Selection and Scaling of Real Accelerograms for Bi

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Selection and Scaling of Real Accelerograms for Bi-Directional Loading: A Review of Current Practice and Code Provisions a

Katrin Beyer & Julian J. Bommer

b

a

European School for Advanced Studies in Reduction of Seismic Risk (ROSE School), Pavia, Italy b

Department of Civil and Environmental Engineering, Imperial College London, London, UK Version of record first published: 25 May 2007.

To cite this article: Katrin Beyer & Julian J. Bommer (2007): Selection and Scaling of Real Accelerograms for Bi-Directional Loading: A Review of Current Practice and Code Provisions, Journal of Earthquake Engineering, 11:S1, 13-45 To link to this article: http://dx.doi.org/10.1080/13632460701280013

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Journal of Earthquake Engineering, 11:13–45, 2007 Copyright © A.S. Elnashai & N.N. Ambraseys ISSN: 1363-2469 print / 1559-808X online DOI: 10.1080/13632460701280013

Selection and Scaling of Real Accelerograms for Bi-Directional Loading: A Review of Current Practice and Code Provisions

1559-808X 1363-2469 UEQE Journal of Earthquake Engineering Engineering, Vol. 11, No. s1, March 2007: pp. 1–39

KATRIN BEYER

Selection K. Beyer and and J. Scaling J. Bommer of Real Accelerograms for Bi-Directional Loading

Downloaded by [EPFL Bibliothèque] at 11:41 31 October 2012

European School for Advanced Studies in Reduction of Seismic Risk (ROSE School), Pavia, Italy

JULIAN J. BOMMER Department of Civil and Environmental Engineering, Imperial College London, London, UK The seismic behavior of asymmetric building structures is often complex and reductions to plane problems which can be analyzed with a single horizontal ground-motion component are often deemed unsatisfactory. As a consequence, dynamic structural analyses with both horizontal groundmotion components become more common, both in research as well as in practice. A review of code provisions regarding selection and scaling of ground motions for bi-directional analysis has, however, revealed that the guidelines provided are frequently inconsistent or are lacking transparency regarding the underlying assumptions. The aim of this study is to shed some light on a number of aspects involved when selecting and scaling records for bi-directional analysis and post-processing results of such analyses. Keywords Bi-directional Dynamic Analysis; Real Strong-motion Records; Selection of Records; Scaling of Records

1. Introduction Seismic ground motion at a point consists of three translational and three rotational components. In earthquake engineering it is customary to only consider the translational components when performing structural analysis. The effect of the rotational component is commonly considered as small and is therefore neglected [Kubo and Penzien, 1979]. To simplify matters further, the focus of this study is on the horizontal components of ground motions. In many cases the vertical component of a ground-motion record would not be used as an input for structural analysis because its effect on the seismic response of buildings may be neglected. The analysis of complex structures with uni-directional seismic input often requires crude assumptions regarding the interaction of the structural system in the two horizontal directions or the application of simplifying combination rules, such as the “30%-rule.” According to the “30%-rule,” the total response is computed as 100% of the maximum response for excitation in one direction plus 30% of the maximum responses for excitation Received 18 September 2006; accepted 31 January 2007. Address correspondence to Julian J. Bommer, Department of Civil and Environmental Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK; E-mail: [email protected]

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K. Beyer and J. J. Bommer

in the other horizontal direction; the combination leading to the largest response is considered for design [Clough and Penzien, 1993]. Both approaches of analysis can be unsatisfactory and hence dynamic analysis of structures with bi-directional horizontal excitation becomes more common. However, there are several aspects which require consideration that are not relevant when uni-directional analysis is carried out. These concern selection criteria for records intended as input motion for bi-directional analysis as well as the scaling of the two horizontal components. The assessment of different scaling procedures will depend on the conceptual framework in which first the seismic hazard assessment of the building site and then the analysis of the structure are carried out. In this study the seismic hazard is represented by a scenario spectrum, which it is assumed is obtained by disaggregation of the uniform hazard spectrum for a certain annual probability of exceedance; the aim of the structural analysis and post-processing of the results is to aim for a similar probability of exceedance for the seismic demand on the structure. A recent study by Baker and Cornell [2006a] has highlighted that inconsistencies between the seismic hazard assessment and structural analysis have been very common arising from different definitions of the horizontal spectral component. The objective of this study is to provide some guidelines for the selection and scaling of real records for bi-directional analysis of structures. First, different definitions of spectral components are given and some code provisions regarding the selection and scaling of records are reviewed (Sec. 2). Then, criteria for the selection of component pairs are discussed and different selection strategies outlined (Sec. 3). In Sec. 4 different scaling options, the orientation of structural axes relative to ground-motion axes, and the post-processing of results are discussed. Only linear scaling is considered in this study where the amplitudes of the records are scaled by a factor while the frequency content of the records remains unaltered. The differences between the selection and scaling procedures are illustrated by means of an example structure (Sec. 5). The main findings of this study are summarized in the last section (Sec. 6). The study is limited to records without pronounced directivity effects; analysis of structures with near-source records would require additional considerations regarding selection and scaling of records and the orientation of ground-motion axes to structural axes.

2. Definitions and Review of Code Provisions In this section the variation of spectral ordinates with the orientation of the ground-motion axes is discussed (Sec. 2.1) and the most common definitions of spectral ordinates are summarized (Sec. 2.2). Although there are different definitions for the horizontal component, the terms acceleration or displacement spectra are always used in this study to refer to elastic response spectra with 5% of critical viscous damping. In Sec. 2.3 the geometric mean component is selected as the preferred definition of the horizontal component when bi-directional analysis is carried out. Section 2.4 gives an overview of selected code provisions regarding selection and scaling of records for bi-directional analysis, application of records in structural analysis and post-processing of results. 2.1 Ground-Motion Axes In most strong-motion databases the horizontal components of ground motion are given with the orientation in which they were recorded, i.e., the orientation of the components is determined by the orientation of the recording instruments, which in most cases is arbitrary with respect to the fault on which the earthquake event occurred. An exception is the new issue of the NGA database [PEER, 2005] in which the components of the records have been rotated to the fault-normal and fault-parallel orientation. It is worth noting that

Selection and Scaling of Real Accelerograms for Bi-Directional Loading

15

unless the fault rupture is perfectly linear, which is almost never the case, definition of the angle q to define the fault-normal and fault-parallel components is not straightforward and in some cases will depend strongly on the judgement of the seismologist. By a simple matrix multiplication of the two time histories, the orientation of the horizontal axes system can be rotated by an angle q:

(2.1)

where ax(t) and ay(t) are the horizontal components of the record in the original orientation, ax(q)(t) and ay(q)(t) the components of the record when rotated anti-clockwise by an angle q. Both sets of axes are orthogonal and horizontal. To visualize the effect of rotating the horizontal axes along which the ground motion is expressed, the components of an example ground motion were rotated at intervals of 1°. For each angle q, the spectra of the two horizontal components were computed. The results for four different spectral periods (T = 0.2, 0.5, 1.0, and 4.0 s) are shown in Fig. 1. Note that the spectral accelerations are symmetric about the origin; this is illustrated by using the same shade of grey for components orientated within the first and third quadrants and the second and fourth quadrants,

Period T = 1s

Period T = 0.2s 0.5

Sa [g]

0.5 0

0

–0.5 −0.5 −0.5

0

−0.5

0.5

0

0.5

Period T = 4s

Period T = 2s 0.1 0.2 0.05 Sa [g]


⎛ a x(q ) (t )⎞ ⎡cosq sinq ⎤ ⎛ a x (t )⎞ ⎜ a (t )⎟ = ⎢ − sinq cosq ⎥ ⋅ ⎜ a (t )⎟ . ⎝ y(q ) ⎠ ⎣ ⎦ ⎝ y ⎠

0

0

−0.05 –0.2 −0.2

0 Sa [g]

0.2

−0.1 −0.1 −0.05

0 0.05 Sa [g]

0.1

FIGURE 1 Imperial Valley, 1979, Station Delta [PEER, 2005]: Spectral acceleration as a function of orientation angle q (thick dark and light lines). The outer circle represents the maximum spectral acceleration of one component obtained for all possible orientations of axes. The horizontal and vertical axes correspond to fault-normal and fault-parallel orientation. The thick black radial lines give the orientation of the principal axes with qp = 18.8°. The solid black line is the geometric mean of the two components as a function of q. The dashed black line represents GMRotD50 as defined by Boore et al. [2006].


16


respectively. The plots show that the spectral accelerations of one horizontal component depend on the orientation of the horizontal axes and on the spectral period considered. Papers on response spectrum analysis representing bi- or tri-directional excitation often refer to the principal axes of ground motion [e.g., Hernández and López, 2002], a set of ground motion axes which was first introduced by Arias [1970]. If ground motion is considered as a random process the principal axes can be determined as the set of axes for which the covariance disappears. The set of principal axes sets itself apart from any other orientation of axes in the respect that the motions a1 (t) and a2 (t) along the principal axes 1 and 2 are uncorrelated. This is of importance in response spectrum analysis and also when generating artificial records with more than one component. The latter was the objective of Penzien and Watabe [1975] whose work was motivated by the lack of recorded ground motions at that time and the consequent need to generate artificial time histories which could be used for structural analysis. From the analogy of Mohr’s circle, the angle qp between the x-axis, and the major principal axis can be written in terms of the 2 2 variances s xx and s yy and the covariance mxy of the two horizontal ground motions ax(t) and ay(t) [Clough and Penzien, 1993]:

tan(2q p ) =

2m xy 2 s xx

2 − s yy

.

(2.2)

with the variances and covariance defined as

2 = s xx

2 = s yy

m xy =

1 td 1 td 1 td

td

∫ (ax (t ) − ax (t )) dt 2

0

td

∫ (ay (t ) − ay (t ))

2

dt

(2.3)

0

td

∫ (ax (t ) − ax (t ))(ay (t ) − ay (t ))dt. 0

where td is the considered duration, ai(t) the time history, and ai (t ) the mean value of the time history ai(t) over the duration td. The orientation of the principal axes is hence always computed for a specific time interval [0, td] which may be selected to represent any portion of the entire duration of the motion [Clough and Penzien, 1993]. By selecting successive time intervals over the entire duration of motion, Penzien and Watabe [1975] found that the orientation of principal axes is fairly constant over the strong interval of motion. However, the smaller the time interval, the larger is the fluctuation of the principal axes over time [Penzien and Watabe, 1975]. Hence, when referring to principal axes of ground motion it is necessary to specify the time interval for which the orientation was computed. Figure 1 also shows the orientation of the principal axes of the example record which were computed for the entire duration of the record. 2.2 Different Definitions of Spectral Ordinates In the previous section it was shown that the spectral ordinate of one component depends on the orientation of the ground-motion axes. The three most common definitions which retain the two components were already discussed in the previous section:


17

• x, y: The orientation of the two horizontal components as recorded. • FN, FP: The components rotated to align in the fault-normal and fault-parallel directions. • Principal 1, Principal 2: The components are orientated along the principal axes (Sec. 2.1). Besides computing the spectral ordinates for a single component, there are a number of definitions of spectral ordinates expressed as a single value derived from the vector of the two perpendicular horizontal components. The most common of these are listed in the following; a more complete list is given in Beyer and Bommer [2006]:


• GMxy: The geometric mean spectrum of the as-recorded components x and y is computed as follows:

SaGMxy (T ) = Sa x (T ) ⋅ Sa y (T ).

(2.4)

• AMxy: The arithmetic mean of the recorded components x and y is:

Sa AMxy (T ) =

Sa x (T ) + Sa y (T ) 2

.

(2.5)

• Envxy: The envelope spectrum is defined as the larger spectral ordinate of the x and y components at each period. • SRSSxy: The square root of the sum of squares spectrum is used in several codes to combine the spectra of the components x and y:

SaSRSSxy (T ) = Sa x2 (T ) + Sa y2 (T ).

(2.6)

Two new definitions have recently been proposed by Boore et al. [2006] which aim at reducing the variance of the ground-motion measure and at producing less arbitrary approximations to components that have genuinely random orientation: • GMRotD50: At each response period, the median value of the geometric mean from all possible orientations of the ground-motion axis system is computed. The orientation corresponding to the median value might vary between different spectral periods. • GMRotI50: This ground-motion measure is an approximation of GMRotD50 with a constant axis orientation for all periods, which minimizes the sum of differences between GMRotD50 and GMRotI50 over all considered periods. The geometric mean SaGMxy for the different orientations is included as a thin solid black line in Fig. 1 and the orientation independent measure SaGMRotD50 is included as the black dotted line. From the number of definitions for spectral ordinates it seems mandatory to always clearly state which ground-motion measure is used when a spectrum is defined. 2.3 Preferred Definition of the Target Spectrum when Selecting and Scaling Records for Bi-directional Structural Analysis The definition of the spectral ordinate of the target spectrum depends on the groundmotion prediction equations (GMPEs) which have been used to derive the spectrum. Most


18


GMPEs use either the geometric mean (GMxy) or the envelope spectrum (Envxy) of two components with the orientation as recorded. Lately, the geometric mean has been the preferred choice, but might be replaced in the future by either GMRotD50 or GMRotI50 once new ground-motion prediction equations for these component definitions have been adopted in practice. Preliminary results of deriving empirical prediction equations using these new definitions have indicated that they do not result in aleatory variability appreciably smaller than that obtained using the simple GMxy definition [Beyer and Bommer, 2006]. In structural analysis with uni-directional input the spectrum of an arbitrarily selected component and the envelope spectrum of two components have traditionally been widely employed. The seismic hazard at a project site can be either determined by carrying out a hazard assessment of the site or by using code spectra. If a hazard assessment is carried out the definition of the spectra are usually given by the GMPEs. If a codified spectrum is used, the definition of the spectra is not always clearly visible to the practicing engineer (Sec. 2.4.2). This study is focused on a consistent approach of selecting and scaling records to a target spectrum where the definition of the spectral ordinate is known. Previous studies by Malhotra [2003] and Baker and Cornell [2006a] which have been concerned with bi-directional input for dynamic structural analysis have chosen the geometric mean spectra as the preferred definition of the spectral ordinates of the target spectrum; the same definition will be used here for the following reasons: • A relatively large set of GMPEs based on this definition is available for use in hazard assessment. • The measure results in a single spectrum and hence the comparison of target and record spectrum is straightforward. • The variation of the spectrum with orientation of the ground-motion axes is small. Hence, selecting and scaling of records is less sensitive to the orientation of the ground-motion axes than for other definitions. • The measure is also meaningful in logarithmic space since it corresponds to the arithmetic mean of the logarithmic values. This can be important in structural reliability analysis where logarithmic response parameters are commonly linked to the logarithm of spectral ordinates. • If the analysis results with bi-directional input are to be compared against results from analysis with uni-directional input, the conversion of the geometric mean spectrum to the spectrum of a single randomly chosen component is fairly straightforward since the median of the two measures are identical while the standard deviation is smaller for the geometric mean than for the single component. Conversion procedures have been proposed by Baker and Cornell [2006b] and Beyer and Bommer [2006]. Other definitions such as the envelope spectrum and the SRSS spectrum (which is frequently used in codes) can also be used but it is more difficult to define procedures which are consistent over the process of defining the hazard and selecting and scaling the records. After the geometric mean, the envelope of the two components is probably the most frequently used component definition for GMPEs and might hence be used to define the hazard at a given site. Methods for scaling of the two components to the envelope spectrum have been developed (Sec. 2.4.2). However, since the envelope spectrum might not be governed by the same component at all periods, a consistent scaling procedure seems less obvious, although a relatively simple procedure would be to scale both components by the same factor such that their envelope matched or exceeded the target spectrum. Another option is simply to convert the spectrum to the equivalent ordinates for another component definition, such as the geometric mean to create a new target for scaling.


19

Empirical conversion factors between median values of most of the definitions listed in Sec. 2.2 and the geometric mean spectrum have been derived by Beyer and Bommer [2006]; however, the small differences in aleatory variabilities, for which Beyer and Bommer [2006] also provide scaling factors, could generally not be accounted for in such simple adjustments if the original spectrum has been obtained from PSHA.

2.4 Code Provisions for Selecting and Scaling of Records for Bi-directional Structural Analysis and Processing of Analysis Results


In the following, a summary of code provisions for the following aspects involved in structural analysis with bi-directional ground motion input is given: • • • •

Selection of records Scaling of records Direction of loading Post-processing of results

For a general review of accelerogram specification in codes the reader is referred to Bommer and Ruggeri [2002]. The aim here is not to give a comprehensive overview of all seismic design codes currently used in practice but to focus on the few in which these issues are more devleoped. In fact, when reviewing different codes, it becomes obvious that guidelines have been copied from codes used in other parts of the world without significant review of the recommendations given therein. The provisions included in this study are: • Eurocode 8, Part 1 [CEN, 2003], abbreviated in the following as EC8; it was chosen because it is the main seismic design code in Europe. • “NEHRP recommended provisions for seismic regulations for new buildings and other structures” [FEMA, 2001], abbreviated in the following as FEMA 368. These guidelines are often acknowledged to mirror the state-of-the-art in seismic design. • The ASCE Standards 7-05 [ASCE, 2006] “Minimum design loads for buildings and other structures” and 4-98 [ASCE, 2000] “Seismic analysis of safety-related nuclear structures,” abbreviated in the following as ASCE 7-05 and ASCE 4-98, respectively. These two documents were included since they are legally binding standards in the United States. • Code and Supplement of the New Zealand Standard 1170.5 [NZS, 2004] abbreviated in the following as NZS. This code has been added since it includes guidelines regarding the scaling of component pairs which are different to the approaches adopted in most other codes. 2.4.1 Selection of records. Most codes do not distinguish between record selection for uni-directional analysis and record selection for bi- or tri-directional analysis. The obvious requirement that records for bi-directional analysis need to consist of at least the two horizontal components while records where only one horizontal component has been recorded can be used for uni-directional analysis, is mentioned by some of the codes. The use of the same component for both horizontal directions is prohibited by all the guidelines reviewed; ASCE 4-98 also explicitly states that the same component for both horizontal directions must not be used even if the starting time of one component is shifted with respect to the other. According to FEMA 368, records for linear and nonlinear time-history analysis should be selected to match magnitude, fault distance, and source mechanism that control the hazard (Table 1). The guidelines for record selection in ASCE 7-05 are identical to

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TABLE 1 Selection criteria for component pairs for dynamic analysis in different seismic codes

EC 8 FEMA 368 ASCE 7-05 ASCE 4-98 NZS

M1

d2

⻫⻫⻫

⻫⻫⻫

⻫

⻫

Rupture Mechanism

Site Class

⻫⻫⻫⻫⻫

⻫⻫⻫

D3

Spectral Shape

Correlation of Components

⻫

(⻫)+

⻫

1

Magnitude; Source-site distance; 3 Duration of ground motion + indirectly through PGA, PGV and PGD


2

those in FEMA 368. In addition to the source and path characteristics of the design earthquake, EC8 requires inclusion of the site class of the building location as selection criteria. The same selection criteria are specified in NZS. ASCE 4-98 requires that geological and seismological settings and local subsurface conditions are appropriate for those of the considered site. It further specifies that the records should be free-field ground motions at the top of the foundation layer and that duration and amplitude of ground-motion parameters such as peak ground acceleration, velocity and displacement shall be representative for the expected ground-motion at the site for that level of hazard. In this way ASCE 4-98 includes to a certain degree the goodness-of-fit between target spectrum and record spectrum as selection criteria, while all other codes which were reviewed suggested selecting records from earthquake events with geophysical features similar to the design earthquake and in some cases also to the site conditions. In practice, problems often arise since the earthquake scenario which contributes most to the hazard at a site is unknown to the engineer. Most codes determine the seismic hazard in terms of uniform hazard spectra but do not give the information regarding the underlying earthquake scenarios. Differences exist between the codes regarding the usage of real, modified or artificial records (Table 2). While FEMA 368 recommends using records from real seismic events which are only to be supplemented by artificial ones if less than three suitable records could be found, EC8 leaves the choice to the designer whether real, modified or artificial records are selected for the structural analysis. NZS only permits real records for structural analysis, which are also the only group of records considered in this study. One should note that it is much more elaborate to generate artificial ground motions with two horizontal components than with a single component only [e.g., Fernández-Dávila and Cruz, 2005]. If ground motions with two components are generated, assumptions regarding the dependence of the two components are mandatory. Different ground-motion models exist on which the generation of artificial motions with two or three components can be based. One of the earliest and most popular ones is the model proposed by Penzien and Watabe [1975]. The minimum number of records required for structural analysis is three for all reviewed codes except for ASCE 4-98 which specifies that at least one record should be used unless the structure is sensitive to long-period motion; in this case the minimum required number of records is also three. The insufficiency of three records, let alone a single record, is widely acknowledged and is discussed further in Sec. 5.


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TABLE 2 Application of component pairs for dynamic analysis in different seismic codes

EC 8 FEMA 368 ASCE 7-05 ASCE 4-98 NZS

Min. number of records

Type of records

Direction of application

3 (7)+ 3 (7)+ 3 (7)+ 1 3

Artificial/Recorded/Simulated‡ Recorded (Simulated)† Recorded (Simulated)† Recorded/Modified/Simulated‡ Recorded

0° and 180° Critical direction Critical direction 0° Critical direction


+

If 3 to 6 records are used the maximum response from all records has to be considered for design. If at least 7 records are used for the analysis, the average of the response to the individual records can be used as design value. ‡ Any of the listed record types can be used as gound-motion input for structural analysis. † Recorded time-histories are to be used as input for structural analysis and only supplement by simulated ones if the number of suitable real records which can be found is too small.

The only code to the authors’ knowledge which introduces a new selection criteria if the record is used for bi-directional analysis instead of uni-directional analysis is ASCE 498. This code states that the components “shall be statistically independent. (. . .) Two time histories shall be considered statistically independent if the absolute value of the correlation coefficient does not exceed 0.3.” For structures sensitive to long-period motion “the input motions in the three orthogonal directions shall, in the frequency range 0.2 to 1.0 Hz, have a correlation coefficient representative of empirical data recorded at sites of similar geotechnical conditions and tectonic environment.” These recommendations seem impractical for the following reasons: • It is not specified whether the correlation coefficient refers to time histories, response spectra, or power spectral density spectra of the components. Moreover, the correlation coefficients of acceleration, velocity, and displacement time histories of the same record are very different [Morris, 2005]. The correlation coefficient further depends on the orientation of the components. ASCE 4-98 does not specify whether the requirements regarding the correlation coefficient applies only to the directions of the horizontal components as they are applied to the structure or whether the correlation coefficient for all possible orientations has to meet the requirements. • The authors are unaware of studies which give correlation coefficients as a function of geotechnical and tectonic settings at a site and ASCE 4-98 provides no reference values. A brief investigation into the distribution of correlation coefficients of the horizontal acceleration time histories of records in the NGA-database [PEER, 2005] showed no trends with respect to site class and fault mechanism. The correlation coefficient was computed as

rxy =

m xy s xx s yy

,

(2. 7)

where mxy, sxx, and syy have been defined in Eq. (2.3). 2.4.2 Scaling of records. Scaling the amplitude of records allows one to match the spectrum of the record to the design spectrum either at a single period or—with a goodness-of-fit


22


depending on the spectral shapes of the design spectrum and the record spectrum—over a period range. An alternative approach is to use the Fast Fourier Transform or a wavelet transformation to achieve an improved match by effectively scaling different parts of the record by different factors [e.g., Hancock et al., 2006]; however, in this article only linear scaling is considered. In Sec. 2.2 it was shown that there are many different definitions of spectra of the horizontal components. When scaling records to a target design spectrum, it is important that the definition of the spectral ordinates, in terms of treatment of the two horizontal components, is consistent between the design spectrum and the spectrum of the scaled record. However, the underlying definition of the horizontal component of code spectra is not always clear. An exception is NZS which states in the commentary that the design spectrum was derived from attenuation equations for the envelope component. The scaling procedure in NZS does not use the envelope spectrum of two components of a record but determines the stronger component which is defined as the component with the larger spectral values over the period range 0.4–1.3 T1, where T1 is the fundamental period of the structure in one specific direction of the structure. A record scale factor k1 is determined which minimizes the error between the target spectrum and the spectrum of the stronger component over the period range of interest. This is done for all records of the suite which will be used for the structural analysis. Finally, a record family scale factor k2 is determined which ensures that at each period within the period range of interest at least one spectrum of a stronger component scaled with the respective factor k1 is larger than the target spectrum. The two components of each record are hence scaled with the total factor k1 · k2. The stronger component of every record is applied in the direction in which the structural period T1 was determined. This procedure is repeated for all directions of the structure. In EC8, although the authors assume that is has been likewise defined as envelope spectrum (since this is the most commonly used definition in European GMPEs), this is not reflected in the scaling procedure. EC8 Part 1, which concerns buildings, states that accelerograms should be scaled to match the peak ground acceleration without commenting on whether this should be done for uni-directional analysis only or whether it also applies to bi-directional analysis for which no specific guidelines are given. In the latter case comments would be lacking on the exact scaling procedure, e.g., whether the same or different scaling factors are to be applied to the three components. EC8 Part 2 [2000] which concerns bridges, however, gives guidelines for the scaling of record components for bi-directional analysis. According to EC8 Part 2, uni-directional analysis may not be carried out. The design spectra are the same for buildings and bridges. As in ASCE 7-05 and FEMA 368, scaling of records with two horizontal components is based on the SRSS spectrum of the two components. EC8 Part 2 states that the average of all SRSS spectra should be scaled not to fall below 1.3 times the design spectrum for a single component, i.e., a single scaling factor is determined for the suite of records. FEMA 368 and ASCE 7-05 allow individual scaling of the records while both components of the record are scaled with the same scaling factor. The average SRSS spectrum of all records must match or exceed the design spectrum for a single component scaled up by a factor of 1.3 (FEMA 368) or 1.17 (ASCE 7-05), respectively. It remains unclear why the SRSS spectrum was chosen as the spectrum on which the scaling procedure was based. The period range over which matching of design spectrum and the scaled average spectrum of the records is required is 0.2T1 –1.5T1 according to the three provisions (EC8 Part 2, FEMA 368 and ASCE 7-05), where T1 is the fundamental period of the structure. Independent of the definition of the horizontal component, most design spectra in codes are approximations of uniform hazard spectra (UHS), the ordinates of which all have the same frequency of exceedance. Due to the different frequency content of small,


23


local events and large, distant events it might often be the case that the UHS at different response periods is dominated by different earthquake scenarios [Reiter, 1990]. Hence, if spectra of real records are scaled to match the UHS over either the entire or a very broad frequency range, the seismic input used for the analysis does not represent a single earthquake scenario. It has become widely accepted in practice that records should not be scaled to the UHS; this limitation applies to all of the codified guidelines cited herein for scaling of records and indeed represents a major shortcoming in current code definitions of seismic actions. 2.4.3 Direction of loading. Figure 1 has shown that the spectral ordinates vary when the two horizontal components are rotated. Structural systems commonly have stronger and weaker axes when loaded horizontally. The response of the structural system will hence depend on the orientation of the structural axis system relative to the ground-motion axes. Therefore, rotating the ground motion by a certain degree will lead to a different structural response. In EC8 it is specified that the seismic action shall “be applied in both positive and negative directions.” However, no specifications are made regarding the original orientation. It is therefore likely that the components are applied with an arbitrary orientation first and in a second analysis run the polarities of both components are switched. Changing the sign of both horizontal time history components corresponds to rotating the components by 180 degrees. Changing the sign of one component at a time does not correspond to a rotation. In fact, there are examples of ground-motion records where the polarity of a single horizontal component has been wrongly reported. In ASCE 4-98 it is stated that the axes of the ground motion “shall, in general, be aligned with the principal axes of the structure.” However, it is not stated how the ground motion axes should be orientated. The provisions ASCE 7-05, FEMA 368 and NZS require that the components are applied in the direction that will produce the most adverse effect of the considered parameter. They do not specify, however, how the most critical direction should be established. Normally the direction is found by rotating the ground-motion components at a certain angle interval (e.g., 1° or 5°) and analyzing the structure for all orientations of the components. The critical direction is then the one which leads to the most adverse effect. 2.4.4 Post-processing of analysis results. There are two steps involved when determining the design quantity of a response parameter from time-history analyses. First, the response quantity for each component pair needs to be determined and second, a final response value on the basis of all component pairs used for structural analysis needs to be computed. This final response value is then compared to the capacity of the structure. To distinguish between the final response value and the response value gained from analysis of a single component pair under several orientations of the components to the structural axes, the latter is referred to in the following as ‘response to an individual record’. With the exception of ASCE 4-98, which does not discuss the orientation of the ground-motion components with respect to the structural axes, all the reviewed codes require that for each component pair the maximum response from all analyzed directions is considered. According to EC8 only two directions need to be analyzed and the maximum response resulting from the application of the components in positive and negative directions shall be considered for design. As stated above, in the case of the provisions ASCE 7-05, FEMA 368 and NZS the relevant direction is the one which leads to the most adverse response. The provisions of EC8, FEMA 368, and ASCE 7-05 all require that the maximum of the response to the individual records is used as final response value if the number of

24


records n is 3 ≤ n < 7. If at least 7 records are used for the analysis, the average of the response to the individual records can be used as final response value. NZS requires that the maximum response to individual records is used, independent of the number n of records for which the structure was analyzed.


3. Selection of Horizontal Pairs The aim of selecting a set of accelerograms from a pool of ground-motion records is to find records which represent best (after scaling) the expected ground shaking at the site. In most codes (see Sec. 2.4.1) some or all of the parameters such as magnitude of the earthquake, source-site distance, source mechanism, and site classification are listed as selection criteria. However, a few codes (e.g., ASCE 4–98), as well as some researchers, propose different parameters as selection criteria. Baker and Cornell [2005] propose that the residual e of the ground motion should be considered when selecting the records. The residual e of the spectral ordinate is the number of standard deviations from the median ground motion as predicted by the GMPE. Shome et al. [1998] and Iervolino and Cornell [2005] conclude from parametric studies that magnitude and distance do not influence the median response if the records are scaled to match the design spectrum at the fundamental period. Watson-Lamprey and Abrahamson [2006a] suggest selecting records based on the response of a simple nonlinear model which can serve as a proxy of a more complicated nonlinear model. As an example they used the Newmark sliding block as proxy for more complex slope-stability models; the methodology was later extended to structures [Watson-Lamprey and Abrahamson, 2006b]. Malhotra [2003] suggests selecting records by their significant duration and their spectral shape. Amongst the studies cited here that by Malhotra [2003] is the only one which considers analyses with bi-directional input. This brief list illustrates the wide range of selection strategies which have been proposed. The aim of this section is neither to declare one of the existing selecting procedures as the best approach nor to propose a new one but rather to point out issues which are important to consider when selecting records intended as input for bi-directional dynamic analysis. These issues are discussed regarding the two most widely adopted selection strategies: • Earthquake scenario-based selection (Sec. 3.2.1) • Selection according to spectral matching and duration (Sec. 3.2.2) Before a record is selected, one needs to check that it is suitable as input for bi-directional analysis; desirable properties are discussed in Sec. 3.1. 3.1 Pre-selection of Records Before a record can be considered for selection, it is necessary to check that the properties of the record are such that it is suitable as bi-directional input for dynamic structural analysis. The obvious necessity that the record contains at least the two horizontal components if an analysis with bi-directional input motion is to be conducted has already been mentioned above. Other properties of the record depend on the recording technique of the ground motion and the processing of the data. Most databases provide the processed records only while the raw data is rarely published. All ground-motion records contain noise due to imperfections in the recording (and, for analogue records, the digitizing) process and the aim of processing the recorded data is to limit the data to frequency ranges where the signal-to-noise ratio is satisfactory [Boore and Bommer, 2005]. To achieve the



25

best results it is in most cases necessary to process the ground-motion records on an individual basis. There are many different processing techniques and the final choice of techniques and parameters will be the personal choice of the person performing the processing. However, certain techniques seem clearly preferable over others. If ground motions are to be used for bi-directional analysis, the choice of the filter types and parameters are of particular concern: Acausal filters should be preferred to causal filters since they do not distort the phase spectra [Boore and Akkar, 2003]. Other characteristics such as the order of the filter are of lesser importance. The horizontal components should, however, be filtered with the same filter parameters (same order and corner periods of the filter); it is also important that the leading zeroes, which should be retained in the filtered record, are of equal length on both components [Boore, 2005]. On the other hand, if the vertical component is also included in the analysis, it is not recommended to use the same filter parameters for the vertical as for the horizontal components. Processing all three components with the same filter parameters would lead to loss of low-frequency content of the horizontal components which is valuable to the structural engineer [Boore and Bommer, 2005]. Other aspects of recording and processing of ground-motion data are equally valid whether the record is used as uni- or bi-directional input for structural analysis. These concern for example: • The recording technique. The data quality of digital recordings is generally higher than the data quality of analogue recordings. However, a very large percentage of records from large seismic events which are currently available from databases are analog recordings. • The choice of whether or not residual displacements are retrieved. Retrieving residual displacements is only possible if baseline correction instead of low-cut filtering is employed to remove baseline errors in the accelerogram. Boore et al. [2002] showed that the magnitude of residual displacement is very sensitive to the parameters of the baseline correction procedure. However, residual displacements of ground motions is not only important if permanent differential displacements are of concern: Boore and Akkar [2003] and Bazzurro et al. [2004] showed that whether residual displacements are removed or retained also has an effect on mediumto-long period spectral displacements. In this study almost all records have been low-cut filtered, the residual displacements have hence been removed; the chosen records were recorded at some distance from the fault, i.e., it is reasonable to assume no permanent displacement. • The usable period range. Of great significance to any user of the processed record is the range of usable periods, i.e., the period interval which contains physically meaningful information. The raw data is usually filtered by a high-cut filter (removing frequency content above the high-cut corner frequency) and a low-cut filter (removing frequencies with lower frequencies than the corner frequency); frequency content outside this window of the processed record is not meaningful. Whether the entire frequency band between the corner frequencies is usable depends on the order of the filter: low order filters modify the frequency content over a considerable frequency band around the corner frequency [Boore and Bommer, 2005]. Akkar and Bommer [2006] suggested that—depending on the type of recording instrument, the magnitude of event and the site class—only spectral displacement ordinates up to 0.65–0.97 times the corner period of the low-cut filter should be trusted. All frequencies of modes of the structure which contribute significantly to the structural response should fall within the range of usable periods. The

26



influence of longer period motion on the response to shorter period motion should be considered. Furthermore, the period lengthening due to inelastic response of the structure needs to be included when the required usable frequency window is determined. For most structural engineering applications the corner frequency of the low-cut filter will decide whether the record is suitable for the analysis or not; the corner frequency of the high-cut filter is commonly less critical. In particular, if displacements of structures with medium-to-long periods are analyzed, one will find that the number of records which are suitable from a database will be significantly reduced. If all of the criteria for pre-selection of records were to be fulfilled the pool of records from which one could finally select would be in many cases very small. For example, from the 3,551 records in the NGA database [PEER, 2005], which was used in this study, only 48 records are digitally recorded and acausally filtered. These records were obtained from five events with magnitudes in the range Mw = 5.0–5.6. The one criterion which should not be compromised concerns the usable period range: If records are used beyond the maximum usable period the analysis results are meaningless. Figure 2 shows the magnitude-distance distribution of the records in the NGA database [PEER, 2005]. The records were grouped in three bins according to the maximum usable period which is

FIGURE 2 Distribution of records in the NGA database [PEER, 2005] with respect to magnitude, hypocentral distance, and maximum usable period. The maximum usable period is the one given in the document accompanying the database; records where the hypocentral distance was not given are plotted with dhypo = 1km (such records were not used for the scenario selection).


27

given in a table accompanying the database. The maximum usable period of the record is the smaller of the maximum usable periods of the two horizontal components. Less than half of the records (1,615 out of 3,551) were filtered with the same filter settings for the two horizontal components; for ten records the filter parameters were not reported.


3.2 Different Selection Strategies A comprehensive discussion of the selection and scaling of real records for uni-directional analysis is included in Bommer and Acevedo [2004]. They suggested that a first search for records is conducted using an earthquake scenario with magnitude, distance and site class as selection criteria. If this search yields more records than needed they suggested to search amongst the accelerograms from the first sweep for those which match the spectral shape of the target spectrum best and, to a lesser extent, the amplitude of the target spectrum. In the present study, the two selection strategies are considered independently, either one or the other is used for selection of the records. This is neither necessary nor most likely the best choice but was done to simplify the selection and to focus on aspects which concern the choice of records for bi-directional analysis. 3.2.1 Scenario-based selection. If scenario based selection is applied, records are selected which fall in bins around central values of seismic parameters. In most cases, not only one parameter but two or more parameters are used for selection. The three most traditional selection parameters are magnitude, source-to-site distance, and site class. The reason for this is that important characteristics of the record such as frequency content, spectral amplitudes, spectral shape, and duration are correlated to magnitude, distance, and site class. Site classes are commonly based on the shear velocity of the uppermost ground layers. One of the most widely adopted site classification systems is that presented in NEHRP which is also used for the classification of the records in the NGA database. Instead of selecting records with a matching site class it is also possible to select ground motions recorded on rock sites and conduct site response analyses. Baker and Cornell [2005] suggested to include the ground-motion residual e(Ti) as selection parameter because it controls the shape of the spectrum in the vicinity of the period Ti. They noted that positive values of e(Ti) are commonly associated with a local peak of the spectrum, i.e., with values locally higher than the median values predicted by the GMPE. Negative values of e(Ti) indicate a local ‘valley’ of the spectrum. Another selection parameter is the source mechanism. Bommer and Acevedo [2004] recommended to omit this parameter unless the search by all other parameters has yielded a large number of records. For all parameters except the ground-motion residual e(Ti), there is no difference whether records are selected for uni-directional or bi-directional analysis if the ordinate of the design spectrum used for the bi-directional analysis is a single component measure, such as for example GMxy. If a probabilistic seismic hazard analysis is carried out, the scenario parameters for magnitude and distance are gained from disaggregation of the hazard analysis results; the parameters correspond to the earthquake which contributes most to the hazard at the size. For bi-directional analysis it would also be possible to choose an ordinate definition which retains the two components and to disaggregate the joint ordinate pairs using Vector PSHA [Bazzurro and Cornell, 2002]; although this is conceptually feasible, the analysis is difficult to perform in practice and this option is hence not considered in the following. If the hazard at a site is described by means of a design code, it is often impossible to determine the underlying earthquake scenario (Sec. 2.4.1) and hence scenario-based selection is not an option unless the scenario parameters are estimated by


28


trying to fit an appropriate GMPE equation to the code spectrum. If magnitude and distance of the earthquake scenario are known, however, the only missing parameters are the bin widths which are used for the selection of the records. Stewart et al. [2001] suggested a magnitude half bin width of ±0.25Mw while Bommer and Acevedo [2004] recommended ±0.20Mw. For their case study, Bommer and Acevedo [2004] used the distance bin [0 km, 40 km] around the scenario value of 10 km. They recommended to relax the distance criterion if the search yields too few records. In the case of insufficient records, they also suggested to be not too rigorous regarding matching of the site class but to solely exclude records with very different site classification from that of the project site. If the ground-motion residual e(Ti) is included in the set of selection parameters it is important that the spectrum of the record matches the definition of the GMPE that is used to determine the ground-motion residual. In this study the geometric mean spectrum is used (Sec. 2.3). The period Ti for which the residual is determined should be the period which controls the response of the structure most. Normally this will be the period of the fundamental mode of the structure in either of the two horizontal directions. The groundmotion residual would be typically determined for one of the fundamental periods of the structure. 3.2.2 Selection according to spectral matching and duration. By selecting according to spectral matching and duration one tries to identify records which match best—after scaling of the records—the expected seismic impact on the structure. If codified spectra are used, selection on the basis of spectral ordinates is easier to apply than selection by earthquake scenario since the target spectrum is readily available to the engineer. Most duration prediction equations are, however, linked to magnitude and source-site distance and hence using duration as selection parameter, if no information on the seismogenic features of the controlling earthquake are available, is as unfeasible as the scenario-based selection. There are different methods to identify the records which match the target spectrum best after scaling. Malhotra [2003] suggested to fit a smooth spectrum defined by nine parameters to the geometric mean spectrum of each record by minimizing the sum-of-square difference between actual and smooth spectrum. He then proposed to select records with smooth spectra which have similar corner periods as the target spectrum. The records are scaled to match the spectral ordinate of the target spectrum at one of the corner periods. Naeim et al. [2004] suggested using genetic algorithms to select and scale a family of records whose average matches the target spectrum best. Although the result of such a search algorithm might be very satisfactory, for someone unfamiliar with the methodology of genetic algorithms it is difficult to understand and to implement correctly. The European Strong Motion Database [Ambraseys et al., 2004] can be searched for records with spectral shapes similar to the target spectrum using the following equation for the root-mean-square difference:

Drms =

1 N

2

⎛ SaR (Ti ) SaT (Ti ) ⎞ − . ∑ ⎜⎝ PGA PGA ⎟⎠ N

i =1

R

(3.1)

T

where SaR(Ti) is the spectral acceleration of the real record at the period Ti, PGAR the peak ground acceleration of the real record, SaT(Ti) is the spectral acceleration of the target record at the period Ti, PGAT the target peak ground acceleration and N the number of periods at which the spectra are defined. This method anchors the spectral shape at the peak ground acceleration. For many structural engineering problems longer periods are of greater interest. To make allowance for the need of matching the target spectrum over the


29

period range which is of prime interest for the structural analysis, the method was modified as follows: For each record a scale factor a was determined which minimized the root-mean-square difference Drms between the scaled geometric mean spectrum of the real record and the target spectrum:


Drms =

k 1 (a SaR (Ti ) − SaT (Ti ))2 , ∑ k − j + 1 i= j

(3.2)

where T, and Tk are the jth and kth entries of the period vector for which the spectral accelerations are defined. The interval [Tj, Tk] defines the period range for which spectral matching is desired; guidelines for the selection of the period interval are given below. From all records those with the smallest root-mean-square difference are selected. Another approach to matching which eliminates the influence of the variation of amplitude of the spectral acceleration with period is to normalize the error by the target value at each period: 2

Drms =

k ⎛ a SaR (Ti ) − SaT (Ti ) ⎞ 1 ∑ ⎟⎠ . k − j + 1 i = j ⎜⎝ SaT (Ti )

(3.3)

The period range for which spectral matching should be aimed is given in most codes as with 0.2T1 –1.5T1 (Sec. 2.3.2) where T1 is the fundamental period of the structure. However, it is believed that the upper period limit of 1.5 T1 might be too low if the structure is undergoing large inelastic deformations causing elongation of the period of the structure [N. Priestley, personal communication, 2005]. It is suggested that a limit be used which is dependent on the expected displacement demand on the structure. In this study the period range [Tm , m Δ T1 ] is considered when matching record with target spectrum, where Tm is the period of the highest mode which contributes significantly to the elastic response of the structure and mΔ the displacement demand on the structure. The period m Δ T1 corresponds to the effective period as defined in the framework of direct displacement-based design [Priestley et al., 2007]. Some researchers suggest to include the duration or number of effective cycles as selection criteria. Hancock and Bommer [2006] have, however, pointed out that the influence of duration or effective cycles on the structural response is still debated in the scientific community. Before duration or effective cycles are included as selection criteria one should therefore consider whether duration or effective cycles are expected to affect the structural response. This depends not only on the structure but also on the response parameter which is used to measure the structural response. Cumulative damage parameters often used to assess the damage to reinforced concrete members are, for example, more dependent on the effective number of cycles than the maximum roof displacement of a structure. Another feature that increases the effect of duration or effective cycles is the use of material models which degrade in strength with successive cycles. However, few analysis programs are capable to model strength degradation effects correctly. If it is decided that duration should be considered when selecting records, the choice of definition of duration or effective cycles requires attention. There is a large number of definitions available in the literature for duration and effective cycles [Bommer and Martínez-Pereira, 1999; Hancock and Bommer, 2006]. Bommer et al. [2006] have also shown that the correlation between different duration and effective number of cycles


30


measures is commonly very poor. If a correlation between duration or effective cycles and structural response is expected, the choice of an appropriate definition for these parameters is hence important. Defining the duration or effective cycles for in-plane motion is not straightforward. Malhotra [2003] suggested to take simply the arithmetic mean of the durations of each component. The same suggestion is made by Green et al. [2004] for the number of effective cycles of in-plane motion: The number of effective cycles was defined as the arithmetic mean of the cycles of the two components. However, both definitions seem a bit simplistic, in particular since their dependence on the orientation of the components has not been investigated. Another common way to count cycles of in-plane motion is to consider the SRSS sum of the component time histories. Hancock and Bommer [2005] have shown that this definition leads to very different results for harmonic motions which are either in or out-of-phase since the polarity (sign) of the time histories is lost. Neither of the presented definitions for duration or effective cycles of in-plane motion seems to have a robust physical basis. Duration and effective cycles are not considered as selection parameter in this study.

4. Options for Scaling Horizontal Pairs of Components Before the scaling options of horizontal pairs of components are considered a number of issues regarding the response quantities are discussed. A typical displacement response quantity is, for example, the lateral displacement at the effective height of a wall, which is required to determine the displacement ductility demand on the wall. In general, not one but a set of records will be used for the analysis of the structure. Depending on the type of the project: • only the mean or median of the structural responses from all records is of interest, • or an estimate of the distribution of the structural response might be required, too. For most engineering projects an estimate of the median is sufficient and this quantity will be the focus of the further discussion. Note that most codes require the computation of the mean rather than the median response from the analysis of n records (mostly 3 or 7 records). However, it is argued herein that the median response is of greater engineering significance since the mean response gives too much weight to singular events (e.g. structural failure for one single record leading to infinite response). The aim of scaling of the records and applying the records to the structure is hence to gain a good estimate of the median response with as few records as possible. With respect to the response of the structure to a single record, one needs to decide whether • One is interested in the maximum response the selected ground motion can cause, i.e., the maximum response from all possible angles of incidence between the ground-motion axes and the structural axes (Fig. 3a). Most codes demand that the most critical orientation of ground-motion axes and structural axes is considered (Sec. 2.4.4). If the structural response is computed for the most critical angle of incidence, i.e., if the angle of incidence is selected which leads to the maximum response, then the probability of exceedance of the structural response will be smaller than the probability of exceedance of the spectral acceleration. It is assumed that the structure is modelled with median physical properties. The probability of exceedance of the seismic hazard is often chosen as 10% in 50 years, although this value was originally chosen somewhat arbitrarily [Bommer and


b)

a)

p(θ) 1

y

360°

FP

θ

31

dθ/360°

θ

FN

Structural Response

x θ Max. Median


θ

FIGURE 3 (a) Angle of incidence q between structural axes and ground-motion axes as used in the case study in Sec. 5 and (b) asssumed probability distribution and structural response values as a function of q.

Pinho, 2006]. Selecting the angle of incidence which causes the maximum response leads to a smaller probability of exceedance. • One is interested in the structural response with, if not exactly the same, at least similar probability of exceedance as the seismic hazard. Bazzurro et al. [1998] showed that the two probabilities of exceedance are approximately the same if the variation of the structural response is neglected. An exact relationship between the probability of exceedance of the seismic hazard and the probability of exceedance of the structural response depends on the shape of the hazard curve as well as the standard deviation of the structural response. As a rule, the probability of exceeding the structural response will be larger than the probability of exceeding the groundmotion level which on average causes this structural response. This follows from probability theory; a detailed treatment of this aspect can be found, for example, in the aforementioned paper by Bazzurro and his co-authors. To simplify matters the effect of the variability of the structural response is neglected in the following. To assess the likelihood that a certain response value is exceeded, assumptions are also required regarding the distribution of the orientation angle q. For the purpose of this study it is assumed that q is uniformly distributed, i.e., the source of the earthquake is equally likely to lie in any direction with respect to the structure. This assumption does not hold of course for sites close to an active fault, where the expected orientation of the fault-normal and fault-parallel axes with respect to the structural axes are effectively known. The median response of the structure for all possible angles q is the ‘typical’ response which is equally likely to be exceeded or not. It is therefore argued that if the probability of exceedance from the seismic hazard analysis is not to be altered by the selection of the angle q one should consider the median response from all angles q. It is clear that identifying the maximum response for all possible angles q requires a large number of analyses since the ground-motion axes need to be rotated at a sufficiently small interval to capture the maximum response. Strictly speaking, the same applies when the median response is to be determined. However, the response to randomly oriented groundmotion axes can be used as an estimate for the median response. In this case only one analysis per record is required. It is, however, expected that for the same accuracy in the estimate of the median response, analyses with more ground-motion records are required

32


if the records are only analyzed for an arbitrary orientation than if for each record the median response for all angles of incidence is determined (Sec. 5). Regarding scaling of the records to match the geometric mean target spectrum, two options seem possible:


• Scaling of the geometric mean spectrum of the record to match the target spectrum. The record was scaled to minimize the error between record and target spectrum (Eq. 3.2). • Scaling of the components individually so that not only the geometric mean but also each component matches the target spectrum as well as possible. This is done by first scaling the geometric mean spectrum of the record to match the target spectrum; this scaling factor is called a. In a second step one component is scaled by a factor b while the other is scaled by the factor 1/b. In this way the geometric mean spectra of the two components remains unaltered. The second of the scaling procedures is clearly only an option if the median response and not the maximum response is of interest. It is, however, not suitable for determining the variation of response values with seismic input. Moreover, it still remains to be established whether this method of scaling reduces the number of analyses needed to obtain a good estimate of the median response and if it introduces a bias to the median response (Sec. 5). The advantage of this scaling method lies in the reduced intensity variation between the components. It is hence expected that fewer analysis are required to reach a stable estimate of the response.

5. Case Study To illustrate some of the points made in the previous chapter a small case study is carried out which aims to show the effects of different selecting and scaling methods on the structural analysis result. For this case study a reinforced concrete structure (Sec. 5.1) with a fundamental period in the cracked state of about 1 s is analyzed. The earthquake scenario which dominates the seismic hazard at the site is a magnitude 7 earthquake at a distance of 20 km to the closest point on the fault with a ground-motion residual of e = 1.0 at T1 = 1 s. The site is classified as NEHRP class ‘C’. The target spectrum for the site is given by the geometric mean spectra according to the GMPE by Abrahamson and Silva [1997]. Figure 4 shows the acceleration and displacement target spectra; the

FIGURE 4 Target spectrum for case study: acceleration spectrum for Mw = 7.0, Rrup = 20 km, and e(T = 1.0 s) = 1.0 according to Abrahamson and Silva [1997] and displacement spectrum.


33

displacement spectrum has been computed by dividing the spectral acceleration by the square of the circular frequency.

As an example structure a 4-story reinforced concrete building is chosen (Fig. 5). The floor plan of the structure is 25 m × 15 m in size; the story height is 3 m. The lateral strength of the system is provided by four structural walls at the perimeter of the slabs. If the structure is excited parallel to the transverse walls, the response will be purely translational since Wall 3 and 4 are of equal length and strength (it is assumed that the center of mass is at the center of the slab). Wall 1 and Wall 2, however, are of different length and have different bending capacities. An excitation parallel to these walls therefore introduces a rotation into the system in addition to the translation. Since the example structure is regular over the height, the structure can be well approximated by a planar 2-D model (Fig. 6). Each wall is modelled by a nonlinear spring with the modified Takeda hysteresis rule representing the force-displacement characteristics at the effective height of the wall. The mass of all storys is lumped in an effective mass at the effective height of the building (heff = 9.3 m). The three modes of the planar 2-D model have the following shapes: The first mode (T1 = 0.97 s) is a pure translational mode in the transverse direction; the second mode (T2 = 0.88 s) has a translational component in the longitudinal direction and also a rotational component; the third mode (T3 = 0.88 s) is a predominantely rotational mode with some translation in the longitudinal direction. Such a 2-D model is well suited for parametric studies since the required analysis time is very short when compared to the analysis time of a full 3-D model. The model is analyzed using the program Ruaumoko [Carr, 2004].

3.2

b) Gravity columns

0.2

Wall 4

0.2

0.3

5

12

y Wall 1

2.5 15 longitudinal direction

a)

x

3


5.1 Example Structure

Wall 2

Wall 3 5

0.2 3.2 25 transverse direction

FIGURE 5 Example structure: 4-story reinforced concrete building, elevation (a) and plan view (b).

Wall 4

Wall 1

M, Irot

Wall 2

Wall 3

FIGURE 6 In-plane 2-D model of example structure.

34



5.2 Selection of Records Records were selected from a subset of the 949 records in the NGA database. From the NGA database with 3,351 records chiefly those from the 1999 Chi-Chi earthquake or from any of its aftershocks were excluded; the exact definition of the subset of the records is given in Beyer and Bommer [2006]. Three groups of 20 records were selected. With 20 records the 95% confidence intervals of the mean response values given in Table 3 are about ±10% of the mean values. The computation time required to analyse a very simple model such as the 2-D stick-model is not very significant. Based on the analysis results of the simple model the required number of records for a more complicated model of the same structure can be estimated. All selected records were scaled to match the target spectrum in the period range of interest (Eq. 3.2). The period range of interest was chosen to include all periods which are expected to significantly contribute to the response of the example structure: The natural periods of the 2-D model with 3 degrees of freedom are 0.97, 0.88, and 0.48 s. A 3-D model including more degrees of freedom will have modes with periods smaller than 0.48 s. Since the chosen records should also be suitable for the analysis of a more elaborate 3-D model of the same structure, the smallest period of interest was estimated as 0.1 s. The largest significant period was estimated using the relationship m Δ T1 (Sec. 3.1.6). Using the direct displacement-based design method [Priestley et al., 2007] it was estimated that the expected displacement ductility of the system should not be larger than 3.0; the largest significant period is hence about 1.7 s, which is rounded to 2.0 s. The period range of interest which was considered when scaling the records is hence [0.1 s, 2.0 s]. To account for the fact that periods longer than this might influence the spectrum, only records with a minimum usable period of 3 s were selected. Also excluded were records for which the velocity time histories suggested that near-source directivity effects might have been present. The selection strategies for the three groups of 20 records were the following: • Set A: From the 949 records the closest distance (as used to define the target spectrum) was only reported for 690 records. Out of these 690 records, all records were selected which fall into the following bins: Mw = [6.8, 7.2], Rrup = [0,50], e(T = 1s) = [0.3; 1.7] and had site classes not more than one class apart from the project site class, i.e., records with site classes between B and D were accepted. This search yielded 34 records. From this set, records with near-source effects and some of the records of the Loma Prieta earthquake in 1989 were excluded. The original set included 23 records from the Loma Prieta earthquake, these were reduced to 11 records to limit possible bias due to overrepresentation of this event. The remaining 20 records were scaled to match the acceleration target spectrum.

TABLE 3 Median, mean and coefficient of variation for different response quantities obtained for Sets A, B, and C Median

Mean

CoV

Set A Set B Set C Set A Set B Set C Set A Set B Set C Response for qmax Response for qmed Response for qrnd1 Response for qrnd2

2.94 2.09 2.23 1.99

2.47 1.89 1.87 1.86

2.46 1.95 1.98 1.93

2.74 2.10 2.19 2.24

2.45 1.94 1.95 1.89

2.49 1.99 2.04 2.01

0.24 0.23 0.28 0.34

0.19 0.18 0.28 0.28

0.20 0.16 0.22 0.24


35


• Set B: 20 records were selected which best matched the acceleration target spectrum over the period range of interest. No requirements regarding magnitude, distance, residual or soil class were imposed. All selected records have, however, maximum usable periods greater than 3 s. • Set C: The selection strategy is very similar to the one for Group B but this time 20 records were selected which matched the displacement instead of the acceleration target spectrum over the period range of interest best. The difference between matching the acceleration and displacement spectrum lies in the weighting of the error at short and long periods: matching the displacement spectra puts more emphasis on the longer periods. Whether the displacement or the acceleration spectrum should be used for matching depends on the response quantity which is of interest. The records from Set A, B, and C originate from 5, 12, and 13 earthquake events, respectively. It is not surprising that records in Set A come from only a few earthquakes since the admissible earthquake events are limited by magnitude and distance bins. The acceleration and displacement spectra of the records are plotted in Fig. 7. With the exception of the mean acceleration spectra of Set A, all mean spectra match the target spectra fairly well. The mean spectra of Sets B and C are fairly similar. Differences between the two sets become obvious when the individual records are considered: Within the period range of interest the divergence of the spectra from the individual records is small for the acceleration spectra of Set B and the displacement spectra of Set C. These spectra were used to assess the goodness-of-fit between target and record spectra and to determine the scale factors, hence the good agreement between target spectrum and spectra of the individual records is not surprising. Figure 8 shows the distribution of the records with respect to magnitude and distance (top row of plots) and with respect to scale factor and distance (bottom row of plots). The variation of the scale factor is significantly larger for Sets B and C than for Set A. Since the records in Set A originate from events with similar magnitude, distance, and ground-motion residual as well as soil class as the design scenario, the spectral amplitudes of the unscaled records are comparable to those of the target spectrum. Records in Set B and C chiefly originate from events with magnitudes smaller than the magnitude of the design scenario (Mw = 7.0); the scale factors are hence in most cases considerably larger than unity. 5.3 Analysis of Structure and Definition of Response Quantities For each of the three sets of records, the following analyses were carried out: Each record with two components was rotated in 36 steps of 5°. The total angle covered is hence 180°, which includes all possible combinations of relative orientation of structural axes and the axes of the input components since the structural system is symmetric about the z-axis. The orientation angle is defined as zero when fault-normal and fault-parallel the groundmotion axes (i.e., the orientation of the components given in the NGA-database [PEER, 2005]) align with the structural axes (Fig. 3a). The analysis of one set of records which contains 20 ground motions required therefore 20 ´ 36 = 720 runs. Since the model is very simple each run required only a couple of seconds of computation time and the analysis of one set of records took between 30 and 45 min. As an example response quantity, the displacement ductility on Wall 4 is considered (Fig. 5). Three different definitions of the response quantity are used in the following: • Maximum response: For each record, the maximum response from all 36 groundmotion axes orientations is determined. The corresponding displacement ductilities are referred to as the response for qmax.



36

FIGURE 7 Acceleration and displacement spectra of the scaled records in Set A, B, and C. The target spectrum is plotted with a thick black line, the mean spectrum of the scaled records is plotted with a thick grey line, and the individual spectra of the scaled records are plotted with thin grey lines. The two black vertical lines define the period range which is of interest for the analysis of the example structure, i.e., [0.1 s, 2.0 s]. • Median response: For each record, the median response from all 36 ground-motion axes orientations is determined. The resulting displacement ductilities are referred to as the response for qmed. • Random Choice: For each record, two directions (Random Choice 1 and 2) are randomly selected. The resulting displacement ductilities are referred to as the



37

FIGURE 8 Top row: Distribution of the records in Set A, B, and C with respect to magnitude and distance. Records for which the closest distance Rrup was not defined were plotted with Rrup = 1km; these records were excluded when the mean of the distance was computed. Bottom row: Distribution of records in Set A, B, and C with respect to scale factor and distance. The black line indicates the mean value of the scale factor, the grey lines the mean value ± standard deviation of the scale factor.

responses for qrnd1 and qrnd2. The random orientation is the orientation of the components as given in most databases. The new NGA-database [PEER, 2005] is an exception since the components are orientated in fault-normal/fault-parallel direction. Figure 9 shows the comparison of the responses for qmax and qmed for all records. The ratio of these response values varies between 1.05 and 1.68. The mean and median values of these response values for the three sets of records are given in Table 3. The median values of Sets B and C are fairly similar; the median values of Set A for the responses for qmax and qmed are, however, between 7 and 20% larger than those of Sets B and C. This is likely to be caused by the selection strategy: selecting by the spectral shapes avoids spectra with high peaks and low troughs, which are present in Set A. Carballo and Cornell [1998] suggested that spectra with smoother shapes (such as Sets B and C) tend to be less aggressive than spectra with pronounced troughs and peaks (such as Set A). Moreover, due to the smoother spectral shape the coefficients of variation (CoV) of the response values are about 20% smaller for Set B and Set C than for Set A (Table 3). The CoV indicates how many analysis runs are required to get a good estimate of the response quantity; the smaller the CoV the fewer analysis runs are required to achieve the same level of accuracy. The graphs in Fig. 9 illustrate that 3 records—which is a typical minimum number of


38


FIGURE 9 Displacement ductility demand on Wall 4: Comparison of maximum and median response values. For each record the maximum (black line) and median response (grey line) to each record for all angles of incidence are plotted. The dashed lines are the median response from the 20 records. records required by codes—are, in general, insufficient to estimate the maximum or median response. Figure 10 illustrates this finding in more detail. From the analysis of 20 records all possible combinations of three records were considered; these are in total 1,140 combinations. For seven out of 20 records there are 77,520 such combinations. The left plot of Fig. 10 shows the distribution of the mean values if only three (black line) or seven records (grey line) are considered out of the 20 records. As an example, the distributions are plotted for records of Set A with a random orientation of ground-motion axes with respect to the structural axes (response for qrnd1). The thin dashed lines represent the actual distribution of the mean values, while the thick solid lines are fitted normal distributions.

FIGURE 10 Mean displacement ductilities computed for 3 and 7 records, respectively: The left figure shows the distribution of the mean ductilities computed for 3 (black lines) and 7 (grey lines) records, respectively. The thick lines are fitted normal distributions, the thin lines the actual distribution. The vertical lines indicate the interval between 90 and 110% of the median ductility demand obtained from the 20 records. The right figure shows the same information, but this time the mean values for 3 records only are plotted. The grey shaded areas correspond to groups of 3 records whose mean value is outside the interval between 90 and 110% of the median ductility demand obtained from the 20 records.



39

For the 77,520 combinations when seven records are considered, the actual and the fitted distribution are almost identical. The vertical lines indicate the median response obtained from the 20 records (m^ 20 ). Also shown as vertical lines are 90% and 110% of m^ 20 The graph shows that a large percentage of combinations, for both 3 and 7 records, lead to estimates of the median response which are more than 10% off the median response obtained from 20 records. This is illustrated in more detail in the right hand figure: All combinations which are represented by the grey shaded area underneath the density curve correspond to combinations which lead to mean values smaller than 90% of m^ 20 or larger than 110% of m^ 20 . For three records, these are 49.2% of all combinations while for seven records the percentage reduces to 23.5% records. Figure 11 shows similar results as Fig. 9 but instead of the response for qmax the results for the two random choices of the orientation angle (qrnd1 and qrnd2) are compared against the response for qmed. While the median values (Table 3) of the random choices are fairly similar to the median values of the response for qmed, the CoV of the random choices are considerably larger than the CoV of the response for qmed. Therefore, if each record is only analyzed for a random orientation (instead of all possible orientations) more records are required to get a good estimate of the median response value. However, per record, only one analysis is required instead of 36 analyses for simple symmetric buildings or 72 analyses for buildings which do not have a symmetry axis (for dq = 5°). Although computer power is continuously increasing 36 or 72 analyses per record might cause relatively large computational costs if a complex 3-D model is analyzed. It is therefore suggested to use—as in the presented case study and as suggested by Watson-Lamprey and Abrahamson [2006a]—a simple model as a proxy for a more detailed model. The simple model can be used to identify the orientation which leads to the median response. The complex model is then analyzed only for this predetermined orientation. Figure 12 shows the response for qmax and the response for qmed as a function of the scale factors which were applied to the 20 records. For none of the three sets can a clear trend of the response with scale factor be observed. This underlines the statement by Bommer and Acevedo [2005] that most limits for scale factors are chiefly based on “folklore” rather than scientific reasons. As a further option, scaling of the components with different factors was explored. As in the previous analysis sets, the geometric mean spectrum was scaled with a factor a to match the target spectrum over the period range of interest. Then,

FIGURE 11 Displacement ductility demand on Wall 4: For each record the median response (thick black line) is compared against the results from two randomly chosen orientations of ground-motion axes with respect to structural axes (thin grey lines). The dashed lines are the median response from the 20 records.


40


FIGURE 12 Distribution of maximum and median response of Wall 4 with respect to the scale factor which was applied to the record.

in a second step, the components were scaled by a factor b and 1/b respectively (section 4). An example of this scaling procedure is shown in Fig. 13. On the left, spectra and response values of the record which has been scaled with a = 2.23 only are shown. On the right, equivalent plots for the same record are shown but this time the components have been scaled by a · b and a/b, respectively; the spectra of the two components are now closer to the geometric mean spectrum than when both components were scaled by a. The plots in the bottom row show the variation of the response value with orientation of the ground motion. The range of values obtained if a uniform scale factor a is applied is greater than the difference between maximum and minimum value obtained when the components are scaled with different factors. However, this is not a generally applicable finding. Among the 60 records in Sets A, B, and C there is also a significant number of records where the difference between maximum and minimum for the two scaling procedures are almost identical or where the difference is smaller if a uniform scaling factor is applied. Figure 14 shows the response for qmed for a uniform scaling factor and for different scaling factors for the two components. The response values for angle qmed obtained for the two scaling procedures are almost identical. This is also reflected in the median, the mean values and the CoV of the three sets (Table 4). The same finding applies if a random orientation of ground-motion axes (qrnd1) to structural axes rather than the response for angle qmed is considered (Fig. 15). These analysis results suggest that individual scaling of components does not reduce the variability of the results and as a consequence the number of records required to yield a stable estimate of the response parameter.



41

FIGURE 13 Scaling of components with different scaling factors. Top row: Target spectrum (thick black line), geometric mean spectrum (thick grey line), and spectra of the fault-normal and fault-parallel components (thin grey lines) if both component are scaled by a = 2.23 (left) and if the fault-normal component is scaled by a factor a · b = 1.81 and the fault-parallel component by a factor a/b = 2.75 (right). Bottom row: Variation of response with orientation angle q.

FIGURE 14 Median displacement demand on Wall 4 if both components are scaled by the same factor a (black line) and if components are scaled by a · b and a/b, respectively (grey line).

42


TABLE 4 With and without component scaling: Median, mean, and coefficient of variation for different response quantities obtained for Sets A, B, and C Median

Mean

CoV

Set A Set B Set C Set A Set B Set C Set A Set B Set C


Response for qmed, b = 1 Response for qmed, b ≠ 1 Response for qdrnd1, b = 1 Response for qdrnd1, b ≠ 1

2.09 2.03 2.23 1.70

1.89 1.96 1.87 1.78

1.95 1.95 1.98 1.75

2.10 2.11 2.19 2.02

1.94 1.96 1.95 1.89

1.99 1.96 2.04 1.76

0.23 0.25 0.28 0.35

0.18 0.19 0.28 0.30

0.16 0.14 0.22 0.29

FIGURE 15 Displacement demand on Wall 4 for a random orientation of ground-motion axes to structural axes if both components are scaled by the same factor a (black line) and if components are scaled by a · b and a/b, respectively (grey line).

6. Discussion and Conclusions This article addresses a series of issues related to ground-motion input for bi-directional analysis. These issues concern the selection, scaling and application of ground motions with two components for nonlinear dynamic structural analysis. The study has been initiated since guidelines in codes which are currently available seem unsatisfactory regarding their consistency and their lack of transparency. It has been shown in Sec. 2.2 that there are a number of different definitions of the horizontal component which can be grouped into definitions which retain the two components and definitions which reduce the horizontal motion to a single ground-motion measure. To achieve consistency over the selection and scaling process it is mandatory to clearly state the chosen definition of the horizontal component at the beginning of the seismic hazard assessment when defining the target spectrum for the considered building site and to maintain this definition throughout the analysis process of the structure. In this study, the geometric mean of the spectral ordinate of the two horizontal components was used to define the target spectrum and to select and scale ground-motion records. The geometric mean spectrum has been chosen for a number of reasons among which are the relatively large set of GMPEs which are available at present for this definition of the horizontal component, the simple comparison between target and record spectrum since the two horizontal components are reduced to a single spectrum, and its clear mathematical formulation which is also meaningful in logarithmic space. Other definitions of the horizontal component such as the envelope spectrum can also be used but it seems more difficult to define clear and consistent selection and scaling procedures.



43

It has been shown that the structural response varies depending on the angle of incidence of the ground motion with respect to the structural axes. It is up to the seismologist and structural engineer to decide whether the maximum response (qmax) or median response (qmed) from all possible angles of incidence or any other response measure should be considered. It is argued in this study that the response for qmed is the most appropriate response quantity if the chosen probability of exceedance in the seismic hazard study (e.g., 10% in 50 years) is not to be altered by the selection of the angle q. The response of the structure to a random orientation (qrnd) of the ground-motion axes with respect to the structural axes can serve as an approximation of the median response. The aim of the case study presented in Sec. 5 was to compare selection and scaling strategies regarding their efficiency in estimating the median response caused by a set of ground motions. It has been shown that selecting records according to their goodness-of-fit with the target spectrum leads to smaller coefficients of variations than if the records were selected according to an earthquake scenario defined in terms of magnitude, source-site distance, and ground-motion residual (e) at the fundamental period of the structure. Hence, fewer records are required to yield a stable estimate of the median response if records are selected for their goodness-of-fit with the target spectrum than if scenario-based selection is applied. The coefficient of variation of the response quantity could be further reduced if the records were not applied with a random orientation with respect to the structural axes but if the orientation was determined which leads to the median response amongst all possible orientation angles. Determining the orientation angle which leads to the median response inevitably requires a large number of analyses per record. However, it is argued that a simple model with only few degrees of freedom can be used as proxy for more complex models to determine the relevant orientation—similar to the methodology developed by WatsonLamprey and Abrahamson [2006a,b] for selecting ground motions. As another alternative to reduce the coefficient of variation of the response quantity scaling of the two horizontal components by the scaling factors b and 1/b, respectively, was explored. The aim was to make the spectra of the two components more similar to their geometric mean spectrum. However, this scaling method did not lead to a reduction in the coefficient in variation in the structural response. All the scaling procedures discussed in this paper used linear scaling of the time histories; the option of adjusting the two components of a record with wavelets [Hancock et al., 2006] to achieve a better match between target and record spectrum has not yet been investigated but will be the topic of a future study.

Acknowledgments The authors firstly wish to thank Prof. Nigel Priestley who initiated this project with his thought-provoking keynote lecture at the 5th International Seminar at the ROSE School in Pavia, Italy in 2005. The authors would like to sincerely thank Dr. Paolo Bazzurro and Dr. Iunio Iervolino for the pertinent and insightful comments which significantly improved the article regarding both content and readability. The authors would also like to express their gratitude towards Prof. Paolo Pinto and Dr. Paolo Franchin for the fruitful discussions at the start of this study. The first author would also like to express her gratitude to John Alarcón, Guillermo Aldama, John Hancock, Rishmila Mendis, and Fleur Strasser who contributed to the work during many discussions related to different aspects of engineering seismology.

References Abrahamson, N. A. and Silva, W. J. [1997] “Empirical response spectral acceleration relations for shallow crustal earthquakes,” Seismological Research Letters 68(1), 94–127.


44


Ambrayses, N. N., Douglas, J., Rinaldis, D., Berge-Thierry, C., Suhadolc, P., Costa, G., Sigbjörnsson, R., and Smit, P. [2003] “Dissemination of European strong-motion data, Vol. 2,” CD-ROM Collection, Engineering and Physical Science Research Council, United Kingdom. Akkar, S. and Bommer, J. J. [2006] “Influence of long-period filter cut-off on elastic spectral ordinates,” Earthquake Engineering and Structural Dynamics 35, 1145–1165. Arias, A. [1970] “A measure of earthquake intensity,” In Seismic Design for Nuclear Power Plants, Hansen, R. J., Ed., The MIT Press, Cambridge Massachusetts, and London, England, pp. 438–483. ASCE [2000] “Seismic analysis of safety-related nuclear structures and commentary,” ASCE Standard No. 004-98, American Society of Civil Engineers. ASCE [2006] “Minimum design loads for buildings and other structures,” ASCE Standard No. 007–05, American Society of Civil Engineers. Baker, J. W. and Cornell, A. [2005] “A vector-valued ground motion intensity measure consisting of spectral acceleration and epsilon,” Earthquake Engineering and Structural Dynamics 34, 1193–1217. Baker, J. W. and Cornell, A. [2006a] “Which spectral acceleration are you using?” Earthquake Spectra 22(2), 293–312. Baker, J. W. and Cornell, A. [2006b] “Correlation of response spectral values for multicomponent ground motions,” Bulletin of the Seismological Society of America 96, 215–227. Bazzurro, P., Shome, N., Cornell, C. A., and Carballo, J. E. [1998] “Three proposals for characterizing MDoF non-linear seismic response’,” Journal of Structural Engineering, ASCE, 124(11), 1281–1289. Bazzurro, P. and Cornell, C. A. [2002] “Vector-valued Probabilistic Seismic Hazard Analysis (VPSHA),” Proc. of 7th U.S. National Conference on Earthquake Engineering, Boston, MA. Bazzurro, P., Sjoberg, P., Luco, N., Silva, W., and Darrangh, R. [2004] “Effects on strong motion processing procedures on time histories, elastic and inelastic spectra,” Proc. of the Invited Workshop on Strong-Motion Record Processing, The Consortium of Organisations for Strong-Motion Observation Systems (COSMOS), Richmond, CA, available online www.cosmos-eq.org. Beyer, K. and Bommer, J. J. [2006] “Relationships between median values and between aleatory variabilities for different definitions of the horizontal component of motion,” Bulletin of the Seismological Society of America 96(4A), 1512–1522. Bommer, J. J. and Acevedo, A. [2004] “The use of real earthquake accelerograms as input to dynamic analysis,” Journal of Earthquake Engineering 8 (special issue 1), 43–91. Bommer, J. J., Hancock, J. and Alarcón, J. E. [2006] “Correlations between duration and number of effective cycles of earthquake ground motion,” Soil Dynamics and Earthquake Engineering 26, 1–13. Bommer, J. J. and Martínez-Pereira, A. [1999] “The effective duration of earthquake strongmotion,” Journal of Earthquake Engineering 3(2), 127–172. Bommer, J. J. and Pinho, R. [2006] “Adapting earthquake actions in Eurocode 8 for performancebased design,” Earthquake Engineering and Structural Dynamics 35(1), 39–55. Bommer, J. J. and Ruggeri, C. [2002] “The specification of acceleration time-histories in seismic design codes,” European Earthquake Engineering 16(1), 3–17. Boore, D. M. [2005] “On pads and filters: processing strong-motion data,” Bulletin of the Seismological Society of America 965(2) 745–750. Boore, D., Stephens, D., and Joyner, W. [2002] “Comments on baseline correction of digital strongmotion data: Examples from the 1999 Hector Mine, California, Earthquake,” Bulletin of the Seismological Society of America 96, 1543–1560. Boore, D. and Akkar, S. [2003] “Effect of causal and acausal filters on elastic and inelastic response spectra,” Earthquake Engineering and Structural Dynamics 32, 1729–1748. Boore, D. and Bommer, J. J. [2005] “Processing of strong-motion accelerograms: Needs, options and consequences,” Soil Dynamics and Earthquake Engineering 25(2), 93–115. Boore, D., Watson-Lamprey, J., and Abrahamson, N. [2006] “Orientation-independent measures of ground motion,” Bulletin of the Seismological Society of America 96(4A), 1502–1511. Carballo, J. E. and Cornell, C. A. [1998] “Input to nonlinear structural analysis: Modification of available accelerograms for different source and site characteristics,” Proc. of the 6th US National Conference on Earthquake Engineering, Seattle, Washington.



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Carr, A. J. [2004] “Ruaumoko – a program for inelastic time-history analysis,” Program manual, Department of Civil Engineering, University of Canterbury, New Zealand. CEN [2003] “Eurocode 8: Design of structures for earthquake resistance. Part 1: General rules, seismic actions and rules for buildings,” Final Draft prEN 1998, European Committee for Standardization, Brussels. CEN [2005] “Eurocode 8: Design of structures for earthquake resistance. Part 2: Bridges,” Final Draft prEN 1998-2, European Committee for Standardization, Brussels. Clough, R. and Penzien, J. [1993] Dynamics of Structures, McGraw-Hill, Inc., New York. FEMA [2001] “NEHRP recommended provisions for seismic regulations for new buildings and other structures, 2000 Edition, Part 1: Provisions,” FEMA 368, Building Seismic Safety Council for the Federal Emergency Management Agency, Washington D.C. Fernández-Davila, V. I. and Cruz, E. F. [2005] “Generación de sismos artificiales a partir de una caracterización de un conjunto de registros de un sismo real,” Proc. Congresso Chileno de Sismología e Ingeniería Antisísmica IX Jornadas (in Spanish), Concepción, Chile. Hancock, J. and Bommer, J. J. [2005], “The effective number of cycles of earthquake ground motion,” Earthquake Engineering and Structural Dynamics 34, 637–664. Hancock, J. and Bommer, J. J. [2006], “A state-of-knowledge review of the influence of strongmotion duration on structural damage,” Earthquake Spectra 22(3), 827–845. Hancock, J., Watson-Lamprey, J., Abrahamson, N. A., Bommer, J. J., Markatis, A., McCoy, E., and Mendis, R. [2006] “An improved method of matching response spectra of recorded earthquake ground motion using wavelets,” Journal of Earthquake Engineering 10 (special issue 1), 67–89. Hernández, J. J. and López, O. A. [2002], “Response to three-component seismic motion of arbitrary direction,” Earthquake Engineering and Structural Dynamics 31, 55–77. Iervolino, I. and Cornell, C. [2005] “Record selection for nonlinear seismic analysis of structures,” Earthquake Spectra 21(3), 685–713. Kubo, T. and Penzien, J. [1979] “Analysis of three-dimensional strong ground motions along principal axes, San Fernando Earthquake,” Earthquake Engineering and Structural Dynamics 7, 265–278. Malhotra, P. K. [2003] “Strong-motion records for site-specific analysis,” Earthquake Spectra 19(3), 557–578. Morris, I. [2005] “What you see is what you get – or is it?,” SECED Newsletter June, 7–10. Naeim, F., Almoradi, A., and Pezeshk, S. [2004] “Selection and scaling of ground motion time histories for structural design using genetic algorithms,” Earthquake Spectra 20(2), 413–426. NZS 1170.5 [2004] “Structural design actions, Part 5: Earthquake actions – New Zealand,” Code and Supplement, Standards New Zealand, Wellington, New Zealand. PEER [2005] NGA database (where NGA stands for “Next Generation of Attenuation”) with records orientated in fault-normal and fault-parallel orientation, PEER strong-motion database (http://peer.berkeley.edu/nga/index.html), Pacific Earthquake Engineering Research Centre, Berkeley. Penzien, J. and Watabe, M. [1975] “Characteristics of 3-dimensional earthquake ground motion,” Earthquake Engineering and Structural Dynamics 3, 365–373. Priestley, M. J. N., Calvi, G. M., and Kowalsky, M. J. [2007] Direct Displacement-based Seismic Design of Structures, IUSS Press, Pavia (draft, book in preparation). Reiter, L. [1990] Earthquake Hazard Analysis Issues and Insights, Columbia University Press, New York. Shome, N., Cornell, C, Bazzurro, P., and Carballo, J. [1998] “Earthquake, records and nonlinear responses,” Earthquake Spectra 14(3), 469–500. Stewart, J. P., Chiou, S.-J., Bray, J. D., Graves, R. W., Somerville, P. G., and Abrahamson, N. A. [2001] “Ground motion evaluation procedures for performanced-based design,” PEER Report 2001/09, Pacific Earthquake Engineering Research Centre, University of California, Berkeley. Watson-Lamprey, J. and Abrahamson, N. [2006a] “Selection of ground motion time series and limits to scaling,” Soil Dynamics and Earthquake Engineering 26, 477–482. Watson-Lamprey, J. and Abrahamson, N. [2006b] “Selection of time series for analyses of response of buildings,” Proc. of the First European Conference on Earthquake Engineering and Seismology, Geneva, Switzerland.

Selection and Scaling of Real Accelerograms for Bi

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