Effects of soil-foundation-structure interaction on fundamental frequency and radiation damping ratio of historical masonry building sub-structures

Large scale simulations and forensic analyses of the seismic behaviour of real case studies are often based on simplified analytical approaches to estimate the reduction in fundamental frequency and the amount of radiation damping induced by dynamic soil-foundation-structure (SFS) interaction. The accuracy of existing closed-form solutions may be limited because they were derived through single degree-of-freedom structural models with shallow rigid foundations placed on a homogeneous, linear elastic half-space. This paper investigates the effectiveness of those formulations in capturing the dynamic out-of-plane response and failure of single load-bearing walls within unreinforced masonry buildings having either a shallow foundation or an underground storey embedded in layered soil. To that aim, analytical predictions based on the replacement oscillator approach are compared to results of two-dimensional dynamic analyses of coupled SFS elastic models under varying geotechnical and structural properties such as the soil stratigraphy, foundation depth and number of building storeys. Regression models and a relative soil-structure stiffness parameter are proposed to quickly predict the frequency reduction induced by SFS interaction, accounting for the presence of an embedded foundation, an underground storey and a layered soil. The effects of SFS interaction are also evaluated in terms of equivalent damping ratio, showing the limitations of simplified approaches. Since the geometric layouts considered in this study are rather recurrent in the Italian and European built heritage, the proposed procedure can be extended to similar structural configurations.