Rational PGA modulation for seismic demand assessment of structural systems under far-field long-period ground motions

Far-field long-period ground motions (FLGMs) exhibit pronounced low-frequency content and prolonged duration, posing challenges to conventional peak ground acceleration (PGA)-based intensity measures. This study proposes a rational PGA modulation framework to improve seismic response prediction under FLGMs. A dataset comprising 1351 ground motion records from the Japanese NIED KiK-net database was compiled, and the influence of epicentral distance, earthquake magnitude and site conditions on the intensity characteristics of FLGMs was statistically investigated. Comparative analyses between FLGMs and ordinary ground motions (OGMs) were performed using seismic design spectra from multiple countries, revealing that conventional PGA-based scaling may lead to significant discrepancies in seismic demand estimation. To address this limitation, a weighted scaling factor incorporating structural resonance characteristics was introduced, and a resonance-weighted PGA modulation scheme was developed for FLGMs. The proposed method was further validated through nonlinear time-history analyses of a high-pier continuous rigid-frame bridge. Compared with the Chinese Bridge Code-based PGA modulation approach, the proposed method significantly reduced response dispersion, with the coefficients of variation reduced by 42.6–78.7%. In addition, the consistency between predicted and reference responses was improved, with response ratios reduced by 67.1–79.5%. The proposed approach provides a practical basis for improving seismic demand assessment of displacement-dominated structures subjected to FLGMs, with its effectiveness demonstrated through a high-pier continuous rigid-frame bridge.