Analytical Solution for Axisymmetric Active Earth Pressure Based on the Characteristics Method considering Orthoradial Geometric Condition

Abstract

The current analytical solutions for axisymmetric active earth pressure are based on certain hypothetical relationships between the circumferential stress, the average stress of the meridional plane, and the main shear stress of the meridional plane. To get a stricter analytical solution, the strict mathematical relationship between them is derived based on the circumferential geometric condition, plastic flow theory, and plastic potential theory in this study. A new axisymmetric characteristics theory, which takes into account the friction angle, the dilatation angle of the soil, and the flow velocity, is established. A new analytical solution for axisymmetric active earth pressure is derived based on the new axisymmetric characteristics theory and the hypothesis of the active static state. The solutions developed in this study and the active static-state hypothesis are demonstrated to be reasonably accurate compared with a set of experimental data obtained from the literature. Various comparative analyses were conducted, and many interesting conclusions are obtained; it is found that the analytical solution is greater than the numerical solution. The analytical and numerical solutions for pressure caused by surcharge and weight fall between the solutions of Berezantzev (λ=1) and Cheng (λ=KO), whereas the analytical and numerical solutions for pressure caused by cohesion are greater than those of Berezantzev and Cheng.