Research And Application Of Finite Element Limit Equilibrium Method For Three-dimensional Slope Stability

The stability analysis and safety evaluation of slopes are of great significance for preventing and controlling geotechnical disasters and ensuring the safety of people's lives and property.The actual slope failure has a spatial effect,and the two-dimensional slope stability analysis cannot reflect this failure characteristic.Therefore,a three-dimensional method is needed to analyze the slope stability.At the same time,the three-dimensional method can also solve the problems of difficult selection of two-dimensional cross-sections and overestimation of material strength parameters in two-dimensional back analysis.In order to solve the problem of three-dimensional slope stability,this paper establishes a three-dimensional finite element limit equilibrium method based on the theoretical basis of the two-dimensional finite element limit equilibrium method.Based on the three-dimensional limit equilibrium state,the local safety factor is defined,combined with the necessary and sufficient conditions of the three-dimensional limit equilibrium of the slope,the main sliding direction and the sliding direction of the slip surface,the global safety factor of the slip surface is defined.Two methods of parameterized construction of slope slip surface are given:improved ellipsoid construction method and key point interpolation construction method.Combining the two slip surface construction methods with the particle swarm optimization method,a two-stage search mode for the most dangerous slip surface is proposed.This search mode can search for slip surfaces of any shape,and improves the efficiency and accuracy of the slip surface search.Using an object-oriented programming method,a three-dimensional finite element limit equilibrium method program was written,which decoupled into three calculation parts:the most dangerous slip surface search,slip surface construction and safety factor calculation,and realized the scalability of the program.The program completes the automation of importing the finite element calculation results,realizes the visual output of the calculation results,and can be used for the three-dimensional slope stability analysis of the actual project.Four special calculation examples(slope with weak interlayer,wedge slope,slope with local load on the top and shallow slope)are calculated.The calculation results are compared with the limit equilibrium method and the finite element strength reduction method,and the validity,rationality and superiority of the three-dimensional finite element limit equilibrium method are verified.The influence of mesh sensitivity,Poisson's ratio,dilatancy angle,and boundary conditions on the calculation results is analyzed,and the results of the stress field calculation safety factor obtained by elastic finite element is analyzed for rationality.An engineering example of a tailings pond was selected,and the stress field was calculated by the fluid-solid coupling model finite element method,and the stability analysis of the upstream stacking method and dry stacking method of the main dam slope of the tailings pond was carried out.The influence of different dam construction methods on slope stability is compared,and the reliability and practicability of the three-dimensional finite element limit equilibrium method program are tested.Through the discussion and analysis of the above content,the following conclusions are drawn:(1)The three-dimensional finite element limit equilibrium method can calculate the safety factor of a three-dimensional slip surface of arbitrary shape.For the safety factor of the same slip surface,the result of the finite element limit equilibrium method is slightly larger than that of most of the limit equilibrium methods that adopt simplified assumptions and is similar to the result of the strict limit equilibrium method.The two-stage search method obtained by combining the parametric slip surface construction method and the particle swarm optimization method can find the position of the most dangerous slip surface and the corresponding minimum safety factor.The minimum safety factor obtained by this method is slightly smaller than the safety factor obtained by the finite element strength reduction method according to the calculation non-convergence judgment.(2)The grid size of the sliding surface will affect the safety factor.As the grid size decreases and the number of grids increases,the safety factor gradually converges.The finite element calculation parameter Poisson's ratio will affect the safety factor.As the Poisson's ratio increases,the safety factor increases.When the Poisson's ratio is close to 0.5,the result of the finite element limit equilibrium method is close to the result of the limit equilibrium method,and the two are more comparable.The dilatancy angle has little effect on the safety factor of wedge slope with asymmetric structure surface,but has an effect on the main sliding direction.(3)There is no significant difference between the safety factors obtained by the improved ellipsoid structure slip surface and the key point interpolation structure slip surface.However,the slip surface positions of the two methods are different.It is worth noting that the key point interpolation structure surface can reflect the influence of the model's boundary conditions and geometric properties on the slip surface.The local safety factor distribution on the slip surface obtained by the key point interpolation method is smoother.(4)The three-dimensional elastic finite element limit equilibrium method can be applied to the slope stability problem with a safety factor close to 1.The calculation results of the safety factor and the position of the slip surface are similar to the strength reduction method.The effective stress field calculated by the fluid-structure coupling finite element can be used by the three-dimensional finite element limit equilibrium method to analyze the slope stability under consolidation and seepage conditions.(5)The three-dimensional finite element limit equilibrium method can give a clear safety factor and corresponding critical slip surface according to its safety factor definition formula,which solves the problem of using the same reduction for different soil layers of the tailings dam slope in the strength reduction method.Whether the coefficient is reasonable and the safety coefficient is difficult to distinguish and other issues.The three-dimensional finite element limit equilibrium method can also show the local safety factor,which is helpful for the stability analysis of progressive failure.