Abstract: The shaking-induced vibration energy and below count of standard penetration tests are two key factors for evaluating the liquefaction potential of sand. A revised model based on Zeeman equation of cusp catastrophe, which can display the development of liquefaction, is established. In the proposed model, the ratio of shaking-induced pore water pressure with effective confining pressure is taken as the state variable while the earthquake-induced energy function modified by earthquake duration and the below count of SPT corrected by the clay content and overburden confining pressure are taken as two individual controlling variables. In the study, triggering condition of liquefaction based on pore water pressure, development pattern of pore water pressure induced by cyclic loading under undrained condition achieved by experimental tests and seismically-incuced damage records of liquefaction observed in previous earthquakes are taken into account. Compared with the conventional cusp model widely employed in engineering practice, an additional term and three non-unity coefficients are included in the revised model. Therefore the fundamental feature of Zeeman equation and the linear correlation between two independent variables are fully contained in the proposed model and furthermore the model can adequately simulate the liquefaction development. Based on the proposed model, the statistical method based on the validation hypothesis for controlling first type of error is used to define the related parameters, bifurcated curve and transformation relationship between the two coordinate systems. The proposed model is verified by the test results. It is shown that the proposed model is reasonable and can be used to predict liquidation potential of sites in practice.