PSI - Issue 78

Giulia Giuliani et al. / Procedia Structural Integrity 78 (2026) 952–959

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The preliminary design of the isolation system is performed using an equivalent single-degree-of-freedom (SDOF) model, with the superstructure idealized as a rigid mass. High Damping Rubber Bearings (HDRBs) are designed assuming a nominal shear modulus of G = 0.4 MPa and an effective damping ratio ξ = 15%. Where applicable, Flat Sliding Bearings (FSBs) are included through equivalent linearized stiffness and damping contributions, based on a constant friction coefficient of 1%. Spectral displacement demand is estimated via linear spectral analysis using the RotD50 horizontal spectrum, amplified by a factor of 1.3 to obtain an equivalent RotD100 representation. The target isolation periods are set to 2.5 s and 3.5 s for the 3-story and 9-story buildings, respectively. The total rubber thickness H r of the HDRBs is computed to satisfy a target design shear strain γ d =2.5, aimed at minimizing the overall bearing height. A primary shape factor S1=20 is adopted, consistent with common commercial values in Europe. The number and size of HDRBs are selected to ensure compliance with the European standard EN 15129:2009, requiring a secondary shape factor S2>3.5 and a displacement-to- diameter ratio δ=d/D<0.7 . The resulting design configurations, including the number of bearings and sliders, as well as HDRB dimensions, are summarized in Tables 3 and 4. As expected, isolation displacement demand increases markedly as the distance to the fault decreases. To maintain the target shear strain γ d , the total rubber thickness H r must be increased. To preserve the isolation system’s lateral stiffness, the rubber area (and hence the bearing diameter D) must also increase. However, if the number of bearings remains constant, increasing diameter leads to a reduction in the secondary shape factor S2, potentially violating the stability threshold of 3.5 for near-fault cases. Indeed, without design adjustments, both the 3-story and 9-story buildings exhibit S2 values below the acceptable limit for the 0 km and 5 km scenarios. To resolve this, an increased number of FSBs is introduced for the near-fault configurations (0 km and 5 km), thereby reducing the shear strain demand on individual HDRBs and ensuring S2>3.5. Conversely, for the 15 km and 30 km cases, the lower displacement demands allow the use of HDRBs alone, resulting in S2 values well above the minimum requirement. This is due to the effective shear strain being reduced below the target value of 2.5%, as will be shown in the subsequent stability domain analysis.

Fig. 4. Plan view of the case study.

Table 4. Results of the isolation system design for the 9-storey building R JB [Km] D [mm] Hr [mm] S2 n HDRB n FSB d [mm] γ d 0 1049 290 3.62 18 10 724 2,50 5 857 236 3.63 22 6 590 2,50 15 587 141 4.16 28 0 353 2,50 30 467 89 5.23 28 0 223 2,51

Table 3. Results of the isolation system design for the 3-storey building. R JB [Km] D [mm] Hr [mm] S2 n HDRB n FSB d [mm] γ d 0 786 211 3.73 14 14 527 2,50 5 619 168 3.68 18 10 420 2,50 15 374 95 3.92 28 0 238 2,51 30 290 57 5.06 28 0 143 2,51