Solution And Application Research Of Material Nonlinearity Problem For Numerical Manifold Method

Numerical Manifold Method(NMM)is a powerful numerical calculation method.Finite Element Method(FEM)and Discontinuous Deformation Analysis(DDA)are special cases of NMM.In the nonlinear analysis of numerical manifold method,an appropriate solution method needs to be selected to solve the equilibrium equation.The Newton-Rapson iteration(N-R)method is an important method for finding the root of an equation.Its essence is second order gradient descent,which reflects the characteristic of fast convergence.In this paper,the non-linear numerical manifold problem is taken as the starting point,and the Newton-Rapson iteration method is selected as the solution method.The Newton-Rapson iteration method is used to solve the non-linear numerical manifold problems.And it is applied to slope stability analysis.The specific research work is as follows:Based on the theory of NMM and Newton-Rapson iteration method,the Newton module is developed and some examples of linear elasticity are analyzed.The basic principles of NMM are explained from the four aspects of NMM’s finite coverage system and weight function,balance equation,internal and external force matrix composition,and treatment of fixed boundaries.Several types of nonlinear equation solving methods are introduced,and the relationship and differences between the traditional Newton-Rapson iteration method and the modified Newton method in the iteration method are explained.Based on the object-oriented programming method and the principle of Newton’s method,the related data in Newton module is defined,and the developed Newton module is used as the core calculation module of nonlinear NMM.Combined with NMM,the M-C module and D-P module in the constitutive model are realized.The general constitutive models in geotechnical engineering are summarized.The Mohr-Coulomb(M-C)model and the Drucker-Prager(D-P)model are selected.The basic principles of M-C strength criterion and D-P strength criterion are explained,the corresponding stress-return mapping methods are described,and the relevant class data in the constitutive model is defined.Finally,the M-C module and the D-P module are prepared.Based on the modified N-R method,the nonlinear NMM slope examples corresponding to M-C module and D-P module were selected for stability analysis.The calculation results show that the N-R method can solve the nonlinear NMM problem of homogeneous slopes and heterogeneous slopes,and it has certain accuracy and solution precision.For cracked structures,developed an refinement algorithm that performs mathematical grid refinement in the crack tip area.The refinement levels range from one to four levels.An additional function at the crack tip is introduced to handle the singular physical coverage.In addition,in order to calculate the stress intensity factor,the J integral method is selected.Numerical examples of finite plates with unilateral cracks and finite plates with bilateral cracks show that,under the condition of fixed radius of integral circle of J integral method,the displacement field distribution of crack tip is more refined with the improvement of the level of mathematical mesh infusing around the crack tip,and the solution accuracy of SIF is also gradually improved.The N-R method for solving nonlinear NMM is applied to some engineering examples.The stratified soil slope in the Chengding collapse project of Wailong Village and a dangerous rock mass with structural plane in The Western Taiping Mountain of Zhangjiakou city were selected for stability analysis,and the safety and stability coefficients of the slope and dangerous rock mass under the condition of natural dead weight were calculated.The calculation and analysis of soil slope and rock engineering cases show that the N-R method is feasible in the stability analysis of geotechnical engineering,and the safety and stability coefficient calculated by soil and rock engineering has a certain accuracy.