The term “powder factor” is almost universally accepted as the measure of the efficiency of a blasting program. It represents the economics of blasting since it designates quantity of explosive (thereby providing quality control in rock fragmentation) in terms of the associated volume broken.
It is the wide use of this concept that explains the interest shown in an approach to rock blasting preferred by A. W. and Z. W. Daw in a treatise on blasting substantiating its use in the form, Q = CvW³ for single shot hole,
Q = quantity of explosive lb
Cv = blasting coefficient
W³ = unit volume of rock
It is obvious that the term Cv could also be called the apparent powder factor should the equation be written in the form, Cv = Q/W³ (lb per cubic unit). However, while the approach was ingenious and the practical applications straightforward, their original, rather limited experimental work, along with certain assumptions, was questioned.
Summary of Experimental Results
The postulations fundamental to the “One-Shot” pin and its performance is that the peak force causing rupture of rock to a free face below an impacting pin, as measured on the pin, is a measure of the resistance of that rock to impact failure; and the peak strain measured on the impacting pin is, concomitantly, a measure of that resistance.
The successful, performance of the “One-Shot” measuring method previously described calls for the use of a load cell pin to transmit the force of a falling weight to the rock and instrumentation which will record the strain time record of the pin during the impact event.
With the dependability of the measurement system reasonably established, its use in determining rock resistance becomes practical.
To eliminate the possibility of the limited dimensions of a 7 x 7 x 3 in. block inducing a contribution to the measured strain-by reflected tension from its sides, tests were also carried to 18 x 18 x 6 in. models. Theoretically, the energy of the reflected tensional waves from the sides of a block would be greatly dispersed by the time they arrived at the potential fracture plane.
Positioning strain gages on the faces of test blocks below the bottoms of impacted boreholes permits reliable measurement of peak strain due to rupturing force. Results by this method, described under Mechanical Testing, supports the straight line relationship εp/εg = q · W · S from which F/εg = B · S · W is derived. This, for impact, expresses an important correlation among burden, hole diameter, rupturing strain and force. Therefore, by test, since the ratio εp/εg remains constant for constant ratios of W/S, the ratio of the corresponding stresses should have a constant relationship. If the stress in the impacting pin is that transmitted to the rock burden, then the ratio of that of the latter to that corresponding to εg should follow the same constant rate increase; and since this ratio bears a constant relationship to W/S, a significant correlation is therefore demonstrated.
For any type of dynamic loading, deformation is proportionate to the magnitude of the load to and including rupture of a system. With definite correlation between peak strain during rupture and W/S ratios established by the two types of loading, especially hydro-impact and supported by supplementary mechanical testing herein described, it is reasonable to deduce that if a similar such correlation should result when explosive charges are used, then such a relationship as the aforementioned would hold for impulsive loading by detonating explosive.
One-Shot” Pin Performance
By experiment and calculation, when the impact weight was dropped from random heights, constant peak forces were obtained for constant ratios (W/S) of rock burden to hole periphery ( S = π x diameter) for direct and by hydroimpact loading of the laboratory models. From this it is concluded that the “One-Shot” device gives measured values of the rupturing force which, for all practical purposes in laboratory work, are valid and close to absolute.
On the basis of the above, it can be further concluded that the rupturing impact force recorded is a measure of the resistance of the rock burden to direct and hydro-impact rupture.
The following conclusions are derived from the laboratory explosive tests.
- The use of electric resistance strain gages in the manner described is adequately established as a valid and workable laboratory method of measuring the effects of explosive detonation in rock rupture.
- The principle that the deformation of the system is proportionate to the applied force, to and including rupture, is upheld in the light of the comparable results in terms of peak strain, plot of dimensionless products, and resulting exponentials from three different types of dynamic loading used. Therefore, this method of mechanical testing holds some possibilities as a means of standardizing a method for dynamic rock strength.
- Finally, that the expression in the form of F = SxWy · R is valid for explosive rupturing forces in laboratory testing. If on the same basis, it should be valid when applied in the field, it can be a useful device in commercial blasting practice. From it, if valid, is foreseen that the apparent “powder factor” in the form of Cv = Q/W³ pounds of explosive per cubic feet could be readily determined for a single shot hole in the field. By this means, the coefficient derived should be of practical economic value in commercial blast design. This is mainly because of the foreseeable relative simplicity by which its determination can be made.