surface blast design equations

some empirical equations for surface blast design

1.   By Fraenkel 1944.

where:

                  = Maximum burden for good fragmentation, in meters (m)
              d            = Borehole diameter (m)

                        = Charge height (m)

              H           = Depth of the blast-hole (m)

2.   By Pearse 1955

where: 

            K    = A constant. its value varies from 0.7 - 1.0

            Ps   = Borehole pressure, MPa

               = Tensile strength,
            d     = Diameter of borehole, m

   

3.    By Langefors and Kihlstrom 1968

Where:

              B max = Maximum burden for good fragmentation (m) 

              D         = diameter of hole (m)
              ρe        =Density of the explosive in the borehole (Kg/m3)
              Se        = Relative Weight strength of the explosive
              f          = Degree of confinement of the blasthole.
             S/B      = Spacing to burden ratio
             Co       = Corrected blastability factor (Kg/m3 )
                         = C + 0.75 for B max =l.4-1.5m
                         = C + 0.07/B for B max < 1.4m
                            When C = rock constant

4.         By Lopez Jimeno, E (1980) 

He modifies the ash’s formula by incorporating the seismic velocity to the rock mass, resulting in

Where:
             B= Burden, m
             D= Diameter of blast-hole, inches
             F= correction factor based on rock group = Fr× Fe

Where: 

•             ρ'        = Specific gravity of rock, gm/cm3 
•             VC     = Seismic propagation velocity of the rock mass 
•             ρ''       = Specific gravity of explosive charge, gm/cm3 
•             VD    = Detonation velocity of explosive, m/s               

The indicated formula is valid for diameter between 165 & 250mm.  For large blasthole the burden value will be affected by a reducing coefficient of 0.9.

5.        By Konya and Walter (1990)

Where:

            B       = Burden, (ft) 

            ρe      = Specific gravity of explosive, (lb/in3) 

            ρr      = Specific gravity of rock, (lb/in3) 

            D       = Diameter of explosive, (in) 

Correction factor, 

Where:

•              Bc = Corrected burden (ft) 
•              Kd = Correction factor for rock deposition. Its value is as follows, 

1. • for bedding steeply dipping into cut Kd = 1. 18 
2. • for bedding steeply dipping into face Kd = 0.95 
3. • for other cases Kd = 1.0 

•              Ks = Correction factor for geologic structure. Its value is as follows, 

1. • for heavily cracked, frequent weak joints, weakly cemented layers Ks = 1.30 
2. • for thin well-cemented layers with tight joints Ks=1.1 
3. • for massive intact rock Ks = 0.95 

•            Kr = Correction factors for number of rows. Its value is as follows, 

1. • for one or two rows of blastholes Kr = 1.0 
2. • for third or subsequent rows Kr = 0.95

Konya and walter also suggested the following empirical relationships- 

 For instantaneous initiations system, 

For delay initiation system, 

Where, 

            H     = depth of blast-hole, m 

            B     =burden, m 

            S      =Spacing, m

Konya and Walter also suggested the following empirical relationship 

Where, 

           S ANFO = relative strength of explosive 

           ρr           = density of rock, gm/c.c. 

           d            = diameter of blast-hole, m

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Surface blast design, drilhole arrangements.