Seismic Effect On Bridges

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1. Introduction A great deal of research effort has been made to improve the design and retrofit methodology for bridge structures in seismic active zones, especially after the 1994 Northridge, 1995 Kobe, and 1999 Chi–Chi earthquakes. Lessons [1] learned from the investigation of highway bridges seriously damaged by these destructive earthquakes are highly valuable to the upgrading of many bridges still in use, as these bridges probably are as seismically deficient as those that already failed the test of nature. General public would think girders, piers, and foundations receive the most attention in the design and construction of a bridge structure. Nonetheless, secondary components such as rubber bearings, hinge restrainers, side stoppers, and expansion joints if not well taken care of are likely to result in undesirable overall performance of a bridge structure during extreme quake events [2]. The rubber bearings commonly used in past decades have been seriously questioned as to their seismic resistance. Expansion-type bearings are vulnerable to un-seating or toppling when deck sliding is excessive. Fix-type bearings may break loose if their hinge-restrainer device is sheared off by lateral seismic loading. New techniques in the form of an isolator or a damper device are introduced to replace or enhance conventional bearings [2] and [3]. Previous studies have shown that the gap of joints between decks can have a significant effect on the response of a bridge [3] and [4]. Using simplified model, it was found when sliding and pounding occurs, accelerations of bridge decks may increase by a factor of ten, as compared to that without pounding [3]. The abrupt increase of accelerations can result in severe impact forces that damage structural members like the deck or pier. Meanwhile, assessment of seismic vulnerability of common types of bridges based on techniques such as fragility analysis is getting more attention. A study on the fragility of a bridge's inventory shows that the most vulnerable bridge type is the multi-span simply supported concrete bridges [5]. This study presents a case analysis involving deck sliding and pounding of a multi-span simply supported concrete bridge damaged by the 1999 Chi–Chi earthquake. Its reference coordinate is (120°46″E, 24°17″N). A brief description of its damages and related photos can be found in public reports [6]. Bridges of the same kind are quite common on highway river-crossings all

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over Taiwan. Site investigation and survey data for this particular bridge collected following the quake indicated that major structural responses that occurred on that day were the sliding of several deck spans relative to pier cap beams and the pounding between adjoining decks, all along the traffic direction. One extra pounding occurred between a special recessed pier cap beam and a deck supported on this pier.

2. Bridge characteristics and observed damages A brief description of the bridge of concern to this study is presented in this section, while more details including bearings and gaps of joints are introduced along sections that follow. Constructed in 1984, the bridge has thirteen segments with abutments at two ends. Fig. 1 provides an elevation view covering four segments on the south end. Each span of the bridge superstructure (i.e. deck) is made of concrete slab cast onto pre-cast T-girders laterally braced by diaphragms. Fig. 2 illustrates the transverse section view of a typical bent. Along the traffic direction, T-girders are simply supported on top of a cap beam (i.e. wing beam) cast in one piece with straight pier column, and embedded into a caisson foundation at the column base. In the transverse direction, concrete side stoppers are installed to prevent excessive sidewise movement. As the designer called for, each girder is simply supported with one end on a fix-type rubber bearing having dowel bars (i.e. hinge) and another on an expansion-type rubber bearing (i.e. roller).

Full-size image (54K) Fig. 1. Elevation view of four segments at south end; the bridge has 13 segments: 13+11@35+13 m.

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Full-size image (54K) Fig. 2. Transverse section view of a typical bridge bent (unit: cm).

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On 21 September 1999, shortly after midnight, a violent quake struck. What was left on the bridge site a minute later were two spans of massive decks falling off at the south end and other deck spans being displaced under South–North sliding motion. Fig. 3 presents the schematic view of the damaged bridge. One particular pier appeared to have been pounded at its cap beam, tilted 10° off the straight position, and left crushing marks at the cap beam and flexural cracks at the column base (in Fig. 3 where star marks show). It is worth noticing in Fig. 1 and Fig. 3 that the top of this pier cap beam is not built flush, in contrast to other piers, but has a special recessed back-wall to accommodate girders of different depths from two adjoining deck spans. Nevertheless, T-girders, piers, and caissons, all remained intact as individual members, except one single pier severely damaged as mentioned. In terms of kinetics, the decks simply acted as rigid masses, and piers as flexible columns fixed at the base in response to the quake.

Full-size image (53K) Fig. 3. Observed damage condition of the bridge: two fallen decks and one severely damaged pier.

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Based on damages data collected form public reports and several rounds of the author's personal field trips, it is reasonably speculated that the fix–expansion bearings, as required by the design engineer for each girder, were not duly in place as constructed. None of the dowel bars necessary for fix-type bearings could be found, not even at the exposed end sections of the two fallen decks. Fig. 4 provides a blowout view of the bearing details according to original design drawings.

Full-size image (57K) Fig. 4. Details of bearings at girder support.

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3. Dynamic model of the bridge To ensure setting up analysis models representative of bridge behaviors, as-built bridge plans were collected and examined to determine dimensions of deck spans and pier cap beams and columns, details of fix/expansion bearings, and material specifications of all material used. Each of the eleven typical spans between piers is 35 m long. Each of the two end spans leading to abutments is 13 m long. Each bent of the bridge has one single pier with cap beam and on top are five girders simply supported using common rubber bearing pads, one pad at each girder end. The girder end supports are classified as fix- or expansion-type, commonly known as hinge or roller. The fix-type girder support on the pier cap beam consists of rubber bearing pads with dowel bars projecting about 300 mm into the pier cap and 150 mm into the T-girder, as shown in Fig. 4. The average column height of all piers is 5.9 m. Adjoining decks and abutments are separated by expansion joints with gaps of 40 mm in between. Each deck superstructure consists of a 13 m wide concrete slab and five 2-m-deep precast T-girders. A typical concrete pier column having an oblong cross section 2 m deep by 4 m plus wide is built into a huge caisson

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having a circular cross section of 6 m in diameter and a height of 12 m, dug deep into the sandy rock stratum under the riverbed. Under extreme seismic actions, this type of bridge, just discussed, may exhibit highly nonlinear behaviors, such as the yielding of dowel bars and sliding at rubber bearings, pounding between decks at expansion joints, cracking and yielding of concrete pier columns, and soil–structure interaction near the foundation. Ideally, an analytical model need incorporate all of these in the dynamic analysis. Damage conditions of the bridge indicated that its major response to seismic action took place in the traffic direction. Except the tilted pier, all other pier columns remained intact. The ground conditions at the site were normal, though heaved pavement approaching the south end abutment was visible. It might be the outcome of severe pounding of the end deck onto the back-wall of the abutment. Altogether, these indicated pier columns had a fairly rigid base at foundations. In effect, the bridge responded mainly along the traffic direction, counting on the stiffness and strength provided by bearings and pier columns. The study adopts a practical but realistic approach to setting up analytical models of the bridge. Nonlinear behaviors incorporated in models include sliding and friction at bearings, closing and pounding at expansion joints. The stiffness of a bridge's deck bodies such as girders and slabs have insignificant effect on the seismic response of the bridge. As shown in Fig. 5, the bridge is idealized as a two-dimensional discrete model with deck bodies lumped as rigid masses, supported by bearings, seated on top of pier columns, and subjected to violent ground motion along both longitudinal and vertical directions. Its dynamic response is to be numerically solved for in the traffic direction of the bridge.

Full-size image (43K) Fig. 5. Analytical model for a bridge showing masses and nonlinear elements.

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The analytical model consists of four spans: three typical spans together with a shorter span connecting to the abutment. For bridges with more spans under seismic motions in the longitudinal direction, the maximum possible one-way sliding toward the river centerline is a variable value bounded by the total sum of gaps in a succession of expansion joints. Consider a 13-span bridge with all decks seated on 2000-mm-wide cap beams and separated by 40 mm nominal gaps. The maximum one-way sliding for any one of the 13 decks is 520 mm, still short of the deck-seating length of 980 mm. Although a more conservative design may call on the remaining 460 mm to be reserved for opposite movement in deformed piers, it is still unlikely to form a 460 mm gap, counting all piers. This is because each pier is strong and deforms elastically with lateral movement below 30 mm. The above is true prior to the failure of Pier 3 under pounding by Deck 2. In the study, the maximum gap for one-way sliding at the north end of the four-span model is set at 160 mm, sufficing to cover three more spans further up north. In fact, responses of the pounded pier are not significantly affected by the number of spans used in the model, as illustrated later. The backfill material is assumed to be granular soils with 30° angle of internal friction. A set of soil springs along the height of the abutment can be constructed to model the lateral force– displacement behavior of the backfill. The summed total stiffness is estimated at 874 000 kN/m. Since soil heaving just behind the abutment was observed after the quake, the passive earth pressure (Pp) of backfill soils is used as the yield strength for soil springs; Pp is estimated at 5300 kN. Though these soil data may seem less deterministic than those of solid materials, they have only localized and limited effects on the backfill and do not significantly change final results of this study.

4. Comparative study of models As stated in the previous section, models used for failure study shall match the site survey data and reflect the mechanical behavior of each element and member. The cause-finding process can then be carried out by varying key parameters in the dynamic analyses of models and relating the results to information disclosed by site survey. Therefore, models are organized in groups. Model group I and II in Table 1 are set up to account for the variation of design-specific parameters, i.e.

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bearing types and arrangement at ends of each deck span. Fig. 1 provides the identity of each bearing. The bearing at each deck end may be chosen as either fix type or expansion type. Model groups subdivided in Table 2 are needed to determine the sensitivity of analyzed results to the variation of uncertain parameters, i.e. the friction coefficient used at the interface where the bearing pad comes into contact with the T-girder as well as the cap beam (Fig. 4).

Table 1. Bearing type (fix or expansion) for bridge models Model group Bearing IDs a

b

c

d

e

I

Fix

Exp. Fix

II

Exp. Exp. Exp. Exp. Exp. Exp. Exp. Exp.

Exp. Fix

f

g

Exp. Fix

h Exp.

Full-size table

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Table 2. Coefficient of friction at bearings used in comparative models Model ID

I1

I2

I3

II1 II2 II3

Coefficient of friction 0.1 0.2 0.3 0.1 0.2 0.3

Full-size table

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5. Ground motions The quake had a magnitude of 7.3 and a focal depth around 10 km [6]. A set of two ground motion data recorded at the Taiwan Weather Bureau TCU068 observation station during the quake is employed in combination as ground waveform inputs to the bridge model. This particular station is located inside a nearby public school. In the dynamic analysis, the primary ground motion input is the N–S component of the strong motion because the major response and subsequent deck falling of the bridge took place in the longitudinal direction which runs nearly parallel to the N–S direction. The peak ground acceleration of the N–S ground motion recorded is 3.61 m/s2. The secondary ground motion, needed to determine the variation of friction force with respect to the vertical reaction at the bearing, is the Z (vertical) component of the quake having a peak ground acceleration of 5.19 m/s2. Fig. 6 presents these two records of ground accelerations.

Full-size image (229K) Fig. 6. (a) Ground acceleration (N–S component), (b) ground acceleration (Z component).

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6. Parameters for dynamic analysis

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Each of the deck and pier bodies is modeled as discrete mass supported by flexible pier column, through interfaces of bearings and gaps of joints. For a typical deck having mass M and damping

C under the longitudinal ground acceleration

, the equation of motion can be expressed as (1)

Fi (also referred to in Eq. (5) later) is the impact spring force initiated by a condition (2)

X2-X1-Gp>0, where X2 and X1 denote, respectively, displacements of two adjoining decks, or displacements of Deck 2 and Pier 3; Gp is the gap at expansion joints. Fs (also referred to in Eq. (8) later) is the friction force at bearings governed by a condition (3)

where

and

denote, respectively, velocities of a deck and its supporting pier.

6.1. Mass Each typical 35 m deck span has a total mass of 633 ton (metric unit), counting in pavement, slabs, girders, diaphragms, and railing. The shorter 13 m deck span connecting to the abutment has 182 ton. Each typical pier has 162 ton, including the cap beam and column. Using Rayleigh's procedure and the first mode shape of a laterally loaded cantilever, we can determine the lumped mass to be 71 ton for a typical pier. 6.2. Pounding When the bearings slide, pounding between deck spans can significantly affect the response of the bridge and thus must be considered in the bridge model. In view of the 40 mm gap at the expansion joint between decks, pounding action is modeled using a compression-only impact spring when the gap is closed. In case of fully elastic impact,

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the stiffness of an impact spring shall be several orders of magnitude of the pier column stiffness [3], [4] and [5]. The following equation is used as an estimate: (4)

Ki=EdAd/Ld, in which Ed, Ad, and Ld are the modulus of elasticity, transverse sectional area, and length of the deck body, respectively. The chosen value for the impact spring stiffness shall not produce inconsistent results. On the basis of numerical tests on a range of values, the stiffness of the impact spring used in the analysis is 4.56×106 kN/m. The impact spring force in Eq. (1) is then determined by (5)

Fi=(X2-X1-Gp)Ki. When two bodies in motion collide with each other, a situation called elastic impact arises, assuming that the plastic deformation occurring in the contact zone is negligible. The usage of an impact spring element at the interface of a deck and a pier merely enables the transfer of mechanical energy from the rigid deck to the flexible pier. At the instant of contact, the action of impact produces an impulsive force that affects local stresses and strains of colliding bodies near the contact zone, given that the duration of contact can be measured. In this study, it is the internal force (shear) developed in the deformed pier that is of major concern. Test cases to illustrate this point are provided later. 6.3. Behaviors of rubber bearing Referring to the details in Fig. 4, the bearing pads mounted on pier cap beams and abutments are composed of interlacing layers of neoprene rubber and steel sheets to provide horizontal flexibility and vertical supports. Ideally, this device is modeled as a spring–dashpot. Under violent quake action, the capability of a dashpot to absorb detrimental earthquake energy is practically small and ignored, when compared with other factors. 6.3.1. Bearing stiffness

Each bearing pad has a total thickness of 61 mm, consisting of five layers of 11-mm-thick neoprene rubber bonded to six layers of 1-mm-thick steel sheet. The steel sheet covers of the pad come into contact with steel plates pre-embedded in the concrete T-girder and the pier cap beam. The neoprene rubber has a hardness of 60 as per ASTM D412. Under severe dynamic loading,

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the sliding friction induced at the interface of the bearing pad and the girder/pier depends on the surface condition of the steel material. The horizontal stiffness against sliding is provided by the rubber material. The total horizontal stiffness provided at each deck end is (6)

Kr=(GrAr/Tr)Nr, where Gr, Ar, Tr are shear modulus, planar area, and thickness of the rubber pad, respectively. Nr (=5) is the number of bearings at each deck end. Table 3 presents data used in the analysis.

Table 3. Stiffness calculation of rubber bearing at each deck end Shear modulus

Gr 1650

kN/m2

Thickness

Tr

5.5

cm

2200

cm2

Bearing area at girder end Ar Number of bearings

Nr 5

Piece

Translation stiffness

Kr 33000 kN/m

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6.3.2. Dowel bar

One dowel bar is planned for each fix-type bearing at one end of each girder. Each bar material, as per AASHTO M183, has a specified tensile strength 4.02×105 kN/m2 and a circular cross section of 60 mm in diameter. The dowel bar shear strength is (7)

Vb=AbFsbNb.

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Nb (=5) is the number of dowel bars at each deck end. Fsb is the shear strength and taken as 0.577 times the tensile strength, referring to von Mises yield criterion. The calculated result is , to be used as a conservative estimate since similar tests reported that Fsb might be the same order of magnitude as the tensile strength [7]. 6.3.3. Bearing friction

Upon sliding of deck bodies under the horizontal quake motion, the behavior of a metal sheetcovered bearing is captured by Coulomb friction. Mechanism of friction is associated with molecular adhesion, surface roughness, and other factors. Experimental data of un-cleaned metal-on-metal contact gave the friction coefficient ranging from 0.15 to 0.30. In railway terms, typical wheel-on-rail friction coefficient is 0.2, a threshold value used in the study. Referring to Fig. 4, for each bearing pad, the friction force in Eq. (1) is (8)

where μ is the coefficient of friction and Wn the normal force exerted on the interface of bearing pad with T-girder and pier cap beam. The total weight of a typical deck body is 6210 kN. Usually, Wn is half the weight, i.e. 3105 kN. In view of the violent vertical quake motion, up to 5.19 m/s2, this may not be the case. Instead, reactive forces exerting on the interfaces with Tgirder and pier cap beam are determined first in response to the vertical motion, and substituted for Wn, simultaneously, for use in response to the horizontal motion. 6.4. Behaviors of concrete pier column Data and calculations described next refer to the original design plans and are judged reasonable for use in the study. The laboratory testing of concrete core samples taken from the site by a local investigation team indicated that the quality of concrete material is quite normal as constructed. 6.4.1. Flexure

Each pier column in Fig. 2 has a longitudinal reinforcement ratio 1.3% and tie reinforcement ratio (volumetric ratio) 0.2%. The specified yield strength of reinforcing bars and specified compressive strength of concrete are 275.6 and 20.6 MPa, respectively. The behavior of a reinforced concrete column under flexural–axial loading depends on the stress–strain model used

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[8]. The effect of properly designed tie reinforcement is to confine and then enhance the concrete strength and ductility. Typical calculation for the complete moment–curvature relationship of a column section involves slicing the concrete sections into fiber layers. Each layer then relates to the specified stress–strain relationship, dependent on whether the layer is confined or unconfined. An in-house code of such a kind has been developed to generate the moment– curvature curve for concrete column sections. The moment and curvature at yield are 24 900 kN m and 1.56×10−3 /m, respectively. Effective flexural rigidity (EIe) up to the yield point is 2.12×107 kN m2. This value is about half that calculated for the un-cracked column section, taking into account the nonlinear behavior of concrete material. With a main reinforcement 1.3% the gross section area and a compressive stress around 3% the concrete strength, these data are on the conservative side. The effective lateral stiffness of the pier column is thus (9)

where Hp (=5.9 m) is pier column height. The typical pier column stiffness used in the analysis is 3.1×105 kN/m. The shear strength of the pier at yield

.

6.4.2. Shear

For concrete members designed in the 1980s, such as the pier column just discussed, the cross sectional shear strength depends mainly on the quality of concrete and amount of tie reinforcement used [9]. The shear capacity of each pier column (Vp) is derived from concrete (Vc) and from tie reinforcing (Vs) together as (10)

Vp=Vc+Vs, with (11)

in which fvc, Ae and dc denote the shear strength, effective area, and effective depth of the concrete cross section, respectively. Ash, fsy and s are the sectional area, tensile strength, and

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spacing of lateral ties. For the pier column here,

,

, and

.

7. Solution scheme Analytical models are set up using a multiple-degree-of-freedom dynamic analysis program GENDYN, developed for research use at NKFUST since 2001 [10]. By means of direct time stepping of the governing differential equations based on the fourthorder Runge–Kutta scheme, nonlinear transient results of motions and forces can be obtained. Solution accuracy is ensured by varying the time stepping size ranging from 1/10 000 to 1/20 000 s and checking for convergent results. Since only localized and limited plastic deformation were observed for this rather massive concrete structure, a uniform damping ratio of 2% is deemed proper and used in the dynamic analysis.

8. Analyzed responses Based on design requirements, Group I models arrange for each deck span the bearings to be fix type at one end and expansion type at the other, in an alternating pattern. Group II models assume all bearings to be expansion type. Fig. 1 has shown the identity of each deck span or pier column referred to in the following. 8.1. Bridge model Group I Here, bearings are of expansion- and fix-type, alternating over the deck spans. To support a full 35 m deck span on a typical pier, such as Pier 1, a fix-type bearing develops large restraining force to carry most of the seismic loading. As depicted in Fig. 7, the maximum restraining force required for the fix-type bearing has exceeded the dowel shear strength (

). In

case the dowel bars were not overcome, the maximum restraining force would exert on Pier 1 and cause plastic cracking at the pier column due to yield by flexure (

), as

indicated in Fig. 8. At Pier 3 in particular, where a fix-type bearing undertakes seismic loading from a lighter 13 m deck span to the right, any damage to the pier or the bearing is deemed unlikely.

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Full-size image (25K) Fig. 7. Shear force at fix bearing (<0).

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Full-size image (21K) Fig. 8. Maximum shear force of Pier 1 (<0).

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8.2. Bridge model Group II Here, all bearings are of the expansion type. The largest seismic load exerted on Pier 1 is 2130 kN, well below its shear capacity. Pier 3, supporting the 35 m Deck 2 to the left, is under the threat of this deck sliding from left onto the special back-wall at the pier cap beam. The quake intensity is indeed excessive enough to shake loose whatever frictional resistance the bearing can provide, and the deck pounds and leans on Pier 3. The pounding produces severe impact load and transmits shear load to Pier 3, as illustrated in Fig. 9 and Fig. 10. Depending on the friction coefficient μ chosen for the bearing, the pounding-induced shear force is able to cause damage to the Pier 3. For a μ value ranging from 0.2 to 0.3, the pier suffers local plastic

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cracks due to yield by flexure ( by yield and fails eventually by direct shear (

). When the μ value dips below 0.2, it first cracks ). Prior to the failure of Pier 3 by

pounding, the analyzed maximum sliding movement of the deck is 100 mm to the left. Photos from personal site trips revealed that several successive deck spans had actually moved off their designed positions by 100–200 mm. Fig. 11 illustrates motions of Deck 2 and Pier 3, when they close in on a 40 mm gap and collide at the high time of quake motions.

Full-size image (52K) Fig. 9. (a) Maximum response of a pier under pounding, (b) maximum response of pier under pounding (coefficient of friction=0.1).

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Full-size image (24K) Fig. 10. Maximum shear force of Pier 3 (>0).

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Full-size image (22K) Fig. 11. Displacements of Deck 2 and Pier 3 involving sliding and pounding (at time=15 s, 4 cm gap closed and first pounding began).

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Referring again to Fig. 9a, as the number of spans for the analytical model goes from two, three, to four, shear forces developed in Pier 3 do not change much. For lower friction at bearings (μ=0.1), the fast-moving decks are bound to shear off Pier 3 in all models. For higher friction (μ=0.2), the corresponding shear force is a bit higher in the four-span model than in others. Regarding the impact force under pounding, Fig. 9b shows results from three test cases for the

four-span model (μ=0.1), in which the value of impact spring stiffness is deliberately set at Ki, and 3Ki,respectively. The shear forces developed in Pier 3 in these cases are nearly the same, though forces in the impact spring vary significantly.

9. Discussions Group I model is the designer's choice, but is bound to suffer damages due to either the shear-off of dowel bars, or the yielding of pier columns. Such damage to the bridge is meant to be extensive and common all over the deck spans. Group II model, assuming that the dowel bars necessary for the fix-type bearings are missing, simply cannot sustain the sliding and pounding. Such damage is most likely at the most vulnerable Pier 3. The impact load hit this pier hard enough to inflict concrete spalling at pier cap beam and serious flexural cracking at pier column base. The 35 m Deck 2 to the left of Pier 3, pinning on its cap beam, and knocking its column off

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to the right, thus fell off the support on the next pier to the left. Further to the left, the 35 m Deck 1, losing its contact with the fallen Deck 2, and sliding freely to the right, eventually fell off too.

10. Conclusions The cause-finding process based on the comparative study of analytical models has presented quantifiable information in good match with the field observation of a bridge structure damaged by the 1999 Chi–Chi earthquake. The models used for failure study reflect the behavior of each element and member by referring to the design specifications, as-built drawings, and damage survey data. In particular, the modeling for sliding and pounding between deck bodies proves to be essential to a realistic dynamic analysis of the bridge under the violent earthquake. Without analytical models and the comparative study, it might be quite convenient to have the nature (the earthquake) to blame for the loss of a bridge. Instead, the technical judgments derived from this study are: (1) The bridge constructor somehow had missed out on installing the dowel bars necessary for restraining the deck bodies, and failing such, the desirable flexural actions in the pier columns did not take effect. Thus things turned otherwise and the free sliding and pounding among deck bodies happened. (2) The bridge designer had arranged a back-wall at the cap beam of one particular pier, resulting in a weak spot. As the pounding and sliding began, it then led to the falling-off of two deck spans near the hardest hit pier. The study demonstrates that details at bearings can significantly affect a bridge's behavior. In fact, since bridges of the similar kind are still around, this study is presented in the hope to help identify sensible changes to specifications used by the designer and constructor alike. In particular, the design of a special back-wall atop the cap beam is to be avoided so as to make way for sliding and pounding among deck spans, when dowel bars are overcome during extreme earthquakes. Retrofitting such cap beams can be done at a feasible cost, compared to what had happened to the case bridge. The point is that a bridge with sliding decks pounding each other still has chance to survive the same earthquake without decks falling off. The analysis also demonstrates that adding dowel bar sizes/numbers to form a hinge at bearings simply transmits even more seismic loading from decks to pier columns, resulting in damages such as the plastic cracking of concrete. Instead, considerations may be given to the use of energy-absorbing bearings such as lead-in-rubbers or viscous dampers.