A rigorous characteristic line theory for axisymmetric problems and its application in circular excavations

Abstract

The existing approaches to solving axisymmetric active earth pressure problems by applying characteristic line theory are based on certain subjective hypotheses, and the resulting solutions for axisymmetric active earth pressure are not rigorous. In this paper, by introducing the compatibility equation in place of various hypotheses, a rigorous characteristic line theory of axial symmetry is established and applied in the calculation of axisymmetric earth pressure. The limit equilibrium equations derived are based on the limit stress components satisfying the Drucker–Prager yield criterion. The limit compatibility equation derived is based on the flow theory, the plastic potential theory and the compatibility equation. By solving the limit equilibrium equations together with the limit compatibility equation, general solutions for the characteristic line and characteristic relationship are found. By introducing boundary conditions, the axisymmetric active earth pressure is obtained, which takes into account the dilatancy angle and the radial flow velocity of the stress boundary. A comparison with existing methods and with experimental data indicates that this method is more accurate than existing methods. Finally, the earth pressure generated by weight, surcharge and cohesion is investigated and many interesting conclusions are drawn. In a shallow excavation, the earth pressure shows a nonlinear development, and it shows an almost linear development in a deep excavation. The pressure produced by weight is affected significantly by the friction angle and the dilatancy angle, and the pressure produced by surcharge and cohesion is greatly affected by the friction angle and the radial flow velocity of the free boundary.