Variation of the fundamental period is regarded as one of the methods to assess the damage of the structures under earthquakes. The inter-relationship among seismic parameters and variation of the fundamental period can identify the potential structural damage of an earthquake. For this purpose, the present paper aimed to study the relations among main seismic parameters, incorporating a variety of information about ground motion and variation of fundamental period. Three RC frames were analyzed under far-fault earthquake records by nonlinear dynamic analyses and mathematical methods applied to assay the correlation between seismic parameters and variation of fundamental period. Based on the results, high correlations were observed between some seismic parameters and variation of fundamental period. Further, based on regression equations, new parameters with a very strong correlation with variations of fundamental periods were achieved, which can be regarded as appropriate indices to estimate the potential structural damage of an earthquake.