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Quantifying the effect of rock mass quality on peak particle velocity for underground drift development Caceres, Cristian Andres Caceres 2011

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QUANTIFYING THE EFFECT OF ROCK MASS QUALITY ON PEAK PARTICLE VELOCITY FOR UNDERGROUND DRIFT DEVELOPMENT  by   Cristian Andres Caceres Doerner   A THESIS SUBMITTED IN PARTIAL FULLFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in  The Faculty of Graduate Studies (Mining Engineering)   THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)   December 2011     Cristian Andres Caceres Doerner, 2011    ii ABSTRACT In prior research the existence of the strong relation between peak particle velocity (PPV), as a result of blasting, and damage to civil structures and mining excavations has been well established. In essence, the higher the PPV levels, the greater has been the observed damage to a structure or excavation. The first part of this thesis examines, through case studies in four underground mines, the relationship observed between measured PPV and induced overbreak. These developed relationships were established through a blast monitoring campaign of drift development headings of markedly dissimilar rock mass qualities, varying from fair/poor to extremely competent. In the second part of this thesis is developed of a new methodology to estimate PPV, which incorporates input parameters that are characteristic of different rock mass qualities, such as propagation velocity and resonance frequency, and explosive characteristics such as velocity of detonation (VOD). This methodology makes use of waveforms to determine vibration levels from which the PPV of a blasthole is established. The developed model estimates PPV by taking into consideration the spatial location of the blasthole with respect to both the drift face, and the point of interest, and the arrival time difference of every incremental charge (or packet) within a blasthole based on the travel distance of the seismic wave, the VOD, and the rock mass propagation velocities. Current state of the art methodologies are solutions to a particular blasting situation; they either consider a specific close range geometry, where they have limited applicability, or they tend to be over simplified in the far-field by considering the explosive charge as a point source. The proposed methodology considers a more realistic close range geometric solution that can be applied specifically to a drifting situation, and improves some of the drawbacks of current methodologies in the far-field range. Finally, a more reliable estimation of PPV levels can help in the assessment of the damage potential of a particular structure or excavation and therefore should help toward preventive measures to make the working environment more safe and cost effective.    iii TABLE OF CONTENTS Abstract.......................................................................................................................................ii	
   Table	
  of	
  Contents ................................................................................................................... iii	
   List	
  of	
  Tables ............................................................................................................................vi	
   List	
  of	
  Figures......................................................................................................................... vii	
   List	
  of	
  Abbreviations	
  and	
  Symbols..................................................................................xvi	
   Acknowledgements..............................................................................................................xix	
   Dedication ................................................................................................................................xx	
   1	
   Introduction........................................................................................................................1	
   1.1	
   Motivation	
  and	
  Significance	
  of	
  the	
  Proposed	
  Research............................................ 1	
   1.2	
   Scope	
  and	
  Objective .............................................................................................................. 2	
   1.3	
   Methodology ............................................................................................................................ 3	
   1.4	
   Statement	
  of	
  Contributions ................................................................................................ 5	
   1.5	
   Thesis	
  Outline ......................................................................................................................... 6	
   2	
   Literature	
  Research .........................................................................................................9	
   2.1	
   Falls	
  of	
  Ground	
  –	
  A	
  Latent	
  Threat	
  to	
  Miners ................................................................. 9	
   2.2	
   Ground	
  Vibrations	
  and	
  Damage	
  Assessment .............................................................11	
  2.2.1	
   Introduction .................................................................................................................................... 11	
  2.2.2	
   Beyond	
  the	
  Detonation	
  Process.............................................................................................. 13	
  2.2.3	
   The	
  Harmonic	
  Seismic	
  Wave	
  Equation ............................................................................... 16	
  2.2.4	
   Seismic	
  Wave	
  Attenuation ........................................................................................................ 18	
  2.2.5	
   Seismic	
  Wave	
  Diffraction........................................................................................................... 19	
  2.2.6	
   Seismographs ................................................................................................................................. 19	
  2.2.7	
   Geophone	
  Damping...................................................................................................................... 20	
  2.2.8	
   Frequency	
  of	
  Vibration............................................................................................................... 21	
  2.2.9	
   Frequency	
  Spectrum ................................................................................................................... 21	
  2.2.10	
   Scaling	
  and	
  Prediction	
  of	
  Ground	
  Vibrations................................................................. 22	
  2.2.11	
   Rock	
  Mass	
  Damage	
  from	
  Blasting....................................................................................... 30	
  2.2.12	
   Particle	
  Velocity	
  Estimates	
  in	
  Relation	
  to	
  Structural	
  Damage................................ 32	
  2.2.13	
   Blast	
  Damage	
  Measurement	
  Techniques......................................................................... 32	
  2.2.14	
   Blast	
  Overbreak .......................................................................................................................... 33	
   2.3	
   Rock	
  Mass	
  Classification....................................................................................................34	
  2.3.1	
   Introduction .................................................................................................................................... 34	
  2.3.2	
   Bieniawski’s	
  Geomechanics	
  Classification	
  -­‐	
  RMR ........................................................... 37	
  2.3.3	
   Barton’s	
  Rock	
  Tunneling	
  Quality	
  Index,	
  Q ......................................................................... 38	
  2.3.4	
   Rock	
  Support	
  Under	
  Dynamic	
  Loading ............................................................................... 42	
  2.3.5	
   Support	
  Design	
  Requirements ................................................................................................ 43	
   3	
   Field	
  Data	
  Collection	
  and	
  Analysis........................................................................... 44	
   3.1	
   Introduction...........................................................................................................................44	
   3.2	
   The	
  Drifting	
  Process ...........................................................................................................44	
   3.3	
   Methods	
  of	
  Field	
  Data	
  Collection ....................................................................................45	
  3.3.1	
   Process	
  of	
  Field	
  Data	
  Collection ............................................................................................. 45	
  3.3.2	
   Rock	
  Mass	
  Quality	
  Assessments............................................................................................. 47	
  3.3.3	
   Blast	
  Monitoring	
  and	
  Equipment........................................................................................... 50	
      iv 3.3.4	
   Explosives	
  Characteristics ........................................................................................................ 55	
   3.4	
   Methods	
  of	
  Analysis	
  of	
  Field	
  Data ..................................................................................56	
  3.4.1	
   PPV	
  and	
  SD ....................................................................................................................................... 56	
  3.4.2	
   Frequency	
  Content	
  of	
  a	
  Waveform........................................................................................ 58	
  3.4.3	
   PPV	
  Analysis	
  using	
  Band-­‐Pass	
  Filter .................................................................................... 58	
  3.4.4	
   Data	
  Processing ............................................................................................................................. 60	
  3.4.5	
   Overbreak	
  Assessments	
  –	
  Scanner	
  Profiles ...................................................................... 65	
  3.4.6	
   Other	
  Analysis	
  of	
  Field	
  Data..................................................................................................... 68	
  3.4.7	
   Structural	
  Mapping ...................................................................................................................... 69	
  3.4.8	
   Detonator	
  Delay	
  Scatter............................................................................................................. 70	
   3.5	
   Limitations	
  and	
  Advantages	
  of	
  the	
  Presented	
  Empirical	
  Data .............................72	
   4	
   Case	
  Studies ..................................................................................................................... 74	
   4.1	
   Introduction...........................................................................................................................74	
   4.2	
   Stillwater	
  Mine	
  –	
  Montana	
  USA .......................................................................................75	
  4.2.1	
   Rock	
  Mass	
  Quality......................................................................................................................... 76	
  4.2.2	
   Vector	
  Sum	
  PPV	
  and	
  Frequency	
  Content............................................................................ 81	
   4.3	
   SSX-­Steer	
  Mine	
  –	
  Nevada	
  USA ..........................................................................................84	
  4.3.1	
   Rock	
  Mass	
  Quality......................................................................................................................... 84	
  4.3.2	
   Vector	
  Sum	
  PPV	
  and	
  Frequency	
  Content............................................................................ 89	
   4.4	
   Turquoise	
  Ridge	
  JV	
  Mine	
  –	
  Nevada	
  USA .......................................................................93	
  4.4.1	
   Rock	
  Mass	
  Quality......................................................................................................................... 94	
  4.4.2	
   Vector	
  Sum	
  PPV	
  and	
  Frequency	
  Content............................................................................ 98	
   4.5	
   Musselwhite	
  Mine	
  –	
  Ontario	
  Canada .......................................................................... 102	
  4.5.1	
   Rock	
  Mass	
  Quality.......................................................................................................................102	
  4.5.2	
   Vector	
  Sum	
  PPV	
  and	
  Frequency	
  Content..........................................................................106	
   4.6	
   Analysis	
  of	
  Results............................................................................................................ 110	
  4.6.1	
   PPV	
  versus	
  SD	
  for	
  a	
  Wide	
  Range	
  of	
  Rock	
  Mass	
  Qualities...........................................110	
  4.6.2	
   Charge	
  Weight	
  per	
  Delay .........................................................................................................113	
   5	
   PPV	
  Modeling	
  –	
  The	
  Proposed	
  Methodology ......................................................115	
   5.1	
   Introduction........................................................................................................................ 115	
   5.2	
   The	
  Semi	
  Empirical	
  Modeling	
  Tool ............................................................................. 116	
  5.2.1	
   Background ...................................................................................................................................116	
  5.2.2	
   Model	
  Set-­‐Up.................................................................................................................................118	
  5.2.3	
   Point	
  of	
  Diffraction	
  (POD) .......................................................................................................119	
  5.2.4	
   Assumptions..................................................................................................................................121	
  5.2.5	
   Analytical	
  Background..............................................................................................................123	
   5.3	
   Arrival	
  Time	
  Analysis ...................................................................................................... 127	
  5.3.1	
   General ............................................................................................................................................127	
  5.3.2	
   Stress	
  Wave	
  Propagation	
  Velocity	
  –	
  Rock	
  Mass	
  Quality	
  Dependence .................130	
  5.3.3	
   Arrival	
  Time	
  –	
  Rock	
  Mass	
  Sound	
  Velocity	
  Dependence.............................................132	
   5.4	
   Particle	
  Velocity	
  Analysis	
  –	
  Drifting	
  Case ................................................................. 141	
  5.4.1	
   Proposed	
  PPV	
  Equation	
  –	
  Analytical	
  Background........................................................141	
  5.4.2	
   Determination	
  of	
  Constants ...................................................................................................144	
  5.4.3	
   Waveform	
  Generation	
  –	
  Frequency	
  Dependence .........................................................145	
  5.4.4	
   Phase	
  Shift	
  -­‐	
  Delayed	
  Arrival	
  Times	
  of	
  Peak	
  Velocities ..............................................147	
  5.4.5	
   Resonance	
  Vibration	
  Frequency	
  Range	
  of	
  a	
  Rock	
  Mass	
  Medium ..........................157	
  5.4.6	
   Model	
  Sampling	
  Rate.................................................................................................................159	
   5.5	
   PPV	
  –	
  Diffraction	
  Case...................................................................................................... 163	
  5.5.1	
   General ............................................................................................................................................163	
      v 5.5.2	
   Arrival	
  Time	
  –	
  Two	
  Blastholes	
  with	
  identical	
  Nominal	
  Delay.................................171	
   5.6	
   PPV	
  for	
  Practical	
  Cases.................................................................................................... 173	
  5.6.1	
   General ............................................................................................................................................173	
  5.6.2	
   Competent	
  Rock	
  Mass	
  –	
  Good	
  Rock	
  Mass	
  Quality;	
  RMR	
  >	
  75..................................174	
  5.6.3	
   Weak	
  Rock	
  Mass	
  –	
  Poor/Fair	
  Rock	
  Mass	
  Quality;	
  RMR	
  >	
  35 ...................................180	
   6	
   Model	
  Testing................................................................................................................186	
   6.1	
   Field	
  Data	
  PPV	
  Measurements	
  –	
  Musselwhite	
  Mine	
  Case.................................... 186	
   6.2	
   PPV	
  Data	
  Measured	
  versus	
  Modeled	
  –	
  Musselwhite	
  Mine	
  Case ........................ 191	
   7	
   Applications	
  of	
  the	
  Proposed	
  Model......................................................................197	
   7.1	
   General ................................................................................................................................. 197	
   7.2	
   Analysis	
  of	
  the	
  PPV	
  for	
  different	
  Explosive	
  Types ................................................. 197	
   7.3	
   Blasthole	
  Interaction	
  Analysis ..................................................................................... 204	
   7.4	
   Other	
  Applications	
  of	
  the	
  Model .................................................................................. 206	
  7.4.1	
   Blasthole	
  Distribution	
  Analysis ............................................................................................206	
  7.4.2	
   Surface	
  and	
  Underground	
  Blasts .........................................................................................206	
  7.4.3	
   Pyrotechnic	
  Caps	
  Delay	
  Scatter ............................................................................................207	
   7.5	
   Limitations	
  of	
  the	
  Model................................................................................................. 207	
   8	
   Conclusions ....................................................................................................................209	
   9	
   Recommended	
  Future	
  Work....................................................................................214	
   References.............................................................................................................................216	
   Appendices............................................................................................................................223	
   Appendix	
  A	
  –	
  Rock	
  Mass	
  Quality	
  Logs..........................................................................223	
   Appendix	
  B	
  –	
  Particle	
  velocity	
  and	
  Frequency	
  Content	
  -­	
  Case	
  Studies .............247	
       vi LIST OF TABLES Table 2.1 Rock Mass Rating System (After Bieniawski, 1976) ....................................... 38	
   Table 2.2 Classification of individual parameters used in the Tunneling Quality Index Q (After Barton et al 1974)................................................................ 40	
   Table 3.1 High Frequency Triaxial Geophone – Instruction Sheet (source: www.instantel.com, June 2011)................................................................................ 53	
   Table 3.2 Explosive utilized – Main specifications (source: www.dynonobel.com, June 2011) ............................................................................ 55	
   Table 4.1 Mine site case studies ....................................................................................... 74	
   Table 4.2 Number of PPV measurements and average RMR ........................................... 75	
   Table 4.3 Barton’s Q index components – Stillwater Mine.............................................. 78	
   Table 4.4 Bieniawski’s RMR ratings – Stillwater Mine ................................................... 79	
   Table 4.5 Summary of blasthole ID, explosive types and relative weights per blasthole – Stillwater Mine ................................................................................. 79	
   Table 4.6 Barton’s Q index components – SSX Mine...................................................... 87	
   Table 4.7 Bieniawski’s RMR ratings – SSX Mine............................................................ 87	
   Table 4.8 Summary of explosive ID, types and relative weights per blasthole – SSX Mine ............................................................................................... 89	
   Table 4.9 Barton’s Q index components – Turquoise Ridge JV Mine............................. 96	
   Table 4.10 Bieniawski’s RMR ratings – Turquoise Ridge JV Mine................................. 96	
   Table 4.11 Summary of explosive ID, types and relative weights per blasthole – Turquoise Ridge JV Mine ...................................................................... 97	
   Table 4.12 Barton’s Q index components – Musselwhite Mine..................................... 105	
   Table 4.13 Bieniawski’s RMR ratings – Musselwhite Mine........................................... 105	
   Table 4.14 Summary of explosive ID, types and relative weights per blasthole – Musselwhite Mine ................................................................................ 105	
   Table 5.1 Table of propagation velocities for different mediums (source: Pavlovic, 1998) ....................................................................................................... 131	
   Table 5.2 Table of explosive detonation velocities ........................................................ 133	
      vii LIST OF FIGURES Figure 2.1 Percentage of underground mining injuries in U.S. classified by accident type (source: U.S. Department of Labor: Bureau of Labor Statistics (http://www.bls.gov/iif/, June 2011)) .......................................................... 9	
   Figure 2.2 Percentage of underground mining fatalities in U.S. classified by accident type (source: U.S. Department of Labor: Bureau of Labor Statistics (http://www.bls.gov/iif/, June 2011)) ........................................................ 10	
   Figure 2.3 Fall of ground related injuries in U.S. (source: U.S. Department of Labor: Bureau of Labor Statistics (http://www.bls.gov/iif/, June 2011)) ........................................................................................................................ 11	
   Figure 2.4 Detonation velocity for ANFO versus charge diameter (modified from source: “Rock Blasting and Explosives Engineering” pg. 101)....................... 15	
   Figure 2.5 Integration of the surface wave effect in the near region of an extended charge (After Persson et. al., 2001) pg. 245 .............................................. 28	
   Figure 2.6 ELOS concept to measure average stope overbreak........................................ 34	
   Figure 2.7 Procedure for measurement and calculation of RQD (after Deere, 1989).............................................................................................................. 36	
   Figure 3.1 Sequential tasks of the drifting process ........................................................... 45	
   Figure 3.2 Pre-blast data collection process ..................................................................... 46	
   Figure 3.3 Post-blast data collection process .................................................................... 46	
   Figure 3.4 Relationship between discontinuity spacing and RQD, after Bieniawski (1989)..................................................................................................... 48	
   Figure 3.5 Cell mapping of both walls and back for each round...................................... 49	
   Figure 3.6 Photograph of the left wall showing structures and rock mass condition ................................................................................................................... 50	
   Figure 3.7 Protective metal box with geophone and datalogger installed ........................ 51	
   Figure 3.8 Minimate Plus® and high frequency triaxial geophone.................................. 52	
   Figure 3.9 SM-7 30Hz geophone response curve (modified from www.iongeo.com, June 2011) .................................................................................. 54	
   Figure 3.10 SM-7 30Hz geophone phase lag (modified from www.iongeo.com, June 2011) .................................................................................. 55	
   Figure 3.11 Perimeter and lifter blastholes - Explosive’s distribution – Stillwater mine .......................................................................................................... 57	
   Figure 3.12 PPV versus time record – With and without band pass filter (0- 100Hz)....................................................................................................................... 58	
   Figure 3.13 PPV versus time record – With and without band pass filter (100-500Hz).............................................................................................................. 59	
   Figure 3.14 PPV versus time record – With and without band pass filter (500-1000Hz)............................................................................................................ 59	
   Figure 3.15 PPV versus time record – With and without band pass filter (1000-1500Hz).......................................................................................................... 60	
   Figure 3.16 Transversal, vertical and longitudinal particle velocity record ..................... 61	
   Figure 3.17 Vector sum of the three individual particle velocity components ............................................................................................................... 62	
   Figure 3.18 Isolated seismic waveform ............................................................................ 63	
      viii Figure 3.19 Frequency content for burn cut blasthole ...................................................... 63	
   Figure 3.20 Planned or as-built profile against final profile ............................................. 65	
   Figure 3.21 Average overbreak measurement over an entire blasted round section ....................................................................................................................... 66	
   Figure 3.22 Leica™ HDS3000® laser scanner................................................................. 67	
   Figure 3.23 Laser scanned profile of a development drift ................................................ 68	
   Figure 3.24 Picture of the face showing dimensions and blasthole long period delay number ................................................................................................. 69	
   Figure 3.25 Representation of major structures on Schmidt stereonet ............................. 70	
   Figure 3.26 Long period cap delay scatter........................................................................ 71	
   Figure 3.27 PPV versus SD............................................................................................... 72	
   Figure 4.1 4400ft level heading – plan view – Stillwater Mine........................................ 76	
   Figure 4.2 Typical 4400ft and 4700ft level headings – support installed – Stillwater Mine.......................................................................................................... 77	
   Figure 4.3 4400ft level heading – blocky ground with support – Stillwater Mine .......................................................................................................................... 77	
   Figure 4.4 4400ft level headings – after-blast picture – Stillwater Mine ......................... 78	
   Figure 4.5 Typical 4400ft and 4700ft level headings – blast pattern – Stillwater Mine.......................................................................................................... 80	
   Figure 4.6 4400ft elevation heading – Laser scanned side view – SSX Mine.................. 81	
   Figure 4.7 PPV versus time – Stillwater Mine ................................................................. 81	
   Figure 4.8 PPV versus SD values – Stillwater Mine ........................................................ 82	
   Figure 4.9 PPV versus SD boundary – 95% confidence level – Stillwater Mine .......................................................................................................................... 83	
   Figure 4.10 Frequency content – Stillwater Mine ............................................................ 84	
   Figure 4.11 7170 cross cut XC11 level heading – plan view – SSX Mine....................... 85	
   Figure 4.12 Rock mass appearance & support installed of right wall – SSX Mine .......................................................................................................................... 86	
   Figure 4.13 Rock mass appearance adjacent to zone under study – SSX Mine .......................................................................................................................... 86	
   Figure 4.14 XC11 heading – blast pattern – SSX Mine ................................................... 88	
   Figure 4.15 XC11 heading – Laser scanned view – SSX Mine........................................ 89	
   Figure 4.16 PPV versus time – SSX Mine........................................................................ 90	
   Figure 4.17 PPV versus SD values – SSX Mine............................................................... 91	
   Figure 4.18 PPV versus SD boundary – 95% confidence level – SSX Mine ................... 92	
   Figure 4.19 Frequency content – SSX Mine..................................................................... 93	
   Figure 4.20 3471 development panel – plan view – Turquoise Ridge JV Mine .......................................................................................................................... 94	
   Figure 4.21 Rock mass at face and support – Turquoise Ridge JV Mine......................... 95	
   Figure 4.22 Rock mass at upper corner – After-blast picture – Turquoise Ridge JV Mine .......................................................................................................... 95	
   Figure 4.23 Shotcreted walls – Pre-blast picture – Turquoise Ridge JV Mine .......................................................................................................................... 96	
   Figure 4.24   3471 development heading – blast pattern – Turquoise Ridge JV Mine..................................................................................................................... 98	
   Figure 4.25  PPV versus time – Turquoise Ridge JV Mine.............................................. 99	
      ix Figure 4.26 PPV versus SD values – Turquoise Ridge JV Mine.................................... 100	
   Figure 4.27 PPV versus SD boundary – 95% confidence level – Turquoise Ridge JV Mine ........................................................................................................ 101	
   Figure 4.28 Frequency content – Turquoise Ridge JV Mine.......................................... 102	
   Figure 4.29 720L C Block East plan view – Musselwhite Mine .................................... 103	
   Figure 4.30 720L C Block East face and drill pattern – Musselwhite Mine .................. 103	
   Figure 4.31 720L C Block East rock mass and rebar bolts pattern – Musselwhite Mine................................................................................................... 104	
   Figure 4.32 720L C Block East back support with rebar and mesh – Musselwhite Mine................................................................................................... 104	
   Figure 4.33 720L C Block East heading – blast pattern – Musselwhite Mine ............... 106	
   Figure 4.34 PPV versus time –– Musselwhite Mine....................................................... 107	
   Figure 4.35 PPV versus SD values – Musselwhite Mine................................................ 108	
   Figure 4.36 PPV versus SD boundary – 95% confidence level – Musselwhite Mine................................................................................................... 109	
   Figure 4.37 Frequency content – Musselwhite Mine...................................................... 110	
   Figure 4.38 PPV versus SD for a range of rock mass qualities ...................................... 111	
   Figure 4.39 PPV versus SD. Solid lines represents 95% confidence level..................... 111	
   Figure 4.40 PPV versus SD – Log scale – for a range of rock mass qualities ................ 112	
   Figure 4.41 Log(PPV) versus Log(SD) – for a range of rock mass qualities ................. 113	
   Figure 4.42 Delay time scatter – Pyrotechnic blasting caps ........................................... 114	
   Figure 5.1 2D representation of a blast pattern............................................................... 117	
   Figure 5.2 Three dimensional projection of the blasthole locations ............................... 118	
   Figure 5.3 Packet representation and location of a centroid ........................................... 119	
   Figure 5.4 Point of diffraction height ZPOD of multiple packets ..................................... 120	
   Figure 5.5 Incidence, reflected and diffracted/refracted rays ......................................... 120	
   Figure 5.6 Packet initiation sequence – Expanding seismic wavefront and ray path.................................................................................................................... 122	
   Figure 5.7 Point of diffraction height ZPOD nth and angle of incidence βnth of nth packet ................................................................................................................. 124	
   Figure 5.8 Point of diffraction height ZPOD ith and angle of incidence βith of ith packet .................................................................................................................. 125	
   Figure 5.9 Ascending arrival times from the initiation point (Packet 17) ...................... 128	
   Figure 5.10 Descending arrival times from the initiation point (Packet 17) .................. 128	
   Figure 5.11 Parabolic ascending arrival times from the initiation point (Packet 17) .............................................................................................................. 129	
   Figure 5.12 Parabolic arrival times. Central packets of the wavefront arrives first .............................................................................................................. 129	
   Figure 5.13 Simultaneous arrival times for all packets................................................... 130	
   Figure 5.14 P-wave velocity (m/s) for various rock types (modified from source: http://science.jrank.org/pages/48110/seismic-properties- rocks.html, January 2011)....................................................................................... 132	
   Figure 5.15 Arrival times for highlighted blasthole location.......................................... 133	
   Figure 5.16 Arrival times – Vbw=6500m/s – Good rock quality – Y=0.9m Z=0.0m.................................................................................................................... 136	
      x Figure 5.17 Arrival times – Vbw=6500m/s – Good rock quality – Y=0.0m Z=0.0m.................................................................................................................... 136	
   Figure 5.18 Arrival times – Vbw=6500m/s – Good rock quality – Y=2.6m Z=3.5m.................................................................................................................... 137	
   Figure 5.19 Arrival times – Vbw=6500m/s – Good rock quality – Y=5.0m Z=3.3m.................................................................................................................... 137	
   Figure 5.20 Arrival times – Vbw=6500m/s – Good rock quality – Y=0.2m Z=3.3m.................................................................................................................... 138	
   Figure 5.21 Arrival times – Vbw=2000m/s – Poor/Fair rock quality – Y=0.9m  Z=0.0m .................................................................................................... 138	
   Figure 5.22 Arrival times – Vbw=2000m/s – Poor/Fair rock quality – Y=0.0m  Z=0.0m .................................................................................................... 139	
   Figure 5.23 Arrival times – Vbw=2000m/s – Poor/Fair rock quality – Y=2.6m  Z=3.5m .................................................................................................... 139	
   Figure 5.24 Arrival times – Vbw=2000m/s – Poor/Fair rock quality – Y=5.0m  Z=3.3m .................................................................................................... 140	
   Figure 5.25 Arrival times – Vbw=2000m/s – Poor/Fair rock quality – Y=0.2m  Z=3.3m .................................................................................................... 140	
   Figure 5.26 User defined modeling parameters flowchart.............................................. 142	
   Figure 5.27 Initial calculations flowchart ....................................................................... 143	
   Figure 5.28 Model waveform generation........................................................................ 143	
   Figure 5.29 Model PPV determination from linear superposition of multiple waveforms ................................................................................................ 144	
   Figure 5.30 High frequency; Packets arrive simultaneously – Zero phase shift ......................................................................................................................... 146	
   Figure 5.31 Low frequency; Packets arrive simultaneously – Zero phase shift ......................................................................................................................... 146	
   Figure 5.32 Waveform time shift between two packets ................................................. 147	
   Figure 5.33 Discrete Hustrulid-Lu values and continuous modeled waveforms............................................................................................................... 148	
   Figure 5.34  High frequency waveform; PPV modeled versus PPV from Hustrulid-Lu equation (2000) – Zero phase shift ................................................... 149	
   Figure 5.35 Low frequency waveform; PPV modeled versus PPV from Hustrulid-Lu equation (2000) – Zero phase shift ................................................... 150	
   Figure 5.36 High Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=10,000m/s....................................................... 151	
   Figure 5.37 Low Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=10,000m/s....................................................... 151	
   Figure 5.38 High Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=8,250m/s......................................................... 152	
   Figure 5.39 Low Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=8,250m/s......................................................... 152	
   Figure 5.40 High Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=6,500m/s......................................................... 153	
   Figure 5.41 Low Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=6,500m/s......................................................... 153	
      xi Figure 5.42 High Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=5,000m/s......................................................... 154	
   Figure 5.43 Low Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=5,000m/s......................................................... 154	
   Figure 5.44 High Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=4,300m/s......................................................... 155	
   Figure 5.45 Low Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=4,300m/s......................................................... 155	
   Figure 5.46 High Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=3,200m/s......................................................... 156	
   Figure 5.47 Low Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=3,200m/s......................................................... 156	
   Figure 5.48 Waveforms generated at various frequency ranges..................................... 158	
   Figure 5.49 Linear superposition of waveforms generated at various frequency ranges ..................................................................................................... 159	
   Figure 5.50 Model sampling rate = 500,000Hz .............................................................. 161	
   Figure 5.51 Model sampling rate = 25,000Hz ................................................................ 161	
   Figure 5.52 Model sampling rate = 16,384Hz ................................................................ 162	
   Figure 5.53 Model sampling rate = 8,192Hz .................................................................. 162	
   Figure 5.54 Model sampling rate = 4,096Hz .................................................................. 163	
   Figure 5.55 Arrival times – Signature blasthole case ..................................................... 166	
   Figure 5.56 PPV waveforms for selected packets – Signature blasthole case................ 166	
   Figure 5.57 PPV waveforms for all 17 packets – Signature hole case ........................... 167	
   Figure 5.58 Linear superposition of individual PPV waveforms – Signature blasthole case .......................................................................................................... 167	
   Figure 5.59 Arrival times – Diffraction case .................................................................. 169	
   Figure 5.60 PPV waveforms for selected packets – Diffraction case............................. 169	
   Figure 5.61 PPV waveforms for all 17 packets – Diffraction case................................. 170	
   Figure 5.62 Linear superposition of individual PPV waveforms – Diffraction case....................................................................................................... 170	
   Figure 5.63 Arrival times for two blastholes at different locations – Zero time scatter .............................................................................................................. 172	
   Figure 5.64 Linear superposition between 2 blastholes with same delay number .................................................................................................................... 173	
   Figure 5.65 Arrival times and PPV for highlighted blasthole location........................... 174	
   Figure 5.66 Good rock mass quality – PPV vs. time waveform – Record & model....................................................................................................................... 175	
   Figure 5.67 Arrival times - Good rock mass quality case - Y=0.0 Z = -1.73 ................. 176	
   Figure 5.68 Particle velocity waveforms - Good rock mass quality case - Y=0.0 Z = -1.73 ...................................................................................................... 177	
   Figure 5.69 Linear superposition - Good rock mass quality case - Y=0.0 Z = -1.73 ..................................................................................................................... 178	
   Figure 5.70 Arrival times - Good rock mass quality case - Y=3.5 Z = -1.73 ................. 179	
   Figure 5.71 Particle velocity waveforms - Good rock mass quality case - Y=3.5 Z = -1.73 ...................................................................................................... 179	
      xii Figure 5.72 Linear superposition - Good rock mass quality case - Y=3.5 Z = -1.73 ..................................................................................................................... 180	
   Figure 5.73 Fair/Poor rock mass quality – PPV vs. time waveform – Record & model ...................................................................................................... 181	
   Figure 5.74 Arrival times - Poor/Fair rock mass quality case - Y=0.0 Z = - 1.73.......................................................................................................................... 182	
   Figure 5.75 Particle velocity waveforms - Poor/Fair rock mass quality case - Y=0.0 Z = -1.73 .................................................................................................... 183	
   Figure 5.76 Linear superposition - Poor/Fair rock mass quality case - Y=0.0 Z = -1.73 ...................................................................................................... 183	
   Figure 5.77 Arrival times - Poor/Fair rock mass quality case - Y=3.5 Z = - 1.73.......................................................................................................................... 184	
   Figure 5.78 Particle velocity waveforms - Poor/Fair rock mass quality case - Y=3.5 Z = -1.73 .................................................................................................... 185	
   Figure 5.79 Linear superposition - Poor/Fair rock mass quality case - Y=3.5 Z = -1.73 ...................................................................................................... 185	
   Figure 6.1 Blasthole’s location and linear charge density .............................................. 188	
   Figure 6.2 Measured PPV values – Musselwhite Mine – 9.5m from the face ............... 189	
   Figure 6.3 Measured PPV values – Musselwhite Mine – 10.5m from the face.......................................................................................................................... 190	
   Figure 6.4 Measured PPV values – Musselwhite Mine – 21.5m from the face.......................................................................................................................... 190	
   Figure 6.5 Measured PPV values – Musselwhite Mine – 26.6m from the face.......................................................................................................................... 191	
   Figure 6.6 Measured versus modeled PPV surface contours – 9.5m from the face .................................................................................................................... 192	
   Figure 6.7 Surface projection of modeled surface contours – 9.5m from the face.......................................................................................................................... 192	
   Figure 6.8 Measured versus modeled PPV surface contours – 10.5m from the face .................................................................................................................... 193	
   Figure 6.9 Surface projection of modeled surface contours – 10.5m from the face .................................................................................................................... 193	
   Figure 6.10 Measured versus modeled PPV surface contours – 21.5m from the face .................................................................................................................... 194	
   Figure 6.11 Surface projection of modeled surface contours – 21.5m from the face .................................................................................................................... 194	
   Figure 6.12 Measured versus modeled PPV surface contours – 26.5m from the face .................................................................................................................... 195	
   Figure 6.13 Surface projection of modeled surface contours – 26.5m from the face .................................................................................................................... 195	
   Figure 7.1 Near-field PPV of ANFO............................................................................... 199	
   Figure 7.2 Near-field PPV of ANFO – Finer discretization around the blasthole .................................................................................................................. 199	
   Figure 7.3 Near-field PPV modeled – 3D surface – SEC Detagel™ ............................. 201	
   Figure 7.4 Near-field PPV modeled – 2D projection – SEC Detagel™......................... 201	
   Figure 7.5 Near-field PPV modeled – 3D surface – ANFO............................................ 202	
      xiii Figure 7.6 Near-field PPV modeled – 2D projection – ANFO ....................................... 202	
   Figure 7.7 Near-field PPV modeled – 3D surface – Dyno AP™ ................................... 203	
   Figure 7.8 Near-field PPV modeled – 2D projection – Dyno AP™............................... 203	
   Figure 7.9 Blasthole Interaction – 3D surface – Dyno AP™ ......................................... 205	
   Figure 7.10 Blasthole Interaction – 2D projection – Dyno AP™................................... 205	
   Figure 7.11 Application to a surface blast situation ....................................................... 207	
    Figure A. 1 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Cross cut 1....................................................................... 223	
   Figure A. 2 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Cross cut 2....................................................................... 224	
   Figure A. 3 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Cross cut 3....................................................................... 225	
   Figure A. 4 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 1............................................................. 226	
   Figure A. 5 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 2............................................................. 227	
   Figure A. 6 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 3............................................................. 228	
   Figure A. 7 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 4............................................................. 229	
   Figure A. 8 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 5............................................................. 230	
   Figure A. 9 Back, right and left wall rock mass classification logs – Stillwater Mine – Footwall lateral 6 ....................................................................... 231	
   Figure A. 10 Back, right and left wall rock mass classification logs – Stillwater Mine – Footwall lateral 7 ....................................................................... 231	
   Figure A. 11 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 8............................................................. 232	
   Figure A. 12 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 9............................................................. 233	
   Figure A. 13 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 10........................................................... 234	
   Figure A. 14 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 11........................................................... 235	
   Figure A. 15 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 12........................................................... 236	
   Figure A. 16 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 13........................................................... 237	
   Figure A. 17 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 14........................................................... 238	
   Figure A. 18 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 15........................................................... 239	
   Figure A. 19 Back, right and left wall pictures and rock mass classification logs – SSX Mine – Cross cut 11-1.......................................................................... 240	
      xiv Figure A. 20 Back, right and left wall pictures and rock mass classification logs – SSX Mine – Cross cut 11-2.......................................................................... 241	
   Figure A. 21 Back, right and left wall pictures and rock mass classification logs – SSX Mine – Cross cut 11-3.......................................................................... 242	
   Figure A. 22 Back, right and left wall pictures and rock mass classification logs – SSX Mine – Cross cut 11-4.......................................................................... 243	
   Figure A. 23 Back, right and left wall pictures and rock mass classification logs – SSX Mine – Cross cut 11-5.......................................................................... 244	
   Figure A. 24 Back, right and left wall pictures and rock mass classification logs – Musselwhite Mine – Footwall lateral 1........................................................ 245	
   Figure A. 25 Back, right and left wall rock mass classification logs – Turquoise Ridge JV Mine – Footwall lateral 1....................................................... 246	
    Figure B. 1 Particle velocity record – Transversal, vertical and longitudinal – Musselwhite Mine................................................................................................ 247	
   Figure B. 2 Particle velocity record – Transversal, vertical and longitudinal – Stillwater Mine..................................................................................................... 248	
   Figure B. 3 Particle velocity record – Transversal, vertical and longitudinal – Turquoise Ridge JV Mine.................................................................................... 249	
   Figure B. 4 Particle velocity record – Transversal, vertical and longitudinal – SSX Mine............................................................................................................. 250	
   Figure B. 5 Original (Trans1) and truncated transversal particle velocity records (Trun1) – Musselwhite Mine ..................................................................... 251	
   Figure B. 6 Frequency content of original (Trans1) and truncated transversal particle velocity records (Trun1) – Musselwhite Mine ........................ 252	
   Figure B. 7 Frequency content of truncated unsmoothed and smoothed (average of 2, 3, 4, 5, 6 and 7 consecutive samples) transversal particle velocity records – Musselwhite Mine ..................................................................... 253	
   Figure B. 8 Frequency content of truncated unsmoothed and smoothed (average of 8 consecutive samples) transversal particle velocity records – Musselwhite Mine................................................................................... 254	
   Figure B. 9 Frequency content of truncated unsmoothed and smoothed blast and quiet portion (average of 4 and 8 consecutive samples) of the transversal particle velocity records – Musselwhite Mine...................................... 255	
   Figure B. 10 Frequency content of transversal, vertical and longitudinal particle velocity records – #0 delay – Stillwater Mine ........................................... 256	
   Figure B. 11 Frequency content of transversal, vertical and longitudinal particle velocity records – #2 (1/2) delay – Stillwater Mine .................................. 257	
   Figure B. 12 Frequency content of transversal, vertical and longitudinal particle velocity records – #2 (2/2) delay – Stillwater Mine .................................. 258	
   Figure B. 13 Frequency content of transversal, vertical and longitudinal particle velocity records – #3 (1/2) delay – Stillwater Mine .................................. 259	
   Figure B. 14 Frequency content of transversal, vertical and longitudinal particle velocity records – #3 (2/2) delay – Stillwater Mine .................................. 260	
   Figure B. 15 Frequency content of transversal, vertical and longitudinal particle velocity records – #4 (1/2) delay – Stillwater Mine .................................. 261	
      xv Figure B. 16 Frequency content of transversal, vertical and longitudinal particle velocity records – #4 (2/2) delay – Stillwater Mine .................................. 262	
   Figure B. 17 Frequency content of transversal, vertical and longitudinal particle velocity records – #5 (1/2) delay – Stillwater Mine .................................. 263	
   Figure B. 18 Frequency content of transversal, vertical and longitudinal particle velocity records – #5 (2/2) delay – Stillwater Mine .................................. 264	
   Figure B. 19 Frequency content of transversal, vertical and longitudinal particle velocity records – #6 (1/2) delay – Stillwater Mine .................................. 265	
   Figure B. 20 Frequency content of transversal, vertical and longitudinal particle velocity records – #6 (2/2) delay – Stillwater Mine .................................. 266	
   Figure B. 21 Frequency content of transversal, vertical and longitudinal particle velocity records – #7 (1/2) delay – Stillwater Mine .................................. 267	
   Figure B. 22 Frequency content of transversal, vertical and longitudinal particle velocity records – #7 (2/2) delay – Stillwater Mine .................................. 268	
   Figure B. 23 Frequency content of transversal, vertical and longitudinal particle velocity records – #8 (1/2) delay – Stillwater Mine .................................. 269	
   Figure B. 24 Frequency content of transversal, vertical and longitudinal particle velocity records – #8 (2/2) delay – Stillwater Mine .................................. 270	
   Figure B. 25 Frequency content of transversal, vertical and longitudinal particle velocity records – #9 (1/2) delay – Stillwater Mine .................................. 271	
   Figure B. 26 Frequency content of transversal, vertical and longitudinal particle velocity records – #9 (2/2) delay – Stillwater Mine .................................. 272	
   Figure B. 27 Frequency content of transversal, vertical and longitudinal particle velocity records – #11 delay – Stillwater Mine ......................................... 273	
   Figure B. 28 Frequency content of transversal, vertical and longitudinal particle velocity records – #12 delay – Stillwater Mine ......................................... 274	
   Figure B. 29 Frequency content of transversal, vertical and longitudinal particle velocity records – #13 delay – Stillwater Mine ......................................... 275	
   Figure B. 30 Frequency content of transversal, vertical and longitudinal particle velocity records – #14 delay – Stillwater Mine ......................................... 276	
   Figure B. 31 Frequency content of transversal, vertical and longitudinal particle velocity records – #15 (1/2) delay – Stillwater Mine ................................ 277	
   Figure B. 32 Frequency content of transversal, vertical and longitudinal particle velocity records – #15 (2/2) delay – Stillwater Mine ................................ 278	
   Figure B. 33 Frequency content of transversal, vertical and longitudinal particle velocity records – #1 delay at 9.5m from face – Musselwhite Mine ........................................................................................................................ 279	
   Figure B. 34 Frequency content of transversal, vertical and longitudinal particle velocity records – #1 delay at 10.5m from face – Musselwhite Mine ........................................................................................................................ 280	
   Figure B. 35 Frequency content of transversal, vertical and longitudinal particle velocity records – #1 delay at 21.5m from face – Musselwhite Mine ........................................................................................................................ 281	
   Figure B. 36 Frequency content of transversal, vertical and longitudinal particle velocity records – #1 delay at 26.5m from face – Musselwhite Mine ........................................................................................................................ 282	
      xvi LIST OF ABBREVIATIONS AND SYMBOLS a - Acceleration A - Amplitude ANFO - Ammonium nitrate and fuel oil c - Characteristic propagation velocity of P/S/Raleigh wave CMRI - Central Mining Research Institute d - Displacement D - Distance E - Original energy stored in a wave ELOS - Equivalent linear overbreak slough ER - Energy ratio f - Frequency fdom - Dominant frequency FFT - Fast Fourier transform GPR - Ground penetrating radar HCF - Half cast factor ISP - Indian Standard Predictor Ja - Joint alteration number Jn - Joint set number Jr - Joint roughness number Jv - Volumetric joint count Jw - Joint water reduction factor l - Linear charge concentration LIDAR - Light Detection and Ranging    xvii NIOSH - National Institute for Occupational Safety and Health POD - Point of diffraction PPV  - Peak particle velocity Q - Barton’s rock tunnelling quality index QE  - Mass of explosive charge Qf  - Quality factor RMR  - Bieniawski's rock mass rating RQD - Deere’s rock quality designation SD - Scaled distance SRF - Stress reduction factor t - Time T - Period TDR - Time domain reflectometry u - Harmonic displacement USBM - U.S. Bureau of Mines V - Velocity VP - Particle velocity VOD - Velocity of detonation ZPOD - Z coordinate at the point of diffraction αP - P-Wave velocity βith - Angle formed between the ith packet (elemental charge) and the horizontal βS - S-Wave velocity ΔE - Energy lost in one cycle ε - Strain    xviii θ - longitudinal shear displacement vector λ - Wavelength ψ - rotational shear displacement vector ω - angular frequency ϕ - phase shift     xix ACKNOWLEDGEMENTS I would like to thank the committee members for all the support they gave me throughout all these years without which it would have been impossible to complete this research and thesis. My greatest thanks goes to my supervisor Dr. Rimas Pakalnis for the immense and invaluable amount of knowledge he has shared with me, for his trust and friendship, patience and financial support. To my co-supervisor Dr. Michael Hitch for his editing support and his exchange of knowledge and ideas, which improved my research findings and helped to produce a better thesis document. To Dr. Malcolm Scoble for his directions and detailed assessment of my research and his key and precise editing contributions. To Dr. Scott Dunbar and David Sprott for their supervision and fundamental directions. The author would like to thank immensely NIOSH Spokane Research Laboratory and the blasting research team for their financial support, and their contribution of knowledge, as well as the support of their qualified personnel, these being fundamental components in the completion of this research. They have also made available their state of the art equipment and assisted in the organization of the field investigations. The author is particularly grateful to the following: Jami Dwyer, Steve Iverson, Bill Hustrulid, Ed McHugh, Ted Williams, Tom Brady, and Joel Warneke. To Trent McColl for his editorial support. With his English expertise, the thesis is now much more comprehensible as before. The author would also like to thank the following mining companies and their personnel involved: Stillwater Mining Company, Queenstake Resources, Barrick Gold Corp. and Newmont Mining Corp., and Goldcorp Inc.. They provided invaluable assistance during the data acquisition phase of the research, and allowed the use of their time, facilities, and equipment, without which this research could not have been conducted.    xx DEDICATION  To my wife Veronica and my daughters Victoria and Javiera and to my son Tomas. To my parents Ximena and Alberto. To my family and friends. They all gave me the strength and confidence necessary to pursue this incredible endeavor.      1 1 INTRODUCTION 1.1 Motivation and Significance of the Proposed Research Since the beginning of the twentieth century, more than 50,000 mining related fatalities have occurred in the U.S. alone (which is approximately half of all fatalities in metal and non-metal mining, excluding coal), according to NIOSH’s Information Circular 9520 (Breslin, 2010). A significant portion of these fatalities would be related to ground falls and pillar failures. According to the U.S. Department of Labor, the incidence of fatal injuries fell dramatically during the period 2006 to 2010 (31 fatalities total due to face/rib/highwall falls of roof and back, pertaining to both surface and underground mining). Reducing fatalities and injuries across the mining industry remains a principle concern. A strong relationship between peak particle velocity (PPV) – as a result of blasting – and damage to civil structures and mining excavations has been well established by previous research. In essence, the higher the PPV, the greater the observed damage to a structure or excavation. Estimating PPV levels occurring at any given location (with respect to the explosive charge) as accurately as possible thus becomes critical toward making better, more reliable predictions of the potential for damage to existing structures and excavations. The primary motivation of this research is to make the drifting process safer by preventing injuries and fatalities from roof and rib falls in underground mines. The triggering of these failures can have diverse origins but one major factor is the excessive vibration levels resulting from blasting. In addition, this research aims to make the drifting process more cost effective by ensuring a better understanding of the working environment, in terms of particle velocity, which has the potential to cause rock instabilities, as a result of the blasting process. From a geotechnical perspective, cost effective solutions are reached when support designs can prevent all potential instabilities from occurring at the minimum possible cost. Hence, if this process can establish a reliable estimation of the maximum vibration levels, and    2 therefore, an estimate of the degree of damage caused by blasting, then there will be advances in the optimization of drift support designs. 1.2 Scope and Objective The information produced by this research can be used by geotechnical and blasting personnel for a more comprehensive analysis of a particular situation, as this information relates to various rock mass conditions existing at their sites. This research provides empirical relationships relating PPV, scaled distance (SD), and overbreak obtained throughout the analysis of data gathered. Mine sites were selected in order to cover a broad range of rock mass qualities assessed in terms of RMR and Q, ranging from fair/poor to extremely competent. In the author’s opinion, there is a lack of tools available to the geotechnical and blasting community that can be used to determine PPV, specifically in a drifting situation. The existing tools produce overly simplistic solutions, which can lead to large calculation errors in PPV value estimation. This research is oriented to the geotechnical and blasting personnel who are engaged in analysis of the stability of development drifts.  The proposed methodology, which has been developed specifically for a drifting situation, can have positive impacts in the reduction of underground rock failure. This methodology considers important geometric and geophysical features not necessarily addressed by traditional methodologies. Moreover, the methodology is also applicable to surface and underground production blasting when the surface layout is similar to that existing in drift development. The proposed methodology has been verified experimentally using a modeling tool developed and tested with commonly used spreadsheet software and is presented by the author to be more accurate than current methodologies, as it incorporates parameters that are characteristic of the quality of the rock mass and the explosives utilized. The main objective is the development of a new methodology and modeling tool that, once calibrated, can be used by the blasting engineer to improve and optimize designs of blasting rounds. A reliable estimation of the PPVs determined at any given location, some distance from the blast or within the blast round, can then be related to the potential for    3 overbreak and damage occurring at these locations and can therefore assess the potential risk to mining personnel. 1.3 Methodology A total of four underground mines located in North America were investigated, and their drill and blast operations monitored with respect to blasthole location, explosive distribution, delay sequence, seismic vibration monitoring, ground support employed, overbreak assessment, and rock mass quality assessment. Each of the four sites investigated showed clear differences with respect to the other three, in that the sites exhibit a broad range of rock mass qualities, all of which were subsequently analyzed in terms of measured PPV and the associated frequency content. Two widely used rock mass classification systems to assess rock mass quality were employed at the mine sites investigated. These are Bieniawski's Rock Mass Rating, RMR (1976) and Barton’s Rock Tunnelling Quality Index, Q (1974). The seismic records of particle velocity versus time were recorded via high-frequency geophones and dataloggers that were installed along the walls of the monitored drifts, some distance from the blast. Measurements of blast-induced overbreak were estimated from laser scanner profiles and planned surface of excavation. A less accurate method using a handheld laser distance meter was also employed to estimate overbreak in those situations where laser scanner equipment was not available. Site-specific characteristic curves were then obtained from the records of PPV versus SD data. These site-specific characteristic curves present further evidence that as rock mass quality improves, the PPV required for fragmenting and displacing the rock increases. From the records of the particle velocity measured over time, frequency spectrum graphs were derived employing the fast Fourier Transform (FFT). The peak frequency and frequency ranges obtained in this way indicate that there is a strong relationship between frequency ranges and rock mass quality, where high frequencies are undetectable and/or decay more rapidly with decreasing rock mass quality.    4 In an attempt to reduce the large scatter of the recorded PPV versus SD data, a modification and improvement to the Hustrulid-Lu method (Hustrulid and Lu, 2002) used for the near-field PPV prediction, was made by the incorporation of geophysical components into the proposed methodology. This methodology – and the result of it, the developed modeling tool – utilizes a waveform seed generator to determine the peak velocities of individual packets that pertain to a single blasthole of the round. PPV for each blasthole can then be calculated from the linear superposition of all individual packet waveforms whose phases are shifted by their respective arrival time differences, that is, when they arrive at the geophone location. The methodology takes into account the travelled distance, and the travelled time of the seismic wave (between the packet centroid and the geophone), which differs for each packet. The methodology also takes into account the vibration frequency of the given rock mass which has an effect on the waveform generated. These three considerations should lead to greater accuracy in the determination of the final PPV values. The properties and characteristics employed in the model are as follows: the location, length, and diameter of every blasthole in the round with respect to the geophone’s location; the explosive’s linear charge density and VOD; the rock mass medium’s body and surface wave velocities and its main resonant frequency; and, the travelled length of the wavefront comprising every individual packet originating at the blasthole. In principle, only the shortest path travelled by the seismic vibration, measured from the packet location to the geophone location, would generate the PPV and any other path would merely add to the residual portion of the original particle velocity. As a result of the frequency content analysis, the importance of analyzing the combined particle velocity determined for a single blasthole from the combination of a wide range of frequencies can be recognized, however, to simplify the analysis performed, only a single predominant resonance frequency was used. To ascertain the model’s capabilities, an example of a waveform generated from the linear superposition of a range of waveforms each with a different frequency, was conducted and documented. The implemented model was constructed keeping in mind that the seismic wavefront originating at the packet location travels through a body of rock at the body wave    5 velocity, and once it has reached the face-wall contact of the blasting round, the wavefront passes through a point of diffraction (POD); from there on, it travels through the surface of the drift’s wall, at the surface wave velocity, to the geophone location. In the proposed methodology, of the two decomposed PPV vectors, the vector parallel to the wall, and, the vector perpendicular to the wall (i.e., the vertical projection of the original PPV vector before it passes through the POD), only the PPV magnitude of the vector parallel to the wall is accounted for, while the other, the PPV magnitude of the vector perpendicular to the wall, is discarded. This was done by the application of a factor to the length of every packet ray trajectory. This factor is a function of the incidence angle of the packet’s trajectory to the POD, explained in more detail below. 1.4 Statement of Contributions As a result of the field investigation and subsequent analysis of the data gathered, graphs of PPV versus SD were developed for a wide range of rock mass qualities (Figure 4.38 and Figure 4.40). In addition, the corresponding average overbreak determination is also provided for each of the mine sites investigated. These graphs were obtained using existing methodologies but the innovation lies in the fact that the PPV versus SD relations were obtained for a broad range of rock mass qualities, varying from fair/poor to extremely competent and these empirical relations are combined into a single graph from which the importance of rock mass quality on the PPV versus SD relations is emphasized. Also, a set of graphs showing the content of resonance frequencies (Figure 4.10, Figure 4.19, Figure 4.28, and Figure 4.37), obtained from the particle velocity versus time records, provides additional evidence of the strong relation existing between resonance frequencies and rock mass quality. The main resonance frequency is also used as an input parameter for the proposed methodology to determine PPV. The primary contribution of this research is to present a new semi-empirical methodology to determine PPV at any given location from any particular blasthole of the round. This methodology was especially designed for a drifting situation and includes analytical formulations (Eq. 41 through Eq. 45) and the development of a computer based modeling tool. This computing tool was validated and tested using spreadsheet software, and applied to determine PPV values at any distance from a given blasthole location. The    6 model takes into consideration the arrival times of a number of individual packets forming the blasthole column, as well as the predicted path of the seismic wavefront. In certain cases, the seismic wave diffracts at the face-wall contact and this phenomenon is also incorporated into the new methodology. The specifics are explained in detail in subsequent sections. In summary, the provided empirical data relating PPV, SD, overbreak, and resonance frequency with rock mass quality constitute valuable information to the reader for whom similar rock mass condition could be present at their sites. In addition, the new methodology proposed to estimate PPV and subsequently the validation and testing of the modeling tool developed, may have a noteworthy positive impact on safety, as well as on cost optimization of drift developments, both being key factors in underground mine operations. 1.5 Thesis Outline The manuscript has been divided into 9 main chapters and a brief summary of each one is given as follows: Chapter 2 Literature Research, presents the theory and background of the main aspects this thesis is focused on, particularly rock blasting and rock mechanics. It describes crucial aspects with regard to PPV, rock mass quality, overbreak, and frequency spectrum. A discussion of limitations of current methodologies follows, as they are employed to assess near-field PPV, close to the blasthole’s perimeter, and also in the intermediate- and far-field case. Also, the scarce number of alternative methods that can be used on a regular basis, other than seismic monitoring, to assess damage caused by an explosive charge of known properties and its relation to the quality of the rock mass, will be addressed. The analytical and applied background regarding ground vibrations, wave theory, seismic monitoring, particle velocity, damage potential, SD, near- and far-field PPV prediction, frequency spectrum, and rock mass quality is also covered in this chapter. Chapter 3 Field Data Collection and Analysis , describes the procedures and processes involved in the data acquisition and analysis of field measurements. The characteristics of    7 the equipment employed are described, as well as the processes of data gathering including examples of a typical rock mass quality logging sheet, a laser scanner profile, a structural mapping record, particle velocity and vector sum versus time records, and a plot of frequency spectrum, among others. The ELOS concept is introduced, normally applied to the determination of the average overbreak thickness of large open stopes, but employed here for drift development type excavations. An example is also presented, of the scatter that could be found in the delay time of pyrotechnic detonators, along with an example of a PPV versus SD graph recorded for a given rock mass quality. Chapter 4 Case Studies, presents details of the information gathered at the four mines investigated including their locations, a brief description of the mining methods employed to extract the ore, the types of ore and rock types under investigation, as well as plan views of the monitoring area, and general descriptions of rock mass quality including pictures of the rock mass conditions and the support system being employed. Results of the analysis of the gathered data, PPV versus SD charts, are presented along with best-fit curves and equations obtained from the point cloud of the recorded data, including the range of frequencies at which a particular rock mass vibrates. Chapter 5 PPV Modeling – The Proposed Methodology, presents the methodology itself including a new set of analytical equations to determine PPV at any location in the vicinity of a blasting round, either at the face where the detonation of the blastholes occurs, or on the walls some distance away from the blast. Details of the semi-empirical modeling tool, including the geophysical and analytical background, are also presented. The geophysical and analytical background provides the working ground for the analysis of the data gathered in the field campaigns, as was presented in Chapter 4 Case Studies. Validation of the modeling tool against current methodologies is performed in this chapter as well as a series of tests to determine potential applications for the model, e.g., PPV analysis based on different rock mass qualities. Chapter 6  Model Testing, tests the proposed semi-empirical modeling tool on one of the four mine sites visited by estimating PPV values and comparing them against the field data gathered. Three-axial plots of the recorded PPV determined for each blasthole location are compared against surface contour plots obtained via the modeling tool. No    8 statistical analysis was performed to compare the modeled and field data owing to the fact that some of the properties and constants used in the model were obtained from literature (due to cost constraints on the data acquisition in the field). Chapter 7 Applications of the Proposed Model, proposes other potential applications for the modeling tool, such as estimation of the PPV values in the boundaries immediately adjacent to the explosive charge. The model can also be used, for example, to perform PPV decay contour plots in the vicinity of blastholes loaded with different types of explosives. The interaction between two or more charges could also be a part of potential applications making use of the analysis of the modeling results. In this chapter the limitations of the modeling tool are also provided. Chapter 8 Conclusions, includes a summary of the main findings and the contributions made by this research. Chapter 9 Recommended Future Work, describes a number of ideas to implement in future studies for the continuation of the research presented herein, in order to expand knowledge in the field of rock blasting. A good portion of the ideas mentioned in this chapter point toward improving the model’s capability and tackling its shortcomings (as mentioned in Chapter 7).    9 2 LITERATURE RESEARCH 2.1 Falls of Ground – A Latent Threat to Miners From time to time, news appears of miners trapped, injured, or becoming part of fatalities statistics that flood the media. News of injuries is a main concern to the families and the community, to the mine, the industry, industrial health and safety organizations, and the public in general. So any effort toward reducing injuries in the workplace should be forefront. Figure 2.1 - Figure 2.3 show percentage injuries and fatalities in the U.S. mining industry occurring in underground (conventional stoping and caving) mining during the period 2000-2011.  Figure 2.1 Percentage of underground mining injuries in U.S. classified by accident type (source: U.S. Department of Labor: Bureau of Labor Statistics (http://www.bls.gov/iif/, June 2011)) Figure 2.2 shows the percentage of fatalities that occurred in the U.S. in underground mining for the same period.    10  Figure 2.2 Percentage of underground mining fatalities in U.S. classified by accident type (source: U.S. Department of Labor: Bureau of Labor Statistics (http://www.bls.gov/iif/, June 2011)) Figure 2.3 shows the total number of injuries related only to fall of roof and fall of face/rib/pillar that occurred in the U.S. during the period January 2000 to June 2011.    11  Figure 2.3 Fall of ground related injuries in U.S. (source: U.S. Department of Labor: Bureau of Labor Statistics (http://www.bls.gov/iif/, June 2011)) The information provided in the previous figure was obtained from the “Accident Injuries Data Set” database. This information was filtered to show only conventional stoping and caving underground mining methods, from which only injury records classified as fall of roof or back and fall of face/rib/pillar/side/highwall is reflected. Underground locations include faces, intersections, vertical, sloping and inclined shafts, underground shops and offices, and others. Coal mining including shortwall, longwall, and continuous miner methods do not form part of the data analyzed as they bear little relation to the drilling and blasting techniques under study. 2.2 Ground Vibrations and Damage Assessment 2.2.1 Introduction It is widely understood that the degree of damage sustained by a given rock mass as a result of blasting is proportional to the quality of that rock mass (Bieniawski, 1989; Barton et al. 1974; Hoek et al., 1980) as well as proportional to the quantity of explosives fired per delay. Logically, the higher the quantity of explosives fired per delay, the higher    12 the resultant seismic vibration, and this vibration has a direct effect on the magnitude of the damage sustained by the rock mass. Given that it is nearly impossible to take measurements of peak vibration levels in the immediate vicinity of a given blasthole, i.e., where the greater damage to the rock actually occurs, these vibration levels have always been estimated by extrapolating measured vibrations at considerable distances from the source. From statistical and physical points of view, the greater the distance from the blast that data points are used for extrapolation, the greater the error generated, thus the lower the reliability of predicting the peak vibration levels responsible for the damage to the rock mass. This is probably the greatest shortcoming of most of the research undertaken so far in this area, and there are several relevant examples (Dey, 2004; Adamson et al., 1999, Murty et al., 2003). Moreover, those who have attempted to monitor vibration levels nearer to a given blast, have not done so for more than a single rock mass quality. Notably, for some of the research undertaken, the methods employed require extra or special operations, such as drilling perpendicular to the strike direction of the drift, which generally conflict with production schedules, and for this reason, are not used on a regular basis. Boreholes for instrumentation drilled in a different orientation than the blastholes, in many cases require bringing in other drilling equipment, and even though they can prove to be useful, the extra setup time may not allow the mining cycle to fit the constraints of the shift. On the other hand, the installation of blast monitoring instrumentation can operate during parts of the mining cycle where they produce insignificant interruptions to the operation. In Murty (2003), peak vibration levels were predicted in the near-field, at a distance of 1m from the blast, while the nearest actual measurements were taken at a distance of 43m from the blast. On the other hand, some research involving single blasthole firing has attempted to monitor in the near-field using experimental rather than real-world mine drift developments (Yang et al., 1994). Yang employed accelerometers rather than the more direct measurement method utilizing geophones, requiring subsequent integration of the acceleration versus time records in order to derive the corresponding particle velocity, which involves an implicit approximation error as well as the use of a much higher frequency band (accelerometers) to record the seismic data.    13 2.2.2 Beyond the Detonation Process The author considers the following two quotes to be representative of a fundamental vision toward a safer and cost effective blasting process. The damage produced to the remaining excavation might not be completely avoidable, but it can be engineered so as to be minimized. “The innocent rock mass is often blamed for insufficient stability that is actually the result of rough and careless blasting. Where no precautions have been taken to avoid blasting damage, no knowledge of the real stability of the undisturbed rock can be gained from looking at the remaining rock wall. What one sees are the sad remains of what could have been a perfectly safe and stable rock face.” Holmberg and Persson (1980). “Blasting for underground construction purposes is a cutting tool, not a bombing operation.” Svanholm et al. (1977). When an explosive charge is detonated inside a borehole, the rock in the periphery of the charge will sustain irreversible plastic deformation. As the seismic wave continues its outwards propagation, its energy will decay very rapidly, up to the point that only elastic stress waves will remain propagating through the volume of rock. From the total available energy produced by the detonation of the explosive charge, only a portion of the energy is transformed into seismic waves, which then propagate as body waves, and also on the surface of the ground as surface waves. These elastic stress waves or seismic waves, as they propagate through the whole volume of rock including its surface, are felt as ground vibrations. Blasting operations inevitably produce ground vibrations that, for the majority of cases, are undesirable and unavoidable. Therefore, it has always been an important consideration in blast design, to control and maintain within acceptable limits the magnitude of these ground vibrations, since they can induce excessive damage to nearby excavations and equipment. Ground vibrations may also dislodge rock wedges that are difficult to recognize but become a latent threat to the safety of personnel and equipment. In the book “Rock Blasting and Explosives Engineering” the authors Persson, Holmberg, and Lee, provided pertinent information regarding the blasting process. The information is summarized as follows: Only a fraction, ranging between 50%-70%, of the detonating    14 energy corresponds to the effective expansion work used for breaking the rock, and this occurs up to the point when pressures on the order of 1000 bar have been reached, and when the blasting products have expanded 10 to 20 times the initial volume. When the rock breakage process is taking place, new and existing cracks are being extended, as extremely high-induced tangential stresses overcome the tensile strength of the rock, triggered by the radial expansion of the borehole walls. Also, new and existing cracks are being formed by the injection of high-pressure gases. The breakage process continues until the pressures have reached approximately 100 bars, then the expanding gases get vented until they reach atmospheric pressure. During this process, the remaining 50%- 30% of the original explosive energy is transformed into heat, seismic energy, and airblast. The seismic energy propagates outward in all directions from the source charge as an expanding sphere or ovoid, and the rate of decay of these seismic waves will vary depending on how the rock mass medium interacts with the vibrations being generated. An explosive charge initiated in a cylindrical column can at best propagate at its maximum propagation velocity, theoretically the stable detonation velocity DCJ (Chapman-Jouguet detonation velocity) that is intrinsic to the explosive type and the diameter and condition of the blasthole. In this sense, the larger the blasthole diameter, the higher the VOD, and similarly, a confined explosive charge will produce a higher VOD as compared to an unconfined charge. Figure 2.4 shows the relation existing between explosive diameter and VOD for an unconfined charge (blue dashed line) and a confined charge (red continuous line).    15  Figure 2.4 Detonation velocity for ANFO versus charge diameter (modified from source: “Rock Blasting and Explosives Engineering” pg. 101) Given that the explosive’s propagation velocity is limited to its maximum velocity, the contribution that each infinitesimal portion of the charge column adds to the ground vibrations generated, and measured some distance from the blast, will be comprised of a complex combination of waves including direct, refracted, reflected, body, and surface waves of the compressive, shear, and tensile types. From a practical point of view, the complex combination of wave types is nearly impossible to separate out, however, this separation is not really necessary since the resultant vibration can be measured directly with seismic instrumentation (for this research, only the magnitude of the particle velocity is relevant. The reader is encouraged to check Green’s paper for a complete discussion of the wave types comprising ground vibration (Green, 1984)). The character of ground vibrations can be fully described by measurements in three orthogonal or mutually perpendicular directions, that of the time history of the acceleration, the velocity, or the displacement at a point (particle) in the ground. These quantities are interrelated, as shown in the following expression where a is acceleration, V is velocity, d is displacement, t is time, and f is the frequency of vibration:    16   a = dVdt = d2d d2t  Eq. 1 and for sinusoidal motion takes the form:   a = 2 ⋅π ⋅ f ⋅V = (2 ⋅π ⋅ f )2 ⋅ d  Eq. 2 In practice, it is generally easier to measure either the velocity or the acceleration. Most commercial blast vibration monitoring equipment is used to record particle velocity (i.e., velocity of ground movement), given that the maximum or PPV of ground movement is closely related to the potential for structural/rock damage, as noted by Forsyth (Forsyth, 1993); Pusch (Pusch et al. 1993), Holmberg (Holmberg, 1993), and Siskind (Siskind, 2000), among others. 2.2.3 The Harmonic Seismic Wave Equation The following equations provided in this section form part of many basic physics and geophysics textbooks. These equations in particular were obtained from “Fundamentals of Geophysics” by William Lowrie, Second Edition, pp. 133-135. Two characteristics of wave motion are important to consider, first, that the wave transmits energy by means of elastic displacement of its particles in the medium, that is, the particles will be displaced momentarily by the shaking of the ground, where there is no net transfer of mass, and subsequently, that they will return to their initial position, once the shaking has ended. The second characteristic is that there is a repetition of the wave pattern in space and time. Because there is such harmonic repetition of the wave pattern, the amplitude variation can be expressed by a sine or cosine function. The amplitude of the disturbance is repeated at regular time intervals (known as the period of the wave), T, while the wave passes through a point in space. Frequency is defined by the number of times the amplitude is repeated per second. Thus, the frequency, f, is equal to the inverse of the period T (f=1/T). The regular repetition distance of the wave motion along the direction of travel is known as the wavelength, λ. The disturbance of the medium by the passage of a wave motion can be expressed by the harmonic displacement, u, of a particle from its initial position, by:    17   u = A ⋅ sin 2 ⋅π ⋅ x λ − t T ⎛ ⎝ ⎞ ⎠ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟  Eq. 3 Where A is the amplitude, x is the position, and t is the time. The angular frequency ω and the wave number k can be expressed by:   ω = 2 ⋅π ⋅ f = 2 ⋅πT  Eq. 4   k = 2 ⋅π λ  Eq. 5 The displacement equation, u, can be written as:   u = A ⋅ sin k ⋅ x −ω ⋅ t( )  Eq. 6 The first and second derivation over time t and position x gives the following:   ∂u ∂t = −A ⋅ω ⋅cos k ⋅ x −ω ⋅ t( )  Eq. 7   ∂ 2u ∂t 2 = −A ⋅ω 2 ⋅ sin k ⋅ x −ω ⋅ t( ) = −ω 2 ⋅ u  Eq. 8    ∂u ∂x = −A ⋅ k ⋅cos k ⋅ x −ω ⋅ t( )  Eq. 9   ∂ 2u ∂x 2 = −A ⋅ k 2 ⋅ sin k ⋅ x −ω ⋅ t( ) = −k 2 ⋅ u  Eq. 10 Which corresponds to solutions to the more general seismic wave equation for the primary or compressional P-Wave, and the secondary or shear S-Wave, respectively:   ∂ 2θ ∂t 2 = αP 2 ⋅ ∂ 2θ ∂x 2 + ∂ 2θ ∂y 2 + ∂ 2θ ∂z2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟  Eq. 11   ∂ 2ψ ∂t 2 = βS 2 ⋅ ∂ 2ψ ∂x 2 + ∂ 2ψ ∂y 2 + ∂ 2ψ ∂z2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟  Eq. 12 Where αP and βS are the P-Wave and S-Wave velocities and θ and ψ are the longitudinal and rotational shear displacement vectors.    18 2.2.4 Seismic Wave Attenuation As the seismic wave travels away from its source, its intensity becomes weaker. The attenuation of a wave refers to the decrease of the amplitude with increasing distance. This decrease of intensity is partly due to geometric propagation and partly due to absorption of energy due to imperfect elastic properties of the medium. As the seismic wave propagates through a medium, the anelastic properties of this medium – in which the particles that comprise it do not react as though perfectly elastic with their neighbors – has negative effects on the intensity of the seismic wave. In anelastic damping, part of the total seismic energy is transformed into, for example, frictional heat and other sources of energy loss. The most important reduction of the intensity of a seismic wave is due to geometric attenuation, where, if considered that there is no anelastic damping, as the wavefront propagates, the original seismic energy amplitude is now distributed over an increasingly larger surface. The attenuation of the waveform equation can be expressed from a modification of the Knopoff (1963) equation, but where the independent variable is converted from offset to arrival time and the dominant wavelength to dominant frequency (Huang et. al, 2009):   A t( ) = A to( ) ⋅exp −t ⋅ fdom ⋅πQf ⎛ ⎝ ⎜ ⎞ ⎠ ⎟  Eq. 13 Where fdom is the dominant frequency and t is the arrival time of peak amplitude. The parameter Qf is called the quality factor defined by the fractional energy loss per cycle:   2 ⋅π Qf = − ΔE E  Eq. 14 Where ΔE is the energy lost in one cycle and E is the original energy stored in the wave. A similar approach is used in the proposed methodology to determine the pre-peak attack and post-peak attenuation of the waveform. This approach is introduced in Chapter 5, where the parameter Qf has been replaced by +1/(2δ1) or -1/(2δ2), which are the pre-peak attack or post-peak decay factors, defined later.    19 2.2.5 Seismic Wave Diffraction When the wavefront plane of a seismic wave hits an acute obstacle, a sharp corner or a more general discontinuous boundary, it experiences a phenomenon called diffraction, which allows the wave to follow a path that is in the shadow zone of the source of the seismic vibration. This discontinuous boundary acts as a source of secondary wavelets in which part of the total energy contributes to the reflected wave and part diffracts into the shadow zone where its intensity is lower than the original wavefront. As the angle away from the incident wavefront progressively increases, the intensity progressively decreases. 2.2.6 Seismographs The vibration waveform generated by the detonation of a blasthole can be directly recorded with the use of motion sensing transducers that are connected to a datalogger, whose function is to record digital or analog data into its internal memory, and to provide the geophone or set of geophones with an electrical power source. The geophones utilized in this research were a class of high frequency, high particle velocity range sensors with a frequency range of between 28Hz and 1000Hz, and particle velocities of up to 2540 mm/s. The seismographs record ground movement in three mutually perpendicular orientations or motion components, with one vertical orientation component and two horizontal components. When properly aligned, the horizontal components are labeled longitudinal and transverse components to measure ground movement parallel, and perpendicular to the direction where the vibration source is coming from, respectively. The datalogger also incorporates a separate channel to record airblast. A series of recommendations and requirements on the installation of seismographs in buildings, soils, and rock structures is specified in various documents (Siskind et al., 1985; Duvall, 1961; USBM RI 5708; Stagg and Engler, 1980; and USBM RI 8506, 17th Edition Blasters’ Handbook (ISEE, 2000)) to avoid slippage, rotation, and tipping, due to insufficient gripping of the seismograph-structure contacting surfaces. A faulty    20 installation would provoke the measurement of unwanted motion not representative of the motion being recorded. Recommendations on appropriate distances from the source of vibration to the seismographs are given in USBM Bulleting 656 (Nicholls et al., 1971), RI 8507 (Siskind, et al., 1980b) and RI 9226 (Siskind, et al., 1989). These recommendations were not followed entirely as recommended as the selection of the location for the installation of the geophones was based on maximum proximity to the blast but at the same time the spot selected gave some protection from the shock wave and fly rock. Performance standards and technical specifications of blasting seismographs are provided in the Blast Vibration and Seismograph section of the International Society of Explosive Engineers September 30, 1990. These specifications are presented in terms of the required accuracy for frequency and vibration records, their minimum and maximum range levels, calibration, range of operating temperatures, sampling rate, and over-swing ratio, among others. The technical specifications of the geophones utilized are given in Chapter 3. A geophone is the mechanism inside these transducers that measures ground vibrations by the movement of a magnet within a field of magnetic flux lines. The speed at which these flux lines are traversed, is proportional to the induced voltage. In principle, as the magnet or the surrounding coil is free to move, when the ground vibrates, it will shake the transducer casing that is coupled to the ground, and the coil or the magnet due to its inertia, will tend not to move. The speed at which the magnet versus coil motion vibrates, results in an induced voltage proportional to the particle velocity in units of Volts/millimeters/seconds. This information gets recorded in the internal memory of the unit. The term geophone is also referred to herein as the instrument capable of monitoring and recording seismic vibrations with all the required components. 2.2.7 Geophone Damping Geophones make use of damping to retard the tendency of the mass and spring to oscillate at its natural vibration frequency. If the sensor has no damping, the amplitude    21 peaks at its natural or resonance frequency and the oscillation of the spring-mass system will eventually stop due to gravity and friction. If a low resonant frequency is desirable, this can be accomplished through a modification of its design by a stiffer spring or a heavier mass. A shorter impulse provided by heavy damping has direct impact on the sensitivity of the sensor. Critical damping of a sensor, measured as a damping ratio, happens when the mass-spring system returns to the rest position with no oscillation or over-swing after being displaced by the seismic vibration.  A geophone can be over-damped or under-damped when its ratio is either over or under the critical damping value. Normal damping for geophones is in the range of 70% of critical (source: High Frequency Geophone manual). 2.2.8 Frequency of Vibration Vibration is the mechanical oscillation around an equilibrium point. These oscillations can be periodic in time or random, depending on the object being analyzed and the source of the oscillation. When the detonation of an explosive charge is set off within a mechanical system such as the rock, the initial input vibration will be allowed to vibrate freely. The mechanical system will vibrate at one or more of its natural vibration frequency or frequencies and then damp down to zero over time and distance. Vibration analysis can be explained by a simple mass-spring-damper model, which is indeed an example of a simple harmonic oscillator. Even a more complex system could possibly be modeled by the superposition of simple mass-spring-damper models. 2.2.9 Frequency Spectrum The representation of a time-domain signal in its frequency domain is called a frequency spectrum. The Fourier transformation can be applied to any time domain signal to obtain its frequency spectrum yielding a plot of amplitude and phase against frequency. The seismic vibration occurring in a volume or surface of rock can be specified by the spectral composition of its vibrations and predominant periods in the rock and their dependence on the intensity of the blast effects, the distance to the source, the depth of    22 the explosive charge, the geological conditions of the rock, and the nature of the reduction of intensity of the seismic waves over distance and time from the source. The frequency spectrum as applied in this analysis is the determination of the range of frequencies (or frequency content) that the rock vibrates at as a result of the high intensity detonation process. After the blast, the rock vibrates in its natural vibration frequencies and a significant part of this frequency range is recorded in the internal memory of the geophones. A frequency spectrum is determined through the application of the fast Fourier Transform (FFT) to the particle velocity versus time records. The FFT can be used to compute the frequency distribution of the seismic records, which are considered non-periodic time series (Nicholls et al., 1971). FFT computes a continuous spectrum without preserving the amplitude of the time signal. Blair (2004) suggests the use of time-frequency analysis to determine the distribution of frequencies over a period of time, although this is impractical for small charges where the entire vibration waveform occurs in a fraction of a second. Blair demonstrated that the popular zero-crossing method could yield invalid results for the frequency obtained at the PPV. For the present work, it is sufficient that FFT be used to obtain the dominant frequency (or range of frequencies) of the peak of the vibration waveform. It is important to mention that the implications of vibration frequency in the damage potential of building type structures have been well established (Siskind, 2000), but there is limited information available for rock type structures using high frequency and high particle velocity instruments, and of records of PPV levels measured in close proximity to an explosive charge. 2.2.10 Scaling and Prediction of Ground Vibrations Spathis (2010) categorized vibration predictions into five procedures that can be used independently of each other or in combination with one or more procedures. Vibration predictions were categorized as: - historical data review, - charge weight scaling laws, - waveform superposition,    23 - scaled charge weight superposition, and - analytical and/or numerical methods such as finite difference or finite element. Of these categories, the last four have direct relation to the research undertaken and they will be addressed in this chapter as well as in the following chapters. Charge weight scaling laws have two types of scaling prediction formulations that can be used to assess PPV values for the purpose of estimating potential damage to rock subjected to blasting. In general, they can be classified as the near-field and far-field scaling formulations, and they are routinely employed to determine PPV at some distance from the explosive source. Particle velocity of the vibration due to blasting is a function of the following:  borehole pressure, confinement, and charge weight, as well as, distance from the blast site, how the compressive wave decays through the rock mass, superposition of the stress created by the firing sequence within the blasthole column, and superposition of the stress created by the firing sequence of adjacent holes. For the far-field case, where the explosive charge can be considered a spherical charge, PPV (in millimeters per second, mm/s), experienced at some distance, D (in meters, m), from an explosive source of given mass, QE (in kilograms, kg), loaded into a volume of rock, is conveniently expressed in the general form of a power law as follows:   PPV = K QE α Dn ⎛ ⎝ ⎜ ⎞ ⎠ ⎟  Eq. 15 Where K, α, and n are constants controlled mainly by the geology and the type of blasting. In most cases, the three-parameter model above reduces to a more convenient, two- parameter form by combining the distance and charge mass into a single SD variable of the form:    24   SD = DQEα ⎛ ⎝ ⎜ ⎞ ⎠ ⎟  Eq. 16 The explosive’s quantity, QE, is determined by the summation of all equivalent explosive weight charges with the same delay number, however, it is commonly accepted that an initiation time difference of 9 milliseconds or greater is required if constructive interference is to be avoided from neighboring charges (Dick et al., 1983). Timing analysis of long period detonators will reveal a large scatter in their delay time, which translates into the absence of constructive interference in the individual particle velocity waveform, reducing the overall vibration intensity (as will be demonstrated in later chapters). The normalizing factor, D/QEα, accounts for changes in the mass of the charge and variations in the propagation distance from the source to the reference point. Square-root scaling (α = 1/2) characterizes the approach normally used in studies of surface blasting. Square root scaling takes into consideration cylindrical wave propagation (two- dimensional) such as that of a body wave close to a cylindrical charge, or, at greater distances, that of a surface wave. Given that the charge mass is proportional to the square of the hole radius, this distance ratio, or SD, can be written as D/QE1/2. Likewise, where three-dimensional wave propagation closely represents the real world situation, cube-root scaling should apply. At substantial distances from a charge, where wave propagation is three-dimensional through an extended medium, cylindrical charges can be approximated as a spherical source. Here, explosive mass varies with the cube of the equivalent spherical-charge radius. Hence, in this case the SD is represented as D/QE1/3. In practical situations, other factors come into play, for example, a higher attenuation rate of high-frequency vibration components in cases where propagation distance is significant. The most appropriate scaling factor for use in a specific application is generally the one that provides the best statistical fit of the experimental data. Square-root scaling is normally used when propagation curves are being developed for vibrations from surface blasting as measured at the surface (which is a common situation). Cube- root scaling provides the best fit of experimental measurements for instances where wave propagation is approximately three-dimensional in reports such as those by Duvall and    25 Atchison (1957), Rupert and Clark (1977), and Naismith (1982); the last two studies measured vibration in underground coal mines from surface mine blasting. General blast vibration prediction formulae have been presented by Du Pont (1977) and by Abraseys and Hendron (1968). Singh and Vogt (1998) gave a classification of the most common blast prediction formulas, some of which are presented in the following set of equations: USBM1  PPV = K DQE ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −β  Eq. 17 AMHEN2  PPV = K DQE3 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −β  Eq. 18 LANKH3  PPV = K QE D 3 2 ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ β  Eq. 19 ISP4  PPV = K QE D 2 3 ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ β  Eq. 20 CMRI5  PPV = n + K DQE ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −1  Eq. 21 USBM1 = U.S. Bureau of Mines (Duval and Fogelson, 1962); AMHEN2 (Ambrasey and Hendron, 1968); LANKH3 (Langefors-Kihlstrom, 1978); and ISP4 (Indian Standard Predictor, 1973); CMRI5  (Central Mining Research Institute, Dhanbad, 1993). Where K, β, and n are site-specific experimental constants. However, given that the absolute charge mass, and the distance, geology, rock mass quality and types of blasting vary widely from site to site, the propagation equation should be developed from measurements taken at the particular site of interest. Where this is not possible, as in planning of the drilling and blasting operation for a new area, the findings obtained from empirical data obtained at other sites, under similar conditions, will provide a reasonable approximation.    26 When distances from the blast and explosive quantities are being determined for a large number of measurements of PPV, the best-fit criterion for the 3-parameter model is based on the minimization of the sum of the square residuals, ssr (Wetherelt et al., 2003):   ssr = PPVi − K ⋅Din ⋅QEiα( )2 i=1 N ∑  Eq. 22 Where PPVi, Di, and QEi, is the i triad, and N is the number of data points. Alternatively, for the two-parameter model, the sum of the square residuals, ssr, is:   ssr = PPVi − K ⋅ SDi−β( )2 i=1 N ∑  Eq. 23 It is common practice to express equation 17 in the log/log form:   logPPV = logK − β ⋅ logSD  Eq. 24 And to determine the parameters K and β by minimizing ssr for equation 24, where:   ssr = logPPVi − logK + β ⋅ logSD( )2 i=1 N ∑  Eq. 25 The resulting PPV-SD equation is considered to be the best-fit equation, which can then be employed for on-site prediction purposes (Dowding, 1985; Wetherelt et al., 2003). For the near-field case, Holmberg and Persson (1978) proposed a generalized PPV equation (Eq. 26) valid solely for distances that are short in comparison to charge length, such that the explosive charge can no longer be considered as concentrated at a point. For an extended charge of linear charge concentration, l (kg/m), a first approximation of the resulting PPV is obtained by integrating the generalized equation over the total charge length. This equation for near-field vibration particle velocity assumes that the vibration PPV resulting from the detonation along the entire column charge is numerically additive:   V = K ⋅ l ⋅ dx r02 + x − x0( )2[ ]n 2⋅αxs xs + H∫ ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ α  Eq. 26 Where    27 - V  = vibration velocity (mm/s, in/s), - K, α ,  n  = site specific constants, - l  = linear charge concentration (kg/m), - xs  = start length of charged blasthole (m), - xs + H  = end length of charged blasthole (m), and - ro  = length between explosive charge and measuring point measured .                          perpendicular to the longitudinal axis of the blasthole. They pointed out that resultant vibration PPV is representative of the stress caused by the vibration. One clear shortcoming of this method is that it is time independent (or basically a static approach). This method does not incorporate the arrival times of waveforms within a blasthole or the arrival times of waveforms from different blastholes within the blast, which limits its applicability for real-world examples. Figure 2.5 illustrates the corresponding dimensions for the estimation of the near-region vibration particle velocity.    28  Figure 2.5 Integration of the surface wave effect in the near region of an extended charge (After Persson et. al., 2001) pg. 245 Holmberg and Persson (1978) found that for competent Swedish bedrock masses the applicable constants are K = 700, α = 0.7, and n = 1.5. The limits of the damage zones can then be estimated from a plot of particle velocity vs. distance. Blair et al. (1996) suggested that the Holmberg-Persson equation requires further investigation. One problem is the way in which the Holmberg-Persson model deals with vibration peaks. For example, the model derives total peak vibration, VT, by the scalar summation of the individual vibration peaks (i.e., V1+V2+V3…). Blair argued that the model is incapable of providing the correct near-field analysis as this model does not incorporate any time delay for the vibration peaks at a given point and the peaks should be summed as vectors and not as scalar magnitudes. In the same context, Baird et al. (1992) shows that a cylindrical column of explosive does not propagate in a spherical radiating pattern as the Holmberg-Persson model. Blair subsequently developed a    29 dynamic finite element model to assess the damage zone and later developed simple analytical tools to assess the non-linear behavior (Blair, 2008) occurring in the very-near- field between charges of the same blasthole or among different blastholes separated by small distances. Persson (1997) showed from comparison of theoretical and experimental values that the effective parts of elemental waves arrive at a given point nearly simultaneously, i.e., the entire charge length detonates instantaneously. This assumption overlooks effects of the timing differences of the arrival of elemental waves originating at different parts of charge. The Holmberg-Persson near-field vibration particle velocity formula (Eq. 26) has been widely used since its introduction, however, Blair and Minchinton (1996) showed that it did not correctly integrate the contribution from each charge element. Later Hustrulid and Lu (2002) showed that the equation was developed using an embedded error, meaning that the Holmberg-Persson equation is mathematically incorrect. Hustrulid and Lu established that the SD equation can be written in differential form, as:   dV = K ⋅ (l ⋅ dx)α ⋅D−n  Eq. 27 Where l is the linear charge concentration (kg/m) and dx is the incremental charge length (m). The incremental form of equation 27 can be expressed as:   ΔV = K ⋅ (l ⋅ Δx)α ⋅D−n  Eq. 28 If the cylindrical charge is divided into N incremental charges, then the total PPV produced by the overall cylindrical charge should be expressed as:   PPV = K ⋅ lα ⋅ (Δx) α ro2 + (xi − xo)2[ ] n 2i=1 N ∑  Eq. 29 Which differs from the Holmberg-Persson equation (Eq. 26) written in the incremental form:    30   PPV = K ⋅ lα ⋅ (Δx) ro2 + (xi − xo)2[ ] n 2i=1 N ∑ ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ α  Eq. 30 One possible explanation for the good estimation capabilities of the Holmberg-Persson equation (Eq. 26) is the fact that the constants (or unknowns) K, α, and n are estimated from the best-fit relation as determined from actual records of seismic data. Even if the equation includes an error, this error is reduced by the fine-tuning of the constants toward those values that minimize the error against the provided data. This can be accomplished, for example, by means of a built-in Microsoft® Excel™ linear equation solver, using the Gauss-Jordan method, which solves systems of equations with two or more unknowns. 2.2.11 Rock Mass Damage from Blasting Extensive research undertaken by many investigators has verified that civil and rock structure damages have a direct relationship with the ground vibrations originating from blasting. The studies conducted by Swedish Detonic Foundation (Holmberg and Persson, 1978) resulted in a damage model, wherein damage to a rock mass is indicated if post-blast cracks exceed the pre-blast cracks. Holmberg (1993) concluded that damage was inflicted mainly in the rock structural discontinuities and joints, cracks, and other weak planes in the rock mass. Paventi’s work (Paventi, 1995), introduces a similar approach for characterizing rock mass damage based on petrofabric rock mass classification and rock units at the Birchtree mine, although the lack of blast monitoring data to relate rock mass damage to the energies generated by the blast makes a comparison to the work presented in this research impractical. The rock mass was considered disturbed through the following mechanisms: - near hole crushing due to high shock wave amplitudes, - generation of radial cracks due to high-pressure gas in the drill hole, - opening of the existing joints because of high-pressure gases produced from detonation of explosive, - fractures through spalling,    31 - reduction of shear strength due to blast induced rock movement, and - vibration induced displacement affecting the local slope stability or tunnel perimeter. Early investigations of blast damage of surface structures performed by the U.S. Bureau of Mines (Thoenen et al., 1937, 1938b and 1942) used criteria relating acceleration, frequency, charge size, and distance. Later research by Duvall (Duvall et al., 1957) established a criterion of 50mm/s (2in/s) particle velocity related to SDs, the latter utilizing a square-root power scaling law as discussed in Section 2.2.10. Crandell (1949) proposed that the damage caused by the blast vibrations was proportional to the energy ratio. The energy ratio, ER, was defined as a ratio of the squares of the acceleration a, and the frequency f:   ER = a 2 f 2  Eq. 31 Edwards et al. (1960), Langefors et al. (1973), Bauer et al. (1978), Holmberg et al. (1978) Mojitabai et al. (1996), and several others proposed particle velocity as a blast damage criterion. In general terms, a simple, single-term criterion such as PPV of ground vibrations can be used to determine the damage potential of rock and civil structures. Dowding (1985) successfully applied elastic theory for plane waves (Kolsky, 1963) to blasting problems from which it was deduced that particle velocity was directly proportional to the strain, ε. Therefore, an increase in the particle velocity should directly translate to an increase in ground strain which, in turn, generally induces greater damage to the structure. Holmberg and Persson (1978) stated that damage is a result of induced strain (ε):   ε = VP c  Eq. 32 Where, - VP = particle velocity, and - c   = characteristic propagation velocity of P/S/Raleigh wave.    32 Furthermore, the relationship between PPV and rock breakage performance has also been established (Cunningham, 1983). Breakage performance indicators include size distribution of the rock fragments, muck pile placement, and oversize occurrence, among others. PPV is also associated with the damage inflicted onto the surroundings of the blasted excavation (Holmberg and Persson, 1978; Holmberg and Persson, 1979, Holmberg and Hustrulid, 1981). 2.2.12 Particle Velocity Estimates in Relation to Structural Damage For the construction industry, the consensus is that a PPV of less than 50mm/s would have low probability of structural damage to residential buildings. Some general data relating PPV to rock damage in underground openings is currently available but is scarce. Even so, Langefors and Kihlstrom (1973) have proposed the following specific criteria for tunnels: PPV’s of 305mm/s and 610mm/s shall result in a fall of rock in unlined tunnels, and the formation of new cracks, respectively. Bauer and Calder (1970) observed that no fracturing of intact rock will occur for a PPV of 254mm/s, PPV of 254 - 635mm/s results in minor tensile slabbing and PPV of 635 - 2540mm/s would cause strong tensile and some radial cracking. Break up of rock mass will occur at a PPV of 2540mm/s. Bogdanhoff (1995) monitored near-field blast acceleration of an access tunnel in Stockholm. Vibration measurements were done at distances between 0.25 and 1.0 meters, outside tunnel perimeter holes with accelerometers. Altogether eight blasts were monitored. The PPV in the assumed damage range was found to be between 2000 and 2500mm/s. 2.2.13 Blast Damage Measurement Techniques Both direct and indirect techniques have been used in the past to measure the amount damage adjacent to the blasted area. Direct measurements include the use of: - visual inspection, - half-cast factor (HCF), - bore hole camera to determine the fractures before and after blasting, and    33 - measurements of overbreak (and underbreak) using survey measurements or laser profiling. Some other less common techniques include the use of borehole dilatometer (Scoble et al., 1987) to measure rock deformation modulus and relate it to the extent of excavation disturbance surrounding an underground opening and also locate open fracture within a rock mass (Koopmans and Hughes, 1985). Indirect measurements are conducted using mainly geophysical techniques to assess the blast damage which include: - vibration analysis, - cross hole seismic scanning, - surface seismic tomography, - ground penetrating radar (GPR), and - time domain reflectometry (TDR), among others. In the author’s opinion, visual inspection, overbreak, HFC, and vibration analysis associated with rock mass characterization are reliable, simple and robust techniques to measure blast damage, and can easily and routinely be carried out by mine personnel. Although the other techniques have their own merits for the purpose of assessing blast damage, these are considered more academic than practical, and thus are less likely to be performed on a regular basis. 2.2.14 Blast Overbreak The Equivalent Linear Overbreak Slough (ELOS) introduced by Clark (1998), is a damage criterion used to assess the stability of open stopes by defining an average thickness of over-broken material. It considers an average thickness of the excess material and can be estimated independently for back and walls. ELOS is an appropriate method to define overbreak since it is relatively simple to determine and yields a linear measure – in length units – and makes it easy to plot and compare. Figure 2.6 shows the design/planned profile, the final profile, and the average overbreak thickness (as per ELOS). A drawback of using ELOS is the apparently small amount of average overbreak    34 even for cases where there is a large localized overbreak zone since that volume is then divided by the surface area of the excavation where this value dilutes over the entire surface excavation. The problem of estimating overbreak in specific locations where the actual overbreak occurred, rather than employing the ELOS method, is the fact that these kinds of estimations are unable to explain why in other cases such overbreak did not occur where a different blasthole was detonated with the same explosive type and quantities. In this sense, ELOS generalizes well the amount of overbreak, whereas overbreak measured in a particular location would not always be explainable.  Figure 2.6 ELOS concept to measure average stope overbreak 2.3 Rock Mass Classification 2.3.1 Introduction For the purposes of producing preliminary assessments, evaluating support requirements, estimating degrees of deformation, and determining the magnitude of the strength of a given rock mass, among others, two complimentary rock mass classification systems are widely used in the field: Bieniawski’s RMR (1976, 1989) and Barton et al.’s Q (1974).    35 Such classification is highly effective in the development of a comprehensive picture of the nature and structure of rock masses. Whether using RMR or Q, it is essential first to describe the rock mass in detail, and from there translate this description into either classification index, rather than simply recording rating values during mapping. Without a fully described rock mass, cost evaluations, stability analysis, and studies of the effectiveness of support systems are almost impossible to carry out. These two classification systems employ somewhat similar parameters – geological, geometric, and design/engineering – where the main differences are the weighting assigned to those parameters, along with differentiations of the use of each parameter found in either system. Both methods evaluate quantitatively the quality of the assessed Rock Quality Designation The Rock Quality Designation (RQD) index (Deere et al., 1967) provides a quantitative estimate of the rock mass quality using logs of rock cores. RQD is defined as the percentage of intact core pieces longer than 100mm (4 inches) within the total length of the core, where the cored samples should be at least NW size (54.7mm or 2.15 inches in diameter), to somehow standardize the sample’s competency. Samples are drilled and extracted with a double-tube core barrel. Figure 2.7 summarizes the measurement procedures of the length of the core pieces and a calculation example of the RQD.    36  Figure 2.7 Procedure for measurement and calculation of RQD (after Deere, 1989) Palmström (1982) suggested that when core samples are not available, the rock discontinuities visible in surface exposures or exploration addits could be used to estimate RQD from the number of discontinuities per unit volume. With respect to clay- free rock masses, the suggested relationship is:   RQD = 115 − 3.3 ⋅ Jv  Eq. 33 where Jv is the sum of the number of joints per unit volume for all joint (discontinuity) sets. Jv is known as the volumetric joint count. Given that RQD is a directionally dependent parameter, its value may change substantially with respect to borehole orientation. To reduce such directional dependence, a volumetric joint count is recommended. In cases of diamond drill core, because RQD is intended to represent rock mass quality in-situ, it is imperative that fractures caused by handling or the drilling process itself are identified and subsequently ignored. Where Palmström's relationship is used for structural mapping of undisturbed rock masses and in estimating Jv, blast induced fractures should be ignored.    37 With regard to the research conducted for the present study, RQD is estimated and employed as a parameter of the RMR and Q rock mass classifications systems, covered later. 2.3.2 Bieniawski’s Geomechanics Classification - RMR Bieniawski (1976) produced a rock mass classification called the Geomechanics Classification or Rock Mass Rating (RMR). The five parameters used to classify a rock mass quality under the RMR system are: - uniaxial compressive strength of rock material, - rock quality designation (RQD), - spacing of discontinuities, - condition of discontinuities, and - groundwater conditions. To employ RMR, a given rock mass is first divided into a number of structural regions. Each region is subsequently classified separately. The boundaries of the structural regions may be determined by consideration of major structural features, such as a fault, or by examining changes in rock type. In some cases, the rock mass will need to be subdivided into a number of small structural regions, where significant changes in discontinuity spacing or characteristics must be accounted for within the same rock type. The system is presented in Table 2.1, which gives ratings for each of the five relevant parameters. These ratings are summed to produce a value of RMR.        38  Table 2.1 Rock Mass Rating System (After Bieniawski, 1976)  The value of RMR can vary from nearly 10 to 100, with values of approximately 25 representing extremely poor ground and values rating around 100 representing exceptionally good, competent unjointed ground. Bieniawski (1989) includes a set of guidelines as an aid to the selection of support for tunnels excavated in rock where RMR is employed. 2.3.3 Barton’s Rock Tunneling Quality Index, Q Using a large number of underground excavation case histories, Barton et al. (1974) of the Norwegian Geotechnical Institute, introduced a Tunneling Quality Index (Q) used to evaluate the characteristics of rock mass employed for the design of the tunnel support requirements. The index Q varies on a logarithmic scale from 0.001 to a maximum of 1,000, and is defined by:   Q = RQDJn ⋅ Jr Ja ⋅ Jw SRF  Eq. 34 Where RQD is the Rock Quality Designation, Jn is the joint set number, Jr is the joint roughness number, Ja is the joint alteration number, Jw is the joint water reduction factor and SRF is the stress reduction factor. To give an explanation of the meaning of the parameters involved in determining Q, Barton et al. (1974) offer the following description: Point-load strength index > 8 MPa 4-8 MPa 2-4 MPa 1-2 MPa Uniaxial compressive strength > 200 MPa 100-200 MPa 50-100 MPa 25-50 MPa 10-25 MPa 3-10 MPa 1-3 MPa 15 12 7 4 2 1 0 90% - 100% 75% - 90% 50% - 75% 25% - 50% 20 17 13 8 > 3 m 1 - 3 m 0.3 - 1 m 50 - 300 mm 20 25 20 10 Very rough surfaces Not continuous No separation Hard joint wall contact Slightly rough surfaces Separation < 1 mm Hard joint wall contact Slightly rough surfaces Separation < 1 mm Soft joint wall contact Slickesided surfaces or Gouge < 5 mm thick or Joint open 1 - 5 mm Continuous joints 25 20 12 6 Inflow per 10m tunnel length None < 25 liters/s 25 - 125 liters/s Ratio of joint water pressure and major principal stress 0 0.0 - 0.2 0.2 - 0.5 General condition Completely dry Moist only (interstitial water) Water under moderate pressure 10 7 4 RANGE OF VALUES Drill core quality RQD For this low range uniaxial compressive test is preferred 5 > 125 liters/s 0 Ground water Severe water problems > 0.5 Rating 2 3 4 PARAMETER 1 Strength of intact rock material Rating Rating Spacing of joints Rating Condition of joints Rating 0 Soft gouge > 5 mm thick or Joint open > 5 mm Continuous joints 5 < 50 mm < 25% 3    39 The first quotient (RQD/Jn), representing the structure of the rock mass, is a crude measure of the block or particle size, with the two extreme values (100/0.5 and 10/20) differing by a factor of 400. If the quotient is interpreted in units of centimeters, the extreme 'particle sizes' of 200 to 0.5cm are seen to be crude but fairly realistic approximations. Probably the largest blocks should be several times this size and the smallest fragments less than half the size. (Clay particles are of course excluded.) The second quotient (Jr/Ja) represents the roughness and frictional characteristics of the joint walls or filling materials. This quotient is weighted in favor of rough, unaltered joints in direct contact. It is to be expected that such surfaces will be close to peak strength, that they will dilate strongly when sheared, and that they will therefore be especially favorable to tunnel stability. The third quotient (Jw/SRF) consists of two stress parameters. SRF is a measure of: 1) loosening load in the case of an excavation through shear zones and clay bearing rock, 2) rock stress in competent rock, and 3) squeezing loads in plastic incompetent rocks. It can be regarded as a total stress parameter. The parameter Jw is a measure of water pressure, which has an adverse effect on the shear strength of joints due to a reduction in effective normal stress. Water may, in addition, cause softening and possible outwash in the case of clay-filled joints. The quotient (Jw/SRF) is a complicated empirical factor describing the 'active stress'. It appears that the rock tunneling quality Q can now be considered to be a function of only three parameters, which are crude measures of: - block size (RQD/Jn), - inter-block shear strength (Jr/ Ja), and - groundwater and active stress (Jw/SRF). The numerical value of the index Q varies on a logarithmic scale from 0.001 for exceptionally poor ground to a maximum of 1,000 for exceptionally good, competent, practically unjointed ground. Table 2.2 gives the classification of individual parameters used to obtain the Tunneling Quality Index Q for a rock mass.    40 Table 2.2 Classification of individual parameters used in the Tunneling Quality Index Q (After Barton et al 1974)     41 Table 2.2 (cont’d.) Classification of individual parameters used in the Tunneling Quality Index Q (After Barton et al 1974)     42 Table 2.2 (cont’d.) Classification of individual parameters used in the Tunneling Quality Index Q (After Barton et al 1974)   2.3.4 Rock Support Under Dynamic Loading It is evident that the rock support employed should be designed to withstand the dynamic loading of nearby blasts. This is especially important when the ground being supported is of weak rock mass, in which the rock excavation is only held up by the supporting elements acting against an otherwise extreme deformation, to the point of caving. For this type of weak ground, where the use of shotcrete is very common, in combination with other means of rock support, there has been extensive work done in the field in terms of    43 empirical design (Pakalnis et. al., 2010), numerical modeling (Zhou and McNeary, 2007; Caceres et. al., 2010), and laboratory testing of shotcrete panels (Bernard and Pireher, 2000; Martin et. al. 2010).  In any case, there remains a need for better understanding of the behavior of shotcrete under the instantaneous dynamic stresses exerted during the blasting process. 2.3.5 Support Design Requirements A better understanding of the dynamic behavior of different rock mass qualities should provide fundamental information to define the type of ground support that requires a specific set of rock mass conditions. Input parameters, such as PPV values and ground vibration frequencies coupled with dynamic (and static) rock support strength, should be regularly assessed to provide the safest and most cost-effective ground support design.    44 3 FIELD DATA COLLECTION AND ANALYSIS 3.1 Introduction There are two main purposes of drifting in underground mining, the first is that the drift itself as driven into ore material constitutes economic benefit to the mine; and the second is to gain access to an orebody. Secondary purposes may include ventilation and material transportation, among others. The main objective of the drifting process is to achieve the desired excavation profile as safely and cost-effective as possible. In this process, key factors include minimizing overbreak and damage to the remaining rock mass, hence reducing the support requirements up to an acceptable risk level while achieving the desired fragmentation for cost-effective material handling. 3.2 The Drifting Process The process of drift development, also known as drifting, comprises a series of tasks performed sequentially. Briefly, the process starts by defining and delineating the direction of the drift and the blasthole location. This is followed by the drilling of blastholes and, subsequently, the loading of explosives. Once personnel and equipment have been vacated from the area, the round is blasted. After gases produced by the chemical reaction of the detonated explosives and the dust are ventilated, mucking of the broken material takes place. Manual and/or mechanical scaling of loose material to ensure there is a safe entrance to the workplace follow this. Once the support system and mining services are installed, the process repeats itself. The drifting process is summarized in the following flow chart. The whole process is guided by planning and engineering and regulated by human, economic, and workplace factors.    45  Figure 3.1 Sequential tasks of the drifting process  3.3 Methods of Field Data Collection 3.3.1 Process of Field Data Collection Data was obtained through a field measurement process and a data collection process, followed by analysis and interpretation of the results. Details of each step and the logistics involved are given below. The following flow chart shows the different tasks involved in the pre-blast site investigation. These tasks can be executed in any given sequence, but they obviously depend on the availability of the workforce operating the machinery in the drift. Ideally, the site investigation should disrupt the drifting process as little as possible.    46  Figure 3.2 Pre-blast data collection process The post-blast site investigation is concentrated in the newly created excavation and includes the following tasks:  Figure 3.3 Post-blast data collection process Although not included as part of the flow chart, a visual inspection to record any extra features that can help future analysis of the information, such as excessive break out in parts of the drift or the condition of the support in use to address rock bolt plate conditions and bagging of mesh with broken material, is performed.    47 During the pre- and post-blast site investigation it was necessary to take extra precautions to avoid injuries as there was more exposure to unsecure conditions like working right at the face or during the drilling and explosive loading of the blasthole round. 3.3.2 Rock Mass Quality Assessments Two systems were employed to characterize rock mass quality: Bieniawski's Rock Mass Rating, RMR (1976), and Barton’s Rock Tunneling Quality Index, Q (1974). See Sections 2.3.2 and 2.3.3 for explanations. Uniaxial compressive strength values were obtained from laboratory test reports (previously completed on similar rock types for each of the mines investigated). No unconfined compressive strength tests had been performed at those particular sites. It is a common practice among geotechnical engineers and technicians to quantify the strength of a rock mass based on a hammer blow to the exposed rock for the purpose of analyzing its soundness. This method was employed along the entire, actual monitored drifts in order to confirm that the values obtained were consistent with those from previous tests performed on similar rock types. RQD values were determined based on the average spacing of the joint sets and the relation existing between average spacing and RQD. As in the case of the strength of the rock mass, it is common practice to assess the RQD values based on average joint set spacing, in the absence of diamond drill core. The graph shown in Figure 3.4 presented by Bieniawski (1989), was used to determine approximated RQD values.    48  Figure 3.4 Relationship between discontinuity spacing and RQD, after Bieniawski (1989) Barton et al. (1974) Tunneling Quality Index (Q) was also determined for the purpose of assessing the rock mass quality. The numerical value of the index Q is defined by:   Q = RQDJn ⋅ Jr Ja ⋅ Jw SRF  Eq. 35 All of the values prescribed by the Q system, such as RQD, Jn (joint set number), Jr (joint roughness number), Ja (joint alteration number), Jw (joint water reduction factor), and SRF (stress reduction factor), were determined based on visual inspection of the sites being monitored.  The data was subsequently reported as three separate ratios RQD/Jn, Jr/Ja, and Jw/SRF. As is the case in RMR, the larger the index Q, the more competent the rock mass. Figure 3.5 shows the rock mass quality information sheet used for each mapped cell, featuring independent descriptions for both walls and back. Each cell constitutes a surface of a previously blasted round. Cells include Bieniawski’s (1976) Rock Mass Rating (RMR), Barton’s (1974) Tunneling Quality Index Q, Deere’s (1976) Rock Quality Designation (RQD), dip and dip direction of major joint sets including persistence, spacing and number of occurrences, as well as field notes of type and condition of support installed, and any other description that may enhance the information detailed, such as number and length of half-barrels visualized, and a visual assessment of the    49 amount of overbreak that might have occurred (obtained with the help of a handheld laser distance meter).  Figure 3.5 Cell mapping of both walls and back for each round In order to have a visual record for future analysis and interpretation of rock mass quality and type and condition of the rock support employed, three pictures of the right and left walls and the back were taken for every round length. As an example, Figure 3.6 shows the left wall of the drift, where the face of the round represents the front.    50  Figure 3.6 Photograph of the left wall showing structures and rock mass condition The dip and dip direction of the structures and joint sets were measured using a Brunton® compass, for which the declination had been previously set up to measure the strike of rock features with respect to mine North. 3.3.3 Blast Monitoring and Equipment High frequency triaxial geophones were installed along drifts to measure particle velocity. These instruments are capable of measuring ground velocities up to 2540mm/s (100in/s) between the 28Hz to 1000Hz range. The geophones were bolted to the ribs of one or both walls, preferentially on solid rock or mounted on an aluminum bracket, and on shotcrete when the circumstances required doing so. The data loggers or monitors were set to begin recording triggered by ground motion exceeding 10mm/s. The location for the installation of each geophone was selected after a thorough inspection, to avoid intersecting rock features that could cause faulty readings (because of loosening of the coupling of the geophone to the rock). Because the geophones were installed as near to the face as possible, in some close distance cases a protective metal box was used to shield the instruments from the shock wave, and from the ejected rock from the blast (Figure 3.7).    51  Figure 3.7 Protective metal box with geophone and datalogger installed The seismic data, consisting of the measurement of particle velocity over a period of time, was recorded on an Instantel™ MiniMate Plus® datalogger (seismic monitor). Figure 3.8 shows the MiniMate Plus®, along with a high frequency triaxial geophone used to monitor blast-produced seismic vibrations.    52  Figure 3.8 Minimate Plus® and high frequency triaxial geophone The geophones were connected to the dataloggers using cables of various lengths, permitting coverage of long lengths (up to 25 meters) with the use of a single datalogger. A maximum of two geophones can be connected to each datalogger of the series employed. The internal batteries of the datalogger were fully charged to ensure that they were able to record during the blasting event, which could be hours after the instruments were installed. Also, they required the setup of the sampling rate (the number of samples recorded per second) to a maximum of 16,384 samples per second, along with the length of time of the measurement once triggered, to ensure that all blastholes of a round were recorded. Ten seconds is sufficient to record all the events of a round when long-period delay detonators are used. In many cases, the dataloggers recorded events other than the blasting episode, triggered by vibration levels in excess of 10mm/s, such as when heavy machinery was passing close to the geophone. As these instruments have a limited memory capacity, it was imperative that the useable records were downloaded immediately following each event, in order to clear and free up available memory.    53 At the end of the monitoring process, all instruments were retrieved, in some cases many hours after the event occurred, when personnel were allowed access to the monitored drift. The technical specifications of the geophones utilized were obtained from the product instruction sheet Table 3.1 – High Frequency Triaxial Geophone – Instantel® web page. Table 3.1 High Frequency Triaxial Geophone – Instruction Sheet (source: www.instantel.com, June 2011) Specifications Amplitude Range 100in/s (2540mm/s) Frequency Range 28Hz to 1000Hz Sensitivity 0.0012674V/in/s (0.33222605V/mm/s) Resolution 0.00310in/s (0.0788mm/s) Trigger Levels 0.05 to 100in/s (1.27 to 2540.00mm/s) Sensor Density 145lb/ft3 (2.33g/cc) Recommended Sample Rate 4096 samples per second Cable Length 100ft (30.48m)  The frequency response curve and the phase lag for model type SM-7 30Hz geophone sensors are shown in Figure 3.9 and Figure 3.10 respectively. The SM-7 sensors are manufactured by Ion Geophysical Corporation. From the response curve it can be seen that sensitivity rapidly decreases for frequencies lower than 30Hz and is negligible below 10Hz. On the upper side, the sensitivity shows an almost flat response for frequencies in the range 30-1000Hz. The equipment utilized is incapable of recording accurately frequencies below the 30Hz threshold and has zero sensitivity for frequencies lower than 8Hz where an important portion of the low frequency particle velocity is to be found. However, rock breakage occurs not because of the PPV at a particular frequency level, but occurs due to the cumulative particle velocity over a wide range of frequencies.     54  Figure 3.9 SM-7 30Hz geophone response curve (modified from www.iongeo.com, June 2011) The phase response starts around 0 degrees at approximately 0Hz, then reaches 90 degrees at 30Hz, ascending to approximately 160 degrees at 100Hz.     55  Figure 3.10 SM-7 30Hz geophone phase lag (modified from www.iongeo.com, June 2011) 3.3.4 Explosives Characteristics The following table (Table 3.2) lists the technical specifications of the explosives utilized in the blasting of development rounds. Some of these specifications can only be taken as average values since they could vary due to a variety of factors. Some of these factors are inherent to the explosive itself, and some are external, dependent upon the surrounding rock, and the size and condition of the blasthole. Table 3.2 Explosive utilized – Main specifications (source: www.dynonobel.com, June 2011) Specifications ANFO Dyno® AP Dynosplit® Density (g/cc) 0.84 1.15 1.40 Energy (cal/g)                (cal/cc) 880 720 775 890 995 1,440 Relative Weight Strength 1.00 0.88 1.13 Relative Bulk Strength 1.00 1.24 2.00 Velocity (m/s) 3,400 4,700 2,600 Detonation Pressure (kbars) 31 63 25 Gas Volume (moles/kg) 43 41 32 Water Resistance None Excellent 24 hrs     56 The relative weight strength is a specified explosive characteristic used to compare the energy content and the production of gases of different explosives with respect to an explosive considered standard. In many cases, including in this research, the standard explosive used is ANFO, a combination of ammonium nitrate and fuel oil, which at a certain percentage, maximizes energy delivered and balances oxygen consumption (i.e., minimizing production of CO and NOx gases). 3.4 Methods of Analysis of Field Data 3.4.1 PPV and SD PPV measurements of each blasthole or combination of blastholes were determined directly from the vector sum of the three independent and perpendicular particle velocities versus time velocities. The larger the amount of explosives detonated per delay, the higher the PPV measured for similar excavation geometries and rock mass conditions, although the quantities of explosive and the distances to the blast must be normalized in order to compare them with different explosive types and quantities, used within the same blasthole or blastholes in the round. It is common practice to use SD (Dowding, 1985), which can be defined as the relation existing between the standardized explosive quantities to its equivalent quantity of ANFO – or any other explosive used as a reference – measured in kilograms or pounds, and the distance to the explosive source measured in meters or feet, from an arbitrary point. For the analysis herein, the standardization of different explosive types was performed using their relative weight strength to that of ANFO, based on information obtained and documented by the explosives companies. Figure 3.11 portrays an example of a section of the combination of explosives loaded into individual blastholes for body, perimeter (contour), and lifter blastholes at the Stillwater mine.    57   Figure 3.11 Perimeter and lifter blastholes - Explosive’s distribution – Stillwater mine  The PPV relationship is presented with respect to the SD as an equation of the type shown in equation 26.   PPV = K Q α Dn ⎛ ⎝ ⎜ ⎞ ⎠ ⎟  Eq. 36 Where n, α, and Κ are the site-specific constants, D is the distance to the source, and Q is the weight of explosives detonated per delay. In this analysis, it was assumed that α=0.5 , and so only K and n are the unknowns to be determined based on the best-fit power law relation, as applied to the cloud of data points recorded.    58 Once these constants are determined (and incorporated back into the Holmberg-Persson equation (Eq. 26)), it then is possible to establish the near-field PPV necessary to produce the measured amount of overbreak, for any given rock mass quality. 3.4.2 Frequency Content of a Waveform The frequency content was obtained from the particle velocity versus time records, and then compared to the differences existing among the range of rock mass qualities being analyzed. As determined in the proposed semi-empirical model, in the upcoming pages, only the main, predominant frequency will be used to assess PPVs. 3.4.3 PPV Analysis using Band-Pass Filter The following figures display the resultant PPV waveforms (after the original waveform has been filtered using a band pass filter). The set of ranges analyzed were 0-100Hz, 100- 500Hz, 500-1000Hz, and 1000-1500Hz. The scale of each pair of graphs, i.e., with and without band pass filtering, is the same.  Figure 3.12 PPV versus time record – With and without band pass filter (0-100Hz)     59  Figure 3.13 PPV versus time record – With and without band pass filter (100-500Hz)   Figure 3.14 PPV versus time record – With and without band pass filter (500-1000Hz)     60  Figure 3.15 PPV versus time record – With and without band pass filter (1000-1500Hz) It is clear from the above graphs that, when the seismic monitors are in close proximity to the blast, the largest PPV values are determined in the high frequency range of the spectrum. In particular, for the Musselwhite Mine case study, this range was between 500-1500Hz yielding an average of more than 90% of the original PPV value. It is important to note that there is practically no literature available regarding such high frequency readings and high levels of PPV measurements. This is because the majority of existing, available data had been recorded at considerable distances from the blast. 3.4.4 Data Processing Data processing included analysis of the various seismic records obtained from each geophone installed along a given drift. The results of the PPV for several events were combined on a single spreadsheet. Seismic data processing was by Instantel® Blastware™ software (v. 4.37). Each seismic record included three independent particle velocity measurements (in millimeters per second), one for each axis (horizontal, vertical, and transversal) of the triaxial geophone, as depicted in Figure 3.16.    61  Figure 3.16 Transversal, vertical and longitudinal particle velocity record The vector sum of the three components is obtained by applying the square root of the sum of the square of the horizontal, vertical, and transversal particle velocity component measurements at any given time, from which PPVs for each individual blasthole or sets of blastholes are determined, as shown in Figure 3.17. Each seismic record has an associated standardized explosive quantity and length, and from each peak (using the vector sum), a single point on the PPV versus SD graph is determined. It is important to note that the vector sum PPV might not coincide with the peak velocity of each of the three individual records.    62  Figure 3.17 Vector sum of the three individual particle velocity components In order to illustrate the relationship that exists between the frequency spectrum range and the rock mass quality assessed, the seismic record waveform of a single blasthole was isolated from the waveforms pertaining to other blastholes, as shown in Figure 3.18. Background noise, which is also mixed with the seismic events, distorts the overall frequency content, and can lead to ambiguous results. It is for these reasons that filtering and isolating individual blasthole waveform are important to determine the most significant frequency range where the PPV is the highest. The fast Fourier transformation was applied to this isolated portion, and the frequency spectrum was thus obtained (Figure 3.19).    63  Figure 3.18 Isolated seismic waveform   Figure 3.19 Frequency content for burn cut blasthole  A number of examples regarding the frequency content obtained for various experiments performed on the information gathered can be found in Appendix B – Particle Velocity and Frequency Content - Case Studies. There, the frequency content of an isolated waveform compared to the frequency content of the entire blast, the frequency content of the blast compared to the quiet portion in between blast records, is shown. Also, the    64 frequency content of an original waveform compared to the frequency content of various filtered waveforms using the smoothing function, which averages successive particle velocity records using a moving box, used to decrease the standard deviation of the original waveform, can be found in Appendix B as well. Also, the frequency content of the waveforms of a number of successive blastholes given by their respective delay number, and the frequency content for the same blasthole measured from different geophone locations at increasingly longer distances from the blast, is included.    65 3.4.5 Overbreak Assessments – Scanner Profiles Overbreak (as defined for this specific research), consists of the average thickness of excess rock, for one section of a blasted round, beyond its design perimeter. Figure 3.20 shows the planned profile, the final profile, and the estimated average thickness of overbreak/underbreak, for a single section of the drift.  Figure 3.20 Planned or as-built profile against final profile The average overbreak/underbreak comprises a number of sections of measurements of overbreak/underbreak as depicted in Figure 3.21.     66  Figure 3.21 Average overbreak measurement over an entire blasted round section To calculate overbreak values, a series of three-dimensional digital profiles were generated utilizing a laser scanner computerized surveying unit (Leica™ Geosystems HDS 3000® (Figure 3.22)) of the family of LIDAR systems. LIDAR stands for Light Detection and Ranging.     67  Figure 3.22 Leica™ HDS3000® laser scanner This LIDAR unit can not only obtain a three-dimensional point cloud image with the actual size and shape of the volume being surveyed, but also detect and record different colorations of the surfaces, depending on their reflective properties (when hit by the laser device), as shown in Figure 3.23. In this particular image, several features can be detected in great detail: the contour of the excavation, the welded mesh installed, a pool of water, and wood pieces in left lower corner of the drift.    68  Figure 3.23 Laser scanned profile of a development drift A less accurate technique was also employed in the absence of the LIDAR surveying system, by using a high-precision handheld laser distance meter. Readings were taken across the drift and the results were recorded manually. 3.4.6 Other Analysis of Field Data Part of the whole field data collection process included photographing the face loaded with the explosives, prior to blasting, and marking the location of each blasthole in the round with the detonator delay numbers. These numbers were subsequently superimposed to the loaded face to track changes to the original design, as shown in Figure 3.24. This helped reconcile the delay numbers and the different explosives loaded within the same round, e.g., ANFO for production holes, Dyno Split D® for perimeter holes, and Dyno AP® for lifter holes.    69  Figure 3.24 Picture of the face showing dimensions and blasthole long period delay number 3.4.7 Structural Mapping The equal area Schmidt stereonet projection shown in Figure 3.25 was obtained using Rocscience™ Dips® software, from the records of dip and dip direction, of all major structures present in every cell mapped. The projection permits visualization and analysis of structures present, in order to examine the potential for wedge failures (which may raise safety concerns or increase the amount of overbreak material that is not in direct relation to the detonation process).    70  Figure 3.25 Representation of major structures on Schmidt stereonet 3.4.8 Detonator Delay Scatter Figure 3.26 shows the measured scatter of the defined delay numbers of the explosive detonators. Zero cap delay scatter implies that the total weight of explosives fired with the same delay number should be numerically summed. Linear superposition of individual particle velocity waveforms would produce constructive interference, generating greater peak values versus peaks of blastholes fired independently of each other.    71  Figure 3.26 Long period cap delay scatter Figure 3.27 shows a set of PPV versus SD measurements (D/Q^½), for one blasting round at the Turquoise Ridge JV mine. Geophones were installed at 3.5m, 6.0m, and 15.0m from the face. The different explosives used for production holes (Dyno AP®) and perimeter back holes (Trimtex®) were then standardized with the relative weight strength to that of ANFO. From the PPV versus SD cloud of data points, graphed in Figure 3.27, the best-fit curve is obtained and the constants K and n are determined.    72  Figure 3.27 PPV versus SD The large scatter of the cloud of data points is due to the fact that a single average distance, from the blasthole to the geophone, is used for all blastholes pertaining to the round, irrespective of their location to the different geophones installed. In the following chapters a different treatment will be used to calculate an approximate distance to each and every blasthole of the round, in an attempt to reduce this large scatter. 3.5 Limitations and Advantages of the Presented Empirical Data There are a number of limitations in relation to the empirical data presented that are noteworthy. It is important though to highlight the fact that the data was obtained from measurements made at real underground operations and under real production conditions, that is, not from laboratory experiments (which can be repeated any number of times). The reader must understand that working with experiments as performed in a laboratory differs greatly from the process of taking measurements at the site. Also, due to the nature of the given rock mass, there could be huge variability in its behavior, making the analysis of the data thus gathered a much more complex procedure.    73 Due to cost constraints, a limited number of overbreak measurements were gathered from the four mine sites in question. From these, a strong correspondence among overbreak values, rock mass qualities, and PPV measurements was established. More measurements should naturally confirm this to a higher degree of certainty. As it stands, the finding is that the higher the rock mass quality, the higher the PPV recorded, and at the same time, the lower the measured overbreak. For two of the four sites, a handheld laser distance meter was used when the LIDAR was not available which would have produced much greater accuracy of overbreak measurements. The high frequency geophones used cover only the intermediate to high frequency range (28Hz – 1000Hz) leaving out the low frequency range (<28Hz), where a portion of the overall PPV would be expected to be encountered. Future research should, if possible, utilize two geophones installed in the same location to record a much wider range of frequencies. The RMR and Q values were provided using the original versions of these rock mass classification systems (that is, not the updated versions). The reason for this is that they are simpler than current versions of these systems which makes comparison with other classification systems easier, provided that not just the ratings are given but a detailed description of the rock mass is included. Rock damage and overbreak occurs relatively close to the explosive charge, normally at distances much closer than the nearest geophone is usually installed. Extrapolation of the recorded PPV versus SD curve, in order to obtain the potentially damage-inducing PPV levels, is therefore typically performed. In an effort to overcome this particular and very common limitation, geophones were installed very close to the explosive charge, which reduced the amount of extrapolation needed for the best-fit curve, thus limiting the error of the estimated PPV.    74 4 CASE STUDIES 4.1 Introduction A total of five underground mines located in North America were investigated and development round blasts were monitored and assessed as previously specified. The purpose of the field investigation was to monitor the blast rounds, characterize the rock mass quality (using RMR and Q geomechanical classification systems) and assess blast induced overbreak (using laser scanning profiles or handheld laser distance meter measurements). Table 4.1 shows the mines site visited as part of the data gathering process. Table 4.1 Mine site case studies Mine Location Company Dates Stillwater Montana, USA Stillwater Mining Co. July 16 – 21, 2006 Stillwater Montana, USA Stillwater Mining Co. Sep 10 – 15, 2006 Steer Nevada, USA Queenstake Resources Ltd. Nov 5 – 11, 2006 Turquoise Ridge JV Nevada, USA Barrick - Gold Corp. Mar 26 – 29, 2007 East Boulder Montana, USA Stillwater Mining Co. Sep 18 – 21, 2007 Musselwhite Ontario, Canada Goldcorp Inc. May 14 – 16, 2008  Table 4.2 shows the total number of PPV measurements available in each case, to derive the PPV versus SD relation and associated overbreak. The author would like to highlight the fact that in the East Boulder Mine investigation no useful data was gathered as mucking equipment destroyed one datalogger – with two geophones connected – and on the second datalogger, one of the connecting cables to the geophone was torn up by fly rock.    75 Table 4.2 Number of PPV measurements and average RMR Mine No. of PPV Measurements Average RMR Stillwater 350 65 Steer 189 35 Turquoise Ridge JV 109 55 East Boulder 0 60 Musselwhite 190 90 TOTAL 838  Details of the geotechnical mapping done at each of the mine sites investigated can be found in Appendix A – Rock Mass Quality Logs. 4.2 Stillwater Mine – Montana USA The J-M Reef ore deposit stretches 28 miles underground in southern Montana's Beartooth Mountain Range, USA. At the beginning of the 1970s the J-M Reef ore deposit was discovered. It is a 45 kilometer-long reef that belongs to the Stillwater Complex. The reef deposit consists of successive layers of ultramafic to mafic rocks, silicate minerals, and rocks rich in magnesium and iron. Platinum group metals (PGMs) such as platinum, palladium, and other precious metals are contained in the ore body. Mining methods employed include sub level open stoping, captive cut and fill, and ramp accessed mechanized cut and fill methods. Figure 4.1 shows a plan view of the 4400ft level heading monitored.     76  Figure 4.1 4400ft level heading – plan view – Stillwater Mine 4.2.1 Rock Mass Quality The rock types at the Stillwater mine, considered to be medium to hard with average compressive strength in the order of 100MPa, consist principally of anorthosites, gabbros, norites and dunites. The rock mass present in the monitored areas and the ground support (wire mesh and straps bolted with 0.9 m friction bolts with face plates for the upper corners of both walls and back) are shown in Figure 4.2, Figure 4.3, and Figure 4.4.     77  Figure 4.2 Typical 4400ft and 4700ft level headings – support installed – Stillwater Mine   Figure 4.3 4400ft level heading – blocky ground with support – Stillwater Mine     78  Figure 4.4 4400ft level headings – after-blast picture – Stillwater Mine The average rock mass quality determined from the 4400ft and 4700ft drift levels (Q and RMR) is presented in Table 4.3 and Table 4.4, respectively. Similar rock characteristics were found at both levels. Rock mass tends to be very blocky where the excavation contour typically begins at a joint set face. Overbreak/underbreak is likely to be higher in this case. There are usually slight signs of stress build-up in the upper corners. Where the ground is less blocky, more massive and silicified, the blasted contour follows the planned profile more closely. Table 4.3 Barton’s Q index components – Stillwater Mine Rock strength  100MPa Block size (RQD/Jn)  7.60 Joint strength (Jr/Ja)  0.63 Jw/SRF (dry/low stress)  1.00 TOTAL  ≈ 4.79      79 Table 4.4 Bieniawski’s RMR ratings – Stillwater Mine Rock Strength R4 12 RQD 80% 15 Spacing 5cm-30cm 13 Joint condition Tight-slightly open 15 Ground water Dry 10  RATING ≈ 65  The size of the 4400ft and 4700ft level drifts monitored were 3.0m wide by 3.5m tall with an arched back. The average length of each blasthole was 4.0m, of which 3.75m was loaded with explosives; no material was used as stemming. The total number of blastholes loaded was 42 with 6 relief holes, as depicted in Figure 4.5. Table 4.5 displays the explosive employed for the different blastholes used throughout the blast pattern and its weight relative to ANFO. The approximate blast efficiency (pull) is 92%, that is, blast depth advancement with respect to original planned blasthole depth. Average overbreak was estimated to be about 0.20m. Table 4.5 Summary of blasthole ID, explosive types and relative weights per blasthole – Stillwater Mine  Blasthole ID   Explosive Type  Weight Relative to ANFO (kg)  Lifters  Dyno AP  4.69  Back  Dynosplit D (22mm x 400mm)   3.72  Production  ANFO  6.00  Perimeter  ANFO  6.00       80  Figure 4.5 Typical 4400ft and 4700ft level headings – blast pattern – Stillwater Mine Figure 4.6 shows the 3D profile of the excavation and blasthole projection at the 4400ft level.    81  Figure 4.6 4400ft elevation heading – Laser scanned side view – SSX Mine 4.2.2 Vector Sum PPV and Frequency Content A representative particle velocity record for the Stillwater Mine is presented in Figure 4.7.  Figure 4.7 PPV versus time – Stillwater Mine Figure 4.8 shows the vector sum of the PPV for multiple numbers of blasted rounds recorded on geophones installed in the 4400ft and 4700ft level drifts.  The PPV values were recorded at SD values as low as 4.2m/kg^0.5 for all heading’s blastholes and 1.1m/kg^0.5 for the nearest signature blasthole. The highest PPV value recorded was 450mm/s corresponding to a burn cut blasthole, and 930mm/s for a signature blasthole.    82 The seismic record used to determine frequency content was recorded at a sampling rate of 8192 records per second (this rate was a compromise between higher data recording versus memory available on the equipment).  Figure 4.8 PPV versus SD values – Stillwater Mine The PPV versus SD power law best-fit curve is estimated from 350 records:   PPV = 412.9 ⋅ DW ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −0.85  Eq. 37 The 95% confidence line is shown in Figure 4.9. This additional curve includes at least 95% of the data points, which fall within or below this boundary. The additional boundary is obtained through the use of the standard error of the estimates applied to the provided data, subjected to a 95% confidence level.    83  Figure 4.9 PPV versus SD boundary – 95% confidence level – Stillwater Mine Figure 4.10 shows a characteristic frequency spectrum for a single burn cut blasthole where peak frequencies are close to 150Hz and nearly all predominant frequencies’ decay occurred around 1100Hz.    84  Figure 4.10 Frequency content – Stillwater Mine  4.3 SSX-Steer Mine – Nevada USA Gold was discovered at the Jerritt Canyon District, Nevada, USA in 1972. Underground mining commenced in 1993 with the SSX-Steer Complex and the Smith mine. Since mining began, Jerritt Canyon has produced over 7 million ounces of gold. The Jerritt Canyon deposits are typical of the Carlin-type deposit of micron to submicron-sized gold particles hosted primarily by carbonaceous, Paleozoic calcareous, and sulfidic sedimentary rocks, and in intermediate to mafic intrusive rock. The SSX deposit formation is controlled by a network of structures running northwest and northeast. Mining methods employed include conventional sublevel stoping, blind bench stoping, ramp bench stoping, and blind uphole stoping. Ground support typically uses friction rock bolts, welded mesh, and shotcrete, with cemented back-fill in mined-out areas. 4.3.1 Rock Mass Quality The average rock mass quality Q and RMR determined from the studied area, zone 7- 7170 cross-cut XC11 (see plan view in Figure 4.11), consisting of in-situ rock for the    85 right wall and face and cemented backfill for the left wall, are given in Table 4.6 and Table 4.7, respectively. The rock consists of black, fine-grained, carbonaceous limestone (Muntean and Henry, 2006). This limestone commonly comprises thin, wavy laminations and contains pods and lenses of black chert (silica mineral); Brecciation and veinlets, and stringers of white calcite, realgar (arsenic sulfide), and orpiment (arsenic sulfide) are typical. It is essentially a black mud, highly foliated, and weathered sedimentary rock (see Figure 4.12 and Figure 4.13). Ground support consists of 2.1m friction bolts with mesh.  Figure 4.11 7170 cross cut XC11 level heading – plan view – SSX Mine     86  Figure 4.12 Rock mass appearance & support installed of right wall – SSX Mine   Figure 4.13 Rock mass appearance adjacent to zone under study – SSX Mine     87 Table 4.6 Barton’s Q index components – SSX Mine Rock strength 30-50MPa Block size (RQD/Jn) 1.90 Joint strength (Jr/Ja) 0.16 Jw/SRF (dry/low stress) 1.00 TOTAL 0.30  Table 4.7 Bieniawski’s RMR ratings – SSX Mine  Rock Strength  R2  5  RQD  20%-40%  8  Spacing  0.5-1.5cm+  5  Joint condition  Slightly open  9-6  Ground water  Dry  10    RATING  37-33  The size of zone 7-7170 cross-cut XC11 drifts monitored was 4.3m wide by 4.3m tall. The average length of each blasthole was 3.7m, of which 3.4m was loaded with explosives; no material was used as stemming. The total number of blastholes loaded was 28 with 2 relief holes, and 15 unloaded holes, as depicted in Figure 4.14. Based on driller’s experience, blast contour tends to finish within the unloaded holes (line drilling).    88  Figure 4.14 XC11 heading – blast pattern – SSX Mine Blasted heading round resulted in overbreak of up to 1.5m deep on the upper right corner and an overbreak across the entire back of approximately 0.8m. Average overbreak was estimated to be in the order of 0.8m for the back and 0.35m for the walls. Figure 4.15 shows the 3D scanned contours of the XC11 heading viewed from the top (plan view).    89  Figure 4.15 XC11 heading – Laser scanned view – SSX Mine Table 4.8 displays the explosive employed for the different blastholes utilized throughout the blast pattern and its weight relative to ANFO. The approximate blast efficiency is in the order of 90%. The diameters of the blast holes were 48mm, and the relief holes were 76mm. Holes in the back and left rib were line-drilled on 0.3m centers and were not loaded, as they were intended to limit the extent of the break. Dyno Nobel Unigel sticks were loaded into the lifters, while the remaining holes were loaded with ANFO. Table 4.8 Summary of explosive ID, types and relative weights per blasthole – SSX Mine Blasthole ID Explosive Type Weight Relative to ANFO (kg) Lifters Dyno Unigel (2.4m total) 3.56 Back Unloaded N/A Production ANFO 3.65 Perimeter ANFO 3.65  The total number of blastholes loaded was 27 including 2 relief holes. 4.3.2 Vector Sum PPV and Frequency Content A representative particle velocity record for the SSX Mine is presented in Figure 4.16.    90  Figure 4.16 PPV versus time – SSX Mine The graph in Figure 4.17 shows the vector sum of the PPV obtained only from geophones anchored on rock; data from geophones anchored on cemented backfill was not included in the analysis. The PPV values were recorded at SD values as low as 4.2m/kg^0.5. The highest value of PPV recorded was 185mm/s for a stoping blasthole. The data loggers were set to record at a sampling rate of 8192 records per second.    91  Figure 4.17 PPV versus SD values – SSX Mine The PPV versus SD power law best-fit curve is estimated from 155 records:   PPV = 310.2 ⋅ DW ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −1.3  Eq. 38 The 95% confidence line is shown in Figure 4.18.    92  Figure 4.18 PPV versus SD boundary – 95% confidence level – SSX Mine Figure 4.19 shows a distinct frequency spectrum for a single burn cut blasthole, where peak frequency is near 110Hz and nearly all predominant frequencies’ decay occurred around 600Hz.    93  Figure 4.19 Frequency content – SSX Mine  4.4 Turquoise Ridge JV Mine – Nevada USA The Turquoise Ridge joint venture Mine is located in Golconda, Humboldt County, Nevada, USA. Operations consist of an underground gold mine owned by Barrick. The Turquoise Ridge ore body was discovered in 1993 and mining began in 1998. The ore deposit is hosted in limy sediments with veinlets of graphite minerals intertwined with the host rock. Gold mineralization is found in the intersection of regional structural fabric and systematic regional structures. The mining method employed at the Turquoise Ridge Mine is underhand cut and fill, due to the generally poor rock mass conditions. Ground support includes friction bolts with face plates, wire mesh, and shotcrete throughout the whole perimeter of the excavation.    94 4.4.1 Rock Mass Quality The rock mass quality present at the 3471 development panel was only assessed at the face since previous round blasts were shotcreted. The Q and RMR values for the face and subsequently blasted round are shown in Table 4.9 and Table 4.10, respectively. Figure 4.20 shows the plan view of the 3471 development panel.  Figure 4.20 3471 development panel – plan view – Turquoise Ridge JV Mine Figure 4.21 to Figure 4.23 show the characteristics of the rock and the support employed.    95  Figure 4.21 Rock mass at face and support – Turquoise Ridge JV Mine  Figure 4.22 Rock mass at upper corner – After-blast picture – Turquoise Ridge JV Mine    96  Figure 4.23 Shotcreted walls – Pre-blast picture – Turquoise Ridge JV Mine  Table 4.9 Barton’s Q index components – Turquoise Ridge JV Mine Rock strength  80-100MPa Block size (RQD/Jn)  6.25 Joint strength (Jr/Ja)  0.50 Jw/SRF (dry/low stress)  1.00 TOTAL  3.13  Table 4.10 Bieniawski’s RMR ratings – Turquoise Ridge JV Mine Rock Strength  R3+  7 RQD  75+  13 Spacing  5-10cm+  10 Joint condition  Tight/slightly open  15 Ground water  Dry  10   RATING  55     97 The size of the 3471 development panel monitored was 4.3m wide by 4.3m tall with arched back. The average length of each blasthole was 2.8m, of which approximately 2.5m was loaded with explosives; no material was used as stemming. Table 4.11 displays the explosive employed for the different blastholes utilized throughout the blast pattern and its weight relative to ANFO. The approximate blast efficiency is on the order of 93%. Blasted heading round resulted in an estimated average overbreak of 0.25m. Table 4.11 Summary of explosive ID, types and relative weights per blasthole – Turquoise Ridge JV Mine  Blasthole ID  Explosive Type  Weight Relative to ANFO (kg)  Lifters  Dyno APTM (6 sticks)  3.05  Back  Trimtex (2 sticks) + Dyno AP (2 sticks)  1.42  Production  Dyno APTM (6 sticks)  3.05  Perimeter  Dyno APTM (6 sticks)  3.05  The total number of blastholes loaded was 49, including 2 relief holes for the burn cut. No stemming was used and only 35cm were left of unloaded blasthole length.    98  Figure 4.24   3471 development heading – blast pattern – Turquoise Ridge JV Mine 4.4.2 Vector Sum PPV and Frequency Content A representative particle velocity record for the Turquoise Ridge JV Mine is presented in Figure 4.25.    99  Figure 4.25  PPV versus time – Turquoise Ridge JV Mine The graph in Figure 4.26 shows the vector sum of the PPV for one blasted round monitored with 3 geophones, installed on the ribs of the 3471 development panel. The PPV values were recorded at SD values as low as 2.8m/kg^½. The highest PPV recorded was 190mm/s, corresponding to a rib contour blasthole. Geophones were anchored at 3.5m, 8.0m, and 15.0m from the face, on shotcreted walls. The data loggers were set to record at a sampling rate of 16384 records per second.    100  Figure 4.26 PPV versus SD values – Turquoise Ridge JV Mine The PPV versus SD power law best-fit curve is estimated from 109 records:   PPV = 255.8 ⋅ DW ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −0.94  Eq. 39 The 95% confidence line is shown in Figure 4.27.    101  Figure 4.27 PPV versus SD boundary – 95% confidence level – Turquoise Ridge JV Mine Figure 4.28 shows a distinct frequency spectrum for a single burn cut blasthole, recorded from the nearest geophone at 3.5m from the face, where frequency peaks near 370Hz, and nearly all predominant frequencies’ decay occurred around 1250Hz.    102  Figure 4.28 Frequency content – Turquoise Ridge JV Mine  4.5 Musselwhite Mine – Ontario Canada Musselwhite Mine is a fly-in fly-out, 4,000 tons per day underground gold producer. The mine is located in Northwestern Ontario, Canada and is owned and operated by Goldcorp Canada Ltd. Gold mineralization is typically hosted in highly foliated – small scale – and folded metamorphic rock masses – larger scale – within oxide-silicates contained in banded iron formations. Musselwhite utilizes sub level open stoping with delayed backfill, in particular the Avoca and transverse (primary/secondary) stoping methods. The area studied corresponds to 720L C Block East, 720 meters below surface. 4.5.1 Rock Mass Quality Figure 4.29 shows the plan view of 720L C Block East and the geophone locations. By far, this is the best rock mass encountered during the field investigations (see Figure 4.30, Figure 4.31 and Figure 4.32). Table 4.12 and Table 4.13 show the average Q and RMR    103 values respectively for the back and walls of the area under study. Ground support consisted of 2.4m resin rebar rock bolts with mesh placed at the back and upper corners of both walls, as shown on Figure 4.32.  Figure 4.29 720L C Block East plan view – Musselwhite Mine   Figure 4.30 720L C Block East face and drill pattern – Musselwhite Mine     104  Figure 4.31 720L C Block East rock mass and rebar bolts pattern – Musselwhite Mine  Figure 4.32 720L C Block East back support with rebar and mesh – Musselwhite Mine     105  Table 4.12 Barton’s Q index components – Musselwhite Mine Rock strength 100-150MPa Block size (RQD/Jn) 45.00 Joint strength (Jr/Ja) 4.00 Jw/SRF (dry/low stress) 1.00 TOTAL 180.00  Table 4.13 Bieniawski’s RMR ratings – Musselwhite Mine  Rock Strength R4+ 13  RQD 90+ 20  Spacing 2m+ 28  Joint condition Tight 20  Ground water Dry 10   RATING ≈ 90  Manual measurements of overbreak were taken using a handheld laser distance meter and they approximately average 3.0cm, where the bulk of overbreak occurred in the upper corners of both walls. Five (5) complete half-barrels were present on the back of the drift (where the strong vertical foliation reduced the likelihood of half-barrels on the walls). Table 4.14 shows the explosive used for each group of blastholes, its quantities in kilograms for each blasthole, and the equivalent quantities relative to ANFO. Values are based on a blasthole diameter of 1¾in (4.45cm) by 4.3m long, with 0.3m of unloaded blasthole at the collar. Table 4.14 Summary of explosive ID, types and relative weights per blasthole – Musselwhite Mine Blasthole ID  Explosive Type  Weight Relative to ANFO (kg) Lifters  Dyno APTM (4.0m total)  6.22 Back  SEC Detagel Presplit (22mm x 400mm)  1.64 Production  ANFO  5.17 Perimeter  ANFO  5.17  The total number of blastholes loaded was 59, including 5 relief holes.    106   Figure 4.33 720L C Block East heading – blast pattern – Musselwhite Mine  4.5.2 Vector Sum PPV and Frequency Content Figure 4.34 shows the particle velocity versus time record and the graph in Figure 4.35 shows the vector sum of PPV for one of the geophones (of 6 geophones installed) recording the blasted round as monitored at the ribs of the 720L C Block East drift, where 2 geophones were damaged by the blasted rock. The PPV values were recorded at SD values as low as 4.7m/kg^0.5. The highest PPV recorded was 390mm/s, corresponding to a rib contour blasthole. Figure 4.37 shows a distinct frequency spectrum for a single burn cut blasthole, recorded from the nearest geophone installed approximately 9.5 m away from the face. The rest of the geophones were located at 10.5m, 21.5m, and 26.6m. In this    107 case, frequency peaks were near 1050Hz and nearly all predominant frequencies’ decay occurred around 2600Hz (Figure 4.37). The data loggers were set to record at a sampling rate of 8192 records per second.   Figure 4.34 PPV versus time –– Musselwhite Mine     108  Figure 4.35 PPV versus SD values – Musselwhite Mine The PPV versus SD power law best-fit curve is estimated from 167 records:   PPV = 1099.6 ⋅ DW ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −1.2  Eq. 40 The 95% confidence line is shown in Figure 4.36.    109  Figure 4.36 PPV versus SD boundary – 95% confidence level – Musselwhite Mine     110  Figure 4.37 Frequency content – Musselwhite Mine  4.6 Analysis of Results The following are the most relevant results obtained from these field investigations: 4.6.1 PPV versus SD for a Wide Range of Rock Mass Qualities The relation between PPV and SD as a function of rock mass quality was obtained from multiple records of particle velocity versus time, in which the highest velocity recorded for each blasthole or set of blastholes is the measurement of the PPV value. Each blasthole or set of blastholes determines a single point on the PPV versus SD graph. Various best-fit exponential curves were established for the various sets of PPV versus SD points obtained at the mine sites investigated.  These best-fit curves represent the site- specific characteristic curves shown in Figure 4.38, and the logarithmic scale graph is shown in Figure 4.40. The 95% confidence lines are shown in Figure 4.39.    111  Figure 4.38 PPV versus SD for a range of rock mass qualities  Figure 4.39 PPV versus SD. Solid lines represents 95% confidence level     112  Figure 4.40 PPV versus SD – Log scale – for a range of rock mass qualities In Figure 4.41, the logarithmic function is applied to the PPV and SD pair and the best-fit Log(PPV) versus Log(SD) line is plotted.    113  Figure 4.41 Log(PPV) versus Log(SD) – for a range of rock mass qualities The best-fit linear equations obtained from the data points of each of the mine sites investigated and presented in the form of equation 24, is as follows: Musselwhite Mine:  Log(PPV) = -1.19 × Log(SD) + 3.04 Stillwater Mine:  Log(PPV) = -0.85 × Log(SD) + 2.62 Turquoise Ridge JV Mine: Log(PPV) = -0.94 × Log(SD) + 2.41 SSX Mine:   Log(PPV) = -1.06 × Log(SD) + 2.42 4.6.2 Charge Weight per Delay At the mine sites investigated it is apparent that the time scatter in long period pyrotechnic blasting detonators (which were used at all four sites), rarely produced constructive interference. This is either due to the time scatter itself, which is greater than the minimum required to produce constructive interference, or due to the spatial location of the blastholes detonated on the same delay. This implies that the total weight of explosive fired per delay should not be numerically summed.  The great majority of the data points plotted on the PPV versus SD graph, shown in previous figures, are the result    114 of a single independently recorded waveform. In all of the monitored rounds, there were up to 5 blastholes detonated with the same nominal delay, but from the analysis of the waveforms, the great majority did not present constructive interference. As an example, the following particle velocity versus time record shows the time scatter present in these long period pyrotechnic blasting caps with same nominal delay number. In this particular case, Figure 4.42 shows that there are four clearly identifiable independent seismic waveforms from the four blastholes fired using the same nominal delay number. Given the location of the installed geophones, no constructive interference was found, and therefore, the weights of explosives for individual blastholes should be treated independently of one another.  Figure 4.42 Delay time scatter – Pyrotechnic blasting caps     115 5 PPV MODELING – THE PROPOSED METHODOLOGY 5.1 Introduction The model reviewed here was originally developed with the objective of finding a way to reduce the substantial scatter of the actual data recorded from the mine sites investigated. In these cases, a single distance from all the blastholes to every geophone installed was used, independent of their individual locations within the round. The resultant PPV versus SD analysis presented a large number of PPV values for a single SD factor, resulting in the large scatter of the data.  The existing near-field Hustrulid-Lu equation (Eq. 29) was modified, and evolved into one that could integrate the physical properties of the rock and the explosives used. The incorporation of these properties made possible the analysis of a variety of geometrical and physical conditions, considered fundamental toward the objective of explaining the behavior of seismic waves generated by an explosive charge. A detailed explanation of the nature of the model, assumptions made, testing, and results, is given throughout this chapter. The proposed (semi-empirical) modeling tool is intended for use in determining the PPV of a blasthole located within the round, at any particular location either on the face of the blasted round itself or within the walls of the drift. If PPV is determined right at the face, this could be considered to be the near field case.  The latter (walls) is likely to be the most appropriate location for the installation of instrumentation, such as geophones, and could be considered to be the intermediate- or far-field cases. The model incorporates geophysical principles, analytical equations, and user-defined parameters, which provide the basis for the analysis of the physical data gathered, and are presented in the previous chapter. The analysis uses a modification of the Hustrulid-Lu equation (Eq. 29) to derive the final PPV by adding up the contributions of small incremental charges within the blasthole, but differs from the Hustrulid-Lu method, in that it incorporates individual incremental charges as waveforms. This generates various particle velocity waveforms for each individual packet, and it incorporates the arrival times of all packets, thus allowing for the superposition of the generated waveforms.    116 The model is highly accessible since it runs on Microsoft™ Excel® or any compatible spreadsheet software. 5.2 The Semi Empirical Modeling Tool 5.2.1 Background In an attempt to reduce the large scatter of the recorded PPV versus SD data obtained from the mine sites investigated, the semi-empirical model (or “model”) was developed. This model modifies the Hustrulid-Lu equation (Eq. 29) by incorporating measurable, physical properties of the rock mass, and the explosives in use. In addition, it uses a waveform seed generator, from which particle velocity waveforms are constructed, thus allowing for the use of the estimated arrival times of every individual packet pertaining to a blasthole of the round, to estimate the final PPV. The PPV for each blasthole is then determined from the linear superposition of all individual packet waveforms whose phases are shifted by their respective arrival time differences (i.e., as they arrive at the geophone or location of interest). It assumes that the travelled path of the seismic wave is unique, and is determined from the shortest possible distance starting at the packet location and ending at the geophone location. Due to the geometry of the blasting round, the seismic wave cannot travel directly to the geophone. It first, must pass through a point located at the edge of the face of the round and the walls of the drift, and from that point travel to the geophone. The physical and geophysical features employed in the model include: the location, length, and diameter of each blasthole with respect to the position of the geophone; the explosive’s linear charge density and VOD; the rock mass medium’s body and surface wave velocities and its main resonant frequency or frequencies; and the travelled length for each individual packet from which the associated travel time is determined. Figure 5.1 depicts a section of a blast pattern in the vicinity of each blasthole, which produces a three-dimensional representation of that section (Figure 5.2), where the strike of the drift is visualized vertically, and the blastholes are projected in space in the vertical direction.    117  Figure 5.1 2D representation of a blast pattern The star in Figure 5.1 represents the location of the geophone or the point of interest, either immediately at the face-wall contact or some distance away from the face, where from the analysis, the PPV is to be determined.    118  Figure 5.2 Three dimensional projection of the blasthole locations 5.2.2 Model Set-Up The model subdivides the total length of a blasthole into “n” packets of equal charge length, and then determines the contribution of each of those packets to the final PPV. As a compromise between full data manipulation and the correspondent model becoming unmanageable, the number of packets “n” was arbitrarily chosen to be 17, as this yields a reasonably good estimation of PPV while maintaining a relatively fast processing time. At present, the model calculates PPVs for 60 different blastholes in about 10-15 seconds using an i7 Intel core processor. The number of packets and/or blastholes can be increased to any value, as deemed necessary in any given situation, assuming a correspondent increase in processing time. A greater number of divisions (i.e., a higher number of packets) would not contribute significantly to the overall accuracy of the modeled results. Increasing the number of packets greatly increases the processing time involved.    119  Figure 5.3 Packet representation and location of a centroid Figure 5.3 is a three-dimensional representation of a single packet located within a particular blasthole, including its centroid and its dimensions, which are used to determine the packet’s explosive charge and location. 5.2.3 Point of Diffraction (POD) The model was constructed with attention to the fact that the trajectory of the seismic wavefront must pass through a point of diffraction (POD) at the face-wall contact of the blasting round, and then travel through the surface of the drift wall, ultimately arriving at the geophone location (as depicted in Figure 5.4).    120  Figure 5.4 Point of diffraction height ZPOD of multiple packets In the event that an elastic stress wave encounters a boundary demanding a sharp turn of 90 degrees or more, only a portion of the total incidence energy of this elastic stress wave will continue through the rock face as refracted and diffracted energy, whereas the remaining portion would be reflected (Figure 5.5).  Figure 5.5 Incidence, reflected and diffracted/refracted rays The contribution of the refracted and diffracted portion of the incident seismic wave is determined by factoring the length of each packet ray (taken from the packet’s origin    121 location to the face-wall contact point, the POD), by the ratio of the depth to the packet’s origin, versus the length from the packet’s origin to the POD. This ratio yields the projection of the velocity vector parallel to the drift orientation. 5.2.4 Assumptions A fundamental aspect of this model is its simplicity, and therefore, results should be based on calibration of recorded data whenever possible. This simplicity is imperative, since, in order to be rigorous, many parameters must be included to account for the aggregate of influences on the physical behavior of a rock-explosive interaction. The model makes the assumption that only the shortest path would generate the peak of the particle velocity and that any other path would add merely to the residual portion of the particle velocity. This assumption is fully consistent with the physics of wave propagation, and it will be used to determine the unique path of travel from the origin of the seismic wave to the point of interest, and from this length and the velocities involved, the total travel time of the seismic wave will be determined. It is assumed that blastholes are bottom initiated (base-primed), which is the most common method of initiating a drift blasthole. In this case, the first initiated packet corresponds to packet 17 and the last packet to be initiated corresponds to packet 1. The explosive column is initiated at the bottom of the cylindrical charge from where the seismic wavefront expands in a spherical manner. As this happens, the explosive in the column charge, which propagates at a finite velocity (i.e., the VOD of the explosive utilized), and reaches the subsequent packet centroid at a certain time. When the detonation front has reached the next packet, a new seismic wavefront begins to propagate in a fashion similar the previous one. This continues as the whole column charge detonates, as depicted in the four images of Figure 5.6.     122  Figure 5.6 Packet initiation sequence – Expanding seismic wavefront and ray path Blastholes are considered to be straight lines, perpendicular to the face and parallel to the walls of the drift. No blasthole deviation was assumed. Notably, a more comprehensive analysis would include particle velocity as determined from the combination of a wide range of frequencies generated from a single blasthole, as indicated in the frequency spectrum analysis of the seismic wave velocity records given in Chapters 3 and 4. However, for ease, all of the analyses performed for the research herein were based on a single predominant resonance frequency. Two assumptions in this case are, that the seismic wave produced by the blasthole packets takes the shortest route to the geophone, and, that it passes through that wall upon which the geophone is located. Although this might not always be the case, given that examples could be found where the shortest path does not pass necessarily through the    123 wall on which the geophone is installed, nevertheless, this assumption likely yields the highest particle velocity measurement as compared with the shortest path, owing to the fact that more points of diffraction will be encountered and the energy will dissipate more rapidly. This could happen, for example, when blastholes are located at the contour of the excavation, where the seismic wave will travel through the surface of the roof or back of the excavation, and then along the wall to the geophone location. As the blastholes detonate and fragment the rock, and as this volume of fragmented rock is displaced, the transitory volume defined by the blasthole sequence becomes empty, which in turn prevents the seismic waves from travelling through the opened space. The actual trajectory of the seismic wave should go around this momentarily emptied space. In this case, the assumption is that the seismic wave travels in a straight line, from the origin of the packet to the POD, and then to the geophone, avoiding any other, more complicated path. 5.2.5 Analytical Background In order to determine the shortest travelled distance from the point of origin to the arrival point (geophone), necessarily passing through the face-wall contact, the height of that unique point (ZPOD), at the face-wall contact must be found, such that the total travelled distance is minimized. Figure 5.7 and Figure 5.8 depict two different points of origin, for the nth and the ith packets, where the seismic wave originating at these points should pass through ZPODnth and ZPODith at the face-wall contact, yielding the total shortest distance. The vertical reference location of the geophone is always assumed to be at 0m elevation but could be set at any distance from the face.      124  Figure 5.7 Point of diffraction height ZPOD nth and angle of incidence βnth of nth packet     125  Figure 5.8 Point of diffraction height ZPOD ith and angle of incidence β ith of ith packet The total travelled distance is determined by summation of the distance from the origin of a particular packet, passing through the ZPOD at the face-wall contact, and continuing to the location of interest, in this case a geophone. The total travelled distance of the seismic wave starting from the ith packet is given by:   DTOTAL ith = xith2 + yBH2 + (zBH + ZPODith )2 + dF −G2 + ZPODith2  Eq. 41 Where:    126 - yBH is the horizontal blasthole location with respect to the geophone, - zBH is the vertical blasthole elevation with respect to the geophone, - xith is the depth of the ith packet with respect to the geophone, - ZPODith is the vertical elevation of the point of diffraction for the ith packet, and - dF-G is the horizontal distance from the face of the round to the geophone. To determine the ZPODith that minimizes the total travelled distance (DTOTALith) of the ith packet the following calculations are required:   ∂DTOTALith ∂ZPODith = 0  Eq. 42 then,   ZPODith = zBH ⋅ dF −G ⋅ (−dF −G ± xith2 + yBH2 ) (xith2 + yBH2 − dF −G2 )  Eq. 43  The total arrival time for the ith packet is composed of the time that it takes for the detonation front to reach the ith packet centroid from the bottom of the charge, (travelling at the VOD of the given explosive), the travelled time from the ith packet centroid to the point of diffraction ZPODith at the face-wall contact (travelling at the body wave velocity), and the travelled time from ZPODith to the geophone location at the surface wave velocity. In this case, the arrival time of the ith packet is given by the following equation:   tith = hBH − xith VODexp losive + xith2 + yBH2 + (zBH − ZPODith )2 VM _ BodyWave + dF −G2 + ZPODith 2 VM _ SurfaceWave  Eq. 44 Where, - tith is the arrival time of the ith packet, - hBH is the total length of the blasthole - VODexplosive is the velocity of detonation of the explosive, - VM_BodyWave is the body wave velocity of the medium, and    127 - VM_SurfaceWave is the surface wave velocity of the medium. 5.3 Arrival Time Analysis 5.3.1 General The most general case for determining PPV of a blasthole from the contribution of its individual incremental charges is by considering that each and every one of these individual incremental charges arrive simultaneously, that is, there is no time delay associated with their arrival time. This is probably the most significant disadvantage of the Holmberg-Persson and Hustrulid-Lu methods, since both only consider simultaneous arrival of all individual incremental charges. In a sense, there is no actual consideration whatsoever of arrival time. Moreover, even if these methods were to incorporate time delay, there can be no solution possible, unless the incremental charges are treated as a waveform, as opposed to an independent numeric value. As will be shown, there could be substantial variation in the final PPV as determined when the arrival time of each incremental charge is considered, i.e., where incremental changes are treated as a waveform, versus final PPV as determined without consideration for arrival times. Given that the explosive charges are bottom initiated (base-primed blastholes), there are many different possible alternatives to the sequence of the arrival of the seismic wave at the geophone location. This of course will depend on the location of the blasthole with respect to the geophone, as well as the VOD of the explosive used, and the propagation velocity of the seismic wave. Among the possible forms of the curve of arrival times with respect to the packet location, several are depicted in Figure 5.9 through Figure 5.13. In all of these examples, the point or points that are lowest with respect to the rest of the points indicates the first to arrive at the geophone location, as opposed to the point or points located at the top. In Figure 5.10, the first stress wave to arrive pertains to the collar of the blasthole. In this case, the detonation velocity of the explosive is much larger than the seismic wave velocity. In Figure 5.9, just the opposite occurs, that is, the seismic wave velocity is greater than the detonation velocity.    128  Figure 5.9 Ascending arrival times from the initiation point (Packet 17)   Figure 5.10 Descending arrival times from the initiation point (Packet 17)     129 Figure 5.11 and Figure 5.12 portray parabolic curves of the arrival time with respect to the packet location. In both cases, there is more than one packet location whose stress waves arrive simultaneously with another.  Figure 5.11 Parabolic ascending arrival times from the initiation point (Packet 17)  Figure 5.12 Parabolic arrival times. Central packets of the wavefront arrives first     130 Figure 5.13 would be an extreme case where all the stress waves arrive simultaneously. This form of arrival time curve is representative of the current state of methods, as employed in the Holmberg-Persson (Eq. 26) and Hustrulid-Lu (Eq. 29) equations.  Figure 5.13 Simultaneous arrival times for all packets  5.3.2 Stress Wave Propagation Velocity – Rock Mass Quality Dependence It is commonly accepted that a relation exists between the types of rock and the sound velocity of a stress wave propagating in that medium, where stronger rocks or better defined, more competent rock masses will present higher propagation velocities, as compared to softer rocks or less competent rock masses. It is clear that the weaker the rock mass, in terms of its quality, the slower the propagation velocity. The presence of more features within the rock mass such as cracks, joint sets, faults, etc., imposes obstacles to the propagation of the stress wave, reducing its energy and velocity.    131 Table 5.1 shows propagation velocities for different mediums. Rock types classified from weak, such as sandstone, to competent, such as metamorphosed hard rock, are relevant to the research conducted herein. Table 5.1 Table of propagation velocities for different mediums (source: Pavlovic, 1998) MEDIUM  Velocity (m/s) min Velocity (m/s) max Air (temperature dependence) 310 360 Gravel, dry sand 100 500 Wet sand (with water) 200 1,800 Clay 1,200 2,500 Water (temperature dependence) 1,430 1590 Sandstone friable 1,500 2,500 Sandstone dense 1,800 4,000 Chalk 1,800 3,500 Limestone 2,500 6,000 Gypsum 4,500 6,500 Ice 3,100 4,200 Granite 4,000 5,700 Metamorphosed 4,500 6,800  Figure 5.14 shows a representation of the primary P-wave velocity propagating in different rock types.    132  Figure 5.14 P-wave velocity (m/s) for various rock types (modified from source: http://science.jrank.org/pages/48110/seismic-properties-rocks.html, January 2011)  5.3.3 Arrival Time – Rock Mass Sound Velocity Dependence There are different forms of arrival time curves and actual time differences for a stress wave originating at a particular packet location within the blasthole. Those differences depend on the location of the blasthole within the round with respect to the location of the geophone and also depend on the VOD of the explosive, and on the body and surface sound velocities of the rock medium. The green triangles in Figure 5.15 mark the locations of the blastholes within the round as they are analyzed in relation to their arrival times at the geophone location. In this case, the geophone was located 10.5m from the face. For convenience, the reference location coordinate of the geophone is always (0.0m, 0.0m). The arrival times for the following blasthole’s collar location coordinates were analyzed: (0.9m, 0.0m), (0.0m, 0.0m), (2.6m, 3.5m), (5.0m, 3.3m), and (0.2m, 3.3m).    133  Figure 5.15 Arrival times for highlighted blasthole location Arrival time analysis takes into consideration the different detonation velocity ranges for different types of commercial explosives, as well as some hypothetical detonation velocities above and below these ranges (for the purpose of testing the model). Table 5.2 illustrates a wide range of explosive types and their associated detonation velocity. Table 5.2 Table of explosive detonation velocities Explosive Name  Abbreviation Detonation Velocity (m/s) Density (g/cm³) Triazido-trinitrobenzene TATNB 7,300 1.71 Trinitrobenzene TNB 7,450 1.6 Dinitro-diazenofuroxan DDF 10,000 2.02 Acetone Peroxide AP 5,300 1.18 Aliphatic explosives Ammonium Nitrate AN 5,270 1.3 Aromatic explosives Cyclotetramethylene Tetranitramine HMX 9,100 1.91    134 Explosive Name  Abbreviation Detonation Velocity (m/s) Density (g/cm³) Cyclotrimethylenetrinitramine RDX 8,750 1.76 Dunnite  7,150 1.6 Ethyl Picrate  6,500 1.55 Ethylenedinitramine EDNA 7,570 1.65 Hexanitrohexaazaisowurtzitane HNIW or CL-20 9,400 2.04 Inorganic explosives Lead azide  4,630 3.0 Lead styphnate  5,200 2.9 Mannitol hexanitrate MHN 8,260 1.73 Mercury Fulminate  4,250 3.0 Methyl nitrate  8,000 1.21 Methyl Picrate  6,800 1.57 Nitrocellulose NC 7,300 1.2 Nitroglycerine NG 7,700 1.59 Nitroglycol EGDN 8,000 1.48 Nitroguanidine NQ 8,200 1.7 Octanitrocubane ONC 10,100 2.0 Organic Explosives Pentaerythritol Tetranitrate PETN 8,400 1.7 Picric Acid TNP 7,350 1.7 Picryl Chloride  7,200 1.74 Silver azide  4,000 4.0 Tetranitroglycoluril Sorguyl 9,150 1.95 Tetryl  7,570 1.71 Triaminotrinitrobenzene TATB 7,350 1.80 Trinitroaniline TNA 7,300 1.72 Trinitrocresol  6,850 1.62 Trinitrotoluene TNT 6,900 1.6 Urea nitrate UN 4,700 1.59 Reference Cooper, Paul W., Explosives Engineering, New York: Wiley-VCH, 1996. ISBN 0-471-18636-8 Figure 5.16 through Figure 5.20 show the arrival time versus the blasthole’s packet depth for each blasthole location as represented by the triangles in Figure 5.15, for a rock with    135 body wave velocity of 6,500m/s, which corresponds to a good, competent rock mass, such as the one studied at the Musselwhite Mine site. At the other extreme, Figure 5.21 through Figure 5.25 show the arrival times for a rock with body wave velocity of 2,000m/s, corresponding to rock with poor to fair rock mass quality, such as the one present at the SSX mine. The different curves represent the ratio between the VOD of the explosive, and the body (Vbw) and surface (Vsw) wave velocity of the rock mass. Note from the following graphs that the arrival times of packet 17, i.e., the one closest to the bottom of the blasthole (at approximately 4.3m into the rock face), turn out to be nearly all equal (Figure 5.16 - Figure 5.25). This happens because packet 17 is the shortest distance into the blasthole column and therefore travels the shortest distance at the explosive’s detonation velocity, i.e., the one varied for this analysis. The great majority of the travelling time occurs in the rock mass medium, in which the body and surface wave velocities were set constant throughout this portion of the analysis.    136  Figure 5.16 Arrival times – Vbw=6500m/s – Good rock quality – Y=0.9m  Z=0.0m  Figure 5.17 Arrival times – Vbw=6500m/s – Good rock quality – Y=0.0m  Z=0.0m    137  Figure 5.18 Arrival times – Vbw=6500m/s – Good rock quality – Y=2.6m  Z=3.5m  Figure 5.19 Arrival times – Vbw=6500m/s – Good rock quality – Y=5.0m  Z=3.3m    138  Figure 5.20 Arrival times – Vbw=6500m/s – Good rock quality – Y=0.2m  Z=3.3m  Figure 5.21 Arrival times – Vbw=2000m/s – Poor/Fair rock quality – Y=0.9m  Z=0.0m    139  Figure 5.22 Arrival times – Vbw=2000m/s – Poor/Fair rock quality – Y=0.0m  Z=0.0m  Figure 5.23 Arrival times – Vbw=2000m/s – Poor/Fair rock quality – Y=2.6m  Z=3.5m    140  Figure 5.24 Arrival times – Vbw=2000m/s – Poor/Fair rock quality – Y=5.0m  Z=3.3m  Figure 5.25 Arrival times – Vbw=2000m/s – Poor/Fair rock quality – Y=0.2m  Z=3.3m    141 5.4 Particle Velocity Analysis – Drifting Case 5.4.1 Proposed PPV Equation – Analytical Background The new proposed model quantifies PPV via the linear superposition of a number of waveforms generated for each of the packets or elements of the original blasthole column based on a scaled distance equation component (equation 29, in Section 2.2.10), a simplified particle velocity wave equation component (equation 7, in Section 2.2.3) and a simplified inelastic attenuation component (equation 13, in Section 2.2.4). The waveform of each packet is generated using a waveform generator, including the travelled distance to the point of interest (equations 41 and 43), the main predominant frequency of vibration, a pre-peak inelastic attack component and a post-peak inelastic attenuation component of the waveform, the standardized linear charge density, and a series of constants associated with these terms. Also, the arrival time delay of every packet is indirectly accounted for, via a phase shift of the waveform peaks by their respective arrival time based on equation 44. This new proposed linear superposition scaled distance general analytical equation (45), has been specifically designed for a drifting situation. The new proposed equation that is used to determine the PPV at any given time is presented as follows:  PPV t( ) = K '⋅ω ⋅ lα ⋅ Δx α xith2 + yBH2 + (zBH − ZPODith )2( ) f 1 Sin f 3(βith ) + dF −G2 + ZPODith 2( ) f 2 ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ n ⋅Cos ω ⋅ t + φith( ) ith=1 N ∑ ⋅e−(δ 1 ,δ 2 )⋅ω ⋅t  Eq. 45 Where, - K’, α, n, f1, f2, and f3 are site specific constants (f1=f2=f3=1, most general case), - ω is the angular frequency of the waveform, - Δx is the packet height, - ϕith is the phase shift, - δ1 or δ2 are the pre-peak attack or post-peak decay constants, - t is the time at which PPV is determined,    142 - N is the number of packets, and - βith is the angle between the ray formed from the ith packet to the PODith with the horizontal. The sinusoidal waveform term of equation 45 is a simplified form of equation 7, in which the position x is considered fixed. Equation 45 incorporates the distance of every packet within the blasthole such that there is no need to define a unique distance value such as in the case of the SD factor, even for the far-field case. The delay in the arrival of every seismic waveform originating at each of the packets in the blasthole is accounted for, identical to the near-field case. In essence, the proposed linear scaled distance equation can incorporate into a single formulation the near- and intermediate/far-field components as a combined body (i.e., distance between packet centroid and POD) and surface (i.e., distance between POD and geophone) component of equation 45. The flowcharts in Figure 5.26 - Figure 5.29 reflect the steps needed to determine PPV at a given distance from the blasthole location.  Figure 5.26 User defined modeling parameters flowchart     143  Figure 5.27 Initial calculations flowchart  Figure 5.28 Model waveform generation     144  Figure 5.29 Model PPV determination from linear superposition of multiple waveforms  5.4.2 Determination of Constants The model makes use of various constants necessary for accurate PPV prediction, which must be determined through a calibration process involving a number of blast rounds monitored using geophones. Various tests of signature blastholes (or blastholes without a free-face) should be done to establish the value of the constant f1 (Eq. 45), owing to the fact that the far-field term is zero. The f3 constants could be determined from, for example, detonation of packet size explosive charges (e.g., one cartridge of dynamite) located at different depths within the blasthole (where the geophone is installed on the drift wall). This enables the determination of the effect of the angle formed between the packet centroid and the point of diffraction at the face-wall intersection, on PPV. In the absence of data, the Sin(β) term could be ignored by defining f3 as equal to zero (0). From records obtained for a number of geophones located at various distances from the blast, and once the f1 and f3 constants have been determined, the K’, α, and f2 constants could be resolved. Angular frequency, ω, is directly determined from the frequency content of the particle velocity versus time records. Similarly, the constants δ1 and δ2 are directly determined from the pre- and post-PPV versus time records.    145 The model calculates the phase shift term ϕith, based on travelled distance, VOD of the explosive and body and surface wave propagation velocities, which can be experimentally determined. 5.4.3 Waveform Generation – Frequency Dependence The following two figures show the results of generating two waveforms for two dissimilar frequencies, that is, dissimilar in terms of their representation of the rock mass quality. One is a high frequency waveform (1000Hz) corresponding to an extremely competent rock mass -- such as the Musselwhite Mine case -- and the other a low frequency (150Hz) waveform corresponding to a fair-poor rock mass quality -- such as the SSX Mine case. Figure 5.30 shows only 5 of the 17 waveforms corresponding to 5 of the 17 packets of a single blasthole generated at a frequency of 1000Hz, and Figure 5.31 shows those waveforms generated at a frequency of 150Hz. The scale of the horizontal time axis (x-axis) is equal for both examples. In these particular cases, there is no phase shift among the peaks of the waveforms, meaning that all the waveform peaks are coincident with the same time value. It is important to note that the peak velocity values of individual packets corresponding to the same location in the explosive column are exactly the same, irrespective of what frequency is used.    146  Figure 5.30 High frequency; Packets arrive simultaneously – Zero phase shift  Figure 5.31 Low frequency; Packets arrive simultaneously – Zero phase shift    147  5.4.4 Phase Shift - Delayed Arrival Times of Peak Velocities When an analysis to determine the PPV is done using the approximate physical values for the detonation velocity of an explosive and the velocity of propagation of the seismic wave in a rock mass medium, the value of taking into consideration the arrival times for each different packet in a given blasthole becomes clear. Figure 5.32 shows two waveforms that, due to excavation geometry, rock mass properties, and the explosive’s properties, have arrived with a time delay (or shift).  Figure 5.32 Waveform time shift between two packets The model can be validated by examining results, in the near-field, using the Hustrulid- Lu equation, comparing them with the results obtained from the model. The Hustrulid-Lu equation is restricted to the near-field and assumes zero delay in the arrival times of the incremental charges. This can be emulated by assigning in the model extremely high velocities of detonation to the explosive and propagation velocities to the rock medium,    148 yielding zero time delay. To emulate this in the near-field, the model may be set to consider the location of the geophone as being at the face of the blasted round. As a result of this, the phase shift between the peaks of the individual packets becomes negligible, and both the Hustrulid-Lu equation (Eq. 29) and the model give equal values, packet by packet (Figure 5.33), in the calculation of particle velocity when of course, the same equivalent set of constants is used. Figure 5.33 shows 5 of the 17 waveforms that form part of the total number of waveforms pertaining to a single blasthole. The circles indicate the equivalent discrete value determined using the Hu-Lu equation. In this case, both the Hu-Lu values and the peaks of the waveforms give exactly same value, although the peaks of the waveforms are shifted in time. The effect is only noticeable when the linear superposition of all individual waveforms is applied.  Figure 5.33 Discrete Hustrulid-Lu values and continuous modeled waveforms The values of every single peak waveform generated for each packet comprising the final PPV value for a given blasthole will be identical to those obtained using the Hustrulid-Lu equation (Eq. 29). On the other hand, if the time shifts are taken into account, the final linear superposition of the set of waveforms pertaining to a single blasthole would yield PPV values that are always lower than those using the Hustrulid-Lu equation (Eq. 29). Hu-Lu    149 The PPV values generated via Hustrulid-Lu will always be the maximum obtainable values. Note that at the peak of each waveform in Figure 5.33, the shape is not smooth but rather sharp. The reason for this is the use of different attack and decay constants in order to adjust the model’s pre- and post-peak waveform shape to the recorded waveform shape. Figure 5.34 and Figure 5.35 compare PPV obtained using both methods, where the model applies frequencies of 1000Hz and 150Hz with zero phase shifts. The results obtained using the Hustrulid-Lu equation (Eq. 29) are plotted with a green circle, whereas the model results are plotted by means of a waveform indicated by a red circle, symbolizing their peaks. As can be seen, both methods yield the same results.  Figure 5.34  High frequency waveform; PPV modeled versus PPV from Hustrulid-Lu equation (2000) – Zero phase shift  Hustrulid-Lu    150  Figure 5.35 Low frequency waveform; PPV modeled versus PPV from Hustrulid-Lu equation (2000) – Zero phase shift Similarly, Figure 5.36 through Figure 5.47 compare PPV obtained using both methods, for the same set of frequencies, but in this case, the phase shift has been varied from zero, and set according to the time delay associated with the packet’s arrival time. Reasonable values for the VOD of the explosive and the rock’s sound velocity have been employed. A series of VOD values ranging from 10,000m/s down to 3,200m/s, corresponding to different explosives types, densities, and confinement conditions were tested. The propagation velocities of the seismic wave for a high velocity (6500m/s), high frequency (1000Hz) good rock mass quality and a slow velocity (2000m/s), low frequency (150Hz) fair/poor rock mass quality, were also part of these modeling experiments. Hustrulid-Lu    151  Figure 5.36 High Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=10,000m/s  Figure 5.37 Low Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=10,000m/s Hustrulid-Lu Hustrulid-Lu    152  Figure 5.38 High Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=8,250m/s  Figure 5.39 Low Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=8,250m/s Hustrulid-Lu Hustrulid-Lu    153  Figure 5.40 High Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=6,500m/s  Figure 5.41 Low Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=6,500m/s Hustrulid-Lu Hustrulid-Lu    154  Figure 5.42 High Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=5,000m/s  Figure 5.43 Low Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=5,000m/s Hustrulid-Lu Hustrulid-Lu    155  Figure 5.44 High Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=4,300m/s  Figure 5.45 Low Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=4,300m/s Hustrulid-Lu Hustrulid-Lu    156  Figure 5.46 High Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=3,200m/s  Figure 5.47 Low Velocity and Frequency; PPV modeled vs. PPV from Hustrulid-Lu equation Vexplosive=3,200m/s Hustrulid-Lu Hustrulid-Lu    157 From the previous results, the significance of arrival times in the determination of the PPV sustained by the rock at a specific location from the blast, becomes clear. The greater the differences in arrival time of individual packet waveforms, the greater the decrease in final PPV value.  Final PPV value is determined by the linear superposition of individual packet waveforms while the peak value of each individual packet remains unchanged. 5.4.5 Resonance Vibration Frequency Range of a Rock Mass Medium So far the model has been used to determine PPV for a unique dominant frequency from a broader range of natural frequencies at which the rock mass vibrates. This section is intended to provide proof that the model can be used to analyze PPV obtained from a range of frequencies that could be generated from a single blasthole. Multi-frequency analysis is beyond the scope of this research and its relevance could be determined through continuation of this research in future investigations. Figure 5.48 shows the PPV of individual waveforms, for a single blasthole location, each generated at a different frequency of oscillation. Each of the waveforms plotted is obtained from the linear superposition of each of the 17 waveforms generated at a single frequency of oscillation. An appropriate multi-frequency analysis should determine the amplitude of the waveform (PPV) obtained within a short range of frequencies, and the propagation velocity for this frequency range. The procedure would be repeated successively, to account for the entire spectrum of frequencies propagating through the rock mass. This is done in the same way as was the case in Chapter 3, shown in Figure 3.12 through Figure 3.15, in which the recorded waveform was filtered on a pre-established frequency range, where the amplitude of the waveform is then determined for that specific frequency range. The procedure would then be repeated for each subsequent frequency range, in turn, until the whole spectrum of frequencies for the given rock mass is covered.    158  Figure 5.48 Waveforms generated at various frequency ranges Figure 5.49 displays the linear superposition of the combined waveforms obtained for each individual frequency tested and displayed in Figure 5.48. It is important to note that there could be a delay in arrival time for each of the waveforms generated at any particular frequency. Kolsky (Kolsky, 1953) addressed this issue where velocity dispersion caused high-frequency plane waves to travel faster than the low frequency waves. In this particular example, no considerations were made with respect to propagation velocities for a particular frequency value tested, which could have potentially yielded differences in their arrival times, and thus their PPV results.    159  Figure 5.49 Linear superposition of waveforms generated at various frequency ranges 5.4.6 Model Sampling Rate Different sampling rates can also be accounted for in the model. The sampling rate is the number of samples per second. This is also a parameter selectable on the dataloggers and can be set up at fixed rates of 1024, 2048, 4096, 8192, and 16384 samples per second. Naturally, the higher the sampling rate, the larger the memory consumption. This is particularly relevant when a limited amount of memory is available, as is the case with Minimate Plus® datalogger, because, for example, an unintentional triggering of the datalogger recording process, as when machinery is operating nearby, could rapidly cause the memory to fill up, and thereby prevent monitoring of the actual blasting event. Another important issue to consider regarding the sampling rate is that lower sampling rates cannot record the peak as accurately as is the case at higher sampling rates. As an illustration, the sampling rate of the model was varied from an extremely high value of 500,000Hz down to 4,096Hz. PPV obtained at a sampling rate of 500,000Hz is 660mm/s (Figure 5.50), whereas PPV obtained at a sampling rate of 16,384Hz is 655mm/s (Figure    160 5.51), which represents a 0.8% error. PPV obtained at a sampling rate of 4,096Hz is 601mm/s (Figure 5.53), or an 8.9% error. Figure 5.50 through Figure 5.54 show the resulting PPV waveform values obtained using different sampling rates.    161  Figure 5.50 Model sampling rate = 500,000Hz  Figure 5.51 Model sampling rate = 25,000Hz    162  Figure 5.52 Model sampling rate = 16,384Hz  Figure 5.53 Model sampling rate = 8,192Hz    163  Figure 5.54 Model sampling rate = 4,096Hz 5.5 PPV – Diffraction Case 5.5.1 General So far, the model has only been used to determine the PPV in the near-field instance, where the travelled distance to the point of interest is relatively short, only a few meters away, and each packet travels in a straight line toward the point of interest (i.e., signature blasthole). Note that the equations prescribed by the Holmberg-Persson and Hustrulid-Lu methods were presented solely for illustration in this simple case scenario. The model determines the distances from each and every packet in the blasthole, passing through a point of diffraction ZPOD or (0,0,ZPOD) at the face-wall contact, to the geophone location or point of interest. Note that for each packet there is a different ZPOD that yields the shortest packet-geophone distance. The model assumes that the vibration travels from the packet centroid to the ZPOD through the body of rock at its body wave velocity. From this point onward the wave travels on the surface of the wall excavation to the geophone at the surface wave velocity. As a consequence of such unfavorable geometry, where an open volume prohibits a direct path of propagation, the vibrational energy experiences a    164 sharp loss at this ZPOD location, which, in the worst case corresponds to a turn angle of nearly 90o. The assumption here is that only a portion of the original packet velocity magnitude continues to propagate parallel to the wall, while the remainder vanishes into the medium, and consequently does not get recorded by the datalogger. In practice, this situation has been incorporated in the model by assuming that only the vertical projection of the original magnitude of the packet’s particle velocity parallel to the wall reaches the geophone. In addition, the user can apply a power factor to the vertical projection, to increase or decrease the weight that the point of diffraction has on the vertical PPV projection. This happens since not all of the seismic energy that makes a turning angle toward the point of interest at the face-wall contact will dissipate, some of the energy diffracts. At this stage, for simplification, the model does not incorporate other constants or variables. Another solution, not being explored as part of this research, is that the original waveforms could have been decomposed as the projection of the magnitude parallel and perpendicular to the wall using the Sin(βith) and Cos(βith) factors respectively (times a constant for each projection), and not just using the one parallel to the wall, as is used for the model. It is of course implied that the vector summation of both components should not generate amplitudes greater than the original. The following two examples illustrate both cases: one in which there are solely straight path lines from the packets to the geophone – signature blastholes case; the other such that the geophone is located on the surface of the excavation and the seismic rays originating in each packet must pass through points of diffraction. In both cases, the propagation velocity of the medium, the VOD of the explosive, the vibrational frequency, and the site constants were all set to be the same values. Figure 5.55 shows the arrival time results for a blasthole located 5.2m from the geophone, the signature blasthole case, whose distance is measured along the surface of the excavation, from the collar of the blasthole to the point of interest. Figure 5.56 shows the particle velocity waveforms for a selected number of packets (1, 5, 9, 13, 17) and Figure 5.57 shows the particle velocity waveforms for all 17 packets of the array, where the red- dashed short-spaced line is the waveform corresponding to packet 1, i.e., the packet closet    165 to the geophone, yielding the highest PPV value. Figure 5.58 shows the linear superposition waveform of all 17 packets.    166  Figure 5.55 Arrival times – Signature blasthole case  Figure 5.56 PPV waveforms for selected packets – Signature blasthole case    167  Figure 5.57 PPV waveforms for all 17 packets – Signature hole case  Figure 5.58 Linear superposition of individual PPV waveforms – Signature blasthole case    168 Figure 5.59 shows the arrival time results of a blasthole located 5.2m from the geophone, where the distance is also measured along the surface of the excavation. The distance is 2.6m from the collar of the blasthole to the point of diffraction at the face-wall contact, and 2.6m from the point of diffraction to the geophone, in the diffraction case. Figure 5.60 shows the particle velocity waveforms for the same selected number of packets (1, 5, 9, 13, 17) and Figure 5.61 shows the particle velocity waveforms for all 17 packets of the array. As in the previous example, the red-dashed short-spaced line represents the waveform corresponding to packet 1 (i.e., closest to the geophone.) In this case, however, it yields the lowest PPV value. Figure 5.62 shows the linear superposition waveform of all 17 packets. In this example, the packets that are closest to the face, even though their distances to the geophone are the shortest, have the greatest reduction in their PPV values due to the sharp (90o) turn at the point of diffraction. Note that with respect to the previous examples, it would not be possible to match all 17 distances for every packet in the array.    169  Figure 5.59 Arrival times – Diffraction case  Figure 5.60 PPV waveforms for selected packets – Diffraction case    170  Figure 5.61 PPV waveforms for all 17 packets – Diffraction case  Figure 5.62 Linear superposition of individual PPV waveforms – Diffraction case    171  5.5.2 Arrival Time – Two Blastholes with identical Nominal Delay The following example is intended to demonstrate that two blastholes with the same nominal delay number, while considering zero time delay scatter, located at a certain distance from each other, should yield no constructive interference. As a consequence, the linear superposition of the two waveforms combined could yield the same, and in some cases even smaller, final PPV than the original PPV of each waveform on its own. Figure 5.63 shows the arrival times of two opposite bottom corner lifter blastholes. For this example, in a real case scenario, such as the Musselwhite mine, both of these lifter blastholes would be detonated with a #19 nominal delay number. No time delay scatter was considered in this example. In this figure, it is clear that the arrival time of the peak of the waveform of one blasthole never intersects with the arrival time of the peak of the waveform of the second blasthole. Each dot on both curves indicates the arrival time of the peak of individual waveforms.    172  Figure 5.63 Arrival times for two blastholes at different locations – Zero time scatter Figure 5.64 shows the two individual waveforms for each lifter blasthole, as indicated by the long-spaced red line and the short-spaced blue line. In Figure 5.64, the linear superposition of both waveforms is combined, indicated by a continuous black line. In this example, destructive rather than constructive interference occurs between both waveforms.    173  Figure 5.64 Linear superposition between 2 blastholes with same delay number In the previous example, the explosive’s VOD, its type and quantities, the velocities of propagation, the frequency, plus all the other constants for both samples are all assumed to have equal values. 5.6 PPV for Practical Cases 5.6.1 General So far, the model has been validated against the Hustrulid-Lu equation using non-real values for the propagation velocity and the VOD of the explosive. In this case, the peak of every packet of a blasthole coincides at time tini, that is, there is no time shift among the arrival times of the peaks of every packet, and the model and equation yield exactly the same results. It has also been tested for the near-field and diffraction case scenarios. In this section, the model will be tested in a more realistic scenario where the VOD of the explosive (4,300m/s) is similar to the cartridge explosive Dyno APTM, used in the lifter blastholes. The body and surface propagation velocities of the seismic wave and the predominant frequencies tested are closer to that of a poor-fair and good rock mass    174 qualities. These cases are, to some extent, representative of the SSX and the Musselwhite mines, respectively. In Figure 5.65, the blue triangles indicate the locations of two blasthole collars. The differences among PPV generated by each of the blastholes for both rock mass qualities will be analyzed.  Figure 5.65 Arrival times and PPV for highlighted blasthole location The analysis includes the arrival time and the individual waveforms of each packet in the array as well as the linear superposition of the combined individual waveforms. In this case, both blastholes are located at the floor level of the drift corresponding to the coordinates (0.0, -1.7) and (3.5, -1.7). The geometry of the drift and the explosive properties are identical for both of these otherwise dissimilar rock mass qualities. 5.6.2 Competent Rock Mass – Good Rock Mass Quality; RMR > 75 Figure 5.66 compares PPV versus time of a single blasthole recorded waveform against the model waveform, for the Musselwhite Mine case. The rock mass dominant vibration    175 frequency was set to 1000Hz and the velocity of propagation of the body wave was set to 6500m/s. The pre- and post-decay constants were varied to achieve similar waveform patterns. The use of similar waveform patterns could improve the reliability of the model’s predictive capabilities as it is expected that the model will better interpret the recorded PPV.  Figure 5.66 Good rock mass quality – PPV vs. time waveform – Record & model The following sets of figures were obtained after adjusting the rock mass and explosive properties to represent a good rock mass quality, such as that encountered at the Musselwhite mine. In this case, constant K was set to 1000, n=-1.5, and α=0.7, and f1=1, f2=1, and f3=1. The distance from the face of the round to the geophone location was set at 5m. Figure 5.67 shows the arrival times of each of the waveforms for every packet in the array. The first vibration waveform to arrive at the geophone corresponds to the packet located at the bottom of the blasthole. This result is expected, as the body wave velocity is faster than the VOD of the explosive.    176  Figure 5.67 Arrival times - Good rock mass quality case - Y=0.0 Z = -1.73 Figure 5.68 shows all the waveforms generated for every packet in the array. In this case, the seismic wavefront has to pass through a point of diffraction, so that the distances are factored by Sin(βith). It is evident that those blastholes located at the perimeter, closest to the geophone, will have a factor approximately equal to one {Sin(≅90°)≅1} in which case the factor applied has no noticeable impact on their distances. The closer the blasthole’s collar is to the perimeter, the less significant this factor becomes.     177  Figure 5.68 Particle velocity waveforms - Good rock mass quality case - Y=0.0 Z = -1.73 Figure 5.69 shows the linear superposition of the combined individual waveforms generated for the blasthole located at (0.0,-1.73).    178  Figure 5.69 Linear superposition - Good rock mass quality case - Y=0.0 Z = -1.73  Figure 5.71, Figure 5.72, and Figure 5.74 show similar sets of figures as the previous cases, but now the collar location at (3.47m,-1.73m) is considered (i.e., farther from the perimeter). In this case, the factor applied to the portion of the distance between the packet centroid and the point of diffraction becomes more significant, as is evident by comparing the peak waveform values for packet 1, the one closest to the collar, where, in the first case, this value was nearer to maximum, and in the second case was closer to minimum (short-spaced red line).    179  Figure 5.70 Arrival times - Good rock mass quality case - Y=3.5 Z = -1.73  Figure 5.71 Particle velocity waveforms - Good rock mass quality case - Y=3.5 Z = -1.73    180   Figure 5.72 Linear superposition - Good rock mass quality case - Y=3.5 Z = -1.73  5.6.3 Weak Rock Mass – Poor/Fair Rock Mass Quality; RMR > 35 As in the previous example, the following sets of figures were obtained after adjusting the rock mass and explosive properties to represent a poor/fair rock mass quality, with an RMR on the order of 35, such as that encountered at the SSX mine. Figure 5.73 compares PPV versus time of a single blasthole waveform against the modeled waveform for the SSX Mine case.    181  Figure 5.73 Fair/Poor rock mass quality – PPV vs. time waveform – Record & model For the following case, the constant K was set to 150 and for comparison purposes, the constants n and α were kept the same as in the previous example, i.e., n = -1.5 and α = 0.7. The rock mass dominant vibration frequency was set to 150Hz and the velocity of propagation of the body wave was set to 2000m/s. The distance from the face of the round to the geophone location was set to 5m. Figure 5.74 shows the arrival times of each of the waveforms for each packet in the array. In this case, the first vibration waveform to arrive at the geophone corresponds to the packet located at the collar of the blasthole. Just as before, this is an expected result, owing to the fact that the body wave velocity is much slower than the VOD of the explosive.    182  Figure 5.74 Arrival times - Poor/Fair rock mass quality case - Y=0.0 Z = -1.73     183  Figure 5.75 Particle velocity waveforms - Poor/Fair rock mass quality case - Y=0.0 Z = -1.73  Figure 5.76 Linear superposition - Poor/Fair rock mass quality case - Y=0.0 Z = -1.73    184 Figure 5.77 shows the arrival times of the waveforms of each packet of the blasthole located at (3.47m,-1.73m). In this case, the first waveform to arrive is the one corresponding to packet 7. Waveforms for packets 6 and 8 arrive nearly simultaneously as do the waveforms for packets 5 and 9 and so on, up until the arrival corresponding to packets 1 and 14. In this case, the simultaneous arrival of two or more packets produces a greater peak when compared to that of individual independent arrival times.  Figure 5.77 Arrival times - Poor/Fair rock mass quality case - Y=3.5 Z = -1.73     185  Figure 5.78 Particle velocity waveforms - Poor/Fair rock mass quality case - Y=3.5 Z = -1.73  Figure 5.79 Linear superposition - Poor/Fair rock mass quality case - Y=3.5 Z = -1.73     186 6  MODEL TESTING 6.1 Field Data PPV Measurements – Musselwhite Mine Case This chapter considers model validation using Musselwhite Mine PPV versus SD data compared with modeling results. One significant difference from current methodologies, as evident in this example, is that the modeling and recorded data points are analyzed using three axes rather than the more common PPV versus SD plotting method. In this example, the recorded PPV data points are plotted on the vertical axis with the magnitude corresponding to PPV values. Although the PPV values are recorded at some distance from the face, the value of the PPV of each blasthole in the round is assigned to its specific location. Similarly, the modeling results are plotted as a colored-surface contour indicating the range of the actual PPV values modeled. By plotting both the actual and the modeled surface contours, their difference enables assessment of how well the input parameters were established. A significant drawback of the far-field PPV versus SD plot, specifically with the use of near-field data points, is the fact that it considers the explosive charge as concentrated into a point, and the distance is therefore considered a discrete quantity, and so it is unclear which value is to be used, that of the collar, the toe, or a location somewhere in between. Regarding this, the model accounts for the distance to every packet regardless if it is in the near or far-field, and the accuracy of the predictions of the PPV should increase accordingly. Due to the fact that the model was developed after the actual gathering of data, that the model can provide the highest possible accuracy for prediction of PPV values is somewhat limited. Some of the parameters utilized to generate the model results were obtained from existing literature, whereas other parameters, such as the frequency of vibration and pre- and post-decay factors were determined by interpretation of recorded data. Among the parameters obtained from the literature are the n and α constants, the estimation of the vibrational propagation velocity of the rock mass, and the VOD of the explosive. It is beyond the scope of this research to determine specific values for the n and α constants that could yield optimum model prediction with the least standard deviation of error.    187 For the recorded data, the PPV values were assigned to each blasthole location based on the nominal delay number and the distance to the geophone, and when there were two or more blastholes detonated with the same nominal delay, the location in the round was assigned based on the PPV magnitude and their distances to the geophone. For each of the blastholes that were detonated with the same cap delay, the greater the distance of the blasthole to the geophone, the lower the PPV that was assigned to a given blasthole location among those possible. In principle, this method is consistent with the theory but can in practice, lead to interpretation errors. This chapter provides PPV predictions, obtained post modeling process, which yielded an acceptable difference with the recorded PPV values. In this regard, in the validation of the model, it was not meant to determine the n, α, and other constants that yield the lowest statistical error. Given that some of the constants were not determined from empirical data but rather were obtained from literature, it should be clear that there is little benefit in performing statistical analysis. Nevertheless, this chapter demonstrates the potential of the modeling tool, featuring three-axial plots through which it is possible to present and compare the modeling results with the data records obtained from the monitoring campaigns. Figure 6.1 shows a plot of a section of the blasthole pattern where the red dots correspond to the locations of the blastholes in the round and the number refers to the linear charge density, in kilograms per meter, for each particular blasthole location. The graphs in this and the following chapters were created using OriginPro 8.5™ plotting software.     188  Figure 6.1 Blasthole’s location and linear charge density Figure 6.2 through Figure 6.5 show PPV values recorded at the geophone location and subsequently assigned to each blasthole in the round, where the PPV is plotted in the vertical axis for almost every location in the round, at face-geophone distances of 9.5m, 10.5m, 21.5m, and 26.6m, respectively.     189  Figure 6.2 Measured PPV values – Musselwhite Mine – 9.5m from the face     190  Figure 6.3 Measured PPV values – Musselwhite Mine – 10.5m from the face  Figure 6.4 Measured PPV values – Musselwhite Mine – 21.5m from the face    191  Figure 6.5 Measured PPV values – Musselwhite Mine – 26.6m from the face  6.2 PPV Data Measured versus Modeled – Musselwhite Mine Case From the model, PPV values corresponding to each blasthole location were determined, and from these values a series of surface contours were plotted against recorded PPV values, as shown in Figure 6.6, Figure 6.8, Figure 6.10, and Figure 6.12. The surface contours indicate the magnitude range of the PPV modeled, in millimeters per second. The surface projections of these three-dimensional surface contours were also plotted in Figure 6.7, Figure 6.9, Figure 6.11, and Figure 6.13, as an aid to the reading of the values.    192  Figure 6.6 Measured versus modeled PPV surface contours – 9.5m from the face  Figure 6.7 Surface projection of modeled surface contours – 9.5m from the face    193  Figure 6.8 Measured versus modeled PPV surface contours – 10.5m from the face  Figure 6.9 Surface projection of modeled surface contours – 10.5m from the face    194  Figure 6.10 Measured versus modeled PPV surface contours – 21.5m from the face  Figure 6.11 Surface projection of modeled surface contours – 21.5m from the face    195  Figure 6.12 Measured versus modeled PPV surface contours – 26.5m from the face  Figure 6.13 Surface projection of modeled surface contours – 26.5m from the face    196 Three main factors that form part of the model’s architecture, which were used to obtain the PPV results in this chapter, are considered to enhance its potential beyond current methodologies: first, the proposed model predicts a PPV value in which the distance to every individual packet is accounted for, including as it is applied to a far-field case type scenario; second, the model uses linear superposition of the generated waveforms after they have been shifted by their respective arrival times; and third, it also accounts for the diffraction of the seismic waves. The combination of these factors with the right set of constants should lead to a much more precise PPV prediction. In contrast, current methodologies make the use of discrete values for the near-field PPV calculation, with its applicability being limited only to “signature blastholes” and without consideration of the time component. For the far-field (as well as the intermediate-field), current methodologies do not consider the time component and it is up to the user to choose whether to use the collar, or a mid-point, or the toe of the blasthole for the geophone- blasthole distance. Although in the far-field, the time component and the appropriate geophone-blasthole distance might not be as relevant as in the near- and intermediate- field cases, it is still valid to apply the model to the far-field situation.    197 7 APPLICATIONS OF THE PROPOSED MODEL 7.1 General A broad range of blasting applications could be analyzed with the proposed modeling tool. All modeling tools, including this one, require calibration of input parameters. This model requires the input of fitting constants to yield an accurate prediction of PPV values, which must be established via numerous particle velocity monitoring records of near-, intermediate-, and far-field detonations. Potential applications include explosive analysis where PPV in the very-near-field, i.e., within a few centimeters of the blasthole, could be estimated. As well, the determination and analysis of the appropriate explosive type and its distribution throughout the blast pattern could be made, aiming to reduce potential damage to rock excavations and structures. The proposed model is not limited to PPV analysis of drifting and tunneling operations, but could also be used in underground and surface production blasting, where the geometry of the blast with respect to the point of interest is similar to that of the model’s set-up, that is, in the near-field or where the seismic waves would pass through a point of diffraction before arriving at the point of interest. 7.2 Analysis of the PPV for different Explosive Types The following example shows the 3-D surface contour of the distribution of the PPV for one blasthole loaded with ANFO, obtained for many location points around the face of the round (Figure 7.1). Figure 7.2 shows PPV results, but in this case the scale of the PPV was increased and discretized to a much finer degree, at a very close range to the blasthole. This greater level of discretization around the zone of interest can easily be achieved in the model by factoring the monitoring’s (x,y) location point with a factor lower than one. The reader should be aware of the non-linear waveform superposition affecting the blastholes at the very close range of the explosive charge (Blair, 2007), where irreversible deformation takes place. The non-linear waveform superposition that should be used for the very-near-filed would yield a smaller or greater PPV calculation value – depending on the constant used – than the linear scheme used in the proposed    198 solution. Also, it would be necessary to make modifications to the model in order to achieve a smooth transition at the boundary of the non-linear and linear zones.     199  Figure 7.1 Near-field PPV of ANFO  Figure 7.2 Near-field PPV of ANFO – Finer discretization around the blasthole    200 Another set of predicted PPV values, obtained in close proximity to the blasthole location, was plotted for each (x,y) location point surrounding the blasthole, but where different types of explosives, commonly employed at the mine sites investigated, were used. In this case, the maximum horizontal distances from the blasthole to the point of interest is approximately 0.6m. Figure 7.3 through Figure 7.7, show the three-dimensional PPV surface contours for SEC Detagel™, ANFO, and Dyno AP™ explosives, respectively. These explosives are commonly employed in the perimeter, body, and lifter blastholes, respectively. Figure 7.4 through Figure 7.8, show the two-dimensional surface projection for the same explosives.            201  Figure 7.3 Near-field PPV modeled – 3D surface – SEC Detagel™  Figure 7.4 Near-field PPV modeled – 2D projection – SEC Detagel™    202  Figure 7.5 Near-field PPV modeled – 3D surface – ANFO  Figure 7.6 Near-field PPV modeled – 2D projection – ANFO    203  Figure 7.7 Near-field PPV modeled – 3D surface – Dyno AP™  Figure 7.8 Near-field PPV modeled – 2D projection – Dyno AP™    204 The height of the column charge corresponds in all cases to the length of the blasthole of 4.3m. By reducing this height to a very small value (a few millimeters), one could obtain results right next to an infinitesimal small explosive charge, allowing for the determination of PPV values along the entire column of explosive. Although this test did not form part of the analysis, it could well be used to calibrate the model using laboratory size blasting samples. 7.3 Blasthole Interaction Analysis The interacting detonating charges can also be analyzed from the modeling results. For example, two or more charges detonated with the same time delay could be used to assess the radius of interaction of each blasthole charge, thus aiding in determining the burden and spacing that could potentially optimize fragmentation and minimize damage inflicted to the perimeter of the excavation. Figure 7.9 and Figure 7.10 show the three-dimensional surface contour and its two-dimensional surface projection for two interacting charges, with 58cm spacing between them. The explosive considered was Dyno AP™. For this example, it was assumed that the samples are detonated at the same nominal delay, and so, there is no phase shift between the waveforms of both blastholes.     205  Figure 7.9 Blasthole Interaction – 3D surface – Dyno AP™  Figure 7.10 Blasthole Interaction – 2D projection – Dyno AP™     206 7.4 Other Applications of the Model 7.4.1 Blasthole Distribution Analysis An extension of the previous subchapter would include determination of the PPV predictions for different types of explosive considering their distribution as employed in a round. With the model, PPV predictions can be determined at any given location, either within the face or in such cases where the seismic vibration has to pass through a point of diffraction, and thus, potential negative implications at any given location could be assessed. 7.4.2 Surface and Underground Blasts The model was originally designed and implemented for drift and tunnel development, but may well be utilized to assess underground and surface production blasting, where the geometric conditions of the excavations are similar to that of the original design. The POIs (geophones) could be located in the same plane of the blasting round or at 90o from it, as shown in Figure 7.11. In this sense, blastholes can be positioned at any given location, while their length and linear charge densities are user defined. Currently the model is limited to parallel blastholes but could be modified to allow for the analysis at any given orientation.    207  Figure 7.11 Application to a surface blast situation  7.4.3 Pyrotechnic Caps Delay Scatter With the model, one could determine, for example, the implications of two or more blastholes detonating at the same nominal delay, with the addition of some time delay, in order to emulate the scatter existing among pyrotechnic caps similar to those of Figure 3.26. Ideally, it would be desirable to avoid linear superposition of waveforms originating with different nominal delay numbers, in order to reduce the PPV levels. This exercise can be easily performed with this model. 7.5 Limitations of the Model The model considers that the location of the geophone or point of interest is either immediately at the face of the blasthole, or on a wall oriented 90o with respect to the blasting round face. It determines the shortest distance to the geophone, however, the model is constrained to a specific geometry by having to determine the distance to the geophone necessarily passing through the point of diffraction located at the face-wall    208 intersection, and from there to the point where the geophone has been installed. This might not always be the case, for example, for some of the perimeter blastholes located at the boundaries of the blast pattern. Also, depending on the blast sequencing of an actual blasting round, for some of the modeled waveform packets of certain blastholes, the direct path from the packet location to the point of diffraction would not be possible; this would be due to the fact that previous detonated blastholes have opened a void, also known as screening influence (Blair, 2007). For these cases, an actual seismic vibration will be forced to go around this newly created opening. The model provides no consideration for an indirect path of the seismic wave but could potentially be modified to factor in this effect. This can be done, for example, by taking into consideration the current open void (based on the detonation sequence) and the semi-perimeter of an ellipse as the distance that the seismic wave should travel from the packet location to the POD. In this case, twice the semi-major axis of the ellipse would be the distance from the packet centroid to the POD, and the diameter of the open void would be twice the semi-minor axis. The blastholes are considered parallel to each other and parallel to the strike orientation of the drift or tunnel. The reality though, is that blastholes normally present some intentional or designed deviation as well as unintentional or unavoidable deviation. For example, in a standard blast pattern, the perimeter blastholes are normally drilled in an outward orientation with a wider angle to maintain the planned area. Since the drilling equipment requires room to position the drill, if these perimeter blastholes are not drilled with a wider angle, the size of the excavation will be reduced as subsequent rounds are blasted. Potential upgrades could include non-parallel blastholes, but this is beyond the scope of this research.    209 8 CONCLUSIONS Analysis of PPV versus time data and assessment of rock mass quality at the sites investigated has experimentally confirmed that as rock mass quality decreases, the rate of decay of the seismic vibration amplitude increases. That is, if the distance travelled by the seismic vibration is the same for two dissimilar rock mass qualities, then the amplitude of the particle velocity for the lower rock mass quality will experience a more rapid decay or damping over that distance.  Similarly, it was experimentally demonstrated that a rock mass of poorer quality generates lower vibration frequencies, and also dampens the higher vibration frequencies faster, as the wave travels through that particular medium, allowing only the lower frequencies to remain. This becomes especially evident when comparing the frequency content of two dissimilar rock mass qualities, such as those existing at the Musselwhite Mine (90 RMR) versus those at the SSX Mine (35 RMR), where observed peak vibration frequencies were approximately 1100Hz and 150Hz, respectively.  The high-frequency geophones installed in close proximity to the explosive charges indicate that, at such a short range, the high frequency amplitude components of the particle velocity have greater influence than the lower frequencies. Peak velocities of greater than 60% that of the original PPV are measured within the 500-1000Hz range, when a PPV versus time record for a good rock mass is analyzed. These results represent a step forward, in respect of the fact that the values that have been commonly observed in the great majority of literature to date have been in the order of 5-50Hz (where the values were obtained at greater distances from the explosive source and utilized lower frequency range geophones).  From analysis of the field measurements, a PPV versus SD relation for various rock mass qualities was developed. This relation confirmed that the more competent the rock mass quality, the higher the PPV required for fragmenting and displacing the rock, and at the same time showed a progressively lower extent of overbreak with improving rock mass quality.    210  Blasting generates ground vibrations that are predominant at the natural vibration frequencies of the rock. The research has produced useful empirical data on the predominant frequencies associated with various rock mass qualities, as determined in close proximity to a given drift development blast. This data could provide some of the input parameters required to assess various ground support elements employed, for example, shotcrete and rock bolts, using numerical modeling tools or other methods, in order to determine dynamic response under a variety of rock mass conditions. Numerical codes such as PFC3D could perform static and dynamic strength analysis of pseudo- materials subjected to vibrational shaking with user defined loading amplitudes and frequencies.  Also, when safety is a principle consideration, should blast monitoring become a regular feature of mining operations, and given that PPV and frequency content are related to rock mass quality, this information could be used to produce much deeper, more thorough assessments and interpretations of the quality of the rock mass and its need for an appropriate type of support system.  The time scatter in long period (LP) pyrotechnic blasting caps suggests that utilizing the total weight of explosive per delay would likely yield erroneous SD factor results. There was very little evidence in this research of constructive interference (productive interaction) between blastholes with same nominal delay, such that the vibration waves would eventually yield higher peak magnitudes of particle velocity, compared to the peak magnitudes for individual blastholes with the same nominal delay time, when this type of blasting cap is utilized.  The use of electronic detonators might have greatly simplified the analysis of the seismic records if each blasthole would have been assigned a different delay number. This would have helped reduced uncertainty with regard to the locations of some of the blastholes since the delay scatter for this electronic detonator is assumed to be negligible. By    211 recognizing the delay time in the seismic records, the recorded PPV could be easily assigned to a particular blasthole location.  The model results were used to demonstrate that two blastholes with exactly the same nominal delay time could generate partial destructive interference of their seismic waveforms, measured at the geophone location, due solely to the spatial location within the round. And so, even though two or more blastholes could detonate at exactly the same time, it is possible that this is not reflected in the particle velocity seismic records as an increase in overall peak value.  Overbreak measurement, as determined through the ELOS method, involves values that in some cases are perceived to be quite small even in the presence of a wedge type breakout of rather large size, owing to the fact that the total volume of the estimated overbreak is normalized by the planned excavation surface, and thus yielding an average of the overbreak thickness. ELOS represents the average depth of the excess of broken material measured normal to the excavation surface. An alternative to the method employed in this research could have been to present simply the total volume of overbreak, without normalizing it to the original volume or surface area being excavated; in this case, it would not be possible to compare the overbreak volume against different excavation sizes.  The semi-empirical model was validated against Hustrulid-Lu (Equation 29), however, the model is not restricted to the near-field particle velocity determination, as in Hustrulid-Lu’s equation. This is due to the fact that the model utilizes a waveform instead of discrete numerical values, and can incorporate the delay in arrival times of each and every packet of the blasthole. One of the major contributions of this research is its wide range of applications to different blasting problems, as the solutions obtained using the model and the equations and methodologies provided therein shows.  The model was used to demonstrate the effects of the sampling rate to accurately record PPV measurements, where an error on the order of 9% could be made if using 4,096    212 samples per second, and on the order of 1% if using 16,384 samples per second, as compared with an infinite sampling rate. It is clear that the sampling rate should be set as high as is possible for the instrument in use, but that the rate should also depend on the number of channels being recorded simultaneously, as well as the memory availability of the monitoring equipment.  The proposed methodology (and its subsequent application) addresses the problem of the reduction of the particle velocity of a wave after it has passed a point of diffraction at the face-wall interface. It is expected that the energy of the seismic waves is reduced after passing the point of diffraction at this interface, and the methodology accounts for part of this reduction by using a portion (the vertical projection) of the original PPV value. This portion of the original PPV value is obtained directly from the value of the angle formed from the location of the incidence ray to the location of the POD at the interface.  As the proposed semi-empirical formulation (Eq. 45) incorporates the distance of each and every packet within the blasthole, there is no need to define a unique distance value for determination of the SD factor, as in the far-field case. The equation also accounts for the delay in the arrival time of every seismic waveform originating at its packet location, for both the near-field and far-field cases. In essence, it incorporates into one formula, the near- and far-field effects as separate body and surface wave propagation components.  The model incorporates various constants, which can be set at their basic, uncalibrated values, i.e., 1, for simplicity but which can also be determined in the calibration process for the chosen number of blast rounds as monitored (the greater the number of blast rounds, the greater the accuracy of the calibration). In this way, the model provides for a great deal of flexibility to the end user. Calibration of these empirical constants does, however, increase complexity, as these constants need to be defined. In Chapter 5, there is a brief explanation of some of the tests that can be performed in order to determine these constants. Due to cost constraints, not all the values for the input parameters were determined from field measurements. Where field data was not available, values for the input parameters were obtained using existing literature data. In this case, there is little    213 value in performing cross-correlation analysis between the modeled and measured PPV values. The general recommendation is to keep in mind that the accuracy of the determination of the values for the empirical constants directly affects the reliability of the predicted PPV values. The more data collected the better. However, there is additional cost to gathering more and more data. Greater accuracy must be weighed against the cost of collecting that data.  In the model’s application chapter (7), various examples were undertaken with the proposed model, accounting for explosive type and interaction between charges in a blasting round. These are basic applications that most blasting engineers should perform systematically. With the new approach, other types of analysis in which similar geometric conditions (as in a drift or tunnel development round) could also be analyzed, such as underground and surface production blasting, expanding its potential even further.  The model presents some limitations regarding the estimation of the distance from a blasthole’s packet to the geophone location, hence affecting the PPV determined from the model. This is due to the fact that the whole blasting sequence is not taken into consideration by the model, and in order to incorporate it into a future proposal, consideration for the loss of part of the original seismic vibration energy should be made. This could be done by estimating the total travel distance of the seismic waves, as they must travel around the void produced by the detonation of previous blastholes, in accord with the blasting sequence.    214 9 RECOMMENDED FUTURE WORK This research has shown that future advances in this new methodology could be made as follows: -­‐ The proposed modeling tool requires the input of different equation constants, some of which were obtained from literature and subsequently adapted to the constants specific to the proposed model. It is imperative that the determination of the particular set of constants used by the model should be generated from a series of blast monitoring campaigns, applicable to one or more rock mass qualities. Some of these constants should be readily available, such as the rock mass body and surface propagation velocities, whereas others, such as the f1 to f3 factors, would have to be obtained from multi-variable statistical analysis of a number of monitored blasts. Once these empirically determined constants are obtained, the accuracy of the model results would be expected to increase. -­‐ As a result of the concussion produced by the detonation of explosive charges, a given rock mass vibrates at many of its natural vibration frequencies. Although the proposed model can determine the particle velocity waveforms for a number of different frequencies, in this research only the particle velocity that results from application of the single predominant vibration frequency was tested. A multi- frequency analysis could potentially yield more accurate results, although certainly this will also increase the model’s complexity. This complexity would include, for example, a determination of the propagation velocity for each range of frequencies being analyzed. To be rigorous in this matter, it would also be necessary to determine the PPV equation constants for each frequency range since, for example, the rate of decay and the propagation velocity is different for different frequencies. -­‐ The proposed model assumes that the blastholes are drilled perpendicular to the surface of the face of the blasting round, whereas the reality is that not all the blastholes are drilled in this way. Some of the blastholes, specifically perimeter or contour blastholes including lifters, are drilled at an angle to increase the dimensions of the excavation. It is obvious that the maximum surface increase will be at the end of the blastholes in these cases, to provide sufficient room to    215 accommodate the drilling equipment. It is also to be expected that by incorporating the actual drillhole direction into the model, PPV prediction accuracy should also increase. -­‐ Among the limitations evident in the model is the fact that as each blasthole detonates, it creates a void through which seismic waves cannot propagate. The modeling design assumed that travelled distance is determined from the straight path between a particular packet location and the point of diffraction. The reality, though, is that the seismic wave must travel around this newly created void. A simple solution to this problem might be to compute the travelled path from the packet to the point of diffraction using the perimeter of an ellipse, in which twice the semi-major axis would correspond to the straight line formed by the detonating packet and the point of diffraction, and twice the semi-minor axis would correspond to the diameter of the void being formed. In this way, the semi-perimeter of an ellipse would correspond to the actual travelled distance from a particular packet centroid to the point of diffraction.      216 REFERENCES Adamson, W. R., Scherpenisse C. R., and Diaz, J. C. (1999). The use of blast monitoring/modelling technology for the optimisation of development blasting. In Proceedings Explo ’99, (The Australasian Institute of Mining and Metallurgy: Melbourne). pp 35-42. Ambraseys, N.N., and Hendron, A.J. (1968). Dynamic behavior of rock masses, in Rock mechanics in engineering practice. Stagg, K.G., and Zieniewicz, O.C (eds.), New York, John Whey. pp. 203–236. Anonymous (2011). The Bureau of Labor Statistics of the U.S. Department of Labor. Accident Classification by Industry. Anonymous (2000). 17th Edition Blasters. Handbook (ISEE, 2000)). Barton, N.R., Lien, R., and Lunde, J. (1974). Engineering classification of rock masses for the design of tunnel support. Rock Mech. Vol. 6(4), pp. 189-239. Barton, N., Lien, L., and Lunde, J. (1974). Analysis of rock mass quality and support practice in tunneling and a guide for estimating support requirements. Internal Report of Norwegian Geotechnical Institute, Oslo, Norway, pp. 6–9. Bauer, A., and Calder, P.N., (1978). Open Pit and Blasting Seminar. Mining Engineering Department, Queens University, Kingston, Ontario. Bernard, E.S., and Pireher, M. (2010). The use of Round Determinate panels for the assessment of flexure performance of fiber reinforced concrete, Cement and Aggregates, ASTM. Bieniawski, Z.T. (1973). Engineering Classification of Jointed Rock masses, Transaction South African Institution of Civil Engineers, Vol. 15. pp. 335-344. Bieniawski, Z.T. (1976). Rock mass classification in rock engineering. In Exploration for rock engineering, proc. of the symp., (ed. Z.T. Bieniawski) Vol. 1, Cape Town: Balkema. pp. 97-106. Bieniawski, Z.T. (1989). Engineering rock mass classifications. New York: Wiley.    217 Baird, G.P., Blair, D.P., and Jiang, J.J. (1992). Particle motions on the surface of an elastic half-space due to a vertical column of explosives. West Aust. Conf. Mining Geomech. pp. 367-374, Kalgoorlie, Australia. Blair, D.P., and Minchinton, A. (1996). On the damage zone surrounding a single blasthole, Proceedings of Rock fragmentation by blasting, FRAGBLAST-5, (Ed) Mohanty, Montreal, Quebec, Canada, 23-24 August. pp. 121-130. Blair, D.P. (2004). The frequency content of ground vibration. International Journal of Blasting and Fragmentation. 8: pp. 151–176. Blair, D.P. (2008). Non-linear superposition models of blast vibration. International Journal of Rock Mechanics & Mining Sciences 45. pp. 235–247. Bogdanoff, I. (1995). Vibration measurements in damage zone in tunnel blasting. Proceedings of Rock fragmentation by blasting, FRAGBLAST-5, (Ed) Mohanty, Montreal, Quebec, Canada, 23-24 August. pp. 177-185. Breslin, J.A. (2010). One Hundred Years of Federal Mining Safety and Health Research. NIOSH’s Information Circular 9520. Clark, L. M. (1998). “Minimizing Dilution in Open Stope Mining with a Focus on Stope Design and Narrow Vein Longhole Blasting”. MASc. Thesis, Faculty of Graduate Studies, Department of Mining and Mineral Process Engineering. CMRI (1993), Vibration standards, Central Mining Research Institute, Dhanbad. Cooper, P. W. (1996). Explosives Engineering, New York: Wiley-VCH. ISBN 0-471- 18636-8. Crandell, F.J. (1949). Ground Vibration due to Blasting and its Effect upon Structures”, J. Boston Soc. Civ. Engineers, Apr. pp. 222-245. Cunningham, C.V.B. (1983). The Kuz-Ram Model for Predicting Fragmentation from Blasting, Proceedings of the First International Symposium on Fragmentation by Blasting, Lulea Sweden. August 22–26. pp. 439–453. Deere, D.U., Hendron, A.J., Patton, F.D. and Cording, E.J. (1967). Design of surface and near surface construction in rock. In Failure and breakage of rock, proc. 8th U.S. symp.    218 rock mech., (ed. C. Fairhurst). New York: Soc. Min. Engrs, Am. Inst. Min. Metall. Petrolm Engrs. pp. 237-302. Dey, K. (2004). Investigation of blast-induced rock damage and development of predictive models in horizontal drivages. PhD Thesis, Indian School of Mines, Dhanbad. Dick, R.A., Fletcher, L.R., and D'Andrea, D. V. (1983). Explosives and Blasting Procedures Manual. U.S. Bureau of Mines, Report IC 8925. Du Pont, E.I. De Nemours and Co. (1977). Blasters handbook. 16th edition, Delaware. Dowding, C.H. (1985). Blast vibration monitoring and control. New Jersey, Prentice- Hall, Englewood Cliffs, NJ, USA. Duvall, W. I., and Atchison, T. C. (1957), Rock Breakage by Explosives", U.S. Bureau of Mines RI 5356. Duvall, W.I. (1961). Design Criteria for Portable Seismographs. U.S. Bureau of Mines RI, 5708. 6 pages. Edwards, A.T., and Northwood, T.D. (1960). Experimental studies of effects of blasting on structures, The Engineer. p. 211. Forsyth, W.W. (1993). A discussion on the blast induced overbreak around underground excavations. Rock Fragmentation by Blasting FRAGBLAST-4. pp. 161-166. Green, R.E. (1984). Vibration damage from blasts and tremors. Proceedings of the South African National Group on Rock Mechanics Conference Monitoring for Safety in Geotechnical Engineering. pp. 89-104. Hoek, E., and Brown, E.T. (1980). Underground Excavations in Rock. London: Institution of Mining and Metallurgy. 527 pages. Holmberg, R., and Persson, P.A. (1978). Swedish approach to contour blasting. Proceedings of the Fourth Conference on explosive and blasting techniques, Society of Explosives Engineers, February 1-3, New Orleans, USA. pp. 113-127. Holmberg, R., and Persson, P.A. (1979). Design of Tunnel Perimeter Blasthole Patterns to Prevent Rock Damage, Proceedings, Tunnelling 1979, March 12-16, Ed. Jones M.J., Institution of Mining and Metallurgy, London, UK.    219 Holmberg, R., and Persson, P.A. (1980). “Design of tunnel perimeter blasthole patterns to prevent rock damage”, Trans. Ins. Min. Metall., London Vol. 89. pp. A37-40. Holmberg, R., and Hustrulid, W. (1981) Swedish Cautious Blast Excavation at the CSM/ONWI test site in Colorado, Proceedings of the Seventh Conference on Explosives and Blasting Technique. Phoenix, AZ, USA. Holmberg, R. (1993). Recent developments in control rock damage. Rock Fragmentation by Blasting, Rossmanith (ed.), A.A. Balkema, Rotterdam. pp. 197-198. Huang J.-W., Bellefleur, G., and Milkereit, B. (1989). Seismic wave attenuation due to scattering and leaky mode mechanisms in heterogeneous reservoirs. Joint convention of CSPG, CSEG and CWLS, Calgary, Alberta. Hustrulid, W., and Lu, W. (2002). Some general design concepts regarding the control of blast induced damage during rock slope excavation. Fragblast 7, Beijing, China, August, pp. 595-604. Indian Standard Institute (1973). Criteria for safety and design of structures subjected to underground blast. ISI Bull; IS-6922. Knopoff, L. (1964). Q: Reviews of Geophysics. 2, 625-660. Kolsky, H. (1963). Stress waves in solids. New York, Dover. Koopmans, R., and Hughes, R.W. (1985). Determination of near field excavation disturbance in crystalline rock. Mater. Res. Soc. Symp. Proc.; Vol/Issue: 50; Materials Research Society international symposium, Stockholm, Sweden. pp. 567-576. Langefors, U., Kihlstrom, B., and Westerberg H. (1958). Ground vibrations in blasting. Water Power. Langefors, U., and Kilstrom, B. (1973). The Modern Techniques of Rock Blasting. John Wiley and sons. pp. 34 - 73. Martin L., Seymour, B., Clark, C., Stepan, M., Pakalnis, R., Roworth, M. and Caceres, C. (2010). An analysis of flexural strength and crack width for fiber-reinforced shotcrete used in weak rock mines”. SME 2010, Phoenix, Nevada.    220 Murthy, V.M.S.R., Dey, K., and Raitani, R. (2003). Prediction of overbreak in underground tunnel blasting - A case study. Journal of Canadian Tunneling Canadien. pp. 109-115. Naismith, W.A. (1982). The influence of large scale surface blasting on the stability of underground coal mines. First International Congress on Rockbursts and Seismicity in Mines. Gay, N.C., and Wainwright, E.H. (eds.). The South African Institute of Mining and Metallurgy. Nicholls, H.R., Johnson, C.F., and Duvall, W.I. (1971). Blasting Vibrations and Their Effects on Structures. U.S. Bureau of Mines Bulletin 656. 105 pages. Pakalnis, R. (2010). Design of underground mine openings utilizing shotcrete. Kencana Mine Presentation, Spokane Research Laboratory, April 8-9. Palmström, A. (1982). The volumetric joint count - a useful and simple measure of the degree of rock jointing. Proc. 4th congr. Int. Assn Engng Geol., Delhi Vol. 5. pp. 221- 228. Paventi, M. (1995). Rock Mass Characteristics and Damage at the Birchtree Mine. PhD. Thesis, McGill University, 445 pages. Pavlovic, V. D., and Velickovic, Z. S. (1998), Measurement of the Seismic Wave Propagation Velocity in the Real Medium. The scientific journal FACTA UNIVERSITATIS, Vol. 1, No. 5. pp. 63-73. Persson, P.A. (1997). The relation between strain energy, rock damage, fragmentation and throw in rock blasting. The International Journal of Blasting and Fragmentation. Vol. 1 No. 1, pp. 99-109. Pusch, R., and Stanfors, R. (1993). Disturbance of rock around blasted tunnels. In: H.P. Rossmanith (ed.), Rock Fragmentation by Blasting, A.A. Balkema, Rotterdam. pp. 153- 159. Rupert, G.B., and Clark, G.B. (1977). Criteria for the proximity of surface blasting to underground coal mines. Proceedings, 18th US. Symposium on Rock Mechanics. June. pp. 3C3-1 to 3C3-1O.    221 Scoble, M.J., Cullen, M., and Makuch, A. (1987). Experimental studies of factors relating to destress blasting. Proceedings, 28th US Symposium on Rock Mechanics. Am. Inst. Mining Engineers, Univ. of Arizona. pp. 901-908. Singh, P.K., and Vogt, W. (1998). Ground vibration: prediction for safe and efficient blasting. Erzmetall; 51 (10): pp. 677-684. Siskind, D.E., Stagg, M.S., Kopp, J.W., and Dowding, C.H. (1980b). Structure response and damage produced by ground vibration from surface mine blasting. U.S. Bureau of Mines RI 8507. 74 pages. Siskind, D. (1985). Blast Vibration measurements near and on structure foundations. U.S. Bureau of Mines RI 8969, 1985. 20 pages. Siskind, D.E., Crum, S.V., Otterness, R.E., and Kopp, J.W. (1989). Comparative study of blasting vibrations from Indiana surface coal mines. U.S. Bureau of Mines RI 9226. 41 pages. Siskind, D. (2000). Vibrations from Blasting. 1st Edition. Published by International Society of Explosives Engineers, Cleveland, OH, USA, 2000. 120 pages. Spathis, A.T. (2009). A brief review of the measurement, modelling and management of vibrations produced by blasting, 9th International Symposium on Rock Fragmentation by Blasting, Granada, Spain. Stagg, M.S., and Engler, A.J. (1980). Measurement of blast-induced ground vibration and seismograph calibration. U.S. Bureau of Mines RI 8506. 62 pages. Svanholm, B. O., Persson, P. A., and Larsson, B. (1977). Smooth blasting for reliable underground openings. In Rockstore 77: Storage in excavated rock caverns, proc. 1st Int. Symp., Stockholm, (ed. M. Bergman), pp. 573-579. Oxford: Pergamon. Thoenen, J. R., and Windes, S. L. (1937). Earth vibrations from quarry blasting. Progress Report No. 1, Bureau of Mines RI 3353. Thoenen, J. R., and Windes, S. L. (1938). Earth vibrations caused by mine blasting, Progress Report No. 2, Bureau of Mines RI 3407.    222 Thoenen, J. R., and Windes, S. L. (1942). "Seismic effects of quarry blasting," Bureau of Mines Bulletin 442. 1942. Wetherelt, A., Hunt, P., and Pepper, J. (2003). Peak particle velocity modelling. Proceedings of EFEE Second World Conference on Explosives and Blasting Technique. Prague, Czech Republic, pp. 81-88. Yang, R.L., Rocque, P., Katsabanis, P., and Bawden, W.F. (1994). Measurement and analysis of near-field blast vibration and damage. Geotechnical and Geological Engineering, Vol. 12. pp. 169-182. Zhou, X.J., and McNeary, R.L. (2007). Modeling of shotcrete under ASTM C-1550 with PFC3. In proceedings 1st Canada-U.S. Rock Mechanics Symposium: Meeting Society’s Challenges and Demands. pp. 1533-1539.        223 APPENDICES APPENDIX A – ROCK MASS QUALITY LOGS   Figure A. 1 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Cross cut 1    224   Figure A. 2 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Cross cut 2     225   Figure A. 3 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Cross cut 3     226   Figure A. 4 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 1     227   Figure A. 5 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 2     228   Figure A. 6 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 3      229   Figure A. 7 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 4      230   Figure A. 8 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 5      231  Figure A. 9 Back, right and left wall rock mass classification logs – Stillwater Mine – Footwall lateral 6  Figure A. 10 Back, right and left wall rock mass classification logs – Stillwater Mine – Footwall lateral 7      232   Figure A. 11 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 8     233   Figure A. 12 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 9     234   Figure A. 13 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 10     235   Figure A. 14 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 11     236   Figure A. 15 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 12     237   Figure A. 16 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 13     238   Figure A. 17 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 14     239   Figure A. 18 Back, right and left wall pictures and rock mass classification logs – Stillwater Mine – Footwall lateral 15     240   Figure A. 19 Back, right and left wall pictures and rock mass classification logs – SSX Mine – Cross cut 11-1      241   Figure A. 20 Back, right and left wall pictures and rock mass classification logs – SSX Mine – Cross cut 11-2     242   Figure A. 21 Back, right and left wall pictures and rock mass classification logs – SSX Mine – Cross cut 11-3     243   Figure A. 22 Back, right and left wall pictures and rock mass classification logs – SSX Mine – Cross cut 11-4      244   Figure A. 23 Back, right and left wall pictures and rock mass classification logs – SSX Mine – Cross cut 11-5      245   Figure A. 24 Back, right and left wall pictures and rock mass classification logs – Musselwhite Mine – Footwall lateral 1     246  Figure A. 25 Back, right and left wall rock mass classification logs – Turquoise Ridge JV Mine – Footwall lateral 1    247 APPENDIX B – PARTICLE VELOCITY AND FREQUENCY CONTENT - CASE STUDIES   Figure B. 1 Particle velocity record – Transversal, vertical and longitudinal – Musselwhite Mine     248  Figure B. 2 Particle velocity record – Transversal, vertical and longitudinal – Stillwater Mine       249  Figure B. 3 Particle velocity record – Transversal, vertical and longitudinal – Turquoise Ridge JV Mine      250  Figure B. 4 Particle velocity record – Transversal, vertical and longitudinal – SSX Mine     251  Figure B. 5 Original (Trans1) and truncated transversal particle velocity records (Trun1) – Musselwhite Mine              252  Figure B. 6 Frequency content of original (Trans1) and truncated transversal particle velocity records (Trun1) – Musselwhite Mine              253  Figure B. 7 Frequency content of truncated unsmoothed and smoothed (average of 2, 3, 4, 5, 6 and 7 consecutive samples) transversal particle velocity records – Musselwhite Mine              254  Figure B. 8 Frequency content of truncated unsmoothed and smoothed (average of 8 consecutive samples) transversal particle velocity records – Musselwhite Mine              255   Figure B. 9 Frequency content of truncated unsmoothed and smoothed blast and quiet portion (average of 4 and 8 consecutive samples) of the transversal particle velocity records – Musselwhite Mine     256  Figure B. 10 Frequency content of transversal, vertical and longitudinal particle velocity records – #0 delay – Stillwater Mine             257  Figure B. 11 Frequency content of transversal, vertical and longitudinal particle velocity records – #2 (1/2) delay – Stillwater Mine            258  Figure B. 12 Frequency content of transversal, vertical and longitudinal particle velocity records – #2 (2/2) delay – Stillwater Mine              259  Figure B. 13 Frequency content of transversal, vertical and longitudinal particle velocity records – #3 (1/2) delay – Stillwater Mine             260  Figure B. 14 Frequency content of transversal, vertical and longitudinal particle velocity records – #3 (2/2) delay – Stillwater Mine              261  Figure B. 15 Frequency content of transversal, vertical and longitudinal particle velocity records – #4 (1/2) delay – Stillwater Mine              262  Figure B. 16 Frequency content of transversal, vertical and longitudinal particle velocity records – #4 (2/2) delay – Stillwater Mine              263  Figure B. 17 Frequency content of transversal, vertical and longitudinal particle velocity records – #5 (1/2) delay – Stillwater Mine              264  Figure B. 18 Frequency content of transversal, vertical and longitudinal particle velocity records – #5 (2/2) delay – Stillwater Mine              265  Figure B. 19 Frequency content of transversal, vertical and longitudinal particle velocity records – #6 (1/2) delay – Stillwater Mine              266  Figure B. 20 Frequency content of transversal, vertical and longitudinal particle velocity records – #6 (2/2) delay – Stillwater Mine              267  Figure B. 21 Frequency content of transversal, vertical and longitudinal particle velocity records – #7 (1/2) delay – Stillwater Mine              268  Figure B. 22 Frequency content of transversal, vertical and longitudinal particle velocity records – #7 (2/2) delay – Stillwater Mine              269  Figure B. 23 Frequency content of transversal, vertical and longitudinal particle velocity records – #8 (1/2) delay – Stillwater Mine              270  Figure B. 24 Frequency content of transversal, vertical and longitudinal particle velocity records – #8 (2/2) delay – Stillwater Mine              271  Figure B. 25 Frequency content of transversal, vertical and longitudinal particle velocity records – #9 (1/2) delay – Stillwater Mine              272  Figure B. 26 Frequency content of transversal, vertical and longitudinal particle velocity records – #9 (2/2) delay – Stillwater Mine              273  Figure B. 27 Frequency content of transversal, vertical and longitudinal particle velocity records – #11 delay – Stillwater Mine              274  Figure B. 28 Frequency content of transversal, vertical and longitudinal particle velocity records – #12 delay – Stillwater Mine              275  Figure B. 29 Frequency content of transversal, vertical and longitudinal particle velocity records – #13 delay – Stillwater Mine              276  Figure B. 30 Frequency content of transversal, vertical and longitudinal particle velocity records – #14 delay – Stillwater Mine              277  Figure B. 31 Frequency content of transversal, vertical and longitudinal particle velocity records – #15 (1/2) delay – Stillwater Mine              278  Figure B. 32 Frequency content of transversal, vertical and longitudinal particle velocity records – #15 (2/2) delay – Stillwater Mine              279  Figure B. 33 Frequency content of transversal, vertical and longitudinal particle velocity records – #1 delay at 9.5m from face – Musselwhite Mine              280  Figure B. 34 Frequency content of transversal, vertical and longitudinal particle velocity records – #1 delay at 10.5m from face – Musselwhite Mine              281  Figure B. 35 Frequency content of transversal, vertical and longitudinal particle velocity records – #1 delay at 21.5m from face – Musselwhite Mine              282  Figure B. 36 Frequency content of transversal, vertical and longitudinal particle velocity records – #1 delay at 26.5m from face – Musselwhite Mine         

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