Circular loads on the surface of a half-space: Displacement and stress discontinuities under the load

Based on the expressions for the surface displacements due to concentrated vertical and tangential forces acting on the free surface of a half-space, available from the well-known Boussinesq and Cerruti elasticity problems, the surface displacements and the surface stresses are derived for a half-space loaded by the vertical and tangential circular ring loads, or by uniform normal and radial shear stresses applied within a circular or annular circular domains. By using different routes of integration, alternative forms of displacement expressions are derived from the concentrated force results. Betti’s reciprocal theorem is used to relate the displacements due to radial and vertical ring loads. The displacement and stress discontinuities under these loads, or along the boundaries of the circular domains within which the uniform stress is applied, are evaluated and discussed. The radial and circumferential components of stress are discontinuous under the load whenever the slope of the radial displacement is discontinuous under that load.