Application Of Three-dimensional Upper Bound Mechanism Of Slope And Its Discretization

On the basis of upper bound analysis and the plastic mechanical characteristics of soil,the stability analysis of the three-dimensional slope is presented in this paper.The genetic algorithm is used to obtain the optimal value of the three-dimensional slope,such as the safety factor,critical height,stability number and so on.After verifying the reliability of the algorithm,the stability of the three-dimensional slope with the consideration of reinforcement and the nonlinear failure criterion is further carried out,and the practical advice is also provided for practical use according to the conclusions.Finally,a three-dimensional slope discrete model based on a spatial discretization technique is proposed.The main research works in this paper can be detailed as follows:（1）The mechanism of the three-dimensional slope with the shape of horn is introduced,and the relationships among the critical height,the stability coefficient,the strength parameters and the three-dimensional characteristic parameters of the slope are expounded.The calculation formulas of internal energy dissipation rate and external force work rate of the three-dimensional slope,considering the volume strain of the damaged part,are derived.And explicit expressions of the critical height and stability coefficient of the slope are given.Also,the genetic algorithm is used to program,calculate and analyze the stability of the three-dimensional slope.（2）According to the mechanism of the three-dimensional slope with the shape of horn,the stability of the three-dimensional reinforced slope considering the nonlinear failure criterion under different reinforcement modes is studied.And the corresponding explicit expressions of the critical height are derived.MATLAB is used to program,calculate and analyze the combined effect of nonlinear parameter m,uniform reinforcement strength k₀ on slope stability.The practical suggestions are also provided for construction and design of slopes.（3）In terms of the spatial discretization technique,three-dimensional slope discrete model with"point to point"is proposed.The calculation formulas of internal energy dissipation rate and external force work rate of this mechanism are derived.Combining strength reduction technique and bisection method,a program for calculating the safety factor is compiled based on genetic algorithm.The safety factors of slope under different geometric and strength parameters are given,and the results are compared with the traditional continuous failure mechanism.The agreement of the results shows that the three-dimensional discrete slope model proposed is feasible.