ABSTRACT
This paper presents a complex variable solution of the displacement and stress induced by the excavation of a shallow circular hole in a ground modelled as a gravitational elastic half-plane. Assuming that the diameter of the hole is adequately small so that the initial stress on the perimeter of the hole can be taken to be equal to the initial stress of the center of the hole, the complex integral of the released initial tractions on the perimeter of the hole is derived analytically, first on the half-plane and then transformed via a holomorphic function onto a mapped annulus. The complex potential functions are expressed as Laurent series, with their coefficients determined by using the stress release condition at the perimeter of the hole as well as the traction free condition of the surface of the half-plane. The comparison with numerical solutions for hypothetical problems verifies the analytical solution.
