An analytical approach to model Structure–Soil–Structure Interaction (SSSI) of arbitrarily distributed buildings under SH waves

In this work, a simplified analytical framework based on the multiple scattering theory is proposed to model the structure–soil–structure interaction of buildings excited by antiplane shear waves. To this purpose, each building is modelled as a single degree-of-freedom oscillator, whereas the soil as a viscoelastic layer laying on an elastic half-space. By neglecting the soil-foundation kinematic interaction and considering only its inertial counterpart, the coupled response of buildings is modelled using a multiple scattering approach, where the buildings scattered wavefields are described via Green’s functions. The developed analytical framework is exploited to discuss the dynamic response of a single building, evaluating the variation of its amplitude with respect to the characteristic site frequencies. The dynamics of two buildings are then studied by modelling their coupled response. In particular, the interaction between them is investigated as a function of the buildings spacing, mass, and relative stiffness. Finally, the analysis is extended to the coupled response of a cluster of five buildings. Through the discussed examples, it is demonstrated how the proposed methodology can serve as a computationally inexpensive tool for predicting the interaction among vibrating structures under shear antiplane waves propagating at different frequencies.