Technical Note - Correcting the burden formula for heave blasting

An AIME transaction by P.L. Allsman (1960), "Analysis of Explosive Action in Breaking Rock," contains many useful concepts applicable to blast design. Of special interest was the derivation of a heave blasting burden formula, which is important in establishing the maximum burden. Unfortunately, its derivation contains a fundamental error and then a compensating one. This formula was: [ ] The derivation used the impulse-momentum principle, with a 0.3 m thick (1 ft thick) radius of rock mass being acted on by an explosive impulse. However, the rock weight was not converted to mass by dividing by the gravitational constant. This mistake can be verified by checking the units in the formula, which resolve into m%-sec instead of meters. Adding the gravitational constant corrects this: [ ] If the minimum velocity is now taken as 0.3 m/sec (1 ft per sec), as was recommended, excessively large burdens result. Any appropriate rock velocity should be capable of throwing the rock mass a minimum distance so that the swell needed for breakage can occur. Unless the burden is extremely small and the bench height is very high, it is unlikely that a velocity of only 0.3 m/sec (1 ft per sec) will be sufficient. A review of the literature indicates that average rock velocities observed by camera studies typically range from 15 to 30 m/sec (50 to 100 ft per sec) (duPont deNemours and Co., 1977; Tansey, 1979). On this basis, a minimum rock velocity of about 15 m/sec (49 ft per sec) would be expected and not 0.3 m/sec (1 ft per sec). When a velocity of 15 m/sec (49 ft per sec) is inserted into the corrected formula, the results approximate those of the original formula with a velocity of 0.3 m/sec (1 ft per sec). The errors were approximately self-compensating [ ] References Allsman, P.L., 1960, "Analysis of Explosive Action in Breaking Rock," Transactions, AIME, Vol. 217, pp. 475-476. E. I. duPont deNemours and Co., 1977, Blasters' Handbook, 175th Anniversary Edition, Dupont, Wilmington, DE, pp. 233. Tansey, D.O., 1979, "The DuPont Sequential Blasting System," CIM Bulletin, Vol. 72, July, p. 80. Thompson, S.D., 1981, "Critical Review and Revision of Surface Blasting Practice," MS thesis, West Virginia University, pp. 308-316.