Study on a Seismic Input Method for Layered Soil with Viscoelastic Artificial Boundaries Based on the Path Cumulative Amplitude Coefficient

To improve seismic input accuracy in layered soil, this study proposes a method based on the path cumulative amplitude coefficient within a viscoelastic artificial boundary framework. Retaining single reflections at interfaces and subsequent transmissions, it selects and truncates paths using cumulative amplitude coefficients, accounting for amplitude variations, delays, spatial phase differences, and mode conversion. Free-field responses are transformed into equivalent nodal forces. Harmonic wave analyses of three-layer soil under SV and P incidence at 0°, 10°, and 20° yield displacement histories with mean normalized root-mean-square errors below 2% and mean Pearson correlation coefficients of at least 0.996. For El Centro excitation at 20°, absolute relative peak-displacement errors do not exceed 0.61% with a threshold of 0.001. Lower thresholds produce a convergence trend with diminishing accuracy gains and increasing path counts and input-processing costs. Under identical prescribed incident SV wave intensity, the Pingyao Ancient City Wall example shows that 10° incidence causes progressive peak delays along the wall, reduces displacement peaks and tensile damage in the incident-wave-side flanking tower, and increases displacement and torsion in the central and back-wave-side towers compared with vertical incidence. The method enables an adjustable accuracy-cost tradeoff for spatially non-uniform seismic response analysis at horizontally layered sites.