Effects of fault rupture on seismic responses of fault-crossing simply-supported highway bridges

Engineering Structures 206 (2020) 110104

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Effects of fault rupture on seismic responses of fault-crossing simplysupported highway bridges

T

Fan Zhanga, Shuai Lia, , Jingquan Wanga, , Jian Zhangb ⁎

a b

⁎

Key Laboratory of Concrete and Prestressed Concrete Structure of China Ministry of Education, Southeast University, Nanjing, China Dept. of Civil and Environmental Engineering, University of California, Los Angeles, United States

ARTICLE INFO

ABSTRACT

Keywords: Fault-crossing bridge Simply-supported highway bridge Permanent ground displacement Seismic response Synthetic ground motion Multi-criteria decision making process

Past earthquakes have demonstrated that fault-crossing bridges were susceptible to damage or even collapse. This study focused on investigating the effects of fault rupture on seismic responses of a simply-supported highway bridge. Six sets of ground motions with fling-step effect in fault-parallel direction and forward directivity effect in fault-normal direction were selected as the inputs from four strike-slip earthquakes. A simplified baseline correction method was used to recover the permanent ground displacement in these records. A typical simply-supported girder bridge located in China was taken as the prototype bridge and the numerical model of the bridge was generated in OpenSees. Effects of fault crossing angles (from 15° to 165°) and the amplitude of permanent ground displacement on the seismic behaviors of the bridge were evaluated. More specially, two special cases, i.e. contact case and separation case, are considered and compared considering the contact and separation between the girder and abutment in bridge longitudinal direction. Results revealed that the piers and bearings in contact case have larger seismic damage compared to separation case, and the separation case causes the unseating of the bridge spans. It was found that the fault crossing angle has a great impact on the seismic responses of the fault-crossing bridge. The fault crossing angle from 60° to 90° causes the lowest structural seismic responses. The permanent ground displacement is another important influence factor of the bridge. Unlike the bridges without crossing fault, the peak values of the responses of the bridge increase as the pulse amplitudes and pulse periods increase.

1. Introduction Simply-supported bridges can be widely found in the transportation network. Following the work of Chen [1], simply-supported bridges account for more than 70% at Sichuan province alone in China. According to the statistics of reconnaissance report on damage of bridges around the world, more than 20 fault-crossing bridges were damaged in the past two decades, in which 16 were simply-supported bridges [2]. The practical applications in bridge construction show that the simplysupported bridges are generally designed and constructed to cross an active fault due to the easiness of retrofit after a large earthquake (e.g., Puqian Approach Bridge in China [3] and Thorndon Overbridge in Newzealand [4]). In some seismic design codes around the world, only generic provisions are outlined and prevention of bridge construction across fault rupture zone is recommended [5,6]. These codes did not provide detailed provisions on how to design the fault crossing bridges. The recommendation cannot be applied in the regions with dense traffic networks of active fault. For example, it was reported that more than

⁎

5% of all bridges in California either cross faults or lie in very close proximity to fault-rupture zones [7]. To consider the effect of fault rupture on bridges, a Caltrans Bridge Memo to Designers [8] proposed a simplified procedure for ordinary bridges crossing strike-slip faults in 2013. However, there are a large number of bridges built before 2013 in California across potentially active fault rupture zones. Once the active fault fractures, these bridges may sustain significant damage if not properly designed or retrofitted. Consequently, it is critical to understand the seismic behaviors of the bridges subjected to a fault rupture. Since the serious damage of fault crossing bridge of 1999 Kocaeli and Duzce, Turkey earthquakes and the 1999 Chi-Chi, Taiwan earthquake, the vulnerability of fault crossing bridges has been attracting increasing attention. Yang and Mavroeidis [2] presented a comprehensive literature review of experimental, analytical and numerical studies on fault-crossing bridges. Up to date, there are still limited studies have investigated the effect of fault rupture on bridges. The main reasons for this limitation are (a) the lack of ground motions with permanent ground displacement, (b) the difficulties in retrieving the

Corresponding authors. E-mail addresses: [email protected] (S. Li), [email protected] (J. Wang).

https://doi.org/10.1016/j.engstruct.2019.110104 Received 13 May 2019; Received in revised form 14 December 2019; Accepted 15 December 2019 0141-0296/ © 2019 Published by Elsevier Ltd.

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F. Zhang, et al.

real permanent ground displacement from accelerograms [9], and (c) the complexity of considering spatially varying ground motion and rigorous nonlinear response history analysis. Therefore, several simplified analysis methods were proposed to explore the seismic response of the bridge crossing fault. Gloyd et al. [10] proposed a special design approach for estimating the effect of ground fault rupture on ordinary bridges by considering two specific loads in addition to the standard loading defined in designed codes in California. Murono et al. [11] used a miniature testing device equipped with two 1300 mm × 650 mm aluminum plates to study the seismic behavior of a bridge (1/50 scale) crossing a fault. One plate can move at arbitrary speed in the horizontal direction and the other plate was fixed. The shift of the movable plate was considered as the permanent ground displacement in fault rupture process. Anastassopoulos et al. [12] developed a two-step methodology for bridge design against the fault rupture deformation. In the first step, a simplified superstructure model with the fault rupture soil-foundation-structure interaction (FR-SFSI) was employed to simulate the displacements and rotation at the base of the piers. Secondly, the computed displacements and rotation were as input for a detail superstructure model without SFSI. Goel and Chopra [7,13] proposed two procedures (response spectrum analysis and linear static analysis) for linear elastic ordinary bridges and three procedures (modal pushover analysis, linear dynamic analysis, and linear static analysis) for nonlinear ordinary bridges crossing fault rupture zones. These procedures estimated the total peak responses of ordinary bridges crossing fault rupture zones in elastic and inelastic range by superposing peak values of quasi-static and dynamic responses. Goel et al. [14] proposed a fault-rupture response spectrum analysis method to investigate the seismic responses of two curved bridges. Compared to the simplified analysis methods, nonlinear response history analysis is a competitive method to investigate the seismic behavior of bridges crossing fault rupture zones. Park et al. [15] analyzed the seismic performance of Bolu Viaduct traversed by the North Anatolian Fault during the 1999 Duzce, Turkey, earthquake using nonlinear time-history analysis method. Considering the fact that no ground motions were recorded during the Duzce earthquake at or in the vicinity of the Bolu Viaduct site, the input ground motions were simulated by combining pulse-type simple mathematic function with a far-field record. The analysis showed that the displacement between the superstructure and the substructure exceeded the capacity of the bearings at an early stage of the earthquake, and the shear keys played a critical role in preventing collapse of the deck spans. Yang et al. [16] also studied the dynamic response of Bolu Viaduct. The Lucerne Valley records processed with and without a displacement offset were considered to excite the bridge. The results demonstrated that the permanent ground displacements are essential to be considered in analyzing the seismic response of the bridges crossing fault rupture. Saiidi et al. [17] conducted a large-scale shake table test for a two-span RC continuous bridge model subjected to a ground motion with permanent ground displacement. Then nonlinear dynamic analyses of the test model revealed that existing analytical techniques can adequately estimate the responses of the fault crossing bridge. A parametric study was conducted to investigate the impact of the bridge configurations and fault locations. The numerical analysis showed that the softer bent on the side of the fault had the largest drift ratio. Ucak et al. [18] generated synthetic broadband ground motions at the site of the Bolu Viaduct by using a hybrid simulation approach based on physical models of the extended seismic source. Time history analysis of the bridge showed that fault crossing location and fault crossing angle were the main factors of seismic responses of bridges fault crossing rupture zones. The seismic responses of the viaduct with two fault crossing angle (e.g. 25° and 90°) were compared. Hui et al. [19] and Zeng [20] investigated the effect of fault crossing location and fault crossing angle on nonlinear responses of a multi-support continuous bridge and a deep-water cable-stayed crossing strike-slip faults respectively. Both the results showed that the fault crossing location and the fault crossing

angle had significant influence on the seismic response of the bridges. Previous researches indicated that the effect of permanent ground displacement, fault crossing location and fault crossing angle on the responses of bridges requires careful consideration. However, most of previous researches mainly investigated the effect of fault crossing location on the responses of bridges. The effect of fault crossing angle on the seismic responses of simply-supported bridge system is still insufficient. Moreover, only one pair of ground motions with permanent ground displacement was used in above researches. Additionally, the influence of amplitude of permanent ground displacement was still not reported. Therefore, the effects of fault crossing angle and amplitude of permanent ground displacement on the seismic responses of simplysupported bridges should be carefully evaluated. The main objective of this study is to investigate the effect of crossing angle and amplitude of permanent ground displacement on a simply-supported bridge across an active fault. A simplified baseline correction method is used to process ground motions with permanent ground displacement. The record-decomposition incorporation (RDI) method proposed by the authors [21] is adopted to generate a series of ground motions with varied permanent displacement amplitude. A three dimensional (3D) model of a typical simply-supported bridge is developed considering the nonlinear behavior of bridge pier, bearing, shear key, abutment, and the contact effects. Multi-criteria decision making (MCDM) method is used for the optimization of crossing angle. The pier responses and the relative displacement between girder and pier are analyzed to evaluate the seismic performance of the bridge considering the effects of fault-rupture. 2. Near-fault ground motions with permanent ground displacement Permanent ground displacement is interpreted as the coseismic deformation of the ground due to dislocation across the fault surfaces [22]. As aforementioned discuss, the investigation of the seismic responses of bridge crossing active fault has attracted the attention of researchers. Unfortunately, accumulating experience indicates that the digital recordings are often plagued by baseline offsets caused by hysteresis in the transducer [22], tilting of the ground [23], or problems in instrumental. Although small offset in acceleration, it can produce totally unrealistic ground velocities and displacements, which cannot be corrected by filtering low-frequency noise from the acceleration records. The main reason is high-pass filtering removes not only the baseline errors but also the low-frequency signal content including the permanent ground displacements. As stated by Graizer [9,24] and Trifunac et al. [25], permanent ground displacement can be accurately calculated from six components of strong-motion accelerations simultaneously recorded at a station. However, most accelerometers can only measure three translational components. Significant efforts have been made to recover the permanent displacement from unprocessed ground motions by empirical and approximate approaches [22,23,26–29]. These empirical methods assume that baseline offset occurs during the strong shaking phase of the entire time history. The baseline offset can be removed by subtracting a polylinear trend from velocity time history. Iwan et al. [22] argued that the baseline offset is caused by hysteresis of transducer when the ground acceleration exceeds 50 cm/s2. Based on the finding, the baseline shift changes in a complicated way during the interval of strong shaking and keeps constant in pre-event and post-event phase. The start and end time (t1 and t2) of the strong shaking phase can be determined by the first and last time points, respectively, when the absolute acceleration exceeds the threshold of 50 cm/s2. Removing the pre-event mean from the whole record is a stable approach to eliminate shift in pre-event phase. The final offset in post-event phase can be determined by leastsquare fit of the final portion of the velocity data. Then, the strongest shift in velocity time history can be approximately assumed a linear trend beginning from 0 at t1 to the velocity shift at t2 in post-event. 2

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Table 1 Details of corrected ground motions in fault-parallel and fault-normal direction. Earthquake

Mw

Station

Rrup (km)

Vs30 (m/s)

Component

PGA (cm/s2)

PGV (cm/s)

PGD (cm)

PD (cm)

Target displacement

Landers, 1992

7.2

LUC

2.19

1369

7.5

YPT

4.83

297

Ducze, 1999

7.14

C1058

0.21

529

Denali, 2002

7.9

PS10

2.74

310

Darfield, 2010

7

GDLC

1.22

344

ROLC

1.54

296

570.6 702.5 226.0 227.7 81.2 89.2 313.3 285.5 747.8 697.5 414.2 250.7

141.1 64.6 83.0 94.5 19.0 18.2 150.5 114.7 131.1 101.9 68.9 97.0

257.2 64.4 239.3 87.2 44.4 13.8 302.6 123.6 212.6 47.5 198.2 103.1

194.3 0.0 188.9 0.0 30.5 0.0 299.1 0.0 176.5 0.0 144.7 0.0

* [42]

Kocaeli, 1999

FP FN FP FN FP FN FP FN FP FN FP FN

179.1 [45] 31.2 [45] * [43] * [44] * [44]

Note: FP, fault-parallel; FN, fault-normal. * means the data has been processed.

Boore [23] showed that the ground tilt is an important source of baseline offset. The start and end time (t1 and t2) of the strong shaking phase should be free parameters. Wu and Wu [26] proposed an iterative way to determine the t1 and t2. Chao et al. [27] and Wang et al. [28] simplified the iterative procedure by using the ratio of energy distribution in accelerograms as the criterion to determine the time points of baseline correction. Lin et al. [29] introduced more subsection in strong shaking phase to modify the permanent displacement to facilitate the agreement between the achieved final displacement and the target final displacement. The empirical approaches provide a reliable method to correct near-fault ground motions with permanent ground displacement. However, the recorded ground motions with permanent ground displacement are still limited. It is essential to synthesize such ground motions using suitable methods. Pulse-type ground motions are attributed mainly to forward directivity effect and fling step effect. Aki [30] demonstrated that fling-step records present one-sided pulses in velocity time histories and permanent ground displacement in displacement time histories. In order to investigate the seismic behavior of various engineering structures subject to near-fault impulsive records, Makris [31], Mavroeidis and Papageorgiou [32], Alavi and Krawinkler [33], Baker [34], He and Agrawal [35], Yang and Zhou [36] proposed synthetic simplified models to simulate pulse-type ground motions. However, most of the simplified models do not contain the high-frequency content portion that may play an important role for structures in which higher modes are significant. To efficiently represent the near-fault ground motions, Mavroeidis and Papageorgious [32] firstly proposed a methodology to generate realistic synthetic ground motions by combining their simplified models mentioned above with high-frequency component synthesize by a stochastic approach. Ghahari et al. [37], Tan et al. [38], Yang and Zhou [36], Yan and Chen [39], Li et al. [21] utilized the same approach but various above-mentioned simplified models for longperiod component and different methods (far-field records, near-field non-pulse records, purely high-frequency components from near-fault impulsive records by high-pass filtering, or synthetic high-frequency by stochastic approach) for synthesis of high-frequency component to generate broadband strong motions. Li et al. [21] validated the effectiveness of combination of the simplified model proposed by Mavroeidis and Papageorgiou [32] and purely high-frequency filtered from nearfault impulsive records in three aspects including time histories, response spectra and bridge responses. This approach can be used to investigate the effects of the pulse parameters on the responses of bridges. To investigate the nonlinear seismic responses of simply-supported bridges, 6 sets of ground motions with fling-step effect in fault-parallel direction and forward directivity effect in fault-normal direction are adopted. A simplified baseline correction method is used to recover the permanent ground displacement of these records. Then two sets of nearfault ground motions with permanent ground displacement are synthesized with the method proposed by the authors [21].

2.1. Selection of ground motions The permanent ground displacement varies from a few centimeters to several meters depending on the rupture mechanism of fault (strikeslip, dip-slip or combined), slip distribution of the fault, the burial depth of the fault, and the fault-to-station distance [16]. For the dip-slip fault case, the hanging-wall effect and vertical ground motion will cause diverse and complicated magnitude of permanent ground displacements at two sides across the fault. Most of the studies focused on seismic responses of bridge crossing strike-slip fault for simplified calculation. For the strike-slip fault case, the permanent ground displacement is only occurred in fault-parallel direction, which is assumed to distribute equally in magnitude along the fault-parallel direction with reversed polarity among the two sides of the fault. The faultnormal direction components are assumed to be identical at the both sides of fault rupture in order to ensure kinematic continuity in the fault-normal direction [18]. In order to satisfy the above assumptions, six groups of bidirectional near-fault records from five different strike-slip earthquakes are selected. These records are considered from earthquakes with a magnitude (Mw) range of 7–7.9 and obtained at the closest distance of 0.21–4.83 km from surface rupture of the fault. Table 1 lists the basic properties of the ground motions such as the closest distance to fault rupture (Rrup), the average shear-wave velocity of the top 30 m (Vs30), and peak ground acceleration (PGA). It should be noted that the 1999 Duzce earthquake and the 2010 Darfield earthquake had predominant strike-slip motions with small dip-slip components [40,41]. The dip-slip motion may cause permanent ground displacement in the fault-normal or vertical directions, which may affect the seismic response of the fault crossing bridge. However, the ground motions with permanent ground displacement from pure strike-slip earthquakes around the world are very rare. In this regard, the ground motions from predominant strikeslip earthquakes with small dip-slip are also selected without considering the vertical components. With the development of the strong ground motion database, more ground motions from pure strike-slip earthquakes should be collected to further validate the accuracy of the conclusions in this study in future research. The ground motions for LUC, PS10, GDLC, and ROLC stations have been processed to preserve static offsets by Chen [42], the United States Geological Survey (USGS) [43] and the New Zealand Strong Motion Database [44]. Raw data for YPT, and C1058 stations derived from the database of the COSMOS Virtual Data Center and the ORFEUS Engineering Strong-Motion Database will be baseline corrected in the following section. 2.2. Baseline correction As mentioned previously, baseline offset could be eliminated by subtracting a poly-linear trend from velocity seismogram. It is assumed that the baseline offset is caused by the tilt of ground during strong 3

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Fig. 1. Illustration of the baseline correction method for YPT-N229.

shaking phase and the tilt is stable after the offset happened (Fig. 1). In this condition, the ground motion can be corrected by removing the offset as a straight line from velocity time history. It should be noted that the beginning time of drift in velocity time history is unknown. But the line can be determined by least-squares fit of the final portion of the velocity data. The baseline can be expressed as follows:

Vf (t ) = V0 + af t ,

tw < t < tend

2.3. Synthetic of Near-fault ground motion with permanent ground displacement To investigate the effect of the amplitude of permanent ground displacement on seismic behavior of bridges, sets of near-fault ground motions with various permanent ground displacements should be first simulated. This study uses the method proposed by the authors [21] to synthesize a series of ground motions considering the permanent ground displacement with different amplitudes and invariant high-frequency component. The background record (BGR) and pulse-type record (PTR) are decomposed using fourth-order Butterworth filter form the fault-parallel component from LUC station. Then the PTR can be simulated by artificial pulse-type motion (APT) proposed by Mavroeidis and Papageorgiou [32] to analyze the effects of pulse parameters (i.e. velocity amplitude, pulse period) on the responses of structures. The mathematical model of the impulsive velocity is given as Eq. (3).

(1)

Then the occurrence of baseline offset can be calculated as follows:

tw =

V0 af

(2)

where af is the correction acceleration and tw is the time at which the line fit to velocity as zero. Finally, the baseline corrected velocity time history can be obtained by subtracting the fitting line from the original motion. The displacement time history can be obtained by integrating the processed velocity time history. It is shown in Fig. 1 that the record N228 in YPT station is as an example to illustrate the processing of baseline correction in this study. The recording from C1058 station is corrected by the same procedure. Boore [23] demonstrated that there are a wide range of final displacements can be obtained for various choices of baseline correction. In order to investigate the seismic responses of fault-crossing bridge, the baseline correction in this paper should satisfy the following two criteria (a) the value of velocity time history after the earthquakes should return back to zero (see Fig. 1a), and (b) the mean displacement after the end of strong motion shaking should be similar to the target of ground offset. The target of ground offset could be GPS, InSAR, or field measurements in the vicinity of the ground motion stations. For this study, the ground offsets measured along fault traces [45] from the Kocaeli earthquake and Ducze earthquake are used to validate the effectiveness of the baseline correction method. The ground offsets at the vicinity of stations were determined using interpolation method based on the coordinate of the station. In fact, the orientation of accelerometers at strong-motion stations are not always at fault-normal or fault-parallel direction. Additionally, the strike direction adjacent to the stations also cannot be determined accurately because it varies along the fault rupture. Therefore, the faultparallel component is supposed to shaking in the direction of maximum permanent ground displacement at a station. Hence, the corresponding fault-normal component does not contain permanent ground displacement and the forward directivity pulse is contained in velocity seismograph. The assumption fits well with the characteristics of ground motions adjacent to strike-slip faults. Fig. 2 illustrates the six sets of baseline corrected acceleration, velocity and displacement time histories in fault-parallel and fault-normal directions. Table 1 summaries the permanent ground displacement (PD) and target ground offset of each ground motion. It shows that the permanent ground displacements of YPT and C1058 stations recovered by the baseline correction method have good fitness with the target ground offsets.

1

A 2 [1 + cos( v (t ) =

2 (t Tp

2

cos[ T (t

Tp

t 0)] t0

t

2

t0 +

Tp 2

,

>1

t0) + ],

p

0,

(3)

otherwise

Parameter A controls the amplitude of the velocity pulse; Tp presents the velocity pulse period; the parameter γ and ν control the shape of the velocity pulse; and t0 specifies the epoch of the envelope’s peak. The ground displacement time history compatible with the ground velocity given by equation (3) are expressed as: 2

sin[ T (t

t0) + ] +

p

ATp

sin

4

+ d (t ) = C,

2 (

t0

Tp

Tp

t0 +

1 2

1

ATp

1 1

2

(t

Tp 2

sin( sin( +

1

t0 ) +

2 ( + 1) (t Tp

sin

>1

ATp

4

+1

t

2

4

1 2

1)

1 2

+

t0) +

, ) + C , t < t0 ) + C , t > t0 +

Tp 2 Tp 2

(4) where C is integration constant. The equation (4) shows that if a permanent ground displacement is contained in a ground motion, the amplitude of the permanent displacement can be determined by the last portion of the piecewise function. It can be found that the permanent ground displacement is positively correlated with the parameters A and Tp. The parameters of the original PTR of LUC record can be estimated using a step by step procedure proposed by Mavroeidis and Papagarous [32]. These parameters are determined so as to optimize the fitting of 4

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Fig. 2. Baseline corrected acceleration, velocity and displacement time histories in fault-parallel and fault-normal direction.

velocity pulse respectively. Fig. 3 shows the time history of synthetic ground motion varying with parameter A. The parameter A is varied from 0 to 0.26 m/s so that the permanent ground displacement ranging from 0 to 0.5 m. It should be noted that other parameters are the same as that of the PTR of LUC station. Fig. 4 illustrates the time history of synthetic ground motion varying with pulse period Tp. The pulse period Tp is varied from 0 to 12 s with the permanent ground displacement changing from 0 to 0.32 m. In this case, the parameter A is fixed as 0.13 m/s (the median value of the previous case).

Table 2 Parameters of the PTR of LUC record. Parameters

Values

A γ ν Tp t0

100 cm/s 1.2 20 9.6 s 10 s

3. Nonlinear finite element model of simply-supported bridge 3.1. Configurations of case study bridge A typical three-span simply-supported bridge with double-pier bents in China is selected for this study. This bridge is a symmetrical structure with three spans. The length of side span is 12 m and the length of middle span is 24 m. The deck of each span is consisted of five precast reinforced concrete box-section girders with a height of 1.5 m. The middle span is supported by two rows of double-pier bents with a height of 8 m. The distance between the double piers is 5 m and each pier has a diameter of 1 m with 18 longitudinal reinforcement bars. The diameter of the reinforcement is 25 mm. The longitudinal reinforcement ratio of the pier is 1.1% and the volumetric reinforcement ratio of the spirals is 0.8%. The width and height of the cap is 0.9 m and 1.6 m. The seat length of the cap for girder in longitudinal direction is 0.43 m. HRB335 (a Chinese steel grade) is used as the reinforcements with a design-yielding strength of 280 MPa. C50 (a Chinese concrete grade) is used as the concrete with a design-compressive strength of 22.4 MPa. The bents are supported on rigid spread footing foundations with stiff soil. 400 mm × 400 mm laminated rubber bearings are placed under right side of the box-section girders and the left side of girders are fixed. The top and bottom sides of the bearings with the girders and caps are restrained by high-strength bolts to prevent the sliding of the bearing. The total thickness of the rubber layer is 0.071 m. Movement of the superstructure is restrained longitudinally by the abutment back-wall with a 0.04 m gap and transversely by shear keys.

Fig. 3. Time history of synthetic ground motions varying with parameter A.

3.2. Finite element model Fig. 4. Time history of synthetic ground motions varying with pulse period.

A three-dimensional nonlinear finite element model is developed in OpenSees [46] to simulate the seismic responses of the simply-supported bridge. Multiple support excitation time history analyses are performed on the bridge model subjected to bidirectional ground displacements with permanent ground displacement. The concrete girders and pier caps are modeled with elastic beam-column elements because they are assumed to remain elastic under earthquake excitations. The

synthetic velocity, displacement, pseudo-velocity response spectrum to the original PTR. Table 2 lists parameters of PTR for LUC record. To examine the effect of different parameters on the dynamic response of the bridge, artificial ground motions with different A and Tp are simulated by combining the BGR of LUC records with the equivalent 5

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Table 3 Material properties of concrete and steel. Material properties

Unconfined concrete

Confined concrete

Material properties

Steel reinforcement

Compressive strength Strain at f′cc Crushing strength Crushing Strain Tensile strength

f′c0 = 32.5 Mpa εc0 = -0.002 fcu0 = 0 Mpa εcu0 = -0.006 ft = 2.64 Mpa

f′cc = 39.9 Mpa εcc = -0.0024 fcu = 27.9 Mpa εcu = -0.0345 ft = 2.64 Mpa

Yield Strength Ultimate Strength Initial elastic modulus Tangent at hardening Stain at hardening Strain at fsu

fy = 387 Mpa fsu = 626 Mpa Es = 200,000Mpa Esh = 10,000 Mpa εsh = 0.01 εsu = 0.154

nonlinear behaviors of the piers, bearings, foundations, abutments, shear keys, and contact between adjacent girders and abutments are taken into consideration in the bridge modeling. Displacement-based beam-column element with fiber sections are used to describe the nonlinearity of bridge piers. Concrete02 material is adopted to model the concrete. Mander’s confinement model [47] is used for unconfined or confined concrete fibers. Reinforcing Steel material is adopted for the steel reinforcement. The material properties of concrete and steel are listed in Table3. The behavior of the bearings is controlled by shear deformations. The bearings are modeled using uniaxial bilinear material. The shear modulus of the elastomeric bearing is determined by the JTG/T 2008 guidelines [5]. The foundation system is established with three translational and three rotational elastic springs. The soil foundation stiffness is calculated from the solution of a rectangular footing bonded to the surface of an elastic half space [24]. The abutments are represented in the backfill passive-pressure force direction by bilinear springs that can only sustain pressure. The stiffness of the abutment is determined according to Caltrans [48]. The shear keys are simulated using an elastic-plastic model considering the contributions of concrete and enforcement proposed by Xu and Li [49]. Two parallel nonlinear springs, with hysteretic behavior, in series with a gap element can be assigned to represent the inelastic behavior of shear keys. A bilinear contact element, zero-length element with ElasticPPGap material, is used to model the contact between girder and girder (or abutment) in longitudinal direction and between girder and shear key in transverse direction. It should be noted that the contact locations will change under the seismic loads. However, for fault crossing bridge, the permanent ground displacement is the major factor to cause the contact effect. Once the girder and shear key contact, the increasing ground dislocation makes the contact tighter and tighter. In order to simplify the simulation, the contact location is assumed not to change in this study. The 3D nonlinear FE model of the bridge system and schematic diagram of various components of the simply-supported bridge are shown in Fig. 5. The mechanical properties of bridge components above-mentioned are listed in Table 4. It should be noted that material properties, the total rubber thickness of bearing, the strength of abutment and shear key, soil properties, the gap between girder and abutment, and the gap between girder and shear key affect the seismic behavior and failure mode of fault crossing bridges under seismic excitations. This study focuses on the effect of fault crossing angle and amplitude of permanent ground displacement on the response of a simply-supported bridge with specified material properties and geometric parameters. A sensitivity study based on fractional factorial analysis method [50] can be adopted in further research to evaluate the effect of these factors and their interactions on the seismic behavior of bridges.

bridge by applying static offset at the bottom of the piers. Table 5 lists the offset capacity of key components of the bridge. The pushover result shows that the bearing failed when 0.31 m static offset applied in longitudinal direction and shear key failed when 0.33 m static offset loaded in transverse direction. However, the maximum permanent ground displacement of selected ground motions in this study is approximate 3 m. Ordinary bridges will collapse inevitably when subjected to such huge ground dislocation. In order to investigate the seismic response of the bridge in an applicable range, the permanent ground displacement of records in fault-parallel direction is scaled to 0.15 m (static offset is 0.3 m). The direct scaling of peak ground motion [21,51], or matching the average of response spectrum for a period range [33,52] are the most conventional approaches for studying the effect of characteristic of ground motions on structures. The direct scaling of permanent ground displacement will excessively underestimate the high-frequency component of the ground motion. The scaling based on the average of response spectrum is not able to control the amplitude of permanent ground displacement. These common scaling methods may not applicable for investigating the seismic response of fault crossing bridge. On the basis of the synthetic of near-fault ground motion with permanent ground displacement, a method of decomposing the baseline corrected records and scaling each component individually is used in the current study. The scaling procedure utilizes a fourth-order Butterworth filter with a corner frequency of 0.08 Hz to decompose the ground motions into low-frequency components and high-frequency components. It should be noted that the corner frequency of 0.08 Hz was applied to filter the high-frequency component of records from LUC station [16], which corresponds to the ~50th percentile of the distribution of high-pass corner frequencies within the NGA-West2 ground motion database for earthquake magnitudes > 60 and distances less than 20 km [53]. The permanent ground displacement for the lowfrequency component of the fault-parallel motion is directly scaled to 0.15 m. The scaling factor for the low-frequency component of faultnormal motion is same as that of fault-parallel motion. The high-frequency component is scaled such that the average acceleration spectra of each individual record matches the JTG B02-2013 design spectrum in the period range of 0.2T to 2.0T (T is the fundamental period of the bridge) suggested by NEHRP Consultants Joint Venture [54]. Subsequently, the scaled broadband ground motions are obtained by combining the scaled low-frequency components with scaled high-frequency components. Fig. 7 illustrates the comparison of the design spectrum with scaled records spectrum. Note that the scaled record may correspond to a different magnitude earthquake from the original one, while the magnitude controls the duration and pulse period of ground shaking. For a rigorous scaling procure, the duration and pulse period should also be modified. Hancock and Bommer [55] have stated that damage measures based on peak response do not depend on duration, while cumulative damage measures such as absorbed hysteretic energy and fatigue damage are correlated with this particular parameter. Furthermore, the pulse period and duration of the low-frequency component affect the rise time required to reach the permanent ground displacement. Appendix A analyzes the effect of the rise time on the seismic response of the fault crossing bridge subjected to synthetic ground motions with varying rise time but the same permanent ground

3.3. Ground motion scaling Ground motions should be scaled appropriately for performing the nonlinear response-history analyses of structures. Previous researches used only one pair of ground motions to investigate the seismic response of fault crossing bridges. The scaling of ground motion for time history analysis of fault crossing structure has not been paid enough attention. Fig. 6 illustrates the results of a static pushover analysis of the 6

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Fig. 5. 3D nonlinear finite element model of the bridge.

displacement. The result shows that the rise time required to reach the permanent ground displacement does not influence the seismic response of the bridge in this study. Therefore, the modification of pulse period and duration is not considered in this study. The scaled records are beneficial to investigate the effect of fault crossing angle on the seismic response of the fault crossing bridge. The effect of pulse period will be discussed in the later section.

three main scenarios according to the location of fault relative to the bridge. The first scenario (“Case A”), in which the fault crossing angle is assumed to be acute (0 < θ < 90°), causes seismic contact between the girders along the longitudinal direction on both sides of the fault. On the contrary, the second scenario named “Case B”, in which the fault crossing angle is assumed to be obtuse (90° < θ < 180°), causes separation of girders along the bridge longitudinal direction on both sides of the faults. The fault crossing angle of the last scenario (“Case C”) was assumed to be 90°. Nonlinear time history analysis is carried out to evaluate the seismic responses of the bridge under the bidirectional baseline corrected ground motions. It should be noted that the Newmark integration method and time step of 0.005 s are used in the

4. Nonlinear seismic response analysis As shown in Fig. 8, the rupture in a strike-slip fault causes the opposite movement of the piers on both sides of the fault. Fig. 8 illustrates Table 4 Mechanical properties of bridge components. Bearing Yield force Stiffness before yield Stiffness after yield Abutment Yield force Stiffness Foundation Horizontal stiffness Horizontal stiffness Vertical stiffness Rocking stiffness Rocking stiffness Torsion stiffness

Shear key Fy = 20.36 kN K1 = 3,130 kN/m K2 = 939 kN/m

Concrete contribution Yield force Yield deformation Ultimate deformation Reinforcement contribution Yield force Yield deformation Ultimate deformation Contact element Yield force Stiffness

Pbw = 3968 kN Kabut = 24,070 kN/m 6

Kx = 4.6 × 10 kN/m Ky = 4.49 × 106 kN/m Kz = 6.12 × 106 kN/m Kθx = 5.23 × 1012 kN·m/rad Kθy = 7.66 × 1012 kN·m/rad Kθz = 9.17 × 1014 kN·m/rad

7

Vc = 632 kN Δn = 17.6 mm Δcu = 57.6 mm Vs = 666 kN Δy = 4 mm Δu = 105.3 mm Fy = 7356 kN Kp = 48900 kN/m

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simulation. The responses of pier, bearing, shear key, abutment and the relative displacement between girder and column are obtained from time history analyses of the bridge. To investigate the effect of the seismic response of the fault-crossing bridge, three fault crossing angles, 45°, 135° and 90°, are chose to represent “Case A”, “Case B” and “Case C” respectively. The maximum responses of the pier happened on the right side along longitudinal axis of the bridge because the supporters of middle span are fixed on the right pier cap. The bearing with maximum deformation in longitudinal direction located on the left abutment for “Case A” but on the left side of the middle span with moveable bearings for “Case B”. The maximum transverse deformation of the bearing and shear key occurred on the left side of the middle span for all cases. Note that the maximum response of shear key occurred on the right side of the pier cap along transverse axis of the bridge. The seismic behavior of each bridge component with maximum response is investigated in this study. Fig. 9 presents the time history responses in longitudinal and transverse directions of the bridge subjected to LUC records for three scenarios. It can be observed that the pier of the fault-crossing bridge is not only subjected to larger residual deformation, but also suffers great postevent invariable internal force caused by permanent ground displacement. Fig. 9(a) shows that the longitudinal peak drift and residual drift of pier for “Case A” are 105% and 144% greater than those for “Case B” respectively. Fig. 9(b) illustrates that the longitudinal peak and residual shear force at the bottom of the pier for “Case A” increase by 26% and 44% compared to those for “Case B” respectively. Fig. 9(c) and (d) reveal that the longitudinal responses of the bearing present similar trends as the pier. In addition, the location of the bearings with longitudinal maximum response are different between “Case A” and “Case B”. The bearings with longitudinal maximum response for “Case A” are on the right side of the abutment accompanying larger pressure and deformation of the abutment back-wall (shown in Fig. 9(e) and (f)). On the contrary, the bearings with longitudinal maximum response for “Case B” located on the right side of the pier cap, which causes translation or unseating of the girder in longitudinal direction. For “Case C”, because permanent ground displacement is not considered in the bridge longitudinal direction, the longitudinal responses of pier and bearing are small. The results for “Case B” and “Case C” are similar to the static tests for a miniature simply-supported bridge model which suffer a lateral dislocation conducted by Murono et al. [11]. However, for “Case A”, Murono et al. reported that the girder away from fault crossing fell off the piers which not happened in this study. It is because the abutments were not considered in the experiment of Murono et al. and consequently, the girder away from fault crossing fell off the piers without any constraint in longitudinal direction. By contrast, the transverse peak and residual responses of the pier

Fig. 6. Static pushover analysis of the bridge (RD: relative displacement, PD: pier drift). Table 5 The offset capacity of key components of the bridge. Damage description

Static offset (m)

Pier collapse in longitudinal direction Bearing failure in longitudinal direction Bearing failure in transverse direction Shear key failure

0.60 0.31 0.39 0.33

Fig. 7. Spectral Acceleration of scaled records.

Fig. 8. Location of fault with respect to structure: contact of girders (“Case A”, left), separation of girders (“Case B”, right), and perpendicular (“Case C”, middle).

8

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Fig. 9. Time history response of the bridge under LUC ground motion.

and bearing are almost same for “Case A” and “Case B”. Because the permanent ground displacement excited in transverse direction for “Case C” is larger than the other two cases, the transverse responses of the bridge for “Case C” are larger. For example, the transverse peak and residual deformation of the bearing for “Case C” are increased by 255% and 192% compared to “Case A”. Fig. 9(e) and (f) show the time history response of shear keys. The ultimate deformation of shear key is 0.0576 m [49]. It is indicated that the shear keys are not destroyed for “Case A” and “Case B” but destroyed for “Case C”. Shear keys restrain the transverse relative displacement between girder and pier. After shear keys are destroyed, the relative displacement will increase immediately. The hysteretic responses of the nonlinear elements of the faultcrossing bridge under LUC ground motion are shown in Fig. 10. According to the damage states demonstrated by Banerjee and Shinozuka [56], the drift of pier for “Case A” combined in longitudinal and transverse direction reaches to 1.69%. It exceeds the drift limit of minor damage state (1%) and would be achieved to the drift limit of moderate damage state (2.5%). The pier cracked and the surface concrete spalled. The drift of pier for “Case B” and “Case C” are less than 1% which indicate that the pier was not damaged in these scenarios. It is evident that the pier of the bridge crossing fault for “Case A” subjects larger damage compared with that for the other two cases. Fig. 10(c) shows that the shear key has not reached ultimate capacity and fail for “Case

A” and “Case B” but collapse for “Case C”. It is the reason that the deformation of bearing for “Case C” is larger than the other two cases. Fig. 10(d) indicates the passive force of the backfill is fully mobilized for “Case A”. The abutment suffered small seismic load in “Case B” and “Case C”, which is not enough to cause damage. The analytical results highlight the significant influence of fault crossing angle on seismic performance of simply-supported bridges. 5. Effect of fault crossing angles As the effect of fault crossing angle has significant influence on the seismic responses of fault crossing bridges, the permanent ground displacement of each record is rotated from 15° to 175° and inputted along the two orthogonal axes of the bridge. Nonlinear time-history analyses are performed to investigate the effects of fault crossing angles on seismic response of the bridge. Fig. 11 illustrates the maximum response of the pier considering various fault crossing angles in longitudinal and transverse directions. It is shown in Fig. 11(a) that the drift of the pier in longitudinal direction decrease with increasing of fault crossing angle from 0° to 90° (“Case A”) and increase with increasing of fault crossing angle from 90° to 180° (“Case B”). On the contrary, the drift of pier in transverse direction increases with the increasing of fault crossing angle from 0° to 90° and decreases with the increasing of fault crossing angle from 90° to 180°. 9

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Fig. 10. Force-displacement responses of various nonlinear elements of the fault-crossing bridge.

Fig. 11. The maximum responses of the pier considering various fault crossing angles.

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Fig. 12. The maximum relative displacement between superstructure and substructure.

slowly for fault crossing angle from 15° to 60°. After that, the relative displacement ascends immediately to a large value for 75°. Finally, the increasing trend becomes slowly with the fault crossing angle from 75° to 90°. The various trend with fault crossing angle from 90° to 175° is symmetrical to the left curves. The phenomenon can be explained as follows. The force to prevent relative displacement between girder and pier in transverse direction is mainly provided by bearings and shear keys. It is shown in Fig. 5 that the shear key can withstand large horizontal forces in small deformation. When the shear key reaches the ultimate capacity (1298 kN), the deformation is 0.0576 m. As mentioned above, the deformations of the shear key and bearing are identical. When the shear key reaches to ultimate deformation, the horizontal force of the bearing is 72 kN, which is far less than the force for shear key. Therefore, once the shear key is damaged, the large horizontal force in shear key previous will be transferred to bearings instantaneously to generate large deformation of bearings.

The increase and decrease trends of the drift are shown in trigonometric distribution patterns. This phenomenon can be attributed that the rotation of the permanent ground displacement varies trigonometric with fault crossing angles. It indicates that permanent ground displacement is the prominent influence factor on the seismic response of the faultcrossing bridge. It will be elaborately discussed in the following sections. Furthermore, comparing the drift of pier in “Case A” with that in “Case B”, the drift of the pier in longitudinal direction reaches to the minimum value near the 90°, whereas the drift in “Case A” has larger values compared to “Case B” at the same crossing angle level (e.g. 30° and 150°). The corresponding drift in transverse direction is symmetrical along 90°. For instance, the average maximum drift of the pier in longitudinal direction for 15° is 1.7 times than that for 165°. The average maximum drifts of pier in transverse direction for 15°, 30°, 45°, 60°, 75° are equivalent to those in cases of 165°, 150°, 135°, 120°, 105°, respectively. A similar trend can be observed in Fig. 11(d) for the shear force at the pier bottom. It is found that the pier exhibits plastic deformation because the drift exceeding the limit of minor damage state (1%), the average maximum shear-force of pier in longitudinal direction for 15° is close to that for 165°. The relative displacements between superstructure and substructure are important responses to access the seismic performance of simplysupported bridge. Fig. 12(a) illustrates the relative displacement in longitudinal direction. Left part of the figure (fault crossing angle: 0–90°) is the relative displacement between abutment and girder, which also represent the deformations of the backfill or corresponding bearing in longitudinal direction (caused by “Case A”). Right part of the figure (fault crossing angle: 90-180°) is the relative displacement between girder and pier which is equals to the deformations of the bearing on the pier cap in longitudinal direction (caused by “Case B”). Fig. 12(b) shows the relative displacement between girder and pier in transverse direction. The relative displacement is consistent to the deformations of the bearing on the pier cap and shear keys in transverse direction. The relative displacement in longitudinal and transverse direction shows the same trend with the drift of pier. It appears that the girders have no contact with the abutment back-wall when the fault crossing angle is between 75° to 90°. When the fault crossing angle decreases from 60° to 15°, the relative displacement between the girder and abutment increases rapidly. It means that the smaller the angle is, the more disadvantage for the abutment back-wall and the corresponding bearing for “Case A”. When the fault crossing angle increases from 90 to 165 degree, the relative displacement between the girder and pier in longitudinal direction presents a quick increase. The greater the angle is, the lager the risk of unseating or falling of the girder in longitudinal direction. Fig. 12(b) reveals that the relative displacement between girder and pier in transverse direction increases with increasing of fault crossing angle from 0° to 90°. It should be noted that the increasing trend is very

6. Optimum analysis of fault crossing angles In order to calculate the optimal fault crossing angle to make the bridge more advantageously under permanent ground displacement, multi-criteria decision making (MCDM) method is used in this study. There are different weighting and scoring methods by which the ranking of alternatives in a MCDM problem is determined. Weights can be assigned to each attribute by the decision maker (direct assignment method) or can be calculated according to the statistical data in the problem through Entropy method [57]. The score of each alternative is computed by taking all criteria into account using different scoring methods such as weighted sum method (WSM) or TOPSIS which are two well-known techniques. The alternative with the highest score is selected as the best one and is placed in the first rank when the goal of MCDM is maximizing all criteria [58]. On the other hand, the worst alternative has the lowest score. The weight of each attribute can be determined according to the qualitative evaluations tabulated in Table 6 [59]. The fault crossing angle is considered as an alternative ranging from Table 6 Assignment of values for a 10-point scale.

11

Attribute evaluation

Value

Extremely unimportant Very unimportant Unimportant Average Important Very important Extremely important

0 1 3 5 7 9 10

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is also a very important criterion for seismic damage of the bridge. The performance of the double cylindrical pier in longitudinal and transverse direction is different. In order to compare the capacity of the double pier bent in longitudinal and transverse direction, lateral loads along the two directions are applied on the top of pier for pushover analyses respectively. Fig. 14 shows the pushover results of the double cylindrical pier of the bridge. The equivalent yield strength of the pier in longitudinal direction is 327 kN, which is 55% smaller than that in transverse direction (731 kN). It shows that the seismic performance of the pier in transverse direction is superior to that in longitudinal direction significantly. The pier in longitudinal direction are more vulnerable under the same seismic load. In this study, the weight of the drift of pier in longitudinal direction (W1) is assigned as 9. Relatively, the weight of the drift of pier in transverse direction (W2) is calculated as about 5. The weights of relative displacement between girder and pier in transverse direction (W4) and the deformation of abutment backfill (W5) cannot be assigned directly. It is generally believed that damage of the bridge caused by the shear key and abutment is not important than that by pier [58,59]. For these reasons, the weights of shear key (W4) and abutment backfill (W5) should be assigned not higher than W2. In order to investigate the influence of different weighting strategies for W4 and W5 on the optimized score, six strategies are compared. For strategies 1 and 5, the C4 and C5 are assumed to be equally important with the same weight. Strategies 2, 3 and 6 assume C4 is less important than C5. Strategy 4 assumes that C4 is more important than C5. The details of these weighting strategies are tabulated in Table 7. Fig. 15 illustrates the score of each alternative (fault crossing angle) for the six weighting strategies. By evaluating the alternatives from highest to lowest scores, the first three optimized fault crossing angle of each strategy are listed in Table 7. The results demonstrate that the optimized fault crossing angle is 60° when W4 is equal or greater than W5, while the optimized fault crossing angle is 90° when W4 is less than W5. It should be emphasized that the prevention of girder falling is considered as the first important for the six weighting strategies. The oversized relative displacement between girder and pier in transverse direction could cause the failure of bearings and shear keys [1]. Therefore, the larger relative displacement in transverse direction may cause more damage than the deformation of abutment. In this condition, for the purpose of ensuring that the girder does not fall in longitudinal direction and the relative displacement in transverse direction is not too large, the fault crossing angle of 60° is the optimized design for simply-supported bridge crossing strike-slip fault. There are also some different opinions that the relative displacement in transverse direction is not so important because the shear key can be considered as a sacrificial component of the bridge [60]. According to these views, the fault crossing angle of 90° is the best design scheme. It is consistent with the research results of Ucak et al. [18] and Hui et al. [19], which did not consider the influence of shear key on the seismic response of the bridges. Although the responses of the piers for 15–90°-fault crossing angle are larger than those for 105–165°, the girder will not fall for 15–90°. It is the reason that the average score of the alternatives in the range of 15–90° is larger than that in the range of 105 to 165 for all of the weighting strategies. Generally, the optimized fault crossing angle is in the range of 60–90° if the girder falling prevention is considered as the first importance. In order to prevent girder from unseating, the slight contact between the girder and girder or girder and abutment during the earthquake can be acceptable.

Fig. 13. Flow chart of multi-objective optimization.

15° to 165°. On the basis of the above analyses, the average drift of pier, the relative displacement between girder and pier in two orthogonal direction of the bridge and the deformation of abutment backfill are chose as criteria in the optimization method. As a result, a multi-criteria decision making problem has been defined with 11 alternatives and five criteria. In the next step, each criterion is divided by the summation of that criterion for all alternatives. The normalized weight for each criterion is calculated by dividing the evaluation value of each one by their summation value. Noted that the method of normalizing the criteria and weight in this study are the same as the reference [59]. According to the WSM method, the score of each alternative is found as follows: 5

Si =

Wj Cj j=1

(5)

where Wj and Cj are normalized weights and criteria respectively. Fig. 13 shows the procedure of optimizing the fault crossing angle through a multi-criteria decision making process. The most serious seismic damage of fault-crossing simply-supported beam bridge is girder falling, which is controlled by relative displacement between girder and pier in longitudinal direction (C3). Here, the weight W3 is assigned as 10. In additional, the performance of the pier

7. Effect of permanent ground displacement As mentioned earlier, the parameter (A) and period (Tp) of velocity pulse are the main factors affecting the amplitude of permanent ground displacement. For the purpose of investigating the influence of permanent ground displacement on seismic performance of the bridge, 12

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Fig. 14. Pushover results of double cylindrical pier.

bridge. The quantitative performance limit states defined for the pier, bearing, shear key and abutment backfill are used to assess the seismic damage of the fault crossing bridge. The qualitative description of the limit states (e.g., slight, moderate, extensive, and collapse) are provided in Table 8. Fig. 16 illustrates the seismic responses of the bridge subjected to the artificial ground motions varying with pulse amplitudes in longitudinal direction. It shows that the ductility of the pier and the relative displacement between girder and pier increase as the parameter A increases. It should be noted that the permanent ground displacement increases from 0 to 0.5 m with the increasing of the parameter A varying from 0 to 0.26 m/s. Furthermore, the permanent ground displacement for separation case could cause lower damage of the bridge compared to that for contact case. For instance, when the pier reaches to the yielding (ductility = 1), the permanent ground displacement is 0.10 m for contact case, whereas that is 0.22 m for separation case. The static pushover analysis of the bridge by applying static offset at the bottom of the piers is used to compare with the dynamic analysis results. Fig. 16 also shows the pushover analysis of ductility of pier and relative displacement between girder and pier in longitudinal direction. In Fig. 16(a), the maximum ductility of the pier is larger than the residual ductility of the pier and pushover analysis result. For contact case, when the permanent ground displacement is less than 0.1 m, the ductility of pier calculated by pushover analysis is nearly the same as the residual ductility of the pier. While the ductility of pier calculated by pushover analysis is slightly larger than the residual ductility of the pier when the permanent ground displacement exceeds 0.1 m. The residual ductility is larger than the ductility of pier calculated by pushover analysis (2% to 25%), when the permanent ground displacement ranges from 0.1 m to 0.5 m. Under the same situation, this difference is from 1% to 18% when the permanent ground displacement ranges from 0.16 m to 0.5 m for separation case. It indicates that the static analysis will underestimate the seismic response of fault crossing bridge if the permanent ground displacement is as the static offset between two pier bents crossing fault. The damage of the bridge for contact case and separation case in longitudinal direction are different (Fig. 16). For contact case, the abutment backfills are destroyed firstly when the permanent ground displacement reaches to 0.10 m. At the same time, the pier experiences yield damage. Then the bearings failed when the permanent ground

Table 7 Weighting strategies and results of scoring. Strategy

S1 S2 S3 S4 S5 S6

Weight of criteria

Optimized angle

W1

W2

W3

W4

W5

1st

2nd

3rd

9 9 9 9 9 9

5 5 5 5 5 5

10 10 10 10 10 10

5 3 1 5 3 1

5 5 5 3 3 3

60 90 90 60 60 90

90 60 75 45 75 75

75 75 60 90 90 60

Fig. 15. Scores various from fault crossing angle for different Weighting strategy.

nonlinear time history analyses of the bridge subjected to the synthetic ground motions in Figs. 3 and 4 are carried out. As shown in Fig. 8, the ground motions are inputted in three different ways, i.e. causing contact of girders in the longitudinal direction (contact case), causing separation of girders in the longitudinal direction (separation case), and in the transverse direction. Here, the maximum displacement ductility of the pier and the relative displacement between girder and pier or abutment are obtained to estimate the seismic performance of the Table 8 Performance limit states of the components of the bridge. Components A B C D

pier bearing shear key abutment backfill

Slight

Moderate

Extensive

Collapse

References

μd > 1.00 γ > 100% ds > 0.041 da > 0.042

μd > 1.20 γ > 150% ds > 0.043 –

μd > 1.76 γ > 200% ds > 0.058 –

μd > 4.76 γ > 250% ds > 0.103 da > 0.198

[61] [62] [49] [63]

Note: μd is the displacement ductility of pier; γ is the shear strain of bearing; ds is the deformation of shear key (m); da is deformation of abutment backfill (m). 13

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Fig. 16. Seismic response of the bridge in longitudinal direction.

Fig. 17. Seismic response of the bridge in transverse direction.

displacement reaches to 0.19 m. The ductility of the pier is 2.7 and the pier suffers extensive damage. Finally, the pier collapses when the permanent ground displacement increases to 0.32 m. For separation case, the pier yields firstly when the permanent ground displacement reaches to 0.22 m. Meanwhile, the bearings suffer moderate damage. Then the bearings are destroyed when the permanent ground displacement reaches to 0.35 m. The ductility of the pier is 3.62 which means the pier suffers extensive damage. The relative displacement between girder and pier exceeds 0.55 m when the permanent ground displacement is > 0.46 m and the girder has fallen. Fig. 17 shows the seismic responses of the bridge subjected to the artificial ground motion varying with parameter A in transverse direction. It indicates that the deformation of the pier increases as the permanent ground displacement increases from 0 to 0.14 m. At this stage, the inertia forces of the girders are transferred to the piers by the shear keys and bearings. After that, the shear keys destroy and the inertia forces are redistributed to the bearings. The damage of the shear keys induces rapidly increasing of the deformation of the bearing. the ductility of the pier remains constant when the permanent ground displacement varies from 0.14 m to 0.2 m. Finally, the deformation of the pier increases with the increasing of the permanent ground displacement. The damage process of the bridge subjected the permanent ground displacement in transverse direction of the bridges is as follows: The shear key destroyed and the pier yielded firstly when the permanent ground displacement reached to 0.14 m. Then the bearing destroyed when the permanent ground displacement reached to 0.33 m. At that time, the pier suffered extensive damage. Finally, the pier collapsed with the permanent ground displacement increasing to 0.53 m. Figs. 18 and 19 illustrate the seismic response of the bridge subjected to the artificial ground motion varying with the pulse period (Tp)

in longitudinal and transverse direction respectively. Because the permanent ground displacement also linearly increases with the increasing of Tp (Fig. 4). The response of the bridge subjected the records with different Tp shows the similar trend with that in the case of the records with various parameter A. Previous study showed that the bridge without crossing fault had the greatest seismic responses when the pulse period coincided with the fundamental period of the bridge [21]. However, the response of the fault crossing bridge increases as the pulse period increases. The reason can be also attributed to the fact that increasing the Tp causes the increasing of permanent ground displacement. In conclusion, when the bridge subjected to permanent ground displacement in longitudinal direction like contact case, the abutment backfill will destroy firstly. The distance of the piers on the both sides of the fault will be shortening. Therefore, girder falling will not happen. When the permanent displacement increases large enough, the bridge will collapse due to the pier collapse. In separation case, the bearing will destroy firstly. When the permanent displacement increases large enough, the bridge will experience girder falling. When the bridge subjected to permanent ground displacement in transverse direction, the shear key will destroy firstly. After that, the bearing will be destroyed. If the permanent ground displacement large enough, the pier will collapse. 8. Conclusions The seismic performance of a simply-supported bridge crossing strike-slip fault is examined in this paper. Six sets of ground motions adjacent faults were selected as the input of nonlinear tiem history analysis. In addition, two sets of ground motions with varying permanent ground displacements were synthetic by combining the high14

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Fig. 18. Seismic response of the bridge in longitudinal direction.

frequency BGR filtered from fault parallel component of LUC station with simple equivalent pulses. The effects of fault crossing angle and permanent ground displacement on the seismic performance of the bridge were evaluated. The following conclusions can be drawn:

5. Shear key was an important component to limit the transverse displacement of simply-supported bridges. At present, due to lack of design for fault crossing bridge, the shear key of typical simplysupported bridges in China cannot withstand larger permanent ground displacement. Once it is damaged, the transverse responses of the bridge will increase dramatically. The shear key should be designed to provide resistant capacity to meet the full seismic demand of fault crossing bridges.

1. When the minimum angle between the fault and bridge are same, the seismic performance of the simply-supported bridge varies greatly with the different behaviors of the bridge induced by the fault rupture, i.e. longitudinal contact of girders and longitudinal separation of girders. The responses of pier caused by longitudinal contact of girders were larger than those by separation of girders. The contact of girders induced greater damage to the bridge, and the separation of girders caused the unseating of bridge. 2. The fault crossing angle was an important factor affecting seismic performance of fault crossing simply-supported bridges. When the fault and bridge were perpendicular, the longitudinal responses of the bridge are smaller than those in any other fault crossing angle. However, the transverse responses of the bridge reached the maximum values. 3. If rupture direction is determined and the prevention of unseating is considered as the first important role, the fault crossing angle between 60° and 90° led to smallest seismic responses of simply-supported bridges. Although the contact of girders will cause large responses of the bridge, slight contact can protect the bridge from unseating. 4. The permanent ground displacement was another predominant influence on the seismic behavior of the fault crossing bridge. With the increasing of the permanent ground displacement, the deformation of the pier and relative displacement between pier and girder increase significantly. The responses of fault crossing bridge increased as the pulse amplitude and pulse period increase and showed similar trend.

The effect of fault crossing angle and permanent ground displacement on the seismic performance of a typical simply-supported bridge was investigated. This study could provide a useful reference for aseismic design of a new highway bridge crossing active fault. However, the presented study was based on parametric analysis of pure numerical simulations. The future study should be expanded to wider range of bridge configurations and shaking table tests. Additionally, the seismic behavior of bridge crossing dip-slip fault and the ground-motion scaling method to scale pulse period and duration of ground motion with permanent ground displacement should be further studied. CRediT authorship contribution statement Fan Zhang: Conceptualization, Methodology, Software, Formal analysis, Writing - original draft, Writing - review & editing, Visualization, Funding acquisition. Shuai Li: Methodology, Investigation, Writing - review & editing, Funding acquisition. Jingquan Wang: Conceptualization, Supervision, Project administration, Funding acquisition. Jian Zhang: Validation, Writing - review & editing, Supervision.

Fig. 19. Seismic response of the bridge in transverse direction. 15

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Declaration of Competing Interest

article. We also would like to thank Dr. Junjun Guo for his kind discussion and helpful suggestion in this study. This study was financially supported by Graduate Student Research Innovation Project of Jiangsu Province (Grant No. KYCX18_0116), the Fundamental Research Funds for the Central Universities (Grant No. 2242019K40082), the Natural Science Foundation of Jiangsu Province (Grant No. BK20190370), and the National Natural Science Foundation of China (Grant No. 51908123).

The authors declared no potential conflicts of interest with respect of to the research, authorship, and/or publication of this article. Acknowledgements The authors would like to thank four anonymous reviewers for their suggestions and comments that helped us significantly improve the Appendix A

The pulse period and duration of the low-frequency component affect the rise time required to reach the permanent ground displacement. In order to investigate the effect of rise time on the response of the fault crossing bridge, synthetic ground motions with various rise time but same permanent ground displacement are generated using the method adopted in Section 2.3. According to the equivalent pulse model proposed by Mavroeidis and Papageorgiou [32], the duration of the low-frequency can be expressed as γTp so that the rise time is controlled by Tp and γ. Furthermore, Eq. (4) shows that the product of A and Tp determines the amplitude of permanent ground displacement when γ and ν are fixed. The value of ATp is 75.0716 cm s when the required permanent ground displacement is 0.15 m and other parameters are used in Table 2. Here, the synthetic low-frequency components varying with the rise time are generate by changing the Tp from 1 s to 10 s and A = 75.0716/Tp with fixed other parameters. Fig. A1 illustrates the synthetic low-frequency components with various rise time. It clearly shows that the rise time required to reach the permanent ground displacement increases with the increasing of the pulse period. Then the synthetic broadband ground motions are obtained by combining the synthetic low-frequency components with the scaled high-frequency component of LUC. Fig. A2 exhibits the seismic response of the fault crossing bridge subjected the synthetic broadband ground motions. It clearly shows that the rise time does not affect the peak response of the bridge in this study. This phenomenon can be attributed that the pulse periods of the ground motions (1.0–10 s) are far away from the fundamental period of the considered bridge (0.54 s) and as a result, changing the rise time has negligible effect on the seismic response of the bridge.

Fig. A1. Synthetic low-frequency components varying with rise time.

Fig. A2. Seismic response of the bridge, the Contact case and Separation case are the response of the bridge in longitudinal direction, Transverse.

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