Seismic Demand of the Liquefaction Potential with Equivalent Number of Cycles for Probabilistic Seismic Hazard Analysis

Equivalent number of cycles ($N_{\text{cyc}}$) is a significant factor in assessing liquefaction potential during earthquakes. However, the effects of $N_{\text{cyc}}$ 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 $N_{\text{cyc}}$ 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 $N_{\text{cyc}}$ is developed as variable dependent on earthquake magnitude, peak ground acceleration (PGA), and ratio of spectral acceleration, $T_s$ and $b$. Then, the $N_{\text{cyc}}$ 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 ($K_{1\text{cyc}}$). The standard deviation of $K_{1\text{cyc}}$ is also modeled on the basis of the aleatory variability of PGA, $r_d$, and $N_{\text{cyc}}$ with correlations between these residuals. This predictive model of $K_{1\text{cyc}}$ is implemented in probabilistic seismic hazard analysis (PSHA) to show the impact of these uncertainties on design practice.