613_earthquake Engineering and Structural Dynamics by Wiryanto Dewobroto

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EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2007; 36:13471362

Published online 15 March 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/eqe.684

A comparison of single-run pushover analysis techniques forseismic assessment of bridges

R. Pinho1,,, C. Casarotti2 and S. Antoniou3

1European Centre for Training and Research in Earthquake Engineering (EUCENTRE), Via Ferrata 1,

Pavia 27100, Italy2Structural Mechanics Department, University of Pavia, Via Ferrata 1, Pavia 27100, Italy

3SeismoSoftSoftware Solutions for Earthquake Engineering, Chalkida, Greece

SUMMARY

Traditional pushover analysis is performed subjecting the structure to monotonically increasing lateralforces with invariant distribution until a target displacement is reached; both the force distribution andtarget displacement are hence based on the assumption that the response is controlled by a fundamentalmode, that remains unchanged throughout.

However, such invariant force distributions cannot account for the redistribution of inertia forces causedby structural yielding and the associated changes in the vibration properties, including the increase ofhigher-mode participation. In order to overcome such drawbacks, but still keep the simplicity of usingsingle-run pushover analysis, as opposed to multiple-analyses schemes, adaptive pushover techniques haverecently been proposed.

In order to investigate the effectiveness of such new pushover schemes in assessing bridges subjectedto seismic action, so far object of only limited scrutiny, an analytical parametric study, conducted on

a suite of continuous multi-span bridges, is carried out. The study seems to show that, with respect toconventional pushover methods, these novel single-run approaches can lead to the attainment of improvedpredictions. Copyright q 2007 John Wiley & Sons, Ltd.

Received 21 August 2006; Revised 1 January 2007; Accepted 29 January 2007

KEY WORDS: displacement based; adaptive pushover; seismic analysis; bridges; DAP; FAP

1. INTRODUCTION

The term pushover analysis describes a modern variation of the classical collapse analysis

method, as fittingly described by Kunnath [1]. It refers to an analysis procedure whereby an

Correspondence to: R. Pinho, European Centre for Training and Research in Earthquake Engineering (EUCENTRE),Via Ferrata 1, Pavia 27100, Italy.

E-mail: [email protected]

Contract/grant sponsor: European Commission

Copyright q 2007 John Wiley & Sons, Ltd.


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1348 R. PINHO, C. CASAROTTI AND S. ANTONIOU

incremental-iterative solution of the static equilibrium equations has been carried out to obtain

the response of a structure subjected to monotonically increasing lateral load patterns. Whilst the

application of pushover methods in the assessment of building frames has been extensively verified

in the recent past, nonlinear static analysis of bridge structures has been the subject of only limited

scrutiny [2]. Since bridges are markedly different structural typologies with respect to buildings,observations and conclusions drawn from studies on the latter cannot really be extrapolated to the

case of the former, as shown by Fischinger et al. [3], who highlighted the doubtful validity of

systematic application of standard pushover procedures to bridge structures.

Recent years have also witnessed the development and introduction of an alternative type of

nonlinear static analysis[410], which involve running multiple pushover analyses separately, each

of which corresponding to a given modal distribution, and then estimating the structural response

by combining the action effects derived from each of the modal responses (i.e. each displacement

force pair derived from such procedures does not actually correspond to an equilibrated structural

stress state). As highlighted by some of their respective authors, the main advantage of this

category of static analysis procedures is that they may be applied using standard readily available

commercial software packages, since they make use of conventional analysis types. The associated

drawback, however, is that the methods are inevitably more complex than running a single pushover

analysis, as noted by Maison[11], for which reason they do not constitute the scope of the current

work, where focus is instead placed on single-run pushover analysis procedures, the simplicity

of which renders them an even more appealing alternative, or complement, to nonlinear dynamic

analysis [12].

In this work an analytical parametric study is thus conducted applying different single-run

pushover procedures, either adaptive or conventional, on a number of regular and irregular con-

tinuous deck bridges subjected to an ensemble of ground motions. The effectiveness of each

methodology in reproducing both global behaviour and local phenomena is assessed by comparing

static analysis results with the outcomes of nonlinear time-history runs. Adaptive pushovers are

run in both their force-based [1317] and displacement-based [18, 19] versions. With respect to

the latter, it is noted that, contrary to what happens in a non-adaptive pushover, where the appli-cation of a constant displacement profile would force a predetermined and possibly inappropriate

response mode that could conceal important structural characteristics and concentrated inelastic

mechanisms at a given location, within an adaptive framework a displacement-based pushover

is entirely feasible, since the loading vector is updated at each step of the analysis according to

the current dynamic characteristics of the structure. The interested reader is referred to some of

the aforementioned publications for details on the underlying formulations of adaptive pushover

algorithms.

It is observed that whilst for regular bridge configurations some conventional single-run pushover

methods may manage to provide levels of accuracy that are similar to those yielded by their more

evolved adaptive counterparts, when irregular bridges are considered the advantages of using the

latter become evident. In particular, the displacement-based adaptive pushover (DAP) algorithm is

shown to lead to improved predictions, which match more closely results from nonlinear dynamicanalysis.

2. PARAMETRIC INVESTIGATION: CASE-STUDIES AND MODELLING ASSUMPTIONS

The parametric study has considered two bridge lengths (four and eight 50 m spans), with regular,

irregular and semi-regular layout of the pier heights and with two types of abutments; (i) continuous

Copyright q 2007 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2007; 36:13471362

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SEISMIC ASSESSMENT OF BRIDGES 1349

Label 213

Label 3332111

Label 2331312

Label 2222222

Label 123

Label 222

SHORT BRIDGES LONG BRIDGES

REGULAR

SEMIREGULAR

IRREGULAR

Figure 1. Analysed bridge configurations.

0.0

1.0

2.0

3.0

4.0

0.0 0.7 1.4 2.1 2.8 3.5

Natural Period (s)

Pseudo-Acceleration(g)

0

30

60

90

120

0.0 0.7 1.4 2.1 2.8 3.5

Natural Period (s)

SpectralDisplacement(cm)

Figure 2. Elastic pseudo-acceleration and displacement spectra.

deck-abutment connections supported on piles, exhibiting a bilinear behaviour (type A bridges),

and (ii) deck extremities supported on pot bearings featuring a linear elastic response (type Bbridges). The total number of bridges is therefore 12, as shown in Figure 1, where the label

numbers 1, 2, 3 characterize the pier heights of 7, 14 and 21 m, respectively.

Since the nonlinear response of structures is strongly influenced by ground motion characteristics,

a sufficiently large number of records needs to be employed so as to bound all possible structural

responses. The employed set of seismic excitation, referred to as LA, is thus defined by an ensemble

of 14 records selected from a suite of historical earthquakes scaled to match the 10% probability of

exceedance in 50 years (475 years return period) uniform hazard spectrum for Los Angeles [20].

The ground motions were obtained from California earthquakes with a magnitude range of 67.3,

recorded on firm ground at distances of 1330 km. The elastic (5% damped) pseudo-acceleration

and displacement response spectra of the records are presented in Figure 2, where the thicker line

represents the median spectrum, and the bounding characteristics of the records are summarized

in Table I, where the significant duration is defined as the interval between the build up of 5 and95% of the Total Arias Intensity [21].

The finite element package used in the present work, SeismoStruct [22], is a fibre-element-

based program for seismic analysis of framed structures, which can be freely downloaded from

the Internet. The program is capable of predicting the large displacement behaviour and the

collapse load of framed structures under static or dynamic loading, duly accounting for geometric

nonlinearities and material inelasticity. Its accuracy in predicting the seismic response of bridge


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Table I. Bounding characteristics of the employed set of records.

Peak Peak response 5% Arias Significant Totalground acceleration intensity duration teff duration ttot teff/ttotal

acceleration (g) (g) threshold (s) (s) (s) (%)

Min 0.30 0.84 1.25 5.3 14.95 9Max 1.02 3.73 12.5 19.66 80.00 52

structures has been demonstrated through comparisons with experimental results derived from

pseudo-dynamic tests carried out on large-scale models [23].

The piers are modelled through a 3D inelastic beamcolumn element, with a rectangular hollow

section of 2.0 4.0 m and a wall thickness of 0.4 m; the constitutive laws of the reinforcing steel

and of the concrete are, respectively, the MenegottoPinto[24]and Manderet al.[25]models. The

deck is a 3D elastic nonlinear beamcolumn element, with assigned sectional properties, to which

a 2% Rayleigh damping (for the first transversal modes of the structure) was also associated. The

deck-piers connections are assumed to be hinged (no transmission of moments), transmitting only

vertical and transversal forces, in order to model the engaging of the sub- and super-structure in

the transversal direction by mean of shear keys. Further details can be found in [26].

Equivalent linear springs are used to simulate the abutment restraints, which should reflect the

dynamic behaviour of the backfill, the structural component of the abutment and their interaction

with the soil (type A bridges). Employed stiffness values for the bilinear and linear models were

found, respectively, in Goel and Chopra [27] and from an actual bridge with similar dimensions

and loads (type B bridges).

3. PARAMETRIC INVESTIGATION: ANALYSES AND RESULTS POST-PROCESSING

The response of the bridge models is estimated through the employment of (i) incremental dynamic

analysis (IDA), (ii) force-based conventional pushover with uniform load distribution (FCPu),

(iii) force-based conventional pushover with first mode proportional load pattern (FCPm), (iv) force-

based adaptive pushover (FAP) and (v) displacement-based adaptive pushover (DAP).

Results are presented in terms of the bridge capacity curve, i.e. a plot of a reference point

displacement versus total base shear and of the deck drift profile. Following Eurocode 8 [28]

recommendations, the independent damage parameter selected as reference is the displacement of

the node at the centre of mass of the deck: each level of inelasticity (corresponding to a given

lateral load level or to a given input motion amplitude) is represented by the deck centre drift, and

per each level of inelasticity the total base shear Vbase and the displacements i at the other deck

locations are monitored.

The true dynamic response is deemed to be represented by the results of the IDA, which is aparametric analysis method by which a structural model is subjected to a set of ground motions

scaled to multiple levels of intensity, producing one or more curves of response, parameterized

versus the intensity level [29]. A sufficient number of records is needed to cover the full range of

responses that a structure may display in a future event. An IDA curve set, given the structural

model and a statistical population of records, can be marginally summarized (with respect to the

independent parameter) by the median, the 16 and 84% fractiles IDA curves.


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=

1,IDA

1

=1

=

2,IDA

=2

4,IDA

=4

4

=

3,IDA

=3

3

2

Figure 3. Normalized transverse deformed pattern.

Comparing pushover results with IDA output, obtained from averaged statistics and fractile

percentiles of all dynamic cases, allows avoiding the unreliable influence of single outlier values,

which, statistically speaking, have reduced significance with respect to the population. From this

point of view, robust measures of the means of the scattered data are used which are less sensitiveto the presence of outliers, such as the median value, defined as the 50th percentile of the sample,

which will only change slightly if a large perturbation to any value is added, and the fractiles as

a measure of the dispersion.

Results of pushover analyses are compared to the IDA median value, for the 14 records, of each

response quantity of interest; pier displacements (i ) and base shear forces (Vbase):

i,IDA= medianj =1:14[i,j IDA] (1a)

Vbase,IDA= medianj =1:44[Vbase,j IDA] (1b)

Results of adaptive pushover analyses with spectrum scaling, which thus become also record-

specific, are statistically treated in an analogous way: medians of each response quantity represent

that particular pushover analysis (i.e. FAP or DAP) with spectrum scaling.

The results of each type of pushover are normalized with respect to the corresponding exact

quantity obtained from the IDA medians, as schematically illustrated in Figure 3, and translated

in the relationships (2a) and (2b). Representing results in terms of ratios between the approximate

and the exact procedures, provides an immediate indication of the bias in the approximate

procedure: the ideal target value of each pushover result is always one.

i,PUSHOVERtype=i,PUSHOVERtype

i,IDA

ideally

1 (2a)

Vbase,PUSHOVERtype=V

base,PUSHOVERtypeVbase,IDA

ideally

1 (2b)

Moreover, normalizing results renders also comparable all deck displacements (i.e. all nor-

malized displacements have the same unitary target value), and thus a bridge index (BI) can be

defined as a measure of the precision of the obtained deformed shape. Per each level of inelasticity,

the BI is computed as the median of normalized results over the m deck locations, together with


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0 0.035 0.07 0.105 0.14

0

1

=

=

=

=

median

-0.5 4,IDA

4

=4

1,IDA

1

=1

3,IDA

3

=3

2,IDA

2

=2

BI

medi

3

2

4

1

centralnode

Figure 4. Graphical representation of normalized transverse displacements.

the standard deviation , to measure the dispersion of the results with respect to the median

BIPUSHOVERtype= mediani =1:m(i,PUSHOVERtype) (3a)

PUSHOVERtype=

m

i =1(i,PUSHOVERtype BIPUSHOVERtype)

2

m 1

0.5

(3b)

The results obtained above can then be represented in plots such as that shown in Figure 4,

where each increasing level of inelasticity (here represented by the deck central node displacement,

indicated in the horizontal axis) of the BI, computed through Equation (3a), is represented with

black-filled symbols, whilst the grey empty marks represent the values of which the BI is themedian, i.e. the normalized deck displacements given by Equation (2a). In this manner, the extent

(in terms of mean and dispersion) to which each pushover analysis is able to capture the deformed

pattern of the whole bridge, with respect to the IDA average displacement values, at increasing

deformation levels is immediately apparent.

4. PRELIMINARY STUDY: SELECTION OF BEST PUSHOVER OPTIONS

According to Eurocode 8 [28] pushover analysis of bridges must be performed by pushing the

entire structure (i.e. deck and piers, see Figure 5 left) with the two aforementioned prescribed

load distributions (uniform load distribution and first mode proportional load pattern). In this

preliminary study, the possibility of pushing the deck alone (Figure 5, right) has been investigated;the choice of pushing just the deck was considered observing that, at least for the case-studies

considered, the superstructure is the physical location where the vast majority of the inertia mass

is found.

An additional preliminary investigation regarded the understanding of which adaptive pushover

modality (with or without spectral amplification) would lead to the best results. Including spectrum

scalingin the computation of the load vector allows accounting for the influence that the frequency


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Figure 5. Pushing deck and piers (left) and pushing just the deck (right) loading scheme options.

(a)

(c) (d)

(b)

Figure 6. Capacity curve results.

content of a given input motion has on the contributions of different modes: the spectral ordinate

at the instantaneous period of each mode is employed to weigh the contribution of such mode to

the incremental load shape at any given analysis step (the reader is referred to [19, 30] for further

details).


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Bridge A123 FAPnss

Bridge A123 DAPnss Bridge A123 DAPssDBridge A123 DAPss

Bridge B3332111 FAPnss

Bridge B3332111 DAPnss Bridge B3332111 DAPss Bridge B3332111 DAPssD

Bridge B3332111 FAPss Bridge B3332111 FAPssD

Bridge A123 FAPss Bridge A123 FAPssD

0 0.035 0.07 0.105 0.14 0.175 0.210

0.5

1

1.5

Deck Displ. @ Central Pier Top (m)

0 0.035 0.07 0.105 0.14 0.175 0.21



0 0.035 0.07 0.105 0.14 0.175 0.21

Deck Displ. @ Central Pier Top (m)0 0.035 0.07 0.105 0.14 0.175 0.21


0 0.035 0.07 0.105 0.14 0.175 0.21


0 0.035 0.07 0.105 0.14 0.175 0.21


0

0.5

1

1.5

0

0.5

1

1.5

0

0.5

1

1.5

0

0.5

1

1.5

0

0.5

1

1.5

0

0.5

1

1.5

0

0.5

1

1.5

0

0.5

1

1.5

0

0.5

1

1.5

1

2

3

0 0.045 0.09 0.135 0.18 0.225 0.27


0 0.045 0.09 0.135 0.18 0.225 0.27


0 0.045 0.09 0.135 0.18 0.225 0.27


0 0.045 0.09 0.135 0.18 0.225 0.27


0 0.045 0.09 0.135 0.18 0.225 0.27


0 0.045 0.09 0.135 0.18 0.225 0.27

0.5

1

1.5

2

2.5

3

(a) (b) (c)

(f)(e)(d)

(g) (h) (i)

(k)(j) (l)

Figure 7. Prediction of the deformed pattern: BI and relative scatter, plottedseparately for each pushover type.

Table II. Global averages of the summaries of results for different adaptive methods.

Bridge index Dispersion Normalized base shear

Mean Min Max Mean Min Max Mean Min Max

FAPnss 0.77 0.67 0.92 0.28 0.20 0.38 0.95 0.85 1.09FAPss 0.86 0.76 0.99 0.23 0.14 0.35 1.00 0.90 1.12FAPssD 0.88 0.78 1.01 0.22 0.13 0.34 0.99 0.89 1.10

DAPnss 1.10 0.95 1.22 0.38 0.27 0.49 1.47 1.20 1.82DAPss 0.84 0.74 0.96 0.18 0.12 0.26 1.08 0.96 1.24DAPssD 0.87 0.78 0.99 0.19 0.14 0.27 1.03 0.95 1.13


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(a) (b)

Figure 8. Capacity curve results.

Within the above framework, FAP and DAP analyses have thus been performed with and without

spectral scaling and pushing both deck and piers or just the deck, for a total of four types of FAP

and DAP. In the following, such analyses will be referred to as FAPnss/DAPnss, FAPss/DAPss,

FAPss-D/DAPssD, respectively, with the nss/ss suffix standing for the exclusion/inclusion of

spectrum scaling, and the D suffix meaning that only the deck is pushed. Results are presented

in terms of the bridge capacity curve (reference point displacement versus total base shear) and

of the deck drift profile.

The following observations were withdrawn from capacity curve plots and the prediction

of the total base shear (Figure 6): (i) generally DAPnss strongly overestimates the base shear

across the whole deformation range (Figure 6(b) and (d)), (ii) such over-prediction is reducedif spectrum scaling is included (DAPss), particularly if only the deck is pushed (DAPssD);

(iii) FAPnss capacity curve is generally quite close to FAPss, even if it is generally lower

(Figure 6(a) and (c)).

As for what concerns the prediction of the inelastic displacement pattern, it was noted that the

drift profiles obtained from the adaptive algorithms were generally very similar to those obtained

from the nonlinear dynamic analyses, with a general trend of underestimation of displacements

(Figure 7(e)(l)), except for DAPnss, that often over-predicts the response and lead also to numerical

instability (analysis reproduced in Figure 7(d) and (j) could not be carried out for the entire target

displacement range).

In addition to the percentage under/overprediction of the deformed shape, it is important to

check the relative scatter, because a good BI estimate associated however to a large scatter means

simply that along the deck all predicted displacements are very small or very large with respect tothe corresponding IDA results. On the contrary, a less precise prediction of the BI coupled with a

lower scatter may indicate a more stable, and thus preferred, estimate of the displacements along

the deck. Table II summarizes global averages of means, maximum and minimum values of the BI

(with the corresponding dispersion) and of the normalized total base shear, over the entire bridge

ensemble. It is noted that (i) DAPnss is the worst pushover option, showing significant scatter and

overestimation (especially for base shear estimates), and (ii) the option of pushing just the deck


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Bridge A2331312 FCPm

Bridge A2331312 FCPu

Bridge A2331312 FAP

Bridge A2331312 DAP

Bridge B123 FCPu

Bridge B123 FCPm

0 0.02 0.04 0.06 0.08 0.1 0.120

0.5

1

1.5

2

0

0.5

1

1.5

2

0

0.5

1.5

1

0

0.5

1.5

1

0123456


0 0.02 0.04 0.06 0.08 0.1 0.12Deck Displ. @ Central Pier Top (m)



0 0.02 0.04 0.06 0.08 0.1 0.12


0 0.02 0.04 0.06 0.08 0.1 0.12


0 0.02 0.04 0.06 0.08 0.1 0.12


0 0.02 0.04 0.06 0.08 0.1 0.12






0

1

0

0.5

1

1.5

2 Bridge A213 FAP

Bridge A213 DAP

Bridge A213 FCPu

Bridge A213 FCPm

0

0.5

1

1.5 Bridge B123 FAP

Bridge B123 DAP

0

0.5

1

1.5

0

0.5

1

1.5

2

0

0.5

1

1.5

0

0.5

1

1.5

-0.5

(a)

(e)

(h)

(j) (k) (l)

(i)(g)

(d)

(b) (c)

(f)

Figure 9. Prediction of the deformed pattern: BI and relative scatter, plottedseparately for each pushover type.

affects only marginally the predictions (whilst in terms of stability and velocity of the analyses it

proved to be very advantageous).

In conclusion, the best performance in terms of both shear and deformed shape predictions was

given by those adaptive techniques that included spectrum scaling and where the loads were applied

to the deck alone, this being thus the reason for which such analysis options have been adopted in

the subsequent parametric study, where comparisons with conventional pushover procedures arecarried out.

5. PARAMETRIC STUDY: RESULTS OBTAINED

A myriad of capacity curve plots, obtained for the different pushover analyses and compared with

the IDA envelopes, were derived in this parametric study, the full collection of which can be


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Table III. Global averages of the obtained results.

Bridge index Dispersion Normalized base shear

Mean Min Max Mean Min Max Mean Min Max

RegularFCPm 0.67 0.52 0.80 0.34 0.27 0.40 0.81 0.72 0.93FCPu 1.07 0.91 1.27 0.19 0.12 0.26 1.03 0.92 1.21FAP 0.93 0.81 1.10 0.19 0.11 0.26 0.94 0.87 1.05DAP 0.79 0.70 0.89 0.17 0.12 0.22 0.94 0.88 1.02

Semi-regularFCPm 0.65 0.55 0.79 0.70 0.60 0.84 0.70 0.62 0.84FCPu 0.79 0.70 0.94 0.33 0.24 0.51 0.99 0.89 1.14FAP 0.87 0.78 0.99 0.33 0.21 0.53 0.97 0.87 1.10DAP 0.83 0.75 0.94 0.22 0.18 0.33 1.03 0.96 1.11

Irregular

FCPm 0.89 0.64 1.15 1.33 0.86 1.77 0.88 0.74 1.08FCPu 0.74 0.64 0.87 0.19 0.14 0.25 1.06 0.96 1.17FAP 0.82 0.74 0.94 0.15 0.08 0.22 1.04 0.94 1.15DAP 0.98 0.88 1.13 0.19 0.11 0.25 1.13 1.01 1.27

consulted in [26]. Herein, and for reasons of succinctness, only the most pertinent observations,

together with some representative plots, are included:

(i) FCPm tends to underestimate the stiffness of the bridge, mainly due to the fact that,

for the same base shear, central deck forces are generally higher compared to the other

load patterns, thus resulting in larger displacement at that location; FCPm capacity curveconstitutes an evident lower bound, often already in the elastic range, where one would,

at least in principle, expect a correct prediction of the response (see Figure 8).

(ii) On occasions, a hardening effect in the pushover curve occurs: once piers saturate their

capacity, the elastic abutments absorb the additional seismic demand, fully transmitted

by the much stiffer and elastic superstructure, thus proportionally increasing shear re-

sponse and hence hardening the capacity curve. This effect, observed also in the dynamic

analyses, is sometimes reproduced only by the DAP procedure, as can be observed in

Figure 8(b).

(iii) The adaptive techniques show often capacity curves quite close one to the other, and very

close to FCPu (Figure 8(a)). In the elastic range, and as expected, the adaptive capacity

curves lie within FCPm and FCPu curve, the same often occurring also in the inelastic

range (Figure 8(a)). In some cases, however, adaptive load patterns lie above the FCPucapacity curve.

Examining instead the predictions of inelastic deformation patterns, the aforementioned under-

performance of FCPm is further confirmed, with poor predictions of deformed shape and/or large

scatter being observed (Figure 9(a)(c)). On the other hand, the drift profiles obtained with adaptive

methods seem to feature the best agreement with those obtained from the nonlinear time-history


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0 50 100 150 200 250 300 350 4000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Inelastic Deformed Pattern - BridgeB3332111

Deck Node Location (m)

DeckNodeDisplacement

(m)

DAPFAPFCPuFCPmIDA

0 50 100 150 200 250 300 350 4000

0.1

0.2

0.3

0.4

0.5

Inelastic Deformed Pattern - BridgeB3332111D


DAPFAPFCPuIDA

0 50 100 150 200 250 300 350 4000

0.05

0.1

0.15Inelastic Deformed Pattern - BridgeA2331312


DeckNodeDisplacement(m)



DeckNodeDisplacement

(m)

DAPFAPFCPuFCPmIDA

0 50 100 150 200 250 300 350 4000

0.05

0.1

0.15

Inelastic Deformed Pattern - BridgeA2331312D


DAPFAPFCPuFCPmIDA

0 50 100 150 2000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

BridgeB123



DAPFAPFCPuFCPmIDA

0 50 100 150 2000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

BridgeB123


DAPFAPFCPuFCPmIDA

(a) (b)

(c) (d)

(e) (f)

Figure 10. Representative examples of deformed pattern results.


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analyses (Figure 9(g)(l)), with DAP seemingly presenting the lower scatter. These observations

may be further confirmed through examination of Table III, where averages of means, maximum

and minimum values of the BI (plus corresponding dispersion) as well as of the normalized total

base shear, over the entire bridge ensemble, are given. It is noted that:

(i) FCPm heavily underestimates predictions of both deformed shape and base shear, featuring

also excessively high BI dispersion values. This pushover modality is, therefore, in the

opinion of the authors, not adequate for seismic assessment of bridges.

(ii) FCPu performs rather well for regular bridges (it leads to the best predictions in this

category), however, its performance worsens considerably as the irregularity of the case-

study structures increases.

(iii) FAP leads to averagely good predictions throughout the entire range of bridge typology

(clearly with better results being obtained for regular bridges), noting however that a

relatively high value of dispersion is observed in the case of semi-regular configurations.

(iv) DAP produces also averagely good results throughout the entire set of bridges considered

in the study, featuring in particular a very high accuracy in the case of irregular bridges

(most regrettably, such high accuracy is conspicuously not present in the case of regular

structures). The values of dispersion are very low, independently of bridge regularity.

Finally, and for the sake of completeness, Figure 10 shows the inelastic deformed pattern of

three bridge configurations at two different levels of inelasticity, with the objective of rendering

somewhat more visual the statistical results discussed previously. It is readily observed how adaptive

methods, and particularly DAP, are able to represent the inelastic behaviour of the bridge with a

higher level of accuracy, when compared with conventional methods.

6. CONCLUDING REMARKS

In the framework of current performance-based design trends, which require, as a matter of

necessity, the availability of simple, yet accurate methods for estimating seismic demand on

structures considering their full inelastic behaviour, a study has been carried out to gauge the

feasibility of employing single-run pushover analysis for seismic assessment of bridges, which

have been so far the object of limited scrutiny, contrary to what is the case of building frames.

Within such investigation, both conventional as well as adaptive pushover methods were used

to analyse a suite of bridge configurations subjected to an ensemble of seismic records. It is noted

that the bridges feature particularly non-standard shapes, both in terms of pier height distribution

(certainly more irregular than what is typically found in the majority of bridges/viaducts), as well

as in terms of spans length (typically, the end spans tend to be slightly shorter that their central

counterparts). Such bridge configurations were intentionally adopted so as to increase the influence

of higher modes in the dynamic response of the structures and in this way place the numericaltools under as tough as possible scrutiny.

The results of this analytical exercise show that, while on the average along regular and irregular

configurations some conventional static force-based procedures (namely, using a uniform load

distribution pattern) give results comparable to adaptive methods in estimating seismic demand

on bridges, the displacement-based variant of the adaptive method associates good predictions in

terms of both shear and deformed shape with a reduced scatter in the results. The latter has also


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proved to be most effective in representing the hardening effect that piers capacity saturation

can sometime introduce in the capacity curve. In other words, whereas the application of a fixed

displacement pattern is a commonly agreed conceptual fallacy, the present work witnesses not only

the feasibility of applying an adaptive displacement profile, but also its practical advantages, with

respect to other pushover methods.It is important to note that the inadequacy of using conventional single-run pushover analysis to

assess non-regular bridges is already explicitly recognized in Eurocode 8[28], where it is stated that

such analysis is suitable only for bridges which can be reasonably approximated by a generalized

one degree of freedom system. The code then provides additional details on how to identify the

cases in which such condition is and is not met, and advises the use of nonlinear time-history

analysis for the latter scenarios. The results of the current work seem to indicate that the use of

single-run pushover analysis might still be feasible even for such irregular bridge configurations,

for as long as a displacement-based adaptive version of the method is employed. The authors feel

that the latter could perhaps constitute an ideal alternative or complementary option to (i) the use

of nonlinear dynamic analyses, (ii) the adoption of multiple-run pushover methods or (iii) the use

of alternative definitions of reference point and force distributions, all of which might also lead to

satisfactory response predictions for irregular bridges, as shown in [2].

Finally, it is re-emphasized that the scope of this paper was confined to the verification of the

adequacy with which different single-run pushover techniques are able to predict the response of

continuous span bridges subjected to transverse earthquake excitation. The employment of such

pushover algorithms within the scope of full nonlinear static assessment procedures, such as the

N2 method [31, 32] or the Capacity Spectrum Method [33, 34], is discussed elsewhere [35, 36].

ACKNOWLEDGEMENTS

The authors are very grateful to two anonymous reviewers whose thorough and insightful reviews of aninitial version of the manuscript led to a significant improvement of the paper. Part of the current workhas been carried out under the financial auspices of the European Commission through the FP6 IntegratedProject LESSLOSS (Risk Mitigation for Earthquakes and Landslides). Such support is also gratefullyacknowledged by the authors.

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32. Fajfar P, Gaspersic P, Drobnic D. A simplified nonlinear method for seismic damage analysis of structures. In

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34. Freeman SA. Development and use of capacity spectrum method. Proceedings of the Sixth U.S. National

Conference in Earthquake Engineering, Seattle, U.S.A., 1998.

35. Casarotti C, Pinho R. Application of an adaptive version of the capacity spectrum method to seismic design

and assessment of bridges. Proceedings of the Eighth US National Conference on Earthquake Engineering,

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EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2007; 36:13631383

Published online 19 March 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/eqe.685

Analysis of the weightiness of site effects on reinforcedconcrete (RC) building seismic behaviour: The Adra town

example (SE Spain)

Manuel Navarro1,,, Francisco Vidal2, Takahisa Enomoto3, Francisco J. Alcala4,Antonio Garca-Jerez1, Francisco J. Sanchez1 and Norio Abeki5

1Department of Applied Physics, University of Almeria, Spain2Andalusian Institute of Geophysics, University of Granada, Spain

3Department of Architecture, University of Kanagawa, Yokohama, Japan4Technical University of Catalonia, Barcelona, Spain

5Department of Architecture, University of Kanto Gakuin, Yokohama, Japan

SUMMARY

The damage distribution in Adra town (south-eastern Spain) during the 1993 and 1994 Adra earthquakes(5.0 magnitude), that reached a maximum intensity degree of VII (European Macroseismic Scale (EMSscale)), was concentrated mainly in the south-east zone of the town and the most relevant damage occurredin reinforced concrete (RC) buildings with four or five storeys. In order to evaluate the influence of groundcondition on RC building behaviour, geological, geomorphological and geophysical surveys were carriedout, and a detailed map of ground surface structure was obtained. Short-period microtremor observationswere performed in 160 sites on a 100 m 100 m dimension grid and Nakamuras method was applied inorder to determine a distribution map of soil predominant periods. Shorter predominant periods (0.10.3 s)were found in mountainous and neighbouring zones and larger periods (greater than 0.5 s) in thickerHolocene alluvial fans. A relationship T= (0.0490.001)N, where T is the natural period of swayingmotion and Nis the number of storeys, has been empirically obtained by using microtremor measurementsat the top of 38 RC buildings (ranging from 2 to 9 storeys). 1-D simulation of strong motion on differentsoil conditions and for several typical RC buildings were computed, using the acceleration record in Adratown of the 1993 earthquake. It is noteworthy that all the aforementioned results show the influence ofsite effects in the degree and distribution of observed building damage. Copyright q 2007 John Wiley &Sons, Ltd.

Received 15 June 2006; Revised 30 December 2006; Accepted 29 January 2007

KEY WORDS: soil conditions; landform classifications; S-wave shallow structure; microtremors; site

effects; dynamic behaviour of RC buildings; Adra earthquake; strong motion simulation

Correspondence to: Manuel Navarro, Department of Applied Physics, University of Almeria, 04120, Almeria, Spain.E-mail: [email protected]

Contract/grant sponsor: CICYT; contract/grant numbers: AMB99-0795-C02-02, REN2003-08159-C02

Copyright q 2007 John Wiley & Sons, Ltd.


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1364 M. NAVARRO ET AL.

1. INTRODUCTION

The softness of the ground surface and the thickness of surface sediments have been observed

as two important local geological factors that affect the level of earthquake shaking. Their local

variations can lead to spatial seismic intensity differences and may have a remarkable influence onthe level of building damage and on significant earthquake damage distribution even in the cases

of moderate earthquakes.

Since the 1985 Michoacan earthquake (Mexico), building damage has been studied analysing

the contribution of site response [1], in particular when resonant phenomenon appears. This

strong influence of site effects on damage distribution has produced extreme consequences, for

example, in the earthquakes of Leninakan, Armenia (1988), or Loma Prieta, California (1989).

More recent destructive earthquakes (e.g. Northridge, California 1994; Kobe, Japan 1995; Izmit,

Turkey 1999 or ChiChi, Taiwan 1999) have shown how unconsolidated soil and sediment deposits

were responsible for important modifications in ground motion amplitude in a range of periods

and how building damage increases when the fundamental vibration period of the building is

close to the predominant period of the soil motion [2]. In the case of the Izmit earthquake on

17 August 1999, the non-uniformity in earthquake damage distribution indicates the site effects

associated with alluvial basins such as motion amplification and low-frequency enhancement,

unfavourable to the structures of longer periods [3]. In Adapazari city, these authors report that

five to six storey buildings located over deep alluvial soil were the most adversely affected by the

earthquake.

The relationship between soil amplification and the level of damage has been recently confirmed

for several large earthquakes (Mw>6.5) and analysed with regard to deep soil structures and

tall buildings. For example, in the 1948 Fukui (Japan) catastrophic earthquake, the degree and

distribution of damage were strongly correlated with local soil conditions of the Fukui basin,

where the ratio of totally collapsed houses ranged from 60 to almost 100% [4]. In the 1967

Caracas (Venezuela) earthquake it was noticed that the most affected areas were linked to geological

characteristics like the thickness of the quaternary alluvial[5]. In the 1999 Izmit (Turkey) earthquakethe varying ground characteristics underlying Adaparazi city played a dominant role in the extent

and distribution of ground motion intensity and in the consequent building damage [3, 6]. In the

1999 ChiChi (Taiwan) earthquake, Seo et al.[2]found, using strong motion data, that earthquake

motions would be amplified several times in the period range from 1 to 3 s in the Taipei basin,

and such ground motion would be very effective for tall buildings.

A large number of observational studies show that local amplification effect has played a role

in the seismic damage distribution in urban areas for several moderate earthquakes [711]. The

agreement is generally quite satisfactory, though only qualitative. Our work tries to estimate how the

resulting ground motions might interact with the built environment in the case of small earthquakes,

not very thick soil layers and damage in buildings of less than six storeys.

In some large earthquakes (e.g. Northridge or Kobe) it has been proved that the pattern of peaks

in ground acceleration and in ground velocity reflect the source proximity and rupture processcausing significant directivity effects. However, site effects are still very important and explain the

ground motion amplification caused by surface geology and the degree of building destruction and

its spatial distribution. Nowadays, it is thought that site effects are more significant in the lower

shaking levels associated with small and moderate earthquakes, particularly at higher frequencies

[12]. For this reason, the analysis of local site effects has a special relevance in regions of small

and moderate earthquakes, like in south-eastern Spain.


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ANALYSIS OF THE WEIGHTINESS OF SITE EFFECTS 1365

Figure 1. (a) Main tectonic units of the Betic Cordillera (southern Spain) and geographical location ofresearch area and (b) geological sketch of Adra town, with II, IIII and IIIIII being the geological

cross-sections shown in Figure 2.

Adra town is situated in the SW of the Almera province (Southeast of Spain) (Figure 1(a)), oneof the most hazardous zones of Spain from the point of view of seismic hazard. Historical seismicity

data reveal that Adra was affected by near destructive earthquakes in 1522 and 1804 (IX maximum

intensity, European Macroseismic Scale (EMS scale)) and in 1910 (mb= 6.2) [13]. Several small

earthquakes (mb= 5.0) in the south-east of Spain, for example, in 1993, 1994 (with an epicentre

near Adra, Almera) and in 1999 (with an epicentre close to Mula, Murcia) reached a VII degree

of intensity (EMS scale) and a detailed macroseismic study revealed areas with different intensities

within the most affected towns. Furthermore, buildings with the same typology placed in areas

underlain by similar surface geology, showed significant damage differentiation from place to place

(some with moderate damages and others undamaged); the only appreciable difference amongst

them was the height of the buildings. In the case of two Adra earthquakes dated 23 December 1993

and 4 January 1994, the most relevant damage in Adra town occurred in reinforced concrete (RC)

buildings of four or five storeys placed on recent alluvial deposits. The other RC buildings onlysuffered light damage or remained intact, and similar occurred with brick and masonry structures

placed outside alluvial deposits. Other nearby towns (Berja, Balanegra and Balerma) suffered a

similar degree of damage. This damage pattern could be related to microscale controlling factors of

ground motion. This paper is concerned with such an influence, based on geological, morphological

and dynamic characteristics of the ground surface and the dynamic behaviour of the buildings in

the affected area of Adra town.


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1366 M. NAVARRO ET AL.

In order to analyse the building/site response relationship we have determined geomorphological

characteristics of Adras urban area (using geotechnical data, drillings, shear velocity values of

shallow layers, etc.). We performed microtremor measurements in the ground surface and the

Nakamura method was applied in order to empirically determine ground predominant periods with

thesein situmeasurements. Finally, building behaviour features were obtained through microtremormeasurements on the top of the buildings.

2. GEOLOGICAL AND GEOPHYSICAL SETTING

During the last decade different kinds of empirical and numerical methods have been proposed

to estimate site effect dependence on surface geological conditions in urban areas. Sometimes,

combined approximations from different methods have been applied to estimate site amplification

characteristics. Frequently, a first step is to perform a geological microzonation based on geologi-

cal and geotechnical identification of materials, their geographical distribution and morphological

conditions[12]. A set of tectonic, edaphological, geomorphological, hydrological, geotechnical and

geophysical data is then involved in the determination of physical properties at each site. After that,

urban area is divided into different zones with almost homogeneous soil conditions allowing us to

reduce the number of sites whose seismic response has to be estimated. Geological microzoning

serves as a starting point in the application of experimental procedure in order to determine site

response based on the measure of ground motions at different sites. Such an estimation can be done

using strong or weak earthquake motion [14] or by microtremor measurements analysis [15, 16].

From a geological point of view, Adra town is located inside the Alpujarride Complex, Internal

Betic Zone (Figure 1(a)) [17]. The older materials (basement) form part of the Adra Unit (Alpu-

jarride Complex), a group of metamorphic nappes constituted by Palaeozoic and Permo-Triassic

phyllites, schist and micaschist [17, 18]. These are covered by a Plio-Quaternary set of sediments

that run from the East to the West of the town with complex geometries and spatial distributions

[1921], marking the Alpujarride bedrock (Figure 1(b)). The Pliocene materials are represented

by deltaic facies formed by poorly rounded pebbles in a sandyclayey matrix, which appear inthe East of Adra town (Figure 1(b)). The Pleistocene is composed of marine and continental sedi-

ments. The marine sediments are formed by two marine terraces composed of gravel and rounded

pebbles fairly or very loose in a sandy matrix. The continental sediments are constituted of three

generations of detrital glacis with red and fine silts, fine sands and gravel in a red siltyclayey

matrix both with scarce internal classification. The Holocene is represented by three principal types

of deposits. The most extensive is a mixed alluvial-marine level of fine sands, silts and gravel

between 2 and 50 m thick. The second deposits are represented by overlaying colluvial deposits of

local rain-fed watercourses that run through the town from North to South, and the recent sandy

marine terrace. The last deposits are represented by recent marine terraces and anthropogenical

fillings [21].

All these preorogenic and postorogenic materials were studiedin situand a stratigraphic correla-

tion of six boreholes and 15 stratigraphic columns was carried out [21]. A detailed urban geologicmap in 1:5000 scale (Figure 1(b)) has been obtained using borehole data of recent Adra river

alluvial sediment, SPT measurements, VS values, together with geological and hydrogeological

features of surface materials [22]. Fifty-five N-values from 30 standard penetration tests (SPT) and

49 real density values of sediments (dry estimation) have been analysed to geotechnically char-

acterize the geological materials (Table I). The ranges of S wave velocity values were obtained

using the relationships of Imai [23] and Kokusho [24].


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ANALYSIS OF THE WEIGHTINESS OF SITE EFFECTS 1367

TableI.Geological,lithologicalandg

eothechnicaldescriptionofthelithologicalunitsofAdratown.

Characteristicsofthematerials

N-value

Thickness

Density

VS,by

VS,by

Geological

(SPT)

(meters)

(g/cm2)

Imai

Kokusho

U

nderlying

formation

Lithology

(average)(average)

(average)(1981)

(1987)

materials

Remarks

Schist

Solidrock

>50

Morefracturedand/ormeteorized

(>50)

areasarevulnerabletolandslides

Phyllites

Solidrock

Vulnerabletolandslides

Pliocene

G

ravelswith

>50

>20

1.90

389

402

Hard

rock


conglomerates

clayeymatrix

(>50)

(5)

Non-saturatematerial

MarineterraceIM

ediumand

3035

15

1.751.80

297

317

Hard

rock


MarineterraceIIth

icksands

(32)

(2)

(1.86)

Perchedgroundwater(high

permeability)

GlacisI

Clayeysands

3550

150

1.801.90

340

344

Marineterraces

Capableoflandslide

GlacisII

andgravels

(41)

(12)

(1.86)

andhardrock

Non-saturatematerial

Alluvias

M

ediumgravels

2530

15

1.801.85

240

240

Hard

rock

Vulnerabletoliquefaction

andsands

(27)

(2.5)

(1.82)

Smallalluvialaquifer

(high

permeability)

AlluvialfanofFinelimesand

1520

15

1.851.90

266

262

Thicktofine

Itisnormallycovered

byfillings

Adrariver

sa

nds

18

3.5

(1.88)

sands

Vulnerabletoliquefaction

M

ediumgravels

3040

150

1.801.90

259

259

Plioceneand

Quitevulnerabletoliquefaction

andsands

(34)

(22)

(1.83)

hard

rock

Majordeltaicaquifer(highand

mediumpermeability)

Recentmarine

T

hicktofine

1520

>15

1.751.85

205

205

Hardrock,

Vulnearabletoliquefaction

terrace

sa

nds

(17)

(7)

(1.81)

GlacisII,

(softmaterials)

Terra

ceIIand

alluvialfan

ofAdrariver

Phreaticaquifer(high

and

mediumpermeability)

Fillings

Blocksand

0.509 46 55.3 47.7 57.30 70.93 5.6 1.5 >0.30

10 47 55.7 55.2 31.95 34.13 6.0 1.9 >0.3011 48 44.5 51.8 28.01 48.66 4.9 3.6 >0.50

12 81 96.0 42.2 71.35 86.38 6.0 1.3 >0.3013 82 69.0 62.4 38.17 51.02 5.3 2.8 >0.3014 84 50.0 40.2 90.63 121.17 5.4 1.2 >0.3015 85 50.0 39.6 40.70 46.57 5.2 2.0 >0.4016 86 81.0 7.9 29.74 31.10 4.9 2.9 >0.5017 87 92.0 52.4 91.30 93.73 5.9 1.0 >0.20

Japan Metrological Agency.


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1412 M. R. GHAYAMGHAMIAN AND G. R. NOURI

Figure 2. Borehole-to-surface spectral ratio for the largest event (event 37), small events(grey lines) and the average of small events.

The largest event among the database is the Chibaken-Toho-Oki earthquake (1987) with thesurface PGA of near 400 and 270 cm/s2 in NS and EW directions, respectively. Thus, the possible

effects of nonlinear soil response need to be examined. This is done by comparing borehole-to-

surface spectral ratio for the largest event (Event 37) and average of the small events for C0

borehole. As shown in Figure 2, there is no clear downward shift in resonance frequency of the

spectral ratios at the site for large event. Therefore, the record of large event is not affected by

the nonlinear soil response. Luet al. [38] also reported the same conclusions by analysing the site

amplification characteristics using cross-spectrum technique for 27 events at the site.

3. ROTATIONAL GROUND MOTION

Let uj (t), vj (t) and wj (t) to be the translational accelerations along the X, Y and Z axes. The

rotational components of surface motion related to a station pair(j = 1, 2)are computed from the

acceleration time histories according to the following finite difference expressions [27, 28, 36]:

z =1

2

u

yv

x

=

1

2

u2(t) u1(t)

y

v2(t) v1(t)

x

(1)

y =w

x=

w2(t) w1(t)

x(2)

x =w

y

=w2(t) w1(t)

y

(3)

The quantities dealt with here are the torsional acceleration z about the vertical axis and the

rocking accelerations x and y about the horizontal axes. u j (t), vj (t)and wj (t)are the recorded

acceleration in the NS, EW and UD directions, respectively. Figure 3 shows an example of typical

recorded translational accelerations and calculated torsional and rocking accelerations for event 37

at stations C0 and C1.


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CHARACTERISTICS OF GROUND MOTION ROTATIONAL COMPONENTS 1413

Figure 3. An example of recorded ground acceleration at stations C0 and C1 and estimatedrotational ground acceleration for event 37.


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Array-derived rotations are subjected to a limitation. The instruments should be closely spaced

enough that the finite difference approximations could be near to true gradients. Specifically, to

obtain array gradient estimates accurate to 90% of true gradients, the array dimensions must be

less than approximately one-quarter wave length of the dominant energy in the wave train [30].

Regarding estimated large wave velocity [39] (see Section 5) and very closely spaced instrumentsin Chiba site, the rotational motions could be evaluated within the acceptable accuracy range using

the above finite difference equations.

4. TORSIONAL GROUND MOTION

Based on Equation (1), the torsional ground acceleration is calculated for different events and

pairs of stations with different separation distances. The standard deviation of motions is used as

a parameter that provides information on the corresponding torsional quantities [40]. The standard

deviation of each torsional time history is calculated and then its variation with separation distance,

magnitude and PGA is investigated. In addition, the ratio of ground motion durations (the timeinterval between 5% and 95% of the total energy) of torsional to translational ground motions is

examined. Figure 4(a) shows an example of the variation of standard deviation of torsional motion

with respect to separation distances for three different events (large, moderate and small event).

It is clear that the standard deviation of torsional motion decreases rapidly as separation distance

increases. The variation of the maximum values of torsional motion with separation distances also

reveals the same trend as shown in Figure 4(b). The analyses of the other events show the same

trend that their figures are not shown due to similarity. Figure 5(a) demonstrates the variation of

standard deviation of torsional motion with earthquake magnitude for three separation distances

(10, 109 and 143 m). From this figure, torsional motion seems to be gradually increased with

increasing magnitude. Although only one event with a magnitude larger than 6.5 is available,

the sudden increase in the torsional value of earthquake motion with a magnitude larger than

6.5 is observable. The similar trend can be seen for other separation distances. In Figure 5(b),

the variation of standard deviation of torsional ground motion with PGA is also shown for the

Figure 4. (a) Standard deviation of torsion vs separation distance and(b) maximum torsionvs separation distance.


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Figure 5. (a) Standard deviation of torsion vs magnitude for three separation distances and (b) standarddeviation of torsion vs PGA for three separation distances.

same three separation distances. As it might be expected, the standard deviation of torsional motion

increases with increasing PGA. Particularly in case of PGA = 0.40g the standard deviation value

for torsional motion displays a large difference with the others.

The duration of ground motion can have a strong influence on earthquake damages. A motion

with short duration may not produce enough loads to damage the structures, even if the amplitude


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Figure 6. (a) Duration of torsional vs translational motions for different separation distances and eventsand (b) duration of torsion vs magnitude for three separation distances.

of the motion is high. On the other hand, a motion with moderate amplitude but long duration

can produce enough loads to cause substantial damage in structures. Since the duration of ground

motion is an important parameter in structural analysis, it is worthy to examine the variation of

rotational motion duration in relation to translational one. Figure 6(a) shows the relation between

torsional and translational durations for different magnitude. This shows that the duration of

torsional ground motion could be generally larger than the translational one. Figure 6(b) illustrates

that the duration of torsional ground motion has an increasing trend with increasing magnitudes

up to MJMA = 6.5 (strong earthquakes) and it seems to be decreased for magnitudes larger than

MJMA = 6.5 (very strong earthquakes). In addition, duration of torsional motion in three separation

distances (Figure 6(b)) shows that with increasing separation distance, duration increases.

5. ESTIMATION OF TORSIONAL MOTION USING TRANSLATIONAL ONES

Since it is difficult to directly record torsional ground motions, attempts are made to predict the

torsional motion from translational ones [36]. Spatial variation of ground motion can be defined by

appropriate coherency function models. Several empirical coherency functions have been suggested

[41]. Although these coherency functions model the spatial variations of translational motions well,

they cannot be directly used to model the torsional ground motions. Hao [36] proposed a new

form of coherency function as

kl (x,y, i)= |kl | exp

ix

va

= exp[(1()x

2 + 2()y2)] exp

ix

va

(4)

where |kl | is the coherency loss function and exp(ix/va)is the phase shift between the motionsat pointskandl , is the circular frequency, va is the apparent velocity of ground motion, x and yare the separation distances between points kandl in the ground motion propagation direction and

its transverse one, respectively. Using this coherency function, the relation between PSD function

of torsional and translational ground motions can be given as

S = Sg()[1() + 2() + /2v2a ] (5)


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where Sg() is the PSD of translational accelerations and is obtained by averaging the recorded

translational PSDs at station pair. 1() and 2() are the parameters with the form

j ()=aj

ln() + bj

, 0.314(rad/s), j = 1, 2 (6)

where aj and bj are determined by regression method from the recorded motions and bj

| ln(0.314)= 1.1584|. Furthermore, the apparent velocity (va) can be obtained by calculating the

cross-correlation functions between motions of each station pair [36].

The obtained apparent velocity values range between 4 km/s to infinity as it is clear from time

lag of cross-correlation coefficients in Figure 7. Yamazaki and Turker [39] analysed the apparent

velocity at Chiba site using FK method and found the apparent velocity is 5 km/s in the average

for a wide frequency range (0.58 Hz). They and Katayama et al. [37] concluded that the wave

propagate almost vertically and the incident angle should be close to normal in Chiba site.

By employing Chiba array data and based on Equation (5), the relations between PSD of

torsional and translational motions are examined. Since the coherency function depends on the

distance between the two stations, accelerometer pairs in Chiba array are categorized in some groups

as summarized in Table I. For obtaining the parameters a j and b j using optimizing scheme, 50%

of data are used in each separation distance group. To this end, the PSDs related to each group

are averaged for each frequency. Having an averaged PSDs for translational and torsional motions

(Sg,S)at each separation group, the coefficientsaj andbj are evaluated by optimization scheme

(Table III). Figure 8 shows the averaged torsional PSD and the predicted one for two events

(events 81 and 82) and three groups of separation distances. In the next step, to check the validity

of the results, the identified coefficients are applied to predict the torsional PSDs for the other 50%

of data in each distance group that are not used in optimization procedure for estimating aj and

bj . Figure 9 shows the comparison between simulated and actual torsional PSDs for the data that

are not used in the optimization (the other 50% of torsional PSDs). As illustrated in Figure 9, the

predicted torsional PSDs are not consistent with the observed ones in small separation distances.

In the contrary, a good agreement between predicted and observed torsional PSDs can be seenfor intermediate and large distances. This trend can be seen for almost all of the events at the

site. Thus, the torsional motion should be calculated with more care using Equation (5) in small

distances. As revealed from Figure 4, the values of torsional motion in close distances are very

discursive. The scattering of torsional values in close separation distances may also support the

idea that some other factors affected the estimation of torsional motion in close distances. However,

we do not have a clear explanation for this discrepancy.

6. ROCKING GROUND MOTIONS

As previously explained, rocking ground motion is also found to be important and there are some

cases in which rocking components of ground motion has largely contributed to the overall responseof structures [9, 2022]. Thus, the rocking component of ground motion and its properties need to

be further analysed using actual data. The rocking ground motion is calculated using Equations (2)

and (3) and their variations with magnitude and PGA for different separation distances are examined

in the same fashion as for torsional ground motion. Figure 10 shows that the standard deviation

and maximum of rocking ground motion decrease rapidly with increasing separation distance as

was the case for torsional motion. Figure 11(a) illustrates the variation of standard deviation of


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Figure 7. Example of cross-correlation coefficient function, estimated lag time and apparent velocity indifferent separation distances for events 81 and 87.


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Table III. Coefficients ofa j and bj .

Mean and standard deviation of coefficients of all events

Separation distance a1 a2 b1 b2

10


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Figure 9. Comparison of the PSDs for the data, which is not employed in optimization,in different separation distances for events 81 and 82; (a) 10


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Figure 9. Continued.

Figure 10. (a) Standard deviation of rocking vs separation distance for three events and (b) maximum

rockingvs separation distance for three events.

rocking motion with different magnitudes for three separation distances (10, 109 and 143 m).

Similar to torsional ground motion the standard deviations of rocking motion are also increased

as magnitude increases. It is interesting to note that for magnitude greater than 6.5 (M= 6.7), the

standard deviation of rocking motion suddenly increases and reach to a value seven times larger


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Figure 11. (a) Standard deviation of rocking vs magnitude for three separation distances and (b) standard

deviation of rocking vs PGA for three separation distances.

than the ones in M


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Figure 12. (a) Duration of rocking motions vs vertical component for different separation distances andevents and (b) duration of rocking vs magnitude for three separation distances.

one for PGA = 0.13g. Unfortunately, there were no available data in the range of 0.150 .40g to

investigate more in regard with the standard deviation increasing trend with PGA.

Figure 12(a) shows the variation of rocking motion duration vs the vertical one. It can be seen

that the duration of rocking ground motion is about equal to the vertical component of ground

motion. Figure 12(b) illustrates that the duration of rocking ground motion increases as magnitude

increases up to 6.5 (strong earthquake) and decreases for magnitudes larger than 6.5 (very strong

earthquake). Furthermore, the duration of rocking motion in three separation distances depicted in

Figure 12(b) shows that there is clear changing in rocking ground motion duration with variation

of separation distances.

7. ROTATIONAL RESPONSE SPECTRA AND ITS RELATION WITH

TRANSLATIONAL ONES

A more meaningful way to compare rotational and translational ground motions and to recognize

their effects on structural response is to obtain the response spectra for each component of ground

motion. The response spectrum for rotational acceleration is defined as the peak value of response

of a single degree of freedom (SDF) rotational oscillator subjected to rotational motion and is

plotted against its rotational vibration period.

As noted earlier, rotational motions are functions of separation distance between the two record-

ing stations. The distance categorization mentioned in Table I is also used here to investigate the

characteristics of rotational response spectra. Torsion and rocking time histories for each station

pair are computed and the response spectra for each of the rotational and translational (horizon-tal and vertical) motions are normalized to their corresponding peak values. For each separation

distance group, the averaged response spectra of each component are calculated.

Considering the importance of noise level, the nine events out of 17 with very small NSR and

reliable frequency range larger than 0.30 Hz (periods


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As demonstrated in Figure 13(a), the effect of separation distance on normalized response spectra

for periods more than 0.2 s is more distinct. In the period range of 0.2


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Figure 13. (a) Normalized acceleration response spectra of torsional motion; (b) normalized accelerationresponse spectra of horizontal motions; and (c) torsional to translational acceleration response spectra

ratio for different separation distances.


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Figure 14. (a) Normalized acceleration response spectra of rocking motion; (b) normalized acceler-ation response spectra of vertical motions; and (c) rocking to vertical acceleration response spectra

ratio for different separation distances.


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that this effect is notable at the periods longer than 0.20 s. For the period range of 0.21.5 s and

in far separation distances, the values of normalized rotational response spectra are larger than

those for near separation distances. This manifested that neglecting the separation distance in this

period range may lead to underestimation of normalized response values. This point needs to be

considered in the response analyses of structures against rotational components. Previous studies[24, 25] suggested a linear trend for spectral ratio of rotational motions to the translational ones.

However, the analysis of the array data revealed that spectral ratios of rotational and translational

motions are not linearly proportional to the period for different separation distances. In addition,

this ratio can be affected by separation distance.

Because of the difficulties in recording of torsional motion, the evaluation of torsional motion

from translational one is focused. The coherency function proposed by Hao [36] was examined

to predict the torsional motion from the translational ones for different separation distances and

events at the site. The estimated torsional motion was found to be well predicted for intermediate

and far distances (100320 m). However, it seems that other factors may need to be considered

for reliable estimation of torsional motion in close separation distances.

ACKNOWLEDGEMENTS

The authors would like to acknowledge the generosity of Tokyo University in sponsoring further investi-gation on earthquake engineering. Without the data provided through their support, this study would nothave been possible. We wish to thank Professor Masayoshi Nakashima and the Earthquake Engineeringand Structural Dynamics anonymous reviewers whose comments led to substantial improvement of thispaper.

REFERENCES

1. Bouchon M, Aki K. Strain, tilt and rotation associated with strong ground motion in the vicinity of earthquake

faults. Bulletin of the Seismological Society of America 1982; 72:17171738.

2. Trifunac MD, Todorovska MI. A note on usable dynamic range in accelerographs recording translation. SoilDynamics and Earthquake Engineering2001; 21:275286.

3. Takeo M, Ito HM. What can be learned from rotational motions excited by earthquakes? Geophysical Journal

International1997; 129:319329.

4. Bycroft GN. Soilfoundation interaction and differential ground motions. Earthquake Engineering and Structural

Dynamics 1980; 8:397404.

5. Trifunac MD, Todorovska MI, Ivanovic SS. Peak velocities, and peak surface strains during Northridge, California

earthquake of 17 January 1994. Soil Dynamics and Earthquake Engineering 1996; 15:301310.

6. Newmark NM. Torsion in symmetrical buildings. Proceedings of the 4th World Conference on Earthquake

Engineering, Santi

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