A simplified vector valued PSHA using principal components for seismic slope displacement hazard estimation

This study proposes a new seismic slope displacement prediction equation based on uncorrelated principal components and implementation in landslide hazard estimation. First, the nonlinear principal component analysis (NLPCA) was performed for 11 mutually correlated ground motion intensity measures (IMs). It was found that these eleven IMs could be represented with three mutually uncorrelated principal components. Additionally, a model to predict the principal components as a function of earthquake magnitude, the closest distance to rupture, average shear wave velocity of soil and rock layers on top 30 m, and fault mechanism was also developed from this work. The corresponding model has total standard deviations of 0.043, 0.013, and 0.011 for PC₁, PC₂, and PC₃, respectively. Further, these principal components and the critical acceleration of slope were used to develop the slope displacement prediction equation. The developed slope displacement prediction model was observed to have lesser variability \(\left({\sigma }_{lnSD}=0.662\right)\) $\left({\sigma }_{\mathit{lnSD}},=,0.662\right)$ , and the attenuation pattern was comparable with other existing relations. Additionally, the application of the equation is demonstrated by developing the slope displacement hazard curves for Shimla City. The slope displacement corresponds to a 2475-year return period exceeding 5 cm for the slopes with a critical acceleration of less than 0.1 g. The proposed slope displacement prediction model based on uncorrelated principal components can simplify landslide hazard estimation significantly.