Dynamic constitutive models and liquefaction characteristics of soil are critical in the seismic stability analysis on embankment dams. The P-Z constitutive model, which is a kind of the multi-mechanism plastic model based on generalized plasticity, is mainly introduced in this paper. Considering soil as two-phase media, based on the Biot fluctuation theory and the P-Z model, the dynamic analysis formulation of two-phase media is established, and the criterion of soil liquefaction is proposed through investigations, where the generation and dissipation process of soil pore pressure and the variations of effective stress are taken into account. Furthermore, the interface conditions between two-phase media and the other types of medium are derived and the examples of verification are presented.

Some dynamic artificial boundaries were summarized, including the local boundary and the global boundary. The viscous-spring artificial boundary is introduced in dynamic analysis, and the wave input method is analyzed. Finally, the precision and stability of visco-spring artificial boundary is proved by the example.