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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8© 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
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 ]
VARIABLES and [UNITS]
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]
VARIABLES and [UNITS]
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
VARIABLES and [UNITS]
FORMULANAME
VARIABLES and [UNITS]
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
9© 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
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
VARIABLES and [UNITS]
H = Face Height [ft]
D = Blast-hole Diameter [in]
DH ��
FaceHeight Formula
5 10
VARIABLES and [UNITS]
BLAST DESIGN FORMULAS
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
VARIABLES and [UNITS]
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
VARIABLES and [UNITS]
Leading underground mining technology.
10© 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
2
����
���SD
DW
MaximumChargeWeight per Delay
SD = Scaled distance factorW = Charge weight per delay [ lb]D = Distance [ft]
VARIABLES and [UNITS]
WSDD ��
MinimumDistance Formula
SD = Scaled distance factorW = Charge weight per delay [lb]D = Distance [ft]
VARIABLES and [UNITS]
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]
VARIABLES and [UNITS]
VARIABLES and [UNITS]
Volume of Rock
Weight of Rock
BLAST DESIGN FORMULAS
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
VARIABLES and [UNITS]
Loading a blast on an iron ore range.
11© 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
� � 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
VARIABLES and [UNITS]
VARIABLES and [UNITS]
VARIABLES and [UNITS]
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
VARIABLES and [UNITS]
VARIABLES and [UNITS]
Pressure Formula
P = Pressure [kbar]VOD = Velocity of detonation of explosive [ft/sec]dE = Density of explosive [g/cm3]
EdVODP ��� 20.000000233
VARIABLES and [UNITS]
BLAST DESIGN FORMULAS
12© 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
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
VARIABLES and [UNITS]
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 [�]
VARIABLES and [UNITS]
BLAST DESIGN FORMULAS
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
VARIABLES and [UNITS]
Stone Stemming Particle Size Formula
Ts = Clean crushed stone stemming particle size [in]
D = Blast-hole diameter [in]
20��
DTs
12
VARIABLES and [UNITS]
Bulk trucks preparing for another day on the job.
13© 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
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
VARIABLES and [UNITS]
BLAST DESIGN FORMULAS
B = Burden [ft]J = Sub-drilling [ft]
Sub-Drilling Formula
� � BJ ��� 0.2 0.5
VARIABLES and [UNITS]
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
VARIABLES and [UNITS]
B = Burden [ft]T = Top stemming length [ft]
� � BT ��� 3.17.0
Top Stemming Length Formula
VARIABLES and [UNITS]
Industry’s leading Detonating Cord
14© 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
BLAST DESIGN FORMULAS
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
VARIABLES and [UNITS]
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
VARIABLES and [UNITS]
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
VARIABLES and [UNITS]
VARIABLES and [UNITS]
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]
VARIABLES and [UNITS]
HEET Truck on display at an open house in 2001
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