Unconfined Explosions

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where,
Wc = weight of casing
W = charge weight
Various formats for determination of F have been suggested by
different investigators (see Some Effects of Light Surrounds and Casings
on the Blast from Explosives by Dewey) with Equation (12c) giving the best
fit for steel-cased explosives.
EQUATION:
F = 0.2 + 0.8/(1 + Wc/W)
(12c)
Equation (12c) should be used for other materials besides steel.
4.
UNCONFINED EXPLOSIONS.
a.  Free-Air Burst.  Free-air burst blast pressures are the blast
loadings acting on a structure due to an explosion in which no amplification
of the initial shock waves occurred.
(1) When the shock wave impinges on a surface oriented so that a
line which describes the path of travel of the wave is normal to the
surface, then the point of initial contact is said to sustain the maximum
(normal reflected) pressure and impulse.  The peak pressures, impulses,
velocities, and other parameters of this shock wave for a bare spherical
TNT explosive charge are given in Figure 4-5 of NAVFAC P-397 vs. the scale
distance, Z = RA/W1/3.
(2) The effect of the angle of incidence on the peak reflected
pressures is shown in Figure 4-6 of NAVFAC P-397.  For design purposes, the
other blast parameters, except the duration of the wave, may be taken as
those corresponding to the reflected pressure Pr and are obtained from
Figure 4-5.  The duration of the blast wave corresponds to the duration of
the free air pressure.
b.  Surface Burst.  An explosion occurring on or very near the ground
surface is considered to be a surface burst.  Unlike a free-air burst, the
initial wave of the explosion is reflected and reinforced by the ground
surface to produce a reflected wave.  There exists a theoretical procedure
used to estimate the magnitude of the incident pressure (NAVFAC P-397);
however, the impulse calculated from this method is generally conservative
relative to test results which were used to construct Figure 4-12 (NAVFAC
P-397).  A quick glance at both Figures 4-5 and 4-12 will show that for a
given distance from a detonation of the same weight of explosive, all of
the parameters of the surface burst environment are larger than those for
the free-air environment.
c.  Pressure-Time Variation.  In the analysis of certain structures
(steel frames, cold-formed members), a more accurate definition of the
variation of the pressure as a function of time is required.  This
variation is usually referred to as the "p-T curve" of the blast wave.
As stated in Appendix A of Blast Capacity Evaluation of Pre-Engineered
Buildings by Stea, et al., this variation can be approximated by the
following functions:
2.08-18