Page 25 - Numerical Analysis and Modelling in Geomechanics

6 JOHN W.BULL AND C.H.WOODFORD
This range of diameters is due to the dissipation and absorption of the detonation
gases into the voids behind the fracture surface [35]. Surrounding the void is a
compacted spherical shell of subgrade with an outer diameter some 20% larger
than that of the void [16, 17, 34].
For a camouflet-producing detonation, it is usual for the concrete runway to
show signs of distress. This distress may range from a small hole to extensive
heaving and cracking [25]. This research considers a detonation that causes no
apparent disturbance to the runway. The possibility of determining the position
of the camouflet from the location of the projectile’s entry point into the
subgrade has been considered, but there is no means by which the penetration
path of the projectile can be predicted from the projectile’s surface penetration
point [26].

Camouflet size and material requirements

This research assumes that prior to the detonation, the clay subgrade is
homogeneous, isotropic, elastic and has a California Bearing Ratio (CBR) of 9.
5%. Notwithstanding the non-linearity of the concrete runway and the subgrade,
the ability to carry out linear elastic analysis has proved useful in developing
runway design methods [36]. The predominant justification for using elastic theory
is that under a single load application, most runways will respond in a resilient
manner. Linear elastic analysis can give reasonable solutions for a single load
path if sufficient care is taken in determining the material properties. This is also
true for the investigation of surface subsidence, provided only compaction takes
place [34, 37]. Thus linear elastic analysis is used in this research [36].
This research makes the same reasoned assumptions concerning the
dimensions and material properties of the camouflet and the subgrade as in
previous research published by the authors [8–14]. That is a 213 kg explosive
charge detonates at a depth of approximately λ =−1.388 under a runway and
c
creates a camouflet.
The detonation depth of 8.354 m (1.401W 0.333 m) is greater than the least value
of 8.286 m (1.39W 0.333 m) for no surface rupture and it is accepted that runway
heave could occur for detonation up to 16.555 m (2.78W 0.333 m). Consideration was
given to the range of void diameters of 4.495 m to 7.0948 m (0.754W 0.333 m to 1.
19W 0.333 m) and the value of 6.246 m (1.048W 0.333 m) was chosen. This is the
diameter of the void shown in Figure 1.1. Surrounding the void is a highly
compacted subgrade shell extending from the void diameter of 6.246 m to a
diameter of 7.495 m [16, 17]. Above the void is a conical-shaped volume of
subgrade that was loosened and then resettled to its original level. For the
subgrade displacement at the underside of the runway a diameter of 17.622 m
was used, giving a cone apex angle of 93.06°.
Earlier it was stated that experimental research had shown that for no surface
rupture, the minimum detonation depth for a 213 kg explosive charge was
between 8.286 m and 16.572 m [23, 33]. The purpose of this research is to