A History of Research and a Review of Recent Developments
A History of Research and a Review of Recent Developments
A History of Research and a Review of Recent Developments
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72<br />
Structural loading from distant explosions<br />
<strong>of</strong> the hole. Dynamic penetration occurs when the warhead <strong>of</strong> a bomb or<br />
missile is contained in a shaped container that hits a structure at high velocity<br />
<strong>and</strong> enters the component before exploding. The component can have the<br />
solidity <strong>of</strong> a reinforced concrete slab, the cellular construction <strong>of</strong> an aircraft<br />
body, or the laminations <strong>of</strong> armour plate.<br />
The loading <strong>of</strong> structures by an extremely concentrated action that damages<br />
the fabric by a cutting action must also be considered. This leads us later to<br />
the consideration <strong>of</strong> hollowed or shaped charges that project molten metal<br />
linings into the structure like jets. This chapter, however, is confined to one<br />
distant explosion, <strong>and</strong> to the analytical history <strong>of</strong> the investigation <strong>of</strong> structural<br />
loading when the loading actions are assumed to be uniform. Much <strong>of</strong> this<br />
history has been set down <strong>and</strong> explained with diagrams in many earlier<br />
publications, <strong>and</strong> there is no point in repeating the details here, so what follows<br />
is a review <strong>of</strong> the major elements <strong>of</strong> the loading analysis.<br />
4.1 UNIFORMLY DISTRIBUTED PRESSURES<br />
The fundamentals <strong>of</strong> reflected shock fronts were discussed briefly in section<br />
2.1, but it is now necessary to look more closely at reflections from aboveground<br />
structures <strong>and</strong> components. An example <strong>of</strong>ten considered is the action<br />
<strong>of</strong> a shock front from a detonation on a surface structure <strong>of</strong> simple rectangular<br />
box-shape, having one face normal to the direction <strong>of</strong> propagation <strong>of</strong> a shock<br />
wave from a distant explosion. If the explosion is directly above the structure,<br />
the shock wave will strike the upper face <strong>and</strong> a reflected shock is formed. The<br />
overpressure on this face rises to pr, which as we saw in Eq. (4.1) is given by<br />
p r/p 0=2(7p a+4p 0)/(7p a+p 0),<br />
(4.1)<br />
where p 0 is the peak ‘free field’ incident pressure, p a is atmospheric pressure,<br />
<strong>and</strong> the angle <strong>of</strong> incidence <strong>of</strong> the shock front is zero. After the shock wave has<br />
impinged on the surface <strong>of</strong> the earth adjacent to the structure, the sides <strong>of</strong> the<br />
structure will be loaded by the same reflected pressure (which acts in all<br />
directions). It is assumed in this analysis that the wavelength considerably<br />
exceeds the dimensions <strong>of</strong> the structure.<br />
If the explosion is at ground level, <strong>and</strong> the centre <strong>of</strong> the explosion lies on the<br />
normal to the side face <strong>of</strong> the structure at its mid-point, then the shock wave will<br />
strike the side face normally <strong>and</strong> a reflected shock is formed having an instantaneous<br />
pressure p r. At the moment this reflected front is formed, the initial non-reflected<br />
pressure p 0, just above the top edge <strong>of</strong> the front face, initiates a rarefaction wave,<br />
travelling at the speed <strong>of</strong> sound, which heads down the front face towards the<br />
ground. This causes disintegration <strong>of</strong> the reflected shock, until it is in equilibrium<br />
with the dynamic pressures due to the following blast winds, q.<br />
Meanwhile, at a time equal to the length <strong>of</strong> the structure divided by the front<br />
velocity, ū, the incident shock front travels over the top <strong>and</strong> along the sides <strong>of</strong>