Numerical simulation of static and dynamic behaviors of saturated sand by an adaptive mesh scheme

Based on the finite element method with a posterior error estimation and the Delaunay triangulation, an adaptive mesh scheme is set up to simulate the saturated sand behaviors when being compressed statically and when being liquefied during earthquakes. The bilinear recovered function, usually being used for quadrilateral elements in superconvergent patch recovery (SPR) error estimation, is confirmed to be available and reliable for triangular element mesh. In both the static and dynamic examples of saturated sand, the changing laws of deformation, strain, excess pore water pressure ratio, etc. due to the adaptive mesh calculation are maintained in the same trend as the normal finite element calculation. The displacement of the reference point is approaching to the exact value as the mesh is regenerated, so is the average relative error of the whole area. The suitable adaptation degree for an initial mesh is discussed and applied to the adaptive numerical simulation of the seismic liquefaction. Also, some improvement for the initial mesh is implemented in the Delaunay triangulation. This adaptive mesh scheme is proved to improve calculating efficiency, and to ensure the desired accuracy as well.