Three-dimensional Analysis Method For Slope Stability With Asymmetric Slip Surface And Its Application

The actual slope instability and failure often presents the form of asymmetric three-dimensional slip surface.Because the movement trend of asymmetric sliding body is the coexistence of translation and rotation around the vertical axis,the route of the main sliding must be in the form of curve.Most of the existing three-dimensional slope limit equilibrium methods were proposed by the linear route of the main sliding,and the influence of the curvilinear route of the main sliding on the safety factor was rarely considered.In this study,based on the limit equilibrium theory,two three-dimensional methods were proposed for slope stability with asymmetric slip surface considering the curvilinear route of the main sliding.The research work was carried out from three aspects: data investigation,theoretical research and engineering cases analysis,and the main research results were as follows:(1)The quasi-rigorous and rigorous three-dimensional limit equilibrium methods were proposed for slope stability with asymmetric slip surface.The basic physical quantities for slope stability analysis were obtained by the mapping function relation of the route of the main sliding.The function of normal stresses over the slip surface was assumed.The four equilibrium equations(a force equilibrium equation and three moment equilibrium equations)were established by the equilibrium conditions of the entire sliding body.The quasi-rigorous limit equilibrium solution of three-dimensional safety factor for the slope stability was deduced by an analytical or a numerical method.Furthermore,The Curvilinear coordinate system along the general form route of the main sliding was established,all the equilibrium conditions of the entire sliding body(three forces and three moments)were considered.,and the expressions of basic physical quantities in the equilibrium equations were derived.Optimizing the route of the main sliding,the rigorous solution of the safety factor involved for asymmetric slip surface was obtained.(2)The rationality and feasibility of the present methods were verified by some representative examples.The research results indicated that: a.the safety factor of the curvilinear route was significantly smaller than that of the linear route and the difference was as high as about 20% involved for the three-dimensional slope with significant asymmetric slip surface,which showed that the curvilinear route of the main sliding was of importance to the stability evaluation of three-dimensional slope.b.the more significant the asymmetry of three-dimensional slip surface,the greater the proportion of rotation around the vertical axis for the sliding body,the more significant the bending degree of the route of the main sliding,and the more obvious the asymmetric distribution of normal stresses over the slip surface.There was hardly any rotation around the vertical axis,the route of the main sliding tended to be a straight line and the distribution of normal stresses over the slip surface was symmetric involved for symmetrical sliding body.(3)The proposed quasi-rigorous and rigorous three-dimensional limit equilibrium methods have been successfully applied to the stability analysis of two slope cases with asymmetric slip surface.The analysis results showed that compared with the linear routes of the main sliding,the values of safety factors of the curvilinear routes of the main sliding were smaller,and the relative errors were about 10%～20%.Because the phenomenon of the curvilinear route of the main sliding was considered in the present methods,it was more consistent with the critical sliding state of asymmetric three-dimensional slope.Compared with the rigorous method,the errors of the safety factors calculated by the quasi-rigorous method were within 6%.Within a certain error range allowed by the engineering,the quasi-rigorous solution can be used as the evaluation value of stability analysis.For the engineerings with high accuracy requirements,the rigorous solution should be used.The research results can provide a theoretical reference for the stability evaluation of three-dimensional slope with asymmetric slip surface.