Study on the theory of three-dimensional limit analysis of soil and practical calculation

¹ Guangxi Key Laboratory of Geomechanics and Geotechnical Engineering Guilin University of Technology, Guilin 541000, China
² Tianjin Port Engineering Institute Co., Ltd. of CCCC First Harbor Engineering Co., Ltd., Tianjin 300222, China
³ Key Laboratory of Port Geotechnical Engineering, Ministry of Communications, PRC, Tianjin 300222, China
⁴ Key Laboratory of Tianjin Port Geotechnical Engineering, Tianjin 300222, China
⁵ CCCC First Harbor Engineering Company Ltd., Tianjin, 300461 China
⁶ China Key Laboratory of failure mechanism and safety control techniques of earth-rock dam of the Ministry of Water Resources, Nanjing 210029 ;

^* Corresponding author: a Bin Li, lee_binbin@163.com.

Abstract

Based on the stress analysis of a point in space, the stress analysis of a point on a surface is performed, and then the relationship among the normal stress, the shear stress, and the stress component of a point on a surface and the first order partial derivative of the surface equation is deduced. Equilibrium equations of soil columns between the sliding surface and the top surface of the slope are established, which include differential equilibrium equation of force, equilibrium equation of force, and equilibrium equation of moment. These equilibrium equations and Coulomb yield condition can form the fundamental equations of three-dimensional slope stability analysis. Applying the supposition similar to that applied in the simplified Bishop method, a kind of three-dimensional slope analysis method can be obtained. An example is presented to show that the computation method is reasonable and applicable.