Seismic demand of the liquefaction potential with equivalent number of cycles for probabilistic seismic hazard analysis

Equivalent number of cycles (N_cyc) is a significant factor in assessing liquefaction potential during earthquakes. However, the effects of Ncyc are considered a deterministic value by using a magnitude scaling factor, and the uncertainties of these effects have not been included in the current design practice. This paper calculates N_cyc within the soil mass by deconvolution analysis as a function of the period of soil layer from the ground surface (T_s) and the soil property (b) using a wide range of acceleration time histories. The predictive model of N_cyc is developed as variable dependent on earthquake magnitude, peak ground acceleration (PGA), and ratio of spectral acceleration, T_s and b. Then, the Ncyc model is combined with the ground-motion prediction equation of PGA and the prediction equation of seismic shear-stress reduction coefficient (r_d) to obtain the prediction equation of the seismic demand of the liquefaction potential (K_1cyc). The standard deviation of K_1cyc is also modeled on the basis of the aleatory variability of PGA, r_d, and N_cyc with correlations between these residuals. This predictive model of K_1cyc is implemented in probabilistic seismic hazard analysis (PSHA) to show the impact of these uncertainties on design practice.