The theoretic solution to elastic half-space subjected to internal circular loading

The elastic half-space problem vertically loaded by internal uniformly distributed circular force is the fundamental theoretical problem of piled foundation engineering. The general solutions of displacement and stress in integral form were derived with Bessel integral transform method. The half-space problem was separated into two parts according to the plane in which the force is loaded. By properly introducing boundary conditions and continuity conditions at the interface between two parts, the theoretical solutions for displacement and stress of the elastic half-space due to internal uniformly distributed vertical loading were given. The formulae of average vertical displacement and vertical normal stress in the loaded area at different depth were put forward for convenience. The numerical results show that the method presented in this paper gives the right solution.