Theory and practical calculation method for axisymmetric active earth pressure based on the characteristics method considering the compatibility condition

• Published in: Applied Mathematical Modelling Vol. 68; p. 563
• Main Authors: Xiong, G J, Wang, J H, Chen, J Chen
• Format: Journal Article
• Language: English
• Published: New York Elsevier BV 01-04-2019
• Subjects: Axisymmetric flow; Boundary conditions; Compatibility; Earth pressure; Equilibrium equations; Flow theory; Hypotheses; Numerical integration; Strain rate; Superposition (mathematics)
• ISSN: 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2018.11.022

The current theories and calculation method for axisymmetric active pressure have been established according to certain hypotheses. This paper presents a strict theory for this problem with the axisymmetric compatibility condition replacing the current hypotheses, and further develops a practical calculation method for engineering applications. The new governing equations are rigorously derived by substituting the limit stress components under the Drucker–Prager criterion into the equilibrium equations and substituting the strain rate obtained by the flow theory into the axisymmetric compatibility equation. The characteristic lines and characteristic relations are got and the numerical integration method for axisymmetric active pressure is established by introducing boundary conditions. The calculation and derivation indicate that the axisymmetric earth pressure not only depends on boundary load but is also related to boundary velocity. Based on the numerical integration method, the pressure coefficients are investigated in detail, and many new conclusions are found. Finally, a practical calculation formula for axisymmetric active earth pressure is presented based on the linear superposition principle and the function fitting of pressure coefficients. Six sets of experimental data are cited to verify and support the theory and practical method.