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

Transcription

1 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,

2 Study of Blast-Induced Damage in Rock with Potential Application to Open Pit and Underground Mines Abstract Leonardo Fabián Triviño Parra Doctor of Philosophy Department of Civil Engineering University of Toronto 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 D 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 D 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. ii

3 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 -4 borehole diameters from stress waves; > 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. iii

4 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. iv

5 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 : Introduction.... Excavation in rock.... Blasting as a rock excavation method Blast design Damage, overbreak and dilution control Research objectives and approach Thesis outline... Chapter : Elements of Theory and State of the Art Physical processes in rock blasting Shock wave and subsequent seismic waves Gas Expansion Stress wave propagation in rock blasting Radiation from a cylindrical source Waves attenuation....3 Damage mechanics Damage as crack density Kachanov's approach for isotropically distributed non-interacting cracks Assessment of blast-induced damage in rock... 7 v

6 .4. Direct measurement of cracks Seismic monitoring: PPV method Explosive gas pressure activity Cross-hole: Variations in P-wave velocity The combined finite and discrete elements (FEM-DEM) method The YD code Constitutive model in YD code Comparison of seismic radiation between YD and Heelan analytical solution.. 37 Chapter 3: Experiments, Instrumentation and Layout Experimental procedures Instrumentation Accelerometers Pressure sensors Explosion (detonation) front pressure measurement VOD measurement Cross-hole seismic system Data acquisition systems Field test sites Surface test site Underground mine Chapter 4: Seismic Radiation from Blast and Damage in Rock: Results from Single-hole Controlled Experiments Measurement of seismic radiation Identification of body waves Amplitude of seismic waves Frequency content of seismic waves... 7 vi

7 4..4 Short vs. long charges Effect of initiation mode (Direct / Reverse) and relative source-sensor location Blasthole pressure function and VOD Measurement of damage Cross-hole measurements Gas pressure activity Discussion Chapter 5: Damage from Stress Waves and Gas Expansion Model input parameters from field and lab experiments Elastic constants Material properties from lab experiments Explosive properties Pressure function Adjustment of attenuation and calibration of other input parameters D model vs. 3D phenomenon: adjustment of geometric attenuation Relationship between PPV and crack density Calibration of material viscous damping and in-hole pressure function decay Material strength parameters Summary of properties for models Relative contribution of stress waves and gas expansion to damage Damage quantification from models Damage quantification from field measurements Quantification of damage from stress waves and gas expansion Sensitivity analysis for variations in input parameters Discussion Chapter 6: Extension of Results to Underground Blasting vii

8 6. Production blast monitoring Blast simulation Model parameters Production blast damage Discussion... 5 Chapter 7: Conclusions Nature of seismic waves by rock blasting in boreholes Mechanisms of wave generation for different explosive initiation modes Blast-induced seismic wave propagation by D numerical method vs. 3D real case Correlation between stress wave amplitude and damage Fracture network development by stress waves and gas expansion Relative contribution of stress waves and gas penetration to blast-induced damage Future work Overall conclusions... 6 References Appendices... 7 Appendix A : Relationship between Elastic Constants... 7 Appendix B : Effective medium theories (EMT) Appendix C : Constitutive model in FEM-DEM code YD Appendix D : List of blast experiments and instrumentation... 8 Appendix E : Laboratory tests and Material Strength Properties E. Measurement of P and S-wave velocities and density E. Static and dynamic uniaxial compressive strength (UCS) E.3 Static and dynamic tensile strength E.4 Strain / Loading rate dependency of strength parameters Appendix F : Analytical-numerical approach for Direct and Reverse initiation modes... 9 viii

9 List of Tables Table. Proposed Classification of Earth Materials by Attenuation Coefficient (after Woods & Jedele 985)... 3 Table. Accelerometers technical data Table 3. Data acquisition systems technical information... 5 Table 4. Principal stresses at Williams mine Table 5. Regular joint sets at Williams mine Table 6. Explosive properties at Williams mine Table 7. Effect of variation in material viscous damping and pressure function decay rate over PPV and frequency of seismic signals... 5 Table 8. Loading and decay rates at various distances from blasthole... 8 Table 9. Summary of material strength properties... 9 Table. Summary of material and explosive properties for numerical models... Table. Summary of material and explosive properties for production blast simulation ix

10 List of Figures Figure. Blasthole cross sections in open pit excavations. a) Typical terminology for blast design (after Yamin 5); b) Events occurring during a typical quarry bench blast (after Morhard 987) Figure. Typical cross Section of a tunnel excavation (after Sen 995). Terms used to refer to boreholes vary from place to place. Here, they are provided only as examples Figure 3. Schematic view of planned and unplanned dilution in underground mines Figure 4. Schematic diagram of the approach and methodology employed in this research.... Figure 5. Zones of damage caused by stress wave (after Yamin 5) Figure 6. Damage by single-hole blast. Network created by gas penetration (after Yamin 5) 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 F (φ) (for P-waves) and F (φ) (for S-waves) (after Heelan 953). 9 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 7). 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)... Figure 9. Various forms of vibration attenuation (after Dowding 996, Woods & Jedele 985). Figure. Schematic view of algorithms built in the combined FEM-DEM program YD Figure. Representation of the Kelvin-Voigt visco-elastic model in the one-dimensional case x

11 Figure. Geometric attenuation of P and S-waves from FEM-DEM elastic models and comparison with D and 3D elastic attenuation. a) FEM-DEM results before correction; b) FEM- DEM results after correction (x r -.5 ) Figure 3. Radiation pattern of particle velocity from FEM-DEM program and Heelan solution considering elastic material (i.e., no damping) with ν =.5. a) FEM-DEM contour plot of PPV (D attenuation); b) Heelan contour plot of PPV (3D attenuation); c) FEM-DEM contour plot modified by a factor r -/ (3D attenuation); d) FEM-DEM contour plot modified by a factor r -/ (3D attenuation) and S/P ratio amplified by a factor.6 (for equal S/P ratio) Figure 4. 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 -/... 4 Figure 5. 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 -/... 4 Figure 6. Comparison between solution to Lamb's problem for a point horizontal load and FEM-DEM results for ν =.5. a) Radial component, and b) Tangential component of Lamb s solution (after Miller & Pursey 954). c) Radial component, and d) Tangential component FEM- DEM program Figure 7. Accelerometer assembly to be grouted in borehole. a) Accelerometer assembly inserted in φ 5 mm aluminum case; b) Detail of case showing three uniaxial accelerometers mounted orthogonally; c) Assembly in 3 mm aluminum case attached to ABS pipe ready to be inserted and grouted in borehole Figure 8. 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 Figure 9. Silicon pressure sensor employed for gas activity in the vicinity of a blasthole. a) Connector, sensor and case; b) Assembly for field tests xi

12 Figure. Sensors installed in monitor holes and connected to power supplies Figure. Cross-hole system layout Figure. General view of the surface test site Figure 3. Surface test site plan view. Distribution of boreholes. 45 and 75 mm boreholes are identified with the nomenclature B45 and B75 respectively Figure 4. Explosive assembly corresponding to 5 g of emulsion to be inserted in φ45 mm borehole Figure 5. 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 6. Experimental setup in surface test site Figure 7. Geometry and experimental layout at Williams mine Figure 8. Typical distribution of blastholes in a production ring (~ m x 6 m, plan view). Numbers in parenthesis indicate delay number (x 5 ms). All holes plunging from collar to toe Figure 9. Initiation method for Production Blasts (drawing facilitated by Williams Operating Corp) Figure 3. Recorded three components of acceleration for a single charge of g of emulsion at surface test site. r = 3. m, θ = 44 (coordinates according to Figure 3). Component Ay is vertical ( A denotes accelerometer id, and xyz its specific orthogonal coordinate system) Figure 3. Recorded three components of acceleration for a single charge of 4.46 kg of emulsion at Williams mine. r = 49.8 m, θ = 67 (coordinates according to Figure 3). AV denotes (approximately) vertical component, ( A denotes accelerometer id, and VLT its specific orthogonal coordinate system) xii

13 Figure 3. 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. Components rˆ, θˆ and φˆ of velocity for a single shot, 6m explosive column, direct primed, executed at Williams mine. r = 34 m, θ = Figure 34. Example of plotting an equal area projection, upper hemisphere stereonet with polar mesh Figure 35. Identification of P and S-waves by analysis of the direction of particle motion for a single shot, g emulsion, executed at the surface test site. r = 3. m, θ = 8. The time window is indicated by highlighting the corresponding signal shown below the stereonet. Direction B corresponds to the blasthole orientation. rˆ, θˆ, φˆ correspond to unit vectors in spherical coordinates as shown in Figure Figure 36. P and S-wave velocities obtained for each test site Figure 37. Peak Particle Acceleration (PPA) and Peak Particle Velocity (PPV) as a function of Scaled Distance. Surface test site Figure 38. Peak Particle Acceleration (PPA) and Peak Particle Velocity (PPV) as a function of Scaled Distance. Williams mine Figure 39. Radial components of velocity for a single cartridge of explosive and its amplitude spectra. Charge:.56 kg,.4 m of emulsion. r = 3 m θ = Figure 4. Average Frequency of Acceleration and Velocity as a function of Distance. Summary of both test sites considering charges of Emulsion Figure 4. 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 xiii

14 Figure 4. Amplitude and orientation of P and S-wave PPV for short explosive charges, projected on the plane rˆ -θˆ. In each case the center of the charge is located at (,) 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 Figure 43. Amplitude and orientation of P and S-wave PPV for long explosive charges, projected on the plane rˆ -θˆ 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 = 9 ; b) Reverse mode, 8.4 kg, 6 m column of emulsion, r = 47 m θ = 66. Williams mine Figure 45. Radial components of velocity and their amplitude spectra. a) Direct mode, 4.4 kg, 3 m column of emulsion, r = 6 m θ = ; b) Reverse mode, 4.4 kg, 3 m column of emulsion, r = 5 m θ = 67. Williams mine 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.. kg emulsion, 9% coupling 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 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 = ; b) Discretization of area around. kg (.45 m) charge ( a =.5 m); c) Discretization of area around.64 kg ( m) charge ( a = m) Figure 5. Cross-hole ray-paths from measurements on P-wave velocity changes to quantify damage caused by a. 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 xiv

15 Figure 5. Cross-hole ray-paths from measurements on P-wave velocity changes to quantify damage caused by a.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 Figure 5. Cross-hole ray-paths from measurements on P-wave velocity changes to quantify damage caused by a.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 Figure 53. Measured variations in P-wave velocity caused by explosive charges of. kg,.5 kg and.64 kg Figure 54. Measured blast-induced damage determined from inversion of P-wave velocities corresponding to a.5 kg charge of emulsion, 9% coupling. a) Vertical plane E-W; b) Vertical plane N-S; c) Plan view at Z =.5 m (top); d) Plan view at Z = -.5 m (bottom)... 9 Figure 55. Comparison of measured and calculated P-wave velocity values after blast for explosive charge of.5 kg Figure 56. Measured blast-induced damage determined from inversion of P-wave velocities corresponding to a.64 kg charge of emulsion, 67% coupling. a) Vertical plane E-W; b) Vertical plane N-S; c) Plan view at Z = m (top); d) Plan view at Z = - m (bottom) Figure 57. Comparison of measured and calculated P-wave velocity values after blast for explosive charge of.64 kg Figure 58. Measured gas pressure activity in monitor holes from blasts corresponding to.5 and.64 kg of explosive (9% and 67% coupling respectively) in φ 45 mm borehole Figure 59. Pressure activity recorded in monitor holes from a blast corresponding to.5 kg of explosive, 9% coupling in φ 45 mm borehole Figure 6. 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.... xv

16 Figure 6. Pressure functions P u (t), P d (t), and P(t)/P max, for parameters LR = GPa/ms, and DR = GPa/ms (with α = -7, α = -3, b ratio =. LR: Loading Rate; DR: Decay Rate) Figure 6. Initial meshes used for models. a) Mesh for.5 kg charge; b) Profile of horizontal particle velocity at 65 µs after initiation; and c) Mesh for.64 kg explosive charge.... Figure 63. Fracture patterns from FEM-DEM models for a) short and b) long charges of explosive, bottom initiated Figure 64. Damage vs. PPV from FEM-DEM models 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 Figure 66. Comparison of rˆ component of particle velocity between single shot experiments and FEM-DEM models. a).5 kg (.45 m) explosive, reverse primed, r =.6 m, θ = 9. b).64 kg ( m) explosive, direct primed, measured on surface, r =.4 m, θ = Figure 67. Contour plots from FEM-DEM model for a short charge of explosive: a) Damage; b) PPV.... Figure 68. Contour plots from FEM-DEM model for a long charge of explosive: a) Damage; b) PPV Figure 69. Damage from FEM-DEM model for short and long charges, after correction D to 3D Figure 7. Contour plots of measured damage for short and long explosive charges considering cylindrical symmetry Figure 7. Relative contribution of stress waves and gas expansion to damage for a short charge, bottom initiated Figure 7. Relative contribution of stress waves and gas expansion to damage for a long charge, bottom initiated xvi

17 Figure 73. Effect of variations in G C over fracture patterns obtained for short and long explosive charges. Short models: σ s = 7 MPa; σ t = 4 MPa; a) Min G C = 3 J/m ; b) Avg. G C = 4 J/m ; c) Max G C = 79 J/m. Long models: σ s = 8 MPa; σ t = 3 MPa; d) Min G C = 3 J/m ; e) Avg. G C = 4 J/m ; f) Max G C = 79 J/m Figure 74. Effect of variations in σ t over fracture patterns obtained for short and long explosive charges. Short models: σ s = 7 MPa; G C = 4 J/m ; a) Min σ t = 6 MPa; b) Avg. σ t = 4 MPa; c) Max σ t = 5 MPa. Long models: σ s = 8 MPa; G C = 4 J/m ; d) Min σ t = MPa; e) Avg. σ t = 3 MPa; f) Max σ t = 47 MPa Figure 75. Effect of variations in σ s over fracture patterns obtained for short and long explosive charges. Short models: σ t = 4 MPa; G C = 4 J/m ; a) Min σ s = 8 MPa; b) Avg. σ s = 7 MPa; c) Max σ s = 78 MPa. Long models: σ t = 3 MPa; G C = 4 J/m ; d) Min σ s = 75 MPa; e) Avg. σ s = 8 MPa; f) Max σ s = 49 MPa Figure 76. Production Blast #, March 5, 7 Dayshift - Accelerometer A. 3 kg Emulsion - Collar Primed - 3 g/m Det Cord r' = 77.3 m Figure 77. Production Blast #3, March 5-6, 7 Nightshift - Accelerometer A. 9 kg Emulsion - Booster Collar Primed - 3 g/m Det Cord r' = 74. m Figure 78. Production Blast #, March, 7 Dayshift - Accelerometer A. 65 kg Water Gel - Booster Collar Primed - 3 g/m Det Cord r' = 43.5 m Figure 79. Components rˆ, θˆ and φˆ of velocity for a production blast shot consisting of holes. r = 4m, θ = 36 ; r = 39m, θ = Figure 8. PPA and PPV for P and S-waves vs. scaled distance in rock. Production and Control Blasts at Williams mine Figure 8. Frequency spectrum of particle Acceleration and Velocity vs. distance. Production and Control Blasts at Williams mine Figure 8. Mesh used to model production blast in FEM-DEM code: Refinement for calibration of parameters (35,+ elements) xvii

18 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 5-6 to estimate equivalent 3D PPV Figure 84. Velocity time history recorded at m horizontally from raise center point (distance to boreholes from 3 to 6 m). The amplitude of signals is not corrected by factor given by Equation 5-6 to estimate equivalent 3D particle velocities Figure 85. Mesh used to model production blast in FEM-DEM code: Refinement to determine fracture pattern, damage and PPV contour (7,+ elements). Symmetry was used, model includes half of stope only Figure 86. Stress wave amplitude from two adjacent blasthole with different delays. Colors show horizontal particle velocity (v x ) at.5 ms after the initiation of each blasthole. PPV at snapshots (wave front in blue): left 5 mm/s; right mm/s Figure 87. Fracturing associated with stress waves obtained from production blast simulation. a) Fracture pattern; b) Crack density calculated directly from D simulation; c) Crack density corrected from D to 3D Figure 88. Comparison of fracture patterns from production blast simulation considering various configurations associated with field stresses and initiation mode xviii

19 List of Appendices Appendix A : Relationship between Elastic Constants... 7 Appendix B : Effective medium theories (EMT) Appendix C : Constitutive model in FEM-DEM code YD Appendix D : List of blast experiments and instrumentation... 8 Appendix E : Laboratory tests and Material Strength Properties Appendix F : Analytical-numerical approach for Direct and Reverse initiation modes... 9 xix

20 List of Symbols 3D Laplace operator, e.g. = ( x + y + z ) in Cartesian coordinates α α Attenuation coefficient Standard charge weight scaling law specific site constant (power of charge weight) α Error of pressure function at t = α α P α S β Error of pressure function at t = t max P-wave attenuation coefficient S-wave attenuation coefficient Standard charge weight scaling law specific site constant (power of distance) δ Dimensionless number to characterize coupling between stress and fluid pressure Volumetric strain, = ( ε + ε + ε ) xx yy zz ΔG ε ε ij ε ij ε ε ζ η η θ θ λ λ μ Change in electric conductance Strain Strain component along i on a plane with normal in the direction j Strain rate component along i on a plane with normal in the direction j Strain tensor Strain rate tensor Crack aspect ratio (thickness / radius) Viscous damping Vertical angle in Prolate coordinate system Vertical angle in spherical coordinate system Angle between borehole axis and direction explosive center to observation point Lamé constant Wavelength Shear modulus xx

21 μ ν ν ξ ρ ρ ρ D ρ 3D ρ C ρ G ρ S σ σ σ σ 3 σ c σ ij σ s σ t σ ϕ ϕ ϕ ω ω i Ω Solid matrix Shear modulus Poisson s ratio (Greek letter nu) Solid matrix Poisson s ratio Prolate coordinate that forms prolate spheroids when kept constant Crack density Material density D crack density 3D crack density Combined blast-induced crack density Crack density due to gas expansion only Crack density due to stress waves only Stress Maximum principal stress Middle principal stress Minimum principal stress Compressive strength Stress component along i on a plane with normal in the direction j Shear strength Tensile strength Stress tensor Borehole diameter Horizontal angle in spherical and Prolate coordinate systems Angle between borehole axis and direction explosive center to observation point Angular frequency Component of rotation according to i Dimensionless angular frequency a Borehole radius xxi

22 a i A Crack radius Area b d Parameter related to the max slope of the decaying part of pressure function, m d b ratio Ratio b d /b u b u B BD c D D D D DR dx dy dz E E E P E S ESS f F G IC h H I Parameter related to the max slope of the rising part of pressure function, m u Sample thickness Borehole diameter Phase velocity Damage (in conventional damage mechanics) Distance Sample diameter Total damage (when damage is taken as crack density) Peak decay rate Infinitesimal length in the x direction Infinitesimal length in the y direction Infinitesimal length in the z direction Young modulus Solid matrix Young modulus Energy (or relative energy) associated to P-waves Energy (or relative energy) associated to S-wave Explained sum of squares Frequency Scaling factor Fracture energy Geometrical factor related to the shape of the cracks Positive scaling parameter Electric current xxii

23 I k k K K K f K IC L i LR m d m u M M n P P d P max PPA PPV PPV D PPV 3D P u Q r R R Identity matrix Bulk modulus Wavenumber Fracture toughness Standard charge weight scaling law specific site constant Fluid bulk modulus Mode I fracture toughness Apparent crack length Peak loading rate Max normalized slope of the decaying part of pressure function Max normalized slope of the rising part of pressure function Elastic modulus Solid matrix elastic modulus Exponent to define rising part of pressure function Pressure Decaying pressure function Peak in-hole pressure Peak particle acceleration Peak particle velocity D peak particle velocity 3D peak particle velocity Rising pressure function Coordinate rotation matrix Radial distance Electric resistance Coefficient of determination RSS Residual sum of squares xxiii

24 S/P SD SE S V t t t d t u Ratio of S-wave peak amplitude to P-wave peak amplitude Scaled distance Standard error Volumetric stretch time Student s t-test statistic Time parameter to define decaying part of pressure function Time parameter to define rising part of pressure function T Wave period (= f - ) u u u Displacement in the x direction Maximum displacement Particle velocity u max Maximum (peak) particle velocity v V V V c V i V P V P Displacement in the y direction (letter vee) Voltage Volume Current volume Initial volume P-wave velocity Solid matrix P-wave velocity V S ENZ S-wave velocity V Vector particle velocity in geographic coordinates, { V V V } rθφ V ENZ = E N Z V Vector particle velocity in spherical coordinates, V { V V V } rθφ = r θ φ VOD w w Velocity of detonation Displacement in the z direction Explosive weight xxiv

25 Chapter 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 blastinduced 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.. 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

26 constructed in rock, including beautiful and elaborate tunnels and caves. The Ellora Caves and Temples, constructed between the 5 th and th centuries AD, were cut out of the hardest rock by using simple hand tools (Beaver 97). 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 98). 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 5). 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 5). 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.

27 3 Water jet: The system consists on cutting the rock by applying directed high pressure water (generally above 7 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 998). 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 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.. 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.

28 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... 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)

29 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)

30 6 Figure 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 shows a typical section of a tunnel excavation in underground mines. a) b) Vs = 3 to 45 m/s Inclination VUP =.5 to 36 m/s Free Face Stemming Face profile Explosive Burden Material: Limestone VP = 4,5 m/s ρ =.3 kg/dm 3 Onset of Movement 5- msec Vf =.5 to 6 m/sec Explosive: ANFO VOD =, m/sec Hole Dia. =.5 cm Ave. Burden = 4.5 m Figure. Blasthole cross sections in open pit excavations. a) Typical terminology for blast design (after Yamin 5); b) Events occurring during a typical quarry bench blast (after Morhard 987). Roof holes Stopping holes Rib holes Cut with cut easer holes Lifter holes Figure. Typical cross Section of a tunnel excavation (after Sen 995). Terms used to refer to boreholes vary from place to place. Here, they are provided only as examples.

31 7.3 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.

32 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 ). Timing: Accurate timing is essential for appropriate blasting. Failure in timing may produce inappropriate initiation of explosive column, lack of programmed collaboration

33 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..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 D 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.

34 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 D 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.

35 A SURFACE TEST SITE B STUDY OF STRESS WAVES IN UNDERGROUND MINE Stress waves Gas expansion phase Inversion of P-wave velocities into damage C NUMERICAL MODELING Ability to reproduce P and S-waves Identification of P and S- waves Single-hole seismic monitoring Blast damage measurements Evaluation of numerical code FEM-DEM Ability to simulate fracture process from blasting PPA & PPV vs. scaled distance (material attenuation) Frequency content (strain rate & strength) Initiation mode effects Single-hole Control blasts Production blast monitoring 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. Contribution of stress waves and gas expansion to damage Production blast modeling Study of wave attenuation Method to overcome limitations of D code FUTURE WORK 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 Figure 4. Schematic diagram of the approach and methodology employed in this research.

36 .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 : 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 : 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 up to 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 D 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

37 3 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.

38 4 Chapter 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.. 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... 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

39 5 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 ). 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.. 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

40 6 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 : 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.5 to 3 borehole diameters. Zone : 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. Pre-existent fractures Damage boundary Blasthole Zone I: Crushing / Extensive fracturing Zone III: Elastic waves, no damage Zone II: Short length fractures Figure 5. Zones of damage caused by stress wave (after Yamin 5).

41 7.. 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. Pre-existent fractures Blasthole Crushing / melting Propagation of fractures Fragmentation Figure 6. Damage by single-hole blast. Network created by gas penetration (after Yamin 5).

42 8. 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... 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 (953). Heelan (953) 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: u w u w P P S S F = r = F ( ϕ) ( ϕ) r d dt d dt sinϕ cosϕ cosϕ sinϕ { p( t r V )} P { p( t r V )} S (-) (-) where u P, w P, u S, and w S 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); V P

43 9 and V S are the medium P and S-wave velocities respectively; and F and F are the following functions: V F ϕ cos (-3) F ( ) S = ϕ 4πµ VP VP = (-4) 4πµ ( ϕ ) sin ϕ V S where is the volume of the loaded cylindrical void, and µ is shear modulus. The functions or coefficients F and F 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 =.5 or λ = µ), for example, approximately 6% of the radiated wave energy goes into S and 4% into P (Heelan 953). 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 9. Z SV SV P Source P ϕ 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 F (φ) (for P-waves) and F (φ) (for S- waves) (after Heelan 953).

44 Another analytical solution was provided by Abo-Zena (977). In this work the Heelan solution was criticized for having mathematical inaccuracies; however, the proposed solution agrees exceptionally well with that of Heelan (White 983, Blair & Minchinton 996, Blair 7). 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 (7) 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: where Frequency limitation: Ω A <., and Far Field limitation: Ω r a > 5 A Ω A = aω A VP is a dimensionless frequency, a is borehole radius, A ω is the average angular frequency of the pressure function, V P 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 r a < 5, irrespective of the frequency. In addition to the Heelan and Abo-Zena solutions, an exact (full-field) solution was developed by Tubman (984), Tubman et al (984), Meredith (99), and Meredith et al (993). 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 968, Bouchon 979, 98 & 3) and fast Fourier transform (Blair 7). 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 f A = 6 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 6).

45 a) b) c) 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 7). 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)... 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 du max d or dr ( lnu ) dr max, where u max 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, r, and the total wave energy remains constant, the energy density at any given point decays by a factor r. 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 r, and geometric attenuation is proportional to r /. A common expression to account for geometric attenuation is: n r u = u r max max, with n = for body waves and n = ½ for surface waves -5

46 where u max and u max are the peak particle velocities at two distances from the source r and r. 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: max max α ( r r ) u = u e -6 where α is the attenuation coefficient. Note that the expression given by Equation -6 implies that the attenuation coefficient α represents the decay d( u ) dr material damping attenuation can be combined in a single expression as follows: ln max. Geometric spreading and r n α ( r r ) max = u max e -7 r u u = u r r u = u r r e α ( r r ) u = k r m Figure 9. Various forms of vibration attenuation (after Dowding 996, Woods & Jedele 985).

47 3 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 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. Proposed Classification of Earth Materials by Attenuation Coefficient (after Woods & Jedele 985) Class Attenuation Coefficient, α (/m) Description of Material 5 Hz 5 Hz I 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 Competent soils: Most sands, sandy clays, silty clays, gravel, silts, weathered rock (can dig with shovel) III Hard soils: Dense compacted sand, dry consolidated glacial till, some exposed rock (cannot dig with shovel, must use pick to break up) IV <.3 <.3 Hard, competent rock: Bedrock, freshly exposed hard rock (difficult to break with hammer).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

48 4 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 and, with representing no damage, and indicating complete material breakage (Lemaitre & Desmorat 5). 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: D n δs = δs D -8 When damage is caused by the presence of microcracks, the method of direct measurement has been proposed to calculate this variable (Lemaitre 996). 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: Li D = -9 L where D is damage, L i represent the apparent size of cracks (measured length), and L 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 996), 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

49 5 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 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 (994). The choice of the method, including a brief comparison with other alternative approaches, is discussed in Appendix B..3. 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 994): ρ = a i, in the two-dimensional case, and - A 3 ρ = a i, in the three-dimensional case - V where A and V represent the area and volume of representative elements in D and 3D respectively, and a i represent the radius of cracks (rectilinear cracks of length a i in D, and circular cracks of diameter a i in 3D).

50 6.3. Kachanov's approach for isotropically distributed non-interacting cracks The simplest case of Kachanov's (994) 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: M = + Hρ - M Where M is the rock effective modulus, the sub-index 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: E ν δ 3 = + Hρ = + hρ E 5 δ + -3 µ ν δ hρ = + H ρ = + µ 5 δ + + ν -4 where ( ν ) 6 h = -5 9 ( ν ) is a geometrical factor related to the shape of the cracks (assumed to be circular) and ν E ζ = h -6 K δ f is a dimensionless number to characterize the coupling between stress and fluid pressure, in which K f is fluid bulk modulus, and ζ is crack s average aspect ratio (thickness / radius). Note that Equation -4 has been corrected from Kachanov's (994) original formulation as developed in Benson et al (6).

51 7.4 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..4. Direct measurement of cracks This method has been executed in blocks of relatively intact rock and also in controlled bench blasting (Olsson et al, Ouchterlony et al 999 &, Mohanty & Dehghan Banadaki 9, Dehghan Banadaki ). 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..4. 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.

52 8 The commonly accepted method to predict blast-induced damage in nearby structures is the standard charge weight scaling law (Hopler 998, Dowding 996), given by Equation -7: α β PPV = K w r -7 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 -7 can be achieved by considering α = β/3 (cube-root scaling) or α = β/ (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 968). 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/w / 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 98, Wiss 98). Typically, PPV is plotted against the term r/w /, usually referred as scaled distance in a logarithmic scale. Thus: ( ) β PPV = K SD -8 with r SD = -9 / w 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

53 9 is the well-known Holmberg-Persson method (Holmberg and Persson 979), 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 (984) proposed some PPV threshold values for different rock conditions: mm/s for hard rock with strong joints; 7-8 mm/s for medium hard rock with no weak joints; and 4 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 996, 6) and even mathematically erroneous (Hustrulid & Lu ). The standard scaling law itself has also been questioned for not considering the wave nature of the radiating signals from a blast (Blair 99), and has also been qualified as inadequate to predict blast-induced damage (Fleetwood et al 9). 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)..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 987, Brent & Smith 996, Yamin 5). 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 preexistent 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.

54 3 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..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 blastinduced 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 (994) described in.3. is used. From Equation -3, the crack density can be calculated as: E ρ = - H E where H is a positive scaling parameter and the sub-index 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:

55 3 V P ρ = - H VP Thus, crack density within the rock mass before and after blasting can be calculated as: V P ρ before =, and - H VP before V P ρ after = -3 H VP after where ρ before, ρ after, V P before and V P 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: V V P P before ρ blast = ρ after ρbefore = -4 H VP before VP after 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 -4: ~ V P after = V P before V + Hρ V P before P -5 where V ~ P after is the calculated the P-wave velocity after blast. Equation -5 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..

56 3.5 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 995, Mohammadi et al 998, Munjiza 4). One software that uses this method is the YD code, which has been applied to blast modeling, including the incorporation of fractures and explosion gas penetration into cracks (Munjiza et al 999a,b). Also, it has been compared to analytical and experimental results of blast seismic radiation (Trivino et al 9). 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 nonplanar waves. Consequently, this code was chosen to be used as part of this research to specifically compute damage from stress waves..5. The YD code The YD code is a D open source program developed by Munjiza () 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

57 33 Figure shows a schematic view of the above mentioned algorithms. A full description of the method can be found in Munjiza (4). Specific stress combination Fracture Intensive fracturing Fragmentation Fracture Discrete Elements Interaction Contact Detection Algorithm Discrete elements separate bodies Contact forces on interacting boundaries equivalent nodal forces z Rotation, Translation, Stretch Deforming stress and strain nodal forces x Deformation y Finite Elements Temporal Discretization Nodal forces discrete elements move in time Time domain / small time steps Direct numerical integration Figure. Schematic view of algorithms built in the combined FEM-DEM program YD. Within blast related problems, some of the application of the YD software are: Modeling of fracturing process Variety of loading conditions Complicated geometries Interaction of different materials Some of the limitations of the code are: D 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

58 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..5. Constitutive model in YD code The constitutive model built into the YD code corresponds to the Kelvin-Voigt model, with the equations corresponding to the D 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. E η Figure. 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: σ µ ε + λ I + ηε = -6 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, = ( ε + ε + ε ) viscous damping. The D version of this model can be written as: is volumetric strain, and η is xx yy zz σ σ σ xx yy xy = λ + µε = λ + µε = µε xy xx yy + ηε + ηε + ηε xy xx yy -7 where is volumetric strain, and ε ij and ε ij are components of strain and strain rate respectively (note that in the YD code the user-input viscous damping parameter is η). The constitutive

59 35 model given by Equation -7 along with Newton s second law of motion ( a m F = ) 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: ( ) x u t x u t u + + = η µ λ ρ for compression waves, and -8 x t x t x x x + = ω η ω µ ω ρ for shear waves -9 where u and ω x are longitudinal and rotational displacements along the x-axis, and ρ is density. The general solutions for these equations can be written as: ( ) = t x V i x P P e e u t x u ω ω α, for compression waves, and -3 ( ) = t x V i x x x S S e e t x ω ω α ω ω, for shear waves -3 where ω is angular frequency and the parameters α P, α S (attenuation coefficients), and V P, V S (wave velocities) have the following approximate expressions for small values of η (Jaeger et al 7): ( ) P P V µ λ ηω α + = and + = ρ µ λ P V for compression waves, and -3 S S µv ηω α = and = ρ µ S V for shear waves, -33 The expressions for the coefficients α P and α S necessarily imply that attenuation of S-waves is always greater than attenuation of P-waves. In the case of a Poisson solid (ν =.5 or λ = μ), for example, the ratio between these coefficients P S α α is.6. The actual equations implemented in the code make use of the volumetric stretch parameter defined as: i c V V V S = -34

60 36 where V c and V i are the initial and current volumes of an element. By using the relationships between volumetric stretch and strain S = V V = + and S = V V (assuming V c i V i c Δ ), the expressions from Equation -7 can be written in terms of the former. Thus, the expressions implemented in the code are: σ σ ii ij = λ SV ii ii S + µε + ηε V SV = µε ij + ηε ij i j S V -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: E µ = ( + ν ) Eν λ = ν E µ = + ν λ = ( ) Eν ( )( ) + ν ν for Plane Stress, and -36 for Plane Strain -37 Note that the expressions for shear modulus in both cases are identical, while the expressions for the Lamé constant differ by a factor ( ν ) ( ν ). Also, both moduli in Plane Strain are identical to those in the general 3D case. Finally, although the YD code considers a single value of viscous damping, the model has potential to incorporate independently shear and volumetric damping, as shown in Appendix C.

61 Comparison of seismic radiation between YD 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 a 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 D 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 -.54 (in log-log scale). This geometric attenuation is very close to the theoretical value for the D case (-.5), but evidently far from the 3D case (-). As a consequence, values of wave amplitude from the YD 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 D wave amplitudes by a factor proportional to r -.5 is a suitable method to compare results from D and 3D cases. This correction consists of scaling (or multiplying) PPV D (PPV from D models) by a factor proportional to r -.5 (with r being distance from the source). Figure b shows the geometric attenuation of waves from the FEM-DEM program, corrected by a factor r -.5. It is clear from this figure than the results corrected by this factor are close to the 3D geometric attenuation.

62 38 a) b) Figure. Geometric attenuation of P and S-waves from FEM-DEM elastic models and comparison with D and 3D elastic attenuation. a) FEM-DEM results before correction; b) FEM-DEM results after correction (x r -.5 ). Figure 3 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 3a shows the pattern obtained directly from FEM-DEM PPV values, whereas Figure 3b shows the results from the Heelan solution (the agreement and differences between the two solutions was discussed by Trivino et al 9). 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.6 (in terms of peak amplitudes) Energy from P and S-waves: E P 4%, E S 59% FEM-DEM: S/P ratio. (in terms of peak amplitudes) Energy from P and S-waves: E P 54%, E S 46%

63 39 a) FEM-DEM b) Heelan c) FEM-DEM x r -.5 d) FEM-DEM x r -.5, S/P x.6 Figure 3. Radiation pattern of particle velocity from FEM-DEM program and Heelan solution considering elastic material (i.e., no damping) with ν =.5. a) FEM-DEM contour plot of PPV (D attenuation); b) Heelan contour plot of PPV (3D attenuation); c) FEM-DEM contour plot modified by a factor r -/ (3D attenuation); d) FEM-DEM contour plot modified by a factor r -/ (3D attenuation) and S/P ratio amplified by a factor.6 (for equal S/P ratio). Figure 3c shows the FEM-DEM results corrected by a factor r -.5 and Figure 3d shows the same results with S/P ratios amplified by a factor.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 -.5 ) FEM-DEM results corresponds approximately to a factor.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 4 and Figure 5 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.5.); this discrepancy may, however, be subject of further study.

64 4 a) b) Figure 4. 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 -/. a) b) Figure 5. 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 -/. The discrepancy in S/P ratios should not be taken as a drawback of the FEM-DEM method. In fact, the results from the D program should not match those from Heelan, as the later is a 3D solution. The problem solved by the D numerical method corresponds actually to Lamb's problem for the surface normal line load source (Miller & Pursey 954, Miklowitz 978, Graff 99). The radiation from this solution in terms of both radial (P-waves) and tangential (Swaves) components is shown in Figure 6a,b. The S/P ratio from this solution is approximately., which is evidently much closer to the. from FEM-DEM, than to the.6 from Heelan s solution. From Figure 6 some singularities of zero amplitude are observed at various angles ( from vertical for radial component or P-wave;, 65, and 9 for tangential component or S- wave). Even though the respective radiation patterns from the FEM-DEM method (Figure 6c,d)

65 4 do not show these singularities, its results are considered acceptable, as such singularities are unlikely to occur in reality. a) b) Singularity of zero amplitude Singularities of zero amplitude load load c) d) Distance (m) 5 Distance (m) Distance (m) Distance (m) Figure 6. Comparison between solution to Lamb's problem for a point horizontal load and FEM-DEM results for ν =.5. a) Radial component, and b) Tangential component of Lamb s solution (after Miller & Pursey 954). 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 -.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.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).

66 4 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 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. whilst the instrumentation is described in section 3.. The

67 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., while the instrumentation is described in section 3.. 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 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.. to 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 to 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

68 44 research ranges from to 5 khz (with ±5% of accuracy). A summary of the accelerometers main specifications is included in Table. Table. Accelerometers technical data Specification Unit Type Type Type 3 Type 4 Model number 87B 8763A5 8763A 864AM Components Uniaxial (*) Triaxial Triaxial Uniaxial (*) Acceleration range g (**) ± ±5 ± ± Acceleration limit g (**) ± ± ± ± Sensitivity (±5%) mv/g (**) Frequency response (±5%) Hz.5,,, 5, Resonant frequency, nom khz Sensing element type Quartz shear Ceramic shear Ceramic shear Quartz compression Case / base material Titanium Titanium Titanium Titanium Weight g (*) (**) Three uniaxial accelerometers are mounted orthogonally to obtain true vectors of motion Acceleration due to gravity ( 9.8 m/s ) 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 7 shows three uniaxial accelerometers in aluminum case to be grouted in borehole. Figure 8 shows the spring mounting system, power supply and detail of installation.

69 45 a) b) c) Figure 7. Accelerometer assembly to be grouted in borehole. a) Accelerometer assembly inserted in φ 5 mm aluminum case; b) Detail of case showing three uniaxial accelerometers mounted orthogonally; c) Assembly in 3 mm aluminum case attached to ABS pipe ready to be inserted and grouted in borehole. a) b) c) Figure 8. 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.

70 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 preexistent 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 -3 or - 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 9 shows a silicon sensor and assembly for field tests. Figure 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 5. a) b) Connector to power supply Protective casing Sensor Sensor Figure 9. Silicon pressure sensor employed for gas activity in the vicinity of a blasthole. a) Connector, sensor and case; b) Assembly for field tests.

71 47 σ c =.8 Steel plate Anchors Rubber plug Figure. Sensors installed in monitor holes and connected to power supplies 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 99 & 995, Cunningham et al ). In this work pressures are calculated according to the following equations by Austing et al (995): ( GPa) P =. 4 G if a a ( GPa) P = G G if a G a. Ω 3- G a >. Ω 3- Where G a is a measure of the change in conductance (in S or Ω - ) of the gauge as a result of dynamic loading. G a is calculated according to the following approximate expression: Ga = 3-3 R R i where R is the resistance of the gauge measured at any given time during the explosion and R i 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:

72 48 V R = 3-4 I 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 999, Nie & Olsson, Olsson et al ), 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 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 MHz). Finally, the VOD is easily calculated as the change in length of the cable per unit of time (MREL 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.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

73 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 6 velocity measurements per explosive source. Figure shows a schematic view of one array of receivers and one source, indicating the main components of the cross-hole system. Firing device Shock tube Recording unit Natural water table Receivers: Piezoelectric sensors Source: Detonator Source-receiver Ray-paths Figure. Cross-hole system layout.

74 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-65A; Measurement Computing DAQ board model USB-68HS; and Agilent oscilloscope model 5464A. 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-65A Board USB- 68HS Oscilloscope 5464A 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 per channel rate MS/s MS/s ( MS/s for VOD) - 5 ks/s MS/s Maximum frequency response Total number of channels per unit Total number of units utilized khz Tests recorded Seismic activity, expl. gas pressure, VOD, det. front pressure, cross-hole VOD, crosshole Seismic activity Seismic activity, explosive gas pressure Cross-hole

75 5 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 Surface test site This test site is located near the town of Verona about 5 km north of Kingston, Ontario. The specific test area consists of a relatively flat rock outcrop with 7 vertical boreholes drilled from the surface of approximately m. The boreholes are 6 m in depth and have a nominal diameter of either 45 or 75 mm. Figure 3 shows a plan view of the test site indicating the relative locations of boreholes. Figure shows a general view of the test area. Figure. General view of the surface test site.

76 B75. B75.6 B45..5 B75. B45. B45.3 B75.6 B45.3 B45.3 B75. B75.4 N (m).5 B45.7 B45.4 B45.7 B45.5 B45.7 B75.4 B45.8 B45. B45.8 B45..5 B75.5 B75.9 B75.9 B75.6 B75. B E (m) Figure 3. 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.4 m and the standard deviation of the collar elevations is.3 m. Also, there is an underground water table in the area, approximately 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 ~ m from the explosive). A total of blasts with various amounts of explosive were monitored

77 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: charges of. kg emulsion in φ45 mm boreholes (9% coupling) charges of.5 kg emulsion in φ45 mm boreholes (9% coupling) charge of. kg emulsion in φ75 mm borehole (9% coupling) charge of.5 kg emulsion in φ75 mm borehole (9% coupling) charges of.6 kg ( m length) of emulsion in φ45 mm boreholes (67% coupling) charges of 9 g/m det. cord (double ~ g/m), m length in φ45 mm boreholes charge of 38 g/m cord (quadruple of ~ g/m), m length in φ45 mm boreholes Figure 4 shows a fully assembled 5 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. Carbon Resistors Emulsion Sand for weight VOD cable Detonator Shock tube Figure 4. Explosive assembly corresponding to 5 g of emulsion to be inserted in φ45 mm borehole. Figure 5 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.

78 54 m cube Figure 5. 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 6 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 5 g and g triaxial accelerometers (types, 3 and 4 in Table, section 3..) 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 3 and psi silicon sensors (see section 3..).

79 55 Firing device Power supplies / signal conditioners Recording unit Shock tube VOD Pressure sensor Water level Source: Emulsion Carbon resistors VOD cable Seismic signal Triaxial Accelerometer (spring loaded) Figure 6. 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..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 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).

80 56 Cross-hole: Pre and post blast damage evaluation is carried out through cross-hole measurements as described in section Three tests were selected to carry out these measurements, corresponding to explosive charges of.,.5 and.6 kg of emulsion. Between 8 and 9 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 Underground mine Starting in January 7, 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 ~, 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, Grabinsky et al 8a, 8b & 8c, Grabinsky & Thompson 9, Grabinsky, Mohanty & Trivino 9, Thompson et al 9, Thompson et al, Trivino & Mohanty 9, Witterman & Simms ). 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 Test site description The blast monitoring program was executed at depths between approximately 75 and 9 m from surface. The values of P and S-wave velocities in rock typically obtained at the mine are around 6 and 34 m/s, respectively. The major rock units strike E-W and dip 6 to 7 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).

81 57 Table 4. Principal stresses at Williams mine Stress Component Magnitude Orientation (Trend / Plunge) σ 3 (MPa).4 * Depth (m) 5 / 6 (closest to vertical) σ / σ 3 ratio / (nearly N-S) σ / σ 3 ratio / 8 (nearly E-W) Five regularly occurring joint sets (foliation) are present at the mine. These are summarized in Table 5. Table 5. Joint set A Set B Set C Set Regular joint sets at Williams mine Description Parallel to the orientation of the rock fabric, locally visible as foliation or bedding depending on the rock unit. Rock foliation ~, ~65 N. Spacing varies from. to.5 m, averaging. m Nearly vertical joints striking roughly North-South and dipping sub-vertically parallel to the major diabase dykes. Spacing ranges from.3 to. m, averaging.5 m Relatively flat lying joints dipping 5 South. Spacing ranges from.3 to. 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 (singlehole 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 9, Trivino et al ). 8 single-hole control blasts and 6 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 7. Up to 3 multi-channel high-frequency (>4 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 55 blasts, as each hole in a production blast round could be clearly identified and analyzed individually.

82 58 Blasthole Overcut Accelerometers Monitor Holes A B 9 Single-hole charges Explosive Production Blast Stope B89 CPB filled Stope Production Holes Undercut Figure 7. Geometry and experimental layout at Williams mine. Figure 7 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 g and the frequency range is from.5 Hz to khz (Type in Table ) Single-hole blasts A total of 8 single-hole blasts (also referred to as control blasts) were executed at different depths along a single 4 m long, 6 mm diameter blasthole (Figure 7). 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: g Pentolite (PETN / TNT) boosters (in strings from one to four boosters, to 88 g, blasts) and strings of φ=4 mm, L=4 mm emulsion cartridges (7 blasts). The emulsion cartridges were assembled in line in lengths of.4 m (single cartridge,.56 kg, 3 blasts), 3 m (7.5 cartridges, 4. kg, blasts) and 6 m (5 cartridges, 8.4 kg, blasts).

83 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. Properties Explosive properties at Williams mine Explosive Type Pentolite Booster Emulsion Cartridges Weight g 56 g Dimensions φ = 46 mm, L = 3 mm φ = 4 mm, L = 4 mm Density.6 g/cm 3. g/cm 3 Velocity of Detonation (VOD) 75 m/s 55 m/s (*) Detonation Pressure (**).5 GPa 8.4 GPa (*) In hole VOD measured for 4 mm cartridges; (**) Calculated values Multiple-hole production blasts Seismic radiation from 6 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 7) is located around 3 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 7 north. The smaller blastholes are 65 mm in diameter, plunging and drilled in a 'fanned' fashion at different levels (rings) (Figure 7 and Figure 8). Stope Boundary Figure 8. Typical distribution of blastholes in a production ring (~ m x 6 m, plan view). Numbers in parenthesis indicate delay number (x 5 ms). All holes plunging from collar to toe.

84 6 Typically, each production blast corresponded to the excavation of to 4 rings, with a total of 6 to kg of explosive per blast. The amount of explosive per delay varied from 7 to 68 kg. In all cases the blasts were initiated with 3 g/m detonating cord connected to a 9 g booster at the toe, as shown in Figure 9. Figure 9. 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: 6 / 8 Number of blastholes: 53 / 94 Number of rings: 4 / 75 Total amounts of explosive: 9,6 / 8, 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.

85 6 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. 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... The accelerometer types (according to Table ) and mounting system used in each test site are as follows: Surface test site: Accelerometers type, 3 and 4, spring loaded Williams mine: Accelerometers type, grouted A total of 9 single-hole blast experiments (also referred to as control blasts) were successfully executed and recorded in both test sites altogether ( at surface test site, 8 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 Hz or

86 6 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 3 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 g of emulsion and the sensor is located at 3 m from it. Voltage (V) 3 - Surface Test - Ax Channel 4 mv/g 5, Hz Voltage (V) Surface Test - Ay Channel 5 mv/g 5, Hz Voltage (V) 3 - Surface Test - Az Channel 6 mv/g 5, Hz Time (ms) Time (ms) Time (ms) Figure 3. Recorded three components of acceleration for a single charge of g of emulsion at surface test site. r = 3. m, θ = 44 (coordinates according to Figure 3). Component Ay is vertical ( A denotes accelerometer id, and xyz its specific orthogonal coordinate system). Likewise, Figure 3 shows the recorded three components of acceleration from a 6 m length column of 4 mm diameter emulsion cartridges. The direct distance from source to sensor in this case is 49.8 m. Voltage (V) Williams Control Blast 9 - AV Channel 4 5 mv/g, Hz Voltage (V) Time (ms) Williams Control Blast 9 - AL Channel 5 5 mv/g, Hz Voltage (V) Time (ms) Williams Control Blast 9 - AT Channel 6 5 mv/g, Hz Time (ms) Figure 3. Recorded three components of acceleration for a single charge of 4.46 kg of emulsion at Williams mine. r = 49.8 m, θ = 67 (coordinates according to Figure 3). AV denotes (approximately) vertical component, ( A denotes accelerometer id, and VLT its specific orthogonal coordinate system).

87 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 Rotation to spherical coordinates As discussed in section.. 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 3. In this coordinate system, the P-wave is expected to be preferably along the rˆ direction, whereas the vertically polarized S-wave is expected to generate motion along the θˆ direction. In the subsequent sections of this thesis, the plane containing the borehole axis and the point of observation is referred as the rˆ -θˆ 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 3.

88 64 Figure 3. 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 rˆ direction, while the S-wave is dominant in the θˆ direction. The φˆ 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. Velocity (mm/s) 5-5 P-wave rˆ Time (ms) Velocity (mm/s) S-wave θˆ Time (ms) Velocity (mm/s) φˆ Time (ms) Figure 33. Components rˆ, θˆ and φˆ of velocity for a single shot, 6m explosive column, direct primed, executed at Williams mine. r = 34 m, θ = 9.

89 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

90 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: V rθφ V = V V r θ φ 4- Where V r, V θ and V φ 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 3; 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: re rˆ = rn, rz θ E φ E θˆ = θ N, and φˆ = φ N 4- θ Z φ Z Thus the vector velocity can be written as: V ENZ VE = V N = Q{ Vrθφ } 4-3 V Z where Q is the rotation matrix defined as: { ˆr ˆ θ ˆ φ} Q = 4-4 Thus, the orientation of the vector velocity can be written in terms of its plunge and trend as follows:

91 67 VZ Plunge = arctan VE + VN 4-5 V E Trend = arctan +ϕ VN 4-6 where ϕ = 8 36 if sign elseif otherwise ( VE ) = sign( VN ) = sign( VZ ) ( V ) = sign( V ) or sign( V ) = sign( V ) sign E N E Z st ( quadrant) nd rd ( or 3 quadrants) th ( 4 quadrant) 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. th 4 quadrant Trend 5 st quadrant Plunge 4 5. V ENZ = V ENZ = 8.4 rd 3 quadrant nd quadrant 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, ( rˆ, θˆ, φˆ). In this case the blasthole is vertical and the sensor is located nearly horizontally to the west from the blast. Consequently, rˆ and θˆ directions are nearly E-W and vertical, respectively.

92 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 θˆ directions (Figure 35b), which allows a preliminary identification of this signal as S-wave. a) P-wave b) S-wave Velocity Velocity Figure 35. Identification of P and S-waves by analysis of the direction of particle motion for a single shot, g emulsion, executed at the surface test site. r = 3. m, θ = 8. The time window is indicated by highlighting the corresponding signal shown below the stereonet. Direction B corresponds to the blasthole orientation. rˆ, θˆ, φˆ correspond to unit vectors in spherical coordinates as shown in Figure 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 -3.5 m at the surface test site to 3- 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.

93 69 a) b) 3.5 V P = 5.9 km/s 3. R = V S = 3.34 km/s.5 R = Surface Distance Source - Sensor (m) Arrival Time (ms) Distance Source - Sensor (m) V P = 6.3 km/s R =.9957 V S = 3.6 km/s R =.9875 Williams 3 Arrival Time (ms) Figure 36. P and S-wave velocities obtained for each test site. 4.. 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 -9), 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..3 to 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 to 5 g of explosive in φ45 and φ75 mm boreholes (~9% coupling). Long charges of emulsion are.6 kg and m long detonated in φ45 mm boreholes (67% coupling). Detonating cord charges are also m long with either 4 or 8 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

94 7 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 sourcesensor 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 a) b) PPA (g) PPV (mm/s) Surface mounted sensor Scaled Distance, R/w / (m/kg / ) Scaled Distance, R/w / (m/kg / ) P-wave Emulsion long P-wave Emulsion short P-wave Det Cord S-wave Emulsion long S-wave Emulsion short S-wave Det Cord 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 (.4 m) and long (3 and 6 m) charges of emulsion (67% coupling) as well as short strings of pentolite boosters ( to 4 boosters per shot, 63% coupling) in a 6 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.5). This is mainly attributed to the sharp angle between the blasthole axis

95 7 and the direction source-sensor (between 3 and ) which causes relatively low amplitudes of S-waves. This phenomenon is further discussed in section 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 a) b) PPA (g) PPV (mm/s).. Scaled Distance, R/w / (m/kg / ) Scaled Distance, R/w / (m/kg / ) P-wave Emulsion long P-wave Emulsion short P-wave Boosters S-wave Emulsion long S-wave Emulsion short S-wave Boosters Figure 38. Peak Particle Acceleration (PPA) and Peak Particle Velocity (PPV) as a function of Scaled Distance. Williams mine 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 Hz high-pass filter, as mentioned earlier.

96 7 a) b) 5 ^ r.5.4 Velocity (mm/s) 5-5 Velocity (mm/s) Time (ms) 5 Frequency (khz) Figure 39. Radial components of velocity for a single cartridge of explosive and its amplitude spectra. Charge:.56 kg,.4 m of emulsion. r = 3 m θ =. 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: fi A( fi ) f = 4-8 A( f ) i where f is the average frequency (Hz), f i represents the individual frequencies in the spectrum (Hz), and A ( f i ) is the amplitude associated with each frequency f i. In order to prevent noise from severely affecting the average frequency, only frequencies with amplitudes greater than % 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 4 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 and 3 khz in terms of acceleration and between.8 and 5 khz in terms of particle velocity, excluding the results from surface mounted sensors.

97 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 8). a) b) Avg.Frequency of Acc. (Hz) Surface mounted Reverse primed Avg.Frequency of Vel. (Hz) Reverse primed Direct primed Surface mounted Direct primed Distance (m) Distance (m) Surface long Surface short Williams long Williams short Figure 4. Average Frequency of Acceleration and Velocity as a function of Distance. Summary of both test sites considering charges of Emulsion Short vs. long charges Figure 4 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. km/s (Figure 36), and the explosive types have similar detonation properties (emulsion in both cases).

98 74 a) b) PPA (g) PPV (mm/s) Reverse primed Scaled Distance, R/w / (m/kg / ) Surface long Surface short Scaled Distance, R/w / (m/kg / ) Williams long Williams short Figure 4. 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 4). 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.

99 Effect of initiation mode (Direct / Reverse) and relative sourcesensor location As discussed in section.., both analytical and numerical solutions to the problem of seismic radiation from a cylindrical source (or lateral pressure source in the D 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 953, Abo-Zena 977, Meredith 99, Meredith 993, Tubman 984) and visco-elastic models (Blair & Minchinton 6), as well as visco-elastic model in a fracturing medium (Trivino et al 9), little experimental work has been previously done to verify this theory. In geophysical exploration work, White & Sengbush (963) 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 9 m, in a medium with relatively low P and S-wave velocities ( and 9 m/s approximately). In the context of production blasting in mining, Trivino & Mohanty (9) carried out blast experiments in an underground mine (Williams) studying the propagation of P and vertically polarized S-waves from blasting. Figure 4 shows the amplitude and orientation of P and S-waves for various blast experiments with relatively short charges of explosive (. to kg,. to.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 sourcesensor 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.5 and in many cases close to ). 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. and.35 (Figure 4c). The

100 76 cases where no S-wave amplitudes are shown (Figure 4a) 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, 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 9). Also, at angles close to 9 (perpendicular to the blasthole) S-waves still exhibit amplitudes close to P-waves (Figure 4a,b). This is at variance with analytical and numerical models (Trivino et al 9) which predict an S/P ratio equal to zero at 9 (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.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 9, 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 ( 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.

101 77 a) Surface:. kg Emulsion 3 c) Williams:.9 kg Boosters Distance z (m) Distance z (m) - - Scale mm/s -3 4 Distance x (m) b) Surface:.5 kg Emulsion P P S S Scale 4 mm/s -3 4 Distance z (m) d) Williams:.56 kg Emulsion 45 5 Scale 5 mm/s Distance x (m) Distance x (m) Distance x (m) Figure 4. Amplitude and orientation of P and S-wave PPV for short explosive charges, projected on the plane rˆ -θˆ. In each case the center of the charge is located at (,) 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 4 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 P S Scale 5 mm/s Distance z (m) P S

102 78 between the two initiation modes. While the direct initiation mode shows a strong concentration of energy towards one particular frequency ( khz), the reverse mode exhibits a more or less uniform distribution of peaks between and 4 khz, with an average of. khz and a periodicity of around.4 khz. a) Surface:.4 kg, m Det Cord 3 b) Surface:.4 kg, m Det Cord 3 c) Williams: 4.4 kg, 3 m Emulsion 8.4 d) kg Williams: Emulsion 8.4 kg, 6 m Emulsion 8 P S 6 4 P S 6 4 P S Distance z (m) - Distance z (m) - Distance z (m) - Distance z (m) - S P Scale mm/s - Scale mm/s -6 Scale mm/s -6 Scale mm/s Distance x (m) Distance z (m) Distance x (m) e) Surface:.64 kg, m Emulsion -8 4 Distance x (m) -3-4 Scale 5 mm/s Distance x (m) P S -8 4 Distance x (m) Figure 43. Amplitude and orientation of P and S-wave PPV for long explosive charges, projected on the plane rˆ -θˆ.

103 79 a) b) Velocity (mm/s) 5-5 ^ r 6 m Direct Time (ms) r^ Velocity (mm/s) Frequency (khz).8 Velocity (mm/s) - Velocity (mm/s) m Reverse Time (ms) Frequency (khz) 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 = 9 ; b) Reverse mode, 8.4 kg, 6 m column of emulsion, r = 47 m θ = 66. 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 (.8 vs. 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 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

104 8 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. a) Velocity (mm/s) 4 - ^ r -4 3 m Direct Time (ms) b) Velocity (mm/s) m Reverse ^ r 5 Time (ms) Velocity (mm/s) Velocity (mm/s) Frequency (khz) Frequency (khz) Figure 45. Radial components of velocity and their amplitude spectra. a) Direct mode, 4.4 kg, 3 m column of emulsion, r = 6 m θ = ; b) Reverse mode, 4.4 kg, 3 m column of emulsion, r = 5 m θ = 67. Williams mine. 4. Blasthole pressure function and VOD Measurements of in-hole dynamic pressure and VOD were executed as described in sections 3..3 and The in-hole pressure measurements were carried out at the surface test site with 5 Ω carbon resistors. A total of 8 signals were successfully recorded at MHz sampling rate. Figure 46 shows the recorded variation of voltage over time and the converted data to pressuretime history (Equation 3-) from a. kg emulsion charge, 9% coupling, in a φ45 mm borehole.

105 8 a) Channel -. V to. V Voltage (V) DataTrapII Scope Data,, Hz Time (ms) 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.. kg emulsion, 9% 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 9% coupling in φ45 and φ75 mm boreholes, and 67% coupling in a φ45 mm borehole. The results of peak pressure vary between.3 and.6 GPa, for distances from the explosive between and cm. Peak Pressure Previous research has shown values between.5 and.7 GPa for emulsion (Nie & Olsson, Olsson et al ), 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 999), as explained in 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 -3 GPa should be expected, Mohanty ). 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. b)

106 8 a) b).8 9% coupling : P =.9 exp(. D).6 R = Excluded.4. 67% coupling : P =. exp(. D) Peak pressure (GPa) Distance from top of explosive (cm) Peak loading rate (GPa/µs) 3.5 LR =.47P R = Peak pressure (GPa) D45,. kg charge, 9% coupling D45,.5 kg charge, 9% coupling D75,.5 kg charge, 9% coupling D75,. kg charge, 9% coupling D45,.64 kg charge, 67% coupling D45,. kg charge, 9% coupling D45,.5 kg charge, 9% coupling D75,.5 kg charge, 9% coupling D75,. kg charge, 9% coupling D45,.64 kg charge, 67% coupling 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 9% coupling show a clearly higher trend (larger pressures) than those from 67% coupling, with the exception of one data point corresponding to g of explosive in a φ75 mm borehole (9% coupling). The lower pressure recorded in this case may be explained by the short length of the charge (only 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 9% coupling. The equations resulting from this regression are as follows: (. ) (. ) P =.9 exp D for 9% coupling, and 4-9 P =. exp D for 67% coupling 4- 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.

107 83 The equation obtained from a linear regression is: LR =. 47P 4- 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 6 mm at the mine, with 67% coupling (i.e., cartridges of φ3 and φ4 mm respectively). The results from these measurements are shown in Figure 48. The measured VOD values correspond to 4.9 and 5.8 km/s for the φ3 and φ4 mm cartridges respectively. The higher VOD for the larger cartridge diameter (~7% higher) is consistent with previous experimental results (Esen 4). The results presented in this section, including in-hole peak pressure, loading rate and VOD are used in damage models included in Chapter 5. a) b).5 Distance (m) VOD = 4.9 km/s R = Surface Distance (m) VOD = 5.8 km/s R =.948 Williams.5 m column φ3 mm cartridges φ45mm borehole Time (ms) 3m column.5 φ4 mm cartridges φ6mm borehole Time (ms) Figure 48. In-hole VOD measurements, water coupled. a) Surface test site; b) Williams mine.

108 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.4.4 and.4.3 respectively. The monitored explosive charges correspond to emulsion cartridges of. kg (.8 m long, mean depth 4.75 m),.5 kg (.45 m long, mean depth 3.7 m), and.64 kg ( m long, mean depth 4.5 m), the first two coupled at 9% 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 Cross-hole measurements The general procedure to determine blast-induced damage from cross-hole measurements is described in section.4.4 and the instrumental layout is schematized in section 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 6 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 6 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.4.4. This method is described in section

109 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.6 (from 5..) the geometrical factor h given by in Equation -5 is equal to.95. For water filled cracks, which is our case, the factor δ (Equation -6) is negligible if the crack aspect ratio is small (ζ < -3 ). Thus, assuming small aspect ratio, Equation -3 becomes: E E = +.76ρ 4- and Equation -5 becomes: V P after = V P before V +.76ρ V P before P 4-3 The general procedure consists on determining a damage distribution which gives results of V P after from Equation 4-3 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 4-3. For this equation V P before blasting is considered to be approximately constant along each ray-path, and the value of V P for the undamaged material (V P ) 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 V P for the nearly undamaged material. Thus, V P is chosen as the average of lab test plus three standard deviations, i.e., V P = 6.3 km/s (see section 5..).

110 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 4-3) and those measured after the blast, according to: RSS = n ( y i y i ) i= ˆ 4-4 Where the variable y in this case is used to denote P-wave velocity after blast, with y i being the measured values, and ŷ i the calculated values from Equation 4-3. 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, R and the Standard Error, SE are estimated according to the following expressions: R ESS = ESS + RSS RSS SE = 4-6 n where RSS is the Residual Sum of Squares calculated from Equation 4-4, and ESS is the Explained Sum of Squares of the model, calculated as: 4-5 ESS = where n ( y i y i ) i= ˆ 4-7 y i 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

111 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 -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: x = a sinh y = a sinh z = a cosh ( ξ ) sin( η) cos( φ) ( ξ ) sin( η) sin( φ) ( ξ ) cos( η) 4-8 Where a is half of the distance between two foci, and ξ, η and φ are the variables that define the coordinate system, with ξ, η π, and φ π. 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. kg (.45 m long) and.64 ( m long) charges, with a =.5 m and m, respectively. a) b) c) Z X 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 = ; b) Discretization of area around. kg (.45 m) charge ( a =.5 m); c) Discretization of area around.64 kg ( m) charge ( a = m).

112 P-wave velocity measurements Figure 5 to Figure 5 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 (6 for. kg charge, 76 for.5 kg charge, and 6 for.64 kg charge). Each of these figures (Figure 5 to Figure 5) show ray-paths, explosive charges and boreholes from different angles, as well as a cylindrical projection on a vertical semi-plane, equivalent to the rˆ -θˆ plane described in section 4... 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. a) b) c). kg charge Figure 5. Cross-hole ray-paths from measurements on P-wave velocity changes to quantify damage caused by a. 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.

113 89 a) b) c).5 kg charge Figure 5. Cross-hole ray-paths from measurements on P-wave velocity changes to quantify damage caused by a.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. a) b) c).64 kg charge Figure 5. Cross-hole ray-paths from measurements on P-wave velocity changes to quantify damage caused by a.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.

114 9 The results of P-wave velocities before and after blast for all three experiments are shown in Figure 53. In the case of the. 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: b b t = 4-9 S b b where b and b are the slopes of the curves after and before blast, and Sb b is the standard error b of the difference between the slopes ( S b b Sb + S, with S b and S b being the standard errors associated to each slope). With values b = 5.8, b = 5.7, S b =.47 and S b =.5, the t-test indicated that the slopes are not significantly different at 95% confidence level (t =.88 > t.5, =.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. Distance (m) a). kg charge b).5 kg charge c).64 kg charge Before: V P = 5.7 km/s R =.9744 After: V P = 5.8 km/s R = Time (ms) Distance (m) Before: V P = 5.89 km/s R = After: V P = 5.3 km/s R = Time (ms) Distance (m) Before: V P = 5.74 km/s R =.9835 After: V P = 4.88 km/s R = Time (ms) Before Blast After Blast Before Blast After Blast Before Blast After Blast Figure 53. Measured variations in P-wave velocity caused by explosive charges of. kg,.5 kg and.64 kg.

115 9 The results of P-wave velocity measurements from the.5 and.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. kg charge, the.5 kg charge caused some severe damage with a non-uniform distribution in the area surveyed. For the case of the.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.5 kg charge is probably due to the higher coupling (9% vs. 67% for the.64 kg charge), which causes higher pressures as seen from Figure Inversion results: 3D images of blast-induced damage The inversion method described in section is applied to the cross-hole measurements carried out around short (.5 kg,.45 m) and long (.64 kg, m) charges of explosive. Figure 54 shows contour plots representing the results of blast-induced damage for the.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 =.5 and -.5 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 m ( borehole diameters) horizontally from the explosive charge.

116 9 a) b).5 kg charge, bottom initiated c) d) Figure 54. Measured blast-induced damage determined from inversion of P-wave velocities corresponding to a.5 kg charge of emulsion, 9% coupling. a) Vertical plane E-W; b) Vertical plane N-S; c) Plan view at Z =.5 m (top); d) Plan view at Z = -.5 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 43 m/s. Although the calculated R value of.5 does not indicate the model to be particularly accurate, it indicates a fair fit to the data.

117 93 8 Vp (m/s) Measurement number R =.5 SE = 43 m/s Measured Model Residuals Figure 55. Comparison of measured and calculated P-wave velocity values after blast for explosive charge of.5 kg. Figure 56 shows the results of damage distribution corresponding to the.64 kg ( m) explosive charge. As expected, damage is observed to propagate farther than the case of.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.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 = m and Z = - 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 m ( 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 R and Standard Error (SE) are.74 and 8 m/s, respectively. These values indicate higher accuracy and a much better fit than the previous case.

118 94 a) b).64 kg charge, bottom initiated c) d) Figure 56. Measured blast-induced damage determined from inversion of P-wave velocities corresponding to a.64 kg charge of emulsion, 67% coupling. a) Vertical plane E-W; b) Vertical plane N-S; c) Plan view at Z = m (top); d) Plan view at Z = - 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.

119 95 8 Vp (m/s) Measurement number R =.74 SE = 8 m/s Measured Model Residuals Figure 57. Comparison of measured and calculated P-wave velocity values after blast for explosive charge of.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.), 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 R 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.

120 Gas pressure activity As indicated in section 3., gas activity is monitored in boreholes surrounding a single blasthole in the surface test site. The method is described in section.4.3 and the instrumentation is detailed in section 3... The experiments involving gas pressure measurements correspond to charges of.5 and.64 kg of emulsion, coupled at 9% and 67% respectively. All measurements associated with the.5 kg charge correspond to the same blast assessed through cross-hole (Figure 5), whereas the measurements around.64 kg charge correspond to two different blasts, being one of them also assessed through cross-hole (Figure 5). The horizontal distances between blasthole and monitor holes vary between.5 and.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.5 kg charge, two events took place at distances between.5 and.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 kpa. Around.64 kg charges, only one of them indicated pressure activity, with a peak of 8 kpa at.3 m. Other measurements between and.5 m showed only some high frequency component which is believed to be unrelated to pressure events, as explained below. 8 Distance in Borehole Diameters ( ) Plug failed Pressure (kpa) Mostly high freq. component Distance (m).5 kg 9% coupling.64 kg 67% coupling Figure 58. Measured gas pressure activity in monitor holes from blasts corresponding to.5 and.64 kg of explosive (9% and 67% coupling respectively) in φ 45 mm borehole.

121 97 The signals corresponding to the four measurements around the.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 (> 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 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 to 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.

122 98 Pressure (kpa) Time (ms) Pressure (kpa) Time (ms) 3 Pressure (kpa) Time (ms) Pressure (kpa) Time (ms) Very low or no pressure (< kpa) Pressure event detected (> kpa) Figure 59. Pressure activity recorded in monitor holes from a blast corresponding to.5 kg of explosive, 9% 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.5 kg charge, for example, the pressure sensors predict a typical limit of damage around 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.3 m from a.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.

123 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 ( to g) and wide frequency-band (up to 5 khz) was essential to obtain reliable and accurate seismic signals for the full range of distances monitored (from to 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 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.

124 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.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.

125 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 6 shows schematically the difference between the two cases indicated. a) b) L t = VOD L t = VOD Sequential initiation of 'fixed' small sources Moving source Figure 6. 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

126 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.5 and.64 kg charges of emulsion, but was not sufficient to assess damage from smaller charges (e.g.. kg). The total number of wave velocity measurements successfully completed for the two larger charges was more than 6 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 D 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.

127 3 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 999, Nie & Olsson, Olsson et al ), 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.

128 4 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 crosshole experiments presented in Chapter 4. Damage from stress waves is computed through the numerical FEM-DEM code YD introduced in section.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. to 5.3. Finally the quantification of damage from stress waves and gas expansion is included in section 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.. Elastic constants Elastic constants are calculated from field measurements of P and S-wave velocity shown in section 4...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 YD code, the complete set of constants is shown here for reference. These are:

129 5 P-wave velocity, V P 59 m/s S-wave velocity, V S 334 m/s Young Modulus, E 75.3 GPa Shear Modulus, µ 9.8 GPa Lamé Constant, λ 33.4 GPa Bulk Modulus, K 53. GPa Poisson's Ratio, ν 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 YD 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 (σ s ) and Tensile Strength (σ t ). 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: V P = 6. km/s V S = 3.46 km/s ρ o =.67 kg/dm 3

130 6 The average values obtained for wave velocities are, as expected, higher than those obtained from field measurements (5.9 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 (~-3%) and the small differences between V S and V S values (Figure E) confirm that the material may be considered as isotropic, at least in absence of significant damage. The values obtained for V P are used to estimate the undamaged material properties required to calculate damage from cross-hole measurements, as detailed in section The average value of density (.67 kg/dm 3 ) 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 σ s is taken equal to half of σ c. Thus, from Figure E3 shear strength is calculated as: σ S = 8 MPa if LR < 35 GPa/s 5- σ S = (.4LR + 37) MPa if LR < 35 GPa/s 5- 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 Tensile Strength: Since fractures from blasting have various orientations, σ t is chosen as an average between the two limit experimental curves (Figure E4). Thus, the expression to calculate tensile strength becomes: ( 8). 9 σ = 3.5 LR t with LR in GPa/s. Equation 5-3 is used to determine tensile strength for models in section Explosive properties Appropriate velocity of detonation VOD, peak pressure, and loading rate for models are chosen from the experimental results included in section 4..

131 7 VOD: VOD for m long charges with 67% coupling is taken from the measurement shown in Figure 48a, equal to 4.9 km/s. For.45 m, 9% 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 % 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.. Considering the explosive-borehole distance equal to.3 cm for 9% coupling, Equation 4-9 predicts a peak pressure P max =.8 GPa. For 67% coupling, considered cm distance, Equation 4- predicts P max =.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 9% and 67% coupling are obtained from Equation 4-. Considering the values of peak pressure indicated in the previous paragraph, peak loading rates are LR =.6 GPa/µs for 9% coupling, and LR =.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 Pressure function The pressure function used in all models in this thesis was initially introduced by Trivino et al (9) with a shape similar to that shown in Figure 6. The equations of this pressure function permit to account independently for both the rapid pressurization and the relatively slower

132 8 pressure decay in the blasthole. The set of equations to define this pressure function P(t) is as follows: P( t) = Pmax P ( t) P ( t) 5-4 P u P b d [ bu ( t t )] ( t) e u bd ( t t ) ( t) e d u d n { } = 5-5 = {[ ] } 5-6 = e 5-7 d m d b = b b 5-8 u d ratio [ ln( α )] n bu [ ln( α )] n [ ln( α )] t u = 5-9 { n } bu t d = 5- n = round ( e b m m ) P max 5- ratio u d m u = LR, and 5- m d = DR 5-3 P max where P max is the peak in-hole pressure; P u (t) and P d (t) are functions to (approximately) define the rise (up) and decay (down) of the pressure function; b u, t u, n, b d, and t d are the parameters that define these curves; b ratio is the ratio b d /b u ; m u and m d are the maximum slopes of P u (t) and P d (t), respectively; α and α are approximately the normalized errors of the resulting curves at t = and t = t max, with t max 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 P max, LR, DR, α, α, and b ratio. The remaining parameters are determined from Equation 5-4 to Equation 5-3. The most relevant input parameters of the pressure function are evidently P max, 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, α, α, and b ratio, 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 α and α are normalized errors, they should have small values compared to ; b ratio should be ). Figure 6 shows an example of pressure function calculated for a particular set of parameters. The parameters P max and LR to be used in numerical models are indicated in 5..3, whereas DR is determined in section 5..

133 9 P u (t) P d (t) P(t)/P max = P u (t) * P d (t) Pressure.6.4 m u Pressure.6.4 m d x = Pressure Time (ms).. Time (ms).. Time (ms) Figure 6. Pressure functions P u(t), P d(t), and P(t)/P max, for parameters LR = GPa/ms, and DR = GPa/ms (with α = -7, α = -3, b ratio =. LR: Loading Rate; DR: Decay Rate). 5. 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 D 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.. D 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 D model has the disadvantage of producing a lower attenuation (geometric spreading) than the real 3D case, as shown in section.5.3 (Figure ). 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 D

134 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 D 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 D 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 D 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 PPV D (PPV from D models) by a factor proportional to r -.5 (with r being distance from the source), as shown in section.5.3 (Figure 3), proved to be a consistent and reasonable method, which allowed to convert D crack density and damage distribution into equivalent 3D values. The conversion of PPV from D to 3D is done according to: PPV3 D = PPVD F 5-4 where F is the aforementioned scaling factor proportional to r -.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 r F = 5-5 r where r is the minimum distance from the blasthole to the observation point, and r is an appropriate distance at which PPV D = PPV 3D. Considering that the pressure function at the borehole boundary has the same shape and amplitude in both D and 3D cases, it is reasonable to assume that the PPV D must equal PPV 3D at this boundary. Thus, considering the distance r as measured from the borehole axis, Equation 5-4 becomes:.5 r PPV3D = PPVD 5-6 BD

135 where BD is the borehole diameter. It is important to notice that Equation 5-6 permits only to obtain an equivalent PPV 3D. 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 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. and those calibrated with experimental field data (section 5..3). At the same time the calibration of parameters (section 5..3) uses the relationship between PPV and crack density determined in this section, in order to compare the results from the D 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.5 kg and.64 kg through the program YD. In both cases the finite VOD was simulated by discretizing the explosive sources in small elements of. to.3 m long. Figure 6 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 ( m x m for the short charge; m x.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

136 the blasthole (horizontal velocity, V x ) as the fracture network resulting from it develops (red lines). In both models the initiation point is about. m above the bottom of the explosive column, as this location corresponds approximately to the initiation point of field experiments. a) Mesh for.5 kg (.45 m) explosive b) V x at 65 µs after initiation c) Mesh for.64 kg ( m) explosive.9 GPa.7 GPa m m Pressure applied at borehole wall at 65 µs after initiation Control points to calculate damage Figure 6. Initial meshes used for models. a) Mesh for.5 kg charge; b) Profile of horizontal particle velocity at 65 µs after initiation; and c) Mesh for.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 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.

137 3 a) b).8 Z (m) R (m) Z (m) R (m) 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 6. 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 -, considering circular areas centered at the same control points (akin to the method of direct measurement described in section.4.). 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.5 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: ( PPV ) b ρ = a ln + 5-7

138 4 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 Crack density, ρ.5.5 ( ). 8 ρ =.7 ln PPV Eliminated for regression PPV (m/s) Figure 64. Damage vs. PPV from FEM-DEM models. Assuming Equation 5-7 valid to estimate damage in both D and 3D: ρ ρ D 3D = a ln = a ln ( PPVD ) + b ( PPV ) + b 3D 5-8 By combining these equations with Equation 5-6, the following relationship between 3D and D crack density is obtained:. 5 r ρ 3D = ρ D + a ln 5-9 BD with a =.7, obtained from the semi-log regression above. Equation 5-9 is used to adjust calculated blast-induced damage from stress waves obtained from D models, in order to represent a 3D configuration.

139 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.,.5 and.64 kg, considering material and explosive properties from 5.. 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 D/3D factor defined in 5.. (Equation 5-6), 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 Decay rate, DR Increasing Decreasing Decreasing Decreasing Increasing Increasing 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:

140 6 Material Damping: η =.55 MPa s Peak Decay Rate: DR = GPa/ms, for. kg charge DR = 9 DR = 8 GPa/ms, for.5 kg charge GPa/ms, for.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 D FEM-DEM code have been modified by the factor defined by Equation 5-6. 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 (. kg). The agreement is nonetheless satisfactory, considering the significant dispersion of results that occur in field measurements. a) 4 b) 4 PPV (mm/s) 3 Scaled Distance (m/kg / ) Avg. Freq. of Velocity (Hz) 3 Distance (m) 4 Measured. kg Measured.5 kg Measured.64 kg Model. kg 3 Model.5 kg Model.64 kg Scaled Distance (m ) 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. (

141 7 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. a) b) 8 6 rˆ r 5 rˆ r Velocity (mm/s) 4 Velocity (mm/s) 5 - Measured r Model Time (ms) -5 Measured r Model - 3 Time (ms) Figure 66. Comparison of rˆ component of particle velocity between single shot experiments and FEM-DEM models. a).5 kg (.45 m) explosive, reverse primed, r =.6 m, θ = 9. b).64 kg ( m) explosive, direct primed, measured on surface, r =.4 m, θ = Material strength parameters Having determined the pressure function and energy dissipation parameters (section 5..3), it is possible to calculate shear and tensile strength (σ s, σ t,) from their relationship with loading rate, according to the expressions indicated in section 5... Fracture toughness, K IC (and therefore fracture energy, G C ) 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.

142 8 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 (σ x ) curve. Table 8. Distance (m) Loading and decay rates at various distances from blasthole Loading rate (GPa/s) Short charge Decay rate (GPa/s) Loading rate (GPa/s) Long charge Decay rate (GPa/s). 4,,,,5. 6,6 3,8 3,6,7.3 5,3,9 4,8,.4 4,3,3 3,7 99.5,6,,6 67.6,7,, 56 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. and. 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 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 σ s and σ t were calculated using the expressions in Equation 5-, Equation 5-, and Equation 5-3.

143 9 Table 9. Parameter Summary of material strength properties Short charge Long charge Min Avg Max Min Avg Max Loading rate (GPa/s), 5,, 56, 8, Shear strength, σ s (MPa) Tensile strength, σ t (MPa) Fracture toughness, K IC (MPa m ½ ) Fracture energy, G C (J/m ) Values of K IC 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 m ½ s - ) were converted to stress over time (GPa/s) according to Equation E-6. Finally, values of G C were calculated from K IC according to the expressions for plane strain given in Appendix E, with the elastic constants indicated in section 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.

144 Table. Summary of material and explosive properties for numerical models Short Charge:.5 kg,.45 m, 9% coupling Models Long Charge:.64 kg, m, 67% coupling Section Material elastic properties P-wave velocity, V P 59 m/s & 5.. S-wave velocity, V S 334 m/s & 5.. Young Modulus, E 75.3 GPa & 5.. Shear Modulus, µ 9.8 GPa & 5.. Lamé Constant, λ 33.4 GPa & 5.. Bulk Modulus, K 53. GPa & 5.. Poisson's Ratio, ν & 5.. Other material properties Density, ρ 67 kg/m Shear Strength, σ s 7 MPa 8 MPa 5.. & 5..4 Tensile Strength, σ t 4 MPa 3 MPa 5.. & 5..4 Fracture Toughness, K IC MPa m / 5.. & 5..4 Fracture Energy, G C 4 J/m 5.. & 5..4 Viscous Damping, η.55 MPa s 5..3 Explosive and explosive / rock interaction properties Velocity of Detonation, VOD 53 m/s 49 m/s 4. & 5..3 In-hole Peak Pressure, P max.7 GPa.9 GPa 4. & 5..3 In-hole peak Loading Rate, LR 5 GPa/ms 3 GPa/ms 4. & 5..3 In-hole peak Decay Rate, DR 9 GPa/ms 8 GPa/ms 5..3

145 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.5 and.64 kg explosive charges, as presented in section 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.. 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 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... Similarly, PPV contour plots are calculated for the same models from velocity time histories recorded at control points, as shown in Figure 6. 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 and.3. The zones corresponding to the long cracks extending radially are represented by values of damage around.5. The PPV contour plot shows significantly larger velocities at both ends of the explosive. The amplitude of PPV in these areas reaches over 3 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 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.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

146 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 Further analyses on this point are included later in section a) Damage D, short charge, bottom initiated b) PPV (mm/s), short charge, bottom initiated 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 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 5% 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 Finally, the contour plot of damage shows values close to unity for the crushed zone around the borehole and about.5 around for the longer radial fractures.

147 3 a) Damage D, long charge, bottom initiated b) PPV (mm/s), long charge, bottom initiated 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 5-9 is applied to the calculated values of damage from the D 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 D/ 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 5-9). It is also apparent that the stress waves cause severe damage only in the first. to. m from the blastholes. Considering a value of damage equal to as an arbitrary limit to determine failure, the average distances from the boreholes to the failed boundaries are. m for the short charge (9% coupling) and only.5 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 to determine the relative contribution of stress waves and gas penetration to blast-induced damage.

148 4 a) Shock wave damage 3D, short charge, bottom initiated b) Shock wave damage 3D, long charge, bottom initiated Figure 69. Damage from FEM-DEM model for short and long charges, after correction D to 3D 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 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 D 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 rˆ -θˆ is calculated as the average damage along the horizontal angle (vertical being collinear with borehole axis). Figure 7 shows the measured damage from.5 kg (.45 m) and.64 kg ( 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..).

149 5 a) Measured damage 3D, short charge, bottom initiated, cylindrical average b) Measured damage 3D, long charge, bottom initiated, cylindrical average Figure 7. Contour plots of measured damage for short and long explosive charges considering cylindrical symmetry. As observed in section 4.3., 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 9% 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 > ) reaches a maximum distance of about.3 m from the explosive charge. For the long charge (67% coupling) severe damage (ρ > ) is observed to propagate from the initiation point and around /3 and /3 of the explosive length, with a maximum extension of.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. for the short charge). The lower maximum damage for the long charge may be explained by the lower coupling of this charge (67% vs. 9%). As shown in section 4., 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

150 6 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 >.5 propagates up to distances around.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 ( m x.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 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 These results were converted into cylindrically symmetrical models in order to properly analyze and compare with numerical models, as explained in section 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 D combined finite and discrete elements method. Since wave propagation in D exhibits different geometrical spreading compared to the 3D case (see sections 5.. &.5.3, Figure ), 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:

151 7 ρ G = ρ ρ 5- C S where ρ G and ρ S are crack densities due to gas expansion and stress waves, respectively, and ρ C is the combined blast-induced damage considering both stress waves and gas. Figure 7 and Figure 7 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 7, respectively. In order to facilitate direct assessment, the scale of colors applied to all these contour plots was taken to be the same range ( ρ ). 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 m, and length of either m (short charge) or.6 m (long charge)). The equation to calculate this measure of total damage is as follows: y x D = ρ V = π x ρ dx dy 5- y= y x= where D refers to total damage over the volume in m 3, 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 [, x] and [y, y]. As the actual computation of crack density is done at discrete points, a discrete version of Equation 5- is used: D π x ρ x y 5- i j i ij Figure 7 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.. 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 (ρ max =.5 for stress waves

152 8 vs. ρ max =. 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 7 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 5), 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.

153 9 a) Combined damage: ρ = 4. max D = ρv =. 3 m 3 b) Shock wave damage: c) ρ =.5 max D = ρv =. 5 m 3 Gas expansion damage: ρ =. max D = ρv =. 7 m 3 - = Figure 7. 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 m long explosive column is shown in Figure 7. 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 (ρ max =. for stress waves vs. ρ max =.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 % and 3% lower. These lower values are probably due to the lower coupling of the longer charge (67%) compared to the shorter one (9%), 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.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

154 3 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 7. Finally, the variations on the extension of damage along the explosive column, particularly the larger damage observed around /3 and /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 7 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. a) Combined damage: b) Shock wave damage: c) ρ = 3. max D = ρv = m 3 ρ =. max D = ρv =. 8 m 3 Gas expansion damage: ρ =.9 max D = ρv = m 3 - = Figure 7. Relative contribution of stress waves and gas expansion to damage for a long charge, bottom initiated.

155 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 G C, tensile strength σ t, and shear strength σ s. 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. Figure 73 shows the resultant fracture patterns with varying fracture energy, G C. 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 3 to 79 J/m ) 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, σ t is shown in Figure 74. The ranges studied for this parameter are 6 to 5 MPa for the short charge and 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 σ t have little contribution to the overall uncertainty of the models. Fracture pattern changes with shear strength, σ s are shown in Figure 75. The ranges studied in this case are 8 to 78 MPa for the short charge, and 75 to 49 MPa for the long charge. From this figure it is clear than σ s produces the most significant variations in fracture patterns for both short and long charges. Figure 75a and Figure 75d (lower values of σ s ) 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 σ s (Figure 75c and Figure 75f) indicated lower crack densities and different fracture patterns, although once again, the maximum extent of fractures remains nearly unchanged.

156 3 a) b) c) d) e) f) Figure 73. Effect of variations in G C over fracture patterns obtained for short and long explosive charges. Short models: σ s = 7 MPa; σ t = 4 MPa; a) Min G C= 3 J/m ; b) Avg. G C= 4 J/m ; c) Max G C= 79 J/m. Long models: σ s = 8 MPa; σ t = 3 MPa; d) Min G C= 3 J/m ; e) Avg. G C= 4 J/m ; f) Max G C= 79 J/m. 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 σ s 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.

157 33 a) b) c) d) e) f) Figure 74. Effect of variations in σ t over fracture patterns obtained for short and long explosive charges. Short models: σ s = 7 MPa; G C = 4 J/m ; a) Min σ t = 6 MPa; b) Avg. σ t = 4 MPa; c) Max σ t = 5 MPa. Long models: σ s = 8 MPa; G C = 4 J/m ; d) Min σ t = MPa; e) Avg. σ t = 3 MPa; f) Max σ t = 47 MPa. In the case of the short charge, it is estimated that deviations in σ s for the ranges considered, cause variations in crack density by about ±3% 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 σ s is increased significantly.

158 34 a) b) c) d) e) f) Figure 75. Effect of variations in σ s over fracture patterns obtained for short and long explosive charges. Short models: σ t = 4 MPa; G C = 4 J/m ; a) Min σ s = 8 MPa; b) Avg. σ s = 7 MPa; c) Max σ s = 78 MPa. Long models: σ t = 3 MPa; G C = 4 J/m ; d) Min σ s = 75 MPa; e) Avg. σ s = 8 MPa; f) Max σ s = 49 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

159 35 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.

160 36 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 D 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 D is lower than in 3D by a factor proportional to r.5 ). In order to account for this difference in attenuation, a simple approach was proposed to convert D wave amplitudes into 3D equivalent (Equation 5-6). 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 5-6. 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 D 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 D and 3D cases, a simple equation was derived to determine 3D crack density from D models (Equation 5-9). 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.

161 37 Despite the relatively long extension of fractures obtained from the D models (up to 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. and. m (i.e., 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, who reported up to ~ 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/D correction (see Figure 64 and Equation 5-9). 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.

162 38 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 7. Typical geometry and initiation method of these production blasts are schematized in Figure 8 and Figure 9. Section 6. 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 Section 6. 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 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 8 and Figure 9). These figures also show the amount of charge weight detonated for each delay round. They are essentially duplicates of what is observed for singlehole 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.

163 39 Velocity (mm/s) - - Design Timing n # Holes with same delay ^ r r ˆ 6 3 Total Charge Weight (kg) Time (ms) Figure 76. Production Blast #, March 5, 7 Dayshift - Accelerometer A. 3 kg Emulsion - Collar Primed - 3 g/m Det Cord r' = 77.3 m. Velocity (mm/s) Design Timing n # Holes with same delay ^ r ˆ r Total Charge Weight (kg) Time (ms) Figure 77. Production Blast #3, March 5-6, 7 Nightshift - Accelerometer A. 9 kg Emulsion - Booster Collar Primed - 3 g/m Det Cord r' = 74. m. Velocity (mm/s) Design Timing n # Holes with same delay ^ r r ˆ Total Charge Weight (kg) Time (ms) Figure 78. Production Blast #, March, 7 Dayshift - Accelerometer A. 65 kg Water Gel - Booster Collar Primed - 3 g/m Det Cord r' = 43.5 m.

164 4 The identification of P and S-waves is carried out by following the methods applied to singlehole blasts shown in 4... and 4... (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 rˆ and θˆ, respectively. 5 3 Velocity (mm/s) P-wave Velocity (mm/s) 5-5 S-wave Velocity (mm/s) Time (ms) Time (ms) Time (ms) Figure 79. Components rˆ, θˆ and φˆ of velocity for a production blast shot consisting of holes. r = 4m, θ = 36 ; r = 39m, θ = 68. Figure 8 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..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.

165 4 a) b) PPA (g) PPV (mm/s) Scaled Distance, R/w / (m/kg / ) Scaled Distance, R/w / (m/kg / ) Single long P-wave Single short P-wave Production P-wave Single long S-wave Single short S-wave Production S-wave Figure 8. 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.

166 4 The frequency content of the vibration signals in rock is shown in Figure 8, 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 m, the maximum frequency of high-amplitude acceleration signal averages around.6 khz; for the corresponding particle velocity signal it is around 5 Hz. a) b) Avg. Frequency of Acc. (Hz) Avg. Frequency of Vel. (Hz) Distance (m) Distance (m) Single long Single short Production Figure 8. 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 5 grain detonating cord (i.e., 3 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 8).

167 43 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 # shows very poor energy release during the first half of the blast (Figure 76), blast #3 shows uneven energy release for similar explosive charge weights (Figure 77), and blast # shows missing holes (Figure 78). Such occurrences were typical of all the production blasts monitored. 6. 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 8, projected on a horizontal plane. 6.. 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 (P max ), decay rate (DR), and material viscous damping (η). Material elastic parameters (E, µ, k, λ, ν) are obtained from the measurement of P and S-wave velocities presented in 4...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 9). Finally material strength parameters (σ s, σ t and G c ) 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 8 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.5 m around the blastholes and. m towards

168 44 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. Control points Half of Raise Approximate stope boundary Blastholes m Figure 8. Mesh used to model production blast in FEM-DEM code: Refinement for calibration of parameters (35,+ elements).

169 45 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 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. Table. Summary of material and explosive properties for production blast simulation Values Source Medium properties P-wave velocity, V P 63 m/s Measured, S-wave velocity, V S 36 m/s Measured, Young Modulus, E 86.8 GPa & Appendix A Shear Modulus, µ 34.8 GPa & Appendix A Lamé Constant, λ 34. GPa & Appendix A Bulk Modulus, K 57. GPa & Appendix A Poisson's Ratio, ν & Appendix A Density, ρ 67 kg/m 3 Arbitrary Shear Strength, σ s 75 MPa Arbitrary Tensile Strength, σ t 5 MPa Arbitrary Fracture Toughness, K IC 6.8 MPa m / Arbitrary Fracture Energy, G C 5 J/m Arbitrary Viscous Damping, η.3 MPa s Fitted Explosive and explosive / rock interaction properties Velocity of Detonation, VOD 55 m/s Tech. specs. In-hole Peak Pressure, P max.5 GPa Fitted In-hole peak Loading Rate, LR 5 GPa/ms Arbitrary In-hole peak Decay Rate, DR GPa/ms Calibrated

170 46 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 D to 3D equivalent PPV according to Equation 5-9. 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. a) 3 b) 4 Model PPV (mm/s) Measured Avg. Freq. of Velocity (Hz) 3 Model Measured Scaled Distance (m/kg / ) 3 Distance (m) 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 5-6 to estimate equivalent 3D PPV. Figure 84 shows the horizontal velocity time history recorded 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. Velocity (mm/s) 4 3 Design Timing 3 n= # Holes with same delay Time (ms) Total Charge Weight (kg) Figure 84. Velocity time history recorded at m horizontally from raise center point (distance to boreholes from 3 to 6 m). The amplitude of signals is not corrected by factor given by Equation 5-6 to estimate equivalent 3D particle velocities.

171 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.5 m around the blastholes and. 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. Half of Raise Blastholes m Approximate stope boundary Figure 85. Mesh used to model production blast in FEM-DEM code: Refinement to determine fracture pattern, damage and PPV contour (7,+ 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 (5 grain), which is considered enough to ignite the emulsion from the collar, as explained in 6.. 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 D 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 D model, this refraction does not correspond with the 3D situation.

172 48 Refracted S-wave Refracted P-wave Incident P-wave Initiation direction m m Blastholes Approximate stope boundary Figure 86. Stress wave amplitude from two adjacent blasthole with different delays. Colors show horizontal particle velocity (v x) at.5 ms after the initiation of each blasthole. PPV at snapshots (wave front in blue): left 5 mm/s; right mm/s. The final fracture pattern and the D 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 D 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 D results by Equation 5-9, 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.

173 49 a) Half raise Initiation direction N (m) b) E (m) Blastholes c) Figure 87. Fracturing associated with stress waves obtained from production blast simulation. a) Fracture pattern; b) Crack density calculated directly from D simulation; c) Crack density corrected from D 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