Page 24 - Numerical Analysis and Modelling in Geomechanics

SURFACE DISPLACEMENTS OF AN AIRFIELD RUNWAY 5
The dome of the void formed at the detonation will collapse in single or
multiple stages [16, 17, 29, 32]. In rock, the time between detonation and dome
collapse may be a few minutes, in water-bearing sands, a few days, while in
unsaturated loamy-water subgrades stability may last for years [26, 29]. Dome
collapse is complete when one of the three following conditions occurs. First, the
height of the collapsed cone develops over the entire detonation to the air–
ground interface with a ground settlement funnel being formed on the exposed
surface [32]. Second, the void is completely filled with collapsed material, but
not extending to the surface. Third, the material in the collapse path is strong
enough to form a temporary stable dome. Which of the three conditions that
occur depends upon the amount and the volume of the compacted and dilated
subgrade. Subgrade compaction occurs close to the point of detonation, with the
amount of compaction reducing as the distance from the point of detonation
increases. Dilation begins to occur as the shock waves approach the air-ground
interface. Hence in the cone of subgrade between the point of detonation and the
air-ground interface there is competition between compaction and dilation which
makes the strength of the subgrade in the cone uncertain and requires a number of
finite element models to be considered. If the camouflet occurs under a runway,
the first condition will cause immediate loss of subgrade support, which will be
obvious to the repair team. For the second condition, loss of subgrade support
will take time to develop, assuming it does actually develop. The second and
third conditions present considerable difficulties for the runway repair team.
They must determine if, when and at what surface loading the dome will
collapse, also the extent of the loss of subgrade support to the runway.
Linked to the difficulties described above and to the possibility of the
detonation of undetected unexploded devices, considerable effort was expended
in the early 1940s on the detection of both camouflets and unexploded devices,
to determine their effect on the subgrade support provided to surface structures
[23, 33]. Research showed that the greater the depth of the detonation, the more
difficult it became to determine the size of the resulting camouflet [23, 33].
Dimensional analysis suggested that the mass of a charge should increase
proportionally to the square root of the depth of detonation to create the same
radius of the zone of disturbance [27]. Further experimental research shows that
for there to be no surface rupture, the detonation depth has to have a minimum
value of between 1.39W 0.333 m and 2.78W 0.333 m, that is between 8.286 m and 16.
572 m for the 213 Kg charge considered later in this chapter [23, 33].
To determine the size of the camouflet void, experimental research suggests
that the void diameter D be between 1.15W 0.333 m and 1.19W 0.333 m [23].
Experimental research also suggests that the apparent camouflet vertical (D ) and
v
horizontal (D ) diameters are equal and between 0.754W 0.33 m and 1.19W 0.33 m
h
[16, 17, 23, 34]. Other experimental research found that the camouflet void was
nearly spherical, with a volume V between 2.738W m 3 and 3.3465W m 3 and a
diameter D between 0.9918W 0.333 m and 1.0711W 0.333 m [33]. Consequently, the
diameter of the camouflet is within the range of 0.754W 0.333 m and 1.19W 0.333 m.