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Rock properties, explosive properties, and design variables are combined using five underlying equations in this modern version of the Kuz-Ram fragmentation model.
Breakage theory (Kuznetsov, 1973): The amount of breakage that occurs with a known amount of explosive energy can be estimated using Kuznetsov's equation.
Size distribution theory (Rosin & Rammler, 1933): The particle size distribution of the broken rock can be determined from the average size if the mode of breakage is known.
Explosive detonation theory (Tidman): The amount of energy released by an explosive is calculated from its detonation behavior using the Tidman equation.
Blast design correlation (Cunningham) A correlation exists between the many different blast configurations and the mode of breakage.
Rock type correlation (Lilly): The properties of a rock will modify the amount of breakage that will occur. Kuznetsov Equation The original equation, developed by Kuznetsov, was modified by Cunningham for ANFO based explosives.
Rosin Rammler Equation
The size distribution is calculated from the Rosin-Rammler equation. 
Where: Y Percentage of material less than the size X (%)
X size of material (m)
Xc characteristic size (m)
n = uniformity |
Characteristic Size The characteristic size is calculated from the average size for use in the Rosin-Rammler equation.
Xc = Xav / ( 0.693 ) Where:
Xc characteristic size (m)
Xav average size of material from the Kuznetsov equation (m) |
Uniformity
The uniformity exponent is calculated from an equation developed by Cunningham.
0.5 0.1
n = [2.2 - 14 (B/D) ] [0.5 (1 + S/B)] [1-Z/B] [0.1 + (Lb - Lt) / L ] [L/H] P
P = 1.0 square pattern
1.1 staggered pattern
Where:
n uniformity exponent
B burden (m)
D hole diameter (mm)
S spacing (m)
Z standard deviation of drilling error (m)
Lb bottom charge length (m)
Lt top charge length (m)
H bench height (m)
P blast pattern factor
Tidman Equation The explosive strength is calculated from a modified equation originally developed by Tidman:
E = [ VODe / VODn ]² RWS
Where:
E effective relative weight strength (%)
VODe effective (field) velocity of detonation (m/s)
VODn nominal (maximum) velocity of detonation (m/s)
RWS weight strength relative to ANFO (%) Blastability Index The Blastability Index (or 'Rock Factor') is calculated from an equation originally developed by Lilly. It is used to modify the average fragmentation based on the rock type and blast direction.
A = 0.06 (RMD + JF + RDI + HF)
Where: A = blastability index
RMD = rock mass description
JF= joint factor
RDI = rock density index, RDI = 25( rr- 2)
HF = hardness factor |
The individual components are:
RMD =10 + 10 Xi
JF = JFs + JFo
JFs = 10 spacing < 0.1
20 0.1 < spacing < oversize
50 oversize < spacing
JFo = 10 dip < 10
20 dr < 30
30 60< dr
40 30< dr < 60
dr = | JDD - FFDD |
UCS/5
Where:
Xi in situ block size (m)
JF= joint factor
JFs= joint spacing factor
JFo= joint orientation factor
dr =relative dip direction (degrees)
JDD= joint dip direction (degrees)
FFDD= free face dip direction (degrees)
rr =rock specific gravity
Y= Young's modulus (GPa)
UCS =unconfined compressive strength (MPa)
Powder Factor
The equation for powder factor is: K = Qe /(B)(S)(H) Where
K =powder factor (kg / cubic m)
B= burden (m)
S =spacing (m)
H =bench height (m)
Qe = charge weight (kg) |
Charge Weight The equation for charge weight is: Qe = 1000 p r² L re Where:
Qe = charge weight (kg)
r = hole radius (m)
L = charge length (m)
re = explosive specific gravity |
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