Effect of Asynchronous Earthquake Motion on ComplexBridges. I: Methodology and Input Motion

Nicholas J. Burdette1; Amr S. Elnashai, F.ASCE2; Alessio Lupoi3; and Anastasios G. Sextos4

Abstract: Based on observed damage patterns from previous earthquakes and a rich history of analytical studies, asynchronous inputmotion has been identified as a major source of unfavorable response for long-span structures, such as bridges. This study is aimed atquantifying the effect of geometric incoherence and wave arrival delay on complex straight and curved bridges using state-of-the-artmethodologies and tools. Using fully parametrized computer codes combining expert geotechnical and earthquake structural engineeringknowledge, suites of asynchronous accelerograms are produced for use in inelastic dynamic analysis of the bridge model. Two multi-degree-of-freedom analytical models are analyzed using 2,000 unique synthetic accelerograms with results showing significant responseamplification due to asynchronous input motion, demonstrating the importance of considering asynchronous seismic input in complex,irregular bridge design. The paper, Part 1 of a two-paper investigation, presents the development of the input motion sets and the modelingand analysis approach employed, concluding with sample results. Detailed results and implications on seismic assessment are presentedin the companion paper: Effect of Asynchronous Motion on Complex Bridges. Part II: Results and Implications on Assessment.

DOI: 10.1061/�ASCE�1084-0702�2008�13:2�158�

CE Database subject headings: Bridges; Seismic analysis; Seismic effects; Earthquakes; Ground motion; Nonlinear analysis;Dynamic analysis.

Introduction

Because curved elevated transportation structures are becoming acommon solution to complex transportation problems, it is impor-tant that a commensurate breadth and depth of research areinvested in understanding these complex structures. Natural disas-ters of the past few decades have provided numerous examples ofbridge damage and collapse for bridges that were designed forseismic forces �Elnashai et al. 1999�. To better protect bridgesfrom future earthquakes, researchers must aid bridge designers byutilizing field observations and expanding on past investigationsto include representative bridges of all types and alignments,striving to make inelastic dynamic analyses as realistic as pos-sible. With advances in computing power, structural and seismo-

1Research Assistant, Mid-America Earthquake �MAE� Center,Dept. of Civil Engineering, Univ. of Illinois at Urbana-Champaign,205 N. Mathews Ave., Urbana, IL 61801 �corresponding author�. E-mail:nick.burdette@arup.com

2Bill and Elaine Hall Endowed Professor, Director, MAE Center,Dept. of Civil Engineering, Univ. of Illinois at Urbana-Champaign,205 N. Mathews Ave., Urbana, IL 61801. E-mail: aelnash@uiuc.edu

3Postdoctoral Research Fellow, Dept. of Structural and GeotechnicalEngineering, Univ. of Rome “La Sapienza,” Via Gramsci 53, 00197Rome, Italy. E-mail: alessio.lupoi@uniroma1.it

4Lecturer, Dept. of Civil Engineering, Division of StructuralEngineering, Aristotle Univ. of Thessaloniki, Thessaloniki GR-54124,Greece. E-mail: asextos@civil.auth.gr

Note. Discussion open until August 1, 2008. Separate discussionsmust be submitted for individual papers. To extend the closing date byone month, a written request must be filed with the ASCE ManagingEditor. The manuscript for this paper was submitted for review and pos-sible publication on August 16, 2006; approved on January 8, 2007. Thispaper is part of the Journal of Bridge Engineering, Vol. 13, No. 2,

March 1, 2008. ©ASCE, ISSN 1084-0702/2008/2-158–165/$25.00.

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logical features previously simplified can be fully included inanalysis.

Utilizing advanced analysis tools, this study seeks to includetwo complicating factors not often considered in seismic analysis:�1� bridge irregularity, including varied pier heights, abutmentend conditions, and a curved horizontal alignment; and �2� spa-tially varied seismic input with a range of incoherence cases.Inclusion of the first factor recognizes that actual bridges mustoften be irregular due to site limitations or alignment require-ments. The second factor is included due to increased understand-ing of the seismological characteristics of earthquakes and thehigher displacement demand possible from asynchronous input,demonstrated in recent studies �Sextos et al. 2004; Lupoi et al.2005�.

To consider the effect of bridge irregularity, equivalent curvedand straight concrete bridge models will be subjected to asynchro-nous earthquake motion and their responses compared in the fol-lowing companion paper. Because the vast majority of previousanalytical studies have been performed on straight bridges, thiscomparison will determine whether asynchronous response am-plification can be expected to be similar for curved versions ofprevious bridges studied. The effect of various levels of earth-quake incoherence will be determined using synthetic accelero-grams generated by means of two specifically developed,state-of-the-art asynchronous record generation softwareprograms.

Spatially Asynchronous Earthquake Motion

Sources of Asynchronous Motion

Consideration of spatially varied seismic input motion is chal-

lenging due to its complexity. Wave travel speed, reflection and

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refraction, and heterogeneous soil conditions all cause deviationsfrom synchronous excitation for distributed foundation structuressuch as bridges. For simplification, asynchronous motion is com-monly divided into three components: �1� wave passage effect;�2� geometric incoherence of the input; and �3� local site condi-tions. The first component is due to the finite travel speed ofseismic waves, resulting in progressive excitation of each supportpoint as a wave front passes. The second component accounts forthe reflection and refraction of seismic waves as they passthrough the ground, changing their signal content between sup-port points. The final component accounts for situations wherestructures are founded on different soil types, such as a bridge thatspans a geologic divide. Though the asynchronous motion ob-served during earthquakes is a complex interaction of all threecomponents, for analytical simplicity, researchers have dividedthe phenomenon into these three sources.

Observations from Previous Earthquakes

In recent earthquakes, there are numerous examples of bridgefailures that may have been caused or aided by differential sup-port motion. During the Northridge earthquake of 1994, a numberof spans of the Gavin Canyon undercrossing fell off of their sup-ports, resulting in the total collapse of substantial portions of thestructure �Tzanetos et al. 2000�. The spans became unseated andcollapsed, despite being retrofitted with restraining devicesfollowing the San Fernando earthquake. While shifting andpounding of deck slabs from synchronous motion could causeunseating, differential support motion is a more likely cause ofthe large displacements, resulting in failure of this retrofittedstructure.

The Kobe earthquake of 1995 provides further examples ofdeck unseating where differential support movement was likelyinvolved. The city of Kobe has many kilometers of elevated high-ways where single spans supported on rollers bridge the gapsbetween piers. Many of these single spans fell off of their sup-ports at expansion joints during this earthquake because of largelongitudinal displacements between piers �Elnashai et al. 1995�.Again, it is difficult to fully attribute these failures to asynchro-nous earthquake motion, but such motion is known to cause largedifferential movement of neighboring supports. As discussed ingreater detail below, several studies have shown that spatiallyvaried ground motion can exact higher demands on a bridgestructure than synchronous motion.

Previous Studies

Studies on the response of extended foundation structures to dif-ferential support excitation began over 40 years ago with a studyby Bodganoff et al. �1965� on the effect of ground transmissiontime on long structures. This and other early studies, such asDumanoglu and Severn �1987a,b� and Leger et al. �1990�, fo-cused on long bridges subjected to wave passage effects only.These studies identified isolated cases of response amplificationdue to asynchronous motion, but their conclusions were limiteddue to their simplicity. Significant advances in computing powerin the early 1990s allowed larger, more involved studies to beperformed. The advent of “spatial” models of asynchronousmotion allowed geometric incoherence to be incorporated intostudies using a stochastic field based on random vibration theory.

The majority of studies, including both the wave passageeffect and geometric incoherence terms, use synthetic ground mo-

tion based on the Luco and Wong coherency function �Luco and

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Wong 1986�. This function provides a mathematical representa-tion of coherence and consists of two terms, one that quantifiesthe severity of the wave passage effect, and another that repre-sents the level of geometric incoherence. While other coherencefunctions have been suggested �see Oliveira et al. �1991�; DerKiureghian and Neuenhofer �1992�; among others�, the functionproposed by Luco and Wong has gained the widest use for itssimplicity and clarity.

One of the first studies based on the random vibration theoryapproach was done by Zerva �1990�. In this study the structuralresponse of beams with varied lengths were evaluated for seismicinput with different degrees of incoherence, including totally syn-chronous excitation. The results showed that asynchronous re-sponse is very complex and a clear trend is hard to define, withincoherence either increasing or decreasing the structural re-sponse, depending on many parameters.

The first major study to include inelastic dynamic analysis wasby Monti et al. �1996� and involved the inelastic response of asimple, symmetric, six-span reinforced concrete bridge to asyn-chronous motion. The results showed that in cases of severe in-coherence, the bridge responds almost entirely pseudostatically,though the response is still less than the synchronous case. Be-cause the simplicity of this study structure limited the scope of theresults, future researchers often introduced irregularities intosimple bridge structures. Tzanetos et al. �2000� varied the pierheights of a straight bridge, which was analyzed using inelasticasynchronous analysis. For this irregular bridge, asynchronousmotion was shown to significantly increase response for manycases, especially in the transverse direction. Tzanetos et al. �2000�identified suppression of the fundamental mode and dominance ofhigher-mode response as a hallmark of asynchronous excitation, afinding supported in future studies.

Two recent asynchronous inelastic bridge analyses includingstructural irregularities are by Sextos et al. �2003a,b� and Lupoi etal. �2005�. The first study involved a broad parametric study of 20bridges with different geometric and dynamic characteristics�though all straight�. Results from this study showed that relativepier displacements are strongly tied to the overall length of thebridge, with these displacements increasing logarithmically forthe study range �up to 600 m� and exceeding synchronous dis-placements frequently above 400 m. The second study by Lupoiet al. �2005� involved the analysis of a straight, 200 m four-spanbridge in the longitudinal direction only, with varied pier heights,deck stiffness, and coherency level of the input motion. Thisstudy showed that asynchronous motion can increase the prob-ability of bridge failure for even relatively short structures.

The analytical study most similar to the current investigationof curved bridges under asynchronous motion is by Sextos et al.�2004�. The study involved the inelastic response history analysisof a curved, prestressed concrete bridge in Greece, the Krystal-lopigi Bridge. The study structure is a 12-span, 638 m, curvedbridge with varied pier heights. The bridge was analyzed withboth a natural record recorded near the bridge site, and a suite ofsynthetic records with varied degrees of correlation. Results ofthis analysis support the conclusion of previous studies that asyn-chronous motion can excite higher dynamic modes, and casesof pier displacement demands doubling were noted. This ledthe authors to propose the 600 m length suggested by Eurocode 8as a threshold for asynchronous analysis be reduced in the caseof curved bridges, although the difficulty in drawing furtherconclusions for such a complex bridge without further study is

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Study Overview

Study Parameters

The two primary parameters considered in this study are �i�bridge plan geometry and �ii� level of incoherence, described by awave passage effect and geometric incoherence contribution. Theeffect of plan geometry on response was evaluated by analyzingtwo equivalent bridge models with straight and curved decks. Inorder to approach the issue of incoherent ground motion in alogical and incremental way, three levels of incoherence werestudied for each of the two contributing phenomenon. These threelevels of incoherence relate to the following ground motion co-herency function proposed by Luco and Wong �1986�

���,�� = exp�− ����

�s�2�exp�i

��L

�app� �1�

where � includes the mechanical characteristics of the soil; �and �L�separation distance between two support points and theprojected distance from the source, respectively; �s�shear wavevelocity; and �app�apparent surface wave velocity. The coherencelevel of generated time histories is controlled by this expression,which in this study is used essentially as a two-parameter func-tion, with inputs of �s /� and �app. The separation distancebetween two bridge piers and the projected distance in the direc-tion of propagation are determined by the geometry of the studystructure.

The first variable input quantity is the lumped shear wavevelocity and soil property term �s /�. This quantity controls thefirst term of the coherency function, and accounts for the geomet-ric incoherence of the ground motion. The second input quantity�app is the apparent surface velocity. This parameter is associatedwith the second term of Eq. �1�, and it controls the severity of thewave-passage effect. Setting �app=� is equivalent to an earth-quake in which the seismic waves travel with infinite speed,reaching all bridge supports simultaneously, and rendering themotion coherent with regard to this parameter. In the coherencyfunction, this is reflected by the second term becoming 1, mean-ing any loss of coherence must be from geometric incoherence�term one�. In the same manner, when �s /�=�, the first term ofthe expression becomes 1 and, thus, any incoherence is from thewave passage effect only �term two�.

By performing a parametric study varying these coherencyinput parameters for a given earthquake, the effect of each sourceof incoherence can be isolated. Table 1 shows the range of coher-ency cases considered with their abbreviations to facilitate easyreference. The level of geometric incoherence increases from leftto right in the table, while wave passage severity increases fromtop to bottom. Thus, the upper left entry “in-in” corresponds tosynchronous input motion, while the bottom right “30-30” repre-sents the most incoherent case, with �s /� and �app values of

Table 1. Incoherence Cases and Their Abbreviations

�s /� value

�app value Infinity 900 m /s 300 m /s

Infinity in-in in-90 in-30

900 m /s in-90 90-90 30-90

300 m /s in-30 90-30 30-30

300 m /s.

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This range of study parameters was selected based on previousstudies and observed shear wave velocities, which can be aslow as 200–300 m /s in soft soil �Wilson and Jennings 1985�. Itis noted that the apparent velocity �app is generally much higherthan the corresponding shear wave velocity; however, the lowvalue of 300 m /s is adopted as the extreme case of maximumwave arrival delay. To compare synchronous and asynchronousresponse, fully coherent �infinite �s/� and �app� motion was alsoanalyzed, which could correspond to a dense rock site. Theintermediate value of 900 m /s is chosen to represent moderatevelocities, and geometric incoherence parameters are selected tocorrespond to �app values, as done in previous studies �Monti et al.1996; Lupoi et al. 2005�. Though highly dependent on the indi-vidual time history records, these levels of incoherence resulted inmaximum relative ground displacements of approximately 20–30 mm for moderate incoherence and 100–150 mm for severelyincoherent records.

Structural Model

The curved, prestressed concrete bridge structure analyzed in thisstudy was proposed as a design example for the Second Interna-tional Workshop on the Seismic Design of Bridges �Priestley1994�. This bridge was selected because all of its structural dataare readily available, and because it was designed as an examplestructure to encourage �synchronous� seismic analyses. Like mostbridges in previous asynchronous studies, it has a cellular con-crete deck. Because pseudostatic deflections play an importantrole in asynchronous response, the stiffness of the bridge deck caninfluence the displacement demand placed on bridge piers, and itis acknowledged that results found using this structure may not beeasily transferable to a steel bridge; however, it represents a com-mon structural form for long-span bridges and a practical studystructure.

The prestressed concrete study bridge is shown in Fig. 1. It issupported by eight piers and two abutments with a total length of344 m rotating 98 deg. The piers consist of 1 m diameter singlecolumn bents supporting a prestressed concrete twin box girdersuperstructure with sliding bearings, which allow rotation andlongitudinal motion, but are restrained transversely. The deck isfixed to abutment 1 and attached through a similar bearing toabutment 10. The abutments are supported by six 1 m diam rein-forced concrete cast in drilled hole �CIDH� cylinders a minimumof 15 m long. Each of the eight bridge piers are supported by amonolithic footing and four similar CIDH cylinders.

Input Motion and Modeling

Synthetic Earthquake Records

Due to the large number of correlated time history records re-quired for such a large parametric study, synthetic records wereused for analysis. These records were provided from two sourcesusing different record generation software. A suite of ten earth-quake events for each of the nine incoherence cases considered inTable 1 were produced using a generation model developed byLupoi et al. �private communication, 2006�. Records simulatingone earthquake event for the nine coherency cases were producedusing software developed by Sextos et al. �2003b� called asyn-chronous support input generator �ASING�.

Both of these software models account for bridge geometry

and desired coherence level to produce spatially variable earth-

ution subject to ASCE license or copyright. Visithttp://www.ascelibrary.org

quake ground motion based on random vibrations. Given thebridge geometry and the �s /� and �app terms, the software pro-duces correlated response history records for any number ofpoints spaced along a line. Records produced using each of theseprograms have been used in previous studies by the developers,with satisfactory verification of record quality �Lupoi et al., 2005;Sextos et al. 2003a,b�. Additionally, the ASING program was cali-brated based on measured seismic excitation from a strong motionarray in Greece, primarily with respect to the effect of local soilconditions, which is one of the main modules of the program.

Because this study structure was excited in both the longitudi-nal and transverse directions, a total of 180 unique time historieswere required for each earthquake event �20 for each coherencycase�. Therefore, a total of 1,800 unique time histories were cre-ated using software developed at the University of Rome and 180time histories were produced using the ASING program. All syn-

Fig. 1. Study structure plan, elevation,

Fig. 2. Example of accelerogram

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thetic earthquake records were generated to closely match thecriteria given with the design example, with a record duration of20 sec and peak ground acceleration of 5 m /s2. To ensure theearthquakes did not miss an important dynamic mode of the studystructure, the synthetic records were generated to closely matchthe Eurocode 8 design spectrum.

To prevent spurious net displacements between bridge supportpoints in the bridge structure, all generated records were baselinecorrected to zero final displacement using a linear baseline cor-rection algorithm. This ensured that the final ground displacementof the entire bridge site is zero while allowing absolute displace-ments of various support points to vary during seismic excitation�resulting in pseudostatic forces�. Fig. 2 demonstrates the effect ofbaseline correction on an example accelerogram. When the origi-nal displacement record is adjusted using a linear function toproduce a zero final displacement, the corrected accelerogram

ection �adapted from Priestley �1994��

re and after baseline correction

and s

befo

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closely matches the original. Slight differences can be seen be-tween the two, but the general shape, amplitude, and frequencycontent of the signal are preserved.

Fig. 3 shows example time history records applied at supportpoints 1, 5, and 10 for moderate wave passage effect and moder-ate geometric incoherence. The simple shift in accelerogramscaused by the wave passage effect is evident in the first figure,with the finite wave travel speed causing a time delay at eachsupport. The records showing geometric incoherence are morecomplex, with variations both in frequency content and signalshape at each support.

Modeling

The inelastic analysis program ZEUS-NL �Elnashai et al. 2002�was used to perform dynamic time history analysis of both bridgemodels. Due to the complexity of the models, a detailed multi-degree-of-freedom �MDOF� model was created for both thestraight and curved cases �Fig. 4�. To accurately model geometricand material nonlinearities in these three-dimensional structures,all deck, pier, and pier cap elements are cubic elastoplastic 3Dbeam-column elements. The model uses confined and unconfined

Fig. 3. Example time history records for �a

Fig. 4. Isometric view of curved a

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concrete, which is modeled using a uniaxial constant confinementconcrete model with confinement determined using a proceduredeveloped by Mander et al. �1988� based on pier cross section andshear reinforcement.

To reduce analysis time due to the large number of nonlinearanalyses performed on the study structure, foundation boundaryconditions were simplified and piers considered fixed to theground. Though this simplification ignores local soil conditions,which are known to be an additional source of asynchronous mo-tion, for clarity, this site effect was not included in the study.Accelerograms were applied �in global coordinates� to the base ofeach pier in both the longitudinal �east-west� and transverse�north-south� directions simultaneously for each earthquakeevent. The software program converts these accelerograms intodisplacement time histories, which are then applied in analysis.Deck-bearing connections at all pier caps and the east abutmentwere modeled in ZEUS-NL using trilinear symmetric elastoplas-tic joint curves, calibrated to a sliding friction ��� of 0.12, asspecified in the design example used for this study �Priestley1994�. The mass of the deck and pier caps was considered usinglumped mass elements, shown as the large boxes at deck level in

passage effect; �b� geometric incoherence

aight bridge models in ZEUS-NL

� wave

nd str

ution subject to ASCE license or copyright. Visithttp://www.ascelibrary.org

Fig. 4. Finally, Rayleigh damping elements were included in themodel, simulating a viscous damping value of 2%.

Modeling of the west abutment was complex due to the fixedboundary condition at this end of the structure. Preliminary analy-sis with a rigid connection between the west abutment anddeck resulted in the monolithic abutment being subjected to ex-tremely high lateral forces. In reality, however, the abutmentwould not remain rigid during seismic excitation, and movementwithin the soil will dissipate energy, significantly reducing theinput force. A ZEUS-NL abutment model, including the six CIDHfoundation cylinders was created for more detailed analysis. Soilstiffness for the structural model was provided �Priestley 1994�with resistance increasing linearly with depth. Springs of linearlyincreasing stiffness were used to simulate soil resistance on thesix foundation cylinders. A static pushover analysis of this abut-ment model resulted in the curve shown with the dotted line inFig. 5.

Using results from the detailed pushover analysis, the abut-ment stiffness was approximated in the full ZEUS-NL bridgemodel using the bilinear curve shown in Fig. 5, with a transitionpoint at 45 mm. As expected, when ground motion was applied tothe west abutment through a spring with these bilinear stiffnesscharacteristics, the lateral force reduced significantly. Though thisbilinear spring adequately represents abutment stiffness to a point,it does not model the reality of abutment pile shear. Preliminaryanalysis using varied shear failure values showed negligiblebridge response variation; however, the simple bilinear springmodel was used in the final bridge model.

It should be noted that the complex dynamic stiffness of thecoupled backfill-abutment-deck system is in general differentfrom the stiffness found through pushover analysis, due to theinherent frequency dependence of the corresponding dynamicstiffness matrix. However, the approach above is a reasonableapproximation for the assessment of the abutment lateral forces,not only because the actual damping at the backfill-abutment in-terface is expected to reduce the demand, but also because theanalysis performed in Part II essentially focuses on the relativeeffect of spatial variability parameters given the soil-foundationsystem conditions.

In addition to the curved bridge model, analysis was per-formed on an identical 344 m long straight bridge structure toexamine the effect of deck geometry on seismic response. The

Fig. 5. West abutment CIDH cylinder group p

model was created with identical boundary conditions and mate-

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rial properties as the curved bridge. The same suite of syntheticearthquake records were applied to this model, isolating deck cur-vature as the only factor modifying bridge response.

Sample Results

When the relative displacement �in global x and y directions�between the top and bottom of each pier is examined, it is clearthat inelastic dynamic analysis of the curved bridge model usingsynthetic asynchronous accelerograms results in significant pierdisplacement increases compared with synchronous input. To helpquantify the number of piers that may be damaged if a bridgedesigned for synchronous displacements was subjected to asyn-chronous motion, a nominal lateral deflection limit of 1.5 timesthe design �synchronous� deflection was defined. Though arbi-trary, this was recognized as a significant increase in pier deflec-tion, indicating substantial asynchronous response amplification.Table 2 shows the number of piers exceeding 1.5 times the maxi-mum displacement of the synchronous case increases sharply asthe input motion becomes less coherent. The study bridge haseight bridge piers and was subjected to 11 earthquake events ateach coherency level, providing 88 opportunities for piers to ex-ceed this limit.

From the pier “failure” rates in Table 2, it is clear that inco-herence from the wave passage effect �increasing from top tobottom� is less damaging than coherence loss from geometricincoherence �increasing from left to right�. The maximum pier“failure” rate from wave arrival delay alone is 8%, while 30% ofpiers exceeded the 1.5 displacement limit when only geometricincoherence is considered. This observation implies that the com-mon design practice of simply applying an earthquake record atthe pier supports with a time shift is incomplete and could beextremely unconservative. These results show significant re-sponse increases are possible when asynchronous motion isconsidered, even without accounting for the effect of local soil

er analysis, with bilinear curve approximation

Table 2. Bridge Piers Reaching Limit State for Nine Incoherence Cases

in-in :0 /88=0% in-90 :2 /88=2% in-30 :26 /88=30%

in-90 :2 /88=2% 90-90 :2 /88=2% 30-90 :32 /88=36%

in-30 :7 /88=8% 90-30 :3 /88=3% 30-30 :31 /88=35%

ushov

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conditions and demonstrate the importance of increasing under-standing of this phenomenon.

Discussion and Conclusions

Over the last 30 years, numerous analytical studies have identifiedasynchronous earthquake motion as an important factor influenc-ing bridge response, especially in cases of long or irregularbridges. Generally, these studies have shown asynchronous mo-tion to suppress fundamental dynamic modes, exciting highermodes as well as creating significant pseudostatic displacementsbetween bridge support points. Seeking to extend general trendsfrom previous analytical studies and further define the nature ofresponse amplification from asynchronous seismic input, a suit-able irregular bridge structure is selected for study. A complexMDOF analytical idealization of the study bridge is created andvalidated through inelastic dynamic analysis. Suites of syntheticasynchronous accelerograms are produced for use in inelasticdynamic analysis using two independent, fully parametrizedcomputer codes combining expert geotechnical and earthquakestructural engineering knowledge. Extensive analysis using nearly2,000 unique input records with varied levels of geometric andspatial incoherence shows asynchronous motion can significantlyincrease �or decrease� structural response compared with synchro-nous excitation.

Preliminary results comparing the effect of the two sources ofasynchronous earthquake input investigated on the curved studystructure indicate that geometric incoherence results in greaterresponse amplification than wave arrival delay for the concretestudy structure. Severe geometric incoherence alone resulted in30% of the piers exceeding the 1.5 displacement limit, comparedwith 8% with only wave passage effect. This notable differencein response amplification is likely due to the nature of each ofthese incoherence sources. The wave passage effect simply re-sults in adjacent support points following the same deflectionrecord with a short delay, limiting the pseudostatic deflectionpossible. Geometric incoherence, however, produces slightlydifferent displacement records at adjacent piers due to randomreflection and refraction. Thus, adjacent displacement records canvary more significantly, resulting in larger pseudostatic deflec-tions and greater response amplification compared with synchro-nous input.

As noted above, asynchronous response consists of a complexcombination of effects including suppression of fundamentaldynamic modes and pseudostatic displacements, which can eitherdecrease or increase structural response compared with synchro-nous strong motion for a given seismic record. Table 2 showsthat though general trends can be found in result comparisons�e.g., greater incoherence results in more cases of significant am-plification�, a degree of variability still remains. For example,when a degree of geometric incoherence is added to the mostsevere wave passage case �in-30�, rather than the occurrence ofpier “failures” increasing, it decreases from 8% to 3%. This couldbe due to a reduction in pseudostatic displacements or greatersuppression of certain dynamic modes for this combination ofincoherence. Because asynchronous response is such a complex,motion-specific phenomenon, it is advisable to use a suite ofground motions to provide opportunities for detrimental responseto manifest.

The multitude of inelastic dynamic analyses performed inthis study results in a wealth of response data. Sample results

presented in the current paper show numerous cases of re-

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sponse amplification due to asynchronous motion for the irregularbridge studied. Further analysis of the data is needed to betterunderstand the nature of this amplification and document re-sponse variation between curved and straight bridges. Thisdetailed analysis of asynchronous response amplification isconsidered extensively in the companion paper, “Effect of Asyn-chronous Motion on Complex Bridges. Part II: Results and Im-plications on Assessment.”

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