Prediction equations for the effective number of cycles of ground motions for shallow crustal earthquakes

The number of ground motion cycles is one of important characteristics of seismic loadings. This paper presents new prediction equations for the effective numbers of cycles using the mixed-effects model and 7447 ground-motion recordings selected from the NGA-West2 database. Four measures of the effective numbers of ground motion cycles, including two absolute and two relative measures, were computed based on the rainflow range-counting approach. The proposed functional forms employ four predictor variables consisting of moment magnitude M, rupture distance Rrup, site condition parameter Vs30, depth-to-top-of-rupture parameter Ztor, and a rupture directivity term Idir. An additional sediment depth parameter Z1 is incorporated in the predictive model for the absolute measures. The proposed models are applicable in predicting the effective numbers of cycles subjected to shallow crustal earthquakes with M ranging from 4 to 7.9, and rupture distance up to 300 km. It is also found that the standard deviations of the relative measures are much smaller than the absolute ones, indicating a higher level of predictability for the relative measures of ground motion cycles. •Definitions of the effective numbers of ground motion cycles: relative and absolute.•Exponent coefficients of 2 and 3 are considered for computing numbers of cycles.•Predictive models are developed for numbers of cycles based on NGA-West2 database.•The performance of proposed models is examined and compared with existing models.