Scholars' Mine Doctoral Dissertations Student Theses and Dissertations Fall 2019 The mechanics of precision presplitting Anthony Joseph Konya Follow this and additional works at: https://scholarsmine.mst.edu/doctoral_dissertations Part of the Civil Engineering Commons, and the Explosives Engineering Commons Department: Mining Engineering Recommended Citation Konya, Anthony Joseph, "The mechanics of precision presplitting" (2019). Doctoral Dissertations. 2836. https://scholarsmine.mst.edu/doctoral_dissertations/2836 This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. THE MECHANICS OF PRECISION PRESPLITTING by ANTHONY JOSEPH KONYA A DISSERTATION Presented to the Faculty of the Graduate School of the MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY in EXPLOSIVE ENGINEERING 2019 Approved by: Dr. Paul Worsey, Advisor Dr. Kyle Perry Dr. Gillian Worsey Dr. Cesar Mendoza Dr. Braden Lusk 2019 Anthony Joseph Konya All Rights Reserved iii ABSTRACT Precision Presplitting is a widely used method of presplit blasting for the mining and construction industries. In recent years considerable effort has gone into the development of empirical equations based on field data to be able to better design the Precision Presplit for various rock types and structural environments. However, the most widely discussed theory about the mechanics of the presplit formation, that of shockwave collisions, does not appear to be applicable for this method of presplitting. This research has disproven this theory based on insufficient magnitude of the shockwave from modeling with basic wave mechanics. Other authors have suggested alternative theories based on the gas pressurization of the borehole. Recently the concept of hoop stresses as a result of the gas pressurization of the borehole was suggested. No method to analyze the gas pressurization of the borehole and magnitude of the hoop stresses existed. This research seeks to develop the basic theory to determine the hoop stress field for a Precision Presplit blast, using basic laws from thermodynamics and mechanics of materials to present a mathematical proof to determine the borehole pressure from a decoupled charge and the magnitude of the hoop stress developed in the rock. This modelling approach analyzes the stress from both the shockwave and gas pressure, which are quantified and compared to the tensile strength of the rock. This research shows that the shockwave magnitude is much too low to cause presplit formation while the hoop stress has sufficient magnitude to cause the split. iv ACKNOWLEDGMENTS The author wishes to express his gratitude to his advisor, Dr. Paul Worsey, for his advice, assistance, and encouragement throughout the author’s schooling and this project; to Dr. Gillian Worsey for her ongoing support and encouragement through the authors schooling and this project; to Dr. Kyle Perry for his assistance and valued ideas in preparation on this project; to Dr. Cesar Mendoza for his support and encouragement on this project; and to Dr. Braden Lusk for his support and encouragement on this project. The author also wishes to express gratitude to the Missouri University of Science and Technology and the Mining Engineering and Explosive Engineering programs for ongoing education without which this project would not have been possible. The author also wishes to thank the Missouri S&T Curtis Laws Wilson Library, Interlibrary Loan Services. The author also wishes to express sincere gratitude to Precision Blasting Services for allowing the author to utilize equipment and unpublished research which were vital to the completion of this project. The author wishes to express his gratitude to Dr. Calvin J. Konya, without whom none of this would have been possible. The mentorship and knowledge imparted has been the basis for the author’s current and ongoing work. v TABLE OF CONTENTS Page ABSTRACT ....................................................................................................................... iii ACKNOWLEDGMENTS ................................................................................................. iv LIST OF ILLUSTRATIONS ............................................................................................. ix LIST OF TABLES ............................................................................................................. xi NOMENCLATURE ........................................................................................................ xiii SECTION 1. INTRODUCTION ........................................................................................................ 1 2. REVIEW OF LITERATURE ....................................................................................... 6 2.1. INTRODUCTION OF BLASTING TECHNIQUES ......................................... 6 2.2. HISTORIC MECHANICS OF BREAKAGE..................................................... 8 2.3. SHOCK BREAKAGE IN COMMERCIAL BLASTING ................................ 17 2.3.1. The Discovery of Shockwaves. .............................................................. 17 2.3.2. Shockwave Research in Commercial Blasting. ...................................... 20 2.3.2.1. Livingston Cratering Theory. ....................................................22 2.3.2.2. U.S. Bureau of Mines Cratering Theory. ...................................26 2.3.2.3. Shockwave Spallation Theory. ..................................................27 2.3.2.4. Strain Wave Theory. ..................................................................32 2.3.2.5. Refutation of the application of shockwaves in blasting. ..........33 2.3.3. Shockwave Theory and Mathematical Concepts. .................................. 37 2.4. GAS PRESSURIZATION BREAKAGE IN COMMERCIAL BLASTING ... 40 vi 2.4.1. Becker-Kistiakowsky-Wilson (BKW) Equation of State ....................... 45 2.4.2. Cook’s Equation of State. ....................................................................... 48 2.4.3. Taylor’s Equation of State. ..................................................................... 49 2.4.4. Outoyne-Skidmore-Konya (OSK) Equation of State. ............................ 49 2.4.5. Theoretical Borehole Pressure Calculations. ...........................................51 2.5. PRESPLITTING ............................................................................................... 52 2.5.1. Traditional Presplitting. .......................................................................... 58 2.5.2. Precision Presplitting. ..............................................................................59 2.5.3. Propellant Presplitting. .............................................................................69 3. EMPIRICAL ANALYSIS OF BOREHOLE PRESSURES ....................................... 71 3.1. DEVELOPMENT OF AN EMPIRICAL BOREHOLE PRESSURE MODEL ............................................................................................................ 71 3.2. MODIFICATION OF THE EMPIRICAL MODEL ........................................ 76 3.3. EMPIRICAL MODEL FOR TYPICAL PRECISION PRESPLIT .................. 81 4. THEORETICAL ANALYSIS OF BOREHOLE PRESSURES ................................. 82 4.1. INTRODUCTION TO THEORETICAL MODELS ........................................ 82 4.1.1. Temperature of Detonation. ................................................................... 83 4.1.2. Specific Heats for Explosive Products. .................................................. 84 4.1.2.1. Dulong-Petit Limit. ....................................................................85 4.1.2.2. PETN detonation products. ........................................................86 4.1.2.3. Specific heat for nitrogen, N2. ...................................................87 4.1.2.4. Specific heat of water vapor, H2O. ............................................87 4.1.2.5. Specific heat for carbon dioxide, CO2. ......................................88 4.1.2.6. Specific heat for carbon monoxide, CO.....................................88 vii 4.1.3. Calculation of the Temperature of the Explosion. ................................. 93 4.2. DETONATION PRESSURE MODEL ............................................................ 98 4.2.1. Validation of Equations of State from Experimental Data..................... 98 4.2.2. Development of Detonation Pressure Model from Taylor EOS. ......... 102 4.3. DEVELOPMENT OF THERMODYNAMIC MODEL ................................ 106 4.4. COMPARISON OF PRESSURE MODELS .................................................. 123 4.5. BOTTOM CHARGE EFFECTS .................................................................... 127 4.6. PRESSURE OF A TYPICAL PRECISION PRESPLIT ................................ 131 5. HOOP STRESS MODEL FOR BLASTING ............................................................ 132 5.1. DEVELOPMENT OF HOOP STRESS MODEL .......................................... 132 5.2. SIMPLIFICATION OF HOOP STRESS MODEL ........................................ 140 5.3. HOOP STRESS OF A PRECISION PRESPLIT BLAST .............................. 141 6. MAGNITUDE OF THE SHOCKWAVE FROM PRESPLITTING ........................ 147 6.1. SHOCKWAVE MECHANICS .....................................................................