Study of Blast-Induced Damage in Rock with Potential Application to ...

Study of Blast-Induced Damage in Rock with Potential Application to Open Pit and Underground Mines

by

Leonardo Fabián Triviño Parra

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Department of Civil Engineering University of Toronto

© Copyright by Leonardo F. Triviño Parra, 2012

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Study of Blast-Induced Damage in Rock with Potential

Application to Open Pit and Underground Mines

Leonardo Fabián Triviño Parra

Doctor of Philosophy

Department of Civil Engineering University of Toronto

2012

Abstract

A method to estimate blast-induced damage in rock considering both stress waves and gas

expansion phases is presented. The method was developed by assuming a strong correlation

between blast-induced damage and stress wave amplitudes, and also by adapting a 2D numerical

method to estimate damage in a 3D real case. The numerical method is used to determine stress

wave damage and provides an indication of zones prone to suffer greater damage by gas

expansion. The specific steps carried out in this study are: i) extensive blast monitoring in hard

rock at surface and underground test sites; ii) analysis of seismic waveforms in terms of

amplitude and frequency and their azimuthal distribution with respect to borehole axis, iii)

measurement of blast-induced damage from single-hole blasts; iv) assessment and

implementation of method to utilize 2D numerical model to predict blast damage in 3D situation;

v) use of experimental and numerical results to estimate relative contribution of stress waves and

gas penetration to damage, and vi) monitoring and modeling of full-scale production blasts to

apply developed method to estimate blast-induced damage from stress waves.

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The main findings in this study are: i) both P and S-waves are generated and show comparable

amplitudes by blasting in boreholes; ii) amplitude and frequency of seismic waves are strongly

dependent on initiation mode and direction of propagation of explosive reaction in borehole; iii)

in-situ measurements indicate strongly non-symmetrical damage dependent on confinement

conditions and initiation mode, and existing rock structure, and iv) gas penetration seems to be

mainly responsible for damage (significant damage extension 2-4 borehole diameters from stress

waves; > 22 from gas expansion). The method has the potential for application in regular

production blasts for control of over-breaks and dilution in operating mines. The main areas

proposed for future work are: i) verification of seismic velocity changes in rock by blast-induced

damage from controlled experiments; ii) incorporation of gas expansion phase into numerical

models; iii) use of 3D numerical model and verification of crack distribution prediction; iv)

further studies on strain rate dependency of material strength parameters, and v) accurate

measurements of in-hole pressure function considering various confinement conditions.

iv

Acknowledgments I need to thank first to my two precious beloved ones: Daisy and Connie, always supporting,

loving and caring…

I would like to thank my supervisor Professor Bibhu Mohanty, who always trusted, supported,

and guided me with his extensive and deep knowledge in this complex field of my research.

Professor Bernd Milkereit, my co-supervisor, was always available for me to discuss anomalies

in my research findings and resolve tricky issues. Professor Antonio Munjiza of Queen Mary

University of London, UK, facilitated the use of his open source FEM-DEM software ‘Y-code’

and provided useful hints to carry out my research.

I would also like to thank those who contributed in a significant way to my research progress,

and in particular to Dr. Benjamin Thompson, Mr. Sheng Huang, and the staff in my Department,

and Professor Takis Katasabanis and Mr. Oscar Rielo of the Queen’s University for assistance

and use of the Queen’s University Explosives Test Site. The help provided by the personnel from

Williams Mine, Ontario for facilitating my field investigations at the mine is also gratefully

acknowledged.

Finally I would like to thank the Natural Sciences and Engineering Research Council of Canada

(NSERC) and the Ontario Research Foundation for their financial support.

v

Table of Contents Acknowledgments .......................................................................................................................... iv

Table of Contents ............................................................................................................................ v

List of Tables ................................................................................................................................. ix

List of Figures ................................................................................................................................. x

List of Appendices ....................................................................................................................... xix

List of Symbols ............................................................................................................................. xx

Chapter 1: Introduction ............................................................................................................. 1

1.1 Excavation in rock .............................................................................................................. 1

1.2 Blasting as a rock excavation method ................................................................................. 3

1.2.1 Blast design ............................................................................................................. 4

1.3 Damage, overbreak and dilution control ............................................................................. 7

1.4 Research objectives and approach ...................................................................................... 9

1.5 Thesis outline .................................................................................................................... 12

Chapter 2: Elements of Theory and State of the Art ............................................................... 14

2.1 Physical processes in rock blasting ................................................................................... 14

2.1.1 Shock wave and subsequent seismic waves .......................................................... 14

2.1.2 Gas Expansion ...................................................................................................... 17

2.2 Stress wave propagation in rock blasting .......................................................................... 18

2.2.1 Radiation from a cylindrical source ...................................................................... 18

2.2.2 Waves attenuation ................................................................................................. 21

2.3 Damage mechanics ........................................................................................................... 23

2.3.1 Damage as crack density ....................................................................................... 25

2.3.2 Kachanov's approach for isotropically distributed non-interacting cracks ........... 26

2.4 Assessment of blast-induced damage in rock ................................................................... 27

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2.4.1 Direct measurement of cracks ............................................................................... 27

2.4.2 Seismic monitoring: PPV method ......................................................................... 27

2.4.3 Explosive gas pressure activity ............................................................................. 29

2.4.4 Cross-hole: Variations in P-wave velocity ........................................................... 30

2.5 The combined finite and discrete elements (FEM-DEM) method .................................... 32

2.5.1 The Y2D code ....................................................................................................... 32

2.5.2 Constitutive model in Y2D code ........................................................................... 34

2.5.3 Comparison of seismic radiation between Y2D and Heelan analytical solution .. 37

Chapter 3: Experiments, Instrumentation and Layout ............................................................ 42

3.1 Experimental procedures .................................................................................................. 42

3.2 Instrumentation ................................................................................................................. 43

3.2.1 Accelerometers ..................................................................................................... 43

3.2.2 Pressure sensors .................................................................................................... 46

3.2.3 Explosion (detonation) front pressure measurement ............................................ 47

3.2.4 VOD measurement ................................................................................................ 48

3.2.5 Cross-hole seismic system .................................................................................... 48

3.2.6 Data acquisition systems ....................................................................................... 50

3.3 Field test sites .................................................................................................................... 51

3.3.1 Surface test site ..................................................................................................... 51

3.3.2 Underground mine ................................................................................................ 56

Chapter 4: Seismic Radiation from Blast and Damage in Rock: Results from Single-hole Controlled Experiments ......................................................................................... 61

4.1 Measurement of seismic radiation .................................................................................... 61

4.1.1 Identification of body waves ................................................................................. 63

4.1.2 Amplitude of seismic waves ................................................................................. 69

4.1.3 Frequency content of seismic waves ..................................................................... 71

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4.1.4 Short vs. long charges ........................................................................................... 73

4.1.5 Effect of initiation mode (Direct / Reverse) and relative source-sensor location . 75

4.2 Blasthole pressure function and VOD ............................................................................... 80

4.3 Measurement of damage ................................................................................................... 84

4.3.1 Cross-hole measurements ..................................................................................... 84

4.3.2 Gas pressure activity ............................................................................................. 96

4.4 Discussion ......................................................................................................................... 99

Chapter 5: Damage from Stress Waves and Gas Expansion................................................. 104

5.1 Model input parameters from field and lab experiments ................................................ 104

5.1.1 Elastic constants .................................................................................................. 104

5.1.2 Material properties from lab experiments ........................................................... 105

5.1.3 Explosive properties ............................................................................................ 106

5.1.4 Pressure function ................................................................................................. 107

5.2 Adjustment of attenuation and calibration of other input parameters ............................. 109

5.2.1 2D model vs. 3D phenomenon: adjustment of geometric attenuation ................ 109

5.2.2 Relationship between PPV and crack density ..................................................... 111

5.2.3 Calibration of material viscous damping and in-hole pressure function decay .. 115

5.2.4 Material strength parameters ............................................................................... 117

5.3 Summary of properties for models ................................................................................. 119

5.4 Relative contribution of stress waves and gas expansion to damage .............................. 121

5.4.1 Damage quantification from models ................................................................... 121

5.4.2 Damage quantification from field measurements ............................................... 124

5.4.3 Quantification of damage from stress waves and gas expansion ........................ 126

5.4.4 Sensitivity analysis for variations in input parameters ....................................... 131

5.5 Discussion ....................................................................................................................... 135

Chapter 6: Extension of Results to Underground Blasting ................................................... 138

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6.1 Production blast monitoring ............................................................................................ 138

6.2 Blast simulation .............................................................................................................. 143

6.2.1 Model parameters ................................................................................................ 143

6.2.2 Production blast damage ..................................................................................... 147

6.3 Discussion ....................................................................................................................... 152

Chapter 7: Conclusions ......................................................................................................... 154

7.1 Nature of seismic waves by rock blasting in boreholes .................................................. 155

7.2 Mechanisms of wave generation for different explosive initiation modes ..................... 155

7.3 Blast-induced seismic wave propagation by 2D numerical method vs. 3D real case ..... 156

7.4 Correlation between stress wave amplitude and damage ............................................... 157

7.5 Fracture network development by stress waves and gas expansion ............................... 157

7.6 Relative contribution of stress waves and gas penetration to blast-induced damage ..... 158

7.7 Future work ..................................................................................................................... 159

7.8 Overall conclusions ......................................................................................................... 161

References ................................................................................................................................... 164

Appendices .................................................................................................................................. 170

Appendix A : Relationship between Elastic Constants ........................................................... 171

Appendix B : Effective medium theories (EMT) .................................................................... 173

Appendix C : Constitutive model in FEM-DEM code Y2D ................................................... 175

Appendix D : List of blast experiments and instrumentation .................................................. 181

Appendix E : Laboratory tests and Material Strength Properties ............................................ 183

E.1 Measurement of P and S-wave velocities and density .................................................... 183

E.2 Static and dynamic uniaxial compressive strength (UCS) .............................................. 184

E.3 Static and dynamic tensile strength ................................................................................. 186

E.4 Strain / Loading rate dependency of strength parameters ............................................... 188

Appendix F : Analytical-numerical approach for Direct and Reverse initiation modes ......... 191

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List of Tables Table 1. Proposed Classification of Earth Materials by Attenuation Coefficient (after Woods &

Jedele 1985) .................................................................................................................................. 23

Table 2. Accelerometers technical data ...................................................................................... 44

Table 3. Data acquisition systems technical information ........................................................... 50

Table 4. Principal stresses at Williams mine .............................................................................. 57

Table 5. Regular joint sets at Williams mine ............................................................................. 57

Table 6. Explosive properties at Williams mine ........................................................................ 59

Table 7. Effect of variation in material viscous damping and pressure function decay rate over

PPV and frequency of seismic signals ........................................................................................ 115

Table 8. Loading and decay rates at various distances from blasthole .................................... 118

Table 9. Summary of material strength properties ................................................................... 119

Table 10. Summary of material and explosive properties for numerical models ....................... 120

Table 11. Summary of material and explosive properties for production blast simulation ....... 145

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List of Figures Figure 1. Blasthole cross sections in open pit excavations. a) Typical terminology for blast

design (after Yamin 2005); b) Events occurring during a typical quarry bench blast (after

Morhard 1987). ............................................................................................................................... 6

Figure 2. Typical cross Section of a tunnel excavation (after Sen 1995). Terms used to refer to

boreholes vary from place to place. Here, they are provided only as examples. ............................ 6

Figure 3. Schematic view of planned and unplanned dilution in underground mines. ................... 7

Figure 4. Schematic diagram of the approach and methodology employed in this research. ....... 11

Figure 5. Zones of damage caused by stress wave (after Yamin 2005). ...................................... 16

Figure 6. Damage by single-hole blast. Network created by gas penetration (after Yamin 2005).

....................................................................................................................................................... 17

Figure 7. Heelan solution of relative P and SV-wave amplitudes for a cylindrical source with

only radial pressure in an infinite elastic medium. The source is represented by a small

cylindrical charge at the center of the coordinate system, with vertical axis of symmetry. Radii in

the figure are proportional to F1(φ) (for P-waves) and F2(φ) (for S-waves) (after Heelan 1953). 19

Figure 8. Comparison of contour plots of peak vibration amplitudes from a short cylindrical

source given by a) Heelan solution; b) Full-field solution, and c) dynamic finite elements method

(after Blair 2007). Amplitude values are normalized at a distance 5 m horizontally from the

origin (i.e., values shown in the isolines represent vibration amplitudes relative to that point). .. 21

Figure 9. Various forms of vibration attenuation (after Dowding 1996, Woods & Jedele 1985). 22

Figure 10. Schematic view of algorithms built in the combined FEM-DEM program Y2D. ...... 33

Figure 11. Representation of the Kelvin-Voigt visco-elastic model in the one-dimensional case.

....................................................................................................................................................... 34

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Figure 12. Geometric attenuation of P and S-waves from FEM-DEM elastic models and

comparison with 2D and 3D elastic attenuation. a) FEM-DEM results before correction; b) FEM-

DEM results after correction (x r -0.5). ........................................................................................... 38

Figure 13. Radiation pattern of particle velocity from FEM-DEM program and Heelan solution

considering elastic material (i.e., no damping) with ν = 0.25. a) FEM-DEM contour plot of PPV

(2D attenuation); b) Heelan contour plot of PPV (3D attenuation); c) FEM-DEM contour plot

modified by a factor r -1/2 (3D attenuation); d) FEM-DEM contour plot modified by a factor r -1/2

(3D attenuation) and S/P ratio amplified by a factor 1.6 (for equal S/P ratio). ............................ 39

Figure 14. Radiation patterns of particle velocity from Heelan analytical solution and FEM-DEM

program considering only radial component. a) Contour plot of PPV from Heelan solution; b)

Contour plot from FEM-DEM modified by a factor r -1/2. ............................................................ 40

Figure 15. Radiation patterns of particle velocity from Heelan analytical solution and FEM-DEM

program considering only tangential component. a) Contour plot of PPV from Heelan solution;

b) Contour plot from FEM-DEM modified by a factor r -1/2. ........................................................ 40

Figure 16. Comparison between solution to Lamb's problem for a point horizontal load and

FEM-DEM results for ν = 0.25. a) Radial component, and b) Tangential component of Lamb’s

solution (after Miller & Pursey 1954). c) Radial component, and d) Tangential component FEM-

DEM program. .............................................................................................................................. 41

Figure 17. Accelerometer assembly to be grouted in borehole. a) Accelerometer assembly

inserted in φ 50 mm aluminum case; b) Detail of case showing three uniaxial accelerometers

mounted orthogonally; c) Assembly in 32 mm aluminum case attached to ABS pipe ready to be

inserted and grouted in borehole. .................................................................................................. 45

Figure 18. Spring mounting system for accelerometers. a) Triaxial accelerometer mounted on

spring for a 45 mm borehole; b) Spring system and power supply; c) Assembly ready to be

installed. ........................................................................................................................................ 45

Figure 19. Silicon pressure sensor employed for gas activity in the vicinity of a blasthole. a)

Connector, sensor and case; b) Assembly for field tests. ............................................................. 46

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Figure 20. Sensors installed in monitor holes and connected to power supplies. ......................... 47

Figure 21. Cross-hole system layout. ............................................................................................ 49

Figure 22. General view of the surface test site. ........................................................................... 51

Figure 23. Surface test site plan view. Distribution of boreholes. 45 and 75 mm boreholes are

identified with the nomenclature B45 and B75 respectively. ....................................................... 52

Figure 24. Explosive assembly corresponding to 500 g of emulsion to be inserted in φ45 mm

borehole. ........................................................................................................................................ 53

Figure 25. 3D view of boreholes (φ45 mm in red & φ75 mm in yellow) indicating explosive

charges (emulsion in blue & det. cord in green). Frame box dimensions (for reference) are 5 m

width, 4 m depth and 7 m height. .................................................................................................. 54

Figure 26. Experimental setup in surface test site. ....................................................................... 55

Figure 27. Geometry and experimental layout at Williams mine. ................................................ 58

Figure 28. Typical distribution of blastholes in a production ring (~20 m x 6 m, plan view).

Numbers in parenthesis indicate delay number (x 25 ms). All holes plunging 20° from collar to

toe. ................................................................................................................................................. 59

Figure 29. Initiation method for Production Blasts (drawing facilitated by Williams Operating

Corp). ............................................................................................................................................ 60

Figure 30. Recorded three components of acceleration for a single charge of 100 g of emulsion at

surface test site. r = 3.0 m, θ = 44° (coordinates according to Figure 32). Component Ay is

vertical (‘A’ denotes accelerometer id, and xyz its specific orthogonal coordinate system). ........ 62

Figure 31. Recorded three components of acceleration for a single charge of 4.46 kg of emulsion

at Williams mine. r = 49.8 m, θ = 167° (coordinates according to Figure 32). AV denotes

(approximately) vertical component, (‘A’ denotes accelerometer id, and VLT its specific

orthogonal coordinate system). ..................................................................................................... 62

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Figure 32. Spherical coordinates system used to express the results of acceleration and velocity.

The origin of coordinates is chosen to be the center of the explosive charge. ............................. 64

Figure 33. Components r , θ and φ of velocity for a single shot, 6m explosive column, direct

primed, executed at Williams mine. r = 34 m, θ = 19°. ................................................................ 64

Figure 34. Example of plotting an equal area projection, upper hemisphere stereonet with polar

mesh. ............................................................................................................................................. 67

Figure 35. Identification of P and S-waves by analysis of the direction of particle motion for a

single shot, 100 g emulsion, executed at the surface test site. r = 3.2 m, θ = 82°. The time

window is indicated by highlighting the corresponding signal shown below the stereonet.

Direction B corresponds to the blasthole orientation. r , θ , φ correspond to unit vectors in

spherical coordinates as shown in Figure 32. ............................................................................... 68

Figure 36. P and S-wave velocities obtained for each test site. .................................................... 69

Figure 37. Peak Particle Acceleration (PPA) and Peak Particle Velocity (PPV) as a function of

Scaled Distance. Surface test site. ................................................................................................. 70


Scaled Distance. Williams mine. .................................................................................................. 71

Figure 39. Radial components of velocity for a single cartridge of explosive and its amplitude

spectra. Charge: 0.56 kg, 0.4 m of emulsion. r = 32 m θ = 21°. ................................................... 72

Figure 40. Average Frequency of Acceleration and Velocity as a function of Distance. Summary

of both test sites considering charges of Emulsion. ...................................................................... 73


Scaled Distance. Summary of all test sites considering charges of Emulsion and Water Gel. .... 74

xiv

Figure 42. Amplitude and orientation of P and S-wave PPV for short explosive charges,

projected on the plane r -θ . In each case the center of the charge is located at (0,0) and the

borehole axis is collinear with the vertical axis. The length and orientation of the lines labeled as

P and S represent the maximum amplitude of the respective waves and their orientation

represents the direction of particle motion at the time of the peak. .............................................. 77

Figure 43. Amplitude and orientation of P and S-wave PPV for long explosive charges, projected

on the plane r -θ . .......................................................................................................................... 78

Figure 44. Radial components of velocity and their amplitude spectra. a) Direct mode, 8.4 kg, 6

m column of emulsion, r = 34 m θ = 19°; b) Reverse mode, 8.4 kg, 6 m column of emulsion, r =

47 m θ = 166°. Williams mine. ..................................................................................................... 79

Figure 45. Radial components of velocity and their amplitude spectra. a) Direct mode, 4.4 kg, 3

m column of emulsion, r = 62 m θ = 10°; b) Reverse mode, 4.4 kg, 3 m column of emulsion, r =

50 m θ = 167°. Williams mine. ..................................................................................................... 80

Figure 46. Measured in-hole pressure. a) Raw data; b) Pressure-time history. Gauge (carbon

resistor) is located 4 cm above the explosive column in a φ45 mm borehole. 0.1 kg emulsion,

90% coupling. ............................................................................................................................... 81

Figure 47. Measurements of in-hole detonation pressure at surface test site. a) Peak pressure vs.

distance from top of explosive; b) Peak loading rate vs. peak pressure. ...................................... 82

Figure 48. In-hole VOD measurements, water coupled. a) Surface test site; b) Williams mine. . 83

Figure 49. Prolate Coordinate System used to discretize area around blasts. a) Curves of constant

ξ and η on Plane ξ -η (constant φ ) for a = 1; b) Discretization of area around 0.1 kg (0.45 m)

charge ( a = 0.225 m); c) Discretization of area around 1.64 kg (2 m) charge ( a = 1 m). .......... 87

Figure 50. Cross-hole ray-paths from measurements on P-wave velocity changes to quantify

damage caused by a 0.1 kg explosive charge. a) 3D view; b) Plan view; c) Cylindrical projection

of ray-paths on a vertical semi-plane with an edge along the blasthole axis. ............................... 88

xv


damage caused by a 0.5 kg explosive charge. a) 3D view; b) Plan view; c) Cylindrical projection

of ray-paths on a vertical semi-plane with an edge along the blasthole axis. ............................... 89


damage caused by a 1.64 kg explosive charge. a) 3D view; b) Plan view; c) Cylindrical

projection of ray-paths on a vertical semi-plane with an edge along the blasthole axis. .............. 89

Figure 53. Measured variations in P-wave velocity caused by explosive charges of 0.1 kg, 0.5 kg

and 1.64 kg. ................................................................................................................................... 90

Figure 54. Measured blast-induced damage determined from inversion of P-wave velocities

corresponding to a 0.5 kg charge of emulsion, 90% coupling. a) Vertical plane E-W; b) Vertical

plane N-S; c) Plan view at Z = 0.225 m (top); d) Plan view at Z = -0.225 m (bottom)................ 92

Figure 55. Comparison of measured and calculated P-wave velocity values after blast for

explosive charge of 0.5 kg. ........................................................................................................... 93

Figure 56. Measured blast-induced damage determined from inversion of P-wave velocities

corresponding to a 1.64 kg charge of emulsion, 67% coupling. a) Vertical plane E-W; b) Vertical

plane N-S; c) Plan view at Z = 1 m (top); d) Plan view at Z = -1 m (bottom).............................. 94

Figure 57. Comparison of measured and calculated P-wave velocity values after blast for

explosive charge of 1.64 kg. ......................................................................................................... 95

Figure 58. Measured gas pressure activity in monitor holes from blasts corresponding to 0.5 and

1.64 kg of explosive (90% and 67% coupling respectively) in φ 45 mm borehole. ..................... 96

Figure 59. Pressure activity recorded in monitor holes from a blast corresponding to 0.5 kg of

explosive, 90% coupling in φ 45 mm borehole. ........................................................................... 98

Figure 60. Comparison of different cases of wave superposition. a) Signals emitted from a series

of 'fixed' small sources (akin to a long blast source); b) Signals emitted a 'moving' small source.

Note the variation of phase of the individual signals in the second case, as the source moves

upwards. ...................................................................................................................................... 101

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Figure 61. Pressure functions Pu(t), Pd(t), and P(t)/Pmax, for parameters LR = 1000 GPa/ms, and

DR = 100 GPa/ms (with α1 = 10-7, α2 = 10-3, bratio = 2. LR: Loading Rate; DR: Decay Rate). ... 109

Figure 62. Initial meshes used for models. a) Mesh for 0.5 kg charge; b) Profile of horizontal

particle velocity at 65 µs after initiation; and c) Mesh for 1.64 kg explosive charge. ................ 112

Figure 63. Fracture patterns from FEM-DEM models for a) short and b) long charges of

explosive, bottom initiated. ......................................................................................................... 113

Figure 64. Damage vs. PPV from FEM-DEM models. .............................................................. 114

Figure 65. PPV vs. Scaled Distance and Average Frequency of Velocity vs. Distance from both

field measurements and FEM-DEM models, considering calibrated material damping and

pressure function decays. ............................................................................................................ 116

Figure 66. Comparison of r component of particle velocity between single shot experiments and

FEM-DEM models. a) 0.5 kg (0.45 m) explosive, reverse primed, r = 1.6 m, θ = 129°. b) 1.64 kg

(2 m) explosive, direct primed, measured on surface, r = 10.4 m, θ = 70°. ............................... 117

Figure 67. Contour plots from FEM-DEM model for a short charge of explosive: a) Damage; b)

PPV. ............................................................................................................................................ 122

Figure 68. Contour plots from FEM-DEM model for a long charge of explosive: a) Damage; b)

PPV. ............................................................................................................................................ 123

Figure 69. Damage from FEM-DEM model for short and long charges, after correction 2D to

3D. ............................................................................................................................................... 124

Figure 70. Contour plots of measured damage for short and long explosive charges considering

cylindrical symmetry. ................................................................................................................. 125

Figure 71. Relative contribution of stress waves and gas expansion to damage for a short charge,

bottom initiated. .......................................................................................................................... 129

Figure 72. Relative contribution of stress waves and gas expansion to damage for a long charge,

bottom initiated. .......................................................................................................................... 130

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Figure 73. Effect of variations in GC over fracture patterns obtained for short and long explosive

charges. Short models: σs= 107 MPa; σt= 41 MPa; a) Min GC= 310 J/m2; b) Avg. GC= 1240

J/m2; c) Max GC= 2790 J/m2. Long models: σs= 82 MPa; σt= 32 MPa; d) Min GC= 310 J/m2; e)

Avg. GC= 1240 J/m2; f) Max GC= 2790 J/m2. .......................................................................... 132

Figure 74. Effect of variations in σt over fracture patterns obtained for short and long explosive

charges. Short models: σs = 107 MPa; GC = 1240 J/m2; a) Min σt = 26 MPa; b) Avg. σt = 41

MPa; c) Max σt = 51 MPa. Long models: σs = 82 MPa; GC = 1240 J/m2; d) Min σt = 22 MPa; e)

Avg. σt = 32 MPa; f) Max σt = 47 MPa. .................................................................................... 133

Figure 75. Effect of variations in σs over fracture patterns obtained for short and long explosive

charges. Short models: σt = 41 MPa; GC = 1240 J/m2; a) Min σs = 82 MPa; b) Avg. σs = 107

MPa; c) Max σs = 178 MPa. Long models: σt = 32 MPa; GC = 1240 J/m2; d) Min σs = 75 MPa;

e) Avg. σs = 82 MPa; f) Max σs = 149 MPa. .............................................................................. 134

Figure 76. Production Blast #12, March 15, 2007 Dayshift - Accelerometer A. 300 kg Emulsion -

Collar Primed - 30 g/m Det Cord r' = 77.3 m. ............................................................................ 139

Figure 77. Production Blast #13, March 15-16, 2007 Nightshift - Accelerometer A. 900 kg

Emulsion - Booster Collar Primed - 30 g/m Det Cord r' = 74.2 m. ............................................ 139

Figure 78. Production Blast #22, March 22, 2007 Dayshift - Accelerometer A. 650 kg Water Gel

- Booster Collar Primed - 30 g/m Det Cord r' = 43.5 m. ............................................................ 139

Figure 79. Components r , θ and φ of velocity for a production blast shot consisting of 2 holes.

r1 = 24m, θ1 = 36°; r2 = 39m, θ2 = 168°. .................................................................................... 140

Figure 80. PPA and PPV for P and S-waves vs. scaled distance in rock. Production and Control

Blasts at Williams mine. ............................................................................................................. 141

Figure 81. Frequency spectrum of particle Acceleration and Velocity vs. distance. Production

and Control Blasts at Williams mine. ......................................................................................... 142

Figure 82. Mesh used to model production blast in FEM-DEM code: Refinement for calibration

of parameters (35,000+ elements). .............................................................................................. 144

xviii

Figure 83. Comparison of PPV and frequency content of stress waves between field data and

FEM-DEM simulation. PPV values are corrected by factor given by Equation 5-16 to estimate

equivalent 3D PPV. ..................................................................................................................... 146

Figure 84. Velocity time history recorded at 20 m horizontally from raise center point (distance

to boreholes from 13 to 16 m). The amplitude of signals is not corrected by factor given by

Equation 5-16 to estimate equivalent 3D particle velocities. ..................................................... 146

Figure 85. Mesh used to model production blast in FEM-DEM code: Refinement to determine

fracture pattern, damage and PPV contour (27,000+ elements). Symmetry was used, model

includes half of stope only. ......................................................................................................... 147

Figure 86. Stress wave amplitude from two adjacent blasthole with different delays. Colors show

horizontal particle velocity (vx) at 0.5 ms after the initiation of each blasthole. PPV at snapshots

(wave front in blue): left 250 mm/s; right 200 mm/s. ................................................................. 148

Figure 87. Fracturing associated with stress waves obtained from production blast simulation. a)

Fracture pattern; b) Crack density calculated directly from 2D simulation; c) Crack density

corrected from 2D to 3D. ............................................................................................................ 149

Figure 88. Comparison of fracture patterns from production blast simulation considering various

configurations associated with field stresses and initiation mode. ............................................. 151

xix

List of Appendices Appendix A : Relationship between Elastic Constants ........................................................... 171

Appendix B : Effective medium theories (EMT) .................................................................... 173

Appendix C : Constitutive model in FEM-DEM code Y2D ................................................... 175

Appendix D : List of blast experiments and instrumentation .................................................. 181

Appendix E : Laboratory tests and Material Strength Properties ............................................ 183

Appendix F : Analytical-numerical approach for Direct and Reverse initiation modes ......... 191

xx

List of Symbols 2∇ 3D Laplace operator, e.g. ( )2222222 zyx ∂∂+∂∂+∂∂=∇ in Cartesian coordinates

α Attenuation coefficient

α Standard charge weight scaling law specific site constant (power of charge weight)

α1 Error of pressure function at t = 0

α2 Error of pressure function at t = tmax

αP P-wave attenuation coefficient

αS S-wave attenuation coefficient

β Standard charge weight scaling law specific site constant (power of distance)

δ Dimensionless number to characterize coupling between stress and fluid pressure

∆ Volumetric strain, ( )zzyyxx εεε ++=∆

ΔG Change in electric conductance

ε Strain

εij Strain component along i on a plane with normal in the direction j

ijε Strain rate component along i on a plane with normal in the direction j

ε Strain tensor

ε Strain rate tensor

ζ Crack aspect ratio (thickness / radius)

η Viscous damping

η Vertical angle in Prolate coordinate system

θ Vertical angle in spherical coordinate system

θ Angle between borehole axis and direction explosive center to observation point

λ Lamé constant

λ Wavelength

μ Shear modulus

xxi

μ0 Solid matrix Shear modulus

ν Poisson’s ratio (Greek letter nu)

ν0 Solid matrix Poisson’s ratio

ξ Prolate coordinate that forms prolate spheroids when kept constant

ρ Crack density

ρ0 Material density

ρ2D 2D crack density

ρ3D 3D crack density

ρC Combined blast-induced crack density

ρG Crack density due to gas expansion only

ρS Crack density due to stress waves only

σ Stress

σ1 Maximum principal stress

σ2 Middle principal stress

σ3 Minimum principal stress

σc Compressive strength

σij Stress component along i on a plane with normal in the direction j

σs Shear strength

σt Tensile strength

σ Stress tensor

ϕ Borehole diameter

ϕ Horizontal angle in spherical and Prolate coordinate systems

ϕ Angle between borehole axis and direction explosive center to observation point

ω Angular frequency

ωi Component of rotation according to i

Ω Dimensionless angular frequency

a Borehole radius

xxii

ai Crack radius

A Area

bd Parameter related to the max slope of the decaying part of pressure function, md

bratio Ratio bd/bu

bu Parameter related to the max slope of the rising part of pressure function, mu

B Sample thickness

BD Borehole diameter

c Phase velocity

D Damage (in conventional damage mechanics)

D Distance

D Sample diameter

D Total damage (when damage is taken as crack density)

DR Peak decay rate

dx Infinitesimal length in the x direction

dy Infinitesimal length in the y direction

dz Infinitesimal length in the z direction

E Young modulus

E0 Solid matrix Young modulus

EP Energy (or relative energy) associated to P-waves

ES Energy (or relative energy) associated to S-wave

ESS Explained sum of squares

f Frequency

F Scaling factor

GIC Fracture energy

h Geometrical factor related to the shape of the cracks

H Positive scaling parameter

I Electric current

xxiii

I Identity matrix

k Bulk modulus

k Wavenumber

K Fracture toughness

K Standard charge weight scaling law specific site constant

Kf Fluid bulk modulus

KIC Mode I fracture toughness

Li Apparent crack length

LR Peak loading rate

md Max normalized slope of the decaying part of pressure function

mu Max normalized slope of the rising part of pressure function

M Elastic modulus

M0 Solid matrix elastic modulus

n Exponent to define rising part of pressure function

P Pressure

Pd Decaying pressure function

Pmax Peak in-hole pressure

PPA Peak particle acceleration

PPV Peak particle velocity

PPV2D 2D peak particle velocity

PPV3D 3D peak particle velocity

Pu Rising pressure function

Q Coordinate rotation matrix

r Radial distance

R Electric resistance

R2 Coefficient of determination

RSS Residual sum of squares

xxiv

S/P Ratio of S-wave peak amplitude to P-wave peak amplitude

SD Scaled distance

SE Standard error

SV Volumetric stretch

t time

t Student’s t-test statistic

td Time parameter to define decaying part of pressure function

tu Time parameter to define rising part of pressure function

T Wave period (= f -1)

u Displacement in the x direction

u0 Maximum displacement

u Particle velocity

maxu Maximum (peak) particle velocity

v Displacement in the y direction (letter vee)

V Voltage

V Volume

Vc Current volume

Vi Initial volume

VP P-wave velocity

VP0 Solid matrix P-wave velocity

VS S-wave velocity

ENZV

Vector particle velocity in geographic coordinates, ′= ZNEENZ VVVV

θφrV

Vector particle velocity in spherical coordinates, ′= φθθφ VVVV rr

VOD Velocity of detonation

w Displacement in the z direction

w Explosive weight

1

Chapter 1

1 Introduction Blast-induced damage in rock is a significant yet poorly understood area in the rock excavation

industries. The prediction and control of blast damage has been traditionally done by

approximate methods mostly based on experience rather than on understanding of the physical

phenomenon. Perhaps the difficulties of experimentation and modeling in blasting, added to the

significant imperfections of natural rock masses at every scale, plus the limited knowledge on

material behaviour at very large stresses and loading rates, has significantly limited the research

in this area and therefore its understanding. The research presented in this thesis intends to

contribute to this knowledge by providing a method to be applied to predict and control blast-

induced damage in rock. This research includes a significant number of field measurements of

small-scale single-hole and full-scale production blasts, as well as numerical models aimed to

understand the action and interaction of stress waves and gas expansion on the rock mass.

This chapter includes historical references to various methods of rock excavation, basic

information on rock blasting and damage, and describes the objectives and content of the thesis.

1.1 Excavation in rock

Excavation in rock is an essential activity for the great majority of mining operations, as well as

for many diverse civil works, such as tunneling, construction of dams, roads, and buildings.

Throughout history rock excavation has evolved from rudimentary manual techniques to a wide

variety of methods using different technologies.

Early civilizations executed rock excavation for a number of different purposes. In the ancient

Egypt, for example, numerous tunnels were excavated in sedimentary rock as part of the

construction of pharaoh tombs in The Valley of the Kings at Thebes. To excavate these tunnels

Egyptians used copper saws and reed drills supplied with abrasive dust and water. The Romans

constructed numerous water tunnels in hard rock across their empire, following examples from

other cultures, such as those from the Kingdom of Judah and the ancient Greece. The excavation

of these tunnels was done by using chisels and hammers. In India, fabulous temples were

2

constructed in rock, including beautiful and elaborate tunnels and caves. The Ellora Caves and

Temples, constructed between the 5th and 10th centuries AD, were cut out of the hardest rock by

using simple hand tools (Beaver 1972). In pre-Columbian America, the Incas built remarkable

structures from sections of hard rock carved to neatly fit together. Although the precise technique

that the Incas used to extract and carve these rocks is not well known, it is believed that they

used hard pebbles (obsidian) from streams to pound and shape the massive stones that would

form their constructions (Hemming & Ranney 1982).

Another technique of rock extraction from quarries developed by a number of ancient societies

was the use of trenches and wedges. First, trenches were carved on the rock, generally with picks

and/or chisels, defining blocks of various sizes. Then the blocks were detached by using wedges,

such as iron fins or "feathers" inserted in holes along a predefined cutting line. The wedges were

gradually and uniformly hammered until the rock was split. This technique is still in use

nowadays, with somewhat more modern tools. Another remarkably clever method was the use of

very dry wooden wedges. These wedges were first tightly inserted into carved grooves and then

soaked with water. The water would cause the wedges to swell, inducing cracks to the rock and

forcing it to split (Rababeh 2005).

Nowadays, several methods for rock excavation are available and the choice of the technique

depends upon the specific necessities and requirements of the project. Some examples of the

most industrialized methods for rock excavation and cutting for extraction are as follows:

• High pressure gas: The general technique consists on inserting a tube or cartridge with

chemicals (liquid carbon dioxide or other propellants) into pre-drilled boreholes. The

propellant is ignited by heat or the action of a chemical energizer, and thus, suddenly

converted into high pressure gases. The system is designed to create and propagate

fractures in tension (Caldwell 2005). Typical uses are rock and concrete breakage, deep

sea excavation, tunneling and shaft sinking, trenching and excavation.

• Expanding grout: Boreholes are drilled into the rock to be filled with an expansive

mortar. The system creates tensile fractures in the rock in a similar way to that of high

pressure gases, but at a much lower rate (hours to days). It is used for mass concrete and

boulder demolition, splitting of large rocks, and relatively small works of trenching and

bench and underground excavations.

3

• Water jet: The system consists on cutting the rock by applying directed high pressure

water (generally above 700 kPa). The high pressure water can create smooth cuts and be

used to obtain large blocks of rock. It works best in relatively weak sedimentary rocks

such as sandstone or limestone, but it can also be used with stronger rocks such as granite

(Wilson et al 1998).

• Wire cutting: Method used to neatly cut blocks of solid stone, consisting of an abrasive

wire, which circulates continuously around the rock. Today diamond wire machines are

used to cut and extract marble from quarries.

• Tunnel boring machine: These machines are used to excavate tunnels with a circular

section through a variety of soil and rock. Modern drilling machines have a rotating head

with disc cutters, which occupies the whole section of the tunnel. They present the main

advantage of excavating with little disturbance of the material surrounding the tunnel and

they have been successfully used in the construction of numerous tunnels in civil works.

• Rock Blasting: The technique of rock excavation by blasting consists on using the

energy of explosives to break the rock, which is later extracted by mechanical means. The

most common method is by drilling boreholes into the rock mass to insert and detonate

either bulk or pre-packed explosives. The method is extensively used in the mining

industry (both open pit and underground) and numerous civil works.

Of all techniques of rock excavation, blasting has been by far the most widely used technology

for over 100 years. This is mainly due to its wide presence in mining operations, which account

for the great majority of rock extraction worldwide. The high production rates that this industry

requires in addition to the relatively reduced cost and high efficiency of explosives are amongst

the main reasons for the primacy of blasting in mines.

1.2 Blasting as a rock excavation method Excavation in competent rock demands considerable amounts of energy. Whether the rock is to

be extracted to obtain its minerals, to serve as a construction material, or as part of a construction

work, the process of rock excavation necessarily implies breaking the target rock to desired

fragments. This is the part of the excavation process where the use of explosives plays a

fundamental role. The large amount of energy that relatively small quantities of explosives can

liberate has made blasting the most universal method to excavate in almost any kind of rock.

4

Energy liberated from the chemical reactions of explosives in the form of high temperature and

high pressure gases is partly utilized to create fractures, fragmentation, and move the rock. In

order to produce an efficient breakage of the target rock, however, proper confinement and

distribution of the explosive within the rock mass are required. Additionally, excavation in rock

usually requires reaching places away from accessible surfaces. For this, the standard procedure

consists in drilling boreholes (also referred as blastholes) into the rock mass to later insert and

detonate the explosive. The resultant rock fragments are usually extracted by mechanical means

(machinery) and transported for final processing. By inserting the explosive in blastholes, the

surrounding rock mass provides confinement (i.e., an enclosed or semi-enclosed volume to

prevent rapid vent of gases) necessary to fracture the rock upon detonation, thus improving the

transmission of energy to create and expand fractures. Oriented blastholes also permit to reach

the target zone and distribute the explosive as desired within the rock mass (usually as uniformly

as operations permit).

Explosives for blasting come in a variety of forms. Some of the predominant forms of explosives

used nowadays are: a) bulk to be pumped (water gels and emulsions); b) dry as small prills

(Ammonium Nitrate and Fuel Oil, commonly known as ANFO), and c) pre-packed in cartridges

(water gels and emulsions). The decisions about explosive type, amount and a number of other

parameters, such as borehole diameter and overall excavation geometry constitute the blast

design. Relevant criteria for blast design and a more detailed description of parameters are

included in the following section.

1.2.1 Blast design

Proper blast design is essential for the economy and safety of excavation operations. This design

is also linked to project requirements and conditioned by environmental aspects and potential

effects on nearby structures and population. The relevant criteria that constitute the basis to

determine blast parameters can be summarized as follows:

• Obtain fractured or crushed pieces of rock that can be extracted, manipulated and that

serve the specific purpose of the project (i.e., reduction of the target rock to desired

fragments)

• Minimize unwanted damage to immediately surrounding rock mass (stability and

integrity of remaining rock)

5

• Minimize vibration and noise levels that can affect nearby structures and people

• Minimize the total cost of the operations (cost of drilling, explosives, mechanical loading

and transport)

• Minimize other unwanted side effects, such as fly rock, excessive fumes, etc.

A blast design considers a series of parameters or variables, including some that cannot be

modified and also parameters that are precisely the output of the design. The most relevant

parameters or factors that cannot be modified, but must be taken into account in blast design are:

• Local geology

• In situ stresses

• Material strength and overall mechanical behaviour

• Structural discontinuities

• Presence of water (sometimes controllable)

The blast design is conditioned also by the overall geometry of the desired excavation and the

specific excavation method, which are also functions of the previous parameters. In particular,

when excavating an ore body, the overall geometry of the excavation is determined by its

boundaries, and the excavation method is determined by the mining procedures, based on

specific site conditions and available technology. The variables that are the output of the blast

design can be summarized as follows:

• Borehole geometry (diameter, length, inclination, sub-drill)

• Drilling pattern (square, rectangular, staggered, fanned)

• Spatial distribution of boreholes, such as spacing (distance between boreholes in a row, in

bench blasting) and burden (distance to a free surface)

• Explosive (type, energy, packing, charge length, coupling (i.e., explosive to borehole

diameter ratio), loading method)

• Stemming (material, height, particle size)

• Initiation (type, delay, accuracy)

• Collar height

• Bench height (for open pit excavations)

6

Figure 1 illustrates typical cross sections in bench (open pit) blasting, including relevant

terminology for blast design and events occurring during a typical quarry bench blast. Similarly,

Figure 2 shows a typical section of a tunnel excavation in underground mines.

Figure 1. Blasthole cross sections in open pit excavations. a) Typical terminology for blast design (after Yamin 2005); b) Events occurring during a typical quarry bench blast (after Morhard 1987).

Figure 2. Typical cross Section of a tunnel excavation (after Sen 1995). Terms used to refer to boreholes vary from place to place. Here, they are provided only as examples.

a) b)

Vf = 0.15 to 60 m/sec

Face profile

Vs = 3 to 450 m/s

Free Face

Explosive

Stemming

Burden

Inclination

Material: Limestone VP = 4,500 m/s ρ = 2.3 kg/dm3

Explosive: ANFO VOD = 1,200 m/sec Hole Dia. = 12.5 cm Ave. Burden = 4.5 m

Onset of Movement 5-110 msec

VUP = 1.5 to 36 m/s

Rib holes

Stopping holes

Roof holes

Cut with cut easer holes

Lifter holes

7

1.3 Damage, overbreak and dilution control Excavation in rock necessarily implies reducing the target rock to fragments that can be easily

loaded and transported. This process inevitably causes some degree of fracturing or cracking

beyond the excavation boundaries, which may be in the form of new fractures or mobilization of

pre-existent discontinuities. When explosives are used, this extra fracturing caused to the

immediately surrounding rock mass is referred to as Blast-induced Damage. In case of severe

damage, more rock than desired is excavated and the newly created boundaries turn out beyond

the planned excavation boundaries. This extra excavation is in general referred as overbreak and

it may be measured either in length (distance from planned to real boundary) or in mass units

(amount of extra rock excavated).

In underground mines, the extra excavation that occurs when extracting an ore body (i.e., the

amount of rock excavated beyond the boundaries of the ore body) is referred to as dilution.

While part of this dilution is generally necessary to completely extract the ore body, another part

corresponds to overbreak. The former is referred to as planned dilution and is considered from

the design stage. The later is the unplanned dilution, which causes an increase in operation costs

and reduction of stability and safety. Consequently, the unplanned dilution constitutes an

unwanted result of the excavation and a problem to minimize. Figure 3 shows a schematic view

of an ore body and corresponding planned and unplanned dilution.

Figure 3. Schematic view of planned and unplanned dilution in underground mines.

8

Blast-induced damage is conditioned by a number of variables, including rock properties, blast

design and geometric conditions. The variables that can be used to control damage are those

corresponding to blast design. The following is a summary of the most important of these

variables, with a brief description of their effects on blast damage.

• Burden: The selection of appropriate burden (i.e., horizontal distance from the blasthole

to the existent bench face) is one of the most important factors in blast design. From the

point of view of damage control, the selection of excessive burden can result in delayed

displacement of the target rock producing higher borehole pressures sustained for longer

periods. As a consequence high levels of ground vibration and excessive gas penetration

occur, both of which are direct causes of damage.

• Blasthole size and coupling: In general, for a fully coupled explosive (i.e., no gap or

material between explosive and borehole walls) or constant coupling (i.e., explosive to

borehole diameter ratio remains constant), a larger blasthole diameter causes greater

damage. This is due to the higher energy transmitted to the rock resulting from the larger

amount of explosive in the blasthole. However, if decoupling is considered, increasing

the borehole diameter while keeping constant explosive size results in lower damage due

to the damping introduced by the coupling material (usually either air or water) between

the explosive and the blasthole wall.

• Coupling material: In decoupled blasts (i.e., gap exists between explosive and borehole

walls), either water or air can be used as coupling material. Other materials, such as clay

may be used in some particular cases. In the case of water, the transmission of energy

from the explosive to the rock is much higher than in the case of air, due to the

significantly lower compressibility of the former. In air coupling, air acts as a "cushion"

reducing the in-hole pressure and thus decreasing the amplitude of the induced stresses

and the fracturing and mobilizing action of the lower pressure gases.

• Spacing: Large spacing results in lack or reduced collaboration (i.e., fragmentation and

displacement of the target rock mass by joint action) between blastholes. As a

consequence more and longer cracks propagate behind the holes causing more extensive

damage (Olson et al 2002).

• Timing: Accurate timing is essential for appropriate blasting. Failure in timing may

produce inappropriate initiation of explosive column, lack of programmed collaboration

9

between holes and over-confinement of some rows. The end results include increased

damage in some areas, lower explosive performance and improper fragmentation.

• Explosive type: Changes in explosive type can result in significantly different

fragmentation and damage. In general, explosives with higher Velocity of Detonation,

VOD, release energy more quickly, causing greater stresses and more damage. Explosives

that produce larger volume of gases may have the potential to cause greater damage upon

expansion; however, this also depends on the velocity of the chemical reactions (also

directly related to VOD), since faster reactions cause higher pressures and hence increase

fragmentation (i.e., decrease fragment sizes) and damage.

1.4 Research objectives and approach The research work presented in this thesis is aimed at improving and understanding rock damage

induced by blasting and its minimization. In order to study and predict blast-induced damage, the

research uses its correlation with seismic wave amplitudes. Thus, the study of seismic waves in

this research is essential to understand the physical interaction between explosive and rock mass,

including the in-hole pressure pulse and the processes of rock breakage by both stress waves and

gas expansion. The specific objectives of this research are as follows:

• Investigate the nature of the seismic waves generated by rock blasting in boreholes.

• Study the mechanisms of wave generation for different explosive initiation modes in

borehole.

• Evaluate the performance of a 2D numerical method on reproducing seismic wave

propagation from blasting, including point source and linear long source with different

initiation modes.

• Seek a correlation between the peak amplitude of seismic waves and the damage induced

by them to the rock mass

• Provide qualitative and quantitative interpretation of the fracture network development

caused by stress waves and gas expansion in blasting, and the interaction between the

two.

• Determine the relative contribution of stress waves and gas penetration to blast-induced

damage in rock in the near field.

10

The final goal of this study is to provide precise recommendations for the development of a

reliable method to quantify and control blast-induced damage, based on actual damage

measurements in rock and numerical analysis. The results from this work are intended to be a

base to incorporate the "blasting variable" in methods or models intended to reduce the risk of

overbreak and dilution in open pit and underground mines. Figure 4 shows the research

methodology in a diagram indicating the various parts of the research project and the future work

on the specific research front. These parts can be summarized as follows:

• Small-scale blast experiments: Single charge experiments are executed and monitored

in boreholes in a surface test site and an underground mine. Blast-induced seismic

radiation is assessed by using high-amplitude and high-frequency oriented triaxial

accelerometers in boreholes in the vicinity of the blastholes. The relative amplitude of

blast-induced P and S-waves, frequency content of these stress signals, effects of

initiation mode, and material attenuation properties are studied from these experiments.

In the case of the surface experiments, blast-induced damage is evaluated by cross-hole

measurements before and after blast, as well as by measuring gas penetration activity

during blasting.

• Modeling of small-scale blast experiments: A 2D combined finite and discrete element

method (FEM-DEM) is utilized to estimate the relative contribution of stress waves and

gas pressure to blast-induced damage. The specific software uses an explicit time scheme

and allows the creation of fractures in the material as strength is overcome by stress.

Geometry, material and explosive parameters in these models correspond to those from

the surface test site. Thus, the relative contribution of stress waves and gas expansion is

assessed from the results of both field experiments and numerical models.

• Monitoring and modeling of full-scale production blasts in underground mine:

Multiple-hole production blasts are executed and monitored in an underground mine.

These experiments are an extension of the study developed with single-hole experiments.

They provide significant understanding of stress waves in full-scale situations and

contribute to validate the method of stress wave monitoring to study blast damage. The

method developed using the FEM-DEM software to determine blast-induced damage

from stress waves is applied to a full-scale production blast. The results are presented and

the potential of the method as a predictive and design tool in rock blasting is discussed.

11

Figure 4. Schematic diagram of the approach and methodology employed in this research.

GOAL: Provide guidelines for the development of a

reliable method to assess blast-induced damage that can be

used as a predictive and design tool for blasting

operations.

SURFACE TEST SITE

STUDY OF STRESS WAVES

IN UNDERGROUND

MINE

Frequency content

(strain rate & strength)

Single-hole Control blasts

Production blast

monitoring

PPA & PPV vs. scaled distance (material

attenuation)

Gas expansion

phase

NUMERICAL MODELING

Single-hole seismic

monitoring

Stress waves

Inversion of P-wave

velocities into damage

Blast damage measurements

Initiation mode effects

Gas expansion phase • In-hole pressure measurements • Gas activity monitoring • Numerical modeling considering gas/solid interaction Further applications of numerical method FEM-DEM • 3D model • Arbitrary geometries • In-situ stresses • Heterogeneity • Discontinuities • Explosives & initiation Prediction of full-scale damage & application • Measurement of damage & overbreak from full-scale

blasts • Implementation and evaluation of method to predict

blast damage: incorporate geomechanical conditions, blast practice, blast monitoring

• Incorporation of method into a model to predict & control over-break and dilution

Identification of P and S-

waves

Evaluation of numerical

code FEM-DEM

Ability to reproduce P and S-waves

Ability to simulate fracture

process from blasting

Study of wave

attenuation

Method to overcome

limitations of 2D code

Contribution of stress

waves and gas

expansion to damage

FUTURE WORK

Production blast

modeling

C

B

A

12

1.5 Thesis outline This thesis summarizes several years of research conducted as part of the Ph.D. program. It is

divided into 7 chapters and appendices as follows:

• Chapter 1: Introduction to the thesis, including background information on rock

excavation, blasting practice, blast-induced damage, and its main consequences. It also

includes the research objectives, approach and thesis outline.

• Chapter 2: Provides elements of theory on the process of fracturing of rock by blasting

and a summary of the state of the art on blast-induced damage. It also includes a

description of the software used to model blast waves in rock and damage.

• Chapter 3: Provides a summary of the experimental procedures, including a detailed

description of instrumentation employed in this research. Additionally, it includes a brief

description of the two test sites (a surface test site and an underground mine) where the

experiments took place.

• Chapter 4: Corresponds to the details and results of single-hole experiments in surface

and underground test sites. The main results include measurements of seismic radiation in

the near field (monitoring distances from 1 up to 100 m from the source) along with

blast-induced damage for short and long linear explosive sources in the area surrounding

the blastholes, determined through an original approach to invert P-wave velocities into

damage from cross-hole measurements. Particular emphasis is placed on the effect of

initiation mode on amplitude and frequency content of seismic signals, and its

significance on seismic radiation and damage.

• Chapter 5: Includes the development and results of numerical models to simulate the

tests executed on the surface test site. The main results include the comparison of fracture

patterns from models and measurements, and the quantification of the relative

contribution of stress waves and gas expansion to damage. An original method to correct

predictions of damage from a 2D model to represent a 3D situation is proposed and

included in this chapter.

• Chapter 6: The results of full-scale blast experiments executed in an underground mine

along with the numerical simulation of a production blast are described in this chapter.

The experiments consist of multiple-hole production blasts, corresponding to regular

13

mine production. The results include seismic measurements with high amplitude and high

frequency accelerometers grouted into the rock mass. The full-scale numerical models

correspond to the application of the method to determine blast-induced damage from

stress waves.

• Chapter 7: Provides the conclusions of the thesis and a discussion of the future work

oriented towards further development of the proposed method to predict blast-induced

damage and its potential application to control overbreak and dilution. It provides

suggestions for new research, including experimentation and modeling of the gas

expansion phase and its interaction with the fractured rock, as well as further

development of numerical methods for the realistic simulation of borehole blasting.

• Appendices: Contain complementary information to the thesis, including constitutive

equations, details of blasts executed, laboratory tests, and an original approach to show

the effect of initiation mode in blasting on seismic waveforms.

14

Chapter 2

2 Elements of Theory and State of the Art The information contained in this chapter is intended to provide background theory on the

processes taking place during rock blasting and the methods to model and assess blast-induced

damage. Significant emphasis is placed on the study of stress waves, given their strong

correlation with blast damage. This chapter includes the approaches to define a damage variable

and to measure blast-induced damage from field experiments, which are utilized later on blast

damage assessment in Chapter 4. Additionally, a description of the numerical method FEM-

DEM, which is used to model stress wave damage in Chapter 5 (single-hole blasts) and Chapter

6 (production blasts), is provided.

2.1 Physical processes in rock blasting The process of rock blasting can be summarized as consisting of two main phenomena: a) shock

wave produced by the rapid reaction of the explosive components and b) penetration of high

pressure gases into the pre-existing or newly created fractures. The shock wave is a high

amplitude pressure pulse that travels through a medium at supersonic speeds. It is responsible for

causing damage to the rock mass in the immediate vicinity of the blasthole and as attenuated

through processes of geometric spreading and energy dissipation, it degenerates into seismic

waves when the velocity of propagation is no longer supersonic. The gases from the explosive

reaction subsequently penetrate into the cracks and discontinuities, generating additional stresses

and causing longer fractures and fragmentation. The details of these two main processes and

their consequences are discussed in the following sections.

2.1.1 Shock wave and subsequent seismic waves

The chemical reaction of the explosive components produces rapid formation of high-pressure

and high-temperature gases. As a result, the medium around the explosive (air, water or rock) is

object of a sudden compression, creating a high amplitude and steep disturbance that propagates

as a mechanical wave. This type of wave is known as shock wave and, in contrast to acoustic

waves (which are of nearly infinitesimal amplitude), possesses four unusual properties: i) a

15

pressure-dependent supersonic velocity of propagation; ii) the creation of a steep wavefront with

abrupt changes in all thermodynamic properties; iii) non-linear reflection and interaction, and iv)

for non-planar waves, a significant decrease in the velocity of propagation with increasing

distance from the source (Krehl 2001).

In (borehole) rock blasting, the shock wave is responsible for crushing the rock around the

borehole, and thus, for initiating the fracturing process of the rock mass. The rapid decrease in

velocity of propagation of the shock wave with distance is the result of amplitude reduction and

shape change due to geometric spreading and energy transformation (typically referred to as

energy dissipation). This decrease in velocity causes the shock wave to degrade into seismic

waves within a short distance from the borehole, when the velocity of propagation is no longer

supersonic (albeit the ability to fracture rock may still remain). As seismic waves move farther

from the source, their amplitude continues decreasing due to geometric spreading and energy

dissipation. When the stress amplitude no longer overcomes the material strength, the generated

waves behave elastically.

Seismic waves propagate in a variety of motion modes and thus, as different seismic waves. The

generation of different wave types depends on geometric conditions and material properties. The

most significant waves generated in borehole blasting are P (longitudinal) and S (shear) waves.

They propagate within the rock mass and are referred to as body waves. Although typical blast

seismic monitoring does not make any distinction between these two waves, they produce

different particle motion modes and propagate at different speeds. P-waves are associated with a

compression-dilation movement (i.e., in the direction of wave propagation), whereas S-waves

correspond to a shear movement (i.e., perpendicular to the direction of propagation). The

presence of P and S-waves in rock blasting is discussed in section 2.2. Other wave types that can

be generated from a blast are surface waves, such as Rayleigh or Love waves, each of them

associated with its own motion mode and speed.

As the shock wave is the precursor of seismic waves, and both shock and seismic waves

correspond to mechanical waves (i.e. inducing stress and strain as they occur), the damage that

they cause to the rock mass (e.g., microcracks, fractures and fragmentation) is generally studied

as a single (albeit complex) phenomenon. Consequently, hereinafter in this study, the term stress

wave is used to refer both shock and seismic waves, while the damage they cause is jointly

16

analyzed. Also, attention is generally focused on seismic waves, as the assessment of this type of

waves is much more practical than that of the shock wave.

In terms of damage caused by stress waves from a single blasthole, various zones have been

identified based on degree of damage. A simple division of these zones has been done according

to the radial distance to the blasthole boundary:

• Zone 1: Extensive damage characterized by material crushing. The extent of this zone is

defined by the initial stress wave energy and dynamic properties of the rock; however, it

is usually considered to be 0.5 to 3 borehole diameters.

• Zone 2: Creation and propagation of cracks. In this zone the dynamic strength of the rock

is overcome by stresses from the stress field. Cracks are created when the stress wave

exceeds the strength of the rock, which is controlled by pre-existing features within the

rock mass.

• Zone 3: Elastic wave propagation. In this zone the energy of the wave front has been

significantly attenuated and its amplitude is not large enough to initiate damage. Thus it

will propagate as a seismic wave.

Figure 5 shows the different zones defined by the stress wave and the rock response.

Figure 5. Zones of damage caused by stress wave (after Yamin 2005).

Blasthole

Pre-existent fractures

Damage boundary

Zone I: Crushing / Extensive fracturing

Zone II: Short length fractures

Zone III: Elastic waves, no damage

17

2.1.2 Gas Expansion

The high pressure gases play an important role in the damage to the rock mass. The solid or

liquid explosive components are converted into high pressure and high temperature gases though

chemical reactions. The surrounding rock in contact with the explosive is not only crushed by the

stress wave, but may also be partly melted or burnt by these high temperature gases. Beyond this

relatively small zone the high pressure gases find their way into previously existing and newly

created fractures and micro fractures, creating a complex network of discontinuities and turning

part of the surrounding rock into fragments. As gases dissipate and pressures drop along the

fractures, their ability to reduce the rock to fragments is decreased and eventually at some

distance no more rock is fractured. Fractures, however, extend beyond the excavation boundary

as long as gas pressures are large enough to expand fractures. Figure 6 shows an example of

fracture network connected by gas penetration.

Figure 6. Damage by single-hole blast. Network created by gas penetration (after Yamin 2005).

Blasthole

Pre-existent fractures

Crushing / melting

Fragmentation

Propagation of fractures

18

2.2 Stress wave propagation in rock blasting Even though both stress waves propagation and gas expansion are different processes that take

place in rock blasting, they are not independent, as both are the result of the same chemical

reactions. Hence, at this stage on the research field of rock blasting, attention is focused on the

study and understanding of stress waves with the aim of developing a method to predict and

control blast-induced damage. The current section includes relevant theory developed to model

the propagation and attenuation of waves from a cylindrical source.

2.2.1 Radiation from a cylindrical source

As the great majority of excavation in rock is done by the method of drilling and blasting, it is

essential to understand the propagation of stresses resulting from loading the cylindrical borehole

by explosion. This problem corresponds in essence to the propagation of waves originating from

a cylindrical void in a solid medium (rock mass). Various authors have developed analytical

solutions to this problem, on the grounds of linear elasticity. The first of these solutions was

provided by Heelan (1953).

Heelan (1953) developed solutions that permit calculation of displacement (and thus velocity and

acceleration) time histories at any point in an infinite medium when a short cylinder (with

vertical axis) is loaded in different modes (radially, vertically and in torsion). One of the results

shown by this approach is that in radial loading mode, only P and vertically polarized S-waves

(SV) occur (hereafter SV-waves are generally referred to simply as S-waves). According to this

solution, given a transient pressure function p(t) acting radially on the walls of a short cylindrical

void in an infinite medium, the displacement field induced at an observation point located in the

far field at a distance r from the source can be expressed as:

( ) ( )

−

−=

ϕϕϕ

cossin1

PP

P Vrtpdtd

rF

wu

(2-1)

( ) ( )

−=

ϕϕϕ

sincos2

SS

S Vrtpdtd

rF

wu

(2-2)

where uP, wP, uS, and wS are the displacements in the horizontal (u) and vertical (w) directions

(considering the cylinder axis as vertical) associated with P and S-waves, respectively; ϕ is the

angle between the cylinder axis and the direction source to observation point (see Figure 7); VP

19

and VS are the medium P and S-wave velocities respectively; and F1 and F2 are the following

functions:

( )

−

∆= 2

22

1 cos214 P

S

P VV

VF ϕ

πµϕ (2-3)

( ) ϕπµ

ϕ 2sin42

SVF ∆

= (2-4)

where ∆ is the volume of the loaded cylindrical void, and µ is shear modulus. The functions or

coefficients F1 and F2 describe the angular variation of the peak amplitude of the radiated P and

S-waves with the angle ϕ. Figure 7 shows a polar plot of these two functions, thus representing

the relative amplitudes of P and S-waves from a small, cylindrical, axially loaded source.

This solution indicates that when a cylindrical borehole is subject only to radial pressure, a

relatively large amount of the radiated energy goes into S-wave, while the rest of it goes into P-

wave. For a Poisson solid (ν = 0.25 or λ = µ), for example, approximately 60% of the radiated

wave energy goes into S and 40% into P (Heelan 1953). This relatively high energy associated

with S-waves means that peak particle velocities are dominated by this type of waves for a wide

range of angles, with maximum occurring at 45°. P-waves are dominant only for angles close to

normal, with maximum at 90°.

Figure 7. Heelan solution of relative P and SV-wave amplitudes for a cylindrical source with only radial pressure in an infinite elastic medium. The source is represented by a small cylindrical charge at the center of the coordinate system, with vertical axis of symmetry. Radii in the figure are proportional to F1(φ) (for P-waves) and F2(φ) (for S-waves) (after Heelan 1953).

SV SV

P P

ϕ

Source

Z

20

Another analytical solution was provided by Abo-Zena (1977). In this work the Heelan solution

was criticized for having mathematical inaccuracies; however, the proposed solution agrees

exceptionally well with that of Heelan (White 1983, Blair & Minchinton 1996, Blair 2007). Both

solutions proposed by Heelan and Abo-Zena are limited to relatively large distances from the

source, due to approximations used in the calculations, which assume a small charge compared

to the distance to the observation point. Moreover, work developed by Blair (2007) indicates that

the Heelan solution overestimates the true vibration amplitudes for waveforms with average

frequency above certain limit. To be precise, two limitations hold for this solution to be valid:

• Frequency limitation: 1.0<Ω A , and

• Far Field limitation: 5>Ω arA

where PAA Vaω=Ω is a dimensionless frequency, a is borehole radius, Aω is the average

angular frequency of the pressure function, VP is the medium P-wave velocity, and r is the radial

distance from the source to the observation point in cylindrical coordinates (i.e., horizontal

distance). Both restrictions combined imply that the Heelan solution is not valid if 50<ar ,

irrespective of the frequency.

In addition to the Heelan and Abo-Zena solutions, an exact (full-field) solution was developed by

Tubman (1984), Tubman et al (1984), Meredith (1990), and Meredith et al (1993). The full-field

solution is much more numerically intensive than the approximate solutions of Heelan and Abo-

Zena, and involves the computation of Bessel functions and integrals. The later can be solved

relatively efficiently through the wavenumber method (White and Zechman 1968, Bouchon

1979, 1980 & 2003) and fast Fourier transform (Blair 2007). Figure 8 shows a comparison of

results given by the Heelan and Full-field solutions with a dynamic finite elements method

(DFEM), through contour plots of peak vibration amplitudes for a short cylindrical charge with a

pressure function with average frequency fA = 600 Hz. The similarity between the Full-field and

DFEM results is obvious. Although the Heelan solution is in good qualitative agreement, it

exhibits two clear differences with the other methods: first it shows lower amplitudes on the

vertical axis, and second it seems to slightly overestimate the S-wave amplitudes (as can be seen

from the larger lobes at 45° angles). Despite the indicated differences and the limitations

mentioned above, the Heelan solution appears to be physically and mathematically well founded,

and useful to quickly estimate vibration amplitudes (Blair & Minchinton 2006).

21

Figure 8. Comparison of contour plots of peak vibration amplitudes from a short cylindrical source given by a) Heelan solution; b) Full-field solution, and c) dynamic finite elements method (after Blair 2007). Amplitude values are normalized at a distance 5 m horizontally from the origin (i.e., values shown in the isolines represent vibration amplitudes relative to that point).

2.2.2 Waves attenuation

The amplitude of a stress pulse or stress wave necessarily decays with distance from the source.

This decay is usually called attenuation. Mathematically, attenuation may be represented by

drud max

or ( )drud maxln , where maxu is the peak particle velocity at a distance r from the source.

The primary reason for attenuation in rock blasting, common to any material, is the geometric

spreading of energy. In order to illustrate geometric spreading, let us consider the case of a point

source in an infinite isotropic elastic material. At any time after the blast, the wave front defines

a sphere centered on the source, so the wave energy is distributed on the surface of this sphere.

As the sphere surface increases with the square of the distance, r2, and the total wave energy

remains constant, the energy density at any given point decays by a factor r2. Since wave energy

is proportional to the square particle velocity amplitude, the geometric attenuation (i.e.,

attenuation by geometric spreading) of body waves is proportional to r. In the case of surface

waves the energy is distributed in a cylinder, rather than a sphere, so the energy density decays

by r instead of r2, and geometric attenuation is proportional to r1/2. A common expression to

account for geometric attenuation is:

n

rruu

−

=

1

21max2max , with n = 1 for body waves and n = ½ for surface waves 2-5

a) b) c)

22

where 1maxu and 2maxu are the peak particle velocities at two distances from the source r1 and r2.

In addition to geometric spreading, seismic waves experience loss of energy caused by friction

and other forms of energy dissipation. It has been shown that the decay of signals is a function of

energy loss per cycle of deformation, i.e., decay is proportional to the number of wavelengths

traveled. Since this energy loss per cycle of deformation is a material property, it is called

material damping. The classical expression for wave attenuation by material damping is:

)(1max2max

12 rreuu −−= α 2-6

where α is the attenuation coefficient. Note that the expression given by Equation 2-6 implies

that the attenuation coefficient α represents the decay ( ) drud maxln . Geometric spreading and

material damping attenuation can be combined in a single expression as follows:

)(

2

11max2max

12 rrn

err

uu −−

= α 2-7

Figure 9. Various forms of vibration attenuation (after Dowding 1996, Woods & Jedele 1985).

( )122112

rrerruu −−= α

2112 rruu =

mrku −=

23

Figure 9 shows the attenuation of waves considering only geometric spreading and also a

combination of both geometrical and material damping for Rayleigh waves. The same figure

shows an approximation to the combined geometric and material damping, which establishes a

linear relationship between peak particle velocity and distance in a log-log scale (considering

same wave type and same source energy).

Since wave decay caused by material damping increases proportionally with the number of

deformation cycles, and a higher frequency wave passes through more deformation cycles than a

lower frequency wave for the same travelled distance, the attenuation coefficient increases with

frequency. Table 1 provides typical ranges of the α coefficient for a variety of earth materials. It

can be observed that the coefficient also decreases with material competence.

Table 1. Proposed Classification of Earth Materials by Attenuation Coefficient (after Woods & Jedele 1985)

Class Attenuation Coefficient,

α (1/m) Description of Material 5 Hz 50 Hz

I 0.01-0.03 0.10-0.3 Weak or soft soils: Lossy soils, dry or partially saturated peat and muck, mud, loose beach sand and dune sand, recently plowed ground, soft spongy forest or jungle floor, organic soils, topsoil (shovel penetrates easily)

II 0.003-0.01 0.03-0.1 Competent soils: Most sands, sandy clays, silty clays, gravel, silts, weathered rock (can dig with shovel)

III 0.0003-0.003 0.003-0.03 Hard soils: Dense compacted sand, dry consolidated glacial till, some exposed rock (cannot dig with shovel, must use pick to break up)

IV <0.0003 <0.003 Hard, competent rock: Bedrock, freshly exposed hard rock (difficult to break with hammer)

2.3 Damage mechanics In conventional damage mechanics, damage corresponds to the presence of microcracks (or

microfractures) and microvoids (or microcavities) which are discontinuities within a solid that is

considered continuous at a larger scale. In general these microcracks or microvoids can be

referred to as microdefects. Even though the conventional damage mechanics definition given

above does not consider ‘macro’ fractures and fragmentation as damage (probably as a

consequence of the many applications in which these are considered material failure or near

failure), in rock blasting it is essential to quantify them. Thus, in this study related to rock

blasting, the term damage is used to refer to the breakage of bonds between rock particles by the

24

physical action of the explosive upon the rock mass, including fractures and fragmentation. The

quantification of this kind of damage, however, is not a trivial problem, as the scale at which

fractures are measured may significantly affect the results.

In conventional damage mechanics, the concept of damage refers to the portion of microdefects

in a given volume of material. In this approach the damage variable is seen as the relative area of

microdefects on a surface and thus, is bounded between 0 and 1, with 0 representing no damage,

and 1 indicating complete material breakage (Lemaitre & Desmorat 2005). Considering a

damaged body and a Representative Volume Element of cross section δS defined on a plane with

normal n , the value of damage at this point on the indicated plane is defined by:

SSD D

n δδ

=

2-8

When damage is caused by the presence of microcracks, the method of direct measurement has

been proposed to calculate this variable (Lemaitre 1996). The method consists on producing

amplified images of the material to count and measure the crack lengths on a plane. For

simplification assuming square cracks, damage can be calculated as:

2

2

LL

D i∑= 2-9

where D is damage, Li represent the apparent size of cracks (measured length), and L2 is the

surface of the plane under analysis.

Even though the concept of damage as defined above has been widely studied and a large

number of measurement methods have been developed (Lemaitre 1996), this definition may not

be appropriate for rock blasting, or in general, for the evaluation of damage around rock

excavations. First, the definition itself makes little sense in the case of fractures, since the

intersection of an arbitrary plane on an arbitrary fracture generally leads to insignificant relative

surface of cracks. Second, crack measurements in a representative volume of rock with

numerous extensive fractures can easily lead to values well beyond unity, even if the rock is still

held together by external forces, such as the case of the rock mass surrounding a tunnel. This

situation would be in contradiction with the upper limit (unity) of the damage variable. As a

25

consequence, the approach of conventional damage mechanics was discarded in this study to

evaluate blast-induced damage.

Another approach to quantify damage is that in which damage is evaluated in terms of crack

density. In this case, the value of damage varies between 0 and ∞. This case is evidently not

appropriate to evaluate damage in general (which includes microvoids), but it is suitable for

brittle materials, where cracks are by far the main source of damage. In this context, a number of

theories have been developed seeking to relate damage (as crack density) and other material

properties. Some of these theories, also referred to as effective medium theories, are described in

Appendix B. The approach of damage as crack density is chosen to evaluate blast-induced

damage in this thesis and the theory to relate elastic constants and crack density corresponds to a

simple and non-controversial method developed by Kachanov (1994). The choice of the method,

including a brief comparison with other alternative approaches, is discussed in Appendix B.

2.3.1 Damage as crack density

Since the great majority of rocks exhibit a brittle nature, damage in rock consists mainly on the

presence, creation and propagation of cracks. Consequently, rock damage is evaluated in terms

of crack density, which is commonly defined according to the following equations (Kachanov

1994):

∑= 21ia

Aρ , in the two-dimensional case, and 2-10

∑= 31ia

Vρ , in the three-dimensional case 2-11

where A and V represent the area and volume of representative elements in 2D and 3D

respectively, and ai represent the radius of cracks (rectilinear cracks of length 2ai in 2D, and

circular cracks of diameter 2ai in 3D).

26

2.3.2 Kachanov's approach for isotropically distributed non-interacting cracks

The simplest case of Kachanov's (1994) non interactive theory considers cracks with centers

uniformly distributed and randomly oriented (isotropic). The ratio between the elastic moduli of

the solid matrix and the corresponding effective elastic moduli is calculated as a linear function

of the crack density as:

ρHMM

+=10 2-12

Where M is the rock effective modulus, the sub-index ‘0’ indicates properties of the solid

(undamaged) matrix, and H is a positive scaling parameter that depends on the matrix and fluid

properties and crack geometry (it also depends on crack interaction, when this is considered).

The precise expressions to calculate effective Young and shear moduli are as follows:

ρδ

δνρ hH

EE

+

−−−+=+=

1211

53111 00 2-13

0

00

11211

52111

νρ

δδν

ρµµ

+

+

−−−+=′+=

hH 2-14

where

( )( )219

116

0

20

νν

−−

=h 2-15

is a geometrical factor related to the shape of the cracks (assumed to be circular) and

hKE

f

ζνδ 00

21

−= 2-16

is a dimensionless number to characterize the coupling between stress and fluid pressure, in

which Kf is fluid bulk modulus, and ζ is crack’s average aspect ratio (thickness / radius). Note

that Equation 2-14 has been corrected from Kachanov's (1994) original formulation as developed

in Benson et al (2006).

27

2.4 Assessment of blast-induced damage in rock Accurate and reliable assessment of blast-induced damage has been attempted by a number of

authors using a wide variety of methods. Some of the generally accepted methods are:

• Direct measurement of cracks

• Seismic monitoring

• Cross-hole: variations in P-wave velocity

• Explosive gas pressure activity

In this section a brief description of the above indicated method is included.

2.4.1 Direct measurement of cracks

This method has been executed in blocks of relatively intact rock and also in controlled bench

blasting (Olsson et al 2002, Ouchterlony et al 1999 & 2001, Mohanty & Dehghan Banadaki

2009, Dehghan Banadaki 2010). It consists of cutting the blasted rock perpendicularly to the

blasthole axis, identification and measurement of length and quantity of blast-induced fractures.

The method has been applied to single-holes in blocks with no significant displacement of

material, and also to bench blasting with fragmentation at the front of a series of blastholes. It is

a relatively complicated method that requires significant effort to measure actual fractures. It is,

however, probably the most direct and reliable method to measure blast-induced damage and it

allows the distinction of fractures induced only by stress waves from those created and enhanced

by gas penetration, by casing the blastholes. Due to its difficulties it has been applied only for

scaled experiments, generally with small laboratory samples.

2.4.2 Seismic monitoring: PPV method

Probably the most common method to determine blast-induced damage is the monitoring of

blast-induced vibrations. Peak particle velocity (PPV) has been found not only theoretically

proportional to blast-induced stress, but also well correlated to actual damage. It is a relatively

simple method compared to others. The disadvantages of this method are that it does not provide

actual determination of blast-induced damage, and it is generally used in combination with some

form of scaling law, disregarding directionality and distinction between different types of waves.

28

The commonly accepted method to predict blast-induced damage in nearby structures is the

standard charge weight scaling law (Hopler 1998, Dowding 1996), given by Equation 2-17:

βα −= rwKPPV 2-17

where PPV = peak particle velocity at a given point; w = explosive weight (generally taken as the

total explosive weight per delay); r = direct distance from source to the point; and the parameters

K, α and β are specific site constants. This method can be seen as a simple fitting method in

which the peak particle velocity at a given point is assumed to be only a function of the total

explosive charge per delay and the distance from the source. Further simplification of Equation

2-17 can be achieved by considering α = β/3 (cube-root scaling) or α = β/2 (square-root

scaling). The cube-root scaling can be derived from dimensional analysis when the energy

released from the explosion is considered proportional to the weight of the explosive (Ambraseys

& Hendron 1968). Square-root scaling is based on the fact that the explosive charge is distributed

in a long cylinder. Thus, per unit length of hole, the diameter of the blasthole is proportional to

the square-root of the charge weight and, therefore, the expression R/w1/2 is somewhat equivalent

to the ratio between the source-receiver distance and the diameter of the blasthole. This approach

is the most traditional form of scaling law and has been widely used to predict and control

vibration levels in construction situations (Siskind et al 1980, Wiss 1981). Typically, PPV is

plotted against the term r/w1/2, usually referred as scaled distance in a logarithmic scale.

Thus:

( ) β−= SDKPPV 2-18

with

2/1wrSD = 2-19

where SD is scaled distance, and the coefficients K and β are determined by simple linear

regression (in log-log space).

Despite the fact that the scaling law is an approximate method that at most can be used to

estimate the order of magnitude of the vibration levels for a given blast configuration, it has been

extrapolated to determine blast-induced damage in rock and mine structures. One example of this

29

is the well-known Holmberg-Persson method (Holmberg and Persson 1979), which assumes the

square-root form of the scaling law to be true for every element of explosive charge within a

blasthole. The method also indicates that the contribution of each element of charge to the PPV

at a given point is numerically additive, resulting in an expression that is a modified version of

the scaling law. In order to estimate blast-induced damage based on this model, Holmberg (1984)

proposed some PPV threshold values for different rock conditions: 1000 mm/s for hard rock with

strong joints; 700-800 mm/s for medium hard rock with no weak joints; and 400 mm/s for soft

rock with weak joints.

The Holmberg-Persson model has, however, been shown to have several shortcomings, including

being physically inconsistent (Blair & Minchinton 1996, 2006) and even mathematically

erroneous (Hustrulid & Lu 2002). The standard scaling law itself has also been questioned for

not considering the wave nature of the radiating signals from a blast (Blair 1990), and has also

been qualified as inadequate to predict blast-induced damage (Fleetwood et al 2009). It is

important to mention here that this inadequacy is not the result of lack of correlation between

PPV and damage (as indicated earlier, these have been found well correlated) but a consequence

of predicting PPV based only on distance and charge weight (i.e., without considering

directionality or wave properties).

2.4.3 Explosive gas pressure activity

It is a more direct determination of blast-induced damage, consisting of measurement of gas

penetration in monitor holes in the vicinity of one or more blastholes (Brinkmann et al 1987,

Brent & Smith 1996, Yamin 2005). Gas pressure is measured when a fracture or network of

fractures connect the blasthole with the monitor hole. The method allows the determination of

the range of distances where fractures are developed from the blasthole, allowing the estimation

of damage depth around or behind a hole. The main advantage of this method is that, in contrast

to vibration measurements, it provides an estimation of the damage zone involving not only

stress waves but also gas expansion. One of the drawbacks of the method, is that it is strongly

affected by the local conditions of the measuring area, in particular by the presence of pre-

existent fractures in the rock mass. Also, when no gas pressure is recorded there is no certainty

that blast-induced fractures do not reach the monitoring distance; it only means that they have

not reached the specific measuring point.

30

Given the advantages and disadvantages of measuring gas activity, it is used as a secondary

method to evaluate blast-induced damage from single-hole controlled blasts as part of this

research work.

2.4.4 Cross-hole: Variations in P-wave velocity

This method consists of determination of P-wave velocities in the rock before and after blasting,

at various distances from the blasthole. In the current research work this is the method utilized to

evaluate blast-induced damage.

The method provides a theoretical estimation of blast-induced damage based on the measured

variation of wave velocities with fractures in the rock mass. Although it does not provide precise

information on the fractures created by blasting (e.g. size, aspect ratio, opening), it allows the

quantification of damage at various locations with respect to the source. It is probably the most

convenient method to evaluate blast-induced damage in rock, not only due to the brittle nature of

rock, but also for being applicable to in-situ measurements, in contrast to most other methods.

Despite its advantages, the method is also somewhat expensive and cumbersome, as it requires

the drilling of boreholes in the vicinity of the blast and appropriate equipment to measure P-wave

velocities. These drawbacks are probably the reason why it is not widely used to determine blast-

induced damage.

The calculation of damage is done by using the relationships between P-wave velocity and

Young's modulus (see Appendix A), and between the latter and damage, according to, for

example, one of the effective medium theories. Here, the approach given by Kachanov (1994)

described in 2.3.2 is used.

From Equation 2-13, the crack density can be calculated as:

−= 11 0

EE

Hρ 2-20

where H is a positive scaling parameter and the sub-index ‘0’ indicates undamaged properties.

Considering the elasticity modulus to be proportional to the square of P-wave velocity, i.e.,

assuming that density and Poisson’s ratio are approximately constant, the above equation can be

re-written in terms of P-wave velocities:

31

−= 11

2

20

P

P

VV

Hρ 2-21

Thus, crack density within the rock mass before and after blasting can be calculated as:

−

= 11

2

0

beforeP

Pbefore V

VH

ρ , and 2-22

−

= 11

2

0

afterP

Pafter V

VH

ρ 2-23

where ρ before, ρ after, VP before and VP after are the crack densities and measured P-wave velocities

before and after blast. Thus, blast damage (i.e., increase in crack density caused by blasting) can

be calculated as:

−

=−= 11

22

0

afterP

beforeP

beforeP

Pbeforeafterblast V

VV

VH

ρρρ 2-24

In practice, as several measurements of wave velocities are executed at various locations before

and after blasting, the damage at any specific point is determined by minimizing the error

between the calculated P-wave velocity from the estimated damage and the measured values of

P-wave velocity after the blast. Velocity calculated from damage is obtained from Equation 2-24:

2

0

1

~

+

=

P

beforeP

beforePafterP

VV

H

VV

ρ

2-25

where afterPV~ is the calculated the P-wave velocity after blast. Equation 2-25 is used in this

research work to invert multiple measurements of P-wave velocities around a single-hole blast

into damage, as shown in section 4.3.1.

32

2.5 The combined finite and discrete elements (FEM-DEM) method

As its name implies, the combined finite and discrete element method (FEM-DEM) is a

numerical method that utilizes both finite and discrete element techniques to model the

behaviour of independent elements and continuous materials (Munjiza et al 1995, Mohammadi et

al 1998, Munjiza 2004). One software that uses this method is the Y2D code, which has been

applied to blast modeling, including the incorporation of fractures and explosion gas penetration

into cracks (Munjiza et al 1999a,b). Also, it has been compared to analytical and experimental

results of blast seismic radiation (Trivino et al 2009). This software was found to be suitable to

evaluate blast-induced damage, as it is capable of simulating the non linear response of solids to

dynamic loading, including fracture creation and propagation, as well as the reproduction of non-

planar waves. Consequently, this code was chosen to be used as part of this research to

specifically compute damage from stress waves.

2.5.1 The Y2D code

The Y2D code is a 2D open source program developed by Munjiza (2000) using a FEM-DEM

technique. In this program, discrete elements are used to model discontinuous materials or to

model the creation of discontinuities in the form of fractures and fragmentation. Finite element

techniques are used within a continuous piece of element in order to properly account for

variations in the state variables within the element. Thus, the method not only allows the

incorporation of complicated geometries, discontinuities and various materials, as most finite and

discrete element methods do, but also permits the creation of fractures when the strength of the

material is exceeded. This program uses an explicit time integration scheme (i.e., direct

integration in time domain), considered suitable for most practical dynamic applications. Within

its code, the software contains a number of algorithms, the most important being as follows:

• Interaction is computed between discrete elements. This interaction produces forces on

boundaries and causes the elements to move;

• Movement is calculated by direct numerical integration over time;

• The forces cause deformation of the elements, and finally

• Fracture and fragmentation occur under specific conditions

33

Figure 10 shows a schematic view of the above mentioned algorithms. A full description of the

method can be found in Munjiza (2004).

Figure 10. Schematic view of algorithms built in the combined FEM-DEM program Y2D.

Within blast related problems, some of the application of the Y2D software are:

• Modeling of fracturing process

• Variety of loading conditions

• Complicated geometries

• Interaction of different materials

Some of the limitations of the code are:

• 2D modeling differs from 3D real problems

• Inability to explicitly handle the phenomenon of gas expansion (lack of explosion model)

• Difficulty on choosing input parameters: material strength (dependency on strain rate),

loading conditions

• Mesh dependence of results. Higher accuracy longer processing times

• Requires verification on the prediction of crack distribution

Specific stress combination Fracture

Intensive fracturing Fragmentation

Contact Detection Algorithm

Discrete elements separate bodies

Contact forces on interacting boundaries equivalent nodal forces

Rotation, Translation, Stretch

Deforming stress and strain nodal forces

Nodal forces discrete elements move in time

Time domain / small time steps

Direct numerical integration

Fracture

Deformation Temporal

Discretization

Interaction

x y

z

Discrete Elements

Finite Elements

34

The following sections include the main equations corresponding to the constitutive model

implemented in the software as well as comparisons with analytical solutions. Details of the

constitutive model are included in Appendix C.

2.5.2 Constitutive model in Y2D code

The constitutive model built into the Y2D code corresponds to the Kelvin-Voigt model, with the

equations corresponding to the 2D case, shown in detail in Appendix C. In this model, energy

dissipation is introduced through a viscous parameter, which simulates the dissipation of kinetic

energy. Thus, the model conserves the strain-stress proportionality and the Poisson effect from

the elastic model in the static case, but introduces viscosity in the dynamic case. The model is

typically represented by an elastic element (spring) acting in parallel to a viscous element

(dashpot) as illustrated in Figure 11.

Figure 11. Representation of the Kelvin-Voigt visco-elastic model in the one-dimensional case.

The general constitutive equation for this model can be written similarly to the elastic model, by

introducing a damping term as follows:

εεσ I ηλµ 22 +∆⋅⋅+= 2-26

where σ, ε, and ε are stress, strain, and strain rate tensors, µ and λ are Shear Modulus and Lamé

constant respectively, I is the identity matrix, ( )zzyyxx εεε ++=∆ is volumetric strain, and η is

viscous damping. The 2D version of this model can be written as:

+=

++∆=++∆=

xyxyxy

yyyyyy

xxxxxx

εηµεσ

εηµελσεηµελσ

222222

2-27

where ∆ is volumetric strain, and εij and ijε are components of strain and strain rate respectively

(note that in the Y2D code the user-input viscous damping parameter is 2η). The constitutive

E

η

35

model given by Equation 2-27 along with Newton’s second law of motion ( amF ⋅= ) govern the

motion of waves through a continuous body. For compression and shear waves with an

approximately plane wavefront (i.e., in the far field for a point source), the equations of motion

(assuming the x-axis in the direction of propagation) can be written as:

( ) 2

2

2

2

2

2

0 22xu

txu

tu

∂∂

∂∂

+∂∂

+=∂∂ ηµλρ for compression waves, and 2-28

2

2

2

2

2

2

0 xtxtxxx

∂∂

∂∂

+∂∂

=∂∂ ω

ηω

µω

ρ for shear waves 2-29

where u and ωx are longitudinal and rotational displacements along the x-axis, and ρ0 is density.

The general solutions for these equations can be written as:

( )

−

−=tx

Vi

x PP eeutxuωω

α0, for compression waves, and 2-30

( )

−

−=tx

Vi

xxx

SS eetxωω

αωω 0, for shear waves 2-31

where ω is angular frequency and the parameters αP, αS (attenuation coefficients), and VP, VS

(wave velocities) have the following approximate expressions for small values of η (Jaeger et al

2007):

( ) PP Vµλ

ηωα2

2

+= and

21

0

2

+=

ρµλ

PV for compression waves, and 2-32

S

S Vµηωα2

2

= and 21

0

=

ρµ

SV for shear waves, 2-33

The expressions for the coefficients αP and αS necessarily imply that attenuation of S-waves is

always greater than attenuation of P-waves. In the case of a Poisson solid (ν = 0.25 or λ = μ), for

example, the ratio between these coefficients PS αα is 2.6.

The actual equations implemented in the code make use of the volumetric stretch parameter

defined as:

icV VVS = 2-34

36

where Vc and Vi are the initial and current volumes of an element. By using the relationships

between volumetric stretch and strain ∆+== 1icV VVS and ∆−≈= 11 ciV VVS (assuming

Δ≪1), the expressions from Equation 2-27 can be written in terms of the former. Thus, the

expressions implemented in the code are:

ji

S

SSS

ijV

ijij

iiV

iiV

Vii

≠+=

++

−=

εηµεσ

εηµελσ

212

212121

2-35

The input values for shear modulus and Lamé constant may be chosen to model the cases of

plane stress or plane strain, by using the following relationships with Young modulus and

Poisson’s ratio:

( )

−=

+=

21

12

ννλ

νµ

E

E

for Plane Stress, and 2-36

( )

( )( )

−+=

+=

νννλ

νµ

211

12E

E

for Plane Strain 2-37

Note that the expressions for shear modulus in both cases are identical, while the expressions for

the Lamé constant differ by a factor ( ) ( )νν 211 −− . Also, both moduli in Plane Strain are

identical to those in the general 3D case.

Finally, although the Y2D code considers a single value of viscous damping, the model has

potential to incorporate independently shear and volumetric damping, as shown in Appendix C.

37

2.5.3 Comparison of seismic radiation between Y2D and Heelan analytical solution

In order to illustrate the applicability of the FEM-DEM program to blast related problems, a

comparison between radiation patterns between this method and the Heelan analytical solution is

provided in this section. This comparison is carried in terms of attenuation and through contour

plots of PPV from a short source in the elastic case. It is important to clarify though that Heelan’s

model is only used to evaluate the ability of the FEM-DEM software to reproduce seismic signals

(applied to blasting in borehole) and is not used to investigate damage.

Figure 12a illustrates the geometric decay of P and S-waves determined from FEM-DEM elastic

models (i.e., no damping), as well as theoretical geometric attenuation curves for 2D and 3D

cases. All curves are normalized in terms of both PPV and distance (r). Attenuation of P-waves

from the FEM-DEM program was determined by calculating PPV values at several points on a

line along the direction of application of a point load. S-waves were determined at 45° angles

with respect to this line. Both wave types show a slightly non-linear attenuation closer to the

source (more significant for S-waves), which is attributed to the numerical approximations

caused by the relatively coarse mesh closer to the source. Despite this non linearity, both curves

exhibit a linear trend at larger distances, with a slope around -0.54 (in log-log scale). This

geometric attenuation is very close to the theoretical value for the 2D case (-0.5), but evidently

far from the 3D case (-1). As a consequence, values of wave amplitude from the Y2D software

are not expected to match those from a 3D situation, but the results from the program are

necessarily of higher amplitude. It is proposed here that correcting 2D wave amplitudes by a

factor proportional to r -0.5 is a suitable method to compare results from 2D and 3D cases. This

correction consists of scaling (or multiplying) PPV2D (PPV from 2D models) by a factor

proportional to r -0.5 (with r being distance from the source). Figure 12b shows the geometric

attenuation of waves from the FEM-DEM program, corrected by a factor r -0.5. It is clear from

this figure than the results corrected by this factor are close to the 3D geometric attenuation.

38

Figure 12. Geometric attenuation of P and S-waves from FEM-DEM elastic models and comparison with 2D and 3D elastic attenuation. a) FEM-DEM results before correction; b) FEM-DEM results after correction (x r -0.5).

Figure 13 shows the results of radiation obtained from a short source (horizontal loading in the

center of each plot) from the FEM-DEM program and Heelan solution. All graphs are

normalized by the PPV value 5 m horizontally from the source. Figure 13a shows the pattern

obtained directly from FEM-DEM PPV values, whereas Figure 13b shows the results from the

Heelan solution (the agreement and differences between the two solutions was discussed by

Trivino et al 2009). Both solutions agree in that P-waves are dominant at angles close to the

horizontal and S-waves dominate at angles close to 45°; however, there is a clear difference

between the relative amplitudes of P and S-waves. The relative amplitudes in terms of S/P ratio

(ratio of S-wave peak amplitude to P-wave peak amplitude) and radiated energy for both cases

are:

Heelan:

• S/P ratio 1.6 (in terms of peak amplitudes)

• Energy from P and S-waves: EP 41%, ES 59%

FEM-DEM:

• S/P ratio 1.1 (in terms of peak amplitudes)

• Energy from P and S-waves: EP 54%, ES 46%

a) b)

39

Figure 13. Radiation pattern of particle velocity from FEM-DEM program and Heelan solution considering elastic material (i.e., no damping) with ν = 0.25. a) FEM-DEM contour plot of PPV (2D attenuation); b) Heelan contour plot of PPV (3D attenuation); c) FEM-DEM contour plot modified by a factor r -1/2 (3D attenuation); d) FEM-DEM contour plot modified by a factor r -1/2 (3D attenuation) and S/P ratio amplified by a factor 1.6 (for equal S/P ratio).

Figure 13c shows the FEM-DEM results corrected by a factor r -0.5 and Figure 13d shows the

same results with S/P ratios amplified by a factor 1.6. The later shows clearly results very close

to the Heelan solution, which indicates that the discrepancy in S/P ratio between the Heelan and

the modified (x r -0.5) FEM-DEM results corresponds approximately to a factor 1.6 (Heelan’s

being higher than FEM-DEM). Despite the discrepancy of S/P ratios, both P and S-waves follow

approximately the same patterns in both modified FEM-DEM and Heelan solution. Figure 14

and Figure 15 show the comparison between both methods for both P and S-waves

independently, confirming an excellent match between the two solutions. It is estimated that this

discrepancy should not make the results of the FEM-DEM method too far from reality,

especially when considering material damping, as S-waves are more strongly attenuated than P-

waves (see section 2.5.2); this discrepancy may, however, be subject of further study.

a) FEM-DEM

c) FEM-DEM x r -0.5 d) FEM-DEM x r -0.5, S/P x 1.6

b) Heelan

40

Figure 14. Radiation patterns of particle velocity from Heelan analytical solution and FEM-DEM program considering only radial component. a) Contour plot of PPV from Heelan solution; b) Contour plot from FEM-DEM modified by a factor r -1/2.

Figure 15. Radiation patterns of particle velocity from Heelan analytical solution and FEM-DEM program considering only tangential component. a) Contour plot of PPV from Heelan solution; b) Contour plot from FEM-DEM modified by a factor r -1/2.

The discrepancy in S/P ratios should not be taken as a drawback of the FEM-DEM method. In

fact, the results from the 2D program should not match those from Heelan, as the later is a 3D

solution. The problem solved by the 2D numerical method corresponds actually to Lamb's

problem for the surface normal line load source (Miller & Pursey 1954, Miklowitz 1978, Graff

1991). The radiation from this solution in terms of both radial (P-waves) and tangential (S-

waves) components is shown in Figure 16a,b. The S/P ratio from this solution is approximately

1.2, which is evidently much closer to the 1.1 from FEM-DEM, than to the 1.6 from Heelan’s

solution. From Figure 16 some singularities of zero amplitude are observed at various angles (0°

from vertical for radial component or P-wave; 0°, 65°, and 90° for tangential component or S-

wave). Even though the respective radiation patterns from the FEM-DEM method (Figure 16c,d)

a) b)

a) b)

41

do not show these singularities, its results are considered acceptable, as such singularities are

unlikely to occur in reality.

Figure 16. Comparison between solution to Lamb's problem for a point horizontal load and FEM-DEM results for ν = 0.25. a) Radial component, and b) Tangential component of Lamb’s solution (after Miller & Pursey 1954). c) Radial component, and d) Tangential component FEM-DEM program.

Finally, the FEM-DEM software is estimated to be suitable to model blasting in boreholes,

provided the correction by a factor proportional to r -0.5 is applied in order to account for the

difference in geometric attenuation with the 3D case. As for the mismatch of S/P ratio with the

3D analytical solution by a factor 1.6, it is estimated that the incorporation of material

attenuation into the models should significantly reduce this discrepancy. Thus, no correction

associated to S/P ratios is attempted as part of this work. Regarding the lack of singularities from

FEM-DEM results (in contrast to the analytical solution to Lamb’s problem), it is estimated that

no negative consequences should arise from it, as in real situations these singularities may never

occur, and the numerical results are closer to the 3D exact solution, which does not show such

singularities (Figure 8b).

a) b) Singularities

of zero amplitude

Singularity of zero

amplitude

12

Distance (m)

Dis

tanc

e (m

)

0 2 4 6 8 100

5

10

1

Distance (m)

Dis

tanc

e (m

)

0 2 4 6 8 100

5

10c) d)

load load

42

Chapter 3

3 Experiments, Instrumentation and Layout The work performed as part of this research project includes an experimental component,

oriented towards the understanding of seismic waves from blasting and blast-induced damage.

This experimental part corresponds to various blast experiments executed in two test sites, as

well as laboratory tests to determine material properties. This chapter provides a description of

the experimental procedures, instrumentation and test sites. The results from these experiments

are presented later in Chapter 4.

3.1 Experimental procedures The study of blast-induced damage in rock involves a significant number of processes taking

place in the rock mass and hence, an important number of variables relevant to the final outcome

of the blast. These variables are associated not only with material and geometrical properties but

also with the complex dynamic interaction between explosive and rock. Consequently, the

current study incorporates the experimental assessment of the most relevant variables through the

execution of single-hole and multiple-hole blast experiments. These experiments are carried out

in hard rock on a surface test and one underground mine.

The field experiments executed include the following measurements:

• Seismic radiation

• Explosion gas activity

• Explosion front pressure

• Velocity of detonation (VOD) of explosive

• Near-field damage assessment

The surface experiments correspond to small-scale blasts executed in a natural exposed rock

mass. Several single-hole blasts are executed in vertical boreholes (or blastholes) and the

aforementioned measurements are executed with the appropriate instrumentation. Details of this

test site and setup are included in 3.3.1 whilst the instrumentation is described in section 3.2. The

43

results from this test site, which are included in Chapter 4, are also utilized for the calibration of

numerical models whose results are presented in Chapter 5.

Underground mine experiments include both single-hole controlled blast experiments and the

monitoring of regular multiple-hole production blasts. The measurements carried as part of these

experiments correspond to seismic studies (blast vibrations), VOD and explosion front pressure.

Information on the test site and experimental setup are provided in 3.3.2, while the

instrumentation is described in section 3.2. The results from single-hole experiments are included

in Chapter 4 along with those from the surface test site, whereas multiple-hole production blast

results are shown in Chapter 6. The later were also used for the calibration of parameters for

numerical models, also presented in Chapter 6.

3.2 Instrumentation The instrumentation utilized to assess the physical phenomena taking place during and as a

consequence of blasting can be summarized as follows:

• Triaxial Accelerometer stations: to measure seismic activity from blasts

• Gas Pressure sensors: to measure gas penetration in the vicinity of single-hole blasts

• Carbon resistors (pressure sensors): to measure explosion front pressure

• VOD device: to measure velocity of detonation, VOD

• Cross-hole system: to assess blast-induced damage through variations in P-wave

velocities

• Data Acquisition systems: to record signals from all the above instruments

A complete description of this instrumentation is given in 3.2.1 to 3.2.6.

3.2.1 Accelerometers

Blast-induced seismic activity is measured during all blast experiments and production blasts at

both test sites. For this, triaxial accelerometer stations were located at various distances and

angles with respect to the explosive source axis. Accelerometers of various capacities ranging

from 100 to 1000 g (acceleration due to gravity) were utilized and selected according to the

expected vibration levels. All accelerometers used have a relatively wide frequency band which

varies according to the model. The maximum frequency response of the models utilized for this

44

research ranges from 10 to 25 kHz (with ±5% of accuracy). A summary of the accelerometers

main specifications is included in Table 2.

Table 2. Accelerometers technical data Specification Unit Type 1 Type 2 Type 3 Type 4

Model number 8702B100 8763A500 8763A1000 8614A1000M1

Components Uniaxial(*) Triaxial Triaxial Uniaxial(*)

Acceleration range g(**) ±100 ±500 ±1000 ±1000

Acceleration limit g(**) ±200 ±1000 ±2000 ±2000

Sensitivity (±5%) mV/g(**) 50 10 5 2.5

Frequency response (±5%) Hz 0.5 … 10,000 1 … 12,000 1 … 10,000 10 … 25,000

Resonant frequency, nom kHz 54 55 55 125

Sensing element type Quartz shear Ceramic shear

Ceramic shear

Quartz compression

Case / base material Titanium Titanium Titanium Titanium

Weight g 8.7 3.3 3 0.7 (*) Three uniaxial accelerometers are mounted orthogonally to obtain true vectors of motion (**) Acceleration due to gravity ( ≈ 9.8 m/s2)

The measurement of seismic signals is intended to provide information on wave propagation in

the near field in terms of amplitude and frequency content, as well as material properties, such as

wave velocities and material attenuation. This information is also used to calibrate the blasthole

pressure function utilized in numerical models.

The accelerometers are inserted into the rock mass in boreholes at various depths. Two

alternative mounting systems are used for this: grouted (permanent) and spring loaded

(retrievable). The first system is used in the underground mine, while the latter is used at the

surface test site. In all cases the orientation of the three accelerometer components is controlled

so that the vectors of motion (acceleration, velocity, displacement) can be fully determined.

Figure 17 shows three uniaxial accelerometers in aluminum case to be grouted in borehole.

Figure 18 shows the spring mounting system, power supply and detail of installation.

45

Figure 17. Accelerometer assembly to be grouted in borehole. a) Accelerometer assembly inserted in φ 50 mm aluminum case; b) Detail of case showing three uniaxial accelerometers mounted orthogonally; c) Assembly in 32 mm aluminum case attached to ABS pipe ready to be inserted and grouted in borehole.

Figure 18. Spring mounting system for accelerometers. a) Triaxial accelerometer mounted on spring for a 45 mm borehole; b) Spring system and power supply; c) Assembly ready to be installed.

a) b)

c)

a) b)

c)

46

3.2.2 Pressure sensors

Gas Pressure activity is monitored by pressure sensors installed in boreholes (monitor holes)

located in the close vicinity of a single blasthole. The monitor holes are plugged at the collar to

create a chamber where the gas activity can be measured. This monitoring is carried out only at

the surface test site and is intended as an indicator of the extent of fracture propagation.

The method relies on the propagation of gases through a fracture network including both pre-

existent and blast created fractures. Thus, the recording of gas pressure at various distances from

the source provides an indication of the extent of the blast-induced damage. The sensors

employed for these measurements correspond to a silicon sensitive element packaged in a plastic

housing with a pressure range between 0-30 or 0-100 psi absolute pressure. Each sensor is

connected to a power supply, which provides energy to the sensor and amplifies its output. Each

sensor is calibrated individually and a calibration curve is determined and applied to each

measurement. Figure 19 shows a silicon sensor and assembly for field tests. Figure 20 shows a

sensor already installed in a monitor hole showing the collar plug and power supply. A drawing

of the mounting system is also included in this figure. A full description and scheme of circuits

and calibration procedures of both sensors and power supplies can be found in Yamin 2005.

Figure 19. Silicon pressure sensor employed for gas activity in the vicinity of a blasthole. a) Connector, sensor and case; b) Assembly for field tests.

Sensor

Connector to power supply

Protective casing

Sensor

a) b)

47

Figure 20. Sensors installed in monitor holes and connected to power supplies.

3.2.3 Explosion (detonation) front pressure measurement

The in-hole explosive front pressure is measured by carbon resistors mounted on top of the

explosive column. The change in pressure caused by reaction of the explosive components

induces variations in the resistance or conductance of the carbon resistors. The resistance is

measured by applying a constant current through the gauge (carbon resistor) and recording the

resulting potential difference (voltage) by a high speed data acquisition unit. The blasthole

pressure can be calculated from previously calibrated formulas or graphs relating pressure and

impedance variations (Austing et al 1991 & 1995, Cunningham et al 2001). In this work

pressures are calculated according to the following equations by Austing et al (1995):

( )GPaGP a∆= 4.212 if 101021.0 −Ω≤∆ aG 3-1

( )GPaGGP aa227871387.71 ∆+∆−= if 101021.0 −Ω>∆ aG 3-2

Where ∆Ga is a measure of the change in conductance (in S or Ω-1) of the gauge as a result of

dynamic loading. ∆Ga is calculated according to the following approximate expression:

i

a RRG 11

−=∆ 3-3

where R is the resistance of the gauge measured at any given time during the explosion and Ri its

initial resistance. The current applied to the gauge is supplied by a high speed constant current

power supply, so the resistance R in Equation 3-3 above is calculated according to:

0282.0=cσ Steel plate

Anchors

Rubber plug

48

IVR = 3-4

where V is the measured voltage and I is the constant current provided by the power supply.

Although studies have been done to protect the sensors from the explosion itself in order to

obtain a measurement of the full explosive pressure function (Nie 1999, Nie & Olsson 2001,

Olsson et al 2002), the protective systems also introduce a boundary between explosive and

sensor, causing a modification to the recorded signals. Consequently, in this research work, the

carbon resistors are placed directly on top of the explosive with only water as transmitting

medium. A thin protective film (shrink-cable) was placed to cover the sensors in order to provide

water isolation. The gauge is destroyed shortly after the detonation, which is the reason why only

the raise of the pressure curve is reliably recorded.

3.2.4 VOD measurement

The in-hole velocity of detonation VOD is measured from in-hole explosive columns in both

surface and underground test sites. The measurement is done through the variation in impedance

of a coaxial cable placed along the explosive column. This cable, which has a constant

impedance per unit of length, is progressively destroyed as the explosive detonates from the

lower end of the blasthole. The conductive plasma created at the detonation front shortens the

circuit as the cable is consumed, allowing the continuous measurement of impedance. Thus, the

reduction in length of the cable is determined by measuring its change of impedance with a high

speed recording unit (usually at a recording rate of 10 MHz). Finally, the VOD is easily

calculated as the change in length of the cable per unit of time (MREL 2005).

3.2.5 Cross-hole seismic system

Blast-induced damage is quantified through the variations in P-wave velocity in the rock mass

caused by the cracks and microcracks generated from the blast, as described in section 2.4.4.

This system is employed only at the surface test site, where P-wave velocities are determined by

measuring wave travel times between a source and a series of receivers in the rock mass.

The measurements are executed between several pairs of monitor holes in the vicinity of the

blasthole before and after blasting. The seismic source is produced by a small amount of

explosive (detonator by shock tube) and the seismic signals (and thus their arrival times) are

49

measured by pressure sensitive piezoelectric sensors. Sensors and sources are always placed

under water for better coupling and consistency of measurements. Typically, four arrays or four

receivers each are used with every source, totaling up to 16 velocity measurements per explosive

source. Figure 21 shows a schematic view of one array of receivers and one source, indicating

the main components of the cross-hole system.

Figure 21. Cross-hole system layout.

Source: Detonator

Receivers: Piezoelectric sensors

Source-receiver Ray-paths

Recording unit

Firing device

Shock tube

Natural water table

50

3.2.6 Data acquisition systems

Five different types of high-speed multi-channel data acquisition (DAQ) systems are utilized to

record signals from the various sensors used in field experiments: MREL DAQ systems

DataTrap II and MicroTrap; Kyowa analog recorder model RTP-650A; Measurement Computing

DAQ board model USB-1608HS; and Agilent oscilloscope model 54624A. The main

specifications of these devices and the tests they are used to record are indicated in Table 3.

Table 3. Data acquisition systems technical information Specification DataTrap II MicroTrap Analog

recorder RTP-650A

Board USB-1608HS

Oscilloscope 54624A

Manufacturer MREL Specialty Explosive Products Limited

MREL Specialty Explosive Products Limited

Kyowa Sensor System

Solutions

Measurement Computing Corporation

(MCC)

Agilent Technologies

Data acquisition Type

Digital Digital Analog (betamax

tapes)

Digital Digital

Stand-alone recording

Yes Yes Yes No (computer required to operate)

Yes

Internal battery

Yes Yes No No No

Maximum recording rate per channel

10 MS/s 1 MS/s (2 MS/s for

VOD)

- 250 kS/s 200 MS/s

Maximum frequency response

- - 40 kHz - -

Total number of channels per unit

8 4 8 14 4

Total number of units utilized

1 1 2 2 1

Tests recorded Seismic activity, expl. gas pressure,

VOD, det. front pressure, cross-hole

VOD, cross-hole

Seismic activity

Seismic activity,

explosive gas pressure

Cross-hole

51

3.3 Field test sites The experimental program of this research work was carried out at two tests sites. The first one

corresponds to an open area with relatively flat exposed natural rock. Here, blast experiments

were conducted in vertical boreholes to measure the main physical phenomena taking place

during and as a consequence of blasting (i.e., stress waves, gas expansion, and blast-induced

damage). The other test site corresponds to an operating underground mine, in which several

boreholes were specifically drilled with the purpose of installing seismic instrumentation and

executing controlled blast experiments. Additionally, regular production blasts were monitored

in terms of seismic activity at this mine. A detailed description of both test sites is presented in

this section.

3.3.1 Surface test site

This test site is located near the town of Verona about 50 km north of Kingston, Ontario. The

specific test area consists of a relatively flat rock outcrop with 27 vertical boreholes drilled from

the surface of approximately 12 m2. The boreholes are 6 m in depth and have a nominal diameter

of either 45 or 75 mm. Figure 23 shows a plan view of the test site indicating the relative

locations of boreholes. Figure 22 shows a general view of the test area.

Figure 22. General view of the surface test site.

52

Figure 23. Surface test site plan view. Distribution of boreholes. 45 and 75 mm boreholes are identified with the nomenclature B45 and B75 respectively.

The natural rock in this test site corresponds to a massive granite with few joints. Although the

area used for the study is relatively flat, the surrounding rock surface is undulated and partly

covered with layers of soil and vegetation. The maximum difference in elevation of any two

borehole collars is 0.4 m and the standard deviation of the collar elevations is 0.13 m. Also, there

is an underground water table in the area, approximately 2 m below surface. The presence of

natural underground water resulted to be an advantage for the blast experiments, as it provided

better conduction of seismic and pressure signals, as well as better explosive and instrument

coupling (e.g. cross-hole and detonation front pressure sensors). Consequently all experiments

were carried out under water.

The experiments in this test site correspond to small-scale blasts in the natural rock mass

specifically designed to study the mechanisms of damage in the near field by blasting (within

~1 m from the explosive). A total of 11 blasts with various amounts of explosive were monitored

B45.01

B45.03

B45.07

B45.08

B45.13

B45.14B45.11

B45.17

B45.18

B45.20

B45.22

B45.23

B45.25B45.27

B75.02

B75.04

B75.05

B75.06

B75.09

B75.10

B75.12B75.15

B75.16

B75.19

B75.21 B75.24

B75.26

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5E (m)

N (m

)

53

with a variety of instruments to characterize explosive performance, stress waves and damage.

The experiments correspond to single-hole blasts with point (short) and line sources of explosive

inserted in selected blastholes. The list of experiments is as follows:

• 2 charges of 0.1 kg emulsion in φ45 mm boreholes (90% coupling)

• 2 charges of 0.5 kg emulsion in φ45 mm boreholes (90% coupling)

• 1 charge of 0.1 kg emulsion in φ75 mm borehole (90% coupling)

• 1 charge of 0.5 kg emulsion in φ75 mm borehole (90% coupling)

• 2 charges of 1.6 kg (2 m length) of emulsion in φ45 mm boreholes (67% coupling)

• 2 charges of 19 g/m det. cord (double ~10 g/m), 2 m length in φ45 mm boreholes

• 1 charge of 38 g/m cord (quadruple of ~10 g/m), 2 m length in φ45 mm boreholes

Figure 24 shows a fully assembled 500 g cartridge of explosive to be inserted in a φ45 mm

borehole. In this particular test the detonator (initiated by shock tube) is inserted through a hole

at the bottom of the cartridge (right side) in order to achieve bottom initiation. Sand is used at the

bottom of the cartridge to provide additional weight to the assembly. Additionally, a VOD cable

is inserted through the explosive and carbon resistors to measure in-hole pressure on top of it.

Figure 24. Explosive assembly corresponding to 500 g of emulsion to be inserted in φ45 mm borehole.

Figure 25 shows a 3D view of the borehole array indicating explosive charge locations. The

complete list of experiments executed is detailed in Appendix D, including charge location,

amount and type, borehole diameter, instrumentation and relative location of accelerometers

respect to the explosive charge.

Carbon Resistors Emulsion Sand for weight

VOD cable

Detonator

Shock tube

54

Figure 25. 3D view of boreholes (φ45 mm in red & φ75 mm in yellow) indicating explosive charges (emulsion in blue & det. cord in green). Frame box dimensions (for reference) are 5 m width, 4 m depth and 7 m height.

Figure 26 shows schematically a typical experimental setup for this test site. The measurements

executed are briefly explained as follows:

• Acceleration time histories: Near field seismic radiation from blasting measured by 500

g and 1000 g triaxial accelerometers (types 2, 3 and 4 in Table 2, section 3.2.1) with the

purpose of obtaining information on amplitude and frequency content for different wave

types (e.g. P and S-waves) and material properties (e.g. wave velocities and attenuation).

This information is also used to calibrate the in-hole pressure function.

• Gas penetration: Pressure sensors are installed in adjacent sealed boreholes and gas

pressure is measured in order to assess blast damage. The method relies on the

propagation of gases through a fracture network including both pre-existent and blast

created fractures. Thus, the recording of gas pressure at various distances from the source

provides an indication of the extent of the blast-induced damage. The sensors employed

for these measurements are 30 and 100 psi silicon sensors (see section 3.2.2).

1 m cube

55

Figure 26. Experimental setup in surface test site.

• Detonation front pressure: The in-hole explosive pressure is measured with water

coupled carbon resistors placed at various distances from the top of the explosive (see

section 3.2.3). The resultant pressure history (reliable only up to the peak pressure) is

used in the determination of the pressure function for numerical models.

• In-hole Velocity of Detonation: The in-hole velocity of detonation, VOD is measured by

inserting a cable with constant resistance per length unit, into or next to the explosive

column, as described in section 3.2.4. The change in length of the cable produced by the

detonation of the explosive is determined by continuous measurement of the cable

impedance, thus providing a continuous VOD. The obtained values are later used in

numerical models (Figure 48).

Recording unit

Water level

Firing device

Source: Emulsion

Shock tube

Triaxial Accelerometer (spring loaded)

Pressure sensor

Seismic signal

Power supplies / signal conditioners

VOD cable

Carbon resistors

VOD

56

• Cross-hole: Pre and post blast damage evaluation is carried out through cross-hole

measurements as described in section 3.2.5. Three tests were selected to carry out these

measurements, corresponding to explosive charges of 0.1, 0.5 and 1.6 kg of emulsion.

Between 81 and 192 signals (i.e., from pairs source-receiver) were recorded in each case.

The results from the experiments executed at this test site are included in Chapter 4.

3.3.2 Underground mine

Starting in January 2007, the Engineering Geoscience Group at the University of Toronto,

through its Department of Civil Engineering, carried out a full-scale study oriented to improve

the design and operations related to cemented paste backfill (CPB) as a stope filling material.

The first stage of the study was executed at Williams mine, one of the largest gold-producing

mines in Canada, with ~10,000 tonnes of ore per day. The research project included the

monitoring of CPB throughout its curing phases with a variety of instruments (pressure cells,

thermometers, piezometers, electrical conductivity probes, etc.) as well as blast monitoring in

both rock and CPB. Results have been published in a number of papers and reports (Bawden et al

2010, Grabinsky et al 2008a, 2008b & 2008c, Grabinsky & Thompson 2009, Grabinsky 2010,

Mohanty & Trivino 2009, Thompson et al 2009, Thompson et al 2010, Trivino & Mohanty 2009,

Witterman & Simms 2010). The blast program included numerous single-hole experiments and

multiple-hole production blast monitoring, as well as a detailed investigation of the seismic

transmission and response characteristics in both rock and CPB. The results of the blast

monitoring program in rock are presented in Chapter 4 and Chapter 6 of this thesis. A detailed

description of this test site, including experimental setup is included in this section.

3.3.2.1 Test site description

The blast monitoring program was executed at depths between approximately 750 and 900 m

from surface. The values of P and S-wave velocities in rock typically obtained at the mine are

around 6000 and 3400 m/s, respectively. The major rock units strike E-W and dip 60° to 70° to

the north. The main rock types consist of interbanded metasedimentary rocks with amphibolite

and feldspathic (granitic) intrusives. The principal far field stresses for the area of the test site, as

considered for mine design, are summarized in Table 4 (note that orientations are referred to the

local coordinate system specific for this mine).

57

Table 4. Principal stresses at Williams mine Stress Component Magnitude Orientation (Trend / Plunge)

σ3 (MPa) 0.0214 * Depth (m) 250 / 60 (closest to vertical)

σ1 / σ3 ratio 2.0421 358 / 10 (nearly N-S)

σ2 / σ3 ratio 1.3972 093 / 28 (nearly E-W)

Five regularly occurring joint sets (foliation) are present at the mine. These are summarized in

Table 5.

Table 5. Regular joint sets at Williams mine Joint set Description

A Set Parallel to the orientation of the rock fabric, locally visible as foliation or bedding depending on the rock unit. Rock foliation ~110°, ~65°N. Spacing varies from 0.1 to 0.5 m, averaging 0.2 m

B Set Nearly vertical joints striking roughly North-South and dipping sub-vertically parallel to the major diabase dykes. Spacing ranges from 0.3 to 2.0 m, averaging 0.5 m

C Set Relatively flat lying joints dipping 15° South. Spacing ranges from 0.3 to 1.0 m

D Set Strikes North-South and dips East at approximately 47°

E Set Strikes North-South and dips West at approximately 45°

The blast monitoring program was divided into two parts: single charges of explosive (single-

hole blasts) and production blasts with multiple holes. Thus, damage potential within the rock

mass was studied through the monitoring and analysis of blast-induced seismic waves and their

dependency on time and distance (Trivino & Mohanty 2009, Trivino et al 2010).

18 single-hole control blasts and 16 regular production blasts were monitored with triaxial wide

frequency band accelerometer stations embedded in rock. A typical arrangement for transducer

assembly for in-hole placement is shown in Figure 17. Up to 32 multi-channel high-frequency

(>40 kHz) analog and digital data acquisition systems were used in the investigation. Because of

the high-resolution recording, all the individual delay rounds in the production blasts could be

clearly identified. Although blast monitoring involved a total of 34 blasts, the high-resolution

recording employed in the study effectively led to analysis of a total of 550 blasts, as each hole

in a production blast round could be clearly identified and analyzed individually.

58

Figure 27. Geometry and experimental layout at Williams mine.

Figure 27 shows the geometry of the test area indicating the location of accelerometer stations,

single-hole charges and production blast charges. The triaxial accelerometers in rock were

grouted in boreholes and their orientation of was carefully controlled. The acceleration range of

the sensors is 100 g and the frequency range is from 0.5 Hz to 10 kHz (Type 1 in Table 2).

3.3.2.2 Single-hole blasts

A total of 18 single-hole blasts (also referred to as control blasts) were executed at different

depths along a single 140 m long, 60 mm diameter blasthole (Figure 27). Its orientation is nearly

parallel to the main rock units with a trend of 357° and a plunge of 73°. Two types of explosive

were used: 220 g Pentolite (PETN / TNT) boosters (in strings from one to four boosters, 220 to

880 g, 11 blasts) and strings of φ=40 mm, L=400 mm emulsion cartridges (7 blasts). The

emulsion cartridges were assembled in line in lengths of 0.4 m (single cartridge, 0.56 kg, 3

blasts), 3 m (7.5 cartridges, 4.2 kg, 2 blasts) and 6 m (15 cartridges, 8.4 kg, 2 blasts).

Accelerometers

Overcut

Undercut

Monitor Holes

Blasthole

Single-hole Explosive charges

A B

B89 Production Blast Stope

Production Holes

10

9

CPB filled Stope

59

All explosive charges were lowered by a cable into the blasthole, and no stemming or sealing

material was used below or above the explosive. Also, all the blasts were initiated with shock

tube detonators and ignited under water. The specifications corresponding to the utilized

explosives are provided in Table 6.

Table 6. Explosive properties at Williams mine Properties Explosive

Type Pentolite Booster Emulsion Cartridges

Weight 220 g 560 g

Dimensions φ = 46 mm, L = 130 mm φ = 40 mm, L = 400 mm

Density 1.6 g/cm3 1.11 g/cm3

Velocity of Detonation (VOD) 7500 m/s 5500 m/s (*)

Detonation Pressure (**) 22.5 GPa 8.4 GPa

(*) In hole VOD measured for 40 mm cartridges; (**) Calculated values.

3.3.2.3 Multiple-hole production blasts

Seismic radiation from 16 multiple-hole blasts executed for the production of a stope in the test

area were successfully monitored at the mine. The production stope (shown in Figure 27) is

located around 30 m east of the closest sensor. The mining method corresponds to long-hole

stoping, which consists on developing a large sub-vertical hole along the stope (raise) to then

execute the main excavation by blasting smaller sub-horizontal holes drilled from the raise. In

this case the raise is sub-vertical along the ore body, which dips 70° north. The smaller

blastholes are 65 mm in diameter, plunging 20° and drilled in a 'fanned' fashion at different

levels (rings) (Figure 27 and Figure 28).

Figure 28. Typical distribution of blastholes in a production ring (~20 m x 6 m, plan view). Numbers in parenthesis indicate delay number (x 25 ms). All holes plunging 20° from collar to toe.

Stope Boundary

60

Typically, each production blast corresponded to the excavation of 1 to 4 rings, with a total of

600 to 1000 kg of explosive per blast. The amount of explosive per delay varied from 17 to 68

kg. In all cases the blasts were initiated with 30 g/m detonating cord connected to a 90 g booster

at the toe, as shown in Figure 29.

Figure 29. Initiation method for Production Blasts (drawing facilitated by Williams Operating Corp).

The summary of monitored and total production blasts in this stope is as follows:

• Number of production blasts: 16 / 28

• Number of blastholes: 532 / 942

• Number of rings: 41 / 75

• Total amounts of explosive: 9,600 / 18,000 kg

• Explosive types: Emulsion (both cartridged and bulk loaded) & Water Gel

(bulk loaded)

where the first number corresponds to the successfully monitored production blasts and the

second number is associated with all the production blasts in this particular stope.

61

Chapter 4

4 Seismic Radiation from Blast and Damage in Rock: Results from Single-hole Controlled Experiments

This chapter corresponds to the results obtained from field experiments executed at the surface

test site and the underground mine, as described in Chapter 3. These experiments include

measurements of seismic radiation, in-hole detonation pressure, VOD, gas activity, and

variations in wave velocities to assess blast-induced damage. The assessment of seismic waves is

later utilized for the calibration of numerical models and the damage measurements are

specifically studied with the results from these models to assess the relative contribution of stress

waves and gas penetration to damage (Chapter 5).

4.1 Measurement of seismic radiation The results contained in this section correspond to seismic activity measured from single-hole

control blasts executed at both surface and underground test sites. All these measurements were

executed with accelerometer stations as described in section 3.2.1. The accelerometer types

(according to Table 2) and mounting system used in each test site are as follows:

• Surface test site: Accelerometers type 2, 3 and 4, spring loaded

• Williams mine: Accelerometers type 1, grouted

A total of 29 single-hole blast experiments (also referred to as control blasts) were successfully

executed and recorded in both test sites altogether (11 at surface test site, 18 at Williams mine).

All control blasts were water coupled. A complete summary of the control blasts executed in

both test sites is included in Appendix D.

The recorded vibration data is analyzed in terms of both particle acceleration and particle

velocity. Acceleration data is converted to velocity through numerical integration. However, in

such conversions, any DC drift in the acceleration record often adds significant error to particle

velocity values. Thus, as common practice, a numerical filter is applied during the integration

process to eliminate this effect. Throughout this work, a sharp Butterworth high-pass filter is

applied to the seismic signals. The threshold used for this high-pass filter is typically 100 Hz or

62

less, so as to minimize baseline shift over time. PPV values were found to be not significantly

affected by this filter, due to the relatively low energy content in the low frequencies.

Figure 30 shows the acceleration time histories recorded by the three components of an

accelerometer station at the surface test site during a control blast. The explosive charge

corresponds to 100 g of emulsion and the sensor is located at 3 m from it.

Figure 30. Recorded three components of acceleration for a single charge of 100 g of emulsion at surface test site. r = 3.0 m, θ = 44° (coordinates according to Figure 32). Component Ay is vertical (‘A’ denotes accelerometer id, and xyz its specific orthogonal coordinate system).

Likewise, Figure 31 shows the recorded three components of acceleration from a 6 m length

column of 40 mm diameter emulsion cartridges. The direct distance from source to sensor in this

case is 49.8 m.

Figure 31. Recorded three components of acceleration for a single charge of 4.46 kg of emulsion at Williams mine. r = 49.8 m, θ = 167° (coordinates according to Figure 32). AV denotes (approximately) vertical component, (‘A’ denotes accelerometer id, and VLT its specific orthogonal coordinate system).

-3

-2

-1

0

1

2

3

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Surface Test 2 - AzChannel 6 10 mV/g 500,000 Hz

Volta

ge (V)

Time (ms)

-4

-3

-2

-1

0

1

2

3

4

5

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Surface Test 2 - AyChannel 5 10 mV/g 500,000 Hz

Volta

ge (V)

Time (ms)

-3

-2

-1

0

1

2

3

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Surface Test 2 - AxChannel 4 10 mV/g 500,000 Hz

Volta

ge (V)

Time (ms)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

7.5 10.0 12.5 15.0 17.5 20.0

Williams Control Blast 9 - ATChannel 6 50 mV/g 100,000 Hz

Volta

ge (V

)

Time (ms)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

7.5 10.0 12.5 15.0 17.5 20.0

Williams Control Blast 9 - ALChannel 5 50 mV/g 100,000 Hz

Volta

ge (V

)

Time (ms)

-1.00

-0.75

-0.50

-0.25

-0.00

0.25

0.50

0.75

1.00

7.5 10.0 12.5 15.0 17.5 20.0

Williams Control Blast 9 - AVChannel 4 50 mV/g 100,000 Hz

Volta

ge (V

)

Time (ms)

63

4.1.1 Identification of body waves

Three methods were utilized to identify body waves from control blasts: analysis of direction of

particle motion, rotation to spherical coordinates, and P and S-wave arrival times. The first two

methods are related to the polarization properties of body waves from an axially loaded

cylindrical hole, whereas the third one is a verification of consistency of results. The three

methods are described in the following sections.

4.1.1.1 Rotation to spherical coordinates

As discussed in section 2.2.1 the axial loading of a cylindrical hole in a homogeneous and

infinite medium causes the generation of only P and vertically polarized S-waves. Vertically

polarized S-waves are such that the direction of particle motion lies on the plane containing the

cylinder axis and the direction of propagation. Thus, all the motion generated by an axially

loaded borehole at any point should be restricted to the plane that contains the borehole axis and

the observation point.

Although in practice it is not expected that the particle motion is totally contained on the plane

indicated (since this would require the medium to be perfectly continuous, homogeneous and

isotropic, and the loading to be identical around the perimeter of a perfect cylinder) the main

seismic waves are expected to be observed with clarity on this plane.

Based on this, the vectors of motion (velocity in this case) are expressed in spherical coordinates

with origin in the explosive charge, as shown in Figure 32. In this coordinate system, the P-wave

is expected to be preferably along the r direction, whereas the vertically polarized S-wave is

expected to generate motion along the θ direction. In the subsequent sections of this thesis, the

plane containing the borehole axis and the point of observation is referred as the r -θ plane.

Also, the relative location of an observation point with respect to the explosive charge is

indicated by the distance r and the angle θ (hereafter referred to as azimuth) shown in Figure 32.

64

Figure 32. Spherical coordinates system used to express the results of acceleration and velocity. The origin of coordinates is chosen to be the center of the explosive charge.

Figure 33 shows the 3 spherical components of velocity time history for a single-hole blast in

direct mode. As expected, the P-wave is dominant in the r direction, while the S-wave is

dominant in the θ direction. The φ component exhibits non-negligible amplitudes, particularly

with the arrival of the P-wave. This situation is commonly observed and is attributed to material

and borehole imperfections, errors in the coordinates and orientation of borehole and sensor, and

possibly the uneven load distribution and fracture creation from the blasthole.

Figure 33. Components r , θ and φ of velocity for a single shot, 6m explosive column, direct primed, executed at Williams mine. r = 34 m, θ = 19°.

5 10 15 20-40

-30

-20

-10

0

10

20

30

Time (ms)

Velo

city

(mm

/s)

5 10 15 20-100

-50

0

50

100

Time (ms)

Vel

ocity

(mm

/s)

P-wave S-wave

r θ5 10 15 20

-40

-20

0

20

40

60

Time (ms)

Vel

ocity

(mm

/s)

φ

65

4.1.1.2 Analysis of direction of particle motion

The identification of wave types through coordinate rotation as shown in the previous section

may not provide accurate results for the arrival time of S-waves in certain cases. This is

particularly true in the presence of significant noise, low S-wave amplitudes and deviations from

the theoretical direction of motion (caused for example, by presence of geological

discontinuities). For the accurate identification of wave types and arrival times, the author

developed a visual method based on the analysis of direction of particle motion from 3-

component vibration data. The method consists on using a technique of map projection to plot

vectors of particle velocity and thus identify wave types from their amplitude and direction of

particle motion. Although several types of projection are available, the author utilizes the

Lambert Azimuthal Equal Area Projection, which along with the stereographic projection is

commonly used for the analysis of geological data. The method developed by the author is

described in detail in the following paragraphs.

The general procedure consists of plotting vectors of particle velocity from the recorded 3

components of seismic signals on an Equal Area (Schmidt) Stereonet (hereinafter referred to

simply as stereonet). For this a time frame containing the signal of interest is chosen and

discretized in a number of data points (each data point having three components), which are

plotted in the stereonet. As each data point is a vector with a specific magnitude, a contour plot is

drawn by tracing isolines associated with magnitude. In sequence, the steps required to plot a

contour stereonet from vibration data are as follows:

• Choose a time window for the vibration data containing the peak magnitude of the signal

of interest;

• Calculate the orientation (trend and plunge) and magnitude (absolute value) of the vector

velocity corresponding to each data point in the time window;

• Plot the orientation of these data points in a stereonet and keep record of its magnitude

(for two vectors with same orientation, only the vector with the highest magnitude

remains);

• Draw contour lines (isolines) of magnitude from the plotted data points

From this procedure, the peak of the contour plot will give the main direction of motion caused

by the wave under analysis. In addition to the particle motion contour plot, some other

66

orientations can be represented in the stereonet, such as borehole orientation and the previously

described spherical coordinate system. In this study stereonets correspond to upper hemisphere,

equal area projection and referred to an arbitrary coordinate system. The procedure to plot a

vector in an upper hemisphere stereonet is as follows:

At any given time the recorded seismic data can be written as:

=

φ

θθφ

VVV

Vr

r

4-1

Where Vr, Vθ and Vφ are the 3 orthogonal components of recorded vibration data (vector

velocity). Note that the symbols used here correspond to spherical coordinates as indicated in

Figure 32; however, the procedure is valid regardless of the coordinate system. The orientation

of each component of velocity must be, however, known and referred to a global or local

coordinate system. If the components of velocity are referred to a coordinate system in terms of

East (E), North (N), and Elevation (Z) as follows:

=

Z

N

E

rrr

r ,

=

Z

N

E

θθθ

θ , and

=

Z

N

E

φφφ

φ 4-2

Thus the vector velocity can be written as:

θφr

Z

N

E

ENZ VVVV

V

Q=

= 4-3

where Q is the rotation matrix defined as:

φθ ˆˆr=Q 4-4

Thus, the orientation of the vector velocity can be written in terms of its plunge and trend as

follows:

67

+=

22arctan

NE

Z

VV

VPlunge 4-5

ϕ+

=

N

E

VVTrend arctan 4-6

where

( ) ( ) ( )

( ) ( ) ( ) ( )

←°==←°

==←°=

otherwiseVVorVVelseif

VVVif

ZENE

ZNE

360signsignsignsign180

signsignsign0ϕ

( )( )( )quadrant

quadrantsorquadrant

th

rdnd

st

432

1 4-7

where quadrants refer to those in the stereonet starting with the N-E quadrant and advancing

clockwise. Figure 34 illustrates an example of stereonet showing the projection of a vector on it.

The mesh included corresponds to a polar mesh, which is practical to measure angles directly

from the stereonet.

Figure 34. Example of plotting an equal area projection, upper hemisphere stereonet with polar mesh.

Figure 35 shows stereonets constructed for the analysis of direction of motion for a single shot at

the surface test site. The figure also shows the blasthole orientation, indicated as B, and the

orientations of the spherical coordinate system with origin at the center of the blasthole, ( r , θ ,

φ ). In this case the blasthole is vertical and the sensor is located nearly horizontally to the west

from the blast. Consequently, r and θ directions are nearly E-W and vertical, respectively.

Trend 52° Plunge 40 °

=

4.541.5

ENZV

4.8=ENZV

quadrantst1

quadrantnd2quadrantrd3

quadrantth4

68

The main direction of motion of the first signal (Figure 35a) is very close to the radial directions,

confirming this signal as a P-wave. This result is not surprising, since P-waves are usually easy

to identify. The method is particularly useful for the identification of S-waves. In this case,

another later major peak shows a direction of motion close to the θ directions (Figure 35b),

which allows a preliminary identification of this signal as S-wave.

Figure 35. Identification of P and S-waves by analysis of the direction of particle motion for a single shot, 100 g emulsion, executed at the surface test site. r = 3.2 m, θ = 82°. The time window is indicated by highlighting the corresponding signal shown below the stereonet. Direction B corresponds to the blasthole orientation. r , θ , φ correspond to unit vectors in spherical coordinates as shown in Figure 32.

4.1.1.3 P and S-wave arrival times

The initiation time for all control blasts was accurately recorded, allowing precise determination

of arrival times of the seismic waves. As a method of control for the identification of P and S-

waves, their arrival times (first breaks) were plotted against distance from source (point of

initiation) to sensor, as shown in Figure 36. These graphs show consistency of arrival times for

both P and S-waves, which supports their correct identification. The higher scatter observed for

S-waves is attributed to the difficulties in picking the arrival time of these waves, mainly due to

the noise caused by waves with earlier arrivals (i.e., coda of P-wave and in some cases P-wave

reflections). The range of source-sensor distances in the experiments is shown in Figure 36.

These ranges are from 1-3.5 m at the surface test site to 30-110 m at Williams mine. The results

for P and S-wave velocities for each test site are shown in the respective graphs in Figure 36.

a) P-wave b) S-wave

Velocity Velocity

69

Figure 36. P and S-wave velocities obtained for each test site.

4.1.2 Amplitude of seismic waves

Figure 37 and Figure 38 show the values of PPA and PPV for P and S-waves vs. scaled distance

in root square form (Equation 2-19), for the experiments conducted at both test sites. The

summary of these tests including explosive amount and relative location of accelerometers can

be found in Appendix D. This section contains a general analysis of variations in peak

amplitudes of seismic waves with scaled distance and explosive type. Specific analysis of

frequency content, initiation mode, charge length and orientation are discussed in detail in

sections 4.1.3 to 4.1.5.

Figure 37 shows the results corresponding to the surface test site, including short and long

charges of emulsion and long charges of detonating cord. The short charges correspond to

amounts from 100 to 500 g of explosive in φ45 and φ75 mm boreholes (~90% coupling). Long

charges of emulsion are 1.6 kg and 2 m long detonated in φ45 mm boreholes (67% coupling).

Detonating cord charges are also 2 m long with either 41 or 82 g of explosive. All accelerometers

are spring loaded in boreholes, with the exception of those recording the long charges of

emulsion, which are surface mounted (screwed in).

The results from short charges clearly indicate a trend of increasing PPA and PPV with

decreasing scaled distance for both P and S-waves. Also, there is no significant difference

between the amplitudes of P and S-waves. The results from detonating cord indicate higher

V P = 6.23 km/sR 2 = 0.9957

V S = 3.61 km/sR 2 = 0.9875

0

20

40

60

80

100

120

0 10 20 30

Arrival Time (ms)

Dis

tanc

e S

ourc

e - S

enso

r (m

)

V P = 5.90 km/sR 2 = 0.9914

V S = 3.34 km/sR 2 = 0.9453

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.2 0.4 0.6 0.8 1.0

Arrival Time (ms)

Dis

tanc

e S

ourc

e - S

enso

r (m

)

a) b)

Surface Williams

70

amplitudes, compared with emulsion in terms of both PPA and PPV, which is attributed to the

higher strength of the former explosive (PETN). Two long charges of emulsion show

significantly lower amplitude in terms of PPA, but similar in terms of PPV, compared to short

charges. This disparity between PPA and PPV is mainly attributed to the difference in frequency

content of long and short charges for a given scaled distance. Effectively, the long charges in

question have a larger amount of explosive than short charges, which means longer source-

sensor distance for equal scaled distance, and hence lower frequency content. Thus, when

integrating the acceleration data, the lower amplitude and lower frequency signals from long

charges are transformed into relatively higher velocity time histories compared to those from

short charges. The frequency content of different signals is further discussed in section 4.1.3.

Figure 37. Peak Particle Acceleration (PPA) and Peak Particle Velocity (PPV) as a function of Scaled Distance. Surface test site.

The results of PPA and PPV from Williams mine are shown in Figure 38. The experiments

include short (0.4 m) and long (3 and 6 m) charges of emulsion (67% coupling) as well as short

strings of pentolite boosters (1 to 4 boosters per shot, 63% coupling) in a 60 mm borehole. These

results indicate that the amplitudes (both PPA and PPV) associated with P-waves are always

larger than those for S-waves (average S/P ratio, i.e., ratio of S-wave peak amplitude to P-wave

peak amplitude, is 0.25). This is mainly attributed to the sharp angle between the blasthole axis

10

100

1000

10000

1 10 100

Scaled Distance, R/w1/2 (m/kg1/2)

PP

A (g

)

10

100

1000

1 10 100


PP

V (m

m/s

)

P-wave Emulsion long P-wave Emulsion short P-wave Det Cord

S-wave Emulsion long S-wave Emulsion short S-wave Det Cord

Surface mounted sensor

a) b)

71

and the direction source-sensor (between 3° and 22°) which causes relatively low amplitudes of

S-waves. This phenomenon is further discussed in section 4.1.5.

As in the case of detonating cord, the results obtained from pentolite boosters show higher

amplitudes than those from emulsion due to the higher detonation pressure of the former. Also,

the results from long charges of emulsion exhibit a high dispersion of results in both graphs. This

is mainly attributed to the variations in initiation mode as explained in section 4.1.5.

Figure 38. Peak Particle Acceleration (PPA) and Peak Particle Velocity (PPV) as a function of Scaled Distance. Williams mine.

4.1.3 Frequency content of seismic waves

The frequency content of seismic waves is calculated by applying the Fast Fourier Transform

(FFT) to the recorded signals. In this work the procedure is applied to both acceleration and

velocity time histories in the radial direction (or close to radial, when the three accelerometer

components are not available). Analyses executed over directions other than radial were verified

and do not provide significant variations in the results. As an illustrating example, Figure 39

shows the radial component of velocity from a single cartridge of emulsion executed at Williams

mine and its corresponding amplitude. Note that the absence of tow frequencies in the spectrum

is due to the application of a 100 Hz high-pass filter, as mentioned earlier.

0.1

1

10

100

1000

1 10 100 1000


PP

A (g

)

0.1

1

10

100

1000

1 10 100 1000


PP

V (m

m/s

)

P-wave Emulsion long P-wave Emulsion short P-wave Boosters

S-wave Emulsion long S-wave Emulsion short S-wave Boosters

a) b)

72

Figure 39. Radial components of velocity for a single cartridge of explosive and its amplitude spectra. Charge: 0.56 kg, 0.4 m of emulsion. r = 32 m θ = 21°.

Although the complete information on frequency content of any waveform is contained in its full

spectrum diagrams (both amplitude and phase spectra), the comparison of a large number of

waveforms through these diagrams may become cumbersome. For this reason the average

frequency of the amplitude spectrum is used as a variable for most of the following analyses.

The average frequency is calculated from the amplitude spectrum as the weighted average of

frequencies according to the following equation:

∑∑ ⋅

=)(

)(

i

ii

fAfAf

f 4-8

where f is the average frequency (Hz), if represents the individual frequencies in the spectrum

(Hz), and )( ifA is the amplitude associated with each frequency if . In order to prevent noise

from severely affecting the average frequency, only frequencies with amplitudes greater than

20% of the peak amplitude in the spectrum were considered. The arrow shown in the spectrum

diagram of Figure 39b indicates the calculated average frequency.

Figure 40 shows the average frequencies of the signals recorded in both test sites in terms of

acceleration and velocity. The data includes only experiments executed with emulsion. The

results indicate average frequencies between 2 and 13 kHz in terms of acceleration and between

0.8 and 5 kHz in terms of particle velocity, excluding the results from surface mounted sensors.

5 10 15-15

-10

-5

0

5

10

15

Time (ms)

Vel

ocity

(mm

/s)

r^

0 5 100

0.1

0.2

0.3

0.4

0.5

Frequency (kHz)

|Vel

ocity

(mm

/s)|

a) b)

73

From this data, the range of distances for a particular test site or blast type (long or short charges)

seems to be too short to determine a reliable trend, given the large dispersion of results. Variation

of frequency with distance is further analyzed in Chapter 6 with data corresponding to

production blasts, which comprises a much wider range of distances. The large amount of data

collected from these blasts allowed the identification of a trend of decreasing average frequency

with distance, despite the high dispersion of values (see Figure 81).

Figure 40. Average Frequency of Acceleration and Velocity as a function of Distance. Summary of both test sites considering charges of Emulsion.

4.1.4 Short vs. long charges

Figure 41 shows the combined results of PPA and PPV for both test sites, considering

experiments done only with Emulsion. In this case the values of PPA and PPV were obtained as

the highest between the corresponding values obtained for P and S-waves. From these graphs it

is apparent that despite the different rock and explosive types and various test conditions, the

signals in both test sites follow approximately the same trend. This similarity is particularly

significant in the case of PPV and most pronounced for short charges. This finding supports the

consistency of the data, as both test sites present competent rock with similar P-wave velocities

from 5.9 to 6.2 km/s (Figure 36), and the explosive types have similar detonation properties

(emulsion in both cases).

100

1000

10000

100000

1 10 100

Distance (m)

Avg

.Fre

quen

cy o

f Vel

. (H

z)

100

1000

10000

100000

1 10 100

Distance (m)

Avg

.Fre

quen

cy o

f Acc

. (H

z)

Direct primed

Surface mounted

Direct primed

Surface mounted

Surface long Williams long

Surface short Williams short

a) b)

Reverse primed

Reverse primed

74

Figure 41. Peak Particle Acceleration (PPA) and Peak Particle Velocity (PPV) as a function of Scaled Distance. Summary of all test sites considering charges of Emulsion and Water Gel.

In terms of PPA, long charges exhibit a trend of lower amplitudes than short charges. In terms of

PPV this difference tends to vanish, due to the lower frequency content of the signals associated

with long charges. The exception to this rule is the case of reverse primed long charges, which

exhibit frequencies similar to short charges. Considering equal scaled distance, these relatively

high frequency and. low PPA signals produce lower PPV values than signals with higher PPA

(such as shorter charges) or lower frequency (such as direct primed long charges) (see Figure

40).

Although the matching trend of PPV for long and short charge somewhat validates the use of the

square root scaling law, it is important to keep in mind that blast-induced seismic signals are the

result of complex superposition of signals generated along the explosive column. Hence the

shape and peak amplitude of the signals for a given blast configuration and medium properties

vary not only with distance to the source but also with the relative location of the observation

point with respect to the source. This phenomenon is analyzed and discussed in the next section.

1

10

100

1000

1 10 100


PP

V (m

m/s

)

10

100

1000

10000

1 10 100


PP

A (g

)

Reverse primed

Surface long Williams long

Surface short Williams short

a) b)

75

4.1.5 Effect of initiation mode (Direct / Reverse) and relative source-sensor location

As discussed in section 2.2.1, both analytical and numerical solutions to the problem of seismic

radiation from a cylindrical source (or lateral pressure source in the 2D case) indicate non

uniform wave amplitudes for varying angle between the direction of wave propagation and the

cylinder axis. In other words, in the case of borehole blasting, as the angle between the blasthole

axis and the direction source to point of observation changes, so does the shape and amplitude of

body waves. Although this has been proven in theory, including elastic (Heelan 1953, Abo-Zena

1977, Meredith 1990, Meredith 1993, Tubman 1984) and visco-elastic models (Blair &

Minchinton 2006), as well as visco-elastic model in a fracturing medium (Trivino et al 2009),

little experimental work has been previously done to verify this theory.

In geophysical exploration work, White & Sengbush (1963) carried out experiments in shale

sediments to determine relative amplitudes of P and S-waves from a cylindrical source,

comparing their results with the Heelan approach. These measurements were limited to the far

field, at distances over 90 m, in a medium with relatively low P and S-wave velocities (2100 and

900 m/s approximately). In the context of production blasting in mining, Trivino & Mohanty

(2009) carried out blast experiments in an underground mine (Williams) studying the

propagation of P and vertically polarized S-waves from blasting.

Figure 42 shows the amplitude and orientation of P and S-waves for various blast experiments

with relatively short charges of explosive (0.1 to 2 kg, 0.02 to 0.45 m long) executed in both test

sites. The lines plotted in each graph indicate the magnitude and orientations of the peak P and S-

waves projected on the r-θ plane (that is the plane containing the blasthole axis and the source-

sensor direction). The middle points of these lines indicate the relative location of the sensor with

respect to the source, with the blasthole axis being collinear with the vertical axis (labeled as

Distance z) and the explosive bottom initiated. All measurements were executed with triaxial

accelerometers and the results and analyses presented here are in terms of particle velocity.

These graphs show that for a variety of distances and orientations, S-waves are generally smaller,

but of amplitudes comparable to P-waves (S/P ratios usually higher than 0.5 and in many cases

close to 1). Exception to this is the case of very sharp angles between the blasthole and the

direction source-sensor, where recorded S/P ratios are between 0.1 and 0.35 (Figure 42c). The

76

cases where no S-wave amplitudes are shown (Figure 42a) are due to excessive noise in the

signals to reliably identify S-waves, and do not necessarily indicate low amplitudes for these

waves.

In contrast to the elasticity theory, measured S/P ratios are never significantly greater than 1,

even for angles close to 45°. The primary cause for this discrepancy is attributed to the presence

of material attenuation or damping in real materials, which attenuates S-waves faster than P-

waves and is not considered in the elastic models (Trivino et al 2009). Also, at angles close to

90° (perpendicular to the blasthole) S-waves still exhibit amplitudes close to P-waves (Figure

42a,b). This is at variance with analytical and numerical models (Trivino et al 2009) which

predict an S/P ratio equal to zero at 90° (i.e., no S-wave is generated in the direction

perpendicular to the blasthole). Two main reasons may explain this situation: first, the charges

are not exactly a point source (they are up to 0.45 m long), hence at any point of observation

there is always a portion of the explosive pressurizing the blasthole at an angle with respect to

the direction to the sensor (i.e., the direction of pressure application is not collinear with the

direction source-sensor); and second, given the rapid theoretical increase on S/P ratio for

increasing or decreasing angles from 90°, any small error in the calculation of this angle can lead

to a significant change in the S/P ratio.

The effect of initiation mode on the seismic signals was an important component of this study.

Specifically, differences in signals between direct and reverse initiation modes were studied.

Figure 43 shows the peak amplitudes of P and S-waves in various directions for several

configurations of long charges of explosive (2 to 6 m long). As before, in these graphs blastholes

are vertical with the explosive center at the origin of coordinates, and the arrows indicate the

direction of the explosive ignition (bottom initiation in all cases).

In all cases it is observed that the peak amplitudes of waves in direct mode (sensor above center

of explosive in these graphs) are larger than those in reverse mode (sensor below explosive

center) at similar distances. This is true for both P and S-waves. Also, the direct/reverse ratio is

observed to be greater for sharper angles with respect to the borehole axis.

77

Figure 42. Amplitude and orientation of P and S-wave PPV for short explosive charges, projected on the plane r -θ . In each case the center of the charge is located at (0,0) and the borehole axis is collinear with the vertical axis. The length and orientation of the lines labeled as P and S represent the maximum amplitude of the respective waves and their orientation represents the direction of particle motion at the time of the peak.

Finally, it is worthwhile to note the effects of the relative location and orientation of charges on

the variation in frequency content of the signals with initiation mode for long charges. In this

analysis the data from the surface test site is excluded due to the effect of surface mounting (in

all other cases accelerometers are mounted in boreholes). From Figure 40 it is possible to

observe that the results in direct primed mode tend to present lower average frequency of

acceleration than other cases. However, the high dispersion of results and the less obvious

differences in frequency of velocity with other cases do not permit one to conclude any

significant differences between direct and reverse initiation modes.

A comparison of waveforms and frequency spectra in direct and reverse mode for 6 m columns

of explosive recorded at Williams mine is shown in Figure 44. From the frequency spectra in this

figure it is obvious that there are significant differences on the distribution of frequencies

0 2 4-3

-2

-1

0

1

2

3

Scale400 mm/s

Distance x (m)

Dis

tanc

e z

(m)

0 2 4-3

-2

-1

0

1

2

3

Scale100 mm/s

Distance x (m)

Dis

tanc

e z

(m)

0 10 200

5

10

15

20

25

30

35

40

45

Scale5 mm/s

Distance x (m)

Dis

tanc

e z

(m)

a) Surface: 0.1 kg Emulsion

d) Williams: 0.56 kg Emulsion

b) Surface: 0.5 kg Emulsion

c) Williams: 0.9 kg Boosters

0 10 200

10

20

30

40

50

60

70

80

90

100

Scale5 mm/s

Distance x (m)

Dis

tanc

e z

(m)

S P

S

P

S

P

S

P

78

between the two initiation modes. While the direct initiation mode shows a strong concentration

of energy towards one particular frequency (1 kHz), the reverse mode exhibits a more or less

uniform distribution of peaks between 0 and 4 kHz, with an average of 2.2 kHz and a periodicity

of around 0.4 kHz.

Figure 43. Amplitude and orientation of P and S-wave PPV for long explosive charges, projected on the plane r -θ .

0 20 40-80

-60

-40

-20

0

20

40

60

80

Scale20 mm/s

Distance x (m)D

ista

nce

z (m

)

a) Surface: 0.04 kg, 2 m Det Cord

0.04 kg Emulsion d) Williams: 8.4 kg, 6 m Emulsion

b) Surface: 0.04 kg, 2 m Det Cord

c) Williams: 4.4 kg, 3 m Emulsion

0 0.5 1 1.5-3

-2

-1

0

1

2

3

Scale200 mm/s

Distance x (m)

Dis

tanc

e z

(m)

0 20 40-80

-60

-40

-20

0

20

40

60

80

Scale20 mm/s

Distance x (m)

Dis

tanc

e z

(m)

0 0.5 1 1.5-3

-2

-1

0

1

2

3

Scale200 mm/s

Distance x (m)

Dis

tanc

e z

(m)

S

P

0 2 4 6 8 10 12-5

-4

-3

-2

-1

0

1

2

3

4

5

Scale50 mm/s

Distance x (m)

Dis

tanc

e z

(m)

e) Surface: 1.64 kg, 2 m Emulsion

S

P

S P

S P

S

P

79

Figure 44. Radial components of velocity and their amplitude spectra. a) Direct mode, 8.4 kg, 6 m column of emulsion, r = 34 m θ = 19°; b) Reverse mode, 8.4 kg, 6 m column of emulsion, r = 47 m θ = 166°. Williams mine.

Similarly, Figure 45 shows the case of 3 m columns of emulsion in direct and reverse mode.

Although in this case the average frequencies are similar (1.8 vs. 2 kHz), once again the direct

mode shows a strong concentration of energy towards the average frequency whereas in reverse

mode at least 5 significant peaks are observed more or less periodically distributed between 0

and 5 kHz.

The differences observed between direct and reverse mode, in terms of both amplitude and

frequency content were found to be due to the superposition of waves originating along the

explosive column at varying time. These differences are mainly controlled by P-wave velocity,

velocity of detonation VOD, and the shape of the in-hole pressure function. In the case of the

examples shown, the P-wave velocities are higher but close to the explosive's VOD, leading in

direct mode for example to a constructive superposition of P-waves generated along the

blasthole. In contrast, in reverse mode the superposition of waves generated along the blasthole

is more destructive and hence, lower amplitudes are obtained. A detailed approach showing the

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

Frequency (kHz)

|Vel

ocity

(mm

/s)|

6 8 10 12 14 16 18-30

-20

-10

0

10

20

Time (ms)

Vel

ocity

(mm

/s)

r^

0 1 2 3 4 50

1

2

3

4

5

Frequency (kHz)

|Vel

ocity

(mm

/s)|

5 10 15-100

-50

0

50

100

Time (ms)

Vel

ocity

(mm

/s)

r^

6 m Reverse

6 m Direct

a)

b)

80

effects of initiation mode on waveform amplitudes and frequencies is included in Appendix F.

The approach is based on simple linear superposition of waves and even though it does not

constitute mathematical proof for the problem of wave superposition for different initiation

modes, it permits to understand variations on wave shape with relative location source observer.

Figure 45. Radial components of velocity and their amplitude spectra. a) Direct mode, 4.4 kg, 3 m column of emulsion, r = 62 m θ = 10°; b) Reverse mode, 4.4 kg, 3 m column of emulsion, r = 50 m θ = 167°. Williams mine.

4.2 Blasthole pressure function and VOD

Measurements of in-hole dynamic pressure and VOD were executed as described in sections

3.2.3 and 3.2.4. The in-hole pressure measurements were carried out at the surface test site with

500 Ω carbon resistors. A total of 8 signals were successfully recorded at 10 MHz sampling rate.

Figure 46 shows the recorded variation of voltage over time and the converted data to pressure-

time history (Equation 3-1) from a 0.1 kg emulsion charge, 90% coupling, in a φ45 mm

borehole.

10 12 14 16 18-60

-40

-20

0

20

40

Time (ms)

Vel

ocity

(mm

/s)

r^

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

1.2

1.4

Frequency (kHz)

|Vel

ocity

(mm

/s)|

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Frequency (kHz)

|Vel

ocity

(mm

/s)|

10 15 20-15

-10

-5

0

5

10

Time (ms)

Vel

ocity

(mm

/s)

r^

3 m Reverse

3 m Direct

a)

b)

81

Figure 46. Measured in-hole pressure. a) Raw data; b) Pressure-time history. Gauge (carbon resistor) is located 4 cm above the explosive column in a φ45 mm borehole. 0.1 kg emulsion, 90% coupling.

Figure 47 shows the results of in-hole peak pressure vs. distance from the top of the explosive

column. In all cases the explosive corresponds to bottom initiated emulsion. Measurements

include experiments with 90% coupling in φ45 and φ75 mm boreholes, and 67% coupling in a

φ45 mm borehole. The results of peak pressure vary between 0.3 and 1.6 GPa, for distances from

the explosive between 2 and 11 cm.

Previous research has shown values between 0.25 and 0.7 GPa for emulsion (Nie & Olsson 2001,

Olsson et al 2002), however, the author is of the opinion that those measurements should be

viewed with caution, as the researchers used a protective device that is likely to attenuate and

modify the signals from the shock wave (Nie 1999), as explained in 3.2.3. Even though the

results presented here are consistent and the method is more appropriate to determine the rise of

the in-hole pressure function, it is also recognized that the values of peak pressure obtained are

somewhat low (emulsion explosives have typical detonation pressure of ~7.5 GPa; with

decoupling values of at least 2-3 GPa should be expected, Mohanty 2012). A possibility is that

the peaks of the recorded pressure curves correspond to the sensors failure, but not to the actual

peak pressure; however, there is no evidence to support this idea. For this reason, the in-hole data

collected here is analyzed assuming that the first peak corresponds to the maximum pressure at

the sensors location. It is clear, however, that further research is required on these measurements.

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

0.014 0.015 0.016 0.017 0.018 0.019 0.020 0.021 0.022 0.023 0.024

DataTrapII Scope DataChannel 2 -10.0 V to 10.0 V 10,000,000 Hz

Volta

ge (V

)

Time (ms)0.014 0.016 0.018 0.020 0.022 0.024

a)

Peak Pressure

b)

82

Figure 47. Measurements of in-hole detonation pressure at surface test site. a) Peak pressure vs. distance from top of explosive; b) Peak loading rate vs. peak pressure.

From Figure 47a, data points from 90% coupling show a clearly higher trend (larger pressures)

than those from 67% coupling, with the exception of one data point corresponding to 100 g of

explosive in a φ75 mm borehole (90% coupling). The lower pressure recorded in this case may

be explained by the short length of the charge (only 2 cm), resulting in reduced explosive

performance (i.e., full strength may not be reached). Discarding this data point, an exponentially

decaying trendline can be fit to the data. Thus, a multiple variable power regression (with

independent variables distance and coupling) was conducted assuming equal decay for both 67%

and 90% coupling. The equations resulting from this regression are as follows:

( )DP 12.0exp9.1 −= for 90% coupling, and 4-9 ( )DP 12.0exp0.1 −= for 67% coupling 4-10

where P is the peak pressure in GPa and D is the distance from the top of the explosive in cm.

In addition to peak pressures, the loading rates from the rising pressure curves were calculated.

Figure 47b shows an approximately linear trend between measured peak loading rate and peak

pressure, which seems to be independent of coupling, borehole size and explosive amount.

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2

Peak pressure (GPa)

Pea

k lo

adin

g ra

te (G

Pa/µs

)

D45, 0.1 kg charge, 90% coupling D45, 0.5 kg charge, 90% coupling


D45, 1.64 kg charge, 67% coupling

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 2 4 6 8 10 12

Distance from top of explosive (cm)

Pea

k pr

essu

re (G

Pa)



D45, 1.64 kg charge, 67% coupling

a) b)

85.047.1

2 =

=

RPLR

( )DPcoupling 12.0exp9.1:%90 −=

( )DPcoupling 12.0exp0.1:%67 −=

Excluded

99.02 =R

83

The equation obtained from a linear regression is:

PLR 47.1= 4-11

where LR is the peak loading rate in GPa/µs, corresponding to the maximum slope in the rising

curve of the pressure time history (Figure 46 (b)).

VOD measurements were conducted in both test sites on charges of emulsion cartridges attached

in line. The experiments were water coupled in boreholes of 45 mm at the surface test site and 60

mm at the mine, with 67% coupling (i.e., cartridges of φ30 and φ40 mm respectively). The

results from these measurements are shown in Figure 48. The measured VOD values correspond

to 4.92 and 5.28 km/s for the φ30 and φ40 mm cartridges respectively. The higher VOD for the

larger cartridge diameter (~7% higher) is consistent with previous experimental results (Esen

2004).

The results presented in this section, including in-hole peak pressure, loading rate and VOD are

used in damage models included in Chapter 5.

Figure 48. In-hole VOD measurements, water coupled. a) Surface test site; b) Williams mine.

0

0.5

1

1.5

2

2.5

-0.1 0 0.1 0.2 0.3 0.4 0.5

Time (ms)

Dis

tanc

e (m

)

VOD = 4.92 km/sR 2 = 0.9995

0

0.5

1

1.5

2

2.5

3

3.5

4

-0.1 0.1 0.3 0.5 0.7

Time (ms)

Dis

tanc

e (m

)

VOD = 5.28 km/sR 2 = 0.948

a) b)

2m column φ30 mm cartridges φ45mm borehole

Surface Williams

3m column φ40 mm cartridges φ60mm borehole

84

4.3 Measurement of damage Quantification of blast-induced damage through experimental methods was carried out at the

surface test site for selected blasts. Damage from three explosive charges of different sizes was

assessed by two methods: cross-hole measurements and gas pressure activity monitoring,

described in sections 2.4.4 and 2.4.3 respectively. The monitored explosive charges correspond

to emulsion cartridges of 0.1 kg (0.08 m long, mean depth 4.75 m), 0.5 kg (0.45 m long, mean

depth 3.7 m), and 1.64 kg (2 m long, mean depth 4.5 m), the first two coupled at 90% and the

last one at 67%. All charges were detonated under water in φ45 mm boreholes.

Description and results of the measurements for each method are presented in the following

sections.

4.3.1 Cross-hole measurements

The general procedure to determine blast-induced damage from cross-hole measurements is

described in section 2.4.4 and the instrumental layout is schematized in section 3.2.5. In this

research work, multiple measurements of P-wave velocity were executed in the area surrounding

each of the three monitored blasts. The source for these measurements is a single explosive

detonator (cap) ignited by shock tube and placed in one of the boreholes surrounding the blast.

Receivers correspond to 16 pressure sensitive piezoelectric sensors located in up to 4 arrays of 4

sensors each. Each of these arrays is inserted in a different borehole and the seismic signals

caused by the detonator were recorded, obtaining P-wave arrival times at up to 16 locations per

source. As signals are recorded in boreholes under water (neither source nor receivers are

attached to the rock, but both are close to the center of their respective borehole), they are

corrected by the travel time in water within both source and receiver boreholes. The procedure is

executed both before and after blast with sources and receives at the same locations, to obtain

variations of P-wave velocity.

The precise determination of the most affected areas by blasting requires the inversion of wave

velocities into damage. For this an original method was developed by the author based on the

relationship between the two variables given in 2.4.4. This method is described in section

4.3.1.1.

85

4.3.1.1 Inversion method considering multiple measurements around a blast

This inversion, consisting on finding the blast-induced damage distribution around the blast, is

executed through an iterative process to minimize the differences (errors or residuals) between

measured and calculated P-wave velocities after blasting. In this procedure damage is assumed to

decrease with increasing distance from the blast, and the minimization of error is achieved

through a minimum squares criterion, similar to the method applied in most linear regressions.

For a Poisson's ratio of 0.26 (from 5.1.1) the geometrical factor h given by in Equation 2-15 is

equal to 1.905. For water filled cracks, which is our case, the factor δ (Equation 2-16) is

negligible if the crack aspect ratio is small (ζ < 10-3). Thus, assuming small aspect ratio, Equation

2-13 becomes:

ρ76.010 +=∗EE 4-12

and Equation 2-25 becomes:

2

0

76.01

+

=

P

beforeP

beforePafterP

VV

VV

ρ

4-13

The general procedure consists on determining a damage distribution which gives results of

VP after from Equation 4-13 closest to those measured for each ray-path. For this, an initial

damage distribution is assumed around the explosive charge considering exponentially

decreasing damage with distance. Then, P-wave velocities after blast are calculated based on this

damage distribution and the measurements before blast from Equation 4-13. For this equation VP

before blasting is considered to be approximately constant along each ray-path, and the value of

VP for the undamaged material (VP0) is considered uniform throughout the whole area. For this

value, and considering that the damage being assessed throughout this research work refers to

macroscopic damage (i.e., it does not include microscopic fractures), lab results are taken as

representative of VP for the nearly undamaged material. Thus, VP0 is chosen as the average of lab

test plus three standard deviations, i.e., VP0 = 6.3 km/s (see section 5.1.1).

86

The RSS (Residual Sum of Squares) value of the model is calculated as the sum of the squares of

the differences between the calculated values (P-wave velocities after blast from Equation 4-13)

and those measured after the blast, according to:

( )∑=

−=n

iii yyRSS

1

2ˆ 4-14

Where the variable y in this case is used to denote P-wave velocity after blast, with yi being the

measured values, and iy the calculated values from Equation 4-13.

The damage distribution is then modified at all points, lines and planes (one point, line or plane

at a time) by increasing and decreasing the damage values by a small amount. The RSS value is

recalculated for each case and the new estimation of damage distribution corresponds to the case

of minimum RSS. The procedure is repeated until a negligible improvement on the residuals is

achieved when modifying the damage distribution (i.e., the method searches for a minimum

RSS).

To determine the reliability of the model, the Coefficient of Determination, R2 and the Standard

Error, SE are estimated according to the following expressions:

RSSESS

ESSR+

=2 4-15

1−

=nRSSSE 4-16

where RSS is the Residual Sum of Squares calculated from Equation 4-14, and ESS is the

Explained Sum of Squares of the model, calculated as:

( )∑=

−=n

iii yyESS

1

2ˆ 4-17

where iy represents the values of P-wave velocity after blast considering uniform damage with

minimum RSS (the value of this uniform damage is calculated similarly to the general procedure,

considering evidently constant damage throughout the area).

The criterion of decreasing damage with increasing distance from the blast, which is maintained

throughout the procedure, is achieved by choosing an appropriate coordinate system in which

87

one of the coordinates approximates the distance to the explosive charge. A standard system that

meets this requirement is provided by the Prolate Coordinates, a 3-dimensional extension of the

2-dimensional Elliptic Coordinate system. Prolate Coordinates are produced by rotating the

Elliptic coordinates around its major axis, generating planar, ellipsoidal and hyperbolic surfaces

when taking one coordinate as constant. The equations that relate Prolate and Cartesian

Coordinates are as follows:

( ) ( ) ( )( ) ( ) ( )( ) ( )

===

ηξφηξφηξ

coscoshsinsinsinhcossinsinh

azayax

4-18

Where a is half of the distance between two foci, and ξ , η and φ are the variables that define

the coordinate system, with 0≥ξ , πη ≤≤0 , and πφ 20 ≤≤ . For convenience, in the modeling

of damage, the foci of the system are located at the end points of the explosive charges. Figure

49 shows Prolate Coordinates on a plane of equal φ . On Figure 49a, ellipses correspond to

curves of constant ξ , whereas hyperbolas are curves of constant η . Figure 49b and Figure 49c

show the discretization of the area used to compute damage around the 0.1 kg (0.45 m long) and

1.64 (2 m long) charges, with a = 0.225 m and 1 m, respectively.

Figure 49. Prolate Coordinate System used to discretize area around blasts. a) Curves of constant ξ and η on

Plane ξ -η (constant φ ) for a = 1; b) Discretization of area around 0.1 kg (0.45 m) charge ( a = 0.225 m); c) Discretization of area around 1.64 kg (2 m) charge ( a = 1 m).

a) b) c)

-2 -1 0 1 2 X

2

1

0

-1

-2

Z

88

4.3.1.2 P-wave velocity measurements

Figure 50 to Figure 52 show various views of the ray-paths (taken as straight lines from source to

receiver) corresponding to the cross-hole measurements executed around each of the three

surveyed blasts. Altogether P-wave velocities were successfully measured through a total of 396

ray-paths (lines source-receiver) before and after blasting (60 for 0.1 kg charge, 176 for 0.5 kg

charge, and 160 for 1.64 kg charge).

Each of these figures (Figure 50 to Figure 52) show ray-paths, explosive charges and boreholes

from different angles, as well as a cylindrical projection on a vertical semi-plane, equivalent to

the r -θ plane described in section 4.1.1.1. For this projection each point maintains its relative

location with respect to the blasthole and explosive charge. In other words, the blasthole

becomes the axis of the cylindrical projection and all distances and angles from this axis are

maintained. Since generally the closest point from a ray-path to the blasthole is some point

between the source and the receiver, ray-paths appear to be curved upon projection. The only

exceptions to this are ray-paths that originate or cross through the blasthole. In all cases the

coordinate system is chosen to have its origin at the center of the explosive charge.

Figure 50. Cross-hole ray-paths from measurements on P-wave velocity changes to quantify damage caused by a 0.1 kg explosive charge. a) 3D view; b) Plan view; c) Cylindrical projection of ray-paths on a vertical semi-plane with an edge along the blasthole axis.

a) b) c) 0.1 kg charge

89





90

The results of P-wave velocities before and after blast for all three experiments are shown in

Figure 53. In the case of the 0.1 kg charge (Figure 53a), the average P-wave velocity does not

appear to decrease after blasting, but rather seems to increase. In order to statistically determine

whether the two curves have significantly different slopes, a Student’s t-test was performed on

both sets of data, with the following t statistic:

21

21

bbSbbt

−

−= 4-19

where b1 and b2 are the slopes of the curves after and before blast, and 21 bbS − is the standard error

of the difference between the slopes ( 222121 bbbb SSS +≈− , with

1bS and 2bS being the standard

errors associated to each slope). With values b1 = 5.82, b2 = 5.72, 1bS = 0.047 and

2bS = 0.025,

the t-test indicated that the slopes are not significantly different at 95% confidence level (t = 1.88

> ∞,05.0t = 1.645). Thus, the apparent increase in slope is not a real change in velocity, but a result

of the relatively high dispersion of results compared to the variations caused by blast damage at

the surveyed locations. The sources of dispersion are both real variations in material properties

(heterogeneity and anisotropy) and measurement errors (distances source-receiver and arrival

times). Consequently, no calculation of damage is possible for this particular blast.

Figure 53. Measured variations in P-wave velocity caused by explosive charges of 0.1 kg, 0.5 kg and 1.64 kg.

Before:V P = 5.74 km/s

R 2 = 0.9835

After:V P = 4.88 km/s

R 2 = 0.9211

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.2 0.4 0.6 0.8

Time (ms)

Dis

tanc

e (m

)

Before Blast After Blast


R 2 = 0.9787


R 2 = 0.67950

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6

Time (ms)

Dis

tanc

e (m

)



R 2 = 0.9744


R 2 = 0.9544

0

0.5

1

1.5

2

2.5

3

0 0.2 0.4 0.6

Time (ms)

Dis

tanc

e (m

)


a) 0.1 kg charge b) 0.5 kg charge c) 1.64 kg charge

91

The results of P-wave velocity measurements from the 0.5 and 1.64 kg charges are shown in

Figure 53b and Figure 53c, respectively. In the first case it is possible to see that in some areas

there is a severe reduction of P-wave velocity, while in others there seems to be no change. This

clearly indicates that in contrast to the 0.1 kg charge, the 0.5 kg charge caused some severe

damage with a non-uniform distribution in the area surveyed. For the case of the 1.64 kg charge

damage seems to be more extended but less severe in some areas, given the more significant

drop in average P-wave velocity and the lower dispersion of values. The more extensive damage

in the later case is likely to be due to the larger amount of explosive, which causes both stronger

stress waves and larger volume of gases, resulting in longer fractures. The more severe damage

observed in some areas around the 0.5 kg charge is probably due to the higher coupling (90% vs.

67% for the 1.64 kg charge), which causes higher pressures as seen from Figure 47.

4.3.1.3 Inversion results: 3D images of blast-induced damage

The inversion method described in section 4.3.1.1 is applied to the cross-hole measurements

carried out around short (0.5 kg, 0.45 m) and long (1.64 kg, 2 m) charges of explosive. Figure 54

shows contour plots representing the results of blast-induced damage for the 0.5 kg explosive

charge. From this figure, two main observations can be made: First, the results show a severe

concentration of damage near the bottom of the charge (initiation point) diagonally down at an

angle of approximately 45° with respect to the blasthole axis; and second, damage seems to

propagate mainly in some specific directions (asymmetry along azimuth). Additionally, the

resulting plots indicate cylindrical asymmetry (along horizontal angles), as it shows damage

being strongly concentrated towards some specific directions. This is more evident in Figure

54c,d showing damage in plan view at Z = 0.225 and -0.225 m (top and bottom of explosive).

From these graphs it is possible to observe that damage is most severe along the east-west

direction. The maximum extent of damage exceeds 1 m (22 borehole diameters) horizontally

from the explosive charge.

92

Figure 54. Measured blast-induced damage determined from inversion of P-wave velocities corresponding to a 0.5 kg charge of emulsion, 90% coupling. a) Vertical plane E-W; b) Vertical plane N-S; c) Plan view at Z = 0.225 m (top); d) Plan view at Z = -0.225 m (bottom).

A comparison between P-wave velocities measured after the blast and those calculated based on

the model is shown in Figure 55. From this figure it is possible to observe that in most cases the

calculated values approximate well the measurements, even though in some cases the residuals

indicate poor accuracy of the model. This happens particularly in some cases of very low

measured wave velocities, which may be due to localized damage not represented by the model.

These cases contribute greatly to the standard error, which reaches a value of 431 m/s. Although

the calculated R2 value of 0.50 does not indicate the model to be particularly accurate, it indicates

a fair fit to the data.

0.5 kg charge, bottom initiated a) b)

c) d)

93

Figure 55. Comparison of measured and calculated P-wave velocity values after blast for explosive charge of 0.5 kg.

Figure 56 shows the results of damage distribution corresponding to the 1.64 kg (2 m) explosive

charge. As expected, damage is observed to propagate farther than the case of 0.5 kg charge, but

with a more reduced area with severe damage close to the blasthole. From Figure 56a,b it is

possible to observe a larger damaged area (ρ > 3) which propagates diagonally down from the

bottom of the explosive charge.

Also, as in the case of the 0.5 kg charge, damage seems to propagate in some preferential

directions. For example, the vertical plane E-W (Figure 56a) shows significantly more damage

than the plane N-S (Figure 56b). Figure 56c and Figure 56d showing plan views at Z = 1 m and

Z = -1 m, also support this observation by clearly showing damage propagating mainly in the

direction E-W. The maximum damage extent in this case seems to significantly exceed 1 m (22

borehole diameters) horizontally from the blasthole.

As in the previous case, the significance of the model is evaluated by comparing measured and

calculated values of P-wave velocity after blast, shown in Figure 57. The calculated values of R2

and Standard Error (SE) are 0.74 and 228 m/s, respectively. These values indicate higher

accuracy and a much better fit than the previous case.

0 20 40 60 80 100 120 140 160-2000

0

2000

4000

6000

8000

Measurement number

Vp

(m/s

)

Measured

Model

Residuals

R2 = 0.5SE = 431 m/s

94

Figure 56. Measured blast-induced damage determined from inversion of P-wave velocities corresponding to a 1.64 kg charge of emulsion, 67% coupling. a) Vertical plane E-W; b) Vertical plane N-S; c) Plan view at Z = 1 m (top); d) Plan view at Z = -1 m (bottom).

Both experiments with short and long charges indicate a strong asymmetry both vertically and

horizontally. The horizontal (i.e., cylindrical) asymmetry is manifested by damage being

propagated mainly in the direction E-W in both models. This kind of asymmetry is likely to be

related to material anisotropy resulting from previously existing fractures, micro-fractures,

foliation or joints in the natural rock mass, which may be the result of previously existing

deviatory stresses in the rock mass. Another potential source of this asymmetric behaviour may

be changes in mineral composition causing both anisotropy and heterogeneity.

1.64 kg charge, bottom initiated a) b)

c) d)

95

Figure 57. Comparison of measured and calculated P-wave velocity values after blast for explosive charge of 1.64 kg.

Another relevant common observation is the concentration of damage close to the explosive's

initiation point. Although this is contrary to the intuitive case when only damage caused by stress

waves is considered (see section 4.1), it can be explained as the result of the expansion of gases.

These, being subject to higher confinement at the initiation point (in these experiments), are

under higher pressures and hence cause a more dense and extended fracture network.

Finally, although the sources of error of the method to determine damage distribution based on

various measurements of P-wave velocity include measurements errors, there are some implicit

and explicit assumptions that contribute to these errors. One of these assumptions is the

imposition of decreasing damage with increasing distance. Although this hypothesis is general, it

necessarily decreases the R2 value of the model, and hence the quality of the fit. Also the P-wave

velocity before blast was assumed to be constant throughout each ray-path, as it is unrealistic to

determine accurately the velocity distribution based on the available data, mainly due to probable

anisotropy of the existent material. As a final point, the fracture network created by explosives is

known to be strongly anisotropic, due to its directional nature. Hence, it is estimated that the

assumption of isotropic damage implicit in the method is the most significant source of error.

Nonetheless, because the measurements are taken in a wide variety of orientations and there is a

significant amount of data, it is reasonable to assume that the calculated distributions of damage

are a fair representation of the average damage throughout most of the surveyed areas.

0 20 40 60 80 100 120 140 160-2000

0

2000

4000

6000

8000

Measurement number

Vp

(m/s

)

R2 = 0.74SE = 228 m/s

Measured

Model

Residuals

96

4.3.2 Gas pressure activity

As indicated in section 3.1, gas activity is monitored in boreholes surrounding a single blasthole

in the surface test site. The method is described in section 2.4.3 and the instrumentation is

detailed in section 3.2.2. The experiments involving gas pressure measurements correspond to

charges of 0.5 and 1.64 kg of emulsion, coupled at 90% and 67% respectively. All measurements

associated with the 0.5 kg charge correspond to the same blast assessed through cross-hole

(Figure 51), whereas the measurements around 1.64 kg charge correspond to two different blasts,

being one of them also assessed through cross-hole (Figure 52). The horizontal distances

between blasthole and monitor holes vary between 0.5 and 2.5 m.

Results of peak pressure are plotted vs. distance in Figure 58. From this figure we can see that

pressure events were detected from both charge sizes. In the case of the 0.5 kg charge, two

events took place at distances between 0.5 and 0.8 m, with peak pressures of 68 and 35 kPa

respectively (the former value is only a lower bound of pressure activity, due to failure (grout

expelled) of the borehole plug). Two other sensors monitoring the same charge recorded only

mild pressure events, below 1 kPa. Around 1.64 kg charges, only one of them indicated pressure

activity, with a peak of 18 kPa at 1.3 m. Other measurements between 1 and 2.5 m showed only

some high frequency component which is believed to be unrelated to pressure events, as

explained below.

Figure 58. Measured gas pressure activity in monitor holes from blasts corresponding to 0.5 and 1.64 kg of explosive (90% and 67% coupling respectively) in φ 45 mm borehole.

0

10

20

30

40

50

60

70

80

0 0.5 1 1.5 2 2.5

Distance (m)

Pre

ssur

e (k

Pa)

0 10 20 30 40 50

Distance in Borehole Diameters ( )

0.5 kg 90% coupling 1.64 kg 67% coupling

Plug failed

Mostly high freq. component

97

The signals corresponding to the four measurements around the 0.5 kg charge are shown in

Figure 59. This figure also shows the location of the monitor holes relative to the source and the

damage contour plot determined through the cross-hole system for the same blast (horizontal cut

across bottom of explosive charge from Figure 54d).

Figure 59 clearly shows that the significant pressure events (> 10 kPa) are consistent in terms of

both amplitude (i.e., increasing amplitude with decreasing distance) and rise time (sharper

pressure rise with decreasing distance). The pressure events less than 1 kPa could be due to rock

movement rather than gas penetration, although this hypothesis needs to be proved. All signals

show some high frequency component (typically 100 to 120 Hz) which is more evident in the

lower pressure graphs. This component is observed in most measurements and is attributed to

noise caused by electromagnetic interference from the AC power supply (voltage inverter),

which is evidently not related with the actual pressure events.

When comparing gas pressure with the results from cross-hole measurements (Figure 59) there

seems to be a mismatch between the two methods. In other words, the direction of damage

development determined by the cross-hole method does not match the highest recorded

pressures. In fact, the highest recorded pressure lies on a zone where no damage appears to be

identified, despite the closeness to the blasthole.

The mismatch between the results of cross-hole and gas penetration on damage, however, is not

discouraging. As indicated earlier, the method of gas penetration relies on the development of

fractures from the blasthole to the particular monitor hole where the sensor is placed. Thus, gas

pressure events can be recorded only if a fracture or network of fractures connects both holes.

Additionally the presence of pre-existent fractures makes the phenomenon of gas expansion even

more dependent on local conditions. Effectively, as fractures are in fact voids and weak planes

within the rock mass, the gas pressure may suffer a quick drop when reaching a fracture. As a

result the gas flow can be deviated from its original course causing higher variations in gas

pressures within the rock mass.

98

Figure 59. Pressure activity recorded in monitor holes from a blast corresponding to 0.5 kg of explosive, 90% coupling in φ 45 mm borehole.

Despite the previously indicated apparent disagreement between cross-hole and gas

measurements, there is still an overall agreement in terms of potential damage with distance. For

the 0.5 kg charge, for example, the pressure sensors predict a typical limit of damage around 1 m

from the blasthole. This limit is evidently highly variable, even for the same blast, due to the

complex development of fracture networks. For the same charge, cross-hole measurements

indicate damaged areas from a few centimeters to over a meter. Similarly, gas pressure

measurements indicate damage at 1.3 m from a 1.64 kg charge, while the cross-hole method

indicates damage from a few decimeters to over a meter. Thus considering the high variability of

damage in blasting, the results of cross-hole and gas penetration are in fair agreement.

0 200 400 600 800 1000-1

-0.5

0

0.5

1

Time (ms)

Pre

ssur

e (k

Pa)

0 20 40 60 80 100 120-10

0

10

20

30

40

50

60

70

Time (ms)

Pre

ssur

e (k

Pa)

0 50 100 150 200-10

0

10

20

30

40

Time (ms)

Pre

ssur

e (k

Pa)

0 100 200 300 400 500-1

-0.5

0

0.5

1

Time (ms)

Pres

sure

(kPa

)

Very low or no pressure (< 10 kPa)

Pressure event detected (> 10 kPa)

99

In the next chapter, damage from seismic signals is assessed by numerical methods through the

use of the combined finite and discrete elements method Y-code. The relative contribution of

stress waves and gas expansion to damage is determined by combining the results of this

numerical method and field measurements. These field measurements include only cross-hole

results and no directly gas expansion, as the former provides a considerably larger amount of

data and has proved to be more reliable and consistent.

4.4 Discussion One of the key components of this research was the monitoring, identification and quantification

of blast-induced seismicity. As part of this, the use of triaxial accelerometers with high amplitude

(100 to 2000 g) and wide frequency-band (up to 25 kHz) was essential to obtain reliable and

accurate seismic signals for the full range of distances monitored (from 1 to 100 m). It was

shown that seismic signals in this range can contain frequencies of significant amplitude up to

several kHz, with typical average values (in terms of frequency of particle velocity) between 1

and 5 kHz. Considering these large frequencies, the use of a more traditional and widely known

technology such as geophones would have not provided accurate signals, as typical ranges of

geophone frequency response have a higher limit from only a few tens to a few hundred Hz. This

finding alone suggests that a great portion of blast-induced seismic studies might be severely

flawed, as signals, which are typically measured by geophones, probably do not represent

accurately the seismic signals in the near field.

Not only the accurate measurement of seismic signals, but also the correct identification of wave

types plays an important role in this study. In all cases recorded signals were carefully analyzed

and despite the significant noise present in many cases, the great majority of first arrivals were

picked with precision. This included P-waves and S-waves, even though the latter showed

amplitudes generally lower than the former. This accurate identification of signals was possible

through the use of three graphical methods: stereonets to analyze true direction of motion;

rotation to spherical coordinates to pick first arrivals with higher accuracy; and plotting arrival

time vs. distance to verify the validity of picked arrivals. Another contributing factor to the

unequivocal identification of signals was the location of charges and sensors away from free

surfaces, whenever possible, thus avoiding the noise commonly induced by free surfaces on the

recorded signals.

100

Amplitude and frequency content of signals are of foremost importance in the study of the

source. With amplitude as a function of scaled distance and frequency as a function of distance,

significant scatter was found. A great part of this scatter was shown to be explained by physical

interaction between waves generated along the explosive column, modeled as simple linear

superposition of waves. Linear superposition indicated modification in both amplitude and

frequency content, which vary not only with distance from the source, but also with charge

length and relative location source-receiver. For example, the measurement of P-waves from 6 m

explosive columns in direct and reverse modes indicated a direct / reverse ratio (i.e., the ratio

between amplitudes in direct and reverse initiation mode) of over 4 in terms of PPV. The same

experiments indicated a reduction in average frequency for both cases with respect to short

charges, with long charges in direct mode showing the lowest average frequencies. Moreover,

the shape of the amplitude spectra in direct and reverse modes was significantly different, with

the former having a clear concentration towards one particular frequency, while the later showed

a spread out spectrum over a larger frequency range. The numerical evaluation of direct and

reverse modes from an initial seed waveform corresponding to a 0.4 m charge showed results in

qualitative agreement with the experimental data (Appendix F).

The specific finding of frequency in direct mode lower than in reverse mode may be thought as

counterintuitive. Generally speaking, when a source emitting a steady signal is in relative motion

towards an observation point, the observer perceives a signal of higher frequency than the one

being emitted (Doppler effect). In the opposite case, i.e., when the observation point and source

are moving relatively away from each other, the signal observed is of lower frequency than the

one being emitted. Hence if an explosion in direct mode is thought of being similar to the case of

the source moving towards the observer, it would be reasonable to expect higher frequencies.

This, however, is not the case with the measured signals, for lower average frequencies are

generally obtained from experimental data in direct mode.

This discrepancy seems to be the result of the difference between a blast source and a moving

source, which causes blast-induced seismic signals to differ from a Doppler effect case. In simple

terms, this may be explained by discretizing the long explosive source into a series of small

sources initiated in sequence. In this case, signals observed from the long charge are seen as the

superposition of a number of signals emitted from the same number of small sources.

101

Each of these sources is located at a fixed point and emitting the same signal at time intervals

equal to ∆L/VOD, where ∆L is the distance between the sources and VOD is the velocity of

detonation. A different situation results from the case of a moving source (with same velocity,

VOD). Although this case may also be seen as the superposition of small sources, the finite time

interval between the initiation of two consecutive small sources (also equal to ∆L/VOD), implies

that the phase of the associated signals will change accordingly, thus causing the discrepancy

between the two conditions. Figure 60 shows schematically the difference between the two cases

indicated.

Figure 60. Comparison of different cases of wave superposition. a) Signals emitted from a series of 'fixed' small sources (akin to a long blast source); b) Signals emitted a 'moving' small source. Note the variation of phase of the individual signals in the second case, as the source moves upwards.

Thus, the reduction in average frequency observed from direct initiation mode blasts seems to be

the result of the superposition (which may or may not be linear) of waves emitted along the

explosive column (i.e., from 'small' charges). This superposition modifies the amplitude

associated with all frequencies in the spectrum, and tends to enhance lower frequencies while

causing destructive superposition at discrete frequency intervals. These frequency intervals are

clearly seen in amplitude spectra recorded in reverse initiation mode (Figure 44b & Figure 45b).

Another significant result from the experimental methods was the successful implementation and

application of a cross-hole system to measure blast-induced damage. In spite of being a relatively

expensive procedure, due to the necessity to drill several monitoring holes and the specific

a)

Sequential initiation of

'fixed' small sources

VODLt ∆

=∆

Moving source

VODLt ∆

=∆

b)

102

requirements of equipment and delicate execution, the method provided clear images of damaged

zones around the blasthole, permitting quantify objectively damage in terms of crack density.

The overall accuracy of method and execution allowed the measurement of damage around 0.5

and 1.64 kg charges of emulsion, but was not sufficient to assess damage from smaller charges

(e.g. 0.1 kg). The total number of wave velocity measurements successfully completed for the

two larger charges was more than 160 in each case. This provided significant duplicate

information necessary to overcome the variations caused by heterogeneity and anisotropy

resulting from both the natural rock mass and blast-induced fractures.

One of the hypotheses in the method to calculate crack density distribution was the assumption

of isotropic damage. Even though this not the case of blast-induced damage, this hypothesis was

assumed in all calculations, and probably represents the main source of error and uncertainty in

the models. An anisotropic model would be more accurate and would probably represent and

permit to identify better the fractures caused by blasting; however, such approach was found

impractical for the purpose of this thesis, as the introduction of anisotropy in the analysis would

have resulted in models impossible to compare with the 2D numerical results. The consideration

of anisotropy would be probably useful and relevant when applying the method to predict blast

damage in a particular rock mass with strong anisotropy.

The measurement of damage from short and long explosive charges indicated a strong

concentration of damage originating at the explosive initiation point. This damage cannot be

accounted for by the stress waves alone, as seen from seismic measurements (since direct

initiation gives higher amplitudes). This result is further discussed in the next chapter with the

assistance of numerical models to account independently for damage from both stress waves and

gas expansion.

On the other hand, the top of the explosive column exhibits relatively low damage, compared to

the bottom and middle portions. This is attributed to the lower confinement conditions at the top

of the explosive due to the lack of stemming material (in the experiments executed the only

source of confinement on top was the column of water above). This lower confinement permits

gases to escape more quickly, causing a rapid drop in pressure and thus reducing damage to the

rock.

103

On the monitoring of gas pressure activity in neighbour boreholes, it is recognized that this may

be an aid to assess blast-induced damage; however, it is also clear that the method requires a

large number of measurements to provide reliable results. One very important application of the

method would be its use in addition to crack mapping to determine pressure of gases penetrating

into the fracture network. This option is further discussed in section 7.7.

Finally, it is essential to mention the importance of measuring other variables on the accuracy of

the results and analysis. These variables include the velocity of detonation VOD, and the in-hole

explosion pressure. In this study, both variables were considered essential to correctly model the

blasts and determine damage. The carbon resistors used to monitor in-hole pressure proved to be

an excellent system to determine the rising part of the pressure function. Its use with no casing

and in water coupled conditions seems to be ideal for this determination. Although other authors

have used and defended the use of special casing to protect the sensors, and thus obtain the full

pressure function curve (Nie 1999, Nie & Olsson 2001, Olsson et al 2002), it is quite evident that

the proposed protective casing causes distortion of the pressure signals, resulting in unreliable

readings of the pressure function. The protective casing may be useful and recommended if

proper study is done to correct the signals from this additional shielding. For the purpose of this

study the use of carbon resistors without casing was found to be the best option to obtain reliable

peak pressures, whereas the decaying part of the pressure function was chosen to be calibrated

with measured seismic signals.

104

Chapter 5

5 Damage from Stress Waves and Gas Expansion This Chapter deals with quantifying the contribution from blast-induced stress waves and gas

expansion to damage, considering a single blasthole. The separation of stress waves and

explosive gases is done by quantifying independently damage from stress waves and combined

damage from waves and gases. Combined damage is assessed by using the results from cross-

hole experiments presented in Chapter 4. Damage from stress waves is computed through the

numerical FEM-DEM code Y2D introduced in section 2.5. All models and experimental results

presented and discussed in this chapter, including material and explosive properties, correspond

to the surface test site.

In order to determine the model input parameters, three different methods are used: a) laboratory

tests, b) field experiments, and c) a calibration process of FEM-DEM models with field recorded

stress signals. All the most relevant material and explosive properties are obtained by one of

these three methods. The process to obtain these parameters and results are included in sections

5.1 to 5.3. Finally the quantification of damage from stress waves and gas expansion is included

in section 5.4.

5.1 Model input parameters from field and lab experiments Field experiments are the source to obtain some of the most relevant material and explosive

parameters, including elastic constants, in-hole pressure and VOD. Other essential material

properties, including density, shear and tensile strength, are determined through laboratory tests.

The results (either values or expressions) obtained from both field and lab experiments are

included in this section.

5.1.1 Elastic constants

Elastic constants are calculated from field measurements of P and S-wave velocity shown in

section 4.1.1.3, by using the relationships included in Appendix A and the average material

density from Appendix E. Although only two elastic constants are required for the isotropic

elements in the Y2D code, the complete set of constants is shown here for reference. These are:

105

• P-wave velocity, VP 5900 m/s

• S-wave velocity, VS 3340 m/s

• Young Modulus, E 75.3 GPa

• Shear Modulus, µ 29.8 GPa

• Lamé Constant, λ 33.4 GPa

• Bulk Modulus, K 53.2 GPa

• Poisson's Ratio, ν 0.26

5.1.2 Material properties from lab experiments

Several material properties are required for the modeling of blast damage. The most important

material properties that affect the fracture process are those corresponding to material strength.

In the case of the Y2D code, an analysis of sensitivity (shown later in section 5.4.4) indicated

that the most relevant strength related input parameters for the models under study are Shear

Strength (σs) and Tensile Strength (σt). The third strength related parameter, Fracture Energy

proved to have little influence on the fracture pattern, even for variations in one order of

magnitude.

Shear and tensile strength are determined through both static and dynamic laboratory tests on

multiple rock samples representative from the surface test site comprising of a granitic rock.

Additionally, material density and wave velocities are also determined from selected samples.

The detailed description and results from these tests are included in Appendix E. The following

is a summary of those results.

• Wave velocities and Density:

The average values of P and S-wave velocities and density are as follows:

VP = 6.02 km/s

VS = 3.46 km/s

ρo = 2.67 kg/dm3

106

The average values obtained for wave velocities are, as expected, higher than those

obtained from field measurements (5.90 and 3.34 km/s respectively, Figure 36a), as

laboratory samples do not have some of the natural fractures present in the field.

Additionally, the relatively low values of standard deviation (~1-3%) and the small

differences between VS1 and VS2 values (Figure E1) confirm that the material may be

considered as isotropic, at least in absence of significant damage. The values obtained for

VP are used to estimate the undamaged material properties required to calculate damage

from cross-hole measurements, as detailed in section 4.3.1. The average value of density

(2.67 kg/dm3) is used in all models.

• Shear Strength:

Considering that the maximum shear stress is half of the compressive stress in UCS tests,

the shear strength σs is taken equal to half of σc. Thus, from Figure E3 shear strength is

calculated as:

MPaS 82=σ if LR < 3250 GPa/s 5-1 ( )MPaLRS 370141.0 +=σ if LR < 3250 GPa/s 5-2

where LR is the loading rate expressed in GPa/s. These equations are used to determine

shear strength to be used in models in section 5.4.1.

• Tensile Strength:

Since fractures from blasting have various orientations, σt is chosen as an average

between the two limit experimental curves (Figure E4). Thus, the expression to calculate

tensile strength becomes:

( ) 29.0285.3 += LRtσ 5-3

with LR in GPa/s. Equation 5-3 is used to determine tensile strength for models in section

5.4.1

5.1.3 Explosive properties

Appropriate velocity of detonation VOD, peak pressure, and loading rate for models are chosen

from the experimental results included in section 4.2.

107

• VOD:

VOD for 2 m long charges with 67% coupling is taken from the measurement shown in

Figure 48a, equal to 4.9 km/s. For 0.45 m, 90% coupling charges the effect of VOD on

model results is minimum, due to the short charge length. In other words, the chosen

VOD value has little influence on the model results, as long as it is reasonably

representative of the explosive. Considering that VOD increases with charge diameter and

confinement, a 10% increase in VOD (i.e., 5.3 km/s) for a fully coupled charge would be

considered reasonable.

• In-hole Peak Pressure:

In-hole peak pressure values are calculated from the empirical equations shown in section

4.2. Considering the explosive-borehole distance equal to 0.3 cm for 90% coupling,

Equation 4-9 predicts a peak pressure Pmax = 1.8 GPa. For 67% coupling, considered 1

cm distance, Equation 4-10 predicts Pmax = 0.9 GPa. These values of peak pressure are

used for the models corresponding to explosive charges with the indicated coupling

percentages at the surface test site.

• In-hole Loading Rate:

Peak loading rate (i.e., raising part of the in-hole pressure function) values for both 90%

and 67% coupling are obtained from Equation 4-11. Considering the values of peak

pressure indicated in the previous paragraph, peak loading rates are LR = 2.6 GPa/µs for

90% coupling, and LR = 1.3 GPa/µs for 67% coupling.

The decay of the pressure function cannot be determined from the executed experiments

due to the destruction of the sensors by the explosion itself. Pressure decay rate is

determined instead by calibrating the maximum slope of this curve with amplitude and

frequency content of measured seismic signals in section 5.2.

5.1.4 Pressure function

The pressure function used in all models in this thesis was initially introduced by Trivino et al

(2009) with a shape similar to that shown in Figure 61. The equations of this pressure function

permit to account independently for both the rapid pressurization and the relatively slower

108

pressure decay in the blasthole. The set of equations to define this pressure function P(t) is as

follows:

)()()( max tPtPPtP du ⋅⋅= 5-4

( ) ( )[ ] nuu ttb

u etP2−⋅−= 5-5

( ) ( )[ ] 2dd ttb

d etP −⋅−= 5-6

dd meb ⋅⋅= 2122 5-7

ratiodu bbb = 5-8

( )[ ] un

u bt 21

1ln α−= 5-9

( )[ ] ( )[ ] unn

d bt 21

22

11 1lnln αα −−−−= 5-10

( )duratio mmberoundn ⋅⋅⋅= 2122 5-11 maxPLRmu = , and 5-12 maxPDRmd = 5-13

where Pmax is the peak in-hole pressure; Pu(t) and Pd(t) are functions to (approximately) define

the rise (up) and decay (down) of the pressure function; bu, tu, n, bd, and td are the parameters that

define these curves; bratio is the ratio bd/bu; mu and md are the maximum slopes of Pu(t) and Pd(t),

respectively; α1 and α2 are approximately the normalized errors of the resulting curves at t = 0

and t = tmax, with tmax being the time at which P(t) is maximum; and LR and DR are the peak

loading and decay rates of the in-hole pressure function.

From the equations above, the input parameters to fully define the in-hole pressure function are

Pmax, LR, DR, α1, α2, and bratio. The remaining parameters are determined from Equation 5-4 to

Equation 5-13. The most relevant input parameters of the pressure function are evidently Pmax,

LR and DR, which depend on the specific blast configuration (i.e., explosive type, amount,

borehole diameter, coupling and coupling material, initiation mode, and interaction with the rock

mass). The other input parameters, α1, α2, and bratio, have a minor influence on the shape of the

function and can be chosen quite arbitrarily without perceivable influence on the results,

provided they are of reasonable value (as α1 and α2 are normalized errors, they should have

small values compared to 1; bratio should be ≥ 2). Figure 61 shows an example of pressure

function calculated for a particular set of parameters. The parameters Pmax and LR to be used in

numerical models are indicated in 5.1.3, whereas DR is determined in section 5.2.

109

Figure 61. Pressure functions Pu(t), Pd(t), and P(t)/Pmax, for parameters LR = 1000 GPa/ms, and DR = 100 GPa/ms (with α1 = 10-7, α2 = 10-3, bratio = 2. LR: Loading Rate; DR: Decay Rate).

5.2 Adjustment of attenuation and calibration of other input parameters

This section comprises two essential parts in the method to estimate blast-induced damage,

developed as part of this research work. The first part is the adjustment of damage from 2D

models to represent a real 3D situation. The second part corresponds to the calibration of

material viscous damping and in-hole pressure function decay rate. Both of these variables

control the amplitude and frequency content of the blast-induced seismic signals. Thus, the

calibration process is done by replicating as closely as possible the field measured seismic

signals in terms of both PPV and frequency.

The aforementioned processes of damage adjustment and parameters calibration are dependent

on each other, as will be shown. Consequently, in practice they are carried out simultaneously

and thus, they are presented together in this section.

5.2.1 2D model vs. 3D phenomenon: adjustment of geometric attenuation

The proper use of a numerical code to evaluate a physical phenomenon involves not only

choosing the correct input parameters but also a correct interpretation of results. The particular

case of a dynamic 2D model has the disadvantage of producing a lower attenuation (geometric

spreading) than the real 3D case, as shown in section 2.5.3 (Figure 12). This disadvantage is,

however, not an impediment to obtain meaningful results if these are properly interpreted. For

this correct interpretation an original procedure to apply the results of crack density from 2D

0 0.01 0.020

0.2

0.4

0.6

0.8

1

Time (ms)

Pre

ssur

e

mu

Pu(t)

0 0.01 0.020

0.2

0.4

0.6

0.8

1

Time (ms)

Pre

ssur

e

P(t)/Pmax = Pu(t) * Pd(t)

0 0.01 0.020

0.2

0.4

0.6

0.8

1

Time (ms)

Pre

ssur

e

md

Pd(t)

x =

110

models to a 3D problem is developed as part of this research. In this section the fundamentals of

this method are presented.

The differences in geometric spreading between the 2D and 3D situations result in severe

differences in PPV, and consequently in stress amplitudes caused by stress waves. The higher

values of PPV in the 2D models result into more severe fracturing for equal distance and angle

from the source. One potential solution considered by the author was to artificially increase

damping in the 2D model, in order to match the magnitudes of PPV from the 3D experiments.

After testing this alternative with the FEM-DEM code it was found that this increase of damping

severely affected the shape of the signals (loss of high frequencies), becoming impossible to

match even approximately both amplitude and frequency of signals simultaneously.

A second alternative, consisting of scaling PPV2D (PPV from 2D models) by a factor

proportional to r -0.5 (with r being distance from the source), as shown in section 2.5.3 (Figure

13), proved to be a consistent and reasonable method, which allowed to convert 2D crack density

and damage distribution into equivalent 3D values. The conversion of PPV from 2D to 3D is

done according to:

FPPVPPV DD ⋅= 23 5-14

where F is the aforementioned scaling factor proportional to r -0.5. In order to maintain physical

consistency, the scaling factor must be a dimensionless expression. Thus, the following simple

equation that meets this requirement is chosen:

5.0

0

−

=

rrF 5-15

where r is the minimum distance from the blasthole to the observation point, and r0 is an

appropriate distance at which PPV2D = PPV3D. Considering that the pressure function at the

borehole boundary has the same shape and amplitude in both 2D and 3D cases, it is reasonable to

assume that the PPV2D must equal PPV3D at this boundary. Thus, considering the distance r as

measured from the borehole axis, Equation 5-14 becomes:

5.0

23 2

−

⋅=

BDrPPVPPV DD 5-16

111

where BD is the borehole diameter. It is important to notice that Equation 5-16 permits only to

obtain an equivalent PPV3D. Equivalent 3D damage can be calculated using this equation

combined with a proper relationship between PPV and crack density. Such relationship should be

determined by using the complete set of parameters from the particular case under study (i.e.,

geometry, initiation mode, material and explosive properties). The process to establish this

relationship and the results for the cases under study are presented in section 5.2.2.

5.2.2 Relationship between PPV and crack density

The relationship between PPV and crack density is established from FEM-DEM models of short

and long charges. This process requires the full set of material and explosive parameters,

including those determined according to 5.1 and those calibrated with experimental field data

(section 5.2.3).

At the same time the calibration of parameters (section 5.2.3) uses the relationship between PPV

and crack density determined in this section, in order to compare the results from the 2D models

with 3D experimental data. Consequently, it should be understood that the two processes are

carried out as an iterative process to minimize the differences between models and field

measurements.

FEM-DEM models were constructed to simulate blasts corresponding to 0.5 kg and 1.64 kg

through the program Y2D. In both cases the finite VOD was simulated by discretizing the

explosive sources in small elements of 0.02 to 0.03 m long. Figure 62 shows the meshes used for

these models. Note that in both cases the symmetry of the problem has been used to reduce the

models size (i.e., only the rock mass on one side of the borehole is modeled) and thus, the

computing time. Both meshes include a uniform area (i.e., elements of uniform size) close to the

borehole. The outer boundaries of the models are beyond these areas in order to minimize the

effect of reflections on the free surfaces. These uniform areas (1 m x 2 m for the short charge; 1

m x 2.6 m for long charge) are the target of the damage analysis and outside them elements of

increasing size are used to reduce computing times.

Additionally control points used to determine velocity time histories are shown on each mesh.

Finally, on the side of each mesh, the shape of the pressure function at 65 µs from initiation is

shown, and a screenshot from the FEM-DEM program shows the stress wave propagating from

112

the blasthole (horizontal velocity, Vx) as the fracture network resulting from it develops (red

lines). In both models the initiation point is about 0.1 m above the bottom of the explosive

column, as this location corresponds approximately to the initiation point of field experiments.

Figure 62. Initial meshes used for models. a) Mesh for 0.5 kg charge; b) Profile of horizontal particle velocity at 65 µs after initiation; and c) Mesh for 1.64 kg explosive charge.

Evaluation of damage is carried out based on the fracture network resulting from the models.

Figure 63 shows the fracture patterns generated from the simulation of both short and long

charges of explosive with the FEM-DEM program (note that the symmetry of fractures with

respect to the vertical axis is only a consequence of the identical models on both sides; an

asymmetrical mesh would not produce symmetrical fracture pattern). From Figure 63a (short

charge), two main features are observed: first, highly crushed areas occur around the blasthole,

particularly close to both ends; and second, longer cracks, up to 1 m long, develop in some

particular directions radially from the blasthole. In the case of a long charge (Figure 63b), the

fracture pattern exhibits a similar shape as that for the smaller charge, with only a slightly higher

concentration of long fractures around the upper half of the column.

1 m1 m

b) Vx at 65 µs after initiation

Pressure applied at borehole wall at 65 µs after initiation

a) Mesh for 0.5 kg (0.45 m) explosive

c) Mesh for 1.64 kg (2 m) explosive

1.7

GP

a

0.9

GP

a

Control points to calculate damage

113

Figure 63. Fracture patterns from FEM-DEM models for a) short and b) long charges of explosive, bottom initiated.

In order to establish the relationship between PPV and damage (i.e., crack density, ρ) from

models, both variables are determined at the controls points shown in Figure 62. At these points,

PPV values are determined from velocity time histories obtained from the FEM-DEM software.

Crack density values are calculated according to Equation 2-10, considering circular areas

centered at the same control points (akin to the method of direct measurement described in

section 2.4.1). The diameter of these circular areas to count and measure cracks is chosen

arbitrarily as the distance between each point and the closest control point towards the borehole,

or 0.05 m, whichever is greater. Consecutive cracks are counted as one, with a total length equal

to the sum of lengths. Control points and the criterion to determine the areas to calculate crack

density are chosen in such way that different damage zones are clearly identified, but at the same

time changes on the location of these points do not introduce significant variations on the results.

The calculated values of ρ are plotted against PPV, as shown in Figure 64, indicating a clear

correlation between ρ and PPV. Upon observation of this correlation, a semi-log curve is fitted to

the data, with the form:

( ) bPPVa +⋅= lnρ 5-17

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

R (m)

Z (m

)

-1 -0.5 0 0.5 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

R (m)

Z (m

)

a) b)

114

where PPV is in m/s, and a and b are parameters to be determined by linear regression. Since

both variables ρ and PPV are the result of modeling, they both have significant uncertainties

associated. Thus, a minimum areas regression is chosen over the typical simple linear regression.

This kind of regression minimizes the products between residuals in both variables, and provides

the most sound results, as it is independent of both scale and order of variables (i.e., same result

is obtained regardless of which variable is chosen as independent, which is not the case with

simple regression). The resulting equation is shown above the fitting curve in Figure 64.

Figure 64. Damage vs. PPV from FEM-DEM models.

Assuming Equation 5-17 valid to estimate damage in both 2D and 3D:

( )( )

+⋅=+⋅=

bPPVabPPVa

DD

DD

33

22

lnln

ρρ

5-18

By combining these equations with Equation 5-16, the following relationship between 3D and

2D crack density is obtained:

⋅+=

− 5.0

23 2ln

BDraDD ρρ 5-19

with a = 0.7, obtained from the semi-log regression above. Equation 5-19 is used to adjust

calculated blast-induced damage from stress waves obtained from 2D models, in order to

represent a 3D configuration.

0

0.5

1

1.5

2

2.5

3

1 10 100 1000

PPV (m/s)

Crac

k de

nsity

, ρ ( ) 8.1ln7.0 −⋅= PPVρ

Eliminated for regression

115

5.2.3 Calibration of material viscous damping and in-hole pressure function decay

Material viscous damping and pressure function decay are calibrated by replicating as closely as

possible measured and simulated particle velocity signals. For this, both parameters are adjusted

in the simulation of explosive charges of 0.1, 0.5 and 1.64 kg, considering material and explosive

properties from 5.1. Curves of particle velocity vs. time are determined at locations that match

those controlled with accelerometers in field experiments. The results from models were

corrected by the 2D/3D factor defined in 5.2.1 (Equation 5-16), and then compared with field

measurements in terms of both amplitude (PPV) and average frequency (Equation 4-8).

Variations in both viscous damping and decay rate were found to produce significant changes in

shape and amplitude of seismic signals. For example, increasing material viscous damping

produces signals of lower amplitude and lower average frequency, as a result of larger energy

dissipation, which is more significant for waves of higher frequency. Table 7 indicates a

summary of the changes in PPV and average frequency caused by variations in damping and

decay rate.

Table 7. Effect of variation in material viscous damping and pressure function decay rate over PPV and frequency of seismic signals PPV Avg. Frequency

Viscous damping, η Increasing Decreasing Decreasing

Decreasing Increasing Increasing

Decay rate, DR Increasing Decreasing Increasing

Decreasing Increasing Decreasing

As can be seen in Table 7 increasing or decreasing damping and decay rate produces the same

effect in PPV but opposite effect in average frequency. This connection between the variables

allows finding a solution that minimizes the differences between models and experimental data

in terms of both PPV and average frequency. Hence, both material damping and peak decay rate

were adjusted to match the available data. For damping, a unique value is calibrated, as all

experiments were carried out in the same rock mass. For decay rate, three different values are

calibrated corresponding to the three charge sizes used in the experiments. The resultant values

of this calibration process are as follows:

116

Material Damping: 2η = 0.55 MPa·s

Peak Decay Rate: DR = 110 GPa/ms, for 0.1 kg charge

DR = 90 GPa/ms, for 0.5 kg charge

DR = 28 GPa/ms, for 1.64 kg charge

Figure 65 and Figure 66 compare results from field experiments and models. Note that in these

two figures the amplitudes (PPV) from the 2D FEM-DEM code have been modified by the factor

defined by Equation 5-16. Figure 65 shows the results of PPV vs. scaled distance and average

frequency of velocity vs. distance. In the case of PPV, very good agreement is found between

models and field data. The trend of PPV is nearly identical in both cases. In terms of average

frequency there is a slight overestimation for long charges and a slight underestimation for the

smallest charges (0.1 kg). The agreement is nonetheless satisfactory, considering the significant

dispersion of results that occur in field measurements.

Figure 65. PPV vs. Scaled Distance and Average Frequency of Velocity vs. Distance from both field measurements and FEM-DEM models, considering calibrated material damping and pressure function decays.

100 101 102102

103

104

Distance (m)

Avg

. Fre

q. o

f Vel

ocity

(Hz)

100 101 102101

102

103

104

Scaled Distance (m/kg1/2)

PP

V (m

m/s

)

104

Measured 0.1 kg

103

)

Measured 0.5 kg

(

Measured 1.64 kg

102

Model 0.1 kg

Model 0.5 kg

100 10110

Scaled Distance (m

Model 1.64 kg

a) b)

117

Figure 66 compares the radial signals recorded from two different blasts with those produced by

the FEM-DEM code. From this figure it is possible to observe the good agreement between

measured and modeled signals. Even though they are evidently not identical, the agreement in

terms of both amplitude and shape indicates also a close match in terms of delivered energy,

which is essential for the results to be comparable when evaluating fracturing.

Figure 66. Comparison of r component of particle velocity between single shot experiments and FEM-DEM models. a) 0.5 kg (0.45 m) explosive, reverse primed, r = 1.6 m, θ = 129°. b) 1.64 kg (2 m) explosive, direct primed, measured on surface, r = 10.4 m, θ = 70°.

5.2.4 Material strength parameters

Having determined the pressure function and energy dissipation parameters (section 5.2.3), it is

possible to calculate shear and tensile strength (σs, σt,) from their relationship with loading rate,

according to the expressions indicated in section 5.1.2. Fracture toughness, KIC (and therefore

fracture energy, GC) is determined from available literature, given its low incidence on the model

results (see section 5.4.4).

As seismic signals decrease in amplitude and frequency with distance due to geometric spreading

and energy dissipation, loading rate also decreases with distance. Thus the appropriate loading

rate to determine strength parameters must be chosen for the distances of interest, i.e., a range of

distances where seismic wave induced fractures are likely to develop.

0 1 2 3 4-400

-200

0

200

400

600

800

Time (ms)

Vel

ocity

(mm

/s)

r

0 10 20 30-100

-50

0

50

100

150

200

Time (ms)

Vel

ocity

(mm

/s)

r

r

MeasuredModel

r

MeasuredModel

a) b)

r r

118

The following table includes the maximum loading and decay rates of seismic signals

determined from short and long charge models at various distances horizontally from the bottom

of the explosive. Both rates were calculated as approximately the average variation of the rising

and decaying parts of the horizontal stress (σx) curve.

Table 8. Loading and decay rates at various distances from blasthole

Distance (m) Short charge Long charge

Loading rate (GPa/s)

Decay rate (GPa/s)

Loading rate (GPa/s)

Decay rate (GPa/s)

0.1 24,000 11,000 12,000 2,500

0.2 6,600 3,800 3,600 1,700

0.3 5,300 2,900 4,800 1,100

0.4 4,300 1,300 3,700 990

0.5 2,600 1,000 2,600 670

0.6 2,700 1,000 2,100 560

As can be seen from Table 8, decay rates are always lower than rising rates. This is found to be

consistent with expected results, as the rising part of the in-hole pressure function is considerably

steeper than the decaying part. As lower loading rates result in lower material strength, it is

estimated that the decaying part of the seismic signals controls the material strength properties.

Also, since the fracture network from seismic signals is likely to be most important within a few

borehole diameters, it seems appropriate to choose an average value of loading rate from the

decaying part of the signals at distances between 0.1 and 0.2 m. Nevertheless, given the high

variability of loading rates close to the borehole, the behaviour of the models with changing

material strength properties will also be analyzed in section 5.4.4 by using limit values of

strength parameters. These limit values as well as the average values chosen for the models are

summarized in Table 9. In this table, values of σs and σt were calculated using the expressions in

Equation 5-1, Equation 5-2, and Equation 5-3.

119

Table 9. Summary of material strength properties

Parameter Short charge Long charge

Min Avg Max Min Avg Max

Loading rate (GPa/s) 1,000 5,000 10,000 560 2,000 8,000

Shear strength, σs (MPa) 82 107 178 82 82 149

Tensile strength, σt (MPa) 26 41 51 22 32 47

Fracture toughness, KIC (MPa m½) 5 10 15 5 10 15

Fracture energy, GC (J/m2) 310 1240 2790 310 1240 2790

Values of KIC were estimated from CCNBD test results shown in Figure E7. For this, loading

rate values reported in terms of stress intensity factor over time (GPa·m½·s-1) were converted to

stress over time (GPa/s) according to Equation E-6. Finally, values of GC were calculated from

KIC according to the expressions for plane strain given in Appendix E, with the elastic constants

indicated in section 5.1.1.

5.3 Summary of properties for models The following table includes a summary of the properties used for the numerical modeling of

single-hole blasts, with the exception of models in section 5.4.4, where limit values of material

strength parameters from Table 9 are used. The table also includes the references to the sections

in this thesis where the parameters are discussed and/or determined.

120

Table 10. Summary of material and explosive properties for numerical models Models

Section Short Charge: 0.5 kg, 0.45 m, 90% coupling

Long Charge: 1.64 kg, 2 m, 67% coupling

Material elastic properties

P-wave velocity, VP 5900 m/s 4.1.1.3 & 5.1.1

S-wave velocity, VS 3340 m/s 4.1.1.3 & 5.1.1

Young Modulus, E 75.3 GPa 4.1.1.3 & 5.1.1

Shear Modulus, µ 29.8 GPa 4.1.1.3 & 5.1.1

Lamé Constant, λ 33.4 GPa 4.1.1.3 & 5.1.1

Bulk Modulus, K 53.2 GPa 4.1.1.3 & 5.1.1

Poisson's Ratio, ν 0.26 4.1.1.3 & 5.1.1

Other material properties

Density, ρ 2670 kg/m3 5.1.2

Shear Strength, σs 107 MPa 82 MPa 5.1.2 & 5.2.4

Tensile Strength, σt 41 MPa 32 MPa 5.1.2 & 5.2.4

Fracture Toughness, KIC 10 MPa·m1/2 5.1.2 & 5.2.4

Fracture Energy, GC 1240 J/m2 5.1.2 & 5.2.4

Viscous Damping, 2η 0.55 MPa·s 5.2.3

Explosive and explosive / rock interaction properties

Velocity of Detonation, VOD 5300 m/s 4900 m/s 4.2 & 5.1.3

In-hole Peak Pressure, Pmax 1.7 GPa 0.9 GPa 4.2 & 5.1.3

In-hole peak Loading Rate, LR 2500 GPa/ms 1300 GPa/ms 4.2 & 5.1.3

In-hole peak Decay Rate, DR 90 GPa/ms 28 GPa/ms 5.2.3

121

5.4 Relative contribution of stress waves and gas expansion to damage

Damage distribution measurements around a single blasthole are combined with the results from

numerical models to determine the relative contribution from stress waves and gas expansion to

damage. The measurements correspond to those executed at the surface test site for 0.5 and 1.64

kg explosive charges, as presented in section 4.3.1. Numerical models for the same charges are

developed with the parameters indicated in 5.3 and the results are computed according to the

method described in 5.2. The final results from both experimental and numerical methods and

the computation of damage distribution from both stress waves and gases are included in this

section.

5.4.1 Damage quantification from models

The fracture patterns shown in Figure 63 are used to construct damage (crack density) contour

plots for short and long charges. The algorithm to compute damage distribution from models is

described in section 5.2.2. Similarly, PPV contour plots are calculated for the same models from

velocity time histories recorded at control points, as shown in Figure 62.

Figure 67 shows contour plots for damage and PPV for a short explosive charge. As expected,

the shape of the contour plot of damage is similar to the fracture pattern shown in Figure 63. The

area around the borehole corresponding to the crushed zone exhibits values of crack density

between 1 and 2.3. The zones corresponding to the long cracks extending radially are represented

by values of damage around 0.5.

The PPV contour plot shows significantly larger velocities at both ends of the explosive. The

amplitude of PPV in these areas reaches over 300 m/s, around twice as much as along the sides

of the borehole. Beyond this highly crushed zone, which extends roughly up to a distance where

PPV is 100 m/s, the radiation pattern exhibits slight lobes diagonally upwards, which are a

consequence of the initiation mode (bottom primed) of the explosive column.

A significant observation from the damage contour plot is the severe concentration of cracks

around the initiation point. Crack density in this area reaches values up to 2.5, about twice as

much as in other zones around the borehole. At the top of the explosive there is also a

concentration of cracks of lower magnitude. Although the fracture pattern in Figure 63 also

122

shows concentration of fractures around both top and bottom of the explosive, the crack density

contour plot makes very clear that fractures at the initiation point are denser. This constitutes an

important observation on fracture patterns from blasting, for it may explain the severe

concentration of damage originated from the initiation point, as measured from the field

experiments included in section 4.3.1. Further analyses on this point are included later in section

5.4.3.

Figure 67. Contour plots from FEM-DEM model for a short charge of explosive: a) Damage; b) PPV.

Figure 68 shows the contour plots of damage and PPV for the long explosive charge. Once again

it is clear that the highest concentration of fractures occurs around both bottom and top of the

explosive, reaching values slightly above 2 in both cases, which represents more than twice the

fracture density around the rest of the column. Also, as in the previous case, the PPV contour

plot shows the highest values just above and below the column, with values of PPV on top 50%

higher than those at the bottom. This difference in PPV is due to the initiation mode (bottom

primed), which causes seismic signals to build up in amplitude, as explained in section 4.1.5.

Finally, the contour plot of damage shows values close to unity for the crushed zone around the

borehole and about 0.5 around for the longer radial fractures.

a) Damage 2D, short charge, bottom initiated b) PPV (mm/s), short charge, bottom initiated

123

Figure 68. Contour plots from FEM-DEM model for a long charge of explosive: a) Damage; b) PPV.

In order to obtain an estimation of 3D damage for each case, Equation 5-19 is applied to the

calculated values of damage from the 2D models. The results of this procedure applied to the

both short and long charges are shown in Figure 69. From this figure it is evident that the 2D/ 3D

correction causes a significant reduction of the apparent damage. As expected, change in damage

is most significant for farther distances from the blasthole, whereas in its immediate vicinity

there is no change (see Equation 5-19). It is also apparent that the stress waves cause severe

damage only in the first 0.1 to 0.2 m from the blastholes. Considering a value of damage equal to

1 as an arbitrary limit to determine failure, the average distances from the boreholes to the failed

boundaries are 0.1 m for the short charge (90% coupling) and only 0.05 m for the long charge

(67% coupling). In both cases the most significant damage is found at both ends of the explosive

charge.

Finally, the results shown in Figure 69 are used in section 5.4.3 to determine the relative

contribution of stress waves and gas penetration to blast-induced damage.

a) Damage 2D, long charge, bottom initiated b) PPV (mm/s), long charge, bottom initiated

124

Figure 69. Damage from FEM-DEM model for short and long charges, after correction 2D to 3D.

5.4.2 Damage quantification from field measurements

Quantification of damage from field measurements was calculated on the basis of change in P-

wave velocity and shown in section 4.3.1. As seen in that section, results indicate non

symmetrical damage, not only on a vertical plane, but also on any horizontal plane (Figure 54

and Figure 56). In order to compare results with 2D models, however, it is necessary to obtain

results representative of any vertical plane. For this, the cylindrical average is considered. In

other words, the damage at any point on the plane r -θ is calculated as the average damage along

the horizontal angle (vertical being collinear with borehole axis).

Figure 70 shows the measured damage from 0.5 kg (0.45 m) and 1.64 kg (2 m) explosive

charges, considering cylindrical average as indicated above (from Figure 54 and Figure 56). Note

that these contour plots have been plotted with the same color scale to allow direct comparison.

These contour plots provide more consistent results and a simpler way to analyze damage results

from 3D data, compared to asymmetrical graphs. As horizontal variations are eliminated, the

effects of anisotropy and heterogeneity are significantly reduced; thus, these plots permit to

visualize more clearly vertical variations of damage due to varying loading conditions for

different orientations respect to the borehole axis (see section 2.2.1).

a) Shock wave damage 3D, short charge, bottom initiated

b) Shock wave damage 3D, long charge, bottom initiated

125

Figure 70. Contour plots of measured damage for short and long explosive charges considering cylindrical symmetry.

As observed in section 4.3.1, damage from both explosive charges is concentrated around

specific points in the explosive column and propagates in specific directions. In the case of the

short charge, which is 90% coupled, a significant part of damage is shown to propagate from the

initiation point (lower end) diagonally away from the borehole, at an angle of approximately 45°

with respect to the borehole axis. The extension of the severely damaged area (ρ > 1) reaches a

maximum distance of about 0.3 m from the explosive charge.

For the long charge (67% coupling) severe damage (ρ > 1) is observed to propagate from the

initiation point and around 1/3 and 2/3 of the explosive length, with a maximum extension of 0.7

m from the borehole. The peak damage in this case is, however, much lower than the case of the

short charge (ρ ≈ 3 vs. 4.2 for the short charge).

The lower maximum damage for the long charge may be explained by the lower coupling of this

charge (67% vs. 90%). As shown in section 4.2, the in-hole pressure from the smaller diameter

charge (67% coupling) is around half of that from the larger diameter. This lower pressure brings

two main consequences: first, the seismic waves in the immediate vicinity of the blasthole are

generally of lower amplitude, and second, gases interact with the rock mass at lower pressures.

Additionally, as the area of a section of the long explosive charge is only about 55% of the area

a) Measured damage 3D, short charge, bottom initiated, cylindrical average

b) Measured damage 3D, long charge, bottom initiated, cylindrical average

126

of the short charge, the amount of gas per unit of length resulting from the former is around the

same fraction of the later. Thus, less severe fracturing should be expected due to a) lower stress

wave amplitudes, b) lower gas pressure, and c) less gas volume per unit of length.

Despite the slightly shorter extension of severe damage, the longer charge exhibits a much more

extensive damaged area. Around the short charge, for example damage with ρ > 0.5 propagates

up to distances around 0.5 m from the blasthole. In contrast, damage for the longer charge,

considering the same fracture density, extends to a much wider area, including almost

completely the area shown in the figure (2 m x 2.6 m) and beyond. It is to be noticed that the

overall pattern of damage in both cases is very similar, with damage being more extensive from

the initiation point diagonally down. Further comments on this are included in section 5.4.3,

when distinction between stress waves and gas damage is made.

5.4.3 Quantification of damage from stress waves and gas expansion

Quantification of total blast-induced damage, caused by both stress waves and gas penetration

was carried out through inversion of P-wave velocities into crack density from cross-hole

measurements, as described in section 4.3.1. These results were converted into cylindrically

symmetrical models in order to properly analyze and compare with numerical models, as

explained in section 5.4.1.

The other front of research to quantify damage is the calculation of stress wave contribution to

damage, which was assessed through numerical models using a 2D combined finite and discrete

elements method. Since wave propagation in 2D exhibits different geometrical spreading

compared to the 3D case (see sections 5.2.1 & 2.5.3, Figure 12), the results from these models

were converted into equivalent 3D damage by using the correlation between crack density and

PPV.

The final part of damage quantification is the determination of the relative contribution of gas

penetration to damage. For this, two assumptions are made: first, that crack densities determined

from both experiments and models are physically equivalent, and second, that the only sources of

blast-induced damage are stress waves and gas expansion. Thus, it is reasonable to assume that

the contribution to damage from gas is equal to the difference between total blast damage and

stress wave damage. In terms of crack density, this can be written as:

127

SCG ρρρ −= 5-20

where ρG and ρS are crack densities due to gas expansion and stress waves, respectively, and ρC

is the combined blast-induced damage considering both stress waves and gas. Figure 71 and

Figure 72 show the results of this operation applied to the results from measurements and models

for short and long charges. For comparison these figures include the results of stress wave

damage and combined damage shown in Figure 69 and Figure 70, respectively. In order to

facilitate direct assessment, the scale of colors applied to all these contour plots was taken to be

the same range (0 ≤ ρ ≤ 2). These figures also show the maximum crack density and a measure

of the total damage caused to the rock in each case. This measure of total damage corresponds to

the crack density integrated over the volume represented by each figure (i.e., the cylindrical

volume with its axis collinear with the borehole axis with a radius of 1 m, and length of either 2

m (short charge) or 2.6 m (long charge)). The equation to calculate this measure of total damage

is as follows:

∫ ∫= =

==2

1

1

0

2y

yy

x

x

dydxxVD ρπρ 5-21

where D refers to total damage over the volume in m3, ρ and ρ are crack density and its average

over the represented volume V, and x and y are the Cartesian coordinates shown in each figure

with limits [0, x1] and [y1, y2]. As the actual computation of crack density is done at discrete

points, a discrete version of Equation 5-21 is used:

∑∑ ∆∆≈i j

iji yxxD ρπ2 5-22

Figure 71 provides a clear image of the contribution from stress waves and gas to damage for a

short charge, not only in terms of extension but also in terms of severity. The most evident

distinction between stress waves and gas damage is the significantly larger extent reached by the

later. This is not a surprising finding, as the greater extent of gas damage compared to stress

waves is a well known characteristic of borehole blasting, as seen in section 2.1. In terms of

maximum crack density, the peak value associated with stress waves is not substantially different

from that corresponding to gas, with the former being slightly higher (ρmax = 2.5 for stress waves

128

vs. ρmax = 2.1 for gas). In terms of total damage, however, gas expansion exhibits a considerably

larger value than stress waves, accounting for over 95% of the total combined damage.

Figure 71 also provides insights to interpret the fracture network development from both stress

waves and gas expansion, as well as the interaction between the two, which is one of the

fundamental objectives of this research. From the stress wave contour plot it is clear that the

zone with the highest crack density occurs around the explosive’s initiation point. This higher

crack density facilitates the penetration of gases into the rock mass in this area. Furthermore, as

the initiation point corresponds to the place where explosive reactions begin to take place, the

fracture network resulting from both stress waves and gas expansion begin to develop precisely

at this point. Thus, it is natural to expect gases to be initially driven into this area as a result of

the newly created stress wave induced fractures. This initial flow of gas creates even more

fractures, thus facilitating more gas to penetrate. At the same time, this process causes a drop in

the overall borehole gas pressure, decreasing the potential of damage from gas penetration into

other areas. The orientation of damage propagating from the explosive bottom (~45°

downwards) can be explained by the directionality of stress wave fractures as shown in Figure

63a. From this figure it is easy to see that long fractures tend to propagate precisely downwards

and out from the bottom of the explosive. These stress wave induced fractures are likely to be

responsible for conducting gases in this direction, causing the observed damage in this area.

Another significant observation in terms of damage is the low crack density measured around the

top of the explosive, despite the model predictions indicating high stress wave induced crack

densities in the same area. Although this could be partly due to low coverage of this zone with

the cross-hole system (Figure 51), there is a significant difference in confinement which may

explain the lower damage in this area. As the detonation front progresses through the blasthole,

gases are produced, preventing the immediate venting of the newly created gases along the

borehole. At the top of the explosive, however, there is no source of confinement other than

water, which evidently doesn’t constitute the same barrier as the high pressure gases. Thus, the

faster venting of gases would cause a faster drop in pressure, thus reducing the damage around

this area.

129

Figure 71. Relative contribution of stress waves and gas expansion to damage for a short charge, bottom initiated.

Finally, the relative contribution of stress waves and gas expansion to damage, for a 2 m long

explosive column is shown in Figure 72. As in the case of the short charge, gas expansion

damage extends considerably farther than stress wave damage. Also, albeit the maximum crack

density caused by stress waves is slightly higher than that caused by gas (ρmax = 2.2 for stress

waves vs. ρmax = 1.9 for gas), the total damage caused by gas represents over 95% of the total

combined damage (both calculated over the cylindrical volume represented in the figure), as

before.

Compared with the results from the short charge, peak values of crack density are between 10%

and 30% lower. These lower values are probably due to the lower coupling of the longer charge

(67%) compared to the shorter one (90%), which causes lower amplitudes in both stress waves

and gas pressure in the rock mass. On the other hand, total damage is higher by a factor of 3.6 for

gas and combined damage, and by a factor of 1.6 for stress wave damage, compared to the short

charge. These higher values of total damage are explained by the larger amount of explosive

used in this case, which evidently is expected to deliver more energy to the rock and thus cause

more damage from both stress waves and gas.

The long explosive charge shows the same features observed for the short charge around the top

and bottom of the explosive (i.e., high amplitude extended damage from the bottom and very

Combined damage: 2.4max =ρ

31.1== VD ρ m3

Shock wave damage: 5.2max =ρ

05.0== VD ρ m3

Gas expansion damage: 1.2max =ρ

27.1== VD ρ m3

b) c) a)

- =

130

little damage on top). In particular the same pattern of damage propagating diagonally down

from the initiation point is observed for both explosive charges. The phenomenon is explained in

detail in the analysis of Figure 71.

Finally, the variations on the extension of damage along the explosive column, particularly the

larger damage observed around 1/3 and 2/3 of the column length, are likely to be the result of the

combined action of both stress waves and gas expansion. Even though stress wave damage

contour plot in Figure 72 does not indicate any extended damage around these areas, from Figure

63b it is easy to see that some long fractures tend to develop radially considerably beyond the

relatively uniformly damaged zone around the borehole. As these long cracks develop, they

conduct gases into the rock mass causing damage to propagate even further. Thus, damage

observed at these points along the column is likely to be due to the long cracks initiated by stress

waves, which are later expanded by explosive gases driven into the rock mass.

Figure 72. Relative contribution of stress waves and gas expansion to damage for a long charge, bottom initiated.

Gas expansion damage: 9.1max =ρ

57.4== VD ρ m3

Combined damage: 0.3max =ρ

65.4== VD ρ m3

Shock wave damage: 2.2max =ρ

08.0== VD ρ m3

a) c) b)

- =

131

5.4.4 Sensitivity analysis for variations in input parameters

The effect of variations in material strength parameters on the results from FEM-DEM models is

analyzed in this section. In particular, changes in fracture patterns of short and long charge

models are studied under variations in fracture energy GC, tensile strength σt, and shear strength

σs. The upper and lower limits considered for each of these variables are indicated in Table 9.

Each variable is studied independently by taking it to these limits while all other variables

remain constant with values summarized in Table 10.

Figure 73 shows the resultant fracture patterns with varying fracture energy, GC. From this figure

it is evident that this parameter has very little influence on the overall fracture process. Even with

a variation of nearly one order of magnitude (from 310 to 2790 J/m2) the fracture networks seem

nearly identical for both short and long charges. This indicates that even though this parameter

was estimated only approximately from the available literature, it provides negligible uncertainty

to the model results.

The effect of variations in tensile strength, σt is shown in Figure 74. The ranges studied for this

parameter are 26 to 51 MPa for the short charge and 22 to 47 MPa for the long charge. Although

in this case more differences are observed between the extreme cases, variations from the

average value are still of very low significance when studying fracture densities. Hence, it is

concluded that variations in σt have little contribution to the overall uncertainty of the models.

Fracture pattern changes with shear strength, σs are shown in Figure 75. The ranges studied in

this case are 82 to 178 MPa for the short charge, and 75 to 149 MPa for the long charge. From

this figure it is clear than σs produces the most significant variations in fracture patterns for both

short and long charges. Figure 75a and Figure 75d (lower values of σs) exhibit higher crack

densities compared to the average values, particularly for the short charge. Nevertheless, the

maximum distances reached by cracks in different directions and the overall shape of the fracture

pattern are nearly the same in both cases. The opposite case with highest values of σs (Figure 75c

and Figure 75f) indicated lower crack densities and different fracture patterns, although once

again, the maximum extent of fractures remains nearly unchanged.

132

Figure 73. Effect of variations in GC over fracture patterns obtained for short and long explosive charges. Short models: σs= 107 MPa; σt= 41 MPa; a) Min GC= 310 J/m2; b) Avg. GC= 1240 J/m2; c) Max GC= 2790 J/m2. Long models: σs= 82 MPa; σt= 32 MPa; d) Min GC= 310 J/m2; e) Avg. GC= 1240 J/m2; f) Max GC= 2790 J/m2.

The change in fracture pattern is more evident from the long charge (Figure 75f), which in

contrast to the other cases indicates most fractures oriented sub-horizontally with a slight

inclination downwards away from the borehole. The reasons for this re-orientation of fractures

with increasing σs are probably related to the loading mode of the material, and hence on the

initiation mode of the explosive, although a deeper examination of this phenomenon is beyond

the scope of this thesis.

a) b) c)

d) e) f)

133

Figure 74. Effect of variations in σt over fracture patterns obtained for short and long explosive charges. Short models: σs = 107 MPa; GC = 1240 J/m2; a) Min σt = 26 MPa; b) Avg. σt = 41 MPa; c) Max σt = 51 MPa. Long models: σs = 82 MPa; GC = 1240 J/m2; d) Min σt = 22 MPa; e) Avg. σt = 32 MPa; f) Max σt = 47 MPa.

In the case of the short charge, it is estimated that deviations in σs for the ranges considered,

cause variations in crack density by about ±30% from the average. For the long charge, however,

there is little variation in terms of crack densities, except at the borehole boundary, even though

the fracture pattern clearly changes when σs is increased significantly.

a) b) c)

d) e) f)

134

Figure 75. Effect of variations in σs over fracture patterns obtained for short and long explosive charges. Short models: σt = 41 MPa; GC = 1240 J/m2; a) Min σs = 82 MPa; b) Avg. σs = 107 MPa; c) Max σs = 178 MPa. Long models: σt = 32 MPa; GC = 1240 J/m2; d) Min σs = 75 MPa; e) Avg. σs = 82 MPa; f) Max σs = 149 MPa.

Finally, it is necessary to mention that even though material strength parameters are chosen to be

constant in each particular model, these parameters actually exhibit a clear strain rate

dependency, as observed from experimental results. In general, higher strain rate or loading rate

means higher strength parameters. Thus, in reality, a proper model should consider strain rate

dependency by assigning higher strength parameters to the areas with higher loading rates. As in

the case of blasting higher loading rates occur closer to the blasthole, such model might predict

lower fracture densities closer to the borehole but higher densities for larger distances. In other

words, it is estimated that there might be a systematic error in the models presented in this thesis

a) b) c)

d) e) f)

135

consisting on a prediction of higher densities close to the blasthole and lower densities farther

away. It is concluded, however, that this potential error does not invalidate the results, as it

probably does not cause severe variations that contradict the analyses and conclusions of this

research. A precise study of strain rate dependency and its implications in rock blasting

experiments and models is clearly required, and is proposed as an important area of future

investigation in the fields of dynamic fracture and rock fragmentation .

5.5 Discussion The construction and interpretation of models for this work required a number of steps from the

measurement and calibration of input parameters, to the development of an appropriate approach

to correctly interpret the results.

The study of seismic waves carried out as part of this work permitted to identify the main

parameters that are significant on the resultant seismic waves. For the models utilized here, the

identified parameters are: i) material viscous damping; ii) P and S-wave velocities (or more in

general elastic constants); iii) VOD; iv) in-hole pressure function; v) relative location of

observation point with respect to explosive charge, and vi) length of explosive charge. Important

to keep in mind is that the choice of parameters above is somewhat arbitrary, as most of them are

dependent on other variables, and thus, other variables may be chosen instead. For example VOD

and in-hole pressure function are dependent on explosive type, coupling, coupling material,

borehole diameter, initiation method, and possibly on confinement conditions (which vary along

the borehole). Thus, the latter 6 parameters might have been chosen instead of the former two. It

is estimated, however, that the chosen parameters provide a relatively simple yet comprehensive

point of view to study blast-induced seismic waves.

Viscous damping and pressure function decay were calibrated by using measured seismic

signals. Amplitude and frequency content of signals were found to be significantly sensitive to

both parameters in contrasting ways (increasing damping causes both decreasing amplitude and

frequency, while a faster pressure decay produces decreasing amplitude but increasing

frequency), which allowed successful calibration with minimum error. Thus, the analysis of

seismic signals in terms of both amplitude and frequency proved to be of significant importance

for reliable calibration of both material attenuation and in-hole pressure function.

136

Material strength properties were determined through laboratory experiments and were found to

be dependent on the loading rate and hence on the frequency content of stress signals. Even

though material strength parameters were determined only approximately, due to the elevated

and highly variable loading rates from blasting, an analysis of sensitivity indicated that only

shear strength would influence significantly the results of damage. Damage calculated from

models was found to be accurate enough for the purpose of this work.

The problem of propagation of seismic signals in 2D vs. 3D case was studied and specially

considered as part of this study. The difference between the two cases is that seismic waves

suffer different geometric attenuation a result of the different volume over which energy is

spread as the wave front moves away from the source (the attenuation of waves in 2D is lower

than in 3D by a factor proportional to r 0.5). In order to account for this difference in attenuation,

a simple approach was proposed to convert 2D wave amplitudes into 3D equivalent (Equation 5-

16). The approach was tested for short and long charges of explosive in the linear elastic case by

comparing the PPV contour plots from the Heelan analytical solution with those given by the

FEM-DEM program, modified by Equation 5-16. The correction was found satisfactory, based

on the comparison of shape and attenuation of contour plots from both P and S-waves.

In addition to PPV correction, the proper use of 2D models required the correction of damage.

Keeping this in mind, damage was quantified from models as crack density and related to PPV

by curve fitting. With the assumption of equal damage for equal PPV in both 2D and 3D cases, a

simple equation was derived to determine 3D crack density from 2D models (Equation 5-19).

Even though the numerical models indicate a good correlation between PPV and damage, which

somewhat justifies the correction of damage based on equivalent PPV, it is also recognized that

the creation and development of fracture networks is a highly complex phenomenon that requires

more than simple PPV estimation to be properly predicted. Even for an isotropic and

homogeneous material, as assumed in the numerical models, the prediction of fractures is limited

to an estimation of zones defined by fracture density. Furthermore, considering that the complex

interaction between stress waves and gas expansion has yet to be accounted for, it is clear that

the method developed here requires further development. This method can, however, be used as

a guideline to estimate areas of greater damage or as a diagnostic tool in blasting.

137

Despite the relatively long extension of fractures obtained from the 2D models (up to 1 m for

both long and short charges), the correction applied to estimate 3D equivalent damage indicates

that actual damage from stress waves has a short range, between 0.1 and 0.2 m (i.e., 2 to 4

borehole diameters) for the analyzed sources. Also, stress wave damage from models is more

severe at both ends of the explosive column, which is coincident with the highest PPV values.

This phenomenon is due to the high gradient of loading existing at these points caused by the

discontinuity in loading conditions, which results in large deviatoric stresses.

Although the extension of damage from stress waves reported here is significantly lower than

measurements carried out in small samples (as in Dehghan Banadaki 2010, who reported up to

~10 borehole diameters of damage from stress waves with detonating cord), it is necessary to

consider that the results from the models in this work are akin to calculating average damage,

due to the application of the 3D/2D correction (see Figure 64 and Equation 5-19). Thus, the

extent of damage reported here does not correspond with maximum crack length, but may be

considered as an average maximum distance where damage is significant.

Additionally, the conditions of initiation and confinement of these particular experiments are

also likely to cause gases to be driven into fractures around the initiation point. Since both stress

waves and gas expansion begin to develop at the initiation point, so does the fracture network

resulting from them. Consequently, gases are likely to be initially driven into this area as a result

of the newly created stress wave induced fractures. This initial flow of gas creates even more

fractures, thus facilitating more gas to penetrate. Also, since boreholes are water filled and the

explosive is bottom initiated, the initiation point is subject to higher confinement, which also

stimulates the penetration of gases in this zone.

Finally, it is important to mention that the analysis of sensitivity indicating shear strength as the

only significant variable on damage, suggests that fractures obtained from models are mostly

controlled by shear. Thus, it is essential to keep in mind that the results shown here, including in

particular the equation relating crack density and PPV, apply to the case of dominant shear

fractures. The case of dominant tensile fractures, which can be found in situations that

incorporate a free surface, should be studied and analyzed independently.

138

Chapter 6

6 Extension of Results to Underground Blasting This chapter presents the results from a full-scale blast monitoring program executed at Williams

mine, and the simulation of one of these blasts with the FEM-DEM code previously described.

The monitored production blasts correspond to the same level as the single-hole control blasts

presented in Chapter 4. The general layout of experimental setup and monitored blasts is shown

in Figure 27. Typical geometry and initiation method of these production blasts are schematized

in Figure 28 and Figure 29.

Section 6.1 includes measured seismic signals from the aforementioned production blasts in

terms of both amplitude and frequency content. As in the case of control blasts, the amplitude of

these signals is measured in terms of peak particle acceleration (PPA) and peak particle velocity

(PPV), and the parameter to study frequency content corresponds to the average frequency

calculated according to section 4.1.3. Section 6.2 shows the method developed in Chapter 5 to

estimate blast-induced damage, applied to a regular production blast. The determination of some

material and explosive properties is carried out by calibration against field data, by following

nearly the same procedure described in 5.2.3.

6.1 Production blast monitoring Figure 76 to Figure 78 show particle velocity time histories recorded from three different

production blasts by triaxial accelerometers grouted in the rock mass (blast geometries and setup

shown in Figure 28 and Figure 29). These figures also show the amount of charge weight

detonated for each delay round. They are essentially duplicates of what is observed for single-

hole control blasts, i.e., each hole or delay round in the production blast generates an analogous

vibration signal representative of the single-hole control blast (see for example Figure 39a). The

symbol r′ˆ is used to refer to the radial direction from the center of gravity of the explosive

charges to the sensor, whereas r' is the distance between these two points.

139

Figure 76. Production Blast #12, March 15, 2007 Dayshift - Accelerometer A. 300 kg Emulsion - Collar Primed - 30 g/m Det Cord r' = 77.3 m.

Figure 77. Production Blast #13, March 15-16, 2007 Nightshift - Accelerometer A. 900 kg Emulsion - Booster Collar Primed - 30 g/m Det Cord r' = 74.2 m.

Figure 78. Production Blast #22, March 22, 2007 Dayshift - Accelerometer A. 650 kg Water Gel - Booster Collar Primed - 30 g/m Det Cord r' = 43.5 m.

0 100 200 300 400 500 600 700-30

-20

-10

0

10

20

r 0

Time (ms)

Vel

ocity

(mm

/s)

0 100 200 300 400 500 600 700

0

30

60

Tota

l Cha

rge

Wei

ght (

kg)

2 2 2 2 2 2 2 1 1

↑ Design Timingn # Holes with same delay

r′ˆ

0 500 1000 1500-30

-20

-10

0

10

20

30

r 0

Time (ms)

Vel

ocity

(mm

/s)

0 500 1000 1500

0

30

60

90

Tota

l Cha

rge

Wei

ght (

kg)

2 2 2 2 2 4 4 3 3 2 4 4 3 3 2 2 2 1 1


r′ˆ

0 100 200 300 400 500 600 700-40

-20

0

20

40

60

r 0

Time (ms)

Velo

city

(mm

/s)

0 100 200 300 400 500 600 700

0

30

60

90To

tal C

harg

e W

eigh

t (kg

)

2 2 2 2 3 2 2 2 2 2 2 2 2


r′ˆ

140

The identification of P and S-waves is carried out by following the methods applied to single-

hole blasts shown in 4.1.1.1 and 4.1.1.2 (i.e., stereonet particle motion analysis and rotation to

spherical coordinates). Arrival time verification was not possible, as the difficulties of cabling in

underground operations made it unfeasible to measure blast ignition times. Nevertheless, a

verification of consistency of difference between arrival times of P and S-waves (i.e., linear

variation with distance) was applied and the results were found satisfactory. Figure 79 shows the

three components of velocity from an individual shot within a production blast. As in the case of

control blast, P and S-waves are clearly identifiable from the components r and θ , respectively.

Figure 79. Components r , θ and φ of velocity for a production blast shot consisting of 2 holes. r1 = 24m, θ1 = 36°; r2 = 39m, θ2 = 168°.

Figure 80 shows PPA and PPV from recorded P and S-waves vs. scaled distance. For

comparison, this figure also includes the results from single-hole control blasts shown in Figure

38. Aside from the variations caused by initiation modes and relative source-sensor location

(discussed in section 4.1.5), the relevant contributors to scatter in both PPA and PPV are varying

charge locations, and lack of control of timing and the exact amount of explosive in each hole.

Another uncertainty comes from the assumption that all holes in each delay round detonated at

the same instant. Other significant sources of scatter are the local geologic, geometric and stress

conditions, which jointly contribute to variations on radiated seismic energy. For example,

blastholes located at the opposite side of the raise are likely to provide little contribution to the

recorded amplitudes compared to those on the same side of sensors. Also, geology and stress

conditions applied to the specific pre-blast excavation geometry constitute major variables that

determine rock fracturing. These pre-blast fractures can also play an important role on the

propagation of stress waves.

0 5 10 15-40

-20

0

20

40

60

80

100

Time (ms)

Velo

city

(mm

/s)

0 5 10 15-100

-50

0

50

100

150

Time (ms)

Velo

city

(mm

/s)

0 5 10 15-30

-20

-10

0

10

20

30

Time (ms)

Velo

city

(mm

/s)

P-wave S-wave

141

Figure 80. PPA and PPV for P and S-waves vs. scaled distance in rock. Production and Control Blasts at Williams mine.

Despite the scatter, a clear trend is observed for the decay of PPA and PPV in rock with charge

weight and distance. The amplitude of S-waves, although slightly lower than P-waves shows a

similar decay rate. Furthermore, the amplitudes generated by the control blasts appear larger

compared to the production blasts for the same scaled distance. This is to be expected due to i)

higher detonation pressure of the boosters employed, ii) better coupling of the explosive in the

borehole, and iii) use of ‘point initiation’ of explosive charge in the control blasts compared to

‘side initiation’ of the explosive columns in the production blasts.

The measurements confirm that the trend of amplitude (i.e., slope of curve amplitude vs. scaled

distance) in terms of PPA does not match the trend in terms of PPV, due to the different

dependency of both variables with time. Effectively, the process of time integration to convert

from particle acceleration to velocity implies not only a shift in phase but also a relative

reduction in amplitude of higher frequencies. Also, the energy dissipation that occurs by several

mechanisms (which is summarized by the coefficient of attenuation) increases with frequency.

Consequently, as higher frequencies are more significant in terms of acceleration, the decay of

PPA is higher compared to the decay of PPV.

1

10

100

1000

1 10 100


PP

V (m

m/s

)

1

10

100

1000

1 10 100


PP

A (g

)

Single long P-wave Single short P-wave Production P-wave

Single long S-wave Single short S-wave Production S-wave

a) b)

142

The frequency content of the vibration signals in rock is shown in Figure 81, for both particle

acceleration and velocity. As expected, the average frequency decreases with increasing distance

from the blast source due to the higher attenuation of higher frequencies. At a distance of 100m,

the maximum frequency of high-amplitude acceleration signal averages around 1.6 kHz; for the

corresponding particle velocity signal it is around 500 Hz.

Figure 81. Frequency spectrum of particle Acceleration and Velocity vs. distance. Production and Control Blasts at Williams mine.

The investigation also revealed the effect of initiation mode on the resulting vibration level. The

current practice at the mine employs a 150 grain detonating cord (i.e., 30 g/m) along the

explosive column in addition to a Pentolite booster at the toe of each hole. Detonating cords of

such strength are likely initiate the explosive column sideways, which would bypass the booster

at the toe. This would result in either deflagration of the explosive column or only partial

detonation across the diameter of the borehole. Both scenarios would result in lower energy

release from the explosive than booster initiation at the toe. This is clearly demonstrated in

comparing the vibrations generated in the control blasts with those of the regular production

blasts. In the former, only booster initiation was employed compared to the production blasts. In

almost every case, the vibration level, and therefore the explosive energy release, was

significantly higher than in production blasts for identical scaled distance (Figure 80).

100

1000

10000

100000

10 100 1000

Distance (m)

Avg

. Fre

quen

cy o

f Vel

. (H

z)

100

1000

10000

100000

10 100 1000

Distance (m)

Avg

. Fre

quen

cy o

f Acc

. (H

z)

Single long Single short Production

a) b)

143

The production blasts monitored also exhibited considerable scatter in hole firing times, as well

as missing holes (Figure 76 to Figure 78). This could be due to any combination of variations in

the firing times of the detonators, ‘tracing’ of the holes by detonating cord, and poor explosive

loading practice. In either case, this leads to serious lowering of explosive performance and

improper fragmentation. For example, production blast #12 shows very poor energy release

during the first half of the blast (Figure 76), blast #13 shows uneven energy release for similar

explosive charge weights (Figure 77), and blast #22 shows missing holes (Figure 78). Such

occurrences were typical of all the production blasts monitored.

6.2 Blast simulation The simulation of a single ring from a production blast with a similar configuration to those

monitored at Williams mine is presented in this section. The chosen geometry and initiation

sequence is the same as shown in Figure 28, projected on a horizontal plane.

6.2.1 Model parameters

The calibration of parameters is done through the comparison of PPV and average frequency

values at various distances from the blast. The calibrated parameters in this case correspond to

the pressure function peak amplitude (Pmax), decay rate (DR), and material viscous damping (2η).

Material elastic parameters (E, µ, k, λ, ν) are obtained from the measurement of P and S-wave

velocities presented in 4.1.1.3, whereas explosive's VOD is taken as the VOD of the detonating

cord used to initiate the explosive from manufacturer's data sheet (see Figure 29). Finally

material strength parameters (σs, σt and Gc) are assigned arbitrary values, due to the lack of

information from the mine. Hence, the results from these models have only an illustrative

purpose, which is to show the application of the method to estimate damage from a real

production blast. The application of this method to estimate damage in a real case requires,

evidently the application of appropriate input parameters for the specific site.

Figure 82 shows the mesh used for the calibration of parameters. In this case, only one side of a

ring from a typical production blast was used, after verifying that peak amplitudes and frequency

spectra in the near field differ little from the modeling of a full ring. In order to improve the

simulation of the fracturing process and finite VOD, higher mesh refinement is used in the

vicinity of the blastholes. Typical element size is 0.05 m around the blastholes and 0.2 m towards

144

the area to record output histories. Outside these areas larger elements were used in order to

place the outer boundaries far away to minimize reflections without significantly increase

running times.

Figure 82. Mesh used to model production blast in FEM-DEM code: Refinement for calibration of parameters (35,000+ elements).

Control points

1 m

Half of Raise

Approximate stope boundary

Blastholes

145

During the process of calibration of parameters it was found that achieving higher frequencies in

seismic signals from the model requires significant mesh refinement, which implies a significant

increase in running times (typically a reduction in element size by a factor of 2 implies an

increase in running times by a factor of 8). Thus, it was decided to tolerate lower frequencies

from the model putting emphasis on the calibration of amplitudes. These lower frequencies are

mostly a result of insufficient mesh refinement, and it is estimated that frequencies calculated

with higher mesh refinement should not differ much from the measured values. The summary of

properties used in this model is presented in Table 11.

Table 11. Summary of material and explosive properties for production blast simulation Values Source

Medium properties

P-wave velocity, VP 6230 m/s Measured, 4.1.1.3

S-wave velocity, VS 3610 m/s Measured, 4.1.1.3

Young Modulus, E 86.8 GPa 4.1.1.3 & Appendix A

Shear Modulus, µ 34.8 GPa 4.1.1.3 & Appendix A

Lamé Constant, λ 34.0 GPa 4.1.1.3 & Appendix A

Bulk Modulus, K 57.2 GPa 4.1.1.3 & Appendix A

Poisson's Ratio, ν 0.25 4.1.1.3 & Appendix A

Density, ρ 2670 kg/m3 Arbitrary

Shear Strength, σs 75 MPa Arbitrary

Tensile Strength, σt 15 MPa Arbitrary

Fracture Toughness, KIC 6.8 MPa·m1/2 Arbitrary

Fracture Energy, GC 500 J/m2 Arbitrary

Viscous Damping, 2η 0.3 MPa·s Fitted

Explosive and explosive / rock interaction properties

Velocity of Detonation, VOD 5500 m/s Tech. specs.

In-hole Peak Pressure, Pmax 1.5 GPa Fitted

In-hole peak Loading Rate, LR 2500 GPa/ms Arbitrary

In-hole peak Decay Rate, DR 100 GPa/ms Calibrated

146

Figure 83 shows the comparison of amplitudes and frequencies from modeling (considering the

above parameters) with those measured in the field. Note that PPV values are corrected from 2D

to 3D equivalent PPV according to Equation 5-19. From this figure it is clear that the peak

amplitudes from the model match fairly well those from experiments, whereas in terms of

frequency, lower values were obtained, as explained above.

Figure 83. Comparison of PPV and frequency content of stress waves between field data and FEM-DEM simulation. PPV values are corrected by factor given by Equation 5-16 to estimate equivalent 3D PPV.

Figure 84 shows the horizontal velocity time history recorded 20 m to the east of the raise middle

point. Although some significant noise occurs after the first event, the main events corresponding

to the arrival of P-waves from each delay are easily identifiable.

Figure 84. Velocity time history recorded at 20 m horizontally from raise center point (distance to boreholes from 13 to 16 m). The amplitude of signals is not corrected by factor given by Equation 5-16 to estimate equivalent 3D particle velocities.

0 10 20 30 40 50 60 70 80-2000

-1000

0

1000

2000

3000

4000

Time (ms)

Vel

ocity

(mm

/s)

0 10 20 30 40 50 60 70 80

0

10

20

30To

tal C

harg

e W

eigh

t (kg

)

1 1 1 1 1

↑ Design Timingn=1 # Holes with same delay

100 101 102100

101

102

103

Scaled Distance (m/kg1/2)

PP

V (m

m/s

)

101 102 103102

103

104

Distance (m)

Avg

. Fre

q. o

f Vel

ocity

(Hz)

a) b)

Model

Measured

Model

Measured

147

6.2.2 Production blast damage

After the calibration of parameters, a similar but finer mesh was used to calculate blast-induced

damage from stress waves. In this case typical element size is 0.05 m around the blastholes and

0.1 m for the rest of the area expected to be damaged. As in the previous case the outer

boundaries are placed away from the area of interest in order to prevent significant reflections.

The mesh use in this case is shown in Figure 85.

Figure 85. Mesh used to model production blast in FEM-DEM code: Refinement to determine fracture pattern, damage and PPV contour (27,000+ elements). Symmetry was used, model includes half of stope only.

Figure 86 shows the stress wave propagation from the first two blastholes in the initiation

sequence. In this case waves propagate outwards from the raise, due to the high strength of the

detonating cord used to trace the explosive (150 grain), which is considered enough to ignite the

emulsion from the collar, as explained in 6.1. The deflection of waves when crossing adjacent

boreholes, generating both P and S-waves is to be noted. The phenomenon is more evident from

the detonation of the first pair of blastholes, as no blast-induced cracks interfere with the process.

This is consistent with the theory of wave's refraction, which indicates precisely the generation

of both types of waves when a single wave crosses through a discontinuity at an angle different

from normal. It is important to note that this refraction is a consequence of 2D models only, due

to the lack of third dimension, which implies that boreholes are ‘seen’ by the model as

significant discontinuities in the rock mass. Thus, although physically correct in a 2D model, this

refraction does not correspond with the 3D situation.

1 m

Half of Raise

Approximate stope boundary

Blastholes

148

Figure 86. Stress wave amplitude from two adjacent blasthole with different delays. Colors show horizontal particle velocity (vx) at 0.5 ms after the initiation of each blasthole. PPV at snapshots (wave front in blue): left 250 mm/s; right 200 mm/s.

The final fracture pattern and the 2D and 3D versions of crack density contour plots obtained

from the production blast simulation are shown in Figure 87. The fracture pattern clearly shows

the highest concentration of fractures developing between the initiation and end points of each

blasthole. In contrast to single-hole simulations shown in the previous chapter, fracture density is

not always significantly higher at the ends of each explosive charge. Upon observation of the

fracturing process throughout the initiation sequence, this was found to be due to the induction of

fractures around boreholes caused by the stress waves of neighbour blastholes. In other words,

the high concentration of fractures along the entire length of each blasthole is caused by the

interaction of stress waves from various blastholes.

The 2D crack density contour plot shows the areas with higher concentration of cracks, which

lead a great portion of the subsequent gas expansion, as shown in the previous chapter. The 3D

version of crack density was obtained by correcting the 2D results by Equation 5-19, considering

the minimum distance to a blasthole. This contour plot shows an estimation of the crack density

that would be obtained by pure stress waves in a real 3D case. As in the case of single blasts,

most of the stress wave damage is limited to only a few borehole diameters from each blasthole;

however, the interaction between blastholes also indicates that some stress wave induced

fractures can develop along the entire space between neighbour blastholes.

Refracted P-wave Refracted S-wave Incident P-wave

1 m 1 m

Approximate stope boundary Blastholes

Initiation direction

149

Figure 87. Fracturing associated with stress waves obtained from production blast simulation. a) Fracture pattern; b) Crack density calculated directly from 2D simulation; c) Crack density corrected from 2D to 3D.

One significant advantage of the FEM-DEM method is its versatility, including the possibility to

incorporate ambient stresses and reverse the initiation mode, providing the possibility of

studying their effect on the fracturing process. Here, models that compare the case with and

0 2 4 6 8 10-5

-4

-3

-2

-1

0

1

2

E (m)

N (m

)

a)

c)

b)

Half raise

Blastholes


150

without field stresses, as well as reverse vs. direct initiation modes are presented as examples of

this versatility. In this case the analysis is carried out from the 2D fracture patterns, as a

qualitative evaluation of the variation of results in different scenarios. The principal field stresses

considered are approximately equal to the horizontal principal stresses found in the test area at

Williams mine (see Table 4). These are:

σ 1 = 38 MPa N-S; σ 2 = 27 MPa E-W

The fracturing patterns obtained for the four cases considered are shown in Figure 88. The case

shown and analyzed earlier in this section corresponds to Figure 88a (reverse initiation with no

ambient stresses). The most significant difference is found between the reverse and direct cases

(Figure 88a,b vs. Figure 88c,d), being the later the one that exhibits highest fracture densities.

This is most noticeable close to the free surface (near the raise), due to superposition of waves

(as seen in section 4.1.5) and the reflection of stress signals at the free boundary. Both

phenomena contribute to increase the stress amplitudes around this area in direct mode. The

presence of ambient stress field (Figure 88b,d) produces more damage around the same area

(close to the raise) but lower damage away from it. The later observation is interpreted as the

result of higher confinement provided by the ambient stresses, which tend to re-orient cracks

towards the direction of the maximum principal stress and reduce the development of fractures

away from the excavation.

As stated earlier, the procedure applied here to determine blast-induced damage considers only

stress wave effects. The calculation of a final fracture pattern from a real blast must include the

effects of gas expansion, which as seen on Chapter 5, causes most of the damage to the rock

mass. This process is extremely complex as it involves interaction between expanding high

pressure and high temperature gases and the far from ideal rock mass. To the best of the author's

knowledge there is no successful method to explicitly model this complex interaction.

151

Figure 88. Comparison of fracture patterns from production blast simulation considering various configurations associated with field stresses and initiation mode.

The closest attempt to do model gas/rock interaction was carried out by Munjiza et al (1999a) by

introducing an ideal gas analytical model into the context of the FEM-DEM method. This

particular model involved a fracture detection algorithm coupled with a flow analysis to calculate

gas pressure along the fractures. Unfortunately the details of the fracture detection algorithm are

not explained in this work and no validation of the method with experimental data is provided, so

the soundness of the results is unknown. An explicit numerical method to model explosive gas

behaviour in interaction with the fracturing process of the rock mass is still to be done.

0 2 4 6 8 10-5

-4

-3

-2

-1

0

1

2

E (m)

N (m

)

0 2 4 6 8 10-5

-4

-3

-2

-1

0

1

2

E (m)

N (m

)

0 2 4 6 8 10-5

-4

-3

-2

-1

0

1

2

E (m)

N (m

)

0 2 4 6 8 10-5

-4

-3

-2

-1

0

1

2

E (m)

N (m

)

a) Reverse initiation, no ambient stresses b) Reverse initiation with ambient stresses

c) Direct initiation, no ambient stresses d) Direct initiation with ambient stresses


Half raise


Initiation direction Initiation direction

152

6.3 Discussion An extensive monitoring program of multiple-hole production blasts was developed and carried

out at Williams mine, Ontario. Blast-induced vibrations were measured by triaxial accelerometer

stations and their seismic characteristics were determined. The collected information on vibration

amplitude and frequency as functions of distance and charge weight was utilized to calibrate

model parameters through a process similar to that of single-hole blasts. Finally, the technique

developed to predict blast-induced damage from stress waves using the 2D FEM-DEM method

was applied to a regular production blast.

Analysis of particle motion and rotation to spherical coordinates employed to distinguish P and

S-waves from single-hole blasts, as described in section 4.1.1, were successfully applied to

regular production blasts. Despite the higher complexity of blast geometry and recorded

waveforms, the contrasting polarization of both wave types permitted their clear identification in

the great majority of cases. The analysis of wave amplitudes indicated a scattered yet clear trend

of decreasing amplitude with increasing scaled distance, for both PPA and PPV. In contrast to

control blasts, there was a clear trend of decreasing average frequency with distance. Average

measured frequencies of particle velocity ranged typically from 400 Hz to 2 kHz, for distances

between 30 and 100 m, and were generally lower than those from control blasts, which range

from 1 to 5 kHz.

The measurements also confirmed that the trend of amplitude (i.e., slope of curve amplitude vs.

scaled distance) in terms of PPA do not match the same for that of PPV, due to the different

dependency of both variables with time and the dependency of attenuation (energy dissipation)

on frequency.

Upon evaluation of the blasting practice itself it is clear that a major drawback has to do with the

initiation practice employed at the mine, which involves tracing of the explosive column with a

high-strength detonating cord (50 g/m) connected to a booster at the toe of the hole. This greatly

increases the probability of outright failure or low-order detonation of the explosive column, and

the resulting adverse effect on fragmentation and wall control. Additionally, the firing time

precision of detonators employed in regular production blasts is of particular concern, as there

are significant variations in firing times of individual delay rounds, as well as missing

153

detonations. The latter could also result from poor delay hook-up practice and/or drilling

accuracy at the mine.

The simulation of a production blast clearly showed the areas expected to suffer greatest damage

from stress waves and their extension. This simulation was carried out assuming collar

detonation induced by the high strength detonating cord. The results are, however, intended only

to show the application of the method, as material strength parameters were not measured for this

test site.

The calibration of peak in-hole pressure with experimental data indicated a value of 1.5 GPa.

This relatively low value clearly shows one of the negative effects of tracing with high-strength

detonating cord, as the relatively lower amplitude (compared with the 1.8 GPa calculated for a

smaller borehole with similar coupling) reveals lower released energy.

Finally, additional models were simulated in the FEM-DEM program to compare the variations

in fracture patterns with the incorporation of field stresses and in-hole initiation mode. The

results indicate more intense fragmentation in direct mode, particularly around the area of the

raise, due to the presence of free surface. The presence of field stresses does not seem to increase

significantly the fracture density on the analyzed models, except around the free surface created

by the raise. In fact ambient stresses seem to shorten the penetration of cracks into the rock mass

around the areas away from the raise, and appear to modify the orientation of fractures from a

non preferred orientation in the unstressed case to an orientation along the maximum principal

stress. This result, although not new, shows the consistency of the FEM-DEM method, by

predicting reasonable fracture pattern variations in presence of far field stresses.

154

Chapter 7

7 Conclusions In order to study and predict blast-induced damage in rock, the research contained in this thesis

uses one of the well known characteristics of rock blasting: the strong correlation between stress

wave amplitude and blast-induced damage. The study of stress waves in this research was

essential to understand the physical interaction between explosive and rock mass, from the in-

hole pressure pulse to the processes of rock breakage by both stress waves and gas expansion.

The approach developed includes the study of blast-induced seismic waves by experimental and

numerical methods and the quantification of blast-induced damage. Specifically, the research

was oriented towards the study of the following components: i) nature of blast-induced seismic

waves; ii) mechanisms of seismic wave generation; iii) blast-induced seismic waves in 2D and

3D media; iv) correlation between stress wave amplitude and damage; v) development of

fractures by stress waves and gas expansion, and vi) relative contribution of stress waves and gas

penetration to damage.

Over one hundred field experiments in surface and underground test sites were conducted as part

of this research work. These experiments included extensive monitoring of seismic signals with

high amplitude and wide frequency-band accelerometers, as well as measurements of blast-

induced damage by a cross-hole system, amongst others. The results from seismic monitoring

permitted identification and quantification of seismic waves, study of the effects of charge length

and initiation mode on induced seismicity, as well as to calibrate material (rock) and explosive

properties. The measurements of damage permitted a clear determination of 3D damage from

single-hole blasts.

In addition to field experiments, a numerical method was applied to determine the relative

contribution of stress waves and gas expansion to damage. This method corresponds to the

combined finite and discrete element method (FEM-DEM), which was used to simulate blasts in

2D models. These models, with the aid of an original procedure to relate 2D and 3D damage,

were successfully used to determine the relative contribution of stress waves and gas expansion

to damage.

155

The detailed conclusions from both experiments and models, as well as the envisioned future

work in the field of blast-induced damage are described in the next sections of this chapter.

7.1 Nature of seismic waves by rock blasting in boreholes Small-scale and full-scale experiments clearly showed the generation of both P and S-waves

from rock blasting in cylindrical holes. Both types of wave were shown to present comparable

amplitudes for a wide range of distances and directions of propagation (referred to the borehole

axis). Only at very sharp angles between the borehole axis and direction of propagation, S-waves

showed significantly lower amplitudes from single-hole blasts. The average S/P ratio (i.e., the

ratio between peak amplitudes of S and P-waves at a given point) in terms of particle velocity

measured from single-hole blasts at angles lower than 22° was 0.25. In contrast, the Heelan

elastic solution gives an average round 1.5 for the S/P ratio in the same range of angles.

The measurement of seismic waves from production blasts, which included nearly the complete

range of angles of propagation (0°–180°), showed that the amplitudes of P and S-waves were not

significantly different, with an average S/P ratio equal to 1. The average S/P value from the

Heelan solution and other numerical models for the full range of angles is 1.7.

The strong differences between measured and analytical S/P ratios suggest that the use of an

elastic approach to model wave propagation is not appropriate. This highlights the necessity to

consider material attenuation, as S-waves show a much stronger attenuation compared to P-

waves.

7.2 Mechanisms of wave generation for different explosive initiation modes

Significant variations on seismic signals were found for different initiation modes. In particular,

the study of signals in reverse and direct initiation modes revealed strong differences in terms of

both amplitude and frequency content. For example, comparisons of vibration measurements

between direct and reverse initiation of 3 and 6 m explosive columns indicate direct/reverse

ratios over 400% in terms of particle velocity. In these cases, the P-wave was found to be the

dominant wave. Also, the comparison of frequency spectra between the same cases indicated a

concentration towards one particular frequency in direct mode, while reverse mode showed a

spread out spectrum (Figure 44 & Figure 45).

156

The physical interaction between waves generated along the explosive column, modeled as a

linear superposition of sequentially initiated identical waves, was found to be a potential

explanation for the differences in both amplitude and frequency spectra. This interaction

modifies the amplitude associated with all frequencies in the spectrum, and tends to enhance

lower frequencies while causing destructive superposition at discrete frequency intervals.

Although this phenomenon holds for both direct and reverse initiation modes, the intervals of

destructive frequency can be significantly different (much larger intervals in the direct case)

which causes the mismatch of both amplitude and frequency between the two cases. The analysis

also showed the importance of target location with respect to initiation mode in borehole in

calculating blast-induced damage.

7.3 Blast-induced seismic wave propagation by 2D numerical method vs. 3D real case

The comparison between 2D and 3D models of seismic propagation from point source indicated

qualitative agreement but quantitative discrepancies in terms of wave amplitudes.

The main difference between 2D and 3D seismic waves is the divergent geometric attenuation

resulting from the different change in area over which energy is spread as the wave front moves

away from the source (the attenuation of waves in 2D is lower than in 3D by a factor

proportional to r 0.5). In order to account for this difference in attenuation, a simple approach to

convert 2D wave amplitudes into 3D equivalent was proposed (Equation 5-16). This approach

consisted of modifying PPV values from 2D models by a factor proportional to r -0.5.

The comparison of contour plots of PPV showed the 2D elastic numerical models (after

correction by factor ~ r -0.5) to be in excellent agreement with the Heelan analytical solution when

P and S-waves were considered independently. The ratio of amplitudes of P and S-waves,

however, showed significant difference with the 2D case having a lower S/P ratio by a factor 1.6.

Despite this discrepancy, the 2D numerical method was estimated as good enough for the

purpose of estimating blast-induced damage.

157

7.4 Correlation between stress wave amplitude and damage Numerical modeling of single-hole blasts carried out with the combined FEM-DEM method

permitted to establish a correlation between stress wave amplitude and the damage induced by

them to the rock mass. After calibration of parameters for the rock mass corresponding to a

surface test site (hard granitic rock), the relationship between crack density and PPV was

calculated as follows:

( ) 8.1ln7.0 −⋅= PPVρ 7-1

where ρ is non-dimensional crack density defined by Equation 2-10 and PPV is expressed in m/s.

Although this equation was obtained from 2D models, it is estimated that considering it valid for

the 3D case is a reasonable assumption, given a) the theoretical linear relationship between

particle velocity and stress (given by the well known equation Vc ⋅⋅= 0ρσ for plane waves,

where σ is stress, ρ 0 is density, c is wave velocity and V is particle velocity), and b) that the

relationship stress – crack density should not be substantially different in 2D (plane strain) and

3D cases.

Equation 7-1 was combined with the approach to relate PPV2D and PPV3D (by using the factor ~

r -0.5) in order to estimate damage in a 3D case from 2D models. The application of this method

permitted to compare results from 2D models with 3D damage measurements.

7.5 Fracture network development by stress waves and gas expansion

Cross-hole system was successfully used to measure blast-induced damage in the vicinity of

single-hole blasts. The overall accuracy of the method was appropriate for measuring damage for

large charge sizes (i.e., 0.5 and 1.64 kg) of emulsion, but not suitable to assess damage for

smaller charges.

The measurement of damage from short and long explosive charges allowed a strong

concentration of damage originating at the explosive initiation point. On the other hand, the top

of the explosive column showed relatively low damage, compared to the bottom and middle

portions. This is attributed to the low confinement conditions at the top of the explosive due to

the lack of stemming material (in the experiments executed the only of confinement on top was

158

the column of water above). This low confinement permits gases to escape more quickly, causing

a rapid drop in pressure and thus reducing damage to the rock.

Despite the relatively long extension of fractures obtained from the 2D models (up to 1 m for

both long and short charges), the correction applied to estimate 3D equivalent damage indicates

that significant damage from stress waves has a short range, between 0.1 and 0.2 m (i.e., 2 to 4

borehole diameters) for the analyzed sources. This extent, however, does not correspond with

maximum crack length, but may be considered as an average maximum distance where damage

is significant, as discussed in section 5.5. Additionally, stress wave damage from models is more

severe at both ends of the explosive column, which is coincident with the highest PPV values.

This is due to the high gradient of loading existing at these points caused by the discontinuity in

loading conditions, which results in large deviatory stresses.

In short, the severe damage measured around the initiation point from two different blasts seems

to be consequence of significant amount of gases driven into this area due to the specific

confinement and initiation conditions of these tests.

7.6 Relative contribution of stress waves and gas penetration to blast-induced damage

The combined experimental and numerical methods to evaluate blast-induced damage allowed

the distinction between damage caused by stress waves and by expansion of gases.

Results from short and long charges (0.45 and 2 m long respectively) indicated that the

significant extent of damage from gas expansion (> 22 borehole diameters) is considerably larger

than that from stress waves (2-4 borehole diameters). In terms of maximum crack density, the

peak value associated with stress waves was not substantially different from that corresponding

to gas, with the former being slightly higher. In terms of total damage, however, gas expansion

showed a considerably larger value than stress waves, accounting for over 95% of the total

combined damage. This conclusion is, however, tentative, as it is based on two assumptions that

require further research: a) that FEM-DEM can accurately predict the crack distribution, and

furthermore, the results can be extended from 2D to 3D with reasonable accuracy, and b) that

Kachanov's non-interactive model relating crack density vs. modulus is valid in all cases. Both of

these points constitute fronts of future research, as will be discussed in section 7.7.

159

Peak values of crack density (stress waves, gas and combined) from the long charge were 10% to

30% lower than those from the short charge. These lower values are probably due to the lower

coupling of the longer charge (67%) compared to the shorter one (90%), which causes lower

amplitudes in both stress waves and gas pressure in the rock mass. On the other hand, total

damage is higher by a factor of 3.6 for gas and combined damage, and by a factor of 1.6 for the

stress wave damage, compared to the short charge. These higher values of total damage are

explained by the larger amount of explosive used in this case, which evidently is expected to

deliver more energy to the rock and thus cause more damage.

Both long and short explosive charges show the same features around the top and bottom of the

explosive. Both cases exhibit high amplitude extended damage from the bottom and very little

damage on top. Also, both cases show the same pattern of damage propagating diagonally down

from the initiation point. In the case of the long charge, variable extension of damage along the

explosive column is observed. These features seem to be the result of a combination of various

confinement conditions along the borehole (open top), initiation mode (bottom initiated) and the

interaction between the fracture network created by the stress waves and expanded by the

penetration of gases. In short, the sequence of events taking place during blasting (stress waves,

gas expansion and the creation of fracture networks) seems to severely condition the resultant

damage envelope around the blasthole.

7.7 Future work The main areas of research to be developed are grouped as follows: i) study of gas / rock

interaction and its consequences on rock blasting; ii) experimental data to calibrate effective

medium theories; iii) FEM-DEM modeling, and iv) application and evaluation of blast-induced

damage prediction into full-scale blasts.

The effect of gas expansion on the rock fracturing process cannot be modeled by only

establishing an in-hole pressure function. Instead, proper modeling of this process must include

the use of an appropriate gas expansion and gas flow model, as well as the physical interaction

between the expanding gases and the fracturing rock mass.

The variations of the pressure function along the blasthole as well as the penetration of gases into

the rock mass require further studies. Appropriate analytical and numerical models that

160

incorporate the interaction between the expanding gases and the breaking rock mass should be

considered. Analytical models should consider constitutive equations for a non-ideal gas

considering at least volume, pressure and temperature as relevant variables. Numerical modeling

may be done by implementing a coupled FEM-DEM method capable of handling both solids and

gases. Also, the full waveform of the in-hole pressure function should be determined

experimentally along the whole explosive column. This may be done by using carbon resistors

inserted in the rock mass at several positions along the blasthole and various distances from it.

These results may be used to calibrate the behaviour and results from numerical models.

In order to further understand the penetration of gases into the rock, gas monitoring may be used

in addition to crack mapping to determine pressures of gas penetrating into the fracture network.

To properly execute and analyze these measurements, a meticulous experimental set up

including the selection and positioning of calibrated pressure sensors is required, in addition to

proper modeling to convert the experimental data into crack pressures. The results (crack

pressures) would be highly useful and possibly essential to validate models of interaction

between expanding gases and fracturing rock.

Finally, as discussed in section 5.4.4, the dependency of rock fracturing on strain rate is a

phenomenon that still requires further studies. Even though efforts are being made to improve

our knowledge in this particular area, the high strain (or loading) rates that take place during

blasting are still beyond the range that most experimental methods (e.g. SHPB) can handle. Thus,

the study of strain rate dependency of rocks at the loading rates observed in blasting is proposed

as an important line of investigation in the fields of fracture and rock mechanics. Such study

needs to be focused specifically on the implications in rock blasting and should be carried out

through a combination of experimental methods and modeling.

Another significant front of future research is the calibration of effective medium theories with

experimental data. Specifically, the actual variation of elastic constants and wave velocities with

crack density needs to be assessed, particularly for relatively large cracks, high crack densities

and both dry and wet conditions. Additionally, the actual relationship between crack density and

PPV from blasting (akin to Figure 64) needs to be assessed experimentally. As a starting point,

small explosive charges could be detonated in samples of intact rock to measure vibrations (e.g.

by carbon resistors embedded in the sample) and crack density (e.g. by cutting and measuring

161

fractures after blast). The independent effect of stress waves and gas expansion can be studied by

lining the borehole with a metallic case, as done in Dehghan Banadaki (2010).

On the results from the FEM-DEM software, there are two relevant aspects to be verified: a) the

method to extend the results from 2D to 3D proposed here, and b) the prediction of crack

distribution. While the first point can be tackled by comparing results from 2D and 3D models,

the second point requires assessment through experimental data. The development of 3D models,

besides solving the discussed issue of geometric spreading in 2D, would allow more realistic

features, such as the incorporation of various free surfaces and displacement of fragments in 3D.

Additionally, on the development of the software itself, modeling of the gas phase is required for

proper blast simulations, as a result of the different fracturing mechanisms caused by gas

expansion compared to stress waves, as extensively discussed throughout this thesis.

Finally, the main assessment that this study needs to pass is its applicability to full-scale blast

operations. Even though part of it has been proved through monitoring and modeling of full-

scale underground production blasts (Chapter 6), the experimental assessment of production blast

damage was not part of the study. Consequently, the design and execution of a method to

measure blast damage in mine operations is required to fully evaluate the proposed method. It is

important, however, to keep in mind that such measurements can be fully compared only with a

model that incorporates gas damage, as discussed earlier.

7.8 Overall conclusions This research work proposes a method to predict and control blast-induced damage in rock. The

method is founded on the consideration of stress waves and gas expansion as the main sources of

damage and uses the study of seismic waves as a fundamental tool to evaluate a number of

required parameters. It also includes the use of a numerical method, such as the combined FEM-

DEM method, to model the creation and development of the blast-induced fracture network.

It is to be noted that because of the complexity of the subject, only a limited number of variables

could be tested and a limited number of tests could be performed. Therefore, the conclusions of

this research, although valid, should be viewed only as stepping stones for future research.

162

The main conclusions from the developed research work presented in this thesis are summarized

in the following points:

• The stress waves that result from rock blasting in cylindrical boreholes propagates in both

longitudinal and shear modes (P and S-waves). Experiments in hard rock showed that

both wave types are of comparable amplitudes.

• The amplitude of stress waves varies significantly for different angles of propagation

(referred to borehole axis) as a result of both the naturally uneven distribution of radiating

energy from an axially loaded cylindrical hole, and the interaction of waves generated

along the explosive column. In particular, the amplitude and frequency spectra in direct

and reverse initiation modes for long explosive columns are substantially different, with

the former showing much larger amplitudes and a narrower frequency band.

• Experiments in water coupled, bottom initiated and open top short and long explosive

charges indicated a strong concentration of damage around the initiation point. This

phenomenon is attributed to a) the strong confinement of the explosive at this point as a

consequence of the initiation mode, and b) the stress wave induced fracture network that

is initiated at this point.

• The use of a 2D FEM-DEM code showed that 2D modeling of blasting is possible

provided that results are corrected by differences in geometric spreading. If gas

expansion is considered in the models, the results would also require this correction, as

the expansion of gases in 2D and 3D differs in a similar way as the geometric spreading

of seismic waves. The method proposed here to extend 2D models to 3D simulate

behaviour requires, nevertheless, verification.

• The results of fracture development from numerical models using the FEM-DEM method

were found to be in good qualitative agreement with damage measurements. Both

methods indicated development of radial fractures at preferential locations along the

explosive column (Figure 63 & Figure 70).

• As a consequence of the generation and interaction of stress waves and the later

participation of gas expansion in the processes of rock fracturing, it is clear that assuming

symmetrical damage envelope (such as an ellipsoidal or cylindrical envelope) is not an

appropriate approach.

163

• Experimental and numerical results showed that gas expansion in the studied

configuration accounts for >95% of total damage in the rock mass. This, however, by no

means imply that damage induced by stress waves is irrelevant, since, as shown in the

study, the final fracture network is strongly conditioned by the initial fractures caused by

stress waves.

• The application of the developed method to regular production blasts showed its potential

to be used as a predictive tool in full-scale blasts. Most parameters required by the

method to construct realistic models (medium and explosive properties, geometric

conditions) can be reliably determined for any blast design. The exceptions to this are the

strain rate dependency of material strength and the precise shape of the in-hole pressure

function, which are proposed as fronts of study in section 7.7.

The results of blast-induced damage determined through the proposed method may be attempted

to be incorporated into a broader model to assess, predict and control dilution and overbreak in

underground and open pit mines. In underground mines for example, the incorporation of blast

damage in such model may be done as a modification of the stability number (Mathew's method)

for an excavation, given the damage distribution predicted for a given blast configuration

(including explosive type and amount, blast geometry, initiation sequence, etc.), rock mass

(including heterogeneity, anisotropy, discontinuities, etc.), stress distribution, and overall

geometry. The precise values that would modify the calculated stability need evidently to be

calibrated with extensive empirical data on dilution and blast damage.

164

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Appendices

171

Appendix A : Relationship between Elastic Constants The equations of linear elasticity can be written in a variety of forms with several different

parameters or elastic constants. In an isotropic material, only two of these constants are

independent, so any of them can be written in terms of other two. The most common elastic

constants to express the properties of a solid are:

• E : Young Modulus, GPa

• ν : Poisson's Ratio, dimensionless

• µ : Shear Modulus, GPa

• λ : Lamé Constant, GPa

• k : Bulk Modulus, GPa

Additionally, any of these elastic constants can be written in terms of the P and S-wave velocities

and material density. Table A1 summarizes the common expressions that relate the above

mentioned elastic constants and wave velocities. These equations are valid for a 3D body and the

2D case of Plane Strain. In Plane Stress, some equations (such as the relationship between λ, E

and ν) differ due to the constraint of null stresses out of plane.

172

Table A1. Relationship between elastic constants, wave velocities and density (after Sheriff 1991)

E ν k µ λ VP VS

( )ν,E ( )ν213 −E

( )ν+12E

( )( )ννν

211 −+E

( )( )( )

21

2111

−+

−ννρ

νE ( )

21

12

+νρ

E

( )kE, k

Ek6

3 −

EkkE−9

3

−−

EkEkk

933

21

933

−+

EkEkk

ρ

( )

21

93

− Ek

kEρ

( )µ,E µµ

22−E

( )EE−µ

µ33

−−

EEµ

µµ3

2

21

34

−−

EE

µµ

ρµ

21

ρµ

( )k,ν ( )ν213 −k

+−νν

121

23k

+νν

13k

21

113

+−νν

ρk

21

121

23

+−νν

ρk

( )µν , ( )νµ +12

−+ννµ21

13

2

− ννµ21

2

21

2112

−−νν

ρµ

21

ρµ

( )λν , ( )( )

νννλ 211 −+

+

ννλ

31

−

ννλ

221

211

−νν

ρλ

21

221

−

νν

ρλ

( )µ,k µµ+kk

39

( )µµ

+−k

k32

23

32µ

−k

2134

+ρ

µk 21

ρµ

( )λ,k

−−λλ

kkk

39

λλ−k3

( )λ−k23

2123

−ρ

λk

( ) 21

23

−ρλk

( )λµ,

+−µλµλµ 23

( )µλλ+2

µλ32

+

21

2

+ρµλ

21

ρµ

( )SP VV ,

−−

22

222 43

SP

SPS VV

VVVρ

( )22

22

22

SP

SP

VVVV

−−

− 22

34

SP VVρ

2SVρ ( )22 2 SP VV −ρ

172

173

Appendix B : Effective medium theories (EMT) Effective medium theories correspond to models to relate damage (as crack density) and elastic

constants. In this appendix, a brief description of some of these theories is provided.

Even though cracks represent a small amount of porosity, they affect significantly elastic and

strength properties. Their presence not only reduces the strength of the rock but also increases its

deformability, which implies elastic moduli reduction. Elastic moduli are affected, however, not

only by crack density, but also by its orientation and aspect ratio. The models that relate elastic

moduli and crack density are known as Effective Medium Theories (EMT), which are discussed

in this section.

Several models have been developed that relate crack density with elastic moduli. These models

are considered as part of the Effective Medium Theory (EMT), which is intended to predict the

overall wave speeds and polarizations of long wavelength waves in cracked materials in terms of

the properties of the uncracked solid and the parameters describing the cracks and their

distribution (Hudson et al 2001). In the following paragraphs some of the approaches within the

EMT are summarized.

Zimmerman (1991):

• Pores are the main factor which determines the compressibility of a material.

• In principle if the precise pore geometry was known, the compressibility could be

calculated by solving the equations of elasticity for the rock with the appropriate

boundary conditions over the exterior and interior surfaces. In practice this is never

feasible, due to the mixture of shapes, orientations, number of pores. Numerical methods

such as finite elements, boundary elements can treat irregular geometries; however, it is

not computationally feasible to simulate the compression of a rock with realistic pore

structure in 3D.

• Progress is being made by relating compressibility to pore structure by finding analytical

solutions for isolated pores or certain shapes, and then using approximate methods to

account for 'many' pores whose stress and strain fields interact.

174

• In 3D, pores are modeled as ellipsoidal pores (three unequal axes), or more simply

spheroidal pores (two axes equal). Spheroids include 'penny shaped' cracks with a certain

aspect ratio.

Hudson et al (2001):

• Since the crack shapes are idealized as circular, and different approximations are made,

confidence in the EMTs would greatly increase with experimental or numerical support

• Numerical:

o 20 boundary element studies have been performed.

o Accurate 3D numerical studies with high order approximations have been out of

reach owing to the computational time required.

• Experimental:

o Challenge for the experimentalist is to find or construct a material with empty or

liquid filled cracks with known positions and orientations.

o Rathmore et al 1995 created a synthetic sandstone with parallel circular cracks of

aspect ratio 0.004, and crack density of 0.1. Interestingly the best fit of velocities

to Hudson EMT model was found if the second order terms were dropped.

Kachanov (1994):

• One argument for the non-interacting assumption, shown by Kachanov (1994) is:

o The stress field is amplified at crack tips, but also shielded on crack flanks

o Therefore overall stress interactions are partially compensating for certain

isotropic and aligned distributions.

• Also versatility for different crack symmetries. Dry or water filled cracks. Allows large

crack densities.

• Considered simple and non-controversial.

To the best of the author’s knowledge, there is no significant available experimental data to

validate or discard any of the EMT theories. Consequently, given the simplicity and versatility of

Kachanov's approach, this method is applied for the inversion of wave velocities from field data

in Chapter 4.

175

Appendix C : Constitutive model in FEM-DEM code Y2D This appendix includes the equations of constitutive model in the FEM-DEM program Y2D.

From the literature, a large number of constitutive models to represent the mechanical behaviour

of materials is available. The simplest and most widely studied model is the linear-elastic model.

Other models include a failure criterion, such as the Mohr-Coulomb or Hoek-Brown criteria. In

the case of the Y2D code, mechanical failure occurs though the creation and propagation of

fractures, which are represented by the loss of bonds between neighbour elements when strength

is overtaken by stress. Hence, material failure is simulated in this program without necessity of

specifying a failure criterion for individual elements.

In addition to fracture creation and propagation, there are other mechanisms of energy

dissipation in real materials. This additional dissipation of energy is typically incorporated in

models through the addition of viscosity, represented by dashpots placed in some configuration

with springs, thus representing visco-elastic behaviour. Some of these models are the Maxwell

model (spring and dashpot in series), the Kelvin-Voigt model (spring and dashpot in parallel) and

the Standard Linear Solid (spring in parallel with an array of spring and dashpot in series). For

background on dynamic response of these models, see Kolsky (1960). In the Y2D code, the

currently implemented model corresponds to the Kelvin-Voigt visco-elastic model, which is

described in the following paragraphs.

The Kelvin-Voigt constitutive model is commonly represented by an elastic element (spring)

acting in parallel to a viscous element (dashpot) as illustrated in Figure C1. In this appendix the

solution for the two dimensional case is shown, in order to illustrate the constitutive equations

built-in the Y2D code, used for the models of this thesis.

Figure C1. Representation of the Kelvin-Voigt visco-elastic model in the one-dimensional case

E

η

176

In order to derive the model equations it is necessary to establish dynamic force equilibrium, as

schematized in Figure C2.

Figure C2. Stress distribution over an element of surface in 2D.

By taking force equilibrium, the following equations are obtained:

−

∂

∂++−

∂

∂+=

∂∂

−

∂

∂++−

∂∂

+=∂∂

dydydxx

dxdxdyy

dydxtv

dxdxdyy

dydydxx

dydxtu

yxyx

yxyyyy

yy

xyxy

xyxxxx

xx

σσ

σσσ

σρ

σσ

σσσ

σρ

2

2

0

2

2

0

C- 1

Thus, by simplifying terms, the dynamic equilibrium can expressed as:

∂

∂+

∂

∂=

∂∂

∂

∂+

∂∂

=∂∂

yxtv

yxtu

yyyx

xyxx

σσρ

σσρ

2

2

0

2

2

0

C- 2

The dissipation of energy from the Kelvin-Voigt model in the 2D case can be represented by:

+=

++∆=++∆=

xyxyxy

yyyyyy

xxxxxx

εηµεσ

εηµελσεηµελσ

222222

C- 3

x

y

dxx

xxxx ∂

∂+

σσ

dxy

yyyy ∂

∂+

σσ

xxσ

yyσ

dyy

xyxy ∂

∂+

σσ

dxx

yxyx ∂

∂+

σσ

dx

dy

xyσ

yxσ

177

where ∆ is volumetric strain, λ is Lamé constant, µ is Shear modulus, η is viscous damping, and

εij and ijε are components of strain and strain rate respectively (note that in the Y2D code the

user-input viscous damping parameter is 2η).

By inserting the constitutive into the equilibrium equations, considering σxy=σyx and εxy=εyx, the

following equations are obtained:

( ) ( )

( ) ( )

+∂∂

+++∆∂∂

=∂∂

+∂∂

+++∆∂∂

=∂∂

xyxyyyyy

xyxyxxxx

xytv

yxtu

εηµεεηµελρ

εηµεεηµελρ

2222

2222

2

2

0

2

2

0

C- 4

The equation for compression waves can be obtained by differentiating the first equation with

respect to x, the second with respect to y, and summing. Rearranging terms and considering the

identities:

xu

xx ∂∂

=ε , yv

yy ∂∂

=ε ,

∂∂

+∂∂

=xv

yu

xy 21ε , and ( )yyxx εε +=∆ , C- 5

the following expressions are obtained:

∆∇

∂∂

++=∂∆∂ 22

2

0 22tt

ηµλρ C- 6

where 2∇ is the Laplace operator,

∂∂

+∂∂

=∇ 2

2

2

22

yx. Similarly, the equation for shear waves

can be obtained by differentiating the first equation with respect to y, the second with respect to

x, and subtracting:

ωηωµωρ 222

2

0 ∇∂∂

+∇=∂∂

tt C- 7

where

∂∂

−∂∂

=yu

xv

21ω . For plane waves moving along the x-axis all derivatives on y become

zero.

178

Thus, the above expressions become:

( ) 2

2

2

2

2

2

0 22xu

txu

tu

∂∂

∂∂

+∂∂

+=∂∂ ηµλρ for compression waves, and C- 8

2

2

2

2

2

2

0 xv

txv

tv xxx

∂∂

∂∂

+∂∂

=∂∂

ηµρ for shear waves, C- 9

where the x sub-index denotes derivative on x. These two equations are forms of the Stokes wave

equation, which has the general form:

2

2

2

2

2

2

0 ˆˆxtx

Et ∂

∂∂∂

+∂∂

=∂∂ χηχχρ C- 10

A general solution to this equation can be written as:

( ) ( )[ ]txcix eetx ωωαχχ −−= 0, C- 11

Where ω is angular frequency and the parameters c and α are given by (Kolsky 1963, Ricker

1977):

( )2121

2

222

222

20 1ˆ

ˆˆ

ˆˆ2

ˆ−

+

++

=E

EE

Ec ωηωη

ωρω , and C- 12

( )2121

2

222

222

20 1ˆ

ˆˆ

ˆˆ2

ˆ

−

++

=E

EE

E ωηωη

ωρα C- 13

which correspond to the exact expressions for attenuation coefficient and wave velocity

respectively. Alternatively, Equation C-10 can be written by using a complex elasticity modulus,

as follows:

( ) 2

2

212

2

0ˆˆ

xEiE

t ∂∂

+=∂∂ χχρ C- 14

with

EE ˆˆ1 = and ωηˆ

2 =E C- 15

179

In this case, the expressions for wave velocity and attenuation coefficient can be written as

(Davis 1960):

( )2sec*ˆ 21

δρ

=

Ec , and C- 16

( )2tan δωα

=

c C- 17

with

( ) 2122

21

ˆˆ*ˆ EEE += and ( ) ( )12ˆˆtan EE=δ C- 18

For small values of η , the above expressions can be expanded and written as (Jaeger et al 2007):

+=

2

0 ˆˆ

831

Ecc ωη , and C- 19

0

2

ˆ2ˆ

cEωηα = C- 20

where ( ) 21

00ˆ ρEc = is the velocity that the elastic wave would have in the absence of any

dissipative mechanisms. The actual velocity c, is larger than c0 and varies with frequency;

however, for small amounts of viscous damping η , it remains nearly unchanged and can be

taken as ( ) 21

0ˆ ρEc = . Thus, in the case of the Y2D code, replacing E by ( )µλ 2+ and η by η2

for compression waves, and E by µ and η by η for shear waves, the expressions of attenuation

and wave velocities result:

( ) PP Vµλ

ηωα2

2

+= and

21

0

2

+=

ρµλ

PV for compression waves, and C- 21

S

S Vµηωα2

2

= and 21

0

=

ρµ

SV for shear waves, C- 22

where 2η is the user-input viscous damping parameter. Although the Y2D code considers only

one value of viscous damping, the Kelvin-Voigt model may also be used to incorporate

independently viscosity associated with volume and shear strains (Ricker 1977).

180

This can be achieved by introducing damping expressions in the classical wave equations:

21

2

12

34

tk

∂∂

=∇

+

χρχµ C- 23

22

2

22

t∂∂

=∇χρχµ C- 24

by replacing the elastic constants k by

∂∂

+t

k Vη and µ by

∂∂

+tSηµ , where k is bulk

modulus, and ηV and ηS are volumetric and shear viscous damping parameters. Thus, the

equations for compression and shear waves become:

21

2

12

12

34

34

ttk SV ∂

∂=∇

∂∂

++∇

+

χρχηηχµ C- 25

22

2

22

22

ttS ∂∂

=∇∂∂

+∇χρχηχµ C- 26

From these equations along with Equation C-8 and Equation C-9, and considering that

( )µλµ 234

+=

+k , it is easy to show the relationship between shear and volumetric damping

and η:

ηη =S , and C- 27

3

2ηη =V C- 28

If, however, the expressions in Equation C-3 are replaced by the following:

( )( )

+=

+++∆=+++∆=

xySxyxy

yySVyyyy

xxSVxxxx

εηµεσ

εηηµελσεηηµελσ

223222232222

C- 29

it is possible to show that the equations of motion are identical to Equation C-25 and Equation C-

26 for compression and shear waves, respectively. Thus, there is potential to incorporate viscous

damping from both volumetric and shear strains independently, by simply including the

expressions given by Equation C-29 in the code.

Appendix D : List of blast experiments and instrumentation This appendix includes the full list of blast experiments executed in both test sites, including explosive charges and instrumentation.

Table D1. List of blast experiments executed at the surface test site

Test # Blasthole Diameter

blasthole Charge weight

Depth of center Length Explosive

Type Instrumentation

Acc A (Type 2, spring

mounted)

Acc B (Type 3, spring

mounted)

Acc C (Type 4, spring

mounted)

r (**) θ (**) r θ r θ

(mm) (kg) (m) (m) (m) (deg) (m) (deg) (m) (deg)

1 B45.18 45 0.1 5.00 0.08 Emulsion Acc, CR, CH 2.3 23 1.9 78 1.1 25

2 B45.23 45 0.1 5.00 0.08 Emulsion Acc 3.0 44 3.2 82 2.4 64

3 B45.23 45 0.5 3.55 0.40 Emulsion Acc, CR 2.3 71 3.3 107 - -

4 B75.10 75 0.5 4.75 0.10 Emulsion Acc, CR 2.4 40 1.9 86 - -

5 B75.10 75 0.1 2.90 0.02 Emulsion Acc, CR 1.5 91 2.6 132 - -

6 B45.18 45 0.5 3.73 0.45 Emulsion Acc, PS, CH 2.4 53 1.6 129 - -

7 B45.14 45 0.041 4.00 2.00 Det. Cord Acc 1.9 145 1.9 146 - -

8 B45.14 45 0.041 4.00 2.00 Det. Cord Acc 1.9 35 1.9 34 - -

9 B45.02 45 0.082 4.30 2.00 Det. Cord Acc 2.2 144 2.0 153 - -

10(*) B45.07 45 1.644 4.20 2.00 Emulsion Acc, PS, CH 10.9 110 - - - -

11(*) B45.22 45 1.644 3.80 2.00 Emulsion Acc, CR, PS, VOD 10.4 70 - - - -

(*) For Tests #10 and 11, accelerometer A was mounted on the rock surface, not spring mounted in borehole as in all other tests (**) r and θ according to coordinate system illustrated in Figure 32 See Figure 23 for borehole locations, Figure 25 for schematic location of explosive charges, and Figure 26 for instrumental layout Acc: Accelerometers, CR: Carbon Resistors, PS: Pressure Sensors, VOD: Cable for Velocity of Detonation, CH: Cross-hole 181

Table D2. List of control blast experiments executed at Williams mine

Test # Blasthole Diameter

blasthole Charge weight

Depth of center

Length of explosive Explosive Type

Acc A (Type 1, grouted)

Acc B (Type 1, grouted)

Acc B89 (Type 1, grouted)

r (**) θ (**) r θ r θ

(mm) (kg) (m) (m) (m) (deg) (m) (deg) (m) (deg)

1 C 60 0.23 135.9 0.13 Pentolite Boosters 106.7 5.5 - - 47.6 7.3




5 C 60 0.91 125.5 0.52 Pentolite Boosters 96.4 6.1 96.9 2.8 - -







12 C 60 4.46 91.0 3 Emulsion 62.1 10.2 62.4 5.2 - -

13 C 60 4.46 78.5 3 Emulsion 49.8 167.2 49.9 173.5 - -

14 C 60 8.37 75.2 6 Emulsion 46.7 166.2 46.8 172.8 - -

15 C 60 0.56 65.8 0.4 Emulsion 37.7 17.2 37.5 8.9 - -

16 C 60 8.37 62.0 6 Emulsion 34.0 19.1 33.7 9.9 - -

17 C 60 0.56 59.3 0.4 Emulsion 31.5 20.7 31.1 10.8 - -

18 C 60 0.56 56.8 0.4 Emulsion 29.2 22.4 28.6 11.7 - - (**) r and θ according to coordinate system illustrated in Figure 32 See Figure 27 for experimental layout 182

183

Appendix E : Laboratory tests and Material Strength Properties

Dynamic and static strength properties were determined through laboratory tests in rock samples

from the surface test site. These tests were executed to provide material input parameters for the

numerical modeling of experiments from this test site. The following tests were executed in

several rock samples along various directions: P and S-wave velocities, compressive strength and

tensile strength. A description of these tests and their results is included in this appendix.

E.1 Measurement of P and S-wave velocities and density

P and S-wave velocities are determined in cylindrical samples with nominal dimensions φ = 38

mm, and L = 76 mm through a high frequency ultrasonic technique. Additionally, rock density

was determined by measuring mass and dimensions of the same samples. All rock samples were

saturated at the time of testing.

To measure wave velocities piezoelectric transducers (transmitter and receiver) are placed on

both sides of each sample to determine the travel time of an initially square pulse. The

construction of the sensors permits each of them to act as a transmitter or receiver but sensors are

specific to measure either P or S-waves. The equation used to calculate the wave velocities is as

follows:

( )0TTLV−

= E- 1

where V is either P or S-wave velocity in km/s, L is the measured distance along the direction of

wave propagation (sample length) in mm, T is the measured travel time along the sample in µs,

and T0 is the travel time between sensors face to face in µs.

Upon examination of the rock samples it was found that most of them exhibit one clear bedding

plane. For this reason core samples were taken at specifically oriented directions with respect to

the bed in order to properly quantify possible anisotropic behaviour.

The test results are shown in Figure E1, with each sample identified including the angle between

its axis and bedding plane. All P and S-waves were measured along the cylindrical axis. VS1 and

184

VS2 correspond to measurements of VS parallel and perpendicular to the lines of the bedding plane

on the planar faces of the samples.

The average values and standard deviations for all samples, excluding surface samples due to

evident weathering, are indicated in this figure as average ± standard dev.

Figure E1. Wave velocities and density from lab experiments.

E.2 Static and dynamic uniaxial compressive strength (UCS)

Both static and dynamic compressive tests were executed in cylindrical rock samples. For static

tests, the same samples used to determine VP and VS (38 mm diameter, 76 mm length) were used,

with the exception of the surface samples which were not used to determine any material strength

property. These tests are executed at constant speed in a servo controlled testing machine.

The samples for dynamic tests correspond to two cylindrical cores, with bedding planes at 0° and

45° from the cylinder axis, with a nominal diameter of 25 mm and length of 19 mm (4:3 aspect

ratio). These tests are executed in a 25 mm Split Hopkinson Pressure Bar (SHPB) apparatus with

loading rates between 1,100 and 5,300 GPa/s (Figure E2). In all tests a copper pulse shaper was

used between the striker and the incident bar with the purpose of obtaining a square stress pulse

and achieving dynamic stress equilibrium (Chen et al 1999, Frew et al 2002 & 2005, Dai et al

2008).

0

1

2

3

4

5

6

7

1 (45°) 1B (45°) 2 (0°) 2B (0°) 3 (70°) 4 (90°)surface

4B (0°)surface

5 (?) 6 (noplane)

Sample Id

Wav

e ve

loci

ties,

Vp V

s (k

m/s

)

2.50

2.60

2.70

2.80

2.90

3.00

3.10

3.20

Den

sity

, ρ (k

g/dm

3 )

Vp Vs1 Vs2 ρ

skmVP /08.002.6 ±=

skmVS /09.046.3 ±=

Excluded for averages

30 /01.067.2 dmkg±=ρ

185

Figure E2. Split Hopkinson Pressure Bar (SHPB) system. a) Diagram x-t of stress wave propagation along the system; b) Schematic view of specimen for compression test; and c) Schematic view of specimen for tensile test (after Dai et al 2010a,b).

Figure E3 shows the results from both compressive static and dynamic tests. Dynamic tests

indicate an evident steady and approximately linear increase of compressive strength, σc with

loading rate, which is consistent with previously published results (Xia 2008). Additionally, no

significant difference is observed between samples with bedding planes at 0° and 45°. It is

important to note that samples at lower loading rates exhibit σc values below static tests.

Although the reasons for this are not clear, one likely possibility is that the energy from the

incident bar at the lower loading rates (dynamic tests) is not enough to cause the sample to reach

its full strength. Consequently, the recorded peak stresses are lower than the samples strength at

those loading rates. As this only occurs at relatively low loading rates (LR < 3250 GPa/s), σc in

this range is taken as the average static value (σc = 164 MPa). For higher loading rates, σc can be

calculated from the equation shown in Figure E3, determined as a simple linear regression of the

dynamic values (σc = 0.0282 LR + 73, for LR ≥ 3250 GPa/s).

a)

b) c)

186

Figure E3. Results from static and dynamic UCS tests.

E.3 Static and dynamic tensile strength The tensile strength of various rock samples was determined in both static and dynamic

conditions. In all cases disk shaped samples were used with nominal dimensions of 38 mm in

diameter and 19 mm in length. As in the case of compressive tests, static tensile tests were

executed in a servo controlled testing machine, whilst dynamic tests were carried out using the

SHPB system. In contrast to the compressive tests, the line of load application in tensile tests

corresponds to a central axis in the sample contained on the plane of its circular section. The

equation to calculate both tensile static and dynamic strength is:

BDP

t πσ 2

= E- 2

where σt is the tensile strength, P is the maximum load, and B and D are the sample thickness

and diameter, respectively.

For the dynamic case, loading rates between 150 and 1,100 GPa/s were utilized. Figure E2 shows

schematic views of the stress wave propagation along the SHPB system through time, as well as

elevations and plan views of the samples for dynamic compressive and tensile tests. A detailed

description of the SHPB device and procedures utilized for both compressive and tensile

dynamic tests can be found in Dai et al (2010).

R 2 = 0.8305

0

50

100

150

200

250

300

0 1000 2000 3000 4000 5000 6000

Loading Rate, LR (GPa/s)

Com

pres

sive

Stre

ngth

, σc (M

Pa)

45° 0° Static tests, various angles

730282.0 += LRcσ

MPac 164=σ

187

The results from these tests are shown in Figure E4. In this case samples are grouped and

identified according to the angle between the bedding plane and the fracturing plane of the

sample. As in the case of compressive tests, dynamic tensile tests show increasing strength with

loading rate. This case, however, also shows differences for varying fracture orientation. Tests

with samples oriented with the fracturing plane along the bedding plane (0°) show consistently

lower values than those oriented perpendicularly (90°). Other cases (samples at 45°, 70°, and

with no bedding plane) present values between these two boundaries.

Figure E4. Tensile strength determined by static and dynamic Brazilian Disc tests. Equations shown correspond to a multiple power regression of tests of samples with 0° and 90° angle between fracturing plane and sample layers.

Given the clear limits set by the extreme cases (0° & 90°) a multiple regression analysis was

performed with the following form, which proved excellent correlation for 0° and 90° samples:

( )γασ 010 LRLRt += E- 3

( )γασ 0290 LRLRt += E- 4

where σt0 and σt90 are the tensile stresses considering fracture along and perpendicular to bedding

plane, respectively, α1, α2 and γ are the object parameters of the regression, and LR0 is a suitable

parameter to be determined by maximizing the determination coefficient R2 of the regression. To

determine the parameters α1, α2 and γ Equation E-3 and Equation E-4 were combined in the

following expression:

0

5

10

15

20

25

30

35

0 200 400 600 800 1000 1200

Loading Rate, LR (GPa/s)

Tens

ile S

treng

th, σ

(MP

a)

0° 45° 70° 90° no plane

( ) 29.00 281.3 += LRσ

( ) 29.090 280.4 += LRσ

188

( )γαβσ 0LRLRx += E- 5

where x is 0 for 0° and 1 for 90° samples, and α, β and γ become the new regression parameters

which are determined by multiple linear regression (after logarithmic transformation) with

independent variables x and LR. The resultant equations are shown in Figure E4.

E.4 Strain / Loading rate dependency of strength parameters

The dependency of rock strength parameters on strain or loading rate is a problem still under

study. According to the results of numerous experiments from various authors, the dependency

of strength parameters is such that higher loading rates produce higher strength properties. A

standard experiment to measure dynamic strength properties is the Split Hopkinson Pressure Bar

(SHPB) test. Experimental setup for this experiment and schemes of samples for compressive

and tensile tests are included in Appendix E. Schematic views of samples for fracture toughness

(Semi-circular bend (SCB) and Cracked Chevron Notched Brazilian Disc (CCNBD) specimens)

are shown in Figure E5.

Figure E5. Schematic view of experimental setup and samples for the measurement of fracture toughness in SHPB apparatus. a) CCNBD sample (after Dai et al 2010a); b) SCB sample (after Chen 2009).

Figure E6 and Figure E7 show variations of compressive strength and fracture toughness

measured in samples of Laurentian Granite (Chen et al 2009, Dai et al 2010a,b, Xia et al 2008).

Compressive tests indicate a clear and approximately linear increase in strength with loading rate

for the tested ranges. The dependency of compressive strength indicates that increasing the

a)

b)

189

loading rate by 1000 GPa/s produces an increment of compressive strength between 15 and 20

MPa. The results do not show significant variations of strength with slenderness ratio (L / D) or

sample orientation, for the rock type being tested.

Figure E6. Variation of dynamic compressive strength with loading rate considering a) various slenderness ratios (L / D) (after Dai et al 2010b); and b) various sample orientations (after Xia et al 2008). In b), the loading rate may be calculated by multiplying strain rate by Young's modulus. The range in this graph (0 – 160 s-1) in terms of loading rate is approximately 0 – 11200 GPa/s.

The results of fracture toughness shown in Figure E7 also indicate a steady increase of this

property with loading rate. In all cases loading rate values are reported in terms of stress intensity

factor over time (GPa·m½·s-1). In the case of CCNBD tests, these loading rate values may be

converted into stress over time (GPa/s) according to the following expression, relating far field

stress and stress intensity factor (Jaeger et al 2007):

c

Kπ

σ = E- 6

where c is in general half of the crack length, which in this case is taken as half of the notch

length in the CCNBD samples (Dai et al 2010a).

Fracture energy, Gc can be related to Fracture Toughness, Kc from the expressions that relate

Stress intensity factor and energy release rate. Since the numerical models in this research are in

two dimensions only, there is no mode III stress intensity factor. Also, for simplicity of

expressions and given that we only wish to estimate fracture energy, only mode I fracture mode

is considered. Thus,

L / D ratio:

a) b)

190

E

KG ICIC

2

= , for Plane Stress E- 7

( )E

KG ICIC

221 ν−= , for Plane Strain E- 8

Where the sub-index I accounts for mode I fracture.

Figure E7. Variation of Fracture Toughness with loading rate. a) Initiation and propagation on SCB specimens (after Chen et al 2009); b) Initiation and propagation on CCNBD specimens (after Dai et al 2010a); c) Initiation on CCNBD & SCB specimens (after Dai et al 2010a).

b) c) a)

191

Appendix F : Analytical-numerical approach for Direct and Reverse initiation modes

The following analysis is intended to show the effect on frequency content of the seismic signals

resulting from a column of explosive of finite length initiated at one end, versus the case of a

point charge. The study of frequency content will lead evidently to conclusions on waveform

shape and amplitude and will provide a validation for the waveforms measured in direct and

reverse modes.

Two main assumptions are made for these analysis: first, that the wave velocity is frequency

independent, which implies that waves corresponding to all frequencies travel at the same speed;

and second, that the distance from explosive to observation point is large compared to the

explosive length, so that observed waveforms caused by all elements or portions of explosive

along the column can be considered approximately the same. This last assumption implies to

neglect variations on waveforms caused by different travel distances and ray-path angles.

Let us consider the geometry of a blast with points of observation A and B as shown in Figure

F1. From the point of view of these observation points the initiation of the explosive column

corresponds to direct mode. This analysis considers the superposition of P-waves; however, it

may be easily extended to other wave types.

For simplicity the analysis starts by considering an observation point directly above the explosive

column, which corresponds to point A in Figure F1. The waveform generated by any element of

charge can be expressed as the superposition of single frequency waves with various amplitudes

and phases. In particular, for the element of charge at the initiation point, the equation in the time

domain for any of these waves may be written as:

( ) ( )tAx

txAx

ωω sin,

0

=∂

∂

=

F- 1

Where Aω is the wave amplitude per unit of length associated with the angular frequency ω, and t

is the time domain variable. Note that the phase corresponding to this wave was chosen to be

zero only for simplicity of notation, but without loss of generality.

192

Figure F1. Geometry of a blast considering observation points in direct mode (detonation front moving towards the point of observation).

Generalizing Equation F-1 for any element along the explosive column:

( ) ( )( )ttAx

txA∆+=

∂∂ ωω sin, F- 2

where ∆t is the difference of arrival time between waves generated at a point P on the explosive

column (t1) and those generated at the initiation point O (t0). The expressions for t0 and t1 are:

PV

Dt =0 , and F- 3

( )PV

xDVOD

xt −+=1 F- 4

And hence,

−=−=∆

PVVODxttt 11

01 F- 5

where D and x are the distances from the initiation point to the observation point A and to any

element along the explosive column P, VOD is the explosive's velocity of detonation, and VP is

the P-wave velocity.

VOD

Observation points

Explosive column

D

D-x

x

Element of explosive

L

V

H

A B

Initiation point

P

O

193

Thus, the expression for wave amplitude per unit of length becomes:

( )

−+=

∂∂

PVVODxtA

xtxA 11sin, ωω F- 6

Adding the contribution of all elements of charge along the explosive column:

( ) ∫

−+=

L

P

dxVVOD

xtAtA0

11sin ωω F- 7

Whose analytical solution is:

( ) ( ) ( )( )[ ]TttV

AtA eq +−= ωωωω coscos F- 8

With:

peq VVODV

111−= , and F- 9

eqVLT = F- 10

The peak amplitude of Equation F-8 above is:

( )

=

2sin2 TV

AA eqpeak

ωω

ω ω F- 11

Thus, the relative peak amplitude in direct mode with respect to a unit charge associated with any

frequency is:

( )

=

2sin

2 TVA

A eqpeak ωω

ω

ω

F- 12

The application of this expression to a waveform caused by a unit element of charge (i.e., unit

length) is equivalent to integrate or sum the contribution of all elements of charge along the

explosive column. This procedure is also akin to apply a filter to the fundamental (seed)

waveform to represent the resultant waveform in direct mode. It can be verified that Equation F-

12 also applies for reverse initiation mode, with only a different expression to calculate Veq:

194

peq VVODV

111+= F- 13

Figure F2 shows the filters in direct and reverse modes (from Equation F-12) for a 6 m column

of explosive, with VP = 6200 m/s and VOD = 5300 m/s. From these graphs it is clear that the

signals associated with most frequencies in direct mode are much larger than those in reverse

mode. Although in both cases the amplification of signals is equal to 6 m (the length of the

explosive column) for frequency zero, in direct mode this amplification decays slowly to zero at

6 kHz, whereas in reverse mode it quickly decays to zero at 0.5 kHz. These frequencies (6 kHz

and 0.5 kHz) represent also the periodicity of the filters, equal to 1/T (Equation F-9 and Equation

F-10 in direct mode; Equation F-10 and Equation F-13 in reverse mode).

Figure F2. Filters in Direct and Reverse modes for a 6 m column of explosive, with VP = 6200 m/s and VOD = 5300 m/s, considering the observation points directly above or below the explosive column.

Note that the filters' unit is of length (Equation F-12), as they are meant to be applied to the

signals corresponding to a charge of unit length. Also, the frequency shown in these graphs, as in

the case of field measurements, corresponds to the ordinary frequency f calculated as:

πω2

=f F- 14

Since in most cases, the measurement of waves is done at an angle with respect to the blasthole

axis, i.e., not directly above or below the explosive column, the calculations of direct and reverse

filters are generalized to any angle. The observation point B in Figure F1 represents this general

case, where a horizontal distance H must be considered. For this point, the equations of arrival

times are as follows:

0 2 4 6 8 100

1

2

3

4

5

6

Frequency (kHz)

Filte

r Am

plitu

e (m

)

0 2 4 6 8 100

1

2

3

4

5

6

Frequency (kHz)

Filte

r Am

plitu

e (m

)6 m Direct 6 m Reverse

195

PV

HDt22

0+

= F- 15

( )

PVHxD

VODxt

22

1+−

+= F- 16

( ) ( )PV

HDDxxHDVOD

xttt22222

012 +−−++

+=−=∆ F- 17

Thus, the filter in direct mode can be calculated from:

( ) ( ) ( )∫

+−−++++=

L

PD dx

VHDDxxHD

VODxtAtA

0

22222 2sin ωω F- 18

And in reverse mode the filter equation is obtained from:

( ) ( ) ( )∫

+−+++++=

L

PR dx

VHDDxxHD

VODxtAtA

0

22222 2sin ωω F- 19

From Equation F-18 and Equation F-19 it can be observed that in the general case the filters in

direct and reverse modes are not independent of the distances (both horizontal and vertical) to the

observation point. Since an analytical solution for the above integrals is cumbersome, numerical

integration is applied to obtain the filters. Direct and reverse filters for a 6 m explosive column

using the same parameters and distances corresponding to measured signals (Figure 44) are

shown in Figure F3. The calculated filters are applied to a signal (frequency spectrum) recorded

from a 0.4 m long charge (Figure 39) and the resulting spectra are shown in the same figure. For

comparison, the recorded spectra from Figure 44 are also shown. Although the calculated and

recorded spectra are not identical, it is patently clear that the mode of initiation of the explosive

is primary responsible for the shape of the frequency spectra. While in direct mode the filter

causes a concentration of energy towards lower frequencies, the reverse filter produces several

periodic peaks in a wider range of frequencies. Additionally, the amplitudes obtained in direct

mode are significantly higher than those in reverse mode, which agrees with the experimental

results.

196

Figure F3. Filters in direct and reverse initiation mode calculated for parameters and distances associated with measured signals from 6 m charges (Figure 44), and its application to a small charge to generate synthetic (calculated) signals. VP = 6200 m/s, VOD = 5300 m/s. Direct: r = 34 m θ = 19°, Reverse r = 47 m θ = 166°. L0 = 0.4 m.

Figure F4 shows the filters corresponding to 3 m columns of explosive considering same

distances and parameters of measured signals (Figure 45). As in the previous case the filters are

applied to a small charge spectrum and the calculated vs. recorded spectra are compared. The

similitude in direct mode is less significant that the 6 m case; however, the presence of periodic

valleys every approximately 1 kHz in both recorded and calculated spectra in reverse mode

confirms the strong effect of the initiation mode on the produced seismic signals.

On the comparison of spectra shown in Figure F3 and Figure F4, there are several factors that

can explain the differences between recorded and calculated spectra. Among these are:

• The small charge used in calculations is not truly a point charge (length to diameter ratio

is 6.7), so the signals are already influenced by its initiation mode.

• Detonation strength of a small (short) charge may not be as high as that of longer charges.

• Non uniform detonation of the explosive (VOD and borehole pressure function).

• The position of the small charge with respect to the blasthole (angle and distance) is not

the same as for the longer charges.

0 1 2 3 4 50

0.2

0.4

0.6

0.8

Frequency (kHz)

|Vel

ocity

(mm

/s)|

0 1 2 3 4 50

1

2

3

4

5

6

Frequency (kHz)

|Vel

ocity

(mm

/s)|

0 1 2 3 4 50

1

2

3

4

5

6

Frequency (kHz)

Filte

r Am

plitu

e (m

)

0 1 2 3 4 50

1

2

3

4

5

6

Frequency (kHz)

Filte

r Am

plitu

e (m

)

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

Frequency (kHz)

|Vel

ocity

(mm

/s)|

0 1 2 3 4 50

1

2

3

4

5

Frequency (kHz)

|Vel

ocity

(mm

/s)|

6 m Direct

6 m Reverse

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

Frequency (kHz)

|Vel

ocity

(mm

/s)|

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

Frequency (kHz)

|Vel

ocity

(mm

/s)|

××0

1L

Calculated Recorded

Calculated Recorded

0.4 m charge

0.4 m charge

××0

1L

197

Figure F4. Filters in direct and reverse initiation mode calculated for parameters and distances associated with measured signals from 3 m charges (Figure 45), and its application to a small charge to generate synthetic (calculated) signals. VP = 6200 m/s, VOD = 5300 m/s. Direct: r = 62 m θ = 10°, Reverse r = 50 m θ = 167°. L0 = 0.4 m.

Finally it is necessary to indicate that an important variable on the effect of the initiation mode

over the seismic signals is the blast pressure function itself. Effectively, as the frequency

spectrum of a small charge depends on the signature of the source, the resultant frequency

spectra in both direct and reverse modes is dependent on the shape of the pressure function. The

effect of the initiation mode will be more significant when higher frequencies (in the kHz range)

are present in the seismic signals, but much lower if the signals contain only low frequencies (up

to a few hundred Hz). It is also evident from the calculated filters that the longer the explosive

charge the larger the effect of the initiation mode.

0 1 2 3 4 50

0.5

1

1.5

2

2.5

3

3.5

Frequency (kHz)

|Vel

ocity

(mm

/s)|

0 1 2 3 4 50

0.5

1

1.5

2

2.5

3

Frequency (kHz)

Filte

r Am

plitu

e (m

)

0 1 2 3 4 50

0.5

1

1.5

2

2.5

3

Frequency (kHz)

Filte

r Am

plitu

e (m

)

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

1.2

1.4

Frequency (kHz)

|Vel

ocity

(mm

/s)|

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

1.2

1.4

Frequency (kHz)

|Vel

ocity

(mm

/s)|

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Frequency (kHz)

|Vel

ocity

(mm

/s)|

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

Frequency (kHz)

|Vel

ocity

(mm

/s)|

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

Frequency (kHz)

|Vel

ocity

(mm

/s)|

3 m Direct

3 m Reverse

Calculated Recorded

Calculated Recorded

0.4 m charge

0.4 m charge

××0

1L

××0

1L

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