Experimental and numerical studies of the seismic behavior of a steel-concrete composite rigid-frame bridge subjected to the surface rupture at a thrust fault

Engineering Structures 205 (2020) 110105

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Experimental and numerical studies of the seismic behavior of a steelconcrete composite rigid-frame bridge subjected to the surface rupture at a thrust fault

T

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Yuanzheng Lina,b, Zhouhong Zonga, , Kaiming Bib, Hong Haob, Jin Lina, Yiyan Chenc a

School of Civil Engineering, Southeast University, Nanjing, Jiangsu 211189, China Centre for Infrastructure Monitoring and Protection, School of Civil and Mechanical Engineering, Curtin University, Bentley, WA 6102, Australia c Shenzhen Municipal Design & Research Institute Co., Ltd., Shenzhen, Guangdong 518028, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: SCCRFB with CSDST piers Surface rupture Thrust fault Shake table test Numerical simulation

Bridges crossing fault are vulnerable to surface fault ruptures. Previous studies on this topic are limited especially for thrust faults. It is necessary to examine the performances of fault-crossing bridges subjected to earthquake-induced surface fault rupture. This study investigates the seismic behavior of a recently proposed steel-concrete composite rigid-frame bridge (SCCRFB) with concrete-filled double skin steel tube (CFDST) piers subjected to the earthquake-induced surface rupture at a thrust fault. Shake table tests on a 1:10 scaled threespan SCCRFB subjected to across-fault ground motions were performed first. Detailed 3D finite element (FE) model of the bridge is then developed by using LS-DYNA and validated by the experimental results. The effects of the key parameters that influence the bridge responses to surface ruptures including the location of the fault, fault-crossing angle and fling-step are systematically investigated. Experimental and numerical results reveal that this novel bridge type has a very good seismic resistance capability.

1. Introduction In seismology, a fault refers to a rock fracture or zone of fractures along which the two sides have been displaced relative to each other. Some fault ruptures are buried below the ground surface and cannot be observed on the ground, these faults are normally known as buried faults. While some others extend to the ground surface, which are referred as surface (fault) ruptures [1]. Depending on the angle of the fault with respect to the ground surface (namely the dip) and the direction of slip, faults can be classified as the strike-slip fault, dip-slip fault and oblique-slip fault (i.e. the combination of strike-slip and dipslip faults). For a strike-slip fault, the two blocks move horizontally and slide past one another (Fig. 1(a)). For a dip-slip fault, depending on the motions of the blocks above (i.e. the hanging-wall block) or below (i.e. the footwall block) the fault plane, it can be classified as the normal fault or reverse fault. In the normal fault, the hanging-wall block moves downward relative to the footwall, while in the reverse fault the hanging-wall block moves upward relative to the footwall (Fig. 1(b)). When the dip angle is less than 45°, a reverse fault is often dubbed thrust fault. Extended engineering structures like bridges across a surface fault

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rupture may suffer significant damages during an earthquake due to the combined effects of ground shaking and tectonic deformation. The damages of bridge structures due to surface fault rupture have been observed in many previous earthquakes. As shown in Fig. 2(a and b), the Bei-Feng Bridge (Fig. 2(a)) and E-Jian Bridge (Fig. 2(b)) which went across the Chelungpu fault (a thrust fault) totally collapsed during the 1999 Chi-Chi earthquake [2–4]. Fig. 2(c and d) show the damages of the Arifiye Bridge (Fig. 2(c)) in the 1999 Kocaeli earthquake [4,5] and the Bolu Viaduct (Fig. 2(d)) in the 1999 Duzce earthquake [5–8]. The strike-slip faults led to the complete collapse and severe damage of the two bridges. Although from the design point of view, the construction of bridges near or above an active fault is generally not recommended [9,10], it is not always possible to avoid construction of such bridges due to various factors and requirements. Moreover, for the buried faults, it may not be easy to detect them in some cases. Many bridges have been constructed either across or very close to the fault-rupture zones (e.g. the bridges as shown in Fig. 2, the Rion-Antirion Bridge in Greece [11], the Puqian sea-crossing bridge in China [12], and more than 5% of the bridges constructed in California [13]). It is therefore imperative to understand the influence of surface fault rupture on the behaviors of bridge structures.

Corresponding author. E-mail address: [email protected] (Z. Zong).

https://doi.org/10.1016/j.engstruct.2019.110105 Received 29 July 2019; Received in revised form 13 November 2019; Accepted 16 December 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.

Engineering Structures 205 (2020) 110105

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Fig. 1. Definitions of (a) strike-slip fault and (b) dip-slip (thrust) fault. Fig. 2. Damages of fault-crossing bridges: (a) Bei-Feng Bridge in the 1999 Chi-Chi earthquake (after [4]); (b) E-Jian Bridge in the 1999 Chi-Chi earthquake (after [2]); (c) Arifiye Bridge in the 1999 Kocaeli earthquake (after [4]); (d) Bolu Viaduct in the 1999 Duzce earthquake (after [8]). In the figure, the dashed lines indicate the surface fault rupture and the arrows indicate the directions of fault movements.

rupture and could therefore subject a bridge to obvious different displacements at the multi bridge supports that locate on the two sides of the surface fault rupture [20,21]. In this case, the bridge structures can be much more vulnerable compared to those under the near-fault ground motions. In the past two decades, the seismic performances of bridge structures crossing fault-rupture zones have been investigated theoretically [13,22–24], experimentally [25–28] and numerically [6,7,29–31]. For example, Goel and Chopra [13,22] proposed approximate procedures to estimate the peak responses of bridges crossing fault-rupture zones based on the structural dynamics theory. Saiidi et al. [25] performed shake table tests of a large scale two-span girder bridge crossing a strike-slip fault. The Bolu Viaduct (see Fig. 2(d)), which was traversed by a surface fault rupture and suffered severe damage in the 1999 Duzce earthquake, has been widely investigated by many researchers [6,7,29,32]. These studies were well reviewed by Yang and Mavroeidis [33]. However, it should be noted that almost all these studies focused on the bridges crossing strike-slip faults (Fig. 1(a)), the effect of dip-slip (thrust) faults (Fig. 1(b)) on the bridge seismic performances is rarely investigated. The seismic responses of a bridge crossing a surface rupture with dip-slip fault could be very different from the strike-slip fault because of the spatial variability of the across-fault ground motions as discussed above, it is necessary to investigate the damage mechanism of the bridges crossing dip-slip faults. On the other hand, it should be noted that the collapses of the faultcrossing bridges mainly occurred to the simply-supported bridges. This

The damages of fault-crossing bridges are related to the special characteristics of across-fault ground motions. The near-fault ground motions are usually characterized by the long-period velocity pulses and permanent ground displacements, which are induced by the forward-directivity effect and fling-step effect respectively. Forward-directivity effect occurs when the rupture is toward the site and the slip direction on the fault plane is aligned with the rupture direction [14], and this effect generates two-sided velocity pulses with no permanent displacements [15]. On the other hand, fling-step is the result of tectonic deformation, and it is associated with a one-sided pulse in its velocity time history and thus generates a discrete step (i.e. the permanent displacement) in its displacement time history that occurs parallel with the direction of slip (i.e. the strike and dip directions for the strike-slip and dip-slip earthquakes respectively) [15,16]. In addition, for the thrust faults, high-frequency ground motions on the hanging-wall tend to be larger than those on the footwall, which is referred as the hanging-wall effect [16]. Extensive studies have been performed to investigate the influence of near-fault velocity pulses on the bridge seismic responses (e.g. [17–19]), the influences of fling-step induced permanent ground displacements and the hanging-wall effect are however rarely considered because uniform excitations were usually assumed. In other words, the earthquake ground motions at different supports of a bridge were assumed to be the same. In fact, the fling-step and hanging-wall effects can result in the significant spatial variability of the ground motions on the two sides of a thrust fault. As a result, the displacements are discontinuous across the surface fault 2

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type of bridges has weak connections between the superstructure and substructure, which makes them vulnerable to the unseating damages since the relative displacements may exceed the supporting length of the bridge piers. For the continuous girder bridges crossing fault-rupture zones (e.g. the Bolu Viaduct [7] as shown in Fig. 2(d)), though they are less vulnerable compared to the simply-supported bridges in terms of complete collapse, they may suffer severe damages in the bearings, shear keys and/or other displacement protective devices. Compared to the simply-supported bridges and continuous girder bridges, the rigidframe bridges have better seismic performance and collapse resistance capacity as evidenced in many previous severe earthquake events (e.g. [34,35]). However, the reinforced concrete (RC) piers in the conventional rigid-frame bridges may suffer severe damages especially in the plastic hinge zones due to the large moment developed in these areas [36]. To improve the seismic performance and overcome the limitations of conventional rigid-frame bridges, a new structural solution, namely the steel-concrete composite rigid-frame bridge (SCCRFB) with concrete-filled double skin steel tube (CFDST) piers, was proposed recently. The CFDST piers can significantly improve the seismic performance of the bridge due to the confinement effect provided by the steel tubes [37–40]. Moreover, the steel-concrete composite box girder is more ductile compared to the prestressed concrete (PC) box girder [41,42], which makes this new bridge type less vulnerable compared to the conventional rigid-frame bridges especially when they are constructed close to or over an active fault. To the best knowledge of the authors, no previous study reports the seismic performance of this type of bridge subjected to the surface rupture at a dip-slip fault. This paper carries out experimental studies and numerical simulations on the seismic behaviors of the SCCRFB with CFDST piers crossing a dip-slip thrust fault. A 1:10 scaled three-span bridge model was constructed and tested by using the two-shake table system at Chongqing Communications Research and Design Institute (CCRDI), China. The bridge design, test procedure and test results are presented in detail first. Then a detailed three-dimensional (3D) finite element (FE) model of the bridge is developed by using the explicit FE code LSDYNA [43] and validated by the experimental results. The influences of the fault-rupture location, fault-crossing angle and fling-step on the bridge seismic responses are systematically investigated using the validated numerical model.

through rigid joints. For the detailed designs of CFDST piers and composite girder, relevant guidelines and design codes are followed [44–46]. Each bridge pier had a RC footing with a dimension of 1200 × 700 × 400 mm (length × width × height), and the RC footing was welded on a 20 mm thick steel plate, which was used to anchor the bridge model to the shake tables (Fig. 3(c and d)). It should be mentioned that the inner and outer steel boxes of the CFDST pier extended through the entire footing and were fully welded on the steel plate, and some holes were drilled in the buried part of the steel boxes so that the rebars could pass through (Fig. 3(d)), thus making the bridge piers rigidly connected with the footing. Fig. 3(e) shows the details at the rigid joints. In particular, the steel box girder had a rectangular opening of 480 × 240 mm (i.e. the crosssection size of the CFDST piers) at the corresponding location of the bottom flange to accommodate each CFDST pier for structural assembly. During the construction, the top region of the CFDST pier was inserted into the opening and then connected with the bridge girder using 16 longitudinal bolts. The dimension of the bolts was 450 × 16 mm (length × diameter), and the spacing was 120 mm and 100 mm in the transverse and vertical directions, respectively. Meanwhile, all the seams were welded, and thereafter the C50 concrete was cast to the joint region between the two closest diaphragms to form the rigid joint. Because the dimensions of the scaled bridge model were relatively large, the scaling on the material level was not employed, and concrete and steel materials were used to construct the bridge model [44–46]. The C40 grade concrete was adopted for the bridge substructures including the concrete footings, side piers and infilled concrete in the middle piers, while the C50 grade concrete was used for the bridge superstructure. The steel plate with the thickness of 4 mm was used for the outer and inner steel boxes of the CFDST piers, as well as the diaphragms and webs of the composite girder. For the top and bottom flanges of the composite girder, the thickness of the steel plate was 8 mm. Each side pier was reinforced by 10 φ8 longitudinal bars and φ6 stirrups spacing at 60 mm (40 mm in the potential plastic-hinge regions). The 10 mm and 16 mm bars were also used in the footings, the bent caps, and the bridge decks. More details can be found in Fig. 3, and Table 1 tabulates the key parameters for different materials.

2. Experimental studies

2.2. Experimental setup

2.1. Bridge model

The shake table system in CCRDI includes two tables. Table A is located at a fixed position and Table B is moveable from 2 m to 20 m in the longitudinal direction away from Table A. Each table has a size of 3 × 6 m (transverse × longitudinal) and is able to carry a specimen with a maximum weight of 35 tonnes. The effective working frequency ranges from 0.1 Hz to 100 Hz. The two shake tables both have six degrees of freedom (DOFs) and can achieve a maximum acceleration of 1.0 g in the three directions with the full weight on the table. The strokes are ± 150 mm and ± 100 mm in the horizontal and vertical directions, respectively. Fig. 4 shows the experimental setup. Because the bridge specimen was a scaled model, additional mass was added to provide enough axial load and inertial forces for the bridge piers. The additional mass included 3.5 tonnes of concrete blocks filled in the steel box girder, 15.36 tonnes of concrete blocks (in total 4) installed on the bridge deck, 300 kg lead blocks attached to each RC column of the side piers and 900 kg concrete-filled steel boxes installed on the two sides of each CFDST column. 23 accelerometers, 7 displacement sensors, and 22 steel strain gauges were installed on the key locations of the bridge model, and they were all wired to the data acquisition system that was placed in the front of the bridge model as shown in Fig. 4. It should be mentioned that before the tests with the across-fault ground motions in the present study, the bridge model had experienced a series of tests with uniform excitations of maximum PGA 0.6 g. The

The bridge prototype considered in this study is an idealized threespan SCCRFB with CFDST piers representing a common medium-span bridge with tall piers [41]. To make the scaled model within the testing capacity of the shake table system and also make the scaled model as large as possible to best represent the seismic behaviors of the bridge specimen, a factor of 1:10 was selected to scale the geometry of the bridge prototype. The details of the bridge model are presented in Fig. 3. As shown, the span arrangement of the bridge model was 4 m + 7 m + 4 m, and the total length was 15.6 m including an additional 0.3 m extended section on the both ends (Fig. 3(a)). The total height of the model was 3.88 m, including the footing thickness of 0.4 m, the pier height of 3.0 m and the girder height of 0.48 m as shown in Fig. 3(a). The bridge superstructure was a steel-concrete composite box girder consisting of an open-section U-shaped steel box girder and a RC deck with stud connectors (see Fig. 3(b)). There were two types of piers serving as the substructures. The piers on the two sides, i.e. Piers 1 and 4, were the RC double-column piers with a sectional diameter of 192 mm (Fig. 3(c)), and each of them supported the bridge girder through two bi-directional sliding bearings. The two middle piers, i.e. Piers 2 and 3, were the rectangular CFDST columns with outer steel box dimension of 480 × 240 mm and inner steel box dimension of 320 × 120 mm (Fig. 3(d)), and they connected with the bridge girder 3

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Fig. 3. Details of the bridge model (unit: mm): (a) general view; (b) cross section of the bridge girder; (c) side piers; (d) middle piers; (e) rigid joints.

2.3. Input ground motions and test procedure

Table 1 Material properties in the tests. Material

Type

Elastic modulus (GPa)

Yield strength (MPa)

Ultimate strength (MPa)

Cubic compressive strength (MPa)

Density (kg/m3)

Steel plate

4 mm 8 mm φ6 φ8 φ10 C40 C50

210 209 201 201 205 31 35

320 470 490 480 430 – –

460 590 520 520 600 – –

– – – – – 40 57

7800 7800 7800 7800 7800 2350 2250

Reinforcement

Concrete

The ground motions recorded at the strong-motion stations TCU049 and TCU052 in the 1999 Chi-Chi earthquake were selected as the raw across-fault ground motions in the shake table tests. These two stations, which were about 37 km to the epicenter, were located on the footwall and hanging-wall of the Chelungpu fault respectively, and the dip angle of the fault was approximately 30° [47]. The closest distances of the two stations to the fault rupture plane were 3.27 km and 1.84 km [48] respectively. These features make the records from the two stations a precious pair of natural across-fault ground motions ever recorded in a thrust earthquake event. The raw ground motion data were downloaded from the Central Weather Bureau (CWB) of Taiwan and were processed through a series of data processing techniques before applying to the shaking tables. Firstly, the raw ground motions were modified using a baseline correction technique to remove the baseline shifting errors and recover the permanent ground displacements [49]. Then the ground motions were decomposed into the low-frequency and high-frequency components by using Butterworth filters at the cut-off frequency of 0.5 Hz. The amplitudes of the low-frequency components

bridge model in this study therefore had some slight damages located at the two ends of the middle piers. These minor damages are considered in the numerical simulations as will be presented in Section 3.

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Fig. 4. Experimental setup: (a) general view; details of the testing instruments of (b) accelerometers; (c) displacement sensors; (d) strain gauges and (e) dataacquisition system.

on the seismic responses will be further discussed in the numerical simulations in Section 4. As shown in Fig. 6, large displacements exist in the input ground motions, which may exceed the stroke limit of the shake tables if not controlled properly. To avoid this possible problem, the displacement control mode was applied to the shake table system. In the tests, four different seismic intensities were considered, and the PGD was used as the control parameter to scale the input ground motions for each case. In particular, the component in the longitudinal direction of shake table B was used as the controlling motion, and four different PGDs with the values of −20 mm, −60 mm, −100 mm and −140 mm were considered. The PGDs for the other components including that on shake table A were accordingly scaled based on the PGD ratios of the reconstructed ground motions. The target PGAs and PGDs for each case are listed in Table 2, and the achieved results are also shown in the table. Fig. 7 shows the target and achieved displacement time histories at the two tables in Case 4 as an example. Those of the other cases have the similar match, but are not presented for brevity. As shown, very good matches were obtained. For the PGAs, the discrepancies were relatively large compared to the PGDs since displacement control was applied to the tables as mentioned above. It should be noted that due to the stroke limits of the hydraulic actuators ( ± 150 mm in the horizontal direction and ± 100 mm in the vertical direction), the shake tables were reset after each test. In other words, the permanent displacements of the two shake tables after the current test were removed, and the shake tables slowly returned to their initial working positions before the following test. This practice was different from the tests performed by Saiidi et al. [25], in which the permanent displacements of the shake tables served as the initial displacements for the subsequent cases, namely the total fault rupture was cumulative. The reset of permanent displacements in this study might

were scaled down so that the peak ground displacements (PGDs) could be within the stroke limit of the shake tables, while the high-frequency components were preserved without modification. These two components were then combined together. By doing so, the reconstructed ground motions reserved the high-frequency properties of the raw data while their PGDs were moderately decreased. Finally, the time duration of the ground motions was compressed by a factor of 0.285 according to the scaling law. In the present study, the surface fault rupture is assumed beneath the middle span of the bridge (see Fig. 5). Piers 1 and 2 locating on Table A were excited by the TCU049 recordings, and Piers 3 and 4 were excited by the TCU052 ground motions by using Table B. It is also assumed that the bridge went across the fault rupture in the normal direction, i.e. the longitudinal (X) and transverse (Y) directions of the bridge are perpendicular and parallel to the surface rupture respectively. Fig. 6 shows the across-fault acceleration and displacement time histories in the longitudinal and vertical (Z) directions of the bridge. It can be seen that the input ground motions were very different for the two shake tables. In particular, the ground motions on the hanging-wall side (namely Table B) had prominent pulse components, higher peak ground accelerations (PGAs), PGDs and larger permanent displacements compared to those on the footwall side (Table A). It should be noted that though the shake table system has six DOFs, the transverse components of the earthquake ground motions were not considered in the tests, i.e. the earthquake ground motions were inputted in the longitudinal and vertical directions of the bridge only. This is because this study focuses on the influence of a pure dip-slip (thrust) fault, the contribution from the strike-slip movement which will further complicate the problem is thus not considered. It also should be noted that the direction of the surface rupture is not necessarily parallel with the transverse direction of the bridge, the influence of fault-crossing angle

Fig. 5. Positions of the bridge model and the assumed fault. 5

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Table A (TCU049)

Table B (TCU052) 0.3

Longitudinal (X)

0.2

Acceleration (g)

Acceleration (g)

0.3 0.1 0.0 -0.1 -0.2

Longitudinal (X)

0.2 0.1 0.0 -0.1 -0.2 -0.3

-0.3 0

5

10

15

20

25

0

5

10

Time (s) 0.3

Vertical (Z)

0.2

Acceleration (g)

Acceleration (g)

0.3 0.1 0.0 -0.1 -0.2 -0.3

5

10

15

20

25

15

20

25

15

20

25

-0.2 0

5

10 Time (s)

Table B (TCU052) Displacement (mm)

Displacement (mm)

20

0.0 -0.1

25

Longitudinal (X)

100 50 0 -50 -100 -150 0

5

10

15

20

150

Longitudinal (X)

100 50 0 -50 -100 -150

25

0

5

10

150 100

Time (s) Displacement (mm)

Time (s) Displacement (mm)

15

0.1

Table A (TCU049) 150

Vertical (Z)

50 0 -50 -100

(b)

25

Vertical (Z)

0.2

Time (s)

-150

20

-0.3 0

(a)

15 Time (s)

0

5

10

15

20

25

150 100

Vertical (Z)

50 0 -50 -100 -150

0

5

Time (s)

10 Time (s)

Fig. 6. Across-fault ground motions in the longitudinal and vertical directions: (a) acceleration; (b) displacement.

identification method [50], and Table 3 tabulates the results. As shown, the first mode of the bridge was the longitudinal girder movement (or longitudinal bending of bridge piers) with a period of 0.418 s and a damping ratio of 2.4%. In the transverse and vertical directions, the fundamental vibration periods were 0.170 s and 0.064 s, respectively, and the corresponding damping ratios were 1.6% and 5.7%, respectively.

induce some additional damages to the bridge model. 2.4. Vibration characteristics Before the test, a white noise motion with duration 60 s and an amplitude of 0.05 g was applied to capture the bridge dynamic characteristics. The fundamental vibration periods in the longitudinal, transverse and vertical directions and the corresponding mode shapes of the initial bridge model (i.e. before the tests in this study) are identified from the acceleration records using the stochastic subspace Table 2 Test cases. Case

Direction

Shake table A (footwall side) PGA (g)

1 2 3 4

X Z X Z X Z X Z

Shake table B (hanging-wall side) PGD (mm)

PGA (g)

PGD (mm)

Target

Achieved

Target

Achieved

Target

Achieved

Target

Achieved

0.03 0.02 0.08 0.06 0.14 0.10 0.20 0.14

0.03 0.02 0.08 0.06 0.13 0.09 0.18 0.13

5.86 1.55 17.59 4.64 29.31 7.74 41.04 10.83

5.84 1.52 17.47 4.56 29.10 7.62 40.86 10.71

0.04 0.02 0.12 0.06 0.20 0.10 0.29 0.14

0.05 0.02 0.14 0.06 0.23 0.10 0.33 0.14

−20.00 14.54 −60.00 43.63 −100.00 72.71 −140.00 101.80

−19.99 14.53 −60.12 43.64 −100.34 72.81 −140.51 102.04

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Table B (TCU052) Displacement (mm)

Displacement (mm)

Table A (TCU049) Longitudinal (X)

40 20 0 -20 0

5

10

15

20

50

Longitudinal (X)

Target Achieved

0 -50 -100 -150

25

0

5

10

20

Vertical (Z)

10 0 -10 -20

0

5

10

15

20

25

15

20

25

Time (s) Displacement (mm)

Displacement (mm)

Time (s)

15

20

25

150

Vertical (Z)

100 50 0 -50

0

5

10

Time (s)

Time (s)

Fig. 7. Comparison of the target and achieved displacement time histories in Case 4.

increased almost linearly with the increase of the ground motion intensity. On the other hand, the bridge showed obvious quasi-static components in the displacement responses. As shown in Fig. 8(b), the bridge girder showed large permanent displacements due to the differential permanent displacements on the two tables, while the dynamic responses (i.e. the flucuations) were relatively small. The different flingsteps on the two sides of the fault also induced obvious residual displacements in the bridge piers, and they were very different in the four cases as shown in Fig. 8(c). In particular, when the PGD was −20 mm (Case 1), piers on each table (i.e. Piers 1 and 2 on Table A and Piers 3 and 4 on Table B) showed the same displacement responses, respectively; when the PGDs were −60 mm (Case 2) and −100 mm (Case 3), Piers 1 and 2 showed the same responses but Piers 3 and 4 showed different; when the PGD was −140 mm (Case 4), all the four piers

Table 3 Vibration characteristics of the initial bridge model. Modal shape

Period (s)

Damping ratio (%)

First longitudinal movement First transverse bending First vertical bending

0.418 0.170 0.064

2.4 1.6 5.7

2.5. Bridge responses, observed performance and damages Fig. 8 shows the bridge responses to the selected across-fault ground motions in the longitudinal direction. It can be seen in (Fig. 8(a)) that the peak acceleration responses of the bridge girder were between the input PGAs on the two shake tables as shown in Table 2, and they

Acceleration (g)

0.3

0.3

Case 2

0.3

Case 3

0.2

0.2

0.2

0.1

0.1

0.1

0.1

0.0

0.0

0.0

0.0

-0.1

-0.1

-0.1

-0.1

-0.2

-0.2

-0.2

-0.2

-0.3

-0.3

-0.3

5

Absolute disp. (mm)

(a)

15

20

25

5

10

15

20

25

10

15

20

25

5

Case 3

20

0

0

0

-20

-20

-20

-40

-40

-40

-40

-60

-60

-60

-60

-80

-80

-80

15

20

25

5

10

Time (s)

80 60 40 20 0 -20 -40 -60 -80 -100 5

10

15 Time (s)

20

25

80 60 40 20 0 -20 -40 -60 -80 -100

10

Pier 2 Pier 4

20

25

5

10

80 60 40 20 0 -20 -40 -60 -80 -100 15

15

20

25

5

10

Time (s)

Case 2

20

25

Time (s)

25

20

25

20

25

-80 5

Time (s)

Case 1

Pier 1 Pier 3

15

20

Case 4

20

0

10

15 Time (s)

-20

5

10

Time (s)

Case 2

20

Case 4

-0.3 5

Time (s)

Case 1

20

(c)

10

Time (s)

(b) Relative disp. (mm)

0.3

Case 1

0.2

80 60 40 20 0 -20 -40 -60 -80 -100

Case 3

5

10

15 Time (s)

15 Time (s)

20

25

Case 4

5

10

15 Time (s)

Fig. 8. Bridge responses to the across-fault ground motions in the longitudinal direction: (a) acceleration and (b) absolute displacement time histories of bridge girder; (c) relative displacement time histories of bridge piers. 7

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Fig. 9. Recorded deformations of the bridge model in Case 4: (a) lifting up at the right end of the bridge girder; tilting of (b) Pier 2 and (c) Pier 3.

upper and lower ends of Piers 2 and 3 (see Fig. 10(a and b)). After the tests, the steel skins around these areas were removed and it was found that the infilled concrete crushed at the bottom of the columns, and there were transverse cracks crossing the entire cross section of the two middle piers as shown in Fig. 10(c and d). It should be noted that some minor cracks also developed on the concrete surfaces of other members including the bridge deck, side piers and concrete footings, while the strain gauge results indicated that the steel plates and reinforcements of these members at the testing locations remained in the elastic range, which indicated that these damages were relatively insignificant compared to the middle piers. It should be noted that the bridge only suffered minor damages at the top and bottom ends of the two middle piers during the tests though the maximum displacements in the longitudinal and vertical directions reached more than 140 mm and 100 mm respectively, which demonstrates the good seismic resistance capability of the bridge due to the special design, i.e. with the steel-concrete composite girder and CFDST piers. It has great application potentials especially when they are constructed near or above an active fault.

showed different responses. The drift responses of the four piers will be further discussed and analyzed in the numerical simulations in Section 4. The behavior and damage of the bridge model were carefully checked after each test. For Cases 1 and 2, the seismic intensities were relatively small, the structural vibrations and deformations were not prominent. When the input PGD increased to −100 mm (Case 3) and −140 mm (Case 4), structural deformations caused by the differential displacements were clearly observed. In particular, the banging noise due to the damage of concrete was heard during the test, and strong vibrations of the bridge model were noted. Fig. 9 shows the deformations of the bridge model in Case 4. It can be seen from Fig. 9(a) that the right span of the bridge model was lifted up by Table B through Pier 3, leading to the separation between the bridge girder and the bearings on Pier 4. Fig. 9(b and c) show the deformations of the two middle piers in Case 4. It can be seen that Piers 2 and 3 tilted away from each other due to the longitudinal movement of the two shake tables. The damages of the bridge model mainly located at the two ends of the middle piers. Fig. 10 shows the damages at the two middle piers after Case 4. As shown, local buckling occurred to the steel skins at the

Fig. 10. Damages occurred to the middle piers: (a and b) local buckling of the steel skins; (c and d) crush and cracks of the infilled concrete (views after cutting and removing the steel skins). 8

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3. Numerical studies

failure surfaces to depict the concrete damage by a damage scalar representing different levels of damage. In particular, the scaled damage measure ranges from 0 to 1 when the material transits from the yield failure surface to the maximum failure surface, and it ranges from 1 to 2 as the material changes from the maximum failure surface to the residual failure surface [43]. This variable is useful in tracking the evolution of damage and measuring the damage occurred in the concrete [51]. The MAT_016 model is used at the columns of the side piers and bridge deck. Instead of modeling reinforcements physically, this material can model the strengthening effect of the reinforcements with only a few parameters. These two material models for concrete modeling have been used in many previous studies and proven yielding good structural response estimations (e.g. [52–54]). As for the concrete footings and bent caps of the side piers, they are normally regarded as elastic components, and are modeled by the *MAT ELASTIC (MAT_001) model in the FE model. The elastic-plastic material model *MAT PIECEWISE LINEAR PLASTICITY (MAT_024) is utilized to model all the steel materials used in the CFDST piers and the composite girder. This is a cost-effective model that allows users to define arbitrary stress-strain curves with isotropic and kinematic hardening plasticity, and the strain rate effect also can be considered by this model [54]. The material model *MAT VISCOELASTIC (MAT_006) is employed to model the rubber bearings on the bent caps of the two side piers, and the parameters are selected based on the data provided by the supplier of the bearings. As demonstrated before, material property tests for both the steel and concrete were carried out before the shake table tests (see Table 1), and the material properties are utilized as the input parameters in the FE model. Table 4 summarizes the material properties in the FE model. The damping of the bridge is modeled by the mass-weighted nodal damping that applies globally to the nodes of the entire FE model by using the damping model *DAMPING GLOBAL in LS-DYNA. The damping constant is determined as 4πζ / T0 , in which T0 (0.418 s) and ζ (2.4%) are the identified fundamental vibration period and the corresponding damping ratio from the test (see Table 3), respectively. The strengths of materials are strain rate dependent as their dynamic properties can be enhanced significantly when subjected to dynamic loads (e.g. [51,53,55–57]). This study utilizes the dynamic increase factor (DIF), a ratio of the dynamic to the static strength with respect to strain rate to account for the material strength enhancement with strain rate effect. The DIF relationships provided by fib Model Code [58] are applied in this study for the concrete strength enhancement. In particular, the DIF of the tensile strength is given by the following equation

In this section, numerical studies are performed to investigate the seismic response and damage mechanism of SCCRFB subjected to the cross-fault ground motions. In particular, the detailed 3D FE model is developed by using the explicit FE code LS-DYNA [43]. This software is chosen because it can well capture the large plastic deformation and the strong nonlinearity of the bridge as demonstrated in the tests. 3.1. Numerical modeling 3.1.1. Element properties Two element types, namely the solid element and shell element, are utilized to construct the FE model in this study. The constant stress 8node solid elements are employed for all the concrete members and the bearings, while the 4-node shell elements are adopted for all the steel plates. The steel bars embedded in the side piers and the bridge deck are not physically modeled as their strengthening effect will be considered in the material modeling, namely a smeared model is adopted for the side piers and the bridge deck. The additional mass blocks are applied to the nodes at the corresponding locations, same as the test model, and they are simulated by the mass elements in LS-DYNA. In order to improve computational efficiency, the reduced integration algorithm (i.e. single integration point for solid elements and 2 integration points for shell elements) is used in the FE model, which, on the other hand, may result in hourglass that leads to the zero energy deformation modes for the elements. To avoid this problem, hourglass control in stiffness form is introduced in the modeling [43]. A numerical convergence test on various mesh sizes (10 mm, 20 mm and 40 mm) is firstly carried out, and it is found that the 20 mm mesh size yields similar results with the smaller mesh but with much less computational cost. Due to the structural layout of the bridge model, the fine mesh size of 20 mm is applied around the rigid joints of the bridge girder and at the two ends of the middle piers, where the most severe damages are expected to occur. Beyond these regions, a mesh size of 50 mm is applied along the piers and at the girder end regions, and a mesh size of 100 mm is applied to the rest portions of the bridge girder. Fig. 11 shows the detailed FE model of the bridge. 3.1.2. Material model and strain rate effect Two material types, i.e. *MAT CONCRETE DAMAGE REL3 (MAT_072R3) and *MAT PSEUDO TENSOR (MAT_016), are applied to model the concrete of the bridge model. The MAT_072R3 model is used at the pier-girder connecting regions and the infilled concrete of the CFDST piers. One primary advantage of this material model is that it allows users to use only one parameter, namely the unconfined compressive strength of concrete, to model the complex behavior of concrete. It should be mentioned that the MAT_072R3 model uses three

(ε /̇ εtṡ )0.018forε ̇ ≤ 10s−1 TDIF = ft / fts = ⎧ ⎨ 0.0062( ε /̇ εtṡ )1/3forε ̇ > 10s−1 ⎩

(1)

Infilled concrete

Fine mesh area Composite girder

Concrete deck

Surface to surface contact

Joint concrete

Inner steel box

Concrete slab Fine mesh area

Top flange

Sharing nodes modeling

Bearings

Concreteencased web

Tie-break contact

Concrete encasing

Outer steel box

Bent cap

Diaphragm Bottom flange CFDST pier

Steel web

RC columns

(a)

(b)

(c)

Fig. 11. Detailed FE model of the bridge: (a) around rigid joints; (b) around girder ends; (c) middle piers. 9

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Table 4 Material properties in the numerical model. Material

Location

LS-DYNA model

Parameter

Value

Concrete

Middle pier

*MAT_CONCRETE_DAMAGE_REL3 (MAT_072R3)

Column of side pier

*MAT_PSEUDO_TENSOR (MAT_016)

Bent cap of side pier/ footing

*MAT_ELASTIC (MAT_001)

Bridge deck

*MAT_PSEUDO_TENSOR (MAT_016)

Rigid joint

*MAT_CONCRETE_DAMAGE_REL3 (MAT_072R3)

Steel

Middle pier/girder

*MAT_PIECEWISE_LINEAR_PLASTICITY (MAT_024)

Rubber bearings

Side pier

*MAT_VISCOELASTIC (MAT_006)

Mass density Compressive strength (cylinder) Mass density Shear modulus Poisson′s ratio Percent reinforcement Mass density Young′s modulus Poisson′s ratio Mass density Shear modulus Poisson′s ratio Percent reinforcement Mass density Compressive strength (cylinder) Mass density Young′s modulus Poisson′s ratio Yield stress Tangent modulus Mass density Bulk modulus Shear modulus

2350 kg/m3 31.6 MPa 2350 kg/m3 11.83 GPa 0.2 1.74% 2350 kg/m3 28.90 GPa 0.2 2250 kg/m3 12.50 GPa 0.2 1.0% 2250 kg/m3 45.0 MPa 7800 kg/m3 210 GPa 0.3 320/470 MPa* 2000 MPa 2300 kg/m3 2000 MPa 1.0 MPa

* For 4 mm thickness and 8 mm thickness steel plates respectively. 2 2 ⎛ |σn | ⎞ + ⎛ |σs | ⎞ ≥ 1 NFLS SFLS ⎝ ⎠ ⎝ ⎠

where ft is the dynamic tensile strength at strain rate ε ̇ in the range from 1 × 10−6 to 3 × 102 s−1, fts is the static tensile strength at εtṡ (=1 × 10−6 s−1, static strain rate). In compression, the equation is given by

(ε /̇ εcṡ )0.014forε ̇ ≤ 30s−1 CDIF = fc / fcs = ⎧ ⎨ 0.012( ε /̇ εcṡ )1/3forε ̇ > 30s−1 ⎩

where σn and σs represent the tensile and shear stress at the interface respectively, and NFLS and SFLS stand for the tensile and shear failure stress. After failure, this model allows the interface to behave as a regular surface-to-surface contact but without interface tension. It should be mentioned that this contact model is only applied to the regions where the delamination is likely to occur, namely the concretesteel interfaces between the outer steel box and the infilled concrete of the two middle piers normal to the longitudinal direction as shown in Fig. 11(c). Beyond these regions, all the concrete-steel interfaces of the composite girder and piers are modeled as sharing nodes. In the explicit analysis, the gravity loading is achieved by applying a constant acceleration of gravity in the vertical direction. As a result, the gravity load is applied dynamically, and leads to the dynamic responses of the structure. This undesirable dynamic effect is removed by using the dynamic relaxation technique in LS-DYNA [43] in the present study. In other words, the simulation is divided into two steps: in the first step, the stress condition of the bridge model under the gravity load is initialized by using the dynamic relaxation technique; and in the second step, the results are applied as the initial condition for the subsequent explicit analysis under seismic loadings.

(2)

where fc is the dynamic compressive strength at strain rate ε ,̇ fcs is the static compressive strength at strain rate εċ s (=30 × 10−6 s−1, static strain rate). The DIF relationship provided by Malvar [59] is adopted for the reinforcements, which is given as

ε ̇ 0.074 − 0.040fy /414 DIF = ⎛ −4 ⎞ ⎝ 10 ⎠

(4)

(3)

where f y is the steel yield strength in MPa. 3.1.3. Contacts and boundary conditions The contact model *CONTACT AUTOMATIC SURFACE TO SURFACE in LS-DYNA is employed to model the contact interfaces between the bottom flanges of bridge girder and the bearings on the two side piers as shown in Fig. 11(b). The penalty algorithm is adopted for this contact model, in which the penetration of slave nodes is resisted via the imaginary normal interface springs between the shooting nodes and contact surface [43]. In the test, a sliding layer with silicone grease existed on the top of each bearing, the Coulomb friction coefficient is set as 0.06 in the numerical simulation [60]. To model the concrete-steel interfaces of a composite member, a commonly used practice is to make the concrete elements and the steel elements share nodes by using the same meshes. This approach is effective to model the perfectly bonded concrete-steel interfaces with reliable connectors. For the CFDST columns in the present study, as observed in the tests, the concrete and steel skins may separate with each other. To consider this effect, *CONTACT TIEBREAK SURFACE TO SURFACE is used to model the connections between the concrete and steel skins in the present study [43]. This contact model defines the tiebreak failure with both normal and shear components at the interface, and the failure criterion is given by

3.2. Model validation, damage and response analyses As mentioned above, the bridge model had been used in a series of uniform excitations before the test of fault-crossing cases. The accumulated damages obviously have certain impacts on the bridge behaviors in the subsequent test cases. This effect is considered in the numerical simulation by using the restart technique in LS-DYNA [43]. In particular, the uniform excitations with the PGA of 0.6 g (the maximum PGA in the uniform tests) are firstly simulated, and then the faultcrossing cases are subsequently applied. After the numerical model is developed, the vibration periods and modal shapes of the numerical model can be obtained by carrying out an eigenvalue analysis. Numerical results show that the fundamental modal periods in the longitudinal, transverse and vertical directions are 0.42s, 0.16s and 0.06s respectively, which are close to the testing results as shown in Table 3. To further demonstrate the accuracy of the 10

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Relative disp. (mm)

(a)

0

5

10

15

20

25

Test FEM

0

5

10

15

20

25

(d)

Time (s)

Test FEM

20 0 -20 -40 -60 -80 0

(b)

Time (s)

20 0 -20 -40 -60 -80 -100

(c)

Absolute disp. (mm)

Test FEM

Relative disp. (mm)

Acceleration (g)

0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3

5

10

15

20

25

Time (s)

80 60 40 20 0 -20

Test FEM

0

5

10

15

20

25

Time (s)

Fig. 12. Comparisons between the test data and numerical simulations of the bridge model in the longitudinal direction in Case 4: (a) acceleration and (b) absolute displacement of the bridge girder; relative displacement of (c) Pier 2 and (d) Pier 3.

deformations induced by the permanent differential displacements of the fault. In particular, for the two middle piers, the compressive and tensile damages of the infilled concrete (Fig. 13(b)) occur at different sides of the piers, and the buckling of the outer steel skins also occurs at opposite locations as shown in Fig. 13(c). For the areas around the two rigid connecting joints, concrete tensile damages occur at the bottom and top of the bridge girder above Piers 2 and 3 (Fig. 13(a)), respectively. As observed during the test, the girder end above Pier 4 separated from the supporting bearings during the test. This behavior is also captured by the numerical model as shown in Fig. 13(a) and Fig. 14. It can be seen in Fig. 14(b and c) that the residual separation height in the simulation is about 12.1 mm, which is close to the measured result in the test, where the residual separation height was about 11.0 mm (Fig. 14(a)). All these damages are in good agreement with the test

numerical model, the seismic responses from the numerical model and testing results are compared. Fig. 12 shows the different responses (acceleration and displacement) of different bridge components (girder and Piers 2 and 3) in the longitudinal direction in Case 4. It can be seen that the numerical results agree well with the testing data. In particular, the peak responses, the vibration periods and the residual displacements are accurately captured by the numerical model, which demonstrates the accuracy of the developed numerical model. The damages obtained from the numerical simulations and test data are also compared. Fig. 13 shows the final damage state of the bridge model after Case 4. As shown in Fig. 13(a), the damages mainly occurred at the two middle piers and the areas around the rigid connecting joints, and the damages at the two middle piers and rigid joints generally distribute at opposite locations due to the reversed bending

Fig. 13. Predicted damages of the bridge model: (a) elevation view; (b) infilled concrete of the middle piers; (c) buckling of the outer steel skins around the two ends of the middle piers (red circles). The fringe levels in (a) and (b) represent the damage measure of concrete, and that in (c) stands for plastic strain. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 11

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Vertical disp. (mm)

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40 30 12.1 mm

20 10 0 0

5

10

(c)

15

20

25

Time (s)

Fig. 14. Separation between the bridge girder and the bearings on Pier 4 in Case 4: Residual separation height observed in (a) experimental and (b) numerical simulation; (c) time history of vertical relative displacement in the simulation.

Energy (103 kJ)

6

signifies the plastic deformations.

Internal Kinetic

5 4

4. Parametric study

3

In the previous sections, experiential and numerical studies are performed to investigate the seismic performances of the SCCRFB with CFDST piers, and to verify the accuracy of the numerical model. To further investigate the influences of across-fault ground motions on the SCCRFB, parametric studies are performed in this section and the influences of the key parameters including the fault-rupture location, fault-crossing angle and fling-step are systematically investigated.

2 1 0 0

5

10

15

20

25

Time (s) Fig. 15. Time histories of the internal and kinetic energies of the bridge in Case 4.

4.1. Influence of fault-rupture location results as shown in Figs. 9 and 10, which further demonstrate the accuracy of the numerical model. The above experimental and numerical results also show that the responses of the bridge are mainly governed by the quasi-static deformation of the bridge caused by the nonuniform movement of the supports, and the contribution of the dynamic effect is relatively small. For example, as shown in Fig. 8(b and c) and Fig. 12(b and d), the fluctuating dynamic components in the displacement responses are much smaller than the quais-static components. The damages as shown in Fig. 13 are also mainly because of the uplift of Pier 3. This is actually expected since as shown in Fig. 6 the earthquake inputs are characterized by the large permanent displacements, while the fluctuating components are not obvious. To more evidently show the contributions of the quais-static and dynamic components, Fig. 15 shows the time histories of internal and kinetic energies of the bridge in Case 4. It should be noted that the internal energy induced by previous cases is removed for a fair comparison. It can be seen that the internal energy is much larger than the kinetic energy and contains large residuals which

In this section, the influence of the fault-rupture location (FRL), i.e. the relative location between the surface fault rupture and the bridge span, is investigated. In addition to the middle-span crossing case as investigated in the test and numerical simulation, another four scenarios as shown in Fig. 16 are also considered, and Table 5 summaries the details. In particular, in Cases FRL-1 and FRL-5, the whole bridge is either located to the right or to the left of the surface fault rupture, namely instead of subjecting to the across-fault ground motions, the bridge is subjected to the near-fault ground motions in these two cases, with the ground motions on the hanging-wall (TCU052) and footwall (TCU049) acting on the bridge respectively. In all these cases, the surface fault rupture is assumed perpendicular to the longitudinal direction of the bridge. Fig. 17 shows the damages occur to the concrete of the two middle piers and rigid joints of the bridge model corresponding to the cases of different fault-rupture locations. In general, the damages are very different for the five cases. Among them, the bridge in Case FRL-3 suffers Fig. 16. Five different fault rupture locations considered in the present study, in which FW and HW represent footwall and hanging-wall respectively.

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Table 5 Details of the fault-rupture locations. Case

FRL-1 FRL-2 FRL-3 FRL-4 FRL-5

Fault location

On the left side Beneath the left span Beneath the middle span Beneath the right span On the right side

Pier locations Footwall (ground motion)

Hanging-wall (ground motion)

– Pier Pier Pier Pier

Pier Pier Pier Pier –

1 (TCU049) 1 and 2 (TCU049) 1, 2 and 3 (TCU049) 1, 2, 3 and 4 (TCU049)

1, 2, 3 and 4 (TCU052) 2, 3 and 4 (TCU052) 3 and 4 (TCU052) 4 (TCU052)

Fig. 17. Concrete damages occur to the two middle piers and rigid joints under across-fault ground motions with different fault-rupture locations: (a) Case FRL-1; (b) Case FRL-2; (c) Case FRL-3; (d) Case FRL-4; (e) Case FRL-5. The fringe levels for Pier 2 and 3 represent the damage measure of concrete, and the fringe level for Pier 4 in (d) stands for plastic strain.

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Table 6 Longitudinal peak and residual displacements of the four piers. Case

Peak displacements (mm)

FRL-1 FRL-2 FRL-3 FRL-4 FRL-5

Residual displacements (mm)

Pier 1

Pier 2

Pier 3

Pier 4

Pier 1

Pier 2

Pier 3

Pier 4

14.48 –23.51 −29.73 5.16 5.92

26.35 26.43 −107.82 −8.50 7.85

26.32 26.78 61.19 7.08 7.88

15.89 15.12 10.76 61.21 6.09

0.13 −0.81 −1.00 0.03 −0.07

0.84 0.85 −75.50 −2.59 0.06

0.80 0.12 31.80 0.74 0.04

0.21 0.16 0.01 24.58 −0.01

4.0

4.0

Peak drift ratio (%)

3.0

Residual drift ratio (%)

Pier 1 Pier 2 Pier 3 Pier 4

3.5

2.5 2.0 1.5 1.0 0.5

Pier 1 Pier 2 Pier 3 Pier 4

3.5 3.0 2.5 2.0 1.5 1.0 0.5

0.0

0.0 FRL-1

FRL-2

(a)

FRL-3

FRL-4

FRL-5

FRL-1

FRL-2

(b)

Case No.

FRL-3

FRL-4

FRL-5

Case No.

Fig. 18. Longitudinal drift ratios of the four piers with different fault-rupture locations: (a) peak; (b) residual.

Fig. 19. Deformations of the bridge structure due to fault dislocation in Case FRL-3. 300

Case FRL-3 Pier 2 Pier 3

200

Axial force (kN)

Axial force (kN)

300

100 0

Gravity loads applied

100 0 Gravity loads applied

-100

-100 0

(a)

Case FRL-4 Pier 3 Pier 4

200

5

10

15

20

0

25

(b)

Time (s)

5

10

15

20

25

Time (s)

Fig. 20. Time histories of axial forces of the bridge piers for Case (a) FRL-3 and (b) FRL-4.

the rigid joint above Pier 2 (Fig. 17(b)). Similarly, in Case FRL-4, Pier 4 is lifted up, and this imposes an upward bending on the right span of the bridge girder, which therefore results in the damages around the rigid joints above Pier 3 due to the bending moment (Fig. 17(d)). In Cases FRL-1 (Fig. 17(a)) and FRL-5 (Fig. 17(e)), the bridge model is uniformly excited by the near-fault ground motions TCU052 and TCU049 respectively, therefore the damages in the two cases are similar showing concrete damages occurring at the lower end of the middle piers but with different damage levels because of the different excitation intensities. It should be mentioned that Pier 4 in Case FRL-4 also

the most severe damages as shown in Fig. 17(c), and these damages have been discussed in Section 3.2. For Cases FRL-2 (Fig. 17(b)) and FRL-4 (Fig. 17(d)), the bridge models show moderate damages but with different damage locations. The damages occur to the two middle piers in Case FRL-2 are more severe compared to Case FRL-4 due to the stronger ground motion intensity and pulse components. In Case FRL-2, the middle and right spans are lifted up due to the vertical displacement, and this causes the left end of the girder separating from the bearings on Pier 1, which in turn leads to a cantilever layout of the left span along with vertical vibration, and thus results in slight damage to 14

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Fig. 21. Four different fault-crossing angles considered in the present study.

in many studies (e.g. [39]), the axial compression ratio in the column is a critical parameter that will significantly influence the lateral bending performance of the column. In particular, the lateral strength of a column increases with the increment of axial compression ratio within a certain level. Because the axial force in Pier 3 is generally much larger than Pier 2 (see Fig. 19), it in turn results in the smaller responses (Fig. 18). The obvious variation of axial forces in the bridge piers is also shown in Case FRL-4 (Fig. 20(b)). It can be seen that the axial force in Pier 4 increases after the fault slip, which makes the piers and bridge girder firmly contact with each other. Accordingly, the friction forces in the sliding bearings increase, which in turn results in the larger lateral responses in Pier 4 with peak drift ratio of 2.0% and residual drift ratio of 0.8% compared to other cases as shown in Fig. 18, and also causes moderate damages at the bottom regions of Pier 4 as shown in Fig. 17(d). Except for these, the rest piers all behave robustly with peak drift ratios less than 1% and almost no residual displacements.

Table 7 Details of the four cases considering different fault-crossing angles. Case

FCA-1 FCA-2 FCA-3 FCA-4

FCA (°)

90 67.5 45 22.5

Peak differential displacement (mm) Longitudinal (X)

Transverse (Y)

Vertical (Z)

170 158 121 66

0 66 121 158

103 103 103 103

undergoes certain nonlinear deformations as shown in Fig. 17(d), and the reasons will be further discussed below. For Pier 4 in other cases and Pier 1 in all the cases, they show no obvious damages, and the reason is that the sliding effect of the bearings releases most of the horizontal forces to the side piers. It also should be noted in Fig. 17(d) that the fringe levels for Piers 2, 3 and 4 are different. For Piers 2 and 3, the fringe shows the damage measure of concrete, while for Pier 4, it represents the plastic strain because the smeared model is applied to this pier as mentioned in Section 3. Table 6 tabulates the peak and residual displacements of the four bridge piers in the longitudinal direction for the five cases, and Fig. 18 shows the corresponding peak and residual drift ratios. It can be seen that the responses of Piers 2 and 3 in Case FRL-3 are the most prominent with peak drift ratios of 3.6% and 2.0% and residual drift ratios of 2.5% and 1.1% respectively. It is worth noting that Pier 2 shows much larger responses than Pier 3 in Case FRL-3, and this result might be related to the differential displacements in the vertical direction. As shown in Fig. 19, the vertical differential displacement results in vertical bending at the middle span of the girder, which in turn changes the axial forces of the two middle piers. Compared to the initial states, the final axial forces in Piers 2 and 3 decrease and increase respectively as observed from the time histories of the axial forces of the two middle piers (Fig. 20(a)). It can be seen that the final axial force in Pier 3 almost doubles compared to the initial axial force which is resulted from gravity, while the final axial force in Pier 2 reduces to nearly zero after undergoing a negative peak of 107 kN (tensile force). As indicated

4.2. Influence of fault-crossing angle The influence of fault-crossing angle (FCA), which is defined as the angle between the bridge longitudinal direction and the fault strike, is investigated in this section. Four different cases, with FCA equaling to 90°, 67.5°, 45° and 22.5° are considered (see Fig. 21). As demonstrated before, the bridge model suffers the most severe damage when its middle span is traversed by the fault rupture, this worst scenario is thus considered in this section. It is obvious that Case FCA-1 is the same as Case 4 in the test and Case FRL-3 in Section 4.1. When FCA is less than 90°, the longitudinal ground motions as shown in Figs. 5 and 6 will have components in both the longitudinal and transverse directions, namely the bridge is actually subjected to the across-fault ground motions with different displacements in the longitudinal, transverse and vertical directions. Therefore, unlike previous simulations under longitudinal and vertical (i.e. two-dimensional, 2D) earthquake ground motions, the simulations and analyses in this section are in three dimensions (3D). The corresponding ground motions in the two horizontal directions (i.e. the X and Y directions) are calculated by projecting the previously used longitudinal ground motions, which is assumed corresponding to the

Fig. 22. Torsional response of the bridge structure. 15

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Fig. 23. Concrete damages occur to the two middle piers and rigid joints under across-fault ground motions with different fault-crossing angles: (a–c) Pier 2; (d–f) Pier 3. The fringe level represents the damage measure of concrete, and the dashed rectangulars indicate the damage evolution with the increment of torsion.

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4.0

4.0

Peak drift ratio (%)

3.5 3.0

Residual drift ratio (%)

Pier 1 Pier 2 Pier 3 Pier 4

2.5 2.0 1.5 1.0 0.5

3.0 2.5 2.0 1.5 1.0 0.5

0.0

0.0 FCA-1

FCA-2

(a)

FCA-3

FCA-4

FCA-1

FCA-2

(b)

Case No.

0.5

FCA-3

FCA-4

Case No.

0.5 Pier 1 Pier 2 Pier 3 Pier 4

0.4

Residual drift ratio (%)

Peak drift ratio (%)

Pier 1 Pier 2 Pier 3 Pier 4

3.5

0.3 0.2 0.1 0.0

Pier 1 Pier 2 Pier 3 Pier 4

0.4 0.3 0.2 0.1 0.0

FCA-1

FCA-2

(c)

FCA-3

FCA-4

FCA-1

FCA-2

(d)

Case No.

FCA-3

FCA-4

Case No.

Footwall side Longitudinal (X)

40

Displacement (mm)

Displacement (mm)

Fig. 24. Peak and residual drift ratios of the four piers with different fault-crossing angles: (a) and (b) in the longitudinal direction; (c) and (d) in the transverse direction.

20 0 -20

0

5

10

15

20

0

-100 -150 0

5

10

15

20

25

20

25

Time (s)

Footwall side Vertical (Z)

Displacement (mm)

Displacement (mm)

Time (s) 20

0.75 1.25

-50

-200

25

PDSF 0.5 1.0 1.5

Hanging-wall side Longitudinal (X)

50

10 0 -10 -20

150

Hanging-wall side Vertical (Z)

100 50 0 -50

0

5

10

15

20

25

0

Time (s)

5

10

15

Time (s)

Fig. 25. Across-fault ground motions with different permanent displacements.

90° fault-crossing case. The calculated peak values are listed in Table 7. It should be noted that earthquake ground motions have three componenets, similar to the longitudinal ground motions, the transverse ground motions (not the transverse components from the longitudinal ground motions) will have components in the longitudinal and transverse directions as well when FCA is not 90°. However, not to further complicate the problem, the transverse ground motions and the corresponding components are not considered in the present study. This simplification will result in different responses to the bridge, but will not influence the general trend and conclusion.

Table 8 Details of the five cases considering different PDSFs. Case

PFD-1 PFD-2 PFD-3 PFD-4 PFD-5

PDSF

0.5 0.75 1.0 1.25 1.5

Permanent differential displacement (mm) Longitudinal (X)

Vertical (Z)

55 82 109 136 164

35 53 71 89 107

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Residual axial force (kN)

300

input intensity shown in Table 7 again, from which it can be seen that the input intensity increases with the decrease of FCA. For the responses between Piers 2 and 3, the results show that larger peak and residual displacement occur to Pier 3. This is because the input intensity on the right two piers is larger than that on the left two piers as shown in Fig. 6.

Pier 1 Pier 2 Pier 3 Pier 4

250 200 150 100

4.3. Influence of fling-step

50

The permanent fault displacement (PFD) is related to the effect of fling-step as discussed in the introduction, which can be characterized by the amplitude of the tectonic deformation and the rise time [16]. The tectonic deformation generally refers to the permanent ground displacement (i.e. the static offset), which is a critical factor of the across-fault ground motion that determines the permanent differential displacements on the two sides of a fault. The rise time refers to the duration of fault slip, which affects the intensity of velocity pulse. Because the structural responses are primarily governed by the quasistatic displacements as demonstrated before, only the influence of the amplitude of fling-step is studied in this section. To quantify the fling-step effect, a parameter dubbed permanent displacement scaling factor (PDSF) is defined, and this factor is determined as the ratio between the desired final displacement and the original one (i.e. the final displacement shown in Fig. 6). In the present study, five values with PDSF equaling to 0.5, 0.75, 1.0, 1.25 and 1.5 are investigated. It should be noted that these five PDSFs are achieved by adopting the baseline correction scheme proposed by Lin et al. [49]. To avoid repetition, this method is not introduced in detail in the present study, interested readers can refer to [49] for more information. Fig. 25 shows the across-fault ground motions in the longitudinal and vertical directions with different PDSFs, and Table 8 summarizes the permanent differential displacements in these cases. It also should be noted that by using the proposed baseline correction scheme, the quasi-static components of the across-fault ground motions are modified while the dynamic components (i.e. the fluctuations) are not affected. Therefore, the amplitude of the fling-step becomes the only variable of these ground motions. Based on the analyses in the previous sections, the across-fault ground motions may result in the most severe responses to the bridge when the fault is beneath the middle span of the bridge and with a FCA of 90°, all the simulations are thus based on this assumption in this section. It is obvious that Case PFD-3 is the same as Case 4 in the test and Cases FRL-3 and FCA-1 in the above two subsections. Fig. 26 shows the axial forces in different piers after the earthquake. It can be seen that with the increment of PFD, the residual axial force in Pier 3 increases while that in Pier 2 decreases. In particular, in Case PFD-5, the axial force in Pier 2 even becomes a negative value, which means Pier 2 is under tension in this case. This is because with the increase of PFD, the right two piers become higher and higher compared to the left two piers (refer to Fig. 19), most of the weight from the

0 -50 PFD-1

PFD-2

PFD-3

PFD-4

PFD-5

Case No. Fig. 26. Residual axial forces developed in the four piers with different PFDs.

Due to the different displacements at the left two and right two piers in the three directions, obvious torsional responses are applied to the bridge. Fig. 22 shows the torsional response illustratively. It should be noted that, as shown in Fig. 6, the input ground motions at the right two piers are much larger than those on the left two piers, the permanent displacements on the left two piers are thus ignored in the illustrative Fig. 22. The torsional behavior is clearly reflected in the numerical results. Fig. 23 shows the damage measures developed in the concrete of the two middle piers and the corresponding rigid joints. As shown in Fig. 23(a–c), the blue area of Pier 2 (where the fringe levels are low) extends from a relatively small portion (FCA = 90°) to almost the whole pier (FCA = 22.5°) with the decrease of FCA. A similar trend is also observed in Pier 3, but the blue area decreases with the decrease of FCA as shown in Fig. 23(d–f). It is also observed from Fig. 23(a and d) that the fringe levels in the rigid joints slightly decrease with the decrease of FCA due to the decreased ground motion intensity in the longitudinal direction, and more discussions will be given in the next paragraph. To more explicitly examine the influence of FCA, Fig. 24 shows the peak and residual drift ratios of the four piers in the longitudinal and transverse directions. It can be seen in Fig. 24(a and b) that the peak and residual drift ratios of the four piers decrease with the decrease of FCA. This is because as tabulated in Table 7, the intensity of ground motion in the longitudinal direction decreases with the decrease of FCA. Smaller input intensity obviously results in smaller structural responses. Comparing Pier 2 with Pier 3, it can be seen that obvious larger peak and residual displacements occur to Pier 2 due to the influence of axial compression ratio as explained above. For the responses in the transverse direction (Fig. 24(c and d)), opposite trend is observed compared to that in the longitudinal direction, namely the peak and residual drift ratios increase with the decrease of FCA. This can be explained by the

5

4

Pier 1 Pier 2 Pier 3 Pier 4

Residual drift ratio (%)

Peak drift ratio (%)

5

3 2 1 0

3 2 1 0

PFD-1

(a)

4

Pier 1 Pier 2 Pier 3 Pier 4

PFD-2

PFD-3

PFD-4

PFD-5

PFD-1

(b)

Case No.

PFD-2

PFD-3

PFD-4

Case No.

Fig. 27. Peak and residual drift ratios of the four piers with different PFDs: (a) peak; (b) residual. 18

PFD-5

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Fig. 28. Concrete damages occur to the two middle piers under across-fault ground motions with different amplitudes of fling-steps: (a) Pier 2; (b) Pier 3. The fringe level represents the damage measure of concrete.

Fig. 29. Plastic strain contours and buckling of the outer steel skins around the two ends of the middle piers. The fringe level represents plastic strain.

Section 4.1. Fig. 28 shows the damages to the infilled concrete of the two middle piers. It can be seen that with the increase of PFD, the two piers show more obvious bending deformations (refer to Fig. 19), which results in the different damage portions in the left and right sides of Piers 2 and 3 (see the left and right views in the figure). In particular, the area and intensity of the blue area on the left side of Pier 2 increase with the increment of PFD, and those on the right side decrease slightly. For Pier 3, an opposite trend is observed. Fig. 29 shows the damages to the steel skins around the two ends of the middle piers. As shown, with the increase of PFD, the plastic areas expand and the buckling potential increases. The above results indicate that larger PFD can result in more severe damages to the bridge.

bridge superstructure is thus supported by Pier 3, and the weight supported by Pier 2 becomes smaller and smaller. Moreover, the bending of the bridge girder mostly concentrates around the areas above Pier 2, and it has a V-shaped deformation as shown in Fig. 19, which in turn tends to pull Pier 2 upward. When the PFD is large enough, the pulling force in Pier 2 can even exceed the gravity load from the superstructure and the pier itself and thus result in tensile residual axial force after the earthquake. With the smaller axial force developed in Pier 2, the axial force in Pier 1 thus increases correspondingly. For Pier 4, the axial force decreases slightly first (from PFD-1 to PFD-2) and then almost maintains at a constant. This is because as shown in the numerical simulations, the bridge girder separates from the supporting bearings when the PDSF is larger than 0.75 (Case PFD-2). The different PFDs also result in the different peak and residual displacements in the four piers. As shown in Fig. 27, obvious peak and residual displacements develop in Piers 2 and 3, and the values increase with the increment of PFD. Moreover, the peak and residual displacements in Pier 2 are larger than those in Pier 3 due to the smaller axial force in Pier 2 as discussed in

5. Summary and conclusions In the present study, seismic behavior of the SCCRFB with CFDST piers subjected to surface rupture at a thrust fault is investigated 19

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through shake table tests and numerical simulations. Parametric analyses are also performed to investigate the influences of the fault-rupture location, fault-crossing angle and fling-step on the bridge seismic responses. Following conclusions can be drawn:

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1. The experimental results indicated that the bridge responses to the across-fault ground motions contained significant quasi-static components. In particular, the residual displacements of the four bridge piers can be very different. In addition, the peak acceleration response of the bridge girder was between the input PGAs of the two shake tables. 2. The experimental studies also revealed that the SCCRFB with CFDST piers only suffered minor damages at the upper and lower ends of the two middle piers, which demonstrates the very good seismic resistance capabilities. It has great application potentials especially when they are constructed near or above an active fault. 3. The developed numerical model can accurately predict the seismic responses and damages of the bridge subjected to the across-fault ground motions. The damages of the bridge are mainly governed by the quasi-static deformations, and the contribution from the dynamic effect is relatively small. 4. The bridge suffers the most severe damage when the fault rupture is beneath the middle span of the bridge. While for the other faultrupture locations, no residual displacements are observed in the bridge piers except for Pier 4 in Case FRL-4. 5. Different transverse ground motion components resulting from different fault-crossing angles can induce different levels of torsional responses and damages to the bridge structure. 6. The amplitude of fling-step significantly affects the responses of the bridge. Larger fling-step results in more severe damages. Large vertical fling-step may result in tensile force in bridge piers. It should be mentioned that all the above conclusions are based on the SCCRFB with CFDST piers only. To more comprehensively demonstrate the benefits of this novel bridge type, comparative studies between the SCCRFB with conventional RC piers and the conventional PC rigid-frame bridge with RC piers deserve further investigations. Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgments This study was supported by the National Key Research and Development Program of China (No. 2017YFC0703405), and the National Natural Science Foundation of China (No. 51678141). The authors are also thankful for the financial support from Shenzhen Municipal Design & Research Institute and the technical support from Chongqing Communications Research & Design Institute in accomplishing the shake table tests. The first author also appreciates the financial support provided by the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX17_0128), the Fundamental Research Funds for the Central Universities, and the China Scholarship Council. References [1] Marsh ML, Buckle IG, Kavazanjian Jr E. LRFD seismic analysis and design of bridges reference manual. United States: Federal Highway Administration; 2014. [2] Lee GC, Loh C-H. The Chi-Chi, Taiwan Earthquake of September 21, 1999: Reconnaissance Report. Report No. MCEER-00-0003. The Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY; 2000. [3] Hsu YT, Fu CC. Seismic effect on highway bridges in Chi Chi earthquake. J Perform Constr Facil 2004;18(1):47–53. [4] Aydan Ö. Actual observations and numerical simulations of surface fault ruptures and their effects engineering structures. In: The eight US-Japan workshop on earthquake resistant design of lifeline facilities and countermeasures against

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