Slope Stability Analysis Based On Three-dimensional Numerical Manifold Method

The disaster caused by slope loss of stability not only poses a direct threat to people’s life and property,but also accompanies the destruction of environment and natural resources.Because the slope instability is a three-dimensional state,the two-dimensional analysis method is often unable to reflect the actual slope instability process,so the three-dimensional slope stability analysis research has great practical significance.However,the research of slope stability is highly required by the experimental cost,experimental conditions and related experimental personnel.At present,most of them are numerical simulation by finite element method.As a new numerical simulation method,the numerical manifold method not only solves the problems of finite element method,continuous and discontinuous deformation analysis method,but also has better adaptability to solving slope problems.At present,the numerical manifold method is less studied in the three-dimensional field,especially in the three-dimensional slope stability analysis.In view of the above problems,the main research contents of this paper are as follows:(1)Based on the basic principle of finite cover of numerical manifold method,a new method of generating finite cover system of three-dimensional manifold method based on set operation is proposed,which generates three-dimensional manifold element by using block set intersection operation between mathematical mesh and solution area.The concept of common mathematical face of three dimensional manifold element is defined,and three dimensional physical covering system is generated by face set operation of the manifold element with common mathematical face in the same mathematical cover.The corresponding algorithm program is programmed by using object-oriented programming technology,and the numerical example results show that it is feasible to generate the finite coverage system of 3D manifold method by using the principle of set operation.(2)The Newton-Rapson iteration is introduced into the numerical manifold method,and the similarities and differences between the traditional and modified Newton-Rapson methods are expounded.A modified Newton-Rapson iteration module is developed to solve the three-dimensional nonlinear numerical manifold.The hexahedral mesh covering system is used to analyze the three-dimensional linear elasticity,and the results of the example are compared with those of ABAQUS.(3)Based on the linear elasticity of the three-dimensional numerical manifold method,the nonlinear stress-strain relationship of soil materials is considered.The strength reduction method is combined with the numerical manifold method,and the Mohr-Coulomb criterion is used to analyze the stability of three-dimensional slope,which is based on the non-convergence of algorithm program.The results of the example are compared with the results of other methods,which verify that the three-dimensional numerical manifold method is reasonable and feasible for slope stability analysis.