Blast Design Formulas

7© 2 0 0 2 A U S T I N P O W D E R C O M P A N Y

T H E B L A S T E R ’ S G U I D E

COMMON FORMULAS USED FOR BLAST DESIGN

Absolute Bulk Strength (ABS)Absolute Weight Strength (AWS)Actual Scaled DistanceBase-Charge LengthBurdenDeck Stemming

-For Dry Holes-For Wet Holes

Face HeightHole-to-Hole Delay TimeLoading DensityMaximum Charge Weight per DelayMinimum DistancePowder Factor

-Volume of Rock Input-Weight of Rock Input

Pre-Splitting Formulas for Air-Decked Charges-Spacing of Air-Decked Charges-Weight of Air-Decked Charges-Stemming Column Length

Pre-Splitting Formulas for De-Coupled Charges-Linear Charge Weight-Spacing between Pre-Split Holes

Pressure FormulaRelative Weight Strength (RWS)Resistance Formulas-For Paralle Circuits-For Series Circuits

Row-to-Row Delay TimeStone Stemming Particle SizeSpacing

-Instant-Delayed

Sub-Drilling“Supersonic” Face VelocityTop-Stemming LengthWater DisplacementWeight of Rock per Blast HoleVibration Level Prediction

-Peak Particle Velocity Prediction-Site Specific Ground Transmission Constant

Volume of Rock per Blast Hole

B L A S T D E S I G N F O R M U L A S

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BLAST DESIGN FORMULAS

Absolute Bulk Strength (ABS)

ABS E = Absolute bulk strength of the explosive[cal/cc]

AWS E = Absolute weight strength of the explosive[cal/g]

dE = Density of the explosive [g/cm3]

EABS � EEAWS � d

VARIABLES and [UNITS]

AbsoluteWeight Strength (AWS)

E

EE

d

RBSAWS

462.7��

AWS E = Absolute weight strength of the explosive[cal/g]

RBS E = Relative bulk strength of the explosive[ANFO = 100]

d E = Density of the explosive [g/cm3 ]


Acutual ScaledDistance Formula

W

DSD �

Actual Scaled Distance

WSDD ��

Minimum Distance

2

��

��

��SD

DW

Maximum Charge Weight per Delay

SD = Scaled distance factorW = Charge weight per delay [ lb]D = Distance [ft]


E b = Length of base charge of high densityexplosives [ft]

B = Average burden [ft]

J = Sub-drilling depth [ft]

Base-Charge Length Formula

� �� JBE b �� 0.3 0.5


FORMULANAME


FORMULA

Variables used in formula and required units in[brackets]. If input variables are not in requiredunits, then you must use the unit conversion tables.

HOW TO READ FORMULAS



B = Burden [ft]de = Density of the explosives [g/cm3]dr = Density of the rock [g/cm3]De = Diameter of fully coupled explosive column [in]

Burden Formula

��

��

��

�

��

��

r

ee d

dDB 1.52


H = Face Height [ft]

D = Blast-hole Diameter [in]

DH ��

FaceHeight Formula

5 10



Td = Minimum length of stone deckconsisting of particles of size Ts [ft]

D = Blast-hole diameter [in]

DTd �� 5.0

For Wet Holes

For Dry Holes

DTd �� 0.1

Deck Stemming Formula


Hole-to-Hole Delay Time Formula

� � SDhth �� 50

Dhth = Delay time between holes in a row [ms]

S = Spacing between holes in a row [ft]

Hole-to-Hole Delay Times to Improve Fragmentation

ms/ft

Sands, Loams, Marls and Coals 1.8 - 2.1

Some Limestones, Rock Shale and some Shales 1.5 - 1.8

Compact Limestones and Marbles, some Granitesand Basalts, Quartzite Rocks and some Gneissesand Gabbros

1.2 - 1.5

0.9 - 1.2

Rock Type ms/ft

Diabase, Diabase Porphyrites, Compact Gneisses,and Mica Schists and Magnetites


Leading underground mining technology.



2

��

��SD

DW

MaximumChargeWeight per Delay

SD = Scaled distance factorW = Charge weight per delay [ lb]D = Distance [ft]


WSDD ��

MinimumDistance Formula

SD = Scaled distance factorW = Charge weight per delay [lb]D = Distance [ft]


V

WPF e�

PF = Powder factor [lb/yd ]3

We = Total weight of explosives used in blast [lb]V = Total volume of rock generated in blast [yd3]

Powder Factor Formula

e

r

W

WPF �

PF = Powder factor [t/lb]Wr = Total weight of rock generated in blast [t]We= Total weight of explosives used in blast [lb]



Volume of Rock

Weight of Rock


dl = Explosives loading density [ lb/ft]

De = Diameter of explosives column [in]

de = Density of explosives [g/cm3 ]

LoadingDensity Formula

eel dDd ��2

0.3404


Loading a blast on an iron ore range.



� � hLSW �� 12.008.0

W = Weight of air-deck charge [lb]S = Spacing between blast-holes [ft]Lh = Length of blast-hole [ft]

� � DS �� 0.25.1

S = Spacing between air-decked holes [ft]D = Diameter of blast-hole [in]

� � DT �� 2.10.1

T = Stemming column length [ft]D = Diameter of blast-hole [in]

Pre-Splitting Formulasfor Air-DeckedCharges




Spacing of Air-Decked Charges

Weight of Air-Decked Charges

Stemming Column Length

Wl = Linear charge weight forpre-splitting explosive [lb/ft]

D = Diameter of blast-hole [in]

S = Spacing between pre-split holes [ft]D = Diameter of blast-hole [in]

Pre-Splitting Formulasfor De-Coupled Charges

Linear Charge Weight

Spacing between Pre-Split Holes

2DS �

2.8

2DWl �28



Pressure Formula

P = Pressure [kbar]VOD = Velocity of detonation of explosive [ft/sec]dE = Density of explosive [g/cm3]

EdVODP �� 20.000000233





RelativeWeight Strength (RWS)

ERWS �

RWSE = Relative weight strength of the explosive[ANFO = 100]

AWS E = Absolute weight strength ofthe explosive [cal/g]

EAWS

91,000


Resistance Formulas

ntotal RRRRR1

...1111

321

��

For Parallel Circuits

ntotal RRRRR �� ...321

For Series Circuits

Rtotal = Total resistance of the electrical circuit [�]R1...Rn = Resistance of individual blasting caps or

circuit branches [�]



Row-to-RowDelay Time Formula

Drtr = Delay time between consecutive rows [ms]

B = Maximum burden in front of a row of holes [ft]

Violent excessive air-blast and back-break 2

High pile close to face, moderate air-blast and back-break 2 - 3

Average pile height, average air-blast and back-break 3 - 4

Scattered pile with minimum back-break 4 - 6

Effects ms/ft

Effects of Various Row-to-Row Delays

� � BDrtr �� 152ms/ft


Stone Stemming Particle Size Formula

Ts = Clean crushed stone stemming particle size [in]

D = Blast-hole diameter [in]

20��

DTs

12


Bulk trucks preparing for another day on the job.



H = Face height [ft]

B = Burden [ft]

S = Blast-hole spacing [ft]

Spacing Formulas

BS �� 2.0)2( BH

S��

�

H

B� 4If:

HB< 4If:

8

)7( BHS

��

3

BS �� 4.1

Instant

Delayed



B = Burden [ft]J = Sub-drilling [ft]

Sub-Drilling Formula

� � BJ �� 0.2 0.5


Dmin = In order to avoid air-blast from "supersonic"lateral face velocity, the delay between holesmust be more than Dmin [ms]

S = Spacing between blast holes [ft]

"Supersonic" FaceVelocity Formula

min

SD �

1.127


B = Burden [ft]T = Top stemming length [ft]

� � BT �� 3.17.0

Top Stemming Length Formula


Industry’s leading Detonating Cord




27

HSBV

��

V = Bank volume of rock per blast-hole [yd3 ]B = Burden [ft]S = Spacing [ft]H = Face height [ft]

Volumeof Rock per Blast Hole Formula


rdVW ��

W = Weight of rock generated per blast-hole [t]V = Bank volume of rock generated

per blast-hole [yd3]dr = Bank density of rock [t/yd3]

Weight of Rock per Blast Hole Formula


Vibration Level Predictation Formulas

6.1-�� SDKPPV

Peak Particle Velocity Prediction

PPV = Peak particle velocity [in/s]K = Ground transmission constant [K=160 if

no other seismic data is available]SD = Scaled distance factor

6.1SDPPVK ��

Site Specific Ground Transmission Constant

PPV = Peak particle velocity [in/s]K = Ground transmission constant

SD = Scaled distance factor



Water Displacement Formula

2

1 ��

��

��

�

h

c

cw

D

D

LLC

C = Number of explosives cartridges requiredto rise above standing water

Lw = Length of the standing water column [ft]

Lc = Length of one explosives cartridge [ft]Dc = Diameter of explosives cartridges [in]Dh = Diameter of blast-hole [in]


HEET Truck on display at an open house in 2001

Blast Design Formulas

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