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.