Analytical fragility curves for non-skewed highway bridges in Chile

Engineering Structures 141 (2017) 530–542

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Analytical fragility curves for non-skewed highway bridges in Chile A. Martínez a, M.A. Hube b,⇑, K.M. Rollins c a

Pontificia Universidad Católica de Chile, Chile Pontificia Universidad Católica de Chile and National Research Center for Integrated Natural Disaster Management CONICYT/FONDAP/15110017, Vicuña Mackenna 4860, Santiago, Chile c Civil and Environmental Engineering Department, Brigham Young University, 368 CB, Provo, UT 84604, USA b

a r t i c l e

i n f o

Article history: Received 23 October 2015 Revised 21 March 2017 Accepted 21 March 2017

Keywords: Bridge Seismic behavior Fragility Experimental analysis Incremental dynamic analysis Damage Bearings

a b s t r a c t Recent earthquakes in Chile and worldwide have caused significant economic losses due to the damage on the road bridge network. To conduct seismic risk assessment studies and to improve resilience of bridges, seismic vulnerability studies are required. The main objective of this study is to construct fragility curves of typical non-skewed highway bridges in Chile. The fragility curves are obtained from an incremental dynamic analysis of a two-dimensional model of the bent cap of a two-span simply supported underpass. As most bridges are constructed with seismic tie-down bars, their constitutive behavior was obtained experimentally. A total of five seismic bar specimens were tested to characterize their cyclic behavior in bridges with and without transverse diaphragms. The incremental dynamic analysis was performed with the two horizontal components of seven seismic records obtained from the Mw 8.8, 2010 Chile earthquake. Additionally, a parametric study is conducted to assess the seismic behavior of bridges with different configurations of seismic bars, with lateral stoppers, and with varying length of the transverse seat width. Results from this study reveal that seismic bars have a limited contribution to the seismic performance of the studied bridge, especially when lateral stoppers are incorporated. Additionally, the transverse seat width is found to be critical to reduce the collapse probability of the superstructure. The provided fragility curves may be used for seismic risk assessment and to evaluate possible improvements in seismic bridge design codes. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction The road infrastructure has been affected by recent earthquakes in Chile (2010 and 2015), Japan (2011) and New Zealand (2011). In Chile, approximately 300 bridges were damaged by the moment magnitude Mw = 8.8 Maule earthquake in 2010, which include 20 bridges with collapsed spans [1]. In the 2015 Chile earthquake, about 7 bridges suffered minor damaged. Damaged bridges in 2010 earthquake represented less than 3% of the total inventory of the country [1], but the connectivity was affected and most of these bridges required repairs. Several authors [1–4] have described and analyzed the damage in bridges due to this earthquake and in general, they all agree in their diagnoses. The most common failure in typical highway bridges during 2010 Chile earthquake was the connection damage between the substructure and the superstructure (Fig. 1a), caused by excessive displacement of the superstructure [1–4]. This type of failure is the most likely reason for the low incidence of column damage ⇑ Corresponding author. E-mail address: [email protected] (M.A. Hube). http://dx.doi.org/10.1016/j.engstruct.2017.03.041 0141-0296/Ó 2017 Elsevier Ltd. All rights reserved.

[1]. In skew bridges, unseating of spans was generated due to rotation of the superstructure, possibly caused by the impact between the abutment and the superstructure. However, tests conducted by Rollins and Jessee [5] suggest that passive resistance at the abutment-superstructure interface may be much less for skewed bridges than for non-skewed bridges. Damage in Chilean bridges was concentrated in lateral stoppers and prestressed concrete girders (Fig. 1b and c), and was attributed mainly to changes in bridge configurations during the last decades. Before the 90s, bridges were designed with transverse diaphragms, reinforced concrete lateral stoppers, and seismic tie-downs bars. These seismic bars are vertical steel rods that connect the slab of the bridge with the bearing table of the substructure, as can be observed in Las Mercedes underpass in Fig. 1c. With the arrival of concession during the 90s, the design of these three elements was modified or they were even eliminated in some bridges. The concessions are private companies that design, built, and maintain highway systems and are supervised by the Ministry of Public Works. Fragility curves are an appropriate tool to evaluate the seismic vulnerability of structures and to estimate the probability of exceeding a certain damage level for a specific seismic ground

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(a) Typical highway bridge

(b) Independecia overpass

(c) Las Mercedes underpass

Fig. 1. Typical highway bridges in Chile and observed damage after the 2010 Maule earthquake.

shaking intensity. Nielson and DesRoches [6] and Pan et al. [7] developed fragility curves for bridges in the US, and Tavares et al. [8] and Siqueira et al. [9] for bridges in Canada. Fragility curves of structures can be estimated from field observations of damage after an earthquake or by analytical approaches. In the provided references, the fragility curves were estimated by analytical methods using nonlinear models of bridges. In this paper, fragility curves for Chilean bridges are also estimated by an analytical approach, specifically by conducting an incremental dynamic analysis. The main objective of this study is to obtain fragility curves for typical non-skewed reinforced concrete bridges in Chile (Fig. 1a). The second objective is to quantify the effect of seismic bars, lateral stoppers, and length of the transverse seat width in the seismic behavior of such bridges. To quantify the contribution of seismic bars to the lateral response of bridges, an experimental program was conducted as part of this research. From the results of these tests, a constitutive model is proposed for the lateral response of seismic bars in bridges with and without transverse diaphragms. For the lateral stoppers, a nonlinear constitutive relationship based on a previous experimental program [10] is used. Previous studies regarding the behavior of Chilean bridges during 2010 Maule earthquake called into question the contribution of seismic bars. Although these bars are designed for vertical forces to prevent the uplift of the deck [11], to some extent they provide lateral stiffness to the bridge deck when the lateral displacement of the superstructure is large, as can be observed in Fig. 1c. Yen et al. [4] doubt that the seismic bars provided vertical restraint during 2010 Maule earthquake because there was no evidence of vertical displacements in beams. Yashinsky et al. [12] postulated that the use of seismic bars had little impact on the seismic performance of bridges. However, both hypotheses contradict the study of Elnashai et al. [2], which concluded that seismic bars contributed to decrease the transverse displacement of the deck. In order to provide objective information to this discussion, the proposed experimental program of seismic bars seeks to quantify their contribution in the seismic behavior of bridges.

2. Experimental program of seismic bars The definition of the seismic bars specimens, test setup, instrumentation, and load application protocol are described in this section. The tests are aimed at determining the contribution of the seismic bars in restraining the transverse displacement of the superstructure of bridges. Two specimens were tested to simulate the behavior of seismic bars in bridges with diaphragms (WD), and three specimens to simulate the behavior of bridges without diaphragms (WOD). The seismic bar specimens were subjected to cyclic lateral displacement and their characteristics are summarized in Table 1. In this table hl corresponds to the clear distance of seismic bars from the bottom of the diaphragm or the slab, to the top of the

Table 1 Test matrix. Specimen

Loading Direction

hl (cm)

WD1, WD2 WOD1, WOD2 WOD3

In both directions In both directions Only in one direction

10 72 72

bearing table, as shown in Fig. 2. The contribution of seismic bars in these two types of bridges are expected to be different, as the clear distance of seismic bars in bridges WD are smaller than that in bridges WOD.

2.1. Definition and design of specimens To define the characteristics of the seismic bar specimens, a statistical analysis of the geometric characteristics of 13 highway bridges located in central Chile was conducted [13]. From this analysis, it was found that two seismic bars are installed between prestressed concrete girders at each side of the spans, and that the average diameter of these bars is 22 mm. The specified steel for these bars is A440-280H (fy = 280 MPa), and the average clear distance (hl in Fig. 2) is 200 mm and 1430 mm in bridges WD and WOD, respectively. The proposed specimens consist of a region of the bridge with two seismic bars between a pair of consecutive girders. Each specimen consists of three main elements: a reinforced concrete block at the bottom representing the bent cap or bearing table of the substructure; a reinforced concrete block on top representing the reinforced concrete diaphragm or slab, depending on the case; and two seismic bars connecting the bottom and top reinforced concrete blocks. Fig. 2 shows the tested regions of the bridges and the constructed specimens for specimens WD and WOD. In each specimen, two rollers were used to simulate the vertical displacement restraint provided by the elastomeric bearings. For conducting the seismic bar tests, a 1:2 scale was selected due to laboratory limitations. Consequently, 16 mm was selected for the diameter of the seismic bars, and a clear distance (hl in Fig. 2) of 100 mm was considered for specimens WD, and 720 mm for specimens WOD. The bent caps of the specimens were 2200 mm long, 400 mm high and 300 mm wide; the diaphragms were 1100 mm long, 740 mm high and 150 mm wide; and the slabs were 1800 mm long, 150 mm high and 300 mm wide. The seismic bars were anchored in the bent cap (bottom reinforced concrete block) with 90-degree hooks and the development length was enough to allow yielding of the bars [14]. At the top edge of the seismic bars a 90 mm long thread was manufactured. This thread was used to bolt the seismic bars to the top diaphragm or slab using a washer and two nuts, following construction practice. The diaphragms and slab were constructed with two cylindrical vertical perforations to allow the seismic bars to pass through

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(a) Bridge WD

(b) Bridge WOD Fig. 2. Definition of seismic bars specimens.

them. To simulate construction practice and to realize the perforations, PVC tubes of 60 mm outside diameter and 3 mm thickness were embedded in the slab and diaphragm. The bent caps of the specimens were reinforced with four 12 mm diameter longitudinal bars at the top and bottom, with two intermediate 8 mm longitudinal bars, and with 8 mm stirrups spaced at 80 mm. The diaphragms were reinforced with 8 mm diameter bars spaced at 200 mm in two layers. Finally, the slabs were reinforced with four 12 mm longitudinal bars at the top and bottom, and with 8 mm stirrups spaced at 80 mm. 2.2. Materials For the seismic bars A440-280H steel (fy = 280 MPa) was specified, and for the reinforcing bars of reinforced concrete elements, A630-420H steel (fy = 420 MPa). The concrete was specified with a characteristic strength of 20 MPa and with a maximum aggregate size of 20 mm. The properties of steel and concrete were measured using standard laboratory tests. The mechanical properties of seismic bars are summarized in Table 2 and were obtained from the tensile tests of three bars. The concrete strength was obtained from compressive tests of three standard cylindrical concrete samples Table 2 Average mechanical properties of seismic bars (16 mm diameter). Parameter

Average

Yield strength [MPa] Ultimate strength [MPa] Yield strain [mm/mm] Hardening strain [mm/mm] Ultimate strain [mm/mm] Modulus of elasticity [GPa]

338.3 506.9 0.0016 0.0153 0.1233 211.9

tested at an age of 407 days, four days before the first seismic 0 bar test. The average concrete strength was f c ¼ 28:1 MPa. 2.3. Test setup and instrumentation The test setups of the specimens WD and WOD are shown in Fig. 3. The bent cap of the specimens was placed on top of concrete blocks in order to adjust the clear distance hl to 100 mm and 720 mm for specimens WD and WOD, respectively. The lateral force was applied from the north side by a hydraulic actuator with a capacity of 610 kN in compression and 340 kN in tension. The actuator was connected to the diaphragm or slab of the specimens with four steel rods that were bolted against steel plates installed on each side of the specimens. The bent cap was anchored to the laboratory strong floor with two transverse steel beams that were bolted to the strong floor. The bent cap was also restrained in the longitudinal direction with steel supports to prevent it from sliding. For the specimen WD, the vertical displacement of the diaphragm was restricted with rollers located at the bottom and top of the diaphragm. The bottom rollers simulate the vertical restraint provided by the elastomeric bearings, and the top rollers prevent the uplift of the diaphragm. During an earthquake, the selfweight of the superstructure is supposed to prevent it from lifting (for vertical acceleration smaller than 1.0 g as in the case of the Maule earthquake). The vertical forces developed at the top rollers were transmitted to the bent cap using a steel reaction beam and four steel rods. For the specimens WOD, the reinforced concrete slab was placed on top of two parallel steel beams to provide flexural stiffness and strength to the slab of the specimen, but allowed the free displacement of the seismic bars between them. These steel beams may prevent flexural or punching failure of the slab, however, to the authors’ knowledge, no damage has been observed

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(a) Specimens WD

(b) Specimens WOD Fig. 3. Test setups of seismic bar specimens.

in slabs due to the action of seismic bars in recent earthquakes. More information of the test setup is available elsewhere [13,15]. The prestress force of the seismic bars is not indicated in the Chilean seismic design code [11] nor in the construction drawings of bridges. Before the execution of the tests, the seismic bars were prestressed with a strain of about 600 mm/m. This value is approximately one third of the yield strain of the bars and was reached by one worker using human force and a regular wrench. A similar prestress in seismic bars is expected to be applied in real bridges by constructors in the field. Each specimen was instrumented with six displacement transducers, two strain gauges, and the load of the actuator was recorded with a load cell. One transducer was installed to measure the longitudinal displacement of the diaphragm or slab; two to measure the uplift of the diaphragm or slab; two to measure the transverse displacement of the diaphragm or slab; and one to measure the eventual longitudinal sliding of the bent cap. The strain gauges were attached in the middle of the clear distance of the seismic bars to measure their deformations.

2.4. Load application and control The horizontal load was applied by controlling the displacement of the actuator. The specimens were subjected to horizontal displacement cycles with increasing amplitude and two cycles at each amplitude. The amplitude of the cycles for specimens WD were ±0.01, ±0.025, ±0.05, ±0.075, ±0.1, ±0.15, ±0.2, ±0.5, ±1.0 and ±1.5 hl, and for specimens WOD1 and WOD2 were ±0.01, ±0.025, ±0.05, ±0.075, ±0.1, ±0.15, ±0.2 and ±0.264 hl. In order to fail the specimen WOD3, it was subjected to two incremental cycles with only positive displacement. The amplitudes of these two cycles were +0.382 and +0.444 hl. 3. Test results 3.1. Observed behavior Before applying the horizontal displacement, the seismic bars were prestressed, and the average tensile strains of such bars in

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specimens WD and WOD were 0.64‰ and 0.59‰, respectively. In all specimens, the initial prestress was totally or partially lost after a few cycles, before reaching the yield point of the bars. The prestress was probably lost due to local yielding of the threads of the seismic bars, or due to local yielding induced by bending of the seismic bars at the contact with the bent cap. For the specimens WD the seismic bars did not touch the PVC tubes embedded in the diaphragm during the first load cycles. Contact was first observed at the cycle with displacement amplitude of 0.2 hl (20 mm). This instant is shown in Fig. 4a for specimen WD2. For cycles with displacement amplitude larger than 0.5 hl (50 mm), the nuts of the seismic bars lifted when the specimens were passing through zero displacement, as can be observed for specimen WD2 in Fig. 4b. This lifting was caused by the plastic deformation of the seismic bars due to yielding at peak displacement amplitudes. Both specimens WD failed at the beginning of the first cycle

with displacement amplitude of 1.5 hl (150 mm), and were not able to reach such displacement amplitude. The failure of both specimens WD was caused by the fracture of the seismic bars at the contact with the bent cap. The fracture may have occurred due to stress concentration and fatigue experienced by the seismic bars. Additionally, the forces generated by the contact between the seismic bars and the PVC tubes in the diaphragm caused damage to the PVC and concrete at the bottom of the diaphragm. Crushing of concrete was observed and the diameter of the perforations through which the seismic bars pass increased its size, as observed in Fig. 4c for specimen WD2. For the specimens WOD the slabs were mounted on top of steel beams, and it was not possible to observe the exact moment at which the seismic bars touched the PVC tubes embedded in the slabs. The nuts of the bars lifted when the specimens were passing through zero displacement for the cycles with displacement ampli-

(a) Contact between the seismic bars and the diaphragm – WD2

(c) Diaphragm damage – WD2

(b) Lifting of the nuts – WD2

Fig. 4. Observed behavior of seismic bar specimens.

(a) WD1

(c) WOD1

(b) WD2

(d) WOD2 Fig. 5. Experimental load-displacement relationship.

(e) WOD3

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tude larger than 0.2 hl (144 mm) and 0.382 hl (275 mm) for specimens WOD1-WOD2 and WOD3, respectively. For the specimens WOD1 and WOD2, failure of the seismic bars was not achieved with the applied displacement cycles. As the displacement amplitude was restricted by the actuator stroke, specimen WOD3 was loaded only with positive displacement to achieve larger displacements. The failure of specimen WOD3 occurred during the cycle with displacement amplitude of 0.444 hl (320 mm), before reaching such displacement. For this specimen, the north seismic bar fractured 15 s before the south bar, and the fracture of the bars occurred at the thread on top of the slab. The damage observed on the concrete of the slab of specimens WOD was less than that on the diaphragms of specimens WD (Fig. 4c). The larger clear distance of seismic bars in specimens WOD required a larger horizontal displacement than specimen WD to generate equivalent contact forces between the seismic bars and the slab. 3.2. Load-displacement relationships

WOD3, the first cycle with amplitude of 0.382 hl was considered to compute the strength reduction ratio. The unloading tangent stiffness (K d ), was calculated as the average unloading stiffness of the same cycles described previously. 4. Load-displacement relationship for seismic bars 4.1. Analytical estimation An analytical model was constructed to reproduce the experimental results of the seismic bars. Fig. 6a shows a diaphragm or slab subjected to a lateral displacement d. In this figure, F is the applied lateral force, hl is the clear distance of the seismic bars, hnl is the height of the diaphragm or slab, F sb is the sum of the axial forces in both seismic bars, and d is the elongation of them. By geometry, the elongation (d) and strain (eA ) of the seismic bars can be obtained from



The load-displacement relationships of the five specimens are shown in Fig. 5 and relevant results are summarized in Table 3. The shown lateral forces correspond to the actuator measured forces minus friction forces generated in the rollers due to the test setup. These friction forces were measured in cycles after the fracture of the seismic bars. However, additional friction forces were identified in specimens WD1 and WD2, as nonzero forces can be observed in Fig. 5a and b in loading cycles with displacement amplitude larger than 0.2 hl. An asymmetry is observed in the load-displacement relationship of specimen WD1 between the positive and negative load cycles (Fig. 5a). This asymmetry was probably generated because the seismic bars in WD1 were not perfectly centered with respect to the PVC tubes embedded in the diaphragm. The fracture of the seismic bars of both specimens WD occurred during the first cycle with displacement amplitude of 1.5 hl (150 mm). For specimen WD1 the first seismic bar to fail was the north bar at a displacement of 0.28 hl (28.3 mm), as shown with a cross in Fig. 5a. For specimen WD2 the first seismic bar to fail was the south bar at a displacement of 0.98 hl (98.4 mm). The fracture of the seismic bars of specimen WOD3 occurred during the first cycle of 0.44 hl (320 mm), and the first seismic bar to fail was the north bar at 0.39 hl (279.7 mm). The yield strength (F y ) and yield displacement (dy ), were determined when yielding was first detected in the seismic bars from the strain gauges readings. The maximum strength (F max ) and the corresponding displacement (dmax ) were defined when the maximum load (positive or negative) was recorded. The ultimate strength (F u ) and ultimate displacement (du ) were defined when fracture of one seismic bar was identified. The strength reduction ratio in successive cycles of equal amplitude (F 2 =F 1 in Table 3) was obtained as the quotient between the strength of the second cycle (F 2 ) and the first cycle (F 1 ). This ratio was obtained considering the average ratio of the last two positive and negative cycles in specimens WD (±0.5 and ±1.0 hl), and the last three cycles in specimens WOD1 and WOD2 (±0.15, ±0.2 and ±0.26 hl). For specimen

d ¼ hl

eA ¼

1 1 cosðhÞ

 ð1Þ

d hl þ hnl

ð2Þ

The initial prestress of the seismic bars was not considered in Eq. (2) because this prestress was lost after a few cycles in the experimental tests. The analytical strain given by Eq. (2) was found to be a good estimate of the strains only for the first two cycles. For cycles of larger amplitude, the analytical strain of the seismic bars was found to overestimate the experimental strain. For the five specimens, on average the analytical strain overestimates the experimental strain by 34% when the maximum displacement (dmax) is considered. This difference occurs owing to several reasons. First, the seismic bars are not only subjected to axial deformation, as the analytical model suggests. Seismic bars are also subjected to bending deformation at the top of the bent cap and at the bottom of the diaphragm or slab. Second, the analytical model does not take into account the gap between the PVC tubes and seismic bars, which reduces the elongation of the seismic bars. Third, the analytical model considers perfect adhesion between the concrete of the bent cap and the seismic bars. Finally, the localized concrete crushing may also contribute to the analytical error. Applying force equilibrium in the free body diagram of Fig. 6a, the relationship between the lateral force F, and the tensile stress f sb of the seismic bars can be written as

F ¼ sinðhÞ

f sb f Asb ¼ cf y Asb fy y

ð3Þ

where Asb corresponds to the total area of seismic bars (two bars in this case) and c results in a dimensionless ratio. For a given lateral displacement, the stress f sb can be obtained assuming an elasticperfectly plastic (EPP) behavior of steel. The comparison between the experimental and analytical maximum strength is summarized in Table 4. For the analytical strength, a yield stress of 338.3 MPa (Table 2) is considered for

Table 3 Summary of test results. Specimen

dy (mm)

dmax (mm)

du (mm)

dy =hl (-)

dmax =hl (-)

du =hl (-)

F y (kN)

F max (kN)

F u (kN)

F 2 =F 1 (-)

K d (kN/m)

WD1 WD2 WOD1 WOD2 WOD3

34.3 60.6 3.2 163.3 150.7

95.9 98.7 189.2 189.7 272.4

28.3 98.4 – – 279.7

0.34 0.61 0.00 0.23 0.21

0.96 0.99 0.26 0.26 0.38

0.96 0.99 – – 0.39

30.5 41.0 2.2 27.5 33.7

86.5 83.0 32.5 32.5 66.4

2.1 20.8 – – 58.1

0.70 0.64 0.75 0.76 0.87

8470 8360 1400 1350 2480

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(a) Analytical model of the test

(b) Load-displacement relationship

Fig. 6. Analytical model of the seismic bars and proposed load-displacement relationship.

the seismic bars, and the angle h of Eq. (3) is obtained with the maximum experimental displacement (dmax in Table 3). The analytical strength at maximum displacement (F amax ) is a good estimate of the experimental strength (F exp max ) for all specimens, except for specimen WOD3. On average, the analytical strength overestimates the experimental strength by 9% for the specimens WD1, WD2, WOD1, and WOD2. For specimen WOD3, the experimental strength is underestimated by 28%. The difference in specimen WOD3 is attributed to the strain hardening of the steel, which is not considered in the analytical model. In this specimen, the maximum strength was recorded in the first cycle under monotonic behavior, where strain hardening is expected to be significant. 4.2. Load-displacement relationship The load-displacement relationship proposed for seismic bars (Fig. 6b) is based on the previous analytical model and consists on a bilinear relationship. This relationship is defined with two points and an unloading stiffness. These two points are obtained from the cross section area, the yield stress, and the clear distance of the seismic bars. The unloading stiffness (K d ) is estimated from the experimental results as a factor of the second loading stiffness (K 2 ). The first point (d1 , F 1 ) corresponds to an experimental point, in which the specimens evidenced a change in the slope of the load-displacement relationship. At this point, the seismic bar changes from a predominantly flexural behavior to a tensile behavior. The second point (d2 , F 2 ) corresponds to an approximation of the maximum displacement (dmax ) and force (F max ) achieved in the specimens tests. The proposed load-displacement relationship for seismic bars is defined from equations in Table 5. The c factor, considered to estimate the force, incorporates the stress ratio (f sb =f y ) and the value of sinðhÞ of Eq. (3) for each case. Additionally, for the WOD case, as the strength estimation is inadequate at displacement d1 , the c factor includes a reduction factor of 0.7 for the estimation of F 1 . A comparison of the proposed model and the experimental results can be found elsewhere [13].

Table 4 Comparison between analytical and experimental strength of the seismic bar specimens at displacements of maximum lateral force. Specimen

F exp max (kN)

F amax (kN)

F amax =F exp max

WD1 WD2 WOD1 WOD2 WOD3

86.5 83.0 32.5 32.5 66.4

94.2 95.6 34.6 34.7 48.1

1.09 1.15 1.06 1.07 0.72

5. Fragility curves of bridges 5.1. Numerical model of bridges To predict the seismic behavior of bridges in the transverse direction, and construct fragility curves, a two-dimensional (2D) model of the central bent of an underpass was constructed with OpenSees [16]. This model is not able to predict the rotation of the superstructure that may occur even in non-skewed bridges. Las Mercedes Bridge was selected as a representative Chilean highway bridge. This bridge is located in the VI Region of Libertador Bernardo O’Higgins, at kilometer 76 of Route 5 (34°040 1900 S, 70°450 4200 W). The bridge is a two-span structure with a continuous reinforced concrete slab and the length of each span is 27 m. The angle of skew is only 11° and the superstructure is comprised of three precast prestressed concrete girders, which are supported by elastomeric bearings in the two-column bent at the center, and in the seat-type abutments at both ends. Additionally, the bridge was structured with four seismic bars at each end of the spans. Las Mercedes Bridge did not have diaphragms and the transverse displacement of the deck was not limited by lateral stoppers. Instead, the bridge was provided with concrete lids. A concrete lid is a vertical element located at the edges of the abutment or bent cap and it is installed for aesthetical reasons, therefore they provide negligible lateral strength [17]. The damage observed on Las Mercedes Bridge after the 2010 earthquake was caused by the lateral displacement of the superstructure which resulted in sliding of the elastomeric bearings and the failure of concrete lids in the abutments. However, the lateral displacement increased in the abutments due to the in-plan rotation of the superstructure. As a result of excessive rotation of the deck, a residual displacement of 1.4 m [18] at the west abutment was measured. The analytical model of the bent of the selected bridge is shown in Fig. 7. The two nodes at the base were fixed at the foundation level and three degrees of freedom were considered at the nodes of the bent cap. For the nodes located at the slab level and at the top of the elastomeric bearings, only the horizontal degrees of freedom were considered. As the bent supports the superstructure of the two spans, the elements of Fig. 7 that represents the prestressed girders, the seismic bars, and the elastomeric bearings, are two identical elements arranged in parallel. These three elements were modeled with two-node link elements acting in the horizontal direction. The bent and the rigid connectors were modeled with beam-column elements. The rigid connectors were used to connect the seismic bars with the bent cap, and to simulate the deck. These rigid elements were modeled with a cross section area of 1.0 m2, with the modulus of elasticity of concrete, and with a

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A. Martínez et al. / Engineering Structures 141 (2017) 530–542 Table 5 Equations of the load-displacement model for seismic bars. Seismic bar configuration WD WOD

Displacement d1 d2 d1 d2

Force

¼ 0:1hl ¼ hl ¼ 0:1hl ¼ 0:35hl

Unloading stiffness

Fi ¼ c

 f y Asb

Fi ¼ c

 f y Asb

K d ¼ 20K 2 K d ¼ 15K 2

c factor 

c¼ c¼



0:04 0:71

for F 1 for F 2

0:07 0:37

for F 1 for F 2



f y corresponds to the real yield stress, 1.2 f ynominal is recommended.

Fig. 7. Analytical 2D model of the bridge bent.

moment of inertia equal to five times the moment of inertia of the bent cap. The seismic mass of the model considered half of the total mass of the superstructure of the bridge, and the total mass of the bent. The considered seismic mass in the model was 282.2 ton. The diameter of the seismic bars of Las Mercedes Bridge is 22 mm, the steel A440-280H, and the clear distance of the seismic bars is 1410 mm. Using the model defined in Table 5 for a bridge WOD, the displacements d1 and d2 are 141 mm and 494 mm, respectively. The forces F 1 and F 2 are 8.9 kN and 47.3 kN, respectively, and the unloading stiffness is 1,628 kN/m. The elastomeric bearings are modeled with an elastic-perfectly plastic constitutive relationship as proposed by Rubilar [19] for Chilean bridges. A coefficient of friction of 0.33 was used for the bearings, which depends on the compressive stress of the bearings. The sliding force of each bearing was 123 kN, and the stiffness of each bearing was 7,800 kN/m, which was calculated using a rubber height of the bearing of 25 mm. Similar constitutive relationships for sliding elastomeric bearings have been used by other researchers [20,21]. The prestressed girders, the slab and the columns of Las Mercedes Bridge were not damaged during the 2010 earthquake, so these elements were modeled elastically. The lateral stiffness provided by each girder was obtained from a three-dimensional (3D) finite elements model of the girder constructed in SAP2000 [22]. The web and the flanges of the girder were modeled with shell elements, and the top flange of the girder was fixed to consider the restraint provided by the slab. The lateral stiffness of the girder (16,200 kN/m) was obtained by applying a transverse concentrated force in the bottom flange at the location of the bearings, and this stiffness was assigned to the link elements of the girders in Fig. 7. The geometrical properties of the bent were obtained from the structural drawings. The diameter of the columns is 1,000 mm, the height between the foundation level and the center of the bent

cap is 7,569 mm, and the center to center distance of the columns is 5,000 mm. The width of the bent cap is 1,600 mm and its height is 1,140 mm. The modulus of elasticity of the bent components was 21,000 MPA, which was obtained from ACI 318 [14] recommendations, considering a characteristic concrete strength of 20 MPa. In the parametric study described in the next section, the effect of including lateral stoppers at both sides of each girder is assessed. The constitutive model for these stoppers was proposed by Rubilar [19] and is shown in Fig. 7. The strength of the stoppers and the gap between the stoppers and the girders are estimated from the Chilean seismic code [11]. For this study, a nominal strength of 126 kN is considered for each stopper and a gap of 84 mm. This gap is equivalent to the bearing height (34 mm) plus 50 mm. The displacement at peak strength is 108 mm and the displacement where the strength is totally lost is 174 mm. First, a modal analysis was conducted to obtain the vibration periods of the structure. The three periods are T1 = 0.67 s, T2 = 0.16 s, and T3 = 0.12 s. For the nonlinear response analyses, Rayleigh damping was considered with 2% damping for the first and third mode. 5.2. Seismic records The incremental dynamic analyses to construct the fragility curves were conducted using the two horizontal components of seven stations that recorded the 2010 Chile earthquake. The vertical ground motion component was not considered in this study because previous researchers [23] have found that the vertical component has no considerable effect in the relative displacement of bridges with sliding isolators. The considered stations are Curicó, Hualañé, Llolleo, Maipú, Peñalolén, Santiago Centro, and Viña del Mar Centro. These stations were selected to include seismic

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records with different soil types. The shear-wave velocity of the sites (VS30 ) of the chosen stations varies between 289 m/s and 541 m/s. To perform the incremental dynamic analysis, the pseudo-acceleration at the fundamental period of the structure (T1 = 0.67 s), considering 5% damping, was chosen as the intensity measure of the ground shaking. For the fundamental period of the structure, the average pseudo-acceleration (Sm a ) of the unscaled fourteen seismic records is 0.72 g. Fig. 8 shows the elastic response spectrum of the fourteen seismic records, where the envelope of the spectrum are shown with black lines. A large variation of the spectral ordinate is observed at the fundamental period of the structure, where the minimum pseudo-acceleration (Smin a ) is ) is 1.22 g. 0.31 g and the maximum pseudo-acceleration (Smax a

5.3. Nonlinear response Fig. 9 shows the results of the nonlinear response history analysis for the Peñalolén EW ground motion scaled to Sa ðT1 Þ ¼ 1:0 g. The relative displacement of an elastomeric bearing is presented in Fig. 9a, where sliding of the bearing is predicted and the maximum relative displacement is 359 mm at 96 s. The residual displacement predicted for this bearing at the end of the ground motion is 328 mm. Fig. 9b shows the history of the base shear, where a maximum base shear of 1,453 kN (51.5% of the seismic weight) is achieved at 71 s. Finally, the load-displacement relationship of a seismic bar is presented in Fig. 9c, where the proposed constitutive model with bilinear loading stiffness can be observed. The sliding of the elastomeric bearings in the analyzed bridge limits the transferred forces between the superstructure and the substructure. In fact, sliding elastomeric bearings can be considered as a quasi-isolation system [20,21]. 5.4. Fragility curves

Fig. 8. Elastic pseudo-acceleration spectrum of the fourteen seismic records considering 5% damping.

(a) Relative displacement of elastomeric bearing

Fragility curves of the considered bridge in the transverse direction are obtained from an incremental dynamic analysis. Each ground motion was scaled from Sa(T1) = 0.0 to 5.0 g, with an increment of 0.1 g. Fig. 10 shows the results of the incremental dynamic analysis for the 14 ground motions, where large dispersion is observed for the maximum relative displacement of the elastomeric bearings (Fig. 10a), and the residual displacement of the elastomeric bearings (Fig. 10b). Additionally, Fig. 10 shows the mean response, and the mean plus and minus one standard devia-

(b) Base shear

(c) Load-displacement relationship of seismic bar Fig. 9. Nonlinear response of the structural model for the Peñalolen EW ground motion scaled to Sa(T1) = 1.0 g.

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(a) Maximum relative displacement of elastomeric bearings

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(b) Residual displacement of elastomeric bearings

(c) Maximum base shear Fig. 10. Results of the incremental dynamic analysis of the considered bridge.

tion. For constructing the fragility curves, three damage levels are defined. Level I is considered when sliding of the elastomeric bearing is predicted. Sliding in the bearings occurs when the maximum relative displacement of the elastomeric bearing is larger than 15.8 mm (i.e. sliding strength of 123 kN). Level II corresponds to a residual displacement of the elastomeric bearings larger than 50 mm. This value was used by the Ministry of Public Works as a rule of thumb criterion to repair bridges after the 2010 Maule earthquake. Finally, level III corresponds to the collapse of the structure, which is achieved when the maximum relative displacement of the elastomeric bearing is larger than 850 mm. This distance corresponds to the transverse seat width, defined here as the distance between the axis of the external prestressed girder and the free edge of the bent cap (Lo in Fig. 7). Damage in the columns and foundations is not considered in this study as no damage was observed in these elements during 2010 Maule earthquake. Additionally, the shear forces transmitted from the bridge deck to the bent are somehow limited by the strength of the connection between the superstructure and the substructure. The fragility curves for the three defined damage levels are presented in Fig. 11. This Figure shows the probability of exceeding the defined damage levels, where DLi correspond to the damage level (i = I, II or III). The markers show the probability of exceeding each damage level at each ground motion intensity. A lognormal cumulative distribution was adjusted for each damage level using MATLAB [24] and the parameters defining the fragility functions are summarized later. For the range of pseudo-accelerations at the fundamental period of the reference bridge for unscaled ground motions, between

Smin ¼ 0:31 g and Smax ¼ 1:22 g, the probability that the elasa a tomeric bearings slide (damage level I) is 100%. For the same range of pseudo-acceleration, the probability of exceeding damage level II ranges between 6% and 59%. According to a previous statistical assessment [17], of 41 underpasses without lateral stoppers that where located in a zone of Route 5, 66% were damage and required to be repaired, which is larger than the probability of damage level II predicted in this analysis. Particularly, of the eleven existing underpasses along the Rancagua By-Pass, all of which had similar characteristics to the Las Mercedes Bridge, five bridges were repaired, corresponding to 45.5%. This percentage of damage is similar to that predicted by this study, and serves to validate the proposed fragility curves for damage level II.

Fig. 11. Fragility curves for three damage levels (model MB).

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The collapse of the bridge (damage level III) is predicted for severe ground motions (Fig. 11). In fact, the probability of collapse for the average pseudo-acceleration of the unscaled ground motions (Sm a ¼ 0:72 g) is zero. This result is not consistent with the observations from the 2010 earthquake, where 7% of underpasses without lateral stoppers collapsed [17]. This discrepancy would reaffirm the studies of Buckle et al. [1], Elnashai et al. [2] and Kawashima et al. [3], who claim that the collapse of some superstructures occurred because of the rotation of the deck. However, this rotation is not considered in the proposed 2D model.

6. Parametric study A parametric study is conducted to quantify the effect of the seismic bars, the lateral stoppers, and the length of the transverse seat width on the seismic behavior of bridges in the transverse direction. Fig. 12 shows the results of the parametric study and Table 6 summarize the statistical parameters of the lognormal fragility curves. To study the effect of seismic bars, three different seismic bars configurations are considered: the reference model described in the previous section (MB), a model with seismic bars with four times the area than those of the reference model (MBx4), and a third model without seismic bars (M). The fragility curves for the three damage levels, and for the three models are shown in Fig. 12a. For the range of pseudo-accelerations at the fundamental period of the reference bridge for unscaled ground motions, between Smin ¼ 0:31 g and Smax ¼ 1:22 g, the probability of exceeda a

ing damage level I and damage level III is 100% and 0%, respectively, for the three seismic bars configurations. A larger difference between the three configurations is obtained for the probability of exceeding damage level II. For the same range of pseudo-accelerations, the probability of exceeding damage level II ranges between 8–65% for the configuration M, 6–59% for the configuration MB, and 5–45% for the configuration MBx4. For the average pseudo-acceleration of the unscaled ground motion (Sm a ¼ 0:72 g), the probability of exceeding damage level II is 38% for the configuration M, 32% for the configuration MB, and 23% for the configuration MBx4. For damage level III, Fig. 11a shows that the collapse vulnerability slightly decreases as the amount of seismic bars increases. The provided results suggest that the seismic bar has limited effect on the vulnerability of bridges. To study the effect of adding lateral stoppers on the seismic behavior of bridges in the transverse direction, three configurations are considered: the reference model described in the previous section (MB), a second model with seismic bars and lateral stoppers (MBS), and a third model without seismic bars and with lateral stoppers (MS). The fragility curves for the three damage levels, and for the three models are shown in Fig. 12b. For the range of pseudo-accelerations at the fundamental period of the reference bridge for unscaled ground motions (between 0.31 g and 1.22 g), again the probability of exceeding damage level I and damage level III is 100% and 0%, respectively, for the three configurations. A larger difference is obtained for the probability of exceeding damage level II. For the same range of pseudo-accelerations, the probability of exceeding damage level II ranges between 6–59% for the configuration MB, 2–37% for the configuration MS, and 1–34% for the

(a) Effect of seismic bars

(b) Effect of lateral stoppers

(c) Effect of transverse seat width Fig. 12. Fragility curves of the parametric study

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A. Martínez et al. / Engineering Structures 141 (2017) 530–542 Table 6 Statistical parameters of lognormal fragility curves. Model

M MB = Lo MBx4 MS MBS 2/3 Lo 1/3 Lo

Level I

Level II

Level III

Med

r

Med

r

Med

r

0.212 0.219 0.225 0.225 0.225 – –

0.101 0.086 0.080 0.080 0.080 – –

0.897 1.062 1.404 1.599 1.648 – –

0.758 0.780 0.888 0.819 0.702 – –

4.290 4.501 4.723 4.573 4.568 3.594 1.870

0.391 0.342 0.363 0.379 0.333 0.454 0.533

configuration MBS. For the average pseudo-acceleration of the unscaled ground motions (Sm a ¼ 0:72 g), the probability of exceeding damage level II is 32% for the configuration MB, 17% for the configuration MS, and 12% for the configuration MBS. It is concluded that the effect of the provided lateral stoppers is more significant than that of seismic bars to reduce the probability of obtaining damage level II. Surprisingly, the fragility curves for damage level III are not affected by the presence of lateral stoppers. Because of the long duration of the imposed ground motions, the energy dissipation capacity of the stoppers may be totally consumed during the first significant cycles, and the effect of the stoppers in subsequent cycles is completely lost due to their cero residual strength. It is expected that this type of stoppers, with limited energy dissipation capabilities, may have a larger contribution to prevent collapse for impulsive ground motions or ground motions with shorter durations. Finally, to study the effect of the transverse seat width, three models are considered: the reference model with a seat width Lo = 850 mm (see Fig. 7), a second model with 2/3Lo (567 mm) and a third model with 1/3Lo (283 mm). The models with reduced set widths, 2/3Lo and 1/3Lo, are equivalent to decrease the total length of the bent cap (9.2 m) by 6% and 12%, respectively. For the three models, the seismic mass was considered equal, and the collapse probability of each case was determined from the predicted maximum relative displacement of the elastomeric bearings, which may cause unseating of the outermost girder. The fragility curves for damage level III (collapse) are shown in Fig. 12c for the three bridge configurations. From this figure it is concluded that the transverse seat width is critical for reducing the collapse probability. For the maximum pseudo-acceleration of the unscaled ground motions (Smax ¼ 1:22 g), the probability of collapse is 0%, 1% a and 24% for a seat width Lo, 2/3Lo, and 1/3Lo, respectively. Additionally, to prevent unseating of the girders in the longitudinal direction, sufficient seat width should be provided in the longitudinal direction of the bridge [25,26]. 7. Conclusions Fragility curves for a representative Chilean non-skewed bridge are calculated in this paper. The fragility curves consider only transverse displacement of the superstructure, and the possible rotation of the superstructure is not accounted for. Therefore, the proposed curves may be considered as an upper bound for seismic risk assessment. Nevertheless, the fragility curves of the parametric study are of great relevance to provide guidelines to improve current seismic bridge design codes. From the tests of the seismic bars it is concluded that they have limited effect on the vertical seismic response of the superstructure. For cycles where yielding of the seismic bars was exceeded, permanent inelastic deformation was induced in these bars and the initial prestress was completely lost. Therefore, the intended design objective of the Chilean bridge design code to control the possible vertical displacement of the superstructure is not properly

accounted for by these bars. Additionally, from the experimental program a constitutive relationship is proposed to simulate the lateral restrain provided by the seismic bars. The developed fragility curves predict that the probability of exceeding damage level I (sliding of elastomeric bearings) is 100%, for an intensity measure equivalent to the average pseudoacceleration of the unscaled ground motions of the 2010 Maule earthquake (Sm a ¼ 0:72 g). For the same intensity measure, the probability of repairing the bridge (i.e. damage level II) is 32%. This probability is slightly less than the percentage of bridges along the Rancagua By-Pass that where repaired after 2010 earthquake. Collapse is predicted for severe ground motions as significant sliding of the elastomeric bearings is required to cause unseating of the girders in the transverse direction. This result is not consistent with observation from 2010 Maule earthquake, where a small percentage of highway bridges collapsed. This inconsistency is attributed to the rotation of the bridge deck experienced by several bridges, which is not accounted for in the proposed 2D model. Further studies using 3D models, including the passive forces developed at the abutment-superstructure interface, are required to simulate this rotational behavior. From the parametric study it is concluded that the effect of the seismic bars in the seismic behavior of bridges without transverse diaphragm is limited. The probability of sliding of elastomeric bearings (damage level I), and the collapse probability (damage level III) is not affected by the seismic bars. The probability of exceeding damage level II slightly decreases as the area of the seismic bars increases. When lateral stoppers are added, the probability of damage level II decreases, but the probability of collapse is not affected because of the limited energy dissipation capacity of the stopper and the long duration of the considered ground motions. Finally, it is concluded that the transverse seat width is the critical parameter that affect the collapse probability of the considered bridge. When the transverse seat width is reduced from 850 mm to 283 mm, the collapse probability increases from 0% to 24%. Therefore, it is strongly recommended to include a minimum transverse seat width in the Chilean seismic design code to improve the seismic vulnerability of bridges. Acknowledgments This research was funded by the Chilean Fondo Nacional de Ciencia y Tecnología, Fondecyt Grant #11121581, and Fondap Grant #15110017. The actuator, pump, and controller used for the experimental program were funded by Fondequip Grant #EQM120198.

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.engstruct.2017. 03.041.

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