## 3 Seismic European Standards  
Eurocode 8 for bridges [19] specifies that nominal design properties (DP) of isolator units shall be evaluated according to EN15129 [20], i.e., for elastomeric bearing 3 rd cycle data at the reference condition: a temperature of 23\({}^{\circ}\), a frequency of 0.5 Hz and a shear strain equal to 100%. However, since environmental or behavioral effects (such as temperature, contamination, ageing or repeated cycles) may significantly influence the dynamic properties of the isolator units and, thus, the seismic response of the isolation system, two sets of design properties should be used in the analyses: UBDPs and LBDPs. This variability should be established in accordance with Annex J and Annex J unless different indications are derived by performing the appropriate tests. In more detail, the influence of the following phenomena should be evaluated: ageing (\(f_{1}\)), temperature (\(f_{2}\)), contamination (\(f_{3}\)) and cumulative travel (\(f_{4}\)). Moreover, by assuming a bi-linear behavior of the bearings, the design properties influenced by the above-mentioned factors are the post elastic stiffness (\(K_{p}\)) and the force at zero displacement (\(F_{0}\)), as shown in Figure 2. The recommended values for the most commonly used isolators, i.e., elastomeric bearings and sliding isolating units, are given. For elastomeric isolators, which are the object of this investigation, the recommended values for ageing and temperature are given (as reported in Tables 1 and 2, respectively), while unitary values are suggested for contamination and cumulative travel. Four categories are considered by this code: low damping rubber  
Figure 2: Post elastic stiffness, \(K_{p}\), and force at zero displacement, \(F_{o}\), of the bi-linear model (**a**) and bi-linear models with upper bound, lower bound and nominal design parameters (**b**). bearings (LDRBs) with an equivalent shear modulus at 100% of strain G \(>\) 0.5 MPa; HDRBs1 with an equivalent damping coefficient of \(\xi\) \(\leq\) 0.15, and an equivalent shear modulus at 100% of strain G \(>\) 0.5 MPa; HDRBs2 with an equivalent damping coefficient of \(\xi\) \(>\) 0.15 and an equivalent shear modulus at 100% of strain G \(>\) 0.5 MPa and LRBs. Furthermore, combination factors (\(\lambda_{U,\beta}\)) are defined to account for the low probability of the simultaneous occurrence of all maximum adverse effects, as shown in Table 3 for important classes I (bridges of less than average importance), II (bridge of average importance) and III (bridges of critical importance). The effective UBDPs used in the design are estimated as follows:  
Footnote 1: equivalent damping coefficient of \(\xi\) \(\leq\) 0.15 and equivalent shear modulus at 100% of strain G \(>\) 0.5 MPa; 2 equivalent damping coefficient of \(\xi\) \(>\) 0.15 and equivalent shear modulus at 100% of strain G \(>\) 0.5 MPa. \[\text{UBDP}=max\ \text{DP}_{\text{nom}}\cdot\lambda_{U,\beta}\cdot\lambda_{U, \beta}\cdot\lambda_{U,\beta} \tag{1}\]  
where modification factors \(\lambda_{U,\beta}\) are defined as follow:  
\[\lambda_{U,\beta}=1+(\lambda_{max,\beta}-1)\cdot\psi_{\beta} \tag{2}\]  
For the effective LBDPs and relevant modification factors, \(\lambda_{U,\beta}\), a similar format should be used, in conjunction with \(\lambda_{min,\beta}\). However, for the commonly used elastomeric and friction bearings, it may be assumed in general that \(\lambda_{min,\beta}=1\) and, therefore, that LBDP = \(min\ \text{DP}_{\text{nom}}\). A similar approach is recommended by the European standard on anti-seismic devices [20] by also considering the variation of the dynamic properties of the bearings within the production supply. Here, again, the code specifies that for all the effects (i.e., the variation in temperature or ageing for elastomeric bearings), UBDPs and LBDPs shall be determined from the type tests carried out before the bearing production. However, when such experimental values are not available, the Annex J provides the same reference factors