The Study Of Three-dimensional Implicit Time Integration For Enriched Convected Particle Domain Interpolation And Its Application To Slope Problems

Slope failure is a hot and difficult problem in the field of geotechnical engineering.Numerical simulation has become one of the main methods to study slope failure because of its characteristics of economy and flexibility.The enhanced Angle points are set at the material interface to improve the simulation accuracy of the discontinuous deformation problem in MPM.In this paper,the enhancement of the watershed material point method is developed and improved,a three-dimensional implicit enhancement of the watershed material point method program is designed and developed,and the deformation and failure process of mule dump landslide is simulated by using the selfprogrammed program.The main research results are as follows:(1)Based on the theory of 2D explicit enriched convected particle domain interpolation,the programming expression of 3D explicit enriched convected particle domain interpolation shape function and its derivative is derived by using isoparametric element and Gaussian integral method.In view of the advantages of the implicit time integration method in the study of quasi static problems,the theory of the enriched convected particle domain interpolation is introduced into the velocity-based MPM implicit solution framework,and the framework of the implicit time enriched convected particle domain interpolation is given,and the assembly scheme of the global stiffness matrix is explained in detail.(2)Based on the object-oriented C + + language,the program framework of implicit time enriched convected particle domain interpolation is designed,Independently developed source programs of particle class,grid class,initialization class,material attribute class,mapping function class,core calculation class and output class and implicit time enriched convected particle domain interpolation data and related operations is realized.(3)A typical example is given to verify the accuracy of implicit time enriched convected particle domain interpolation program.Compared with FEM and MPM,it is found that implicit time enriched convected particle domain interpolation can greatly improve the calculation step size.The calculation efficiency is lower than FEA in the problem of elastic small deformation,and the computational efficiency and accuracy are higher than FEA in large deformation problems.(4)Using the implicit time enriched convected particle domain interpolation program analyzes the near a Beijing steel processing plant residue pile ostentation and extravagance of the slope deformation and failure process,the results show that the implicit time enriched convected particle domain interpolation can accurately record the slope instability failure process,can make people more intuitive,in-depth and systematic description of the slope failure mechanism and assess the risks of damage.