seismic behavior and capacity/demand analyses of three multi-span simply supported bridges

Engineering Structures 30 (2008) 54–66www.elsevier.com/locate/engstruct

Seismic behavior and capacity/demand analyses of three multi-span simplysupported bridges

M. Ala Saadeghvaziria,∗, A.R. Yazdani-Motlaghb

a Department of Civil and Environmental Engineering, New Jersey Institute of Technology, University Heights, Newark, NJ 07102-1982, United Statesb Nishkian and Associates Inc., 1200 Folsom St., San Francisco, CA 94103, United States

Received 17 November 2006; received in revised form 24 January 2007; accepted 25 February 2007Available online 16 April 2007

Abstract

This paper presents the results of an analytical study on the seismic response of three Multi-Span-Simply-Supported (MSSS) bridges in NewJersey. The main goal is to determine the capacity/demand ratio for various components in order to evaluate the seismic vulnerability and todevelop retrofit strategies. Another important objective is to investigate the effect of those response characteristics that are unique to this classof bridges on their seismic performance. Furthermore, the effect of modeling approach and appropriateness of pushover analysis using existingdemand curve are also addressed considering the stiffening-interaction between the bridge and the abutments. The investigation includes detailednonlinear time history analyses of three actual bridges as representatives of typical 2, 3, and 4 span bridges, which are common in New Jerseyand the Eastern United States in general. Both 2-D and 3-D models were employed in order to evaluate the effect of modeling. Several parametersprove to have an important effect on the seismic response of MSSS bridges, such as soil–structure interaction, impact between adjacent spans,steel bearings, and plasticity at pier columns. Therefore, the seismic response of MSSS bridges is evaluated in light of a comprehensive parametricstudy based on these factors and quantified through capacity/demand (C/D) ratios for critical elements. Furthermore, the research needs relatedto the seismic evaluation, retrofit, and design of MSSS bridges are also discussed.c© 2007 Elsevier Ltd. All rights reserved.

Keywords: Bridges; Seismic; Retrofit; Multi-span; Capacity; Demand

1. Introduction

A commonly used type of bridge in the Eastern UnitedStates, including New Jersey, is the Multi-Span-Simply-Supported (MSSS) system. In an MSSS bridge each span issimply supported with separation gaps between the adjacentspans and between the end spans and the abutments. Thegap size is normally in the range of 25–76 mm (1–3 in.).Framing consists of slab-on-girder deck supported on pierbents (normally multi-columns) and seat-type abutment. Bridgecolumns in New Jersey are normally circular or square in crosssection. The lateral reinforcement is different for circular andsquare columns. Generally, abutments are seat-type supportedon footings although some are supported on piles. Steelbearings (fixed and expansion) are normally used as a means of

∗ Corresponding author. Tel.: +1 973 596 5813; fax: +1 973 596 5790.E-mail address: [email protected] (M.A. Saadeghvaziri).

0141-0296/$ - see front matter c© 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2007.02.017

load transfer from the superstructure to the substructure. Thus,in addition to better-understood seismic deficiencies commonto all bridges, such as small seat width, inadequate transversereinforcement in the columns/piers, and soil liquefaction hazardreported during past earthquakes around the world, for MSSSbridges there are other important sources of possible damagein the event of an earthquake. These are related to the steelbearings, impact between adjacent spans and between the end-span and the abutment, soil–structure interaction (especially atthe abutments), and frictional characteristics following possiblebearing failure. The latter parameter is important because evenunder low level of ground motion the impact forces can, atleast theoretically, cause failure of the bearings in the form ofshear failure at the anchor bolts and/or at the connection boltsbetween the girder and the bearing top sole plate. Therefore,post-bearing failure response of the bridge system shouldbe considered using nonlinear models representing Coulombfriction. An equally important factor in the seismic response

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M.A. Saadeghvaziri, A.R. Yazdani-Motlagh / Engineering Structures 30 (2008) 54–66 55

of MSSS bridges is the possibility of abutment backwall failuredue to impact forces.

Due to concerns about the possibility of a damagingearthquake in the Central and Eastern states, the 1988 NEHRPmaps have placed many areas including New Jersey into higherseismic risk categories. Consequently, based on AASHTO [2]seismic design guidelines, which adopted the NEHRP maps, theacceleration coefficient for northern New Jersey has increasedto 0.18, and for the southern coastal areas to 0.1. Thus, theentire state is classified as SPC B. In addition to considerationto seismic load in the design of new bridges, the NewJersey Department of Transportation (NJDOT) also adoptedthe Seismic Retrofitting Manual for Highway Bridges [7]for seismic assessment and rehabilitation of existing bridges.Furthermore, as a part of its seismic retrofit and designefforts, NJDOT sponsored a research program to investigatethe seismic response of MSSS bridges considering their uniquebehavioral characteristics. General issues related to seismicdesign and retrofit of MSSS bridges along with results ofanalyses on the effect of steel bearings on seismic performanceof MSSS bridges, including detailed finite element analysisof critical components, have been reported by Saadeghvaziriand Rashidi [12,13]. This paper presents the results of acomprehensive nonlinear time history analysis of three actualbridges quantified through detailed capacity/demand ratios forkey elements, and discusses design and modeling issues as wellas the research needs related to MSSS bridges. Details of thework presented in this paper can be found in [15].

2. Description of the bridges

Three simple span and simply supported bridges, represen-tative of typical bridges in New Jersey, are evaluated under thisstudy. For these bridges the number of spans varies and is equalto two, three and four. They all have concrete slab decks onsteel girders and reinforced concrete pier bents. The gap sizesbetween adjacent decks or end spans and abutments vary from25 to 76 mm (1 to 3 in.). Pier columns and abutments havespread footings without piles. The pier columns are all circu-lar with spiral or circular lateral reinforcements. The level ofconcrete confinement varies for each bridge. The lowest con-finement belongs to Bridge #1 (3-span bridge) with #3 circularhoops at 305 mm (12′′) spacing. On the other hand Bridges #2and 3 (2 and 4 span bridges, respectively) both have well con-finement details for their pier columns, which consist of spiralreinforcement at small pitch (89–57 mm, or 3.5′′–2.25′′).

Bridge #1 has three spans in lengths of 42.7, 29, and 42.7 m(140′, 95′, and 140′) with skewness equal to 33◦. The widthof the bridge is made of two separated symmetric half-decksand has a total width of 26.2 m (86′). Each half-deck hassix 1626 mm (64′′) high girders supporting a 241 mm (9.5′′)

thick concrete slab. Separate pier bents beneath each half-deckconsist of two 1.22 m (4′) diameter circular columns and a1.4 m (4.6′) high cap beam.

Bridge # 2 is a straight (only 3◦ skewness) bridge with twoequal spans of 29.7 m (97′–4′′). Each deck has fifteen 1143 mm(45′′) high girders supporting a 222 mm (8.75′′) thick concreteslab. The deck cross section has two unequal parts, namely

part 1A (with 9 girders) and part 1B (with 6 girders) and ithas total width equal to 34.1 m (112 feet). Correspondingly,the pier bent consists of two parts with a total of ten 0.91 m (3′)

diameter circular columns.Bridge # 3 has four spans in lengths of 12.8, 39.6, 36.6, and

26.8 m (42′, 130′, 120′ and 88′) with skewness equal to 45◦.Each deck has 7 girders 2184 mm (86′′) apart, supporting a203 mm (8′′) thick concrete slab. Each column bent consistsof five 1.07 m (3.5′) diameter circular columns and a 1.37 m(4.5′) height cap beam. Since the details of steel girders werenot available, typical and estimated dimensions, consideringthe previous two bridges, were assumed. Note that girderinformation is primarily needed in determination of the totalmass and in light of its relatively small weight compared to thedeck this assumption is quite adequate. With regard to stiffness,the deck-girder system is very rigid regardless of the exactvalues for area and moment of inertia for individual elements.The stiffness of the bridge system is controlled by the weakerelements (i.e., columns and abutments).

All three bridges use steel bearings to connect superstructureto the substructure. Typically four 22 mm (7/8′′) diameterA325 steel bolts are used to connect the bearing to the girder,and two 38 mm (1.5′′) diameter A615 steel anchor bolts areused to connect the bearings to the abutments and cap beams.These elements are the weak links in the load transfer fromthe superstructure to the substructure through the bearings. Theedge distance or seat width is in the range of 178–254 mm(7–10 in.).

Plan and elevation for Bridge #1 is shown in Fig. 1. Crosssections for all three bridges are shown in Fig. 2.

3. Analytical modeling

Analysis of MSSS bridges under gravity loads is simpleand straightforward and this is indeed the reason behindusing this system. Under transverse seismic load for straightbridges the system can be easily analyzed as a series ofindependent simply supported beams with boundary springsrepresenting soil–structure interaction. However, the responseof MSSS bridges in the longitudinal direction is complicatedby the impact between adjacent spans as well as soil–structureinteraction [14]. If the displacements due to a design earthquakeobtained from linear analysis exceed the expansion joint widththen a nonlinear dynamic time history analysis that includesimpact will be required. For straight bridges the fundamentalconcepts important to longitudinal motion can be capturedwith a two-dimensional (2-D) model. However, for skewedbridges there is an interaction between the longitudinal andtransverse mode shapes and three-dimensional (3-D) modelsare required. Therefore, in this study both 2-D and 3-D modelswere employed to perform in-depth analyses of these threebridges. Note that the use of 2-D models is more efficient thanperforming unidirectional analysis as a special case of the 3-Dmodels. Special emphasis was placed on detailed parametricstudies under the longitudinal earthquake excitation becausethe study of the damage to MSSS bridges has shown thatseismic waves in this direction have caused more damage than

56 M.A. Saadeghvaziri, A.R. Yazdani-Motlagh / Engineering Structures 30 (2008) 54–66

Fig. 1. Plan and longitudinal elevation of a typical MSSS bridge (Bridge #1).

(a) Bridge #1 (due to symmetry only half of the deck is modeled).

(b) Bridge #2 (columns diameter 91.5 cm).

(c) Bridge #3 (columns diameter 106.7 cm).

Fig. 2. Cross-sections for all three bridges.

transverse waves [18]. Furthermore, under the most likely modeof damage (i.e., bearing failure) the system possesses a highdegree of redundancy in the transverse direction; however, in

the longitudinal direction this may not be the case. Dependingon the available seat length and the soil–structure interaction atthe abutments the system can fail as a result of span unseating.


Fig. 3. A typical 2-D model (Bridge #1 — Concentrated forces are gravity loads).

3.1. 2-D analytical model

All three bridges were analyzed using DRAIN-2DX [4]. The2-D model for Bridge #1 is shown in Fig. 3. Similar modelswere used for the other two bridges, where beam–columnelement (Type 02) is employed to model decks, columns, andcap beams. For the columns nonlinear behavior is modeled byconcentric plastic hinges at the element ends. Plastic hingesare capable of considering P–M interaction curves for steeland reinforced concrete column sections. Bearings, abutmentfoundation and back-fill soil (with inelastic unloading) andsoil springs at the column footings are modeled using simpleconnection element (Type 04). To model gap and impactbetween adjacent spans and between an end-span and theabutment the link element (Type 09) is employed. Notethat expansion bearings are modeled as roller; however, asdetermined by Mander et al. [9] they do possess some stiffnessand friction resistance.

3.2. 3-D analytical model

DRAIN-3DX [5] is used for 3-D nonlinear time historyanalysis. Only Bridges #1 and #3 are modeled since Bridge #2is not skewed and no significant coupling of responses in thehorizontal and longitudinal directions is expected. Fig. 4 showsthe 3-D model for Bridge #1. Similar to the 2-D model, simpleconnection element (Type 04) and compression/tension linkelement (Type 09) are used to model the bearings, abutmentsand foundations, and impact. Elastic beam–column element(Type 17) is used to represent the decks, and cap beams. The

columns are modeled using fiber hinge beam–column element(Type 08) with P–M hinge option. For both 2-D and 3-Dmodels 5% Rayleigh’s damping based on fundamental modesis assumed.

3.3. Properties and capacity of various components

The values of various parameters for analytical modelsand for use in capacity/demand evaluation were determinedusing detailed analyses based on AASHTO LRFD [1], FHWASeismic Retrofitting Manual for Highway Bridges [7], andestablished engineering principles. For the sake of brevity onlya short description of the procedures employed for criticalcomponents is presented here. More detailed information canbe found in the original report [15].

Columns: All three bridges analyzed under this study haveround columns. The exact moment–curvature relationship andmoment–axial load interaction for column cross sections aredetermined. This is achieved by dividing the cross section intoa number of fibers and satisfying compatibility and equilibriumusing commonly used stress–strain relationships for concreteand steel. Per FHWA’s seismic retrofit guidelines [7] theultimate compressive strain of 0.005 is assumed for unconfinedconcrete, and the equation given based on energy balance isused to determine the ultimate compressive strain for confinedconcrete. For this purpose the ultimate compressive stressfor confined concrete is calculated based on the approachproposed by Mander, et al. [10]. The ultimate curvature isreached when concrete strain reaches the ultimate compressivestrain or when the moment decreases to 85% of the maximum

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Fig. 4. A typical 3-D model (Bridge #1).

Fig. 5. A typical fixed bearing.

moment reached on the moment–curvature diagram, whicheverhappens first. The effect of column curvature ductility, thuslateral reinforcement, on shear capacity is also consideredby using the equation given by the FHWA guidelines [7].However, the contribution of axial load to shear capacity isignored to implicitly account for variation in axial load dueto frame action in mutli-columns bents and for the adverseeffect of vertical component of ground motion, which is notconsidered directly. The actual moment–curvature relationshipsalong with the equations given by FHWA [7] for plastic hingerotation and plastic hinge length are used to determine the

plastic rotation capacity. Summary of the calculations is shownin Table 1. The column is then modeled using elasto-plasticbeam elements with an initial stiffness based on the effectivemoment of inertia determined using FHWA’s seismic retrofitguidelines [7]. The plastic moment capacity is determinedby fitting the bilinear model to the actual moment–curvaturerelationship.

Bearings: Typical fixed bearing commonly used in the Stateof New Jersey is shown in Fig. 5. It typically consists ofa parted metal casing with each part welded to the top andbottom steel plates. As was mentioned, the top steel plate


Table 1Basic design parameters along with shear, and flexural capacities for pier columns

Bridge f ′c

(MPa)fy(MPa)

D(m)

Longitudinalrebar

Transversesteel

Vc (kN) Vs(kN)

Mn(kN m)

εcu φu(rad/m) θp (rad)

1 20.7 413.7 1.22#9 #3 @ 305 mm

422–1235 169 3516 0.005 0.022 0.015–0.017(20) Circular hoop

2 27.6 413.7 0.91#10 #5 @ 89 mm

276–800 1164 2120 0.024 0.177 0.126(16) Spiral

3 20.7 275.8 1.07#11 #4 @ 57 mm

324–942 929 1556–2610 0.024 0.157 0.098–0.124(9–20) Spiral

Since there are more than one column type for each bridge, some values are shown as a range accounting for such variation. However, for concrete shear contributionthe range corresponds to curvature ductility factors of 2 and 4 per FHWA.

is connected to the deck steel girder by 4φ22 mm (7/8′′)

connection bolts and the bottom steel plate is connected to theconcrete seat by 2φ38 mm (1.5′′) anchor bolts. Evaluation ofthe shear strength of the weld and the shear strength of theconnecting bolts indicates that the latter is the weak link inthe load transfer from the superstructure to the substructuresthrough the bearing. Based on AASHTO-LRFD [1] theseconnection bolts can provide about 444 kN (100 kips) shearcapacity for each fixed bearings. Impact forces, under evenlow level of ground motion, can easily exceed this capacity.This by itself does not constitute bridge failure and the systemcan function depending on post-failure response. Therefore,post-failure behavior of the bearings is an important factorin proper evaluation of seismic response of MSSS bridges.Assuming Coulomb friction behavior upon shear failure ofthe bolts a bilinear force–deformation relationship is used tomodel the post-failure response. The yield strength is equal tothe coefficient of friction times the normal gravity force perbearing. The coefficient of friction is taken to be in the range of0.2–0.6 as a parameter. Relatively large values are assumed forthe stiffness of the force–deformation relationship representingCoulomb friction.

For roller or expansion bearings, except for the nature ofthe casings, which have a special configuration to allow freemovement of the deck in the longitudinal direction, the detailsare similar to the fixed bearings. Thus, the modeling allows forfree translation in the longitudinal direction and no movementin the transverse direction.

Boundary/Foundation springs: The total bridge displace-ment in the longitudinal direction is limited by the closure ofgaps if the abutment is assumed infinitely stiff and strong. How-ever, in actual situations there are additional movements at theabutments due to their flexibility and yielding, which can com-promise the integrity of the entire bridge system. Movements atthe abutments may be due to elastic deformation of the backfillsoil and sliding of the entire system when supported on foot-ings. An additional source of movement is inelastic deformationas a result of yielding in the soil. Furthermore, the flexibility ofthe foundation can have a significant effect on the level of forcescarried by the columns and on the overall displacement demandfor the bridge system. Therefore, essential to proper estimate ofcapacity/demand ratios for different elements are considerationof the soil–structure interaction (stiffness and strength). In this

study this interaction is modeled through both translational androtational boundary springs at the abutments and at the base ofthe piers.

The procedures given by FHWA’s Seismic Design ofHighway Bridge Foundations [6] and Wilson and Tan [16] areemployed to determine translational and rotational stiffnessesof the boundary springs at the abutments and at the base ofthe piers. Similarly, the stiffness and strength of the abutmentbackfill soil are determined based on FHWA’s procedures [6].Based on these simplified procedures, in addition to geometricdimensions, the shear modulus and internal frictional angle forthe soil are the only parameters needed to define the stiffnessand strength of various foundation elements. The soil shearmoduli (GS) considered are equal to 2.76, 27.6, and 276 MPa(0.4, 4, and 40 ksi), representing soft, medium and stiff soils.The internal frictional angle of 20◦ is assumed for low tomoderately stiff soils (i.e., GS = 2.76 and 27.6 MPa) andit is 45◦ for stiff soil. Various stiffnesses at the abutments inthe longitudinal direction are then lumped (condensed) intoone translational spring at the point of impact between theabutment and the deck as shown in Fig. 6 and detailed in theoriginal report. The only assumption in the process outlinein Fig. 6 is rigid body movement of the abutment, whichhas been corroborated through experimental work by Maroneyet al. [11]. Step one of the process involves determination ofall the translational and rotational springs at various footingsand on the back wall using the above references. In step twothese are moved to the center of stiffness located at the heightx above the base of the footing. In step three, using rigid bodyassumption these are lumped into a single horizontal spring,Kh , which along with the mobilized mass idealize the abutmentas a simple mass spring system.

The horizontal spring at the abutments in the longitudinaldirection are bilinear with their yield strength in compressiondetermined based on Mononobe–Okabe method. Tensilestrength is equal to the friction force at the footinginterface (see Fig. 3). Translational springs in the verticaland transverse directions are assumed to remain elastic. Asan example, using these procedures the abutment springstiffness for Bridge #1 in the longitudinal direction is about332GS kN/mm (1900GS kips/in.), which for a typical soilshear modulus (GS) of 27.6 MPa (4 ksi) results in a stiffnessof 1330 kN/mm (7600 kips/in.). For the same bridge, the


(a) Step-1. (b) Step-2. (c) Step-3.

Fig. 6. Abutment simplified modeling in bridge longitudinal direction.

simplified procedure given by CALTRANS [3], which onlydepends on the width of the bridge, will result in a value of3009 kN/mm (17, 200 kips/in.). The difference by a factor oftwo is consistent with the results reported by Goel and Chopra[8].

An important consideration in modeling the effect ofabutment–bridge interaction during seismic response is toaccount for the possibility of backwall failure. The abutmentwall consists of two segments, namely backwall and breastwall. Backwall is the upper narrow part of the abutment walland it is quite possible for impact forces to cause detachmentof this segment from the breast wall through shear failure.This type of failure is more desirable than total collapse ofthe abutment, since it is much easier to repair. In this studysuch a mode of failure is considered through an iterativeprocedure. That is, in cases that the time history analysisresults indicate the possibility of the backwall failure, the bridgemodel is reanalyzed with damaged abutment configuration. Inthis configuration the mass, stiffness and strength of boundarysprings are modified to correspond to only the backwall portionof the abutment. It should be noted that the shear capacity at thejuncture of two wall segments is controlled by shear frictionand is calculated based on AASHTO LRFD [1].

4. Time history analysis

Using the models described in the previous sections a largenumber of time history analyses were performed to evaluate theseismic response through capacity/demand ratios for criticalcomponents. The parametric study included three types of soils(reflected in shear modulus), two abutment backwall conditions(intact and damaged), and three bearing conditions (intact,failed with low coefficient of friction of 0.2, and failed withhigh coefficient of friction of 0.6). Furthermore, the effect ofmodeling approach (2-D vs. 3-D) on seismic response was alsoevaluated.

Three different set of earthquake ground motion recordsrepresentative of interplate and intraplate earthquakes wereused. These are El Centro (Imperial Valley 1940, with twoorthogonal components with PGA of 341.7 and 210.1 cm/s2),Parkfield (California 1966, with two orthogonal componentswith PGA of 479.6 and 347.8 cm/s2), and Nahanni (Canada1985, one component with PGA of 534.4 cm/s2) records. Fig. 7

Fig. 7. Comparison of response spectra for PGA of 0.18g.

presents response spectra for the primary earthquake records(strongest based on the original PGA) scaled to PGA of 0.18g.In this figure AASHTO design response spectrum is also shownfor comparison purposes. As is seen in the figure, spectralamplitude of the Nahanni record is the lowest in medium to highperiod range, and it has higher demand for high frequency (lowperiod) systems. The input records were scaled by peak groundacceleration (PGA) and two different PGAs of 0.18g and 0.4gwere employed for the time history analyses. The former isthe maximum acceleration coefficient in New Jersey, while thelatter is for higher seismicity regions such as California, andcan be considered as an event with a longer return period for theState of New Jersey. In the 2-D analyses the primary horizontalrecord for each earthquake was used as the input. However, forthe 3-D analyses the orthogonal (i.e., transverse) earthquakecomponent is also considered. Thus, there are two possiblealternatives: namely, primary record as longitudinal input andthe orthogonal horizontal record as transverse input, and viceversa. The same PGA is used in both orthogonal directions.For 3-D analyses only El Centro and Parkfield records areconsidered. This was due to the fact that the Nahanni recorddoes not cause much demand in any of the three bridges.

4.1. 2-D results

Among the three earthquake records used, almost alwaysthe Nahanni record (representative of intraplate earthquakes)


caused the lowest response in all three bridges, regardlessof the level of PGA, soil–structure interaction, and bearingcondition. Although a similar observation cannot be madeabout the other two records (both from California Earthquakes),responses were higher more often for the Parkfield record.For an input motion with PGA of 0.18g the overall seismicresponse in the longitudinal direction, using a 2-D model, ismarginal with the lowest capacity/demand ratio of 1.04 for theseat length. This is aside from bearing performance, which asit will be discussed will most likely fail under impact forces.The minimum capacity/demand (C/D) ratios in Bridge #1,which has the poorest performance, subjected to peak groundacceleration of 0.18g in the longitudinal direction are in therange of 1.04–7.9. Critical response parameters consideredare deck relative displacement (deck sliding), column shear,curvature ductility, and plastic rotation demand. Thus, asidefrom shear failure in the bearing bolts; the bridge is marginallysafe under this level of ground acceleration. Note that the lowestC/D ratio of 1.04 corresponds to the seat length over abutment#2. A C/D of less than unity for the deck relative displacementswill imply fall-off of the span. However, it is for a very soft soilcondition that may not represent actual cases and it is taken asan extreme condition.

Longitudinal response of MSSS bridges is complicated bythe impact between adjacent spans. In general, impact reducesdisplacements, but significantly increases the level of the forcesin the bearings. Consequently, even under low levels of peakground acceleration bearing failure and possibly backwalldamage are likely. The level of impact force depends on thesoil-type and abutment condition (intact vs. damaged backwall). When the abutment is assumed intact the impact forcesare increasing as the soil stiffness decreases. In the case ofdamaged backwall the trend is reversed. For the same soiltype there is less impact force in a damaged backwall casecompared to an intact abutment. These variations have to dowith the relative value of the abutment stiffness with respectto its mobilized mass. Depending on the values of these twoparameters the amplitude of abutment response will changeresulting in different dynamic interaction and impact forceswithin the bridge–abutment system. This should not be takenas a general trend, but it rather highlights the importance ofsoil–structure interaction that should be considered in seismicanalysis of MSSS bridges. For example, the C/D ratios forthe deck relative displacement (deck sliding) at abutment #2 inBridge #1, ranges from 1.04 to more than 2. The C/D is lowerfor softer soil and for smaller coefficient of friction at bearings.

Impact forces between two adjacent spans or between anend-span and the abutment are large enough to cause damageto the bridge in the form of shear failure in the bearings. Fig. 8presents the shear time history in the bearings in Bridge #1under the Parkfield earthquake record (scaled to 0.18 PGA). Asis seen from this figure, because of impact the shear forces in thebearings are several times higher than the capacity of the bolts.Note that in this specific analysis the bearings are assumedelastic and bearing capacity is plotted for comparison purposes.This justifies the assumption of failed-bearing condition in thenonlinear analyses (i.e., assuming Coulomb frictional sliding

Fig. 8. Comparison of the bearings shear response time histories for modelswith impact and without impact between decks (PGA 0.18g, Parkfield EQ,Bridge #1, 2-D model).

at fixed bearings with coefficient of friction as a parameter).Results show that failure of the bolts will not necessarily causelarge displacement in the deck, which can otherwise cause spanfall off. For example, in Bridge #1 subjected to the Parkfieldrecord with PGA of 0.18g, and with medium soil condition(i.e., shear modulus of 27.6 MPa) the C/D ratios for thedeck relative displacement at abutment #2 are 1.9, 1.8, and1.6 for intact, bearing with µ = 0.6, and bearing with µ =

0.2, respectively. For the shear force in the pier columns, asexpected, the trend is even reversed and the C/Ds are higher forbearings with lower coefficient of friction, as shown in Fig. 9.This is further discussed under the 3-D results. Upon failureof the bearings there is a reduction in the seismic demandsbecause of period elongation and higher energy dissipation.Thus, failure of the bearings followed by stable Coulombfriction behavior can act like a fuse and limit the seismicresponse of the bridge system even for higher PGAs. In lightof the importance of this phenomenon, further experimentaland analytical studies should be conducted to validate sucha behavioral characteristic, especially for high bearing wherestability is also an issue. In Fig. 8, impact forces are not ofspike nature and rather continuous and symmetric because thepier impacts an abutment on one side and another bend andabutment on the other side. The frequency of the impact forcetime history appears to be around 11 Hz corresponding tothe lighter abutment with 1330 kN/mm stiffness and weightof 3022 kN. The time history is further compounded by thefrequency of the adjacent bent and second abutment. It is notwithin the scope of this paper to get into the details of impactas such a phenomenon is well studied and quite dependent onnumerical representation, albeit with only local affects. Theemphasis here is on the fact that even under low input groundmotion it is possible to exceed the capacity of the bearingsbecause of impact.

Responses of the bridges under a PGA of 0.4g, which couldbe construed as an earthquake event with much longer returnperiod in New Jersey, are more critical with the possibilities ofspan fall-off (in the case of weak abutments) and column shearfailure. This is further discussed under the 3-D results.


Fig. 9. Shear time histories for Bridge #1, pier #2 — different bearing frictionalcoefficients under Parkfield earthquake (2-D model, G-soil = 4 ksi, PGA =

0.18g).

Table 2Comparison of fundamental periods (Bridge #1, GS = 27.6 MPa)

Model Longitudinal (s) Transverse (s)Pier #1 Pier #2

3-D 1.10 1.67 0.522-D (Longitudinal) 1.40 2.26 N/A

4.2. 3-D results

Only Bridges #1 and #3, which are skewed, were also an-alyzed using 3-D models. As expected, skewness has signif-icant effect on dynamic characteristics and seismic responseby causing coupling of responses in two orthogonal horizontaldirections. Table 2 shows the periods for fundamental modesof Bridge #1 comparing 2-D and 3-D models for medium soil(i.e., GS equal to 27.6 MPa). Note that for the 3-D model themode shapes are coupled and the values shown are for the dom-inant mode shapes in each direction. As it can be seen fromthis table, the periods for longitudinal mode shapes are lowerwhen a 3-D model is employed. This is due to stiffening effectof transverse elements on the longitudinal motion. For example,both fixed and roller support act as fixed in the transverse direc-tion. Consequently, due to skewness there is a restraining effecton the longitudinal movement due to fixity in the transverse di-rection. Similarly, due to framing action the column bents aremuch stiffer in the transverse direction, which has an effect onlongitudinal response. For the same reason, a 3-D model pro-vides a better representation of the axial forces in the columns,which are varying due to frame action even under longitudi-nal motion. Variation in the axial load affects the plastic hingebehavior of the columns. The effect of abutment back wall fail-ure on the displacements in the longitudinal direction is lesssignificant in the case of 3-D model because of higher contribu-tion of the column bents to longitudinal stiffness. Finally, dueto a more distributed representation of the mass and stiffnessof various components, the impact is smoother and the levelsof impact forces appear to be more realistic. For example, us-ing the 2-D model for Bridge #1 (for a typical case) the impactforces are equal to zero and 103,545 kN (23,300 kips) at abut-ments 1 and 2, respectively. However, based on the 3-D modelfor the same case, the impact forces in the longitudinal direc-tion are equal to 15,994, and 33,374 kN (3599, and 7510 kips)

Fig. 10. Time histories of resultant shear force at the right pier in Bridge #1(3-D model, PGA = 0.18g, Parkfield record, and GS = 27.6 MPa).

at abutments 1 and 2, respectively. A similar pattern is observedfor other cases (i.e., different earthquake record, soil-type, etc.)and for Bridge #3.

Skewness and low concrete lateral confinement of the piercolumns are among the seismically undesirable characteristicsof Bridge #1. However, under the PGA of 0.18g, it has C/Dratios larger than 1.0 for most cases. As shown in Table 3,the only condition that leads to pier column shear failure is amodel with elastic bearings (i.e., intact bearings). In an actualsituation, as discussed, most likely the fixed bearings will failunder impact forces, even at a PGA as low as 0.18g. This willcause isolation of the superstructure and provide dissipationof energy through Coulomb friction, which in turn limits thebridge response and the shear demands in the columns. Fig. 10shows the time histories of the resultant shear force demandin right pier columns of Bridge #1 considering both cases ofelastic bearings and failed bearings where post-failure behavioris defined by Coulomb friction with µ = 0.6. It can be seen thatthe maximum shear force demand for pier columns is higherin the case of elastic (intact) bearings than the case of failedbearing. Thus, considering the C/D ratios for shear (Table 3),for medium soil (i.e., GS = 27.6 MPa) the directional C/Dratios have increased from 0.4 to 1.3 in the transverse direction(i.e., y–y axis for shear) and from 1.3 to 2.5 in the longitudinaldirection (i.e., z–z axis for shear). Similarly, the plastic rotationdemands decrease significantly for failed bearings. This can beseen in Table 3 where plastic rotation demands have reducedto almost zero when Coulomb friction was considered at thebearings. Thus, assuming stable post-failure behavior at thebearings over the pier bents, their failure can act like a fuselimiting the seismic response of the bridge, thus, preventingbrittle failure. However, this is a big assumption and should beverified through further studies, especially experimental ones.

To investigate the effect of higher ground motionacceleration many cases were analyzed with PGA of 0.4g. Thesummary of the minimum C/D ratios for both Bridge #1 and3 are shown in Tables 4 and 5, where it can be seen that thecolumns’ shear demands for various conditions greatly exceedthe shear capacities (i.e., C/D lower than unity). Unlike thecase of 0.18g, here column shear failure occurs regardless ofthe bearing condition (i.e., intact or failed). It should be noted


Table 3The minimum C/D ratios for Bridge #1 under PGA of 0.18g (3-D model)

GS (MPa) Clements bridge directional C/D ratiosPier column shear Column plastic rotation Deck slidingC/D ratios in column local axes (y–y, z–z) C/D ratios about column local axes

(y–y, z–z)C/D ratios in bridge longitudinal direction

2.76 (0.8, 1.3) FailureCase: EL, elastic bearing

(1.3, 1.3)Case: EL, elastic bearing

1.1Case: PF, elastic bearing

(2.0, 3.3) for µ = 0.6No shear failure when bearing failure isfollowed by Coulomb-friction behavior

Almost zero demand when bearingfailure is followed by Coulomb-frictionbehavior

27.6 (0.4, 1.3) FailureCase: PF, elastic bearing

(2.5, 1.3)Case: PF, elastic bearing

1.6Case: PF, µ = 0.6



276 (0.4, 1.7) FailureCase: EL, elastic bearing

(1.4, 1.4)Case: EL, elastic bearing

1.8Case: PF, µ = 0.2



In the above table failure is determined by C/D ratios less than one for either one direction or the resultant of two directions. PF = Parkfield Record, EL = ElCentro Record.


GS (MPa) Directional C/D ratiosPier column shear Column plastic rotation Deck slidingC/D ratios in column local axes(y–y, z–z)

C/D ratios about column local axes (y–y, z–z) C/D ratios in bridge longitudinal direction

2.76 (0.4, 1.0) FailureCase: EL, elastic bearing

(3.3, 0.9) FailureCase: EL, elastic bearing

1.0 MarginalCase: EL, µ = 0.2

(0.4, 0.9) FailureCase: EL, µ = 0.6(0.6, 1.3) FailureCase: EL, µ = 0.2

No plastic rotation failure when bearing failureis followed by Coulomb-friction behavior

27.6 (0.2, 0.8) FailureCase: PF, elastic bearing

(3.3, 0.9) FailureCase: PF, elastic bearing

1.2Case: EL, µ = 0.2



276 (0.3, 1.3) FailureCase: EL, elastic bearing

(5.0, 0.8) FailureCase: EL, elastic bearing

1.3Case: EL, µ = 0.2 & 0.6



In the above table failure is determined by C/D ratios less than one for either one direction or the resultant of two directions. PF = Parkfield Record, EL = El CentroRecord.

that Bridge #1 has the poorest response under both levels ofpeak ground acceleration because of low confinement of thecolumns. Bridge #3 performs well under the PGA of 0.18gbecause of better column confinement. However, under 0.4gPGA shear failure of pier columns are possible if the shearcapacities are reduced for curvature ductility demand largerthan 2 [7]. Most column shear failures occur for medium soil

since for very stiff soil restraining effect of the abutments isenhanced resulting in lower displacement and, therefore lowerforce demands on pier bents. For very soft soils the rotationalrestraining at the base of the pier columns is decreasedresulting in more flexible pier bents, which in turn causes largerdisplacements but less curvature ductility and shear demandsin the columns. Thus, it is a balance between these factors that



GS (MPa) Directional C/D ratiosPier column shear Column plastic rotation Deck slidingC/D ratios in column local axes(y–y, z–z)

C/D ratios about column local axes(y–y, z–z)

C/D ratios in bridge longitudinaldirection

2.76 (1.7, 2.0)Case: EL, elastic bearing(1.1, 1.4) FailureCase: EL, µ = 0.6(0.83, 1.0) FailureCase: EL, µ = 0.2

(5, 5)Case: EL, µ = 0.2∼(10, 10) for most cases

1.3Case: EL, µ = 0.2

27.6 (0.9,1.0) FailureCase: EL, elastic bearing(1.0, 1.1) FailureCase: EL, µ = 0.6(0.9, 0.9) FailureCase: EL, µ = 0.2

(5, 10)Case: EL, elastic bearing∼(10, 10) for most cases

1.6Case: PF, elastic bearing

276 (1.4, 1.7)Case: PF, elastic bearing(2.0, 1.7)Case: EL, µ = 0.6(1.4, 1.3) FailureCase: PF, µ = 0.2

(24.7, 10)Case: PF, µ = 0.2Demand is very small for all cases

2.9Case: EL, µ = 0.2

In the above table failure is determined by C/D ratios less than one for either one direction or the resultant of two directions. PF = Parkfield Record, EL = ElCentro Record.

determines the worst situation, which reflects the importance ofconsideration to the soil–structure interaction.

For Bridge #3 under the PGA of 0.4g, unlike Bridge #1,for most cases the maximum response occurs for the case ofbearings with smaller Coulomb frictional coefficient, as it canbe seen by comparing Tables 4 and 5. This is due to the fact thatBridge #3 has fixed bearings over the right abutment, whichresults in higher contribution of the abutment in limiting theresponse of the pier columns. Thus, bearing failure decreasesthe restraining effect of the right abutment on the rest of thebridge causing more displacements and forces in the pier bents.Furthermore, the lower the coefficient of friction the higherwill be pier columns responses for bridges with fixed bearingover the abutment. Therefore, the general statement about failedbearing acting like a fuse should be recast as: bearing failure“over pier bents” acts like a fuse reducing the pier bents shearforces and plastic rotation demands.

5. Pushover analysis

Based on current seismic design guidelines two approachesare common in determining the seismic demand in MSSSbridges or continuous bridges with expansion joints in thelongitudinal direction. The first approach is to find the rangeof demands by using elastic tension and compression models.The former assumes that the gaps are all open and eachsegment of the bridge system is analyzed separately. The latter(compression model) assumes that the gaps are all closed andwill remain close, thus, the entire bridge–abutment systemis used to determine the seismic demands. Generally, thetension model gives the upper bound to displacements and thecompression model provides the lower bound. For example for

Bridge #1 subject to El Centro record with PGA of 0.4g atthe top of Pier-2, the displacement is equal to 11′′ using thetension model and it is equal to 0.94′′ using the compressionmodel. The second approach is to use an iterative procedureusing the effective stiffness of the bridge–abutment system.This procedure will result in more accurate results; howeverit is more involved. A more recent and efficient method isto use pushover analysis. This is a graphically useful methodto compare the demand and capacity. Fig. 11 shows suchanalysis for Bridge #1 based on AASHTO’s response spectrum.AASHTO’s response spectra for 0.18 and 0.4g are plotted inan alternative manner. It is assumed that stiffness is equal toload divided by displacement and then, using the weight of thebridge, the response spectrum is transferred from accelerationvs. period space to load vs. displacement. Thus, on this diagramlines radiating from the origin will show systems with differentperiods (e.g. x-axis is a system with infinite period and y-axis a system with zero period). The load–deformation for thebridge is obtained by applying an increasing force at the levelof the deck in the longitudinal direction. Note that in Fig. 11the load–deformation is obtained by pushing span-3 (betweenright pier and right abutment) to the left. The load–deformationrelationship is, in general, highly nonlinear and originally ofstiffening nature as the gaps close and other elements of thebridge system get involved. Note that pushover analysis isdirection dependent if the gap sizes are not identical at theabutments and at the top of the piers. It also depends on howthe two types of connections (fixed or roller) are combined atvarious locations. The maximum displacement, in this example,is limited by the sum of the gap openings at the left pier andat the left abutment plus the elastic deformation in the left


Fig. 11. Pushover analysis of Bridge #1 (2-D model) with different SSIconditions using AASHTO RS.

abutment (i.e., 121 mm plus the elastic deformation in the leftabutment). Thus, as it can be seen, the stiffness and strengthof the abutments significantly influence the load–deformationbehavior of the system. Comparison of the load–deformationcurves indicates that abutment strength would have more effecton the seismic response of the bridge system than abutmentstiffness. This point is also supported by the time historyanalysis results as discussed. Using compression method underPGA of 0.4g the bridge displacement is about 25 mm (1′′) andfor the tension models of pier-1 and pier-2 the displacementsare 185 and 356 mm (7.3′′ and 14′′), respectively.

Shown in Fig. 11 is also the bridge response usingCALTRANS approximate approach, where the maximumstrength is based on the maximum soil strength of 369 kPa(7.7 ksf) and the stiffness is equal to 114.8 kN/mm per unitwidth of the deck in meters (200 kips/in. per unit width of thedeck in feet). Based on CALTRANS approach the displacementof the bridge in the longitudinal direction is limited due tohigh stiffness and strength at the abutment. Actually, usingthis method there is not much difference in longitudinal deckdisplacement between the two seismic coefficients (0.18 and0.4). The abutment deformation is small due to high stiffnessand this is the reason for only a very small difference betweenseismic coefficients of 0.18 and 0.4.

Note that in obtaining the load–deformation curve in Fig. 11the pier columns are assumed elastic, thus, the demand andsupply are compatible as both are for an elastic system.To advance this approach demand curves that are based onnonlinear behavior of the system needs to be developed. Thus,work on stiffening single degree of freedom systems (S-SDOF)needs to be expanded in order to develop nonlinear responsespectrum that can be used along with pushover analysis [17].A stiffening system consists of an elastic–plastic base system(such as Pier-2 of Bridge #1 and the weight it supports) andthe interacting environment (such as the abutments). Such studymust consider the effect of various parameters, such as ductilityof the base system; size of the gaps; stiffness, strength, and massof the interacting environment; period of the base system; andground motion characteristics.

6. Conclusions and research needs

Based on the results of this comprehensive analytical study,which included many computer simulations, the followingspecific conclusions can be made about the seismic responseof these three bridges, which are representative of typical eastcoast MSSS bridges:

• Impact will cause high shear demand in the steel bearings.Thus, at least analytically, failure of steel bearings is quitelikely, even under low level of PGAs. Assuming a post-failure behavior at the bearings characterized by stableCoulomb friction, bearing failure over pier bents will act likea fuse and reduces the demand on the pier bents. Shouldthe bearing remain elastic (not fail), shear failure of piercolumns with low lateral reinforcement is likely, even underlow levels of PGAs.

• For the bridges considered the seat lengths are onlymarginally adequate. Therefore, it is important to ensuretheir integrity through regular inspections. Furthermore, formore critical bridges or for those with high steel bearingsconsideration should be given to increasing the seat length.

• Seismic response of MSSS bridges is sensitive tosoil–structure interaction and it should be consideredin dynamic analysis of this class of bridges. Amongimportant parameters (mobilized mass, strength, andstiffness) abutment strength has the most significant effecton the overall response of the bridge.

• Three-dimensional models must be used in nonlinear timehistory analyses of skewed MSSS bridges to better representcoupling in orthogonal directions and to model the effect ofvarying axial load on the response of pier columns.

• Under earthquakes with 0.4g PGA, all three MSSS bridgesconsidered would sustain column shear failure that canpossibly lead to collapse of the bridge. However, this levelof ground acceleration is higher (in many locations muchhigher) than AASHTO’s seismic coefficient for New Jersey.Therefore, earthquakes with this level of acceleration maybe considered as an event with significantly higher returnperiod for New Jersey.

In light of the importance of stable post-failure behavior ofthe steel bearing in preventing more critical damage, such asshear failure, which can cause collapse of the bridge severalissues related to this assumption require additional researchwork. Furthermore, there is a great need in developing thetools for a more realistic and effective approach in determiningthe seismic demands that can ultimately be employed withinthe framework of performance-based engineering in the designof this class of bridges. Thus, the following items should beconsidered in future research studies:

• Parametric study of the nonlinear seismic response ofstiffening single degree of freedom (S-SDOF) systems inorder to develop demand diagrams that can be used in thedesign of MSSS bridges.

• Experimental study of the steel bearings to validate theload transfer mechanisms, the mode of failure, frictionalcharacteristics, and stability of response. Such verification is


Fig. 12. Typical fixed steel bearing at an abutment (note seat cracking at theedge and corrosion of its reinforcements).

very important since the post-failure behavior of the bearingshas significant effect on the survival of the bridge.

• Consideration to the possibility that expansion bearingsmay seize up due to build up of corrosion and/or loss oflubrication. These bearings are normally much higher thanthe fixed ones and should they seize and fail during a seismicevent, their post-failure stability is highly questionable.Furthermore, high moments can be exerted on the anchorbolts, which can cause their pull out. These factors mustalso be considered in the seismic evaluation of this class ofbridges.

• Analytical evaluation of the pullout capacity of the concreteseats for the steel bearings using 3-D finite element modelsto ensure that impact will cause bearing shear failure ratherthan pullout/breakage of the concrete seat. The latter cancause span fall off. Furthermore, the actual condition ofthe seat and the availability of adequate seat length/edgedistance should be verified through regular inspection.Fig. 12 shows a typical fixed bearing and its abutment seat.As it can be seen, there appears to be a diagonal crack at theedge of the seat that can compromise the stability of the spanduring a moderate seismic event.

Acknowledgements

This research study was supported by the New JerseyDepartment of Transportation/FHWA and the National Centerfor Transportation and Industrial Productivity (NCTIP) at NJIT.

The results and conclusions are those of the authors and do notnecessarily reflect the views of the sponsors.

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