Deterministic response-band certification of equivalent pulse loads for rockfall impact analysis of high-speed railway bridges

Irregular rockfall impact histories are often represented by simple pulses, although matching peak force and impulse does not ensure an accurate structural response. This study develops a deterministic method for selecting half-sine or triangular pulses for rockfall impact assessment of high-speed railway bridges. A period band determined from bridge responses defines the evaluation domain before pulse selection, and analytical scaling gives the complete amplitude interval satisfying prescribed linear-oscillator response limits. The method separates amplitude mismatch from waveform mismatch and identifies histories that require a more detailed load representation. For 420 finite-element cases, amplitude scaling increases the number of histories meeting response-ratio limits of 0.90–1.15 in the reference band from 283 with peak–impulse matching to 412; 354 histories meet these limits in a shorter-period band. Direct reuse of selected pulses succeeds in 98.02% of transfers from the shorter-period band to the reference band and 62.62% in the reverse direction. Greater temporal dispersion is associated with less scope for extending pulse validity towards shorter periods. In two nonlinear bridge comparisons, reduced histories retaining the original main-impact segment give maximum peak-displacement errors of 4.23% and 0.252% across 24 monitored quantities per case. The method provides a quantitative basis for pulse selection and reuse, with bridge-response comparisons determining the temporal detail needed for engineering assessment.