PSI - Issue 78

Stefano Bracchi et al. / Procedia Structural Integrity 78 (2026) 745–752

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3. A lumped parameters model for SFSI 3.1. Seismic site response analysis

The Local Seismic Response analysis was carried out with an Equivalent Linear approach using code STRATA (Kottke and Rathje 2008). For the purposes of this paper, earthquake levels IML 2-4-6 were considered. For each of them, the average profiles of the shear modulus and damping ratio mobilized by the passage of the seismic waves were therefore defined. In Fig. 2, in addition to the aforementioned profiles, the trends of the mobilized average shear strains,  , are shown, which are compatible with the limit values for all the PGA levels considered for risk analysis of this building.

Fig. 2. Results of seismic site response analysis for IML 2-4-6.

3.2. Foundations impedances Code Dynamat 3.0 (Ensoft 2017) based on the consistent boundary matrix method (Blaney et al. 1976) is adopted to compute foundation impedances. Kausel et al. (1978) have shown that most of non-linearity occurs as a result of the earthquake motion and not as a result of soil-structure interaction. Thus, the soil properties consistent with the mobilized free-field strain levels may be also used without further modification to account for the additional soil motion imposed by the oscillation of the structure. Based on the above, a set of impedance functions is evaluated for each IML adopting as starting point the average shear stiffness and damping ratio profiles mobilized by the passage of seismic waves. The width and the depth of the foundation beam supporting the masonry panels are explicitly taken into account. Also, the foundation beam is idealized as a massless, rigid-body with the same length of the panel and a height equal to its depth from ground surface. As evident from Fig. 1, the symmetry of the problem allows to reduce the overall number of panels to be analyzed. As an example, the shaded lines in Fig. 3 shows the real and imaginary parts of the horizontal, vertical and rotational impedance functions of the foundations of masonry panels No. 127 (b = 2.25 m) and No. 206 (b = 6.5 m) for IML 2. Noticeably, the interval where the imaginary part of any function remains constant is associated with soil hysteretic damping; beyond a cut-off frequency (natural frequency of the subsoil in shearing oscillations for the swaying mode), the effect of radiation damping is prevailing, and the imaginary part varies almost linearly with the frequency excitation. 3.3. Calibration of LPMs In this study, each masonry panel of the URM structure is modeled as an independent shallow foundation. For every pier and each selected IML, a dedicated visco-elastic LPM is calibrated to account for the effects of SFSI under