Foundation Stability Analysis Using Region-dividing Coupling And Fractional-step Coupling Method And The FEM Implementation

Foundation stability is a multiscale progressive failure process that undergoes multiple stages such as elastoplastic deformation,deformation localization,shear band formation,and foundation instability failure.The strength and deformation characteristics of each stage depend on the physical mechanism of different geometric scales.The theoretical formula of the ultimate bearing capacity of the classical foundation and the ideal elastoplastic finite element method based on the macroscopic continuum mechanics theory cannot reflect the discontinuous characteristics of the foundation instability process,and the finite element method has the grid dependence problem.In contrast,the discrete element method can better reflect the mesoscopic behaviors such as contact separation between particles,particle rotation and flying away,but the engineering model has a large amount of calculation and low computational efficiency.Region-dividing coupling analytical method and fractional-step coupling analytical method is an effective means to reproduce the progressive instability of the foundation.In this paper,the stability of foundation is taken as the research object,and the macroscopic and mesoscopic changes of the finite element foundation model and the discrete element foundation model are analyzed from the macroscopic and microscopic scales.The numerical simulation method is also studied.The main research results are as follows:(1)Through the analysis of indoor triaxial test parameters and Monte Carlo finite element analysis results,the sensitivity of the variability of shear strength index to the stability and bearing capacity of the foundation is explored,and the similarities and differences between the calculation results of different numerical methods are analyzed.The reason for discussing macro-mechanical parameter calibration problems.(2)Using ABAQUS software to analyze the stability of the finite element foundation model,recording the bearing capacity and deformation behavior of the foundation under different foundation settlements,revealing the macroscopic changes of the progressive failure process of the foundation,and analyze the grid dependence problem.(3)Using PFC software to carry out the stability analysis of the discrete element foundation model by using the hierarchical load loading method and the linear displacement loading method respectively,revealing the ground progressive from the mesoscopic phenomena such as particle displacement field,corner field,velocity field,contact and force chain.The advantages and disadvantages of the finite element method and the discrete element method are compared from the aspects of bearing capacity,sliding surface and calculation efficiency.(4)Applying FDM-DEM region-dividing coupling analytical method,fractional-step coupling analytical method based on ideal elastoplastic model and soil damage model to multiscale analysis of foundation stability,and verifying the rationality and effectiveness of multiscale analytical method from stress and displacement continuity of coupling domain.(5)According to the results of different numerical simulation methods in this paper,the intrinsic reasons of bearing capacity and deformation difference are discussed,and the corresponding ultimate bearing capacity of foundation is compared with the theoretical calculation formula of ultimate bearing capacity of classical foundation.