Civil Engineering Reference
In-Depth Information
Pressure
Peak positive pressure
p
Positive impulse
i
Equivalent
triangular pulse
Time
Ambient pressure
p
o
Peak negative
pressure
p
-
Time of
arrival
t
A
Equivalent
pulse
duration
t
d
Negative
impulse
i
-
Figure 10.1
Typical blast waveform from a high explosive and equivalent triangular pulse
usually considered for design purposes as an equivalent quan-
tity of trinitrotoluene (TNT), the standard 'reference' explosive
on which empirical load curves are based (US Army Corps of
Engineers, 2002). For convenience, both incident and reflected
blast wave parameters are usually expressed in terms of a scaled
distance Z, defined as the ratio of the stand-off distance from
the centre of a spherical charge to the target and the cube-root
of the charge mass expressed as an equivalent quantity of TNT.
This cube-root scaling law holds that the incident and reflected
pressure are proportional to the cube-root of charge mass, per-
mitting the blast wave parameters to be plotted as variables
which are independent from the mass of the charge. Detonation
in materials other than air, such as detonation in soil and under-
water detonations are beyond the scope of these relationships
and specialist advice should be sought. Similarly, detonations
in enclosed volumes (i.e. internal rooms) and the confinement
effects of objects such as street canyons or reflection from
nearby objects which prevent the free expansion of the blast
wave from a detonation in open air can significantly exacerbate
the blast loads and require specialist methods of analysis.
Unfortunately, and unlike vehicle impact, seismic and other
load types, no simple empirical formulae or 'rules of thumb'
are available for the estimation of blast loads and recourse is
necessary to these curves to derive loads for design. Recourse
is sometimes suggested to the 34 kPa pressure recommended
for design of elements designated as key elements for design
against disproportionate collapse (see Chapter 12:
Structural
robustness
), but this is a notional, static, load for the notional
enhancement of the structural design of critical structural
elements and it is unrelated to the blast pressures derived by an
explosion; therefore the blast pressures due to the event being
considered must be explicitly calculated.
For structural design, the engineer will need to know both
the peak reflected pressure and the reflected impulse of the
blast wave at the relevant scaled distance. The impulse is the
integral of the pressure wave over the duration of the positive
phase (
Figure 10.1
). It is common practice to neglect the nega-
tive phase of the blast wave in most circumstances. The peak
pressure and impulse are the two fundamental loading param-
eters. The shape of the blast pulse is also important, and for
high explosives the pressure rise is almost instantaneous fol-
lowed by a more gradual decay, often approximated by a linear
falling triangular pulse of equal impulse to give an equivalent
pulse duration td (
Figure 10.1
). For vapour cloud explosions,
the 'rise time' is more gradual, and the exact shape will depend
on the strength of the explosion.
The magnitude of blast pressures can be significant: for
high explosives the peak pressures can be in the tens of mega-
pascals (thousands of psi); however, the duration of the pres-
sure pulse may be only a few milliseconds. It is imperative
that the structural engineer design the structure dynamically:
single degree of freedom techniques are industry-standard and
the approach is described in Cormie (2009). The relationship
between the peak pressure and the impulse will govern the
dynamic response of the structure. The dynamic response is
characterised through the ratio of the blast pulse duration td
to either the natural period of the structural element T, or the
time to maximum response of the element tm. If t
d
/T > 10 or
t
d
/t
m
> 3, the structural response is quasi-static and the peak
pressure may be straightforwardly applied as a static load.
If t
d
/T < 0.1 or t
d
/t
m
< 0.3, the load has decayed before the
structure has started to respond and the structural response is
impulsive, being largely governed by its inertia. Between these
limits the structural response is dynamic, being a function of
