PSI - Issue 78

Fabio Mazza et al. / Procedia Structural Integrity 78 (2026) 33–40

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Figure 1. Plan and elevation views of the test structure (units in kNs 2 /m and cm).

Two configurations of the base-isolated test structure are examined with horizontal (i.e. BIH) and horizontal and vertical (i.e. BIHV) base-isolation systems, designed assuming twenty identical HDRBs acting alone and in vertical combination with twenty identical HDRLs (Pourmasoud et al. (2020)). A mixed design approach is adopted, referring to lower- and upper-bound properties of HDRBs in compliance with Eurocode 8 (2005) and EN15129 (2009). Further details can be found in Mazza et al. (2024a). The BIH base-isolation system is designed at the collapse prevention (CP) ultimate limit state, adopting a volumetric compression modulus (E b ) and a shear modulus (G) of the elastomer equal to 2000 MPa and 0.5 MPa, respectively, obtaining an effective stiffness isolation ratio (i.e. α Ke =K eV,HDRB /K eH,HDRB , defined as the ratio between the vertical and horizontal effective stiffnesses of the HDRB) equal to 2400. Specifically, requirements of EN15129 (2009) are fulfilled in terms of: γ tot ≤7 and γ s ≤2.5, with γ tot and γ s being the total and seismic shear strains of the elastomer, respectively; P max /P cr ≤0.5, where P max and P cr represent the maximum compression and the critical axial loads, respectively; a ratio between the horizontal design displacement at the CP limit state (d dC =35.2 cm) and the diameter of the internal steel reinforcing plates (D l =66.5 cm) lower than 0.7; ultimate tensile strength of the elastomer (σ tu ) equal to 1 MPa and maximum compressive stress of steel plates (σ s,max ) lower than f yk (275 MPa). In addition to those defined above, design properties of each HDRB of the BIH base-isolation systems are listed in Table 1: i.e. where primary (S 1 ) and secondary (S 2 ) shape factors; horizontal (ξ eH,BI ) and vertical (ξ eV,BI ) equivalent viscous damping ratios and corresponding horizontal (C eH,HDRB ) and vertical (C eV,HDRB ) viscous damping constants; horizontal (K eH,HDRB ) and vertical (K eV,HDRB ) effective stiffnesses. Horizontal (T BI,1H ) and vertical (T BI,1V ) fundamental vibrations periods are equal to 2.21s and 0.077s, respectively.

Table 1: Design properties of the BIH base-isolation system (units in kN, m and s). α Ke S 1 S 2 P cr ξ eH,BI ξ eV,BI K eH,HDRB K eV,HDRB C eH,HDRB C eV,HDRB 2400 34.2 4.7 13559 0.079 0.050 131054 314530272 6700 61100

A HDRL acting in vertical combination with HDRB, but independent on the horizontal and vertical (in tension) responses of the latter, is designed for the BIHV base-isolated test structure, assuming α Ke equal to 200. It results in a vertical fundamental vibration period (T BI,1V ) equal to 0.167s. Indeed, such a value for α Ke represents a suitable solution both in terms of ductility demand and maximum vertical acceleration reduction at the mid-span section of beams, and for protecting HDRBs from cavitation (Mazza and Braile (2024)). Main design properties of the BIHV base-isolation system are reported in Table 2: i.e. thickness (t HDRL ) and primary shape factor (S HDRL ) of the HDRL, assuming constant values of the diameter (D HDRL = 53cm) and elastic modulus (E=5.12MPa) of the rubber; effective viscous damping ratios in compression (ξ eVc,BI ) and in tension (ξ eVt,BI ); effective compression (K eV,c ) and tension (K eV,t ) vertical stiffnesses and corresponding vertical viscous damping constants (C eV,c and C eV,t ).

Table 2: Design properties of the BIHV base-isolation system (units in kN, m and s). α Ke T BI,1V t HDRL S 1,HDRL ξ eVc,BI ξ eVt,BI K eV,c K eV,t C eV,c C eV,t 200 0.167 0.0446 1.65 0.033 0.050 26210856 314530272 18787 28180