ERS: a tool for relating surface-level or bedrock-level spectral accelerations to seismic response and deformation of earth-slope structures

This paper introduces a new tool termed the Equivalent Response Spectrum (ERS) to characterise depth-averaged, frequency-dependent dynamic loadings within subsurface soils for assessing seismic response and deformation of earth-slope structures. Based on over 520,000 nonlinear ground response analyses, generic models are developed to correlate the ERS ordinates with bedrock- or surface-level spectral accelerations, accounting for soil amplification effects and soil-rock impedance contrasts. Mathematical relationships are then established to relate the ERS to seismically-induced sliding displacements and liquefaction triggering. Results show that the proposed models yield generally unbiased predictions, and their standard deviations remain consistently low across training and testing data (0.05-0.25 for ERS and 0.55-0.8 for sliding displacement in logarithmic scale). Comparison with a case history from the 2000 Orta earthquake demonstrates that the ERS-based model reduces the relative error of permanent displacement estimation for the Güldürcek Dam from 76% (via the Newmark rigid-block model) to 20%. Furthermore, the model is applied to assess liquefaction potential of two sites during the 2011 Christchurch earthquake without relying on seismological parameters. This work could thus bridge readily available rock- or surface-level estimates of spectral accelerations and the seismic performance assessment of earth-slope structures.