SECED 2015 Conference: Earthquake Risk and Engineering towards a Resilient World 9-10 July 2015, Cambridge UK

INFLUENCE OF HIGH DAMPING NATURAL RUBBER BEARING MODEL ON THE SEISMIC RESPONSE EVALUATION OF ISOLATED

BRIDGES

Laura RAGNI1, Hamid AHMADI2, Alan MUHR2, Enrico TUBALDI3, Andrea DALL'ASTA4

Abstract High damping natural rubber (HDNR) bearings are extensively employed in seismic isolation of both bridges and buildings. In HDNR material, a filler is added to the natural rubber to increase its stiffness and dissipation capacity. However, the addition of the filler induces also a stress-softening behaviour under cyclic loadings related to the internal microstructure breakdown or sometime referred to as damage. This phenomenon may significantly influence the seismic response of isolated systems given its recovery characteristics. The present work aims to study the consequences of such softening behaviour on the seismic performance of bridges isolated with HDNR bearings. For this purpose, the response of an isolated bridge pier under different seismic inputs is analyzed by pointing out the differences between the results obtained by considering two different conditions for the bearings, one assuming the "virgin" rubber properties and the other assuming the "stable" or "scragged" properties. Introduction In the last few decades, laminated high damping natural rubber (HDNR) bearings have been extensively employed for seismic isolation of buildings and bridges because of their low horizontal stiffness and high damping capacity, which allows the isolated vibration period to be shifted away from where the earthquake input has the highest energy content and at the same time controlling the motion of the system by accommodating most of the relative displacements and dissipation of energy in the bearings rather than in the structure. Although design codes allow the use of simplified bilinear or visco-elastic models for describing the response of systems isolated with laminated HDNR bearings (AASHTO 2010, EC8 2005), it is well known that the behaviour of the rubber material, which controls the overall bearing behaviour, is complex (Treloar 1975, Dorfmann and Muhr 1999, Muhr 2005). Among the various features of this behaviour there are dependency on strain-amplitude (i.e. Payne effect), on strain-rate, stiffening at large strains due to crystallization, ageing, ambient temperature effects, and stress-softening.  This latter effect consists of a reduction of stiffness and dissipative properties due to deformation that occurs when a rubber specimen is first loaded and also due to repeated cycling (Mullins 1969, Clark 1997). It is often referred to as the "Mullins effect" or "scragging" in the literature. This effect is more pronounced the higher the content of reinforcing filler, and it leads to strain history dependency. The constitutive behaviour of HDNR has been investigated extensively in the last decades and many different models are available for simulating the stress-strain relation of laminated HDNR bearings. These models can be divided into two categories. The first one includes the material models, based on a three-dimensional large strain continuum mechanics approach (e.g., Govindjee and Simo 1991, Dorfmann and Muhr 1999, Lion 1997, Haupt and Sedlan

1 Assistant professor, Department of Civil Engineering, Construction and Architecture (DICEA), Polytechnic University of Marche, Via Brecce Bianche, 60131 Ancona; l.ragni@univpm.it 2Tun Abdul Razak Research Centre (TARRC), Brickendonbury, Brickendon Lane, Hertford SG13 8NL, UK 3 Post-doctoral researcher, Department of Civil Engineering, Construction and Architecture (DICEA), Polytechnic University of Marche, Via Brecce Bianche, 60131 Ancona; etubaldi@gmail.com 4 Full professor, School of Architecture and Design (SAD), University of Camerino, Viale della Rimembranza, 63100, Ascoli Piceno (AP), Italy, a.asta@tin.it

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2001). The second one includes the device phenomenological models, describing only the behaviour of the HDNR isolation bearing in shear under a constant axial load (e.g., Sanò and Di Pasquale 1995, Ahmadi et al. 1996, Kikuchi and Aiken 1997, Hwang et al. 2002, Tsai et al. 2003, Grant et al. 2004, Abe et al. 2004, Bhuiyan et al 2009). It is noteworthy that very few models are capable of describing the stress-softening effect in HDNR bearing. This is probably due to the fact that seismic isolators are often scragged, that is, subjected to several cycles at a large shear amplitude, as part of a manufacturer’s quality control practices (Thompson et al. 2000). However, experimental results have shown that the rubber can recover its initial (i.e. virgin) stress-strain properties (Kulak et al. 1998, Morgan 2000, Thompson et al. 2000) over time. Thus, the unscragged rubber properties should always be considered as initial condition in the assessment/design of systems isolated with HDNR bearings. However, the recovery behaviour probably depends on the elastomeric compound, on the manufacturing process, and on the temperature, but these effects have not been studied comprehensively. It is usually initially very rapid, and then it continues at slower rates. Furthermore, the larger the strain amplitude, the longer the time to recover the initial virgin properties. Seismic codes and standards suggest different procedures to account for this phenomenon. According to the standard EN15129 (2009) on anti-seismic devices the third-cycle response properties at the design displacement should be used as design properties of the isolators, provided that the dependence of the horizontal characteristics on repeated cycles respects some limitations specified by the code. Other codes, such as EC8 (2005) or AASHTO (2010), suggest that the mechanical properties of the isolation system to be used in the analysis shall be the most unfavorable ones attained during the lifetime of the structure. AASHTO (2010) also suggests simplified analysis procedures based on an equivalent bilinear approximation of the bearing behavior and the use of property modification factors. Despite the importance of this aspect, few works have examined the impact of the stress-softening effect on the seismic performance of isolated structures. In this context, Dall’Asta and Ragni (2008a) have evaluated the dynamic response of single-degree-of-freedom systems whose restoring force is provided by dissipative devices based on high damping rubber, showing that the stress-softening effect should not be neglected in the response assessment and should be considered also in elaborating simplified analysis approaches. Similar conclusions were reached based on experimental testing in Stewart et al. (1999). In this paper, some preliminary investigations are carried out on this topic by considering the case study of an isolated bridge. A non linear process-dependent constitutive model based on the model previously developed by some of the authors of this paper for HDNR damping devices (Dall’Asta and Ragni 2006) is used for the analyses. This model allows separation of the contribution to the response due to the path-history dependent component from the contribution resulting from the stable (i.e., non softening) component and its properties are calibrated against double-shear tests carried out at TARRC on HDNR compounds commonly employed for seismic isolators and satisfying the prescriptions of the current European code for anti-seismic devices (EN15129). The response of the isolated bridge is analyzed under ground motions with different characteristics and by considering two different conditions for the bearings, one assuming the virgin (or fully recovered) rubber properties and the other assuming the stable (or scragged) properties at the design strain amplitude. The results obtained for the two different conditions are compared to evaluate the importance of the stress-softening effect on the bridge performance. HDNR bearing model This section briefly describes the constitutive model used in this paper for the isolation bearings. It is based on the model described in Dall’Asta and Ragni (2006) for HDNR damping devices, modified in order to better simulate the behaviour of the rubber manufactured and tested at TARRC for HDNR isolation bearings and complying with the EN15129 indications. The model provides a relation between the shear strain γ and the shear force τ, based on which the force-displacement relationship of the bearing can be

L. RAGNI, H. AHMADI, A. MUHR, E. TUBALDI, A. DALL'ASTA

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evaluated through simple geometrical considerations. The stress-strain material response is decomposed into two contributions:

mτ+τ=τ 0 (1)

where the former ( 0τ ) is the stable component existing for every strain history, whereas the

latter ( mτ ) describes the transient response (stress-softening effect), degenerating as the strain history progresses. The component 0τ of the stress is described by assuming a rheological model (Figure 1) consisting of a nonlinear elastic spring acting in parallel with two rate-dependent elements and can be expressed in the form:

( ) ( ) ( )0 1 1 2 2, , , ,e v v v vfτ γ τ γ γ γ τ γ γ γ= + +& & (2)

where:

( )( ) ( )( ) ( )

5 3

1 1 1 1

2 2 2 2

, ,

, ,

e

v v v v

v v v v

f a b c

E

E

γ γ γ γ

τ γ γ γ γ γ

τ γ γ γ γ γ

= + +

= −

= −

&

& (3a,b,c)

The first term represents a nonlinear elastic contribution, whereas the other two are the overstresses relaxing in time. At least two terms are required to describe different material behaviours related to long-time (second term) and short-time relaxation (third term). The internal variables γv1 and γv2 describe inelastic strains and their evolution is controlled by the two different laws:

( )

( )1 1 1 1 11

, 0v v v v

γγ ν τ γ γ τ γ

η γ

⎡ ⎤= + ≥⎢ ⎥⎣ ⎦

&& & (4a)

( )2 2 2 2,v v vγ ν τ γ γ=& (5b)

where ( )1η γ is a bounding function for the stresses which has the same role of a bounding surface in higher dimensions (Grant et al. 2004, Abe et al.2004). Its expression is:

( ) 21 0 1η γ ξ ξ γ= + (6)

The constant parameters ν1 and ν2 control the rate of relaxation in time while the other terms control the shape of the τ−γ diagram.

τE=f(γ)

τv1=f(..)

τv2=f(..)

Figure 1. Illustration of the rheological model for stable bearing response.

The stress-softening behaviour is described by introducing a damage type parameter qm through the following law:

( )1 01m m mqτ α τ= − (7)

The evolution laws for the damage parameter is:

L. RAGNI, H. AHMADI, A. MUHR, E. TUBALDI, A. DALL'ASTA

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( ) ( )1 1 mod 1 mod 1/ /m m mq q H qχ χ

ζ γ γ γ γ γ⎡ ⎤ ⎡ ⎤= − −⎣ ⎦ ⎣ ⎦&& (8)

where ( )H g denotes the Heaviside step function, ( )mod/χ

γ γ represents the maximum

value that can be reached by 1mq for cycles not exceeding γ , and modγ is the maximum

amplitude for which the model is deemed valid ( modγ =2.5 for this model). By setting the value

of 1mq equal to its limit value for a given maximum strain amplitude, it is possible to simulate the stable response, i.e. the response after the rubber has been fully scragged so further cycles exhibit no stress-softening for strain amplitudes lower than this maximum amplitude. The constitutive behaviour is completely controlled by the shear strain γ and the internal variables 1vγ , 2vγ , 1mq . Table 1 reports the values of the parameters describing the internal variables evolution. These values have been calibrated based on the results of experimental tests carried out at TARRC on double shear specimens made of virgin HDNR. The tests were based on triangular strain histories with different strain amplitudes and strain rates.

Table 1. HDNR model parameters

a [MPa] b [MPa] c [MPa] Ev1 [MPa] ν1 [MPa-1s-1] ζ0 [MPa] 0.014 -0.050 0.290 1.80 0.0765 0.130

ζ1 [MPa] Ev2 [MPa] ν2 [MPa-1s-1] αm1 ζm1 χ 0.080 0.0680 8.5 2.15 0.25 0.7

The accuracy of the model has been also checked by comparing numerical and experimental results for generic strain histories. Figure 2 reports a comparison between test and model results for a displacement history induced by a far field and near field earthquake on an isolation bearing with vibration period T=2.5s, before and after a scragging procedure carried out at the maximum strain amplitude modγ =2.5. (a) (b)

τ [M

Pa]

γ [−] -3 -2 -1 0 1 2 3 -4

-3

-2

-1

0

1

2

3

4

5

6

test model

τ [M

Pa]

γ [−] -3 -2 -1 0 1 2 3 -4

-3

-2

-1

0

1

2

3

4

5

6

test model

(c) (d)

τ [M

Pa]

0 50 100 150 200 250 -5

5

t [s]

test model

0

τ [M

Pa]

0 50 100 150 200 250 -5

0

5 test model

t [s] Figure 2. Comparison between test and model results: strain history induced by a near-fault earthquake (a) and a far-field earthquake (b) before and after scragging at γ=2.5.

L. RAGNI, H. AHMADI, A. MUHR, E. TUBALDI, A. DALL'ASTA

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It is noteworthy that the proposed model can be easily extended to describe the two-dimensional bearing response. However, a further degree of complexity is added by the anisotropy of the stress-softening effect, which controls the influence of scragging along one direction of loading on the response along another direction of loading (Morgan 2000). Seismic response of base-isolated bridge equipped with HDNR bearing model

Case study The case study considered consists of an isolated bridge with a steel-concrete composite continuous deck 200 m long. The two exterior spans are 40 m long, whereas the two interior spans are 60 m long (Figure 3). The superstructure is designed according to the Eurocodes (Tubaldi and Dall’Asta 2011). The permanent loads acting on it are 16.24 kNs2m-1. The reinforced concrete piers are 6.6 m high and have a circular section with diameter D = 2.2 m and longitudinal rebars corresponding to a reinforcement ratio of 1%. The characteristic cubic resistance of concrete is Rck = 24.9 MPa whereas the bars are made of B450C steel.

40 m 60 m 60 m 40 m

Figure 3. Case study

The isolation system has been preliminarily designed by assuming a linear approximation of the rubber behaviour and by considering an EC8 type-1 response spectrum with soil class C and PGA=0.34g. The design values assumed for the period of the isolated system and for the rubber strain of bearings are Tis=2.5s and γis=1.5 respectively. Figure 4 plots the variation with γ of the effective shear modulus Geff of the HDNR considered in this paper for a cyclic strain history at the amplitude γ and at the frequency 1/Tis. The properties of the equivalent linear rubber model are calculated on the basis of the third cycle and they are: effective shear modulus Geff=0.74 MPa and equivalent damping factor ξeff = 0.17.

Geff [

MPa

]

0.00 0.50 1.00 1.50

2.00 2.50 3.00 3.50 4.00 4.50 5.00

0 0.5 1 1.5 2 2.5 γ [−]

1st cycle 3rd cycle 6th cycle

Figure 4. Variation with amplitude γ of the HDNR effective shear modulus Geff

The isolator area and total rubber thickness are A0 =0.568 m2 (corresponding to a diameter D0 = 0.85 m), and h0 = 0.132 m respectively. Two HDNR bearings are positioned on each pier. The maximum design displacement for the bearings is about dd=0.132·1,5=0.198 m, whereas the design restoring force provided by the pair of a pier bearings is fd = 2·Geff ·A0·γ = 1260.1 kN. The piers have been designed to withstand the forces transmitted from the bearings without yielding. By observing Figure 4 it is evident that the stress-softening effect is relevant for the considered rubber, since both stiffness and strength characterizing the first cycle are significantly larger than those of subsequent cycles. In particular, the effective stiffness

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calculated from the first cycle is about 1.5 times larger that the value calculated from the stable cycle, consistently with experimental data for HDR isolators reported in Constantinou et al. (1999) and Thompson et al. (2000). However, the rubber behaviour is within the limits imposed by current European code for anti-seismic devices (EN15129) prescribing that the ratio between the minimum and maximum value of effective stiffness measured in the cycles between the first and the tenth shall not be less than 0.6.

Numerical model A reduced order model of the isolated bridge, consisting of a single pier with the two relevant isolators and the relevant part of the deck (Figure 5a), is considered to investigate the influence of the path-dependent behaviour of the rubber on the seismic response of the isolated bridge. In particular, a 2-degree of freedom model representing the central pier-isolator system is developed, where both the mass of the pier (mp) and the mass of the relevant part of the deck (M) are taken into account. This model permits the pier and isolator displacements to be described. The pier is represented by a Kelvin model with stiffness kp and damping constant cp (Figure 5b). The value of the stiffness accounting for concrete cracking is kp = 82797.2 kN/m whereas the value of the pier damping constant cp is consistent with a pier damping factor ξp = 5%. The mass lumped at the pier top, mp = 108.6 kNs2/m, corresponds to the sum of the mass of the pier cap and the pier tributary mass. The mass lumped at the isolator top, M = 974.4 kNs2/m, represents the tributary deck mass, i.e., half the mass of the adjacent spans.

1.20 0.80

6.00

1.50

(a) (b)

cp

kp

HDNR

mp M

4.50

6.0

Figure 5. Bridge geometrical properties (a) and model (b).

The HDNR bearing behaviour is described by the model introduced in the previous section. In particular, in order to evaluate the influence of the stress-softening effect two different cases are considered. The first case, denoted as "unscragged", describes the virgin rubber behavior and is obtained by assigning a zero initial condition to the damage parameter qm1. The second case, denoted as "scragged", assumes that the stress-softening effect has exhausted at the design strain amplitude γis=1.5 and corresponds to assigning, based on Eq.7, the initial value of qm1=(1.5/2.5)0.7=0.699. Seismic response evaluation The impact of the softening behaviour of HDR bearings on the seismic response of the isolated bridge is investigated by considering two different groups of 7 real ground motion records. These two groups represent respectively far field (FF) and near-fault (NF) seismic inputs. Table 2 reports general information about the records employed. In Figures 7 and 8 the time histories of the ground acceleration, velocity and displacement are reported for one record of each group. It is possible to observe that, as already known, near-fault records, more precisely their fault normal component, contain pulses and thus are characterized by higher peaks of velocity with respect to far-field records (Jangid and Kelly 2001). In the analyses, each of the ground motion records has been scaled to achieve a value of the spectral displacement ordinate Sd(Tis) at the isolation period of Tis=2.5s equal to the design value of 0.2 m, for a damping ratio equal to ξeff. Figure 6 reports the acceleration spectra and scale factors corresponding to the near-fault and the far-field ground motions, respectively.

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Table 2. Ground motions data.

Name Event Station M R(km) Comp. PGA (g) FF1 Northridge-01 Beverly Hills - 12520 Mulhol 6.69 18.4 FN 0.444 FF2 Northridge-01 Beverly Hills - 14145 Mulhol 6.69 17.1 FN 0.5165 FF3 Northridge-01 Castaic - Old Ridge Route 6.69 20.7 FN 0.5143 FF4 Imperial Valley-06 Calexico Fire Station 6.53 10.4 FN 0.2748 FF5 Imperial Valley-06 Delta 6.53 22 FN 0.2378 FF6 Imperial Valley-06 El Centro Array #13 6.53 22 FN 0.117 FF7 Imperial Valley-06 Niland Fire Station 6.53 35.6 FN 0.1088

Name Event Station M Rrup(km) Comp. PGA (g) NF1 Northridge-01 Rinaldi Receiving Sta 6.69 6.5 FN 0.8252 NF2 Northridge-01 Sylmar - Converter Sta 6.69 5.3 FN 0.6125 NF3 Northridge-01 Sylmar - Converter Sta East 6.69 5.2 FN 0.8283 NF4 Landers Lucerne 7.28 2.2 FN 0.4549 NF5 Northridge-01 Newhall - W Pico Canyon 6.69 5.5 FN 0.4105 NF6 Imperial Valley-06 El Centro Array #6 6.53 1.4 FN 0.3375 NF7 Imperial Valley-06 El Centro Array #7 6.53 0.6 FN 0.7268

Rrup= Closest distance to rupture plane FN=fault normal component a) b)

T [s] 0 0.5 1 1.5 2 2.5 3 3.5 4

S a [m

/s2 ]

0

5

10

15

20

25

30

Name Scale factor FF1 2.78 FF2 0.85 FF3 1.10 FF4 3.83 FF5 1.29 FF6 2.96 FF7 5.26

i-th mean

T [s]

S a [m

/s2 ]

0 0.5 1 1.5 2 2.5 3 3.5 4 0

1

2

3

4

5

6

Name Scale factor NF1 3.60 NF2 3.41 NF3 4.51 NF4 3.40 NF5 5.49 NF6 9.19 NF7 4.71

i-th mean

Figure 6. Acceleration spectra for far field (FF) records and near field (NF) records.

Tables 3 and 4 report the results of the analyses in terms of peak values of bearing shear strain γb , bearing shear force fb, pier top displacement up, pier base shear force fp obtained by considering the scragged and the unscragged bearing properties, for the far-field and near-fault records. With reference to the far-field records, it can be observed that the maximum displacements obtained by considering the unscragged bearing properties are smaller or slightly larger than the maximum displacements corresponding to the scregged case, whereas the maximum forces are generally larger. Conversely, with reference to the near-fault records, the maximum displacements obtained by considering the unscragged bearing properties are always less than the maximum displacements of the scregged case, whereas the maximum forces can be smaller or larger depending on the record considered. The differences between the behaviours of the isolated system subjected to the far-field and near-fault ground motions may be explained by observing Figures 7a and 7b, reporting the responses to the FF7 and NF7 records, respectively. In general, when far-field records are

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applied to the isolated system, one or more cycles take place before the maximum displacement is observed. Thus a part of the stress-softening effect has vanished when the maximum displacement occurs. Differently, when near-fault ground motions are applied to the system, the rubber undergoes only short-amplitude cycles before attaining the maximum displacement following the pulse. Thus, in this case the stress-softening effect strongly affects the peak response.

Table 3. Peak response values for far-field ground motions.

FF records unscragged FF records scragged

acc. γb [-] fb [kN] up [m] fp [kN] γb [-] fb [kN] up [m] fp [kN] FF1 1.003 1346.43 0.016 1610.58 1.142 905.73 0.014 1336.01 FF2 1.389 1772.42 0.021 1743.82 1.245 987.84 0.010 825.39 FF3 1.406 1719.95 0.024 2083.58 1.503 1157.98 0.018 1700.63 FF4 1.037 1310.04 0.015 1401.48 1.363 1104.59 0.016 1467.98 FF5 0.638 986.53 0.014 1137.49 1.507 1196.52 0.016 1359.56 FF6 0.792 1208.31 0.018 1603.77 1.441 1150.22 0.016 1410.26 FF7 1.131 1493.58 0.022 1890.92 1.466 1185.67 0.016 1362.29

average 1.057 1405.32 0.019 1638.81 1.381 1098.37 0.015 1351.73

Table 4. Peak response values for near-fault ground motions.

NF records unscragged NF records scragged

acc. γb [-] fb [kN] up [m] fp [kN] γb [-] fb [kN] up [m] fp [kN] NF1 1.133 1568.22 0.021 1734.22 1.161 915.48 0.011 967.77 NF2 0.708 1182.81 0.016 1301.43 1.581 1292.03 0.017 1417.44 NF3 0.800 1283.32 0.017 1419.71 1.161 932.09 0.012 1026.32 NF4 0.912 1386.50 0.019 1601.65 1.492 1177.52 0.016 1309.65 NF5 0.756 1192.83 0.017 1392.34 1.471 1183.60 0.017 1427.90 NF6 0.840 1319.98 0.017 1428.79 1.693 1393.82 0.020 1627.07 NF7 0.989 1477.54 0.021 1731.86 1.638 1336.44 0.018 1583.59

average 0.877 1344.46 0.018 1515.72 1.457 1175.86 0.016 1337.11 a)

b)

-1.5 -1 -0.5 0 0.5 1 1.5 -1.5

-1

-0.5

0

0.5

1

1.5

γ [-]

τ [M

Pa]

unscragged scragged

-1.5 -1 -0.5 0 0.5 1 1.5 γ [-]

τ [M

Pa]

unscragged scragged

-1.5

-1

-0.5

0

0.5

1

Figure 7. Bearing response for FF7 record (a) and NF7 record (b).

Table 5 reports the ratio between the values of these response quantities of interest for the bridge performance assessment estimated by considering the unscragged and scragged

L. RAGNI, H. AHMADI, A. MUHR, E. TUBALDI, A. DALL'ASTA

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rubber properties. In the case of FF ground motions, the value of the average peak bearing displacement obtained by accounting for the stress-softening effect is 40% lower than the corresponding displacement obtained by disregarding the stress-softening effect, whereas the bearing restoring force is 20% larger. Differently, in the case of NF ground motions, the values of the average maximum displacement obtained by using the two rubber models are more similar to each other (the difference being 30%) but the average value of the maximum force is significantly larger if the stress-softening effect is simulated (the difference reaches the 30%). The pier top displacement up and pier base shear force fp show values and trends consistent with those of the bearing restoring forces.

Table 5. Ratios between the response values obtained by accounting for and by disregarding the stress-softening effect.

FF records: ratio unscragged/scragged NF records: ratio unscragged/scragged acc. γb [-] fb [kN] up [m] fp [kN] acc. γb [-] fb [kN] up [m] fp [kN] FF1 0.88 1.49 1.11 1.21 NF1 0.98 1.71 1.86 1.79 FF2 1.12 1.79 2.15 2.11 NF2 0.45 0.92 0.92 0.92 FF3 0.94 1.49 1.31 1.23 NF3 0.69 1.38 1.40 1.38 FF4 0.76 1.19 0.96 0.95 NF4 0.61 1.18 1.22 1.22 FF5 0.42 0.82 0.84 0.84 NF5 0.51 1.01 0.98 0.98 FF6 0.55 1.05 1.10 1.14 NF6 0.50 0.95 0.87 0.88 FF7 0.77 1.26 1.36 1.39 NF7 0.60 1.11 1.12 1.09

average 0.78 1.30 1.26 1.27 average 0.62 1.18 1.20 1.18 Conclusions This paper analyzes the influence of the stress-softening effect on the seismic response of bridges isolated with HDNR bearings. For this purpose, a non linear process-dependent constitutive model for HDNR bearings is developed, which permits the path-history dependent response contribution to be easily separated from the stable one. The response of a realistic isolated bridge is analyzed under both far-field and near-fault ground motions by considering two cases, one accounting for the unscragged rubber properties, the other assuming that rubber is scragged at the design amplitude prior to the earthquake. It is shown that when the near-fault records are considered, in the case of unscragged rubber properties lower values of the bearing displacements and higher values of the bearing forces are obtained compared to the case of scragged rubber properties. Differently, when far-field records are considered, similar values of the bearing displacements and larger values of the forces are obtained for the unscragged model compared to the scragged model. The results of this study should be extended to cover a wider range of isolated systems and seismic input characteristics, also by considering 2D inputs, and may be useful to calibrate simplified approaches to account for the stress-softening effect in the dynamic response assessment of isolated system. REFERENCES Abe M, Yoshida J, Fujino Y (2004) Multiaxial Behaviors of Laminated Rubber Bearings and their Modeling. II: Modelling, Journal of Structural Engineering, 130(8): 1133-1144.

Ahmadi HR, Fuller KNG, Muhr AH (1996), Predicting response of non-linear high damping rubber isolation systems, Proceedings of the Eleventh World Conference on Earthquake Engineering, Acapulco, Mexico, 23–28 June, paper no. 1836.

American Association of State Highway and Transportation Officials (AASHTO) (2010) Guide specifications for seismic isolation design. Washington, D.C.

Bhuiyan AR, Okui Y, Mitamura H, Imai T (2009) A Rheology Model of High Damping Rubber Bearings for Seismic Analysis: Identification of Nonlinear Viscosity, International Journal of Solids and Structures, 46(7-8): 1778-1792.

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Clark P, Aiken ID, Kelly JM (1997) Experimental studies of the ultimate behavior of seismically-isolated structures, Technical Report UCB/EERC 97/18, University of California: Berkeley, CA, USA.

Constantinou MC, Tsopelas P, Kasalanati A, Wolff ED (1999) Property Modification Factors for Seismic Isolation Bearings, Technical Report MCEER-99-0012, Buffalo, USA.

Dall’Asta A and Ragni L (2006) Experimental Tests and Analytical Model of High Damping Rubber Dissipating Devices, Engineering Structures, 28(13): 1874-1884.

Dall'Asta A and Ragni L. (2008), Dynamic systems with high damping rubber: Nonlinear behaviour and linear approximation. Earthquake Engineering and Structural Dynamics, 37(13): 1511-2526.

Dorfmann AL and Muhr A (1999) Constitutive Models for Rubber I, 65-71, Rotterdam, Balkema.

EN 15129:2009 (2009). Anti-seismic devices, CEN, Bruxelles.

EN 1998-2: Design of structures for earthquake resistance, Part 2: bridges, Bruxelles, 2005

Govindjee S, Simo J (1991) A micro-mechanically based continuum damage model for carbon black-filled rubbers incorporating Mullins’ effect. Journal of the Mechanics and Physics of Solids 39(1): 87–112.

Grant DN, Fenves GL, Auricchio F (2005) Modelling and analysis of High-damping Rubber Bearings for the seismic protection of bridges, Iuss Press, Pavia.

Grant DN, Fenves GL, Whittaker AS (2004) Bidirectional modeling of high-damping rubber bearings, Journal of Earthquake Engineering, 8(1): 161-185.

Haupt P and Sedlan K (2001) Viscoplasticity of elastomeric materials: experimental facts and constitutive modelling, Archive of Applied Mechanics, 71(2-3), 2001, 89-109.

Hwang JS, Wu JD, Pan TC, Yang G (2002) A Mathematical Hysteretic Model for Elastomeric Isolation Bearings. Earthquake Engineering and Structural Dynamics, 31(4): 771-789.

Jangid RS, Kelly JM (2001) Base isolation for near-fault motions. Earthquake Engineering and Structural Dynamics, 30(5): 691–707.

Kikuchi M and Aiken ID (1997) An Analytical Hysteresis Model for Elastomeric Seismic Isolation Bearings, Earthquake Engineering and Structural Dynamics, 26(2): 215-231.

Kulak RF, Coveney VA, Jamil S (1998) Recovery characteristics of high-damping elastomers used in seismic isolation bearings, Seismic, Shock, and Vibration Isolation, ASME Publication PVP-Vol. 379, American Society of Mechanical Engineers, Washington DC.

Lion A (1996) A constitutive model for carbon black filled rubber: Experimental investigation and mathematical representation. Continuum Mechanics and Thermodynamics 8(3): 153–169.

Morgan TA (2000) Characterization and seismic performance of high-damping rubber isolation bearings. CE299 Report, University of California, Berkeley.

Muhr A (2005) Modeling the Stress-Strain Behavior of Rubber. Rubber Chemistry and Technology, 78(3): 391-425.

Mullins L (1969), Softening of rubber by deformation, Rubber Chemistry and Technology, 42(1): 339-362 .

Sano T and Di Pasquale G (1995) A Constitutive Model for High Damping Rubber Bearings. Journal of Pressure Vessel Technology, 117(1): 53-57.

Thomson AC, Whittaker AS, Fenves GL, Mahin SA (2000), Property modification factors for elastomeric seismic isolation bearings, Proceedings of the 12th World Conference on Earthquake Engineering, New Zealand: Auckand. January 2000.

Tsai CS, Chiang T-C, Chen B-J, Lin S-B (2003) An Advanced Analytical Model for High Damping Rubber Bearings, Earthquake Engineering and Structural Dynamics, 32(9): 1373-1387.

Treloar LRG (1975) The Physics of Rubber Elasticity, Clarendon Press, Oxford.