Irregular elastic half-plane gravity problem

The analytic solution for stresses in an elastic half-plane with an irregular boundary under gravity is derived in this study. The geometry is treated using a mapping function rationalized from the Schwarz Christoffel transformation and the complex variable method along with the Cauchy integral is used in the derivation. Both Cauchy and logarithmic types of singular integrals, as well as ordinary integrals are evaluated. The body force potential is determined using a restraint condition on horizontal stress at the surface at infinity. The stress functions are decomposed into two parts: a non-holomorphic and a holomorphic one, and are obtained in closed form. Half-planes with finite slopes and steps are considered. Stress concentrations at the toes of slopes of different angles, stress distributions, directions and magnitudes of principal stresses and the Drucker-Prager stress under various internal frictional angles are shown and variation of stresses caused by excavation for slope angles of 30degrees and 60degrees is investigated. (C) 2003 Elsevier Ltd. All rights reserved.