Earthquake-induced poundings of a seismically isolated building with adjacent structures

Engineering Structures 32 (2010) 1937–1951

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Engineering Structures

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Earthquake-induced poundings of a seismically isolated building withadjacent structuresPanayiotis C. Polycarpou, Petros Komodromos ∗Department of Civil and Environmental Engineering, University of Cyprus 75 Kallipoleos Street, P.O. Box 20537, 1678 Nicosia, Cyprus

a r t i c l e i n f o

Article history:Available online 10 April 2010

Keywords:PoundingsImpactSeismic isolationImpactAdjacent structureMoat wall

a b s t r a c t

Past earthquakes have revealed detrimental effects of pounding on the seismic performance ofconventional fixed-supported buildings, ranging from light local damage tomore severe structural failure.However, the potential consequences of earthquake-induced poundings on seismically isolated buildingscan be much more substantial, and, thus, should be assessed. This paper investigates, through numericalsimulations, the effects of potential pounding incidences on the seismic response of a typical seismicallyisolated building. Such impact events may occur either with the surrounding moat wall at the building’sbase or against an adjacent building that may stand at a very close distance. A specialized softwareapplication has been developed in order to efficiently perform numerical simulations and parametricstudies of this problem. The effects of certain parameters, such as the size of the separation distance, thecharacteristics of the adjacent structures and the earthquake characteristics, have been investigated usingthe developed software. The simulations have revealed that even if a sufficient gap is provided,withwhichpoundings with the surrounding moat wall at the base of the building could be avoided, this does notensure that the building will not eventually collide with neighboring buildings due to the deformationsof their superstructures.

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1. Introduction

Seismic isolation technology is an innovative approach of anti-seismic design of structures, which has been more widely used inthe last few years. The incorporation of seismic isolators aims atthe avoidance of damage in the superstructure, in contrast to con-ventionally designed structureswhere damage is very likely duringstrong earthquakes. However, seismically isolated buildings areexpected and allowed to experience large displacements relative tothe ground during strong earthquake excitations, especially whenthe latter contain long period impulses [1–3]. In order to accommo-date such large displacements, a sufficiently wide clearance mustbe provided around the building, which is known as ‘‘seismic gap’’.Nevertheless, the width of the provided seismic gap in most

cases cannot be unlimited due to practical constraints, especiallyin cases of retrofitting existing structures. In addition, it iswidely accepted that there are several uncertainties about thecharacteristics of the expected earthquake and the methods thatare used to estimate themaximum induced relative displacementsof the structure.Therefore, a reasonable concern is the possibility of poundings

of a seismically isolated building against either the surrounding

∗ Corresponding author. Tel.: +357 22892276; fax: +357 22892295.E-mail address: [email protected] (P. Komodromos).

0141-0296/$ – see front matter© 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2010.03.011

moat wall or adjacent buildings during a very strong earthquake.From a research perspective, there is a scientific interest and apractical necessity to investigate thoroughly the complex researchproblem of earthquake-induced poundings of seismically isolatedbuildings, since there is an increasing number of seismic isolationapplications in earthquake-prone areas.

1.1. Pounding incidences during past earthquakes

Although seismic isolation technology began to be imple-mented in structures only during the last few decades, a case ofpounding occurrences, during a strong earthquake, can already befound in the literature [4]. In particular, the base-isolated Fire Com-mand and Control (FCC) building in Los Angeles experienced im-pacts at its base during the 1994 Northridge earthquake, as it wasobserved in the recorded strongmotion data. The building is a two-story steel frame structure with an isolation system consisting ofhigh damping elastomeric bearings. According to the reconnais-sance report, one-sided impact occurred against the concrete entrybridge in the northeast corner of the building. The accelerometersthat were attached on each floor of the building recorded an am-plification of the acceleration response at the isolation level, in thedirection of pounding, from 0.22g , which was the peak ground ac-celeration, to 0.35g , while in the other direction the ground accel-erations were reduced, thanks to seismic isolation, from 0.18g to0.07g .

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1938 P.C. Polycarpou, P. Komodromos / Engineering Structures 32 (2010) 1937–1951

Fig. 1. Damage of a four-story conventional building due to pounding withits adjacent two-story building, during the L’Aquila earthquake in Italy, in April2009 [12].

Poundings of fixed-supported buildings have been more fre-quently observed around the world, especially during very strongearthquakes, ranging from light local to heavier damage thatmighteven have initiated collapse [5–9]. After the 1985 Mexico Cityearthquake, great attention was given to structural poundings,since they had been considered as a leading cause of building col-lapses, based on an exaggeration concerning the actual damagedue to poundings [10]. Although the number of buildings thatwere severely damaged due to poundings was initially overesti-mated [11], after reconsideration, a few years later, it was reportedthat only in 4% of the severely damaged or collapsed buildings, dur-ing theMexico City earthquake, poundings could have played a sig-nificant factor [5,10]. Furthermore, it has been observed that themost severe damage due to poundings occurred in cases of unequalheights, different structural systems and different configurationsof the adjacent buildings [6].The photograph in Fig. 1 shows a pounding incidence between

two neighboring buildings, as reported from an EERI/PEERreconnaissance team, after the L’Aquila earthquake, which hitcentral Italy in April 2009 [12]. During that seismic event, theroof of the two-story building hit the adjacent four-story structurecausing significant damage to the columns of the latter at that level.Nevertheless, the third and the fourth stories of the building donot seem to experience significant damage. The confinement of thedamage of the four-story building at the level of impact indicatesthe destructive effect of structural poundings.

1.2. Past research studies on poundings

Since poundings of conventional fixed-supported buildingshave been frequently observed around the world, especiallyduring very strong earthquakes, extensive research work has beenconducted regarding that case. Anagnostopoulos [13] was one ofthe pioneers who used numerical simulations to investigate theproblem, considering single-degree-of-freedom (SDOF) systemsin series, undergoing the same seismic excitations. Later on,several research studies focused on the numerical or experimentalinvestigation of earthquake-inducedpoundings of fixed-supportedbuildings [14–19].Compared to the extensive research work on poundings of

conventional buildings and bridges, very limited research studieshave been carried out for poundings of seismically isolatedbuildings. Tsai [20] and Malhotra [21] were the first two who,

through their similar research studies, analytically investigatedthe possibility of a seismically isolated building pounding againstthe surrounding moat wall. Both researchers simulated thesuperstructure of an isolated building as a continuous shear beambumping against a stopper at its base, representing the moatwall, in order to investigate, using wave propagation theory, theeffects of impact on its seismic response. Tsai observed very highacceleration response during poundings with the surroundingmoat wall at the isolation level, while Malhotra concluded that thebase shear force increases with the stiffness of the superstructureor retainingwall, while sometimes it becomes higher than the totalweight of the seismically isolated building.Matsagar and Jangid [22] also numerically and parametrically

examined the case of poundings of seismically isolated multi-degree-of-freedom (MDOF) structures, for various types of seismicisolation systems. They concluded that poundings affect the re-sponse of a seismically isolated buildingmorewhen the latter has aflexible superstructure, an increasednumber of stories or relativelystiff adjacent structures. Komodromos et al. [23] and Komodro-mos [24] investigated, through parametric analyses, the effects ofpoundings of a seismically isolated building with the surroundingmoatwall, revealing the detrimental effects of structural impact onthe effectiveness of seismic isolation. In those research works, thebehavior of the seismic isolation system was assumed to be linearelastic, while no other adjacent buildings were considered in thesimulations. Recently, Agarwal et al. [25] have examined the caseof poundings between two-story buildings that were taken to beeither fixed-supported or seismically isolated. In the case of seis-mically isolated buildings, a sliding isolation system with varyingfriction was considered. Nevertheless, the case of poundings be-tween a seismically isolated building and a fixed-supported build-ing was not taken into account, while the simulation involved onlybuildings with two degrees of freedom.Based on the observations from past earthquakes about the

detrimental effects of pounding on the seismic response ofconventional buildings, it would be interesting to investigatethe possibility of poundings of seismically isolated buildings,which exhibit quite different dynamic characteristics from fixed-supported buildings. Furthermore, it is more likely to have morerigorous performance requirements and higher expectations forbuildings that utilize an innovative earthquake-resistant design,such as the seismic isolation technology, than for conventionallyfixed-supported buildings.Although the previous research on earthquake-induced pound-

ings of seismically isolated buildings that has been describedabove provides some basic information about the effects of im-pacts on the response, there is still a need for further investiga-tion of the problem, using more effective modeling approachesand taking into account more influencing parameters. In this pa-per, a part of an extensive researchwork concerning the numericalinvestigation of poundings of seismically isolated buildings withadjacent structures is presented. In particular, using a specially de-veloped software application, a large number of dynamic analysesand parametric studies of seismically isolated buildings poundingwith adjacent structures has been performed. From this investi-gation some indicative results are presented and some useful re-marks are derived.

2. Modeling assumptions

The modeling of the simulated structures was performed intwo dimensions (2D), while the superstructure of the seismicallyisolated building and the adjacent conventionally fixed-supportedbuildings are modeled as MDOF systems, with shear–beambehavior and themasses lumped at the floor levels, assuming linearelastic behavior during earthquake excitations.

P.C. Polycarpou, P. Komodromos / Engineering Structures 32 (2010) 1937–1951 1939

Fig. 2. Bilinear inelastic model for the behavior of the seismic isolation system.

2.1. Modeling of the seismic isolation system

The behavior of the seismic isolation system is simulated usinga bilinear inelastic model, which is a more representative andappropriate model, since it represents satisfactorily the responseunder cyclic loading of the most commonly used seismic isolationsystems, such as the Lead Rubber Bearings (LRB) and the FrictionPendulum Systems (FPS). In the case of the LRB, the bilinearbehavior is justified by the yielding of the lead core after theexceedance of a certain shear force level. The three parameters thatdetermine the bilinear inelastic model are the yielding force (fy),the initial elastic stiffness (K1) and the post-yield stiffness (K2). Forall performed simulations, in the frame of the currently presentedwork, the values of these parameters were empirically selected,based on the assumption that the corresponding equivalentstiffness would render the fundamental period of the seismicallyisolated building about three times larger than the correspondingperiod of the superstructure. The selected values are presented inFig. 2 along with the pre-described bilinear inelastic model.

2.2. Damping

Classical Rayleigh damping has been used for the constructionof the viscous damping matrices of the simulated fixed-supportedbuildings.In the case of seismically isolated buildings undergoing earth-

quake excitations, the energy dissipation mechanisms of thecorresponding MDOF systems are not uniformly distributed, astheymay differ significantly between the seismic isolation systemsand the superstructures. In such cases, the usage of classicalRayleigh damping for the construction of the damping matrix maynot be appropriate [26]. Therefore, in the current study a differentapproach has been adopted in order to take into account thedissipation of energy in a more appropriate, yet simple, manner.Assuming, initially, a uniformly distributed energy dissipation

mechanism along the height of the superstructure, a primarydamping matrix Cp is constructed, according to Rayleigh damp-ing [26], assuming the viscous damping ratios for the two extremeeigenmodes of the MDOF system to represent the viscous energydissipation due to the deformation of the superstructure.Then, considering an almost ‘‘rigid body’’ behavior for the

superstructure of the seismically isolated building, due to therelatively excessive flexibility at the seismic isolation level, anequivalent SDOF system is formed, using the total mass of thebuilding (mtot ) and the effective stiffness (kiso) of the isolationsystem. For this SDOF system, the equivalent viscous dampingcoefficient is calculated to correspond to the excess in dampingthat is provided by the seismic isolation system, beyond theuniform viscous damping that is assumed for the entire MDOFsystem:

ciso = 2 · (ζiso − ζsstr) ·√mtot · kiso (1)

where ζiso and ζsstr are the selected damping ratios for the seis-mic isolation and the superstructure, respectively. The viscousdamping ratio that corresponds to the superstructure is sub-tracted from the corresponding seismic isolation damping ratio(Eq. (1)), since it has already been taken into account during theconstruction of the primary viscous damping matrix, using theRayleigh damping assumption.The final damping matrix C is assembled by superposing

the primary damping matrix to the equivalent viscous dampingcoefficient ciso that corresponds to the supplemental dampingprovided by the seismic isolation system. In particular, the valueof ciso is added to the first element (first row and first column) ofthe primary damping matrix Cp, since the seismic isolation systemis located at the base of the building. In the current study a value ofsupplemental damping ratio ζiso equal to 0.05 has been considered.Nevertheless, the effect of the value of the supplemental viscousdamping ratio of the isolation system is examined in Section 7.

2.3. Impact modeling

The numerical modeling of impact and the estimation of theimpact forces acting on the colliding bodies is an essential topic,not only for cases of structural poundings, but also for otherproblems involving numerical simulation of impact. In the caseof structural poundings, simple impact models, which estimatethe impact forces, are usually used by researchers to investigatestructural impact [13,27,28]. In the current study, a force-basedimpact model is used, assuming an impact spring and an impactdashpot exerting, in parallel, impact forces to the collidingstructures whenever their separation distances are exceeded.Actually, it is a small variation of the linear viscoelastic impactmodel that had been initially proposed byAnagnostopoulos [13], inwhich the tensile forces arisen at the end of the restitution periodare omitted and a small plastic deformation is introduced, whichincreases the available clearance. In particular, when a contact isdetected, the impact force is estimated at each time-step using thefollowing formulas [23]:

Fimp (t +1t) ={kimp · δ (t)+ cimp · δ̇ (t) when Fimp (t) > 00 when Fimp (t) ≤ 0

(2)

where δ(t) is the interpenetration depth, δ̇(t) is the relativevelocity between the colliding bodies, kimp is the impact spring’sstiffness and cimp is the impact damping coefficient. The lateris computed according to the following formulas, provided byAnagnostopoulos [13], based on the conservation of energy beforeand after impact:

cimp = 2 · ξimp

√kimp ·

m1 ·m2m1 +m2

(3)

ξimp = −ln (COR)√

π2 + (ln (COR))2. (4)

In the above formulas,m1,m2 are themasses of the two bodies andCOR represents the coefficient of restitution,which is defined as theratio of relative velocities after and before impact (0 < COR ≤ 1).The exact value of the impact stiffness term (kimp) is practicallyunknown, since its physical meaning is not clearly determined.However, it seems that its value depends on the mechanical prop-erties of thematerial and the geometry of the contact surface of thecolliding bodies. In order to examine the influence of the selectedvalue for the impact stiffness, as well as the value of the coefficientof restitution, on the overall response, a parametric analysis wasperformed, fromwhich selected results are presented in Section 6.In all presented simulations, the stiffness of the impact spring hasbeen assumed to be 2500 kN/mm, while the coefficient of restitu-tion (COR) has been taken to be equal to 0.7.


a b

Fig. 3. Computed maximum impact force in terms of the considered time-step for various values of (a) the impact stiffness and (b) the impact velocity.

2.4. Numerical integration

The equations of motion are directly integrated using theCentral DifferenceMethod (CDM), computing the displacements attime (t + 1t). In order to ensure the stability and the accuracy ofthe CDM, a sufficiently small time-step must be used for the time-integration, according to the following formula:

1t < 1tcr2ωmax

=Tminπ

(5)

where ωmax is the maximum eigenfrequency of the system. How-ever, during impacts, ωmax should be the equivalent eigenfre-quency of the force-based impact model, which equals

ωimp =

√kimpmeff

(6)

where meff =m1·m2m1+m2

. For example, for a kimp = 2500 kN/mmand two colliding masses of 250 tons each, the equivalenteigenfrequency of the impact model is equal to 141.42 rad/s.Therefore, according to the above stability criterion (Eq. (5)) of theCDM, the critical time-step is about 1.4 × 10−2 s. In the currentstudy, the time-step is taken to be equal to 2 × 10−5 s, which ismuch smaller than the aforementioned critical time-step.The selection of a small time-step is also important for the

accuracy of the computed impact force when simulating pound-ings using a ‘‘penalty method’’. This effect is presented in Fig. 3,considering two colliding rigid bodies, each with a mass equal to300 tons, and the pre-described impact model to compute the im-pact forces. In particular, the computed impact force is plotted interms of the size of the time-step in logarithmic scale. It is observedthat, as the time-step size increases, the dispersion in the impactforce values increases. In addition, for higher values of the impactstiffness or the impact velocity, a smaller time-step is needed toavoid errors in the computed responses. According to the plots, avalue of the time-step size smaller than 2×10−3 smay provide suf-ficient accuracy for the particular case. As mentioned previously,the selected value of the time-step size that is used in the con-ducted analyses in the context of this study ismuch lower than thatlimit, avoiding this kind of numerical errors and instabilities in thecomputed responses. Such small time-steps can be easily used innumerical simulations and parametric studies, considering the sig-nificant increase of the computational speed of the available com-puting resources.

2.5. Vertical location of impacts

Two different configurations of a seismically isolated buildingare used in the performed simulations. The first case concerns thepossibility of the seismically isolated building hitting against thesurroundingmoatwall, during a strong earthquake excitation, onlyat the isolation level,whenever the limitedwidth of the seismic gapis exceeded (Fig. 4(a)). In the other case, the seismically isolatedbuilding is considered to be adjacent to other conventionally fixed-supported buildings, with the possibility of poundings occurringnot only at its base, but also at the upper floors of the buildingsdue to the deformation of their superstructures (Fig. 4(b)).(a) Poundings with the moat wallThis configuration represents the case where the seismic gap is

limited and for some reason the relative horizontal displacement atthe base of the seismically isolated building exceeds the availableclearance, during a strong earthquake. Then, the slab at theisolation level hits against the surrounding moat wall, whichis assumed to be rigid and move with the ground during theearthquake excitation. The effective mass of the moat wall, whichis used for the estimation of the impact forces, has been consideredto be 500 tons.(b) Poundings with adjacent buildingsIn this configuration, one or two fixed-supported multistory

buildings are considered to be located next to a seismically isolatedbuilding at the same distance as the surrounding moat wall.Therefore, poundings may occur either with the moat wall atthe base of the seismically isolated building or with the adjacentbuildings at the levels of the upper floors of their superstructures.For simplicity, it is assumed that the slabs of the neighboringbuildings are located at the same levels. Therefore, the impactforces act directly on the concentrated masses of the MDOFsystems. Modeling buildings in series, like in this case, requiresthe simultaneous solution of the equations of motion of theneighboring structures in order to detect potential contacts amongthe oscillating systems. The selected force-based impact model,as described previously, allows the simulation of more than oneimpact occurring on the structure simultaneously.

3. Developed software

Considering the limited, if any, number of commercial struc-tural analysis software applications that are able to performdynamic analysis of more than one structures in series, interact-ing with each other through structural impacts, it was necessary,


a b

Fig. 4. Two considered configurations of a seismically isolated building regarding the possible locations of impacts: (a) poundings only at the base; (b) poundings at all floorlevels, including the base.

Fig. 5. Relative displacement at the isolation level of the four-story seismically isolated building due to the Kobe earthquake for the two cases ofwithout andwith poundings.

for the fulfillment of the aims of this investigation, to develop aspecialized software tool in order to be able to perform the re-quired simulations and parametric studies effectively, based onthe previously described assumptions. Therefore, a software appli-cation has been specifically developed in order to efficiently per-form large numbers of dynamic simulations of seismically isolatedbuildings in series with other structures taking into account po-tential pounding incidences. In particular, an Object-Oriented Pro-gramming (OOP) approach and the Java programming languagehave been utilized to design and implement a flexible and extend-able software application with effective visualization capabilitiesthat can be used in relevant numerical simulations and parametricanalyses. Among other features, the developed software enablesthe user to observe, through appropriate animations, the seismicresponses of the analyzed structures in series, facilitating the ver-ification of the results and the understanding of the analysis out-comes. Large numbers of simulations can be performed, varyingautomatically a certain parameter for each analysis, in order toparametrically investigate its effects on the overall dynamic re-sponse.

4. Analyses considering impacts with the surrounding moatwall

A four-story building is considered, under the followingthree different circumstances: (a) fixed-supported, (b) seismicallyisolated without the possibility of pounding, and (c) seismically

isolated with a seismic gap on either of its sides, to illustrate thepounding effects on its structural response. The superstructure isassumed to have four floors, each with a lumped mass of 320 tons,except for the top floor, where a mass of 250 tons is considered.Each story has a horizontal stiffness of 600 MN/m. The seismicallyisolated building has an additional mass of 320 tons lumped at theisolation level, while the isolation system’s behavior is simulatedusing the bilinear inelastic model. The fundamental period of thefixed-supported four-story building is equal to Tfixed = 0.398 s.In order to observe the effects of poundings on response time-

histories of the seismically isolated building, dynamic analysis ofthe building for each of the cases described above was performed,using the 1995 Kobe earthquake record (KJMA Station) as theground excitation. For the case of poundings, the size of the seismicgap is taken to be equal to 15 cm, which is 10% smaller thanthe maximum relative displacement (16.74 cm) at the isolationlevel of the seismically isolated building under the same excitation(Fig. 5). This assumption is based on the uncertainties concerningthe characteristics of the design earthquake and the estimationof the maximum design displacement of the seismically isolatedbuilding.Fig. 5 presents the displacement time-histories at the base

of the seismically isolated building under the Kobe earthquakefor the case without poundings and the case of a seismic gapequal to 15 cm, where the base mat unavoidably hits against thesurrounding moat wall at two time instances. It is observed thatthe differences in the two plots are very difficult to be identified.Only a slight reduction of the peak values due to impact is detected.


Fig. 6. Acceleration time-histories at the top of the seismically isolated building, with and without poundings.

Fig. 7. Peak responses of the four-story seismically isolated building with and without poundings compared with the peak responses of the corresponding fixed-supportedbuilding.

In contrast to the relative displacement response, the flooraccelerations, as expected, are found to be more sensitive toimpact occurrences. Although the width of the clearance is lessthan 2.0 cm smaller than the maximum relative displacement, theeffects of poundings are significant, especially on the accelerationresponse at the isolation level where impacts occur. Fig. 6presents the acceleration time-histories at the top floor of theseismically isolated building during poundings, compared to thecorresponding time-histories for the casewithout poundings. Highvalues of the acceleration response are observed at the time ofimpact. Nevertheless, due to damping, a short time after impact,the response tends to become identical to the correspondingresponse without poundings.The peak values of the interstory deflections and absolute floor

accelerations of the seismically isolated building with impacts areplotted in Fig. 7 and compared with the corresponding values ofthe fixed-supported and base-isolated building without impact.It is observed that, during poundings, interstory deflections atthe upper floors reach the peak values of the deflections of thecorresponding fixed-supported building. Consequently, on theparticular stories of the superstructure, we observe almost thesame shear forces that act on the fixed-supported buildingwith thesame structural characteristics. If insufficient strength is providedto the structural elements, taking into account these effects ofpotential poundings during the design of the superstructure of aseismically isolated building, considerable damage may occur insuch cases.Considering the computed peak absolute floor accelerations of

the building, the influence of poundings in its response is muchmore pronounced at the lower floors, where the peak floor accel-erations become much higher than those for the correspondingfixed-supported building. Due to poundings with the moat wall,

the structure may experience maximum floor accelerations at theisolation level, where impacts occur, instead of the top floor of thebuilding. It is well known from previous studies [14,16,29] thatthe acceleration response is highly affected from impact. Thesehigh values of floor acceleration that are generated due to pound-ings can damage sensitive equipment that may be housed in thebuilding.The specially developed software tool provides the ability to

create animations of the simulated structures that are subjectedto ground excitations. Fig. 8 presents some snapshots that havebeen created using the developed software, for the case of theaforementioned four-story seismically isolated building, consider-ing a seismic gap that is 15 cm wide. It is observed that pound-ings excite highermodes of deformation of the seismically isolatedbuilding, instead of moving, according to its fundamental mode asan almost rigid body.However, in some cases, more detailed examination of the re-

sults is needed to validate the information that is given by the ani-mations. For example, in this case, two impact events are observedin the animation. In particular, the first impact happens at time 8.4s on the left side and the second at time 8.8 s on the right side ofthe seismically isolated building (Fig. 8). Nevertheless, in Fig. 9, thetime-history data of the impact force indicate that there are threeimpact events. Specifically, the first pounding event on the left sideis followed in very short time by a second smaller impact due tothe effect of the deformation of the superstructure and the inertiaforces acting at the upper stories in the opposite direction from theimpact force.While the impact forces push the basemat apart fromthe moat wall, the inertia forces of the superstructure are drivingthe building against thewall. Consequently, the basemat reboundson the moat wall.


Fig. 8. Snapshots of the animated seismically isolated building under the Kobe earthquake, considering a seismic gap equal to 15 cm.

Fig. 9. Impact force time-history at the base of the four-story seismically isolated building under the Kobe earthquake, considering a gap width equal to 15 cm.

Table 1First two natural modes and periods of the fixed-supported structures consideredadjacent to the seismically isolated building.

First twoeigenmodes:

Number ofstories

2 3 4 5 6

T1 (s) 0.216 0.306 0.398 0.490 0.58T2 (s) 0.086 0.111 0.139 0.168 0.20

5. Analyses considering impacts at all floors

A series of dynamic analyses has been conducted in order toinvestigate the case of having the seismically isolated buildingadjacent to other fixed-supported buildings, compared to the caseof the seismically isolated building standing alone surrounded onlyby the moat wall. For this reason, five types of fixed-supportedbuildingswhich differ only in the number of stories are considered,assuming the same story stiffness and floor mass values as forthe superstructure of the seismically isolated building. The firsttwo modes and their corresponding natural periods of the fivefixed-supported buildings used in the simulations are presentedin Table 1.Five selected earthquake records, which are presented in

Table 2, are used in order to examine the effects of the excita-tion characteristics on the seismic response of the seismically iso-lated building during poundings. All selected earthquake recordsare characterized by low-frequency content, in order to inducelarge relative displacements to the seismically isolated building,since this is one of the most decisive factors for the occurrenceof poundings in such structures. The normalized response spectra,i.e. the spectral acceleration divided by the peak ground accelera-tion, of all five seismic records are plotted together in Fig. 10The size of the seismic gap is considered to be different for each

case of seismic action. In particular, the width of the seismic gap istaken to be 10% smaller than the maximum relative displacementat the isolation level of the seismically isolated building underthe specific seismic excitation. The maximum induced relativedisplacements at the base and the top of the seismically isolated

Table 2Earthquake records that are used in the simulations.

Earthquake Mw Station PGA (g)

Kobe, Japan 1995 6.9 0 KJMA 0.821Northridge, USA 1994 6.7 74 Sylmar - Converter Station 0.897Northridge, USA 1994 6.7 24514 Sylmar - Olive View Med

FF0.604

Kocaeli, Turkey 1999 7.4 Sakarya 0.628San Fernando, USA1971

6.6 Pacoima Dam, S16 1.170

building, as well as the displacements of the tops of the fixed-supported buildings, for each earthquake record, are provided inTable 3.Figs. 11 and 12 present the amplification factors of the peak

floor accelerations and interstory deflections, respectively, of thefour-story seismically isolated building considering poundingswith the adjacent structures. The amplification factor is definedas the ratio of the maximum response quantity of interest whenpoundings occur divided by the correspondingmaximum responsevalue without poundings.According to the simulation results, the peak total accelerations

as well as the interstory deflections and, therefore, the story shearforces of the seismically isolated building significantly increase dueto poundings that occur when the available seismic gap is slightlyexceeded. In the specific cases under investigation, the availableclearance is only 10% less thanwhat is needed to avoid impact and,nevertheless, the responses are amplified significantly regardingthe corresponding responses without poundings.In addition, it is observed that the amplification of the peak

floor accelerations is, in general, greater than the amplificationof the peak interstory deflections, since the former are muchmore sensitive to local impacts. Themaximum amplification of theacceleration response is usually located (i) at the isolation level(for the case of poundings occurring only with the moat wall), (ii)at the floor that is at the same level with the roof of the adjacentstructures or (iii) at the top floor of the seismically isolated buildingwhen that is shorter than the neighboring buildings.Moreover, the amplifications of the response of the seismically

isolated building with poundings seem to depend on the earth-quake characteristics in combination with the number of stories


Fig. 10. Normalized response spectra of the five selected seismic records, considering a viscous damping ratio of 5%.

Table 3Maximum relative displacements (cm) of the seismically isolated building and the fixed-supported buildings, under the five seismic excitations.

Earthquake excitation

(Base - Top) (Top) (Top) (Top) (Top) (Top)

Kobe 16.74–18.85 1.49 5.57 11.40 16.88 15.22Northridge (Converter) 31.71–35.25 1.49 3.41 6.43 10.50 17.70Northridge (Olive) 15.63–17.07 1.18 3.28 5.60 9.75 13.54Sakarya 11.40–12.51 2.12 4.50 5.23 6.30 7.51San Fernando 26.78–29.52 3.47 5.67 14.61 13.40 8.66

and, consequently, the flexibility of the adjacent buildings. The am-plification of the response due to poundings occurring only at thebase of the building is more or less the same for all seismic excita-tions. However, in the case where the seismically isolated buildingis between other multistory buildings, which have different dy-namic responses under each excitation, the amplification curvesfor each earthquake record have significant dispersions. Theworst-case scenario for the seismically isolated building is when theadjacent fixed-supported buildings have fundamental eigenfre-quencies in resonance with the dominant frequencies of the earth-quake excitation.Another set of parametric analyses was performed in order to

examine how the width of the seismic gap affects the response ofthe seismically isolated building in the six different cases regardingthe type of adjacent structures. In particular, the width of thegap between the seismically isolated building and the adjacentstructures is varied between 10 and 45 cm, with a step of 0.5 cm,simultaneously on both sides of the building. Fig. 13 presents themaximum responses of the seismically isolated building in termsof the size of the available clearance for the six configuration casesand for the five seismic excitations.It is observed that the response is, in general, decreasing with

the increase of the available clearance around the seismicallyisolated building. However, the variations of some curves indicatethat this is not always true, especially for relatively narrowgap sizes in combination with the earthquake characteristics.Specifically, very small widths of the seismic gap, in combinationwith a strong earthquake ground excitation, do not allow thestructure to develop high impact velocities as in cases of widerseismic gaps, leading to relatively milder consequences frompotential poundings.Some modern anti-seismic codes suggest the use of the SRSS

(Square Root of the Sum of Squares) approach for the determi-nation of the minimum required seismic gap between two adja-cent buildings in order to avoid structural poundings during strong

earthquakes [30–32]. Relevant research on the investigation ofpoundings of fixed-supported buildings showed that the SRSS ofthe maximum displacements of two adjacent buildings can be suf-ficient [13], while in fewer times it may be insufficient, but withminor impact effects [14,15]. In almost half of the cases that havebeen analyzed in the current study, a seismic gap, equal to theSRSS of the design peak relative displacements of the adjacentstructures, is insufficient under the specific earthquake excitations.Table 4 displays the difference1d = dRSSS−dReq for each one of thecases of the configurations of the adjacent buildings and for all five

seismic records, where dRSSS =√(max diso)2 +

(max dfixed

)2 anddReq is the minimum required seismic gap in order to avoid pound-ings according to the simulations. The termsmax diso andmax dfixedrepresent themaximumhorizontal displacement of the seismicallyisolated building and its adjacent fixed-supported building, respec-tively, under the same excitation. Therefore, a negative sign of thedifference1d denotes that a seismic gap width equal to dSRSS is in-sufficient. The computed dSRSS is also plotted in the graphs of Fig. 13with vertical lines.Considering the type of the adjacent structure, the results

indicate that the presence of fixed-supported buildings at closedistance to a seismically isolated building significantly affects theresponse of the latter during poundings. In general, the plotsindicate that the amplifications of the peak floor accelerations dueto impact are, in general, increasing with the number of stories ofthe adjacent building. An important observation is that, in such acase, poundings may occur for much wider widths of the seismicgap compared to the case of impacts occurring only at the basewith the moat wall. This is justified by the fact that the adjacentmultistory buildings have some horizontal flexibility in contrast tothe surrounding moat wall, which remains undeformed relativeto the ground during the excitation. Therefore, the seismicallyisolated building may pound against the neighboring buildings at


Fig. 11. Amplification of the maximum floor accelerations of the seismically isolated building due to poundings with adjacent structures.

Table 4The difference1d = dRSSS − dReq (cm), where the negative sign denotes insufficiency.

Earthquake excitation

Kobe −0.09 −0.34 −5.47 −6.70 −1.77

Northridge (Converter) 0.78 1.91 −3.17 −7.72 −5.06

Northridge (Olive) 0.61 −0.62 2.46 1.66 0.29

Sakarya 0.69 −0.70 −1.44 0.01 3.59

San Fernando 0.72 1.06 3.31 0.42 −3.74

the upper stories, due to the deformation of the superstructures ofthe buildings in series, before hitting the surrounding moat wall.Fig. 13 also suggests that the peak interstory deflections duringpoundings for the case of buildings in series are most of the timessmaller than those for the case of having impacts only with themoatwall. This indicates that, inmost cases, the adjacent buildingsact as constrainers, preventing the large horizontal displacementsthat may take place when the seismically isolated building hitsonly against the moat wall at the isolation level.The earthquake characteristics and, in particular, the range

of predominant periods, in combination with the fundamentalperiods of the adjacent structures seem to play a significantrole in the severity of the structural impact. Specifically, thedetrimental effects of poundings are more pronounced when thefundamental periods of the adjacent fixed-supported buildings fallwithin the predominant periods of the seismic ground motion.

A representative example is the case of having five-story fixed-supported buildings adjacent to the seismically isolated building,under the Kobe earthquake record.

6. Influence of the impact parameters

As mentioned previously, a series of parametric analyses hasbeen performed in order to examine the influence of selectingdifferent values for the impact parameters, when using thecorresponding linear viscoelastic impact model. Considering thecase where the four-story seismically isolated building is standingbetween two same four-story fixed-supported buildings, theimpact stiffness and the coefficient of restitution were varied inthe ranges 500–5000 kN/mm and 0.1–1.0, respectively. Two casesof seismic gap sizewere examined and the Kobe earthquake record


Fig. 12. Amplification of the maximum interstory deflections of the seismically isolated building due to poundings with adjacent structures.

was selected as the imposed seismic excitation. In the first case(Fig. 14), the width of the seismic gap equals 25 cm and poundingsoccur only at the two top floor levels of the seismically isolatedbuilding, while in the second case, where the separation distanceequals 15 cm (Fig. 15), poundings occur at all floor levels.The plots in Fig. 14 indicate that the influence of the value of

the impact parameters on the interstory deflections is negligible,while a small variation is observed for the acceleration response atthe two floors where impacts occur. Specifically, for values of thecoefficient of restitution (COR) lower than 0.5, the acceleration in-creases and reaches its maximum value when the impact becomeshighly overdamped. For values greater than 0.5, the accelerationresponse is almost insensitive to the variation of the COR.On the other hand, the increase of the impact stiffness increases

the peak floor acceleration at the impacting floor, while at therest of the floor levels the acceleration remains almost constantwith the variation of kimp. An interesting observation is that thepeak floor accelerations at the top floor are more sensitive tothe variation of the impact stiffness than that at the third floor,indicating that the rate with which the accelerations increasedepends on the impact velocity. This is also shown in Fig. 15, wherethe rate of the increase of the peak floor accelerations is greater,since the seismic gap’s width is smaller and causes more severeimpacts. In addition, in the case of relatively narrow seismic gaps,the interstory deflections are not as insensitive to the variationof the impact parameters as in the first case. Conclusively, theinfluence of the values of the impact parameters on the overallresponse during poundings is greater in cases of high impactvelocities. The values of the coefficient of restitution and theimpact stiffness that were used in the performed simulations are

shown with dotted lines in both figures, indicating the relativelylimited influence of their selected values.

7. Influence of supplemental viscous damping

Recent studies have shown that the use of supplementaldamping devices may reduce the relative displacements at thebase of a seismically isolated building under extreme seismicactions that are characterized by near-fault effects [33]. Since thedeveloped software provides the ability of introducing additionaldamping explicitly at the isolation level, this scenario wasalso investigated. In order to examine the effect of introducingexcessive viscous damping at the isolation level, using specialdevices such as viscous dampers, some parametric analyses havebeen conducted.The plots in Fig. 16 provide themaximum relative displacement

at the isolation level as well as the peak floor acceleration at thetop floor of the four-story seismically isolated building (withoutconsidering any pounding) in relation to the supplemental damp-ing ratio of the isolation system. It is observed that the responseis substantially decreasing with the increase of the supplementaldamping ratio. Consequently, in this case, the possibility of pound-ing due to insufficiently wide seismic gap is reduced when suchsupplemental damping devices are implemented. However thereis always an upper limit, since excessive damping may lead to in-creased interstory deflections and absolute floor accelerations ofthe superstructure [33].Furthermore, the case with a seismic gap size equal to 10%

of the maximum unconstrained displacement of the base ofthe seismically isolated building was also considered in order


Fig. 13. Peak responses of the seismically isolated building in terms of the width of the seismic gap. The vertical lines indicate the SRSS of the peak displacements of theneighboring buildings for each earthquake excitation, plotted with the corresponding color and line-type. (For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this article.)

to demonstrate the effect of supplemental viscous damping onimpact velocity. In Fig. 17, the computedmaximum impact velocityof the base of the seismically isolated building is plotted interms of the supplemental damping ratio. It is observed thatthe impact velocity decreases substantially with the increase ofthe supplemental damping, while impacts are avoided after acertain damping ratio value. Therefore, it seems that the use ofsupplemental viscous damping at the isolation system can bean efficient measure for mitigating the detrimental effects ofpounding.

8. Software validation

Finally, in order to validate the accuracy of the aforemen-tioned developed software, the commercial analysis softwareSAP2000 [34] has been used to simulate the previously describedfour-story seismically isolated building. Since the Central Differ-ence Method is not available in the particular software, New-mark’s method has been selected and used as the time-integrationscheme. The Kobe earthquake record has been used as the ground


Fig. 14. Variation of the response of the seismically isolated building during poundingswith adjacent fixed-supported structures, in terms of the COR and the impact stiffnessfor a 25 cm gap width.

Fig. 15. Variation of the response of the seismically isolated building during poundingswith adjacent fixed-supported structures, in terms of the COR and the impact stiffnessfor a 15 cm gap width.

excitation, while a non-linear time-history analysis has been per-formed. Fig. 18 demonstrates comparative results of the time-histories of the relative displacements at the seismic isolation leveland the absolute accelerations at the top floor of the building,with-

out considering any impact. It is observed that the computed re-sponses fromboth software applications are very similar,with neg-ligible differences, considering that a different integration schemeand time-step have been used.


Fig. 16. Effect of supplemental viscous damping on the response of the four-story seismically isolated building without impact.

Fig. 17. Effect of supplemental viscous damping on the maximum value of impact velocity with which the base of the four-story seismically isolated building hits againstthe surrounding moat wall on the left and on the right side of the building, respectively.

Fig. 18. Validation of the computed results without considering any impacts.

In order to take into account the case of poundings with thesurrounding moat wall in the SAP2000 model, two gap elementshave been used with a linear stiffness equal to the impact stiffnessthat is used in the developed software and an opening equalto 15 cm, which corresponds to the width of the seismic gap.Fig. 19 compares the results of the analysis using SAP2000with thecorresponding results from the developed software. It is observed

that, in general, the computed responses are very similar, and themaximum responses are very close.Some variations on the time-history responses exist probably

due to the different integration algorithms that are used and theway of constructing the damping matrices. Specifically, SAP2000uses classical Rayleigh damping, calculating the damping matrixterms based on the viscous damping ratios that are provided


Fig. 19. Validation of the computed results with impact, considering a seismic gap width equal to 15 cm.

from the user for two extreme eigenmodes of the structure, whilethe developed software uses non-classical damping, as previouslydescribed in Section 2.2.It is worth mentioning that conducting a simulation with

SAP2000 requires about 2–3 orders of magnitude more timethan conducting the corresponding analysis with the developedsoftware. This significant efficiency allows us to perform largenumbers of parametric studies, which could not be performedwithcommercial software within a realistic time span.

9. Concluding remarks

Past earthquakes have revealed that poundings of fixed-supported buildings can cause damage ranging from light localto heavier damage that might even have initiated collapse,especially during very strong earthquakes. Although there is notmuch experience from poundings of seismically isolated buildings,since it is a relatively recent anti-seismic technology, numericalsimulations reveal that poundings may have very detrimentalconsequences on such buildings.This paper presents some representative results that are se-

lected from a wide range of simulations, which have been per-formed in order to investigate the effects of poundings withadjacent structures on the response of seismically isolated build-ings during very strong earthquakes. The results presentedconsider only the case of a typical four-story seismically isolatedbuilding with specific structural characteristics under differentcases of neighboring structures and under a range of different seis-mic excitations.Summarizing the observations regarding the results, it has been

found that poundings occurring either at the base of the seismicallyisolated building or at its upper floors are particularly unfavorablefor the structure, since they significantly increase the peak absolutefloor accelerations and the interstory deflections. The parametricanalyses show that even if a ‘‘sufficient’’ gap is provided, withwhich poundings with the surrounding moat wall at the baseof the building could be avoided, this does not ensure that thebuilding will not eventually collide with neighboring buildings. Itis expected that the superstructures of the neighboring buildingswill be considerably deformed during a strong earthquake andthe floors will have such horizontal interstory deflections that,in combination with the expected large horizontal relativedisplacements of the seismically isolated building, unwantedpounding incidences may occur. The results also indicate thatthe detrimental effects of pounding are more pronounced whenthe structures adjacent to the seismically isolated building are in

resonance with the seismic excitation. Therefore, it is importantto take into account the presence and characteristics of theadjacent buildings on the estimation of the required width of theseismic gap around a seismically isolated building, as the designdisplacement at its base may not be sufficient as a sole criterionfor the determination of the required width of the seismic gap.The SRSS method for the estimation of the required separationdistance between a seismically isolated building and its adjacentfixed-supported buildings is found to be insufficient for half ofthe configurations and earthquake excitations that have beenconsidered in the simulations performed. Moreover, the valuesof the impact parameters that are used for the estimation ofthe impact forces have insignificant effects on the response ofthe seismically isolated building during poundings, except forthe cases of very severe impacts. Finally, the implementationof supplemental viscous damping devices seems to mitigate thedetrimental effects of pounding, while in some cases the impact isavoided due to the reduction of the maximum horizontal relativedisplacements of the seismically isolated building.

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Earthquake-induced poundings of a seismically isolated building with adjacent structures

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