Gravity‐induced stresses near axisymmetric topography of small slope

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Abstract
An approximate, analytical solution is found for the gravity‐induced stresses in the neighbourhood of an axisymmetric topographic feature on an elastic half‐space. The solution is in the form of a perturbation expansion in powers of the characteristic slope, ϵ. The leading order problem, at O(1), is for a distributed normal load on a plane half‐space. The O(ϵ) correction is due to a distributed shear traction. The vertical variation of the near‐surface stress perturbation and the rotation of the principal stress directions are O(ϵ) effects, and thus include contribution s of like order from both the normal and shear loads. The method requires general solutions for axisymmetric, normal and shear tractions of arbitrary radial distribution, and these are found in terms of Hankel transforms.

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