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Seismic response analysis of an irregular base isolated building

Article in Bulletin of Earthquake Engineering · October 2011

DOI: 10.1007/s10518-011-9267-1

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Bulletin of Earthquake EngineeringOfficial Publication of the EuropeanAssociation for EarthquakeEngineering ISSN 1570-761XVolume 9Number 5 Bull Earthquake Eng (2011)9:1673-1702DOI 10.1007/s10518-011-9267-1

Seismic response analysis of an irregularbase isolated building

L. Di Sarno, E. Chioccarelli & E. Cosenza

1 23

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Bull Earthquake Eng (2011) 9:1673–1702DOI 10.1007/s10518-011-9267-1

ORIGINAL RESEARCH PAPER

Seismic response analysis of an irregular base isolatedbuilding

L. Di Sarno · E. Chioccarelli · E. Cosenza

Received: 21 August 2010 / Accepted: 31 March 2011 / Published online: 19 April 2011© Springer Science+Business Media B.V. 2011

Abstract This paper assesses the reliability of code-compliant linear and nonlineardynamic analyses for irregular buildings with base isolation system (BIS). Comprehensiveanalyses are carried out for a case study comprising a large reinforced concrete multi-storeyframed hospital with 327 high-damping rubber bearings. Spectral and time history (linearand nonlinear) analyses were performed on the three-dimensional (3D) finite element model(FEM) of the structure; simplified analyses were also conducted on single-degree-of-freedom(SDOF) systems. It is found that, at damageability limit state, the values of maximum in-terstorey drifts (d/h) computed with spectral analyses on the three-dimensional FEM rangebetween 1/6 and 1/10 of the code limit (d/h = 0.33%); thus more stringent code limits shouldbe required for buildings with BISs. The maximum floor acceleration is reduced by about70% with respect to the ground acceleration (free field site); the acceleration profile is uni-form along the height of the multi-storey frame. Threshold values of floor accelerations toassess the seismic performance of equipments in buildings with BIS are lacking. At ultimatelimit state (ULS), spectral analyses provide values of actions and deformations that are lessconservative than those derived through time history analyses. To perform reliable dynamicanalyses of base isolated buildings it is crucial to select natural earthquake ground motionscompliant with the fundamental period of vibration of the structural system. Nevertheless, itis not straightforward to select adequate natural strong motions in the catalogues availableworld-wide; buildings incorporating BISs possess periods of vibration which are generallyhigher than 2.0 s. As a result, distant and high-magnitude earthquakes are effective for baseisolated buildings; nevertheless, such earthquakes are scarce in the seismic databases. Theoutcomes of the present study also demonstrate that simplified linear analyses tend to provideestimates of the response quantities, displacements of base isolators and base shear of thesuperstructure, which can be reliably employed at preliminary design stage. Spectral analysis

L. Di Sarno (B)Department of Engineering, University of Sannio, Benevento, Italye-mail: [email protected]

E. Chioccarelli · E. CosenzaDepartment of Structural Engineering, University of Naples Federico II, Naples, Italy

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Author's personal copy

1674 Bull Earthquake Eng (2011) 9:1673–1702

results of the 3D model tend to match those of the SDOF systems, even for irregular super-structure, provided that modal mass participating ratios are greater than 85–90%. The resultsof spectral analyses on both SDOF and three-dimensional FEM envelope the outcomes oflinear time histories.

Keywords Base isolation · Seismic assessment · Structural analysis · Modeling ·Rubber isolators · Seismic codes

1 Introduction

Base isolation systems (BISs) are being employed in several earthquake-prone regions forthe design of new and existing critical facilities building structures, e.g. hospitals, schools,city halls, fire stations and computer centres. The use of BISs gained wide acceptance inCalifornia and Japan in the aftermath of the 1994 Northridge and 1995 Kobe earthquakes,respectively. In Europe, several buildings and bridges, employing primarily laminated rubberbearings, have been built in the last few years. The spread of such passive control strategywas stimulated by the provisions implemented in new seismic standards, e.g. Eurocode 8(CEN 2006) and DM (2008), in Italy. Simplified rules and requirements have been for-mulated for easy application in ordinary design offices; linear and/or nonlinear structuralanalysis methods, with different level of complexity, can be employed. However, there arestill a number of unsolved issues which are of paramount importance, especially when largeirregular base isolated multi-storey building structures are considered (e.g. Tena-Colungaand Zambrana-Rojas 2006; Tena-Colunga and Escamilla-Cruz 2007). Furthermore, the reli-ability of simplified linear analyses methods should be further investigated (Ramirez et al.2002a,b).

Several comprehensive experimental and numerical studies focusing on the performanceof isolators, either made of rubber (with or without lead cores) or based on sliding sur-faces (single or double), exist in the literature (see for example Braga et al. 2005; Jain andThakkar 2005; Jangid 2005, 2007; Ozbulut and Hurlebaus 2010, among many others). Addi-tional studies have focused on the assessment of the structural performance of buildings andbridges employing BISs (see for example, Nagarajaiah et al. 1991; Hwang and Sheng 1994;Franchin et al. 2001; Ryan and Chopra 2004; Dolce et al. 2007; Kikuchi et al. 2008; Kilarand Koren 2009). The global response of as-built structures has been tested experimentallyon site to determine the periods of vibration and the actual structural equivalent viscousdamping (e.g. Moroni et al. 1998; Braga and Laterza 2004). The response of non structuralcomponents and building interior contents (equipments, machineries, occupants) have alsobeen investigated, primarily with numerical simulations (e.g. Kelly and Tsai 1985; Tsai andKelly 1989; Fan and Ahmadi 1992; Yang and Huang 1993; Lu and Yang 1997; Alhan andGavin 2005; Iemura et al. 2007). The above existing studies rely predominantly on the useof advanced nonlinear dynamic analyses, e.g. classical or incremental inelastic time histo-ries. On the other hand, the preliminary design of building structures is often carried out byutilizing simplified single-degree-of-freedom (SDOF) systems; the results are then validatedon the basis of three-dimensional finite element models (FEMs) of the structure. Modal andspectral analyses are commonly utilized to design both the BISs and the superstructure. Thereliability of simplified models and the use of linear analyses, either spectral or time histories,has not been yet investigated in a comprehensive manner, especially for irregular reinforcedconcrete (RC) buildings with BIS.

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Bull Earthquake Eng (2011) 9:1673–1702 1675

This paper illustrates the results of extensive dynamic analyses performed on a largeirregular base-isolated framed hospital building. The latter frame has an irregular shapedplan layout of about 144 m × 144 m; the frame is also irregular in elevation (two blockswith different heights). It employs 327 high-damping rubber bearings (HDRBs) as base iso-lation system (BIS). The earthquake response of the sample building is assessed throughcode-compliant linear and nonlinear dynamic analyses. The reliability of such analyses andtheir conservatism, if any, is investigated in a detailed fashion.

2 Code provisions for the analysis of isolated buildings

Modern seismic codes (e.g. FEMA 450, 2004; Eurocode 8, 2006 and D.M. 2008, amongmany others) provide rules to analysis and design base isolated structures (BISs) in whichthe isolation system is located below the main mass of the structure. The seismic performanceassessment of such BISs can be carried out by linear and/or nonlinear structural analysis meth-ods. For example, in the recent Italian seismic codes (D.M. 2008) the structural analysis ofstructures with base isolation can be conducted as follows:

• Equivalent static linear analysis;• Linear dynamic analysis (either modal or linear response history);• Nonlinear dynamic analysis (nonlinear response history).

Nonlinear static analysis, i.e. also termed pushover, is not allowed to assess BISs. On theother hand, nonlinear dynamic analysis is deemed compulsory whenever the isolation systemcannot be represented by an equivalent linear model; an adequate constitutive relationshipshould thus be formulated and implemented in the structural analysis scheme.

Linear analyses, either static or dynamic, may be employed if the isolation system can bemodeled with equivalent linear visco-elastic behaviour. This is the case of devices such aslaminated elastomeric bearings, or with bilinear hysteretic behaviour if the system consists ofelasto-plastic types of devices. Effective stiffness (keff ) and effective viscous damping (ξeff )are utilized to model each isolator unit. The effective response quantities (keff and ξeff ) arecomputed at lateral displacements relative to the limit state under consideration. The effectivestiffness keff corresponds to the secant stiffness at the total design displacement. The effectivedamping ξeff of the bearing devices quantifies the energy dissipated under cyclic loads. Forhigher modes outside this range, the modal damping ratio of the complete structure shouldbe that of a fixed base superstructure. The linearization of the isolator constitutive law is aniterative procedure. However, the number of iterations for convergence tends to be rather lowto match the 5% error recommended in the seismic standards; generally less than 5 iterationsare sufficient.

The dynamic response of the base isolated structural system is generally analyzed in termsof accelerations, inertia forces and displacements, as also presented hereafter.

3 Case study

3.1 General description

The benchmark building employed herein to assess the reliability of code-compliant dynamicanalyses is the structural system of a large and irregular base isolated hospital, which wasrecently built in Naples, in the Southern Italy.

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Fig. 1 Longitudinal cross-section of the structure (top) and aerial view of the construction site (bottom)

The plan layout of the hospital building is about 144 × 144m and the total height is about29 m. Structural system utilized for the super-structure is a spatial reinforced concrete (RC)multi-storey moment-resisting frame (MRF). The latter exhibits a large mass eccentricitybecause of the different height (3 and 8 storeys, respectively) of the two L-shape blocks ofthe super-structure. The interstorey for the low-rise block is 3.90 m for all but the basement;for the latter floor the interstorey height is 3.50 m. The second-to-fifth floors in the high riseblock have a 3.90 m interstorey. The upper floors are 3.60 m high. The basement of the high-rise block is 3.50 m. The thickness of the slabs is equal to 40 cm for all but the ground floor;for the latter a RC 50 cm thick solid slab was adopted. The concrete slabs employ specialfoam blocks and are partially cast in situ. The grade of concrete is C25/30. The steel forreinforcement bars is FeB44k (or equivalently B450C), with yield stress equal to 430 MPa.The cross-sections of the columns vary at storey level and in elevation (the maximum dimen-sions are 120 × 100 cm). Deep beams (40 × 70 cm) are located along the storey edges;in the interior bays, flat beam cross-sections range between 90 × 40 cm and 120 × 40 cm.The 8-storey building has an external block, in structural steel. Metal frames are also locatedon the roofs of the building to protect the air unit systems from the natural environmentalactions, e.g. wind, rain and snow. The longitudinal cross-section of the structure and an aerialview relative to the construction stage are shown Fig. 1.

The adopted foundation system includes the following structural parts (Fig. 1):

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Fig. 2 Plan layout of theisolation devices. Red 600 mm;Green 650 mm and Blue 800 mm

Table 1 Mechanical properties of the seismic isolation devices used for the sample frame

Diameterofisolators( mm)

Number ofisolators

Totalrubberthickness( mm)

ShearModulus( MPa)

Viscousdamping(%)

HorizontalStiffness(kN/ mm)

Verticalstiffness(kN/ mm)

Primaryshapefactor (S1)

Secondaryshapefactor (S2)

600 115 150 0.80 ± 0.12 15 1.51 1802 24.58 3.93

650 124 156 1.40 ± 0.21 15 2.98 2472 26.67 4.10

800 88 144 1.40 ± 0.21 15 4.89 3949 24.69 5.49

- Foundation substructure (inferior slab);- Foundation (piled foundation).

The design of the above foundation components was carried out in compliance with the pro-visions included in the seismic national regulations (OPCM 3431, 2005 and DM 2008). TheRC foundation mat rests on piles of medium diameter (800 mm) with a length of 15.00 m.The thickness of the RC mat is 1200 mm while the superior slab includes a RC solid slabwith a thickness of 500 mm. The concrete grade used for the deep foundations is C20/25.Steel reinforcement grade is FeB44k, as for the superstructure.

The base isolation (BI) system employed for the sample frame comprises 327 circular-shaped high damping rubber bearings (HDRBs) with three diameters, namely 600, 650 and800 mm, as pictorially displayed in the plan layout provided in Fig. 2.

The design of the BI structure was based on the application of the rules implementedin CEN (2006) and in the seismic national code (OPCM 3431, 2005, which was recentlyreplaced by DM 2008); the latter codes employ the same provisions for base isolated build-ings. Rubber isolators are placed under each column of the superstructure (see also Fig. 1).The mechanical properties of the rubber devices used for the sample structure are summa-rized in Table 1. The values of horizontal stiffness and shear modulus have been derivedfrom dynamic tests with a maximum frequency of 0.5 Hz and maximum shear deformationγ equal to 2.

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0.00

0.40

0.80

1.20

1.60

2.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Shear deformation (γ)

She

ar S

tres

s (M

Pa)

HDRB φ600

HDRB φ650

HDRB φ800

Fig. 3 Hysteretic behaviour of high damping rubber bearings (HDRBs) used for the sample base isolatedbuilding

Figure 3 shows the hysteretic behaviour of the three types of HDRBs used for the samplebase isolated hospital building; the response curves plotted in the figure correspond to thethird cycle of loading, which is utilized to compute the mechanical properties of the devices.

Qualifying cyclic tests were carried out on a sample of HDRBs following the protocolrequired by the national seismic code (OPCM 3431, 2005). It is noted that the devices exhibitstable energy dissipation capacity at large shear deformations under cyclic loads. Details onthe modelling of the BIS are further illustrated in Sect. 5.

3.2 Design gravity loads

The structural design of the base isolated building was carried out in compliance with partialsafety factor methods as implemented in the national (DM 2008) and European standards(CEN 2006). Amplification coefficients were thus employed to multiply the characteristicvalues of the applied loads. The (force) partial safety factors γg and γq are assumed equal to1.3 and 1.5, respectively. The combination factor ψ0i varies between 0.3 and 0.6 for hospitalbuildings. The coefficients ψ1i and ψ2i are equal to 0.6 and 0.3 in the (rare, frequent andquasi-permanent) combinations for the serviceability limit state.

4 Seismic input characterization

The structural analyses of the sample system were carried out by utilizing dynamic modalanalysis with response acceleration spectrum, linear and nonlinear response history analysiswith spectrum-compatible natural records. The modelling of the seismic input is discussedhereafter.

4.1 Modal analysis with acceleration response spectrum

The seismic input was defined with reference to the 5% damping acceleration response spec-tra evaluated for the four limit states compliant with the recent Italian code of practice (DM2008), namely the operational (OLS), damageability (DLS), life safety (LSLS) and collapse(CPLS) limit states.

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Table 2 Parameters used to define the spectra of the horizontal earthquake components

Limit state (type) PVR (%) TR (year) PGA (g)

ServiceabilityOLS 81 120 0.095

DLS 63 201 0.120

UltimateLSLS 10 1898 0.260

CPLS 5 2475 0.281

OLS operational limit state, DLS damageability limit state, LSLS life safety limit state, CPLS collapse limitstate, PVR probability of exceedance, TR return period of the seismic action, PGA peak ground acceleration

Table 3 Parameters used to define the spectral shape of the horizontal earthquake components

Limit state (type) SS(−) ST(−) FO (−) T∗C (s) CC (−) TB (s) TC (s) TD (s)

ServiceabilityOperational (OLS) 1.20 1.00 2.327 0.331 1.37 0.142 0.427 1.627

Damageability (DLS) 1.20 1.00 2.300 0.300 1.37 0.150 0.451 1.635

UltimateLife safety (LSLS) 1.13 1.00 2.542 0.345 1.36 0.167 0.501 1.691

Collapse prevention (CPLS) 1.10 1.00 2.578 0.346 1.36 0.172 0.517 1.715

S amplification factor for soil profile and topography, FO amplification factor for earthquake horizontal compo-nent, TB,TC and TD are periods corresponding to constant acceleration, velocity and displacement branches

Computed values of return period (TR) for each limit states are summarized in Table 2.Buildings whose integrity during earthquakes is of vital importance for civil protection, e.g.hospitals, are classified of importance class IV in Eurocode (CEN 2006), the importancefactor γI = 1.4.

The soil type comprises deposits of very dense sand with a gradual increase of mechanicalproperties with depth (shear velocity vs ranging between 300 and 800 m/s); such soil corre-sponds to the soil type B in the European seismic standards (CEN 2006). The design valuesof the peak ground accelerations (PGAs) vary between 0.095g (OLS) and 0.281g (CPLS) asshown in Table 2; the site of construction has thus moderate seismicity. The values of theparameters employed to define the spectral shape of the horizontal earthquake componentsat the design limit states are outlined in Table 3.

The viscous damping due to the rubber isolators was accounted for in the analysis byusing the factor η given by:

η = √10/(5 + ξ) ≥ 0.55 (1)

where ξ is the equivalent structural viscous damping expressed in percentage. Therefore, thedesign spectrum is scaled down through the η-factor in the range T ≥ 0.8 Tis. For the samplestructure with BI it was estimated that on average Tis = 2.0 s thus the aforementioned scalingis applicable for T ≥ 1.6 s. The BI system used for the hospital is characterized by equivalentviscous damping ξ equal to 15% and hence η = 0.71.

The design acceleration spectra for horizontal components of earthquake ground motionsare displayed in Fig. 4 along with the displacement response spectra at the four limit statesimplemented in the national seismic code (DM 2008).

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0.0

0.2

0.4

0.6

0.8

1.0

0.0 1.0 2.0 3.0 4.0

CPLS LSLS DLS OLS

Spec

tral

Acc

eler

atio

n (g

)

Period (sec)

Viscous Damping ξ=15%

0

10

20

30

0.00 1.00 2.00 3.00 4.00

LSLS DLS OLS CPLS

Spec

tral

Dis

plac

emen

t (cm

)

Period (sec)

Viscous Damping ξ =15%

Fig. 4 Design acceleration (left) and displacement (right) response spectra

The behaviour factor, namely q-factor, employed for the design of the super-structure iscomputed as follows (DM 2008):

q = 1.15 · αu/α1 = 1.15 · 1.3 = 1.5 (2)

where the ratio αu/α1 = 1.3 (RC frame building with several bays and storeys). The adoptedvalue of the q-factor shows that the super-structure behaves almost linearly even under severearthquake ground motion. The above assumption for the evaluation of q-factor is also com-pliant with the provisions implemented in Eurocode 8 (CEN 2006). The latter code statesthat, in buildings, the resistance condition of the structural elements of the super-structuremay be satisfied taking into account seismic action effects divided by a behaviour factor notgreater than 1.5.

The spatial model was assessed by considering the synchronous input motion Ex and Ey

along the orthogonal directions; the 100%–30% combination rule was used for the earthquakecomponents in compliance with the national seismic regulation (DM 2008). The vertical com-ponent of the earthquake ground motion was not accounted as the site of construction is farfrom the fault.

4.2 Linear and nonlinear dynamic analyses with natural acceleration time-histories

The use of time-history to perform earthquake analyses of structural systems for buildings isallowed by the Italian seismic design code (DM 2008) in compliance with European standards(CEN 2006) and selected records have to be compatible with design spectra.

In case of base isolated structures it is possible to use a single acceleration time-his-tory. Nevertheless, in this study a group of seven pairs of time-histories fulfilling the coderequirements for fixed base structures were utilized. The analysis results can thus be esti-mated as the average of results of the seven analyses. The seismic design codes allow theuse of artificially, mathematically generated or natural records. Natural records are, however,the most direct ground motion representations because they incorporate characteristics likeenergy, frequency and duration of real earthquake ground motions (e.g. Naeim and Lew 1995;Bommer and Acevedo 2004; Iervolino and Cornell 2005; among many others).

There is nowadays a great number of websites with a large number of records. In this workreference was made to the European Strong-motion Database (ESD) (http://www.isesd.cv.ic.ac.uk) where a selection of records has been derived by Iervolino et al. 2007. The timehistories used are summarized in Table 4.

The fundamental period of vibration of fixed and isolated based systems are (see alsoTable 7) Tbf = 0.78 s and Tis = 1.96 s; thus the conditions for spectrum-compatibility of

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http://www.isesd.cv.ic.ac.uk

http://www.isesd.cv.ic.ac.uk


Table 4 Set of earthquake natural records

Site/Zone Code Event name Country Date Station name

B-2 000197 Montenegro Yugoslavia 15/04/1979 Ulcini-Hotel Olimpic

000199 Montenegro Yugoslavia 15/04/1979 Bar-Skupstina Opstine

000228 Montenegro (aftershock) Yugoslavia 24/04/1979 Bar-Skupstina Opstine

000231 Montenegro (aftershock) Yugoslavia 24/04/1979 Tivat-Aerodrom

004673 South Iceland Iceland 17/06/2000 Hella

006263 South Iceland Iceland 17/06/2000 Kaldarholt

006334 South Iceland (aftershock) Iceland 21/06/2000 Solheimar

0.00

0.50

1.00

1.50

2.00

2.50

0.00 1.00 2.00 3.00 4.00

Average X 0,9 x Sel. Xa 000197

Xa 000199 Xa 000228 Xa 000231

Xa 004673 Xa 006263 Xa 006334

Period (sec)

Spec

tral

Acc

eler

atio

n (g

)

Scale Factor = 0.60

0.00

0.50

1.00

1.50

2.00

2.50

0.00 1.00 2.00 3.00 4.00

Average Y 0,9 x Sel. Ya 000197

Ya 000199 Ya 000228 Ya 000231

Ya 004673 Ya 006263 Ya 006334

Scale Factor = 0.44

Period (sec)

Spec

tral

Acc

eler

atio

n (g

)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Average X 0,9 x Sel Xa 000197

Xa 000199 Xa 000228 Xa 000231

Xa 004673 Xa 006263 Xa 006334

Period (sec)

Scale Factor = 1.50

Spec

tral

Acc

eler

atio

n (g

)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Average Y 0,9 x Sel./g Ya 000197

Ya 000199 Ya 000228 Ya 000231

Ya 004673 Ya 006263 Ya 006334

Period (sec)

Scale Factor = 0.96

Spec

tral

Acc

eler

atio

n (g

)

Fig. 5 Spectrum-compatibility at DLS (top) and LSLS (bottom) for the selected natural records: X- (left) andY-direction (right)

the ensemble of time-histories are as follows:

T ∈ [0.62; 2.35] ⇒ Sm−90%Se > 0 (3)

T /∈ [0.62; 2.35] ⇒ Sm−80%Se > 0 (4)

The spectrum compatibility for X- and Y-directions is provided in Fig. 5 for DLS and LSLS.The scaling factors employed for the code-compliant spectrum compatibility of the nat-

ural earthquake records are lower than 2.0; the latter values vary between 0.34 (OLS, alongY-direction) and 1.60 (CPLS, along X-directions), as also summarized in Table 5.

Fourier spectra were also evaluated for the sample suite of earthquake records. The com-puted results demonstrate that the fundamental frequency of the structures is lower thanpredominant frequencies of the natural records.

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Table 5 Scaling factorsemployed for the spectrumcompatibility of the naturalrecords

Direction Limit state

CPLS LSLS DLS OLS

X 1.60 1.50 0.60 0.47

Y 1.03 0.96 0.44 0.34

Fig. 6 Three-dimensional finite element model used to analyze the sample hospital building: perspective (left)and plan (right) views

5 Structural modelling

The RC multi-storey framed structure of the sample hospital building was modelled throughlinear elastic finite elements (FEs). Monodimensional FEs (frame elements) were utilizedto discretize both beams and columns of the three-dimensional bare framed system. Theframe element uses a general, three-dimensional, beam-column formulation which includesthe effects of bi-axial bending, torsion, axial deformation, and bi-axial shear deformations.Shear deformability of beams and columns were also included in the structural model. Panelzone strengths and deformations were not considered in the spatial FEM of the framed system.The implemented FEM encompasses about 8,000 beam elements for the super-structure. Thefloor slabs were modelled through 1500 shell elements. The adopted shell (bidimensional)element is a four node formulation that combines separate membrane and plate bendingbehaviour. The membrane behaviour uses an isoparametric formulation that includes trans-lational in-plane stiffness components and a rotational stiffness component in the directionnormal to the plane of the element. The modeling of the floor diaphragms with shell elementswas deemed accurate and efficient for the present case study because it reliably accounts forthe large openings due to the gardens in the roofs. Notwithstanding, the adopted modellingresulted cumbersome, from a computational standpoint, as it prevents the condensation ofthe degrees of freedom used typically in dynamic analyses of building systems with rigiddiaphragms at storey levels. An additional model with shells and beam elements was adoptedfor the foundation system (inferior slab and piles); spring elements (Winkler model) wereutilized to model the effect of soil along the pile length. Figure 6 displays the FE modelutilised for the response analyses of the sample building superstructure.

The structural response of the base isolation system, comprising 327 HDRBs, was sim-ulated using different numerical models for the rubber isolators as implemented in the FEpackage SAP2000 (CSI, 2008). For each HDRB, horizontal stiffness (khx = khy) were

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specified along with their relevant vertical stiffness kv. It is worth mentioning that the adopteddevices exhibit kv > 800kh (see the values of the mechanical properties summarized inTable 1); it is thus assumed that the contribution of the vertical stiffness is negligible.

In the linear analyses the isolators are modelled as linear rubber isolator link elements; thelatter elements are defined by two mechanical parameters, i.e. secant stiffness and dampingconstant. A link element is assumed to be composed by six separate springs, one for eachof six deformational degrees of freedom (axial, shear, torsion and pure bending). The stiff-nesses of devices are not constant values: they depend on the limit state under considerationand hence on the target design displacement. The value of such stiffnesses were based onexperimental tests on sample devices carried out by the manufacturer. The linear effectivedamping represents the total viscous damping of the link element that is used for responsespectrum analyses, for linear and periodic time histories. For response spectrum and linearmodal time history analysis, the effective damping values are converted to modal damp-ing ratios assuming proportional damping, i.e. the modal cross-coupling damping terms areignored. These effective modal-damping values are added to any other modal damping thatis specified directly. Damping coefficients are assumed equal to zero because damping ratiois accounted for through the setting of the analyses parameters.

Nonlinear analyses were carried out assuming linear elastic behaviour for frame and shellelements of the superstructure; the nonlinearity is concentrated at the base isolation system. Itis thus of paramount importance to simulate reliably the nonlinear response under earthquakeground motions of the rubber isolators.

To perform nonlinear dynamic analyses, it is assumed that damping coefficients are zerobecause the dissipated energy is accommodated by the nonlinear isolator behaviour.

To assess the equivalent damping coefficient ξeq of each isolator the following relationshipmay be used; it is computed at resonance, i.e. with ω = ωn :

ζeq = 1

4π· 1

ω/ωn· ED

Eso(5)

where ζeq , equivalent damping coefficient; ED , hysteretic dissipated energy; Eso, strain elas-tic energy; ω, circular frequency of the system; ωn , circular frequency of the external force.

The equivalent viscous damping ratio is estimated from the results of the experimentaltests carried out by the manufacturer. The actual response of the devices is derived fromlaboratory tests, thus the rubber isolators can be simulated numerically in a reliable manner.In particular a nonlinear elastic-plastic model with hardening has been chosen. This is a biax-ial hysteretic isolator that has coupled plasticity properties for the two shear deformations,and linear effective stiffness properties for the remaining four deformations. The plasticitymodel is based on the hysteretic behaviour proposed by Wen (1976), Park et al. (1986) andrecommended for base isolation analysis by Nagarajaiah et al. (1991). It is assumed that thedissipated energy gives the same value of equivalent damping ratio (energy equivalence).The model parameters of seismic isolators are summarised in Table 6.

Figure 7 provides the typical experimental response of 600 mm rubber devices. Thenumerical models used to perform linear and nonlinear dynamic analyses are compared withthe experimental data. Nonlinear uni-axial constitutive relationships were employed in bothhorizontal directions. It is assumed that deformations are independent along orthogonal direc-tions. Such assumption can be considered reliable for the benchmark case study because ofthe uncoupled modes of vibrations of the isolated structure. The above approximation tendsto be less reliable when bidirectional earthquake loading is accounted for. Table 6 summa-rizes the fundamental parameters used to model the rubber isolators of the sample structure.

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Table 6 Model parameters of seismic isolation devices

Isolatordiameter( mm)

Linearstiffness(kN/ mm)

InitialstiffnessK1(kN/ mm)

Post-yieldstiffnessK2(kN/ mm)

HardeningratioK2/K1

Yieldingforce Fy(kN)

Equivalentdampingratio (%)

600 1.51 1.90 1.01 0.53 197.66 8.10

650 2.98 4.45 2.15 0.48 459.27 9.22

800 4.89 6.68 3.32 0.50 545.75 9.56

-300

-200

-100

0

100

200

300

-200 -100 0 100 200

Experimental

Non linear model

Linear model

Displacement

Shea

r (k

N)

Fig. 7 Rubber seismic isolator model

It is worth noting that the equivalent elastic stiffness does not correspond to the same valueof the force corresponding to the test and assumed in the bilinear model.

The nonlinear response history analyses were carried out utilizing the nonlinear modaltime history analysis (Fast Nonlinear Analysis—FNA), a numerical integration scheme devel-oped by Wilson (1997) and implemented in SAP 2000 (CSI, 2008). The latter algorithm isextremely efficient and designed to be employed for the structural systems which are primar-ily elastic, but they have a limited number of nonlinear elements, such as for the sample baseisolated structure. The nonlinear elements are the isolation devices at the base of the framedsystem.

The structural models utilized to perform the dynamic analyses employ masses lumpedat structural nodes. The lumped masses were estimated by assuming the dead loads and partof the live loads in compliance with seismic code provisions. The structural analyses andperformance assessment was carried out by employing the computer program SAP2000 ver-sion 11.01 (CSI, 2008). The latter program possesses a powerful graphical interface with auser-friendly environment for the input/output data.

5.1 Remarks on nonlinear isolator modelling

To investigate the reliability of the adopted nonlinear isolator model (see Sect. 5) and to fur-ther assess the response of the rubber devices under dynamic loading, simplified sinusoidaltime-histories with different fundamental period of vibrations and amplitudes which leadto the same maximum displacement on the linear elastic model were assumed. Linear andnonlinear response history analyses were carried out along the X-direction of the plan layout

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Table 7 The modal responseproperties of the fixed and baseisolated models

Mode (–) Period (s) Participating mass ratios

X (%) Y (%) X(%) Y(%)

Fixed base

1 0.78 24.0 20.0 24.0 20.0

2 0.76 24.0 29.0 48.0 49.0

3 0.69 5.8 3.8 54.0 53.0

Isolated base

1 1.96 0.1 64.0 0.1 64.0

2 1.89 99.0 0.0 99.0 64.0

3 1.77 0.0 35.0 99.0 99.0

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0.10 1.50 1.70 1.99 2.10 2.20 2.40 2.60 2.80

Min

Sine wave period (sec)

C1

X

TD=12.90cm

0.00

0.50

1.00

1.50

2.00

2.50

3.00

Max (Kln) Min (Kln) Max (K=K1) Min (K=K1)

2.8X

TD=4cmC

1

Max 0.1 1.5 1.7

1.99 2.1 2.2

2.4 2.6

Fig. 8 Coefficient C1 for sinusoidal time-histories: TD = 12.90 cm (left) and TD = 4 cm (right)

of the structure because it activates nearly 100% of the total seismic mass along this direction(see Table 7). Results are expressed through the coefficient C1 equal to the ratio betweenmaximum (or minimum) displacement of nonlinear and linear models. Target displacements(TDs), i.e. the value of maximum displacement obtained by linear model subjected to elasticspectrum at LSLS (see also Table 14), is initially equal to 12.90 cm. These results, providedpictorially in Fig. 8, are compliant with Eq. (5). The coefficient C1 is 1.0 only when sinusoidalperiod corresponds to first natural period of the structure in X-direction. As a result, for suchvalue of sinusoidal time-histories linear and nonlinear models are equivalent. Additionally,a TD equal to 4 cm, which is a value lower than the yielding displacement of nonlinearlinks (9–10 cm), was assumed. The nonlinear system corresponds to a linear system withstiffness equal to K1 and without damping: C1 is variable because two systems have differentdynamic behaviour. Conversely, whether the linear system is characterized by K1 stiffness,C1 is always higher than unity, as displayed in Fig. 8.

A further case considered herein is TD = 30 cm; the results are provided in Fig. 9. Undersuch displacement the equivalent stiffness of the nonlinear system is lower than the stiffnessof the linear counterpart but the dissipated energy is almost the same as in the elastic model(see also results displayed in Fig. 10). Consequently, C1 is higher than unity for all the periodof sine-wave input motion (Fig. 9).

For the sake of completeness, Fig. 10 provides, for each nonlinear link, the equivalentstiffness and damping ratio respectively divided by linear stiffness and equivalent dampingratio reported in Table 1 versus the maximum device displacements.

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0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.50 1.70 1.99 2.10 2.20 2.40 2.60 2.80

MaxMin

Sine wave period (sec)

C1

TD=30cm

Fig. 9 Coefficient C1 for sinusoidal time-histories: TD = 30 cm

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 30 60 90 110 140 170 200 230 260 290 320 350 380

Stiffness 600

Stiffness 650

Stiffness 800

Damping ratio 600

Damping ratio 650

Damping ratio 800

Isolator displacement (mm)

Dim

ensi

onle

ss s

tiffn

ess

Dim

ensi

onle

ss d

ampi

ng

Fig. 10 Equivalent stiffness and damping ratio for each base isolator

6 Performance criteria

Hospital buildings are critical facilities which are vital in the aftermath of earthquake groundmotions; it is thus essential to warrant immediate occupancy performance level under mod-erate-to-intense seismic events. Failure of mechanical and electrical components, damageto medical machineries and equipments may endanger the seismic performance level of theentire building system, although the integrity of the non-structural architectural components,e.g. partitions, claddings and ceilings. Furthermore, failure of nonstructural building com-ponents may prevent the safe evacuation of building occupants and/or undermine rescueoperations. Mechanical and electrical components, as well as machineries and equipmentsare sensitive to horizontal floor accelerations. The seismic performance of nonstructuralbuildings components is, in turn, controlled by interstorey drifts of the structural system.The structural response of the sample system is investigated hereafter with reference to thefollowing performance parameters:

• Storey and interstorey drifts;• Horizontal storey accelerations of the superstructure;• Axial loads in the HDRBs;• Horizontal displacements of HDRBs.

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Axial loads in the HDRBs is computed to identify tensile forces, if any, in the devices. Lowvariations of axial loads under gravity loads and seismic loads points out the efficacy of thebase isolation system. Moreover, the estimation of the deformation demand imposed on eachdevice is essential to check the capacity of the HDRBs.

7 Structural response analysis

The structural response assessment of the irregular frame of the hospital building was carriedout through spectral and time history (both linear and nonlinear) analyses. Such analyses werecarried out in compliance with code provisions (e.g. CEN 2006; DM 2008). Modal analysiswas also carried out to evaluate the eigenvalues and eigenvectors of the framed structure, asillustrated in the next paragraph.

7.1 Modal analysis results

The dynamic properties of the fixed and base isolated models of the sample building are sum-marized in Table 7. The base isolation ratio (BIR = Tbi/Tfb), i.e. the ratio of the fundamentalperiod of the base isolated structure (Tbi = 1.96 s) and the natural period of the fixed basesystem (Tfb = 0.78 s), is 2.5. The latter value demonstrates the efficacy of the base isolationfor the irregular framed building.

The results derived from eigenvalue analysis show that the participating mass ratios forthe isolated structure are characterized by the onset of the 99% of the total mass in the firstthree modes of vibration. The modal translation response is uncoupled along the X- andY-directions. Conversely, the dynamic response of the fixed base structure is extremely com-plex and higher modes affect significantly the global response, for translation and rotationcomponents of the lateral displacements. The participating mass relative to the first threemodes of vibration is about 50% (54 and 53% along X- and Y-direction, respectively) of thetotal structural mass. Additionally, the modal response is coupled along the X- and Y-direc-tions of the lateral translation.

The dynamic properties of the base isolated model summarized in Table 7 were eval-uated for the structural system, modeled using mechanical properties at ULS according toDM (2008). However, modern seismic standards require that values of physical and mechani-cal properties of the isolation system to be used in the analysis shall be the most unfavourableones to be attained during the lifetime of the structure. The properties of the isolation devicesshould reflect adequately the influence of (1) rate of loading; (2) magnitude of the simul-taneous vertical load; (3) magnitude of the simultaneous horizontal loads in the transversedirection, (4) temperature effects due to the thermal gradient and (5) change of propertiesover projected service life, i.e. aging effects. Additionally, accelerations and inertia forcesinduced by the earthquake should be evaluated taking into account the maximum value ofthe stiffness and the minimum value of the damping and friction coefficients. Moreover,displacements should be evaluated taking into account the minimum value of stiffness anddamping and friction coefficients.

The hysteretic behaviour of the three types of HDRBs used for the base isolated building,as displayed in Fig. 3, shows that for low lateral displacements the increase of horizontalstiffness of the devices is significant. Conversely, it has been demonstrated that for valuesof deformations up to 50% of the design values, the equivalent viscous damping increasesslightly, i.e. on average less than 20% (e.g. Kelly 1996; Naeim and Kelly 1999, among

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Table 8 Secant horizontalstiffness of the isolators atdifferent limit states

Limit state Isolator (diameter, mm) Horizontal stiffness (kN/ mm)

OLS 600 2.03

650 4.34

800 6.22

DLS 600 1.79

650 3.78

800 5.58

LSLS 600 1.62

650 3.46

800 5.45

CPLS 600 1.61

650 3.48

800 5.58

Table 9 Periods of vibration atdifferent limit states

Limit state Periods (s)

1st Mode 2nd Mode 3rd Mode

OLS 1.84 1.75 1.63

DLS 1.96 1.84 1.72

LSLS 1.96 1.89 1.77

CPLS 1.95 1.88 1.77

others). The enhanced lateral stiffness at small deformations shortens the fundamental periodof vibration of the base isolated structure and, in turn, augments the inertial forces on thesuper-structure. As a result, it is essential to estimate the secant horizontal stiffness of theisolators at different limit states considered in the analysis and design of the hospital building.Table 8 summarizes the results computed with an iterative solution strategy for the three typesof HRDBs employed for the case study structure, based on a target design displacement ateach limit state. The secant horizontal stiffness of the isolation devices at OLS can be 35%higher than the counterpart stiffness at CPLS. Nevertheless, the effect on the modal responseof the base isolated structure is not significant.

The periods of vibration of the base isolated building at four LSs considered for the samplestructures are listed in Table 9 for the first three modes, i.e. the modes relative to the baseisolation system. The computed values of the periods of vibration show than the horizontalstiffness relative to the OLS can be conservatively used to determine the internal actions inthe superstructures; conversely, the stiffness associated to CPLS can be employed to checkthe deformation capacity of the isolation devices.

The computed results show that the variations of the fundamental period of vibration tendto be less than 10%, when the OLS and CPLS are considered, and hence they can be neglected.Similarly, the modal mass do not change at the four LSs. The modal response values derivedfor the four LSs, i.e. OLS, DLS, LSLS and CPLS, are summarized in Tables 10, 11, 12, 13.

To investigate the reliability of the prediction of global structural response quantities forirregular base isolated structures, the dynamic analysis results, design acceleration spectra

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Table 10 Modal response quantities of the base isolated building at OLS

Mode (–) Participating mass

Period (s) X (%) Y (%) X(%) Y(%)

1st 1.84 0.08 63.00 0.08 63.00

2nd 1.81 99.00 0.28 99.00 64.00

3rd 1.72 0.26 36.00 99.00 99.00

Table 11 Modal response quantities of the base isolated building at DLS


Period (s) X (%) Y (%) X(%) Y(%)

1st 1.96 0.02 64.00 0.02 64.00

2nd 1.89 99.00 0.00 99.00 64.00

3rd 1.78 0.04 35.00 99.00 99.00

Table 12 Modal response quantities of the base isolated building at LSLS


Period (s) X (%) Y (%) X(%) Y(%)

1st 1.96 0.18 64.00 0.18 64.00

2nd 1.89 99.00 0.12 99.00 64.00

3rd 1.77 0.00 35.00 99.00 99.00

Table 13 Modal response quantities of the base isolated building at CPLS


Period (s) X (%) Y (%) X(%) Y(%)

1st 1.95 0.42 64.00 0.42 64.00

2nd 1.88 99.00 0.38 99.00 64.00

3rd 1.77 0.02 35.00 99.00 99.00

and earthquake time-histories are applied along the X-direction of the plan layout of the casestudy building. The participating mass along X-direction is 99% for the first translation modeof vibration (see also Table 7). The seismic response of the multi-degree of freedom model(MDOF) of the irregular three-dimensional framed building is equivalent to the single-degreeof freedom system (SDOF). Such equivalence is a typical beneficial effect for the buildingstructures employing base isolation.

7.2 Spectral response analyses

The spectral response analyses of the base isolated structure were carried out with respectto horizontal acceleration 15% damping spectra defined in Sect. 4.1. Uniaxial (along X- and

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0

500

1000

1500

2000

2500

3000

3500

0 5

OLS DLS LSLS CPLS

Displacement (cm)

Hei

ght (

cm)

X

Vertical 1 X Direction

0

500

1000

1500

2000

2500

3000

3500

0 510 15 20 10 15 20

OLS DLS

LSLS CPLS

Displacement (cm)

Hei

ght (

cm)


X

Fig. 11 Spectral lateral displacement distribution of base isolated system (earthquake spectrum alongX-direction)

0.00

0.25

0.50

0.75

1.00

X Direction Y Direction

Inte

rsto

ry D

rift

d/h

(%

)

Code Limit (DM 2008) 0.33%

Level

1.0X + 0.3Y

0.00

0.25

0.50

0.75

1.00

I II III IV V VI VII VIII I II III IV V VI VII VIII

X Direction Y Direction

Inte

rsto

ry d

rift

d/h

(%

)

Code limit (DM 2008) 0.33%

0.3X + 1.0Y

Level

Fig. 12 Inter-storey drift distribution along the height of the base isolated structure

Y-directions, separately) and biaxial combinations of the seismic input motions wereconsidered. Four structural models were assessed as the mechanical properties of the HDRBsvary with the limit state, as discussed earlier (see also Table 8).

The spectral lateral displacement distribution along the base isolated building height isprovided in Fig. 11 for two corner locations of the plan layout. The vertical deformed shapesshow a nearly rigid deflection of the superstructure both at serviceability (OLS and DLS) andultimate (LSLS and CPLS) limit states. The horizontal floor displacements at CPLS are closeto those computed at LSLS; the maximum variations are about 8% and 6%, for the roof ofthe low- and high-rise blocks, respectively. The values of the spectral lateral displacementsin Fig. 11 are computed for the spectral accelerations acting along X-direction only. Similarresults were also found when earthquake loading is applied along Y-direction and for thecode-compliant seismic combinations.

The inter-storey drifts d/h along the building height at DLS were also computed. Figure 12shows the results derived for the seismic combinations 1.0X + 0.3Y and 0.3X + 1.0Y. Thevalues of d/h do not exceed 0.06% and are significantly lower than the code-based thresholdvalue, i.e. 0.33%. Higher interstorey drifts are computed at lower storeys; the maximum d/h(=0.056%) is found at second level. The upper floors have d/h lower than 0.04%.

To evaluate the damageability of non structural components, the mechanical and electri-cal equipments, building contents and the comfortability of the patients, their relatives andmedical staff of the hospital building, it was deemed necessary to estimate the floor responsespectra. The distribution of the spectral horizontal accelerations along the building height isprovided in Figs. 13 and 14 for the seismic combinations 1.0X + 0.3Y and 0.3X + 1.0Y.

For the low-rise block of the framed structure, the roof acceleration is lower the peakground acceleration (PGA) at OLS, i.e. 0.095g. For the high-rise block, the horizontal accel-erations of the seventh and eighth floors is slightly higher than 0.10g for the LSLS and CPLS.

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0

500

1000

1500

2000

2500

3000

3500

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

PGA (OLS) PGA (DLS)

PGA (LSLS) PGA (CPLS)

OLS DLS

LSLS CPLS

Acceleration (g)

Hei

ght (

cm)

X

Vertical 1 Direction X1.0X + 0.3Y

0

500

1000

1500

2000

2500

3000

3500

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

PGA (OLS) PGA (DLS)PGA (LSLS) PGA (CPLS)OLS DLSLSLS CPLS

X

Acceleration (g)

Hei

ght (

cm)

Vertical 2 X Direction1.0X + 0.3Y

Fig. 13 Spectral lateral acceleration distribution of base isolated system (earthquake response spectrum:combination 1.0X + 0.3Y)

0

500

1000

1500

2000

2500

3000

3500

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

PGA (OLS) PGA (DLS)


OLS DLS

LSLS CPLS

Y

Acceleration (g)

Hei

ght (

cm)

Vertical 1 Y Direction0.3X + 1.0Y

0

500

1000

1500

2000

2500

3000

3500

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

PGA (OLS) PGA (DLS)

PGA (LSLS) OLS

DLS LSLS

CPLS PGA (CPLS)

Y

Acceleration (g)

Hei

ght (

cm)

Vertical 2 Y Direction0.3X + 1.0Y

Fig. 14 Spectral lateral acceleration distribution of base isolated system (earthquake response spectrum:combination 0.3X + 1.0Y)

0

500

1000

1500

2000

2500

3000

3500PGA (OLS) PGA (DLS)


OLS DLS

LSLS CPLS

Acceleration (g)

Hei

ght (

cm)

Vertical 1 Direction X

X X

0

500

1000

1500

2000

2500

3000

3500

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

PGA (OLS) PGA (DLS)


OLS DLS

LSLS CPLS

Acceleration (g)

Hei

ght (

cm)


Fig. 15 Spectral lateral acceleration distribution of base isolated system (earthquake spectrum alongX-direction)

The PGAs relative to the latter LSs are, however, halved (see also Table 2). On average, areduction of the soil acceleration equal to 70% was estimated for the sample hospital build-ing. Such reduction confirms the effectiveness of base isolation to prevent the occurrence ofstructural and non structural damage of the superstructure.

Acceleration profiles similar to those computed for the seismic combinations 1.0X + 0.3Yand 0.3X + 1.0Y were derived for the earthquake loading acting along the X-direction only,as pictorially shown in Fig. 15.

The lateral deformations of the base isolators were also computed. Figure 16 shows theresults of the 600 m and 800 mm HDRBs when loaded along X- and Y-directions, separately.The maximum lateral displacements are similar along both the main directions of the planlayout, i.e. 12.4 versus 12.3 cm.

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-20

-16

-12

-8

-4

0

4

8

12

16

20

0 50 100 150 200 250

Is. 600 mm_Displacements x

Is. 600 mm_Displacements y

Expected Displacements

Dis

plac

emen

t (cm

)

Node (number)

DX,max = 12.4 cmDX,min = -12.4 cm

DY,max = 11.9 cmDY,min = -11.9 cm

-20

-16

-12

-8

-4

0

4

8

12

16

20

0 50 100 150 200 250


Is. 800_Displacements y

Expected displacements



Dis

plac

emen

t (cm

)

Node (number)

Fig. 16 Spectral lateral displacements of base isolators (earthquake response spectrum: X- and Y-directions,respectively)

Table 14 Horizontal displacements of the rubber isolators calculated by spectral analysis

Isolator ( mm) Mean displacements along X Mean displacements along Y

Max (cm) C O V (%) Max (cm) C O V (%)

Only X

600 11.5 1.0 0.2 38.9

650 11.4 1.3 0.1 40.6

800 11.4 1.2 0.2 29.3

Only Y

600 1.6 57.8 11.2 3.5

650 1.6 51.1 11.2 2.9

800 1.6 41.6 11.4 3.8

X + 30% Y

600 12.0 3.1 3.5 4.0

650 11.9 2.7 3.5 2.9

800 11.8 2.1 3.6 4.0

Y + 30% X

600 5.0 18.6 11.2 3.5

650 5.0 16.5 11.2 2.9

800 5.0 13.5 11.4 3.8

The prediction of the maximum lateral displacements derived from the horizontal responsespectra, i.e. assuming a single-degree-of-freedom (SDOF) approximation, matches reliablythe estimated horizontal displacements of the devices computed with the spectral analysis ofthe three dimensional framed system, as further discussed in Sect. 8. The lateral deformationsof the HDRBs provided in Fig. 16 prove that the displacement demand on the rubber devicesis uniformly distributed; the base isolation system exhibits a predominant pure translationalong both X- and Y-directions. The mean displacements of the rubber isolators along withthe coefficient of variations (COVs) are summarized in Table 14 for the earthquake loadingacting along X and Y, separately, and for the seismic combinations 1.0X + 0.3Y and 0.3X+ 1.0Y.

The values of the horizontal displacements were derived for the seismic input along theX- and Y-directions only, for each group of isolator diameters. Such values match closelythe counterpart deformations relative to the seismic combinations. This finding is compliant

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-100

-50

0

50

100

550 600 650 700 750 800 850

Axial force Mean

Axi

al L

oad

Var

iatio

n

N (

%)

Isolator Diameter (mm)

Fig. 17 Variation of axial forces in the rubber isolators derived with spectral analysis

with the uncoupled modes of vibrations of the irregular base isolated structure, as discussedearlier.

The seismic isolation system reduces internal actions generated in the structure duringearthquakes. The mean axial force on isolators with seismic vertical loads are equal to 2,086kN for 600 mm isolators, 3,082 kN for isolators of 650 mm and 5,460 kN for devices withdiameter of 800 mm. The variation of axial forces at ULS is shown in Fig. 17. The meanstress in the HDRBs is lower than 10 MPa and it is uniformly distributed in the three groupsof isolators (the variations of the normal stress range between 12 and 14%). Net tensile forceswere not detected in the rubber devices.

The base shear were computed along X-and Y-directions; the values are similar, i.e.1.14E+05 kN (along X) and 1.11E+05 kN (along Y). The total seismic mass of the super-structure is 1.06E+05 tons. As a result, the seismic coefficients are 1.07 and 1.05 m/s2, forX and Y-direction, respectively, thus confirming that the dynamic response of the samplestructure does not depend on the main direction of the plan layout of the building.

7.3 Response history analyses

Linear and nonlinear response history analyses of the base isolated building structure werecarried out considering the ensemble of natural earthquake records selected as discussed inSect. 4.2. The mean lateral displacements of the first floor solid slab of the superstructurecomputed with linear dynamic analyses are summarized in Table 15; the records were appliedseparately along X- and Y-directions, respectively.

At CPLS the spectral values of the lateral displacements of solid slab are close to thosecomputed with linear dynamic analyses for the rubber isolators (compare values given inTables 14 and 15). Along X-direction the spectral displacement is 11.5 cm, which is simi-lar to the counterpart value 10.54 cm (variation of 9.1%). Along Y-direction, the variationbetween the spectral displacements and those computed with linear dynamic analyses are onaverage 20%. This response is compliant with the slightly coupled modes of vibration (seemodal response quantities in Table 13) along Y-direction.

The mean lateral displacement distributions pictorially summarized in Fig. 18 are similarto those shown in Fig. 11 and relative to spectral analyses. The values of the drifts are alsoclose to those estimated with spectral analyses.

Similarly the acceleration profiles evaluated with the spectral analyses (see Fig. 15) matchthose computed with linear dynamic analyses, as provided in Fig. 19. It is thus proved that,

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Table 15 Mean lateraldisplacements of the firts floorsolid slab (linear dynamicanalyses)

X-direction Y-direction

Max Min Max Min

OLS

X-direction 2.94 −2.84 0.05 −0.05

Y-direction 0.62 −0.63 4.37 −4.12

DLS

X-direction 3.90 −3.89 0.06 −0.06

Y-direction 0.79 −0.79 5.83 −5.34

LSLS

X-direction 9.93 −10.09 0.14 −0.15

Y-direction 1.70 −1.69 13.32 −12.06

CPLS

X-direction 10.54 −10.67 0.17 −0.17

Y-direction 1.79 −1.78 14.23 −12.92

0

500

1000

1500

2000

2500

3000

3500

0 5

OLS DLS LSLS CPLS

Displacement (cm)

Hei

ght (

cm)

X


0

500

1000

1500

2000

2500

3000

3500

0 510 15 20 25 10 15 20 25

OLS DLS

LSLS CPLS

Displacement (cm)

Hei

ght (

cm)


X

Fig. 18 Mean lateral displacement distribution of base isolated system (elastic response history analysis,earthquake records applied along X-direction)

0

500

1000

1500

2000

2500

3000

3500

0

PGA (OLS) PGA (DLS)


OLS DLS

LSLS CPLS

Hei

ght (

cm)

Acceleration (g)

X

0

500

1000

1500

2000

2500

3000

3500

0-0.6 -0.4 -0.2 0.2 0.4 0.6 -0.6 -0.4 -0.2 0.2 0.4 0.6

PGA (OLS) PGA (DLS)


OLS DLSLSLS CPLS

Hei

ght (

cm)

Acceleration (g)

X

Fig. 19 Mean lateral acceleration distribution of base isolated system (elastic response history analysis,earthquake records applied along X-direction)

for base isolated structures, the spectral analyses approximate reliably the structural responseestimated through linear dynamic analyses, provided that the modal participation mass ratiosare higher than 85–90%, as for the X-direction of the sample framed system. The maximumfloor accelerations are on average lower than 0.15g, i.e. the PGA corresponding to the DLS(=1.20 × 0.120 = 0.144g, see also Table 2).

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0.00

0.50

1.00

1.50

2.00

2.50

197(T=1.12)

199 (T=1.02)

228 (T=0.66)

231 (T=0.18)

4673 (T=0.37)

6263 (T=0.33)

6334 (T=0.11)

Max displacementsMin displacements

Earthquake record (label)

Lat

eral

dis

plac

emen

t rat

io

(Non

linea

r/L

inea

r)

Fig. 20 Ratios of the minimum and maximum lateral displacements of base isolators (earthquake recordsapplied along X-direction)

Table 16 Mechanical propertiesof the rubber isolator modellingat LSLS

Mechanical property Rubber isolator diameter ( mm)

600 650 800

K1 (kN/ mm) 2.72 6.06 9.04

K2 (kN/ mm) 1.01 2.15 3.32

Fy (kN) 147.28 367.67 513.31

r = K2/K1 0.37 0.35 0.37

Nonlinear time history response of the base isolated structure was also investigated. In theFE model employed herein, the nonlinearity was lumped in the HDRBs; the superstructure isassumed to behave in a linear manner. The mechanical properties of the rubber isolators wereevaluated at all LSs as in the reference seismic standards (i.e. D.M. 2008). Table 16 summa-rizes the properties of the nonlinear model employed to assess the seismic performance atLSLS.

The values of the mean lateral displacement of first floor slab are provided in Table 17. Thevalues were estimated for the X- and Y-directions, respectively. The computed displacementsare close to those derived from linear response history and spectral analyses. For example,the maximum displacement along X-direction is 10.09cm for the elastic response history(see Table 15) and 11.52cm in the nonlinear analysis; the variation is about 14%. Higherdifferences in the evaluation of horizontal displacements were evaluated for the Y-direction;the variation is up to 26.5%, i.e. 13.32 cm versus 14.14 cm. It can thus be argued that thecoupled modes of vibration along Y-directions leads to underestimations of the displace-ment demand on the isolation devices. The participating mass is about 100% (i.e. 99% alongX-direction) the elastic displacements match the inelastic counterparts, in compliance withthe equal displacement rule.

The comparisons between elastic and inelastic minimum and maximum lateral displace-ments of the rubber isolators are summarized in Fig. 20 for each considered records. The val-ues of the displacements demonstrate the equivalence between elastic and inelastic responsefor the X-direction (with 99% participating mass). The ratios of the minimum and maximumdisplacements are on average close to the unity. This results comply also with “equal dis-placement rule” formulated by Newmark and Hall (1982) for long period structures, such asthose employing BIS.

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Table 17 Mean values of thelateral displacements of first floorsolid slab (at LSLS, nonlineartime history response)

X-direction Y-direction

Max Min Max Min

X-direction 11.52 −10.72 0.76 −0.75

Y-direction 2.53 −2.50 16.85 −14.14

0

500

1000

1500

2000

2500

3000

3500

-25 -15 -5 5 15 25

OLS DLS

LSLS CPLS

Hei

ght (

cm)

Displacement (cm)

X


0

500

1000

1500

2000

2500

3000

3500

-25 -15 -5 5 15 25

LSLS CPLS

OLS DLS

Hei

ght (

cm)

Displacement (cm)

X


Fig. 21 Mean lateral displacement distribution of base isolated system (inelastic response history analysis,earthquake records applied along X-direction)

-45

-35

-25

-15

-5

5

15

25

35

45

30

Linear Noninear Response spectrum

Time (sec)

Dis

plac

emen

t (cm

)

X

-45

-35

-25

-15

-5

5

15

25

35

45

0 5 10 15 20 25 0 5 10 15 20 25 30

Linear Noninear Response spectrum

Time (sec)

Dis

plac

emen

t (cm

)

X

Fig. 22 Lateral displacement time history for two corner points (earthquake records label 199 applied alongX-direction)

The response history analyses show that the mean elastic and inelastic lateral displace-ments along the building height are similar for the X-direction. The results provided in Fig. 21for the inelastic response are close to those elastic shown in Fig. 18. The distribution of thedrifts tend also to be symmetric (in the positive and negative directions) along the height ofthe building.

The displacement time histories of the first floor solid slab were computed using bothlinear and nonlinear response history analyses. The comparisons of the corner points of thefloor slab are provided in Fig. 22 of earthquake records number 199 (see Sect. 4.2). Thevalues derived using the response spectrum analyses approximate closely the displacementsevaluated with linear and nonlinear time history analyses; the mean peak values refer to5% equivalent viscous damping. The maximum variations range between 10 and 20%; thelatter are, however, dependent on the characteristics of the selected earthquake records. Thedifferences of the mean values of the time-history response are generally less than 10%.

The time history response of the displacements of isolation devices was also investigatedby using linear and nonlinear dynamic analyses. Earthquake records were applied alongX- and Y-directions, separately. Figure 23 shows the results of the 600 mm rubber devices.

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-25

-20

-15

-10

-5

0

5

10

15

20

25

0 50 100 150 200 250


Is. 600 mm_Displacements yDisplacements expected X

Displacements expected Y

Dis

plac

emen

t (c

m)

Node Number



-25

-20

-15

-10

-5

0

5

10

15

20

25

0 50 100 150 200 250


Is. 800 mm_Displacements y

Displacements expected X

Displacements expected Y



Dis

plac

emen

t (c

m)

Node Number

Fig. 23 Maximum and minimum time history response of lateral displacements of 600 mm base isolators(earthquake records along X- and Y-directions, respectively)

Fig. 24 Hysteretic response of a typical 600 mm rubber isolator (inelastic response history analyses, earth-quake records applied along X-direction)

The distribution of displacements matches the findings obtained through spectral analyses.However, the values are higher than those displayed in Fig. 16: the maximum (absolute)nonlinear displacements are 20.1 cm (X-direction) and 18.1 cm (Y-direction), while thosederived from linear analyses are 12.4 and 11.8 cm, respectively. It is instructive to note thatthe threshold values of spectral displacements included in Fig. 23 refer to 5% damping, asper code spectral compatibility requirements (see Sect. 4). Conversely, those in Fig. 16 werederived assuming 15% viscous damping. The above discussion points out the controversialrules of seismic code relative to the spectral compatibility for structures with high damping,e.g. with base isolation systems and dissipative dampers. For such structures the compati-bility should be referred to the actual value of the equivalent viscous damping (ξ < 5%), tocompare reliably the results derived with different dynamic analyses. This is also the case ofthe definition of the earthquake input within the displacement-based seismic design.

The inelastic time histories were also employed to assess the energy absorption and dis-sipation of the HDRBs used for the BIS of the irregular sample building. The hystereticresponse of a typical 600 mm rubber isolators is also displayed in Fig. 24.

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Table 18 Mean displacements for LSLS (X direction)

Diameterisolator ( mm)

SDOFpredictionfrom designspectrum (cm)

Responsespectrumanalysis (cm)

SDOFpredictionfrom mediumtime-historiesspectrum (cm)

Lineartime-historyanalyses (cm)

Nonlineartime-historyanalyses (cm)

600 14.24 12.98 14.12 12.12 14.07

650 14.24 12.90 14.12 12.04 14.03

800 14.24 12.81 14.12 11.96 13.98

Average 14.24 12.90 14.12 12.04 14.03

Table 19 Ratios of the maximum lateral displacements derived from dynamic analyses

Displacements ratios for LSLS (X direction)

Isolator diameter( mm)

SDOF predictionvs. spectrumanalysis

Lineartime-history-analysesvs. spectrum analysis

Nonlineartime-history-analyses vs.linear time-history-analyses

600 1.10 0.93 1.16

650 1.10 0.93 1.17

800 1.11 0.93 1.17

Average 1.10 0.93 1.17

The hysteretic response curves were computed for the suite of seven natural groundmotions. It is shown that the nonlinear element (nonlinear link) enters into the inelasticregime and dissipate the earthquake-induced energy.

8 Further comparisons of analysis results

Further comparisons were also carried out to investigate the reliability of the results estimatedwith spectral and time history dynamic analyses and structural models with different levelsof complexity, e.g. SDOF versus spatial framed system. The mean maximum displacementscomputed with the different dynamic analyses are listed in Table 18; comparisons of suchdisplacements are summarized in Table 19.

Response spectrum analysis carried out on the spatial FE structural model gives lowerdisplacements that spectrum previsions. Linear time-history analysis provides lower valuesof displacements than the spectrum method. On the other hand, the ratio between nonlinearand linear time-history analyses should be lower than unity. This is, however, significantlyaffected by the record characteristics and the expression used to estimate the equivalentdamping coefficient. Equation (5) leads to the equivalence between nonlinear and linearmodels merely under a sinusoidal time-history with frequency equal to 0.50 Hz. The sam-ple earthquake time-histories possess, however, higher frequencies. Thus, ratios higher thanunity are expected. Results similar to those summarized in Tables 18 and 19 were estimatedfor horizontal accelerations.

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0

500

1000

1500

2000

2500

3000

3500

1.0X+0.3Y

0.3X+1.0Y

Code-limit

Interstorey drift D/H (%)

Hei

ght (

cm)

X

0

500

1000

1500

2000

2500

3000

3500

-1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00

0197

0199

0228

0231

4673

6263

6334

Average

Code Limit

Interstorey drift D/H (%)

Hei

ght

(cm

)

Fig. 25 Horizontal displacement profiles along the building height: spectral (left) and time history (right)analyses

Table 20 Seismic base shears derived from spectral and response history analyses

Spectral analysis Response history analysis

X-direction Y-direction X-direction Y-direction

Base shear (kN) 1.14E + 05 1.11E + 05 1.75E + 0.5 1.75E + 0.5

Seismic coefficient (3D model) (m/s2) 1.07 1.05 1.65 1.62

Seismic coefficient (SDOF model) (m/s2) 1.38 1.38 1.41 1.81

Variation (%) + 22.2 23.9 −17.1 + 10.5

The distribution height-wise of the lateral displacements were also computed with spectraland time history analyses. The results derived from the different dynamic methods are closeapproximations as shown in Fig. 25.

The evaluation of the seismic base shear can be derived from simplified models. Table 20compares the base shears (for X- and Y-directions) computed with the three-dimensionalmodels and those obtained from simplified SDOF system. The approximation is within 20%and hence acceptable for preliminary design of base isolated superstructure. The seismiccoefficient is also computed assuming that the total seismic mass is 1.06E+05 tons.

9 Conclusions

The present analytical work discussed the results of comprehensive dynamic analyses carriedout on a large irregular multi-storey framed building employing 327 high-damping rubberbearings (HDRBs) as base isolation system (BIS). The structure of the hospital buildingis utilized to assess the reliability of linear and nonlinear dynamic analyses implemented inmodern design standards world-wide and their conservatism, if any. To do so, code-compliantmodal (eigenvalue), spectral and time history analyses were performed on the three-dimen-sional finite element model (FEM) of the structure; simplified analyses were also conductedon single-degree-of-freedom (SDOF) systems. The earthquake response analysis of the hos-pital building is performed chiefly with reference to the (1) storey and interstorey drifts,(2) horizontal storey accelerations of the superstructure, (3) axial loads in the high dampingrubber bearings (HDRBs) and (4) horizontal displacements of HDRBs.

For the sample structure, the base isolation ratio (BIR = Tbi/Tfb), i.e. the ratio of thefundamental period of the base isolated structure (Tbi = 1.96 s) and the natural period of

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the counterpart fixed base system (Tfb = 0.78 s), is 2.5. Although the relatively flexiblefixed-base structure (period of vibration equal to about 0.8 s), the results of the structuralanalyses confirm that the BIS may lead to a number of advantages for both structural andnon structural components.

At damageability limit state (DLS), the values of maximum interstorey drifts (d/h) com-puted with spectral analyses on the three-dimensional FEM range between 1/6 and 1/10 ofthe code limit (d/h = 0.33%), at lower and upper storeys, respectively. The above values ofd/h were also derived with response history analyses (linear and nonlinear); the computedspectral values envelope the values of d/h computed through time history analyses. Codelimits for interstorey drifts at DLS should be more conservative for structures with BISs.

The deformed shape of the assessed superstructure is rigid and the damage to the nonstructural components is inhibited. Additionally, the maximum floor acceleration is reducedby about 70% with respect to the ground acceleration (free field site). Moreover, the accelera-tions are virtually constant over the height of the multi-storey frame. The functionality of thebuilding contents is thus guaranteed, even in the aftermath of moderate-to-high magnitudeearthquake ground motions. Codes of practice should implement threshold values for thefloor acceleration to assess the seismic performance of buildings with BIS. Experimentaland numerical research is, however, deemed necessary to establish reliable floor accelerationlimits.

At ultimate limit state (ULS), spectral analyses provide values of actions and deformationsthat are less conservative than those derived through time history analyses. These outcomesare due to the spectrum-compatibility requirements of the recent Italian seismic code (D.M.2008) and Eurocode 8 (CEN 2006). The latter design standards lead to time-history analysesat ULS which are more restrictive than spectral analyses. It may, therefore, be argued that, toperform reliable dynamic analyses of base isolated buildings, it is of paramount importanceto select natural earthquake ground motions that are compliant with the fundamental periodof vibration of the structural system. However, such systems exhibit periods greater than2.0 s, generally between 2.5 and 3.0 s; it is not straightforward to select adequate naturalstrong motions in the catalogues available world-wide. Distant and high-magnitude earth-quakes are effective for buildings with BIS; nevertheless, such earthquakes are scarce in theseismic databases.

The results of this preliminary analytical study also demonstrate that the selection ofsuites of natural accelerograms based merely on the spectrum compatibility may, however,result misleading and gives rise to underestimations of the deformation quantities derived bysimplified code-based dynamic analyses. The calibration of the linear and nonlinear modelsadopted to simulate the dynamic response of the isolators should be based on the actual fun-damental frequency of the structural system. This assumption may be effective to reduce theunderestimation of the earthquake effects evaluated through linear dynamic analyses, whichranges between 15 and 20%. A suite of seven natural accelerograms should be utilised in thedynamic analyses to estimate the mean values of the response quantities. It is believed thatactual code-spectrum requirements for the selection of natural earthquake records should berevised, especially for long period structures, such as base isolated structures, and/or in thelight of new deformation-based design methodologies.

Simplified linear analyses tend to provide estimates of the response quantities, displace-ments of base isolators and base shear of the superstructure, which can be reliably employedat preliminary design stage. Spectral analysis results of the 3D model tend to match those ofthe SDOF systems, even for irregular superstructure, provided that modal mass participatingratios are greater than 85–90%. The results of spectral analyses on both SDOF and three-dimensional FEM envelope the outcomes of linear time histories. However, when the latter

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analyses are carried out, the spectrum compatibility should be checked with respect to theactual viscous damping (ξ ) of the response spectra utilized to assess the BIS, i.e. ξ > 5%. It isalso found that the nonlinear modal time history analysis (FNA) is an appropriate and efficientintegration scheme to perform nonlinear time history analyses of on irregular base-isolatedstructures.

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