A History of Research and a Review of Recent Developments

Table 2.3
Below-ground explosions 39
Chadwick, Cox and Hopkins used a theory of spherical plastic-elastic flow
in ideal soils to study the formation and size of the camouflet chamber in deep
explosions and produced numerical values for the variation of camouflet radius
with time during the first expansion phase for explosions at a depth of 100 feet
for three idealized soils: fully saturated clays, partly saturated clays or mixed
soils, and dry sands. The first of these has a cohesion >0 and an angle of internal
friction=0; the second has values of both constants >0; the third has a cohesion=0
and angle of internal friction >0. The numerical results for the explosion of a 1
lb spherical charge (radius 0.137 ft) at a depth of burial of 100 ft were as given
in Table 2.3 (figures are given for the end of the first expansion).
These results show that the main influence on camouflet radius is the angle
of internal friction, because when φ>0 the figures coincide, irrespective of the
cohesion. When φ=0 there is a noticeable increase in camouflet size.
There is a good description of the underground nuclear explosion in the
book on the effect of nuclear weapons, compiled and edited by Glasstone and
Dolan [2.9]. In their analysis of shallow explosions they point out that the
ground surface moves upwards in the shape of a dome, which disintegrates
and throws soil and rock fragments upwards. Much of this material falls back
into the crater, entraining air and dust particles which are carried downwards
and then outwards to produce a ‘base surge’ of dirt particles. It is carried
downwind, and can occur several minutes after the original explosion.
Meanwhile the ‘main cloud’ of the explosion, containing expanding gases
and vapours, rises to a height of many thousands of feet.
They describe an underground nuclear explosion of 1.7 kilotons in 1957 at a
depth of 790 feet. During the hydrodynamic phase of the explosion, when the
shock wave is initiated and begins to expand outwards, the original chamber in
which the bomb was placed expanded outwards to form a spherical cavity 62
feet in radius. Eventually this cavity could not support the overlying soil and the
roof fell in to form a tall ‘chimney’ extending about 400 feet upwards from the
burst point. Very roughly, the volume of the cavity was proportional to the cube
root of the energy yield (assumed proportional to the equivalent weight of the
charge in TNT). For contained explosions the constants for granite are 35 feet/
KT 1/3 , and for limestone 25 feet/KT 1/3 . These figures apply to burst depths below
2000 feet. From the rough data assembled in this way it was concluded that in
deep underground tests, where radioactive gases must not be allowed to escape,