On the axisymmetric Mindlin's problem for a semi-space of granular material

Abstract

The methods of images and Hankel transforms are used to construct solution to an axisymmetric boundary value problem of a semi-space of transversely isotropic (granular) material due to a point force applied at a distanceh beneath its stress free plane boundaryz=0. Exact closed form expressions are determined for the components of displacements and stresses throughout the interior of the granular semi-space. The solution is then used to derive the surface displacements due to a uniformly distributed force over a circle of radius ‘a’ with centre at (0, 0, −h) in the planez=−h of the semi-space. By a suitable choice of material constants and through a limit process as α1, α2 approach 1, the granular semi-space becomes isotropic and the corresponding results derived in this particular case agree with those presented in [14].