Response of Seismic-Isolated Bridges in Relation to Intensity

Measures of Ordinary and Pulselike Ground Motions

Özgür Avşar, Ph.D.1; and Gökhan Özdemir, Ph.D.2
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Abstract: This study concentrates on the efficiency of numerous ground motion intensity measures (IMs) to be used in estimating the response
of seismic-isolated bridges (SIBs). Efficiency of commonly used IMs was investigated through their correlation with maximum isolator dis-
placement (MID) obtained from nonlinear dynamic analyses. Two sets of ground motions (GMs), classified as ordinary and pulse-like, were
used in nonlinear dynamic analyses of SIBs. In the analyses, varying isolation parameters, such as the isolation period, T, and the characteristic
strength of the isolator, Qd =W, were studied. Sensitivity to varying T and Qd =W and the effect of ground motion type on the correlation of IMs
with MID of SIBs were examined. To improve the correlation of existing IMs, modified IMs were proposed. The results revealed that
the isolation period has a pronounced effect on the correlation of IMs with MID of SIBs, especially for pulse-like GMs. Among the investigated
IMs, modified velocity spectrum intensity appears to have the strongest correlation with MID of SIBs for a wide range of isolation parameters
and ground motion type. DOI: 10.1061/(ASCE)BE.1943-5592.0000340. © 2013 American Society of Civil Engineers.
CE Database subject headings: Bridges; Ground motion; Seismic analysis; Isolation; Correlation.
Author keywords: Bridges; Ground motion; Seismic analysis; Isolation; Correlation.

Introduction Various aspects of a proper IM were defined in detail by Mackie and

Stojadinovic (2005) and Mehanny (2009). Efficiency was defined as
Seismic isolation of bridges is a very effective way of protecting the amount of variability of a response quantity given an IM. The
bridges from the damaging effects of earthquakes in seismically measure used to evaluate efficiency is the dispersion. An efficient
active regions. A seismic-isolated bridge (SIB) is designed to control demand model requires a smaller number of nonlinear dynamic
its seismic response through the yielding of isolation units placed analyses to achieve a desired level of confidence. This study con-
between the superstructure and substructure. Hence, behavior of a centrates on the efficiency of several IMs by comparing their correlation
SIB is generally dominated by response quantities of employed with the seismic response of SIBs. However, definitions of sufficiency
isolation systems, such as maximum isolator displacement (MID) and scaling robustness of a proper IM are also given for completeness of
(Dicleli 2006; Ozdemir et al. 2011). Calculation of the MID is the subject. Tothong and Cornell (2008) defined a sufficient IM as the
essential for a SIB, because it is generally used to determine the one that renders structural responses conditionally independent of
isolator size as well as the width and type of the expansion joints. In ground motion properties (e.g., earthquake moment magnitude [Mw ],
some cases, the widths of the substructures may also be governed by distance, epsilon, pulse period) at a given intensity level. Hence, se-
the MID. This is the reason why calculation of the MID is one of lection of a sufficient IM makes selection of ground motion records
the most important steps in performance-based seismic design of more simple. Finally, scaling robustness is desired in order not to bias
SIBs, as well as their seismic performance assessment. Tothong and the results with scaling compared with the ones obtained by
Cornell (2008) defined performance-based seismic evaluation as “a employing as-recorded ground motions (Tothong and Luco 2007).
process that results in realistic understanding of the quantified risk In the light of previous studies, it is evident that selection of
due to future earthquakes for a proposed new structure or the upgrade a proper IM results in a great computational saving together with an
of an existing structure.” Performance-based seismic evaluation increased confidence level. However, there is a lack of agreement on
can be performed through probabilistic seismic demand analysis selection of a proper IM, which serves as a link between the seismic
(PSDA), where response of the considered structure from nonlinear hazard of the bridge site and the seismic response of SIBs. To in-
dynamic analyses is combined with a proper ground motion intensity vestigate the correlation between seismic damage of structures
measure (IM). There are basically three aspects of a proper IM, and various IMs, numerous research studies have been conducted
namely, efficiency, sufficiency, and scaling robustness (Tothong and (Giovenale et al. 2004; Riddell 2007; Tothong and Luco 2007;
Cornell 2008). Padgett et al. 2008; Narasimhan et al. 2009). Giovenale et al. (2004)
carried out studies to investigate the efficiency of different IMs with
1 _
Assistant Professor, Dept. of Civil Engineering, Anadolu Univ., Iki the response variables based on single-degree-of-freedom (SDOF)
Eylül Kampüsü, Eskişehir 26555, Turkey (corresponding author). E-mail: systems with various periods in the range of 0.25–1.0 s. Giovenale
ozguravsar@anadolu.edu.tr et al. (2004) excluded ground motion records with near-field effects.
2
Research Assistant, Dept. of Civil Engineering, Kocaeli Univ., Umut- In his rigorous study, Riddell (2007) investigated the correlation
tepe Yerleşkesi, Kocaeli 41380, Turkey. E-mail: gokas3050@yahoo.com
between various IMs and response quantities of SDOF systems. He
Note. This manuscript was submitted on June 30, 2011; approved on
November 17, 2011; published online on November 19, 2011. Discussion
investigated the correlation of IMs with response quantities in three
period open until August 1, 2013; separate discussions must be submitted spectral regions, namely, acceleration-sensitive, velocity-sensitive,
for individual papers. This paper is part of the Journal of Bridge Engi- and displacement-sensitive. Riddell (2007) showed that no single IM
neering, Vol. 18, No. 3, March 1, 2013. ©ASCE, ISSN 1084-0702/2013/ correlates satisfactorily with response quantities in these three spectral
3-250–260/$25.00. regions simultaneously by stating that “acceleration related indices

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J. Bridge Eng., 2013, 18(3): 250-260

 are best for rigid systems, velocity related indices are better for isolator parameters, such as isolation period (T) and characteristic
intermediate-frequency systems, and displacement related indices strength to weight ratio (Qd =W), were varied widely. Analyses were
are better for flexible systems.” However, Riddell (2007) did not performed with near-field records with and without a pulse-like feature,
classify the considered ground motions as ordinary or pulse-like, and named as pulse-like and ordinary records, respectively. The results
instead employed a single heterogeneous set of ground motions enlighten the efficiency of ground motion IMs in predicting the seismic
composed of both ordinary and pulse-like records. Tothong and response of SIBs as a function of isolation parameters and ground motion
Luco (2007) investigated the correlation of numerous IMs with characteristics. Identification of the optimal IMs was performed through
response quantities of reinforced concrete buildings with different various previously defined IMs, as well as an improved IM, by con-
story numbers (3–15) and periods (0.3–3.0 s). They explicitly sidering the procedure followed in the scaling of ground motions defined
differentiate pulse-like ground motions from the ordinary ones by in building codes (ASCE 2005). The MID was the considered response
considering two different ground motion bins. Tothong and Luco quantity of SIBs obtained from analyses and was used to investigate the
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(2007) pointed out that inelastic spectral displacement, Sdi , exhibits correlation of ground motion IMs with the seismic response of SIBs.
all of the three desirable aspects of a proper IM, namely, efficiency,
sufficiency, and scaling robustness for both ordinary and pulse-like
ground motion records for fixed-based moment-resisting frames Description of Seismic-Isolated Bridges and
with a variety of structural properties. Another study conducted by Analytical Model
Padgett et al. (2008) focused on assessing the characteristics of
optimal IMs for portfolios of bridges that exhibit considerable The investigated bridge geometry is identical to the one studied by
nonlinearity under seismic loading. The periods of the investigated Ozdemir et al. (2011). It is a continuous, three-span, cast-in-place
bridges ranged from 0.17 to 0.32 s. The authors considered both concrete box girder structure with a 30
skew. The two intermediate
synthetic and recorded motions but excluded the ones with near-field bents consist of two circular columns with a cap beam [Fig. 1(a)]. Two
characteristics. Padgett et al. (2008) revealed that peak ground isolators are placed at each abutment, and each isolator is assumed
acceleration (PGA) is the optimal IM for the considered bridge to carry half of the tributary weight of the deck, which is 8,335 kN
portfolios. The study carried out by Narasimhan et al. (2009) differs (4,167.5 kN per isolator). The idealized bridge model was analyzed in the
from the previously discussed research studies in terms of the OpenSees platform (Pacific Earthquake Engineering Research Center
structural type considered, base-isolated buildings. In their study, the 2009), as described in detail by Ozdemir et al. (2011). Fig. 1(b) sche-
authors did not seek the best IM, but rather focused on the potential matically shows the employed analytical model of the isolated bridge.
efficiency of existing IMs by employing a combination of several
IMs. However, Narasimhan et al. (2009) did not address the dif- Considered Isolation Systems
ference between ordinary and pulse-like ground motions, because
a single heterogeneous ground motion bin was considered. The isolation systems are represented by a generic bilinear hysteretic
Most of the previous studies concentrated on conventional fixed- representation without considerations for cycle-to-cycle deterioration
base structures, whereas few research studies exist regarding the of properties. Fig. 2 illustrates the idealized force-deformation re-
seismic-isolated systems. Furthermore, studies that considered the lationship in which Qd is the characteristic strength, kd is the postelastic
seismic-isolated systems did not address the difference between or- stiffness, and ke is the elastic stiffness. Fy and Dy are the yield force
dinary and pulse-like ground motions explicitly. This may not be an and yield displacement, respectively. The isolation period, T, is
issue for fixed-base buildings where periods under investigation are related to postelastic stiffness, kd , through Eq. (1). W is the weight
generally less than 1 s. However, for seismic-isolated systems, where acting on an isolator, and g is the gravitational acceleration
isolation periods are greater than 2 s, near-field characteristics are
rffiffiffiffiffiffiffi
especially pronounced (Bommer and Ruggeri 2002). Hence,
the correlation of IMs with response quantities of seismic-isolated T ¼ 2p W ð1Þ
kd g
systems should be investigated separately for ordinary and pulse-like
ground motions. However, it should not be forgotten that the
The MID, Dmax in Fig. 2, is determined following an iterative
earthquake hazard at any site cannot be associated purely with pulse-
procedure in compliance with the code (ASCE 2005) requirements
like or ordinary ground motions. Thus, any IM that works well only
for stability and strength. Detailed information about the iterative
for pulse-like motions but not for ordinary motions (and vice versa)
procedure can be found Ozdemir et al. (2011). In the analyses,
can be misleading in probabilistic seismic analysis. Therefore, it is
various T and Qd =W values are employed to cover a wide range of
meaningful to differentiate two types of motions in studying the MID-
probable cases representative of typical bridge isolation systems
IM correlation with the emphasis on the IMs that work for both types
(Warn and Whittaker 2004). For this purpose, four different isolator
of ground motions. For this purpose, the study presented herein in-
periods, T (2.5, 3.0, 3.5, and 4.0 s), and four different characteristic
vestigated the correlation between existing various IMs and MIDs of
strengths, Qd =W (0.03, 0.05, 0.07, and 0.09), are considered for SIBs
SIBs subjected to near-field records clustered as ordinary and pulse-
with a total of 16 individual cases. In all of these 16 cases, a constant
like ground motions. Moreover, an improved IM has been suggested
value is assumed for Dy, which is equal to 25 mm.
to provide higher correlation between IMs and MIDs. The results are
believed to be useful for future studies, which aim to provide elaborate
methodologies for reliable seismic performance assessment of SIBs. Description of Ground Motion Data

All of the ground motions considered are near-field records having

Research Objectives and Methodology a closest source-to-site distance of less than 20 km. Selected near-
field records are classified into two sets, depending on whether
The main objective of the research presented herein was to in- they contain a distinguishable velocity pulse or not. Records with a
vestigate the correlation between MID of SIBs with existing ground pulse are named pulse-like, while the rest are called ordinary records. In
motion IMs and to recommend an improved IM especially for SIBs. the literature, to capture the pulse-like features of near-field ground
Hence, numerous nonlinear dynamic analyses were conducted where motions, several pulse models have been proposed and various pulse

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Fig. 1. Bent elevation and analytical model of a seismic-isolated bridge in the transverse direction

Yilmaz (2008). Because it is not the main purpose of the current

study to discuss the IMs in detail, definitions of IMs employed and
relevant references are given in Table 3. Period-independent and
period-dependent GM IMs are the two main categories employed
for classifying IMs. Period-independent IMs can be obtained directly
from time series of ground motions or computed by doing simple
calculations with available time series. These IMs are further classified
into three groups as acceleration-related, velocity-related, and
displacement-related GM IMs. Among these IMs, the estimation of
displacement-related IMs is highly sensitive to the parameters em-
ployed during record processing, such as filtering and baseline cor-
rection (Yang et al. 2009; Narasimhan et al. 2009). Therefore, great
care should be given when using displacement-related IMs. Despite
Fig. 2. Idealized bilinear hysteretic loop of a typical isolator the drawback in the reliability of calculation of displacement-related
IMs, the two most common are investigated. There are some other
period-independent IMs that can fall in any of the three groups. IMs
identification methods have been employed (He and Agrawal 2008; that are in the same group have very strong correlations with each
Tang and Zhang 2011). In this study, pulse-like records were recog- other (Riddell 2007; Yakut and Yilmaz 2008; Narasimhan et al. 2009).
nized by observing a pulse signal in the velocity time history, following Therefore, only the most common ones are investigated for the
Akkar et al. (2005). Ordinary and pulse-like ground motions differ from sake of brevity.
each other in terms of seismic demands imposed on the structure (Alavi The response spectra of ground motion records are used together
and Krawinkler 2004; Dicleli 2006). Because of the forward directivity with the period of structure under investigation to determine period-
effect, pulse-like ground motions represent larger-level seismic in- dependent IMs. Although period-dependent IMs are considered to be
tensity resulting in higher structural demands. Ground motion sets are effective IMs that show good correlation with the structural damage,
composed of 93 pulse-like and 48 ordinary records and are taken from the answer to the question of which period or period range is to be used
Günay (2008). Properties of selected pulse-like and ordinary ground for calculations plays a very important role for the reliability of these
motions are presented in Tables 1 and 2, respectively. Fig. 3 dem- IMs. Spectral acceleration (SA), which is obtained from the accelera-
onstrates the difference between the two ground motion sets by tion response spectrum of ground motion at certain periods as well as at
showing their mean response spectra in each bin. the fundamental period of structures, is extensively used as an IM in the
literature (FEMA 2003; Luco and Cornell 2007; Padgett et al. 2008). In
Definition of Ground Motion Intensity Measures this study, SA is calculated from the 5% damped acceleration response
spectrum at the isolation period of the SIBs, which are specified as 2.5,
Although simple and common IMs, such as peak ground accel- 3.0, 3.5, and 4.0 s. Rather than dealing with a single period to determine
eration (PGA) and peak ground velocity (PGV), are generally spectral values, a period range is assumed for various period-dependent
employed in earthquake engineering, numerous ground motion IMs IMs to consider the higher mode effects as well as the period
have been proposed in the literature for seismic response estimation elongation as a result of structural softening. Acceleration spec-
of different structures. Detailed review of GM IMs and their effi- trum intensity (ASI) was first introduced by Von Thun et al. (1988)
ciency have been investigated by Ridell (2007) and Yakut and for the analysis of concrete dams, whose fundamental period generally

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 Table 1. Properties of Pulse-Like GMs
Earthquake Station Mw d (km) Component PGA (g) PGV (cm/s) PGD (cm)
Cape Mendocino Petrolia 7.0 8.2 0 0.590 48.1 21.9
Cape Mendocino FF 7.0 14.3 270 0.385 43.8 21.6
Chi-Chi CHY006 7.6 9.8 E 0.364 55.4 25.6
Chi-Chi CHY028 7.6 3.1 N 0.822 67.0 23.3
Chi-Chi CHY035 7.6 18.1 W 0.252 45.6 12.0
Chi-Chi CHY080 7.6 2.7 N 0.902 102.5 34.0
Chi-Chi CHY080 7.6 2.7 W 0.968 107.6 18.6
Chi-Chi CHY101 7.6 10.0 N 0.440 115.0 68.8
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Chi-Chi CHY101 7.6 10.0 W 0.353 70.7 45.3

Chi-Chi NSY 7.6 13.2 E 0.145 47.5 50.7
Chi-Chi NSY 7.6 13.2 N 0.128 41.9 28.7
Chi-Chi TCU036 7.6 16.7 W 0.139 59.7 63.6
Chi-Chi TCU052 7.6 0.7 N 0.419 118.5 246.3
Chi-Chi TCU052 7.6 0.7 W 0.348 159.0 184.5
Chi-Chi TCU053 7.6 6.0 N 0.140 41.1 48.1
Chi-Chi TCU057 7.6 11.8 N 0.093 42.6 56.3
Chi-Chi TCU059 7.6 17.8 W 0.165 59.4 63.7
Chi-Chi TCU060 7.6 9.5 W 0.201 36.3 51.9
Chi-Chi TCU063 7.6 9.8 N 0.134 73.2 59.3
Chi-Chi TCU064 7.6 16.6 N 0.117 54.1 59.1
Chi-Chi TCU068 7.6 0.3 N 0.462 263.2 430.2
Chi-Chi TCU068 7.6 0.3 W 0.566 176.7 324.3
Chi-Chi TCU084 7.6 11.2 W 1.157 114.8 31.4
Chi-Chi TCU087 7.6 3.2 N 0.122 37.1 25.6
Chi-Chi TCU087 7.6 3.2 W 0.128 40.8 62.7
Chi-Chi TCU101 7.6 2.9 W 0.202 67.9 75.4
Chi-Chi TCU102 7.6 1.5 N 0.169 77.2 44.9
Chi-Chi TCU103 7.6 4.0 W 0.134 61.9 87.6
Chi-Chi TCU104 7.6 12.9 N 0.085 47.2 52.7
Chi-Chi TCU122 7.6 9.4 W 0.220 42.5 43.0
Chi-Chi TCU128 7.6 13.2 N 0.170 68.8 41.9
Chi-Chi TCU128 7.6 13.2 W 0.139 73.1 90.7
Chi-Chi WGK 7.6 10.0 E 0.334 69.0 35.7
Chi-Chi WGK 7.6 10.0 N 0.484 74.5 67.0
Duzce Bolu 7.1 12.0 90 0.822 62.1 13.6
Duzce Duzce 7.1 8.2 180 0.348 60.0 42.1
Duzce Duzce 7.1 8.2 270 0.535 83.5 51.6
Erzincan Erzincan 6.9 4.4 EW 0.496 64.3 21.9
Imperial Valley EC Meloland 6.5 0.5 270 0.296 90.4 31.7
Imperial Valley Brawley Airport 6.5 10.4 225 0.160 35.9 22.4
Imperial Valley El Centro Array No. 4 6.5 7.1 140 0.485 37.4 20.1
Imperial Valley El Centro Array No. 4 6.5 7.1 230 0.360 76.5 59.1
Imperial Valley El Centro Array No. 5 6.5 4.0 140 0.519 46.9 35.4
Imperial Valley El Centro Array No. 5 6.5 4.0 230 0.379 90.5 63.1
Imperial Valley El Centro Array No. 6 6.5 1.4 140 0.411 64.9 27.6
Imperial Valley El Centro Array No. 6 6.5 1.4 230 0.439 109.8 65.8
Imperial Valley El Centro Array No. 7 6.5 0.6 230 0.463 109.3 44.7
Imperial Valley El Centro Array No. 8 6.5 3.9 230 0.454 49.1 35.6
Imperial Valley El Centro Array No. 10 6.5 6.2 50 0.171 47.5 31.1
Imperial Valley El Centro Array No. 10 6.5 6.2 320 0.224 41.0 19.5
Imperial Valley EC County Center 6.5 7.3 92 0.235 68.8 39.4
Imperial Valley El Centro Differential 6.5 5.1 270 0.352 71.2 45.8
Imperial Valley El Centro Differential 6.5 5.1 360 0.480 40.8 14.0
Imperial Valley EC Meloland 6.5 0.5 0 0.314 71.8 25.6
Imperial Valley Holtville Post Office 6.5 7.7 225 0.253 48.8 31.6
Imperial Valley Holtville Post Office 6.5 7.7 315 0.221 49.8 31.9
Kobe Kobe University 6.9 0.9 0 0.290 54.8 13.5
Kobe KJMA 6.9 1.0 0 0.821 81.3 17.7
Kobe KJMA 6.9 1.0 90 0.599 74.4 20.0
Kobe Takatori 6.9 1.5 0 0.611 127.2 35.8

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 Table 1. (Continued.)

Earthquake Station Mw d (km) Component PGA (g) PGV (cm/s) PGD (cm)
Kobe Takatori 6.9 1.5 90 0.616 120.7 32.7
Kocaeli Duzce 7.4 15.4 180 0.312 58.9 44.1
Kocaeli Duzce 7.4 15.4 270 0.358 46.4 17.6
Kocaeli Gebze 7.4 10.9 0 0.244 50.3 42.8
Kocaeli Yarimca 7.4 4.8 60 0.268 65.7 57.0
Kocaeli Yarimca 7.4 4.8 330 0.349 62.2 51.0
Landers Lucerne 7.3 1.1 275 0.721 97.7 70.3
Loma Prieta Corralitos 7.0 3.9 90 0.479 45.2 11.3
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Loma Prieta Gilroy Array No. 2 7.0 13.7 90 0.322 39.1 12.1
Loma Prieta Gilroy Array No. 3 7.0 13.0 90 0.367 44.7 19.3
Loma Prieta Los Gatos Lexington Dam 7.0 5.0 0 0.420 73.5 20.0
Loma Prieta Los Gatos Lexington Dam 7.0 5.0 90 0.433 86.3 30.1
Loma Prieta Saratoga-Aloha Ave 7.0 8.5 90 0.324 42.6 27.6
Loma Prieta Saratoga-W Valley Coll. 7.0 9.3 0 0.255 42.4 19.5
Morgan Hill Coyote Lake Dam (SW Abut) 6.1 0.5 285 1.298 80.8 9.6
North Palm Springs North Palm Springs 6.2 4.0 210 0.594 73.2 11.5
Northridge Canoga Park-Topanga Can 6.7 14.7 196 0.420 60.7 20.3
Northridge Canyon Country-W Lost Cany 6.7 12.4 270 0.482 44.9 12.5
Northridge Newhall-Fire Sta 6.7 5.9 360 0.590 96.9 38.1
Northridge Rinaldi Receiving Sta 6.7 7.1 228 0.838 166.0 28.1
Northridge Sylmar-Converter Sta 6.7 5.4 52 0.613 117.4 54.3
Northridge Sylmar-Converter Sta 6.7 5.4 142 0.897 102.2 45.1
Northridge Sepulveda VA 6.7 8.9 270 0.753 84.5 18.7
Northridge Sylmar-Olive View Med FF 6.7 5.3 90 0.605 78.1 16.8
Northridge Sylmar-Olive View Med FF 6.7 5.3 360 0.843 129.4 31.9
Northridge Tarzana-Cedar Hill A 6.7 15.6 90 1.779 109.6 32.9
Northridge Newhall-W Pico Canyon Road 6.7 5.5 46 0.455 92.8 56.6
Northridge Newhall-W Pico Canyon Road 6.7 5.5 316 0.325 67.4 16.1
San Fernando Pacoima Dam 6.6 2.8 164 1.226 112.5 35.4
San Fernando Pacoima Dam 6.6 2.8 254 1.160 54.1 11.8
Superstition Hills ElCentro Imp. Company Cent 6.6 18.2 90 0.258 40.9 20.1
Superstition Hills Parachute Test Site 6.6 1.0 225 0.455 112.0 52.8
Tabas-Iran Tabas 7.5 2.1 LN 0.836 97.8 38.7
Note: Mw 5 moment magnitude; d 5 depth; PGD 5 peak ground displacement; E 5 east; W 5 west; N 5 north; EW 5 east-west; LN 5 longitudinal.

ranges between 0.1 and 0.5 s. The ASI has a strong correlation with the corresponding ordinate of the target response spectrum by more
structural damage for short-period structures. A different period range than 10%. TD and TM are the effective periods of the isolated
is suggested to calculate the ASI for different types of structures structure at the design displacement and maximum displacement,
having an intermediate fundamental period (Yakut and Yilmaz respectively (ASCE 2005). A similar consideration is followed to
2008). Similar to ASI, constant period ranges were suggested for define Ti and Tf for ASI, VSI, and HI. It is assumed that Ti 5 0:5T
the velocity spectrum intensity (VSI) and the Housner intensity and Tf 5 1:25T (e.g., Ti 5 1:5 s and Tf 5 3:75 s for a system with an
(HI), as given in Table 3. isolation period T 5 3:0 s.) to represent the period range for SIBs,
where T is the isolation period. IMs denoted as modified accel-
eration spectrum intensity (MASI), modified velocity spectrum
Proposed Period-Dependent Ground Motion intensity (MVSI), and modified Housner intensity (MHI) are
Intensity Measures specified in a similar way to the ASI, VSI, and HI, respectively. The
only difference between ASI, VSI, and HI and their modified
Period-dependent IMs, namely, ASI, VSI, and HI are highly sen- counterparts (MASI, MVSI, and MHI) is the period range defined
sitive to the definitions of Ti and Tf (Table 3), which are specified for by Ti and Tf , at which the SIBs are considered to be effective.
the period ranges of structures for which they are considered to be
effective. When using ASI, VSI, and HI, structure-specific period
ranges need to be employed to obtain a higher correlation with the Discussion and Results
seismic response of the structure. In this section, an effective period
range for SIBs is defined in a similar way as specified in the pro- The MIDs of the SIBs, as a structural response parameter, are ob-
cedure followed by AASHTO (1999) and ASCE (2005) to scale tained from the results of the nonlinear dynamic analyses of the SIB
as-recorded ground motions to be used in nonlinear dynamic analyses models in OpenSees (Pacific Earthquake Engineering Research
of seismic isolated systems. It ensures that for each period between Center 2009). To quantify the correlation between the MID and
0:5TD and 1:25TM , the average of the square root sum of the squares IMs for each ground motion set and the isolation parameters, best-
spectra from all ground motion pairs does not fall below 1.3 times the fitted curves of the form given in Eq. (2) are utilized. The form of the

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 Table 2. Properties of Ordinary GMs
Earthquake Station Mw d (km) Component PGA (g) PGV (cm/s) PGD (cm)
Cape Mendocino Rio Dell Overpass 7.0 14.3 360 0.549 41.9 19.5
Chi-Chi CHY006 7.6 9.8 N 0.345 42.8 15.2
Chi-Chi CHY028 7.6 3.1 W 0.653 72.8 14.7
Chi-Chi TCU084 7.6 11.2 N 0.417 45.6 21.3
Chi-Chi TCU122 7.6 9.4 N 0.261 34.1 36.1
Chi-Chi WNT 7.6 1.8 E 0.958 68.8 31.1
Chi-Chi WNT 7.6 1.8 N 0.626 42.0 18.8
Duzce Bolu 7.1 12.0 0 0.728 56.4 23.1
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Imperial Valley Bonds Corner 6.5 2.7 140 0.588 45.2 16.8
Imperial Valley Bonds Corner 6.5 2.7 230 0.775 45.9 15.0
Imperial Valley Brawley Airport 6.5 10.4 315 0.220 38.9 13.5
Imperial Valley Calexico Fire Station 6.5 10.5 225 0.275 21.2 9.0
Imperial Valley Calexico Fire Station 6.5 10.5 315 0.202 16.0 9.2
Imperial Valley El Centro Array No. 2 6.5 15.3 140 0.315 31.5 14.3
Imperial Valley El Centro Array No. 7 6.5 0.6 140 0.338 47.6 24.7
Imperial Valley El Centro Array No. 8 6.5 3.9 140 0.602 54.2 32.3
Imperial Valley El Centro Array No. 11 6.5 12.5 140 0.364 34.4 16.1
Imperial Valley El Centro Array No. 11 6.5 12.5 230 0.380 42.1 18.6
Imperial Valley EC Country Center FF 6.5 7.3 2 0.213 37.5 16.0
Imperial Valley Parachute Test Site 6.5 12.7 315 0.204 16.1 10.0
Kobe Kobe University 6.9 0.9 90 0.311 34.2 7.2
Kocaeli Izmit 7.4 7.2 90 0.220 29.8 17.1
Kocaeli Izmit 7.4 7.2 180 0.152 22.6 9.8
Landers Lucerne 7.3 1.1 0 0.785 31.9 16.4
Loma Prieta Corralitos 7.0 3.9 0 0.644 55.1 10.8
Loma Prieta Gilroy Array No. 2 7.0 13.7 0 0.367 32.9 7.2
Loma Prieta Gilroy Array No. 3 7.0 13.0 0 0.555 35.7 8.3
Loma Prieta Gilroy Array No. 4 7.0 14.3 0 0.417 38.8 7.1
Loma Prieta Gilroy Array No. 4 7.0 14.3 90 0.212 37.9 10.1
Loma Prieta UCSC Lick Observatory 7.0 18.4 0 0.450 18.7 3.8
Loma Prieta UCSC Lick Observatory 7.0 18.4 90 0.395 17.5 5.0
Loma Prieta Saratoga-Aloha Avenue 7.0 8.5 0 0.513 41.2 16.2
Loma Prieta Saratoga-W Valley Coll. 7.0 9.3 270 0.332 61.5 36.3
Morgan Hill Anderson Dam (downstream) 6.1 3.3 250 0.423 25.3 4.6
Morgan Hill Anderson Dam (downstream) 6.1 3.3 340 0.289 27.6 6.3
Morgan Hill Coyote Lake Dam (SW Abut) 6.1 0.5 195 0.711 51.6 12.0
Morgan Hill Gilroy Array No. 4 6.1 5.7 270 0.224 19.3 4.3
Morgan Hill Gilroy Array No. 4 6.1 5.7 360 0.348 17.4 3.1
Morgan Hill Gilroy Array No. 6 6.1 9.9 0 0.222 11.4 2.5
Morgan Hill Gilroy Array No. 6 6.1 9.9 90 0.292 36.7 6.1
North Palm Springs North Palm Springs 6.2 4.0 300 0.694 33.8 3.9
Northridge Canoga Park-Topanga Can 6.7 14.7 106 0.356 32.1 9.1
Northridge Canyon Country-W Lost Cany 6.7 12.4 0 0.410 43.0 11.7
Northridge Newhall-Fire Sta 6.7 5.9 90 0.583 74.9 17.7
Northridge Pacoima Kagel Canyon 6.7 7.3 90 0.301 31.3 11.2
Northridge Pacoima Kagel Canyon 6.7 7.3 360 0.433 51.2 8.0
Superstition Hills El Centro Imp. Comoany Cent 6.6 18.2 0 0.358 46.4 17.6
Superstition Hills Parachute test site 6.6 1.0 315 0.377 43.9 15.3
Note: Mw 5 moment magnitude; d 5 depth; PGD5 peak ground displacement; E 5 east; W 5 west; N 5 north; EW 5 east-west; LN 5 longitudinal.

best-fitted curves is a power function, as considered by Riddell of a linear relationship between the two data sets. Values equal to 1.0
(2007), to represent the nonlinear relationship between the response indicate a positive linear relationship, and 21.0 indicates a negative
parameter and the IMs through nonlinear regression parameters a linear relationship between the investigated IM and MID. Values
and b. Eq. (2) can be rearranged to perform linear regression between close to or equal to zero suggest that there is no linear relationship
logarithms of the variables. In this case, Pearson’s linear correlation between the IM and the MID. For the sake of completeness, it
coefficients (r) can be applied, as shown in Eq. (3), to quantify the is assumed that r . 0:80 indicates a strong correlation, 0:80 .
correlation between the IMs and the MIDs of the SIBs, where n is the r . 0:50 indicates a medium correlation, and 0:50 . r indicates
number of data points. Pearson’s linear correlation coefficient (r) is a a poor correlation to quantify the correlation between the IMs and the
dimensionless index that ranges from 21.0 to 1.0, reflecting the extent MID. In the following sections, Pearson’s correlation coefficient (r) of

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Fig. 3. Comparison of mean and 61 SD of response spectra

Table 3. Definition of GM Intensity Measures Used in This Study

Type of intensity measure Intensity measure Name Definition
Period-independent GM intensity measures
Acceleration-related Peak ground acceleration Peak ground acceleration maxjaðtÞj; aðtÞ5 acceleration time series
(PGA) Ðt
Arias intensity (AI) Arias intensity for undamped case ðp=2gÞ 0f aðtÞ2 dt; tf 5 total duration
(Arias 1970) Ð tf
Cumulative absolute Cumulative absolute velocity (Electrical 0 jaðtÞjdt; tf 5 total duration
velocity (CAV) Power Research Institute 1988)
pffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Ðt
IC Characteristic intensity (Park et al. 1985) Ic 5 ðarms Þ3=2 td ; arms 5 ð1=td Þ t12 aðtÞ2 dt ;
arms = root-mean-square of acceleration
td 5 t2  t1 ; t1 5 t (5% AI); t2 5 t (95% AI)
[significant duration; Trifunac and Brady (1975)]
1=3
Ia Compound acceleration-related intensity PGA 3 td
measure (Riddell and Garcia 2001)
Velocity-related Peak ground velocity Peak ground velocity maxjvðtÞj; vðtÞ5 velocity time series
(PGV)
IF Compound velocity-related intensity PGV 3 td0:25
measure (Fajfar et al. 1990)
1=3
Iv Compound velocity-related intensity PGV2=3 3 td
measure (Riddell and Garcia 2001)
Displacement-related Peak ground displacement Peak ground displacement maxjdðtÞj; dðtÞ5 displacement time series
(PGD)
1=3
Id Compound displacement-related intensity PGD 3 td
measure (Riddell and Garcia 2001)
Period-dependent GM intensity measures
Existing Spectral acceleration (SA) Spectral acceleration PSAðTÞ;
h T 5 isolation
i. period; PSA 5 pseudoacceleration
Tf 50:5s
Effective peak acceleration Effective peak acceleration (Applied avg ðPSAÞj T 50:1s
2:5; PSA 5 pseudoacceleration
i
(EPA) Technology Council 1978) Ð Tf 5 0:5s
Acceleration spectrum Acceleration spectrum intensity Ti 5 0:1s PSAðj 5 5%, TÞdT; PSA 5 pseudoacceleration
intensity (ASI) (Von Thun et al. 1988) Ð Tf 5 2:5s
Velocity spectrum intensity Velocity spectrum intensity Ti 5 0:1s SVðj 5 5%, TÞdT; SV 5 actual velocity
(VSI) (Von Thun et al. 1988) Ð Tf 5 2:5s
Housner intensity (HI) Housner intensity (Housner 1952). Ti 5 0:1s PSVðj 5 5%, TÞdT; PSV 5 pseudovelocity
Ð Tf 5 1:25T
Proposed Modified acceleration Modified acceleration spectrum intensity Ti 5 0:5T PSAðj 5 5%, TÞdT;
spectrum intensity (MASI) PSA 5 pseudoacceleration
Ð Tf 5 1:25T
Modified velocity spectrum Modified velocity spectrum intensity Ti 5 0:5T SVðj 5 5%, TÞdT; SV 5 actual velocity
intensity (MVSI) Ð Tf 5 1:25T
Modified Housner intensity Modified Housner intensity Ti 5 0:5T PSVðj 5 5%, TÞdT; PSV 5 pseudovelocity
(MHI)

various IMs is presented in a graphical manner to compare the ef- P P P

n ðln IM  ln MIDÞ 2 ln IM ln MID
ficiency of each IM to relate the seismic response of the SIBs r ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
h P P 2 ih P P 2 i
n ðln IMÞ2 2 ln IM n ðln MIDÞ2 2 ln MID

MID ¼ a IMb ð2Þ ð3Þ

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 Although the current study concentrates on finding the optimal IMs purpose, an isolation system with Qd =W 5 0:09 is selected and an-
for the response of the SIBs by comparing the correlation coef- alyzed for isolation periods of 2.5, 3.0, 3.5, and 4.0 s. Figs. 5(a and b)
ficients between pulse-like and ordinary records, seismic response display the variation of r as a function of the isolation period for
of the SIBs in terms of the mean MIDs obtained from analyses is pulse-like and ordinary records, respectively. For the particular
also compared with the differences between the response of pulse- isolators considered, the MVSI gives the best correlation with the
like and ordinary records. Fig. 4 shows the variation of the mean MID. However, the degree of correlation slightly decreases with
MIDs for pulse-like and ordinary records with a changing Qd =W increasing isolation period, T, for the MVSI with pulse-like records
ratio and isolation period T. It is clear that pulse-like records result in [Fig. 5(a)]. On the other hand, correlation of the MSVI is almost not
larger isolator displacements compared with ordinary ones. sensitive to any change in the isolation period for ordinary records.
Change in correlation of the MVSI with the MID can be negligible
under an increasing isolation period for ordinary records. The MVSI
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Sensitivity to Varying Isolation Period, T is followed by the HI in terms of correlation with the MID among the
period-dependent IMs. The correlation coefficient of the PGV is not
In this section, the sensitivity to the varying isolation period, T, of the affected by any change in the isolation period for both of the ground
correlation of the MID with the considered IMs is studied. For this motion bins. Fig. 5(b) also demonstrate that the PGD might be
considered a proper IM for predicting the MID of SIBs subjected to
ordinary records; however, it is the worst IM among the investigated
ones for pulse-like records [Fig. 5(a)]. A decrease in the correlation
of the MID with the MASI, MHI, and SA by increasing the isola-
tion period is more apparent. The EPA and ASI have a very close
correlation with the MID, which has a similar tendency with
acceleration-related IMs. This is an expected result because of their
perfect correlation among each other as well as the definitions
of EPA and ASI, whose effective period range (Ti 5 0:1 s and
Tf 5 0:5 s) is in the acceleration sensitive region. In Fig. 5(a), the
correlation of the MHI gets worse compared with the HI for pulse-
like GMs as the isolation period, T, increases. The period range
employed in calculating the MHI and the HI is the main reason for
the variation. Therefore, the period range used in the definition of the
Fig. 4. Mean maximum isolator displacement of seismic-isolated MHI is ineffective for pulse-like GMs and higher isolation periods.
bridges for pulse-like and ordinary records The SA has an acceptable level of correlation coefficients for
ordinary GMs. Although the SA results in a good correlation

Fig. 5. Sensitivity to varying isolation period, T, on the correlation of maximum isolator displacement and intensity measures: (a) pulse-like records;
(b) ordinary records

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 coefficient for a smaller isolation period for pulse-like GMs, the regardless of the ground motion bin. Variation in the correlation of
correlation of the SA with the MID of SIBs reduces sharply with the PGV, PGD, and MSVI because of change in the Qd =W ratio is
increasing isolation period. Another inference from Fig. 5(a) is that minimal, and therefore it can be considered negligible. Hence, the
for all period-dependent and acceleration-related IMs, an increasing sensitivity to varying the Qd =W ratio on the correlation of the IMs
isolation period results in a decreasing correlation with the MIDs of with the MIDs is of less importance compared with that of the
SIBs for pulse-like records. However, the trend is just the opposite isolation period.
for displacement-related IMs. Sensitivity to the varying isolation Mean and standard deviation results of the correlation coefficient
period on the correlation coefficient for velocity-related IMs is of the IMs computed for the 16 SIBs with varying isolation period,
negligible, especially for PGV. On the other hand, Fig. 5(b) shows T, and characteristic strength, Qd =W are presented in Fig. 7 for both
that the change in the isolation period for ordinary records has almost ordinary and pulse-like records. There is a significant difference
no effect on the correlation coefficient of IMs. This is because of the between the results of ordinary and pulse-like records in terms of the
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negligible amount of variation in the spectral shape of ordinary GMs mean correlation coefficient of displacement-related IMs. Although
in the long period range, at which SIBs are effective. As shown in displacement-related IMs have an acceptable level of correlation
Fig. 3, the standard deviation of ordinary GMs is in the negligible (r 5 0:650 for PGD) for ordinary records, they have the worst
order in the long-period range. correlation coefficient (r 5 0:275 for PGD) for pulse-like ones
among the other IMs. Although the mean correlation coefficient
of the EPA, ASI (r 5 0:452), and the acceleration-related IMs for
Sensitivity to Varying Qd =W pulse-like records are better than the ones for ordinary records
(r 5 0:280), their overall correlation is not sufficient for estimating
In this section, the sensitivity to the varying characteristic strength of the response of SIBs. This finding is consistent with the findings of
isolator, Qd =W, on the correlation of the MID with the considered Riddell (2007), because IMs related to the acceleration sensitive
IMs is studied. For this purpose, the isolation period, T, is kept region of the spectrum does not correlate well with the response of
constant (T 5 0:3 s), while the Qd =W ratio varies from 0.03 to 0.09. flexible systems, where SIBs are considered to be one of the flexible
Figs. 6(a and b) show the variation of r as a function of the Qd =W systems. The PGV has the best mean correlation coefficient among
ratio for both pulse-like and ordinary records, respectively. Similar the velocity-related IMs, especially for pulse-like records (r 5 0:71).
to Fig. 5, the MVSI is the best IM that correlates well with the MID of The mean correlation coefficient of the MVSI has the highest
the SIBs under investigation, as shown in Figs. 6(a and b) for both ranking when compared with the other IMs for both ordinary
pulse-like and ordinary records, respectively. The MSVI is followed (r 5 0:761) and pulse-like records (r 5 0:755). Although the VSI,
by PGV for pulse-like records, while it is followed by PGD for MHI, and SA have acceptable levels of mean correlation coefficients
ordinary records among the period-independent IMs. Furthermore, for ordinary records, they are not satisfactory for pulse-like records,
these IMs are almost not sensitive to any change in the Qd =W ratio, especially for SA (r 5 0:50).

Fig. 6. Sensitivity to varying Qd =W on the correlation of the maximum isolator displacement and intensity measures: (a) pulse-like records;
(b) ordinary records

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Fig. 7. Effect of GM type on the mean correlation of maximum isolator displacement and GM intensity measures

Conclusions • Although the sensitivity to varying Qd =W on correlation of IMs

and MIDs can be negligible, it is relatively more pronounced
This study investigated the correlation of widely used ground mo- when pulse-like records are of concern.
tion IMs with MIDs of SIBs. Hence, a series of nonlinear dynamic
analyses were conducted using near-field GMs classified as pulse-
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