Theoretical model for limit equilibrium anti-sliding stability of stress vectors on three-dimensional sliding surface based on projection direction extreme principle

According to the projection direction extreme principle, in which the unbalance characteristics of non-collinear forces formed by tangential stress vectors on the complex sliding surface are revealed and the sliding potential energy ratio of the unbalance stress vectors in the equilibrium direction has the maximum, and minimum potential energies in the dissipation direction, in view that the difference of the stress state of the joints on the three-dimensional sliding surface leads to slight difference between direction of the tangential sliding force and that of the anti-sliding force in the micro-element plane, a theoretical model for calculating the stability of a three-dimensional complex sliding surface against sliding in the plastic limit equilibrium is proposed in the direction of the projection-dissipation orthogonal extreme. The three-dimensional expansion for the theoretical model is completed, and the concrete calculation steps of the theoretical model are given. The reasonable reliability of the model is proved by the curve of the extreme value of potential energy ratio between tangential sliding force and anti-sliding force on the sliding surface of typical stability problems and the degree of agreement between the calculated extreme point and the model. The sensitivity of the change of the factors affecting the finite element stress field to the solution of the theoretical model is also discussed. The vector theoretical model is an innovative research on the basic mechanics theory of anti-slide stability, which is of important theoretical development and practical economic value.