λ -Factors for the Upper and Lower Bound Analyses of Base-Isolated Structures: Historical Review of Code Provisions for Elastomeric Bearings †

: The seismic response of base-isolated structures is notably inﬂuenced by mechanical properties of isolation devices due to their essential role in structural behavior. Consequently, the variability of such properties should be accounted for in the design process. The current seismic codes prescribe a simpliﬁed approach based on structural analyses in two extreme situations resulting from the upper and lower bound design properties of bearings (upper and lower bound analyses). In the case that experimental data are not provided by manufacturers, seismic codes provide the so-called “property modiﬁcation factors” or “ λ -factors”, i.e., modiﬁcation coefﬁcients to be applied to the nominal dynamic properties of bearings to obtain their upper or lower design properties. The aim of this paper is to provide a historical review of values provided for such factors by the main seismic codes by highlighting the limits, as well as some clerical errors, present in some codes. In particular, the European seismic codes are illustrated in detail, i.e., the Eurocode for bridges (EN 1998-2) and product standard on anti-seismic devices (EN 15129). Both these codes account for different sources of variability, such as the bearings production and the environmental and behavioral effects. For all these effects, the same λ -factor values are provided by the two codes, deriving from the second version of the AASHTO guide speciﬁcations for seismic isolation of bridges (AASHTO 1999), which are based on limited and/or old data, especially for high damping rubber bearings (HDRBs), and were never updated in the successive versions. More recent standards are also illustrated, providing different perspectives that deserve attention, even though they require further investigations to be applied in the design practice.


Introduction
The fundamental principle of seismic base isolation is to modify the structural response by introducing a "soft layer" made of isolation bearings able to decouple the soil motion from that of the structure above, which almost behaves rigidly above the isolation system [1][2][3]. Consequently, the behavior of isolation devices plays a fundamental role in the seismic response of base-isolated structures, and the variability of their properties during the service life significantly influences the seismic response of both the isolation system itself and the superstructure. Thus, this variability cannot be neglected in the the case, for example, for the temperature effect and the so-called "scragging" effect (or repeated cycles effect) of HDRBs. Concerning the temperature effect, indeed, a transcription error was made by passing from the American to the European standard. This error was corrected in the updated version of Eurocode 8-part 2 [25] but not in the EN15129 [20]. For the repeated cycles effect, instead, American values were not included in the European standards. In this regard, it is worth noting that the difference between scragged and unscragged properties suggested by the AASHTO code is remarkable, and this aspect has limited the use of this kind of bearings in the USA, especially for strategic structures, such as nuclear power plants and bridges [26][27][28][29]. For this kind of structure, natural rubber bearings (NRBs) or lead rubber bearings (LRBs) are only allowed as alternative systems to friction pendulum (FP) systems. However, this paper explains that such a remarkable effect refers to old bearings (with incomplete curing) that could differ significantly from the current ones. For this reason, the values of AASHTO were not transposed by the European standards; however, alternative values were not provided, leaving a lack of data regarding this aspect. In the last part of the paper, more recent international regulations orientated towards new approaches [30][31][32][33] are examined to provide a complete overview and to open new perspectives. In detail, the indications of ASCE 7 seismic standards for new and existing buildings [30,31] are illustrated. These codes, which are also taken as a reference by high-risk countries other than the U.S., such as Chile, Turkey, and New Zealand, provide updated values of the λ-factors, which, however, must be verified by mandatory experimental tests. Finally, the approach of recent international regulations to elastomeric bearings, the ISO 22726 for buildings and bridges [32,33], is also reported. However, these documents provide few values only, since, following the Japanese approach described in the design recommendations for seismically isolated buildings [34], they specify that the ranges of variation for most of the effects should be defined in agreement between the structural engineer and the manufacturers.

Behavior of HDRBs
HDRBs are composed by alternating layers of steel and rubber; thus, under horizontal loads, they inherit the shear behavior of the rubber compound adopted in their manufacturing. Figure 1 shows the shear behavior of a compound typically used for HDRBs (furnished by FIP MEC) at two different strain amplitudes, i.e., 100% and 150%. As can be observed from the hysteresis loops, the strain amplitude dependence and the repeated cycle effect are not negligible, even though they are limited. Differently, the strain rate dependence is generally negligible in the range of velocities relevant to seismic applications [7,8].  These behavioral effects can be accounted for in advanced numerical models [7,8,11,35,36]. Alternatively, simplified models can be adopted, such as linear models [37] (defined in terms of equivalent linear stiffness, G, and damping, ξ) or bi-linear equivalent models [38,39] (defined in terms of strength at zero displacement, F 0 , and post-elastic stiffness, K p ), by assuming different sets of parameters properly calibrated to simulate these effects. Similarly, for the environmental effects of ageing and temperature, two simplified models can be calibrated to simulate the two extreme conditions (i.e., aged and not-aged conditions or the behaviors under maximum and minimum design temperatures).
In Figure 2a, a general representation of UBDPs, LBDPs and NDPs is depicted, with reference to the bi-linear model. It is worth noting that the stiffness of the bearings directly influences the isolation period, T is , while their dissipation capacity influences the displacements of the bearings themselves. Moreover, both the parameters influence the base shear and the absolute acceleration experienced by the superstructure. Thus, LBDPs usually maximize the isolation system displacements, while UBDPs maximize the isolation system reactions, i.e., the base shear and floor accelerations of the superstructure.  The following sections summarize the code recommendations in the most seismically active counties on the U/L bound approach to account for these sources of variability in the design and analysis of base-isolated structures. The main aim is to illustrate the limits of the current approach of the European codes, which are still based on outdated American standards and present some omissions and transcription errors, and to highlight and promote more modern approaches.

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 3rd cycle data at the reference condition: a temperature of 23°, 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 JJ unless different indications are derived by performing the appropriate tests. In more detail, the influence of the following phenomena should be evaluated: ageing (f1), temperature (f2), contamination (f3) and cumulative travel (f4). Moreover, by assuming a bi-linear behavior of the bearings, the design properties influenced by the above-mentioned factors are the post elastic stiffness (Kp) and the force at zero displacement (F0), 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 following sections summarize the code recommendations in the most seismically active counties on the U/L bound approach to account for these sources of variability in the design and analysis of base-isolated structures. The main aim is to illustrate the limits of the current approach of the European codes, which are still based on outdated American standards and present some omissions and transcription errors, and to highlight and promote more modern approaches.

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 3rd cycle data at the reference condition: a temperature of 23 • , 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 JJ 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 bearings (LDRBs) with an equivalent shear modulus at 100% of strain G > 0.5 MPa; HDRBs 1 with an equivalent damping coefficient of ξ ≤ 0.15, and an equivalent shear modulus at 100% of strain G > 0.5 MPa; HDRBs 2 with an equivalent damping coefficient of ξ > 0. 15 and an equivalent shear modulus at 100% of strain G > 0.5 MPa and LRBs. Furthermore, combination factors (λ U,fi ) 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: where modification factors λ U,fi are defined as follow: For the effective LBDPs and relevant modification factors, λ L,fi , a similar format should be used, in conjunction with λ min,fi . However, for the commonly used elastomeric and friction bearings, it may be assumed in general that λ min,fi = 1 and, therefore, that LBDP = min DP 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 as Annex JJ of [19]. For the production variability, a tolerance of ±20 % is allowed unless a lower variability agreed upon for the factory production control tests. In combining these effects, a combination factor equal to ψ fi = 0.7 is suggested for both the production variability and temperature variation, whereas a factor ψ fi = 1.0 is recommended for the ageing variation. In any case, the ratio between the UBDPs and LBDPs should be less than 1.8 for the elastomeric bearings.
As is illustrated in the next section, the λ-factors currently suggested by both the European codes derive from the second AASHTO edition [21], whose data are based on the report of Constantinou et al. [40]. It is highlighted that these documents, dated back to 1999, were never updated for elastomeric bearings.

Second Edition of AASHTO Guide Specification (1999)
The upper and lower bound properties of isolation bearings were provided for the first time by the second edition of AASHTO [21] to increase the reliability of the design of base-isolated bridges. To obtain such bounding values, property modification factors (λ) were proposed and then used to obtain the adjusted maximum and minimum system property modification factors (accounting for the reduced probability of the occurrence of joint events) by applying the following expressions: where a is the adjustment factor. Based on engineering judgment and on the desire to employ a conservative approach for mission-critical bridges, the following adjustment factors (a) are proposed for bridges: 1.0 for critical bridges, 0.75 for essential bridges and 0.66 for all other bridges. In more detail, λ-factors are provided for different effects (ageing, contamination, travel, temperature and scragging for sliding and/or elastomeric isolators), based on the experimental and theoretical knowledge of the behavior of seismic isolation bearings at the code drafting time. Furthermore, all the proposed values are based on the report of Constantinou et al. [40], containing background information that led to the definition of λ-factor values. In this regard, it is worth noting that, while for sliding bearings, several data are reported and commented, those related to elastomeric devices are limited and briefly reported. In Section 5.6 of [40], "system property modification factors for elastomeric bearings", the authors themselves affirm that for elastomeric bearings, λ-factors strongly depend on the elastomeric compound, that a variety of compounds is used for their manufacturing and that experimental data are scarce. Thus, the values presented in their document and assumed in [21] are primary based on a "proposal of the Authors". In the following subsections, the λ-factors are reported and commented on for each considered effect with reference to elastomeric systems. The proposed values refer to the post-elastic stiffness (K d ) and the characteristic strength (Q d ), corresponding, respectively, to K p and F 0 in the Eurocodes.

Ageing Effect
Concerning the ageing effect, the authors of the report again affirm that "given the rather recent origin of the seismic isolation technology, there is a complete lack of data on aged isolation bearings. During the research several laboratories and in field data are collected for sliding bearings, while very limited data are collected for elastomeric bearings". In detail, the λ-factors for both K d and Q d are assumed equal to 1.1 for LDRBs, 1.2 for HDRBs with small differences between scragged and unscragged properties (smaller than 25%) and 1.3 for HDRBs with large differences between scragged and unscragged properties (larger than 25%, as reported in Table 4). It can be observed that the values suggested by the European codes (Table 1) agree with those proposed by AASHTO ( Table 4) by assuming that HDRBs 1 and HDRBs 2 correspond to HDRBs with small and large differences between scragged and unscragged properties, respectively. Nevertheless, it should be noted that the authors themselves write that the first two values are based on limited data and the last one is mainly based on the engineering judgement. In more detail, the authors cite in their report some papers dealing with old natural rubbers that are not provided with sufficient anti-oxidant properties, as opposed to what happens with modern compounds. The most relevant paper considered by the report is the one of Clark et al. [41], which concerns some tests carried out on some LDRBs and HDRBs in 1983, in conjunction with the construction of the Foothill Communities Law and Justice Center in California. After 12 years of service, some HDRBs were removed from the building and tested again. Although there is uncertainty in the interpretation of the results, since original tests and re-tests were performed with different machine configurations and probably with different rates of loading, the authors conclude that the effective stiffness increment is approximately 25%. Based on this study, they conclude that the mechanical properties modestly increase due to ageing: the increment is in the order of 10% for LDRBs (made by natural rubber) and 20% for HDRBs over a period of approximately 30 years. They also introduce a difference between elastomeric isolators with small or large differences between unscragged and scragged properties. In their opinion, such a large difference is typical of high damping elastomeric isolators characterized by incomplete curing of the elastomer, which implies the continuation of chemical processes in the rubber and, therefore, a potential source for ageing. To account for this aspect, they advanced the proposal of increasing the ageing effect (over the same period) up to 30% for HDRBs with large differences between scragged and unscragged properties.

Temperature Effect
Concerning the temperature effect, the λ-factors assumed in the AASHTO code are reported in Table 5. It is explained in the report that such values are based on results described in [42,43], referring to LDRBs and HDRBs with effective damping less than 15% and moderate differences between unscragged and scragged properties, whereas no data are available for HDRBs with effective damping larger than 15%. Thus, as outlined by the authors, the difference between values of these two kinds of HDRBs (see Table 5) "has been arbitrarily assumed" by the task group writing the code. A further interesting remark of the authors is that all the analyzed studies focus on the effect of low temperature on the properties of elastomeric bearings, neglecting the influence of the duration of exposure to such low temperatures. In more detail, some of them do not report the duration of exposure at all, while others report an approximate exposure time. This aspect introduces a significant source of uncertainty affecting all the proposed data.
Moreover, it should be observed that, differently from the ageing effect, in this case, the suggested values for Q d and K d are different and they coincide with those proposed by the European codes for F 0 and K p (Table 2) (by assuming that HDRBs 1 and HDRBs 2 correspond to HDRBs with small and large differences between scragged and unscragged properties) only if the values referring to K p and F 0 in Table 2 are inverted. This suggests that a transcription error was made when writing the annexes of [19,20]. This error was later corrected in the updated version of the Eurocode 8 [25], but it remains in the EN 15129 [20].

Repeated Cycles Effect
Regarding the repeated cycles effect, it is generally recognized that LDRBs do not exhibit much difference between unscragged and scragged properties. Differently, the additives used in the rubber compound to enhance the damping capacity of HDRBs and the curing process are responsible for a significant loading history dependence of the rubber behavior, leading to a bigger difference between the unscragged (virgin) and scragged (stable) properties. It is also known that rubber bearings recover their virgin properties and that significant recovery occurs within a short period of time. Based on these observations, the authors of the report specify that if nominal properties of HDRBs refer to the scragged condition (i.e., stable hysteretic cycles), the λ-factors may be used to estimate the unscragged (virgin) properties of the isolation bearings. However, at the drafting time of the report, few published results were available in a form that could be suitable for the calibration of the appropriate values of λ-factors. In [44], by testing small scale HDRBs with effective damping less than approximately 0.15, it was found that the λ-factors for both the characteristic strength and the post-yield stiffness were of the order of 1.2 (or even less). However, the authors of the report here again declare that improperly cured bearings may exhibit much higher damping and a much higher ratio between unscragged and scragged properties, as is also confirmed by data reported in [45], relevant to bearings with effective damping in the range 0.15-0.20. Based on these limited data, the factors shown in Table 6 were proposed by the task group writing the second edition of the AASHTO code [21]. It is important to remark that such values of property modification factors for scragging were never adopted by the European codes because they refer to scragged properties, i.e., stable properties, whereas Eurocodes define 3rd cycle data as nominal properties. However, alternative values were not given, thus, in the case where experimental data are unavailable, there are no indications in the European context regarding how to account for the repeated cycles effect.

Updated Editions of AASHTO Guide Specification (2010 and 2014)
The 1999 report [40] first proposed indications to account for the effects of the change in the mechanical properties of isolation bearings, which were implemented in [21], as well as in other successive seismic codes such as [19,20,46]. In 2007, a new technical report, Constantinou et al. [12], was developed to update the previous one, i.e., to better predict the behavioral and environmental effects on seismic isolators and dampers. In detail, Section 12 of [12] focuses on system property modification factors and clearly specifies that the approach based on λ-factors is a simplified one and that the most probable maximum and minimum values of the mechanical properties of isolation bearings should be established by statistical analysis of the distribution of the properties. However, since the exact approach is challenging, the λ-factors approach may be used for most of the base-isolated structures. In this case, it is specified that the maximum and minimum values of the mechanical properties presented in the document are default values that should be verified with appropriate test data and that all manufacturers are encouraged to develop these kinds of tests. However, the default values are also maintained in the case of unavailable experimental data, but here, again, for friction bearings (widely used in American applications), the updated values are based on a large experimental campaign carried out at the University of Buffalo and at Queen's University in Canada and/or on the analyses of the extensive technical literature. Differently, for elastomeric bearings the experimental tests concern LDRBs only (tested at the Buffalo University), while for HDRBs (scarcely used in American applications), few of the new data available in the technical literature are collected and discussed.

Temperature Effect
For the temperature effect on elastomeric bearings, the same references of the past report [40] are reported, except for one paper [47], which was published after 1999 and which investigates the low temperature performance of LDRBs as a function of temperature and duration of exposure for four materials. Based on these studies, the λ-values collected in Table 7 are proposed by specifying that the data for HDRBs are for elastomers named as HDRB a in Table 5. Table 7. λ-factors for scragging, coherently to [12]. However, the task group in charge of updating the AASHTO guide specifications decided to not change values of the previous edition. Thus, in both the 3rd edition [22] and 4th edition [23], the values of Table 5 are maintained.

Repeated Cycles Effect
For the repeated cycles effect, notably influencing the behavior of HDRBs, two further studies [10,48] were analyzed in addition to the references already commented on in the previous section. The first one reports an experimental campaign carried out on 23 moderate-scale rubber bearings with effective damping in the range between 0.05-0.17 and establishes that the scragging effect increases as the shear modulus of rubber decreases and the effective damping increases. The second paper extends the first one and presents results from tests performed on 45 moderate-scale rubber bearings fabricated by six manufacturers using a total of 12 compounds. The outcomes show that the percentage reduction in the effective shear modulus from the first to third cycle strongly depends on the formulation of the rubber compound, the vulcanization procedure used to fabricate the isolator and the imposed strain history. The data reported in these two works suggest that the greater the volume of filler (to obtain high damping and low shear modulus), the greater the potential scragging effect. Furthermore, all rubber bearings recover their virgin properties, but the time to fully recover them depends on the rubber compound, the extent of its curing and the ambient temperature. Finally, experimental cruciform tests also indicate that scragging along one axis significantly influences the response on the perpendicular axis, as was also found in more recent papers [8,11], but here, again, the degree of interaction is strongly compound dependent. Based on these considerations, the values reported in Table 8 are proposed in [12] as defaults ones to apply to full scragged properties (assumed as nominal properties). Differently. for low damping and low modulus elastomers (usually used in lead-rubber bearings), little-to-no scragging is assumed. Basically, the two previous papers [10,48] deftly advise against the use of HDRBs because their load history dependent behavior (leading to the scragging effect) was too compound-dependent and difficult to predict. This is one of the reasons why λ-factors have not been updated in AASHTO guide specifications [22,23].

Ageing Effect
The data reported in [10,48] are also discussed for the ageing effect. In the 2007 report, it is affirmed that HDRBs are generally not significantly affected by ozone and oxygen because they are fabricated with a layer of cover rubber, including anti-oxidants, to protect the core of the bearing from significant infiltrations and that age-related stiffening or hardening is rather due to the vulcanization process of the elastomer, which continues over time. Thus, the percentage of increase in the effective modulus varies depending on several factors, including the level of the initial curing and the temperature. The ongoing vulcanization of the rubber matrix occurs more rapidly in the first few years after the rubber is compounded, while it slows later. Although the authors recognize in their new report that experimental data on this specific topic do not exist, they confirmed the λ-factors of Table 4, including the value of 1.3 for HDRBs with large differences between scragged and unscragged properties. Concerning LRBs, it is confirmed that they generally show an insignificant change in the characteristic strength (which is mainly dictated by the yield strength of the lead core) and a minor (and negligible) increase in the post-elastic stiffness.

ASCE 7 and ASCE 41
As known, AASHTO guide specifications are mainly oriented to bridges; however, the λ-factors approach proposed by this code was assumed also by other American seismic codes focusing on new buildings and existing buildings [30,31], which are also taken as reference for the design of isolation systems in high-risk countries other than the USA, such as Chile, Turkey, and New Zealand. The effects considered by [30] are heating (caused by cyclic dynamic motion), loading rate, scragging and recovery, variability in bearing production, temperature, ageing, environmental exposure, and contamination. As the last versions of AASHTO, this code also specifies that property modification factors should be derived by manufacturer-specific qualification tests data. However, when the manufacturer does not provide qualification test data about property variability (or the manufacturer is unknown), the default lambda factors are suggested by assuming the most unfavorable conditions, characterized by significant uncertainties affecting the isolator unit properties (i.e., friction for sliding bearings, dynamic properties of elastomeric bearings and the yield strength for LRBs). The default λ-factors are also suggested for the most common types of isolators fabricated by quality manufacturers, which can be used in the design phase when the specific manufacturer is not known. However, in this case, the qualification tests about property variability are mandatory and the data provided by the specific manufacturer must agree with those assumed in the design. For HDRBs, it is particularly recommended that the manufacturer presents data on the behavior of the rubber under virgin conditions (immediately tested after vulcanization) so that the scragging property modification factor can be determined. This factor is defined as the ratio of the effective stiffness shown in the first cycle to the effective stiffness of the third cycle, typically obtained at a representative rubber shear strain (e.g., 100%). In this regard, an important remark is reported in the code commentary, where it is explained that this factor is generally equal or larger than 2.0 for rubbers with shear-modulus less than or equal to 0.45 MPa, but it is also recognized that some manufacturers can produce rubber with a shear modulus of 0.45 MPa and a scragging factor approximately equal to 1.2 or lower. Furthermore, it is specified that ageing in elastomeric bearings has in general a small effect if scragging is also low. It is indeed specified that scragging and ageing are related only in the case of manufacturers producing low shear modulus elastomers by incomplete vulcanization. Thus, in the case of experienced manufacturers scragging and ageing may be limited also for low shear modulus bearings. This code also clarifies other important aspects: first, that ambient temperature effects can be ignored for most isolation systems if they are in a conditioned space where the expected temperature does not drop below 0 • C (internal spaces buildings); second, that other variation effects (e.g., velocity, axial load, bilateral displacement and instantaneous temperature due to heating effects) can be considered by adopting advanced numerical models. All these indications are applied to both new and existing buildings, since ASCE dealing with existing buildings [31] completely refers to ASCE 7 [30].
In Tables 9 and 10, the values suggested by the ASCE 7 commentary for new buildings [30] are reported for unknown manufacturers and quality manufacturers, respectively. In detail, λ ae,max/min is the factor that represents the ageing and environmental effect; the λ test,max/min accounts for all the testing effects, while λ spec,max/min is the factor representing the allowed variation in production. The codes also specify how to combine these factors by giving the following expressions: λ min = (1 − 0.75 · (1 − λ ae,min )) · λ test,min · λ spec,min ≤ 0.85 (6) where λ max and λ min are the final factors to be applied to the NDPs.

ISO 22726
A similar approach was suggested by the recently published international standards on elastomeric seismic-protection isolators for bridges [32] and for buildings [33]. First, in these standards, elastomeric isolators are classified by their tolerance on the shear stiffness (which is specified by the structural engineer in the design) by identifying two classes: the S-A class and S-B class, that differ in the allowed tolerance for the production variability. For bridges, a tolerance of ±10% is required for the S-A class, whereas for the S-B class the allowed tolerance is ±20%. The tolerance allowed for buildings are similar: ±15% and ±10% as individual and global requirements for the S-A class, ±25% and ±20% as individual and global requirements for the S-B class. Differently, for the equivalent damping ratio, the code indication is that experimental values should satisfy the requirement specified by the structural engineer in the design. For the other dependencies of shear properties (i.e., shear-strain dependency, compressive stress dependency, frequency dependency, repeated loading dependency and temperature dependency), the general requirement is that the variability is within the specified range agreed upon by both the structural engineer and the manufacturer. Only for the ageing effect of isolation bearings used in bridges is it prescribed that the change in the shear stiffness and in the damping shall be within ±30%. This approach is in line with the design recommendations for seismically isolated buildings edited by the Architectural Institute of Japan [34]. This document clearly specifies the need for performing the design of isolation systems by considering the change in their properties during the service life but without providing any specific values and prescribing that manufacturers carry out tests at factories to give this kind of information on their product line-up, such as, for example, the Bridgestone corporation [49].
In the European context, manufacturers are currently required to respect prescriptions imposed by [20], thus, the ISO 22726 approach indirectly implies that variability ranges allowed for type tests and factory production control tests can be assumed as the maximum variabilities agreed with the manufacturer, unless otherwise specified by the specific manufacturer. However, it is observed that the EN 15129 standard for elastomeric bearings allows the manufacturer to carry out material tests (which are simpler and less demanding) during the qualification procedure to evaluate the effects of frequency, temperature, ageing, and repeated cycles, instead of reduced-scale or full-scale isolation bearings. The results of these tests were collected and commented on in a recent paper of some of the authors of this work [50]; however, the correspondence between the results of the material tests and bearing tests still represents a very sensitive topic to be investigated.

Conclusions
In this paper, a historical review of the approaches proposed by current seismic codes to account for the variability of the dynamic properties of elastomeric bearings is presented. Based on the information collected, the following issues can be highlighted: • in the European context, the informative annexes of Eurocodes propose a simplified approach, based on the so-called λ-factors that can be used to obtain upper and lower bound properties starting from the nominal ones; • the proposed values come from the second edition of AASHTO guide specification, and those related to HDRBs are based on old and/or limited data. • more recent international codes face the problem with a different perspective; • ASCE 7 suggest updated values to be used in the design phase, prescribing that the data of experimental tests concerning property variability provided later by the manufacturer must agree with the values assumed for the design; • the approach followed by international standards for elastomeric isolators, ISO 22726, is similar: the allowed variability range for each specific effect should be agreed upon between the structural engineer and the manufacturer (i.e., established by the structural engineer and verified by the manufacturer during type tests and factory production tests).
In conclusion, it is strongly recommended that in the future versions of the European provisions (which are currently under discussion), the λ-factor values will be updated (by following the ASCE 7 approach) or eliminated (by following the approach of the ISO 22726 international standard). Future actions should also involve the following topics: • form the side of type tests concerning the variability of mechanical properties, it would be important to verify that all the most significant effects for the specific bearing typology are considered (at a device or material scale) and to carefully evaluate the correspondence between material tests (allowed by the product standards during type tests) and tests at the device scale; • at the same time, from the side of numerical analysis, structural engineers and researchers in this field are encouraged to numerically investigate the influence of such variations on the response and reliability of base-isolated structures to establish admissible and reliable variation ranges.
All these efforts will make it possible to design base-isolated structures by properly considering all the uncertainties affecting the bearings during their lifetime, thus, significantly increasing the safety and reliability of such structures.
Author Contributions: All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by L.R., F.M. and L.G. in collaboration with M.G.C. and S.I. (who sheared some experimental data and their knowledge about design and testing requirements of national and international standards on base-isolation) and under the supervision of A.D. The first draft of the manuscript was written by L.R. and all authors commented on previous versions of the manuscript. All authors have read and agreed to the published version of the manuscript.
Funding: Partial financial support was received by the Italian Department of Civil Protection, within the ReLUIS projects 2022-2024.
Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.
Data Availability Statement: All the data analyzed in the current study are all available in national and international published seismic standards and scientific papers, but they can be also requested from the corresponding author.

Conflicts of Interest:
Authors Castellano, M.G. and Infanti, S., working for FIPMEC S.R.L. as coordinator of Academy unit and Test Laboratory director, respectively, declare they have no financial or non-financial interests. The other authors have no relevant financial or non-financial interests to disclose.