Keywords: underground voids, runways, fatigue life, finite elements, subgrade, camouflet.

This research considers the fatigue life of the subgrade beneath a cement concrete runway when an explosive has detonated in the subgrade beneath the runway. The military requirement is that, following an underground detonation, the runway must be repaired and remain operative for up to thirty days. Having identified that an underground detonation has occurred, the repair team must then identify the changes that have taken place in the subgrade and estimate the fatigue life of both the disturbed subgrade and the apparently undisturbed subgrade.

In this research it is assumed that a detonation takes place in the subgrade such that a camouflet is formed and that the runway does not heave or crack. The subgrade between the void and the runway, the cone of disturbance may or may not be affected, depending upon the depth of detonation. There is a potential inherent weakness in the subgrade due to the void but, if the runway surface remains undisturbed, then compaction of the subgrade has occurred giving the subgrade additional strength. However, as the distance from the detonation point increases beyond the void, the compaction of the subgrade reduces. This reduction is related to the proximity of the runway and the ground surface, plus the ground surface's ability to reflect the compression waves from the detonation.

In this paper it is assumed that prior to the detonation the clay subgrade is homogeneous, isotropic and elastic. Notwithstanding the non-linearity of the concrete runway and of the subgrade, the ability to carry out linear elastic analysis has proved most useful in developing runway design methods. Linear elastic analysis is used in this research, with nonlinearity being included in the fatigue relationship.

This research assumes that a 213kg explosive charge detonates at a range of depths between 8.35m and 18.35m, producing a void with a horizontal diameter of 6.25m and a vertical diameter of 6.18m. Surrounding the void is a highly compacted subgrade shell extending to a diameter of 7.50m. Above the void is the cone of disturbance. The base of the cone, on the underside of the runway, has a diameter of 17.622m. In the cone of disruption, this paper considers the seventeen material property sets that cover a range of subgrade possibilities, from the Young's moduli being increased, to the Young's moduli being reduced.

To determine the serviceability limit-state for the subgrade, the number of load repetitions, the subgrade can sustain is predicted from the maximum downward vertical stress in the subgrade and the California Bearing Ratio [] of the subgrade, in percent, using the equation, .

PAFEC software is used to model the camouflet and perform the computational analysis. For computational modelling purposes the camouflet void is assumed to be almost spherical and enclosed in a cylinder having a flat surface uppermost. The full model is constructed by rotating a three-dimensional slice about its vertical axis using the interactive facilities of the PAFEC software. Three dimensional isoparametric finite elements from the PAFEC 37110 element library are used. These elements have curved faces and are provided in a 20-node brick shape and a 15-node wedge shape. Element nodes have three translatory degrees of freedom.

For six of the seventeen material property sets considered in this paper as not being realistic in the cone of disturbance, this paper identifies that their fatigue life is less that 0.1%. The seventh material property set identified as being not realistic had a reduced fatigue life.

For the ten realistic material property sets, where the Young's modulus has been increased the fatigue life of those zones has also, in general, been increased. Where the Young's modulus has reduced the fatigue life has reduced to between 9 0.1% of the original fatigue life and as the depth of detonation increases the fatigue life at least stays the same, or increases. Where the Young's modulus has not changed, the fatigue life shows, either, an increase, a decrease or no change. However, some of the zones show a reduction in fatigue life as the depth of detonation increases, with other zones showing an increase in fatigue life as the depth of detonation increases.

For sixteen of the seventeen material property sets, the fatigue life of zone 7, the undisturbed subgrade outside the cone of disruption, is reduced for all depths of detonation.

With the exception of one material property set, all the material property sets have one or more zones where the fatigue life is reduced. Thus it is necessary for the repair team to determine the material property set with which they are dealing to estimate the resulting fatigue life.

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