Back to Basics – The Fundamentals of Blast Design

 

This document was originally presented at the Golden West Chapter 1999 workshop.

 

(Click on the title to open a copy of the document.)

 

 

 

Understanding Blast Vibration and Airblast,

Their Causes and Their Damage Potential

 

Originally presented at the Golden West Chapter workshops in 2006 and 2007.

 

 

 

*  *  *  *  *  *

 

 

        Useful Conversion Factors for Blasters:

 

 

Official Metric Equivalents (according to U.S. and Canadian law):

 

1 inch (in.)    =    25.4 millimeters (mm)

 

1 pound (lb.) =    453.59237 grams (g)

 

 

Distance:

feet (ft)

x

0.3048

=

meters (m)

 

meters

x

3.2808

=

feet

 

 

 

 

 

 

Weight:

pounds (lbs)

x

0.4536

=

kilograms (kg)

 

kilograms

x

2.2026

=

pounds

 

 

 

 

 

 

Peak Particle

Velocity:

in/sec

x

25.4

=

mm/sec

 

mm/sec

x

0.3937

=

in/sec

 

 

 

 

 

 

Volume:

cubic yards (yd3)

x

1.308

=

cubic meters (m3)

 

cubic meters

x

0.7645

=

cubic yards

 

 

 

 

 

 

Powder Factor:

lbs/yd3

x

0.93

=

kg/m3

 

kg/m3

x

1.6863

=

lbs/yd3

 

 

 

 

 

 

Square Root

Scaled Dist:

ft/lbs1/2

x

0.45236

=

m/kg1/2

 

m/kg1/2

x

2.2106

=

ft/lbs1/2

 

 

 

 

 

 

Cube Root

Scaled Dist:

ft/lbs1/3

x

0.3965

=

m/kg1/3

 

m/kg1/3

x

2.5221

=

ft/lbs1/3

 

 

 

 

 

 

Pressure:

lbs/in2

x

0.145

=

Pascals

 

Pascals

x

6.895

=

lbs/in2

 

lbs/in2

x

.0000689

=

kilobars*

 

kilobars*

x

14504

=

lbs/in2

 

feet of water

x

0.434

=

lbs/in2

 

lbs/in2

x

2.31

=

feet of water

 

* 1 Bar  =  14.5 lbs/in2

 

 

 

 

        Other Miscellaneous Calculations:                        

 

 

                    Pounds of explosive loading per foot of borehole  =  D2  x  S.G.  x  0.34*

 

Where:                  D  =   explosive diameter (inches)

 

                              S.G.   =   specific gravity of

                                                  explosive in g/cc

 

                                *   The factor 0.34 is used to convert g/cc to lbs/cu ft and to calculate

                                           the volume of the explosive charge.  It is the result of the equation,

 

                                                                              0.7854  x 12  x  62.4

                                                                                      1728

 

          where:          0.7854 = ¼ of pi                                               

                              12 = the number of inches in a foot

                              62.4 = the weight of 1 cu ft of water

                                        in lbs (at approx. 45oF)

                              1728 = the number of cu in in a cu ft

 

 

 

 

                    Displacement of water in a borehole:               H  =  D2 / (D2 – De2)  x  h  

 

                                        Where:                  H  =   final height of water

 

                                                                      h  =   initial height of water

 

                                                                      D  =   hole diameter

 

                                                                      De  =   explosive cartridge diameter

 

                                      Determine H, the final height of water, and then divide H by the cartridge length

                                      to determine the number of cartridges that will be required to build out of the water.

 

 

 

 

                    Square Root Scaled Distance = Distance / Explosive Weight 1/2

 

 

                    Cube Root Scaled Distance = Distance / Explosive Weight 1/3

 

 

 

 

The following equations express the relationships between Velocity, Displacement, Frequency and Acceleration for sinusoidal waveforms:

 

 

                               Velocity (in/sec)  =  2 π  f  D

 

                             Velocity (in/sec)   =  386.1 Gs / (2 π f)

 

                             Displacement (inches)  =  V  /  (2 π f)

 

                             Acceleration (in/sec2)  =  2 π  f  V

 

                               Acceleration (in Gs)  =  (2 π  f  V) / 386.1

 

                               frequency (Hertz)  =  V / (2 π D)

 

                               frequency (Hertz)  =  A  / (2 π V)

 

                              = pi  =  3.14159…..)        

 

 

 

 

                    Cole’s Formula for determining peak pressure from an explosive

                              charge detonating underwater (assumed TNT or its equivalent):

 

 

                                             P  =  2.25 x 104 (W1/3 / R) 1.14

 

 

                                        Where:                  P  =  peak pressure in psi

 

                                                                      W =  explosive charge weight in pounds

 

                                                                      R  =  distance (ft) from the detonating charge

 

 

 

 

 

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