Technical Note - Correcting The Burden Formula For Heave Blasting (7bae40b5-e418-4e78-bd77-bdbd2be4dc27)

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: [bImpulse _P d At max =nwuwu where: bmax = maximum burden in m (ft). P= average detonation pressure in N/m2 (lb per ft2). A= duration of the average detonation pressure in sec. n= 3.1416. w= specific weight of rock in N/m3 (lb per ft3). u= minimum velocity that must be imparted to the rock in m/sec (ft per sec). d= borehole diameter in m (ft).] 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 m1/2-sec instead of meters. Adding the gravitational constant corrects this: [P d Atbmax =gu g = gravitational constant equal to 9.81 m/sect (32.2 ft per sec2).] 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 see). 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 [(9 = 1.24)]. ? 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.