Seismic isolation of bridges using isolation systems ... - Springer Link

Bull Earthquake Eng (2007) 5:491–509 DOI 10.1007/s10518-007-9044-3 ORIGINAL RESEARCH PAPER

Seismic isolation of bridges using isolation systems based on flat sliding bearings Mauro Dolce · Donatello Cardone · Giuseppe Palermo

Received: 28 August 2006 / Accepted: 26 July 2007 / Published online: 7 September 2007 © Springer Science+Business Media B.V. 2007

Abstract Three different isolation systems (IS’s) for bridges and viaducts are considered in the present study. All of them are made of steel-PTFE sliding bearings (SB) to support the weight of the deck and auxiliary devices, based on different technologies and materials (i.e. rubber, steel and shape memory alloys), to provide re-centring and/or additional energy dissipating capability. An extensive numerical investigation has been carried out in order to (i) assess the reliability of different design approaches, (ii) compare the response of different types of IS’s, (iii) evaluate the sensitivity of the structural response to friction variability due to bearing pressure, air temperature and state of lubrication and (iv) identify the response variations caused by changes in the ground motion, bridge and isolation characteristics. The nonlinear time-history analyses have been carried out using a simplified pier-deck model, where the pier is modelled as an elastic cantilever beam and the mass of the deck is connected to the pier through suitable nonlinear elements, simulating the behaviour of the IS. Both artificial and natural seismic excitations have been used in the nonlinear dynamic analyses. Keywords Bridges · Sliding bearings · Seismic isolation systems · Performance-based design · Shape memory alloys

1 Introduction There are several conditions that, alone or together, may lead to the use of seismic isolation in a bridge: (i) to avoid brittle failure in some piers, (ii) to avoid concentration of damage in non-regular bridges (e.g. continuous bridges with piers of significantly different height), (iii) to reduce spectral accelerations in very stiff piers, (iv) to increase the energy dissipation capacity of the bridge in order to reduce strength and displacement demands of piers, etc. Obviously, the first two conditions mainly apply to the retrofit of existing bridges, while the latter two conditions are better related to the design of new bridges.

M. Dolce · D. Cardone (B) · G. Palermo DiSGG, University of Basilicata, Macchia Romana Campus, Potenza, 85100, Italy e-mail: [email protected]

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In principle, the design of a seismically isolated bridge is simpler than the design of a conventional bridge, as all the structural members (with the obvious exception of the isolation system (IS)) can be assumed to behave elastically. On the other hand, this condition makes the q-factor approach of conventional bridges (CEN 1998) inadequate for the design of isolated bridges. Alternative design procedures are then needed. When designing an isolated bridge, the bridge geometry and the pier/deck sections are usually known, as they result from non-seismic load conditions. Thus, the pier strength and the characteristics of the IS are the only design variables. When dealing with the retrofit of existing bridges, the pier reinforcement is also known and the characteristics of the IS become the only design variables. Three different IS’s are considered in the present study. All of them are made of steelPTFE sliding bearings (SB), to support the weight of the deck, and auxiliary devices based on different technologies and materials (i.e. rubber, steel and shape memory alloys (SMA’s)), to provide re-centring and/or additional energy dissipating capability. Common practice for the design of isolated structures typically utilises an equivalent visco-elastic model (Hwang et al. 1994; Miranda et al. 2002) to account for the characteristics of the IS. The linearisation of the IS is appealing, as it greatly simplifies the analysis. However, since the visco-elastic parameters of the equivalent IS depend on the structural response, an iterative procedure is needed. Two main parameters characterise the response of an IS, whichever its cyclic behaviour is: the maximum force and the maximum displacement reached during the earthquake. In this study, two different procedures have been set up for the design of the IS’s. They are respectively aimed at getting either a given maximum force (design force approach) or a given maximum displacement (design displacement approach) in the IS. Both are based on the Capacity Spectrum Method, as defined in (ATC 1996). The design force approach is particularly useful for the retrofit of existing bridges, while the design displacement approach is better suited for the design of new bridges. A comprehensive parametric analysis has been carried out, in order to assess the reliability of the two design approaches and evaluate the variation of the bridge response with changes in the ground motion, bridge and IS characteristics. Particular attention has been devoted to the friction variability of the steel-PTFE SB with contact pressure, air temperature and state of lubrication of steel-PTFE interfaces. Both artificial and natural seismic excitations have been used in the non-linear analysis of the isolated bridge. In this paper the design procedures and the main results of the parametric investigation are described and discussed.

2 Isolation systems Sliding isolation devices reduce seismic force transmission to piers and abutments by limiting shear transfer across the sliders. Once their friction threshold is exceeded, the structural response is governed by the frictional characteristics of the sliding interfaces, which in turn are a function of velocity, contact pressure, air temperature and state of lubrication (Mokha et al. 1990). In any case, auxiliary recentering and/or dissipating devices are needed, in order to limit the maximum displacements experienced by the IS’s during the earthquake and the residual displacements at the end of the seismic excitation. In this study three different IS’s are considered. All of them are based on the coupling between lubricated steel-PTFE SB and auxiliary devices based on different technologies and materials, namely: (i) rubber, (ii) steel and (iii) shape memory alloys (SMA’s) (Duerig et al.

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493

( KN )

(K N )


600

600

0

0 -130

0

130 (mm)

-130

0

-600

-600

(b) SMA wires

600

0 -130

(K N )

(a) (K N )

130 (mm)

600

0 0

-600

(c)

130 (mm)

-130

0

130 (mm)

-600

(d)

Fig. 1 Experimental (thin line) and numerical (thick line) force-displacement relationships for (a) pure steelPTFE sliding bearings, (b) steel-, (c) rubber- and (d) SMA-based auxiliary devices

1990). The rubber devices are low-damping elastomeric isolators (Naeim and Kelly 1999), with approximately 10% damping ratio, as obtained from experimental cyclic tests at 0.5 Hz and shear strain from 10% to 100% (see Fig. 1c). In this case, the rubber isolators are used just as re-centring devices with no bearing function. The steel devices are made of U-shaped steel plates deformed in roller bending (Dolce et al. 1996). The SMA devices are of the same type as the device presented in (Dolce et al. 2000), based on the superelastic behaviour of pre-tensioned SMA wires. These three types of IS’s have been selected to examine different mechanical behaviours of IS’s, ranging from highly dissipating to strongly recentering, while keeping a strong correlation to real applications. Figure 1 shows some experimental force-displacement relationships of the SB and of the above said devices as drawn from experimental tests carried out at the University of Basilicata (Dolce et al. 1996, 2003, 2005; Dolce and Cardone 2001 ). All of them were obtained from sinusoidal cyclic tests at 0.3/0.5 Hz. The tests on the sliding device (see Fig. 1a) were carried out on pure steel-PTFE interfaces, under a normal load producing 18.72 MPa contact pressure at 20◦ C air temperature. The friction coefficient at the peak velocity is equal to about 12.5%. It decreases while increasing temperature (Mokha et al. 1990; Dolce et al. 2005) and is < 3% if interfaces are lubricated. It is worth also to note the totally different recentering and energy dissipation capability of the three auxiliary devices and their different sensitivity to temperature variations. Steel

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494


(a)

IS

Force f

k1 µ

µP EP JP

m

k2 d

v(t)

SB

(k2*KP)/(k2+KP) PIER

(k1*KP)/(k1+KP)

Fy

Ug(t)

(b)

Fr

(c)

KP Displacement

Fig. 2 (a) Reference structure selected for the analysis, (b) simplified analytical model and (c) schematic monotonic response of the pier-isolator system

is practically insensitive to temperature variations. Rubber reduces its stiffness and energy dissipation capacity while increasing temperature (HITEC 1998). SMA, instead, shows an opposite trend (Dolce et al. 2000). All that has been properly taken into account in their modelling, as explained below.

3 Numerical model Figure 2a shows the reference structure of the present study. It is a perfectly symmetric bridge with single-column piers having the same height and cross section and sustaining a horizontal continuous deck. In the basic configuration, the bridge is characterised by piers of 10 m height and hollow circular cross section, with 4 m external diameter and 0.35 m thickness. The mass of the deck supported by each pier (see Fig. 2a) is taken equal to 572.5 ton, corresponding to a compressive stress of about 1.4 MPa in the pier concrete section. The attention is focused on the transverse response of the bridge, which is in most cases more critical than the longitudinal response. The effects of different soil conditions under the piers, as well as of non-synchronous motion, are neglected. These latter assumptions, though drastically simplify the numerical model, can limit the applicability of the design procedure in a number of situations. In the proposed procedure, each pier-isolator system has been regarded as an independent system and analysed separately from the others, by taking into account a proper amount of

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deck mass. This assumption is justified by the regular bridge configuration, which leads the centre of stiffness to coincide with the centre of mass of the structure. In first approximation, indeed, the stiffness of each pier-isolator system can be taken equal to the effective stiffness of the IS, since this latter is one order of magnitude lower than the post-cracking stiffness of pier. The isolators are all the same and symmetrically placed with respect the centre of mass of the deck. Finally, the flexural stiffness of the deck is more than one order of magnitude greater than the stiffness of each pier-isolator system. As a result, the transverse response of the bridge is characterised by a rigid translation of the deck only. Reference is, therefore, made to the simplified model shown in Fig. 2b, in which the pier is modelled as an elastic beam with distributed mass, while the effective mass of the deck (calculated according to a tributary principle) is lumped at the top and connected to the pier through a suitable number of nonlinear elements, describing the mechanical behaviour of each IS component. To account for concrete cracking, the flexural stiffness of the pier is reduced by 30%, according to the recommendations provided by (ATC 1996) for columns in compression. A viscous damping ratio equal to 5% has been adopted for the soil-foundation-pier system. Figure 2c shows the idealised monotonic behaviour of the pier-isolator system assumed in the design. It is derived from pushover analysis of the structural model of Fig. 2b, in which the frictional behaviour of the steel-PTFE SB is described through the Coulomb’s model and the mechanical behaviour of the auxiliary devices through an elasto-plastic model. Before sliding in the bearings (F < Fr ), the response of the system is elastic, with lateral stiffness equal to the non-isolated pier stiffness (Kp ). Then, the effective tangent stiffness of the overall system reduces to (k1 · Kp )/(k1 + Kp ), k1 being the initial stiffness of the auxiliary device. When the yielding force is exceeded in the auxiliary device (F > Fy ), the effective tangent stiffness of the overall system reduces to (k2 · Kp )/(k2 + Kp ), k2 being the post-yield stiffness of the auxiliary device. In the time-history analyses, the steel-PTFE SB have been modelled with the modified viscoplastic model (Constantinou et al. 1990), which accounts for the variability of the friction coefficient (µ) with the sliding velocity (v), through the following equation: µ = µmax − (µmax − µmin ) · e−α·v

(1)

in which µmax and µmin are the friction coefficients at very high and very low velocities and α is a function of the bearing pressure and the air temperature (see below). The frictional resistance is directly proportional to the compressive axial force in the element, according to the following equation: F =µ·W · Z

(2)

where W is the vertical load, while Z is a dimensionless hysteretic quantity, which is calculated by solving the following differential equation (Wen 1976): µmin v(1 − Z 2 ) if v · Z > 0 Z˙ = (3) v otherwise µ with the significance of the symbols defined above. The element cannot carry axial tension. In this study, µmax , µmin and α have been analytically expressed as a function of bearing pressure (P) and air temperature (T ), through a second-order polynomial model: f (P, T ) = λ1 + λ2 · T + λ3 · T 2 + λ4 · P + λ5 · P 2

(4)

whose coefficients (λi ) have been derived from a multivariate nonlinear regression with the SPSS package (SPSS 1999), based on the results of experimental tests on pure and lubricated

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steel-PTFE interfaces (Dolce et al. 2005). Three different values of contact pressure between steel and PTFE interfaces (i.e. 9.4 MPa, 18.72 MPa and 28.1 MPa) and air temperature (i.e. −10◦ C, 20◦ C and 50◦ C) were considered in the experimental tests. In this study, the same values of contact pressure and air temperature have been assumed in the numerical analyses. The experimental force-displacement relationship of each auxiliary device has been modelled by a suitable combination (in parallel) of link elements having elasto-plastic, linear elastic, nonlinear elastic and viscous behaviour (see Fig. 1). Figure 1 compares the experimental and numerical force-displacement relationships of each IS component. The numerical curves of Fig. 1 have been obtained by using the same displacement-time histories applied in the experimental tests. Thus, the diagrams of Fig. 1 account for the accuracy of the numerical models in reproducing the actual force levels acting in the device under a given displacement amplitude. From this point of view, the accordance between experimental and numerical results appears to be very suitable. Temperature was one of the main parameters considered in the numerical investigation. To account for the sensitivity of the mechanical behaviour of SMA devices to temperature variations, reference has been made to the experimental outcomes reported in (Dolce et al. 2000), which show a linear dependence on temperature in the range 0◦ C/50◦ C, with a force increase of about 10% every 10◦ C increase, and an equivalent damping decrease of about 13% every 10◦ C increase. As far as rubber-based devices are concerned, reference has been made to (HITEC 1998), which provides detailed information on the effects of extreme temperatures (−20◦ C and 40◦ C, specifically) on effective stiffness and effective damping of rubber isolators.

4 Design of the isolation systems Two different procedures, the design displacement and the design force approach, have been set up to design the IS’s. Both are based on the Capacity Spectrum Method (CSM), as defined in (ATC 1996). The CSM is an iterative procedure that compares the capacity curve of the structure with a response spectrum representation of the earthquake demand to get the Performance Point of the structure, i.e. an estimate of the expected maximum global response of the structure during the ground motion. The comparison between capacity and demand curves is made in the so-called Acceleration Displacement Response Spectrum (ADRS) format, in which spectral accelerations (Sa) vs. spectral displacements (Sd) are plotted, with periods represented by radial lines passing through the origin of the axes. For the structural system under examination, the capacity curve is represented by the multilinear force-displacement relationship shown in Fig. 2c. The capacity curve is converted into spectral coordinates by means of simple equations (ATC 1996). The demand curve is represented by a highly damped elastic response spectrum. In this study, reference has been made to the elastic response spectra provided by Eurocode 8 (CEN 1998) for soil type A and D, with PGA equal to 0.35 g and 0.4725 g, respectively. In the CSM, the location of the Performance Point (PP) must satisfy two conditions. First, PP must lie on the Capacity Spectrum (CS) curve, in order to represent the structural response at a given displacement. Second, PP must lie on the Demand Spectrum (DS) curve representing the nonlinear seismic demand at the same structural displacement. In the case under consideration, the PP must also satisfy the performance objective of the design, which is expressed through a condition on the maximum force or maximum displacement of the IS. In the CSM, the demand curve is iteratively derived from the 5%-damped reference response spectrum, by applying proper reduction factors (Lin et al. 2005), which depend on

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497

Table 1 Design force approach: comparison of the results of preliminary design and nonlinear analysis for each isolation system and soil condition (H = 10 m, T = −10◦ C, P = 9.4 MPa) System Soil Design

Non linear analysis (average over eight accelerograms) ξef F (kN) RMS_F ERR_F D (mm) RMS_D

F (kN) D (mm) Tef (sec)

(%) Steel Rubber SMA

(%)

(%)

(%)

ERR_D (%)

A

760

44

1.14

46

734

1

−3

47

11

7

D

1027

206

2.12

47

926

1

−10

144

6

−30

A

760

82

1.55

22

651

6

−14

65

9

−21

D

1027

304

2.58

19

901

3

−12

234

5

−23

A

760

143

2.06

10

658

5

−13

106

13

−26

D

1027

409

2.99

8

1072

10

4

431

18

5

the equivalent damping (ξeq ) of the soil-pier-isolation system as a whole. The equivalent damping can be viewed as a combination of the inherent viscous damping of the soil-pier system (ξo = 5%) and the effective hysteretic damping of the IS (ξef ). This latter is a function of the IS under consideration (more precisely of the shape of its hysteresis loops) and of the expected maximum displacement. It can be evaluated through the well known formula (Chopra 1995): ξe f =

1 WD · 4π W S

(5)

where W D is the energy dissipated by the IS in a single cycle at the maximum expected displacement. It can be seen as sum of two contributes: the energy dissipated by friction in the SB and that dissipated through the hysteretic or viscous behaviour of the auxiliary devices. W S is the strain energy of the entire IS at the maximum displacement amplitude. The equivalent damping of the soil-pier-isolator system as a whole is then estimated as follows (Priestley et al. 1996): ξeq =

D P · ξo + D I · ξe f DP + DI

(6)

where D P and D I are the maximum expected displacements in the pier and in the IS, respectively. In this study, the damping reduction factors are calculated through the relationship derived by (Bommer et al. 2000) and included in the European Seismic Code (CEN 1998): η = 10/(5 + ξeq ) (7) In order to consider the high levels of damping (45–50%) of the steel-based IS’s (see Tables 1, 2), the limitation η ≥ 0.55 suggested by the EC8 (corresponding to equivalent damping lower than 28%) has been neglected. Since the equivalent damping is a function of the initially unknown maximum response of the IS, the performance point requires an iterative procedure to be evaluated. In the design force approach, the performance objective was to limit the maximum force transmitted by the IS to a fraction of the yielding strength of the pier. This latter was calculated as the maximum shear force in the non-isolated bridge, as obtained from spectral analysis by assuming a behaviour factor (q-factor in EC8) equal to 3.5. A further protection factor

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Table 2 Design displacement approach: comparison of the results of preliminary design and nonlinear analysis for each isolation system and soil condition (H = 10 m, T = 50◦ C, P = 28.1 MPa) System Soil Design

Non linear analysis (average over eight accelerograms)

F (kN) D (mm) Tef (sec)

ξef F (kN) RMS_F ERR_F D (mm) RMS_D (%)

Steel Rubber SMA

(%)

(%)

(%)

ERR_D (%)

A

418

80

2.07

50

401

1

−4

84

10

5

D

1187

220

2.04

45

1036

2

−13

140

9

−36 −18

A

1159

80

1.25

13

988

5

−15

66

7

D

3710

220

1.16

10

2635

3

−29

134

3

−39

A

975

80

1.44

14

864

8

−11

70

22

−12

D

4182

220

1.2

6

3473

4

−17

184

11

−16

was then applied, in order to take into account possible overstrength of the IS or larger than expected displacement demand. Practically, the force transmitted by the IS at the expected maximum displacement was taken equal to 50% of the design nominal strength of the pier. The design values of contact pressure and air temperature were selected so as to maximise the force transmitted to the pier. To this end, reference was made to the lowest available experimental values (i.e. 9.4 MPa and −10◦ C, respectively) for both steel-IS and rubber-IS. For the SMA-IS, on the contrary, a design temperature of 50◦ C was assumed, in order to take into account that the force levels in the SMA device increase while increasing temperature. In the design displacement approach, the performance objective was to limit the maximum displacement of the IS to a fraction of its ultimate displacement capacity. However, the selection of such a limit was also affected by the maximum values of the spectral displacement for high-damping levels (ξeq up to 50% for the steel-IS). Indeed, the iterative procedure does not converge if the target displacement results greater than the maximum spectral displacement, at a given damping ratio, since the D-line of Fig. 3b do not intercept the DS in any point. For simplicity, the maximum allowable displacement was directly taken equal to the peak value of the ground displacement (i.e. dg = 0.025 · TC · TD · PGA), for all the IS’s. For what concerns the friction characteristics of the steel-PTFE SB, reference was made to the higher experimental values of contact pressure and air temperature (i.e. 28.1 MPa and 50◦ C, respectively), in order to maximise the pier-deck displacement. Obviously, for the SMA IS a completely different design temperature was assumed (−10◦ C precisely), due to the different thermal behaviour of the SMA device (Dolce et al. 2000). Figure 3 summarises the two different iterative procedures used in this study. The F-line and the D-line represent the target force and the target displacement, respectively. The curve indicated with CSi represents the capacity spectrum at the ith step of the analysis, the curve indicated with DS(ξi ) represents the DS for the corresponding damping ratio. At the beginning of the analysis a trial value for the maximum displacement (F-based approach) or maximum force (D-based approach) of the IS is assumed. A preliminary IS (hence a preliminary CS and PP) is thus defined. The equivalent damping ratio of the system is then evaluated, through Eq. 6, and a provisional DS derived. The interception between the F-line (or D-line) and the DS provides a new estimate of the PP, hence a new trial value of the maximum displacement or maximum force to be used in the next step of the analysis. The iterative process ends when the error is smaller than a given tolerance.

123


Sa

499

(a) DS(ξ1)

PPi+1 PPi F-line CSi

err DS(ξi)

Tef,i di Sa

Sd

di+1

(b) DS(ξ1)

D-line

PPi+1 fi+1 fi

err CSi Tef,i

PPi

DS(ξi)

Sd

Fig. 3 Summary of the design force (top) and design displacement (bottom) procedures used for the isolation systems, as derived from the Capacity Spectrum Method

Obviously, the first segment of the capacity spectrum does not change during the iterative procedure, as it depends on the pier stiffness and the friction resistance of the SB (KP and Fr in Fig. 2c). The effective period of the system (Tef in Fig. 3), on the contrary, varies according to the displacement levels (for the design force approach of Fig. 3a) or force levels (for the design displacement approach of Fig. 3b) in the isolation device. At each step of the analysis, the displacement levels in the IS have been adjusted so as to correspond to predetermined values of maximum strain or ductility demand in the isolation devices. At the end of the iterative procedure (step n), the performance point PPn provides the expected maximum response of the system. The first six columns of Tables 1 and 2 summarise the results of the two design procedures, for each IS and soil condition. Besides the maximum expected force (Fdesign ) and displacement (Ddesign ), the associated effective period of vibration (Tef ) and effective damping (ξef ) are reported. This latter accounts for the energy dissipation occurring in the whole IS (SB included). It is interesting to compare the results relevant to the different IS’s. Generally speaking, the steel-IS is the less demanding in terms of displacement, when the design force approach is applied, and, vice versa, in terms of force when the design displacement approach is applied. The opposite occurs to the SMA-IS. This is to be ascribed to the different values of the effective damping, which is 45–50% in the steel-IS and 6–14% for the SMA-IS, and assumes intermediate values for the rubber-IS. A direct comparison between the two approaches

123

500


cannot be made, as different temperature and pressure parameters have been assumed for the SB. However it is evident that, for the same IS, the effective period depends strongly on the type of soil, in the design force approach, while it is almost insensitive to the type of soil in the design displacement approach.

5 Nonlinear response of seismically isolated bridges As said above, a parametric investigation based on a large number of nonlinear dynamic analyses was required to assess the reliability of the proposed design procedure and evaluate the variations of the structural response when varying the bridge and IS characteristics, as well as the ground motion. The nonlinear seismic responses of the reference bridge models have been evaluated with the SAP2000_Nonlinear program (Computers and Structures 2002), which has the capability of modelling the different IS’s considered in the present study. Two groups of eight artificial acceleration profiles, each group compatible with the 5%damped response spectra used in the design procedure, have been generated to carry the non-linear dynamic analyses of the isolated bridge. Moreover, three near-fault records of historical earthquakes (see Fig. 4) have been considered, namely: (a) the S90W component of the El Centro—Imperial Valley Earthquake (18/5/1940), (b) the N90E component of the Caleta de Campos—Michoacan Earthquake (19/9/1985) and (c) the 090 component of the Takatori (Kobe)—Great Hanshin-Awaji earthquake (17/1/1995). In order to compare the results relevant to different input motions, the natural records have been normalised according to two different criteria: (i) same PGA and (ii) same spectral acceleration, at the effective period of vibration (Tef ) of each bridge model, as the design earthquake for soil type A. Figure 5a shows the response spectra of the three natural records normalised with respect to PGA, while Fig. 5b shows an example of normalisation, for a given Tef value, with respect to the spectral acceleration. The structural parameters considered in this study are as follows: (i) the inherent characteristics of the auxiliary devices, from highly dissipating to strongly recentering, (ii) the pier height, taken equal to 10 m and 30 m, (iii) the air temperature, taken equal to −10◦ C, 20◦ C and 50◦ C, (iv) the bearing pressure in the steel-PTFE SB, taken equal to 9.4 MPa, 18.72 MPa and 28.1 MPa, and (v) the state of lubrication of the steel-PTFE interfaces. In the following, the structural response of the bridge is described through the force transmitted by the IS to the pier and the pier-deck displacement. Artificial and natural earthquakes are considered separately. 5.1 Structural response to artificial earthquakes The main results of both design procedures and non-linear analyses are compared in Tables 1 and 2, for the bridge with 10 m tall piers. In the design force approach (Table 1) the air temperature and the contact pressure are taken equal to −10◦ C and 9.4 MPa, respectively, with the only exception of the SMA IS, for which a design temperature of 50◦ C is assumed. The contrary holds for the design displacement approach (Table 2), in which reference is made to a contact pressure of 28.1 MPa and a temperature of 50◦ C, for the steel-IS and rubber-IS, while −10◦ C for the SMA-IS. The same values of contact pressure and air temperature are assumed in the corresponding nonlinear analyses. In both the cases, the PTFE-steel interfaces are supposed to be perfectly lubricated.

123


(a/PGA)

(a)

501

1 0.5 0 0

10

20

30

40

-0.5

50 (sec)

-1

(a/PGA)

(b)

1 0.5 0 0

10

20

30

40

50 (sec)

0

10

20

30

40

50 (sec)

-0.5 -1

(a/PGA)

(c)

1 0.5 0 -0.5 -1

Fig. 4 Acceleration profiles of the near-fault records of historical earthquakes used in numerical analyses

In the “Nonlinear Analysis” section of Tables 1 and 2, the data labelled with “RMS” (Root Mean Square differences) account for the scattering in the maximum force/displacement (with respect to the corresponding mean value) due to different ground motions, while those labelled with “ERR” correspond to the percent differences between the average (over eight accelerograms) maximum force/displacement obtained from the time-history analyses and the force/displacement values predicted in the design. Generally speaking, the design procedures are conservative, as they overestimates the maximum expected response of the bridge, with percent errors in the attainment of the performance objective somewhat greater than the dispersion in the response due to the difference in the input motions, all consistent with the same response spectrum. As could be expected, the design procedures are more accurate in predicting the maximum forces than the maximum displacements. Moreover, they work better for stiff soils (type A) than for soft soils (type D). The differences between design and seismic simulation results can be partly ascribed to the different models (i.e. rigid perfectly plastic vs. modified visco-plastic) of the SB in the design procedures and in the time-history analyses. Although the design of the steel-IS seems to provide better prediction of the nonlinear response, the limited number of cases examined cannot provide a definite proof of this apparent trend. Figures 6 and 7 show the sensitivity of the structural response to temperature variations, as obtained from time-history analyses. They refer to the same bridge configurations as Tables 1 and 2, with the bearing pressure in the sliders at the design values (i.e. 9.4 MPa and 28.1 MPa, respectively). The results relevant to different soil conditions are reported separately. The

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502


(a)1.5

Kobe

Sa (g)

1 El Centro Caleta

0.5 EC8_A

0 0

1

2

3

2

3

T (sec)

(b)1.5 EC8_A Caleta

Sa (g)

1

Kobe

El Centro

0.5

Teff

0 0

1 T (sec)

Fig. 5 (a) Response spectra of the natural records normalised with respect to PGA, and (b) example of normalisation with respect to the spectral acceleration corresponding to the effective period of the isolation system

structural response (average over eight accelerograms) is described through the maximum force transmitted by the IS to the pier (left) and the maximum pier-deck displacement (right), divided by the corresponding values obtained from the preliminary design. As can be seen, the choice of a suitable design temperature is fundamental in order to achieve a structural response which satisfies the performance objective of the design over the whole operational range of temperature. This holds especially when also the auxiliary device (in addition to the SB) exhibits a mechanical behaviour which depends on temperature, like rubber and SMA devices. As far as the force-based design approach is concerned (Fig. 6), the assumption of the lowest values of the temperature range (i.e. −10◦ C) is suitable for the steel-IS and the rubber-IS, while for the SMA-IS the best choice results the highest temperature value (i.e. 50◦ C). The contrary holds for the design displacement approach (see Fig. 7). As regards the sensitivity of the structural response to temperature, the SMA-IS performs worse, showing a higher sensitivity to temperature variations, especially in terms of maximum force transmitted to the piers. By assuming 20◦ C as reference temperature and ±30◦ C as thermal excursion, indeed, the maximum force variations range between 24% and 33%

123

Bull Earthquake Eng (2007) 5:491–509 steel_D

rubber_A

2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

rubber_D

Dmax /Dd

Fmax /Fd

steel_A

503

-10

20 (°C)

50

sma_A

sma_D

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Fig. 6 Sensitivity of the structural response to temperature variations: maximum force (left) and maximum displacement (right) normalised with respect to the corresponding design values. Hp = 10 m, IS’s designed according to the F-approach (P = 9.4 Mpa; T = −10◦ C, 50◦ C for SMA)

rubber_A 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

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50

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Fig. 7 Sensitivity of the structural response to temperature variations: maximum force (left) and max. displacement (right) normalised with respect to the corresponding design values. Hp = 10 m, IS’s designed according to the D-approach (P = 28.1 Mpa; T = 50◦ C, −10◦ C for SMA)

(depending on the design approach and soil conditions) for the SMA-IS, 2% and 20% for the rubber-IS and, finally, 3% and 9% only for the steel-IS. Under the same circumstances as before, the maximum displacement variations range between 39% and 103% for the SMA-IS, 14% and 28% for the rubber-IS and 4% and 21% for the steel-IS. Figures 8 and 9 compare the displacement-time histories and force-displacement relationships of the three IS’s, for the same bridge configuration (pier of 10 m height), bearing pressure (18.72 MPa), air temperature (20◦ C) and seismic input (the first artificial accelerogram generated from the EC8 response spectrum for soil type A). The IS’s considered in Figs. 8 and 9 have been designed according to the force-based and the displacement-based design approach, respectively. As can be seen, the choice of the best IS is not so easy, each one presenting some advantages and disadvantages with respect to the others. The steel-IS shows the best control of force when the performance objective of the design is to limit the maximum pier-deck displacement. On the other hand, it also exhibits a large residual displacement at the end of the seismic action.

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Fig. 8 Comparison between the displacement-time histories and force-displacement relationships of the three types of IS designed according to the F-approach (760 kN). Hp = 10 m; P = 18.72 MPa; T = 20◦ C; Seismic input = acc1 from EC8_A response spectrum 100

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Fig. 9 Comparison between the displacement-time histories and force-displacement relationships of the three types of IS designed according to the D-approach (80 mm). Hp = 10 m; P = 18.72 MPa; T = 20◦ C; Seismic input = acc1 from EC8_A response spectrum

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The SMA-IS suffers the large operational range of temperature, which implies high levels of force and low damping capacity. On the other hand, it exhibits a strong supplemental recentering capability, which can be exploited to counteract possible increases in the friction resistance of the SB (e.g. due to grease deterioration) or to remedy installation imperfections (e.g. out of levels, etc.). It probably suffers of its low energy dissipation capability, which implies a strong variability of the response. The addition of energy dissipating devices (e.g. viscous dampers), could produce important benefits in terms of both control of the maximum seismic response and reduction of its sensitivity to temperature variations and ground motion characteristics. The rubber-IS, finally, appears to be a good compromise between the previous two types of IS. Another key parameter in the seismic response of the bridge is the state of lubrication of the steel-PTFE interfaces in the SB. Two limit values of the friction coefficient can be identified. The lower limit (so forth denoted with µLUB ) corresponds to the friction coefficient, at high velocities, of lubricated steel-PTFE interfaces, which can be assumed of the order of 3%, based on experimental outcomes (Dolce et al. 2005). The upper limit (so forth denoted with µPURE ) corresponds to the friction coefficient, at high velocities, of pure steel-PTFE interfaces, which can be assumed of the order of 12.5%, based on experimental outcomes (Dolce et al. 2005). A series of numerical analyses have been conducted in order to evaluate the sensitivity of the bridge response to the state of lubrication of steel-PTFE SB. The IS’s have been designed assuming perfectly lubricated SB (i.e. characterised by µLUB as friction coefficient). Then, the time-history analyses have been performed by increasing the friction coefficient, respectively, by 30%µ and by 50%µ, being µ = µPURE − µLUB . Figure 10 shows the maximum force (left) and maximum displacement (right) experienced by each IS, at different temperatures, while increasing the friction coefficient from µLUB up to µLUB + 0.5 · µ. The IS’s considered in Fig. 10 have been designed according to a force-based approach (760 kN threshold force), by assuming the steel-PTFE interfaces as perfectly lubricated (µ = µLUB ). As expected, the maximum force transmitted by the IS to the piers increases and the pier-deck displacement progressively reduces while increasing friction. However, the variability of the structural response with friction is more or less pronounced, depending on the mechanical behaviour of the auxiliary device. In particular, the higher percent increase in terms of maximum force transmitted to the pier is observed for the steel-IS (on average by about 45% when passing from µLUB to µLUB + 0.5 · µ), while the greater percent decrease in terms of maximum pier-deck displacement is observed for the SMA-IS (on average by about 55% when passing from µLUB to µLUB + 0.5 · µ). This different behaviour is to be ascribed to the substantially different energy dissipation capability of the three systems. In particular the SMA-IS, which has the smallest energy dissipation, is the most sensitive to the friction increase, which turns out to a substantial percent increase of energy dissipation and therefore a substantial percent decrease of displacement. 5.2 Structural response to natural earthquakes Figures 11 and 12 refer to the IS’s designed according to the design force and design displacement approach, respectively. They show, for each natural record and for both normalisation criteria, the ratio between the maximum force experienced by the three IS’s at different temperatures and the assumed design force. Thus, values less than or equal to 1 mean compliance with the design objective, while the contrary holds for values > 1.

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Fig. 10 Max. forces (left) and max. displacements (right) experienced by the (a) steel-, (b) rubber- and (c) SMA-IS while increasing the friction coefficient of the sliding bearings, at different air temperatures. IS’s designed according to the F-approach (760 kN)

As expected, the compliance with the design objective strongly depends on how the inherent nonlinear characteristics of the IS couples with the frequency content of the earthquake. Due to the small number of natural earthquakes taken into consideration, no general conclusions can be drawn. However, some aspects appear to be apparent, e.g. the greater reliability of the design force approach, compared to the design displacement approach. The examination of Figs. 11, 12 also emphasises the great sensitivity of the seismic response of the bridge to air temperature variations: IS’s which fully satisfy the performance objective of the design at the design temperature, do not comply with it at different temperatures.

6 Conclusion In this paper, bridge structures protected by strongly nonlinear IS’s, based on the coupling between steel-PTFE flat SB and auxiliary re-centering and/or dissipating devices, are considered. An iterative procedure for the preliminary design of such IS’s, which explicitly

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Fig. 11 Force ratios (Max. value from NTHA vs. design value) generated in the IS’s by different natural earthquakes, characterised by same PGA (left) or same spectral acceleration (right) at the effective period of vibration of the isolated structure

acknowledges their nonlinear behaviour, is presented. More in detail, two design approaches have been set up to design the IS. One is aimed at controlling the maximum force and is more suitable for the seismic retrofit of existing bridges, the other is aimed at controlling the maximum displacement and is normally more appropriate for new bridges. A parametric study based on nonlinear dynamic analyses has been carried out, in order to assess the reliability of the design procedures and evaluate the sensitivity of the structural response to changes in ground motion, bridge and IS characteristics. Particular attention has been paid to the variability of the frictional behaviour of the SB with contact pressure, air temperature and state of lubrication of steel-PTFE interfaces. The results of the numerical analyses prove the accuracy of the design procedure in predicting the maximum response of the structure, when the same temperature and friction conditions are considered. In any case the design procedures provide conservative predictions of the seismic response. The selection of a suitable design temperature is fundamental in order to obtain a structural response that satisfies the performance objective of the design

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Fig. 12 Displacement ratios (Max. value from NTHA vs. design value) generated in the IS’s by different natural earthquakes, characterised by same PGA (left) or same spectral acceleration (right) at the effective period of vibration of the isolated structure

over the whole operational range of temperature. The appropriate design temperature appears to be strictly related to the inherent behaviour of the auxiliary device. As far as the behaviour of the different IS’s (as well as their sensitivity to temperature and friction variations) is concerned, the most stable behaviour is obtained for the steel-IS, due to the constancy of the steel yield force and its high intrinsic energy dissipation capability, which makes the effects of the variability of the friction force in the SB almost negligible. On the contrary, the maximum sensitivity is observed for the SMA-IS, due to both the considerable variations of force with temperature and the inherent low energy dissipation capability. This latter accentuates the effects of the friction variability on the seismic response. A more stable behaviour could be obtained by complementing the SMA-IS with additional energy dissipating devices, e.g. viscous dampers.

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The design procedure proposed in this study relies upon a simplified pier-deck model, in which each single pier is modelled through an elastic cantilever beam with the contributory mass of the deck lumped at the top. Actually, this structural idealisation has several limitations, when applied to real bridge structures. First of all, highly irregular bridge configurations (e.g. bridge characterised by a continuous deck with piers of very different heights) affect the seismic response of the structure as a whole, to a greater or lesser degree. The effects of different soil conditions under the piers, as well as the effects of near-fault or nonsynchronous ground motions, may also lead to significant modifications in the design force or displacement. Further studies are then needed to extend the proposed design procedures to cover a wider range of ground motion and structural situations. Acknowledgements The studies presented in this paper have been partially funded by the MIUR-COFIN 2002 project “Innovative Aspects in the Seismic Design of Bridges”.

References ATC—Applied Technology Council (1996) ATC-40: seismic evaluation and retrofit of concrete buildings. Report No. SSC 96-01, Redwood City, California (USA) Bommer JJ, Elnashai AS, Weir AG (2000) Compatible acceleration and displacement spectra for seismic design codes. Proceedings of the 12th World conference on earthquake engineering, Auckland, Paper no. 207 Chopra AK (1995) Dynamics of structures. Prentice Hall International Inc., London CEN ENV-1-1 European Committee for Standardisation (1998) Eurocode 8: design provisions for earthquake resistance of structures, Part 1.1: General rules, seismic actions and rules for buildings Computers and Structures Inc. (2002) SAP2000 analysis ref. manual. Version 8.0, Berkeley, CA Constantinou M, Mokha A, Reinhorn AM (1990) PTFE bearings in base isolation: modelling. J Earthquake Eng 116(2):455–472 Dolce M, Filardi B, Marnetto R, Nigro D (1996) Experimental tests and applications of a new biaxial elastoplastic device for the passive control of structures. Proc 4th World congress on joint sealants and bearing systems for concrete structures. Sacramento, California (USA) Dolce M, Cardone D, Marnetto R (2000) Implementation and testing of passive control devices based on shape memory alloys. Earth Eng Struct Dyn 29:945–958 Dolce M, Cardone D (2001) Mechanical behaviour of shape memory alloys for seismic applications: part 1 and 2 Martensite and Austenite N.T. bars subjected to torsion. J Mech Sci 43(11):2631–2676 Dolce M, Cardone D, Marnetto R, Nigro D, Palermo G (2003) A new added damping rubber isolator (ADRI): experimental tests and numerical simulations. Proc 8th world seminar on seismic isolation, energy dissipation and active vibration control of structures, Yerevan, Armenia Dolce M, Cardone D, Croatto F (2005) Frictional behaviour of steel-PTFE interfaces for seismic isolation. Bull Earthquake Eng 3(1):75–99 Duerig TW, Melton KN, Stoeckel D, Wayman CM (eds) (1990) Engineering aspects of shape memory alloys. Butterworth-Heinemann Ltd, London HITEC—Highway Innovative Technology Evaluation Center (1998) Evaluation findings for skellerup base isolation elastomeric bearings, USA Hwang JS, Change LH, Gates JH (1994) Practical analysis of base-isolated bridges with bi-linear hysteresis characteristics. Earthquake Spectra 10(4):705–727 Lin Y-Y, Miranda E, Chang K-C (2005) Evaluation of damping reduction factors for estimating elastic response of structures with high damping. Earthquake Eng Struct Dyn 34:1427–1443 Miranda E, Ruiz-Garcia J (2002) Evaluation of approximate methods to estimate maximum inelastic displacement demands. Earthquake Eng Struct Dyn 31:539–560 Mokha A, Constantinou M, Reinhorn AM (1990) PTFE bearings in base isolation: testing. J Earthquake Eng 116(2):438–454 Naeim F, Kelly JM (1999) Design of seismic isolated structures. Wiley Priestley MJN, Seible F, Calvi GM (1996) Seismic design and retrofit of bridges. Willey SPSS Inc. (Berkeley, California, USA): SPSS Advanced Models 9.0 (1999) Wen YK (1976) Method for random vibration of hysteretic systems. J Eng Mech Div, ASCE 102(EM2): 249–263

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