Characterization of far-field long-period ground motion and rational modulation of PGA in seismic analysis

Far-field long-period ground motion (FFLPGMs) significantly impacts long-period structures that are distant from the seismic source. To systematically identify the key factors affecting the intensity of FFLPGMs, this study selected 1,351 far-field records from the NIED database in Japan and quantitatively analysed the influences of epicentral distance, earthquake magnitude, and site category on the basic intensity parameters of ground motion. Subsequently, this paper conducted an in-depth evaluation of the adaptability of seismic design spectra from China, the United States, Europe, and Japan to both ordinary ground motions and FFLPGMs under different defense intensity levels. The paper found that directly considering the FFLPGMs based on current standards by adjusting the peak ground acceleration (PGA) would lead to significant deviations in the seismic performance assessment of long-period structures. To address this issue, this study introduced a scaling factor (S _F ) into the standard PGA calculation formula, using the resonance curve of reinforced concrete structures as a weighting function. A method for reasonably modulating PGA under FFLPGMs was proposed. The application of the modified method to a continuous steel girder bridge case demonstrated that, compared with the standard design PGA, the modified PGA modulation significantly reduced the dispersion of structural responses, with the coefficient of variation ( CV ) decreasing by 42.47–79.16%. The modified PGA modulation also significantly improves the accuracy of structural responses, with the structural response ratio ( R) decreasing by 68.13–79.47%. The results indicate that the modified PGA modulation method can more accurately reflect the response characteristics of structures under FFLPGMs.