Basics on detonation theory and explosive rock interaction
Parameters that impact on rock breakage and damage • Explosive characteristics and performance: VOD, Density: controlling shock and gas energy and rate of loading • Intact rock properties: density, elasticity, shock properties and dynamic strength • Rock mass characteristics: Degree of jointing, condition of joints and orientation • Degree of confinement: free surface boundaries and blast pattern geometry • Decoupling ratio: controlling pressure and energy • Charge concentration: controlling energy • Time of initiation: controlling shock and gas energy and rate of loading
What do engineers need to know ? •
Ideal and non ideal detonation
•
Effect of confinement on explosive performance
•
Role of shock, stress and gas
•
Intact rock and rock mass response to shock stresses and gas
•
Effect of decoupling
•
Explosive energy concepts
•
Modelling capabilities
Basic terminology • Shock wave – Intense compression wave produced by detonation of explosives
• Shock front – The outer side of a shock wave
• Chapman-Jouguet (CJ) plane – Interface separating the steady and the non steady regions at the detonation front
• Reaction zone or detonation driving zone (DDZ) – Region behind the shock front which drives the shock wave
• Particle velocity – A mechanical wave in which displacements are in the direction of the wave propagation
Explosive detonation Shock/stress wave in the surrounding media
Stable by-products, mainly gases
Chapman-Jouguet (CJ) Plane Shock front in the explosive
Direction of detonation
Primary reaction zone
Expanding gases
Explosive
Undisturbed explosive
Explosive detonation
Basic terminology CJ (Sonic) DDZ Plane Nothing that happens behind the CJ plane can affect the DDZ.
Rho CJ > RhoZ
Particle velocity follows Shock Front, but slower and decelerating
Shock Plane
DDZ drives Shock Wave
Shock initiates reaction
Reaction
Explosive Rho Z
D
u After Cunningham 2003 (HSBM)
Detonation Modelling of Explosives
• Ideal Detonation • 1-D, chemical equilibrium •governed by thermodynamics of detonation products • Non-ideal detonation – eg slightly divergent flow • curved shock front • detonation velocity diameter/ confinement dependence • partial reaction • Hydrocode simulations
Basic terminology •
Ideal detonation – – – –
•
One dimensional, infinite diameter Shock wave planar Complete instantaneous reaction Maximum attainable performance
Non ideal detonation – Shock front curved – Flow diverges – Detonation driving zone (DDZ) terminates at sonic locus where relative particle speed equals local sound speed – Reaction is always incomplete in DDZ – Velocity of detonation decreases with 1/diameter – If diameter of cylindrical charge is too small detonation fails
1- D ideal detonation Braithwaite, 2003
Non ideal detonation
After Bill Byers Brown (2002)
Ideal vs non ideal detonation After Cunningham 2003 (HSBM)
Non-Ideal: WK/MIG
Ideal: CJ/ZND • No Divergence/ effect of confinement • Reaction zone = CJ zone • Ideal VoD
• • • •
Divergence/ effect of confinement Reaction zone>CJ zone Sub-Ideal VoD Critical diameter
Note: WK, MIG model curvature, not edge losses
Basic terminology •
Confinement – Constraining effect of the environment surrounding the explosive – Function of density, strength, sonic velocity and thickness of confining media – Determines the detonation velocity (VoD) and peak pressure
•
Confined detonation velocity – Velocity of detonation (VoD) measured under confined conditions (e.g. in situ) – The higher the confinement the higher the VoD – VoD says how much reaction energy was released in the DDZ
•
Critical diameter – Minimum diameter at which the detonation reaction is sustained
•
Critical density – Density at which detonation fails. Also known as “dead pressing density”
VoD vs charge diameter for some explosives Persson et al , 1994
Unconfined VoD data Heavy ANFO
Unconfined VoD (m/s)
5000 4500 4000 3500 3000 2500 2000 1500 0
50
100
150
200
Diameter (mm) Microtrap System
ShotTrack System
250
300
Confined VoD MicroTrap VOD Data 6.5
6.0
3736 m/s
3735.5 m/s
5.5
5.0
4.5
Distance (m )
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0 -1.25
-1.00
-0.75 Time (ms)
-0.50
-0.25
0.00
Significance of VoD • VoD a critical aspect of explosive characterisation – The only direct report from the detonation front – Defines non-ideal performance – Vital role in verification of model
• Claims that lower VoD = less energy – Debates over relevance to energy delivery
Basic terminology • Energy – Measure of the potential for an explosive to do work
• Energy partitioning – Types of energies released during various phases of the blasting process (e.g. shock, heave and wasted)
Energy model: Ideal Detonation Braithwaite, 2003
Reaction zone Fully reacted Explosive products
Planar shock front CJ plane Kinetic energy of products
Energy delivered by expanding gases behind CJ plane
Energy partitioning
A
1 2 1+2 2+3
Kinetic componenet of shock energy Strain component of shock energy Shock energy Fragmentation and heave energy
4
Strain energy in the burden at the time of gas escape Waste energy
5
Pressure 1
B
Response of the blasthole wall to explosive loading C 3
2 O
4 D
Volume
5 E
By Udy and Lownds (1990)
Energy partitioning Cunningham, 2003 (HSBM)
Anfex Adiabat (Density 0.8) 5.0
Detonation pressure
Pressure, GPa
4.0
“Borehole pressure” Kinetic energy
3.0
Internal energy 2.0
1.0
Net available expansion energy
200 MPa rock strength
0.0 0 CJ volume 0.92
Start volume 1.25
1
10 Specific volume, cc/g
20 MPa End pressure
100
Energy partitioning definitions Cunningham, 2003 (HSBM)
•
Shock Energy – The stage of energy transfer in which the material responds to the impulse of the detonation wave – Characterised by permanent displacement, volume increase, and alteration of material.
•
Heave Energy – The stage of energy transfer in which material response is primarily to an identifiable pressure regime. – Characterised by elastic reaction, movement and cracking but not alteration of the nature of the material.
Energy partitioning experimental findings (Singh, 1993)
•
Percentage depth of damage by shock energy increases with increase in VoD
•
The VOD of the explosive charge controls the rate of release of the explosive energy and also influences the energy partitioning with respect to shock and gas
•
An explosive with a low VOD releases its energy at a slower rate and usually a larger proportion of the total energy in the form of gas energy
•
In low VOD explosives the bulk of the energy is contained in high pressure gases which work on the rock mass for a much longer duration, helping the crack propagation process
Energy models • Conventional energy tables • RWS, REE (Relative Effective Energy): – Calculated using ideal detonation codes – Expansion Energy from detonation state to cut off pressure (e.g. 20MPa) – Relative to ANFO (94:6) density 0.8 g-cm-3
Basic terminology • Relative Bulk Strength – Strength per unit volume of an explosive calculated from its weight strength and density relative to ANFO
• Relative Weight strength – The energy of an explosive material per unit weight relative to ANFO
Energy of Bulk Explosives (AEL) 200 180 160 140 120 100
% Emulsion Density g/cc*100 RBS
80 60 40 20
Pump
Augur
E3 00 1 AN FE X
E4 00 1 E3 50 1
E5 00 1 E4 50 1
P7 01
P4 01
P1 01
0
Basic terminology • Detonation pressure – Pressure achieved within the reaction zone in a detonating explosive measured at the CJ plane
• Borehole pressure – Pressure exerted on the borehole walls by the expanding gases of detonation after chemical reaction
• Decoupling – Borehole diameter greater than explosive charge diameter
• Decoupling ratio – Ratio of charge diameter to borehole diameter
Effect on pressure intensity from decoupling
Miller et al 2005
Experimental work with decoupled charges Olsson and Bergqvist ,1996 The rock mass consisted of a fine-grained massive granite with a uniaxial compressive strength of approximately 200 MPa and a tensile strength of 12 MPa.
Explosive Type Gurit Gurit Emulet 20 Kimulux 42 Detonex 80
Description
A nitroglycerin/nitroglycole sensitized explosive in plastic cartridges A nitroglycerin/nitroglycole sensitized explosive in plastic cartridges A low density ANFO type bulk explosive An emulsion type explosive in plastic pipe cartridges Detonating cord (80g/m)
Hole diameter (mm) Charge diameter (mm) Decoupling ratio
Explosive Diameter (mm) 17
Hole diameter (mm)
Density (kg/L)
VOD (m/s)
Energy (MJ/kg)
2000
Gas Volume (l/kg) 930
3.4
Charge concentration (kg/m) 0.21
38, 51
1
22
24, 51, 64
1
2000
930
3.4
0.4
Bulk
51
0.25
1800
1117
2.6
0.51
22
64
1.15
4800
903
3.2
0.37
11
51
1.05
6500
780
5.95
0.08
24 22 0.92
38 17 0.45
51 17 0.33
64 22 0.34
Olsson and Bergqvist ,1996
Crack Extension B = 0.5m, S = 0.5m
51 mm hole
Gurit 17
Explosive type
2000 m/s
d.c. ratio= 0.33
Gurit 22
2000 m/s
d.c. ratio= 0.43
Emulet 20
1800 m/s
Detonex 80
6500 m/s
0
5
10
15
20
25
Maximum crack length (cm)
30
35
40
Olsson and Bergqvist ,1996
Crack extension B = 0.5m, S = 0.5m
64 mm hole
Explosive Type
Gurit 22 2000 m/s
d.c. ratio= 0.34
Kimulux 42 4800 m/s
d.c. ratio= 0.34
0
5
10
15
20
25
Maximum crack length (cm)
30
35
40
Olsson and Bergqvist ,1996
Explosive Type
Crack extension B= 1m , S= 0.8m
24 mm hole
Gurit 22 2000 m/s
d.c. ratio= 0.92
0
10
20
30
40
50
60
70
Maximum crack length (cm)
80
90
100
Summary of decoupling experiments
Explosive
VOD
Maximum
Charge
Hole
Decoupling
m/s
crack length
Diameter
diameter
ratio
(cm)
(mm)
(mm)
Detonex 80
6500
16
-
-
-
Emulet 20
1800
37
-
-
-
Kimulux 42
4800
26
22
64
0.34
Gurit 22
2000
30
22
51
0.43
Gurit 22
2000
15
22
64
0.34
Gurit 17
2000
5
17
51
0.33
*Gurit 22
*2000
*90
*22
*24
*0.92
All tests were carried out on a 0.5x0.5 m pattern (B xS), except for (*) where B = 1 and S = 0.8m.
Olsson and Bergqvist ,1996
Summary of decoupling experiments Olsson and Bergqvist ,1996
•
Crack length and hence pre-conditioning behind the blast decreases with a reduction in decoupling ratio (charge diameter/hole diameter)
•
Data shows the influence of confinement and velocity of detonation. An increase in burden and spacing and hence confinement showed a clear increase in the zone of damage
•
Higher VOD explosives appeared to generate a high frequency of cracking near the zone of the blast hole
•
Crack length increased with an increased in charge concentration
Explosive performance – detonation codes
Braithwaite, 2003
Thermodynamic codes Theoretical description of the chemical reactions, their rates, products and energy released . A large number of computer codes have been published. The principle difference between the predictions of the codes are due to different chemistry explicit fluid and solid Equations of State Codes include:
Empirical – BKW, Virial – Tiger, Fortran BKW Semi-Empirical – JCZ3 – Tiger Fundamental – WCA or similar – CHEQ, IDeX, Cheetah, TDS, Vixen-i
Ideal Detonation Computer Programs For Condensed Phase Detonations Braithwaite, 2003
Military/ Governmental Institutions TIGER, CHEQ, CHEETAH Commercial Companies IDEX, Vixen_i Consultants TIGERWIN Academic/ University QUATTOR, TDS
LLNL Code, CHEETAH Braithwaite, 2003
CHEETAH
Braithwaite, 2003
TDS Braithwaite, 2003
Typical ideal detonation predictions Braithwaite, 2003
Explosion/ Detonation Property
Base Emulsion Explosive
Aluminized Emulsion Explosive
Detonation Velocity (m/s)
5400
5230
Particle Velocity
1350
1320
Detonation Pressure (Gpa)
7.75
7.25
Detonation Density (kg/m3)
1390
1400
Detonation
(m/s)
Energetics Ideal Shock Energy
(MJ/kg)
0.53
0.51
Ideal Strain Energy
(MJ/kg)
0.11
0.1
Ideal Gas Energy
(MJ/kg)
1.71
2.01
Typical ideal detonation predictions Braithwaite, 2003
Explosion/ Detonation Property
Base Emulsion Explosive
Aluminized Emulsion Explosive
27.5
25.1
CO2
3.5
2.3
N2
9.5
9.1
0
0.2
0
1.1
Detonation products
H2O
H2 Al2O3
(moles/kg explosive)
Aims of modelling explosive performance • • • •
Energy release and rate of energy release Pressure history Detonation velocity Critical VOD/ diameter
• Applications of performance modelling – Formulators’ tool – Blasting optimisation – Front end for rock breaking modeling
Performance modelling process (HSBM approach)
Formulation & density
Vixen_I – ideal detonation
Vixen_N – non-ideal detonation and rarefaction
Unconfined Characteristics
Confinement Model Refinement
Itasca – rock breaking simulation/ rarefaction
Rock Properties
Explosive primers • Every explosive has an energy requirement to be initiated (activation energy) – Nitroglycerin = very small – ANFO = very high
• Priming of explosives with both packaged and cast boosters provides this activation energy • If the activation energy level is not exceeded, the explosive will not perform to optimum Source : Dyno Nobel, 2005
Effect of primer detonation pressure on VoD of ANFO
Source : Dyno Nobel, 2005
Effect of primer diameter on VoD of ANFO
Source : Dyno Nobel, 2005
Explosive rock interaction Rapid generation of gaseous products at high temperatures and pressures Rapid expansion of the borehole wall Formation of dynamic stress waves Crushing/pulverising of the rock Undamaged zone
Radial crack formation and extension Circumferential crack formation from pressure drop (unloading) Gas penetration and extension of cracks and discontinuities
Radial fracturing
Mechanisms of breakage • The main mechanisms of breakage are: – Shock and stress drive • Failure in compression and shear • Radial fracturing • Reflection
– Gas driven • Gas expansion
– Combined mechanisms
Compression and shear
rc
• Level of stresses exceed both the static and dynamic strength of the rock material in both shear and compression
ro • Rock is pulverised as the borehole expands (Udy and Lownds, 1990; Whittaker et al, 1992 and Szuladzinski, 1993)
Radial fracturing
• Tangential strains generated from radial compression during the passage of the “shock” (stress) wave • Radial fractures are developed when the intensity of the tangential strains is greater than the dynamic tensile strength of the rock
Reflection
• Compressive shock wave is reflected as a tensile wave at a free face boundary or open discontinuity • Tensile fractures are generated when the tensile stresses exceed the dynamic tensile strength of the rock mass
Gas expansion • The propagation of fractures due to gas was demonstrated in laboratory scale conditions by Kutter and Fairhurst (1971), Dally et al (1975) and McHugh (1983) • It is almost impossible with current methods to independently measure the processes of shock and gas in full scale conditions.
The combined theory •
Mosinets (1966) argued that fracturing due to stress waves is dominant, contributing approximately 75-88% of the total volume broken with a contribution of 12-25% by the action of gaseous explosion products. This is also supported by experiments with blasthole liners reported by Brinkmann (1990) – Shock and stresses condition the rock mass (crushing, radial and circumferential fractures) – Explosive gases enlarge the primary radial cracks together with the sudden release of energy contained in the rock mass – As compressive stresses are reduced through rock mass displacement, additional tensile fracturing occurs
Rock breakage mechanisms
Relevant rock properties (Cundall, 2007)
• For the full rock breakage process, the relevant rock properties are: – – – –
Density Confined modulus Shock properties (e.g. yield strength HEL) Dynamic tensile strength
Plate Impact test for shock properties (Cambridge University, Field 2005 HSBM) • Designed and built in house • Single stage gas gun, compressed air or helium • 50mm bore • 5m barrel • Pressure up to 350 bar • Velocity range 100-1100 m s-1
Hopkinson Bar test (NIOSH Laboratories, USA) – Provide dynamic properties and design formulas – Split Hopkinson Pressure Bar (SHPB) and Hustrulid modification
Gas gun – Laurance Livermore National Laboratory Braithwaite, 2003
