Page 27 - Numerical Analysis and Modelling in Geomechanics

8 JOHN W.BULL AND C.H.WOODFORD
The numerical model
To satisfy finite element modelling requirements, slight modifications were made
to the initial camouflet dimensions used in previous publications by the authors
[9–14]. The detonation depth was increased to 8.354 m. The central void of the
camouflet has a horizontal diameter of 6.246 m and a vertical diameter of 6.183
m, giving (D /D ) as 99%. The outer radius of the compacted zone, the interface
h
v
between zones 4 and 5 and 6 and 7 is set at 3.748 m. The radius of the interface
between zones 3 and 4 is 5.149 m, with the radius of the interface between zones
2 and 3 being 6.601 m. The origin of the radii is the detonation point. The
interfaces of zones 2 and 3, 3 and 4, and 4 and 5 are spherical and contained
completely within the frustum of the cone.

Deflection model
For each of the 17 material sets, the depth of the point of detonation λ =−1.388
c
was considered as depth 0. Then the depth of the detonation point was increased
by 1 m, 2 m, 3 m, 4 m, 7 m and 10 m. For each depth, the 17 material sets were
computationally modelled. For each depth an additional material set comprising
the same finite element model, but with the void filled and representing the
subgrade before the detonation took place, was also run. This model was used as
a baseline and as a means of checking the accuracy of the displacements obtained
from material sets 1 to 17. A total of 136 computer simulations were run.
A uniform downward pressure load of 0.1 MPa was applied to the upper
surface of the runway. The origin of the coordinate system for the finite element
model was on the top surface of the runway, immediately above the point of
detonation. Along the runway surface, measured outwards from the origin, were
a series of equally spaced points. The points extended from point 1 at the origin
of the coordinates to point 17 at 8.811 m at the zone 1–8 interface. The distance
between each point was 0.5507 m. The distances from point 1 to points 4, 8, 12,
16 and 20 were 1.652 m, 3.855 m, 6.058 m, 8.260 m and 10.188 m respectively.
For data-recording purposes they were recorded to the third decimal point.
Beyond the zone 1–8 interface, there were 12 further points, 18 to 29, at a
distance of 0.459 m apart. Points 1 to 16 were located over the area affected by
the cone of the camouflet, while points 18 to 29 were located over the subgrade
theoretically undisturbed by the camouflet.
To determine the downward vertical deflection of the runway over the
undisturbed subgrade, the average of the deflections of points 17 to 29 inclusive
were used, provided they did not exceed ± 1 % of the point 29 value. Points 17 to
29 were used as the baseline deflection because it was initially considered that
all the increased deflections due to the camouflet would be confined to points 1
to 16 inclusive, directly over the base of the cone. As the research proceeded it
became clear that for some material sets, the effect of the camouflet extended
beyond point 17. Consequently, for those material sets, not all the points beyond