LPI-based correction factor for response spectrum at liquefied sites

Liquefaction can significantly alter the ground response. However, no existing design spectrum accounts for the severity of soil liquefaction. This work aims to develop correction factors that can be used to adjust code-based design spectra to reflect the specific liquefaction susceptibility of a site. The correction factor is derived as the ratio of response spectra calculated by two types of 1D nonlinear site response analyses: effective stress analysis, which can model porewater pressure (PWP) generation, and total stress analysis. We considered seven real profiles and 200 motions in our analysis. Four combinations of soil nonlinear models and PWP generation models are also utilized to account for epistemic uncertainties. Results show that the response spectral ratio for liquefied sites typically falls below one for periods less than 1-2 s and rises above one for longer periods. Meanwhile, the response spectral ratio reflects the overall liquefaction susceptibility influenced by PWP, factor of safety, and liquefiable layer depth, while the liquefaction potential index (LPI) captures their complex interplay. Accordingly, we propose four LPI-dependent factors: three correction factors for peak ground acceleration, 0.2 s spectral acceleration (Sa), and 1.0 s Sa, and a long-period adjustment factor applicable for periods exceeding 1 s. The correction factors linearly decrease with increasing LPI, while the adjustment factor exhibits the opposite trend. A design spectrum for a liquefiable site can be readily constructed by adjusting the code-based design spectrum using the proposed correction factor, as illustrated in the example. This approach is applicable as long as LPI is available from a simplified liquefaction analysis or a liquefaction hazard map.