in figure 6-17, the foam increases the displacement at which failure occurs, thereby 

increasing the capability of the wall to yield to the simulated roof-to-floor closure of the mine 

entry. 

Figure 6-15. Damage of a stopping caused by roof-to-floor convergence of a mine entry. 
59

Figure 6-16. Two-inch-thick foam plank used to reduce the stiffness and extend 

the life of a block stopping by allowing the wall to absorb some deformation prior 

to failure. Only vertical loading is applied in this test. 

0

50

100

150

200

250

300

350

400

0.00 0.50 1.00 1.50 2.00 2.50 3.00

VERTICAL DISPLACEMENT, in

VERTICAL LOAD, kips ..

MRS Test -- 4 ft wide wall -- 7 courses high -- no strain softening material

MRS Test -- 4 ft wide wall -- 7 courses high -- 2 in thick foam strain softening material

Figure 6-17. Comparison of a block stopping wall’s response to vertical loading with 

and without a strain softening foam layer. 
60

 Although the foam is effective in enhancing the yield capability of the wall and 

extending the service life of the stopping in response to the closure of the mine opening, what 

does it do to the transverse load capacity of the stopping? As previously demonstrated, the 

transverse load capacity of a stopping is dramatically increased if arching can be established. 

As described in section 6.7.1 in the discussion of abutment stiffness, it was seen that an 

abutment deformation as little as 0.1 inches can degrade the transverse load capacity of a 

stopping by 80 pct (see figure 6-12 and 6-13). Figure 6-10 showed the theoretical 

relationship between the deformation of the abutment and the lateral displacement of the 

wall, and figure 6-6 showed the impact of increasing wall displacement on reducing the 

transverse load capacity of a stopping. The hypothesis developed from this assessment is 

that low-density foam, such as that commonly used in strain softening for mine ventilation 

stoppings, will not preserve the arching loading mechanism, and as such, severely degrade 

the transverse load capacity of the stopping. 

 In order to evaluate this hypothesis, a series of 

half-wall tests in accordance with the protocol developed 

in chapter 4, section 4.2, were conducted in the Mine 

Roof Simulator with foam as a strain softening material. 

The foam utilized in these tests was a 2 lb/cu ft density, 

polystyrene product manufactured by OPCO, Inc. in 

Latrobe, Pennsylvania. The product trade name is MS 

Blox EPS Squeeze Blocks. The foam plank was placed 

between the top two blocks in the half-wall as shown in 

figure 6-18. 

Figure 6-18. Half-wall test in the 

MRS with 2-inch-thick foam 

plank placed between the top two 

blocks.
61

 Figure 6-19 compares the results of two half-wall tests conducted in the MRS, one with 

the foam as shown in figure 6-18 and an identical block column without any foam. The peak 

transverse pressure without foam was 510 psf, while the peak transverse pressure with the 

foam-softening layer was 28 psf. The foam reduced the transverse load capacity in this test 

by 95 pct. 

 Further analysis reveals why the foam degraded the transverse pressure so severely. 

The low density foam has a very low modulus of elasticity. The stress-strain behavior is 

shown in figure 6-20 for a 12-inch long section of foam plank as tested in a MTS rock testing 

load frame. As seen in this figure, the modulus of elasticity is negligible through nearly 20 

pct strain. This means that the foam provides very little resistance to the extension of the 

tension side of the wall as it rotates about the hinge points under the application of transverse 

pressure. The consequence of this is that little arching thrust will be developed and excessive 

lateral displacement will occur, the combination of which severely limits the transverse load 

capacity of the wall. Figure 6-21 shows the condition of the half-wall tested in the MRS 

Figure 6-19. Comparison of transverse pressure development from half-wall testing in 

the MRS on a block wall with and without a strain-softening foam layer. 

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, in

TRANSVERSE PRESSURE, psf ..

MRS Half-wall Test # SD1 -- 45.75 in height -- 2 in foam strain softening material

MRS Half-wall Test #46 -- 45.75 in height -- no strain softening
62

shown at 3 inches of lateral displacement and a second wall after 7 inches of lateral 

displacement. It is seen from figure 6-21 that the hinge is formed below the foam layer as 

opposed to the interface of the top block with the upper platen of the load frame. This 

indicates that the foam is unable to transfer any significant load between the two blocks, thus 

limiting the development of the arching thrust. 

0

100

200

300

400

500

600

700

800

900

1,000

0 10 20 30 40 50 60

% Strain

Vertical Stress (psi)

EPS Squeeze Block -- 2 lb density foam -- 2 in thick

Figure 6-20. Stress-strain relationship for ESP Squeeze Block foam plank 

commonly used in stoppings to reduce the stiffness of the wall. 
63

 A closer examination of the transverse pressure that does develop with the foam 

reveals that the peak loading occurred at 0.57 inches of lateral displacement (see figure 6-19). 

At first, this seems contradictory to the theory presented thus far, which would suggest that 

the low modulus foam would result in a large lateral displacement at the peak transverse 

pressure. However, the foam is so soft that the stress distribution across the foam is more 

uniform and extends over the full width of the block. By examining the photo in figure 6-21, 

it is seen that the top block in contact with the foam does not rotate away from the upper 

platen of the load frame unlike the bottom block. The rotation of the wall is occurring at the 

block below the foam layer. It too remains fully in contact with the foam across its entire 

area. This implies that the resultant thrust, although very small, is acting more as a 

distributed load across the entire block and the resultant is closer to the middle of the block 

compared to conditions without the foam. In this sense, it is similar to the preloading theory 

explained in the next section. 

Figure 6-21. Half-walls with foam between the top two blocks shown with 3 

inches of lateral displacement (left) and 7 inches of lateral displacement (right). 
64

6.7.3 Impact of Ground Pressures From Roof to Floor Convergence 

Even without arching, a superimposed axial or vertical load acting on a stopping wall 

can greatly increase the transverse load capacity of the stopping. This can be analyzed using 

conventional beam bending analysis. In essence, vertical loading applied to a wall will act to 

offset the lack of tensile strength in the joints of a dry-stacking block stopping. The vertical 

load resists the moment induced by the application of transverse pressure. This condition can 

be expressed by equation 6.12 (Drysdale, 1994). 

 (6.12)

Where ρ = transverse pressure, psf, 

 S = section modulus, in3

/in of wall width or t2/6 where t is the wall 

 thickness, 

 Fv = axial load per unit area, psi, and 

 L = wall height, in. 

 As an example, consider a 5-ft-high wall constructed from conventional concrete block 

with a thickness of 5.625 inches. This is equivalent to the wall evaluated in test #46 

previously analyzed. Using equation 6.12, if a 400-psi pressure is applied to the wall from 

the ground movement, the transverse load capacity (ρ) of a stopping wall would be computed 

as 675 psf. Without the ground pressure, this wall would have no transverse load capacity if 

the weight of the block were ignored as the term Fv would be zero. 

 (6.13) 

 Next, the impact of ground pressure from the perspective of arching conditions will be 

examined. Arching relies on the force couple developed from the thrust force to provide the 

transverse load capacity in a stopping wall. When ground pressure is applied to a stopping, it 

can be assumed that a uniform load distribution is acting on the top and bottom contact 

surfaces of the wall. The resultant force under these conditions is acting along the centerline 

of the wall thickness. In the arching analysis conducted in chapter 5, the resultant thrust load 

from the arching was assumed to act a distance of one-tenth the wall thickness from the edge 

144

L

8

ρ S Fv 2 = × × ×

144 675 psf 60

8 400

6

5.625

ρ 2

2

= × × × =
65

of the block. When these two loading elements, arching thrust and ground pressure, are 

combined, the resultant force will act somewhere between the two, moving more towards the 

block centerline as the magnitude of the ground pressure increases (see figure 6-22). 

 

 Equation 5.1, which satisfies the moment equilibrium requirement for the half-wall 

loading, can be used to back calculate the position of the resultant thrust if the thrust force 

(P), lateral displacement (δh), and horizontal force (HF) are known. The wall thickness and 

height must also be known, allowing the equation to be solved for an adjusted factor to 

replace the “0.8” term. Hence, by substituting the variable “d” for the value 0.8, the equation 

can then be solved for “d” to determine the adjusted factor for the position of the resultant 

thrust force that will satisfy moment equilibrium for a specific axial preload. 

+ =

FV

FV

P

P

Pm

Pm

Resultant load from

ground pressure

Resultant load 

from arching

Modified 

resultant load 

+ =

FV

FV

P

P

Pm

Pm

+ =

FV

FV

P

P

Pm

Pm

Resultant load from

ground pressure

Resultant load 

from arching

Modified 

resultant load 

Resultant load from

ground pressure

Resultant load 

from arching

Modified 

resultant load 

Figure 6-22. Combining arching with axial loading caused by ground pressures 

moves the resultant arch thrust force more towards the centerline of the wall. 
66

 (6.14)

Where P = arching thrust, lbs, 

 t = thickness of the wall, in, 

 δh = lateral displacement of wall at the mid span, in, 

 HF = horizontal force, lbs, and 

 L/2 = half-wall height, in. 

 (6.15) 

 (6.16) 

 (6.17) 

Where d = position factor for resultant arching thrust, 

Pm = modified resultant arching thrust, lbs, 

 t = thickness of the wall, in, 

 δh = lateral displacement of wall at the mid span, in, 

 HF = horizontal force, lbs, and 

 L/2 = half-wall height, in. 

 The result of the preload will be that the maximum transverse pressure will occur at a 

smaller lateral displacement. An example for a 30-in half-wall height with conventional 

Portland cement concrete block is shown in figure 6-23. In this example, the lateral 

displacement at which the maximum transverse pressure occurred decreased from 1.06 

inches to 0.23 inches when the preload was increased from 0 to 491 psi. In essence, the axial 

load makes it more difficult for the half wall to rotate due to the increased compressive forces 

acting on the wall. Thus, the transverse pressure is generated more quickly relative to the 

lateral displacement of the wall. 

P (0.8 t δ ) HF L/2 × × − h = ×

Pm ×(d× t − δh ) = HF× L/2

Pm × d × t − Pm × δh = HF× L/2

P t

HF L/2 P δ d

m

m h

×

× + × =
67

 Preloading should also be examined from the perspective of the abutment stiffness and 

deformation. If the wall strength is sufficient to transfer the loading to the mine roof and 

floor, then a concern might be any damage to the immediate roof and floor may significantly 

degrade the arching capability of the wall. The highest strength stopping blocks have 

material compressive strengths of less than 3,000 psi and most have material compressive 

strengths of less than 1,500 psi. Since the wall structure is able to sustain stresses of only 

about 50 pct of the materials strength, in most cases the wall structure will be damaged long 

before the mine roof or floor material strength is exceeded. 

 Boussinesq analyses of linear elastic foundation responses also show that the stress is 

dissipated or attenuated quickly with depth below the contact area. At a depth of twice the 

width of the loaded area, the stress is less than 10 pct of the initial vertical stress and equals 

90 pct of the initial stress at a depth equal to one-half the radius of the contact area. For a 

stopping wall that is 6-inches thick, this means that the 90 pct of the stress is relieved with 

the first 12 inches of ground (Perloff, 1976). Hence, the immediate roof or floor material 

properties are the most important when considering the abutment stiffness and its impact on 

Figure 6-23. Peak transverse pressure occurs at less lateral displacement when 

preload is applied to the wall. 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE PRESSURE, psf .

Test #102

Test # 109 (Preload 155 psi)

Test # 108 (Preload 280 psi)

Test # 115 (Preload 428 psi)

Test # 120 (Preload 491 psi)

(Preload 51 psi) 
68

arching of a stopping wall. For layered strata that is common in coal mines, the presence of a 

strong layer below a weak immediate layer will focus more of the stress in the immediate 

layer than that indicated in figure 6-24. Even so, the relatively weak block material 

compared to the strength of mine roof or floor material is likely to prevent failure or 

punching of the block into the mine roof and floor. 

 

 Although it is suggested from the previous assessment that arching is likely to occur 

under almost all geologic conditions in a coal mine, it is not to say that arching will not be 

degraded from the deformation of the immediate mine roof and floor. In fact, any 

deformation including the elastic response of the roof and floor abutments will reduce the 

transverse load capacity by causing more lateral displacement of the wall. However, a 

comparison of modulus between the stopping block wall and the ground also suggests that 

Figure 6-24. Boussinesq diagram shows that 90 pct of the 

stress is relieved within the first 12 inches of ground for a 

6-in-thick stopping.
69

the deformations are likely to be small. For example, the modulus of coal is generally about 

300,000 psi and the modulus of overburden rock can reach as high as 3,000,000 psi. These 

are 1 to 2 orders of magnitude higher than the effective modulus of a block stopping wall. 

Assuming an axial pressure of 300 psi acting on a stopping, this equates to only 0.1 pct strain 

in an abutment with a modulus of 300,000 psi. If the abutment is 12 inches thick in 

accordance with the Boussinesq stress analysis, then this translates into only 0.012 inches of 

deformation. This is an order of magnitude less deformation than will occur in the wall itself 

at the peak transverse pressure, so the impact will be small, i.e. less than 10 pct in most cases 

depending on the wall geometry and wall modulus. 

 If the abutment response is purely elastic, the preload or pressure applied by the wall 

will not change the deformation response of the abutment. If however, the load-deformation 

characteristic of the roof or floor material is inelastic, then the preloading may help to stiffen 

the response of the abutments, and thereby enhance the transverse load capacity of the 

stopping. 

6.6.4 Impact of Wedging the Wall Against the Mine Roof 

 A common practice when constructing a stopping wall is to use wooden wedges to 

tighten the wall against the mine roof. Since the wedges are installed at the hinge point, 

proper installation is critical to preserve the arching action of the wall during transverse 

loading. The wedges should always be driven in from the low pressure side of the stopping if 

done from one direction only, or they should be driven from both sides. This is necessary to 

ensure contact with the face of the wall where the arching hinge will occur. If the wedges are 

driven from the high pressure side of the stopping only, there will be a gap at the hinge 

contact face which will completely destroy the arching capability (see figure 6-25). Figure 

6-26 shows this effect including wedges that are driven from the ends of the block, which 

would be unlikely but possible if the wall was built in step form. As seen in the figure, the 

transverse pressure is reduced from 500 psf to less than 20 psf when the wedges are applied 

from the high-pressure side. Figure 6-27 shows that if properly installed, wooden wedges 

will provide equal transverse pressure capability to walls that do not have any wedges but are 

in tight contact with the abutment. Some reduction in transverse pressure is realized when a 

softer pine plank board is used to interface between the top of the wall and the roof abutment. 
70

Finally, figure 6-27 shows that the arching thrust is also preserved when the wedges are 

properly applied. 

Figure 6-25. Wedges driven into stopping high pressure side allow gap to occur at 

tension side of stopping which completely destroys arching capability. 

Transverse 

Pressure 

Figure 6-26. Comparison of direction of wedging on top of block stopping relative 

to impact on transverse load capacity.

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE PRESSURE, psf .

Test #126 -- Wedges driven from low pressure side

Test #127 -- Wedges driven from low pressure side

Test #128 -- Wedges driven from sides
71

Figure 6-28. Arching thrust can also be preserved if wedging is done properly. 

0

5

10

15

20

25

30

35

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, in

THRUST LOAD, kips ..

Test # 126 -- Wedges driven from Low Pressure side

Test # 131 -- 1.5 inch wooden plank

Test # 46 -- No wedges -- Thrust Load -- Klondike (1330) 

Figure 6-27. Transverse load capacity is preserved when wedges are driven from the 

low pressure side of the stopping. 

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE LOAD, psf ..

Test # 126 -- Wedges driven from low pressure side

Test #131 -- 1.5 in wood plank

Test #46 -- No wedges
72

6.6.5 Impact of Preloading the Stopping with Grout Bags 

 Within the past 5 years, grout bags have been utilized to seal the perimeter around a 

stopping (see figure 6-29). The bags can be made in various lengths, but typically are about 

4 feet long and a few inches wider than the thickness of the stopping. The bags are 

pressurized with a fast setting cementitious grout that expands the bag to fill the gap between 

the wall and surrounding coal or rock. They are pressurized by a hand pump with up to 50 

psi of pressure to provide a preload to the stopping wall. Only about 50 pct of the preload is 

sustained with creep in the grout accounting for the loss of load with time. 

 Figure 6-30 shows that the grout bag softens the response of the wall, and thereby can 

delay the failure induced by the ground convergence. In this laboratory example, a 4-ft-wide 

wall was tested with vertical loading, and the grout bag doubled the displacement at which 

failure of the block wall occurred (0.3 compared to 0.6 inches). It is also seen from the chart 

that the wall failed at less load when the grout bag was in place (310 kips compared to 445 

kips). Since the grout bag would tend provide a uniform load distribution across the block 

wall and alleviate stress concentrations from block tolerances at the contact interface, the 

reduction in loading must be due to asymmetric loading across the thickness of the wall 

induced by the bag due to stretching of the grout bag. 

Figure 6-29. Installation of seal with preloading grout bags used to seal around the 

perimeter of the block wall. 
73

 Tests were also conducted in the Mine Roof 

Simulator on a 4-ft-wide half wall to determine the 

impact of the grout bag on the transverse load capacity of 

the stopping (see figure 6-31). Bags were placed on top 

of the half-walls with a 1.5 in gap between the top of the 

wall and the load frame platen. The bags were 

pressurized to about 25 psi to fill the gap. The bags were 

then removed and allowed to cure for 10 to 15 days prior 

to the transverse pressure tests. A total of 7 tests were 

conducted with preload pressures induced by the load 

frame ranging from 11 to 435 psi. The results are shown 

in figure 6-32 along with equivalent tests conducted 

without the grout bags. The bags reduced the boundary 

stiffness, which resulted in less transverse pressure. The 

transverse pressure without the bags was 2 to 3 times 

0

50

100

150

200

250

300

350

400

450

500

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

VERTICAL DISPLACEMENT, inches

VERTICAL LOAD, kips ...

Test #268 -- Vertical Force Only -- Klondike 1727 psi -- 62 inches long -- 8 Courses - Cure Time 2 Days

Test #269 -- Vertical Force Only -- Klondike 1727 psi -- 62 inches long -- 8 Courses - No Bag

Figure 6-30. Grout bag increased the amount of displacement that can occur before 

the block wall fails. 

Figure 6-31. Testing of a halfwall with grout bag in the 

Mine Roof Simulator. 
74

greater at a given preload than measured with the grout bags. However, the grout bags would 

have prevented failure of the stopping by absorbing the ground deformation. The closure 

absorbed by the grout bag during the preloading ranged from 0.35 to 0.55 inches as shown in 

figure 6-33. 

y = 0.0005x + 0.34

R2

 = 0.86

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0 50 100 150 200 250 300 350 400 450 500

PRELOAD, psi

VERTICAL CLOSURE, in .

Figure 6-33. Closure absorbed by grout bag during prestressing. 

Figure 6-32. Comparison of laboratory tests with and without the grout bags. 

0

500

1,000

1,500

2,000

2,500

0 50 100 150 200 250 300 350 400 450 500

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

 Klondike Block (1727 psi) -- 62 in long -- 7.5 in thick -- 8 Courses High -- Strata Grout Bag 

 Klondike Block (1727 psi) -- 62 in long -- 7.5 in thick -- 8 Courses High -- No Bags 

 Klondike Block (1330 psi) -- 16 in long -- 7.5 in thick -- 8 Courses High -- No Bags 
75

CHAPTER 7: DEVELOPMENT OF PREDICTIVE TRANSVERSE 

PRESSSURE MODELS 

 The final goal is to be able to predict the transverse pressure capacity of a stopping. In 

order to do this, predictive models are developed based on the theoretical relationships 

presented in chapters 5 and 6. Two models have been developed: (1) prediction model where 

the lateral displacement is known, and (2) predictive model where the arching thrust force is 

known. A description of these two models including examples is provided. 

7.1 PREDICTING THE TRANSVERSE PRESSURE FROM THE LATERAL 

WALL DISPLACEMENT 

 The first procedure assumes that the lateral displacement is known or measured. The 

flowchart shown in figure 7-1 describes the procedure. The first step is to calculate the 

deformation that occurs in the hinge areas. This is accomplished from the geometrical 

relationship between the lateral displacement and hinge point deformation. Next, the arching 

thrust can be computed from the stiffness of the wall and the mine roof and floor. From the 

moment equilibrium requirements, the horizontal force acting on the base of the wall can be 

calculated and transformed into a resultant force, which can be normalized to the transverse 

pressure acting on the wall. 

Figure 7-1. Flowchart for predicting the transverse pressure capacity of stoppings 

from the lateral wall displacement. 

8

2 L 4 L 32 t 16

y

2

h h

2 × ± × × ×δ + ×δ = -

L / 2

2 A E y P

× × × =

( )

L / 2

P 0.8 t HF h × × − δ =

Lateral displacement Measured (δh) 

Procedure Formula Used 

Calculate “hinged point 

deformation” 

Calculate arch thrust 

Calculate horizontal 

force 

w L / 2

2 HF

×

×

ρ = Calculate transverse 

pressure 
76

7.1.1 Example using Rigid Boundary Conditions. 

 The example chosen is a stopping constructed from conventional, Portland cement 

block, manufactured by Klondike Block and Masonry Supplies, Inc. A 6-course-high halfwall was utilized in the test providing a half-wall height of 45.75 inches, which equates to a 

full-wall height of 91.50 inches. The wall was 5.625 inches thick. The Klondike block has a 

compressive strength of 1,330 psi. The half-wall response from the biaxial test conducted in 

the Mine Roof Simulator is shown in figure 7-2. As seen in the figure, the peak lateral 

loading occurred at 1.92 inches of lateral displacement. The thrust force at the peak lateral 

loading was 22.8 kips as shown by the blue curve in figure 7-2. 

0

200

400

600

800

1,000

1,200

1,400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs ..

0

5

10

15

20

25

30

35

THRUST LOAD, kips

Test #46 -- Lateral Load -- Klondike (1330) -- 5.625 in thick -- 85 psi preload

Test #46 -- Thrust Load -- Klondike (1330) -- 5.625 in thick -- 85 psi preload

Figure 7-2 MRS test of a 6-course-high half-wall showing the measured lateral 

and thrust load development as a function of the applied lateral displacement.
77

0.098 inches

8

2 91.5 4 91.5 32 5.625 1.92 16 1.92

y

2 2

= × − × − × × + × =

( ) 23,134 lbs

45.75

2 5.625 16 60,000 0.098

L / 2

2 A E y P = × × × × = × × × =

( ) ( ) 1,305 lbs

45.75

23,134 0.8 5.625 1.92

L/ 2

P 0.8 t HF h = × × − = × × − δ =

144 514 psf 16 45.75

2 1,305 144

w L / 2

2 HF

× = ×

×

× = ×

×

ρ =

 The hinge point deformation at a lateral displacement of 1.92 inches where the peak 

lateral loading occurred is calculated using equation 7.1 to be 0.098 inches. 

 (7.1) 

 The arching thrust can then be calculated from equation 7.2 using the hinge point 

deformation calculated in equation 7.1 and an elastic modulus of 60,000 psi for this particular 

block material. The modulus can be determined from laboratory testing or can be back 

calculated from the transverse pressure test results provided in this study. A unit block 

arching thrust of 23,134 lbs at the peak lateral loading was computed for this example. 

 (7.2)

Where P = thrust load per unit block width, lbs, 

 A = axial loading area of the wall, in2

, 

 E = elastic modulus, psi, 

 y = deformation in each of two crush zones on half-wall section, in, and 

 L = full-wall height, in. 

 Equation 7.3 is then used to compute the horizontal force acting on the half-wall. The 

result is 1,305 lbs. This compares to the measured horizontal load from the half-wall test of 

1,296 lbs, an error of only 0.7 pct. 

 (7.3) 

The transverse pressure per unit area of the wall can then be determined using equation 7.4. 

 (7.4)

 

 
78

 Figure 7-3 compares the calculated thrust force as a function of the lateral displacement 

to the measured thrust force for test #46. As seen in this figure, the calculated thrust force 

closely predicts the measured thrust force, until near the end of the test when the measured 

thrust force peaked and began to decline. The peak thrust force can be caused from either the 

mechanics of the wall behavior (i.e. moment equilibrium as described in figure 5-1) or failure 

of the material. The calculated thrust force is determined from the elastic response of block 

material and does not consider the strength of the block. The predicted thrust force simply 

continues to increase with increasing lateral displacement as a function of the material 

modulus. In this particular test, since the calculated thrust force closely matched the 

measured thrust force, the response of the wall was accurately predicted throughout the test 

(through the full range of the applied lateral displacement) as shown in figure 7-3. This also 

indicates that the block material strength was not controlling the transverse pressure in this 

particular example. The transverse pressure (see figure 7-4) was limited by the lateral 

displacement in this case and not the block strength. This implies that there is optimum 

block strength for a particular material modulus. 

0

5

10

15

20

25

30

35

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

THRUST LOAD, kips

Test #46 -- Thrust Load -- Klondike (1330) -- 5.625 in thick -- 85 psi preload

Calculated thrust load based on δh and y -- no material failure

Figure 7-3. Half-wall test with theoretically calculated thrust shown by the blue line. 
79

 Another example is depicted in figure 7-5. In this case, the predicted thrust force again 

closely matches the measured thrust force until the measured force peaks and begins to 

decline. The peak thrust force is in this case is most likely caused by failure of the material. 

The material has a compressive strength of 1,330 psi. The measured thrust force was 

approximately 37,000 lbs acting in this particular test across a single concrete block since the 

half-wall was only one block wide. Since the wall is rotating, forming the two hinges in the 

half-wall test (see figure 4-1), the contact area of the hinge zone can vary and was not 

measurable in the test arrangement. However, if it is assumed that the block material is 

failing, then the width of the contact zone can be calculated from equation 7.5. The 

calculated width of the hinge zone of 1.74 inches seems reasonable, and it can be speculated 

that the load exceeding the strength of the material caused the peak thrust force. As the 

lateral displacement progresses beyond the peak thrust force, moment equilibrium 

requirements control the thrust force response. 

 (7.5) 1.74inches

1,330 16

37,000

f w

P

t

c

cr = × = × =

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE PRESSURE, psf .

MRS Half-Wall Test #46 -- Klondike (1330) Block -- Measured Transverse Pressure

Calculated transverse Pressure from measured lateral displacement -- 60,000 psi Elastic

Modulus

Figure 7-4. Comparison of the measured transverse pressure and the calculated 

transverse pressure. 
80

Where tcr = hinge zone width, in, 

 P = thrust load, lbs, 

 fc = compressive strength of the material, psi, and 

 w = width of the wall, in. 

 Figure 7-6 shows the transverse pressure as determined from the MRS half-wall test 

and the predicted transverse pressure using equation 5.4. Unlike test #46 where the 

transverse pressure was accurately predicted though the full range of applied lateral 

displacement, the wall response was accurately predicted up to and including the peak 

transverse pressure, but since there was no limit to the calculated thrust force, the post-peak 

response of the wall was not accurately predicted in this test. Figure 7-6 shows the predicted 

transverse pressure with the thrust force limited to 30,858 lbs. Interestingly, limiting the 

thrust force to a constant value is essentially implying an elastic-plastic material response 

(see figure 7-7). As seen in figure 7-8, the constant thrust force resulted in a linear decrease 

in the post-peak transverse pressure. This suggests that the post-peak behavior is governed 

primarily by the material failure. 

0

10

20

30

40

50

60

70

80

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

THRUST LOAD, kips

Test #102 -- Thrust Load -- Klondike (1330) -- 5.625 in thick -- 51 psi preload

Calculated thrust load based on δh and y -- no material failure"

Figure 7-5. Four-course (30 in) high half-wall test result including comparison of the 

measured and theoretically calculated thrust load. 
81

0

500

1,000

1,500

2,000

2,500

3,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE PRESSURE, psf .

MRS Half-wall Test # 102 -- Klondike 1330 Block -- Measured Transverse Pressure

Calulated transverse pressure from measured lateral displacement -- 60,000 psi modulus

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

THRUST LOAD, kips

Thrust load limited to 30,858 lbs

Figure 7-7. The thrust load is limited to 30,858 lbs based on the observed axial 

load at the measured peak transverse pressure from the MRS test. 

Figure 7-6. Comparison of the measured transverse pressure with that calculated 

theoretically from the lateral displacement. 
82

7.1.2 Example using Non-Rigid Boundary Conditions. 

 If the boundary is not rigid, the same basic theory applies. As described in the section 

on theoretical factors, the system stiffness can be defined using equation 6.11 and referenced 

here as equation 7.6. A system modulus can also be computed using equation 7.7. 

 

 (7.6) 

 (7.7) 

wall abutment

wall abutment

System K K

K K K

+

× =

1 2 2 1

1 2 1 2

c L E L E

E E (L L ) E

× + ×

× × + =

Figure 7-8. Limiting the thrust load improves the post-peak theoretical prediction of the 

transverse pressure in this half-wall MRS test. 

0

500

1,000

1,500

2,000

2,500

3,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE PRESSURE, psf .

MRS Half-wall Test # 102 -- Klondike 1330 Block -- Measured Transverse Pressure

Calulated transverse pressure from measured lateral displacement -- 60,000 psi modulus

Calculated transverse load with axial thrust load limited to 31,500 lbs
83

Where: L1 = thickness of the roof or floor material, in, 

 L2 = height of the half-wall, in, 

 E1 = Young’s modulus of the wall material, psi, and 

 E2 = Young’s modulus of the roof or floor material, psi. 

 

 Reviewing the example provided in the Chapter 6 using the drywall as the roof contact 

material, the predictive model can be explained. The drywall has a relatively low modulus of 

420 psi compared to the 80,000 psi for the concrete block. Using equation 7.7, the system 

modulus is computed as 25,995 psi. Using the system of equations documented in the 

flowchart in figure 7-1, the transverse pressure can be computed as a function of the lateral 

displacement as shown in figure 7-9. 

Figure 7-9. Comparison of theoretically predicted transverse pressure using the 

26,000 psi system modulus for the drywall abutment test and the measured 

transverse pressure. 

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE PRESSURE, psf ...

MRS Half-Wall Test # 179 -- Klondike (1727) Block -- Measured Transverse Load

Calculated transverse load from measured lateral displacement -- 26,000 psi elastic

modulus
84

Figure 7-10. Flowchart for predicting the transverse pressure capacity of stoppings 

from the lateral displacement with preload applied from ground pressures. 

7.1.3 Example considering preloading of the wall from ground pressures. 

 The flowchart shown in figure 7-10 can be used to determine the transverse pressure if 

the wall is preloaded from convergence produced by the ground pressures. The flow chart is 

similar to that depicted in figure 7-1 with two additional steps added as highlighted in the 

yellow text boxes. The additional requirements are that the preload needs to be measured or 

computed and the preload needs to be added to the arching thrust developed from the wall 

rotation. 

8

2 L 4 L 32 t 16

y

2

h h

2 × ± × − × ×δ + ×δ =

Lateral displacement 

Calculate arch thrust 

Calculate horizontal 

force 

Calculate transverse 

pressure w L/ 2

2 HF

×

×

ρ =

Measured (δh) 

Procedure Formula Used 

Calculate “hinge point 

deformation” 

Add preload to arch 

thrust 

Pm = Parch + PL

L / 2

2 A E y Parch

× × × =

Determine preload Measured or 2 PL = ∆L×k

( )

L/ 2

P d t HF m h × × − δ =
85

 An example considering the same wall conditions as the first example documented in 

section 7.1.1 will be examined for the preload condition. The half-wall height is again 45.75 

inches and the wall is constructed from the same Portland cement block manufactured by 

Klondike Block and Brick Company. In this case, a preload of 373 psi is measured equating 

to a unit block preload of 33.57 kips. The laboratory test result is shown in figure 7-11. 

 The preload could also be determined from the crosscut convergence if the axial 

stiffness of the wall is known (see equation 7.8). For the wall construction considered in this 

example, tests in the Mine Roof Simulator have shown that the wall exhibits a biaxial 

stiffness (see figure 7-12). The initial response is soft and somewhat nonlinear. Once the 

block contact becomes uniform through the initial loading, the response is stiffer. In this 

case, a stiffness of 400 kips/inch is computed for a single block column half-wall constructed 

from conventional Portland cement block. The initial load prior to the stiff response could be 

added to the preload assessment to provide a more accurate prediction of preload based on 

convergence (see equation 7.8). If the convergence is less than 0.16 inches, the stiffness is 

computed from the initial response of the wall using equation 7.9. 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

6

12

18

24

30

36

42

THRUST LOAD, kips

Test #74 -- Lateral Load -- Klondike (1300) -- 5.625 in thick -- 373 psi preload

Test #74 -- Thrust Load -- Klondike (1300) -- 5.625 in thick -- 373 psi preload

Figure 7-11. MRS test of 45.75-inch-high half-wall with 373 psi of preload. 
86

0

10

20

30

40

50

60

70

80

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

VERTICAL DISPLACEMENT, inches

VERTICAL LOAD, kips .

k = 80/0.20 = 400 kips/inch

k = 5/0.16 = 310 kips/inch

 (7.8) 

 

 (7.9) 

Where P = Axial preload on unit block, kips, 

 ∆L = Roof to floor convergence, in, 

 k1 = initial stiffness of the stopping, kips/in, and 

 k2 = final stiffness of the stopping, kips/in. 

 

( ) 16 k1 PL = 5 + ∆L − 0. ×

PL = ∆L× k2

If ∆L > 0.16 in 

If ∆L < 0.16 in 

Figure 7-12. Laboratory test to determine stiffness of block column. Example 

shows single block column constructed from six courses of Klondike block. 
87

 The next step in the process is to compute the arch thrust force. This is computed in 

the same manner as the first example through the geometric relationship between the 

measured lateral displacement and the hinge point deformation. In this case, the hinge zone 

deformation is computed as 0.030 inches as shown in equation 7.10. From this, the arch 

thrust force can be computed as 7,150 lbs using equation 7.11. 

 (7.10) 

 (7.11) 

 

 (7.12) 

 The next step (see flowchart in figure 7-10) is to calculate the horizontal force acting to 

produce the transverse pressure of the stopping. In order to do this, the thrust adjustment 

factor (d) must be determined so that the modified thrust resultant force location can be 

incorporated into the equation. If the lateral load and thrust force were known, the thrust 

adjustment factor as a function of the lateral displacement could be calculated. Figure 7-13 

displays the thrust adjustment factor for the test #74 examined in this example. As shown 

figure 7-13, the thrust adjustment factor moves outward from the center of the block toward 

the ends of the block thickness as the lateral displacement initially occurs. It peaks at 0.8 

(the factor used when there is no preload), and then declines back below 0.8 toward 0.7 as the 

lateral displacement continues. Using this thrust adjustment factor, the transverse pressure 

curve can be duplicated (see figure 7-14) using the predictive equations for horizontal force 

and transverse pressure shown in the flowchart in figure 7-10. 

 

 (7.13) 

Where Pm = modified resultant arching thrust, lbs, 

 t = thickness of the wall, in, 

 δh = lateral displacement of wall at the mid span, in, 

 HF = horizontal force, lbs, and 

 L/2 = half-wall height, in. 

0.030inches

8

2 91.5 4 91.5 32 5.625 0.52 16 0.52

y

2 2

= × − × − × × + × =

( ) 7,150 lbs

45.75

2 5.625 16 60,000 0.030

L/ 2

2 A E y P = × × × × = × × × =

P P PL 7.15 33.57 40.72 kips m = arch + = + =

P t

HF L / 2 P d

m

m h

×

× + × δ =
88

 

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

THRUST ADJUSMENT FACTOR (d) ..

Test #74 -- Klondike (1330) block -- 5.625 in thick -- 45.75 in height -- 373 psi preload

Figure 7-13. Plot of the change in the thrust adjustment factor as a function 

of lateral displacement of a half-wall test conducted in the MRS. 

0

200

400

600

800

1,000

1,200

1,400

1,600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE PRESSURE, psf . ..

Test # 74 (Preload 373 psi) Transverse Pressure using calculated d, Lateral Disp
89

 However, the horizontal force is not known, therefore, the thrust adjustment factor 

cannot be computed for the complete loading cycle that will allow prediction of the full 

transverse pressure cycle. The peak transverse pressure can still be predicted by developing 

a regression equation for the thrust adjustment factor at the peak loading based on laboratory 

test results. Table 7-1 summarizes half-wall tests conducted in the Mine Roof Simulator for 

45-in-high, half-wall tests using the arching test protocol described in Chapter 4. A vertical 

preload was applied to the wall prior to the initiation of the lateral displacement of the base 

of the half wall. This preload simulates the axial loading that would be caused by ground 

pressures. The preload in this series of tests was increased from 0 to 763 psi. The calculated 

thrust adjustment factor at the maximum transverse pressure is shown in the last column of 

the table, and compares to the “0.8” term used in the initial analysis without preloading. 

Table 7-1. MRS Half-wall tests on conventional concrete block with preload applied. 

Test 

No. 

Block 

Type 

Wall 

Thickness 

(in) 

Half-wall 

Height 

(in) 

Preload 

(psi) 

Peak 

Lateral 

Load 

(lb) 

Lateral 

disp (in) 

Thrust 

(kips) 

Thrust 

Adjustment 

Factor 

60 Klondike 5.625 45.75 28 1,120 2.05 20.48 0.809 

59 Klondike 5.625 45.75 43 1,032 1.88 19.23 0.771 

46 Klondike 5.625 45.75 85 1,296 1.92 22.79 0.804 

45 Klondike 5.625 45.75 90 978 2.38 19.30 0.835 

34 Klondike 5.625 45.75 109 1,246 2.10 22.11 0.832 

36 Klondike 5.625 45.75 122 1,597 1.15 25.33 0.717 

35 Klondike 5.625 45.75 139 1,795 1.27 28.87 0.731 

37 Klondike 5.625 45.75 202 1,992 0.97 32.01 0.678 

38 Klondike 5.625 45.75 247 1,579 0.98 37.92 0.513 

63 Klondike 5.625 45.75 252 2,268 0.46 29.52 0.707 

61 Klondike 5.625 45.75 313 2,359 0.33 34.02 0.623 

74 Klondike 5.625 45.75 373 3,166 0.52 37.76 0.774 

75 Klondike 5.625 45.75 390 3,617 0.41 40.59 0.798 

76 Klondike 5.625 45.75 474 3,365 0.44 43.47 0.708 

77 Klondike 5.625 45.75 471 3,831 0.72 52.38 0.722 

78 Klondike 5.625 45.75 577 2,499 0.44 45.54 0.525 

79 Klondike 5.625 45.75 534 2,779 0.56 53.48 0.620 

81 Klondike 5.625 45.75 568 3,358 0.71 47.02 0.707 

82 Klondike 5.625 45.75 618 3,922 0.65 59.35 0.652 

83 Klondike 5.625 45.75 623 3,960 0.45 56.30 0.652 

85 Klondike 5.625 45.75 763 3,776 0.45 61.08 0.583 
90

( ) ( ) 144 1,190 psf 16 45.75

2 40.72 1000 .0042 40.72 0.8678 5.625 0.52

2 × = ×

× × × − × + × − ρ =

 As speculated, the adjustment factor, which is an indication of the position of resultant 

thrust, decreases with increasing preload pressure. A plot of the adjustment factor as a 

function of total axial load is shown in figure 7-15, and a trendline based on a linear 

regression analysis of the data is added to evaluate the correlation between the two 

parameters. There is considerable scatter in the data and the R2 factor of 0.45 does not 

suggest a strong correlation, but the trend is towards a decreasing value for the thrust position 

factor as the total thrust increases. 

Substituting the trendline regression equation for the 0.8 term yields equation 7.14. 

The transverse pressure can then be calculated from the measured thrust load and lateral 

displacement using this equation. For the example being discussed, the peak transverse 

pressure is computed as 1,190 psf. This compares with the measured transverse pressure of 

1,244 psf, an error of 4 pct.

 (7.14) 

 (7.15) 

y = -0.0042x + 0.87

R2 = 0.45

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0.800

0.850

0.900

20 25 30 35 40 45 50 55 60 65

TOTAL AXIAL LOAD = PRELOAD + ARCH LOAD, kips

THRUST ADJUSTMENT FACTOR (d) ...

Figure 7-15. Regression trendline developed for the thrust adjustment factor for 

45-in half-wall tests conducted in the MRS. 

( )

( )

( ) 144

w L/2

2 P [ .0042 P 0.8678 t δ ] 144

w L/2

2 P (0.8 t δ ) ρ 2

m m h

2

h ×

×

× × − × + × − × = ×

× × × − =
91

Figure 7-16 shows that the calculated transverse pressure using this prediction 

methodology is very well correlated to the preload. Figure 7-17 illustrates the comparison 

between the measured peak transverse pressure and the calculated transverse pressure for the 

set of tests documented in table 7-1. The graph shows that the calculated transverse pressure 

is consistently less than the measured transverse pressure by about 50 to 100 psf. 

y = 0.89x + 231

R2 = 0.98

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0 100 200 300 400 500 600 700 800

PRELOAD, psi

CALCULATED TRANSVERSE PRESSURE, psf .. 

.

Klondike 1330 Block -- 45 in half-w all height -- Preload assessment

Figure 7-16. Correlation between calculated transverse pressure and the preload 

acting on the wall.

y = 0.94x - 11.39

R2 = 0.85

200

400

600

800

1,000

1,200

1,400

1,600

1,800

200 400 600 800 1,000 1,200 1,400 1,600 1,800

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf .

Figure 7-17. Correlation between the measured peak transverse pressure and the 

calculated transverse pressure from the lateral wall displacement. 
92

7.2 PREDICTING THE TRANSVERSE PRESSURE FROM THE THRUST FORCE 

 In this model, the thrust force is known. The thrust force could be measured by placing 

a hydraulic load cell at the roof or floor interface or somewhere within the wall construction. 

In the laboratory, the thrust force was measured by the MRS load frame. The procedure is 

similar to that of the first model, except that thrust force is used to determine the deformation 

of the hinge points, which in turn is used to calculate the lateral displacement. The procedure 

is outlined in the flowchart in figure 7-18. 

7.2.1 Example using Rigid Boundary Conditions.

 For comparative purposes, the same test used in the previous model (section 7.1.1) will 

be examined here. Again, this is a 45-in-high half-wall that is nominally 6 inches thick. As 

shown in figure 7-2 and documented in table 7-1, the thrust force in this test was measured at 

22.79 kips. Using an elastic modulus of 60,000 psi, equation 7.16 can be used to estimate the 

( )

L / 2

P 0.8 t

HF m × × − δ h =

Thrust Force 

Calculate lateral 

displacement 

Calculate horizontal 

force 

Calculate transverse 

pressure w L / 2

2 HF

×

×

ρ =

Measured (Pm) 

Procedure Formula Used 

Calculate “hinged point 

deformation” 

( )

2

2 t 4 t 4 2 L y 4 y 2 2

h

× ± × − × × × − ×

δ =

2 A E

P L / 2

y

× ×

× =

Figure 7-18. Flowchart for predicting the transverse pressure capacity of stoppings 

if the thrust load is known. 
93

deformation of the hinge zone occurring at each of two hinge zones on the half-wall block 

column evaluated in test #46. 

 (7.16)

Where y = deformation in each of two hinge zones on half-wall section, in, 

 P = thrust load = 22,800 lbs, 

 L/2 = half-wall height = 45.75 in, 

 A = axial loading area of the wall = 90 in2

, and 

 E = Elastic modulus = 60,000 psi. 

The lateral displacement can then be determined from equation 7.17 as follows. 

 (7.17) 

 ...(7.18) 

Where δh = lateral displacement of wall at the mid span = 1.89 in, 

 t = thickness of the wall = 5.625 in, 

 y = deformation in each of two hinge zones on half-wall section = 0.097 in, and 

 L = full-wall (arching) height = 91.5, in. 

 The measured lateral displacement at the peak horizontal loading, which defines the 

maximum transverse pressure capacity of the stopping, was 1.92 inches. The predicted 

lateral displacement based on the measured thrust load was 1.89 inches. The error in the 

lateral displacement prediction is less than 2 pct, which is considered very good considering 

the assumptions made in this analysis. 

 The horizontal force can be determined using equation 7.19. In this case, the 

calculated horizontal force was 1,300 lbs, which compares to the measured MRS horizontal 

force for the laboratory test of 1,296 lbs, and error of less than 1 pct. The transverse pressure 

( )

2

2 t 4 t 4 2 L y 4 y 2 2

h

× − × − × × × − ×

δ =

( ) 0.097 inches

2 16 5.625 60,000

22,800 45.75

2 A E

P L / 2

y = × × ×

× = × ×× =

( ) 1.89 inches

2

2 5.625 4 5.625 4 2 91.5 0.097 4 0.097 2 2

h = × − × − × × × − ×

δ =
94

is then computed from equation 7.20 to equal 512 psf, again an error of less than 1 pct when 

measured against the laboratory test. 

 (7.19) 

 (7.20) 

 Figure 7-19 shows the predicted transverse pressure compared to the measured 

transverse pressure for test #46 for the full loading cycle. This is very similar to the 

prediction made from the lateral displacement (see figure 7-4). 

( ) ( ) 1,300 lbs

45.75

22,790 0.8 5.625 1.89

L / 2

P 0.8 t HF h = × × − = × × − δ =

144 512 psf 16 45.75

2 1,300 144

w L/ 2

2 HF

× = ×

×

× = ×

×

ρ =

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE PRESSURE, psf ..

Measured Transverse Pressure from MRS Test #46

Predicted Transverse Pressure -- Thrust Force Model

Figure 7-19. Comparison of predicted transverse pressure from the thrust force to 

the laboratory measured transverse pressure for a 45-inch-high half-wall test. 
95

7.2.2 Example using Non-Rigid Boundary Conditions. 

 The same theory applies to the non-rigid boundary conditions for the thrust 

measurement model prediction as was used in the lateral displacement measurement model 

described in section 7.1.2. Figure 7-20 demonstrates the thrust load model using the nonrigid boundary conditions. 

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE PRESSURE, psf ..

MRS Half-Wall Test # 179 -- Klondike (1727) Block -- Measured Transverse Pressure

Calculated transverse pressure from measured thrust force

Figure 7-20. Demonstration of the thrust load model using non-rigid boundary 

conditions. 
96

Figure 7-21. Flowchart for predicting the transverse pressure capacity of stoppings if 

the thrust load is known. 

7.2.3 Example considering preloading of the wall from ground pressures. 

 A similar process to that presented in figure 7-18 can be used for predicting the 

transverse pressure from the thrust forces if the wall is also preloaded from the roof-to-floor 

convergence produced by ground pressures. The procedure is illustrated in figure 7-21. 

Total Thrust Force 

Calculate horizontal 

force 

Calculate transverse 

pressure w L/ 2

2 HF

×

×

ρ =

Measured (Pm) 

Procedure Formula Used 

Determine preload Measured or 2 PL = ∆L×k

Parch = Pm - Ppreload 

( )

2

2 t 4 t 4 2 L y 4 y 2 2

h

× ± × − × × × − ×

δ =

Calculate “hinged point 

deformation” 2 A E

P L / 2

y arch

× ×

× =

Calculate lateral 

displacement 

Determine Arch Thrust

( )

L / 2

P d t

HF m h × × − δ =
97

 Test #74 will again be used as an example of the procedure. The test results were 

presented in figure 7-11. In this case, a preload of 373 psi equating to a unit block preload of 

33.57 kips and a total thrust force of 37.76 kips at the peak transverse pressure was measured 

from the MRS half-wall test. Following the flowchart in figure 7-21, the thrust load 

produced by arching equals 4.19 kips. Equation 7.21 then computes the hinge point 

deformation as 0.018 inches. The lateral displacement is calculated from equation 7.22 as 

0.30 inches. 

 (7.21) 

 (7.22) 

 The next step (see flowchart in figure 7-21) is to calculate the horizontal force acting to 

produce the transverse pressure of the stopping. As described in section 7.1.3, the thrust 

adjustment factor (d) must be determined so that the modified thrust resultant force location 

can be incorporated into the equation. Using the thrust adjustment factor as plotted in figure 

7-13, the transverse pressure can be predicted for the full loading cycle as depicted in figure 

7-22. 

0

200

400

600

800

1,000

1,200

1,400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

TRANSVERSE PRESSURE, psf ..

Test # 74 (Preload 373 psi) Thrust Adj Factor

( ) 0.018 inches

2 16 5.625 60,000

4190 45.75

2 A E

P L/ 2

y = × × ×

× = × ×× =

( ) 0.30 inches

2

2 5.625 4 5.625 4 2 91.5 0.018 4 0.018 2 2

h = × − × − × × × − ×

δ =

Figure 7-22. Comparison of predicted transverse pressure for full loading using the 

thrust prediction model compared to the measured transverse pressure from the MRS 

test. 
98

 As was described in the example in section 7.1.3, the peak transverse pressure can be 

computed using the trendline regression of the d factor computed from the empirical test data 

(see figure 7-15). Using this term, the maximum transverse pressure for this particular test is 

computed as 600 psf using equation 7.24. This compares with the measured transverse 

pressure of 622 psf, an error of less than 4 pct.

 

 (7.24) 

 (7.25) 

 Figure 7-23 illustrates the comparison between the measured peak transverse pressure 

and the calculated transverse pressure for the set of tests documented in table 7-1. The graph 

shows that the calculated transverse pressure is consistently less than the measured transverse 

pressure by about 100 to 200 psf. The prediction becomes worse at transverse pressures 

above 1,400 psf, which occurs at the higher preloads. One explanation for the low prediction 

at these high preloads is that the block may be damaged from the preload and the full arching 

potential is not attained in these tests. The prediction is more accurate when these high 

transverse pressure tests are omitted (see figure 7-24).

( )

( )

( ) 144

w L/ 2

2 P ( .0042 P 0.8678 t ) 144

w L/ 2

2 P (0.8 t )

2

m m h

2

h ×

×

× × − × + × − δ

× = ×

× × × − δ

ρ =

( ) ( ) 144 1,200 psf 16 45.75

2 37.76 1000 .0042 37.76 0.8678 5.625 0.30

2 × = ×

× × × − × + × − ρ =

y = 0.86x

R2

 = 0.78

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

2,200

200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000 2,200

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf .. Figure 7-23. Comparison of calculated peak transverse pressure to the measured 

peak transverse pressure for all 45-in-high tests of this block type. 
99

7.3 SUMMARY OF PREDICTIVE MODELS FOR COMPUTING TRANSVERSE 

PRESSURE CAPACITY OF MINE VENTILATION STOPPINGS 

 Two different models were developed to predict the transverse pressure capacity of 

dry-stacked mine ventilation stoppings. The same basic theory was utilized in both models; 

the differences were the result of the required known parameters necessary to compute the 

transverse pressure capacity. The two models are based on knowing: (1) the lateral 

displacement of the wall or (2) the thrust force acting on the wall. Since they rely on the 

same fundamental theory of the arching mechanics, all provide similar predictions of the 

transverse pressure capacity. Figure 7-25 compares an example prediction of the transverse 

pressure for each model with the measured transverse pressure from the MRS laboratory 

testing. 

y = 0.97x

R2

 = 0.89

200

400

600

800

1,000

1,200

1,400

1,600

200 400 600 800 1,000 1,200 1,400 1,600

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf.. Figure 7-24. Comparison of calculated peak transverse pressure to the measured peak 

transverse pressure for 45-in-high tests less than 1,500 psf. 
100

0

200

400

600

800

1000

1200

1400

No Preload Examples Examples with Preload

TRANSVERSE PRESSURE, psf ..

Predicted - Disp Model

Predicted - Thrust Model

Measured

Figure 7-24. Comparison of the two predicted models and the measured transverse 

pressure. 
101

CHAPTER 8: SUMMARY AND ANALYSIS OF EXPERIMENTAL TEST DATA 

Several manufacturers produce blocks for the stopping construction. In addition, there 

are several different types of block materials. Recently, the trend has been towards lighter 

weight materials to reduce the construction effort and material handling injuries. Figure 8-1 

depicts the strength variations of the materials used in these blocks and figure 8-2 compares 

the material modulus for the block materials utilized in this research. The compressive 

strengths range from 84 to 2,450 psi and the modulus ranges from 1,785 to 80,000 psi. The 

blocks can be categorized as follows: (1) conventional masonry units, (2) cellular concrete 

blocks, and (3) low strength or specialty type blocks. Using this classification, the average 

compressive strength for the conventional masonry units was 1,742 psi with an average 

elastic modulus of 61,000 psi. The average compressive strength for the cellular block 

materials was 572 psi with an average modulus of 28,000 psi. The low strength blocks had 

an average compressive strength of 85 psi and an elastic modulus of 5,000 psi. Also shown 

in figures 9-1 and 9-2 is a hollow block value of 900 psi for the compressive strength and 

48,000 psi for the elastic modulus. For arch loading conditions, these differences in material 

properties provide a wide range of transverse pressure capacities for mine ventilation 

stoppings. 

Figure 8-1. Comparison of compressive strength measured from unit block loading 

of various block materials examined in this research. 

0

500

1,000

1,500

2,000

2,500

BLOCK TYPE

COMPRESSIVE STRENGTH (UNIT ... 

BLOCK), psi .

Klondike Solid (Low) Klondike Solid (High)

Peerless High Strength Back Saver ACCOA

Ytong Kingsway

Omega Peerless Super Block

Klondike Hollow Core

Avg. 1742

Standard CMU

Avg. 572

Cellular Block

Avg. 85

Low Strength Block

Hollow Core 

Block

Avg. 900

BLOCK TYPE
102

A series of tests were conducted in the NIOSH Mine Roof Simulator following the 

protocol described in chapter 4. Tests were conducted on half-wall single or triple column 

block walls as documented in the protocol. The parameters varied in the test program were 

the wall height, wall thickness if appropriate, and the axial preload. All walls were drystacked block configurations, which is consistent with the practice utilized in U.S. mines. 

Generally, three tests were conducted of each configuration to evaluate consistency of the 

results. The objective of the tests was to determine the transverse loading characteristics and 

capacity limitations of the various block constructions under arching conditions. 

8.1 KLONDIKE SOLID BLOCK 

 Klondike Block and Masonry Supplies Inc is located in Uniontown, PA and supplies 

general masonry products including concrete blocks used for mine ventilation stoppings. 

The block is made from conventional Portland cement and standard aggregate and is similar 

to conventional block using in the construction industry, just weaker in strength. These 

blocks are commonly used by many mines in the local area and are sometimes referred to as 

CMU’s or concrete masonry units. Figure 8-3 shows a photo of the block. 

Figure 8-2. Comparison of material modulus of various block materials examined in 

this research for stopping construction. 

BLOCK TYPE

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

90,000

MODULUS OF ELASTICITY, psi . Klondike Solid (Low) Klondike Solid (High) Peerless High Strength Back Saver

ACCOA Ytong Kingsway

Omega Peerless Super Block Klondike Hollow Core

Standard CMU

Avg. 61,000

Cellular Block

Avg. 28,000

Hollow Core 

Block

Avg. 48,000

Low Strength Block

Avg. 5,000
103

 The blocks measure 5.625 inches 

in thickness, 16 inches in width and 

7.5 inches high as shown in the figure. 

This block weighs on average 47 lbs. 

The compressive strength varies 

depending on the amount of Portland 

cement used in the mix. Several 

batches of block were purchased for 

laboratory testing. These units had 

compressive strengths of 1,330, 1,727, 

and 1,780 psi as measured from a unit 

block load test. 

8.1.1 Overview of the Test Program 

A total of 91 tests were conducted with Klondike block. The results of the MRS halfwall tests are summarized in the tables 8-1, 8-2, and 8-3. Table 8-1 shows the results for the 

1,330-psi compressive strength block with the narrow dimension used to establish the wall 

thickness. Table 8-2 documents the results of this same block with the wide dimension used 

for the wall thickness. Table 8-3 documents the results of selected tests conducted on the 

higher strength batches (1,727 and 1,780 psi) of the Klondike block. This batch of block 

produced some inconsistency in the results and it is suspected that the Portland cement 

content was not well controlled in this batch resulting in higher than normal variations in 

compressive strength and other material properties. 

The standard test protocol was to evaluate three half-wall heights of 30, 45.75 and 60 

inches from half-walls constructed from 4, 6, and 8 courses of block. This equates to a full 

stopping height ranging from 5 to 10 feet. The preload was varied in increments of 50-100 

psi from 0 to 763 psi. Graphs of the measured lateral load and thrust load as a function of the 

lateral displacement of the wall for each test are documented in Appendix B. A tabular 

summary of the pertinent parameters and loading values for each test is also included 

Appendix C. 

Figure 8-3. Klondike conventional Portland 

cement and aggregate block. 
104

Table 8-1. Summary of Klondike 1330 block tests with narrow block thickness. 

Block Type Test 

No. 

Block 

Width 

(in) 

Block 

Height 

(in) 

Block 

Length 

(in) 

Halfwall 

Height 

(in) 

Preload 

(psi) 

Measured 

Transverse 

Pressure, 

(psf) 

Klondike 1330 102 5.625 7.5 16 30 51 2,136 

Klondike 1330 110 5.625 7.5 16 30 68 2,314 

Klondike 1330 104 5.625 7.5 16 30 188 2,358 

Klondike 1330 105 5.625 7.5 16 30 160 2,890 

Klondike 1330 109 5.625 7.5 16 30 155 2,454 

Klondike 1330 111 5.625 7.5 16 30 141 2,436 

Klondike 1330 106 5.625 7.5 16 30 295 3,304 

Klondike 1330 107 5.625 7.5 16 30 326 3,090 

Klondike 1330 108 5.625 7.5 16 30 280 2,676 

Klondike 1330 112 5.625 7.5 16 30 385 2,620 

Klondike 1330 114 5.625 7.5 16 30 428 3,090 

Klondike 1330 115 5.625 7.5 16 30 428 3,088 

Klondike 1330 118 5.625 7.5 16 30 470 3,406 

Klondike 1330 119 5.625 7.5 16 30 521 2,746 

Klondike 1330 113 5.625 7.5 16 30 567 3,376 

Klondike 1330 60 5.625 7.5 16 45.75 28 440 

Klondike 1330 59 5.625 7.5 16 45.75 43 406 

Klondike 1330 46 5.625 7.5 16 45.75 85 510 

Klondike 1330 45 5.625 7.5 16 45.75 90 384 

Klondike 1330 34 5.625 7.5 16 45.75 109 490 

Klondike 1330 36 5.625 7.5 16 45.75 122 628 

Klondike 1330 35 5.625 7.5 16 45.75 139 706 

Klondike 1330 37 5.625 7.5 16 45.75 202 784 

Klondike 1330 63 5.625 7.5 16 45.75 252 892 

Klondike 1330 61 5.625 7.5 16 45.75 313 928 

Klondike 1330 74 5.625 7.5 16 45.75 373 1,246 

Klondike 1330 75 5.625 7.5 16 45.75 390 1,424 

Klondike 1330 76 5.625 7.5 16 45.75 474 1,324 

Klondike 1330 77 5.625 7.5 16 45.75 471 1,508 

Klondike 1330 78 5.625 7.5 16 45.75 577 984 

Klondike 1330 79 5.625 7.5 16 45.75 534 1,094 

Klondike 1330 81 5.625 7.5 16 45.75 568 1,322 

Klondike 1330 82 5.625 7.5 16 45.75 618 1,544 

Klondike 1330 83 5.625 7.5 16 45.75 623 1,558 

Klondike 1330 85 5.625 7.5 16 45.75 763 1,486 

Klondike 1330 89 5.625 7.5 16 60 43 96 

Klondike 1330 90 5.625 7.5 16 60 42 102 

Klondike 1330 91 5.625 7.5 16 60 143 234 

Klondike 1330 92 5.625 7.5 16 60 150 452 

Klondike 1330 93 5.625 7.5 16 60 128 480 

Klondike 1330 94 5.625 7.5 16 60 310 328 

Klondike 1330 95 5.625 7.5 16 60 308 424 

Klondike 1330 96 5.625 7.5 16 60 347 562 

Klondike 1330 97 5.625 7.5 16 60 394 546 

Klondike 1330 98 5.625 7.5 16 60 398 486 

Klondike 1330 99 5.625 7.5 16 60 442 584 

Klondike 1330 100 5.625 7.5 16 60 592 672 

Klondike 1330 101 5.625 7.5 16 60 645 510 
105

Table 8-2. Summary of Klondike 1330 block wide orientation for wall thickness. 

Block Type Test 

No. 

Block 

Width 

(in) 

Block 

Height 

(in) 

Block 

Length 

(in) 

Halfwall 

Height 

(in) 

Preload 

(psi) 

Measured 

Transverse 

Pressure, 

(psf) 

Klondike 1330 65 7.5 5.75 16 45 17 1,330 

Klondike 1330 66 7.5 5.75 16 45 39 1,262 

Klondike 1330 64 7.5 5.75 16 45 41 1,178 

Klondike 1330 73 7.5 5.75 16 45 85 1,332 

Klondike 1330 39 7.5 5.75 16 45 99 1,212 

Klondike 1330 72 7.5 5.75 16 45 104 1,044 

Klondike 1330 40 7.5 5.75 16 45 118 1,314 

Klondike 1330 41 7.5 5.75 16 45 121 898 

Klondike 1330 67 7.5 5.75 16 45 146 1,586 

Klondike 1330 47 7.5 5.75 16 45 169 1,814 

Klondike 1330 68 7.5 5.75 16 45 174 2,000 

Klondike 1330 69 7.5 5.75 16 45 237 2,056 

Klondike 1330 70 7.5 5.75 16 45 254 1,444 

Klondike 1330 71 7.5 5.75 16 45 279 2,138 

Table 8-3. Summary of Klondike 1,727 and 1,780 block 

Klondike 1780 17 5.625 7.5 16 45.75 0 300 

Klondike 1780 18 5.625 7.5 16 45.75 228 1,080 

Klondike 1780 23 5.625 7.5 16 45 287 1,438 

Klondike 1780 24 5.625 7.5 16 45 290 1,166 

Klondike 1780 25 5.625 7.5 16 45 356 940 

Klondike 1780 21 7.5 5.75 16 46 23 918 

Klondike 1780 20 7.5 5.75 16 46 201 3,062 

Klondike 1780 19 7.5 5.75 16 46 210 3,288 

Klondike 1727 151 5.625 7.5 16 30 77 1,980 

Klondike 1727 152 5.625 7.5 16 30 43 2,936 

Klondike 1727 153 5.625 7.5 16 30 50 1,830 

Klondike 1727 154 5.625 7.5 16 30 66 2,750 

Klondike 1727 155 5.625 7.5 16 30 63 2,216 

Klondike 1727 156 5.625 7.5 16 30 40 2,286 

Klondike 1727 157 5.625 7.5 16 30 77 2,850 

Klondike 1727 200 5.625 7.5 16 37.5 41 1,102 

Klondike 1727 202 5.625 7.5 16 37.5 87 1,536 

Klondike 1727 158 5.625 7.5 16 45 65 842 

Klondike 1727 159 5.625 7.5 16 45 69 498 

Klondike 1727 161 5.625 7.5 16 45 67 888 

Klondike 1727 162 5.625 7.5 16 45 59 896 

Klondike 1727 199 5.625 7.5 16 52.5 89 400 

Klondike 1727 203 5.625 7.5 16 52.5 107 512 

Klondike 1727 198 5.625 7.5 16 60 68 248 

Klondike 1727 204 5.625 7.5 16 60 73 310 
106

8.1.2 Parametric Relationships and Trends. 

Examining tables 8-1 and 8-2, it is seen that the transverse pressure capacity of the 

stoppings constructed from Klondike (1330-psi compressive strength) block varied from a 

low of 96 to a high of 3,376 psf or 0.67 to 23.44 psi. Putting this in perspective, the CFR 

requirement for stoppings is 39 psf (0.27 psi) and 2,880 psf (20 psi) for seals. Further 

examination shows that the transverse pressure is significantly affected by the wall height 

and then by the amount of preload and the wall thickness. Figure 8-4 displays the transverse 

pressure as a function of preload for 30, 46, and 60-in half-wall heights equating to full wall 

heights of 5.0, 7.6 and 10.0 ft. The peak transverse pressures for the 30-in-high half-walls 

are 6 to 8 times higher for preloads above 100 psi than that of the 60-in half-walls and 2 to 4 

times higher than the 46-in-high half-walls. It is also seen from figure 8-4 that the transverse 

pressure is nonlinearly related to the preload and that the transverse pressure reaches an 

asymptotic maximum between 500-550 psi of preload. This suggests that the wall is being 

stressed to its maximum strength from the combination of the preload and arch compressive 

forces when the wall is preloaded to this level. The 1,727 and 1,780-psi block are designated 

separately and the inconsistency in expected results is highlighted with transparent yellow 

ovals. Again, it is suspected that this inconsistency in this particular block is due to quality 

control of the cement material mixes and the resulting block strength. 

Figure 8-5 shows that the lateral displacement at the peak transverse pressure also 

approaches an asymptotic minimum as the preload exceeds 550 psi. This is consistent with 

the transverse pressure behavior expressed in figure 8-4, indicating a limitation of the 

transverse pressure capacity. It is seen from this figure that the lateral displacement is 

reduced quickly for preload pressures up to 200 psi, and then the impact diminishes for 

higher preloads. This indicates that it the initial addition of preload will produce a big 

increase in the transverse load capacity of a stopping. 

The impact of the wall thickness can be seen from figure 8-6. The wall thickness was 

varied from the narrow block dimension (5.625 in) to the wide block dimension (7.5 in) in 

this graph. The wide-wall construction provides 2 to 3 times the transverse pressure capacity 

of the narrow thickness construction, and a similar relationship to the preload. 
107

R2 = 0.70

R2 = 0.74

R2 = 0.86

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 100 200 300 400 500 600 700 800

PRELOAD, psi

HORZ DISPLACEMENT @ PEA

K.

 TRANSVERSE PRESSURE, in

30-in half-wall height 46-in half-wall height 60-in half-wall height

Figure 8-5. Lateral displacement at which peak transverse pressure occurs also 

reaches an asymptotic minimum as the preload exceeds 600 psi.

Figure 8-4. Transverse pressure as measured for MRS laboratory testing as a 

function of preload for three different half-wall heights.

y = -0.0035x2 + 3.9991x + 2003.8

R2 = 0.62

y = -0.0022x2 + 3.2112x + 251.34

R2 = 0.87

y = -0.0017x2 + 1.89x + 60.06

R2 = 0.77

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 100 200 300 400 500 600 700 800

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

30-in half-wall height 46-in half-wall height 60-in half-wall height
108

Further examination of the parametric relationships confirms the arching theory as 

presented in chapters 5 and 6. Figure 8-7 shows that the transverse pressure is directly 

related to the lateral force acting on the half-wall during the laboratory tests. Figure 8-8 

shows that the lateral force is also directly related to the thrust force. This is also consistent 

with the arching theory. Finally, figure 8-9 shows the relationship between the transverse 

pressure and the arch thrust. This graph resembles the plot of transverse pressure versus 

preload shown in figure 8-4. The preload also limits the thrust load for the 46 and 60-in halfwall tests. The 30-in half-wall test appears to be linear, suggesting that the thrust load is not 

yet reaching its limit for this configuration and could possible sustain higher preloads. 

0

500

1,000

1,500

2,000

2,500

0 100 200 300 400 500 600 700 800

PRELOAD, psi

TRANSVERSE PRESSURE, psf. ..

46-in half-wall height -- narrow thickness (5.625 inches)

46-in half-wall height -- wide thickness (7.5 inches)

Figure 8-6. Comparison of narrow and wide wall thickness for Klondike block as a 

function of preload. 
109

y = 42.865x + 101.8

R2 = 0.89

y = 73.884x - 238.31

R2 = 0.89

y = 91.326x + 765.47

R2 = 0.89

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

0 10 20 30 40 50 60 70 80

THRUST FORCE @ PEAK TRANSVERSE LOAD, kips

PEAK LATERAL FORCE, lbs .

4 course half-wall height 6 course hall-wall height 8 course half-wall height

Figure 8-8. Lateral force is also directly related to the thrust force. 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0 1,000 2,000 3,000 4,000 5,000 6,000

LATERAL LOAD @ PEAK TRANSVERSE PRESSURE, lbs

PEAK TRANSVERSE PRESSURE, psf. ..

30-in half-wall height 46-in half-wall height 60-in half-wall height

Figure 8-7. Transverse pressure is directly related to the lateral load acting on the 

half-wall in the MRS laboratory test. 
110

Figure 8-10 depicts the relationship for tests with less than 100 psi preload between the 

transverse pressure and the calculated material modulus (E), the wall thickness (t), and the 

wall height (L) expressed as by the term E x (t/L)2. Included in this data set are the 1,727 and 

1,780 psi compressive strength block results documented in table 8-3 and a few 

miscellaneous, high strength (2,450 psi) Portland cement block tests of uncertain 

manufacturer. The chart shows that 90 pct of the transverse pressure of a stopping is 

determined by this relationship. The material modulus is a significant parameter since it 

determines the amount of thrust force developed and ultimately the amount of lateral 

displacement of the wall, both of which control the arching mechanics of the wall. If the 

modulus is related to the compressive strength of the block material, the modulus factor 

could be replaced by the compressive strength as previous research suggests (Barczak, 2004). 

R2 = 0.82

R2 = 0.92

R2 = 0.92

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0 10 20 30 40 50 60 70

ARCH THRUST @ PEAK TRANSVERSE PRESSURE, kips

PEAK TRANSVERSE PRESSURE, psf .

30 in half-wall height 46 in half-wall height 60 in half-wall height

Figure 8-9. Relationship between the transverse pressure and the arch thrust for 

MRS laboratory tests conducted at three different half-wall heights. 
111

8.1.3 Evaluation of the Predictive Models 

The next goal is to evaluate the capability to predict the transverse pressure. If the 

thrust force and its resultant location and lateral force are known, the transverse pressure 

capacity of a stopping can be predicted with nearly 100 pct accuracy. If the thrust force 

location is instead calculated from the empirical relationship described in chapter 6 and 

shown in figure 8-11 for three half-wall heights considered in this analysis, the transverse 

pressure can still be predicted with a 98 pct accuracy as depicted by the open red square data 

points shown in figure 8-12. Each data point in figure 8-12 represents an individual 

laboratory test. As seen in the figure, the accuracy of the prediction is fairly consistent 

throughout the full range of transverse pressure conducted in the laboratory testing for three 

different wall heights, and includes preloading of wall from 0 to 763 psi. 

Figure 8-10. Correlation of factors involving the material modulus (E), wall 

thickness (t), and wall height (L) to the transverse pressure capacity of a stopping. 

y = 4.31x - 527.34

R2

 = 0.83

0

500

1,000

1,500

2,000

2,500

3,000

0 100 200 300 400 500 600 700 800

Ex(t/L)2

TRANSVERSE PRESSURE, psf ..

1330 block 1727 block 1780 Block CMU -- Unknown manufacturer
112

y = 0.94x

R2

 = 0.97

y = 1.00x

R2

 = 1.00

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERS

E

PRESSURE, psf ...

Transverse pressure prediction based on measured thrust force and resultant

location and measured lateral displacement 

Transverse pressure prediction based on measured thrust force and calculated

resultant location and measured lateral displacement 

Figure 8-12. Prediction of transverse pressure when both the lateral load and arch 

thrust are known. Blue curves predicts transverse pressure when resultant thrust force 

location is also known and red squares show predicted transverse pressure when 

resultant thrust force location is calculated from empirical data. 

y = -0.0049x + 0.92

R2

 = 0.56

y = -0.0042x + 0.86

R2

 = 0.45

y = -0.0061x + 0.80

R2

 = 0.64

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0.800

0.850

0.900

0 10 20 30 40 50 60 70

TOTAL THRUST P (SUM OF ARCH AND PRELOAD), kips 

THRUST RESULTANT POSITION FACTOR 

. Figure 8-11. Resultant thrust force location for three wall heights as a function of the 

total arch thrust (Klondike solid block). 
113

 If either the thrust force or the lateral displacement is known, then the transverse 

pressure can still be calculated. It is recalled from chapter 7 that two methods were 

developed. Method 1 predicts the transverse pressure from the measured lateral 

displacement. Method 2 predicts the transverse pressure from the measured thrust force. 

Figure 8-13 illustrates the predictive capability of these models showing the measured 

transverse pressure vs. the predicted transverse pressure for each half-wall laboratory test. 

Both methods predict the transverse pressure with reasonably good accuracy with regression 

coefficients for the slope of the line comparing the predicted to the measured transverse 

pressure equaling 0.91 and 0.95, respectively. The trend line can be thought of as an average 

measure of the model’s capability. For example, the slope of the trend line for the lateral 

displacement model indicates that the model over predicts the measured transverse pressure 

by 5 pct, while the thrust model over predicts the measured response by 4 pct. 

8.1.4 Theoretical Impact of Boundary Stiffness 

A theoretical assessment of the impact of the boundary stiffness is conducted by 

varying the system modulus of elasticity (see equation 6.11 and 7.7). Recalling the 

y = 0.94x

R2

 = 0.95

y = 0.95x

R2

 = 0.96

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf .

Method 1 - Calculate transverse pressure with preload factor from measured lateral

displacement and preload

Method 2 - Calculate transverse pressure with preload factor from measured arch

thrust and preload

Figure 8-13. Prediction of transverse pressure from known thrust and lateral loads. 
114

theoretical assessment of arching mechanics described in chapters 5 and 6, the modulus of 

elasticity determines the deformations of the wall and the boundary, i.e. the mine roof and 

floor. The system modulus reflects the series stiffness equivalent of the wall and roof and 

floor structure. The theoretical assessment is made by reducing the system modulus to 75, 

50, and 25 pct of the rigid boundary condition, and computing the transverse pressure using 

the lateral displacement model developed in chapter 7. For comparative purposes, if the 

boundary stiffness were equal to the wall stiffness, the system stiffness would be reduced by 

50 pct. Likewise, if the boundary stiffness were 3 times that of the wall, the system stiffness 

would be 75 pct of the rigid boundary condition, and if the boundary stiffness were one third 

of the wall stiffness, the system stiffness would be 25 pct of the rigid boundary condition. 

Figure 8-14 shows the impact of the reduction in system modulus to 25, 50, and 75 pct 

of the rigid boundary condition at 3 different wall heights as a function of preload. First, it 

can be concluded from figure 8-14 that as the boundary modulus is reduced, the transverse 

pressure capacity of the stopping will also be reduced. It is seen from this figure that the 

impact of reductions in boundary modulus will have a greater impact in terms of absolute 

reductions in transverse pressure for shorter walls than it will for taller walls. For the 

example shown in figure 8-14, the transverse pressure for test number 102 for the 30-in halfwall height, the transverse pressure was reduced from 2,256 psf for the rigid boundary 

condition to 940 psf when the boundary modulus is one third of the wall modulus, thereby 

reducing the system modulus to 25 pct of the rigid boundary condition. This represents a 58 

pct decrease in the transverse pressure capacity of the stopping. The percent reduction in 

transverse pressure remains the same for all wall heights. 

Figures 8-15 through 8-17 show the impact of reductions in system modulus for halfwall heights of 30, 46, and 60 inches. In these figures, the transverse pressure is plotted as a 

function of preload, which varies from zero to 600 psi. These figures indicate the reductions 

in transverse pressure because of reduction in boundary stiffness (lower system modulus) are 

reduced as the preload increases. Using the 30-in-high half-wall as an example, the 58 pct 

decrease in transverse pressure which occurred by reducing the system modulus to 25 pct of 

the rigid boundary condition, drops to a 7 pct reduction at a preload of 567 psi. 
115

y = -543.34x2 + 2433x + 367.34

R2 = 1

y = -289.65x2 + 761x + 37.75

R2 = 1.0

y = -169.96x2 + 272x + 30.41

R2 = 0.95

0

500

1,000

1,500

2,000

2,500

0% 20% 40% 60% 80% 100% 120%

REDUCTION IN SYSTEM MODULUS RELATIVE TO RIGID BOUNDARY 

CONDITIONS, pct

TRANSVERSE PRESSURE, psf .

30-in half-wall height 45-in half-wall height 60-in half-wall height

y = 0.0001x2 + 3.1236x + 2063.8

y = -0.0003x2 + 3.9332x + 1655.6

y = -0.001x2 + 4.9828x + 1171.8

y = -0.0018x2 + 6.2722x + 612.52

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0 100 200 300 400 500 600

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Rigid Boundary Conditions 75% reduction in system modulus

50% reduction in system modulus 25% reduction in system modulus

Figure 8-14. Impact of reducing the boundary stiffness on transverse pressure 

capacity of stopping. Data shows individual test at different wall heights with no 

preload. 

Figure 8-15. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 30-in-high half-walls. 
116

y = -0.0009x2 + 2.45x + 390

y = -0.0013x2 + 2.75x + 324

y = -0.0015x2 + 3.04x + 205

y = -0.0018x2 + 3.41x + 65

0

200

400

600

800

1,000

1,200

1,400

1,600

0 100 200 300 400 500 600

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Rigid Boundary Conditions 75% reduction in system modulus

50% reduction in system modulus 25% reduction in system modulus

y = -0.0012x2 + 2.05x + 73

y = -0.0013x2 + 2.15x + 42

y = -0.0014x2 + 2.26x + 112

y = -0.0015x2 + 2.37x - 22

0

100

200

300

400

500

600

700

800

900

1000

0 100 200 300 400 500 600

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Rigid Boundary Conditions 75% reduction in system modulus 50% reduction in system modulus 25% reduction in system modulus

Figure 8-17. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 60-inch-high half-wall constructions.

Figure 8-16. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 46-inch-high half-wall constructions. 
117

8.2 PEERLESS BACKSAVER 

Peerless Block & Masonry 

Company is located in St. Albans, WV 

and has been supplying masonry 

products to the mining industry for over 

50 years. The block is made from 

lightweight aggregate, cement, and 

bottom ash. The blocks are 

manufactured in 6x8x16-in and 8x8x16-

-in sizes. The 6x8x16-in units were 

purchased for the laboratory tests. A 

6x8x16-in block weighs approximately 

39 lbs. Figure 8-18 shows a photo of the block. Two batches of this block were purchased. 

The first blocks were cured for over 2 years before being tested. At the time of the 

laboratory testing, these block exhibited a unit block compressive strength of 2,169 psi. 

Additional block were purchased later and were cured only 2 weeks prior to testing. These 

blocks exhibited a unit block compressive strength of 1,070 psi. Tests of a six-course 

column of block provided compressive strengths of about 75 pct of the unit block tests. It is 

believed the reduction in apparent strength is due to the stress concentrations at the block 

joints caused by differences in dimensional tolerances. 

8.2.1 Overview of the Test Program 

A total of 33 tests were conducted with Peerless Backsaver block. The results of the 

MRS half-wall tests are summarized in the tables 8-4, and 8-5. Table 8-4 shows the results 

for the fully cured, 2,169-psi compressive strength block with the narrow dimension used to 

establish the wall thickness. Table 8-5 documents the results of the same style block that was 

only cured for two weeks resulting in a reduced compressive strength. The standard test 

protocol was to evaluate three half-wall heights of 30, 45 and 60 inches from half-walls 

constructed from 4, 6, and 8 courses of block. This equates to a full stopping height ranging 

from 5 to 10 feet. Limited block quantities forced a reduced scope of testing relative to 

preloading. The preload was varied from 3 to 165 psi for the 30-in-high half-walls, from 12 

Figure 8-18. Peerless Backsaver block. 
118

to 362 psi for the 45-in-high half-walls, and from 22 to 447 for the 60-in-high half-walls. 

Nominal preloads of 50-75 psi were applied to the partially cured block tests shown in table 

8-5. Graphs of the measured lateral load and thrust load as a function of the lateral 

displacement of the wall for each test are documented in Appendix B. A tabular summary of 

the pertinent parameters and loading values for each test is also included Appendix C. 

Table 8-4. Summary of normal strength Peerless Backsaver block tests. 

Block Type Test 

No. 

Block 

Width 

(in) 

Block 

Height 

(in) 

Block 

Length 

(in) 

Halfwall 

Height 

(in) 

Preload 

(psi) 

Measured 

Transverse 

Pressure 

(psf) 

Peerless Backsavers 297 5.875 7.5 16 30 3 2,072 

Peerless Backsavers 298 5.875 7.5 16 30 10 1,928 

Peerless Backsavers 295 5.875 7.5 16 30 16 2,174 

Peerless Backsavers 296 5.875 7.5 16 30 19 2,766 

Peerless Backsavers 292 5.875 7.5 16 30 21 2,492 

Peerless Backsavers 293 5.875 7.5 16 30 50 2,130 

Peerless Backsavers 301 5.875 7.5 16 30 100 2,732 

Peerless Backsavers 294 5.875 7.5 16 30 104 2,132 

Peerless Backsavers 299 5.875 7.5 16 30 80 2,508 

Peerless Backsavers 300 5.875 7.5 16 30 165 3,136 

Peerless Backsavers 261 5.875 7.5 15.5 45 12 268 

Peerless Backsavers 260 5.875 7.5 15.5 45 25 438 

Peerless Backsavers 262 5.875 7.5 15.5 45 78 614 

Peerless Backsavers 266 5.875 7.5 15.5 45 94 706 

Peerless Backsavers 289 5.875 7.5 15.5 45 121 1,032 

Peerless Backsavers 291 5.875 7.5 15.5 45 143 1,122 

Peerless Backsavers 264 5.875 7.5 15.5 45 178 1,302 

Peerless Backsavers 265 5.875 7.5 15.5 45 182 756 

Peerless Backsavers 290 5.875 7.5 15.5 45 210 884 

Peerless Backsavers 267 5.875 7.5 15.5 45 265 752 

Peerless Backsavers 288 5.875 7.5 15.5 45 362 828 

Peerless Backsavers 282 5.875 7.5 15.5 60 22 126 

Peerless Backsavers 283 5.875 7.5 15.5 60 57 202 

Peerless Backsavers 284 5.875 7.5 15.5 60 132 220 

Peerless Backsavers 285 5.875 7.5 15.5 60 183 374 

Peerless Backsavers 286 5.875 7.5 15.5 60 239 680 

Peerless Backsavers 287 5.875 7.5 15.5 60 447 400 
119

Table 8-5. Summary of low strength Peerless Backsaver block tests. 

Block Type Test 

No. 

Block 

Width 

(in) 

Block 

Height 

(in) 

Block 

Length 

(in) 

Halfwall 

Height 

(in) 

Preload 

(psi) 

Measured 

Transverse 

Pressure 

(psf) 

Peerless Backsavers 355 5.625 7.5 15.5 30 72 1,900 

Peerless Backsavers 356 5.625 7.5 15.5 30 60 1,652 

Peerless Backsavers 357 5.625 7.5 15.5 45 45 428 

Peerless Backsavers 358 5.625 7.5 15.5 45 54 500 

Peerless Backsavers 359 5.625 7.5 15.5 60 66 84 

Peerless Backsavers 360 5.625 7.5 15.5 60 52 156 

8.1.2 Parametric Relationships and Trends. 

Examining tables 8-4 and 8-5, it is seen that the transverse pressure capacity of the 

stoppings constructed from fully cured Peerless Backsaver block varied from a low of 84 to a 

high of 3,136 psf or 0.058 to 21.78 psi. As with the Klondike block discussed in the previous 

section, the transverse pressure is most significantly affected by the wall height and the 

amount of preload. Figure 8-19 displays the transverse pressure as a function of preload for 

30, 45, and 60-in half-wall heights. The transverse pressures for the 30-in-high half-walls are 

6 to 8 times higher than that of the 60-in-high half-walls and 3 to 5 times higher than the 45-

in-high half-walls for preloads above 50 psi. It is also seen from figure 8-19 that the 

transverse pressure is nonlinearly related to the preload for the 30-in-high and 45-in-high 

half-walls and reaches an asymptotic maximum between 250-300 psi of preload for these 

wall heights. Preloads above 175 psi were not applied to the 30-in-high half-walls. As a 

result, the asymptotic maximum for these wall constructions was not reached. The partially 

cured block walls are shown in figure 8-19 designated with open square data point labels. As 

seen in the figure, the 60-in-high and 45-in-high partially cured block walls match the fully 

cured wall responses reasonably well with only slightly lower transverse pressure capacities. 

However, the transverse pressure responses for the partially cured, 30-in-high half-walls 

were considerably less than the fully cured walls. Upon closer examination of the wall 

response, it is seen from the test data in figure 8-20 that the partially cured wall begins with 

the same transverse pressure response, but at approximately 2,500 lbs of lateral loading, it 

slows in its load development, most likely due to partial failure of the material. 
120

Figure 8-20. Decrease in lateral load development with partially cured Peerless 

Backsaver block. 

Figure 8-19. Transverse pressure as measured from MRS laboratory testing as a 

function of preload for three different half wall heights (Peerless Backsaver block). 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

Test #296 - Lateral Load -- Peerless Backsaver (Fully cured block)

Test #355 - Lateral Load -- Peerless Backsaver (Partially cured block)

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 50 100 150 200 250 300 350 400 450 500

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

30-in half-wall height 45-in half-wall height 60-in half-wall height
121

 Figure 8-21 shows that the lateral displacement at the peak transverse pressure also 

approaches an asymptotic minimum as the preload exceeds 250 psi. This is consistent with 

the transverse pressure behavior expressed in figure 8-19, indicating a limitation of the 

transverse loading capacity. 

 

Further examination of the parametric relationships confirms the arching theory as 

presented in chapters 5 and 6. Figure 8-22 shows that the transverse pressure is directly 

related to the lateral force acting on the half-wall during the laboratory tests. Figure 8-23 

shows that the lateral force is also directly related to the thrust force. This is also consistent 

with the arching theory. Finally, figure 8-24 shows the relationship between the transverse 

pressure and the arch thrust. This graph resembles the plot of transverse pressure versus 

preload shown in figure 8-19. The preload also limits the thrust load for the 45-in-high halfwall tests. The transverse pressure for 30-in half-wall test increases throughout the loading 

range, suggesting that the thrust load has not yet reached its limit for this configuration and 

could possible sustain higher preloads. The 60-in-high half-wall test also does not reach a 

clear asymptote. 

Figure 8-21. Lateral displacement at which peak transverse pressure occurs also 

reaches an asymptotic minimum as the preload exceeds 250 psi.

R2 = 0.899

R2 = 0.5166

R2 = 0.5487

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 50 100 150 200 250 300 350 400 450 500

PRELOAD, psi

HORZ DISPLACEMENT @ PEA

K

TRANSVERSE PRESSURE, in .

30-in half-wall height 45-in half-wall height 60-in half-wall height

R2 = 0.52

R2 = 0.55 

R2 = 0.90
122

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 1,000 2,000 3,000 4,000 5,000 6,000

LATERAL LOAD @ PEAK TRANSVERSE PRESSURE, lbs

PEAK TRANSVERSE PRESSURE, psf . ..

30-in half-wall height 45-in half-wall height 60-in half-wall height

Figure 8-22. Transverse pressure is directly related to the lateral load acting on the 

half wall in the MRS laboratory test (Peerless Backsaver block).

y = 69.672x - 153.29

R2

 = 0.80

y = 103.47x + 363.06

R2

 = 0.67

y = 46.113x - 14.75

R2

 = 0.88

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

0 5 10 15 20 25 30 35 40 45

ARCH THRUST FORCE @ PEAK TRANSVERSE PRESSURE, kips

PEAK LATERAL FORCE, lbs .

30-in half-wall height 45-in half-wall height 60-in half-wall height

Figure 8-23. Lateral force is also directly related to the thrust force (Peerless. . 

Backsaver block).
123

 

Figure 8-25 depicts the relationship for tests with less than 75 psi preload between the 

transverse pressure and the material modulus (E), the wall thickness (t), and the wall height 

(L) expressed as by the term E x (t/L)2. Both the fully cured and partially cured blocks are 

included in this analysis. The chart shows that 96 pct of the transverse pressure of a stopping 

is determined by this relationship. The material modulus is a significant parameter since it 

determines the amount of thrust force developed and ultimately the amount of lateral 

displacement of the wall, both of which control the arching mechanics of the wall. If the 

modulus is related to the compressive strength of the block material, the modulus factor 

could be replaced by the compressive strength as previous research suggests (Barczak, 2004). 

R2 = 0.83

R2 = 0.85

R2 = 0.87

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 5 10 15 20 25 30 35 40 45 50

ARCH THRUST FORCE @ PEAK TRANSVERSE PRESSURE, kips

PEAK TRANSVERSE PRESSURE, psf ....

30-in half-wall height 45-in half-wall height 60-in half-wall height

Figure 8-24. Relationship between the transverse pressure and the arch thrust for 

MRS laboratory tests conducted at three different half-wall heights (Peerless 

Backsaver block).
124

8.2.3 Evaluation of Predictive Models 

 

 If the thrust force and its resultant location and lateral load are known, the transverse 

pressure capacity of a stopping can be predicted with nearly 100 pct accuracy. If the thrust 

force location is instead calculated from the empirical model described in chapter 6 and 

shown in figure 8-26 for three half-wall heights considered in this analysis, the transverse 

pressure can still be predicted to within 1 pct of the measured transverse pressure from the 

laboratory tests. Each data point in figure 8-27 represents an individual laboratory test. As 

seen in the figure, the accuracy of the prediction is consistent throughout the full range of 

transverse pressure conducted in the laboratory testing for three different wall heights, and 

includes preloading of wall from zero to 447 psi. 

0

500

1,000

1,500

2,000

2,500

3,000

0 50 100 150 200 250 300 350 400

Ex(t/L)2

TRANSVERSE PRESSURE, psf .

Peerless (fully cured block) Peerless (2 week cured block)

y = 4.15x - 318

R2 = 0.96

Figure 8-25. Correlation of factors involving the material modulus (E), wall thickness 

(t), and wall height (L) to the transverse load capacity of a stopping (Peerless 

Backsaver block).
125

y = 1.00x

R2

 = 1.00

y = 0.975x

R2

 = 0.973

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 500 1,000 1,500 2,000 2,500 3,000 3,500

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERS

E

PRESSURE, psf .

 Transverse pressure prediction based on measured thrust force and resultant load

location and measured lateral displacement 

Transverse pressure prediction based on measured thrust force and calculated

resultant load location and measured lateral displacement 

y = -0.0051x + 0.97

R2

 = 0.26

y = -0.0084x + 1.00

R2

 = 0.46

y = -0.0076x + 0.96

R2

 = 0.53

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

0 5 10 15 20 25 30 35 40 45 50

TOTAL THRUST P (SUM OF ARCH AND PRELOAD), kips 

THRUST RESULTANT POSITION FACTOR .

30-in half-wall height 45-in half-wall height 60-in half-wall height

Figure 8-26. Resultant thrust force location for three wall heights as a function of 

the total arch thrust (Peerless Backsaver block).

Figure 8-27. Prediction of transverse pressure when both the lateral load and arch 

thrust are known. Blue curves predicts transverse pressure when resultant thrust 

force location is also known and red squares show predicted transverse pressure 

when resultant thrust force location is calculated from empirical data. 
126

 If either the lateral displacement or the arch thrust is known, then the transverse 

pressure can still be calculated. Again, it is recalled from chapter 7 that two methods were 

developed. Method 1 predicts the transverse pressure from the measured lateral 

displacement. Method 2 predicts the transverse pressure from the measured thrust force. 

Figure 8-28 illustrates the predictive capability of these models showing the measured 

transverse pressure vs. the predicted transverse pressure for each half-wall laboratory test. 

Based on the calculated trend lines, both models very accurately predicted the measured 

transverse pressure. 

8.2.4 Theoretical Impact of Boundary Stiffness 

A theoretical assessment of the impact of the boundary stiffness is conducted by 

varying the system modulus of elasticity (see equation 6.11 an 7.7). Recalling the theoretical 

assessment of arching mechanics described in chapters 5 and 6, the modulus of elasticity 

determines the deformations of the wall and the boundary, i.e. the mine roof and floor. The 

system modulus reflects the series stiffness equivalent of the wall and roof and floor 

y = 1.01x

R2

 = 0.96

y = 1.00x

R2

 = 0.96

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 500 1,000 1,500 2,000 2,500 3,000 3,500

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERS

E

PRESSURE, psf .

Method 1 - Calculate transverse pressure with preload factor from measured lateral

displacement and preload

Method 2 - Calculate transverse pressure with preload factor from measured arch

thrust and preload

Figure 8-28. Prediction of transverse pressure from two methods (Peerless 

Backsaver block). 
127

structure. The theoretical assessment is made by reducing the system modulus to 75, 50, and 

25 pct of the rigid boundary condition, and computing the transverse pressure using the 

lateral displacement model developed in chapter 7. For comparative purposes, if the 

boundary stiffness were equal to the wall stiffness, the system stiffness would be reduced by 

50 pct. Likewise, if the boundary stiffness were three times that of the wall, the system 

stiffness would be 75 pct of the rigid boundary condition, and if the boundary stiffness were 

one third of the wall stiffness, the system stiffness would be 25 pct of the rigid boundary 

condition. 

Figure 8-29 shows the impact of the reduction in system modulus to 25, 50, and 75 pct 

of the rigid boundary condition at 3 different wall heights as a function of preload. First, it 

can be concluded from figure 8-29 that as the boundary modulus is reduced, the transverse 

pressure capacity of the stopping will also be reduced. It is seen from this figure that the 

impact of reductions in boundary modulus will have a greater impact in terms of absolute 

reductions in transverse pressure for shorter walls than it will for taller walls. For the 

example shown in figure 8-29, the transverse pressure for test number 297 for the 30-in halfwall height, the transverse pressure was reduced from 2,268 psf for the rigid boundary 

condition to 580 psf when the boundary modulus is one third of the wall modulus, thereby 

reducing the system modulus to 25 pct of the rigid boundary condition. This represents a 74 

pct decrease in the transverse pressure capacity of the stopping. The percent reduction in 

transverse pressure remains the same for all three wall heights. 

Figures 8-30 through 8-31 show the impact of reductions in system modulus for halfwall heights of 30, 46, and 60 inches. In these figures, the transverse pressure is plotted as a 

function of preload, which varies from 0 to 450 psi. These figures indicate the reductions in 

transverse pressure because of reduction in boundary stiffness (lower system modulus) are 

reduced as the preload increases. Using the 30-in-high half-wall as an example, the 74 pct 

decrease in transverse pressure which occurred by reducing the system modulus to 25 pct of 

the rigid boundary condition, drops to a 41 pct reduction at a preload of 165 psi. 
128

Figure 8-29. Impact of reducing the boundary stiffness on transverse pressure 

capacity of stopping (Peerless Backsaver block). 

y = -0.0003x2 + 3.99x + 1693

y = -0.0038x2 + 3.40x + 2257

y = 0.0032x2 + 4.59x + 1129

y = 0.0067x2 + 5.19x + 565

0

500

1,000

1,500

2,000

2,500

3,000

0 20 40 60 80 100 120 140 160 180

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Rigid Boundary Conditions 75% Reduction in system modulus

50% Reduction in system modulus 25% Reduction in system modulus

y = 462.76x + 21.50

y = 2249.9x + 18.40

y = 160.58x + 24.04

0

500

1,000

1,500

2,000

2,500

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

REDUCTION IN SYSTEM MODULUS RELATIVE TO RIGID BOUNDARY CONDITIONS, pct

TRANSVERSE PRESSURE, psf .

30-in half-wall height 45-in half-wall height 60-in half-wall height

Figure 8-30. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 30-inch-high half-wall constructions (Peerless 

Backsaver block).
129

8.1

y = -0.0032x2 + 3.05x + 314

y = -0.0033x2 + 2.30x + 432

y = -0.003x2 + 3.13x + 196

y = -0.0029x2 + 3.21x + 79

0

200

400

600

800

1000

1200

0 50 100 150 200 250 300 350 400

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Rigid Boundary Conditions 75% Reduction in system modulus

25% Reduction in system modulus 25% Reduction in system modulus

y = -0.0019x2 + 1.73x + 109

y = -0.0019x2 + 1.66x + 151

y = -0.002x2 + 1.80x + 67

y = -0.0021x2 + 1.87x + 25

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350 400 450 500

PRELOAD, psi

TRANSVERSE PRESSURE, psf ..

Rigid Boundary Conditions 75% Reduction in system modulus

50% Reduction in system modulus 25% Reduction in system modulus

Figure 8-31. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 46-inch-high half-wall constructions (Peerless 

Backsaver block).

Figure 8-32. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 60-inch-high half-wall constructions (Peerless 

Backsaver block).
130

8.3 KLONDIKE HOLLOW CORE BLOCK 

Klondike Block & Masonry 

Supplies Inc is located in Uniontown, 

PA and supplies general masonry 

products including concrete blocks used 

for mine ventilation stoppings. The 

block is made from conventional 

Portland cement and standard aggregate 

with the same basic formulation that is 

used to make the solid blocks. Figure 

8-33 shows a photo of the block. The 

blocks measure 5.625 inches in 

thickness, 15.5 inches in width and 7.5 

inches high. The core holes measure 3.5 x 3.5 inches leaving an edge thickness of 

approximately one inch. This block weighs on average 32 lbs. The unit block compressive 

strength was measured at 907 psi compared to the 1,330 psi strength of the solid block (see 

figure 8-34). The thin webs and facing obviously contribute to the lower strength. 

Figure 8-33. Hollow core concrete block 

(manufactured by Klondike). 

0

200

400

600

800

1,000

1,200

1,400

0.000 0.005 0.010 0.015 0.020 0.025 0.030

STRAIN, in/in

STRESS, psi

Klondike Solid BLock Klondike Hollow Block

Figure 8-34. Comparison of the compressive strength of solid and hollow core block.
131

8.3.1 Overview of the Test Program 

A total of 23 tests were conducted with hollow core Klondike block. The results of the 

MRS half-wall tests are summarized in the table 8-6. The standard test protocol was to 

evaluate three half-wall heights of 30, 45.75 and 60 inches from half-walls constructed from 

4, 6, and 8 courses of block. This equates to a full stopping height of 5 to 10 feet. The 

preload was varied in increments of approximately 50 psi from 0 to 212 psi. Graphs of the 

measured lateral load and thrust load as a function of the lateral displacement of the wall for 

each test are documented in Appendix B. A tabular summary of the pertinent parameters and 

loading values for each test is also included Appendix C. 

Table 8-6. Summary of Klondike, hollow-core block, half-wall tests in the MRS. 

Block Type Test 

No. 

Block 

Width 

(in) 

Block 

Height 

(in) 

Block 

Length 

(in) 

Halfwall 

Height 

(in) 

Adjusted 

Preload 

(psi) 

Measured 

Transverse 

Pressure, 

(psf) 

Klondike Hollow Block 330 5.625 7.5 15.5 30 29 1,338 

Klondike Hollow Block 331 5.625 7.5 15.5 30 55 1,062 

Klondike Hollow Block 340 5.625 7.5 15.5 30 57 1,384 

Klondike Hollow Block 334 5.625 7.5 15.5 30 80 1,586 

Klondike Hollow Block 338 5.625 7.5 15.5 30 91 1,600 

Klondike Hollow Block 332 5.625 7.5 15.5 30 116 1,168 

Klondike Hollow Block 339 5.625 7.5 15.5 30 117 1,544 

Klondike Hollow Block 337 5.625 7.5 15.5 30 140 966 

Klondike Hollow Block 336 5.625 7.5 15.5 30 155 938 

Klondike Hollow Block 335 5.625 7.5 15.5 30 172 1,282 

Klondike Hollow Block 333 5.625 7.5 15.5 30 212 1,424 

Klondike Hollow Block 321 5.625 7.5 15.5 45 22 150 

Klondike Hollow Block 314 5.625 7.5 15.5 45 28 130 

Klondike Hollow Block 315 5.625 7.5 15.5 45 99 472 

Klondike Hollow Block 323 5.625 7.5 15.5 45 87 456 

Klondike Hollow Block 320 5.625 7.5 15.5 45 120 634 

Klondike Hollow Block 322 5.625 7.5 15.5 45 129 708 

Klondike Hollow Block 318 5.625 7.5 15.5 45 131 746 

Klondike Hollow Block 317 5.625 7.5 15.5 45 188 540 

Klondike Hollow Block 319 5.625 7.5 15.5 45 184 768 

Klondike Hollow Block 324 5.625 7.5 15.5 45 207 828 

Klondike Hollow Block 325 5.625 7.5 15.5 60 78 134 

Klondike Hollow Block 327 5.625 7.5 15.5 60 80 168 

Klondike Hollow Block 328 5.625 7.5 15.5 60 129 158 

Klondike Hollow Block 329 5.625 7.5 15.5 60 212 222 
132

8.3.2 Parametric Relationships and Trends. 

Examining table 8-6, it is seen that the transverse pressure capacity of the stoppings 

constructed from Klondike hollow core block varied from a low of 130 to a high of 1,600 psf 

or 0.90 to 11.11 psi for the test configurations documented in the table. In general, the 

hollow core block transverse pressure performance was less consistent than the solid core 

block. Figure 8-35 displays the transverse pressure as a function of preload for 30, 45, and 

60-in half-wall heights. The transverse pressures for the 30-in-high half-walls were 6 to 8 

times higher for preloads above 25 psi than that of the 60-in-high half-walls and 2 to 4 times 

higher than the 45-in-high half-walls. The 45-in half-wall height displays the nonlinear 

behavior between the transverse pressure and the preload as was observed in the solid core 

block walls, reaching an asymptotic level at about 175 psi of preload. Compared to the solid 

core block, which reached as asymptotic load at about 550 psi, it appears that the hollow core 

block is not able to sustain preload stresses as well as the solid core block. The 30 and 60-

inch high half-wall tests did not provide the same trend. For these wall configurations, it 

appears that the preload made relatively little difference in the transverse pressure capacity of 

the stopping. The 30-in-high half-wall trend line even suggests that the transverse pressure 

capacity decreases slightly with increasing preload. The most likely cause of this behavior 

was the walls were damaged from even minimal preload. 

Figure 8-35. Transverse pressure as measured from MRS laboratory testing as a 

function of preload for three different half-wall heights (Klondike hollow core block).

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0 50 100 150 200 250

PRELOAD, psi

TRANSVERSE PRESSURE, psf ..

30-in half-wall height 45-in half-wall height 60-in half-wall height
133

 A review of the test results shows that localized failures of the block at the hinge points 

were occurring as the transverse pressure was developing for the 30-inch-high half-wall 

configurations. Figure 8-36 shows one example. In this example, the wall was preloaded 

with 172 psi. The lateral load began to build as expected with the onset of the induced lateral 

displacement, but at approximately 0.3 inches of lateral displacement, the lateral load 

decreased as the wall was not able to sustain the arch thrust force (i.e. decrease in thrust load 

shown by blue curve in figure 8-36). Following this load-shedding event, the lateral load 

recovered and increased until another load-shedding event occurred at 1.1 inches of lateral 

displacement. The lateral load again recovered reaching a maximum of 2,070 lbs at 1.6 

inches of lateral displacement. Figure 8-37 gives another example at only 90 psi of preload 

pressure. Figure 8-38 shows that the lateral displacement at the peak transverse pressure also 

approaches an asymptotic minimum as the preload exceeds 200 psi. This is consistent with 

the transverse pressure behavior expressed in figure 8-35, indicating a limitation of the 

transverse pressure capacity. 

0

500

1,000

1,500

2,000

2,500

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

4

8

12

16

20

THRUST LOAD, kips

Test #335 -- Lateral Load -- Klondike Hollow Core Block -- 5.5 in thick -- 172 psi preload

Test #335 -- Thrust Load -- Klondike Hollow Core Block -- 5.5 in thick -- 172 psi preload

Figure 8-36. Example of 30-in-high half wall test where the wall was not able to 

sustain the arch thrust load during localized failure of the block during transverse 

pressure resulting in lateral load shedding twice during the loading cycle. 
134

0

500

1,000

1,500

2,000

2,500

3,000

0.0 0.5 1.0 1.5 2.0 2.5

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

4

8

12

16

20

24

THRUST LOAD, kips

Test #338 -- Lateral Load -- Klondike Hollow Core Block -- 5.5 in thick -- 90 psi

preload

Test #338 -- Thrust Load -- Klondike Hollow Core Block -- 5.5 in thick -- 90 psi

preload

Figure 8-37. Another example where the arch thrust force was not sustained 

during the full loading cycle. 

R2 = 0.52

R2 = 0.40

R2 = 0.96

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 50 100 150 200 250

PRELOAD, psi

HORZ DISPLACEMENT @ PEA

K

TRANSVERSE PRESSURE, in .

30-in half-wall height 45-in half-wall height 60-in half-wall height

Figure 8-38. Lateral displacement at which peak transverse pressure occurs 

approaches asymptotic minimum as preload exceeds 200 psi (Klondike hollow core 

block).
135

Further examination of the parametric relationships confirms the arching theory as 

presented in chapter 6. Figure 8-39 shows that the transverse pressure is directly related to 

the lateral force acting on the half-wall during the laboratory tests, despite the inconsistency 

in the transverse pressure performance. Figure 8-40 shows that the lateral force is also 

directly related to the thrust force. This is also consistent with the arching theory. Finally, 

figure 8-41 shows the relationship between the transverse pressure and the arch thrust. The 

preload also limits the thrust force for the half-wall tests. The maximum lateral force and 

arch thrust force attained at the highest preloads in the 60-in-high half-wall test was 

significantly less than that of the other two wall heights. 

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0 500 1,000 1,500 2,000 2,500 3,000

LATERAL LOAD @ PEAK TRANSVERSE PRESSURE, lbs

PEAK TRANSVERSE PRESSURE, psf . 

30-in half-wall height 45-in half-wall height 60-in half-wall height

Figure 8-39. Transverse pressure is directly related to the lateral load acting on the 

half wall in the MRS laboratory test (Klondike hollow core block).
136

y = 76.76x + 29

R2

 = 0.84

y = 93.09x + 614

R2

 = 0.84

y = 54.96x - 1616

R2

 = 0.91

0

500

1,000

1,500

2,000

2,500

3,000

0 5 10 15 20 25 30

ARCH THRUST FORCE @ PEAK TRANSVERSE PRESSURE, kips

PEAK LATERAL FORCE, lbs .

30-in half-wall height 45-in half-wall height 60-in half-wall height

Figure 8-40. Lateral force is also directly related to the thrust force (Klondike hollow 

core block).

Figure 8-41. Relationship between the transverse pressure and the arch thrust for MRS 

laboratory tests conducted at three different half-wall heights (Klondike hollow core 

block).

y = 76.76x + 29

R2 = 0.84

y = 93.09x + 614

R2

 = 0.84

y = 54.96x - 1616

R2 = 0.91

0

500

1,000

1,500

2,000

2,500

3,000

0 5 10 15 20 25 30

ARCH THRUST FORCE @ PEAK TRANSVERSE PRESSURE, kips

PEAK LATERAL FORCE, lbs .

30-in half-wall height 45-in half-wall height 60-in half-wall height
137

Figure 8-42 depicts the relationship for tests with less than 100 psi preload between the 

transverse pressure and the material modulus (E), the wall thickness (t), and the wall height 

(L) expressed as by the term E x (t/L)2

. The chart shows that 91 pct of the transverse 

pressure of a stopping is determined by this relationship. The material modulus is a 

significant parameter since it determines the amount of thrust force developed and ultimately 

the amount of lateral displacement of the wall, both of which control the arching mechanics 

of the wall. If the modulus is related to the compressive strength of the block material, the 

modulus factor could be replaced by the compressive strength as previous research suggests 

(Barczak, 2004). 

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0 100 200 300 400 500 600

Ex(t/L)2

, psi

TRANSVERSE PRESSURE, psf ,,.

30-in half-wall height 45-in half-wall height 60-in half-wall height

y = 1.64x-207.34

R2

 = .91

Figure 8-42. Correlation of factors involving the material modulus (E), wall thickness 

(t), and wall height (L) to the transverse pressure capacity of a stopping (Klondike 

hollow core block).
138

8.3.3 Evaluation of the Predictive Models 

The next goal is to evaluate the capability to predict the transverse pressure. If the 

thrust force and its resultant location and lateral force are known, the transverse pressure 

capacity of a stopping can be predicted with less than 1 pct error. Figure 8-43 shows the 

calculated resultant thrust force location factor for each of the three half-wall heights. A few 

comments are made relative to this factor for the hollow core block. First, the factor for the 

30 and 45-in-high half-wall constructions is larger than it was for the solid core block. For 

these wall heights, there is less reduction in the factor when the thrust force increases than 

was seen for the solid block. It is believed that these differences are attributed to the damage 

and localized failure of the block during the transverse pressure development as described in 

section 8.3.2 and illustrated in figures 8-36 and 8-37. The 60-in half-wall height 

constructions showed a large change in the resultant thrust location factor with increasing 

arch thrust. This change appears abnormally large primarily due to the high initial values at 

the lower thrust forces. 

 

y = -0.0033x + 0.97

R2

 = 0.10

y = -0.0036x + 0.99

R2

 = 0.54

y = -0.0458x + 1.47

R2

 = 0.86

0.70

0.75

0.80

0.85

0.90

0.95

1.00

0 5 10 15 20 25 30

TOTAL THRUST P (SUM OF ARCH AND PRELOAD), kips 

THRUST P RESULTANT POSITION FACTOR 

..

30-in half-wall height 45-in half-wall height 60-in half-wall height

Figure 8-43. Resultant thrust force location for three wall heights as a function of 

the total arch thrust (Klondike hollow core block). 
139

 If the thrust force location is instead calculated from the empirical model described in 

chapter 6 and shown in figure 8-43 for three half-wall heights considered in this analysis, the 

transverse pressure can still be predicted with a 94 pct accuracy as depicted by the open red 

square data points shown in figure 8-44. Each data point in figure 8-44 represents an 

individual laboratory test. As seen in the figure, the accuracy of the prediction is fairly 

consistent throughout the full range of transverse pressure conducted in the laboratory testing 

with one exception at the highest calculated transverse pressure (high preload condition) 

where the predicted transverse pressure was nearly 400 psf lower than the measured 

transverse pressure for this one test. 

y = 0.99x

R2

 = 0.57

y = 0.94x

R2

 = 0.98

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0 200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE ... 

PRESSURE, psf . ....

Transverse pressure prediction based on measured thrust force and resultant load

location and measured lateral displacement 

Transverse pressure prediction based on measured thrust force and calculated

resultant load location and measured lateral displacement 

Figure 8-44. Prediction of transverse pressure when both the lateral load and arch 

thrust are known. Blue curves predicts transverse pressure when resultant thrust 

force location is also known and red squares show predicted transverse pressure 

when resultant thrust force location is calculated from empirical data. 
140

If either the arch thrust or lateral displacement is known, then the transverse pressure 

can still be calculated. It is recalled from chapter 7 that two methods were developed. 

Method 1 predicts the transverse pressure from the measured lateral displacement. Method 2 

predicts the transverse pressure from the measured thrust force. Figure 8-45 illustrates the 

predictive capability of these two methods showing the measured transverse pressure vs. the 

predicted transverse pressure for each half-wall laboratory test. It is seen from figure 8-45 

that both methods significantly over predict the measured transverse pressure when the 

regression trend lines are employed. Method 2, where the thrust force is known, is the more 

accurate of the two models and does a reasonable job (less than 15 pct error) of predicting the 

transverse pressure. Upon closer examination, it is seen that the transverse pressure 

predictions for both methods are much more accurate for transverse pressures below 1,000 

psf. Only the 30-in-high half-walls provide transverse pressure capacities greater than 1,000 

psf. Again, it is believed that these walls are being damaged prematurely from the preload 

resulting in the lower than expected transverse pressure. 

y = 0.64x

R2

 = 0.80

y = 0.85x

R2

 = 0.95

0

500

1,000

1,500

2,000

2,500

0 500 1,000 1,500 2,000 2,500

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf .

Method 1 - Calculate transverse pressure with preload factor from measured lateral

displacement and preload

Method 2 - Calculate transverse pressure with preload factor from measured arch

thrust and preload

Figure 8-45. Prediction of transverse pressure from known thrust and lateral loads 

with a constant material modulus for all tests.
141

 Figure 8-46 shows the prediction of the two models when the material modulus for the 

30-in-high half-walls is reduced by 50 pct from 65,000 psi to 32,500 psi. This modification 

significantly improves the prediction of all three models, in particular for the 30-in-high halfwall constructions. The justification for doing this again lies in the premature failures of the 

block during the transverse pressure development for the short wall constructions. 

Essentially, these failures increase the lateral displacement of the wall, which can be 

accounted for by a reduced material modulus (see chapter 6). 

y = 0.94x

R2

 = 0.82

y = 0.98x

R2

 = 0.93

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0 200 400 600 800 1,000 1,200 1,400 1,600 1,800

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERS

E

PRESSURE, psf 

Method 1 - Calculate transverse pressure with preload factor from measured lateral

displacement and preload

Method 2 - Calculate transverse pressure with preload factor from measured arch

thrust and preload

Figure 8-46. Prediction of transverse pressure from known thrust and lateral 

loads where the material modulus for the 30-in-high half-walls was reduced by 50 

pct.
142

8.3.4. Theoretical Impact of Boundary Stiffness 

Figure 8-47 shows the impact of the reduction in system modulus to 25, 50, and 75 pct 

of the rigid boundary condition at three different wall heights. It is seen from this figure that 

the impact of reductions in boundary modulus will have a greater impact in terms of absolute 

reductions in transverse pressure for shorter walls than it will for taller walls. For the 

example shown in figure 8-47, the transverse pressure for test number 330 for the 30-in halfwall height, the transverse pressure was reduced from 1,152 psf for the rigid boundary 

condition to 398 psf when the boundary modulus is one third of the wall modulus thereby 

reducing the system modulus to 25 pct of the rigid boundary condition. This represents a 65 

pct decrease in the transverse pressure capacity of the stopping. The percent reduction in 

transverse pressure remains the same for all three wall heights. 

y = 413x + 59

y = 1006x + 150

0

200

400

600

800

1,000

1,200

1,400

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

REDUCTION IN SYSTEM MODULUS RELATIVE TO RIGID BOUNDARY 

CONDITIONS, pct

TRANSVERSE PRESSURE, psf .

30-in half-wall height 45-in half-wall height 60-in half-wall height

Figure 8-47. Impact of reducing the boundary stiffness on transverse pressure 

capacity of stopping. Data shows individual test at different wall heights with no 

preload.
143

 Figures 8-48 through 8-50 show the impact of reductions in system modulus for halfwall heights of 30, 45, and 60 inches. In these figures, the transverse pressure is plotted as a 

function of preload, which varies from 0 to 212 psi. These figures indicate the reductions in 

transverse pressure as a result of reduction in boundary stiffness (lower system modulus) are 

reduced as the preload increases. Using the 30-in-high half-wall as an example, the 65 pct 

decrease in transverse pressure which occurred by reducing the system modulus to 25 pct of 

the rigid boundary condition drops to a 48 pct reduction at a preload of 212 psi. 

y = -0.0031x2 + 3.74x + 791

y = -0.0058x2 + 3.73x + 1032

y = -0.0002x2 + 3.74x + 542

y = 0.0029x2 + 3.75x + 285

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0 50 100 150 200 250

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Rigid Boundary Conditions 75% reduction in system modulus

50% reduction in system modulus 25% reduction in system modulus

Figure 8-48. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 30-inch-high half-wall constructions (Klondike 

hollow core block).
144

Figure 8-49. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 45-inch-high half-wall constructions (Klondike 

hollow core block).

y = -0.0015x2 + 1.81x + 336

y = -0.0035x2 + 2.10x + 429

y = 0.0006x2 + 1.56x + 234

y = 0.0027x2 + 1.34x + 123

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Rigid Boundary Conditions 75% reduction in system modulus

50% reduction in system modulus 25% reduction in system modulus

y = -0.0005x2 + 0.71x + 101

y = -0.0005x2 + 0.75x + 75

y = -0.0006x2 + 0.80x + 96

y = -0.0009x2 + 1.03x + 61

0

50

100

150

200

250

300

0 50 100 150 200 250

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Rigid Boundary Conditions 75% reduction in system modulus

50% reduction in system modulus 25% reduction in system modulus

Figure 8-50. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 60-inch-high half-wall constructions 

(Klondike hollow core block).
145

8.4 ACCOA AUTOCLAVED AERATED CONCRETE BLOCK 

Aerated Concrete Corporation of 

America (ACCOA) located just north of 

Orlando, Florida is the largest 

manufacturer of autoclaved aerated 

concrete (AAC) in the United States. Its 

primary use is the construction industry 

where the block is used for both load 

bearing and non-load bearing 

applications. Autoclaved aerated 

concrete is a process where material 

with entrained air is cured in an 

autoclaved oven to formulate air pockets within the concrete structure. This provides a very 

low-density material that is light weight, durable, and easy to cut, making it attractive for 

mine ventilation stopping (see figure 8-51). Silica is the largest dry raw material. Copper 

mine tailings are often used for the silica source. Other materials include sand and flyash 

fillers. The silica reacts with the aluminum to form a chemical reaction, which creates 

millions of tiny air cells that give AAC its unique properties. Only about 20 pct of the 

material is cement. The material is 

more air than anything else. 

Interestingly, AAC was invented in 

Sweden in 1923 as an alternative to 

their rapidly depleting timber 

supplies. Unlike normal concrete, 

AAC block are very resistant to 

thermal change. Figure 8-52 

shows a house in California 

constructed from AAC block that 

survived a devastating fire that 

destroyed 336 homes and 17,000 acres. 

Figure 8-51. AAC block manufactured by 

Aerated Concrete Corporation of America. 

Figure 8-52. Fire resistance capability of aerated 

concrete block is shown by this house which 

survived devastating fire in California. 
146

They were approved for mine use by MSHA in 2003. This product is currently 

distributed to the mining industry through Lee Supply in Charleroi, Pennsylvania. The block 

is manufactured in thicknesses of 6 and 8 inches with heights of 12 inches and a width of 24 

inches. Figure 8-51 shows a photo of a 6-in-thick block. This block weighs on average 16 

lbs. The unit block compressive strength was measured from laboratory testing at 421 psi. 

8.4.1 Overview of the Test Program 

A total of 18 tests were conducted with ACC block. DSA Sales Inc of Pittsburgh, PA. 

donated a limited supply of the block. Due to the limited supply, only the 48-in half-wall 

height was evaluated in the research program. Efforts to obtain additional block for testing 

were unsuccessful due to limited funding. The results of the MRS half-wall tests are 

summarized in the table 8-7. The preload was varied in increments of 50 psi from zero to 

300 psi. Graphs of the measured lateral load and thrust load as a function of the lateral 

displacement of the wall for each test are documented in Appendix B. A tabular summary of 

the pertinent parameters and loading values for each test is also included Appendix C. 

Table 8-7. Summary of ACC block tests. 

Block Type Test 

No. 

Block 

Width 

(in) 

Block 

Height 

(in) 

Block 

Length 

(in) 

Halfwall 

Height 

(in) 

Preload 

(psi) 

Measured 

Transverse 

Pressure, 

(psf) 

ACC 6 26 6 12 24 48 3 166 

ACC 6 27 6 12 24 48 3 186 

ACC 6 48 6 12 24 48 30 184 

ACC 6 49 6 12 24 48 60 228 

ACC 6 50 6 12 24 48 75 264 

ACC 6 28 6 12 24 48 120 358 

ACC 6 32 6 12 24 48 132 340 

ACC 6 29 6 12 24 48 136 276 

ACC 6 33 6 12 24 48 136 326 

ACC 6 31 6 12 24 48 293 338 

ACC 6 30 6 12 24 48 300 320 

ACC 8 56 8 12 24 48 18 498 

ACC 8 55 8 12 24 48 20 552 

ACC 8 54 8 12 24 48 38 434 

ACC 8 53 8 12 24 48 40 528 

ACC 8 62 8 12 24 48 97 794 

ACC 8 51 8 12 24 48 111 682 

ACC 8 58 8 12 24 48 238 678 
147

8.4.2 Parametric Relationships and Trends. 

Examining table 8-7, it is seen that the transverse pressure capacity of the stoppings 

constructed from Florida block varied from a low of 166 to a high of 678 psf or 1.15 to 4.71 

psi. Figure 8-53 displays the transverse pressure as a function of preload for the 6-in and 8-in 

thick block walls. The transverse pressures for the 8-in-thick half-walls are 2 to 3 times 

higher than the 6-in-thick half-walls. It is also seen from figure 8-52 that the transverse 

pressure is nonlinearly related to the preload and that the transverse pressure approaches an 

asymptotic maximum at approximately 200 psi for the 6-in-thick walls and 150 psi for the 8-

in-thick walls. This suggests that the wall is being stressed to its maximum strength from the 

combination of the preload and arch compressive forces when the wall is preloaded to this 

level. 

Figure 8-54 shows that the lateral displacement at the peak transverse pressure also 

approaches an asymptotic minimum as the preload exceeds 150-200 psi. This is consistent 

with the transverse pressure behavior expressed in figure 8-53, indicating a limitation of the 

transverse pressure capacity. 

0

100

200

300

400

500

600

700

800

900

0 50 100 150 200 250 300 350

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

6-in-thick -- 48-in half-wall height 8-in-thick -- 48-in half-wall height

Figure 8-53. Transverse pressure as measured from MRS laboratory testing as a 

function of preload for 48-inch-high half-walls (AAC Block from Florida).
148

 

 

Further examination of the parametric relationships confirms the arching theory as 

presented in chapters 5 and 6. Figure 8-55 shows that the transverse pressure is directly 

related to the lateral load acting on the half-wall during the laboratory tests. Figure 8-56 

shows that the lateral load is also directly related to the thrust force. This is also consistent 

with the arching theory. Finally, figure 8-57 shows the relationship between the transverse 

pressure and the arch thrust. This graph resembles the plot of transverse pressure versus 

preload shown in figure 8-53, showing that the arch thrust also reaches an asymptotic value. 

R2 = 0.96

R2 = 0.75

0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200 250 300 350

PRELOAD, psi

HORZ DISPLACEMENT @ PEA

K

TRANSVERSE PRESSURE, in .

6-in-thick -- 48-in half-wall height 8-in-thick -- 48-in half-wall height

Figure 8-54. Lateral displacement at which peak transverse pressure occurs also 

reaches an asymptotic minimum as the preload approaches 150 psi (AAC Block from 

Florida).
149

0

100

200

300

400

500

600

700

800

900

0 500 1,000 1,500 2,000 2,500 3,000 3,500

LATERAL LOAD @ PEAK TRANSVERSE PRESSURE, lbs

PEAK TRANSVERSE PRESSURE, psf .

6-in thick -- 48-in half-wall height 8-in thick -- 48-in half-wall height

Figure 8-55. Transverse pressure is directly related to the lateral load acting in 

the 48-inch-high half-wall MRS laboratory tests (AAC Block from Florida).

y = 104.48x - 193.95

R2

 = 0.73

y = 44.606x + 314.37

R2

 = 0.96

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 5 10 15 20 25 30 35

ARCH THRUST FORCE @ PEAK TRANSVERSE PRESSURE, kips

PEAK LATERAL LOAD, lbs .

6-in thick -- 48-in half-wall height 8-in thick -- 48-in half-wall height

Figure 8-56. Relationship between the lateral load and the arch thrust for MRS 

laboratory tests for the 48-inch half-wall height (AAC Block from Florida).
150

Figure 8-58 depicts the relationship for tests with less than 100 psi preload between the 

transverse pressure and the material modulus (E), the wall thickness (t), and the wall height 

(L) expressed as by the term Ex(t/L)2. The chart shows that 93 pct of the transverse pressure 

of a stopping is determined by this relationship. The material modulus is a significant 

parameter since it determines the amount of thrust force developed and ultimately the amount 

of lateral displacement of the wall, both of which control the arching mechanics of the wall. 

If the modulus is related to the compressive strength of the block material, the modulus factor 

could be replaced by the compressive strength as previous research suggests (Barczak, 2004). 

R2 = 0.75

R2 = 0.94

0

100

200

300

400

500

600

700

800

900

0 5 10 15 20 25 30 35 40 45 50

ARCH THRUST FORCE @ PEAK TRANSVERSE PRESSURE, kips

PEAK TRANSVERSE PRESSURE, psf .

6-in thick -- 48-in half-wall height 8-in thick -- 48-in half-wall height

Figure 8-57. Relationship between the transverse pressure and the arch thrust for MRS 

laboratory tests conducted at 48-inch half-wall height (AAC Block from Florida).
151

Evaluation of Predictive Models 

 The next goal is to evaluate the capability to predict the transverse pressure. If the 

thrust force and its resultant location and lateral load are known, the transverse pressure 

capacity of a stopping can be predicted with nearly 100 pct accuracy. If the thrust force 

location is instead calculated from the empirical model described in chapter 6 and shown in 

figure 8-59 for the two block thicknesses considered in this analysis, the transverse pressure 

can still be predicted with 99 pct accuracy as depicted by the open red square data points 

shown in figure 8-60. Each data point in figure 8-60 represents an individual laboratory test. 

As seen in the figure, the accuracy of the prediction is consistent throughout the full range of 

transverse pressure conducted in the laboratory testing, and includes preloading of wall from 

zero to 300 psi and three different wall heights. 

y = 3.23x - 177

R2

 = 0.94

0

100

200

300

400

500

600

0 50 100 150 200 250

Ex(t/L)2

, psi

TRANSVERSE PRESSURE, psf .

6-in thick -- 48-in half-wall height 8-in thick -- 48-in half-wall height

Figure 8-58. Correlation of factors involving the material modulus (E), wall 

thickness (t), and wall height (L) to the transverse pressure capacity of a stopping 

(AAC Block from Florida).
152

y = -0.0166x + 0.95

R2

 = 0.88

y = -0.0147x + 1.08

R2

 = 0.855

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 5 10 15 20 25 30 35 40 45 50

TOTAL THRUST P (SUM OF ARCH AND PRELOAD), kips 

THRUST RESULTANT POSITION FACTOR .

6-in thick -- 48-in half-wall height 8-in thick -- 48-in half-wall height

Figure 8-60. Prediction of transverse pressure when both the lateral load and arch 

thrust are known. Blue curves predicts transverse pressure when resultant thrust force 

location is also known and red squares show predicted transverse pressure when 

resultant thrust force location is calculated from empirical data (AAC block from 

Florida).

Figure 8-59. Resultant thrust force location for two block thicknesses as a function of 

the total arch thrust (AAC block from Florida).

y = x

R2 = 1

y = 0.99x

R2 = 0.94

0

100

200

300

400

500

600

700

800

900

0 100 200 300 400 500 600 700 800 900

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf .

Transverse load prediction based on measured thrust force and resultant load location and

measured lateral displacement 

Transverse load prediction based on measured thrust force and calculated resultant load location

and measured lateral displacement 
153

 If either the arch thrust or the lateral displacement is known, then the transverse 

pressure can still be calculated. It is recalled from chapter 7 that two methods were 

developed. Method 1 predicts the transverse pressure from the measured lateral 

displacement. Method 2 predicts the transverse pressure from the measured thrust force. 

Figures 8-61 illustrates the predictive capability of these models showing the measured 

transverse pressure vs. the predicted transverse pressure for each half-wall laboratory test. 

The overall accuracy of the predictive models is reasonably good (error less than 10 pct). 

However, as highlighted in this graph with yellow colored ovals, some laboratory tests are 

not accurately predicted. Further examination of these tests indicates that failure was 

occurring during the preloading of the half-wall prior to the application of transverse 

pressure. Figure 8-62 shows an example where the thrust force decreased immediately after 

the preload was applied and continued to decrease throughout the loading cycle. Figure 8-63 

shows that the predictive models are improved when these premature failures are eliminated 

from the data set. 

y = 1.00x

R2

 = 0.86

y = 0.95x

R2

 = 0.87

0

100

200

300

400

500

600

700

800

900

0 100 200 300 400 500 600 700 800 900

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf . .

Method 1 - Calculate transverse pressure with preload factor from measured lateral displacement and

preload

Method 2 - Calculate transverse pressure with preload factor from measured arch thrust and preload

Figure 8-61. Prediction of transverse pressure from known thrust and lateral loads 

(AAC block from Florida).
154

y = 1.00x

R2

 = 0.94

y = 0.98x

R2

 = 0.93

0

100

200

300

400

500

600

700

800

900

0 100 200 300 400 500 600 700 800 900

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf..

Method 1 - Calculate transverse pressure w ith preload factor from measured lateral displacement and preload

Method 2 - Calculate transverse pressure w ith preload factor from measured arch thrust and preload

Removed tests w here failure 

occurred during preloading.

Figure 8-63. Prediction of transverse pressure from known thrust and lateral loads with 

premature failures removed (AAC block from Florida).

0

200

400

600

800

1,000

1,200

1,400

0.00 0.50 1.00 1.50 2.00 2.50 3.00

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lb

0

8

16

24

32

40

48

56

THRUST LOAD, kips

Test #30 -- Lateral Load -- FL Block -- 6 in thick -- 288 psi preload

Test #30 -- Thrust Load -- FL Block -- 6 in thick -- 288 psi preload

Figure 8-62. Example of test with high preload showing how the thrust force 

decreases immediately after the preload is applied and continues to decrease through 

the full loading cycle. 
155

8.4.4 Theoretical Impact of Boundary Stiffness 

A theoretical assessment of the impact of the boundary stiffness is conducted by 

varying the system modulus of elasticity (see equation 6.11 and 7.7). The modulus of 

elasticity determines the deformations of the wall and the boundary, i.e. the mine roof and 

floor. The system modulus reflects the series stiffness equivalent of the wall and roof and 

floor structure. The theoretical assessment is made by reducing the system modulus to 75, 

50, and 25 pct of the rigid boundary condition, and using the lateral displacement model to 

calculate the transverse pressure. For comparative purposes, if the boundary stiffness were 

equal to the wall stiffness, the system stiffness would be reduced by 50 pct. Likewise, if the 

boundary stiffness were three times that of the wall, the system stiffness would be 75 pct of 

the rigid boundary condition, and if the boundary stiffness were one third of the wall 

stiffness, the system stiffness would be 25 pct of the rigid boundary condition. 

 Figure 8-64 shows the impact of the reduction in system modulus to 25, 50, and 75 pct 

of the rigid boundary condition for both the 6-in and 8-in thickness configurations. First, it 

can be concluded from figure 8-64 that as the boundary modulus is reduced, the transverse 

pressure capacity of the stopping will also be reduced. It is seen from this figure that the 

impact of reductions in boundary modulus will have a greater impact in terms of absolute 

reductions in transverse pressure for thicker walls than it will for thinner walls. For the 

example shown in figure 8-64, the transverse pressure for test number 56 for the 8-in-thick 

half-wall, was reduced from 498 psf for the rigid boundary condition to 156 psf when the 

boundary modulus is one third of the wall modulus, thereby reducing the system modulus to 

25 pct of the rigid boundary condition. This represents a 69 pct decrease in the transverse 

pressure capacity of the stopping. Figures 8-65 and 8-66 show the impact of reductions in 

system modulus for both the 6-in-thick and 8-in-thick walls including the walls with preload. 

The transverse pressure is plotted as a function of preload, which is scaled from 0 to 160 psi 

in these plots to eliminate the cases where premature failures were occurring from the higher 

preloads. These figures indicate the reductions in transverse pressure because of reduction in 

boundary stiffness (lower system modulus) are reduced as the preload increases through this 

range. Using the 8-in-thick half-wall as an example, the 69 pct decrease in transverse 

pressure which occurred by reducing the system modulus to 25 pct of the rigid boundary 

condition drops to a 19 pct reduction at a preload of 143 psi. 
156

y = 309.83x + 206.67

y = 155.17x + 7.97

0

100

200

300

400

500

600

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

REDUCTION IN SYSTEM MODULUS RELATIVE TO RIGID BOUNDARY 

CONDITIONS, pct

TRANSVERSE PRESSURE, psf .

6 inch wide -- 48-in half-wall height 8 inch wide -- 48-in half-wall height

Figure 8-64. Impact of reducing the boundary stiffness on transverse pressure 

capacity of stopping. Data shows individual test at different wall heights with no 

preload (AAC block from Florida).

y = -0.0033x2 + 2.08x + 1171

y = -0.0025x2 + 1.78x + 1561

y = -0.0042x2 + 2.37x + 781

y = -0.005x2 + 2.677x + 391

0

50

100

150

200

250

300

350

400

0 20 40 60 80 100 120 140 160

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Rigid Boundary Conditions 75% reduction in system modulus

50% reduction in system modulus 25% reduction in system modulus

Figure 8-65. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 6-inch-thick half-wall constructions (AAC 

block from Florida).
157

8.4 YTONG BLOCK 

Ytong is also an 

autoclaved aerated concrete 

(AAC) block, similar in 

material properties to that of 

the block described in the 

previous section. This block is 

now manufactured by Safecrete 

in Ringgold, Georgia, although 

the block that was tested was 

believed to be from a Florida 

plant. As previously described, 

the air pores within the formed structure characterize the material. The Ytong block had a 

unit block compressive strength of 705 psi, a 67 pct increase compared to the previously 

y = -0.0118x2 + 4.27x + 291

y = -0.0057x2 + 2.85x + 454

y = -0.014x2 + 5.27x + 1707

y = -0.0173x2 + 6.29x + 44

0

100

200

300

400

500

600

700

800

0 20 40 60 80 100 120 140 160

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Rigid Boundary Conditions 75% reduction in system modulus

50% reduction in system modulus 25% reduction in system modulus

Figure 8-66. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 8-inch-thick half-wall constructions (AAC 

block from Florida).

Figure 8-67. Ytong autoclaved aerated concrete 

block. 
158

discussed ACCOA block. The block that was tested measured nominally 8 inches thick and 

8 inches high by 24 inches wide. Figure 8-67 shows a photo of a 7.875-inch-thick block. 

This block weighs on average 29 lbs. 

8.5.1 Overview of the Test Program 

A total of 16 tests were conducted with Ytong block. The scope of testing included three 

half-wall heights of 31.50, 47.25, and 63.00 inches. The preload was varied in increments of 

50 psi from 0 to 145 psi. The results of the MRS half-wall tests are summarized in the table 

8-8. Graphs of the measured lateral load and thrust load as a function of the lateral 

displacement of the wall for each test are documented in Appendix B. A tabular summary of 

the pertinent parameters and loading values for each test is also included Appendix C. 

Table 8-8. Summary of Ytong block tests. 

Block Type Test 

No. 

Block 

Width 

(in) 

Block 

Height 

(in) 

Block 

Length 

(in) 

Halfwall 

Height 

(in) 

Preload 

(psi) 

Measured 

Transverse 

Pressure, 

(psf) 

Ytong 239 7.875 7.875 24 31.5 3 2,150 

Ytong 249 7.875 7.875 24 31.5 7 1,822 

Ytong 243 7.875 7.875 24 31.5 51 2,016 

Ytong 250 7.875 7.875 24 31.5 58 2,272 

Ytong 251 7.875 7.875 24 31.5 94 2,186 

Ytong 241 7.875 7.875 24 31.5 107 2,160 

Ytong 242 7.875 7.875 24 31.5 145 2,590 

Ytong 234 7.875 7.875 24 47.25 15 562 

Ytong 235 7.875 7.875 24 47.25 53 772 

Ytong 237 7.875 7.875 24 47.25 109 1,034 

Ytong 238 7.875 7.875 24 47.25 132 1,060 

Ytong 245 7.875 7.875 24 63 10 262 

Ytong 246 7.875 7.875 24 63 38 386 

Ytong 252 7.875 7.875 24 63 69 360 

Ytong 247 7.875 7.875 24 63 99 384 

Ytong 248 7.875 7.875 24 63 142 448 
159

8.5.2 Parametric Relationships and Trends. 

Examining table 8-8, it is seen that the transverse pressure capacity of the stoppings 

constructed from Ytong block varied from a low of 262 to a high of 2,590 psf or 1.82 to 

17.99 psi. The transverse pressure is most significantly affected by the wall height as with 

previous block tests. Figure 8-68 displays the transverse pressure as a function of preload for 

the three different wall heights and preload varying from 0 to 150 psi. The transverse 

pressures for the 31.5-in-high half-walls are 5-6 times that of the 63-in-high half-walls and 

two to 4 times higher than the 47.25-in-high half-walls. The impact of the preload was less 

than was observed with the conventional Portland cement block (section 8.1), which is 

consistent with the results observed for the Florida AACOA block as well. The 47.25-inhigh half-wall showed the familiar trend of nonlinear response with preload, but here too the 

impact was rather small, with a decrease of 47 pct in transverse pressure when the preload 

was decreased from 132 psi to 15 psi. In terms of percent, the least impact was observed 

with the shortest wall height (31.5 inches). It is also seen from figure 8-68 that the transverse 

pressure approaches an asymptotic maximum at approximately 125 psi, suggesting the block 

strength is being exceeded at this loading. 

Figure 8-68. Transverse pressure as measured from MRS laboratory testing as a 

function of preload for three different half-wall heights (Ytong AAC block).

0

500

1,000

1,500

2,000

2,500

3,000

0 20 40 60 80 100 120 140 160

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

31.5-in half-wall height 47.25-in half-wall height 63-in half-wall height
160

 Figure 8-69 shows that the lateral displacement at the peak transverse pressure also 

approaches an asymptotic minimum as the preload approaches 125 psi. This is consistent 

with the transverse pressure behavior expressed in figure 8-68, indicating a limitation of the 

transverse pressure capacity. 

 Further examination of the parametric relationships confirms the arching theory as 

presented in chapters 5 and 6. Figure 8-70 shows that the transverse pressure is directly 

related to the lateral load acting on the half-wall during the laboratory tests. Figure 8-71 

shows that the lateral load is also directly related to the thrust force. This is also consistent 

with the arching theory. Finally, figure 8-72 shows the relationship between the transverse 

pressure and the arch thrust. This graph is somewhat inconsistent with the previous analysis 

in that the transverse pressure does not reach an asymptotic level with the increasing arch 

thrust, suggesting that the material strength has not been reached at the preloads considered 

in this analysis. 

R2 = 0.29

R2 = 0.47

R2 = 0.69

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 20 40 60 80 100 120 140 160

PRELOAD, psi

HORZ DISPLACEMENT @ PEAK .

TRANSVERSE PRESSURE, in .

31.5-in half-wall height 47.25-in half-wall height 63-in half-wall height

Figure 8-69. Lateral displacement at which peak transverse pressure occurs also 

reaches an asymptotic minimum as the preload approaches 130 psi (Ytong AAC 

block).
161

0

500

1,000

1,500

2,000

2,500

3,000

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000

LATERAL LOAD @ PEAK TRANSVERSE PRESSURE, lbs

PEAK TRANSVERSE PRESSURE, psf .

31.5-in half-wall height 47.25-in half-wall height 63-in half-wall height

Figure 8-70. Transverse pressure is directly related to the lateral load acting on 

the half-wall in the MRS laboratory tests (Ytong AAC block).

y = 78.42x + 649

R2

 = 0.95

y = 94.07x + 1792

R2

 = 0.69

y = 40.17x + 817.99

R2

 = 0.83

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

0 5 10 15 20 25 30 35 40 45 50

ARCH THRUST FORCE @ PEAK TRANSVERSE PRESSURE, kips

PEAK LATERAL FORCE, lbs .

31.5-in half-wall height 47.25-in half-wall height 63-in half-wall height

Figure 8-71. Relationship between the lateral load and the arch thrust for MRS 

laboratory tests for three different wall heights (Ytong AAC block).
162

Figure 8-73 depicts the relationship for tests with less than 100 psi preload between the 

transverse pressure and the material modulus (E), the wall thickness (t), and the wall height 

(L) expressed as by the term Ex(t/L)2. The chart shows that 98 pct of the transverse pressure 

of a stopping is determined by this relationship. The material modulus is a significant 

parameter since it determines the amount of thrust force developed and ultimately the amount 

of lateral displacement of the wall, both of which control the arching mechanics of the wall. 

If the modulus is related to the compressive strength of the block material, the modulus factor 

could be replaced by the compressive strength as previous research suggests (Barczak, 2004). 

R2 = 0.96

R2 = 0.72

R2 = 0.83

0

500

1,000

1,500

2,000

2,500

3,000

0 5 10 15 20 25 30 35 40 45 50

ARCH THRUST FORCE @ PEAK TRANSVERSE PRESSURE, kips

PEAK TRANSVERSE PRESSURE, psf . .

31.5-in half-wall height 47.25-in half-wall height 63-in half-wall height

Figure 8-72. Relationship between the transverse pressure and the arch thrust for 

MRS laboratory tests conducted at three different wall heights (Ytong AAC block).
163

8.5.3 Evaluation of Predictive Models 

 The next goal is to evaluate the capability to predict the transverse pressure. If the 

thrust force and its resultant location and lateral load are known, the transverse pressure 

capacity of a stopping can be predicted with nearly 100 pct accuracy. If the thrust force 

location is instead calculated from the empirical model described in chapter 6 and shown in 

figure 8-74 for three half-wall heights considered in this analysis, the transverse pressure can 

still be predicted with a 99 pct accuracy as depicted by the open red square data points shown 

in figure 8-75. Each data point in figure 8-75 represents an individual laboratory test. As 

seen in the figure, the accuracy of the prediction is consistent throughout the full range of 

transverse pressure conducted in the laboratory testing, and includes preloading of wall from 

0 to 160 psi and three different wall heights. 

Figure 8-73. Correlation of factors involving the material modulus (E), wall thickness 

(t), and wall height (L) to the transverse pressure capacity of a stopping (AAC Block 

from Florida).

y = 6.29x - 280

R2

 = 0.98

0

500

1,000

1,500

2,000

2,500

0 50 100 150 200 250 300 350 400

Ex(t/L)2

, psi

TRANSVERSE PRESSURE, psf . .

31.5-in half-wall height 47.25-in half-wall height 63-in half-wall height
164

y = 1.00x

R2

 = 1.00

y = 1.00x

R2

 = 0.99

0

500

1,000

1,500

2,000

2,500

3,000

0 500 1,000 1,500 2,000 2,500 3,000

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE

 PRESSURE, psf .

Transverse pressure prediction based on measured thrust force and calculated

resultant load location and measured lateral displacement 

Transverse pressure prediction based on measured thrust force and resultant load

location and measured lateral displacement 

y = -0.0083x + 1.016

R2

 = 0.69

y = -0.0061x + 0.94

R2

 = 0.91

y = -0.0116x + 1.05

R2

 = 0.894

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

15 20 25 30 35 40 45 50

TOTAL THRUST P (SUM OF ARCH AND PRELOAD), kips 

THRUST RESULTANT POSITION FACTOR .

31.5-in half-wall height 47.25-in half-wall height 63-in half-wall height

Figure 8-74. Resultant thrust force location for three wall heights as a function of the 

total arch thrust (AAC block from Florida).

Figure 8-75. Prediction of transverse pressure when both the lateral load and arch thrust are 

known. Blue curves predicts transverse pressure when resultant thrust force location is also 

known and red squares show predicted transverse pressure when resultant thrust force 

location is calculated from empirical data (Ytong AAC block).
165

 If either the arch thrust or the lateral displacement is known, then the transverse 

pressure can still be calculated. It is recalled from chapter 7 that two methods were 

developed. Method 1 predicts the transverse pressure from the measured lateral 

displacement. Method 2 predicts the transverse pressure from the measured thrust force. 

Figure 8-76 illustrates the predictive capability of these two methods showing the measured 

transverse pressure vs. the predicted transverse pressure for each half-wall laboratory test. 

Methods 1 and 2, which either utilize the measured lateral displacement or measured thrust 

load, on average provide very accurate predictions (1 pct error based on trend line). 

8.5.4 Theoretical Impact of Boundary Stiffness 

A theoretical assessment of the impact of the boundary stiffness is conducted by 

varying the system modulus of elasticity (see equation 6.11 and 7.7). The modulus of 

elasticity determines the deformations of the wall and the boundary, i.e. the mine roof and 

y = 1.01x

R2 = 0.98

y = 1.01x

R2 = 0.98

0

500

1,000

1,500

2,000

2,500

3,000

0 500 1,000 1,500 2,000 2,500 3,000

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf .... .

Method 1 - Calculate transverse pressure with preload factor from measured lateral

displacement and preload

Method 2 - Calculate transverse pressure with preload factor from measured arch thrust and

preload

Figure 8-76. Prediction of transverse load from known thrust and lateral loads with 

premature failures removed (Ytong AAC block). 
166

floor. The system modulus reflects the series stiffness equivalent of the wall and roof and 

floor structure. The theoretical assessment is made by reducing the system modulus to 75, 

50, and 25 pct of the rigid boundary condition, and the transverse pressure is calculated using 

the lateral displacement model developed in chapter 7. For comparative purposes, if the 

boundary stiffness were equal to the wall stiffness, the system stiffness would be reduced by 

50 pct. Likewise, if the boundary stiffness were three times that of the wall, the system 

stiffness would be 75 pct of the rigid boundary condition, and if the boundary stiffness were 

one third of the wall stiffness, the system stiffness would be 25 pct of the rigid boundary 

condition. 

Figure 8-77 shows the impact of the reduction in system modulus to 25, 50, and 75 pct 

of the rigid boundary condition at three different wall heights as a function of preload. First, 

it can be concluded from figure 8-77 that as the boundary modulus is reduced, the transverse 

pressure capacity of the stopping will also be reduced. It is seen from this figure that the 

impact of reductions in boundary modulus will have a greater impact in terms of absolute 

reductions in transverse pressure for thicker walls than it will for thinner walls. For the 

example shown in figure 8-77, the transverse pressure for test number 239 for the 31.5-inhigh half-wall, the transverse pressure was reduced from 1,988 psf for the rigid boundary 

condition to 744 psf when the boundary modulus is one third of the wall modulus, thereby 

reducing the system modulus to 25 pct of the rigid boundary condition. This represents a 63 

pct decrease in the transverse pressure capacity of the stopping. 

 Figures 8-78 through 8-80 show the impact of reductions in system modulus for halfwall heights of 31.5, 47.25, and 63 inches. In these figures, the transverse pressure is plotted 

as a function of preload, which is scaled from 0 to 160 psi in these plots. These figures 

indicate the reductions in transverse pressure as a result of reduction in boundary stiffness 

(lower system modulus) are reduced as the preload increases through this range. Using the 

31.5-in-high half-wall as an example, the 63 pct decrease in transverse pressure which 

occurred by reducing the system modulus to 25 pct of the rigid boundary condition, drops to 

a 15 pct reduction at a preload of 145 psi. 
167

y = 4382x + 115

y = 1659x + 400

y = 190x + 52

0

500

1,000

1,500

2,000

2,500

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

REDUCTION IN SYSTEM MODULUS RELATIVE TO RIGID BOUNDARY 

CONDITIONS, pct

TRANSVERSE PRESSURE, psf .

31.5-in half-wall height 47.25-in half-wall height 63-in half-wall height

Figure 8-77. Impact of reducing the boundary stiffness on transverse pressure capacity 

of stopping. Data shows individual test at different wall heights with no preload (Ytong 

AAC block).

y = -0.009x2 + 5.75x + 1671

y = -0.0015x2 + 3.30x + 1967

y = -0.0133x2 + 8.48x + 1246

y = -0.0144x2 + 11.47x + 692

0

500

1,000

1,500

2,000

2,500

3,000

0 20 40 60 80 100 120 140 160

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Rigid Boundary Conditions 75% reduction in system modulus 50% reduction in system modulus 25% reduction in system modulus

Figure 8-78. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 31.5-in-high half-wall constructions (Ytong 

AAC block).
168

y = -0.0132x2 + 5.82x + 366

y = -0.0148x2 + 5.63x + 470

y = -0.0103x2 + 5.87x + 254

y = -0.0062x2 + 5.76x + 137

0

200

400

600

800

1,000

1,200

0 20 40 60 80 100 120 140

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Rigid Boundary Conditions 75% reduction in system modulus

50% reduction in system modulus 25% reduction in system modulus

Figure 8-79. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 47.25-in-high half-wall constructions (Ytong 

AAC block).

y = -0.0059x2 + 2.62x + 167

y = -0.0053x2 + 2.27x + 211

y = -0.0068x2 + 3.05x + 116

y = -0.0081x2 + 3.55x + 60

0

50

100

150

200

250

300

350

400

450

0 20 40 60 80 100 120 140 160

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Rigid Boundary Conditions 75% reduction in system modulus

50% reduction in system modulus 25% reduction in system modulus

Figure 8-80. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 63-in-high half-wall constructions (Ytong 

AAC block).
169

8.6 KINGSWAY BLOCK 

Kingsway is another autoclaved 

aerated concrete (AAC) block, similar in 

material properties to that of the block 

described in the previous two sections. This 

block was manufactured by KTL 

Technologies in England, and was the block 

that was utilzied as part of the underground 

verification of the arching mechanism and 

laboratory testing protocol. As previously 

described, the air pores within the formed 

structure characterize the material. The 

Kingsway block had a unit block 

compressive strength of 546 psi. A photo of 

the block is shown in figure 8-81, including 

a close-up of the block showing the air 

pockets within the concrete structure. The 

block that was tested measured nominally 5-

7/8 inches thick and 8-3/8 inches high by 15-

1/4 inches wide. This block weighs on average 21 lbs.

8.6.1 Overview of the Test Program 

A total of 9 tests were conducted with Kingsway block. The scope of testing included 

four half-wall heights of 33.5, 41.875, 50.25, and 58.625 inches. Due to the limited number 

of block available, there was no attempt to vary the preload as part of the test program. A 

nominal preload of 50-100 psi was applied for all tests. The results of the MRS half-wall 

tests are summarized in the table 8-9. Graphs of the measured lateral load and thrust load as 

a function of the lateral displacement of the wall for each test are documented in Appendix 

B. A tabular summary of the pertinent parameters and loading values for each test is also 

included Appendix C. 

Figure 8-81. Kingsway AAC block

including close-up of highlighted section 

showing air pockets within concrete 

structure.. 
170

Table 8-9. Summary of test configurations and results for the Kingsway block. 

Block Type Test 

# 

Block 

Width 

(in) 

Block 

Height 

(in) 

Block 

Length 

(in) 

Halfwall 

Height 

(in) 

Preload 

(psi) 

Measured 

Transverse 

Pressure, 

(psf) 

Kingsway 147 5.875 8.375 17.25 33.5 65 758 

Kingsway 148 5.875 8.375 17.25 33.5 54 834 

Kingsway SD2 5.875 8.375 17.25 41.875 50 462 

Kingsway SD1 5.875 8.375 17.25 41.875 50 388 

Kingsway 137 5.875 8.375 17.25 41.875 80 448 

Kingsway 138 5.875 8.375 17.25 41.875 66 406 

Kingsway 139 5.875 8.375 17.25 50.25 89 226 

Kingsway 135 5.875 8.375 17.25 58.625 45 174 

Kingsway 136 5.875 8.375 17.25 58.625 64 138 

8.6.2 Parametric Relationships and Trends. 

Examining table 8-9, it is seen that the transverse pressure capacity of the stoppings 

constructed from Kingsway block varied from a low of 138 to a high of 834 psf or 0.95 to 

5.79 psi. The transverse pressure is most significantly affected by the wall height as with 

previous block tests. Figure 8-82 shows that the transverse pressure is directly related to the 

lateral load acting on the half-wall during the laboratory tests. In this graph, the data are 

grouped by wall height. The 50.25 and 58.625 half-wall height, which amounts to one 

course of block height difference, are grouped together for the regression analysis since there 

is only one test at the 58.625-in height. This degrades the analysis slightly. This data 

grouping is also included in figures 8-83 and 8-84. Figure 8-83 shows that the lateral load is 

also directly related to the thrust force. This is also consistent with the arching theory. 

Finally, figure 8-84 shows the relationship between the transverse pressure and the arch 

thrust. Unlike previous analyses, there is insufficient change in preload in this data set to 

cause the transverse pressure to reach an asymptotic level with the increasing arch thrust. 

Due to the small changes in preload, the arch thrust for a specific height also changes 

relatively little (less than 5 kips) for each of the height evaluations. 
171

0

100

200

300

400

500

600

700

800

900

0 200 400 600 800 1,000 1,200 1,400 1,600 1,800

LATERAL LOAD @ PEAK TRANSVERSE PRESSURE, lbs

PEAK TRANSVERSE PRESSURE, psf .

33.5-in half-wall height 41.875-in half-wall height

50.25-in half-wall height 58.625-in half-wall height

Figure 8-82. Transverse pressure is directly related to the lateral load acting on the 

half-wall in the MRS laboratory tests (Kingsway AAC block).

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

8 9 10 11 12 13 14 15

ARCH THRUST FORCE @ PEAK TRANSVERSE PRESSURE, kips

PEAK LATERAL FORCE, lbs .

33.5-in half-wall height 41.875-in half-wall height

50.25-in half-wall height 58.625-in half-wall height

Figure 8-83. Relationship between the lateral load and the arch thrust for MRS 

laboratory tests for different wall heights (Kingsway AAC block).
172

Figure 8-85 depicts the relationship for tests with less than 100 psi preload between the 

transverse pressure and the material modulus (E), the wall thickness (t), and the wall height 

(L) expressed as by the term E x (t/L)2

. The chart shows that 98 pct of the transverse 

pressure of a stopping is determined by this relationship. The material modulus is a 

significant parameter since it determines the amount of thrust force developed and ultimately 

the amount of lateral displacement of the wall, both of which control the arching mechanics 

of the wall. If the modulus is related to the compressive strength of the block material, the 

modulus factor could be replaced by the compressive strength as previous research suggests 

(Barczak, 2004). 

0

100

200

300

400

500

600

700

800

900

8 9 10 11 12 13 14 15

ARCH THRUST FORCE @ PEAK TRANSVERSE PRESSURE, kips

PEAK TRANSVERSE PRESSURE, psf .

33.5-in half-wall height 41.875-in half-wall height

50.25-in half-wall height 58.625-in half-wall height

Figure 8-84. Relationship between the transverse pressure and the arch thrust for 

MRS laboratory tests conducted at different wall heights (Kingsway AAC block).
173

8.6.3 Evaluation of Predictive Models 

The next goal is to evaluate the capability to predict the transverse pressure. If the 

thrust force and its resultant location and lateral load are known, the transverse pressure 

capacity of a stopping can be predicted with nearly 100 pct accuracy. If the thrust force 

location is instead calculated from the empirical model described in chapter 6 and shown in 

figure 8-86 for three half-wall heights considered in this analysis, the transverse pressure can 

still be predicted with a 92 pct accuracy as depicted by the open red square data points shown 

in figure 8-87. Each data point in figure 8-87 represents an individual laboratory test. As 

seen in the figure, the accuracy of the prediction is consistent throughout the full range of 

transverse pressure conducted in the laboratory testing. 

Figure 8-85. Correlation of factors involving the material modulus (E), wall thickness 

(t), and wall height (L) to the transverse pressure capacity of a stopping (Kingsway 

AAC Block).

y = 5.01x - 179

R2

 = 0.98

0

100

200

300

400

500

600

700

800

900

0 50 100 150 200 250

Ex(t/L)2

, psi

TRANSVERSE PRESSURE, psf.

33.5-in half-wall height 41.875-in half-wall height

50.25-in half-wall height 58.625-in half-wall height
174

Figure 8-87. Prediction of transverse pressure when both the lateral load and arch 

thrust are known. Blue curves predicts transverse pressure when resultant thrust 

force location is also known and red squares show predicted transverse pressure 

when resultant thrust force location is calculated from empirical data (Kingsway 

AAC block).

y = -0.0119x + 1.02

R2

 = 1.00

y = -0.0391x + 1.32

R2

 = 0.98

y = -0.0657x + 1.48

R2 = 0.81

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

8 9 10 11 12 13 14 15

TOTAL THRUST P (SUM OF ARCH AND PRELOAD), kips 

THRUST RESULTANT POSITION FACTOR . .

33.5-in half-wall height 41.875-in half-wall height

50.25-in half-wall height 58.625-in half-wall height

Figure 8-86. Resultant thrust force location for three wall heights as a function of the 

total arch thrust (Kingsway AAC block).

y = x

R2

 = 1.00

y = 1.08x

R2

 = 0.98

0

100

200

300

400

500

600

700

800

900

0 100 200 300 400 500 600 700 800 900

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERS

E

PRESSURE, psf 

Transverse pressure prediction based on measured thrust force and resultant load location

and measured lateral displacement 

Transverse pressure prediction based on measured thrust force and calculated resultant

load location and measured lateral displacement 
175

If either the thrust force or lateral displacement is known, then the transverse pressure 

can still be predicted. It is recalled from chapter 7 that two methods were developed. 

Method 1 predicts the transverse pressure from the measured lateral displacement. Method 2 

predicts the transverse pressure from the measured thrust force. Figure 8-88 illustrates the 

predictive capability of these two methods showing the measured transverse pressure vs. the 

predicted transverse pressure for each half-wall laboratory test. Method 1 slightly under 

predicts the transverse pressure by about 3 pct, while method 2 slightly over predicts the 

transverse pressure by about 1 pct. 

8.6.4 Theoretical Impact of Boundary Stiffness 

A theoretical assessment of the impact of the boundary stiffness is conducted by varying 

the system modulus of elasticity (see equation 6.11 or 7.7). The modulus of elasticity 

determines the deformations of the wall and the boundary, i.e. the mine roof and floor. The 

system modulus reflects the series stiffness equivalent of the wall and roof and floor 

structure. The theoretical assessment is made by reducing the system modulus to 75, 50, and 

y = 1.02x

R2

 = 0.97

y = 0.99x

R2

 = 0.94

0

100

200

300

400

500

600

700

800

900

0 100 200 300 400 500 600 700 800 900

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERS

E

PRESSURE, psf. .

Method 1 - Calculate transverse pressure with preload factor from measured lateral

displacement and preload

Method 2 - Calculate transverse pressure with preload factor from measured arch thrust

and preload

Figure 8-88. Prediction of transverse pressure from known thrust and lateral loads with 

premature failures removed (Kingsway AAC block).
176

25 pct of the rigid boundary condition. For comparative purposes, if the boundary stiffness 

were equal to the wall stiffness, the system stiffness would be reduced by 50 pct. Likewise, 

if the boundary stiffness were three times that of the wall, the system stiffness would be 75 

pct of the rigid boundary condition, and if the boundary stiffness were one third of the wall 

stiffness, the system stiffness would be 25 pct of the rigid boundary condition. 

Figure 8-89 shows the impact of the reduction in system modulus to 25, 50, and 75 pct of 

the rigid boundary condition at 3 different wall heights as a function of preload. For the 

example, the transverse pressure for test number 239 for the 33.5-in-high half-wall, the 

transverse pressure was reduced from 780 psf for the rigid boundary condition to 540 psf 

when the boundary modulus is one third of the wall modulus, thereby reducing the system 

modulus to 25 pct of the rigid boundary condition. This represents a 31 pct decrease in the 

transverse pressure capacity of the stopping. 

0

100

200

300

400

500

600

700

800

900

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

REDUCTION IN SYSTEM MODULUS RELATIVE TO RIGID BOUNDARY 

CONDITIONS, pct

PEAK TRANSVERSE PRESSURE, psf .

33.5-in half-wall height 41.875-in half-wall height 58.625-in half-wall height

Figure 8-89. Impact of reducing the boundary stiffness on transverse pressure 

capacity of stopping. Data shows individual test at different wall heights with no 

preload (Kingsway AAC block).
177

8.7 OMEGA BLOCK 

 Omega block are manufactured by 

Burrell Mining Products Inc. located in 

New Kensington, Pennsylvania near 

Pittsburgh. The block is composed of 

Portland cement and flyash and also 

contains air pores within the concrete 

structure to create a very low density 

material (22 lbs per cubic foot). The block 

can easily be cut with a handsaw. The 

block as shown in figure 8-90 measures 

nominally 8 in thick, 24 in wide, and 16 in 

in height and weighs just less than 40 lbs, yet it covers the same area as three regular 

concrete blocks that weigh as much as 50 lbs each. The compressive strength is only 84 psi, 

making it the weakest block evaluated in this research effort thusfar. The block is brittle and 

susceptible to damage from handling. Small fiberglass fibers are imbedded in the mix to help 

hold the material together and improve its post failure loading characteristics. 

8.7.1 Overview of the Test Program 

 A total of 22 tests were conducted with Omega block. Half-wall configurations at 

heights of 32, 48, and 64 inches from 2, 3, and 4 courses of block were evaluated in the test 

program. The results of the MRS half-wall tests are summarized in the table 8-10. The low 

compressive strength of the block did not allow much variation of preload. A nominal 

preload was applied and measured once the test began, although the magnitude could not be 

precisely controlled, with the result that the preload varied from 1 to 27 psi. The low 

strength of the block resulted in thrust loading that was near the measurable limits of the load 

frame. This contributed to some of the inconsistency in the test results. Graphs of the 

measured lateral load and thrust load as a function of the lateral displacement of the wall for 

each test are documented in Appendix B. A tabular summary of the pertinent parameters and 

loading values for each test is also included Appendix C. 

Figure 8-90. Omega block manufactured 

by Burrell Mining Products Inc. 
178

Table 8-10. Summary of Omega block tests. 

Block Type Test 

No. 

Block 

Width 

(in) 

Block 

Height 

(in) 

Block 

Length 

(in) 

Halfwall 

Height 

(in) 

Preload 

(psi) 

Measured 

Transverse 

Pressure, 

(psf) 

Omega Block 221 8 16 24 32 2 176 

Omega Block 220 8 16 24 32 5 184 

Omega Block 174 8 16 24 32 8 254 

Omega Block 169 8 16 24 32 8 210 

Omega Block 143 8 16 24 32 9 188 

Omega Block 170 8 16 24 32 15 282 

Omega Block 175 8 16 24 32 27 288 

Omega Block 144 8 16 24 32 28 230 

Omega Block 172 8 16 24 48 1 42 

Omega Block 222 8 16 24 48 6 40 

Omega Block 173 8 16 24 48 8 110 

Omega Block 168 8 16 24 48 14 70 

Omega Block 167 8 16 24 48 20 128 

Omega Block 141 8 16 24 48 23 130 

Omega Block 142 8 16 24 48 27 100 

Omega Block 223 8 16 24 64 8 16 

Omega Block 165 8 16 24 64 12 16 

Omega Block 176 8 16 24 64 14 14 

Omega Block 177 8 16 24 64 15 18 

Omega Block 145 8 16 24 64 20 24 

Omega Block 166 8 16 24 64 21 30 

Omega Block 146 8 16 24 64 27 50 

8.7.2 Parametric Relationships and Trends. 

 Examining table 8-10, it is seen that the transverse pressure capacity of the stoppings 

constructed from Omega block varied from a low of 14 to a high of 288 psf or 0.03 to 2.00 

psi. Figure 8-91 displays the transverse pressure as a function of preload for the three halfwall heights. The transverse pressures for the 32-in-high half-walls are an order of 

magnitude higher than the 64-in-high half-walls. It is also seen from figure 8-91 that the 

transverse pressure is nonlinearly related to the preload and that the transverse pressure 

approaches an asymptotic maximum at approximately 20 psi for the 32 and 48 in-high walls. 

The upward slope 64-in high wall curve suggests the peak loading has not been reached, but 

the data at the low preloads is inconsistent and it is likely that the 64-in-high walls are also 

approaching a transverse pressure limit. Figure 8-92 plots the lateral displacement at which 

the peak transverse pressure is achieved as a function of preload using the complete data set. 
179

Although the correlation is very weak, the trend is that the lateral displacement also 

approaches an asymptotic level at about 20 psi. 

Figure 8-92. Lateral displacement at which peak transverse pressure occurs also 

reaches an asymptotic minimum as the preload approaches 150 psi (Omega Block).

Figure 8-91. Transverse pressure as measured from MRS laboratory testing as a 

function of preload for three half-wall heights (Omega Block).

R2 = 0.13

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 5 10 15 20 25 30

PRELOAD, psi

HORZ DISPLACEMENT @ PEAK . 

TRANSVERSE PRESSURE, in .

32-in half-wall height 48-in half-wall height 64-in half-wall height

y = -0.15x2 + 7.12x + 29

R2

 = 0.62

y = -0.32x2 + 13.12x + 137

R2

 = 0.64

y = 0.12x2 - 2.40x + 26

R2

 = 0.99

0

50

100

150

200

250

300

350

0 5 10 15 20 25 30

PRELOAD, psi

TRANSVERSE PRESSURE, psf . .

32-in half-wall height 48-in half-wall height 64-in half-wall height
180

 Further examination of the parametric relationships confirms the arching theory as 

presented in chapter 6. Figure 8-93 shows that the transverse pressure is directly related to 

the lateral force acting on the half-wall during the laboratory tests. Figure 8-94 shows that 

the lateral force is also directly related to the thrust force. This is also consistent with the 

arching theory. Finally, figure 8-95 shows the relationship between the transverse pressure 

and the arch thrust. This graph resembles the plot of transverse pressure versus preload 

shown in figure 8-91, showing that the arch thrust also reaches an asymptotic value. 

0

50

100

150

200

250

300

350

0 100 200 300 400 500 600 700 800 900

LATERAL LOAD @ PEAK TRANSVERSE PRESSURE, lbs

PEAK TRANSVERSE PRESSURE, psf .

32-in half-wall height 48-in half-wall height 64-in half-wall height

Figure 8-93. Relationship between the lateral load and the arch thrust for MRS 

laboratory tests for three half-wall heights (Omega Block).
181

y = 99.68x + 53.55

R2

 = 0.93

y = 117.5x + 178.25

R2

 = 0.90

y = 49.99x + 17.86

R2

 = 0.85

0

100

200

300

400

500

600

700

800

900

0123456

ARCH THRUST FORCE @ PEAK TRANSVERSE PRESSURE, kips

PEAK LATERAL FORCE, lbs .

32-in half-wall height 48-in half-wall height 64-in half-wall height

Figure 8-94. Relationship between the lateral load and the arch thrust for MRS 

laboratory tests for three half-wall heights (Omega Block).

R2 = 0.95

R2 = 0.88

R2 = 0.88

0

50

100

150

200

250

300

350

0123456

ARCH THRUST FORCE @ PEAK TRANSVERSE PRESSURE, kips

PEAK TRANSVERSE PRESSURE, psf . .

32-in half-wall height 48-in half-wall height 64-in half-wall height

Figure 8-95. Relationship between the transverse pressure and the arch thrust for 

MRS laboratory tests conducted at three half-wall heights (Omega Block).
182

 Figure 8-96 depicts the relationship between the transverse pressure and the material 

modulus (E), the wall thickness (t), and the wall height (L) expressed as by the term 

E x (t/L)2

. The general trend of increasing transverse pressure with increasing E x (t/L)2 is 

typical of other block types. However, as seen in the chart, the data for the Omega block is 

scattered resulting in a poor correlation compared to other block types. The chart shows that 

24 pct of the transverse pressure of a stopping is determined by this relationship. This 

material is very weak and prone to damage even from handling. Small amounts of preload 

can substantially damage the block. This accounts for the scatter and poor correlation. The 

material modulus is a significant parameter since it determines the amount of thrust force 

developed and ultimately the amount of lateral displacement of the wall, both of which 

control the arching mechanics of the wall. However, the air pores and weak concrete matrix 

and localized damage to the block from the test preparation or transverse pressure 

development cause the material modulus to vary from block to block. 

y = 15.74x + 52.39

R2

 = 0.24

0

50

100

150

200

250

300

0 2 4 6 8 10 12

Ex(t/L)2

TRANSVERSE PRESSURE, psf . Figure 8-96. Correlation of factors involving the material modulus (E), wall 

thickness (t), and wall height (L) to the transverse pressure capacity of a stopping 

(Omega Block).
183

8.7.3 Evaluation of Predictive Models 

 The next goal is to evaluate the capability to predict the transverse pressure. If the 

thrust force and its resultant location and lateral load are known, the transverse pressure 

capacity of a stopping can be predicted with nearly 100 pct accuracy. If the thrust force 

location is instead calculated from the empirical model described in chapter 6 and shown in 

figure 8-97 for three half-wall heights considered in this analysis, the transverse pressure can 

still be predicted to better than 99 pct accuracy as depicted by the open red square data points 

shown in figure 8-98. Each data point in figure 8-98 represents an individual laboratory test. 

As seen in the figure, the accuracy of the prediction is consistent throughout the full range of 

transverse pressure conducted in the laboratory testing, and includes preloading of wall from 

0 to 27 psi and three different wall heights. Hence, while the wall performances may not be 

very consistent, if the thrust and lateral displacement are known, the arching mechanics still 

dictate a good measure of the transverse pressure capacity. 

Figure 8-97. Resultant thrust force location for three wall heights as a function of the 

total arch thrust (Omega block).

y = -0.0271x + 0.98

R2

 = 0.34

y = -0.0474x + 1.07

R2

 = 0.52

y = -0.0811x + 0.88

R2

 = 0.85

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0123456

TOTAL THRUST P (SUM OF ARCH AND PRELOAD), kips 

THRUST RESULTANT POSITION FACTOR .

32-in half-wall height 48-in half-wall height 64-in half-wall height
184

 If either the thrust force or the lateral displacement is known, then the transverse 

pressure can still be calculated. It is recalled from chapter 7 that two methods were 

developed. Method 1 predicts the transverse pressure from the measured lateral 

displacement. Method 2 predicts the transverse pressure from the measured thrust force. 

Figures 8-99 illustrates the predictive capability of these models showing the measured 

transverse pressure vs. the predicted transverse pressure for each half-wall laboratory test. 

The accuracy of the predictive models is less than that developed for previous blocks, due in 

large part to the inconsistency of the block material properties and low thrust loads. Overall, 

the accuracy of the models is within 15 pct of the measured transverse pressure based on the 

trend line, although individual test predictions can be considerably less accurate. Models 1 

and 2, which are based on measured lateral displacements (method 1) or measured thrust 

forces (method 2) tend to over predict the transverse pressure. 

Figure 8-98. Prediction of transverse pressure when both the lateral load and arch 

thrust are known. Blue curves predicts transverse pressure when resultant thrust force 

location is also known and red squares show predicted transverse pressure when 

resultant thrust force location is calculated from empirical data (Omega block).

y = 1.00x

R2

 = 1.00

y = 1.00x

R2

 = 0.99

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERS

E

PRESSURE, psf .

Transverse pressure prediction based on measured thrust force and resultant load

location and measured lateral displacement 

Transverse pressure prediction based on measured thrust force and calculated resultant

load location and measured lateral displacement 
185

y = 0.88x

R2

 = 0.81

y = 0.84x

R2

 = 0.79

0

50

100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350 400 450

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf .

Method 1 - Calculate transverse pressure with preload factor from measured

lateral displacement and preload

Method 2 - Calculate transverse pressure with preload factor from measured arch

thrust and preload

Figure 8-99. Prediction of transverse pressure from known thrust and lateral loads 

(Omega block).
186

8.7.4 Theoretical Impact of Boundary Stiffness 

 A theoretical assessment of the impact of the boundary stiffness is conducted by 

varying the system modulus of elasticity (see equation 6.11 and 7.7). The modulus of 

elasticity determines the deformations of the wall and the boundary, i.e. the mine roof and 

floor. The system modulus reflects the series stiffness equivalent of the wall and roof and 

floor structure. The theoretical assessment is made by reducing the system modulus to 75, 

50, and 25 pct of the rigid boundary condition, and using the lateral displacement model 

developed in chapter 7 to calculate the transverse pressure. For comparative purposes, if the 

boundary stiffness were equal to the wall stiffness, the system stiffness would be reduced by 

50 pct. Likewise, if the boundary stiffness were three times that of the wall, the system 

stiffness would be 75 pct of the rigid boundary condition, and if the boundary stiffness were 

one third of the wall stiffness, the system stiffness would be 25 pct of the rigid boundary 

condition. 

 Figure 8-100 shows the impact of the reduction in system modulus to 25, 50, and 75 

pct of the rigid boundary condition at each of the three half-wall heights. Unlike other walls 

where the block material modulus was considerably higher, reductions in boundary stiffness 

have less impact on the Omega block especially at the higher wall heights. For the example 

shown in figure 8-100, the transverse pressure is reduced by 30 pct for the shortest wall 

construction (32-in-high half-wall) when the system modulus is reduced to 25 pct of the rigid 

boundary condition, 12 pct for the 48-in-high half-wall construction, and is essentially 

unchanged for the 64-in-high half-wall construction. 

 Figures 8-101 and 8-103 show the impact of reductions in system modulus for the three 

half-wall construction heights as a function of the preload. Since the preload range was very 

limited (only 28 psi maximum preload applied), these figures show that there was not much 

impact by the preload, although in general, the reductions in transverse pressure as a result of 

reduction in boundary stiffness (lower system modulus) are reduced as the preload increases 

through this range. 
187

0

50

100

150

200

250

0% 20% 40% 60% 80% 100%

REDUCTION IN SYSTEM MODULUS RELATIVE TO RIGID BOUNDARY 

CONDITIONS, pct

PEAK TRANSVERSE PRESSURE, psf . .

32-in half-wall height 48-in half-wall height 64-in half-wall height

Figure 8-100. Impact of reducing the boundary stiffness on transverse pressure 

capacity of stopping. Data shows individual test at different wall heights with no 

preload (Omega block).

y = -0.1186x2 + 13.85x + 60.66

y = -0.1499x2 + 14.67x + 74.67

y = -0.0847x2 + 12.93x + 46.69

y = -0.0482x2 + 11.93x + 32.77

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Rigid Boundary Conditions 75% reduction in system modulus

50% reduction in system modulus 25% reduction in system modulus

Figure 8-101. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 32-inch-high half-wall constructions (Omega 

block).
188

y = -0.0544x2 + 5.63x + 41.21

y = -0.0432x2 + 4.98x + 54.33

y = -0.0679x2 + 6.35x + 27.03

y = -0.0837x2 + 7.16x + 11.81

0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Rigid Boundary Conditions 75% reduction in system modulus 50% reduction in system modulus 25% reduction in system modulus

Figure 8-102. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 48-inch-high half-wall constructions (Omega 

block).

y = -0.0574x2 + 2.67x - 7.61

y = -0.0785x2 + 3.51x - 15.31

y = -0.0442x2 + 2.20x - 3.84

y = -0.0389x2 + 2.07x - 4.02

0

5

10

15

20

25

30

0 5 10 15 20 25 30

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Rigid Boundary Conditions 75% reduction in system modulus

50% reduction in system modulus 25% reduction in system modulus

Figure 8-103. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 64-inch-high half-wall constructions (Omega 

block).
189

8.8 PEERLESS SUPER BLOCK 

 Peerless Block & Masonry Company from St. 

Albans, West Virginia also makes an ultra light weight 

block called the Super Block (figure 8-104). This block is 

characterized by styrofoam pellets that are imbedded in 

the concrete mix to provide a low density material. 

Included in the mix is polypropelene fibers to help hold 

the weak material together during failure. With a density 

of only 38 lbs per cubic foot, this allows an oversized 

block to be produced that maintains a reasonable lifting 

weight of less than 50 lbs for a 6x16x24-in block. The 

block is also manufactured in a conventional 6x8x16-in 

block that weighs about 16 lbs. The unit block 

compressive strength is 86 psi, comparable to the Omega 

block described in the previous section. 

8.8.1 Overview of the Test Program 

 A total of 31 tests were conducted with Peerless Super Block, 25 with the 6x16x24-in 

size block and 6 with the 6x8x16-in size block with half-wall configurations at heights of 32, 

46, 48, and 64 inches. A single column of block was used for the large size Super Block 

while 3 blocks were used to form the width of the half-wall for the small Super Block tests. 

The small block tests were conducted at the 46-in half-wall height only. The results of the 

MRS half-wall tests are summarized in the table 8-11. The low compressive strength of the 

block did not allow much variation of preload. These blocks also have a low compressive 

strength, which limited the amount of preload that could be applied. For the single block 

column tests with the large block, the preload varied from 7 to 60 psi and from 5 to 89 psi for 

the three-column wide small block tests. The low strength of the block resulted in thrust 

loading that was near the measurable limits of the load frame. This contributed to some of 

the inconsistency in the test results. Graphs of the measured lateral load and thrust load as a 

function of the lateral displacement of the wall for each test are documented in Appendix B. 

Figure 8-104. Peerless 

Super Block test set up 

(showing two blocks stacked 

on top of one another). 
190

A tabular summary of the pertinent parameters and loading values for each test is also 

included Appendix C. 

Table 8-11. Summary of Peerless Super Block Testing. 

Block Type Test 

No. 

Block 

Width 

(in) 

Block 

Height 

(in) 

Halfwall 

Length 

(in) 

Halfwall 

Height 

(in) 

Preload 

(psi) 

Measured 

Transverse 

Pressure, 

(psf) 

Peerless Super Block 216 5.8 16 24 32 7 114 

Peerless Super Block 218 5.8 16 24 32 16 104 

Peerless Super Block 217 5.8 16 24 32 17 130 

Peerless Super Block 219 5.8 16 24 32 21 86 

Peerless Super Block 208 5.8 16 24 32 54 96 

Peerless Super Block 209 5.8 16 24 32 56 104 

Peerless Super Block 214 5.8 16 24 48 12 30 

Peerless Super Block 195 5.8 16 24 48 29 48 

Peerless Super Block 190 5.8 24 24 48 37 38 

Peerless Super Block 191 5.8 16 24 48 38 42 

Peerless Super Block 211 5.8 16 24 48 41 68 

Peerless Super Block 197 5.8 16 24 48 42 54 

Peerless Super Block 193 5.8 16 24 48 42 48 

Peerless Super Block 192 5.8 16 24 48 45 46 

Peerless Super Block 210 5.8 16 24 48 56 50 

Peerless Super Block 196 5.8 16 24 48 60 58 

Peerless Super Block 194 5.8 16 24 48 63 62 

Peerless Super Block 231 5.8 16 24 64 4 6 

Peerless Super Block 225 5.8 16 24 64 14 10 

Peerless Super Block 230 5.8 16 24 64 22 6 

Peerless Super Block 205 5.8 16 24 64 33 16 

Peerless Super Block 229 5.8 16 24 64 34 20 

Peerless Super Block 232 5.8 16 24 64 54 18 

Peerless Super Block 233 5.8 16 24 64 53 24 

Peerless Super Block 206 5.8 16 24 64 56 10 

Peerless Super Block 

(small) 302 5.75 7.625 46.5 45.75 5 12 

Peerless Super Block 

(small) 303 5.75 7.625 46.5 45.75 20 24 

Peerless Super Block 

(small) 304 5.75 7.625 46.5 45.75 30 42 

Peerless Super Block 

(small) 305 5.75 7.625 46.5 45.75 57 66 

Peerless Super Block 

(small) 307 5.75 7.625 46.5 45.75 80 70 

Peerless Super Block 

(small) 308 5.75 7.625 46.5 45.75 89 84 
191

8.8.2 Parametric Relationships and Trends. 

 Examining table 8-11, it is seen that the transverse pressure capacity of the stoppings 

constructed from Peerless Super Block varied from a low of 14 to a high of 126 psf or .01 to 

0.88 psi. Figure 8-106 displays the transverse pressure as a function of preload for the three 

half-wall heights. The transverse pressures for the 32-in-high half-walls are 5 to 7 times 

higher than the 64-in-high half-walls. It is also seen from figure 8-106 that the transverse 

pressure is nonlinearly related to the preload and that the transverse pressure approaches an 

asymptotic maximum at approximately 35-40 psi for the 64-in-high half-walls. The upward 

slope of the 48-in-high half-wall curve suggests the peak loading has not been reached, and it 

appears that for this data the 32-in-high half-walls was damaged when the preload was 

applied. Figure 8-106 plots the lateral displacement at which the peak transverse pressure is 

achieved as a function of preload for the 32-in-high and 48-in-high half-walls. The 64-inhalf-wall response was inconsistent and did not follow a clear trend. Although the 

correlation is very weak, the trend is that the lateral displacement also approaches an 

asymptotic level. 

y = -0.003x2 + 1.03x + 11.78

R2

 = 0.83

y = -0.0064x2 + 0.63x + 1.92

R2

 = 0.50

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60 70 80 90 100

PRELOAD, psi

TRANSVERSE PRESSURE, psf. .

32-in half-wall height 48-in half-wall height

64-in half-wall height 46-in half-wall height

Figure 8-105. Transverse pressure as measured from MRS laboratory testing as a 

function of preload for three half-wall heights (Peerless Super Block).
192

 Further examination of the parametric relationships confirms the arching theory as 

presented in chapter 6. Figure 8-107 shows that the transverse pressure is directly related to 

the lateral force acting on the half-wall during the laboratory tests. Figure 8-108 shows that 

the lateral force is also directly related to the thrust force. In this case, the short wall 

correlation is not good. The thrust forces are relatively low and are at the limit of the load 

frame can accurately measure, but the block performance was also inconsistent at the short 

heights with failure and damage to the block occurring during the loading cycle to a greater 

extent than in the other test configurations. Finally, figure 8-109 shows the relationship 

between the transverse pressure and the arch thrust. This graph resembles the plot of 

transverse pressure versus preload shown in figure 8-105, showing that the arch thrust also 

reaches an asymptotic value. Here again, the correlation is not good for the short wall tests. 

Figure 8-106. Lateral displacement at which peak transverse pressure occurs also 

reaches an asymptotic minimum as the preload approaches 70-80 psi (Peerless Super 

Block).

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 10 20 30 40 50 60 70 80 90 100

PRELOAD, psi

HORZ DISPLACEMENT @ PEAK .

 TRANSVERSE PRESSURE, in.

32-in half-wall height 48-in half-wall height

64-in half-wall height 46-in half-wall height
193

0

20

40

60

80

100

120

140

0 100 200 300 400 500 600 700

LATERAL LOAD @ PEAK TRANSVERSE PRESSURE, lbs

PEAK TRANSVERSE PRESSURE, psf .

32-in half-wall height 48-in half-wall height

64-in half-wall height 46-in half-wall height

Figure 8-107. Relationship between the lateral load and the arch thrust for MRS 

laboratory tests for three half-wall heights (Peerless Super Block).

y = 33.49x + 53.47

R2

 = 0.96

y = 14.63x + 25.38

R2

 = 0.51

0

100

200

300

400

500

600

700

0 2 4 6 8 10 12 14 16 18

ARCH THRUST FORCE @ PEAK TRANSVERSE PRESSURE, kips

PEAK LATERAL FORCE, lbs .

32-in half-wall height 48-in half-wall height

64-in half-wall height 46-in half-wall height

Figure 8-108. Relationship between the lateral load and the arch thrust for 

MRS laboratory tests for three half-wall heights (Peerless Super Block).
194

 Figure 8-110 depicts the relationship between the transverse pressure and the material 

modulus (E), the wall thickness (t), and the wall height (L) expressed as by the term 

E x (t/L)2. The general trend of increasing transverse pressure with increasing E x (t/L)2 is 

typical of other block types. The chart shows that 63 pct of the transverse pressure of a 

stopping is determined by this relationship. It is noted that the shortest half-wall (32-in) were 

eliminated from this data set. As shown in the previous analyses of the arching parameters, 

the 32-in-high half-walls did not correlated well to the observed trends in the 48 and 64-inhigh half-wall tests. This material is very weak and prone to damage even from the initial 

preloading. Figure 8-111 compares two 32-in-high half-wall tests where the thrust load 

development is nearly identical in each test with the exception of a slight difference in the 

initial preload. However, as seen in the graph, the lateral load responses are significantly 

different. This type of behavior accounts for the scatter and poor correlation of the data. The 

material modulus is a significant parameter since it determines the amount of thrust force 

developed and ultimately the amount of lateral displacement of the wall, both of which 

control the arching mechanics of the wall, and the distribution of the Styrofoam pellets is not 

consistent and cause localized changes in the block material properties (see figure 8-112). 

R2 = 0.67

R2 = 0.45

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

ARCH THRUST FORCE @ PEAK TRANSVERSE PRESSURE, kips

PEAK TRANSVERSE PRESSURE, psf . .

32-in half-wall height 48-in half-wall height

64-in half-wall height 46-in half-wall height

Figure 8-109. Relationship between the transverse pressure and the arch thrust for 

MRS laboratory tests conducted at three half-wall heights (Peerless Super Block).
195

Figure 8-110. Separation of weak block from thrust empirical prediction equation 

provides more accurate model predictive capability for Peerless Super Block. 

y = 0.49x + 11.13

R2

 = 0.63

0

10

20

30

40

50

60

70

80

90

0 20 40 60 80 100 120 140

Ex(t/L)2

TRANSVERSE PRESSURE, psf .

Peerless Super Block (large) Peerless Super Block (small)

Figure 8-111. Two tests on 32-in-high half-walls show very similar thrust load 

development except at the initial preloading and significantly different transverse 

pressure (Peerless Super Block). 

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

2

4

6

8

10

12

THRUST LOAD, kips .

Test #207 -- 24 inches wide -- Lateral Load -- Peerless -- 33 psi preload

Test #208 -- 24 inches wide -- Lateral Load -- Peerless -- 46 psi preload

Test #207 -- 24 inches wide -- Thrust Load --Peerless-- 6.0 in thick -- 33 psi preload

Test #208 -- 24 inches wide -- Thrust Load --Peerless -- 6.0 in thick -- 46 psi preload
196

8.8.3 Evaluation of Predictive Models 

 The next goal is to evaluate the capability to predict the transverse pressure. If the 

thrust force and its resultant location and lateral load are known, the transverse pressure 

capacity of a stopping can be predicted with nearly 100 pct accuracy. If the thrust force 

location is instead calculated from the empirical model described in chapter 6 and shown in 

figure 8-113 for three half-wall heights considered in this analysis, the transverse pressure 

can still be predicted to better than 98 pct accuracy as depicted by the open red square data 

points shown in figure 8-114. Each data point in figure 8-114 represents an individual 

laboratory test. As seen in the figure, the accuracy of the prediction is consistent throughout 

the full range of transverse pressure conducted in the laboratory testing, and includes 

preloading of wall from zero to 89 psi and three different wall heights. Hence, while the wall 

performances may not be very consistent, if the thrust and lateral displacement are known, 

the arching mechanics still dictate a good measure of the transverse pressure capacity. 

Figure 8-112. Photo of Peerless Super Block with close-up showing Styrofoam pellets 

(small white objects in photo) imbedded in concrete mix. 
197

y = -0.2277x + 1.41

R2

 = 0.94

y = -0.0521x + 0.74

R2

 = 0.53

y = -0.0703x + 0.74

R2

 = 0.49

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

01234567

TOTAL THRUST P (SUM OF ARCH AND PRELOAD), kips 

THRUST RESULTANT POSITION FACTOR .

32-in half-wall height 48-in half-wall height 64-in half-wall height

y = 1.00x

R2

 = 1.00

y = 0.98x

R2

 = 0.63

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140 160

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERS

E

PRESSURE, psf. .

Transverse pressure prediction based on measured thrust force and resultant load

location and measured lateral displacement 

Transverse pressure prediction based on measured thrust force and calculated

resultant load location and measured lateral displacement 

Figure 8-114. Prediction of transverse pressure when both the lateral load and arch 

thrust are known. (Peerless Super Block).

Figure 8-113. Resultant thrust force location for three wall heights as a function of 

the total arch thrust (Peerless Super Block).
198

 If either the thrust force or the lateral displacement is known, than the transverse 

pressure can still be calculated. Method 1 predicts the transverse pressure from the measured 

lateral displacement. Method 2 predicts the transverse pressure from the measured thrust 

force. Figures 8-115 illustrates the predictive capability of these two models showing the 

measured transverse pressure vs. the predicted transverse pressure for each half-wall 

laboratory test. The accuracy of the predictive models is not very good, due in large part to 

the inconsistency of the block material properties and low thrust loads. Method 2, which is 

based on the measured thrust forces over predicts the transverse pressure by a considerable 

amount. This is due in large part to the fact that the thrust load never increases during the 

transverse pressure development. Figure 8-111 was one example of this behavior. About 80 

pct of the tests as highlighted in bold print in table 8-8 were this way. The block just deforms 

as the transverse pressure is developed, resulting in poor correlations in the model 

predictions. 

.

y = 0.79x

R2

 = 0.59

y = 0.53x

R2

 = 0.50

0

50

100

150

200

250

0 50 100 150 200 250

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERS

E

PRESSURE, psf

Method 1 - Calculate transverse pressure with preload factor from measured lateral

displacement and preload

Method 2 - Calculate transverse pressure with preload factor from measured arch thrust

and preload

Figure 8-115. Prediction of transverse pressure from known thrust and lateral loads 

(Peerless Super Block).
199

8.8.4 Theoretical Impact of Boundary Stiffness 

The inconsistency in the test results due to the very low material modulus for the Super 

Block make the theoretical assessment of the impact of boundary stiffness somewhat 

unreliable. Figure 8-116 shows the impact at 46-in half-wall height, which provided the most 

consistent test results. In this figure, the trend is consistent with other weak block materials, 

showing that the preload does reduce the transverse pressure for rigid boundary conditions, 

but has relatively little impact at very low boundary stiff nesses. 

Figure 8-116. Impact of boundary stiffness reductions compared to rigid arching 

conditions as a function of preload for 46-in-high half-wall constructions (Peerless 

Super Block).

y = -0.0075x2 + 1.38x + 11.18

y = -0.007x2 + 1.29x + 15.11

y = -0.0078x2 + 1.47x + 7.02

y = -0.008x2 + 1.55x + 2.62

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60 70 80 90 100

PRELOAD, psi

TRANSVERSE PRESSURE, psf....

Rigid Boundary Conditions 75% reduction in system modulus

50% reduction in system modulus 25% reduction in system modulus
200

CHAPTER 9: UNIVERSAL DESIGN EQUATIONS FOR 

STOPPING BLOCK WALLS 

Chapter 8 showed that if either the arching thrust or the lateral displacement is known, 

then the maximum transverse load of the stopping could be predicted with reasonable 

accuracy using the two predictive models developed in chapter 7. While these measurements 

could be made on stoppings in a mine and these models used to provide valuable information 

of the transverse loading of the stopping, a more generic model that does not require in 

service performance measurements is needed to develop design equations for stoppings. To 

fulfill this objective, models are developed based on the wall geometry (thickness and height) 

and the elastic modulus of the material, which utilize empirical data from the laboratory 

testing to provide for transverse load determinations of various stopping constructions. 

 The wall thickness and height are known parameters for any stopping construction. 

The elastic modulus can be determined from material property testing. Tests were conducted 

on a column of full size stopping blocks, whereby vertical load was applied to the block 

column of equivalent height to the half-wall MRS tests. The wall is tilted slightly to a 

configuration that is consistent with the orientation of the wall during the applied transverse 

loading. The result is shown in figure 9-1 for a Portland cement block that has been utilized 

in several examples in this dissertation, where it is shown that the block has a modulus of 

50,000 psi. The modulus is computed at the early loading stage where the strains are 

consistent with the wall deformation during arching as measured in the MRS laboratory tests. 

Although this modulus is an order of magnitude less than what the elastic modulus is 

reported for concrete materials, the value should be considered an “apparent modulus” rather 

than a true elastic modulus since the block is being loaded in an unconventional manner 

compared to ASTM laboratory test requirements for modulus determinations. The important 

point is that this value is consistent with the theoretical analysis of arching where back 

calculation of the modulus computed a value of 60,000 psi for this particular block. 
201

 It was shown in chapter 8 that when the modulus is back calculated for a specific test 

then a strong correlation exists between the transverse load and the term Ex(t/L)2 where E is 

the modulus, t is the wall thickness, and L is wall height. The goal of this generalized design 

is to develop a design equation, which uses a constant modulus for a specific block type. 

Since preloading of the wall from ground pressures is also possible in any underground mine, 

incorporating preload pressure into this generalized design equation was also considered a 

necessary requirement. 

 Modulus values for each block type were back-calculated from the half-walls tests 

conducted in the MRS. From this, a modulus representing each block was determined as part 

of a profile characterization for that block. These values were shown in the chart in figure 

8-2 and are summarized here in tabular form (table 9-1). With these values, and known 

parameters for wall thickness and height, the Ex(t/L)2

 term was computed and correlated to 

the measured transverse pressure. The next step was to incorporate preload into the process. 

A full empirical model is developed by performing a multivariable regression analysis, that 

in addition to the Ex(t/L)2

, includes the preload pressure. A hybrid theoretical model is also 

developed whereby the normalized total thrust force is determined from a multivariable 

0

200

400

600

800

1,000

1,200

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014

STRAIN, in/in

STRESS, psi

Test #344 -- Vertical Force w/ wedges -- Klondike 1727 psi -- 5.625 inches thick

E = 400/0.008 = 50,000 psi

Figure 9-1. Test conducted in MRS on 6-course-high half wall to determine apparent 

elastic modulus for the block material. 
202

regression of the Ex(t/L)2

 term and preload. As part of this process, a multivariable 

regression analysis is also made to determine the thrust resultant position factor as a function 

of the wall height and thrust. Then using the flowchart shown in figure 9-2, the hinge point 

deformation and lateral displacement are computed from the arching theory presented in 

chapter 5. This model is an empirical equivalent to Model 2 (Thrust Model) presented in 

Chapter 8. A second hybrid theoretical model is developed which utilizes a multivariable 

regression analysis to compute the lateral displacement as a function of the Ex(t/L)2 term and 

preload. This model would be an empirical equivalent to Model 1 (Lateral Displacement 

Model) presented in Chapter 8 and is expressed by the flowchart in figure 9-3. A third model 

combines the two by using empirical multivariable regression analysis to compute both the 

normalized thrust and the lateral displacement as illustrated in the flowchart in figure 9-4. 

The inclusion of the lateral displacement into the design equation through this process 

improves the prediction accuracy. The hybrid theoretical models also provide more 

information that can be beneficial to a design engineer or researcher. Also included in the 

block profile listing in table 9-1 is a preload limit. This represents the maximum preload that 

the block wall can sustain relative to the transverse loading. If the preload exceeds these 

amounts, localized failures will limit and sometimes reduce the transverse load capacity of 

the stopping. 

 The design equations using these two approaches are presented for each specific block 

manufacturer as well as a more general category of block type, namely (1) standard concrete 

masonry block made from Portland cement and aggregate fillers, (2) cellular concrete block 

materials, and (3) low strength or specialty type block categories which at present include 

Omega Block and the Peerless Super Block composed of Styrofoam-imbedded concrete (see 

table 9-1). The standard concrete block or CMU as they are sometimes called is represented 

by the Klondike and Peerless Backsaver block in this data set. The cellular concrete block is 

represented by the Ytong, Aerated Concrete Corporation, and Kingsway block. As with any 

empirical model, these models will improve as additional test data become available. 

However, with the data set provided from the MRS half-wall testing, these design equations 

are shown to provide good approximations of the transverse load capacity of the various 

mine ventilation stopping constructions currently being utilized throughout the U.S. 
203

Table 9-1. Profile characteristics for various block materials examined in this study. 

1

 Unit block compressive strength. 

Specific Block Block Category Modulus 

(psi) 

Compressive 

Strength 

(psi)1 

Preload 

limit 

(psi) 

Klondike Solid Block (standard) Standard Solid CMU 60,000 832 500 

Klondike Solid Block (High strength) Standard Solid CMU 80,000 1,564 500 

Peerless Back Saver Standard Solid CMU 40,000 1637 250 

Klondike Hollow Core Standard HollowCore CMU 65,000 882 200 

Ytong Cellular Concrete 40,000 705 150 

Aerated Concrete Corp Cellular Concrete 20,000 446 250 

Kingsway Cellular Concrete 24,000 546 150 

Omega Specialty Block 4,500 70 25 

Peerless Super Block Specialty Block 5,000 32 40 
204

Figure 9-2. Flowchart for predicting the transverse load capacity of stoppings (Hybrid 

Theoretical Thrust Model). 

Determine preload 

Calculate horizontal force

Measured or PL = ∆L× k2

Determine total thrust 

force 

Multivariable regression 

analysis relating thrust to 

Ex(t/L)2

 and preload 

( )

L / 2

P d t HF m h × × − δ =

Compute Arch Thrust Parch = Pm - Ppreload 

( )

2

2 t 4 t 4 2 L y 4 y 2 2

h

× ± × − × × × − ×

δ = Calculate lateral 

displacement 

Calculate “hinged point 

deformation” 2 A E

P L / 2

y

arch

× ×

× =

Determine resultant 

thrust position factor (d)

Multivariable regression analysis 

relating d factor to wall height 

and thrust. 

Calculate transverse 

pressure w L/ 2

2 HF

×

×

ρ =

Procedure Formula Used 
205

Figure 9-3. Flowchart for predicting the transverse load capacity of stoppings 

(Hybrid Theoretical Lateral Displacement Model).

8

2 L 4 L 32 t 16

y

2

h h

2 × ± × − × ×δ + ×δ =

Determine preload 

Calculate arch thrust 

Calculate horizontal 

force 

Calculate transverse 

pressure w L / 2

2 HF

×

×

ρ =

Measured or PL = ∆L × k2

Procedure Formula Used 

Calculate “hinge point 

deformation” 

Add preload to arch 

thrust Pm = Parch + PL

L/ 2

2 A E y Parch

× × × =

Determine lateral 

displacement 

Multivariable regression 

analysis relating displacement 

to Ex(t/L)2

 and preload 

Multivariable regression analysis 

relating d factor to wall height 

and thrust. 

Determine resultant 

thrust position factor (d)

( )

L / 2

P d t HF m h × × − δ =
206

Determine lateral 

displacement 

Calculate horizontal 

force 

Calculate transverse 

pressure w L/ 2

2 HF

×

×

ρ =

Multivariable regression 

analysis relating displacement 

to Ex(t/L)

2 and preload 

Procedure Formula Used 

Determine preload Measured or PL = ∆L× k2

( )

L / 2

P d t HF m h × × − δ =

Determine resultant 

thrust position factor (d)

Multivariable regression 

analysis relating displacement 

to Ex(t/L)2

 and preload 

Determine total thrust 

force 

Multivariable regression 

analysis relating d factor to 

wall height and thrust. 

Figure 9-4. Flowchart for predicting the transverse load capacity of stoppings 

(Combined Hybrid Theoretical Thrust and Lateral Displacement Model).
207

9.1 SPECIFIC BLOCK DESIGN 

 Design equations are developed for each block of a specific manufacturer. The first 

design formulation will be based on the full empirical model where the transverse load is 

determined from a multivariable regression analysis of the half-wall tests conducted for that 

particular block. Following this, hybrid theoretical design formulations based part on 

empirical evaluations and part theoretical calculations will be presented. 

9.1.1 Klondike Solid Block 

 As described in Chapter 8, these are standard CMU block made from Portland cement 

and aggregate. Most of the testing was done with these blocks, since historically they have 

been the most commonly used style of block. The block measures nominally 6x8x16 inches 

and weighs about 50 lbs each. 

9.1.1.1 Full Empirical Model 

 Table 9-2 shows the results of the multivariable regression analysis correlating the 

transverse load to the Ex(t/L)2

 term and preload. From this regression analysis, the design 

equation for Klondike solid core block is shown in equation 9.1 

Transverse Load = 5.3208 x Ex(t/L)2

 + 2.3123 x Preload – 994 (9.1)

Where E = material modulus = 60,000 psi for Klondike block, 

 t = wall thickness, in, 

 L = full wall height, in, and 

 Preload = ground pressure preload, psi. 

Regression Statistics

Multiple R 0.9173

R Square 0.8415

Adjusted R Square 0.8379

Standard Error 403.7352

Observations 91

ANOVA

df SS MS F Significance F

Regression 2 76138801 38069401 233.5516 0.0000

Residual 88 14344187 163002

Total 90 90482988

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept -993.8975 123.4804 -8.0490 0.0000 -1239.2890 -748.5060 -1239.2890 -748.5060

E x (t/L)2 5.3208 0.2555 20.8222 0.0000 4.8130 5.8286 4.8130 5.8286

Preload 2.3123 0.2202 10.5018 0.0000 1.8747 2.7499 1.8747 2.7499

Table 9-2. Regression analysis for determining transverse 

load from modulus and wall geometry parameters. 
208

 Figure 9-5 displays the accuracy of the model for the three wall heights that were 

evaluated in the laboratory test program. Plotted on this graph are the measured transverse 

pressure from the laboratory tests and the transverse pressure for that condition that was 

calculated using equation 9-1 for a particular wall construction and preload pressure. As 

seen in the figure, the model predictions are most accurate for the 45-in half-wall height and 

least accurate for the 30-in half-wall height. The transverse capacity is under predicted 

throughout the preload range for the 30-in half-wall height. Since the performance in the 

laboratory testing were least consistent at the low heights, and this is an empirical model, 

then it makes sense that the model is least accurate for the low height as well. The 45-inhigh performance is accurately predicted by the empirical formula. The transverse pressure 

is also under predicted for preloads less than 300 psi for the 60-in-high configurations. 

Figure 9-6 shows transverse pressure predictions using this empirical design model for 6-inthick walls constructed from Klondike block ranging in height from 5 to 10 feet in one foot 

increments with preloads ranging from 0 to 600 psi. The negative y-intercept on this chart 

for the 9 and 10-ft-high walls indicates the inaccuracies of this model for the high heights at 

lower preloads. 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0 100 200 300 400 500 600 700 800

PRELOAD, psi

TRANSVERSE PRESSURE, psf . Empirical model -- 30-in half-wall height Measured Transverse Load -- 30-in half wall height

Empirical model -- 45-in half-wall height Measured Transverse Load -- 45-in half-wall height

Empirical model -- 60-in half-wall height Measured Transverse Load -- 60-in half-wall height

Figure 9-5. Comparison of design equation predictions with measured transverse 

load from laboratory testing (Full Empirical Model – Klondike block). 
209

9.1.1.2 Hybrid Theoretical Models 

 Transverse load capacity forecasts will be made using the three hybrid theoretical 

models: (1) Hybrid Thrust Model, (2) Hybrid Lateral Displacement Model, and (3) Hybrid 

Combination Thrust and Lateral Displacement Model. 

9.1.1.2.1 Hybrid Thrust Model

As seen in the flowchart in figure 9-2, the Hybrid Thrust Model determines the 

normalized thrust force from a multivariable relationship between the thrust force and the 

Ex(t/L)2

 term and preload, both of which are considered to be known parameters. The 

multivariable linear regression analysis based on 91 laboratory tests of various wall 

constructions is summarized in table 9-3. Equation 9.2 is used to compute the normalized 

thrust force per unit width of wall. Table 9-4 documents the multivariable regression 

analysis results used to determine the resultant thrust position factor (d). 

Figure 9-6. Transverse load capacity predictions for 6-in-thick walls constructed from 

Klondike solid block for walls heights ranging from 5 to 10 ft (Full Empirical Model). 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0 100 200 300 400 500 600

PRELOAD, psi

TRANSVERSE PRESSURE, psf ..

Klondike solid block -- 5 ft wall height Klondike solid block -- 6 ft wall height

Klondike solid block -- 7 ft wall height Klondike solid block -- 8 ft wall height

Klondike solid block -- 9 ft wall height Klondike solid block -- 10 ft wall height
210

Table 9-3. Multivariable regression analysis for determining arching thrust. 

P/BL = 0.0025 x Ex(t/L)2

 + 0.0034 x Preload + 0.6100 (9.2)

Where P/BL = Normalized thrust per unit width of block, kips/in, 

 E = Elastic modulus = 60,000 psi for Klondike solid block, 

 t = wall thickness, in, 

 L = height of wall, in, and 

 Preload = preload pressure, psi. 

Table 9-4. Multivariable regression analysis for determining resultant thrust position 

factor. 

Resultant Thrust Position Factor (d) = -.0021 x Half-wall height - .0036 x Thrust + .9547 (9.3)

Regression Statistics

Multiple R 0.8126

R Square 0.6603

Adjusted R Square 0.6525

Standard Error 0.5130

Observations 91.0000

ANOVA

df SS MS F Significance F

Regression 2.0000 45.0061 22.5031 85.5116 0.0000

Residual 88.0000 23.1579 0.2632

Total 90.0000 68.1640

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 0.6100 0.1569 3.8878 0.0002 0.2982 0.9218 0.2982 0.9218

E * (t/L)2 0.0025 0.0003 7.8052 0.0000 0.0019 0.0032 0.0019 0.0032

Preload 0.0034 0.0003 12.0278 0.0000 0.0028 0.0039 0.0028 0.0039

Regression Statistics

Multiple R 0.4564

R Square 0.2083

Adjusted R Square 0.1903

Standard Error 0.0946

Observations 91.0000

ANOVA

df SS MS F Significance F

Regression 2 0.2073 0.1036 11.5767 0.0000

Residual 88 0.7878 0.0090

Total 90 0.9951

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 0.9547 0.0629 15.1796 0.0000 0.8297 1.0797 0.8297 1.0797

Half-wall Height -0.0021 0.0011 -2.0121 0.0473 -0.0043 0.0000 -0.0043 0.0000

Thrust -0.0036 0.0008 -4.7918 0.0000 -0.0052 -0.0021 -0.0052 -0.0021
211

 Figure 9-7 compares the results of the predicted transverse load capacities from the 

hybrid theoretical thrust model with the measured laboratory test results for half-wall heights 

of 30, 45, and 60 inches with varying preloads. As seen from the graph, the predictions 

overall are improved compared to the full empirical model presented in figure 9-5, especially 

for the 60-in half-wall height. Figure 9-8 shows transverse load predictions using this Hybrid 

Thrust Model for 6-in-thick walls constructed from Klondike block ranging in height from 5 

to 10 feet in one foot increments with preloads ranging from 0 to 600 psi. 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0 100 200 300 400 500 600 700 800

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Hybrid Thrust Model -- Half-w all Height 30 inches Measured Transverse Load -- Half-w all Height 30 inches

Hybrid Thrust Model -- Half-w all Height 45 inches Measured Transverse Load -- Half-w all Height 45 inches

Hybrid Thrust Model -- Half-w all Height 60 inches Measured Transverse Load -- Half-w all Height 60 inches

Figure 9-7. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Thrust Model). 
212

9.1.1.2.2 Hybrid Lateral Displacement Model

As seen in the flowchart in figure 9-3, the Hybrid Lateral Displacement Model 

determines the lateral displacement force from a multivariable relationship from the Ex(t/L)2 

term and preload, both of which are considered to be known parameters. The multivariable 

linear regression analysis based on 91 laboratory tests of various wall constructions is 

summarized in table 9-5. Equation 9.4 is used to compute lateral displacement of the wall. 

Table 9-4 documented the multivariable regression analysis results used to determine the 

resultant thrust position factor (d) for the Hybrid Thrust Model. This equation is also used 

for computing the resultant thrust adjustment factor for this model, except the calculated 

thrust forces are used instead of the measured thrust forces. 

Lateral Displacement = -0.0009 x Ex(t/L)2

 - 0.0023 x Preload + 1.8776 (9.4)

Figure 9-8. Transverse load capacity predictions for 6-in-thick walls constructed 

from Klondike solid block for walls heights ranging from 5 to 10 ft (Hybrid 

Theoretical Thrust Model).

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0 100 200 300 400 500 600

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Klondike solid block -- 5 ft wall height Klondike solid block -- 6 ft wall height

Klondike solid block -- 7 ft wall height Klondike solid block -- 8 ft wall height

Klondike solid block -- 9 ft wall height Klondike solid block -- 10 ft wall height
213

 Figure 9-9 compares the results of the predicted transverse load capacities from the 

hybrid theoretical lateral displacement model with the measured laboratory test results for 

half-wall heights of 30, 45, and 60 inches with varying preloads. As seen from the graph, the 

predictions overall are similar to the hybrid theoretical thrust model presented in figure 9-7, 

slightly more accurate for the highest wall and slightly less accurate for the shortest wall. 

Figure 9-10 shows transverse load predictions using the hybrid theoretical lateral 

displacement for 6-in-thick walls constructed from Klondike block ranging in height from 

5 to 10 feet in one foot increments with preloads ranging from 0 to 600 psi. 

Figure 9-9. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Lateral 

Displacement Model).

Regression Statistics

Multiple R 0.7499

R Square 0.5623

Adjusted R Square 0.5524

Standard Error 0.3978

Observations 91

ANOVA

df SS MS F Significance F

Regression 2 17.8906 8.9453 56.5349 0.0000

Residual 88 13.9239 0.1582

Total 90 31.8146

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 1.877627 0.121658 15.433636 0.000000 1.635857 2.119397 1.635857 2.119397

E * (t/L)2 -0.000862 0.000252 -3.422179 0.000945 -0.001362 -0.000361 -0.001362 -0.000361

Preload -0.002297 0.000217 -10.588914 0.000000 -0.002728 -0.001866 -0.002728 -0.001866

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0 100 200 300 400 500 600 700 800

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Hybrid Lateral Displacement Model -- Half-wall Height 30 inches Measured Transverse Load -- Half-wall Height 30 inches

Hybrid Lateral Displacement Model -- Half-wall Height 45 inches Measured Transverse Load -- Half-wall Height 45 inches

Hybrid Lateral Displacement Model -- Half-wall Height 60 inches Measured Transverse Load -- Half-wall Height 60 inches

Table 9-5. Multivariable regression analysis for 

determining lateral displacement.
214

9.1.1.2.3 Hybrid Combination Model

 The Hybrid Combination Model combines the previous two models by empirically 

determining both the thrust and lateral displacement. Figure 9-11 compares this model’s 

predictions of transverse load capacity to the measured transverse load capacities from the 

laboratory testing. The results are similar to the other two models, but overall are slightly 

more accurate, especially for the higher walls. For completeness, figure 9-12 is included 

which displays the transverse load predictions using the hybrid theoretical combination 

model for 6-in-thick walls constructed from Klondike block ranging in height from 5 to 10 

feet in one foot increments with preloads ranging from 0 to 600 psi. 

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400 500 600

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Klondike solid block -- 5 ft wall height Klondike solid block -- 6 ft wall height

Klondike solid block -- 7 ft wall height Klondike solid block -- 8 ft wall height

Klondike solid block -- 9 ft wall height Klondike solid block -- 10 ft wall height

Figure 9-10. Transverse load capacity predictions for 6-in-thick walls constructed 

from Klondike solid block for walls heights ranging from 5 to 10 ft (Hybrid 

Theoretical Lateral Displacement Model).
215

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0 100 200 300 400 500 600 700 800

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Hybrid Combination Model -- Half-w all Height 30 inches Measured Transverse Load -- Half-w all Height 30 inches

Hybrid Combination Model -- Half-w all Height 45 inches Measured Transverse Load -- Half-w all Height 45 inches

Hybrid Combination Model -- Half-w all Height 60 inches Measured Transverse Load -- Half-w all Height 60 inches

Figure 9-11. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Combination 

Model).

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0 100 200 300 400 500 600

PRELOAD, psi

TRANSVERSE PRESSURE, psf..

Klondike solid block -- 5 ft wall height Klondike solid block -- 6 ft wall height

Klondike solid block -- 7 ft wall height Klondike solid block -- 8 ft wall height

Klondike solid block -- 9 ft wall height Klondike solid block -- 10 ft wall height

Figure 9-12. Transverse load capacity predictions for 6-in-thick walls constructed 

from Klondike solid block for walls heights ranging from 5 to 10 ft (Hybrid 

Theoretical Combination Model).
216

9.1.1.3 Summary of Design Equations for Klondike Block

 In summary, a full empirical design model and three hybrid theoretical design models 

were developed for the Klondike block stopping constructions. Figure 9-13 displays the 

calculated transverse load capacities from the full empirical model compared to the measured 

capacities from the MRS tests. The dashed line represents a perfect correlation between the 

calculated and measured capacities. The red trend line represents the linear regression 

between the measured and calculated capacities. The regression line shows that on average 

the model tends to under predict the transverse pressure by 3 pct. The shaded blue area is a 

+/- 400 psf variation from the perfect correlation. Examining the chart, it is seen that 85% of 

the data falls within this variation. Figure 9-14 displays this same information for the three 

hybrid theoretical design models. Based on the regression trend line correlating the 

calculated transverse pressures to the measured transverse pressures, the combination model, 

which computes both the thrust and lateral displacement from laboratory test data, is the most 

accurate of the three, with a 3 pct difference between the calculated and measured pressures. 

The least accurate is the lateral displacement model with a 12 pct difference. Examining the 

+/-400 psf variation (blue shading), the thrust model and the combination model have 90% of 

the data within this variation, while the lateral displacement model has only 81 pct of the data 

within this tolerance. 

Figure 9-13. Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Full Empirical Model). 

y = 1.03x

R2

 = 0.85

0

400

800

1,200

1,600

2,000

2,400

2,800

3,200

3,600

0 400 800 1,200 1,600 2,000 2,400 2,800 3,200 3,600

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf . ..
217

9.1.4 Peerless Backsaver Block 

 The Peerless Backsaver block is also a conventional Portland cement block with 

lighter weight aggregate to reduce the block weight. The block measures nominally 6x8x16-

in and weighs about 40 lbs compared to the 50 lb weight of the Klondike block. 

9.1.2.1 Full Empirical Model 

 Table 9-6 shows the results of the multivariable regression analysis correlating the 

transverse pressure to the Ex(t/L)2

 and preload. From this regression analysis, the design 

equation for Peerless Backsaver block is shown in equation 9.5. 

Transverse Load = 7.2992 x Ex(t/L)2 + 1.4732 x Preload – 823.0570 (9.5)

Where E = material modulus = 45,000 psi for Peerless Backsaver block, 

 t = wall thickness, in, 

 L = full wall height, in, and 

 Preload = ground pressure preload, psi. 

y = 0.93x

R2

 = 0.87

y = 0.88x

R2

 = 0.88

y = 0.97x

R2

 = 0.85

0

400

800

1,200

1,600

2,000

2,400

2,800

3,200

3,600

0 400 800 1,200 1,600 2,000 2,400 2,800 3,200 3,600

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf .

Hybrid Theoretical Thrust Model

Hybrid Theoretical Lateral Displacement Model

Hybrid Theoretical Combination Model

Figure 9-14. Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Hybrid Theoretical Models). 
218

Table 9-6. Multivariable regression analysis for determining transverse load from 

modulus and wall geometric parameters. 

 Figure 9-15 displays the accuracy of the model for the three wall heights that were 

evaluated in the laboratory test program. Plotted on this graph are the measured transverse 

pressure from the laboratory tests and the calculated transverse pressure using equation 9-5 

for that particular construction. As seen in the figure, the model predictions are most 

accurate for the 45-in half-wall height and least accurate for the 30-in half-wall height. The 

transverse capacity is under predicted at high preloads for the 30-in half-wall height. Since 

the laboratory tests results were least consistent at the low heights, and this is an empirical 

model, then it makes sense that the model is least accurate for this height as well. The 45-in 

high performance is accurately predicted by the empirical formula. The transverse pressure 

is consistently under predicted by about 150 psf for the 60-in-high tests. Figure 9-16 shows 

transverse load predictions using this empirical design model for 6-in-thick walls constructed 

from Peerless Backsaver block ranging in height from 5 to 10 feet in one foot increments 

with preloads ranging from 0 to 500 psi. 

Regression Statistics

Multiple R 0.9646

R Square 0.9305

Adjusted R Square 0.9255

Standard Error 266.6961

Observations 31

ANOVA

df SS MS F Significance F

Regression 2 26644022.68 13322011 187.2994 0.0000

Residual 28 1991550.617 71126.81

Total 30 28635573.3

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept -823.0570 137.3686 -5.9916 0.0000 -1104.4442 -541.6698 -1104.4442 -541.6698

E x (t/L)2 7.2992 0.3856 18.9316 0.0000 6.5094 8.0889 6.5094 8.0889

Preload 1.4732 0.4763 3.0932 0.0045 0.4976 2.4488 0.4976 2.4488
219

Figure 9-16. Transverse load capacity predictions for 6-in-thick walls constructed 

from Peerless Backsaver block for walls heights ranging from 5 to 10 ft (Full 

Empirical Model).

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 50 100 150 200 250 300 350 400 450 500

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Empirical Model -- Half-wall Height 30 inches Measured Transverse Load -- Half-wall Height 30 inches

Empirical Model -- Half-wall Height 45 inches Measured Transverse Load -- Half-wall Height 45 inches

Empirical Model -- Half-wall Height 60 inches Measured Transverse Load -- Half-wall Height 60 inches

Figure 9-15. Comparison of design equation predictions with measured transverse load 

from laboratory testing (Full Empirical Model – Peerless Backsaver block).

0

500

1,000

1,500

2,000

2,500

3,000

0 50 100 150 200 250 300 350 400 450 500

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Peerless Back Saver Block -- 5 ft wall height Peerless Back Saver Block -- 6 ft wall height

Peerless Back Saver Block -- 7 ft wall height Peerless Back Saver Block -- 8 ft wall height

Peerless Back Saver Block -- 9 ft wall height Peerless Back Saver Block -- 10 ft wall height
220

9.1.2.2 Hybrid Theoretical Models 

 Transverse load capacity forecasts will be made using the three hybrid theoretical 

models: (1) Hybrid Thrust Model, (2) Hybrid Lateral Displacement Model, and (3) Hybrid 

Combination Thrust and Lateral Displacement Model. 

9.1.2.2.1 Hybrid Thrust Model

As seen in the flowchart in figure 9-2, the Hybrid Thrust Model determines the 

normalized thrust force from a multivariable relationship between the thrust force and the 

Ex(t/L)2

 term and preload, both of which are considered to be known parameters. The 

multivariable linear regression analysis based on 31 laboratory tests of various wall 

constructions is summarized in table 9-7. Equation 9.6 is used to compute the normalized 

thrust force per unit width of wall. Table 9-8 documents the multivariable regression 

analysis results used to determine the resultant thrust position factor (d). 

Table 9-7. Multivariable regression analysis for determining arching thrust. 

P/BL = 0.0041 x Ex(t/L)2

 + 0.0045 x Preload + 0.2142 (9.6)

Where P/BL = Normalized thrust per unit width of block, kips/in, 

 E = Elastic modulus = 45,000 psi for Peerless Backsaver block, 

 t = wall thickness, in, 

 L = height of wall, in, and 

 Preload = preload pressure, psi. 

Regression Statistics

Multiple R 0.9347

R Square 0.8736

Adjusted R Square 0.8646

Standard Error 0.2333

Observations 31

ANOVA

df SS MS F Significance F

Regression 2 10.5350 5.2675 96.7916 0.0000

Residual 28 1.5238 0.0544

Total 30 12.0588

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 0.2142 0.1202 1.7828 0.0855 -0.0319 0.4604 -0.0319 0.4604

E*(t/L)^2 0.0041 0.0003 12.1584 0.0000 0.0034 0.0048 0.0034 0.0048

Preload 0.0045 0.0004 10.7029 0.0000 0.0036 0.0053 0.0036 0.0053
221

Resultant Thrust Adjustment Factor (d) = -.0016 x half-wall height - .0026 x Thrust + .9222 (9.7)

 Figure 9-17 compares the results of the predicted transverse load capacities from the 

hybrid theoretical thrust model with the measured laboratory test results for half-wall heights 

of 30, 45, and 60 inches with varying preloads. As seen from the graph, the predictions 

overall are improved compared to the full empirical model presented in figure 9-15 for all 

three wall heights. Figure 9-18 shows transverse pressure predictions using this empirical 

design model for 6-in-thick walls constructed from Peerless Backsaver ranging in height 

from 5 to 10 feet in one foot increments with preloads ranging from 0 to 500 psi.

Figure 9-17. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Thrust Model).

Regression Statistics

Multiple R 0.4035961

R Square 0.1628898

Adjusted R Square 0.1030963

Standard Error 0.0856843

Observations 31

ANOVA

df SS MS F Significance F

Regression 2 0.0400 0.0200 2.7242 0.0830

Residual 28 0.2056 0.0073

Total 30 0.2456

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 0.9222 0.0764 12.0676 0.0000 0.7657 1.0787 0.7657 1.0787

Half-wall Height -0.0016 0.0013 -1.2474 0.2226 -0.0044 0.0011 -0.0044 0.0011

Thurst -0.0026 0.0013 -2.0064 0.0546 -0.0052 0.0001 -0.0052 0.0001

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 50 100 150 200 250 300 350 400 450 500

PRELOAD, psi

TR A N SVER SE PR ESSU R E, psf .

Hybrid Thrust Model -- Half-wall Height 30 inches Measured Transverse Load -- Half-wall Height 30 inches

Hybrid Thrust Model -- Half-wall Height 45 inches Measured Transverse Load -- Half-wall Height 45 inches

Hybrid Thust Model -- Half-wall Height 60 inches Measured Transverse Load -- Half-wall Height 60 inches

Table 9.8. Multivariable regression analysis for 

determining resultant thrust position.
222

9.1.2.2.2 Hybrid Lateral Displacement Model

As seen in the flowchart in figure 9-3, the Hybrid Lateral Displacement Model 

determines the lateral displacement from a multivariable relationship from the Ex(t/L)2 term 

and preload, both of which are considered to be known parameters. The multivariable linear 

regression analysis based on 31 laboratory tests of various wall constructions is summarized 

in table 9-9. Equation 9.8 is used to compute the lateral wall displacement. Table 9-8 

documented the multivariable regression analysis results used to determine the resultant 

thrust position factor (d) for the Hybrid Thrust Model. This equation is also used for 

computing the resultant thrust adjustment factor for this model, except the calculated thrust 

forces are used instead of the measured thrust forces. 

Lateral Displacement = -0.0023 x Ex(t/L)2

 - 0.0026 x Preload + 2.3454 (9.8)

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 50 100 150 200 250 300 350 400 450 500

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Peerless Back Saver Block -- 5 ft wall height Peerless Back Saver Block -- 6 ft wall height

Peerless Back Saver Block -- 7 ft wall height Peerless Back Saver Block -- 8 ft wall height

Peerless Back Saver Block -- 9 ft wall height Peerless Back Saver Block -- 10 ft wall height

Figure 9-18. Transverse load capacity predictions for 6-in-thick walls constructed 

from Peerless Backsaver block for walls heights ranging from 5 to 10 ft (Hybrid 

Theoretical Thrust Model).
223

 Figure 9-19 compares the results of the predicted transverse load capacities from the 

hybrid theoretical lateral displacement model with the measured laboratory test results for 

half-wall heights of 30, 45, and 60 inches with varying preloads. As seen from the graph, the 

predictions overall are slightly worse than those provided by the hybrid thrust model. Figure 

9-20 shows transverse load predictions using the hybrid theoretical lateral displacement for 

6-in-thick walls constructed from Peerless Backsaver block ranging in height from 5 to 10 

feet in one foot increments with preloads ranging from 0 to 500 psi. 

Figure 9-19. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Lateral 

Displacement Model).

Regression Statistics

Multiple R 0.7190

R Square 0.5169

Adjusted R Square 0.4824

Standard Error 0.3377

Observations 31

ANOVA

df SS MS F Significance F

Regression 2 3.4179 1.7090 14.9814 0.0000

Residual 28 3.1940 0.1141

Total 30 6.6120

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 2.3454 0.1740 13.4823 0.0000 1.9891 2.7018 1.9891 2.7018

E*(t/L)^2 -0.0023 0.0005 -4.6992 0.0001 -0.0033 -0.0013 -0.0033 -0.0013

Preload -0.0026 0.0006 -4.3164 0.0002 -0.0038 -0.0014 -0.0038 -0.0014

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 50 100 150 200 250 300 350 400 450 500

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Hybrid Lateral Displacement M odel -- Half-wall Height 30 inches M easured Transverse Load -- Half-wall Height 30 inches

Hybrid Lateral Displacement M odel -- Half-wall Height 45 inches M easured Transverse Load -- Half-wall Height 45 inches

Hybrid Lateral Displacement M odel -- Half-wall Height 60 inches M easured Transverse Load -- Half-wall Height 60 inches

Table 9-9. Multivariable regression for determining 

lateral displacement.
224

9.1.2.2.3 Hybrid Combination Model

 The Hybrid Combination Model combines the previous two models by empirically 

determining both the thrust and lateral displacement. Figure 9-21 compares this model’s 

predictions of transverse load capacity to the measured transverse load capacities from the 

laboratory testing. The results are similar to the other two models, but overall are slightly 

more accurate, especially for the shorter walls. For completeness, figure 9-21 is included 

which displays the transverse load predictions using the hybrid theoretical combination 

model for 6-in-thick walls constructed from Peerless Backsaver block ranging in height from 

5 to 10 feet in one foot increments with preloads ranging from 0 to 500 psi. 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 50 100 150 200 250 300 350 400 450 500

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Peerless Back Saver Block -- 5 ft wall height Peerless Back Saver Block -- 6 ft wall height

Peerless Back Saver Block -- 7 ft wall height Peerless Back Saver Block -- 8 ft wall height

Peerless Back Saver Block -- 9 ft wall height Peerless Back Saver Block -- 10 ft wall height

Figure 9-20. Transverse load capacity predictions for 6-in-thick walls constructed from 

Peerless Backsaver block for walls heights ranging from 5 to 10 ft (Hybrid Theoretical 

Lateral Displacement Model).
225

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 50 100 150 200 250 300 350 400 450 500

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Hybrid Combination Model -- Half-wall Height 30 inches Measured Transverse Load -- Half-wall Height 30 inches

Hybrid Combination Model -- Half-wall Height 45 inches Measured Transverse Load -- Half-wall Height 45 inches

Hybrid Combination Model -- Half-wall Height 60 inches Measured Transverse Load -- Half-wall Height 60 inches

Figure 9-21. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Combination 

Model).

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0 50 100 150 200 250 300 350 400 450 500

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Peerless Back Saver Block -- 5 ft wall height Peerless Back Saver Block -- 6 ft wall height

Peerless Back Saver Block -- 7 ft wall height Peerless Back Saver Block -- 8 ft wall height

Peerless Back Saver Block -- 9 ft wall height Peerless Back Saver Block -- 10 ft wall height

Figure 9-22. Transverse load capacity predictions for 6-in-thick walls constructed 

from Peerless Backsaver block for walls heights ranging from 5 to 10 ft (Hybrid 

Theoretical Combination Model).
226

9.1.2.3 Summary of Design Equations for Peerless Backsaver Block 

 In summary, a full empirical design model and three hybrid theoretical design models 

were developed for the Peerless Backsaver block stopping constructions. Figure 9-23 

displays the calculated transverse load capacities from full empirical model compared to the 

measured capacities from the MRS tests. The dashed line represents a perfect correlation 

between the calculated and measured capacities. The red trend line represents the linear 

regression between the measured and calculated capacities. The regression line shows less 

than 1 pct difference between the measured and calculated transverse pressure for the 

empirical model. The shaded blue area is a +/- 400 psf variation from the perfect correlation. 

Examining the chart, it is seen that 93% of the data falls within this variation. Figure 9-24 

displays this same information for the three hybrid theoretical design models. All three 

models produced very accurate results based on the regression trend line correlating the 

calculated transverse loads to the measured transverse loads with less than 1 pct differences 

between measured and calculated transverse load. Examining the +/-400 psf variation (blue 

shading), all three models have 96% of the data within this variation. 
227

y = 1.01x

R2

 = 0.93

0

400

800

1,200

1,600

2,000

2,400

2,800

3,200

0 400 800 1,200 1,600 2,000 2,400 2,800 3,200

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf . .

Figure 9-24. Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Hybrid Theoretical Models).

Figure 9-23. Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Full Empirical Model).

y = 0.99x

R2

 = 0.95

y = 0.99x

R2

 = 0.95

y = 0.99x

R2

 = 0.96

0

400

800

1,200

1,600

2,000

2,400

2,800

3,200

3,600

0 400 800 1,200 1,600 2,000 2,400 2,800 3,200 3,600

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf . ...

Hybrid Theoretical Thurst Model

Hybrid Theoretical Lateral Displacement Model

Hybrid Theoretical Combination Model
228

9.1.3 ACCOA Autoclaved Aerated Concrete Block 

 The ACCOA Autoclaved Aerated Concrete Block is an aerated concrete block that is 

a different class of block than the conventional CMU. The low density allows for a larger 

block size. The block measures nominally 6x12x24 inches or 8x12x24 inches. The 6-inthick block weighs 16 lbs, comparable to that the smaller-sized CMU blocks. 

9.1.2.1 Full Empirical Model 

 Table 9-10 shows the results of the multivariable regression analysis correlating the 

transverse load to the Ex(t/L)2

 and preload. From this regression analysis, the design 

equation for ACCOA block is shown in equation 9.9. 

Transverse Load = 5.7270 x Ex(t/L)2

 + 0.6562 x Preload – 252.8541 (9.9)

Where E = material modulus = 20,000 psi for ACCOA block, 

 t = wall thickness, in, 

 L = full wall height, in, and 

 Preload = ground pressure preload, psi. 

Table 9-10. Multivariable regression analysis for determining transverse load from 

modulus and wall geometric parameters. 

 Figure 9-25 displays the accuracy of the model. Only one height was evaluated in the 

test program. Two block widths, 6 and 8 inches, were evaluated. Plotted on this graph are 

Regression Statistics

Multiple R 0.9254

R Square 0.8564

Adjusted R Square 0.8373

Standard Error 75.4559

Observations 18

ANOVA

df SS MS F Significance F

Regression 2 509362 254681 44.7311 0.0000

Residual 15 85404 5694

Total 17 594766

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept -252.8541 71.6948 -3.5268 0.0031 -405.6681 -100.0402 -405.6681 -100.0402

E x (t/L)2 5.7270 0.6126 9.3486 0.0000 4.4213 7.0328 4.4213 7.0328

Preload 0.6562 0.2009 3.2659 0.0052 0.2280 1.0845 0.2280 1.0845
229

the measured transverse pressure from the laboratory tests and the calculated transverse 

pressure using equation 9-9. As seen in the figure, the model predictions are most accurate 

for the 6-in-thick half-walls. In general, thicker wall constructions for all block types behave 

more erratic. A limited number of tests, particularly with the 8-inch-thick walls due to 

limited block availability, are also contributing to the variability in the model predictions. 

Figure 9-26 shows transverse pressure predictions using this empirical design model for 6-inthick walls constructed from ACCOA block ranging in height from 5 to 10 feet in one foot 

increments with preloads ranging from 0 to 300 psi. 

0

100

200

300

400

500

600

700

800

900

0 50 100 150 200 250 300 350

PRELOAD, psi

TRANSVERSE PRESSURE, psf . Empirical Model -- Half-wall thickness 6 inches Measured Transverse Load -- Half-wall thickness 6 inches

Empirical Model -- Half-wall thickness 8 inches Measured Transverse Load -- Half-wall thickness 8 inches

Figure 9-25. Comparison of design equation predictions with measured transverse load 

from laboratory testing (Full Empirical Model – ACCOA block).
230

9.1.3.2 Hybrid Theoretical Models 

 Since testing was conducted at only one height, the hybrid theoretical models, which 

require empirical assessment of the thrust force, became erratic at heights other than the test 

height. As a result, no further development of the hybrid theoretical models was pursued. 

9.1.3.3 Summary of Design Equation for ACCOA block

 Figure 9-27 displays the calculated transverse load capacities from the full empirical 

model compared to the measured capacities from the MRS tests. The dashed line represents 

a perfect correlation between the calculated and measured capacities. The red trend line 

represents the linear regression between the measured and calculated capacities. The 

regression trend line shows less than 1 pct difference between the measured and calculated 

transverse pressure. The shaded blue area is a +/- 100 psf variation from the perfect 

correlation. Examining the chart, it is seen that 89% of the data falls within this variation. 

Figure 9-26. Transverse load capacity predictions for 6-in-thick walls constructed 

from ACCOA block for walls heights ranging from 5 to 10 ft (Full Empirical Model).

0

200

400

600

800

1,000

1,200

0 50 100 150 200 250 300

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Aerated Concrete Corp Block -- 5 ft wall height Aerated Concrete Corp Block -- 6 ft wall height

Aerated Concrete Corp Block -- 7 ft wall height Aerated Concrete Corp Block -- 8 ft wall height

Aerated Concrete Corp Block -- 9 ft wall height Aerated Concrete Corp Block -- 10 ft wall height
231

9.1.4 Ytong Block 

 The Ytong Block is also a cellular concrete block designed to provide a low density 

material that allows a large block size with a reasonable block weight. The block measures 

nominally 8x8x24 inches and weighs about 29 lbs. 

9.1.4.1 Full Empirical Model 

 Table 9-11 shows the results of the multivariable regression analysis correlating the 

transverse load to the Ex(t/L)2

 and preload. From this regression analysis, the design 

equation for Ytong block is shown in equation 9.10. 

Transverse Load = Ex(t/L)2

 x 3.8807 + 2.9706 x Preload - 452 (9.10)

Where E = material modulus = 40,000 psi for Ytong block, 

 t = wall thickness, in, 

 L = full wall height, in, and 

 Preload = ground pressure preload, psi. 

y = 1.01x

R2 = 0.86

0

100

200

300

400

500

600

700

800

900

0 100 200 300 400 500 600 700 800 900

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf . . Figure 9-27. Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Full Empirical Model).
232

 Figure 9-28 compares the results of the predicted transverse load capacities from the 

hybrid theoretical thrust model with the measured laboratory test results for half-wall heights 

of 31.5, 47.25, and 63 inches with varying preloads. As seen from the graph, the predictions 

from the full empirical model are good for all three half-wall heights. Figure 9-29 shows 

transverse load predictions using this empirical design model for walls constructed from 

Ytong block ranging in height from 5 to 10 feet in one foot increments with preloads ranging 

from 0 to 200 psi. 

Figure 9-28. Comparison of design equation predictions with measured transverse load 

from laboratory testing (Full Empirical Model – Ytong block).

0

500

1,000

1,500

2,000

2,500

3,000

0 20 40 60 80 100 120 140 160

PRELOAD, psi

TRANSVERSE PRESSURE, psf . Empirical Model -- 31.5 inch half-w all height Measured Transverse Load -- 31.5 inch half-w all height

Empirical Model -- 47.25 inch half-w all height Measured Transverse Load -- 47.25 inch half-w all height

Empirical Model -- 63 inch half-w all height Measured Transverse Load -- 63 inch half-w all height

Regression Statistics

Multiple R 0.9907

R Square 0.9815

Adjusted R Square 0.9787

Standard Error 124.8443

Observations 16

ANOVA

df SS MS F Significance F

Regression 2 10753022 5376511 344.9557 0.0000

Residual 13 202619 15586

Total 15 10955642

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept -451.5333 83.2427 -5.4243 0.0001 -631.3683 -271.6984 -631.3683 -271.6984

E x (t/L)2 3.8807 0.1485 26.1297 0.0000 3.5598 4.2015 3.5598 4.2015

Preload 2.9706 0.6612 4.4924 0.0006 1.5420 4.3991 1.5420 4.3991

Table 9-11. Multivariable regression analysis for determining 

transverse load from modulus and wall geometric 

parameters. 
233

9.1.4.2 Hybrid Theoretical Models 

 Transverse load capacity forecasts will be made using the three hybrid theoretical 

models: (1) Hybrid Thrust Model, (2) Hybrid Lateral Displacement Model, and (3) Hybrid 

Combination Thrust and Lateral Displacement Model. 

9.1.4.2.1 Hybrid Thrust Model

As seen in the flowchart in figure 9-2, the Hybrid Thrust Model determines the 

normalized thrust force from a multivariable relationship between the thrust force and the 

Ex(t/L)2

 term and preload, both of which are considered to be known parameters. The 

multivariable linear regression analysis based on 15 laboratory tests of various wall 

constructions is summarized in table 9-12. Equation 9.11 is used to compute the normalized 

thrust force per unit width of wall. Table 9-13 documents the multivariable regression 

analysis results used to determine the resultant thrust position factor (d). 

0

500

1,000

1,500

2,000

2,500

3,000

0 20 40 60 80 100 120 140 160 180 200

PRELOAD, psi

TRANSVERSE PRESSURE, psf . .

Ytong Block -- 5 ft wall height Ytong Block -- 6 ft wall height Ytong Block -- 7 ft wall height Ytong Block -- 8 ft wall height Ytong Block -- 9 ft wall height Ytong Block -- 10 ft wall height

Figure 9-29. Transverse load capacity predictions for 6-in-thick walls constructed 

from Ytong block for walls heights ranging from 5 to 10 ft (Full Empirical Model).
234

Table 9-12. Multivariable regression analysis for determining arching thrust. 

P/BL = Ex(t/L)2 x .0012 + 0.0061 x Preload + 0.5809 (9.11)

Where P/BL = Normalized thrust per unit width of block, kips/in, 

 E = Elastic modulus = 40,000 psi for Ytong block, 

 t = wall thickness, in, 

 L = height of wall, in, and 

 Preload = preload pressure, psi. 

Table 9-13. Multivariable regression analysis for determining resultant thrust position 

factor. 

d = -0.0011 x Half-wall Height - 0.0080 x Thrust + 1.0308 (9.12)

Regression Statistics

Multiple R 0.9304

R Square 0.8657

Adjusted R Square 0.8433

Standard Error 0.1645

Observations 15

ANOVA

df SS MS F Significance F

Regression 2 2.0940 1.0470 38.6840 0.0000

Residual 12 0.3248 0.0271

Total 14 2.4188

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 0.5809 0.1106 5.2544 0.0002 0.3400 0.8218 0.3400 0.8218

E*(t/L)^2 0.0012 0.0002 5.6695 0.0001 0.0007 0.0016 0.0007 0.0016

Preload 0.0061 0.0009 6.4907 0.0000 0.0040 0.0081 0.0040 0.0081

Regression Statistics

Multiple R 0.8945

R Square 0.8001

Adjusted R Square 0.7668

Standard Error 0.0383

Observations 15

ANOVA

df SS MS F Significance F

Regression 2 0.0703 0.0352 24.0127 0.0001

Residual 12 0.0176 0.0015

Total 14 0.0879

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 1.0308 0.0839 12.2918 0.0000 0.8481 1.2135 0.8481 1.2135

Half-wall Height -0.0011 0.0010 -1.1802 0.2608 -0.0032 0.0010 -0.0032 0.0010

Thrust -0.0080 0.0013 -5.9816 0.0001 -0.0109 -0.0051 -0.0109 -0.0051
235

 Figure 9-30 compares the results of the predicted transverse load capacities from the 

hybrid theoretical thrust model with the measured laboratory test results for half-wall heights 

of 31.5, 47.25, and 63 inches with varying preloads. As seen from the graph, the predictions 

overall are less accurate than the full empirical model presented in figure 9-28, especially for 

the 31.5-in half-wall height. Figure 9-31 shows transverse load predictions using this hybrid 

thrust model for walls constructed from Ytong block ranging in height from 5 to 10 feet in 

one foot increments with preloads ranging from 0 to 200 psi. 

0

500

1,000

1,500

2,000

2,500

3,000

0 20 40 60 80 100 120 140 160

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Hybrid Thrust Model -- Half-wall height 31.5 inches Measured Transverse Load -- Half-wall Height 31.5 inches

Hybrid Thrust Model -- Half-wall height 47.25 inches Measured Transverse Load -- Half-wall Height 47.25 inches

Hybrid Thrust Model -- Half-wall height 63 inches Measured Transverse Load -- Half-wall Height 63 inches

Figure 9-30. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Thrust Model).
236

9.1.4.2.2 Hybrid Lateral Displacement Model

As seen in the flowchart in figure 9-3, the Hybrid Lateral Displacement Model determines 

the lateral displacement force from a multivariable relationship from the Ex(t/L)2 term and 

preload, both of which are considered to be known parameters. The multivariable linear 

regression analysis based on 15 laboratory tests of various wall constructions is summarized 

in table 9-14. Equation 9.13 is used to compute lateral wall displacement. Table 9-13 

documented the multivariable regression analysis results used to determine the resultant 

thrust position factor (d) for the Hybrid Thrust Model. This equation is also used for 

computing the resultant thrust adjustment factor for this model, except the calculated thrust 

forces are used instead of the measured thrust forces. 

Lateral Displacement = -0.0007 x Ex(t/L)2 - 0.0037 x Preload + 1.55778 (9.13)

0

500

1,000

1,500

2,000

2,500

3,000

0 20 40 60 80 100 120 140 160 180 200

PRELOAD, psi

TRANSVERSE PRESSURE, psf . . 

Ytong Block -- 5 ft wall height Ytong Block -- 6 ft wall height Ytong Block -- 7 ft wall height

Ytong Block -- 8 ft wall height Ytong Block -- 9 ft wall height Ytong Block -- 10 ft wall height

Figure 9-31. Transverse load capacity predictions for 6-in-thick walls constructed 

from Ytong block for walls heights ranging from 5 to 10 ft (Hybrid Theoretical 

Thrust Model).
237

Table 9-14. Multivariable regression for determining lateral displacement. 

 Figure 9-32 compares the results of the predicted transverse load capacities from the 

hybrid theoretical lateral displacement model with the measured laboratory test results for 

half-wall heights of 31.5, 47.25, and 63 inches with varying preloads. As seen from the 

graph, the predictions overall are similar to the hybrid theoretical thrust model presented in 

figure 9-29 and slightly less accurate than the empirical model. Figure 9-33 shows transverse 

load predictions using the hybrid theoretical lateral displacement for walls constructed from 

Ytong block ranging in height from 5 to 10 feet in one foot increments with preloads ranging 

from 0 to 200 psi. 

Figure 9-32. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Lateral 

Displacement Model).

0

500

1,000

1,500

2,000

2,500

3,000

0 20 40 60 80 100 120 140 160

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Hybrid Lateral Displacement Model -- Half-wall height 31.5 inches Measured Transverse Load -- Half-wall Height 31.5 inches

Hybrid Lateral Displacement Model -- Half-wall height 47.25 inches Measured Transverse Load -- Half-wall Height 47.25 inches

Hybrid Lateral Displacement Model -- Half-wall height 63 inches Measured Transverse Load -- Half-wall Height 63 inches

Regression Statistics

Multiple R 0.8545

R Square 0.7301

Adjusted R Square 0.6852

Standard Error 0.1587

Observations 15

ANOVA

df SS MS F Significance F

Regression 2 0.8177 0.4089 16.2343 0.0004

Residual 12 0.3022 0.0252

Total 14 1.1200

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 1.5578 0.1066 14.6072 0.0000 1.3254 1.7901 1.3254 1.7901

E*(t/L)^2 -0.0007 0.0002 -3.7989 0.0025 -0.0012 -0.0003 -0.0012 -0.0003

Preload -0.0037 0.0009 -4.0903 0.0015 -0.0057 -0.0017 -0.0057 -0.0017
238

9.1.4.2.3 Hybrid Combination Model

 The Hybrid Combination Model combines the previous two models by empirically 

determining both the thrust and lateral displacement. Figure 9-34 compares this model’s 

predictions of transverse load capacity to the measured transverse load capacities from the 

laboratory testing. The combination model is considerably more accurate than the thrust or 

lateral displacement model. For completeness, figure 9-35 is included which displays the 

transverse load predictions using the hybrid theoretical combination model for 6-in-thick 

walls constructed from Ytong block ranging in height from 5 to 10 feet in one foot 

increments with preloads ranging from 0 to 200 psi. 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0 20 40 60 80 100 120 140 160 180 200

PRELOAD, psi

TRANSVERSE PRESSURE, psf.. .

Ytong Block -- 5 ft wall height Ytong Block -- 6 ft wall height Ytong Block -- 7 ft wall height

Ytong Block -- 8 ft wall height Ytong Block -- 9 ft wall height Ytong Block -- 10 ft wall height

Figure 9-33. Transverse load capacity predictions for 6-in-thick walls constructed 

from Ytong block for walls heights ranging from 5 to 10 ft (Hybrid Theoretical 

Lateral Displacement Model).
239

Figure 9-34. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Combination 

Model).

0

500

1,000

1,500

2,000

2,500

3,000

0 20 40 60 80 100 120 140 160

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Hybrid Combination Model -- Half-wall height 31.5 inches Measured Transverse Load -- Half-wall Height 31.5 inches

Hybrid Combination Model -- Half-wall height 47.25 inches Measured Transverse Load -- Half-wall Height 47.25 inches

Hybrid Combination Model -- Half-wall height 63 inches Measured Transverse Load -- Half-wall Height 63 inches

0

500

1,000

1,500

2,000

2,500

3,000

0 20 40 60 80 100 120 140 160 180 200

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Ytong Block -- 5 ft wall height Ytong Block -- 6 ft wall height Ytong Block -- 7 ft wall height

Ytong Block -- 8 ft wall height Ytong Block -- 9 ft wall height Ytong Block -- 10 ft wall height

Figure 9-35. Transverse load capacity predictions for 6-in-thick walls constructed 

from Ytong block for walls heights ranging from 5 to 10 ft (Hybrid Theoretical 

Combination Model).
240

9.1.4.3 Summary of Design Equations for Ytong Block

 In summary, a full empirical design model and three hybrid theoretical design models 

were developed for the Ytong block stopping constructions. Figure 9-36 displays the 

calculated transverse load capacities from full empirical model compared to the measured 

capacities from the MRS tests. The dashed line represents a perfect correlation between the 

calculated and measured capacities. The red trend line represents the linear regression and 

shows that on average the model predicts the transverse pressure to within a 1 pct error. The 

shaded blue area is a +/- 400 psf variation from the perfect correlation. Examining the chart, 

it is seen that 100% of the data falls within this variation. Figure 9-37 displays this same 

information for the three hybrid theoretical design models. The hybrid combination model 

which empirically determines both the arching thrust and lateral displacement provides the 

most accurate predictions of the transverse pressure. The difference between the measured 

and calculated transverse pressure with this model is less than 1 pct. The hybrid thrust and 

hybrid lateral displacement model both over predict the transverse pressure with an error of 6 

pct. Examining the +/-400 psf variation (blue shading), all three models have 100% of the 

data within this variation. 
241

y = 0.94x

R2

 = 0.98

y = 0.94x

R2

 = 0.98

y = 1.01x

R2

 = 0.98

0

400

800

1,200

1,600

2,000

2,400

2,800

0 400 800 1,200 1,600 2,000 2,400 2,800

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf .

Hybrid Theoretical Thrust Model

Hybrid Theoretical Lateral Displacement Model

Hybrid Theoretical CombinationModel

y = 1.00x

R2

 = 0.98

0

400

800

1,200

1,600

2,000

2,400

2,800

0 400 800 1,200 1,600 2,000 2,400 2,800

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf .... .

Figure 9-37. Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Hybrid Theoretical Models).

Figure 9-36. Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Full Empirical Model).
242

9.1.5 Kingsway Block 

 Kingsway is another cellular concrete block used for stopping construction. This block 

measures nominally 6x8x17 inches and weighs on average 21 lbs. It has a moderate 

compressive strength of 546 psi. Only 8 tests were conducted with the Kingsway block. 

Although more test results would produce a better block model, it is believed that there were 

sufficient test variables to construct a useful model. 

9.1.5.1 Full Empirical Model 

 Table 9-15 shows the results of the multivariable regression analysis correlating the 

transverse load to the Ex(t/L)2

 and preload. From this regression analysis, the design 

equation for Kingsway block is shown in equation 9.14. 

Transverse Load = 5.3608 x E(t/L)2

 - 0.2822 x Preload – 172 (9.14)

Where E = material modulus = 24,000 psi for Kingsway block, 

 t = wall thickness, in, 

 L = full wall height, in, and 

 Preload = ground pressure preload, psi. 

Table 9-15. Multivariable regression analysis for determining transverse load from 

modulus and wall geometric parameters. 

 Figure 9-38 compares the predicted transverse load capacities from the empirical 

model with the measured laboratory results for the three half-wall heights with varying 

preloads. Due to limited availability of the block, the preload was not varied much in this 

Regression Statistics

Multiple R 0.9879

R Square 0.9759

Adjusted R Square 0.9663

Standard Error 40.6704

Observations 8

ANOVA

df SS MS F Significance F

Regression 2 335241 167620 101.3372 0.0001

Residual 5 8270 1654

Total 7 343511

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept -172.6684 104.0557 -1.6594 0.1579 -440.1517 94.8149 -440.1517 94.8149

E x (t/L)2 5.3608 0.4124 12.9984 0.0000 4.3006 6.4210 4.3006 6.4210

Preload -0.2822 1.1932 -0.2365 0.8224 -3.3495 2.7851 -3.3495 2.7851
243

series of tests. As seen in the figure, the model predictions are reasonably accurate for the 

42-in and 50-in half-wall heights. Only two tests were conducted at the 33-in half-wall 

height, and the model prediction is a reasonable approximation of the average of these two 

tests. Figure 9-39 shows transverse load predictions using this empirical design model for 

walls constructed from Kingsway block ranging in height from 5 to 10 feet in one foot 

increments with preloads ranging from 0 to 100 psi. The model shows little variation with 

preload. This is due to the lack of variation of preload in the test data. 

Figure 9-38. Comparison of design equation predictions with measured transverse 

load from laboratory testing (Full Empirical Model – Kingsway block).

0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90

PRELOAD, psi

TRANSVERSE PRESSURE, psf. Empirical Model -- Half-wall height 33.5 inches Measured Transverse Load -- Half-wall Height 33.5 inches

Empirical Model -- Half-wall height 41.875 inches Measured Transverse Load -- Half-wall Height 41.875 inches

Empirical Model -- Half-wall height 50.25 inches Measured Transverse Load -- Half-wall Height 50.25 inches
244

9.1.5.2 Hybrid Theoretical Models 

 Transverse load capacity forecasts will be made using the three hybrid theoretical 

models: (1) Hybrid Thrust Model, (2) Hybrid Lateral Displacement Model, and (3) Hybrid 

Combination Thrust and Lateral Displacement Model. 

9.1.5.2.1 Hybrid Thrust Model

As seen in the flowchart in figure 9-2, the Hybrid Thrust Model determines the 

normalized thrust force from a multivariable relationship between the thrust force and the 

Ex(t/L)2 term and preload, both of which are considered to be known parameters. The 

multivariable linear regression analysis based on 8 laboratory tests of various wall 

constructions is summarized in table 9-16. Equation 9.15 is used to compute the normalized 

thrust force per unit width of wall. Table 9-17 documents the multivariable regression 

analysis results used to determine the resultant thrust position factor (d). 

0

200

400

600

800

1,000

1,200

0 10 20 30 40 50 60 70 80 90 100

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Kingsway Block -- 5 ft wall height Kingsway Block -- 6 ft wall height

Kingsway Block -- 7 ft wall height Kingsway Block -- 8 ft wall height

Kingsway Block -- 9 ft wall height Kingsway Block -- 10 ft wall height

Figure 9-39. Transverse load capacity predictions for walls constructed from 

Kingsway solid block for walls heights ranging from 5 to 10 ft (Full Empirical Model).
245

Table 9-16. Multivariable regression analysis for determining arching thrust. 

P/BL = .0018 x Ex(t/L)2

 + 0.0034 x Preload + 0.2850 (9.15) 

Where P/BL = Normalized thrust per unit width of block, kips/in, 

 E = Elastic modulus = 24,000 psi for Kingsway block, 

 t = wall thickness, in, 

 L = height of wall, in, and 

 Preload = preload pressure, psi. 

Table 9-17. Multivariable regression analysis for determining resultant thrust position 

factor. 

d = -0.0087 x Half-wall Height - 0.0453 x Thrust + 1.7532 (9.16)

 Figure 9-40 compares the results of the predicted transverse load capacities from the 

hybrid theoretical thrust model with the measured laboratory test results for half-wall heights 

Regression Statistics

Multiple R 0.6356

R Square 0.4040

Adjusted R Square 0.1656

Standard Error 0.1024

Observations 8

ANOVA

df SS MS F Significance F

Regression 2 0.0356 0.0178 1.6944 0.2743

Residual 5 0.0525 0.0105

Total 7 0.0880

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 0.2850 0.2621 1.0873 0.3265 -0.3888 0.9588 -0.3888 0.9588

E*(t/L)^2 0.0018 0.0010 1.7771 0.1357 -0.0008 0.0045 -0.0008 0.0045

Preload 0.0034 0.0030 1.1396 0.3061 -0.0043 0.0112 -0.0043 0.0112

Regression Statistics

Multiple R 0.8682

R Square 0.7538

Adjusted R Square 0.6553

Standard Error 0.0509

Observations 8

ANOVA

df SS MS F Significance F

Regression 2 0.0396 0.0198 7.6528 0.0301

Residual 5 0.0129 0.0026

Total 7 0.0525

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 1.7532 0.2443 7.1759 0.0008 1.1251 2.3812 1.1251 2.3812

Half-wall Height -0.0087 0.0027 -3.2620 0.0224 -0.0155 -0.0018 -0.0155 -0.0018

Thrust -0.0453 0.0123 -3.6724 0.0144 -0.0770 -0.0136 -0.0770 -0.0136
246

of 33, 42, and 50 inches with varying preloads. As seen from the graph, this theoretical 

model over predicts the transverse load for all three heights. As a result, this model does not 

provide an improvement over the full empirical model presented in figure 9-38. Figure 9-41 

shows transverse load predictions using this empirical design model for walls constructed 

from Kingsway block ranging in height from 5 to 10 feet in one foot increments with 

preloads ranging from 0 to 140 psi. 

Figure 9-40. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Thrust Model).

0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Hybrid Thurst Model -- Half-wall height 33.5 inches Measured Transverse Load -- Half-wall Height 33.5 inches

Hybrid Thrust Model -- Half-wall height 41.875 inches Measured Transverse Load -- Half-wall Height 41.875 inches

Hybrid Thrust Model -- Half-wall height 50.25 inches Measured Transverse Load -- Half-wall Height 50.25 inches
247

9.1.5.2.2 Hybrid Lateral Displacement Model

As seen in the flowchart in figure 9-3, the Hybrid Lateral Displacement Model 

determines the lateral displacement force from a multivariable relationship from the Ex(t/L)2 

term and preload, both of which are considered to be known parameters. The multivariable 

linear regression analysis based on 8 laboratory tests of various wall constructions is 

summarized in table 9-18. Equation 9.17 is used to compute the lateral wall displacement. 

Table 9-17 documented the multivariable regression analysis results used to determine the 

resultant thrust position factor (d) for the Hybrid Thrust Model. This equation is also used 

for computing the resultant thrust adjustment factor for this model, except the calculated 

thrust forces are used instead of the measured thrust forces. 

Lateral Displacement = -0.0057 x Ex(t/L)2

 - 0.0020 x Preload + 2.0018 (9.17)

0

200

400

600

800

1,000

1,200

1,400

0 20 40 60 80 100 120 140

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Kingsway Block -- 5 ft wall height Kingsway Block -- 6 ft wall height

Kingsway Block -- 7 ft wall height Kingsway Block -- 8 ft wall height

Kingsway Block -- 9 ft wall height Kingsway Block -- 10 ft wall height

Figure 9-41. Transverse load capacity predictions for 6-in-thick walls constructed from 

Kingsway solid block for walls heights ranging from 5 to 10 ft (Hybrid Theoretical 

Thrust Model).
248

Table 9-18. Multivariable regression analysis for determining lateral displacement. 

 Figure 9-42 compares the results of the predicted transverse load capacities from the 

hybrid theoretical lateral displacement model with the measured laboratory test results for 

half-wall heights of 33, 42, and 50 inches with varying preloads. As seen from the graph, the 

Regression Statistics

Multiple R 0.8920

R Square 0.7956

Adjusted R Square 0.7138

Standard Error 0.1327

Observations 8

ANOVA

df SS MS F Significance F

Regression 2 0.3425 0.1713 9.7297 0.0189

Residual 5 0.0880 0.0176

Total 7 0.4306

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 2.0018 0.3395 5.8971 0.0020 1.1292 2.8743 1.1292 2.8743

E*(t/L)^2 -0.0057 0.0013 -4.2282 0.0083 -0.0091 -0.0022 -0.0091 -0.0022

Preload -0.0020 0.0039 -0.5033 0.6361 -0.0120 0.0080 -0.0120 0.0080

0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90

PRELOAD, psi

TRANSVERSE PRESSURE, psf. Hybrid Lateral Displacement Model -- Half-wall height 33.5 inches Measured Transverse Load -- Half-wall Height 33.5 inches

Hybrid Lateral Displacement Model -- Half-wall height 41.875 inches Measured Transverse Load -- Half-wall Height 41.875 inches

Hybrid Lateral Displacement Model -- Half-wall height 50.25 inches Measured Transverse Load -- Half-wall Height 50.25 inches

Figure 9-42. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Lateral 

Displacement Model).
249

predictions are significantly better than the hybrid theoretical thrust model presented in figure 

9-40. Figure 9-43 shows transverse load predictions using the hybrid theoretical lateral 

displacement for walls constructed from Kingsway block ranging in height from 5 to 10 feet 

in one foot increments with preloads ranging from 0 to 140 psi. 

9.1.5.2.3 Hybrid Combination Model

 The Hybrid Combination Model combines the previous two models by empirically 

determining both the thrust and lateral displacement. Figure 9-44 compares this model’s 

predictions of transverse load capacity to the measured transverse load capacities from the 

laboratory testing. This model provides a more accurate prediction of the transverse pressure 

than the thrust model, but since it utilizes the thrust model information, it is not quite as 

accurate as the lateral displacement model. Figure 9-45 displays the transverse load 

predictions using the hybrid theoretical combination model for walls constructed from 

Kingsway block ranging in height from 5 to 10 feet in one foot increments with preloads 

ranging from 0 to 140 psi. 

0

200

400

600

800

1,000

1,200

0 20 40 60 80 100 120 140

PRELOAD, psi

TRANSVERSE PRESSURE, psf ..

Kingsway Block -- 5 ft wall height Kingsway Block -- 6 ft wall height Kingsway Block -- 7 ft wall height

Kingsway Block -- 8 ft wall height Kingsway Block -- 9 ft wall height Kingsway Block -- 10 ft wall height

Figure 9-43. Transverse load capacity predictions for walls constructed from 

Kingsway block for heights ranging from 5 to 10 ft (Hybrid Theoretical Lateral 

Displacement Model).
250

0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Hybrid Combination Model -- Half-wall height 33.5 inches Measured Transverse Load -- Half-wall Height 33.5 inches

Hybrid Combination Model -- Half-wall height 41.875 inches Measured Transverse Load -- Half-wall Height 41.875 inches

Hybrid Combination Model -- Half-wall height 50.25 inches Measured Transverse Load -- Half-wall Height 50.25 inches

Figure 9-44. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Combination 

Model).

0

200

400

600

800

1,000

1,200

1,400

0 20 40 60 80 100 120 140

PRELOAD, psi

TRANSVERSE PRESSURE, psf ...

Kingsway Block -- 5 ft wall height Kingsway Block -- 6 ft wall height

Kingsway Block -- 7 ft wall height Kingsway Block -- 8 ft wall height

Kingsway Block -- 9 ft wall height Kingsway Block -- 10 ft wall height

Figure 9-45. Transverse load capacity predictions for walls constructed from 

Kingsway block for walls heights ranging from 5 to 10 ft (Hybrid Theoretical 

Combination Model).
251

9.1.5.3 Summary of Design Equations for Kingsway Block

 In summary, a full empirical design model and three hybrid theoretical design models 

were developed for the Kingsway block stopping constructions. Figure 9-46 displays the 

calculated transverse load capacities from full empirical model compared to the measured 

capacities from the MRS tests. The dashed line represents a perfect correlation between the 

calculated and measured capacities. The red trend line represents the linear regression 

between the measured and calculated capacities. The regression lines shows that on average 

the model tends to over predict the transverse load by a slight amount. The regression trend 

line shows a 2 pct difference between the measured and calculated transverse load. The 

shaded blue area is a +/- 100 psf variation from the perfect correlation. Examining the chart, 

it is seen that 100% of the data falls within this variation. Figure 9-47 displays this same 

information for the three hybrid theoretical design models. Based on the regression trend 

line correlating the calculated transverse loads to the measured transverse loads, the lateral 

displacement model is the most accurate, slightly better than the combination model. Both 

models predict the load to within 2 pct of the measure transverse load. The least accurate is 

the thrust model with a 10 pct difference. Examining the +/-100 psf variation (blue shading), 

all models have 100% of the data within this variation. 
252

y = 0.90x

R2

 = 0.98

y = 0.98x

R2

 = 0.98

y = 0.96x

R2

 = 0.98

0

100

200

300

400

500

600

700

800

900

0 100 200 300 400 500 600 700 800 900

CALCUALTED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf 

Hybrid Theoretical Thrust Model

Hybrid Theoretical Lateral Displacement Model

Hybrid Theoretical Combination Model

Figure 9-47. Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Hybrid Theoretical Models).

Figure 9-46. Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Full Empirical Model).

y = 0.98x

R2

 = 0.98

0

100

200

300

400

500

600

700

800

900

0 100 200 300 400 500 600 700 800 900

CALCUALTED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf ....
253

9.1.6 Omega Block 

 Omega is another cellular concrete block used for stopping construction. This block 

measures nominally 8x16x24 inches and weighs on average 47 lbs. The material is very 

weak with a compressive strength of only 80 psi. It is also a brittle material that is often 

damaged in places simply from handling of the stopping block. These characteristics lead to 

inconsistencies in performance and difficulty in constructing accurate predictive models. A 

total of 22 tests were conducted with the Omega block, sufficient to produce a valid set of 

theoretical and empirical prediction models. 

9.1.5.1 Full Empirical Model 

 In order to improve the accuracy of the model predictions, the modulus was varied as a 

function of half-wall height according to equation 9.18. In reality, the modulus is not 

changing, but the deformation zone associated with the wall rotation produces a differing 

behavior. Changing the modulus is one way to adjust for this issue and incorporate the 

response into the existing prediction models. Table 9-19 shows the results of the 

multivariable regression analysis correlating the transverse load to the Ex(t/L)2

 and preload. 

From this regression analysis, the design equation for Omega block is shown in equation 

9.19. 

Modulus (E) = 0.0271 x Half-wall height 2.8681 (9.18)

Table 9-19. Multivariable regression analysis for determining transverse load from 

modulus and wall geometric parameters. 

Regression Statistics

Multiple R 0.8074

R Square 0.6520

Adjusted R Square 0.6153

Standard Error 59.0914

Observations 22

ANOVA

df SS MS F Significance F

Regression 2 124275 62137 17.7953 0.0000

Residual 19 66344 3492

Total 21 190619

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 325.9738 48.3696 6.7392 0.0000 224.7351 427.2126 224.7351 427.2126

E x (t/L)2 -19.9940 3.4063 -5.8697 0.0000 -27.1234 -12.8646 -27.1234 -12.8646

Preload 2.5990 1.5544 1.6720 0.1109 -0.6544 5.8523 -0.6544 5.8523
254

Transverse Load = -19.9940 x Ex(t/L)2

 + 2.5990 x Preload + 325.9738 (9.19)

Where E = material modulus = 600 to 4,500 psi for Omega block, 

 t = wall thickness, in, 

 L = full wall height, in, and 

 Preload = ground pressure preload, psi. 

 Figure 9-48 compares the predicted transverse load capacities from the empirical 

model with the measured laboratory results for the half wall heights with varying preloads. 

Due to the relative weakness of the block, the preload was not varied much. As seen in the 

figure, the model over predicts the transverse load for the 48-in and 64-in half-wall heights 

and under predicts the load for the 32-in half-wall height. In part, this is reflection of the 

difference in the hinge point deformation at the different wall heights. Figure 9-49 shows 

transverse load predictions using this empirical design model for walls constructed from 

Omega block ranging in height from 5 to 10 feet in one foot increments with preloads 

ranging from 0 to 30 psi, which is the limiting preload to prevent premature failure of the 

stopping wall. Again, the inconsistencies in the transverse loading are largely due to 

localized failures of this weak block material. 

Figure 9-48. Comparison of design equation predictions with measured transverse load 

from laboratory testing (Full Empirical Model – Omega block).

0

50

100

150

200

250

300

350

0 5 10 15 20 25 30

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Empirical Model -- Half-wall height 32 inches Measured Transverse Load -- Half-wall Height 32 inches

Empirical Model -- Half-wall height 48 inches Measured Transverse Load -- Half-wall Height 48 inches

Empirical Model -- Half-wall height 64 inches Measured Transverse Load -- Half-wall Height 64 inches
255

9.1.6.2 Hybrid Theoretical Models 

 Transverse load capacity forecasts will be made using the three hybrid theoretical 

models: (1) Hybrid Thrust Model, (2) Hybrid Lateral Displacement Model, and (3) Hybrid 

Combination Thrust and Lateral Displacement Model. 

9.1.6.2.1 Hybrid Thrust Model

As seen in the flowchart in figure 9-2, the Hybrid Thrust Model determines the 

normalized thrust force from a multivariable relationship between the thrust force and the 

Ex(t/L)2

 term and preload, both of which are considered to be known parameters. The 

multivariable linear regression analysis based on 22 laboratory tests of various wall 

constructions is summarized in table 9-20. Equation 9.20 is used to compute the normalized 

thrust force per unit width of wall. Table 9-21 documents the multivariable regression 

analysis results used to determine the resultant thrust position factor (d). 

0

50

100

150

200

250

0 5 10 15 20 25 30

PRELOAD, psi

TRANSVERSE PRESSURE, psf ..

Omega Block -- 5 ft wall height Omega Block -- 6 ft wall height Omega Block -- 7 ft wall height

Omega Block -- 8 ft wall height Omega Block -- 9 ft wall height Omega Block -- 10 ft wall height

Figure 9-49. Transverse load capacity predictions for 8-in-thick walls constructed 

from Omega block for walls heights ranging from 5 to 10 ft (Full Empirical Model).
256

Table 9-20. Multivariable regression analysis for determining arching thrust. 

P/BL = - 0.0083 x Ex(t/L)2 + 0.0046 * Preload + 0.1586 (9.20)

Where P/BL = Normalized thrust per unit width of block, kips/in, 

 E = Elastic modulus = 600 to 4,500 psi for Omega block, 

 t = wall thickness, in, 

 L = height of wall, in, and 

 Preload = preload pressure, psi. 

Table 9-21. Multivariable regression analysis for determining resultant thrust position 

factor. 

d = -0.0080 x Half-wall Height - 0.0524 x Thrust + 1.3723 (9.21)

 Figure 9-50 compares the results of the predicted transverse load capacities from the 

hybrid theoretical thrust model with the measured laboratory test results for half-wall heights 

of 32, 48, and 64 inches with varying preloads. As seen from the graph, the predictions 

Regression Statistics

Multiple R 0.8319

R Square 0.6920

Adjusted R Square 0.6596

Standard Error 0.0331

Observations 22

ANOVA

df SS MS F Significance F

Regression 2 0.0468 0.0234 21.3487 0.0000

Residual 19 0.0208 0.0011

Total 21 0.0677

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 0.1586 0.0271 5.8515 0.0000 0.1019 0.2154 0.1019 0.2154

E*(t/L)^2 -0.0083 0.0019 -4.3563 0.0003 -0.0123 -0.0043 -0.0123 -0.0043

Preload 0.0046 0.0009 5.2978 0.0000 0.0028 0.0064 0.0028 0.0064

Regression Statistics

Multiple R 0.7478

R Square 0.5592

Adjusted R Square 0.5128

Standard Error 0.0876

Observations 22

ANOVA

df SS MS F Significance F

Regression 2 0.1852 0.0926 12.0531 0.0004

Residual 19 0.1460 0.0077

Total 21 0.3311

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 1.3723 0.1137 12.0712 0.0000 1.1343 1.6102 1.1343 1.6102

Half-wall Height -0.0080 0.0016 -4.8343 0.0001 -0.0114 -0.0045 -0.0114 -0.0045

Thrust -0.0524 0.0163 -3.2092 0.0046 -0.0866 -0.0182 -0.0866 -0.0182
257

overall are improved compared to the full empirical model presented in figure 9-48, 

especially for the 32 and 48-in half-wall height. The transverse load for the 32-in half-wall 

height is now over predicted, while is was under predicted for the empirical model. Overall, 

the accuracy for the 32-in half-wall response remains about the same with this model. Figure 

9-51 shows transverse load predictions using this empirical design model for 8-in-thick walls 

constructed from Omega block ranging in height from 5 to 10 feet in one foot increments 

with preloads ranging from 0 to 30 psi. 

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Hybrid Thrust Model -- Half-wall height 32 inches Measured Transverse Load -- Half-wall Height 32 inches

Hybrid Thrust Model -- Half-wall height 48 inches Measured Transverse Load -- Half-wall Height 48 inches

Hybrid Thrust Model -- Half-wall height 64 inches Measured Transverse Load -- Half-wall Height 64 inches

Figure 9-50. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Thrust Model).
258

9.1.6.2.2 Hybrid Lateral Displacement Model

As seen in the flowchart in figure 9-3, the Hybrid Lateral Displacement Model determines 

the lateral displacement force from a multivariable relationship from the Ex(t/L)2 term and 

preload, both of which are considered to be known parameters. The multivariable linear 

regression analysis based on 22 laboratory tests of various wall constructions is summarized 

in table 9-22. Equation 9.22 is used to compute the lateral displacement. Table 9-21 

documents the multivariable regression analysis results. Equation 9.21 is also used for 

computing the resultant thrust adjustment factor for this model, except the calculated thrust 

forces are used instead of the measured thrust forces. 

Lateral Displacement = 0.0333 x Ex(t/L)2

 - 0.0293 x Preload + 1.6449 (9.22)

0

50

100

150

200

250

300

350

400

450

500

0 5 10 15 20 25 30

PRELOAD, psi

TRANSVERSE PRESSURE, psf ..

Omega Block -- 5 ft wall height Omega Block -- 6 ft wall height Omega Block -- 7 ft wall height

Omega Block -- 8 ft wall height Omega Block -- 9 ft wall height Omega Block -- 10 ft wall height

Figure 9-51. Transverse load capacity predictions for 8-in-thick walls constructed 

from Omega block for walls heights ranging from 5 to 10 ft (Hybrid Theoretical 

Thrust Model).
259

 Figure 9-52 compares the results of the predicted transverse load capacities from the 

hybrid theoretical lateral displacement model with the measured laboratory test results for 

half-wall heights of 32, 48, and 64 inches with varying preloads. As seen from the graph, the 

prediction for the 32-in high half-wall is significantly improved compared to the thrust 

model. Prediction at the other two wall heights is about the same as that of the thrust model. 

Figure 9-53 shows transverse load predictions using the hybrid theoretical lateral 

displacement for walls constructed from Omega block ranging in height from 5 to 10 feet in 

one foot increments with preloads ranging from 0 to 30 psi. 

Regression Statistics

Multiple R 0.4002

R Square 0.1602

Adjusted R Square 0.0717

Standard Error 0.6337

Observations 22

ANOVA

df SS MS F Significance F

Regression 2 1.4549 0.7275 1.8116 0.1905

Residual 19 7.6297 0.4016

Total 21 9.0846

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 1.6449 0.5187 3.1710 0.0050 0.5592 2.7305 0.5592 2.7305

E*(t/L)^2 0.0332 0.0365 0.9102 0.3741 -0.0432 0.1097 -0.0432 0.1097

Preload -0.0293 0.0167 -1.7575 0.0949 -0.0642 0.0056 -0.0642 0.0056

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30

PRELOAD, psi

TRANSVERSE PRESSURE, psf ..

Hybrid Lateral Displacement Model -- Half-wall height 32 inches Measured Transverse Load -- Half-wall Height 32 inches

Hybrid Lateral Displacement Model -- Half-wall height 48 inches Measured Transverse Load -- Half-wall Height 48 inches

Hybrid Lateral Displacement Model -- Half-wall height 64 inches Measured Transverse Load -- Half-wall Height 64 inches

Figure 9-52. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Lateral 

Displacement Model).

Table 9-22. Multivariable regression analysis for 

determining lateral displacement.
260

9.1.6.2.3 Hybrid Combination Model

 The Hybrid Combination Model combines the previous two models by empirically 

determining both the thrust and lateral displacement. Figure 9-54 compares this model’s 

predictions of transverse load capacity to the measured transverse load capacities from the 

laboratory testing. Overall, the results with the combination thrust and lateral displacement 

model are improved over the individual models. The transverse load predictions for the low 

(32-in-high half-wall) and high (64-in-high half-wall) wall heights are significantly 

improved. The prediction at the 48-in half-wall height is slightly worse. For completeness, 

figure 9-55 is included which displays the transverse load predictions using the hybrid 

theoretical combination model for 8-in-thick walls constructed from Omega block ranging in 

height from 5 to 10 feet in one foot increments with preloads ranging from 0 to 30 psi. 

0

50

100

150

200

250

300

350

400

450

500

0 5 10 15 20 25 30

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Omega Block -- 5 ft wall height Omega Block -- 6 ft wall height Omega Block -- 7 ft wall height

Omega Block -- 8 ft wall height Omega Block -- 9 ft wall height Omega Block -- 10 ft wall height

Figure 9-53. Transverse load capacity predictions for 8-in-thick walls constructed 

from Omega block for walls heights ranging from 5 to 10 ft (Hybrid Theoretical 

Lateral Displacement Model).
261

0

50

100

150

200

250

300

350

0 5 10 15 20 25 30

PRELOAD, psi

TRANSVERSE PRESSURE, psf ..

Hybrid Combination Model -- Half-wall height 32 inches Measured Transverse Load -- Half-wall Height 32 inches

Hybrid Combination Model -- Half-wall height 48 inches Measured Transverse Load -- Half-wall Height 48 inches

Hybrid Combination Model -- Half-wall height 64 inches Measured Transverse Load -- Half-wall Height 64 inches

Figure 9-54. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Combination 

Model).

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30

PRELOAD, psi

TRANSVERSE PRESSURE, psf ..

Omega Block -- 5 ft wall height Omega Block -- 6 ft wall height Omega Block -- 7 ft wall height

Omega Block -- 8 ft wall height Omega Block -- 9 ft wall height Omega Block -- 10 ft wall height

Figure 9-55. Transverse load capacity predictions for 8-in-thick walls constructed 

from Omega block for walls heights ranging from 5 to 10 ft (Hybrid Theoretical 

Combination Model).
262

9.1.6.3 Summary of Design Equations for Omega Block

 In summary, a full empirical design model and three hybrid theoretical design models 

were developed for the Omega block stopping constructions. Figure 9-56 displays the 

calculated transverse load capacities from full empirical model compared to the measured 

capacities from the MRS tests. The model over predicts the short and medium height walls 

and under predicts the high wall height performance. The dashed line represents a perfect 

correlation between the calculated and measured capacities. The red trend line represents the 

linear regression between the measured and calculated capacities. The regression lines 

shows that on average the model tends to under predict the transverse load. The regression 

trend line shows a 10 pct difference between the measured and calculated transverse load. 

The shaded blue area is a +/- 40 psf variation from the perfect correlation. Examining the 

chart, it is seen that 73% of the data falls within this variation. Figure 9-57 displays this 

same information for the three hybrid theoretical design models. Based on the regression 

trend line correlating the calculated transverse loads to the measured transverse loads, the 

combination model, which computes both the thrust and lateral displacement from laboratory 

test data, is the most accurate of the three, with a 4 pct difference in calculated and measured 

loads. The least accurate is the thrust model with 23 pct difference, largely due to the over 

prediction of high wall performance. Examining the +/-50 psf variation (blue shading), the 

combination model has 100% of the data within this variation. The lateral displacement 

model has 86 pct of the data within this variation, while the thrust model has only 68 pct of 

the data within the +/-50 psf variation. 
263

y = 0.77x

R2 = 0.93

y = 0.90x

R2

 = 0.89

y = 0.96x

R2

 = 0.92

0

50

100

150

200

250

300

350

400

0 50 100 150 200 250 300 350 400

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf ..

Hybrid Theoretical Thurst Model

Hybrid Theoretical Lateral Displacement Model

Hybrid Theoretical Combination Model

Figure 9-57. Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Hybrid Theoretical Models).

y = 1.10x

R2

 = 0.84

0

40

80

120

160

200

240

280

320

0 40 80 120 160 200 240 280 320

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf . ...

Figure 9-56. Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Full Empirical Model).
264

9.1.7 Peerless Super Block 

 Peerless Super Block is unique block construction with imbedded Styrofoam pellets 

in a very weak concrete mix. It has a compressive strength of only 86 psi, comparable to the 

Omega block. This block measures nominally 6x16x24 inches and weighs approximately 16 

lbs. Thirty tests were conducted with the Peerless Super block, providing a good data set to 

construct the prediction models; however, the non-uniform distribution of the foam pellets 

and very weak concrete material led to inconsistent performance of the stopping walls. 

9.1.7.1 Full Empirical Model 

 In order to improve the accuracy of the model predictions, the modulus was varied as a 

function of half-wall height according to equation 9.23. In reality, the modulus is not 

changing, but the deformation zone associated with the wall rotation produces a differing 

behavior. Changing the modulus is one way to adjust for this issue and incorporate the 

response into the existing prediction models. Table 9-23 shows the results of the 

multivariable regression analysis correlating the transverse load to the Ex(t/L)2

 and preload. 

From this regression analysis, the design equation for Peerless Super Block is shown in 

equation 9.24. 

Modulus (E) = 5.5098 x Half-wall height1.7793 (9.23)

Table 9-23. Multivariable regression analysis for determining transverse load from 

modulus and wall geometric parameters. 

Regression Statistics

Multiple R 0.6405

R Square 0.4102

Adjusted R Square 0.3665

Standard Error 26.2746

Observations 30

ANOVA

df SS MS F Significance F

Regression 2 12965 6482 9.3898 0.0008

Residual 27 18640 690

Total 29 31604

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept -142.1965 46.0870 -3.0854 0.0047 -236.7591 -47.6340 -236.7591 -47.6340

E x (t/L)2 8.3052 2.1515 3.8602 0.0006 3.8907 12.7198 3.8907 12.7198

Preload 0.6435 0.2355 2.7320 0.0110 0.1602 1.1268 0.1602 1.1268
265

Transverse Load = 8.3052 x E x (t/L)2

 + .6435 x Preload – 142.1965 (9.24)

Where E = material modulus = 3,000 to 10,000 psi for Peerless Super Block, 

 t = wall thickness, in, 

 L = full wall height, in, and 

 Preload = ground pressure preload, psi. 

 Figure 9-58 compares the predicted transverse load capacities from the empirical 

model with the measured laboratory results for the half wall heights with varying preloads. 

As seen in the figure, the model predictions are reasonably accurate only for the 48-in halfwall height. The transverse load is considerably over predicted for the 64-in half-wall height 

and under predicted for the 32-in half-wall height. This discrepancy is a tradeoff in the 

modulus adjustment values, which were adjusted to give the best-fit overall for all the 

models. Figure 9-59 shows transverse load predictions using this empirical design model for 

walls constructed from Peerless Super Block ranging in height from 5 to 10 feet in one foot 

increments with preloads ranging from 0 to 100 psi. 

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60 70 80 90 100

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Empirical Model -- Half-wall height 32 inches Measured Transverse Load -- Half-wall Height 32 inches

Empirical Model -- Half-wall height 48 inches Measured Transverse Load -- Half-wall Height 48 inches

Empirical Model -- Half-wall height 64 inches Measured Transverse Load -- Half-wall Height 64 inches

Figure 9-58. Comparison of design equation predictions with measured transverse 

load from laboratory testing (Full Empirical Model – Peerless Super Block).
266

9.1.7.2 Hybrid Theoretical Models 

 Transverse load capacity forecasts will be made using the three hybrid theoretical 

models: (1) Hybrid Thrust Model, (2) Hybrid Lateral Displacement Model, and (3) Hybrid 

Combination Thrust and Lateral Displacement Model. 

9.1.7.2.1 Hybrid Thrust Model

As seen in the flowchart in figure 9-2, the Hybrid Thrust Model determines the 

normalized thrust force from a multivariable relationship between the thrust force and the 

Ex(t/L)2

 term and preload, both of which are considered to be known parameters. The 

multivariable linear regression analysis based on 30 laboratory tests of various wall 

constructions is summarized in table 9-25. Equation 9.26 is used to compute the normalized 

thrust force per unit width of wall. Table 9-26 documents the multivariable regression 

analysis results used to determine the resultant thrust position factor (d). 

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70 80 90 100

PRELOAD, psi

TRANSVERSE PRESSURE, psf ..

Peerless Super Block -- 5 ft wall height Peerless Super Block -- 6 ft wall height

Peerless Super Block -- 7 ft wall height Peerless Super Block -- 8 ft wall height

Peerless Super Block -- 9 ft wall height Peerless Super Block -- 10 ft wall height

Figure 9-59. Transverse load capacity predictions for 6-in-thick walls constructed 

from Peerless Super Block for walls heights ranging from 5 to 10 ft (Full Empirical 

Model).
267

Table 9-25. Multivariable regression analysis for determining arching thrust. 

P/BL = - 0.0012 x Ex(t/L)2 + .0033 x Preload + .0603 (9.26)

Where P/BL = Normalized thrust per unit width of block, kips/in, 

 E = Elastic modulus = 3,000 to 10,000 psi for Peerless Super Block, 

 t = wall thickness, in, 

 L = height of wall, in, and 

 Preload = preload pressure, psi. 

Table 9-26. Multivariable regression analysis for determining resultant thrust position factor. 

d = -0.0034 x Half-wall Height - 0.0188 x Thrust + 0.7892 (9.27)

 Figure 9-60 compares the results of the predicted transverse load capacities from the 

hybrid theoretical thrust model with the measured laboratory test results for half-wall heights 

Regression Statistics

Multiple R 0.8994

R Square 0.8089

Adjusted R Square 0.7948

Standard Error 0.0358

Observations 30

ANOVA

df SS MS F Significance F

Regression 2 0.1461 0.0731 57.1581 0.0000

Residual 27 0.0345 0.0013

Total 29 0.1807

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 0.0603 0.0627 0.9612 0.3450 -0.0684 0.1890 -0.0684 0.1890

E*(t/L)^2 -0.0012 0.0029 -0.4027 0.6903 -0.0072 0.0048 -0.0072 0.0048

Preload 0.0033 0.0003 10.3648 0.0000 0.0027 0.0040 0.0027 0.0040

Regression Statistics

Multiple R 0.6405

R Square 0.4102

Adjusted R Square 0.3665

Standard Error 13.1373

Observations 30

ANOVA

df SS MS F Significance F

Regression 2 3241.1529 1620.5764 9.3898 0.0008

Residual 27 4659.9095 172.5892

Total 29 7901.0624

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept -71.0983 23.0435 -3.0854 0.0047 -118.3796 -23.8170 -118.3796 -23.8170

E*(t/L)^2 4.1526 1.0758 3.8602 0.0006 1.9453 6.3599 1.9453 6.3599

Preload 0.3218 0.1178 2.7320 0.0110 0.0801 0.5634 0.0801 0.5634
268

of 32, 48, and 64 inches with varying preloads. As seen from the graph, the model over 

predicts the transverse load with the exception of the 32-in half-wall height at the lower 

preloads. This is caused primarily by discrepancies in the lateral displacement, which is 

theoretically determined from the thrust load. In several tests, the block would fail causing 

temporary transverse load shedding during the transverse load development. This would 

produce a large lateral displacement at times that would not be accurately predicted by the 

model. The thrust model is also hampered by inconsistent thrust development. At times, the 

thrust would decrease from the initial preload, instead of building thrust as the arching 

develops. This is due to weak material and inconsistent presence of the foam pellets in the 

hinge area. Figure 9-61 shows transverse load predictions using this empirical design model 

for 6-in-thick walls constructed from Peerless Super Block ranging in height from 5 to 10 

feet in one foot increments with preloads ranging from 0 to 100 psi. 

0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90 100

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Hybrid Thrust Model -- Half-wall height 32 inches Measured Transverse Load -- Half-wall Height 32 inches

Hybrid Thrust Model -- Half-wall height 48 inches Measured Transverse Load -- Half-wall Height 48 inches

Hybrid Thurst Model -- Half-wall height 64 inches Measured Transverse Load -- Half-wall Height 64 inches

Figure 9-60. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Thrust Model).
269

9.1.7.2.2 Hybrid Lateral Displacement Model

 As seen in the flowchart in figure 9-3, the Hybrid Lateral Displacement Model 

determines the lateral displacement force from a multivariable relationship from the Ex(t/L)2 

term and preload, both of which are considered to be known parameters. The multivariable 

linear regression analysis based on 30 laboratory tests of various wall constructions is 

summarized in table 9-27. Equation 9.28 is used to compute the lateral wall displacement. 

Table 9-26 documented the multivariable regression analysis results used to determine the 

resultant thrust position factor (d) for the Hybrid Thrust Model. This equation is also used 

for computing the resultant thrust adjustment factor for this model, except the calculated 

thrust forces are used instead of the measured thrust forces. 

Lateral Displacement = 0.0038 x Ex(t/L)2 - 0.0177 x Preload + 1.5636 (9.28)

0

20

40

60

80

100

120

140

160

180

200

0 10 20 30 40 50 60 70 80 90 100

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Peerless Super Block -- 5 ft wall height Peerless Super Block -- 6 ft wall height

Peerless Super Block -- 7 ft wall height Peerless Super Block -- 8 ft wall height

Peerless Super Block -- 9 ft wall height Peerless Super Block -- 10 ft wall height

Figure 9-61. Transverse load capacity predictions for 6-in-thick walls constructed from 

Peerless Super Block for walls heights ranging from 5 to 10 ft (Hybrid Theoretical 

Thrust Model).
270

 Figure 9-62 compares the results of the predicted transverse load capacities from the 

hybrid theoretical lateral displacement model with the measured laboratory test results for 

half-wall heights of 32, 48, and 64 inches with varying preloads. As seen from the graph, the 

predictions overall are similar to the hybrid theoretical thrust model presented in figure 9-60. 

Figure 9-63 shows transverse load predictions using the hybrid theoretical lateral 

displacement for walls constructed from Peerless Super Block ranging in height from 5 to 10 

feet in one foot increments with preloads ranging from 0 to 100 psi. 

Regression Statistics

Multiple R 0.6082

R Square 0.3699

Adjusted R Square 0.3233

Standard Error 0.5098

Observations 30

ANOVA

df SS MS F Significance F

Regression 2 4.1200 2.0600 7.9263 0.0020

Residual 27 7.0170 0.2599

Total 29 11.1370

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 1.5636 0.8942 1.7485 0.0917 -0.2712 3.3983 -0.2712 3.3983

E*(t/L)^2 0.0038 0.0417 0.0918 0.9276 -0.0818 0.0895 -0.0818 0.0895

Preload -0.0177 0.0046 -3.8736 0.0006 -0.0271 -0.0083 -0.0271 -0.0083

0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90 100

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Hybrid Lateral Displacement Model -- Half-wall height 32 inches Measured Transverse Load -- Half-wall Height 32 inches

Hybrid Lateral Displacement Model -- Half-wall height 48 inches Measured Transverse Load -- Half-wall Height 48 inches

Hybrid Lateral Displacement Model -- Half-wall height 64 inches Measured Transverse Load -- Half-wall Height 64 inches

Figure 9-62. Comparison of transverse load capacities from design equations to 

the measured transverse load from laboratory tests (Hybrid Theoretical Lateral 

Displacement Model).

Table 9-27. Multivariable regression analysis for determining 

lateral displacement. 
271

9.1.7.2.3 Hybrid Combination Model

 The Hybrid Combination Model combines the previous two models by empirically 

determining both the thrust and lateral displacement. Figure 9-64 compares this model’s 

predictions of transverse load capacity to the measured transverse load capacities from the 

laboratory testing. The results are much improved over the other two models, especially for 

32 and 48-in half-wall heights. This improved prediction capability is due to use of empirical 

data for both the thrust and lateral displacement parameters. For completeness, figure 9-65 is 

included which displays the transverse load predictions using the hybrid theoretical 

combination model for 6-in-thick walls constructed from Peerless Super Block ranging in 

height from 5 to 10 feet in one foot increments with preloads ranging from 0 to 100 psi. 

Figure 9-63. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Lateral 

Displacement Model).

0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90 100

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Peerless Super Block -- 5 ft wall height Peerless Super Block -- 6 ft wall height

Peerless Super Block -- 7 ft wall height Peerless Super Block -- 8 ft wall height

Peerless Super Block -- 9 ft wall height Peerless Super Block -- 10 ft wall height
272

Figure 9-65. Transverse load capacity predictions for 6-in-thick walls constructed 

from Peerless Super Block for walls heights ranging from 5 to 10 ft (Hybrid 

Theoretical Combination Model).

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90 100

PRELOAD, psi

TRANSVERSE PRESSURE, psf ..

Peerless Super Block -- 5 ft wall height Peerless Super Block -- 6 ft wall height

Peerless Super Block -- 7 ft wall height Peerless Super Block -- 8 ft wall height

Peerless Super Block -- 9 ft wall height Peerless Super Block -- 10 ft wall height

Figure 9-64. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Combination Model).

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60 70 80 90 100

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Hybrid Combination Model -- Half-wall height 32 inches Measured Transverse Load -- Half-wall Height 32 inches

Hybrid Combination Model -- Half-wall height 48 inches Measured Transverse Load -- Half-wall Height 48 inches

Hybrid Combination Model -- Half-wall height 64 inches Measured Transverse Load -- Half-wall Height 64 inches
273

9.1.7.3 Summary of Design Equations for Peerless Super Block

 In summary, a full empirical design model and three hybrid theoretical design models 

were developed for the Peerless Super Block stopping constructions. Figure 9-66 displays 

the calculated transverse load capacities from full empirical model compared to the measured 

capacities from the MRS tests. The dashed line represents a perfect correlation between the 

calculated and measured capacities. The red trend line represents the linear regression 

between the measured and calculated capacities. The regression line shows that on average 

the model under predicts the transverse load, although this is largely due to the poor 

prediction of the shortest wall height. The regression trend line shows a 20 pct difference 

between the measured and calculated transverse load. The shaded blue area is a +/- 20 psf 

variation from the perfect correlation. Examining the chart, it is seen that 73% of the data 

falls within this variation. Figure 9-67 displays this same information for the three hybrid 

theoretical design models. Based on the regression trend line correlating the calculated 

transverse loads to the measured transverse loads, the combination model, which computes 

both the thrust and lateral displacement from laboratory test data, is clearly the most accurate 

of the three, with a 3 pct difference in calculated and measured loads. The thrust and lateral 

displacement model produce similar results with an error of 39 pct. Examining the +/-20 psf 

variation (blue shading), the hybrid combination model has 73 pct of the data within this 

variation, while the thrust model and the lateral displacement models only 27 and 43 pct 

respectively of their data within this variation. 
274

Figure 9-67. Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Hybrid Theoretical Models).

y = 0.61x

R2

 = 0.53

y = 0.61x

R2

 = 0.73

y = 1.05x

R2

 = 0.57

0

20

40

60

80

100

120

140

160

180

200

0 20 40 60 80 100 120 140 160 180 200

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf ... .

Hybrid Theoretical Thrust Model

Hybrid Theoretical Lateral Displacement Model

Hybrid Theoretical Combination Model

Figure 9-66. Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Full Empirical Model).

y = 1.2x

R2 = 0.44

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf ...
275

9.1.8 Klondike Hollow Core Block 

 Klondike Hollow Core Block is a standard Portland cement block with three hollow 

core areas to reduce the material volume and weight of the block. This block measures 

nominally 6x8x16 inches, but weighs only 32 lbs compared to the 47 lbs weight of the 

standard solid block. Its compressive strength is 907 psi compared to 1,330 psi for the solid 

block. A total of 23 tests were conducted with the Klondike Hollow Core Block, sufficient to 

produce good block models for transverse load prediction. 

9.1.8.1 Full Empirical Model 

 In order to improve the accuracy of the model predictions, the modulus was varied as a 

function of half-wall height according to equation 9.29. In reality, the modulus is not 

changing, but the deformation zone associated with the wall rotation produces a differing 

behavior. Changing the modulus is one way to adjust for this issue and incorporate the 

response into the existing prediction models. Table 9-28 shows the results of the 

multivariable regression analysis correlating the transverse load to the Ex(t/L)2

 and preload. 

From this regression analysis, the design equation for Klondike Hollow Core Block is shown 

in equation 9.30. 

Modulus (E) = 1491.2 x Half-wall height - 5263.2 (9.29)

Table 9-28. Multivariable regression analysis for determining transverse load from 

modulus and wall geometric parameters. 

Regression Statistics

Multiple R 0.7523

R Square 0.5660

Adjusted R Square 0.5226

Standard Error 342.4931

Observations 23

ANOVA

df SS MS F Significance F

Regression 2 3059879 1529939 13.0428 0.0002

Residual 20 2346031 117302

Total 22 5405910

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept -1186.8305 409.3905 -2.8990 0.0089 -2040.8038 -332.8572 -2040.8038 -332.8572

E x (t/L)2 7.3129 1.4371 5.0888 0.0001 4.3152 10.3106 4.3152 10.3106

Preload 1.2685 1.3743 0.9231 0.3670 -1.5982 4.1352 -1.5982 4.1352
276

Transverse Load = 7.3129 x Ex(t/L)2

 + 1.2685 x Preload – 1187 (9.30)

Where E = material modulus = 32,500 to 85,000 psi for Klondike Hollow Core Block, 

 t = wall thickness, in, 

 L = full wall height, in, and 

 Preload = ground pressure preload, psi. 

 Figure 9-68 compares the predicted transverse load capacities from the empirical 

model with the measured laboratory results for the half wall heights with varying preloads. 

As seen in the figure, the transverse load predictions do not change much with preload, 

which is uncharacteristic of most other block materials. The empirical predictions of 

transverse pressure are reasonably accurate for the 60-in half-wall height and the 48-in halfwall height at higher preloads, but the transverse pressure prediction for the 30-in half-wall 

height is considerably lower than the measured results. Figure 9-69 shows transverse load 

predictions using this empirical design model for walls constructed from Klondike Hollow 

Core Block ranging in height from 5 to 10 feet in one foot increments with preloads ranging 

from 0 to 300 psi. 

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0 50 100 150 200 250

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Empirical Model -- Half-wall Height 30 inches Measured Transverse Load -- Half-wall Height 30 inches

Empirical Model -- Half-wall Height 45 inches Measured Transverse Load -- Half-wall Height 45 inches

Empirical Model -- Half-wall Height 60 inches Measured Transverse Load -- Half-wall Height 60 inches

Figure 9-68. Comparison of design equation predictions with measured transverse 

load from laboratory testing (Full Empirical Model – Klondike Hollow Core Block).
277

9.1.8.2 Hybrid Theoretical Models 

 Transverse load capacity forecasts will be made using the three hybrid theoretical 

models: (1) Hybrid Thrust Model, (2) Hybrid Lateral Displacement Model, and (3) Hybrid 

Combination Thrust and Lateral Displacement Model. 

9.1.8.2.1 Hybrid Thrust Model

As seen in the flowchart in figure 9-2, the Hybrid Thrust Model determines the 

normalized thrust force from a multivariable relationship between the thrust force and the 

Ex(t/L)2

 term and preload, both of which are considered to be known parameters. The 

multivariable linear regression analysis based on 23 laboratory tests of various wall 

constructions is summarized in table 9-29. Equation 9.31 is used to compute the normalized 

thrust force per unit width of wall. Table 9-30 documents the multivariable regression 

analysis results used to determine the resultant thrust position factor (d). 

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0 50 100 150 200 250 300

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Klondike Hollow Block -- 5 ft wall height Klondike Hollow Block -- 6 ft wall height

Klondike Hollow Block -- 7 ft wall height Klondike Hollow Block -- 8 ft wall height

Klondike Hollow Block -- 9 ft wall height Klondike Hollow Block -- 10 ft wall height

Figure 9-69. Transverse load capacity predictions for 6-in-thick walls constructed from 

Klondike Hollow Core Block for walls heights ranging from 5 to 10 ft (Full Empirical 

Model).
278

Table 9-29. Multivariable regression analysis for determining arching thrust. 

P/BL = 0.0015 x Ex(t/L)2 + 0.0028 x Preload + 0.2936 (9.31)

Where P/BL = Normalized thrust per unit width of block, kips/in, 

 E = Elastic modulus = 32,500 to 85,000 psi for Klondike Hollow Core Block, 

 t = wall thickness, in, 

 L = height of wall, in, and 

 Preload = preload pressure, psi. 

Table 9-30. Multivariable regression analysis for determining resultant thrust position factor. 

d factor = -0.0013 x Half-wall Height - 0.0033 x Thrust + 1.0272 (9.32)

 Figure 9-70 compares the results of the predicted transverse load capacities from the 

hybrid theoretical thrust model with the measured laboratory test results for half-wall heights 

Regression Statistics

Multiple R 0.4695

R Square 0.2204

Adjusted R Square 0.1425

Standard Error 0.3223

Observations 23

ANOVA

df SS MS F Significance F

Regression 2 0.5875 0.2937 2.8278 0.0829

Residual 20 2.0775 0.1039

Total 22 2.6650

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 0.2936 0.3853 0.7622 0.4548 -0.5100 1.0973 -0.5100 1.0973

E*(t/L)^ 2 0.0015 0.0014 1.1424 0.2668 -0.0013 0.0044 -0.0013 0.0044

Preload 0.0028 0.0013 2.1860 0.0409 0.0001 0.0055 0.0001 0.0055

Regression Statistics

Multiple R 0.4086

R Square 0.1670

Adjusted R Square 0.0837

Standard Error 0.0511

Observations 23

ANOVA

df SS MS F Significance F

Regression 2.0000 0.0105 0.0052 2.0044 0.1609

Residual 20.0000 0.0522 0.0026

Total 22.0000 0.0627

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 1.0272 0.0557 18.4469 0.0000 0.9110 1.1433 0.9110 1.1433

Half-wall Height -0.0013 0.0010 -1.3059 0.2064 -0.0034 0.0008 -0.0034 0.0008

Thrust -0.0033 0.0020 -1.6450 0.1156 -0.0076 0.0009 -0.0076 0.0009
279

of 30, 45, and 60 inches with varying preloads. As seen from the graph, the predictions for 

the 30-in half-wall height are improved over that of the empirical model. Conversely, the 60-

in half-wall height predictions are less accurate for this model. Figure 9-71 shows transverse 

pressure predictions using this empirical design model for 6-in-thick walls constructed from 

Klondike Hollow Core Block ranging in height from 5 to 10 feet in one foot increments with 

preloads ranging from 0 to 300 psi. 

Figure 9-70. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Thrust Model).

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0 50 100 150 200 250

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Hybrid Thrust Model -- Half-wall Height 30 inches Measured Transverse Load -- Half-wall Height 30 inches

Hybrid Thrust Model -- Half-wall Height 45 inches Measured Transverse Load -- Half-wall Height 45 inches

Hybrid Thust Model -- Half-wall Height 60 inches Measured Transverse Load -- Half-wall Height 60 inches
280

9.1.8.2.2 Hybrid Lateral Displacement Model

As seen in the flowchart in figure 9-3, the Hybrid Lateral Displacement Model determines 

the lateral displacement force from a multivariable relationship from the Ex(t/L)2 term and 

preload, both of which are considered to be known parameters. The multivariable linear 

regression analysis based on 23 laboratory tests of various wall constructions is summarized 

in table 9-31. Equation 9.33 is used to compute the lateral displacement. Table 9-32 

documented the multivariable regression analysis results used to determine the resultant 

thrust position factor (d) for the Hybrid Thrust Model. This equation is also used for 

computing the resultant thrust adjustment factor for this model, except the calculated thrust 

forces are used instead of the measured thrust forces. 

Lateral Displacement = -0.0095 x Ex(t/L)2 - 0.0085 x Preload + 4.9588 (9.33)

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0 50 100 150 200 250 300

PRELOAD, psi

TRANSVERSE PRESSURE, psf .....

Klondike Hollow Block -- 5 ft wall height Klondike Hollow Block -- 6 ft wall height

Klondike Hollow Block -- 7 ft wall height Klondike Hollow Block -- 8 ft wall height

Klondike Hollow Block -- 9 ft wall height Klondike Hollow Block -- 10 ft wall height

Figure 9-70. Transverse load capacity predictions for 6-in-thick walls constructed 

from Klondike Hollow Core Block for walls heights ranging from 5 to 10 ft (Hybrid 

Theoretical Thrust Model).
281

 Figure 9-72 compares the results of the predicted transverse load capacities from the 

hybrid theoretical lateral displacement model with the measured laboratory test results for 

half-wall heights of 30, 45, and 60 inches. As seen from the graph, the predictions less 

accurate than those determined from the hybrid theoretical thrust model presented in figure 

9-70. Figure 9-73 shows transverse load predictions using the hybrid theoretical lateral 

displacement for walls constructed from Klondike Hollow Core Block ranging in height from 

5 to 10 feet in one foot increments with preloads ranging from 0 to 300 psi. 

Figure 9-72. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Lateral 

Displacement Model).

Regression Statistics

Multiple R 0.8575

R Square 0.7353

Adjusted R Square 0.7089

Standard Error 0.3966

Observations 23

ANOVA

df SS MS F Significance F

Regression 2 8.7406 4.3703 27.7826 0.0000

Residual 20 3.1461 0.1573

Total 22 11.8867

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 4.9588 0.4741 10.4597 0.0000 3.9699 5.9477 3.9699 5.9477

E*(t/L)^ 2 -0.0095 0.0017 -5.7071 0.0000 -0.0130 -0.0060 -0.0130 -0.0060

Preload -0.0085 0.0016 -5.3216 0.0000 -0.0118 -0.0051 -0.0118 -0.0051

0

500

1,000

1,500

2,000

2,500

0 50 100 150 200 250

PRELOAD, psi

TRANSVERSE PRESSURE, psf . Hybrid Lateral Displacement Model -- Half-wall Height 30 inches Measured Transverse Load -- Half-wall Height 30 inches

Hybrid Lateral Displacement Model -- Half-wall Height 45 inches Measured Transverse Load -- Half-wall Height 45 inches

Hybrid Lateral Displacement Model -- Half-wall Height 60 inches Measured Transverse Load -- Half-wall Height 60 inches

Table 9-31. Multivariable regression analysis for 

determining lateral displacement.
282

9.1.8.2.3 Hybrid Combination Model

 The Hybrid Combination Model combines the previous two models by empirically 

determining both the thrust and lateral displacement. Figure 9-74 compares this model’s 

predictions of transverse load capacity to the measured transverse load capacities from the 

laboratory testing. The results are considerably more accurate, especially for the short and 

high walls, than those of the thrust or lateral displacement models. Figure 9-75 is included 

which displays the transverse load predictions using the hybrid theoretical combination 

model for 6-in thick walls constructed from Klondike Hollow Core Block ranging in height 

from 5 to 10 feet in one foot increments with preloads ranging from 0 to 300 psi. 

0

200

400

600

800

1,000

1,200

1,400

1,600

0 50 100 150 200 250 300

PRELOAD, psi

TRANSVERSE PRESSURE, psf ...

Klondike Hollow Block -- 5 ft wall height Klondike Hollow Block -- 6 ft wall height

Klondike Hollow Block -- 7 ft wall height Klondike Hollow Block -- 8 ft wall height

Klondike Hollow Block -- 9 ft wall height Klondike Hollow Block -- 10 ft wall height

Figure 9-73. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Lateral 

Displacement Model).
283

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0 50 100 150 200 250 300

PRELOAD, psi

TRANSVERSE PRESSURE, psf ....

Klondike Hollow Block -- 5 ft wall height Klondike Hollow Block -- 6 ft wall height

Klondike Hollow Block -- 7 ft wall height Klondike Hollow Block -- 8 ft wall height

Klondike Hollow Block -- 9 ft wall height Klondike Hollow Block -- 10 ft wall height

Figure 9-75. Transverse load capacity predictions for 6-in-thick walls constructed 

from Klondike Hollow Core Block for walls heights ranging from 5 to 10 ft (Hybrid 

Theoretical Combination Model).

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0 50 100 150 200 250

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Hybrid Combination Model -- Half-wall Height 30 inches Measured Transverse Load -- Half-wall Height 30 inches

Hybrid Combination Model -- Half-wall Height 45 inches Measured Transverse Load -- Half-wall Height 45 inches

Hybrid Combination Model -- Half-wall Height 60 inches Measured Transverse Load -- Half-wall Height 60 inches

Figure 9-74. Comparison of transverse load capacities from design equations to the 

measured transverse load from laboratory tests (Hybrid Theoretical Combination 

Model).
284

9.1.8.3 Summary of Design Equations for Klondike Hollow Core Block

 In summary, a full empirical design model and three hybrid theoretical design models 

were developed for the Klondike Hollow Core Block stopping constructions. Figure 9-76 

displays the calculated transverse load capacities from full empirical model compared to the 

measured capacities from the MRS tests. The dashed line represents a perfect correlation 

between the calculated and measured capacities. The red trend line represents the linear 

regression between the measured and calculated capacities. The regression lines shows that 

on average the model tends to under predict the transverse load. The regression trend line 

shows a 4 pct difference between the measured and calculated transverse load. The shaded 

blue area is a +/- 200 psf variation from the perfect correlation. Examining the chart, it is 

seen that 52% of the data falls within this variation. Most of the poor predictions occur for 

the short wall configuration (30-in half-wall height) where the transverse load was 

inconsistent with premature localized failures occurring in block near the hinge point contact 

zones. Figure 9-77 displays this same information for the three hybrid theoretical design 

models. Based on the regression trend line correlating the calculated transverse loads to the 

measured transverse loads, the combination model, which computes both the thrust and 

lateral displacement from laboratory test data, is the most accurate of the three, with a 3 pct 

difference in calculated and measured loads. The least accurate is the lateral displacement 

model with 12 pct difference. Examining the +/-400 psf variation (blue shading), the thrust 

model and the combination model have 83% of the data within this variation, while the 

lateral displacement model has only 35 pct of the data within this variation. 
285

y = 0.58x

R2

 = 0.82

y = 0.80x

R2

 = 0.77

y = 0.98x

R2

 = 0.71

0

400

800

1,200

1,600

2,000

2,400

0 400 800 1,200 1,600 2,000 2,400

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf ..

Hybrid Theoretical Thurst Model

Hybrid Theoretical Lateral Displacement Model

Hybrid Theoretical Combination Model

Figure 9-77. Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Hybrid Theoretical Models).

y = 1.04x

R2

 = 0.59

0

200

400

600

800

1,000

1,200

1,400

1,600

0 200 400 600 800 1,000 1,200 1,400 1,600

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf ...

Figure 9-76. Comparison of predicted transverse load capacities compared to the 

measured capacities for the MRS laboratory tests (Full Empirical Model).
286

9.2 GENERIC BLOCK MODELS 

 The previous section developed models for a specific block. These models will 

provide the best design information if that particular block is being utilized. The goal of this 

section is to broaden the design formulations to permit design of stoppings constructed of a 

different block type. One approach would be to select a specific block model that most 

closely matches the physical characteristics of the block in question and use that model for 

design. Another approach is to generalize the specific block models into categories by 

grouping the performance parameters for similar style block materials. This is the approach 

that is described in this section. The categories selected for analysis are as follows: (1) 

standard CMU block with compressive strengths ranging from 1,000 to 2,000 psi, (2) cellular 

block materials with compressive strengths ranging from 250 to 750 psi, and (3) low strength 

block materials with compressive strengths less than 100 psi. The approach utilized in 

developing the specific block models whereby an empirical model and three hybrid 

theoretical models, is also pursued in the development of these generic models. 

9.2.1 Standard CMU Block 

Two block materials were evaluated that fit this category: (1) the Klondike block and 

(2) the Peerless Backsaver block. These blocks were similar in size and density, but the 

Peerless Backsaver block had a 60 pct higher compressive strength. Also included in this 

data set was a group of partially cured Peerless Backsaver block, which had a 50 pct 

reduction in compressive strength. In summary, the compressive strength of these blocks 

ranged from 1,070 to 2,160 psi. 

9.2.1.1 Generic Empirical Model 

The Generic Empirical Model is developed from a multivariable regression analysis 

of the data using the Ex(t/L)2

 term and the preload. Equation 9.34 documents the resulting 

design equation. 

Transverse pressure = 5.2021 x Ex(t/L)2 + 1.8325 x Preload – 962 (9.34)

Where E = material modulus, psi, 

 t = wall thickness, in, 

 L = full wall height, in, and 

 Preload = ground pressure preload, psi. 
287

 Figure 9-78 compares the measured transverse pressure from the Klondike block tests 

to the Generic Empirical Model. Based on the regression line comparing the measured and 

calculated transverse pressures, the Generic Empirical Model predicts the transverse pressure 

to within 4 pct error. The blue shaded area represents a +/- 400 psf variation. It is seen that 

77 pct of the data falls within this load variation. 

9.2.1.2 Generic Hybrid Theoretical Models 

 Transverse pressure capacity forecasts will be made using the three hybrid theoretical 

models developed from the full generic standard CMU data set: (1) Hybrid Thrust Model, (2) 

Hybrid Lateral Displacement Model, and (3) Hybrid Combination Thrust and Lateral 

Displacement Model. The design equations and graph showing a comparison of the 

predicted and measured transverse pressure are included in the next sections. 

y = 0.96x

R2

 = 0.83

0

400

800

1,200

1,600

2,000

2,400

2,800

3,200

3,600

0 400 800 1,200 1,600 2,000 2,400 2,800 3,200 3,600

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSSURE, psf ..

Figure 9-78. Comparison of predicted transverse pressure capacities compared to measured 

capacities for the MRS laboratory tests for the Klondike block (Generic Empirical Model). 
288

9.2.1.2.1 Generic Hybrid Thrust Model

 The Hybrid Thrust Model determines the normalized thrust force from a multivariable 

relationship between the thrust force and the Ex(t/L)2

 term and preload, both of which are 

considered to be known parameters. The multivariable linear regression analysis based on 

120 laboratory tests of various wall constructions consisting of Klondike and Peerless 

Backsaver block constructions. Equation 9.35 is used to compute the normalized thrust force 

per unit width of wall. This can be multiplied by the block length to determine the full thrust 

on a single column block wall or whatever is appropriate for the analysis being conducted. A 

multivariable regression analysis results used to determine the resultant thrust position factor 

(d), which can be computed using equation 9.36. These parameters can then be substituted 

into the equations shown if the flowchart in figure 9-2 to compute the transverse pressure for 

that particular stopping construction. 

P/BL = 0.0023 x Ex(t/L)2

 + 0.0033 x Preload + 0.6137 (9.35)

Where P/BL = Normalized thrust per unit width of block, kips/in, 

 E = Elastic modulus, psi, 

 t = wall thickness, in, 

 L = height of wall, in, and 

 Preload = preload pressure, psi. 

d = -0.0018 x Half-wall Height - 0.0031 x Thrust + 0.9301 (9.36)

 Figure 9-79 compares the predicted transverse pressure with the measured transverse 

pressure for the Klondike block as an example of the accuracy of the model. As seen from 

the regression trend line in the figure, the Generic Thrust Model predicts the transverse 

pressure to within a 9 pct error, however 87 pct of the data was within the +/- 400 psf 

variation compared to only 77 pct for the empirical model shown in figure 9-78. 
289

9.2.1.2.2 Generic Hybrid Lateral Displacement Model

 The Hybrid Lateral Displacement Model determines the lateral displacement from a 

multivariable relationship between the lateral displacement and the Ex(t/L)2 term and 

preload, both of which are considered to be known parameters. The multivariable linear 

regression analysis based on 120 laboratory tests of various wall constructions consisting of 

Klondike and Peerless Backsaver block constructions. Equation 9.37 is used to compute the 

lateral displacement of wall. The same multivariable regression analysis that was used in the 

thrust model is also used to determine the resultant thrust position factor (d), which can be 

computed using equation 9.36. These parameters can then be substituted into the equations 

shown if the flowchart in figure 9-3 to compute the transverse pressure for that particular 

stopping construction. 

Lateral Displacement = -0.0012 x Ex(t/L)2

 - 0.0024 x Preload + 2.0058 (9.37)

Figure 9-79. Comparison of predicted transverse pressure capacities compared to 

measured capacities for the MRS laboratory tests for the Klondike block (Generic 

Thrust Model).

y = 0.91x

R2

 = 0.87

0

400

800

1,200

1,600

2,000

2,400

2,800

3,200

3,600

4,000

4,400

0 400 800 1,200 1,600 2,000 2,400 2,800 3,200 3,600 4,000 4,400

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf ..

Hybrid Theoretical Thrust Model -- Standard Solid CMU
290

Figure 9-80 compares the predicted transverse pressure with the measured transverse 

pressure for the Klondike block as an example of the accuracy of the model. As seen from 

the regression trend line in the figure, the Generic Lateral Displacement Model predicts the 

transverse pressure to within a 10 pct error. In this example, 85 pct of the data was within 

the +/- 400 psf variation. 

9.2.1.2.3 Generic Hybrid Combination Thrust and Lateral Displacement Model

 The Hybrid Combination Model determines both the lateral displacement and the thrust 

from a multivariable relationship between these parameters and the Ex(t/L)2

 term and preload 

using the equations presented in the previous sections. The same multivariable regression 

analysis that was used in the thrust model is also used to determine the resultant thrust 

position factor (d), which can be computed using equation 9.36, is also used in this model. 

These parameters can then be substituted into the equations shown if the flowchart in figure 

9-4 to compute the transverse pressure for that particular stopping construction. Figure 9-81 

compares the predicted and measured transverse pressures using this model for the Klondike 

y = 0.90x

R2

 = 0.88

0

400

800

1,200

1,600

2,000

2,400

2,800

3,200

3,600

4,000

4,400

0 400 800 1,200 1,600 2,000 2,400 2,800 3,200 3,600 4,000 4,400

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf ...

Hybrid Theoretical Lateral Displacement Model -- Standard Solid CMU

Figure 9-80. Comparison of predicted transverse pressures capacities compared to 

measured capacities for the MRS laboratory tests for the Klondike block (Generic 

Lateral Displacement Model).
291

tests. The regression line indicates that the transverse pressure can be predicted to within an 

8 pct difference with this model. The chart also shows that 90 pct of the data falls within the 

+/- 400 psf variation as illustrated by the shaded blue area. 

9.2.2 Cellular Concrete Block Materials 

All of the lightweight block materials examined in this study utilized air-entrained 

concrete to provide a low density material that can effectively reduce the weight of the block 

per unit volume, or by taking advantage of the lower density material, allow larger blocks to 

be fabricated within an acceptable weight limit. Three blocks fit into this category: (1) 

Ytong, (2) ACCOA, and (3) Kingsway. The blocks vary in size and compressive strength, 

which ranges from 446 to 705 psi. 

9.2.2.1 Generic Empirical Model 

The Generic Empirical Model is developed from a multivariable regression analysis 

of the data using the Ex(t/L)2

 term and the preload from the Ytong, ACCOA, and Kingsway 

block performance data. Equation 9.38 documents the resulting design equation. 

Figure 9-81. Comparison of predicted transverse pressure capacities compared to 

measured capacities for the MRS laboratory tests for the Klondike block (Generic 

Combination Model).

y = 0.92x

R2

 = 0.84

0

400

800

1,200

1,600

2,000

2,400

2,800

3,200

3,600

4,000

4,400

0 400 800 1,200 1,600 2,000 2,400 2,800 3,200 3,600 4,000 4,400

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf ...

Hybrid Theoretical Combination Model -- Standard Solid CMU
292

Transverse pressure = 3.5096 x Ex(t/L)2

 + 1.0386 x Preload – 100.9456 (9.38)

Where E = material modulus, psi, 

 t = wall thickness, in, 

 L = full wall height, in, and 

 Preload = ground pressure preload, psi. 

Figure 9-82 compares the measured transverse pressure from the Ytong block tests to 

the Generic Empirical Model. Based on the regression line comparing the measured and 

calculated transverse pressures, the Generic Empirical Model predicts the transverse pressure 

to within 1 pct error. The blue shaded area represents a +/- 200 psf variation. It is seen that 

100 pct of the data falls within this load variation. 

9.2.2.2 Generic Hybrid Theoretical Models 

 Transverse pressure capacity forecasts will be made using the three hybrid theoretical 

models developed from the full generic Cellular Concrete data set: (1) Hybrid Thrust Model, 

Figure 9-82. Comparison of predicted transverse pressure capacities compared to 

measured capacities for the MRS laboratory tests for the Ytong block (Generic 

Empirical Model).

y = 0.99x

R2

 = 0.96

0

400

800

1,200

1,600

2,000

2,400

2,800

0 400 800 1,200 1,600 2,000 2,400 2,800

CALCULATED TRANSVERSE PRESSURE, psf 

MEASURED TRANSVERSE PRESSURE, psf ....

Empirical Model -- Ytong Block -- Cellular Concrete
293

(2) Hybrid Lateral Displacement Model, and (3) Hybrid Combination Thrust and Lateral 

Displacement Model. The design equations and graph showing a comparison of the 

predicted and measured transverse pressure are included in the next sections. 

9.2.2.2.1 Hybrid Thrust Model

 The Hybrid Thrust Model determines the normalized thrust force from a multivariable 

relationship between the thrust force and the Ex(t/L)2

 term and preload, both of which are 

considered to be known parameters. The multivariable linear regression analysis based on 43 

laboratory tests of various wall constructions consisting of Ytong, ACCOA, and Kingsway 

block constructions. Equation 9.39 is used to compute the normalized thrust force per unit 

width of wall. This can be multiplied by the block length to determine the full thrust on a 

single column block wall or whatever is appropriate for the analysis being conducted. A 

multivariable regression analysis results used to determine the resultant thrust position factor 

(d), which can be computed using equation 9.40. These parameters can then be substituted 

into the equations shown if the flowchart in figure 9-2 to compute the transverse pressure for 

that particular stopping construction. 

P/BL = 0.0019 x Ex(t/L)2 + 0.0044 x Preload + 0.3257 (9.39) 

Where P/BL = Normalized thrust per unit width of block, kips/in, 

 E = Elastic modulus, psi, 

 t = wall thickness, in, 

 L = height of wall, in, and 

 Preload = preload pressure, psi. 

d = -0.0028 x Half-wall Height - 0.0076 x Thrust + 1.0181 (9.40)

Figure 9-83 compares the predicted transverse pressure with the measured transverse 

pressure for the Ytong block as an example of the accuracy of the model. As seen from the 

regression trend line in the figure, the Generic Thrust Model predicts the transverse pressure 

to within a 1 pct error, however 100 pct of the data was within the +/- 400 psf variation 

compared to only 77 pct for the empirical model shown in figure 9-82. 
294

9.2.2.2.2 Generic Hybrid Lateral Displacement Model

 The Hybrid Lateral Displacement Model determines the lateral displacement from a 

multivariable relationship between the thrust force and the Ex(t/L)2 term and preload, both of 

which are considered to be known parameters. The multivariable linear regression analysis 

based on 43 laboratory tests of various wall constructions consisting of Ytong, ACCOA, and 

Kingsway. Equation 9.41 is used to compute the lateral displacement of wall. The same 

multivariable regression analysis that was used in the thrust model is also used to determine 

the resultant thrust position factor (d), which can be computed using equation 9.40. These 

parameters can then be substituted into the equations shown if the flowchart in figure 9-3 to 

compute the transverse pressure for that particular stopping construction. 

Lateral Displacement = -0.0004 x Ex(t/L)2 -0.0045 x Preload + 1.4303 (9.41)

Figure 9-84 compares the predicted transverse pressure with the measured transverse 

pressure for the Ytong block as an example of the accuracy of the model. As seen from the 

regression trend line in the figure, the Generic Lateral Displacement Model predicts the 

Figure 9-83. Comparison of predicted transverse pressure capacities compared to 

measured capacities for the MRS laboratory tests for the Ytong block (Generic Thrust 

Model).

y = 1.01x

R2

 = 0.97

0

400

800

1,200

1,600

2,000

2,400

2,800

0 400 800 1,200 1,600 2,000 2,400 2,800

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf ...

Hybrid Theoretical Thrust Model -- Cellular Concrete
295

transverse pressure to within a 6 pct error. In this example, 85 pct of the data was within the 

+/- 400 psf variation. 

9.2.2.2.3 Generic Hybrid Combination Thrust and Lateral Displacement Model

 The Hybrid Combination Model determines both the lateral displacement and the thrust 

from a multivariable relationship between these parameters and the Ex(t/L)2 term and preload 

using the equations presented in the previous sections. The same multivariable regression 

analysis that was used in the thrust model is also used to determine the resultant thrust 

position factor (d), which can be computed using equation 9.40, is also used in this model. 

These parameters can then be substituted into the equations shown if the flowchart in figure 

9-4 to compute the transverse pressure for that particular stopping construction. Figure 9-85 

compares the predicted and measured transverse pressures using this model for the Ytong 

tests. The regression line indicates that the transverse pressure can be predicted to within a 9 

pct difference with this model. The chart also shows that 90 pct of the data falls within the 

+/- 400 psf variation as illustrated by the shaded blue area. 

y = 1.06x

R2

 = 0.97

0

400

800

1,200

1,600

2,000

2,400

2,800

0 400 800 1,200 1,600 2,000 2,400 2,800

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf ..

Hybrid Theoretical Lateral Displacement Model -- Cellular Concrete

Figure 9-84. Comparison of predicted transverse pressure capacities compared to 

measured capacities for the MRS laboratory tests for the Ytong block (Generic Lateral 

Displacement Model).
296

9.2.3 Low Strength Block Materials 

A separate model is made for blocks with compressive strengths less than 100 psi. 

These relatively very weak materials behave differently than the other block materials 

examined in this study. Two blocks fell into this category: (1) Omega Block and (2) Peerless 

Super Block. Both of these are cellular type concrete materials, but they are much weaker 

than the cellular materials examined in the Cellular Concrete Models in the previous section. 

The Peerless Super Block incorporates small Styrofoam pellets into the mix to provide 

additional yield capabilities. As noted in the previous chapters, the performance of these two 

block materials was the least consistent of all materials examined. 

9.2.3.1 Generic Empirical Model 

The Generic Empirical Model is developed from a multivariable regression analysis 

of the data using the Ex(t/L)2

 term and the preload from the Omega and Super Block 

performance data. Equation 9.42 documents the resulting design equation. 

Transverse pressure = - 8.8762 x Ex(t/L)2 + 0. 2252 x Preload + 221 (9.42)

Figure 9-85. Comparison of predicted transverse pressure capacities compared to 

measured capacities for the MRS laboratory tests for the Ytong block (Generic 

Combination Model).

y = 1.09x

R2

 = 0.97

0

400

800

1,200

1,600

2,000

2,400

2,800

0 400 800 1,200 1,600 2,000 2,400 2,800

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf ...

Hybrid Theoretical Combination Model
297

Where E = material modulus, psi, 

 t = wall thickness, in, 

 L = full wall height, in, and 

 Preload = ground pressure preload, psi. 

Figure 9-86 compares the measured transverse pressure from the Omega block tests 

to the Generic Empirical Model. Based on the regression line comparing the measured and 

calculated transverse pressures, the Generic Empirical Model predicts the transverse pressure 

to within 11 pct error. However, it is seen that only 36 pct of the data falls within a +/- 40 psf 

variation as represented by the blue shaded area, indicating that in this particular case, the 

generic empirical model is not a well suited to this block. 

9.2.3.2 Generic Hybrid Theoretical Models 

 Transverse pressure capacity forecasts will be made using the three hybrid theoretical 

models developed from the full generic low strength block data set: (1) Hybrid Thrust Model, 

(2) Hybrid Lateral Displacement Model, and (3) Hybrid Combination Thrust and Lateral 

y = 1.11x

R2 = 0.45

0

40

80

120

160

200

240

280

320

0 40 80 120 160 200 240 280 320

CALCULATED TRANSVERSE PRESSURE, psf 

MEASURED TRANSVERSE PRESSURE, psf ...

Empirical Model -- Omega Block -- Low Strength Block

Figure 9-86. Comparison of predicted transverse pressure capacities compared to 

measured capacities for the MRS laboratory tests for the Omega block (Generic 

Empirical Model).
298

Displacement Model. The design equations and graph showing a comparison of the 

predicted and measured transverse pressure are included in the next sections. 

9.2.3.2.1 Hybrid Thrust Model

 The Hybrid Thrust Model determines the normalized thrust force from a multivariable 

relationship between the thrust force and the Ex(t/L)2

 term and preload, both of which are 

considered to be known parameters. The multivariable linear regression analysis based on 53 

laboratory tests of various wall constructions consisting of Omega and Peerless Super Block. 

Equation 9.43 is used to compute the normalized thrust force per unit width of wall. This can 

be multiplied by the block length to determine the full thrust on a single column block wall 

or whatever is appropriate for the analysis being conducted. A multivariable regression 

analysis results used to determine the resultant thrust position factor (d), which can be 

computed using equation 9.44. These parameters can then be substituted into the equations 

shown if the flowchart in figure 9-2 to compute the transverse pressure for that particular 

stopping construction. 

P/BL = -0.0046 x Ex(t/L)2 + 0.0033 x Preload + 0.1325 (9.43)

 

Where P/BL = Normalized thrust per unit width of block, kips/in, 

 E = Elastic modulus, psi, 

 t = wall thickness, in, 

 L = height of wall, in, and 

 Preload = preload pressure, psi. 

d = -0.0060 x Half-wall Height - 0.0361 x Thrust + 1.0924 (9.44)

 Figure 9-87 compares the predicted transverse pressure with the measured transverse 

pressure for the Omega block as an example of the accuracy of the model. As seen from the 

regression trend line in the figure, the Generic Thrust Model predicts the transverse pressure 

to within a 8 pct error, however 87 pct of the data was within the +/- 40 psf variation 

compared to only 36 pct for the empirical model shown in figure 9-86. 
299

9.2.3.2.2 Generic Hybrid Lateral Displacement Model

 The Hybrid Lateral Displacement Model determines the lateral displacement from a 

multivariable relationship between the thrust force and the Ex(t/L)2 term and preload, both of 

which are considered to be known parameters. The multivariable linear regression analysis 

based on 53 laboratory tests of various wall constructions consisting of Omega and Peerless 

Super Block. Equation 9.45 is used to compute the lateral displacement of wall. The same 

multivariable regression analysis that was used in the thrust model is also used to determine 

the resultant thrust position factor (d), which can be computed using equation 9.44. These 

parameters can then be substituted into the equations shown if the flowchart in figure 9-3 to 

compute the transverse pressure for that particular stopping construction. 

Lateral Displacement = -0.0114 x Ex(t/L)2

 -0.0204 x Preload + 2.0080 (9.45)

y = 1.02x

R2

 = 0.82

0

40

80

120

160

200

240

280

320

0 40 80 120 160 200 240 280 320

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf ...

Hybrid Theoretical Thrust Model -- Low Strength Block

Figure 9-87. Comparison of predicted transverse pressure capacities compared to 

measured capacities for the MRS laboratory tests for the Omega block (Generic Thrust 

Model).
300

 Figure 9-88 compares the predicted transverse pressure with the measured transverse 

pressure for the Omega block as an example of the accuracy of the model. As seen from the 

regression trend line in the figure, the Generic Lateral Displacement Model predicts the 

transverse pressure to within a 21 pct error. In this example, 68 pct of the data was within 

the +/- 40 psf variation. 

9.2.3.2.3 Generic Hybrid Combination Thrust and Lateral Displacement Model

 The Hybrid Combination Model determines both the lateral displacement and the thrust 

from a multivariable relationship between these parameters and the Ex(t/L)2 term and preload 

using the equations presented in the previous sections. The same multivariable regression 

analysis that was used in the thrust model is also used to determine the resultant thrust 

position factor (d), which can be computed using equation 9.44, is also used in this model. 

These parameters can then be substituted into the equations shown if the flowchart in figure 

9-4 to compute the transverse pressure for that particular stopping construction. Figure 9-89 

compares the predicted and measured transverse pressures using this model for the Omega 

Figure 9-88. Comparison of predicted transverse pressure capacities compared to 

measured capacities for the MRS laboratory tests for the Omega block (Generic 

Lateral Displacement Model).

y = 1.21x

R2

 = 0.84

0

40

80

120

160

200

240

280

320

0 40 80 120 160 200 240 280 320

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf ...

Hybrid Theoretical Lateral Displacement Model -- Low Strength Block
301

tests. The regression line indicates that the transverse pressure can be predicted to within a 

32 pct difference with this model. The chart also shows that 65 pct of the data falls within 

the +/- 40 psf variation as illustrated by the shaded blue area. 

y = 1.32x

R2

 = 0.93

0

40

80

120

160

200

240

280

320

0 40 80 120 160 200 240 280 320

CALCULATED TRANSVERSE PRESSURE, psf

MEASURED TRANSVERSE PRESSURE, psf ....

Hybrid Theoretical Combination Model -- Low Strength Block

Figure 9-89. Comparison of predicted transverse pressure capacities compared to 

measured capacities for the MRS laboratory tests for the Omega block (Generic 

Combination Model).
302

CHAPTER 10: RECOMMENDED DESIGN FORMULATIONS FOR STOPPING 

BLOCK WALLS 

 The previous chapter documented the development of several design models for 

evaluating the transverse pressure capacity of mine ventilation stoppings. The purpose of 

this chapter is to recommend one model that provides the best potential for accurately 

predicting the transverse pressure capacity of a particular stopping construction. This 

information can also be used to design a stopping using the appropriate block materials and 

construction geometry to meet specific design criteria for a particular application. Design 

formulations for each of the specific block materials evaluated in this study are presented. 

 In addition, models that are more generic are provided. These allow approximation 

of the transverse load capacity of any block construction to be determined, providing the 

material modulus is known. However, a word of caution about the modulus values. The 

effective modulus as used in this design formulation is based on testing of a column of block 

representing the half-wall height of the stopping wall. Furthermore, the wall is rotated by a 

few degrees to provide a one-inch offset between the top and bottom edge of the column 

prior to vertical load application. The modulus is then determined by the initial loaddeformation response. Values should be comparable to the block materials examined in this 

study. 

10.1 SPECIFIC BLOCK DESIGN FORMULATIONS 

Charts depicting the transverse pressure determinations at 1 foot height increments 

for the most common block thickness construction are presented in this section. The design 

formulation from which this chart was derived is also indicated. Four formulations were 

considered: (1) Full Empirical, (2) Hybrid Theoretical Thrust, (3) Hybrid Theoretical Lateral 

Displacement, (4) Hybrid Theoretical Combination Thrust and Lateral Displacement. 

Reference is made to chapter 9 if the user wants to examine the particular formulation in 

detail. The flowcharts presented in figures 9-2, 9-3, and 9-4 can be used to compute the 

transverse pressure directly using either the Hybrid Theoretical Thrust, Hybrid Theoretical 

Lateral Displacement, or Hybrid Theoretical Combination Thrust and Lateral Displacement 

respectively. 
303

10.1.1 Klondike Block Constructions 

Klondike is a conventional concrete block made from Portland cement with a 

moderate compressive strength ranging from 1,300 to 1,700 psi. The block measures 

nominally 5-5/8 x 7-1/2 x 16 inches. The best model for this block was the Hybrid 

Theoretical Combination Thrust and Lateral Displacement model. Figure 10-1 shows the 

transverse pressure estimates for 6-in-thick walls constructed at heights ranging from 5 to 10 

ft in one ft height increments with preload pressures ranging from 0 to 600 psi. These graphs 

can then be used to approximate the transverse pressure capacity for a particular set of 

conditions. For example, the transverse pressure capacity of a 6-ft-high wall with 200 psi of 

ground pressure would be approximately 1,600 psf. 

 The transverse pressure for any condition can also be calculated using the formulation 

documented in chapter 9 and outlined in the flowchart in figure 9-4. Using the previous 

example, the following calculations are made to determine the transverse pressure capacity of 

the stopping using the narrow block dimension to establish the wall thickness with a 6-ft 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0 100 200 300 400 500 600

PRELOAD, psi

CALCULATED TRANSVERSE PRESSURE, psf ......

Klondike solid block -- 5 ft wall height Klondike solid block -- 6 ft wall height

Klondike solid block -- 7 ft wall height Klondike solid block -- 8 ft wall height

Klondike solid block -- 9 ft wall height Klondike solid block -- 10 ft wall height

Figure 10-1. Design chart for Klondike solid block showing transverse load as a 

function of preload for wall heights ranging from 5-10 ft (Hybrid Combination Model). 
304

height and a preload of 200 psi. A parametric analysis can also be made and a regression line 

fitted to the resulting data to provide a chart similar to that shown in figure 10-1. 

Normalized thrust load (P/BL) = 0.0025 x Ex(t/L)2

 + 0.0034 x Preload + 0.6100 

P/BL = 0.0025 x 60,000 x (5.625/72)2 + 0.0034 x 200 + 0.6100 = 2.21 kips/in 

Thrust (Pm) = 2.21 x 16 = 35.38 kips 

Thrust resultant position factor (d) = -.0021 x Half-wall Height - .00361 x Thrust + 0.9547 

Thrust resultant position factor (d) = -.0021 x 36 - .00361 x 35.38 + 0.9547 = 0.75 

Lateral Displacement (δh) = -0.0009 x Ex(t/L)2

 - 0.0023 x Preload + 1.8776 

(δh) = -0.0009 x 60,000 x (5.625/72)2 - 0.0023 x 200 + 1.8776 = 1.10 in 

( ) ( ) 3,065 lbs

72 / 2

35.38 1000 0.75 5.625 1.10

L 2

P d t δ m h = × × × − = × × − Horizontal Force (HF) =

144 1,532psf 16 72/ 2

2 3,065

w L/2

2 HF

× = ×

× = ×

× Transverse Pressure =

10.1.2 Peerless Backsaver Block Constructions 

 Peerless Backsaver is also a conventional concrete block made from Portland cement. 

One set of blocks tested as part of this study were fully cured for over a year and had a high 

compressive strength of 2,169 psi. Partially cured blocks (two-week cure) were also tested, 

and these had a compressive strength of only 1,070 psi. The block measures nominally 5-7/8 

x 7-1/2 x 15-1/2 inches. The best model for this block was the Hybrid Theoretical Thrust 

model. Figure 10-2 shows the transverse pressure estimates for 6-in-thick walls constructed 

at heights ranging from 5 to 10 ft in one ft height increments with preload pressures ranging 

from 0 to 500 psi. These graphs can then be used to approximate the transverse pressure 

capacity for a particular set of conditions. For example, the transverse pressure capacity of 

an 8-ft-high wall with 200 psi of ground pressure would be approximately 800 psf. 
305

 The transverse pressure capacity for any condition can also be calculated using the 

formulation documented in chapter 9 and outlined in the flowchart in figure 9-2. Using the 

previous example, the following calculations are made to determine the transverse pressure 

capacity of the stopping using the narrow block dimension to establish the wall thickness 

with an 8-ft height and a preload of 200 psi. A parametric analysis can also be made and a 

regression line fitted to the resulting data to provide a chart similar to that shown in figure 

10-2. 

Normalized thrust load (P/BL) = 0.0041 x Ex(t/L)2

 + 0.0045 x Preload + 0.2142 

P/BL = 0.0041 x 45,000 x (5.875/96)2

 + 0.0045 x 200 + 0.2142 = 1.80 kips/in 

Thrust (Pm) = 1.80 x 15.5= 27.90 kips 

Preload (PL) = (200 x 15.5 x 5.875)/1000 = 18.21 

Arch Thrust (Parch) = 27.90 – 18.21 = 9.69 

0.0568 inches

2 15.5 5.875 45,000

9.69 1000 96/ 2

2 A E

Parch L 2 = × × ×

× × = × ×

× Hinge Point Deformation (y) =

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 50 100 150 200 250 300 350 400 450 500

PRELOAD, psi

TRANSVERSE PRESSURE, psf .....

Peerless Back Saver Block -- 5 ft wall height Peerless Back Saver Block -- 6 ft wall height

Peerless Back Saver Block -- 7 ft wall height Peerless Back Saver Block -- 8 ft wall height

Peerless Back Saver Block -- 9 ft wall height Peerless Back Saver Block -- 10 ft wall height

Figure 10-2. Design chart for Peerless Backsaver Block showing transverse load as a 

function of preload for wall heights ranging from 5-10 ft (Hybrid Thrust Model).
306

( )

2

2 t 4 t 4 2 l y 4 y 2 2 × − × − × × × − ×

Lateral Displacement (δh ) =

( ) 1.003 in

2

2 5.875 4 5.875 4 2 96 .0562 4 .0562 2 2

= × − × − × × × − ×Lateral Displacement (δh ) =

Thrust resultant position factor (d) = -.0017 x Half-wall Height - .0026 x Thrust + 0.9222 

Thrust resultant position factor (d) = -.0017 x 48 - .0026 x 27.90 + 0.9222 = 0.768 

( ) ( ) 2,040 lbs

96/ 2

27.90 1000 0.768 5.875 1.003

L 2

P d t δ m h = × × × − = × × − Horizontal Force (HF) =

144 790psf 15.5 96/ 2

2 2,040

w L/2

2 HF

× = ×

× = ×

× Transverse Pressure =

10.1.3 Klondike Hollow Core Block Constructions 

Klondike Hollow Core Block is the same material as the solid block except that three 

3.5 x 3.5-in hollow cores are created to reduce the material volume and cost of the block. 

Obviously, this also reduces the weight of the block since the overall size is the same as the 

solid block. Although the concrete mix is similar, the effective block strength is less because 

the webs are not as strong as the solid structure. The unit block compressive strength was 

measured at 907 psi. The best model for this block was the Hybrid Theoretical Combination 

Thrust and Lateral Displacement model. Figure 10-3 shows the transverse pressure estimates 

for 6-in-thick walls constructed at heights ranging from 5 to 10 ft in one ft height increments 

with preload pressures ranging from 0 to 300 psi. These graphs can then be used to 

approximate the transverse pressure capacity for a particular set of conditions. Using the 

same example as was used for the solid block construction, the transverse pressure capacity 

of a 6-ft-high wall with 200 psi of ground pressure would be approximately 1,110 psf. 
307

 The transverse pressure for any condition can also be calculated using the formulation 

documented in chapter 9 and outlined in the flowchart in figure 9-4. Using the previous 

example, the following calculations are made to determine the transverse pressure capacity of 

the stopping using the narrow block dimension to establish the wall thickness with a 6-ft 

height and a preload of 200 psi. A parametric analysis can also be made and regression line 

fitted to the resulting data to provide a chart similar to that shown in figure 10-3. Two 

additional factors need to be considered when analyzing the Klondike Hollow Core Block. 

First, the effective modulus was adjusted as a function of wall height. Second, the preload 

limit is set at 150 psi for this particular block. 

Effective Modulus (E) = 1,491 x Half-wall height – 5,263 = 1,491 x 36 - 5,263 = 48,420 psi 

Normalized thrust load (P/BL) = 0.0015 x Ex(t/L)2

 + 0.0028 x Preload + 0.2936 

P/BL – 0.0015 x 48,420 x (5.625/72)2

 + 0.0028 x 150 + 0.2936 = 1.16 kips/in 

Thrust (Pm) = 1.16 x 15.5 = 17.98 kips 

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0 50 100 150 200 250 300

PRELOAD, psi

TRANSVERSE PRESSURE, psf ....

Klondike Hollow Block -- 5 ft wall height Klondike Hollow Block -- 6 ft wall height

Klondike Hollow Block -- 7 ft wall height Klondike Hollow Block -- 8 ft wall height

Klondike Hollow Block -- 9 ft wall height Klondike Hollow Block -- 10 ft wall height

Figure 10-3. Design chart for Klondike Hollow Core block showing transverse load 

as a function of preload for wall heights ranging from 5-10 ft (Hybrid Combination 

Model).
308

Thrust resultant position factor (d) = -.0013 x Half-wall Height - .0033 x Thrust + 1.0272 

Thrust resultant position factor (d) = -.0013 x 36 - .0033 x 17.98 + 1.0272 = 0.921 

Lateral Displacement (δh) = -0.0095 x Ex(t/L)2

 + 0.0085 x Preload + 4.9588 

(δh) = -0.0095 x 48420 x (5.625/72)2

 - 0.0085 x 150 + 4.9588 = 0.88 in 

( ) ( ) 2,148 lbs

72/ 2

17.98 1000 0.921 5.625 0.88

L 2

P d t δ m h = × × × − = × × − Horizontal Force (HF) =

144 1,108psf 15.56 72/ 2

2 2,148

w L/2

2 HF

× = ×

× = ×

× Transverse Pressure =

10.1.4 ACCOA Block Constructions 

ACCOA Block is a cellular concrete block. The autoclaved aerated concrete is made 

from sand, flyash, and copper mine tailings as a source for the silica, which reacts with the 

aluminum to form a chemical reaction which creates millions of tiny air cells within the 

concrete matrix. The block has a compressive strength of 421 psi. The block measures 

nominally 6 x 12 x 24 inches. An 8-in-thick block is also manufactured. The best model for 

this block was the Hybrid Cellular Thrust Model, meaning that due to the limited test data, all 

cellular block materials were analyzed to produce a design model for this block. Figure 10-4 

shows the transverse pressure estimates for 6-in-thick walls constructed at heights ranging 

from 5 to 10 ft in one ft height increments with preload pressures ranging from 0 to 200 psi. 

These graphs can then be used to approximate the transverse pressure capacity for a 

particular set of conditions. For example, the transverse pressure capacity of a 6-ft-high wall 

with 100 psi of ground pressure would be approximately 800 psf. 
309

 The transverse pressure for any condition can also be calculated using the formulation 

documented in chapter 9 and outlined in section 9.2.3.2.1 and the flowchart in figure 9-2. 

Using the previous example, the following calculations are made to determine the transverse 

pressure capacity of the stopping using the narrow block dimension to establish the wall 

thickness with a 6-ft height and a preload of 100 psi. A parametric analysis can also be made 

and a regression line fitted to the resulting data to provide a chart similar to that shown in 

figure 10-4. 

Normalized thrust load (P/BL) = 0.0019 x Ex(t/L)2

 + 0.0044 x Preload + 0.3257 

P/BL = 0.0019 x 20,000 x (6/72)2

 + 0.0044 x 100 + 0.3257 = 1.03 kips/in 

Thrust (Pm) = 1.03 x 24 = 24.72 kips 

Preload (PL) = (100 x 24 x 6)/1000 = 14.40 kips 

Arch Thrust (Parch) = 24.72 – 14.40 = 10.32 kips 

0

200

400

600

800

1,000

1,200

1,400

1,600

0 20 40 60 80 100 120 140 160 180 200

PRELOAD, psi

TRANSVERSE PRESSURE, psf ...

Aerated Concrete Corp Block -- 5 ft wall height Aerated Concrete Corp Block -- 6 ft wall height

Aerated Concrete Corp Block -- 7 ft wall height Aerated Concrete Corp Block -- 8 ft wall height

Aerated Concrete Corp Block -- 9 ft wall height Aerated Concrete Corp Block -- 10 ft wall height

Figure 10-4. Design chart for ACCOA block showing transverse load as a function of 

preload for wall heights ranging from 5-10 ft (Hybrid Thrust Model).
310

0.065 inches

2 24 6 20,000

10.32 1000 72/ 2

2 A E

Parch L 2 = × × ×

× × = × ×

×

Hinge Point Deformation (y) =

( )

2

2 t 4 t 4 2 L y 4 y 2 2 × − × − × × × − ×

Lateral Displacement (δh ) =

( ) 0.837 inches

2

2 6 4 6 4 2 72 .065 4 .065 2 2

= × − × − × × × − ×Lateral Displacement (δh ) =

Thrust resultant position factor (d) = -.0028 x Half-wall Height - .0076 x Thrust + 1.0181 

Thrust resultant position factor (d) = -.0028 x 36 - .0076 x 24.72 + 1.0181 = 0.729 

( ) ( ) 2,429 lbs

72/ 2

24.72 1000 0.729 6 0.837

L 2

P d t δ m h = × × × − = × × − Horizontal Force (HF) =

144 810psf 24 72/ 2

2 2,429

w L/2

2 HF

× = ×

× = ×

× Transverse Pressure =

10.1.5 Ytong Block Constructions 

Ytong is another cellular concrete block, similar to the ACCOA block. The Ytong 

block has a compressive strength of 705 psi. The block measures nominally 8 x 8 x 24 

inches. The best model for this block was the Hybrid Theoretical Combination Thrust and 

Lateral Displacement model. Figure 10-5 shows the transverse pressure estimates for 8-inthick walls constructed at heights ranging from 5 to 10 ft in one ft height increments with 

preload pressures ranging from 0 to 200 psi. These graphs can then be used to approximate 

the transverse pressure capacity for a particular set of conditions. For example, the 

transverse pressure capacity of an 8-ft-high wall with 80 psi of ground pressure would be 

approximately 800 psf. 
311

 The transverse load for any condition can also be calculated using the formulation 

documented in chapter 9 and outlined in the flowchart in figure 9-4. Using the previous 

example, the following calculations are made to determine the transverse load capacity of the 

stopping which the narrow block dimension to establish the wall thickness with an 8-ft height 

and a preload of 80 psi. A parametric analysis can also be made and regression line fitted to 

the resulting data to provide a chart similar to that shown in figure 10-5. 

Normalized thrust load (P/BL) = 0.0012 x Ex(t/L)2

 + 0.0061 x Preload + 0.5809 

P/BL = 0.0012 x 40,000 x (7.875/96)2

 + 0.0061 x 80 + 0.5809 = 1.39 kips/in 

Thrust (Pm) = 1.39 x 24 = 33.36 kips 

Thrust resultant position factor (d) = -.0011 x Half-wall Height - .0080 x Thrust + 1.0308 

Thrust resultant position factor (d) = -.0011 x 48 - .0080 x 33.36 + 1.0308 = 0.711 

Lateral Displacement (δh) = -0.00075 x Ex(t/L)2

 - 0.0037 x Preload + 1.5578 

(δh) = -0.00075 x 40,000 x (7.875/96)2

 - 0.0037 x 80 + 1.5578 = 1.06 in 

0

500

1,000

1,500

2,000

2,500

3,000

0 20 40 60 80 100 120 140 160 180 200

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Ytong Block -- 5 ft wall height Ytong Block -- 6 ft wall height Ytong Block -- 7 ft wall height

Ytong Block -- 8 ft wall height Ytong Block -- 9 ft wall height Ytong Block -- 10 ft wall height

Figure 10-5. Design chart for Ytong Block showing transverse load as a function of 

preload for wall heights ranging from 5-10 ft (Hybrid Combination Model).
312

( ) ( ) 3,154 lbs

96/ 2

33.36 1000 0.711 7.875 1.06

L 2

P d t δ m h = × × × − = × × − Horizontal Force (HF) =

144 788psf 24 96/ 2

2 3,154

w L/2

2 HF

× = ×

× = ×

× Transverse Pressure =

10.1.6 Kingsway Block Constructions 

Kingsway is another cellular concrete block, similar to the ACCOA block. The 

Kingsway block has a compressive strength of 546 psi. The block measures nominally 5-7/8 

x 8-3/8 x 17-1/4 inches. The best model for this block was the Hybrid Theoretical 

Combination Thrust and Lateral Displacement model. Figure 10-6 shows the transverse 

pressure estimates for 8-in-thick walls constructed at heights ranging from 5 to 10 ft in one ft 

height increments with preload pressures ranging from 0 to 140 psi. These graphs can then 

be used to approximate the transverse pressure capacity for a particular set of conditions. For 

example, the transverse pressure capacity of a 9-ft-high wall with 80 psi of ground pressure 

would be approximately 200 psf. 

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120 140

PRELOAD, psi

TRANSVERSE PRESSURE, psf. Kingsway Block -- 5 ft wall height Kingsway Block -- 6 ft wall height Kingsway Block -- 7 ft wall height

Kingsway Block -- 8 ft wall height Kingsway Block -- 9 ft wall height Kingsway Block -- 10 ft wall height

Figure 10-6. Design chart for Kingsway Block showing transverse load as a function of 

preload for wall heights ranging from 5-10 ft (Hybrid Combination Model).
313

 The transverse pressure for any condition can also be calculated using the formulation 

documented in chapter 9 and outlined in the flowchart in figure 9-4. Using the previous 

example, the following calculations are made to determine the transverse pressure capacity of 

the stopping using the narrow block dimension to establish the wall thickness with a 9-ft 

height and a preload of 80 psi. A parametric analysis can also be made and regression line 

fitted to the resulting data to provide a chart similar to that shown in figure 10-6. 

Normalized thrust load (P/BL) = 0.0018 x Ex(t/L)2 + 0.0034 x Preload + 0.2850 

P/BL = 0.0018 x 24,000 x (5.875/108)2

 + 0.0034 x 80 + 0.2850 = 0.69 kips/in 

Thrust (Pm) = 0.69 x 17.25 = 11.90 kips 

Thrust resultant position factor (d) = -.0087 x Half-wall Height - .0453 x Thrust + 1.7532 

Thrust resultant position factor (d) = -.0087 x 54 - .0453 x 11.90 + 1.7532 = 0.744 

Lateral Displacement (δh) = -0.0057 x Ex(t/L)2

 - 0.0020 x Preload + 2.0018 

(δh) = -0.0057 x 24,000 x (5.875/108)2

 - 0.0020 x 80 + 2.0018 = 1.44 in 

( ) ( ) 646 lbs

108/ 2

11.90 1000 0.744 5.875 1.44

L 2

P d t δ m h = × × × − = × × − Horizontal Force (HF) =

144 200psf 17.25 108/ 2

2 646

w L/2

2 HF

× = ×

× = ×

× Transverse Pressure =

10.1.7 Omega Block Constructions 

Omega is also a cellular concrete block, but with a compressive strength of only 84 

psi, it is much weaker than any of the other cellular block materials. The low density 

material allows the block to be fabricated in an 8 x 16 x 24 inch size, which is also the largest 

of any stopping block evaluated in this study. The low strength of the block leads to 

inconsistent transverse pressure behavior, making models also more difficult to develop. The 

best model for this block was the Hybrid Theoretical Combination Thrust and Lateral 

Displacement model. Figure 10-7 shows the transverse pressure estimates for 8-in-thick 

walls constructed at heights ranging from 5 to 10 ft in one ft height increments with preload 

pressures ranging from 0 to 30 psi. These graphs can then be used to approximate the 

transverse pressure capacity for a particular set of conditions. For example, the transverse 

pressure capacity of an 8-ft-high wall with 15 psi of ground pressure would be approximately 

80 psf. 
314

 The transverse pressure for any condition can also be calculated using the formulation 

documented in chapter 9 and outlined in the flowchart in figure 9-4. Using the previous 

example, the following calculations are made to determine the transverse pressure capacity of 

the stopping using the narrow block dimension to establish the wall thickness with a 8-ft 

height and a preload of 15 psi. A parametric analysis can also be made and regression line 

fitted to the resulting data to provide a chart similar to that shown in figure 10-7. 

Effective Modulus (E) = .027 x Half-wall height2.87 = 1,805 psi 

Normalized thrust load (P/BL) = -0.0083 x Ex(t/L)2

 + 0.0046 x Preload + 0.1590 

P/BL = -0.0083 x 1,805 x (8/96)2

 + 0.0046 x 15 + 0.1590 = 0.12 kips/in 

Thrust (Pm) = 0.12 x 24 = 2.88 kips 

Thrust resultant position factor (d) = -.0080 x Half-wall Height - .0524 x Thrust + 1.3723 

Thrust resultant position factor (d) = -.0080 x 48 - .0524 x 2.88 + 1.3723 = 0.837 

Lateral Displacement (δh) = 0.0333 x Ex(t/L)2

 - 0.0293 x Preload + 1.6449 

(δh) = 0.0333 x 1805 x (8/96)2

 - 0.0293 x 15 + 1.6449 = 1.62 in 

( ) ( ) 305 lbs

96/ 2

2.88 1000 0.837 8 1.62

L 2

P d t δ m h = × × × − = × × − Horizontal Force (HF) =

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30

PRELOAD, psi

TRANSVERSE PRESSURE, psf.

Omega Block -- 5 ft wall height Omega Block -- 6 ft wall height Omega Block -- 7 ft wall height

Omega Block -- 8 ft wall height Omega Block -- 9 ft wall height Omega Block -- 10 ft wall height

Figure 10-7. Design chart for Omega Block showing transverse load as a function of 

preload for wall heights ranging from 5-10 ft (Hybrid Combination Model).
315

144 76psf 24 96/ 2

2 305

w L/2

2 HF

× = ×

× = ×

× Transverse Pressure =

10.1.8 Peerless Super Block Constructions 

Peerless Super Block is a unique block design. Styrofoam pellets are imbedded in a 

weak cement to provide a very low density material. The measured compressive strength is 

86 psi, about the same as the Omega block. The low-density material allows the block to be 

fabricated in a 6 x 16 x 24 inch size, second only to the Omega block in physical size. The 

low strength of the block and non-uniform distribution of the Styrofoam pellets leads to 

inconsistent transverse pressure behavior, making models also more difficult to develop. The 

best model for this block was the Hybrid Theoretical Combination Thrust and Lateral 

Displacement model. Figure 10-8 shows the transverse pressure estimates for 6-in-thick 

walls constructed at heights ranging from 5 to 10 ft in with preload pressures ranging from 0 

to 100 psi. These graphs can then be used to approximate the transverse pressure capacity 

for a particular set of conditions. 

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90 100

PRELOAD, psi

TRANSVERSE PRESSURE, psf .

Peerless Super Block -- 5 ft wall height Peerless Super Block -- 6 ft wall height

Peerless Super Block -- 7 ft wall height Peerless Super Block -- 8 ft wall height

Peerless Super Block -- 9 ft wall height Peerless Super Block -- 10 ft wall height

Figure 10-8. Design chart for Peerless Super Block showing transverse load as a function 

of preload for wall heights ranging from 5-10 ft (Hybrid Combination Model).
316

 The transverse pressure for any condition can also be calculated using the formulation 

documented in chapter 9 and outlined in the flowchart in figure 9-4. Using the previous 

example, the following calculations are made to determine the transverse pressure capacity of 

the stopping using the narrow block dimension to establish the wall thickness with a 10-ft 

height and a preload of 30 psi. A parametric analysis can also be made and regression line 

fitted to the resulting data to provide a chart similar to that shown in figure 10-8. 

Effective Modulus (E) = 5.51 x Half-wall height1.78 = 8,058 psi 

Normalized thrust load (P/BL) =- 0.0018 x Ex(t/L)2

 + 0.0034 x Preload + 0.0603 

P/BL = -0.0018 x 8058 x (5.8/120)2

 + 0.0034 x 30 + 0.0603 = 0.13 kips/in 

Thrust (Pm) = 0.13 x 24 = 3.12 kips 

Thrust resultant position factor (d) = -.0036 x Half-wall Height - .0188 x Thrust + 0.7892 

Thrust resultant position factor (d) = -.0036 x 60 - .0188 x 3.12 + 0.7892 = 0.515 

Lateral Displacement (δh) = 0.0038 x Ex(t/L)2

 + 0.0177 x Preload + 1.5636 

(δh) = 0.0038 x 8058 x (5.8/120)2

 - 0.0177 x 30 + 1.5636 = 1.10 in 

( ) ( ) 98 lbs

120/ 2

3.12 1000 0.515 5.8 1.10

L 2

P d t δ m h = × × × − = × × − Horizontal Force (HF) =

144 19.6psf 24 120/ 2

2 98

w L/2

2 HF

× = ×

× = ×

× Transverse Pressure =

10.2 GENERIC BLOCK DESIGN FORMULATIONS 

The same suite of models that was developed for the specific block constructions was 

also developed by categorizing the blocks into groups with similar material properties. 

Specifically, the categories were defined as follows: (1) standard CMU block with 

compressive strengths ranging from 1,000 to 2,000 psi, (2) cellular block materials with 

compressive strengths ranging from 250 to 750 psi, and (3) low strength block materials with 

compressive strengths less than 100 psi. These models were discussed in detail in Chapter 9. 

When compared with actual test data, the hybrid combination thrust and lateral displacement 

model generally provides the most accurate predictions of the transverse pressure capacities 

of the stopping. This model uses a combination of empirical formulations from multivariable 

regression analysis of test data and theoretical calculations of various parameters affecting 
317

the transverse loading capacity of the stopping. The formulations are presented in figures 10-

9, 10-10, and 10-11 for the three block categories. 

Calculate horizontal 

force (HF) 

Calculate transverse 

pressure (ρ) 

Procedure Formula Used 

Determine preload 

Determine Resultant 

Thrust Position 

factor (d) 

Determine Lateral 

Displacement (δh) 

Multivariable regression analysis 

relating lateral displacement to 

E*(t/L)2 and preload. 

Determine total thrust 

(Pm)

Determine normalized 

thrust force 

Measured or PL = ∆L× k2

Multivariable regression analysis 

relating thrust to E*(t/L)2

 and preload

P/BL = .0027 x E*(t/L)2 + .0033 x Preload + .6137 

Total Thrust (Pm) = P/BL x Block Length 

Multivariable regression analysis 

relating d factor to wall height and 

thrust.

d = -.0018 x Half-wall Height - .0031 x Thrust + .93

δh = -.0012 x E*(t/L)

2 - .0024 x Preload + 2.0058

( )

L / 2

P d t HF m h × × − δ =

w L / 2

HF

×

ρ =

Figure 10-9. Flowchart for Standard CMU model. 

w L / 2

2 HF

×

×

ρ =

P/BL = .0027 x Ex(t/L)

2 + .0033 x Preload + .6137

δh= -.0012 x Ex(t/L)2 - .0024 x Preload + 2.0058 

Multivariable regression analysis 

relating thrust to Ex(t/L)2

 and preload

Multivariable regression analysis 

relating lateral displacement to 

Ex(t/L)

2 and preload. 
318

( )

L / 2

P d t HF m h × × − δ =

Determine Resultant 

Thrust Position 

factor (d) 

Multivariable regression analysis 

relating d factor to wall height and 

thrust.

Determine Lateral 

Displacement (δh) 

Multivariable regression analysis 

relating lateral displacement to 

Ex(t/L)

2 and preload. 

Figure 10-10. Flowchart for the Cellular Concrete Model. 

Calculate horizontal 

force (HF) 

Calculate transverse 

pressure (ρ) 

Procedure Formula Used 

Determine preload 

P/BL = .0019 x Ex(t/L)2 + .0044 x Preload + .3257 

Determine total thrust 

(Pm) Total Thrust (Pm) = P/BL x Block Length 

d = -.0028 x Half-wall Height - .0076 x Thrust + 1.02

δh = -.0004 x Ex(t/L)

2 - .0045 x Preload + 1.43

Determine normalized 

thrust force 

Measured or PL = ∆L× k2

Multivariable regression analysis 

relating thrust to Ex(t/L)2

 and preload

w L / 2

2 HF

×

×

ρ =
319

Calculate horizontal 

force (HF) 

Calculate transverse 

pressure (ρ) w L / 2

2 HF

×

×

ρ =

Multivariable regression analysis 

relating thrust to Ex(t/L)2

 and preload

Procedure Formula Used 

Determine preload Measured or PL = ∆L× k2

( )

L / 2

P d t HF m h × × − δ =

Determine Resultant 

Thrust Position 

factor (d) 

Multivariable regression analysis 

relating d factor to wall height and 

thrust. 

Determine Lateral 

Displacement (δh) 

Multivariable regression analysis 

relating lateral displacement to 

Ex(t/L)2 and preload. 

P/BL = -.0046 x Ex(t/L)2 + .0033 x Preload + .1325 

Determine total thrust 

(Pm) Total Thrust (Pm) = P/BL x Block Length 

d = -.0060 x Half-wall Height - .0361 x Thrust + 1.09

δh = -.0114 x Ex(t/L)

2 - .0204 x Preload + 2.01

Determine normalized 

thrust force 

Figure 10-11. Flowchart for the Low Strength Specialty Block Model. 
320

SUMMARY AND CONCLUSIONS 

 Stoppings are an integral part of any underground mine ventilation system. In coal 

mines, stoppings may be either classified as temporary or permanent structures. Permanent 

stoppings are generally constructed from some form of concrete block, typically dry-stacked 

to form a wall, equal in thickness to the narrow dimension of the block, and bridging between 

the mine roof and floor and pillar ribs. The CFR specifies that stoppings must be able to 

withstand 39 psf of transverse loading on the face of the stopping in a freestanding loading 

condition to be suitable for coal mine use in the United States. This specification is based on 

ASTM E 72 testing requirements, which is intended for building construction of masonry 

panels and walls. The author does not believe that this testing requirement provides an 

accurate representation of the loading conditions that occur in mining situations. For drystacked stopping constructions, the transverse load capacity under the CFR criteria, as studies 

clearly show, is primarily determined by the tensile strength of the sealant. Any block 

material, regardless of its physical properties, can be made to pass the acceptance test for use 

in underground coal mines provided the sealant is strong enough and can adhere to the 

surface of the block. As such, the 39-psf transverse load requirement is an irrelevant, 

arbitrary, and a misleading performance measure that does not accurately correspond to the 

true transverse loading capability of stoppings in the mine. 

 The restraint provided by the mine roof and floor and coal pillars allow the stopping 

wall to arch between these abutments as the wall bends from the application of transverse 

loading. Arching has long been recognized as a valid loading mechanism that can 

dramatically improve the capability of jointed structures to resist loading induced by 

bending. Arching relies on compressive forces within the wall structure to offset the bending 

moment induced by the deflection of the wall from the application of transverse loading. For 

dry-stacked stopping constructions, which have no tensile strength across the joints except 

for the sealant on the face of the joint, these compressive forces can increase the transverse 

load capacity of a stopping by an order of magnitude or more. Transverse loading 

theoretically causes a three-hinge arch to form in a stopping wall as the joint running 

horizontally across the wall opens at the mid vertical span between the mine roof and floor. 

This creates two half-sections of wall, one above and one below the middle joint. Hinges 

also form at the mine roof and floor interface as the half-wall sections remain together as 
321

unit, but also try to rotate at the roof and floor interface. Vertical compressive forces are 

developed in the wall as it is restrained from horizontal rotation by the mine roof and floor. 

These compressive forces allow powerful force couples to be developed that control the 

transverse loading capacity of a jointed structure that otherwise would have very little 

capability to resist bending induced by transverse loading. 

 A lab testing protocol to simulate arching of stopping walls by biaxial loading in the 

NIOSH Mine Roof Simulator was developed. This process is simulated in the MRS by 

testing a half-height section of wall. The wall is restrained vertically by the fixed vertical 

position of the load frame platens, thereby acting as rigid end restraints simulating the mine 

roof and floor. The lower platen is then moved laterally, causing the base of the wall to 

displace with the platen and causing the wall to rotate accordingly, similar to the three-hinge 

theory. Deformation zones are created at the face edges of the half-wall in the areas where 

these two hinges would occur in a full-height wall. By measuring the lateral load applied to 

the wall by the simulator, the transverse load capacity of the wall can be determined. This 

load is normalized to the area of the wall to determine a transverse pressure in psf units 

equivalent to that used in the CFR specifications. 

 The MRS arch testing protocol was validated through two full-scale tests of 

stopping walls in the NIOSH Experimental Coal Mine at the Pittsburgh Research Laboratory. 

In these tests, two different block types with different physical characteristics were evaluated. 

One block was made from a low density, autoclaved concrete material with a compressive 

strength of 540 psi, while the other block was made from more conventional materials 

including Portland cement, sand, and aggregate and had a compressive strength of 1,330 psi. 

Half-walls equivalent to the seam height in the Experimental Coal Mine were constructed in 

the MRS using these block materials and tested in accordance with the arch testing protocol. 

Transverse pressure capacities from the laboratory tests were computed and compared to the 

in-mine tests with full-scale stoppings of the same construction, which were conducted in a 

fabricated air pressure chamber in a remote cross section of the mine. The laboratory test 

results closely matched the full-scale mine tests. The peak transverse pressure measured in 

the laboratory for the lower strength cellular concrete block (Kingsway) was 417 psf 

compared to 400 psf for the full-scale mine tests, an error of only 4 pct. For the stronger 

conventional block, the laboratory measured transverse pressure (1.067 psf) was within 6 pct 
322

of the measured transverse pressure on the full-scale mine stopping (975 psf). Additional 

verification of the laboratory model was provided to develop a mathematical relationship 

based on the arching mechanics between the compressive strength of the block and the wall 

geometry, namely the wall thickness (t) and the wall height (L). It was postulated, based on a 

static analysis of the arching mechanics, that the transverse pressure should be related to the 

product of the block compressive strength (fc) and the squared ratio of the wall thickness and 

length, mathematically expressed by the term fc X (t/L)2. Using this relationship, the 

transverse pressure of an untested wall construction at the NIOSH Lake Lynn facility was 

predicted to within a 10 pct error. 

 Further examination of the arching mechanics indicated that the transverse load 

capacity of a stopping is also related to the lateral displacement of the wall in addition to the 

arching thrust that is developed. The following formulation was used to describe the arching 

mechanics and would serve to provide a mathematical basis for developing various design 

models to define the transverse load capacity of any hypothetical stopping construction. 

Where 

 ρ = transverse load, psf, 

 P = arching force, lbs, 

 T = wall thickness, in, 

 δh = lateral displacement of wall at the mid span, in, 

 w = width of the wall, in, and 

 L/2 = half-wall height, in. 

From this formulation, it is seen that several parameters will affect the transverse load 

response of a mine ventilation stopping, none of which are included in the current CFR 

criteria. The impacts of these parameters are summarized as follows: 

 Wall height – Wall height is a critical parameter in controlling the transverse load 

capacity of a stopping. An increase in wall height will significantly reduce the transverse 

load capacity, since the transverse load varies inversely with the square of the half-wall 

height. Hence, the transverse load capacity of a 10-ft-high stopping wall will be reduced 

( )

( ) 144

w L/2

2 P (0.8 t δ ) 144

w L/2

L/2

2 P 0.8 t δ

ρ 2

h

h

×

×

× × × − × = ×

× × × −

=
323

by a factor of 4 for a 5-ft-high stopping wall of the same construction. From a mechanics 

perspective, the wall height controls the horizontal force couple upon which the arching 

is dependent for moment equilibrium requirements. 

 Wall thickness – The transverse load capacity of a stopping is directly related to the 

thickness of the stopping. Ultimately, the thickness of the wall determines the arch 

moment arm (distance between the resultant thrust forces at the hinge points as 

represented by the factor 0.8 x t - δh term). Since most blocks are dimensionally 

anisotropic, the orientation of the block (wide-side-down or wide-side-up) during wall 

construction can have a significant impact on the transverse load capacity of the stopping. 

The thicker the wall, the greater the transverse load capacity will be. 

 Wall Width -- The wall width does not affect the transverse pressure capability of the 

stopping, despite the width generally being greater than the height of the stopping. Since 

the blocks are dry-stacked, the joints have no tensile strength and create a hinge line 

causing the arch to form from the mine floor to the mine roof instead of from coal pillar 

to coal pillar, as is generally the case in seal behavior. 

 Arch Thrust -- The compressive arch thrust force is the key to the how much transverse 

capacity a stopping of a given geometry can develop. The development of arching thrust 

depends on several factors including the geometry of the wall (i.e. height and thickness). 

However, it is primarily determined by the material properties of the block and boundary 

stiffness of the roof and floor, both of which control how much lateral displacement of 

the wall will occur as the transverse pressure is applied to the face of the stopping. 

 Lateral Displacement -- The lateral displacement also plays a big role in determining 

the transverse capacity of a block stopping. The width of the arch thrust, represented by 

the distance between the resultant thrust forces and mathematically expressed as 0.8 x tδh, will decrease as the lateral deflection of the wall increases. The decrease in the width 

of the arch will cause a proportional decrease in the transverse load capacity of the wall, 

since the force couple produced by the arch thrust will decrease. The lateral 

displacement will increase as the boundary stiffness decreases, thereby reducing the 

transverse load capacity of the stopping. Likewise, walls constructed from a lower 

modulus block material will also have reduced transverse load potential, since the thrust 

force developed, as a function of the lateral displacement will be reduced. 
324

 The transverse load capacity of a stopping wall is limited even if the material strength 

has not been exceeded, because the rotation of the wall impacts the development of the 

arching thrust and moment equilibrium requires that the force couple developed with the 

arching thrust and the transverse loading must balance. This indicates that there is an 

optimum block strength that is needed to ensure that the full transverse load potential is 

realized. Beyond this, the transverse loading will be controlled by the arching mechanics and 

the benefit of the higher block strength will not be realized in the transverse load 

development of the stopping. Due to the arching mechanics, the optimum block strength will 

also depend on the material modulus, since the modulus controls the deformation from the 

thrust forces in the hinge areas. The lower the modulus, the higher the optimum compressive 

strength requirement for a particular block geometry. 

 The full arching potential for any stopping will be realized for rigid boundary 

conditions, which will then establish the maximum transverse loading capacity for the 

stopping. Under rigid arching conditions, the lateral displacement of the wall is controlled by 

the stiffness and elastic response of the block wall. The transverse load capacity will 

decreases as the block modulus decreases since more lateral displacement of the wall will 

occur. The increase in lateral displacement reduces the force couple provided by the arching 

thrust and this causes a decrease in the transverse load capacity of the stopping. If the 

abutments are not rigid, then the lateral displacement will increase further, resulting in a 

further reduction in the transverse load capacity of the stopping. Therefore, a small change 

in the abutment stiffness can cause significant changes in the arching capacity and transverse 

load capacity of a stopping. A theoretical assessment of the impact of the boundary stiffness 

was made by varying the system modulus, which is the equivalent stiffness of the wall and 

the roof and floor acting in series with one another. The system stiffness was reduced to 75, 

50, and 25 pct of the rigid boundary condition, and the transverse load capacity determined 

using the arching mechanics formulations. To put this in perspective, if the boundary 

stiffness was equal to the wall stiffness, the system stiffness would be reduced by 50 pct. 

Likewise, if the boundary stiffness were three times that of the wall, the system stiffness 

would be 75 pct of the rigid boundary condition, and if the boundary stiffness were one third 

of the wall stiffness, the system stiffness would be 25 pct of the rigid boundary condition. 

The percent reduction in transverse pressure remains the same for all wall heights, but the 
325

absolute reductions in transverse pressure for shorter walls than it will for taller walls. As an 

example, the transverse pressure for a 30-in half-wall height is reduced from 1,128 psf for the 

rigid boundary condition to 470 psf when the boundary modulus is one third of the wall 

modulus thereby reducing the system modulus to 25 pct of the rigid boundary condition. 

This represents a 58 pct decrease in the transverse pressure capacity of the stopping. 

 Another important factor in considering the transverse load capacity of a stopping is the 

axial loading induced from the ground pressures. Even without arching, a superimposed 

axial or vertical load acting on a stopping wall can greatly increase the transverse load 

capacity of the stopping by resisting the moment induced by the transverse pressure. For 

arching conditions, the superimposed axial loading will act to strengthen the force couple 

created by the arching thrust. The result of the superimposed axial pressure will be that the 

transverse load development will occur at smaller lateral displacements of the wall, which 

results in higher transverse loading capacities. Increases in transverse loading by a factor of 

5 can be attained with an 8-ft wall constructed from conventional solid concrete block 

materials when the ground pressure is increased from 0 to 600 psi. The ground pressure can 

also help to offset the impact of reductions in boundary stiffness. Using the previous 

example which indicated a 58 pct reduction in transverse loading due to a reduction in 

system modulus to 25 pct of the rigid boundary condition, a theoretical analysis indicates that 

this would drop to a 7 pct reduction if an axial preload pressure of 567 psi was applied to the 

same stopping. 

 A systematic study of various stopping constructions using the arch testing protocol 

was conducted for the following different block materials. The block materials fall into three 

basic categories, which characterize their material properties and physical characteristics: 

(1) Standard concrete masonry units or CMU’s -- These blocks made from conventional 

Portland cement and various aggregate fillers. Historically, these have been the most 

commonly used concrete block materials for stopping construction. They can be 

fabricated in either solid or hollow core fashion. They have compressive strengths 

ranging from 1,000 to 2,000 psi, dependent primarily on how much Portland cement is 

used in the mix. Generally, the blocks measure nominally 6x8x16 inches and weigh 

approximately 50 lbs. Three specific blocks were evaluated in this study: (a) Klondike 

solid block, (b) Peerless Backsaver block, (c) Klondike hollow core block. 
326

(2) Cellular concrete materials -- These blocks utilize autoclaved aerated concrete where 

entrained air is cured in an autoclaved oven to formulate air pockets within the concrete 

structure that provides a very low-density material that is lightweight, durable, and easy 

to cut, making it attractive for mine ventilation stoppings. Silica is the largest dry raw 

material. Sand, flyash, and copper mine tailings are often used for the silica source. 

The silica reacts with aluminum incorporated into the mix to form a chemical reaction 

that creates millions of tiny air cells, which give AAC its unique properties. Only about 

20 pct of the material is cement. Due to the low material density, the block size is 

enlarged to block thicknesses of 8 inches and lengths to 24 inches. Compressive 

strengths range from 464 to 705 psi for the products tested in this study. Three specific 

blocks were evaluated from this category in this study: (a) Ytong block, (b) ACCOA 

block, and (c) Kingsway block. 

(3) Low strength specialty type materials – These blocks have relatively low strengths 

and material modulus such that they behave differently than the products in the other 

two categories. The Omega block has been used for over a decade and was the first 

cellular type material to gain acceptance for use in stopping construction. The block is 

separated from the cellular category due to its weaker strength (84 psi). Another unique 

block is the Peerless Super Block. This block is characterized by styrofoam pellets that 

are imbedded in the concrete mix to provide a low density material. Included in the 

mix is polypropelene fibers to help hold the weak material together during failure. It 

has a compressive strength of 86 psi comparable to that of the Omega block.

 A series of tests were conducted in the Mine Roof Simulator using these block 

materials. The experimental design was to evaluate 3 different heights, typically 30, 48, and 

60-in half-walls representing full wall heights of 5, 8, and 10 ft. Preloading to evaluate the 

impact of ground pressures was varied in 50 to 100 psi increments to the limit of the block 

strength. Generally, a minimum of two tests were conducted for each configuration to 

evaluate consistency in the wall response. Additional tests were conducted as needed if the 

data was inconsistent. 
327

 Several predictive models 

were developed to define the 

transverse load capacity of 

mine ventilation stoppings. 

Chapter 7 presented two 

models, which utilized either 

the measured arch thrust or the 

measured lateral displacement 

to predict the laboratory arch 

test results. The procedures are 

summarized in the flowcharts 

below, first for the lateral 

displacement method and 

second for the arch thrust 

method. 

 Chapter 8 utilized these 

models to evaluate the test 

results for each of the block 

materials and examine 

parametric trends in the 

transverse load performance of 

the various stopping 

constructions. It was clearly 

shown in the analysis that if 

either the lateral wall 

displacement or the arching 

thrust is known, the transverse 

load capacity of the stopping 

could be predicted to within a 

few percent error. One or both 

of the models predicted the 

8

2 L 4 L 32 t 16

y

2

h h

2 × ± × − × ×δ + ×δ =

Lateral displacement 

Calculate arch thrust 

Calculate horizontal 

force 

Calculate transverse 

pressure w L/ 2

2 HF

×

× ρ =

Measured (δh) 

Procedure Formula Used 

Calculate “hinge point 

deformation” 

Add preload to arch 

thrust 

Pm = Parch + PL

L / 2

2 A E y Parch

× × × =

Determine preload Measured or 2 PL = ∆L×k

( )

L/ 2

P d t HF m h × × − δ =

Total Thrust Force 

Calculate horizontal 

force 

Calculate transverse 

pressure w L/ 2

2 HF

×

× ρ =

Measured (Pm) 

Procedure Formula Used 

Determine preload Measured or 2 PL = ∆L×k

Parch = Pm - Ppreload 

( )

2

2 t 4 t 4 2 L y 4 y 2 2

h

× ± × − × × × − × δ =

Calculate “hinged point 

deformation” 2 A E

P L / 2

y arch

× ×

× =

Calculate lateral 

displacement 

Determine Arch Thrust

( )

L / 2

P d t

HF m h × × − δ =
328

transverse load to within 5 pct error for all but the Omega and Peerless Super Block 

constructions. The performance of these blocks was much less consistent than all the other 

blocks due to the low strength and inconsistent material properties. The Omega block 

transverse loading was predicted to within 16 pct accuracy and the Peerless Super Block 

error prediction was 21 pct. 

 Chapter 9 took this analysis one-step further. Instead of using measured lateral 

displacement or thrust information, methods were developed that would allow these 

measures to be estimated and then utilized in the models for transverse load prediction. Four 

formulations were developed: (1) Full Empirical, (2) Hybrid Theoretical Thrust, (3) Hybrid 

Theoretical Lateral Displacement, (4) Hybrid Theoretical Combination Thrust and Lateral 

Displacement. These models were constructed for each particular block that was examined 

in the study. A more generic model was constructed using data grouped into the three 

categories previously described: (1) Standard CMU, (2) Cellular Concrete, and (3) Specialty 

Block. The generic models allow transverse load approximations to be developed for any 

hypothetical block material that fits within these broad criteria. 

 Full Empirical Model – This model uses empirical data from the laboratory half-wall 

tests to construct a multivariable regression analysis correlating the term Ex(t/L)2

 and 

preload to the transverse pressure. In this formulation, E is the material modulus, t is 

the wall thickness, and L is the height of the wall. 

 Hybrid Theoretical Thrust Model – This model uses a multivariable regression 

analysis of test data to correlate the thrust force to the Ex(t/L)2 term and preload 

pressure. Once this is determined, the formulation previously shown is used to 

compute the hinge area deformation and lateral displacement. Then using the moment 

equilibrium requirements for arching, the horizontal force and transverse pressure is 

determined. 

 Hybrid Theoretical Lateral Displacement Model – This model is similar to the 

Hybrid Theoretical Thrust Model except the empirical data is use to estimate the lateral 

displacement instead of the thrust force. Once the lateral displacement is determined, 

the hinge area deformation and arch thrust is computed using the previously described 

formulation. Then using the moment equilibrium requirements for arching, the 

horizontal force and transverse pressure is determined as is done in the thrust model. 
329

 Hybrid Theoretical Combination Model – This model essentially combines the thrust 

model and lateral displacement models. In the Hybrid Combination Model, both the 

thrust and lateral displacement are estimated from a multivariable regression analysis of 

the laboratory test data, again correlating these measures to the Ex(t/L)2 term and 

preload pressure. The transverse pressure is then computed using the moment 

equilibrium requirements that satisfy the arching mechanics.

 Finally, chapter 10 examines each of these design formulations and recommends a 

specific design formulation, which provides the most accurate approximation of the 

transverse load capacity of the stopping. Design formulations are recommended for the 

specific block materials examined in this study as well as for the three generic categories. 

For the most part, the Hybrid Theoretical Combination Model was the recommended design 

formulation. The transverse load capacities for all blocks were predicted to within a 4 pct 

error using the recommended design models. 

 In conclusion, arching stopping design would be a radical departure from the current 

freestanding wall design required by the CFR. The physical properties of the block and the 

size of the mine opening would need to be examined to determine the proper design for a 

stopping application. The sealant would no longer be considered to affect the transverse load 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Klondike

Solid Block

Peerless

Backsaver

Block

Klondike

Hollow

Core Block

Ytong

Block

ACCOA

Block

Kingsway

Block

Omega

Block

Peerless

Super

Block

PREDICTION ACCURACY, percent error ...

Best Model Prediction
330

capability of the stopping. Since the actual transverse load capacity of the stopping can be 

determined, the stopping can be designed based on the required transverse load capacity for a 

specific set of conditions in the mine, as opposed to the current system that permits stoppings 

of widely ranging transverse loading capabilities to be employed in the same environment. 

This approach should lead to a safer mine environment for the tens of thousands of 

mineworkers in underground coal mines. 

FUTURE RESEARCH RECOMMENDATIONS 

This study conducted a comprehensive evaluation of arching in laboratory 

conditions for dry-stacked mine ventilation stoppings. The laboratory test protocol was 

verified with some full-scale testing of stoppings including two tests in a coal mine 

environment. The results of these underground trials did confirm the laboratory test 

procedure and experimental design, but the overriding question remains the issue 

significance of the abutment stiffness and its impact on arching. It is clear that arching can 

occur in a mine environment as was demonstrated by the full-scale in mine testing. An 

extensive theoretical analysis of the impact of the abutment stiffness was also conducted as 

part of this research. That analysis indicates that the abutment stiffness can significantly 

affect the arching capability and degrade the transverse load capacity of a stopping, but it 

also indicates that arching will continue to occur even under relatively soft boundary 

conditions. It was also shown by the analysis that the superimposed axial loading from the 

ground pressures can do much to offset the impact of lower stiffness boundary conditions. 

Nonetheless, additional data needs to be acquired on actual roof and floor stiffness relative to 

a stopping construction to further define the range of boundary conditions that actually exist 

in the mine. It is proposed that some in mine studies of ground stiffness be conducted 

relative to stopping block contact conditions to further define this problem. 

 Although this study was comprehensive in scope, the current industry practice of 

using strain softening materials to absorb ground deformation and thereby extend the service 

life of the stopping, remains a major detriment to preserving the arching and transverse load 

capacity of stoppings. First, the industry needs to be made aware of the impact of the strain 

softening materials relative to transverse loading to avoid creating hazardous ventilation 

conditions with poor stopping construction. Research needs to be done to develop a material 
331

that is more compatible to the block physical properties so that a reasonable compromise can 

be made to preserve both the service life and transverse load capacity of the stopping. 

Additional approaches could also be pursued in which the hinge element would be removed 

while still allowing vertical deformation to occur. This could be some sort of mechanical 

device or some form of membrane control that would provide this function. 

 Finally, the very weak block materials taxed the limits of the laboratory system to 

accurately evaluate the arching thrust and transverse loading. Some additional testing with a 

higher resolution of measurement should be conducted to improve the accuracy of the design 

formulations for these materials. 
334

APPENDIX A: DESCRIPTION OF THE MINE ROOF SIMULATOR 

 The Mine Roof Simulator (MRS) is a servo-controlled hydraulic press custom built 

by MTS Systems Corporation to U.S. Bureau of Mines (USBM) specifications. The 

simulator was built in 1979 at a cost of $7.5 million. It was designed specifically for 

longwall shield testing, and is the only active load frame in the United States that can 

accommodate full-size shields. However, its size and unique capabilities provides a 

facility for testing a wide variety of large-scale structures, including various forms of 

standing roof support structures and mine ventilation stoppings. 

 A functional diagram of the load frame is shown in figure A-1. The load frame has 

several distinctive characteristics. The size of the upper and lower platen is 20 ft x 20 ft. 

The upper platen can be moved up or down and hydraulically clamped into a fixed 

position on the directional columns to establish a height for testing. With a maximum 

vertical opening between the upper and lower platen of 16-ft, the load frame can 

accommodate the largest shields currently in use. Load application is provided by 

controlled movement of the lower platen, operating in either force of displacement 

control. The load frame is a biaxial frame, capable of applying both vertical and 

horizontal loads. Load actuators are equipped with special hydrostatic slip bearings to 

permit simultaneous load and travel. This allows vertical and horizontal loads to be 

applied simultaneously. The capability to provide controlled loading simultaneously in 

two orthogonal directions is unique at this scale. 

 Vertical loading is provided by a set of four actuators, one on each of the corners of 

the lower platen. Loads of up to 3 million pounds can be applied in the vertical direction 

by upward movement of the lower platen. Each actuator is capable of applying the full 3 

million pounds of force, so that the specimen can be placed anywhere on the platen 

surface and the full 3 million pound capacity can be provided. The vertical (upward) 

range of motion of the lower platen is 24 inches. 

 Horizontal loading is also provided by four actuators, with two actuators located on 

both the left and right side of the load frame just below the floor level. These actuators 

act in pairs to provide horizontal displacement of the lower platen in either a positive or a 
335

negative (x) direction, reacting off the corner columns of the load frame. The horizontal 

range of motion of the lower platen is 16 in. 

 There is no programmable control of the lower platen in the lateral horizontal axis 

(y-direction). The load frame has a reactive capacity of 1.6 million pounds in this 

direction, but loads cannot be applied in the lateral direction. The range of motion of the 

lower platen in this direction is + 0.5 in. 

Figure A-1 Diagram of the Mine Roof Simulator. 
336

 Six degrees of freedom control of the lower platen are provided by the unstressed 

reference frame, which provides feedback on platen displacements and rotations to the 

closed-loop control system. Pitch, yaw, and roll of the lower platen are controlled to 

keep the lower and upper platens parallel during load application. 

 A shock absorber actuator is positioned on the left and right side of the lower 

platen. These shock absorbers will control the displacement of the lower platen to less 

than 0.1 in in the event of sudden failure of the support specimen. This system absorbs 

energy stored in the load frame to maintain control of the platen and to avoid releasing 

stored energy into the specimen immediately following an abrupt specimen failure. 

 Two hydraulic pumps provide up to 3,000 psi of pressure to the vertical and 

horizontal actuators during load application. The rate of movement of the lower platen is 

limited by the 140-gpm capacity of the hydraulic pumps. The maximum platen velocity 

assuming simultaneous vertical and horizontal displacement is 5.0 inches per minute. 
337

APPENDIX B: MRS HALF-WALL TEST DATA 
338

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs ..

0.0

5.6

11.3

16.9

22.5

28.1

33.8

39.4

45.0

THRUST LOAD, kips .

Test #102 -- Lateral Load -- Klondike (1330) -- 51 psi preload

Test #102 -- Thrust Load -- Klondike (1330) -- 51 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

5

10

15

20

25

30

35

40

45

THRUST LOAD, kips .

Test #110 -- Lateral Load -- Klondike (1330) -- 68 psi preload

Test #110 -- Thrust Load -- Klondike (1330) -- 68 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

4.5

9.0

13.5

18.0

22.5

27.0

31.5

36.0

40.5

THRUST LOAD, kips

Test #104 -- Lateral Load -- Klondike (1330) -- 188 psi preload

Test #104 -- Thrust Load -- Klondike (1330) -- 188 psi preload

0

1,000

2,000

3,000

4,000

5,000

6,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

10

20

30

40

50

60

THRUST LOAD, kips

Test #105 -- Lateral Load -- Klondike (1330) -- 160 psi preload

Test #105 --Thrust Load -- Klondike (1330) -- 160 psi preload

KLONDIKE BLOCK 
339

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

05

10

15

20

25

30

35

40

45

50

THRUST LOAD, kips .

Test #108 -- Lateral Load -- Klondike (1330) -- 280 psi preload

Test #108 -- Thrust Load -- Klondike (1330) -- 280 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

05

10

15

20

25

30

35

40

45

50

THRUST LOAD, kips .

Test #112 -- Lateral Load -- Klondike (1330) -- 385 psi preload

Test #112 -- Thrust Load -- Klondike (1330) -- 385 psi preload

0

1,000

2,000

3,000

4,000

5,000

6,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

10

20

30

40

50

60

THRUST LOAD, kips .

Test #114 -- Lateral Load -- Klondike (1330) -- 428 psi preload

Test #114 -- Thrust Load -- Klondike (1330) -- 428 psi preload

0

1,000

2,000

3,000

4,000

5,000

6,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

10

20

30

40

50

60

THRUST LOAD, kips .

Test #115 -- Lateral Load -- Klondike (1330) -- 428 psi preload

Test #115 -- Thrust Load -- Klondike (1330) -- 428 psi preload
340

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

4.5

9.0

13.5

18.0

22.5

27.0

31.5

36.0

40.5

THRUST LOAD, kips

Test #109 -- Lateral Load -- Klondike (1330) -- 155 psi preload

Test #109 -- Thrust Load -- Klondike (1330) -- 155 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

05

10

15

20

25

30

35

40

45

THRUST LOAD, kips .

Test #111 -- Lateral Load -- Klondike (1330) -- 141 psi preload

Test #111 -- Thrust Load -- Klondike (1330) -- 141 psi preload

0

1,000

2,000

3,000

4,000

5,000

6,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

10

20

30

40

50

60

THRUST LOAD, kips .

Test #106 -- Lateral Load -- Klondike (1330) -- 295 psi preload

Test #106 -- Thrust Load -- Klondike (1330) -- 295 psi preload

0

1,000

2,000

3,000

4,000

5,000

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0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

10

20

30

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THRUST LOAD, kips .

Test #107 -- Lateral Load -- Klondike (1330) -- 326 psi preload

Test #107 -- Thrust Load -- Klondike (1330) -- 326 psi preload
341

0

1,000

2,000

3,000

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0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

10

20

30

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THRUST LOAD, kips .

Test #118 -- Lateral Load -- Klondike (1330) -- 470 psi preload

Test #118 -- Thrust Load -- Klondike (1330) -- 470 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

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0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

06

12

18

24

30

36

42

48

54

60

THRUST LOAD, kips .

Test #119 -- Lateral Load -- Klondike (1330) -- 521 psi preload

Test #119 -- Thrust Load -- Klondike (1330) -- 521 psi preload

0

1,000

2,000

3,000

4,000

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0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

10

20

30

40

50

60

THRUST LOAD, kips .

Test #113 -- Lateral Load -- Klondike (1330) -- 567 psi preload

Test #113 -- Thrust Load -- Klondike (1330) -- 567 psi preload

0

200

400

600

800

1,000

1,200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs ..

048

12

16

20

24

THRUST LOAD, kips .

Test #60 -- Lateral Load -- Klondike (1330) -- 28 psi preload

Test #60 -- Thrust Load -- Klondike (1330) -- 28 psi preload
342

0

200

400

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0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs ..

0

5

10

15

20

25

30

THRUST LOAD, kips .

Test #59 -- Lateral Load -- Klondike (1330) -- 43 psi preload

Test #59 -- Thrust Load -- Klondike (1330) -- 43 psi preload

0

200

400

600

800

1,000

1,200

1,400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs ..

0

5

10

15

20

25

30

35

THRUST LOAD, kips .

Test #46 -- Lateral Load -- Klondike (1330) -- 85 psi preload

Test #46 -- Thrust Load -- Klondike (1330) -- 85 psi preload

0

200

400

600

800

1,000

1,200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

4

8

12

16

20

24

THRUST LOAD, kips .

Test #45 -- Lateral Load -- Klondike (1330) -- 90 psi preload

Test #45 -- Thrust Load -- Klondike (1330) -- 90 psi preload

0

200

400

600

800

1,000

1,200

1,400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

VERTICAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

4

8

12

16

20

24

28

THRUST LOAD, kips .

Test #34 -- Lateral Load -- Klondike (1330) -- 109 psi preload

Test #34 -- Thrust Load -- Klondike (1330) -- 109 psi preload

Photo 

Not 

Available

Photo 

Not 

Available
343

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0.0 0.5 1.0 1.5 2.0 2.5 3.0

VERTICAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

4

8

12

16

20

24

28

32

36

THRUST LOAD, kips .

Test #36 -- Lateral Load -- Klondike (1330) -- 122 psi preload

Test #36 -- Thrust Load -- Klondike (1330) -- 122 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

VERTICAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

4

8

12

16

20

24

28

32

36

40

THRUST LOAD, kips .

Test #35 -- Lateral Load -- Klondike (1330) -- 139 psi preload

Test #35 -- Thrust Load -- Klondike (1330) -- 139 psi preload

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

7

14

21

28

35

THRUST LOAD, kips .

Test #37 -- Lateral Load -- Klondike (1330) -- 202 psi preload

Test #37 -- Thrust Load -- Klondike (1330) -- 202 psi preload

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

8

16

24

32

40

THRUST LOAD, kips .

Test #63 -- Lateral Load -- Klondike (1330) -- 252 psi preload

Test #63 -- Thrust Load -- Klondike (1330) -- 252 psi preload

Photo 

Not 

Available

Photo 

Not 

Available
344

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

08

16

24

32

40

THRUST LOAD, kips .

Test #61 -- Lateral Load -- Klondike (1330) -- 313 psi preload

Test #61 -- Thrust Load -- Klondike (1330) -- 313 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

06

12

18

24

30

36

42

THRUST LOAD, kips .

Test #74 -- Lateral Load -- Klondike (1330) -- 373 psi preload

Test #74 -- Thrust Load -- Klondike (1330) -- 373 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

06

12

18

24

30

36

42

48

THRUST LOAD, kips .

Test #75 -- Lateral Load -- Klondike (1330) -- 390 psi preload

Test #75 -- Thrust Load -- Klondike (1330) -- 390 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

06

12

18

24

30

36

42

48

THRUST LOAD, kips .

Test #76 -- Lateral Load -- Klondike (1330) -- 474 psi preload

Test #76 -- Thrust Load -- Klondike (1330) -- 474 psi preload
345

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

07

14

21

28

35

42

49

56

63

THRUST LOAD, kips .

Test #77 -- Lateral Load -- Klondike (1330) -- 471 psi preload

Test #77 -- Thrust Load -- Klondike (1330) -- 471 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

10

20

30

40

50

60

THRUST LOAD, kips .

Test #78 -- Lateral Load -- Klondike (1330) -- 577 psi preload

Test #78 -- Thrust Load -- Klondike (1330) -- 577 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

10

20

30

40

50

60

THRUST LOAD, kips .

Test #79 -- Lateral Load -- Klondike (1330) -- 534 psi preload

Test #79 -- Thrust Load -- Klondike (1330) -- 534 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

08

16

24

32

40

48

56

64

THRUST LOAD, kips .

Test #81 -- Lateral Load -- Klondike (1330) -- 568 psi preload

Test #81 -- Thrust Load -- Klondike (1330) -- 568 psi preload
346

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

8

16

24

32

40

48

56

64

72

THRUST LOAD, kips .

Test #82 -- Lateral Load -- Klondike (1330) -- 618 psi preload

Test #82 -- Thrust Load -- Klondike (1330) -- 618 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

8

16

24

32

40

48

56

64

72

THRUST LOAD, kips .

Test #83 -- Lateral Load -- Klondike (1330) -- 623 psi preload

Test #83 -- Thrust Load -- Klondike (1330) -- 623 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

10

20

30

40

50

60

70

80

THRUST LOAD, kips .

Test #85 -- Lateral Load -- Klondike (1330) -- 763 psi preload

Test #85 -- Thrust Load -- Klondike (1330) -- 763 psi preload

0

50

100

150

200

250

300

350

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs ..

0

2

4

6

8

10

12

14

THRUST LOAD, kips

Test #89 -- Lateral Load -- Klondike (1330) -- 43 psi preload

Test #89 -- Thurst Load -- Klondike (1330) -- 43 psi preload

Photo 

Not 

Available

Photo 

Not 

Available
347

0

50

100

150

200

250

300

350

400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .. 

0.0

1.8

3.5

5.3

7.0

8.8

10.5

12.3

14.0

THRUST LOAD, kips .

Test #90 -- Lateral Load -- Klondike (1330) -- 42 psi preload

Test #90 -- Thrust Load -- Klondike (1330) -- 42 psi preload

0

100

200

300

400

500

600

700

800

900

0.0 0.5 1.0 1.5 2.0 2.5 3.0

VERTICAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0369

12

15

18

21

24

27

THRUST LOAD, kips .

Test #91 -- Lateral Load -- Klondike (1330) -- 143 psi preload

Test #91 -- Thrust Load -- Klondike (1330) -- 143 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

048

12

16

20

24

28

32

THRUST LOAD, kips .

Test #92 -- Lateral Load -- Klondike (1330) -- 150 psi preload

Test #92 -- Thrust Load -- Klondike (1330) -- 150 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

048

12

16

20

24

28

32

36

THRUST LOAD, kips .

Test #93 -- Lateral Load -- Klondike (1330) -- 128 psi preload

Test #93 -- Thrust Load -- Klondike (1330) -- 128 psi preload
348

0

200

400

600

800

1,000

1,200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

06

12

18

24

30

36

THRUST LOAD, kips .

Test #94 -- Lateral Load -- Klondike (1330) -- 310 psi preload

Test #94 -- Thrust Load -- Klondike (1330) -- 310 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

0.0 0.5 1.0 1.5 2.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

048

12

16

20

24

28

32

THRUST LOAD, kips .

Test #95 -- Lateral Load -- Klondike (1330) -- 308 psi preload

Test #95 -- Thrust Load -- Klondike (1330) -- 308 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0.0 0.5 1.0 1.5 2.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

048

12

16

20

24

28

32

36

40

THRUST LOAD, kips .

Test #96 -- Lateral Load -- Klondike (1330) -- 347 psi preload

Test #96 -- Thrust Load -- Klondike (1330) -- 347 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0.0 0.5 1.0 1.5 2.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

05

10

15

20

25

30

35

40

45

50

THRUST LOAD, kips .

Test #97 -- Lateral Load -- Klondike (1330) -- 394 psi preload

Test #97 -- Thrust Load -- Klondike (1330)-- 394 psi preload
349

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0.0 0.5 1.0 1.5 2.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

05

10

15

20

25

30

35

40

45

THRUST LOAD, kips .

Test #98 -- Lateral Load -- Klondike (1330) -- 398 psi preload

Test #98 -- Thrust Load -- Klondike (1330) -- 398 psi preload

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

10

20

30

40

50

THRUST LOAD, kips

Test #99 -- Lateral Load -- Klondike (1330) -- 442 psi preload

Test #99 -- Thrust Load -- Klondike (1330) -- 442 psi preload

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

12

24

36

48

60

THRUST LOAD, kips

Test #100 -- Lateral Load -- Klondike (1330) -- 592 psi preload

Test #100 -- Thrust Load -- Klondike (1330) -- 592 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0.0

7.5

15.0

22.5

30.0

37.5

45.0

52.5

60.0

67.5

THRUST LOAD, kips

Test #101 -- Lateral Load -- Klondike (1330) -- 645 psi preload

Test #101 -- Thrust Load -- Klondike (1330) -- 645 psi preload
350

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs ..

0.0

4.3

8.6

12.9

17.1

21.4

25.7

30.0

THRUST LOAD, kips .

Test #65 -- Lateral Load -- Klondike (1330) -- 17 psi preload

Test #65 -- Thrust Load -- Klondike (1330) -- 17 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs ..

05

10

15

20

25

30

35

THRUST LOAD, kips .

Test #66 -- Lateral Load -- Klondike (1330) -- 39 psi preload

Test #66 -- Thrust Load -- Klondike (1330) -- 39 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs ..

0.0

4.3

8.6

12.9

17.1

21.4

25.7

30.0

THRUST LOAD, kips .

Test #64 -- Lateral Load -- Klondike (1330) -- 41 psi preload

Test #64 -- Thrust Load -- Klondike (1330) -- 41 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

06

12

18

24

30

36

42

THRUST LOAD, kips .

Test #73 -- Lateral Load -- Klondike (1330) -- 85 psi preload

Test #73 -- Thrust Load -- Klondike (1330) -- 85 psi preload
351

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0.0

5.5

11.0

16.5

22.0

27.5

33.0

38.5

THRUST LOAD, kips

Test #39 -- Lateral Load -- Klondike (1330) -- 99 psi preload

Test #39 -- Thrust Load -- Klondike (1330) -- 99 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

05

10

15

20

25

30

THRUST LOAD, kips

Test #72 -- Lateral Load -- Klondike (1330) -- 104 psi preload

Test #72 -- Thrust Load -- Klondike (1330) -- 104 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

06

12

18

24

30

36

42

THRUST LOAD, kips

Test #40 -- Lateral Load -- Klondike (1330) -- 118 psi preload

Test #40 -- Thrust Load -- Klondike (1330) -- 118 psi preload

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

06

12

18

24

30

THRUST LOAD, kips .

Test #41 -- Lateral Load -- Klondike (1330) --121 psi preload

Test #41 -- Thrust Load -- Klondike (1330) -- 121 psi preload
352

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

5

10

15

20

25

30

35

40

45

THRUST LOAD, kips .

Test #67 -- Lateral Load -- Klondike (1330) -- 146 psi preload

Test #67 -- Thrust Load -- Klondike (1330) -- 146 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs ,

0.0

4.5

9.0

13.5

18.0

22.5

27.0

31.5

36.0

40.5

45.0

THRUST LOAD, kips ,

Test #47 -- Lateral Load -- Klondike (1330) -- 169 psi preload

Test #47 -- Thrust Load -- Klondike (1330) -- 169 psi preload

0

1,000

2,000

3,000

4,000

5,000

6,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

9

18

27

36

45

54

THRUST LOAD, kips .

Test #68 -- Lateral Load -- Klondike (1330) -- 174 psi preload

Test #68 -- Thrust Load -- Klondike (1330) -- 174 psi preload
353

0

1,000

2,000

3,000

4,000

5,000

6,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

9

18

27

36

45

54

THRUST LOAD, kips .

Test #69 -- Lateral Load -- Klondike (1330) -- 237 psi preload

Test #69 -- Thrust Load -- Klondike (1330) -- 237 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

5

10

15

20

25

30

35

40

THRUST LOAD, kips .

Test #70 -- Lateral Load -- Klondike (1330) -- 254 psi preload

Test #70 -- Thrust Load -- Klondike (1330) -- 254 psi preload

0

1,000

2,000

3,000

4,000

5,000

6,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0

10

20

30

40

50

60

THRUST LOAD, kips .

Test #71 -- Lateral Load -- Klondike (1330) -- 279 psi preload

Test #71 -- Thrust Load -- Klondike (1330) -- 279 psi preload
354

0

100

200

300

400

500

600

700

800

900

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

-2

0

2

4

6

8

10

12

14

16

THRUST LOAD, kips

Test #17 -- Lateral Load -- Klondike (1780 psi) -- 0 psi preload

Test #17 -- Thrust Load -- Klondike (1780 psi) -- 0 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

8

16

24

32

40

48

THRUST LOAD, kips

Test #18 -- Lateral Load -- Klondike (1780 psi) -- 228 psi preload

Test #18 -- Thrust Load -- Klondike (1780 psi) -- 228 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

6.5

13.0

19.5

26.0

32.5

39.0

45.5

52.0

THRUST LOAD, kips

Test #23 -- Lateral Load -- Klondike (1780 psi) -- 287 psi preload

Test #23 -- Thrust Load -- Klondike (1780 psi) -- 287 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

6

12

18

24

30

36

42

THRUST LOAD, kips

Test #24 -- Lateral Load -- Klondike (1780 psi) -- 290 psi preload

Test #24 -- Thrust Load -- Klondike (1780 psi) -- 290 psi preload

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available
355

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

8

16

24

32

40

THRUST LOAD, kips

Test #25 -- Lateral Load -- Klondike (1780 psi) -- 356 psi preload

Test #25 -- Thrust Load -- Klondike (1780 psi) -- 356 psi preload

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

7

14

21

28

35

THRUST LOAD, kips

Test #21 -- Lateral Load -- Klondike (1780 psi) -- 23 psi preload

Test #21 -- Thrust Load -- Klondike (1780 psi) -- 23 psi preload

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

10

20

30

40

50

60

70

80

90

THRUST LOAD, kips

Test #20 -- Lateral Load -- Klondike (1780 psi) -- 201 psi preload

Test #20 -- Thrust Load -- Klondike (1780 psi) --201 psi preload

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

11

22

33

44

55

66

77

88

99

THRUST LOAD, kips

Test #19 -- Lateral Load -- Klondike (1780 psi) -- 210 psi preload

Test #19 -- Thrust Load -- Klondike (1780 psi) --210 psi preload

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available
356

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

06

12

18

24

30

36

42

THRUST LOAD, kips

Test #151 -- Lateral Load -- Klondike (1727) -- 77 psi preload

Test #151 -- Thrust Load -- Klondike (1727) -- 77 psi preload

0

1,000

2,000

3,000

4,000

5,000

6,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

0.0

8.3

16.7

25.0

33.3

41.7

50.0

THRUST LOAD, kips .

Test #152 -- Lateral Load -- Klondike (1727) -- 43 psi preload

Test #152 -- Thrust Load -- Klondike (1727) -- 43 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

06

12

18

24

30

36

42

THRUST LOAD, kips

Test #153 -- Lateral Load -- Klondike (1727) -- 50 psi preload

Test #153 -- Thrust Load -- Klondike (1727) -- 50 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

05

10

15

20

25

30

35

40

45

50

AXIAL LOAD, kips .

Test #154 -- Lateral Load -- Klondike (1727) -- 66 psi preload

Test #154 -- Thrust Load -- Klondike (1727) -- 66 psi preload
357

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

06

12

18

24

30

36

42

48

THRUST LOAD, kips

Test #155 -- Lateral Load -- Klondike (1727) -- 63 psi preload

Test #155 -- Thrust Load -- Klondike (1727) -- 63 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs .

06

12

18

24

30

36

42

48

54

60

THRUST LOAD, kips .

Test #157 -- Lateral Load -- Klondike (1727) -- 77 psi preload

Test #157 -- Thrust Load -- Klondike (1727) -- 77 psi preload

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

09

18

27

36

45

THRUST LOAD, kips

Test # 200 -- Lateral Load -- Klondike (1727) -- 41 psi preload

Test # 200-- Thrust Load -- Klondike (1727) -- 41 psi preload

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

09

18

27

36

45

THRUST LOAD, kips

Test # 202 -- Lateral Load -- Klondike (1727) -- 87 psi preload

Test # 202-- Thrust Load -- Klondike (1727) -- 87 psi preload
358

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

08

16

24

32

40

THRUST LOAD, kips

Test #158 -- Lateral Load -- Klondike (1727) -- 65 psi preload

Test #158 -- Thrust Load -- Klondike (1727) -- 65 psi preload

0

200

400

600

800

1,000

1,200

1,400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

048

12

16

20

24

28

THRUST LOAD, kips

Test #159 -- Lateral Load -- Klondike (1727) -- 69 psi preload

Test #159 -- Thrust Load -- Klondike (1727) -- 69 psi preload

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

08

16

24

32

40

THRUST LOAD, kips

Test #161 -- Lateral Load -- Klondike (1727) -- 67 psi preload

Test #161 -- Thrust Load -- Klondike (1727) -- 67 psi preload

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

05

10

15

20

25

30

35

40

45

THRUST LOAD, kips

Test #162 -- Lateral Load -- Klondike (1727) -- 59 psi preload

Test #162 -- Thrust Load -- Klondike (1727) -- 59 psi preload
359

0

200

400

600

800

1,000

1,200

1,400

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

05

10

15

20

25

30

35

THRUST LOAD, kips

Test # 199 -- Lateral Load -- Klondike (1727) -- 89 psi preload

Test # 199-- Thrust Load -- Klondike (1727) -- 89 psi preload 

0

200

400

600

800

1,000

1,200

1,400

1,600

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

05

10

15

20

25

30

35

40

THRUST LOAD, kips

Test # 203 -- Lateral Load -- Klondike (1727) -- 107 psi preload

Test # 203-- Thrust Load -- Klondike (1727) -- 107 psi preload 

0

100

200

300

400

500

600

700

800

900

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0369

12

15

18

21

24

27

THRUST LOAD, kips

Test # 198 -- Lateral Load -- Klondike (1727) -- 68 psi preload

Test # 198-- Thrust Load -- Klondike (1727) -- 68 psi preload 

0

200

400

600

800

1,000

1,200

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

05

10

15

20

25

30

THRUST LOAD, kips

Test # 204 -- Lateral Load -- Klondike (1727) -- 73 psi preload

Test # 204-- Thrust Load -- Klondike (1727) -- 73 psi preload 
360

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

5

10

15

20

25

30

35

40

THRUST LOAD, kips 

Test #297 -- Lateral Load -- Peerless Backsavers -- 3 psi preload

Test #297-- Thrust Load -- Peerless Backsavers -- 3 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

6

12

18

24

30

36

42

THRUST LOAD, kips 

Test #298 -- Lateral Load -- Peerless Backsavers -- 10 psi preload

Test #298-- Thrust Load -- Peerless Backsavers -- 10 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

5

10

15

20

25

30

35

40

THRUST LOAD, kips 

Test #295 -- Lateral Load -- Peerless Backsavers -- 16 psi preload

Test #295-- Thrust Load -- Peerless Backsavers -- 16 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

4.5

9.0

13.5

18.0

22.5

27.0

31.5

36.0

40.5

45.0

THRUST LOAD, kips 

Test #296 -- Lateral Load -- Peerless Backsavers-- 19 psi preload

Test #296-- Thrust Load -- Peerless Backsavers -- 19 psi preload

Photo 

Not 

Available

PEERLESS BACKSAVER 
361

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

05

10

15

20

25

30

35

40

45

THRUST LOAD, kips 

Test #292 -- Lateral Load -- Peerless Backsavers -- 21 psi preload

Test #292-- Thrust Load -- Peerless Backsavers -- 21 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

05

10

15

20

25

30

35

40

THRUST LOAD, kips 

Test #293 -- Lateral Load -- Peerless Backsavers -- 50 psi preload

Test #293-- Thrust Load -- Peerless Backsavers -- 50 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

05

10

15

20

25

30

35

40

45

50

THRUST LOAD, kips 

Test #301 -- Lateral Load -- Peerless Backsavers -- 100 psi preload

Test #297-- Thrust Load -- Peerless Backsavers -- 100 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

05

10

15

20

25

30

35

40

THRUST LOAD, kips 

Test #294 -- Lateral Load -- Peerless Backsavers -- 104 psi preload

Test #294-- Thrust Load -- Peerless Backsavers -- 104 psi preload
362

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

05

10

15

20

25

30

35

40

45

THRUST LOAD, kips 

Test #299 -- Lateral Load -- Peerless Backsavers -- 80 psi preload

Test #299-- Thrust Load -- Peerless Backsavers -- 80 psi preload

0

1,000

2,000

3,000

4,000

5,000

6,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

09

18

27

36

45

54

THRUST LOAD, kips 

Test #300 -- Lateral Load -- Peerless Backsavers -- 165 psi preload

Test #300-- Thrust Load -- Peerless Backsavers -- 165 psi preload

0

100

200

300

400

500

600

700

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0369

12

15

18

21

THRUST LOAD, kips 

Test #261 -- Lateral Load -- Peerless Backsavers -- 12 psi preload

Test #261-- Thrust Load -- Peerless Backsavers -- 12 psi preload

0

200

400

600

800

1,000

1,200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

048

12

16

20

24

THRUST LOAD, kips 

Test #260 -- Lateral Load -- Peerless Backsavers -- 25 psi preload

Test #260-- Thrust Load -- Peerless Backsavers -- 25 psi preload
363

0

200

400

600

800

1,000

1,200

1,400

1,600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

05

10

15

20

25

30

35

40

THRUST LOAD, kips 

Test #262 -- Lateral Load -- Peerless Backsavers -- 78 psi preload

Test #262-- Thrust Load -- Peerless Backsavers -- 78 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

048

12

16

20

24

28

32

36

THRUST LOAD, kips 

Test #266 -- Lateral Load -- Peerless Backsavers -- 94 psi preload

Test #266 -- Thrust Load -- Peerless Backsavers -- 94 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

07

14

21

28

35

42

THRUST LOAD, kips 

Test #289 -- Lateral Load -- Peerless Backsavers -- 121 psi preload

Test #289 -- Thrust Load -- Peerless Backsavers -- 121 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

08

16

24

32

40

48

THRUST LOAD, kips 

Test #291 -- Lateral Load -- Peerless Backsavers -- 143 psi preload

Test #291 -- Thrust Load -- Peerless Backsavers -- 143 psi preload
364

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

07

14

21

28

35

42

49

THRUST LOAD, kips 

Test #264 -- Lateral Load -- Peerless Backsavers -- 178 psi preload

Test #264-- Thrust Load -- Peerless Backsavers -- 178 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0369

12

15

18

21

24

27

30

THRUST LOAD, kips 

Test #265 -- Lateral Load -- Peerless Backsavers -- 182 psi preload

Test #265-- Thrust Load -- Peerless Backsavers -- 182 psi preload

0

400

800

1,200

1,600

2,000

2,400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

06

12

18

24

30

36

THRUST LOAD, kips 

Test #290 -- Lateral Load -- Peerless Backsavers -- 210 psi preload

Test #290 -- Thrust Load -- Peerless Backsavers -- 210 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

048

12

16

20

24

28

32

36

40

THRUST LOAD, kips 

Test #267 -- Lateral Load -- Peerless Backsavers -- 265 psi preload

Test #267-- Thrust Load -- Peerless Backsavers -- 265 psi preload
365

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

9

18

27

36

45

THRUST LOAD, kips 

Test #288 -- Lateral Load -- Peerless Backsavers -- 362 psi preload

Test #288 -- Thrust Load -- Peerless Backsavers -- 362 psi preload

0

50

100

150

200

250

300

350

400

450

500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

1

2

3

4

5

6

7

8

9

10

THRUST LOAD, kips

Test #282 -- Lateral Load -- Peerless Backsavers -- 28 psi preload

Test #282-- Thrust Load -- Peerless Backsavers -- 28 psi preload

0

100

200

300

400

500

600

700

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

0

3

6

9

12

15

18

21

THRUST LOAD, kips

Test #283 -- Lateral Load -- Peerless Backsavers -- 57 psi preload

Test #283-- Thrust Load -- Peerless Backsavers -- 57 psi preload

0

100

200

300

400

500

600

700

800

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

3

6

9

12

15

18

21

24

THRUST LOAD, kips

Test #284 -- Lateral Load -- Peerless Backsavers -- 132 psi preload

Test #284-- Thrust Load -- Peerless Backsavers -- 132 psi preload
366

0

200

400

600

800

1,000

1,200

1,400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

0

5

10

15

20

25

30

35

THRUST LOAD, kips

Test #285 -- Lateral Load -- Peerless Backsavers -- 183 psi preload

Test #285 -- Thrust Load -- Peerless Backsavers -- 183 psi preload

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

0

12

24

36

48

60

THRUST LOAD, kips

Test #286 -- Lateral Load -- Peerless Backsavers -- 239 psi preload

Test #286-- Thrust Load -- Peerless Backsavers -- 239 psi preload

0

200

400

600

800

1,000

1,200

1,400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

0

8

16

24

32

40

48

56

THRUST LOAD, kips

Test #287 -- Lateral Load -- Peerless Backsavers -- 447 psi preload

Test #287-- Thrust Load -- Peerless Backsavers -- 447 psi preload
367

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

6

12

18

24

30

36

42

THRUST LOAD, kips

Test #355 -- Lateral Load -- Peerless Low Strength Backsavers -- 72 psi preload

Test #355 -- Thrust Load -- Peerless Low Strength Backsavers -- 72 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

0

6

12

18

24

30

36

THRUST LOAD, kips

Test #356 -- Lateral Load -- Peerless Low Strength Backsavers -- 60 psi preload

Test #356 -- Thrust Load -- Peerless Low Strength Backsavers -- 60 psi preload

0

200

400

600

800

1,000

1,200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

4

8

12

16

20

24

THRUST LOAD, kips

Test #357 -- Lateral Load -- Peerless Low Strength Backsavers -- 45 psi preload

Test #357 -- Thrust Load -- Peerless Low Strength Backsavers -- 45 psi preload

0

200

400

600

800

1,000

1,200

1,400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

4

8

12

16

20

24

28

THRUST LOAD, kips

Test #358 -- Lateral Load -- Peerless Low Strength Backsavers -- 55 psi preload

Test #358 -- Thrust Load -- Peerless Low Strength Backsavers -- 55 psi preload
368

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

3

6

9

12

15

18

THRUST LOAD, kips

Test #359 -- Lateral Load -- Peerless Low Strength Backsavers -- 66 psi preload

Test #359 -- Thrust Load -- Peerless Low Strength Backsavers -- 66 psi preload

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

3

6

9

12

15

18

THRUST LOAD, kips

Test #358 -- Lateral Load -- Peerless Low Strength Backsavers -- 52 psi preload

Test #358 -- Thrust Load -- Peerless Low Strength Backsavers -- 52 psi preload
369

0

100

200

300

400

500

600

700

800

0.0 0.5 1.0 1.5 2.0 2.5 3.0

VERTICAL DISPLACEMENT, inches

LATERAL LOAD, lbs

-8

-4

0

4

8

12

16

20

24

THRUST LOAD, kips

Test #26 -- Lateral Load -- ACCOA Block -- 3 psi preload

Test #26 -- Thrust Load -- ACCOA Block -- 3 psi preload

0

100

200

300

400

500

600

700

800

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

2

4

6

8

10

12

14

16

THRUST LOAD, kips

Test #27 -- Lateral Load -- ACCOA Block -- 0 psi preload

Test #27 -- Thrust Load -- ACCOA Block -- 0 psi preload

0

100

200

300

400

500

600

700

800

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

3

6

9

12

15

18

21

24

THRUST LOAD, kips

Test #48 -- Lateral Load -- ACCOA Block -- 30 psi preload

Test #48 -- Thrust Load -- ACCOA Block -- 30 psi preload

0

100

200

300

400

500

600

700

800

900

1,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

5

10

15

20

25

THRUST LOAD, kips

Test #49 -- Lateral Load -- ACCOA Block -- 78 psi preload

Test #49 -- Thrust Load -- ACCOA Block -- 78 psi preload

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available

ACCOA BLOCK 
370

0

200

400

600

800

1,000

1,200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

4

8

12

16

20

24

THRUST LOAD, kips

Test #50 -- Lateral Load -- ACCOA Block -- 85 psi preload

Test #50 -- Thrust Load -- ACCOA Block -- 85 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

3

6

9

12

15

18

21

24

THRUST LOAD, kips

Test #28 -- Lateral Load -- ACCOA Block -- 120 psi preload

Test #28 -- Thrust Load -- ACCOA Block -- 120 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

VERTICAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

3

6

9

12

15

18

21

24

THRUST LOAD, kips

Test #32 -- Lateral Load -- ACCOA Block -- 139 psi preload

Test #32 -- Thrust Load -- ACCOA Block -- 139 psi preload

0

200

400

600

800

1,000

1,200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lb

0

4

8

12

16

20

24

THRUST LOAD, kips

Test #29 -- Lateral Load -- ACCOA Block -- 150 psi preload

Test #29 -- Thrust Load -- ACCOA Block -- 150 psi preload

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available
371

0

200

400

600

800

1,000

1,200

1,400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

VERTICAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

4

8

12

16

20

24

28

THRUST LOAD, kips

Test #33 -- Lateral Load -- ACCOA Block -- 157 psi preload

Test #33 -- Thrust Load -- ACCOA Block -- 157 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

8

16

24

32

40

48

56

64

THRUST LOAD, kips

Test #31 -- Lateral Load -- ACCOA Block -- 300 psi preload

Test #31 --Thrust Load -- ACCOA Block -- 300 psi preload

0

200

400

600

800

1,000

1,200

1,400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

8

16

24

32

40

48

56

THRUST LOAD, kips

Test #30 -- Lateral Load -- ACCOA Block -- 288 psi preload

Test #30 -- Thrust Load -- ACCOA Block -- 288 psi preload

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

6

12

18

24

30

THRUST LOAD, kips

Test #56 -- Lateral Load -- ACCOA Block -- 18 psi preload

Test #56 -- Thrust Load -- ACCOA Block -- 18 psi preload

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available
372

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

06

12

18

24

30

THRUST LOAD, kips

Test #55 -- Lateral Load -- ACCOA Block -- 20 psi preload

Test #55 -- Thrust Load -- ACCOA Block -- 20 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

05

10

15

20

25

THRUST LOAD, kips

Test #54 -- Lateral Load -- ACCOA Block -- 38 psi preload

Test #54 -- Axial Load -- ACCOA Block -- 38 psi preload

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

06

12

18

24

30

THRUST LOAD, kips

Test #53 -- Lateral Load -- ACCOA Block -- 40 psi preload

Test #53 -- Thrust Load -- ACCOA Block -- 40 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.00 0.50 1.00 1.50 2.00 2.50 3.00

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

05

10

15

20

25

30

35

THRUST LOAD, kips

Test #62 -- Lateral Load -- ACCOA Block -- 97 psi preload

Test #62 -- Thrust Load -- ACCOA Block -- 97 psi preload
373

0

500

1,000

1,500

2,000

2,500

3,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

6

12

18

24

30

36

THRUST LOAD, kips

Test #51 -- Lateral Load -- ACCOA Block -- 111 psi preload

Test #51 -- Thrust Load -- ACCOA Block -- 111 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

9

18

27

36

45

54

THRUST LOAD, kips

Test #58 -- Lateral Load -- ACCOA Block -- 238 psi preload

Test #58 -- Thrust Load -- ACCOA Block -- 238 psi preload
374

0

1,000

2,000

3,000

4,000

5,000

6,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

5

10

15

20

25

30

35

40

THRUST LOAD, kips

Test #239 -- Lateral Load -- Ytong -- 3 psi preload

Test #239-- Thrust Load -- Ytong -- 3 psi preload

0

1,000

2,000

3,000

4,000

5,000

6,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

0

5

10

15

20

25

30

35

THRUST LOAD, kips

Test #249 -- Lateral Load -- Ytong -- 7 psi preload

Test #249-- Thrust Load -- Ytong -- 7 psi preload

0

1,000

2,000

3,000

4,000

5,000

6,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

0

10

20

30

40

50

60

THRUST LOAD, kips

Test #243 -- Lateral Load -- Ytong -- 51 psi preload

Test #243-- Thrust Load -- Ytong -- 51 psi preload

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

0

10

20

30

40

50

60

THRUST LOAD, kips

Test #250 -- Lateral Load -- Ytong -- 58 psi preload

Test #250-- Thrust Load -- Ytong -- 58 psi preload

YTONG BLOCK 
375

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

10

20

30

40

50

60

THRUST LOAD, kips

Test #251 -- Lateral Load -- Ytong -- 94 psi preload

Test #251-- Thrust Load -- Ytong -- 94 psi preload

0

1,000

2,000

3,000

4,000

5,000

6,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

0

10

20

30

40

50

60

THRUST LOAD, kips

Test #241 -- Lateral Load -- Ytong -- 107 psi preload

Test #241-- Thrust Load -- Ytong -- 107 psi preload

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

10

20

30

40

50

60

THRUST LOAD, kips

Test #242 -- Lateral Load -- Ytong -- 145 psi preload

Test #242-- Thrust Load -- Ytong -- 145 psi preload

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

5

10

15

20

25

THRUST LOAD, kips

Test #234 -- Lateral Load -- Ytong -- 15 psi preload

Test #234-- Thrust Load -- Ytong -- 15 psi preload

Photo 

Not 

Available

Photo 

Not 

Available
376

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

06

12

18

24

30

36

42

THRUST LOAD, kips

Test #235 -- Lateral Load -- Ytong -- 53 psi preload

Test #235-- Thrust Load -- Ytong -- 53 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

06

12

18

24

30

36

42

48

54

THRUST LOAD, kips

Test #237 -- Lateral Load -- Ytong -- 109 psi preload

Test #237-- Thrust Load -- Ytong -- 109 psi preload

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

06

12

18

24

30

36

42

48

54

THRUST LOAD, kips

Test #238 -- Lateral Load -- Ytong -- 132 psi preload

Test #238-- Thrust Load -- Ytong -- 132 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

0.0 0.5 1.0 1.5 2.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0369

12

15

18

21

24

THRUST LOAD, kips

Test #245 -- Lateral Load -- Ytong -- 10 psi preload

Test #245-- Thrust Load -- Ytong -- 10 psi preload
377

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

07

14

21

28

35

THRUST LOAD, kips

Test #246 -- Lateral Load -- Ytong -- 38 psi preload

Test #246-- Thrust Load -- Ytong -- 38 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

048

12

16

20

24

28

32

36

40

THRUST LOAD, kips

Test #252 -- Lateral Load -- Ytong -- 69 psi preload

Test #252-- Thrust Load -- Ytong -- 69 psi preload

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

08

16

24

32

40

THRUST LOAD, kips

Test #247 -- Lateral Load -- Ytong -- 99 psi preload

Test #247-- Thrust Load -- Ytong -- 99 psi preload

0

500

1,000

1,500

2,000

2,500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

09

18

27

36

45

THRUST LOAD, kips

Test #248 -- Lateral Load -- Ytong -- 142 psi preload

Test #248-- Thrust Load -- Ytong -- 142 psi preload
378

0

200

400

600

800

1,000

1,200

1,400

1,600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

2.3

4.5

6.8

9.0

11.3

13.5

15.8

18.0

THRUST LOAD, kips

Test #147 -- Lateral Load -- Kingsway -- 65 psi preload

Test #147 -- Thrust Load -- Kingsway -- 65 psi preload

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

2

4

6

8

10

12

14

16

18

THRUST LOAD, kips

Test #148 -- Lateral Load -- Kingsway -- 54 psi preload

Test #148 -- Thrust Load -- Kingsway -- 54 psi preload

0

150

300

450

600

750

900

1,050

1,200

1,350

1,500

0.0 0.5 1.0 1.5 2.0 2.5

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

2

4

6

8

10

12

14

16

18

20

THRUST LOAD, kips

Test SD2 -- Lateral Load -- Kingsway -- 50 psi preload

Test SD2 -- Thrust Load -- Kingsway -- 50 psi preload

Photo 

Not 

Available

Photo 

Not 

Available

KINGSWAY BLOCK 
379

0

100

200

300

400

500

600

700

800

900

1,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

0

1.2

2.4

3.6

4.8

6

7.2

8.4

9.6

10.8

12

THRUST LOAD, kips

Test SD1 -- Lateral Load -- Kingsway -- 50 psi preload

Test SD1 -- Thrust Load -- Kingsway -- 50 psi preload

0

200

400

600

800

1,000

1,200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

3

6

9

12

15

18

THRUST LOAD, kips

Test #137 -- Lateral Load -- Kingsway -- 80 psi preload

Test #137 -- Thrust Load -- Kingsway -- 80 psi preload

0

200

400

600

800

1,000

1,200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

3

6

9

12

15

18

THRUST LOAD, kips

Test #138 -- Lateral Load -- Kingsway -- 66 psi preload

Test #138 -- Thrust Load -- Kingsway -- 66 psi preload

Photo 

Not 

Available

Photo 

Not 

Available
380

0

100

200

300

400

500

600

700

800

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

0

2

4

6

8

10

12

14

16

THRUST LOAD, kips

Test #139 -- Lateral Load -- Kingsway -- 89 psi preload

Test #139 -- Thrust Load -- Kingsway -- 89 psi preload

0

100

200

300

400

500

600

700

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

0.0

2.3

4.6

6.9

9.1

11.4

13.7

16.0

THRUST LOAD, kips

Test #135 -- Lateral Load -- Kingsway -- 45 psi preload

Test #135 -- Thrust Load -- Kingsway -- 45 psi preload

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

2.3

4.7

7.0

9.3

11.7

14.0

THRUST LOAD, kips

Test #136 -- Lateral Load -- Kingsway -- 64 psi preload

Test #136 -- Thrust Load -- Kingsway -- 64 psi preload
381

0

50

100

150

200

250

300

350

400

450

500

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

THRUST LOAD, kips

Test #221 -- Lateral Load -- Omega Block -- 2 psi preload

Test #221 -- Thrust Load -- Omega Block -- 2 psi preload

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

1

2

3

4

5

6

THRUST LOAD, kips

Test #220 -- Lateral Load -- Omega Block -- 5 psi preload

Test #220 -- Thrust Load -- Omega Block -- 5 psi preload

0

100

200

300

400

500

600

700

800

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

1

2

3

4

5

6

7

8

THRUST LOAD, kips

Test #174 -- Lateral Load -- Omega Block -- 8 psi preload

Test #174 -- Thrust Load -- Omega Block -- 8 psi preload

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

0

1

2

3

4

5

6

THRUST LOAD, kips

Test #169 -- Lateral Load -- Omega Block -- 8 psi preload

Test #169 -- Thrust Load -- Omega Block -- 8 psi preload

OMEGA BLOCK 
382

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

1.5

3.0

4.5

6.0

7.5

9.0

THRUST LOAD, kips

Test #143 -- Lateral Load -- Omega Block -- 25 psi preload

Test #143 -- Thrust Load -- Omega Block -- 25 psi preload

0

100

200

300

400

500

600

700

800

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

012345678

THRUST LOAD, kips

Test #170 -- Lateral Load -- Omega Block -- 15 psi preload

Test #170 -- Thrust Load -- Omega Block -- 15 psi preload

0

100

200

300

400

500

600

700

800

900

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0123456789

THRUST LOAD, kips

Test #175 -- Lateral Load -- Omega Block -- 27 psi preload

Test #175 -- Thrust Load -- Omega Block -- 27 psi preload

0

100

200

300

400

500

600

700

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

01234567

THRUST LOAD, kips

Test #144 -- Lateral Load -- Omega Block -- 28 psi preload

Test #144 -- Thrust Load -- Omega Block -- 28 psi preload
383

0

20

40

60

80

100

120

140

160

180

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

THRUST LOAD, kips

Test #172 -- Lateral Load -- Omega Block -- 1 psi preload

Test #172 -- Thrust Load -- Omega Block -- 1 psi preload

0

20

40

60

80

100

120

140

160

180

200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

THRUST LOAD, kips

Test #222 -- Lateral Load -- Omega Block -- 6 psi preload

Test #222 -- Thrust Load -- Omega Block -- 6 psi preload

0

50

100

150

200

250

300

350

400

450

500

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

0.8

1.6

2.4

3.2

4.0

4.8

5.6

6.4

7.2

8.0

THRUST LOAD, kips

Test #173 -- Lateral Load -- Omega Block -- 8 psi preload

Test #173 -- Thrust Load -- Omega Block -- 8 psi preload

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0123456

THRUST LOAD, kips

Test #168 -- Lateral Load -- Omega Block -- 14 psi preload

Test #168 -- Thrust Load -- Omega Block -- 14 psi preload
384

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

1.5

3.0

4.5

6.0

7.5

9.0

THRUST LOAD, kips

Test #167 -- Lateral Load -- Omega Block -- 20 psi preload

Test #167 -- Thrust Load -- Omega Block -- 20 psi preload

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

1.5

3.0

4.5

6.0

7.5

9.0

THRUST LOAD, kips

Test #141 -- Lateral Load -- Omega Block -- 23 psi preload

Test #141 -- Thrust Load -- Omega Block -- 23 psi preload

0

50

100

150

200

250

300

350

400

450

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0123456789

THRUST LOAD, kips

Test #142 -- Lateral Load -- Omega Block -- 27 psi preload

Test #142 -- Thrust Load -- Omega Block -- 27 psi preload

0

10

20

30

40

50

60

70

80

90

100

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

THRUST LOAD, kips

Test #223 -- Lateral Load -- Omega Block -- 8 psi preload

Test #223 -- Thrust Load -- Omega Block -- 8 psi preload
385

0

10

20

30

40

50

60

70

80

90

100

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

THRUST LOAD, kips

Test #165 -- Lateral Load -- Omega Block -- 12 psi preload

Test #165 -- Thrust Load -- Omega Block -- 12 psi preload

0

10

20

30

40

50

60

70

80

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

-2.00

-1.25

-0.50

0.25

1.00

1.75

2.50

3.25

4.00

THRUST LOAD, kips

Test #176 -- Lateral Load -- Omega Block -- 14 psi preload

Test #176 -- Thrust Load -- Omega Block -- 14 psi preload

0

20

40

60

80

100

120

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

THRUST LOAD, kips

Test #177 -- Lateral Load -- Omega Block -- 15 psi preload

Test #177 -- Thrust Load -- Omega Block -- 15 psi preload

0

20

40

60

80

100

120

140

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

01234567

THRUST LOAD, kips

Test #145 -- Lateral Load -- Omega Block -- 20 psi preload

Test #145 -- Thrust Load -- Omega Block -- 20 psi preload
386

0

20

40

60

80

100

120

140

160

180

200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

THRUST LOAD, kips

Test #166 -- Lateral Load -- Omega Block -- 21 psi preload

Test #166 -- Thrust Load -- Omega Block -- 21 psi preload

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

1.5

3.0

4.5

6.0

7.5

9.0

THRUST LOAD, kips

Test #146 -- Lateral Load -- Omega Block -- 27 psi preload

Test #146 -- Thrust Load -- Omega Block -- 27 psi preload
387

0

50

100

150

200

250

300

350

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

1

2

3

4

5

6

7

THRUST LOAD, kips

Test #216 -- Lateral Load -- Peerless Super Block -- 7 psi preload

Test #216 -- Thrust Load -- Peerless Super Block -- 7 psi preload

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

2

4

6

8

10

12

THRUST LOAD, kips

Test #218 -- Lateral Load -- Peerless Super Block -- 16 psi preload

Test #218 -- Thrust Load -- Peerless Super Block -- 16 psi preload

0

50

100

150

200

250

300

350

400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

1

2

3

4

5

6

7

8

THRUST LOAD, kips

Test #217 -- Lateral Load -- Peerless Super Block -- 17 psi preload

Test #217 -- Thrust Load -- Peerless Super Block -- 17 psi preload

0

50

100

150

200

250

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

2

4

6

8

10

THRUST LOAD, kips

Test #219 -- Lateral Load -- Peerless Super Block -- 22 psi preload

Test #219 -- Thrust Load -- Peerless Super Block -- 21 psi preload

PEERLESS SUPER BLOCK 
388

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

0

2

4

6

8

10

12

THRUST LOAD, kips

Test #208 -- Lateral Load -- Peerless Super Block -- 54 psi preload

Test #208 -- Thrust Load -- Peerless Super Block -- 54 psi preload

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

2

4

6

8

10

12

14

THRUST LOAD, kips

Test #209 -- Lateral Load -- Peerless Super Block -- 56 psi preload

Test #209 -- Thrust Load -- Peerless Super Block -- 56 psi preload

0

20

40

60

80

100

120

140

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

1

2

3

4

5

6

7

THRUST LOAD, kips

Test #214 -- Lateral Load -- Peerless Super Block -- 12 psi preload

Test #214 -- Thrust Load -- Peerless Super Block -- 12 psi preload

0

50

100

150

200

250

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

2

4

6

8

10

THRUST LOAD, kips

Test #195 -- Lateral Load -- Peerless Super Block -- 29 psi preload

Test #195 -- Thrust Load -- Peerless Super Block -- 29 psi preload

Photo 

Not 

Available

Photo 

Not 

Available
389

0

20

40

60

80

100

120

140

160

180

200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs 

-2.00

-0.75

0.50

1.75

3.00

4.25

5.50

6.75

8.00

9.25

10.50

THRUST LOAD, kips

Test #190 -- Lateral Load -- Peerless Super Block -- 37 psi preload

Test #190 -- Thrust Load -- Peerless Super Block -- 37 psi preload

0

20

40

60

80

100

120

140

160

180

200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

1.5

3.0

4.5

6.0

7.5

9.0

10.5

12.0

13.5

15.0

THRUST LOAD, kips

Test #191 -- Lateral Load -- Peerless Super Block -- 38 psi preload

Test #191 -- Thrust Load -- Peerless Super Block -- 38 psi preload

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

2

4

6

8

10

12

THRUST LOAD, kips

Test #211 -- Lateral Load -- Peerless Super Block -- 41 psi preload

Test #211 -- Thrust Load -- Peerless Super Block -- 41 psi preload

0

50

100

150

200

250

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

2

4

6

8

10

THRUST LOAD, kips

Test #197 -- Lateral Load -- Peerless Super Block -- 42 psi preload

Test #197 -- Thrust Load -- Peerless Super Block -- 42 psi preload
390

0

20

40

60

80

100

120

140

160

180

200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

2

4

6

8

10

12

14

16

18

20

THRUST LOAD, kips

Test #193 -- Lateral Load -- Peerless Super Block -- 42 psi preload

Test #193 -- Thrust Load -- Peerless Super Block -- 42 psi preload

0

20

40

60

80

100

120

140

160

180

200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

1

2

3

4

5

6

7

8

9

10

THRUST LOAD, kips

Test #192 -- Lateral Load -- Peerless Super Block -- 45 psi preload

Test #192 --Thrust Load -- Peerless Super Block -- 45 psi preload

0

50

100

150

200

250

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

2

4

6

8

10

THRUST LOAD, kips

Test #210 --- Lateral Load -- Peerless Super Block -- 56 psi preload

Test #210 -- Thrust Load -- Peerless Super Block -- 56 psi preload

0

50

100

150

200

250

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

2

4

6

8

10

THRUST LOAD, kips

Test #196 -- Lateral Load -- Peerless Super Block -- 60 psi preload

Test #196 -- Thrust Load -- Peerless Super Block -- 60 psi preload

Photo 

Not 

Available

Photo 

Not 

Available
391

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

3

6

9

12

15

18

THRUST LOAD, kips

Test #194 -- Lateral Load -- Peerless Super Block -- 63 psi preload

Test #194 -- Thrust Load -- Peerless Super Block -- 63 psi preload

0

5

10

15

20

25

30

35

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

1

2

3

4

5

6

7

THRUST LOAD, kips

Test #231 -- Lateral Load -- Peerless Super Block -- 4 psi preload

Test #231 -- Thrust Load --Peerless Super Block -- 4 psi preload

0

10

20

30

40

50

60

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

1

2

3

4

5

6

THRUST LOAD, kips

Test #225 -- Lateral Load -- Peerless Super Block --14 psi preload

Test #225 -- Thrust Load --Peerless Super Block -- 14 psi preload

-5

0

5

10

15

20

25

30

35

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

1

2

3

4

5

6

7

8

THRUST LOAD, kips

Test #230 -- Lateral Load -- Peerless Super Block -- 22 psi preload

Test #230 -- Thrust Load --Peerless Super Block -- 22 psi preload

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available
392

0

10

20

30

40

50

60

70

80

90

100

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

0.7

1.4

2.1

2.8

3.5

4.2

4.9

5.6

6.3

7

THRUST LOAD, kips

Test #205 -- Lateral Load -- Peerless Super Block -- 33 psi preload

Test #205 -- Thrust Load --Peerless Super Block -- 33 psi preload

0

20

40

60

80

100

120

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

1

2

3

4

5

6

THRUST LOAD, kips

Test #229 -- Lateral Load -- Peerless Super Block -- 34 psi preload

Test #229 -- Thrust Load --Peerless Super Block -- 34 psi preload

0

20

40

60

80

100

120

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

2

4

6

8

10

12

THRUST LOAD, kips

Test #232 -- Lateral Load -- Peerless Super Block -- 54 psi preload

Test #232 -- Thrust Load --Peerless Super Block -- 54 psi preload

0

20

40

60

80

100

120

140

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

2

4

6

8

10

12

14

THRUST LOAD, kips

Test #233 -- Lateral Load -- Peerless Super Block -- 53 psi preload

Test #233 -- Thrust Load --Peerless Super Block -- 53 psi preload

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available

Photo 

Not 

Available
393

0

10

20

30

40

50

60

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

1.5

3

4.5

6

7.5

9

THRUST LOAD, kips

Test #206 -- Lateral Load -- Peerless Super Block -- 56 psi preload

Test #206 --Thrust Load -- Peerless Super Block -- 56 psi preload

0

10

20

30

40

50

60

70

80

90

100

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

THRUST LOAD, kips

Test #302 -- Lateral Load -- Peerless Super Block (small) -- 5 psi preload

Test #302 -- Thrust Load -- Peerless Super Block (small) -- 5 psi preload

0

20

40

60

80

100

120

140

160

180

200

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

1

2

3

4

5

6

7

8

9

10

THRUST LOAD, kips

Test #303 -- Lateral Load -- Peerless Super Block (small) -- 20 psi preload

Test #303 -- Thrust Load -- Peerless Super Block (small) -- 20 psi preload

0

50

100

150

200

250

300

350

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

3

6

9

12

15

18

21

THRUST LOAD, kips

Test #304 -- Lateral Load -- Peerless Super Block (small) -- 30 psi preload

Test #304 -- Thrust Load -- Peerless Super Block (small) -- 30 psi preload
394

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

3

6

9

12

15

18

THRUST LOAD, kips

Test #305 -- Lateral Load -- Peerless Super Block (small) -- 57 psi preload

Test #305 -- Thrust Load -- Peerless Super Block (small) -- 57 psi preload

0

100

200

300

400

500

600

0.0 0.2 0.4 0.6 0.8 1.0 1.2

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

5

10

15

20

25

30

THRUST LOAD, kips

Test #307 -- Lateral Load -- Peerless Super Block (small) -- 80 psi preload

Test #307 -- Thrust Load -- Peerless Super Block (small) -- 80 psi preload

0

100

200

300

400

500

600

700

0.0 0.5 1.0 1.5 2.0 2.5 3.0

LATERAL DISPLACEMENT, inches

LATERAL LOAD, lbs

0

4

8

12

16

20

24

28

THRUST LOAD, kips

Test #308 -- Lateral Load -- Peerless Super Block (small) -- 89 psi preload

Test #308 -- Thrust Load -- Peerless Super Block (small) -- 89 psi preload

Photo 

Not 

Available
395

APPENDIX C: MRS TABULAR HALF-WALL TEST DATA 
396

KLONDIKE BLOCK 

Klondike 1330 102 30 51 39.13 1.62 3559 1.02 31.54

Klondike 1330 110 30 68 40.29 1.15 3855 1.01 36.77

Klondike 1330 104 30 188 36.35 1.46 3929 0.71 30.44

Klondike 1330 105 30 160 50.34 1.51 4818 0.90 44.54

Klondike 1330 109 30 155 35.15 0.927 4090 0.74 34.60

Klondike 1330 111 30 141 39.49 0.937 4059 0.64 35.63

Klondike 1330 106 30 295 49.42 0.654 5506 0.53 48.34

Klondike 1330 107 30 326 51.09 0.714 5151 0.59 49.27

Klondike 1330 108 30 280 43.66 0.837 4459 0.63 41.04

Klondike 1330 112 30 385 45.45 0.722 4368 0.60 43.41

Klondike 1330 114 30 428 51.00 0.621 5150 0.48 45.93

Klondike 1330 115 30 428 56.57 0.666 5148 0.47 52.18

Klondike 1330 118 30 471 50.48 0.583 5675 0.42 48.63

Klondike 1330 119 30 521 50.10 0.518 4578 0.41 49.17

Klondike 1330 113 30 567 54.83 0.363 5625 0.35 54.10

Klondike 1330 116 30 600 63.71 0.574 6882 0.49 61.24

Klondike 1330 121 30 599 68.97 0.458 6830 0.41 66.99

Klondike 1330 60 45.75 28 22.80 2.99 1120 2.05 20.48

Klondike 1330 59 45.75 43 25.08 2.6 1032 1.88 19.23

Klondike 1330 46 45.75 85 29.38 2.41 1296 1.92 22.79

Klondike 1330 45 45.75 90 22.40 2.94 978 2.38 19.30

Klondike 1330 34 45.75 109 25.24 2.83 1246 2.10 22.11

Klondike 1330 36 45.75 122 32.40 2.26 1597 1.15 25.33

Klondike 1330 35 45.75 139 30.47 1.59 1795 1.27 28.87

Klondike 1330 37 45.75 202 33.24 1.97 1992 0.97 32.01

Klondike 1330 63 45.75 252 36.16 1.18 2268 0.46 29.52

Klondike 1330 61 45.75 313 37.01 0.909 2359 0.33 34.02

Klondike 1330 74 45.75 373 40.35 0.909 3166 0.52 37.76

Klondike 1330 75 45.75 390 41.87 0.731 3617 0.41 40.59

Klondike 1330 76 45.75 474 45.76 0.418 3365 0.44 43.47

Klondike 1330 77 45.75 471 57.76 0.984 3831 0.72 52.38

Klondike 1330 78 45.75 577 57.87 0.005 2499 0.44 45.54

Klondike 1330 79 45.75 534 49.17 0.017 2779 0.56 43.48

Klondike 1330 81 45.75 568 52.05 0.072 3358 0.71 47.02

Klondike 1330 82 45.75 618 59.35 0.647 3922 0.65 59.35

Klondike 1330 83 45.75 623 58.36 0.563 3960 0.45 56.30

Klondike 1330 85 45.75 763 69.46 0.044 3776 0.45 61.08

Klondike 1330 89 60 43 12.70 3.02 320 1.90 8.02

Klondike 1330 90 60 42 13.06 3.05 341 2.10 8.91

Klondike 1330 91 60 143 20.14 2.49 781 1.25 14.78

Klondike 1330 92 60 150 29.79 1.86 1507 1.55 27.51

Klondike 1330 93 60 128 36.42 2.78 1601 1.89 29.71

Klondike 1330 94 60 310 29.90 1.086 1091 0.36 26.00

Klondike 1330 95 60 308 31.57 0.398 1415 0.39 30.09

Klondike 1330 96 60 347 38.60 0.617 1871 0.46 35.66

Klondike 1330 97 60 394 40.89 0.801 1821 0.46 37.68

Klondike 1330 98 60 398 39.08 0.091 1618 0.26 37.25

Klondike 1330 99 60 442 41.23 0.13 1946 0.26 38.64

Klondike 1330 100 60 592 54.73 0.03 2239 0.65 50.59

Klondike 1330 101 60 645 56.29 0.019 1698 0.52 47.16

Thrust Load at 

Peak Horz 

Load (kips)

Displ at 

Peak 

Thrust 

Force (in)

Peak 

Horz. 

Load 

(lbs)

Peak 

Thrust 

Force 

(kips)

Displ at 

Peak Horz. 

Load (in)

Block Type Test No.

Half Wall 

Height 

(in)

Preload 

(psi)
397

Klondike 1330 65 45 17 27.54 1.46 3327 1.09 26.71

Klondike 1330 66 45 39 31.33 1.53 3154 1.32 29.11

Klondike 1330 64 45 41 27.78 0.969 2944 0.87 27.14

Klondike 1330 73 45 85 34.78 1.06 3329 0.91 31.99

Klondike 1330 39 45 99 35.56 1.14 3028 0.98 32.34

Klondike 1330 72 45 104 25.86 0.645 2610 0.56 23.86

Klondike 1330 40 45 118 36.77 1.02 3285 0.98 35.35

Klondike 1330 41 45 121 26.67 1.16 2245 0.93 25.01

Klondike 1330 67 45 146 38.17 0.619 3964 0.59 36.70

Klondike 1330 47 45 169 40.84 0.719 4536 0.66 39.34

Klondike 1330 68 45 174 44.74 0.754 5002 0.70 44.12

Klondike 1330 69 45 237 46.59 0.632 5139 0.53 45.16

Klondike 1330 70 45 254 37.21 0.568 3611 0.56 35.37

Klondike 1330 71 45 279 50.68 0.43 5345 0.42 54.48

Thrust Load at 

Peak Horz 

Load (kips)

Displ at 

Peak 

Thrust 

Force (in)

Peak 

Horz. 

Load 

(lbs)

Peak 

Thrust 

Force 

(kips)

Displ at 

Peak Horz. 

Load (in)

Block Type Test No.

Half Wall 

Height 

(in)

Preload 

(psi)

Klondike 1780 17 45.75 0 14.27 2.23 761 2.25 14.20

Klondike 1780 18 45.75 228 42.55 2.15 2744 1.38 38.04

Klondike 1780 23 45 287 46.48 1.12 3595 0.81 42.88

Klondike 1780 24 45 290 36.98 1.20 2917 0.72 34.09

Klondike 1780 25 45 356 35.93 0.890 2350 0.70 35.05

Klondike 1780 21 46 23 29.67 2.61 2346 1.78 22.89

Klondike 1780 20 46 201 76.93 1.67 7826 1.69 76.66

Klondike 1780 19 46 210 92.87 1.36 8400 1.35 92.40

Klondike 1727 151 30 77 36.55 1.58 3300 1.39 34.07

Klondike 1727 152 30 43 45.60 1.3922 4892 0.90 39.93

Klondike 1727 153 30 50 39.35 2.204 3050 1.32 34.03

Klondike 1727 154 30 66 45.66 1.482 4585 1.32 44.18

Klondike 1727 155 30 63 42.64 2.504 3693 1.58 37.53

Klondike 1727 156 30 40 44.76 1.875 3811 1.55 38.68

Klondike 1727 157 30 77 47.87 1.887 4752 1.02 44.22

Klondike 1727 200 37.5 41 40.35 2.566 2294 1.35 31.15

Klondike 1727 202 37.5 87 38.63 2.021 3198 1.42 31.35

Klondike 1727 158 45 65 36.56 2.357 2104 1.43 27.51

Klondike 1727 159 45 69 26.71 2.388 1243 1.82 23.28

Klondike 1727 161 45 67 35.97 1.521 2218 1.35 34.30

Klondike 1727 162 45 59 39.03 2.076 2239 1.44 33.81

Klondike 1727 199 52.5 89 32.01 3.027 1169 1.96 23.18

Klondike 1727 203 52.5 107 37.01 3.325 1493 1.85 29.54

Klondike 1727 198 60 68 23.64 3.144 828 2.55 20.31

Klondike 1727 204 60 73 26.48 3.59 1036 2.22 20.05

Block Type Test No.

Half Wall 

Height 

(in)

Preload 

(psi)

Thrust Load at 

Peak Horz 

Load (kips)

Displ at 

Peak 

Thrust 

Force (in)

Peak 

Horz. 

Load 

(lbs)

Peak 

Thrust 

Force 

(kips)

Displ at 

Peak Horz. 

Load (in)
398

PEERLESS BACKSAVER 

Peerless Backsavers 297 30 3 37.66 1.89 3452 1.41 33.43

Peerless Backsavers 298 30 10 36.65 1.89 3213 1.50 32.51

Peerless Backsavers 295 30 16 35.99 1.68 3625 1.23 28.33

Peerless Backsavers 296 30 69 41.77 1.43 4611 1.33 40.39

Peerless Backsavers 292 30 21 39.68 1.80 4154 1.45 34.44

Peerless Backsavers 293 30 50 39.26 2.00 3549 1.20 29.19

Peerless Backsavers 301 30 100 44.57 1.34 4553 0.87 37.28

Peerless Backsavers 294 30 89 39.22 1.55 3554 1.07 35.28

Peerless Backsavers 299 30 80 39.42 1.42 4181 1.28 37.58

Peerless Backsavers 300 30 165 46.02 0.82 5227 0.73 44.48

Peerless Backsavers 261 45 12 15.77 2.98 650 2.51 13.64

Peerless Backsavers 260 45 25 21.09 2.94 1063 2.57 18.56

Peerless Backsavers 262 45 78 30.30 2.91 1487 1.96 24.35

Peerless Backsavers 266 45 94 32.13 2.26 1710 1.67 26.58

Peerless Backsavers 289 45 128 39.33 1.94 2499 1.29 30.99

Peerless Backsavers 291 45 188 43.52 1.89 2719 1.22 38.92

Peerless Backsavers 265 45 182 29.19 2.33 1832 1.45 25.37

Peerless Backsavers 290 45 210 33.78 1.89 2142 1.13 30.40

Peerless Backsavers 267 45 265 37.92 1.90 1823 1.15 32.73

Peerless Backsavers 288 45 362 39.24 1.24 2007 1.08 37.82

Peerless Backsavers 282 60 22 13.62 3.26 406 2.55 7.49

Peerless Backsavers 283 60 57 17.74 3.62 652 2.24 13.35

Peerless Backsavers 284 60 132 20.07 2.17 710 1.04 17.32

Peerless Backsavers 285 60 183 30.45 1.75 1205 1.31 28.35

Peerless Backsavers 286 60 344 48.41 2.46 2000 1.53 42.20

Peerless Backsavers 287 60 447 49.21 0.00 1291 1.35 35.78

Peerless Backsavers 

(partially cured) 355 30 72 36.44 1.21 3069 1.12 32.00

Peerless Back savers 

(partially cured) 356 30 60 32.69 1.33 2667 1.29 31.97

Peerless Backsavers 

(partially cured) 357 45 60 22.63 2.72 1038 1.36 16.22

Peerless Back savers 

(partially cured) 358 45 54 25.81 1.93 1209 1.40 21.84

Peerless Backsavers 

(partially cured) 359 60 66 14.16 3.21 269 1.49 8.00

Peerless Back savers 

(partially cured) 360 60 52 13.84 3.25 501 1.87 13.13

Block Type Test 

No.

Displ at 

Peak 

Thrust 

Force (in)

Thrust 

Load at 

Peak Horz 

Load (kips)

Half W all 

Height 

(in)

Preload 

(psi)

Peak 

Thrust 

Force 

(kips)

Peak 

Horz. 

Load 

(lbs)

Displ at 

Peak 

Horz. 

Load (in)
399

KLONDIKE HOLLOW CORE BLOCK 

Klondike Hollow Block 330 30 29 18.21 1.39 2160 1.39 18.21

Klondike Hollow Block 334 30 80 18.84 1.63 2561 1.50 20.00

Klondike Hollow Block 338 30 91 22.53 1.94 2583 1.50 22.53

Klondike Hollow Block 339 30 117 16.84 0.70 2494 0.72 16.66

Klondike Hollow Block 340 30 57 13.69 1.14 2235 1.16 16.20

Klondike Hollow Block 335 30 172 15.53 1.52 2071 1.00 14.47

Klondike Hollow Block 333 30 212 19.63 0.55 2300 0.50 18.43

Klondike Hollow Block 336 30 155 9.25 0.54 1515 0.54 9.25

Klondike Hollow Block 337 30 140 12.75 1.08 1559 1.08 12.75

Klondike Hollow Block 331 30 55 12.80 1.12 1716 1.13 12.46

Klondike Hollow Block 332 30 116 14.35 1.35 1886 1.35 14.35

Klondike Hollow Block 314 45 28 9.32 3.98 313 2.86 5.48

Klondike Hollow Block 321 45 22 7.09 3.81 364 2.50 5.31

Klondike Hollow Block 315 45 99 20.20 3.18 1145 1.87 15.85

Klondike Hollow Block 323 45 87 19.41 3.07 1106 2.36 16.82

Klondike Hollow Block 320 45 120 26.82 3.14 1535 2.12 22.77

Klondike Hollow Block 322 45 129 19.77 1.30 1713 1.32 18.89

Klondike Hollow Block 318 45 131 25.16 1.77 1805 1.66 24.33

Klondike Hollow Block 317 45 188 13.28 0.66 1309 0.60 12.97

Klondike Hollow Block 319 45 184 25.47 1.73 1859 1.73 25.47

Klondike Hollow Block 324 45 207 19.71 0.82 2005 0.81 19.70

Klondike Hollow Block 325 60 78 13.80 4.14 434 3.01 11.00

Klondike Hollow Block 327 60 80 15.34 4.64 543 2.75 12.00

Klondike Hollow Block 328 60 129 14.65 3.24 511 2.33 12.99

Klondike Hollow Block 329 60 212 17.18 2.05 715 1.54 15.78

Thrust 

Load at 

Peak Horz 

Load (kips)

Displ at 

Peak 

Thrust 

Force (in)

Displ at 

Peak Horz. 

Load (in)

Block Type Test 

No.

Peak 

Thrust 

Force 

(kips)

Half 

Wall 

Height 

(in)

Preload 

(psi)

Peak 

Horz. 

Load 

(lbs)

ACCOA BLOCK 

AAC 6 26 48 3 12.81 3.22 668 1.25 7.20

AAC 6 27 48 3 15.2 2.72 742 1.61 10.40

AAC 6 48 48 30 22.26 2.58 735 0.62 9.6

AAC 6 49 48 60 22.26 2.63 912 0.82 12.5

AAC 6 50 48 75 19.76 1.87 1052 0.78 17.01

AAC 6 32 48 132 23.35 0.63 1363 0.57 21.63

AAC 6 29 48 136 24.43 0.00 1104 0.35 20.00

AAC 6 33 48 136 26.27 0.00 1302 0.57 22.66

AAC 6 28 48 120 26.38 0.00 1429 0.39 24.20

AAC 6 31 48 293 46.85 0.00 1353 0.48 40.20

AAC 6 30 48 300 48.83 0.00 1283 0.22 38.00

AAC 8 56 48 18 25.73 2.68 1990 1.86 22.48

AAC 8 55 48 20 27.36 2.40 2210 1.65 24.59

AAC 8 54 48 38 23.06 2.03 1733 1.35 19.51

AAC 8 53 48 40 24.58 2.39 2115 1.22 19.87

AAC 8 51 48 111 31.79 0.79 2730 0.39 30.25

AAC 8 62 48 97 31.42 1.69 3179 0.58 28.02

AAC 8 58 48 238 46.88 0.13 2710 0.19 46.03

Block Type Test No.

Thrust Load 

at Peak Horz

Load (kips)

Displ at 

Peak 

Thrust 

Force (in)

Peak 

Thrust 

Force 

(kips)

Peak 

Horz. 

Load 

(lbs)

Displ at 

Peak Horz. 

Load (in)

Half W all 

Height 

(in)

Preload 

(psi)
400

YTONG BLOCK 

Ytong 239 31.5 3 37.97 1.47 5645 1.13 37.53

Ytong 249 31.5 7 33.27 1.62 4785 1.02 31.70

Ytong 243 31.5 51 47.93 1.58 5292 0.94 41.00

Ytong 250 31.5 58 52.40 1.10 5966 0.92 45.00

Ytong 251 31.5 94 52.60 0.99 5737 0.95 46.00

Ytong 241 31.5 107 48.54 1.29 5672 0.63 42.32

Ytong 242 31.5 145 50.79 0.56 6797 0.42 47.17

Ytong 234 47.25 15 19.51 1.04 2212 1.07 18.92

Ytong 235 47.25 53 37.25 1.26 3040 1.27 33.70

Ytong 237 47.25 109 47.61 1.93 4068 0.99 44.57

Ytong 238 47.25 132 46.02 1.73 4172 0.78 41.77

Ytong 245 63 10 20.00 2.08 1376 1.65 17.46

Ytong 246 63 38.5 29.62 2.25 2023 1.07 23.94

Ytong 252 63 69 30.86 1.69 1885 1.28 27.21

Ytong 247 63 99 33.47 2.45 2012 0.94 30.50

Ytong 248 63 142 39.63 1.17 2349 1.05 39.15

Block Type Test 

No.

Thrust Load at 

Peak Horz 

Load (kips)

Displ at 

Peak 

Thrust 

Force (in)

Peak 

Horz. 

Load (lbs)

Peak Thrust 

Force (kips)

Half Wall 

Height (in)

Displ at 

Peak Horz. 

Load (in)

Preload 

(psi)

KINGSWAY BLOCK 

Kingsway 147 33.5 65 15.75 1.26 1520 0.56 10.92

Kingsway 148 33.5 54 16.95 0.74 1675 0.74 12.93

Kingsway SD2 41.875 50 17.01 1.63 1161 1.13 14.51

Kingsway SD1 41.875 50 10.86 1.40 973 1.34 9.63

Kingsway 137 41.875 80 16.78 2.13 1126 1.22 13.83

Kingsway 138 41.875 66 17.11 1.61 1021 1.39 13.64

Kingsway 139 50.25 89 15.28 1.91 679 1.28 12.53

Kingsway 135 58.625 65 13.51 2.20 614 1.43 9.78

Kingsway 136 58.625 64 12.20 2.76 484 1.56 10.45

Block Type Test 

No.

Thrust Load at 

Peak Horz 

Load (kips)

Displ at 

Peak 

Thrust 

Force (in)

Peak 

Horz. 

Load (lbs)

Peak Thrust 

Force (kips)

Half Wall 

Height (in)

Displ at 

Peak Horz. 

Load (in)

Preload 

(psi)
401

OMEGA BLOCK 

Omega Block 143 32 9 8.53 2.47 504 1.70 3.00

Omega Block 144 32 28 6.41 0.39 615 1.42 4.00

Omega Block 169 32 8 5.50 2.94 559 2.05 3.60

Omega Block 170 32 15 7.49 3.00 753 1.73 4.50

Omega Block 174 32 8 8.08 3.73 679 1.57 3.75

Omega Block 175 32 27 7.30 3.48 769 1.94 5.20

Omega Block 220 32 5 5.60 1.56 491 1.09 2.50

Omega Block 221 32 6 7.24 1.55 471 1.20 2.50

Omega Block 141 48 23 7.20 2.58 522 1.78 5.00

Omega Block 142 48 27 6.00 2.69 400 1.37 4.00

Omega Block 167 48 20 7.03 1.80 511 0.83 4.00

Omega Block 168 48 14 4.93 0.04 278 0.96 2.00

Omega Block 222 48 6 5.17 2.69 160 1.55 1.25

Omega Block 172 48 1 2.38 2.65 165 2.30 1.30

Omega Block 173 48 8 6.06 3.62 436 2.09 3.50

Omega Block 145 64 20 4.99 0.16 128 1.88 2.70

Omega Block 146 64 27 6.01 2.43 262 0.58 4.65

Omega Block 165 64 12 3.43 2.06 80 1.45 1.00

Omega Block 166 64 21 3.89 1.26 159 0.66 2.00

Omega Block 176 64 8 3.16 3.83 73 2.92 1.75

Omega Block 177 64 15 3.57 0.41 99 3.00 2.00

Omega Block 223 64 8 7.98 0.10 82 2.41 1.25

Omega Block 224 64 15 7.30 0.11 90 1.29 1.25

Block Type Test 

No.

Thrust Load at 

Peak Horz 

Load (kips)

Displ at 

Peak 

Thrust 

Force (in)

Peak 

Horz. 

Load (lbs)

Peak Thrust 

Force (kips)

Half Wall 

Height (in)

Displ at 

Peak Horz. 

Load (in)

Preload 

(psi)
402

PEERLESS SUPER BLOCK 

Peerless Super Block 216 32 7 3.16 2.15 302 0.99 2.70

Peerless Super Block 218 32 16 4.06 2.34 278 1.07 2.60

Peerless Super Block 217 32 17 3.19 1.69 344 1.08 2.80

Peerless Super Block 219 32 21 0.00 0.00 229 1.42 3.20

Peerless Super Block 208 32 54 7.85 0.04 257 0.51 4.40

Peerless Super Block 209 32 56 8.93 0.05 275 0.29 4.50

Peerless Super Block 190 48 37 5.91 0.04 153 0.53 2.50

Peerless Super Block 191 48 38 6.87 0.07 166 0.43 2.75

Peerless Super Block 192 48 45 7.06 0.03 181 0.24 3.8

Peerless Super Block 193 48 42 9.80 0.01 192 0.45 3.90

Peerless Super Block 194 48 63 9.77 0.03 248 0.76 6.30

Peerless Super Block 195 48 29 4.90 0.11 191 0.76 3.20

Peerless Super Block 196 48 60 8.68 0.13 232 0.52 6.00

Peerless Super Block 197 48 42 7.41 0.10 216 0.23 4.50

Peerless Super Block 210 48 56 8.45 0.13 204 0.52 6.00

Peerless Super Block 211 48 41 6.47 0.80 275 0.79 0.79

Peerless Super Block 214 48 12 1.30 1.91 120 2.14 3.00

Peerless Backsavers (small foam) 302 45.75 5 4.74 2.38 82 0.75 0.75

Peerless Backsavers (small foam) 303 45.75 20 6.62 0.02 182 1.42 1.42

Peerless Backsavers (small foam) 304 45.75 30 7.55 0.07 304 1.34 1.34

Peerless Backsavers (small foam) 305 45.75 57 15.04 0.09 488 0.67 0.67

Peerless Backsavers (small foam) 307 45.75 80 22.88 0.01 524 0.67 0.67

Peerless Super Block 205 64 33 5.85 0.03 88 1.26 2.80

Peerless Super Block 206 64 56 8.08 0.06 54 0.30 3.75

Peerless Super Block 225 64 14 5.12 0.00 54 1.86 1.60

Peerless Super Block 229 64 34 5.51 0.00 102 0.81 2.50

Peerless Super Block 230 64 22 3.33 0.00 33 2.71 1.60

Peerless Super Block 231 64 4 4.19 0.00 33 2.10 2.50

Peerless Super Block 232 64 54 12.74 0.00 96 0.81 5.60

Peerless Super Block 233 64 53 12.67 0.00 128 1.29 6.00

Block Type Test 

No.

Thrust Load at 

Peak Horz 

Load (kips)

Displ at 

Peak 

Thrust 

Force (in)

Peak 

Horz. 

Load (lbs)

Peak Thrust 

Force (kips)

Half Wall 

Height (in)

Displ at 

Peak Horz. 

Load (in)

Preload 

(psi)