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Blast Design Formulas for opencast mining.for more visit www.blastconsulting.co.za

Transcript of Blast Design Formulas

THE BLASTERS GUIDE

COMMON FORMULAS USED FOR BLAST DESIGN

BLAST DESIGN FORMULASAbsolute Bulk Strength (ABS) .................................................................................... Absolute Weight Strength (AWS) ................................................................................ Actual Scaled Distance ............................................................................................ Base-Charge Length ............................................................................................... Burden .................................................................................................................. Deck Stemming ......................................................................................................-For Dry Holes -For Wet Holes

8 8 8 8 9 9

Face Height ........................................................................................................... 9 Hole-to-Hole Delay Time .......................................................................................... 9 Loading Density .................................................................................................... 10 Maximum Charge Weight per Delay .......................................................................... 10 .................................................................................................. 10 Minimum Distance Powder Factor ...................................................................................................... 10-Volume of Rock Input -Weight of Rock Input

Pre-Splitting Formulas for Air-Decked Charges .......................................................... 11-Spacing of Air-Decked Charges -Weight of Air-Decked Charges -Stemming Column Length

Pre-Splitting Formulas for De-Coupled Charges ......................................................... 11-Linear Charge Weight -Spacing between Pre-Split Holes

Pressure Formula .................................................................................................. 11 Relative Weight Strength (RWS) ............................................................................... 12 Resistance Formulas ............................................................................................. 12-For Paralle Circuits -For Series Circuits

Row-to-Row Delay Time ......................................................................................... 12 Stone Stemming Particle Size .................................................................................. 12 Spacing ............................................................................................................... 13-Instant -Delayed

Sub-Drilling .......................................................................................................... Supersonic Face Velocity ..................................................................................... Top-Stemming Length ........................................................................................... Water Displacement .............................................................................................. Weight of Rock per Blast Hole ................................................................................. Vibration Level Prediction .......................................................................................-Peak Particle Velocity Prediction -Site Specific Ground Transmission Constant

13 13 13 14 14 14

Volume of Rock per Blast Hole ................................................................................ 14 7

2 0 0 2 AU S T I N PO W DE R C O M P AN Y

THE BLASTERS GUIDE

BLAST DESIGN FORMULASHOW TO READ FORMULAS

FORMULA NAME

Base-Charge Length Formula

FORMULAVARIABLES and [UNITS]

Eb

0.3

0.5 B J

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

VARIABLES and [UNITS]

E b = Length of base charge of high density explosives [ft] B = Average burden [ft] J = Sub-drilling depth [ft]

Absolute Bulk Strength (ABS)

ABS E AWSE dEVARIABLES and [UNITS]

Acutual Scaled Distance Formula

Actual Scaled Distance

ABS E = Absolute bulk strength of the explosive [cal/cc] AWS E = Absolute weight strength of the explosive [cal/g] d E = Density of the explosive [g/cm 3 ]

SD

D W

Maximum Charge Weight per Delay

Absolute Weight Strength (AWS)

D W SD

2

AWS E VARIABLES and [UNITS]

RBS E 7 . 462 dE

Minimum Distance

D SD VARIABLES and [UNITS]

W

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/cm 3 ] 2 0 0 2 AU S T I N PO W DE R C O M P AN Y

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

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THE BLASTERS GUIDE

BLAST DESIGN FORMULAS

Burden Formula Hole-to-Hole Delay Time Formula d B De 2 e 1.5 dr VARIABLES and [UNITS] VARIABLES and [UNITS]

D hth 0 5 Sms/ft

B = Burden [ft] de = Density of the explosives [g/cm 3 ] dr = Density of the rock [g/cm 3 ] De = Diameter of fully coupled explosive column [in]

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

Deck Stemming Formula

Rock TypeSands, Loams, Marls and Coals

ms/ft 1.8 - 2.1 1.5 - 1.8 1.2 - 1.5

For Dry Holes For Wet Holes

Td 0.5 D Td 1.0 D

Some Limestones, Rock Shale and some Shales Compact Limestones and Marbles, some Granites and Basalts, Quartzite Rocks and some Gneisses and Gabbros Diabase, Diabase Porphyrites, Compact Gneisses, and Mica Schists and Magnetites

VARIABLES and [UNITS]

0.9 - 1.2

Td = Minimum length of stone deck consisting of particles of size Ts [ft] D = Blast-hole diameter [in]

Face Height Formula

HVARIABLES and [UNITS]

5

10 D

H = Face Height [ft] D = Blast-hole Diameter [in]

Leading underground mining technology.

2 0 0 2 AU S T I N PO W DE R C O M P AN Y

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THE BLASTERS GUIDE

BLAST DESIGN FORMULAS

Loading Density Formula

Minimum Distance Formula

d l 0.3404 De d eVARIABLES and [UNITS]

2

D SD VARIABLES and [UNITS]

W

d l = Explosives loading density [lb /ft] De = Diameter of explosives column [in] de = Density of explosives [g/cm 3 ]

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

Powder Factor FormulaVolume of Rock

PF VARIABLES and [UNITS]

We V

Loading a blast on an iron ore range.

PF = Powder factor [lb/yd 3 ] We = Total weight of explosives used in blast [lb] V = Total volume of rock generated in blast [yd3 ]

Maximum Charge Weight per Delay

Weight of Rock

W VARIABLES and [UNITS]

D SD

2

PF VARIABLES and [UNITS]

Wr We

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

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

2 0 0 2 AU S T I N PO W DE R C O M P AN Y

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THE BLASTERS GUIDE

BLAST DESIGN FORMULAS

Pre-Splitting Formulas for Air-Decked ChargesSpacing of Air-Decked Charges

Pre-Splitting Formulas for De-Coupled ChargesLinear Charge Weight

S

1 .5 2 .0 DVARIABLES and [UNITS]

D Wl 28

2

VARIABLES and [UNITS]

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

Wl = Linear charge weight for pre-splitting explosive [lb/ft] D = Diameter of blast-hole [in]

Spacing between Pre-Split Holes Weight of Air-Decked Charges

W

0 .08 0 .12 S LhVARIABLES and [UNITS]

S

D

2

2.8

VARIABLES and [UNITS]

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

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

Pressure FormulaStemming Column Length

T 1 .0 1 .2 DVARIABLES and [UNITS]

P 0.000000233 VOD d EVARIABLES and [UNITS]

2

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

P = Pressure [kbar] VOD = Velocity of detonation of explosive [ft/sec] d E = Density of explosive [g/cm 3 ]

2 0 0 2 AU S T I N PO W DE R C O M P AN Y

11

THE BLASTERS GUIDE

BLAST DESIGN FORMULAS

Relative Weight Strength (RWS) Row-to-Row Delay Time Formula RWS E VARIABLES and [UNITS]

AWS E 91,000 Drtr 2 15 Bms/ft

RWS E = Relative weight strength of the explosive [ANFO = 100] AWS E = Absolute weight strength of the explosive [cal/g]

VARIABLES and [UNITS]

D rtr = Delay time between consecutive rows [ms] B = Maximum burden in front of a row of holes [ft]

Resistance FormulasEffects

Effects of Various Row-to-Row Delaysms/ft 2 2-3 3-4 4-6

For Parallel Circuits1 1 1 1 1 ... Rtotal R1 R2 R3 Rn

Violent excessive air-blast and back-break High pile close to face, moderate air-blast and back-break Average pile height, average air-blast and back-break Scattered pile with minimum back-break

For Series Circuits Rtotal R1 R2 R3 ... RnVARIABLES and [UNITS]

Stone Stemming Particle Size Formula

Rtotal = Total resistance of the electrical circuit [ ] R1 .