3-Basics on Detonation Theory_FINAL

Basics on detonation theory Basics on detonation theory and explosive rock interactionand 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 patterngeometry

• 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

ExplosiveExplosive

Stable by-products,mainly gases

Shock/stress wave in the surrounding media

Chapman-Jouguet (CJ) Plane

Direction of detonationDirection of detonation

Undisturbed explosivePrimaryreaction zone

Shock front in theexplosive

Expanding gases

Explosive detonation

Basic terminology

CJ(Sonic)Plane

ShockPlaneDDZ

Reaction

Nothing that happens behind the CJ plane can affect the DDZ.

Particle velocity follows Shock Front, but slower and decelerating

ExplosiveRho ZRho CJ > RhoZ

u

D

Shock initiates reaction

DDZ drives Shock Wave

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 detonationBraithwaite, 2003

Non ideal detonation

After Bill Byers Brown (2002)

Ideal vs non ideal detonationAfter Cunningham 2003 (HSBM)

Ideal: CJ/ZNDIdeal: CJ/ZND• No Divergence/ effect of confinement • Reaction zone = CJ zone• Ideal VoD

NonNon--Ideal: WK/MIGIdeal: WK/MIG• 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

1500

2000

2500

3000

3500

4000

4500

5000

0 50 100 150 200 250 300

Diameter (mm)

Unc

onfin

ed V

oD (m

/s)

Microtrap System ShotTrack System

Confined VoD

3735.5 m/s

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

-1.25 -1.00 -0.75 -0.50 -0.25 0.00

MicroTrap VOD Data

Dis

tanc

e (m

)

Time (ms)

3736 m/s

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 DetonationBraithwaite, 2003

Fully reactedFully reactedproductsproducts

Explosive Explosive

Reaction Reaction zonezone

PlanarPlanarshock frontshock front

CJ planeCJ plane

Energy deliveredEnergy deliveredby expanding gases behindby expanding gases behindCJ planeCJ plane

Kinetic Kinetic energy of energy of productsproducts

Energy partitioning

By Udy and Lownds (1990)

Pressure

Volume

1

2

A

B

C

O

34 5

Response of the blastholewall to explosive loading

D E

1 Kinetic componenet of shock energy

2+3 Fragmentation and heave energy

5 Waste energy

2 Strain component of shock energy

4 Strain energy in the burden at thetime of gas escape

1+2 Shock energy

Anfex Adiabat (Density 0.8)

0.0

1.0

2.0

3.0

4.0

5.0

0 1 10 100Specific volume, cc/g

Pre

ssur

e, G

Pa

200 MPa rock strength

“Borehole pressure”

Detonation pressure

20 MPa End pressure

Internal energy

Kinetic energy

Start volume 1.25

CJ volume 0.92

Net availableexpansion energy

Energy partitioningCunningham, 2003 (HSBM)

Energy partitioning definitionsCunningham, 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 notalteration of the nature of the material.

Energy partitioning experimental findings

• 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

(Singh, 1993)

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)

0

20

40

60

80

100

120

140

160

180

200

P101

P401

P701

E5001

E4501

E4001

E3501

E3001

ANFEX

% EmulsionDensity g/cc*100RBS

PumpPump AugurAugur

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.

ExplosiveType

Description ExplosiveDiameter

(mm)

Hole diameter(mm)

Density(kg/L)

VOD(m/s)

GasVolume(l/kg)

Energy(MJ/kg)

Chargeconcentration

(kg/m)Gurit A nitroglycerin/nitroglycole sensitized

explosive in plastic cartridges17 38, 51 1 2000 930 3.4 0.21

Gurit A nitroglycerin/nitroglycole sensitizedexplosive in plastic cartridges

22 24, 51, 64 1 2000 930 3.4 0.4

Emulet 20 A low density ANFO type bulkexplosive

Bulk 51 0.25 1800 1117 2.6 0.51

Kimulux 42 An emulsion type explosive in plasticpipe cartridges

22 64 1.15 4800 903 3.2 0.37

Detonex 80 Detonating cord (80g/m) 11 51 1.05 6500 780 5.95 0.08

Hole diameter (mm) 24 38 51 64Charge diameter (mm) 22 17 17 22Decoupling ratio 0.92 0.45 0.33 0.34

Olsson and Bergqvist ,1996

51 mm holeCrack Extension B = 0.5m, S = 0.5m

0 5 10 15 20 25 30 35 40

Detonex 80

Emulet 20

Gurit 22

Gurit 17

Expl

osiv

e ty

pe

Maximum crack length (cm)

6500 m/s

1800 m/s

2000 m/s

2000 m/sd.c. ratio= 0.33

d.c. ratio= 0.43

Olsson and Bergqvist ,1996

64 mm holeCrack extension B = 0.5m, S = 0.5m

0 5 10 15 20 25 30 35 40

Kimulux 42

Gurit 22

Expl

osiv

e Ty

pe

Maximum crack length (cm)

2000 m/s

4800 m/s

d.c. ratio= 0.34

d.c. ratio= 0.34

Olsson and Bergqvist ,1996

24 mm holeCrack extension B= 1m , S= 0.8m

0 10 20 30 40 50 60 70 80 90 100

Gurit 22

Expl

osiv

e Ty

pe

Maximum crack length (cm)

d.c. ratio= 0.922000 m/s

Summary of decoupling experiments

Olsson and Bergqvist ,1996

Explosive VOD

m/s

Maximum

crack length

(cm)

Charge

Diameter

(mm)

Hole

diameter

(mm)

Decoupling

ratio

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.

Summary of decoupling experimentsOlsson 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 codesTheoretical 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 aredue to different chemistry explicit fluid and solid Equations of State

Codes include:

Empirical – BKW, Virial – Tiger, Fortran BKWSemi-Empirical – JCZ3 – TigerFundamental – WCA or similar – CHEQ, IDeX, Cheetah, TDS, Vixen-i

Ideal Detonation Computer ProgramsFor Condensed Phase Detonations

Braithwaite, 2003

Military/ Governmental InstitutionsTIGER, CHEQ, CHEETAH

Commercial CompaniesIDEX, Vixen_i

ConsultantsTIGERWIN

Academic/ UniversityQUATTOR, TDS

LLNL Code, CHEETAHBraithwaite, 2003

CHEETAHBraithwaite, 2003

TDSBraithwaite, 2003

Typical ideal detonation predictionsBraithwaite, 2003

Explosion/ Detonation Property

Base Emulsion Explosive

Aluminized Emulsion Explosive

Detonation

Detonation Velocity (m/s) 5400 5230

Particle Velocity (m/s) 1350 1320

Detonation Pressure (Gpa) 7.75 7.25

Detonation Density (kg/m3) 1390 1400

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 predictionsBraithwaite, 2003

Explosion/ Detonation Property

Base Emulsion Explosive

Aluminized Emulsion Explosive

Detonation products

H2O (moles/kg explosive) 27.5 25.1

CO23.5 2.3

N29.5 9.1

H20 0.2

Al2O30 1.1

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

Vixen_I – ideal detonation

Vixen_N – non-ideal detonation and rarefaction

Itasca – rock breaking simulation/ rarefaction

ConfinementModelRefinement

Formulation& density

UnconfinedCharacteristics

Rock Properties

Performance modelling process (HSBM approach)

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

Crushing/pulverising of the rock

Rapid expansion of the borehole wall

Rapid generation of gaseous products at high temperatures and pressures

Radial crack formation and extension

Circumferential crack formation frompressure drop (unloading)

Formation of dynamic stress waves

Gas penetration and extension of cracks and discontinuities

Undamaged zone

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

• Level of stresses exceed both the static and dynamic strength of the rock material in both shear and compression

• Rock is pulverised as the borehole expands (Udy and Lownds, 1990; Whittaker et al, 1992 and Szuladzinski, 1993)

rcro

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