Seismic evaluation of arbitrary number of buildings resting on a layered half-space under incident Rayleigh waves

Understanding the Site-City Interaction (SCI) induced by surface wave is vital for accurate seismic analysis and urban planning. Based on the elastodynamics theory and wave equations, this paper proposes a semi-analytical method to investigate SCI effect induced by Rayleigh wave. The proposed approach integrates the Dynamic Stiffness Matrix Method (DSMM) with substructure method, and can effectively model the complex interplay between seismic surface waves, layered half-space, and arbitrary distributed buildings. The feasibility of the proposed method is validated through comparison with numerical results obtained from the Finite Element Method (FEM). Compared with some numerical methods, our method can be easily implemented and does not require artificial boundaries or seismic motion input methods. Furthermore, to demonstrate the applicability for different cases, the analysis of the impact of incident waves with different frequency bandwidths and energy distributions, as well as the effects of different soil layer characteristics on the SCI effect, are conducted. The results indicate that the proposed method can effectively address the structural response and site variation characteristics within a specific area under complex conditions. Given its capabilities, the proposed method has the potential to be a powerful predictive tool for enhancing urban resilience by offering comprehensive seismic risk assessments and targeted hazard mitigation strategies associated with Rayleigh waves.