Investigation on artificial boundary problem in the combined finite-discrete element method (FDEM)

The combined finite-discrete element method (FDEM) is an advanced finite and discrete element coupling method, which can commendably simulate the large deformation and fracture process of materials. The explicit solution method in FDEM is naturally suitable for solving dynamic problems, and the key to dynamic analysis is to establish artificial boundary conditions that can be prepared to simulate infinite domain motion. At present, there is only the viscous boundary condition in the original FDEM, but this is only applicable for solving the internal source wave problems (e.g., blasting, mechanical vibration), and there are no artificial boundary conditions for solving the external source wave problems (e.g., earthquake). Therefore, three artificial boundary conditions have been developed in the present study to enhance the ability of FDEM to conduct dynamic response analysis. Firstly, the basic principle of FDEM and the existing viscous boundary condition are briefly introduced. Then, three newly added boundary conditions are introduced in sequence: (1) viscous-spring boundary condition, which can absorb stress wave energy at the boundary and restore the residual displacement to meet the actual engineering; (2) free-field boundary condition, which is coupled with free-field motion to absorb scattered waves at the lateral boundaries of the model, and the algorithms of mesh matching retrieval and coupling calculation are also introduced; (3) static-dynamic unified boundary condition, which can accurately transform the fixed boundary under the quasi-static analysis into the non-reflective boundary condition under the dynamic analysis. Finally, several classic models are built to verify the feasibility of the newly added boundary conditions. The comparison with the shaking table test also shows that the improved FDEM can be used for seismic response analysis under actual earthquakes.