Study On The Rigorous Three-dimensional Limit Equilibrium Method Based On A Common Model

It is the key to analysis slope stability of the slop engineering,that the results directly affect the selection and implementation of the governance program slope.Because of The limit equilibrium method intuition and ease of use,it has become the most commonly used method for slope stability analysis.After years of development,the two-dimensional limit equilibrium of slope stability tends to be mature.However,the problem of the slope transformation and destruction is actually three-dimensional problem,so,through the analysis of two-dimensional model,the calculated results always tend to deviate from the real situation,and estimates the stability on the high side,making necessary waste in the latter governance as the calculation results are conservative.To this end,it is significance that investigate the stability of the slope from the three dimensions of great practical.In recent decades,the study of the three-dimensional limit equilibrium method has achieved fruitful results,but the three-dimensional analysis has more unknowns than the two-dimensional.In order to obtain the solution,it is necessary to reduce the unknown quantity by introducing the hypothesis condition,and the formation of a different three-dimensional analysis methods to different assumptions.This methods are non-strict three-dimensional limit equilibrium analysis method,the results and the actual there is a certain gap.Some scholars try to establish a quasi-strict or strict three-dimensional limit equilibrium method without introducing assumptions or reduce the assumptions and have achieved some results,but have not yet reached the desired results.For this reason,the study of strict three-dimensional limit equilibrium method needs to be further explored and studied.This paper makes deeper studies of the three-dimensional limit equilibrium methods,mainly carried out the following aspects of the work:(1)The unified model establish by Zhang-model extended,extending two equations to three equations in the original model.By introducing the weight coefficients,the three equations are combined into an equation which can reflect the equilibrium of the whole slope along the arbitrary direction and the torque balance and equilibrium of the micro strip in any direction.Through the adjustment of the weight coefficient and the assumptions introduced by the classical non-strict three-dimensional limit equilibrium method,can obtain the integral form of each method.The problem of the boundary is difficult to be processed can avoid when the column is divided,and the number of columns is difficult to be determined.The unified model can obtain a variety of methods in the meantime.(2)Based on the unified model,establish a strict three-dimensional limit equilibrium method that satisfy the three forces and moment balance of the whole slope along x,y and z.The correction coefficients f1,f2 and the reciprocal f3 of the stability coefficient are calculated by using the correction criteria λ1,λ2,λ3 for the direction of the shear force acting on each side of the micro strip,and the correction coefficient f1,f2 and the reciprocal f3 of the stability coefficient are calculated using the strength criterion.Strictly solvable solution of strictly three-dimensional limit equilibrium method.And the formula for finding the normal force between microtones is established.(3)By using the method of spatial interpolation and binary cubic function least squares fitting,obtain the fitting function of the slope and the sliding surface;To find the value of the integral equation using double Gauss-Legendre quadrature formula;To obtaine the optimal solution of the constructed method by the simulated annealing method in the optimization algorithm.(4)The feasibility and accuracy of the strict three-dimensional limit equilibrium method are verified by two examples of computational analysis.