Nonlinear time-history analysis of degrading structures under spectrum-compatible shallow moonquakes synthesized from Apollo records

Shallow moonquakes are characterized by long durations and slow energy attenuation, posing a significant threat to the seismic safety of future lunar surface structures. Based on high-quality short-period records obtained from the Apollo Passive Seismic Experiment, this study employs the continuous wavelet transform to generate strong ground motion time histories compatible with uniform hazard spectra corresponding to return periods of 475, 2500, and 5000 years. Nonlinear single-degree-of-freedom structural models incorporating stiffness and strength degradation are then established. Dynamic time-history analyses under lunar seismic excitations are performed for various structural periods and strength levels to evaluate displacement responses and cumulative damage characteristics. The results indicate that, under prolonged excitations, structural displacement responses and collapse probabilities increase significantly when degradation effects are considered. At the lunar seismic level corresponding to a 2,500-year return period, the oscillating center can shift by more than 20% of the peak response, and residual displacements can exceed the yield displacement, reflecting the cumulative damage induced by long-duration moonquake excitations. Compared with non-degrading cases, the median maximum displacement of degrading structures can increase by over 20%, and the collapse probability of certain models rises significantly. These findings highlight the necessity of explicitly accounting for degradation effects in the seismic design of lunar surface structures. In the development of lunar construction materials and structural systems, particular emphasis should be placed on high-ductility materials and systems that are resistant to stiffness and strength degradation, thereby reducing the failure risk under prolonged moonquake loading.