Satisfying Boundary Conditions in Homogeneous, Linear-Elastic and Isotropic Half-Spaces Subjected to Loads Perpendicular to the Surface: Distributed Loads on Adjacent Contact Areas

Abstract

This work originates from an experimental program on strain distribution near the loaded surface of an airfield concrete pavement,which provided us with results that contrast with the rheological predictions of Boussinesq for a homogeneous, linear-elastic and isotropic half-space. We already reviewed and extended the original work carried out by Boussinesq in previous papers, to provide a closed form second order solution that enabled us to establish a good match between analytical and experimental findings for point-loads. In this paper, we have explained why Boussinesq’s closed form solution for a homogeneous linear-elastic and isotropic half-space subjected to a point-load is not exact, as believed until now, but approximated. Then, we have shown that our second order solution is the actual solution of Boussinesq’s problem. We have also presented the numerical analysis of second order for rectangular and elliptical contact areas, both loaded by uniform and parabolic laws of external pressure. Moreover, we have evaluated the interaction effect provided on the surface of a concrete half-space by the twin wheels of an aircraft landing gear. Extension of the solution to layered systems is also possible, for improving the knowledge of stress propagation into airfield pavements and promoting more effective design standards.

Keywords

• boussinesq’s problem
• non-uniform load
• interaction effect
• airfield concrete pavement
• twin wheels