Advances in Civil Engineering
Volume 2019 (2019), Article ID 3858457, 22 pages
https://doi.org/10.1155/2019/3858457

Research Article

Optimal Seismic Intensity Measure Selection for Isolated Bridges under Pulse-Like Ground Motions

Linwei Jiang,¹ Jian Zhong,¹ Min He,¹ and Wancheng Yuan²

¹Department of Civil Engineering, Hefei University of Technology, Hefei 230009, China
²State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China

Correspondence should be addressed to Jian Zhong; jzhong@hfut.edu.cn

Received 22 July 2019; Revised 27 October 2019; Accepted 14 November 2019; Published 30 December 2019

Academic Editor: Annan Zhou

Copyright © 2019 Linwei Jiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

Isolated bridges are commonly designed in the near-fault region to balance excessive displacement and seismic force. Optimal intensity measures (IMs) of probabilistic seismic demand models for isolated bridges subjected to pulse-like ground motions are identified in this study. Four typical isolated girder bridge types with varied pier height (from 4 m to 20 m) are employed to conduct the nonlinear time history analysis. Totally seven structure-independent IMs are considered and compared. Critical engineering demand parameters (EDPs), namely, pier ductility demands and bearing deformation along the longitudinal and transverse directions, are recorded during the process. In general, PGV tends to be the optimal IM for isolated bridges under pulse-like ground motions based on practicality, efficiency, proficiency, and sufficiency criterions. The results can offer effective guidance for the optimal intensity measure selection of the probabilistic seismic demand models (PSDMs) of isolated bridges under pulse-like ground motions.

1. Introduction

It has been observed that ground motion recordings in the near-fault region, which is usually taken as within 20 km from the fault rupture, tend to differ from far-field rivals in three main characteristics, that is, velocity pulse, directivity effect, and large vertical acceleration component [1]. Some of these differences are usually shown in the velocity and displacement time series, which have been attributed to two effects: the rupture directivity effect and the fling step. The rupture directivity denotes the effect of rupture propagation relative to the site [2]. The near-fault directivity often manifests in the fault-normal direction, which is the direction perpendicular to the surface of the fault rupture. A site may experience forward directivity when the rupture propagates towards the site with a velocity almost equal to the shear-wave velocity of the soil. This effect appears in the form of a large, long-period velocity pulse. And the fling step effect is observed in the fault-parallel direction, that is, the direction paralleled to the fault slip, which appears in the form of a permanent displacement. Due to the above features, the near-fault ground motions impose high input energy on structures and result in severe damage. This phenomenon was originally discovered by Bertero et al. [3, 4]. However, it is only after the 1994 Northridge earthquake that the severe effect of near-fault ground motions on the demand of structures and the necessity of incorporating the effect into the design process were recognized [5, 6].

The probabilistic seismic demand models conditioned on a single intensity measure (IM) of ground motions are a common and necessary step in generating the analytical fragility curves. The intensity measures (IMs) represent characteristics of ground motions and play an important role in the probabilistic seismic demand analysis. Tracking and reducing uncertainty associated with the PSDM can be accomplished by selecting an optimal IM upon which the demand models are conditioning [7].

Researchers have done a lot of work on the selection of optimal IMs for far-field ground motions in the recent years. The Modified Mercalli Intensity Scale was chosen by the Applied Technology Council [8] as the preferred IM. These data were adopted in the risk assessment software package HAZUS. The recent versions of HAZUS selected the spectral acceleration at a period of 1 s (Sa−1) and peak ground displacement (PGD) as the IMs. Padgett et al. [7] investigated the seismic response of the multispan simply supported steel girder bridge class and found that peak ground acceleration (PGA) and spectral acceleration at the fundamental period (Sa) tended to be the most optimal IMs for synthetic ground motions and cumulative absolute velocity was also a contender for recorded motions. In addition to the common IMs, more complex parameters, multiparameter, or vector-based IMs have been proposed [9–12]. Within the bridge engineering community, PGA and Sa are the widely accepted IMs [7, 13].

However, there is relatively less research on the optimal intensity measures of pulse-like ground motions [14]. Yakhchalian et al. [15] proposed that the commonly used scalar intensity measure, namely, the spectral acceleration at the fundamental period of the structure (Sa), is deficient and insufficient to predict the seismic response with respect to the pulse periods of pulse-like ground motions and developed an optimal integral-based IM (I-Sa) with 15 generic frame structures. Baker and Cornell [16] demonstrated that the near-fault pulse-like ground motions are not well described by traditional intensity measures and proposed a vector intensity measure that combines Sa with a measure of the spectral shape. Li et al. [17] proposed two fuzzy-valued (FV) structure-specific intensity measures (one is based on the squared spectral velocity and the other is based on the inelastic spectral displacement) to characterize near-fault pulse-like ground motions. Zhong et al. [1] investigated the response of cable-stayed bridges under synthetic and recorded pulse-like ground motions and found that PGV tends to be the optimal intensity measure compared to other six structure-independent IMs.

In general, the existing IMs can be classified into two categories, that is, structure-dependent IMs and structure-independent IMs. The former combine structure characteristics with intensity measures, while the latter only consider the features of ground motions. However, Padgett et al. [7] proposed that structure-dependent IMs are difficult to obtain in a regional risk assessment for bridge portfolios due to the lack of sufficient information such as fundamental periods of structures. Isolated bridges display totally different seismic response compared to the ordinary short period bridges. Consequently, this study aims to identify the optimal IM for isolated bridges under pulse-like ground motions by evaluating seven existing structure-independent IMs. Four typical isolated bridge types with varied pier height (from 4 m to 20 m) are employed to conduct the nonlinear time history analysis. Efficiency, practicality, proficiency and sufficiency, and hazard computability are selected to evaluate the candidate intensity measures.

2. Fragility Function Methodology

As an emerging tool, the seismic fragility is a useful tool for evaluating the potential seismic damage of bridges during the earthquakes. Seismic fragility refers to the conditional probability that the seismic demand meets or exceeds the seismic capacity of structures subjected to a series of specific ground motions, generally expressed in equation (1):

where Pvulnerability is the conditional failure probability, SD and are the median and dispersion of seismic demand, respectively, SC and βc are the corresponding median and dispersion of seismic capacity, respectively, and is the cumulative normal distribution function. In this paper, probabilistic seismic demand analysis (PSDA) is utilized to derive the fragility curves of bridges, which can establish the probabilistic relationship between the engineering demand parameters (EDPs) of components and the ground motion intensity measures (IMs) [18]. During the process, the peak demands (Di) of the critical components, namely, the curvature ductility of the pier and deformation of the bearing, are recorded for the ith ground motion.

If it is assumed that the seismic demand coincides with the lognormal distribution, the relationship between the median of seismic demand (SD) and the intensity measure (IM) can be written in equation (2):

where a and b are regression coefficients obtained from the response data of the nonlinear time history analysis. The dispersion is theoretically related to ground motions. But, for the sake of simplification, it is usually assumed that is constant [19] as follows:

where n is the number of ground motions.

3. Characteristics of an Optimal IM

Selection of an approximate IM plays a vital role in the probabilistic demand seismic models, which provides the link between EDPs and IMs. An optimal IM should satisfy the following five requirements [1, 7].

3.1. Practicality

Practicality is used to examine the correlation between the demands placed on the structure and the intensity measures of ground motions, which is measured by the regression parameter b in equation (2). A larger value of b indicates a more practical IM.

3.2. Efficiency

Efficiency is known as the common metric that characterizes an optimal IM. An efficient IM can reduce the variation in the estimated demand median, which is represented by the lower regression parameter in equation (3).

3.3. Proficiency: A Composite Metric of Efficiency and Practicality

The conventional selection of an optimal IM based on practicality and efficiency may lead to a challenge in balancing the two parameters. To deal with the problem, Padgett et al. [7] proposed a composite measure ζ to combine practicality and efficiency, which is defined in equation (4). A more proficient IM yields a lower ζ.

3.4. Sufficiency

Sufficiency is an alternative measure to identify an optimal IM of PSDMs [19]. A sufficient IM is statistically independent of ground motion characteristics, such as the magnitude (M), the epicentral distance (R), and fault characteristics. The sufficiency of IMs is assessed with a regression analysis on the residual ε/IM to obtain the corresponding value, from the PSDM to the ground motion characteristics, M or R [1]. A larger value of the regression evaluation indicates a more sufficient IM.

3.5. Hazard Computability

Hazard computability is also a viable measure of an optimal IM. As defined in Giovenale et al. [20], the hazard computability is the level of effort to assess the seismic hazard or derive the hazard curve. PGA or spectral accelerations at the period of 0.2 s or 1 s are readily available in hazard maps; however, other structure-dependent IMs need even more effort and there is difficulty in calculating some IMs from hazard maps.

Therefore, only structure-independent IMs, namely, seven existing IMs in Padgett et al. [7], are considered and compared in this paper. The detailed IMs are listed in Table 1 with their formulas.

Table 1: List of intensity measures compared in this paper.

IMs
Description
Equation
Units

PGA
Peak ground acceleration

g

PGV
Peak ground velocity

m/s

PGD
Peak ground displacement

m

CAV
Cumulative absolute velocity

m/s

CAD
Cumulative absolute displacement

m

Ia
Arias intensity

m/s

Iv
Velocity intensity

m

4. Characteristics and Modeling of Isolated Bridges

Four typical isolated girder bridge types that are common in transportation networks are adopted in this paper as case studies, namely, multicell box girder (MCBG), multibeam box girder (MBBG), concrete I-girder bridge (CIGB), and steel I-girder bridge (SIGB). To generate PSDMs that are representative of each bridge type, some generalizations of the configurations are necessary to be made. As-built bridge data are collected from the various departments of transportation and the advice of engineers who are experienced in designing and restoring bridges is taken to determine pier details, superstructure geometry, isolation bearing parameters, and so forth. The Guidelines for Seismic Design of Highway Bridges [21] are also referred to in order to ensure that the crucial characteristics (e.g., stiffness, mass, and natural period) are generally consistent with the existing bridges. In particular, the pier dimension is determined to guarantee that the axial compression ratio of piers is about 10% for the ductility demand. In this way, the conclusion obtained in this paper is representative of the isolated girder bridge types rather than a certain bridge (Figure 1).

(a)

(b)

(c)

(d)

Figure 1: Typical beam cross sections of (a) MCBG, (b) MBBG, (c) CIGB, and (d) SIGB (unit: mm).

To demonstrate the effect of structure periods on the optimized results, the pier height varies from 4 m to 20 m to generate a wide period range. The typical longitudinal layout of the bridge is given in Figure 2. The vertical reinforcement ratio of the piers is set as 1.2% uniformly with 16 mm circular ties spaced at 100 mm vertically. The configuration of the pier is also presented in Figure 2, where n is 7 for CIGB and MBBG, 9 for MCBG, and 5 for SIGB and D refers to the side length of the pier. The detailed geometry of each bridge type is summarized in Table 2.

Figure 2: Elevation and pier section properties of simply supported girder bridge.

Table 2: Characteristics of the four isolated girder bridge types.

Bridge type
Height (m)
Column section size (m)
Span length (m)
First order period (s)
Rayleigh damping parameters

α₀
α₁

MCBG
4
1.8 × 1.8
35
0.80
0.3927
0.0064

6
0.84
0.3762
0.0066

8
0.91
0.3471
0.0072

10
1.02
0.3110
0.0080

12
1.17
0.2720
0.0092

14
1.35
0.2362
0.0106

16
1.56
0.2047
0.0122

18
1.8
0.1775
0.0141

20
2.06
0.1551
0.0161

MBBG
4
1.5 × 1.5
30
0.71
1.7453
0.0014

6
0.76
1.1635
0.0017

8
0.83
0.8055
0.0019

10
0.94
0.6100
0.0020

12
1.09
0.4760
0.0022

14
1.28
0.3762
0.0029

16
1.49
0.3050
0.0037

18
1.74
0.2513
0.0048

20
2.00
0.2130
0.0058

CIGB
4
1.5 × 1.5
25
0.54
2.0943
0.0011

6
0.58
1.3368
0.0013

8
0.67
0.9240
0.0015

10
0.78
0.6829
0.0017

12
0.94
0.5150
0.0022

14
1.12
0.4054
0.0029

16
1.33
0.3272
0.0037

18
1.56
0.2720
0.0046

20
1.82
0.2293
0.0057

SIGB
4
1.2 × 1.2
35
0.57
0.5511
0.0045

6
0.64
0.4947
0.0051

8
0.75
0.4245
0.0059

10
0.91
0.3491
0.0072

12
1.11
0.2964
0.0084

14
1.35
0.2371
0.0105

16
1.62
0.1976
0.0126

18
1.91
0.1675
0.0149

20
2.23
0.1434
0.0174

As an effective measure for earthquake resistance and disaster prevention, isolation devices play a vital role in reducing the seismic response of structures. The common types of isolation devices applied in transportation networks include elastomeric bearings (ERB), lead-rubber bearings (LRB), and friction pendulum systems (FPS) [22]. In this paper, LRB is selected to be equipped in the bridge systems. The mechanical properties of LRB can be modeled with a bilinear relationship, which are decided with three parameters, namely, characteristic strength Q, elastic stiffness K₁, and postyielding stiffness K₂. The specific formulas of these parameters are given in Table 3, where Alead is the cross section area of the lead core, G is the shear modulus of the rubber, A is the area of rubber, and Σtr is the total thickness of rubber layers. Since the parameters rely on the specific site scenarios and there is an available LRB portfolio [23], the bearing parameters are determined directly according to the superstructure gravity, which are listed in Table 4.

Table 3: Formulas of the mechanical parameters of LRB.

Parameter
Elastic stiffness K₁
Postyielding stiffness K₂
Characteristic strength Q

LRB
K₁ = (15∼30)K₂
K₂ = (1.15∼1.20)GA/Σtr
Q = fyAlead

Table 4: Mechanical properties of LRB of the four bridge types.

Bridge type
Q (kN)
K₁ (kN/m)
K₂ (kN/m)

MCBG
384
28400
4544

MBBG
193
16400
2624

CIGB
171
24700
3952

SIGB
96
14500
2320

The four bridge types considered in this paper include elements that would undergo highly nonlinear behavior under earthquakes, which are incorporated into the three-dimensional detailed nonlinear OpenSees models [24]. The superstructure usually remains elastic subjected to the earthquakes and is simulated with elastic beam-column elements. Due to the constraint effect of stirrups in the piers, we should divide the concrete into cover parts and confined parts, respectively. Therefore, we adopt fiber elements to model the substructures. Each fiber element has its own stress-strain relationship and can simulate the confined concrete, cover concrete, and longitudinal reinforcement, respectively. The response of isolation devices is simulated by a nonlinear bilinear element to account for the yielding of lead. Figure 3 gives the schematic of the analytical model of isolated girder bridges with the reinforcement, concrete, and LRB relationships, where σy, εy, fc, εuu, εcu, and K are yield strength, yield strain, compressive strength, strain at compressive strength for unconfined concrete, strain at compressive strength for confined concrete, and amplification factor due to constraint effect, respectively.

Figure 3: Nonlinear analytical model with models of materials and isolation devices.

In the model, the yield strength, strain-hardening ratio, and elasticity modulus of steel are 400 MPa, 0.5%, and 2.0 × 105 MPa, respectively. With Concrete01 and Steel01 material models in OpenSees, a modified uniaxial Kent-Scott-Park [25] core concrete model is established considering the degraded unloading/reloading stiffness. The compressive strengths of core concrete and cover concrete are set as 29.8 MPa and 26.8 MPa, respectively, and the crushing strains are 0.016 and 0.0035.

In addition, the damping is taken into account for each sample in this paper. The common damping used for structure dynamic analysis includes viscous damping, modal damping, and structure damping [26, 27]. Although many damping models have been proposed, the ideal damping is still difficult to be determined. In this paper, viscous damping is taken into consideration with Rayleigh damping. Rayleigh damping has the characteristics of algebraic manipulation, uniform mathematic expression, and easy application, which is applied widely in structural dynamic response analysis. It is assumed that the damping matrix [C] is the combination of mass matrix [M] and stiffness matrix [K] [26]:

where α₀ and α₁ are two proportionality coefficients calculated from equation (6):

where ξ is the damping ratio (assumed as 0.05 in this paper) and ωi and ωj are the natural vibration frequencies of structures. Since both the longitudinal and transverse seismic responses of bridges are the focus of this paper, the first two-order longitudinal and transverse frequencies are selected as the values of ωi and ωj. The detailed calculation results of Rayleigh damping are given in Table 1.

5. Ground Motion Database

A database consisting of 243 pulse-like ground motions was established by Shahi and Baker [28] in the June 2012 version of the NGA-West2 database by rotating the ground motions and identifying pulses in all orientations. Dabaghi and Kiureghian [29] selected 121 pulse-like ground motions from the database excluding the aftershocks and the records at sites far from the fault (larger than 30 km). Therefore, the remaining pulse-like ground motions database contains 121 pairs in the 2014 version of NGA-West2 database. Figure 4 shows the distribution of pulse-like ground motions with respect to M and R, PGA, PGV, and the pulse period (Tp). The ground motions were recorded from earthquakes, where M ranges from 5.4 to 7.9 and R changes from 0.07 to 28.04 km. The mechanisms of the fault include reverse, strike slip, and reverse oblique. Each record in the pulse-like ground motion database is rotated into the direction containing the largest pulse amplitude and the corresponding orthogonal horizontal direction following the method proposed by Baker [2] and Dabaghi and Kiureghian [29].

(a)

(b)

(c)

(d)

Figure 4: Distribution of pulse-like ground motions with respect to (a) magnitude and source-to-site distance, (b) PGA, (c) PGV, and (d) pulse period Tp.

In this paper, the nonlinear history analysis is conducted using the abovementioned 121 pairs of pulse-like ground motions. EDPs including curvature ductility demands (μx and μy: the subscripts x and y refer to the longitudinal and transverse directions), bearing deformation at the pier (δx, δy), are tracked and recorded during the process.

With the seismic demands and IMs of ground motions, PSDMs are easily developed. For illustration purpose, PSDMs for curvature ductility μx conditioned on PGA and PGV of MCBG (pier height is 18 m) are given in Figure 5, where R² is the correlation coefficient. As illustrated in the figure, b values are 0.84 and 1.81, respectively, and are 1.42 and 0.93, which indicates that PGV is more practical and efficient. The corresponding ζ are 1.69 and 0.51, respectively, demonstrating that the more proficient IM is PGV. The sufficiency of PGA is examined with conditional statistical dependence on M and R, which is plotted in Figure 6. As shown in the figure, the values are 0.2527 and 2.3308 × 10⁻⁴ with respect to M and R, respectively. This phenomenon reveals that PGV is more independent of M and dependent on R.

(a)

(b)

Figure 5: PSDMs for the curvature ductility demand μx conditioned on (a) PGA and (b) PGV.

(a)

(b)

Figure 6: Sufficiency examination of PGV with conditional statistical dependence on (a) M and (b) R.

To highlight the pulse effect on the seismic demand of structures, the optimal intensity measure selection process is repeated for far-field ground motions case. A set of 80 far-field ground motions in Shafieezadeh et al. [30] is used in this paper as the seismic excitation. Figure 7 shows the distribution of far-field ground motions. The ground motions were recorded from earthquakes with M ranging from 5.5 to 7 and R varying from 12.3 to 60 km.

Figure 7: Distribution of far-field ground motions.

6. Optimal Intensity Measure under Pulse-Like Ground Motions

6.1. Practicality

The practicality comparison of IMs can be estimated with the regression parameter b. A more practical IM yields a larger b. The practicality comparison of the four bridge types with different pier heights is shown in Figures 8 and 9. As illustrated in the figures, PGV tends to be the most practical IM for the pier curvature ductility in the longitudinal and transverse directions, followed by CAV. In contrast, for the lower height cases (from 4 m to 12 m), Iv tends to be the least practical IM, and for the higher height cases (from 14 m to 20 m), PGA is the least practical IM. For the whole height range, Iv, PGD, CAD, and PGA are less appropriate due to relatively low practicality parameter b. Similarly, for the displacement-related EDPs, namely, the bearing displacements, PGV is the most practical in the longitudinal and transverse directions, followed by CAV; the least practical IM is Iv. For the considered height range, Iv, CAD, and PGD tend to be less appropriate because of the relatively low practicality parameter b. In general, PGV tends to be the most practical IM, followed by CAV. In particular, one should notice that, for the long-period cases (e.g., 16–20 m), PGA is not a practical IM under pulse-like ground motions, which is a commonly used IM to establish the analytical fragility curves [22].

(a)

(b)

Figure 8: IMs practicality comparison for (a) the pier curvature ductility along the longitudinal direction and (b) the pier curvature ductility along the transverse direction.

(a)

(b)

Figure 9: IMs practicality comparison for (a) the bearing deformation along the longitudinal direction and (b) the bearing deformation along the transverse direction.

As mentioned above, the optimal intensity measure subjected to far-field ground motions is also identified in this paper. Table 5 summarizes the practicality comparison of the seven structure-independent IMs under far-field ground motions of MCBG. For simplicity, the comparison in the transverse direction is not given because it follows a similar tendency. The practicality comparison results of the other three bridge types are also not listed here due to a similar tendency. As shown in the table, CAV tends to be the most practical IM, followed by PGV; however, Iv tends to be the least practical. To demonstrate the pulse effect on the practicality comparison results graphically, Figure 10 shows the comparison results under pulse-like ground motions and far-field ground motions, where PGA, PGV, Iv, and CAV are chosen as the candidate IMs (conditioning on μy, the other cases follow the similar tendency). As shown in the figure, PGV can be chosen as the appropriate IM to assess the seismic demand under far-field and pulse-like ground motions. In addition, PGA is less appropriate to develop PSDMs with respect to practicality, especially for higher piers (larger than 16 m) under pulse-like ground motions. For example, b values are 0.69 and 0.35 for 8 m and 16 m cases subject to pulse-like ground motions, respectively, and, for far-field ground motions, b varies in a narrow range. This phenomenon reveals that PGA should not be chosen as the IM for long-period structures under pulse-like ground motions.

Table 5: Demand models and practicality comparison of IMs subjected to far-field ground motions.

Height (m)
μx
δx

PGA
PGV
PGD
CAD
Ia
Iv
CAV
PGA
PGV
PGD
CAD
Ia
Iv
CAV

4
0.35
0.37
0.25
0.34
0.23
0.19
0.45
0.79
0.82
0.50
0.71
0.47
0.41
0.91

6
0.41
0.42
0.20
0.36
0.27
0.21
0.54
0.70
0.77
0.40
0.62
0.46
0.37
0.90

8
0.45
0.52
0.26
0.45
0.30
0.26
0.63
0.73
0.82
0.42
0.66
0.48
0.39
0.94

10
0.43
0.53
0.30
0.49
0.30
0.27
0.64
0.70
0.81
0.44
0.67
0.47
0.40
0.94

12
0.54
0.64
0.37
0.58
0.37
0.33
0.79
0.76
0.83
0.46
0.72
0.50
0.42
1.00

14
0.66
0.79
0.47
0.70
0.44
0.40
0.92
0.76
0.86
0.51
0.76
0.50
0.44
1.03

16
0.68
0.85
0.55
0.79
0.47
0.44
0.99
0.75
0.90
0.56
0.79
0.51
0.46
1.03

18
0.70
0.91
0.64
0.90
0.48
0.50
1.05
0.75
0.86
0.55
0.79
0.50
0.44
1.05

20
0.75
1.02
0.71
1.02
0.53
0.56
1.17
0.67
0.74
0.48
0.68
0.44
0.38
0.93

Note: bold values indicate more practical IM.

Figure 10: Practicality comparison of IMs under pulse-like and far-field ground motions. The solid lines and dashed lines refer to the cases of pulse-like and far-field ground motions, respectively.

6.2. Efficiency

As indicated, the efficiency of IMs can be evaluated with the dispersion obtained from the PSDMs. The larger is, the less efficient IM is. Figures 11 and 12 present the efficiency comparison of the four bridge types under pulse-like ground motions. As illustrated in the figures, PGV tends to be the most efficient IM with the pier height ranging from 4 m to 16 m for the pier curvature ductility. However, when the height is 18 m or 20 m, Iv tends to be the most efficient IM. For the bearing deformation, Ia tends to be the most efficient in the longitudinal direction and PGV is the most efficient IM in the transverse direction. In general, PGV tends to be the most efficient IM. An interesting phenomenon observed is that PGA is not efficient similar to the practicality comparison for the long-period structures, which supports the abovementioned assumption strongly.

(a)

(b)

Figure 11: IMs efficiency comparison for (a) the pier curvature ductility along the longitudinal direction and (b) the pier curvature ductility along the transverse direction.

(a)

(b)

Figure 12: IMs efficiency comparison for (a) the bearing deformation along the longitudinal direction and (b) the bearing deformation along the transverse direction.

Similarly, Table 6 lists the efficiency comparison of the seven structure-independent IMs under far-field ground motions. As shown in the table, Iv tends to be the most efficient IM. For the considered height range, PGA and PGD are less efficient because of relatively large efficiency parameter . Similarly, to demonstrate the pulse effect on the comparison results, Figure 13 shows the efficiency comparison of IMs under pulse-like ground motions and far-field ground motions, where PGA, PGV, Iv, and Ia are chosen as the candidate IMs (conditioning on μy, the other cases follow the similar tendency). As shown in the figure, PGV can be chosen as the appropriate IM to predict the seismic response of bridges under either far-field or pulse-like ground motions with respect to efficiency. In addition, PGA is the least efficient IM under either pulse-like or far-field ground motions due to the largest dispersion .

Table 6: Demand models and efficiency comparison of IMs subjected to far-field ground motions.

Height (m)
μx
δx

PGA
PGV
PGD
CAD
Ia
Iv
CAV
PGA
PGV
PGD
CAD
Ia
Iv
CAV

4
0.27
0.22
0.27
0.23
0.23
0.21
0.23
0.47
0.33
0.53
0.44
0.42
0.35
0.45

6
0.31
0.29
0.36
0.31
0.29
0.28
0.29
0.56
0.47
0.60
0.54
0.51
0.49
0.53

8
0.38
0.30
0.40
0.33
0.34
0.30
0.34
0.60
0.50
0.64
0.58
0.55
0.52
0.57

10
0.44
0.37
0.43
0.37
0.40
0.35
0.39
0.64
0.53
0.65
0.58
0.58
0.54
0.59

12
0.50
0.41
0.48
0.42
0.45
0.39
0.43
0.64
0.56
0.67
0.60
0.60
0.55
0.60

14
0.56
0.43
0.53
0.46
0.51
0.41
0.50
0.61
0.49
0.60
0.53
0.55
0.47
0.55

16
0.65
0.51
0.56
0.50
0.59
0.46
0.57
0.64
0.49
0.58
0.53
0.58
0.47
0.58

18
0.73
0.58
0.59
0.53
0.68
0.50
0.65
0.60
0.47
0.54
0.48
0.53
0.43
0.51

20
0.82
0.63
0.65
0.56
0.75
0.53
0.71
0.53
0.45
0.50
0.45
0.49
0.42
0.47

Note: bold values indicate more efficient IM.

Figure 13: Efficiency comparison of IMs under pulse-like and far-field ground motions. The solid lines and dashed lines refer to the cases under pulse-like and far-field ground motions, respectively.

6.3. Proficiency

The composite measure ζ can be utilized to estimate the proficiency of IMs, which combines practicality and efficiency. A more proficient IM has a lower ζ. The proficiency comparison of IMs is given in Figures 14 and 15. As illustrated in the figures, ζ is smaller for PGV conditioning on the curvature ductility and bearing deformation in the longitudinal and transverse directions, which indicates that PGV is the most proficient IM, followed by CAV. For the considered height range, Iv, CAD, PGD, and PGA tend to be less appropriate because of the relatively high proficiency parameters ζ. Similarly, for long-period cases, PGA is not a proficient IM, which is consistent with the practicality and efficiency comparison results. This phenomenon reveals that PGA is not appropriate to be chosen as the IM to develop PSDMs of long-period structures under pulse-like ground motions.

(a)

(b)

Figure 14: IMs proficiency comparison for (a) the pier curvature ductility along the longitudinal direction and (b) the pier curvature ductility along the transverse direction.

(a)

(b)

Figure 15: IMs proficiency comparison for (a) the bearing deformation along the longitudinal direction and (b) the bearing deformation along the transverse direction.

Similarly, Table 7 summarizes the proficiency comparison of the seven structure-independent IMs under far-field ground motions. As shown in the table, CAV tends to be the most proficient IM, followed by PGV. To demonstrate the pulse effect on the comparison results, Figure 16 shows the proficiency comparison of IMs under pulse-like ground motions and far-field ground motions, where PGA, PGV, CAV, and Ia are chosen as the candidate IMs (conditioning on μy, the other cases follow the similar tendency). As shown in the figure, PGV can be chosen as the appropriate IM to assess the seismic demand under both far-field and pulse-like ground motions with respect to proficiency. In addition, PGA is less appropriate to perform the vulnerability analysis under either pulse-like or far-field ground motions because of the relatively large ζ. One should notice that ζ value of PGA increases extremely with the height of pier under pulse-like ground motions, which reveals that PGA is the least proficient under pulse-like ground motions. This phenomenon is consistent with the practicality and efficiency comparison results.

Table 7: Demand models and proficiency comparison of IMs subjected to far-field ground motions.

Height (m)
μx
δx

PGA
PGV
PGD
CAD
Ia
Iv
CAV
PGA
PGV
PGD
CAD
Ia
Iv
CAV

4
0.76
0.59
1.06
0.68
1.01
1.08
0.51
0.59
0.40
1.05
0.62
0.89
0.86
0.50

6
0.77
0.66
1.83
0.86
1.06
1.38
0.53
0.79
0.61
1.51
0.88
1.12
1.32
0.59

8
0.85
0.58
1.50
0.74
1.13
1.16
0.54
0.82
0.62
1.54
0.88
1.16
1.32
0.61

10
1.02
0.69
1.40
0.76
1.36
1.27
0.61
0.91
0.66
1.48
0.87
1.25
1.35
0.63

12
0.91
0.64
1.30
0.72
1.19
1.17
0.55
0.85
0.67
1.47
0.83
1.20
1.31
0.60

14
0.85
0.54
1.13
0.65
1.15
1.02
0.53
0.81
0.57
1.19
0.69
1.09
1.08
0.54

16
0.94
0.60
1.03
0.64
1.26
1.04
0.58
0.85
0.56
1.05
0.66
1.14
1.02
0.55

18
1.05
0.63
0.92
0.59
1.40
1.01
0.62
0.80
0.55
0.98
0.60
1.05
0.98
0.49

20
1.09
0.62
0.92
0.55
1.43
0.96
0.61
0.80
0.61
1.03
0.67
1.10
1.10
0.51

Note: bold values indicate more proficient IM.

Figure 16: Proficiency comparison of IMs under pulse-like and far-field ground motions. The solid lines and dashed lines refer to the cases of pulse-like and far-field ground motions, respectively.

6.4. Sufficiency

The value, which is obtained with a regression analysis on the residual, ε/IM, from the PSDM relative to the ground motion characteristics, that is, M or R, is an indicator of sufficiency of IMs. Generally, the value of 0.1 is regarded as the cutoff of an insufficient IM.

A larger value signifies that the IM is more sufficient. The sufficiency comparison of the four candidate IMs, namely, PGV, PGA, CAV, and Ia, is given in Figures 17 and 18. As indicated in the figures, PGA tends to be the most sufficient IM conditioning on the pier curvature ductility for the lower height range (from 4 m to 6 m) with respect to M and R in the longitudinal and transverse directions. For the higher height cases (larger than 8 m), CAV tends to more sufficient, followed by PGV. For the displacement-related EDP, namely, bearing deformation, PGA tends to be the most sufficient IM for the lower height cases (4 m to 8 m) with respect to M; with height increasing, PGV is more sufficient. However, CAV tends to be the most sufficient IM with respect to R for the lower height range (4 m to 8 m) in the longitudinal and transverse directions. As height increases, CAV and PGV tend to be the most sufficient IMs in the longitudinal and transverse directions, respectively. In general, both PGA and PGV can be selected as the most sufficient IMs for PSDMs of isolated bridges.

(a)

(b)

(c)

(d)

Figure 17: IMs sufficiency comparison with respect to M for (a) the pier curvature ductility along the longitudinal direction, (b) the pier curvature ductility along the transverse direction, (c) the bearing deformation along the longitudinal direction, and (d) the bearing deformation along the transverse direction.

(a)

(b)

(c)

(d)

Figure 18: IMs sufficiency comparison with respect to R for (a) the pier curvature ductility along the longitudinal direction, (b) the pier curvature ductility along the transverse direction, (c) the bearing deformation along the longitudinal direction, and (d) the bearing deformation along the transverse direction.

Similarly, Table 8 shows the sufficiency comparison of the seven structure-independent IMs under far-field ground motions. As shown in the table, Iv tends to be the most sufficient IM, followed by PGV and CAV. To demonstrate the pulse influence on the sufficiency comparison results, Figure 19 shows the sufficiency comparison of IMs under pulse-like ground motions and far-field ground motions, where PGA, PGV, CAV, and Ia are chosen as the candidate IMs (conditioning on μy, the other cases follow the similar tendency). As shown in the figure, PGV is found to be more sufficient with respect to R and less sufficient with respect to M under pulse-like ground motions. Under far-field ground motions, PGV is appropriately independent of M and R. Similarly, PGA is relatively dependent on M and R, which implies that PGA is less sufficient.

Table 8: Demand models and sufficiency comparison using values of IMs subjected to far-field ground motions.

Height (m)
μx
δx

PGA
PGV
PGD
CAD
Ia
Iv
CAV
PGA
PGV
PGD
CAD
Ia
Iv
CAV

M
4
0.18
0.47
0.41
0.79
0.77
0.73
0.82
0.14
0.28
0.24
0.85
0.50
0.97
0.68

6
0.05
0.87
0.15
0.92
0.63
0.58
0.98
0.03
0.71
0.10
0.47
0.26
0.87
0.35

8
0.02
0.63
0.18
0.65
0.43
0.26
0.88
0.06
0.89
0.16
0.62
0.35
0.95
0.45

10
0.01
0.91
0.23
0.57
0.26
0.30
0.70
0.05
0.79
0.17
0.64
0.30
0.97
0.41

12
0.01
0.99
0.18
0.76
0.25
0.34
0.60
0.06
0.67
0.15
0.60
0.30
0.95
0.39

14
0.01
0.87
0.18
0.82
0.17
0.30
0.42
0.01
0.26
0.05
0.24
0.08
0.43
0.13

16
0.002
0.41
0.08
0.62
0.05
0.92
0.12
0.03
0.43
0.13
0.43
0.14
0.70
0.20

18
0.002
0.16
0.04
0.28
0.02
0.50
0.06
0.01
0.13
0.05
0.17
0.05
0.24
0.09

20
0.002
0.16
0.03
0.25
0.02
0.50
0.05
0.05
0.61
0.28
0.75
0.28
0.99
0.45

R
4
0.52
0.97
0.47
0.29
0.59
0.85
0.19
0.11
0.18
0.04
0.03
0.10
0.13
0.02

6
0.63
0.95
0.10
0.18
0.50
0.65
0.14
0.14
0.34
0.02
0.03
0.11
0.16
0.02

8
0.69
0.52
0.16
0.31
0.64
0.82
0.18
0.13
0.33
0.02
0.03
0.10
0.16
0.02

10
0.47
0.76
0.16
0.29
0.44
0.91
0.14
0.17
0.46
0.04
0.05
0.15
0.27
0.04

12
0.45
0.77
0.13
0.22
0.43
0.95
0.10
0.31
0.60
0.08
0.09
0.27
0.41
0.08

14
0.37
0.65
0.11
0.18
0.33
0.93
0.07
0.25
0.55
0.09
0.10
0.23
0.39
0.08

16
0.23
0.92
0.09
0.10
0.21
0.80
0.05
0.10
0.26
0.03
0.03
0.09
0.16
0.03

18
0.24
0.83
0.18
0.17
0.26
0.88
0.11
0.25
0.47
0.16
0.18
0.25
0.44
0.14

20
0.20
0.78
0.13
0.12
0.22
0.84
0.10
0.19
0.38
0.07
0.08
0.16
0.30
0.06

Note: bold values indicate more sufficient IM.

Figure 19: Sufficiency comparison of IMs under pulse-like and far-field ground motions. The solid lines and dashed lines refer to the cases under pulse-like and far-field ground motions, respectively.

In general, based on the practicality, efficiency, proficiency, and sufficiency comparison results, PGV can be selected as the optimal IM to assess the seismic demand of isolated bridges under pulse-like and far-field ground motions. However, PGA is not an appropriate IM to establish PSDMs of isolated bridges, which is commonly used in the fragility analysis of structures.

7. Conclusion

The intensity measure (IM) plays a vital role in linking the seismic hazard analysis with the structural demand (e.g., curvature ductility and bearing deformation). Traditional ground motion models used in the probabilistic seismic hazard demand analysis do not account for pulse effect and may underestimate the seismic demand of structures located in the near-fault region. In addition, the research of the optimal intensity measure selection targeted at pulse-like ground motions is rare and there is no widely accepted optimal intensity measure for pulse-like ground motions in the bridge engineering community, which emphasizes the necessity of the research of optimal intensity measures targeted at the pulse-like ground motions.

The objective of this paper is to identify the optimal IM of PSDMs for isolated bridges subjected to pulse-like ground motions. For this purpose, we select four common isolated girder bridge types with varied pier height (from 4 m to 20 m), that is, multicell box girder (MCBG), multibeam box girder (MBBG), concrete I-girder bridge (CIGB), and steel I-girder bridge (SIGB), as case studies. Totally seven structure-independent IMs, namely, peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), Arias intensity (Ia), velocity intensity (Iv), cumulative absolute velocity (CAV), and cumulative absolute displacement (CAD), are selected as the candidate IMs. The probabilistic seismic demand analysis is performed using 121 pairs of pulse-like ground motions. The engineering demand parameters (EDPs), namely, pier curvature ductility (μx, μy) and bearing deformation (δx, δy), are monitored and reordered. Efficiency, practicality, proficiency, sufficiency, and hazard computability are selected as the selection metrics of an optimal intensity measure.

In general, PGV tends to be the optimal IM for conditioning PSDMs of isolated bridges with the considered pier height range based on the five metrics mentioned above. This phenomenon can be explained in that the response of isolated bridges under pulse-like ground motions is dominated by the pulse characteristic. In addition, as a commonly used IM, PGA is not an appropriate choice to establish the fragility curves of isolated bridges under pulse-like ground motions, which signifies that special attention should be paid to the intensity measure selection when the pulse effect cannot be ignored. The results obtained in this paper are intended to offer guidance for probabilistic seismic demand analysis of isolated bridges near the fault.

Data Availability

All data, models, and codes generated or used during the study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This research was supported by the National Natural Science Foundation of China (51608161 and 51778471), the China Postdoctoral Science Foundation (2016M602007), the Fundamental Research Funds for the Central Universities of China (PA2019GDPK0041), and the Ministry of Science and Technology of China (SLDRCE19-B-19). The supports are gratefully acknowledged.

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