EQTools 3.0 ®

EQTools 3.0  ®
EQTools 3.0
®
Computational Tools for Characterization, Evaluation,
and Modification of Strong Ground Motions within
Performance-Based Seismic Design Framework
User’s Guide
Virginia Polytechnic Institute and State University
Department of Civil and Environmental Engineering
200 Patton Hall
Virginia Tech, Blacksburg, VA 24061
USA
E-mail: [email protected]
While every precaution has been taken to in the preparation of this documentation, the author
assumes no responsibility for errors or omissions, or for damages from the use of information
contained in this document of from the use of programs or source code that may accompany it. In
no event shall the author be liable for any loss of profit or any other commercial damage caused
or alleged to have been caused directly or indirectly by this document.
Printed: August 2010 in Blacksburg, Virginia.
© Copyright Finley A. Charney, 2010.
All rights reserved.
Virginia Polytechnic Institute and State University
Department of Civil and Environmental Engineering
200 Patton Hall
Virginia Tech, Blacksburg, VA 24061
USA
E-mail: [email protected]
August, 2010
Table of Contents
1 About the User’s Guide ......................................................................................................... 1 2 Welcome to EQTools ............................................................................................................ 2 3 4 5 2.1 What is EQTools? ............................................................................................... 2 2.2 New Features ...................................................................................................... 3 2.3 Application Design and Concepts ....................................................................... 4 2.4 System Requirements.......................................................................................... 5 2.5 Installing EQTools .............................................................................................. 6 2.6 Acknowledgments............................................................................................... 7 Strong Ground Motion Database ........................................................................................ 8 3.1 About the Strong Ground Motion Database ....................................................... 8 3.2 Sources of Ground Motion Records ................................................................... 9 3.3 Adding Records to the Database ....................................................................... 10 3.4 File Naming Convention for Time History Files .............................................. 14 3.5 Data Format for Strong Motion Time History Files ......................................... 16 Ground Motion Database Search Tools............................................................................ 19 4.1 Main Program Window..................................................................................... 19 4.2 EQTools Database Search Engine .................................................................... 20 4.3 Database Search Parameters ............................................................................. 21 4.4 Searching for Records in EQTools Environment ............................................. 27 4.5 Viewing the Details of Searched Records ........................................................ 29 4.6 Selecting Records for Study.............................................................................. 31 4.7 Sorting the Searched and Selected Records ...................................................... 34 4.8 Saving and Opening Bin of Earthquakes .......................................................... 34 Investigating Amplitude and Duration Parameters ........................................................ 36 6 7 5.1 Generating Time History Plots ......................................................................... 36 5.2 Time History Plots for Single Record ............................................................... 37 5.3 Time History Plots for Multiple Records.......................................................... 40 5.4 Time History Plot Controls ............................................................................... 42 5.5 Creating Time History Files.............................................................................. 45 5.6 Investigating Incremental Velocities ................................................................ 46 5.7 Investigating Incremental Displacements ......................................................... 49 5.8 Investigating Bracketed Durations.................................................................... 49 Fourier Amplitude Spectrum............................................................................................. 51 6.1 Generating Fourier Amplitude Spectrum using EQTools ................................ 51 6.2 Fourier Amplitude Spectrum for a Single Record ............................................ 54 6.3 Fourier Amplitude Spectrum for Multiple records ........................................... 55 6.4 Fourier Amplitude Spectrum Plot Controls ...................................................... 56 6.5 Exporting the Computed Fourier Amplitude Spectra Data............................... 62 6.6 Fourier Amplitude Spectrum Analysis Tools ................................................... 62 Elastic Response Spectra and Scaling of Time Histories ................................................ 71 7.1 Generating Elastic Response Spectra Using EQTools...................................... 71 7.2 Generating Elastic Response Spectrum for a Single Record ............................ 73 7.3 Generating Elastic Response Spectra for Multiple Records ............................. 75 7.4 Response Spectrum Plot Controls..................................................................... 76 7.5 ASCE-7 Design Spectrum ................................................................................ 80 7.6 Scaling of Elastic Response Spectra for Selected Records ............................... 81 7.7 Saving the Scaled Bin of Earthquakes .............................................................. 86 7.8 Exporting the Computed Response Spectrum Data .......................................... 87 7.9 Generating and Saving DrainPro Data Files ..................................................... 88 8 Ground Motion Attenuation Tools .................................................................................... 89 8.1 Overview of Ground Motion Attenuation Relationships .................................. 89 8.2 Ground Motion Attenuation Relationships ....................................................... 98 8.2.1 N. A. Abrahamson and W. Silva Attenuation Relationship ......................... 98 8.2.2 Kenneth W. Campbell Attenuation Relationship........................................ 103 8.2.3 David M. Boore, William B. Joyner, and Thomas E. Fumal Attenuation
Relationship ............................................................................................................ 106 8.2.4 K. Sadigh, C.-Y. Chang, J.A. Egan, F. Makdisi, and R.R. Youngs
Attenuation Relationship ........................................................................................ 109 8.2.5 P. Spudich, J.B. Fletcher, M. Hellweg, J. Boatwright, C. Sullivan, W.B.
Joyner, T.C. Hanks, D.M. Boore, A. McGarr, L.M. Baker, and A.G. Lindh
Attenuation Relationship ........................................................................................ 113 8.2.6 R.R. Youngs, S.-J. Chiou, W.L. Silva, and J.R. Humphrey Attenuation
Relationship ............................................................................................................ 115 8.2.7 Gail M. Atkinson and David M. Boore Attenuation Relationship (1997a) 117 8.2.8 Atkinson and Boore Attenuation Relationship (1997b).............................. 119 8.3 9 Ground Motion Attenuation Plot Controls ..................................................... 123 New Attenuation Relationships ....................................................................................... 125 9.1.1 Abrahamson and Silva (2008) .................................................................... 125 9.1.2 Boore and Atkinson (2008)......................................................................... 132 9.1.3 Campbell and Bozorgnia (2008) ................................................................. 134 9.1.4 Chiou and Youngs (2008) ........................................................................... 138 9.1.5 Idriss (2008) ................................................................................................ 140 9.2 New Ground Motion Attenuation Plot Control .............................................. 141 10 Site Response Analysis Using EQTools ........................................................................... 149 10.1 Overview of Site Response Analysis Procedures ........................................... 149 10.2 Analysis Control Information for Site Response ............................................ 150 10.3 Base Input Ground Motions ............................................................................ 151 10.4 Geometric and Dynamic Properties of Soil Model ......................................... 152 10.5 Running the Site Response Analysis .............................................................. 153 10.6 Interpreting the Site Response Analysis Results ............................................ 154 11 Horizontal Pair Window: ................................................................................................. 156 12 New Scaling Window ........................................................................................................ 161 12.1 Data to Scale: .................................................................................................. 162 12.2 Combination Options: ..................................................................................... 162 12.3 Scaling Options: .............................................................................................. 163 12.4 Scaling Criteria: .............................................................................................. 164 12.5 Target Spectrum: ............................................................................................. 166 12.6 Plot Options: ................................................................................................... 168 12.7 Steps for Scaling ............................................................................................. 170 12.8 Using Horizontal Pair tool in scaling tool: ..................................................... 172 13 References .......................................................................................................................... 173 1
About the User’s Guide
This User’s Guide contains an introduction to EQTools features and environment, including
resources available in the application for getting more out of EQTools.
The User’s Guide uses the following notations and conventions:
Italics represent error or cautionary messages.
Bold Courier represents the input expected of the user.
Bold represents a menu command.
An arrow such as that in “File → Search Database for Records” indicates a submenu
command.
Function keys and other special keys are enclosed in brackets. For example, [ ↑ ], [ ↓ ], [ ← ] and [
→
] are the arrow keys on the keyboard. [F1], [F2], etc., are function keys; [BkSp]is the
Backspace key for backspacing over characters; [Del] is the Delete key for deleting characters
to the right; [Ins] is the Insert key for inserting characters to the left of the insertion point.
The symbol [ ↵ ] and [Enter] refer to the same key.
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2
Welcome to EQTools
2.1 What is EQTools?
EQTools 3.01 is a Microsoft Windows2 based application that comprises of requisite
computational tools to provide a rapid and consistent means towards systematic assembly of
representative strong ground motions and their characterization, evaluation, and modification
within a performance-based seismic design framework. The application is graphics-intensive
and every effort has been made to make it as user-friendly as possible. The application seeks to
provide processed data which will help the user address the problem of determination of the
critical earthquakes by identification of the severity and damage potential of more than 700
components of recorded earthquake ground motions. Computational tools are also developed to
estimate the ground motion parameters for different geographical and tectonic environments and
to perform one-dimensional linear/nonlinear site response analysis as a means to predict ground
surface motions at sites where soft soils overlay the bedrock.
One of the most difficult tasks towards designing earthquake resistant structures is the
determination of critical earthquake(s). Conceptually, these are the ground motions that would
drive the structure being designed to its critical response. The quantification of this concept,
however, is not so easy. Unlike the linear response of a structure, which can often be obtained
using a single spectrally modified ground motion time history the nonlinear response is strongly
dependent on the phasing of input ground motion and the detailed shape of its spectrum. This
necessitates the use of a suite (bin) of time histories having phasing and spectral shapes
appropriate for the characteristics of the earthquake source, wave propagation path, and site
conditions that control the design spectrum. Computational tools are available in the EQTools
environment to accomplish this. The suite of assembled records may have to be scaled to match
the design spectrum over a period range of interest, rotated into strike-normal and strike-parallel
1
EQTools, Copyright © 2010, Virginia Polytechnic Institute and State University, Blacksburg, Virginia.
2
Windows is a trademark of Microsoft Corporation, Redmond, Washington
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directions for near fault effects, modified for local site conditions before they can be input into
time-domain nonlinear analysis of structures.
The generation of these time histories is
cumbersome and daunting. This is especially due to the sheer magnitude of the data processing
involved. EQTools provides the means to carry out these operations in a systematic manner.
While EQTools may be used for professional practice or academic research, the fundamental
purpose behind the development of the software is to make an available integrated
classroom/laboratory tool that provides a visual basis for learning the principles behind the
selection of time histories and their scaling/modification for input into time domain nonlinear (or
linear) analysis of structures. EQTools in association with NONLIN, a Microsoft Windows
based application for the dynamic analysis of single and multi-degree of freedom structural
systems (Charney, 2003) may be used for learning the concepts of earthquake engineering,
particularly as related to structural dynamics, damping, ductility, and energy dissipation.
2.2 New Features
Since the last version of EQTools was released, the program has added the following features to
its capabilities.
(1) New source category containing records from ATC63 seismic qualification
(2) Orbit Spectrum
(3) Next generation attenuation models
(4) New tool to scale individual, pair or pair and vertical components records for earthquake
events.
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2.3 Application Design and Concepts
All the input in the EQTools environment is carried out interactively through the use of the
computer keyboard and the mouse.
For the current version, plots generated using the
computational tools in the EQTools environment are written to the screen in several different
“windows” and tabular output information can be written to tab-delimited files with the .XL1
tension. These tabular data files are intended for use with a spreadsheet program such as
Microsoft Excel. This allows the user to perform further processing of the data or to graph the
output data for inclusion in reports and other documents. The .XL1 files can be viewed or
printed from a simple text processing program such as Microsoft WordPad. Graphical screen
plots of several different types are produced during program execution. Hard copies of any of
the screen plot windows may be obtained as described later in this manual.
The application has been developed using Microsoft’s Visual Basic 8.0, Enterprise Edition.
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2.4 System Requirements
EQTools must be run on Windows XP SP2 or later. The system should have a minimum
hardware configuration appropriate to the operating system you are using.
For best results, your system's video should be set to 1024 by 768 resolution or more,
displaying not less than 256 simultaneous colors (32 bit preferred). The computer must be
equipped with a Microsoft compatible mouse, trackball, or other pointing device.
Warning: EQTools will not run properly if the system's video resolution is set lower than
1024 by 768 pixels.
In order to install and run EQTools 3.0, the following are recommended or required:
•
Windows XP or higher
•
Pentium 233MHz or greater processor
•
Minimum 64MB of RAM.
Additional memory is recommended for improved
performance
•
SVGA or graphics card and monitor. The software is optimized to run on a screen
resolution of 1024 x 768 or higher.
•
Mouse or compatible pointing device
•
At least 200MB of disk space
Direct Internet connection or Internet access through a service provider is recommended.
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2.5 Installing EQTools
Note
This installation of EQTools 3.0 requires the uninstallation of any previous versions of
EQTools from your computer before installing the new version. We have found that
running more than one version of EQTools from the same computer can lead to
instability and unexpected behavior. To uninstall previous versions of EQTools, use
“Add/Remove Programs” from your Windows Start menu under Settings → Control
Panel
Instructions in this section are intended for single-user edition of EQTools. Currently, it is
possible to run EQTools on a single stand-alone machine only.
To install EQTools, run the SETUP utility provided on the CD. The installation procedure given
below will work for both all the Windows versions.
1. Insert CD EQTools CD in the appropriate drive, D: or E:.
2. Run setup.exe.
3. Follow the setup instructions on the screen.
4. EQTools and associated compressed files are expanded and placed in the newly created
“C:\Program Files\Advanced Structural Concepts\EQTools V3\” directory by
default. You can change the directory name during the setup process.
You can run EQTools from the Start button on the Taskbar by highlighting Programs
→
Advanced Structural Concepts and then clicking on the EQTools V3 icon. Alternatively, you
can drag the EQTools program icon to your desktop. A shortcut icon is created in the dragging
process. To run EQTools, double click the shortcut icon.
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2.6 Acknowledgments
EQ-Tools was developed by Dr. Finley A. Charney, President of Advanced Structural Concepts,
Inc., Blacksburg, Virginia, and Associate Professor of Structural Engineering, Virginia Tech,
Blacksburg, Virginia. Several other individuals have contributed significantly to the program,
including Riaz Syed, Brian Barngrover, and Rohan Talwalker. The program documentation and
Help system was developed by Finley Charney, Riaz Syed, Rohan Talwalker, Jordan Jarrett, and
Ozgur Atlayan.
Funding for the development of EQ-Tools has come from a variety of sources including
Advanced Structural Concepts, Inc., the Federal Emergency Management Agency (FEMA), and
the Building Seismic Safety Council (BSSC).
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3
Strong Ground Motion Database
3.1 About the Strong Ground Motion Database
In the EQTools environment, the access to recorded strong ground motions is made available
through a strong motion database. Central to the EQTools architecture is a large database of
corrected instrumental records of seismic accelerations measured at the ground level during
earthquakes with magnitude greater than 4.5. Besides the actual acceleration records (all stored
in a unique format and unit system) and information on earthquake events, each record contains
information on the geographic location, source characteristics, site-source distance, site geology,
local site conditions, amplitude parameters, and duration parameters. EQTools allows the user to
search the database for records (using various search criteria), display/print the search results,
and retrieve the desired acceleration time histories. As more information becomes available to
the user, new records can be easily added and old records can be updated.
The EQTools strong motion database currently contains over 900 records of engineering interest
from tectonically active regions. Three orthogonal components are available for each recording
in the database, except for those records which do not have vertical ground motion component in
NGA database. This is because all the records are collected from NGA website. The records are
categorized into those recorded within the continental United States and those recorded outside
of continental United States. The contents of the database utilize publicly available processed
data from Pacific Earthquake Engineering Research Center (PEER), Berkeley. For engineering
applications, strong motion is what is of interest. Hence, the database contains only those
records that have a peak ground acceleration of more than or equal to 0.05g.
Microsoft Access has been used to create the relational database of ground motion records. The
database file, named “eqrecords.mdb” is stored in the default installation directory
C:\Program Files\Advanced Structural Concepts\EQTools V3\.
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3.2 Sources of Ground Motion Records
As mentioned before, the contents of the database utilize the publicly available processed records
from the PEER website. Following is a list of primary data providers to PEER. The developer
gratefully acknowledges the providers' efforts in making data available to the engineering
community.
ACOE
Army Corps of Engineers (USACE)
BYU
Brigham Young University
CDMG
California Division of Mines and Geology
CDOT
California Department of Transportation
CDWR
California Division of Water Resources
CEOR
Committee of Earthquake Observation and Research in the Kansai Area
(CEORKA), Osaka, Japan
CIT
California Institute of Technology
CUE
Conference on the Usage of Earthquakes, Railway Technical Research
Institute, Tokyo, Japan
CWB
Central Weather Bureau (Taiwan)
DWP
Los Angeles Department of Water and Power
ERD
Earthquake Research Department (Turkey)
ITU
Istanbul Technical University (Turkey)
KOERI
Kandilli Observatory and Earthquake Research Institute, Bogazici
University (Turkey)
LAFC
Los Angeles Flood Control
LAMONT
Lamont Doherty Earth Observatory, Columbia University
MWD
Metropolitan Water District
SCE
Southern California Edison
UCSC
University of California, Santa Cruz
UNAM
Universidad Nacional Autonoma de Mexico
USBR
US Bureau of Reclamation
USC
University of Southern California
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USGS
United States Geological Survey
VADVA
VA Department of Veterans Affairs
PEERNGA
ATC63/FEMA695 Qualification Records Set
3.3 Adding Records to the Database
The Microsoft Access database of the ground motion records can be updated with new records
with ease. The ground motion database file "eqrecords.mdb" is available in the installation
directory of EQTools. This file can be opened using Microsoft Access and additional records
can be appended to the database. To exploit the power of 32-bit databases, it is recommended
that Access 95 or later versions be used to add records to the database. The database has a
specific field format and the user must strictly follow this format while updating the database
with additional records. A brief description of the fields in the database is given below:
Database filename
:
eqrecords.mdb
Location
:
drive:\ProgramFiles\InstallationDirectory
(default Î C:\Program Files\Advanced Structural Concepts\EQTools V3\)
Field EqName
-
Name of the earthquake event. The name is followed by the date and
time of occurrence as shown in the example.
Example: Borrego Mtn. 1968/04/09 02:30
Field DateAndTime -
Date and time of the earthquake event.
Example: 4/9/1968 2:30:00 AM
Field Station
-
Name of the station where the ground motion was recorded
Example: 5160 Anza Fire Station
Field DataSource
-
Name of party that actually recorded the ground motion data.
Example: USGS United States Geological Survey
Field Location
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Location category.
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Example: Continental United States
Field Component
-
Component of the recorded ground motion. It can be either of the
following:
Field Deg
-
-
Vertical
-
Horizontal (Maximum PGA)
-
Horizontal (Minimum PGA)
Orientation of the recorded ground motion
= "-" if the component is vertical
= XXX if the orientation was XXX degrees (e.g. 230o)
Field Mechanism
-
Fault mechanism
Example: Strike-Slip
Field MinMagAny
-
Minimum value of all available magnitudes for the record
Field MaxMagAny
-
Maximum value of all available magnitudes for the record
Field AvgMag
-
Average of the minimum and maximum magnitude values (i.e.
average of MinMagAny and MaxMagAny…needs to be calculated
by the user)
Field MagM
-
Moment magnitude of the earthquake event.
Type "999999999" if not known
Field MagML
-
Local magnitude of the earthquake event
Type "999999999" if not known
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Field MagMS
-
Surface wave magnitude of the earthquake event
Type "999999999" if not known
Field MagOther
-
Any other or unknown available magnitude measure
Type "999999999" if not known
Field Directivity
-
Whether near-field record or not. This filed has following possible
entries:
Field DistClose
-
-
Near Field (Distance <= 20 Km)
-
Near Field (Classified)
-
Far Field
Closest distance to the fault (in Kilometers)
Type "999999999" if not known
Field DistHypo
-
Hypo-central distance to fault (in Kilometers)
Type "999999999" if not known
Field DistJB
-
Projected distance on fault plane (in Kilometers)
Type "999999999" if not known
Field MinDist
-
Minimum of all available distance (in Kilometers)
Type "999999999" if not known
Field MaxDist
-
Maximum of all available distance (in Kilometers)
Type "999999999" if not known
Field AvgDist
-
Average distance to fault (in kilometers)
(i.e. average of MinDist and MaxDist … needs to be calculated by the
user). Type "999999999" if not known
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Field SiteClass
-
USGS site class, e.g. A, B, etc. If not known, type "Unknown" in this
field if the site classification is not available
Field PGA
-
Peak ground acceleration (in "g" units)
Field PGV
-
Peak ground velocity (in "cm/s" units)
Field PGD
-
Peak ground displacement (in "cm" units)
Field PGAFlag
-
Flag to discern the PGA for a set of 3 components for a record.
= 0 if vertical component.
= 1 for horizontal component with lesser PGA
= 2 for horizontal component with more PGA
Field Duration
-
Duration of the earthquake in seconds
Field FileTH
-
Name of the file containing the acceleration, velocity and displacement
time histories for the earthquake.
Once the above fields are supplied, the time history file should be added to the database. The
data file containing the time histories for the added record should be copied to the following
directory.
Drive:\InstallationDirectory\records
(default Î C:\Program Files\Advanced Structural Concepts\EQTools V3\records)
EQTOOLS, by default, looks for the data files in this directory.
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3.4 File Naming Convention for Time History Files
The strong motion data files (.ACC) in the database contain the acceleration, velocity and
displacement time histories. The data format and the unit system are highly specific. A unique
file name convention has been used for the data files whereby the file names are meant to
describe the contents. A tool has been created to convert .nga files to .ACC files, called ‘Ground
Motion Wizard’. This tool is available on the menu bar of EQTools. Following figure shows the
location of the tool in the menu.
The ground motion wizard can only read the format used in the Pacifica Earthquake Engineering
Research (PEER-NGA) strong ground motion database. Hence, before adding a new record in
EQTools database, the user should make sure to have acceleration time history of that record in
the same format. When the recorded acceleration time histories are saved, they should be saved
with .nga extensions to make them readable by the Ground Motion Wizard. The figure below
shows the screenshot of this tool. When the file is converted through this wizard, it gets stored in
the Records folder.
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NGA files can be opened using the browse key called Load EQ Record. Once a record is
opened, the program will automatically read and display Name, Date, Data Source, Station, and
Duration from the file. The user has to manually set the remaining required options such as
Directivity and Mechanism to complete the information.
Each record is identified by 13
characters as follows. All the files are stored in a specific pre-defined directory. Characters 1-4
identify the earthquake event; characters 5-8 identify the recording station. If there are multiple
records with the same earthquake event name and recording station, the first three characters of
5-8 characters are used to designate the recording station and the remaining one character is used
to identify the record in chronological order by using A, B, C, etc. For example, the records at
117 El Centro Array #9 station for the Imperial Valley Earthquakes of 1938 an 1951 would be
identified as IMPVELCA and IMPVELCB respectively. Characters 9-11 hold the information
for the component. For example, a vertical component would be identified as IMPVELCA-UP
and N45E component would be identified as IMPVELCA045. The three letter extension is
always ACC signifying that the file contains acceleration values as the primary recorded
quantity. Thus, the entire file name would read as: IMPVELC-045.ACC.
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3.5 Data Format for Strong Motion Time History Files
In the EQTools database, the actual acceleration, velocity and displacement records are stored in
a unique format and unit system. The file formats and naming conventions are consistent for all
the records.
Each time history file has the three letter extension “ACC” signifying that
acceleration time history is the primary recorded quantity and the velocity and displacement
histories are obtained by integrating acceleration and velocity time histories respectively. As
mentioned earlier, the contents of the database utilize publicly available processed data from
Pacific Earthquake Engineering Research Center (PEER) NGA Database, Berkeley. PEER NGA
does not have separate files for acceleration, velocity and displacement time histories. Velocity
and displacement time histories are obtained by integrating acceleration time history through the
Ground Record Wizard. In the EQTools database, the three quantities are stored in a single file
by concatenating the three PEER files for a given recording. Consequently, the data file has
three blocks of data – one each for acceleration, velocity and displacement, in that order.
Acceleration Data Block
This block of data has following header lines:
1. Comment (may be used to indicate the data provider)
2. Earthquake name, date and time; station location; recorded component; data source and
station number (if available)
3. Acceleration and units; Filter points
4. Number of points and DT (time step)
The header lines are followed by a single data trace from a strong motion record.
The
FORTRAN format for each line is “5(1E15.7E2)”. Five values are given on each line, and there
are as many lines as are required to provide the number of time-series values indicated in the
value given in the fourth header line.
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Velocity Data Block
This block of data has following header lines:
1. Comment (may be used to indicate the data provider)
2. Earthquake name, date and time; station location; recorded component; data source and
station number (if available)
3. Velocity and units; Filter points
4. Number of points and DT (time step)
The header lines are followed by velocity values obtained by integrating the acceleration time
history. The FORTRAN format for each line is “5(1E15.7E2)”. Five values are given on each
line, and there are as many lines as are required to provide the number of time-series values
indicated in the value given in the fourth header line of the velocity data block.
Displacement Data Block
This block of data has following header lines:
1. Comment (may be used to indicate the data provider)
2. Earthquake name, date and time; station location; recorded component; data source and
station number (if available)
3. Displacement and units; Filter points
4. Number of points and DT (time step)
The header lines are followed by displacement values obtained by integrating the velocity time
history. The FORTRAN format for each line is “5(1E15.7E2)”. Five values are given on each
line, and there are as many lines as are required to provide the number of time-series values
indicated in the value given in the fourth header line of the displacement data block.
A partial listing of the file SAN_LA_A90_.ACC is given below.
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Example Acceleration Record for Imperial Valley Earthquake:
PEER NGA STRONG MOTION DATABASE RECORD
SAN FERNANDO 02/09/71 14:00, LA HOLLYWOOD STOR LOT, 090 (USGS STATION 135)
ACCELERATION TIME HISTORY IN UNITS OF G
2800
0.0100
NPTS, DT
0.502735E-03
0.748869E-03
0.112548E-02
0.126848E-02
0.127161E-02
0.113219E-02
0.132489E-02
0.194844E-02
0.242433E-02
0.273864E-02
0.247960E-02
0.155848E-02
0.167540E-02
0.246211E-02
0.181961E-02
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4
Ground Motion Database Search Tools
4.1 Main Program Window
After EQTools is started, the main EQTools window automatically appears. This windows is
shown below.
The EQTools main window consists of a title bar, a menu bar and Earthquake Record Search
Tool. This window is always open, and serves as a "container" for all other windows used by the
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program. Closing the EQTools window terminates the program, and minimizing the window
reduces the entire EQTools environment to an icon. The title bar displays the program name.
4.2 EQTools Database Search Engine
The search query form in the EQTools environment appears on the screen as the starting window
of the program. Through the inputs in this window, the user can search the database for ground
motion records by various parameters or combinations of the parameters.
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4.3 Database Search Parameters
The user can search the database by using the following control parameters (or a combination of
these control parameters).
Geographical Location: The user can choose ground motions recorded either on the continental
United States or outside of continental United States or both. The default location is "Any".
Earthquake Event: The user can choose the name of a particular earthquake available in the
databse by using the drop-down list of earthquakes. The default event is "Any".
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Record Component: This parameter lets the user search a record on the basis of horizontal or
vertical component. Also, the user can search the record based on the dominant or nondominant orthogonal horizontal components. The available options for these parameters are
shown below. The default component is "Vertical and Horizontal Pairs".
Fault Mechanism: This parameter lets the user search a record on the basis of the mechanism
of the fault causing the earthquake. The available options for these parameters are shown
below. The default mechanism is "Strike-Slip".
Zone of Recording: The user can choose between near field or far field records. The
database can be searched without including this parameter as well. The available options are as
shown below.
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Magnitude or Peak Ground Acceleration (PGA): This control allows the user to search the
records on the basis of the Magnitude of the event OR the Peak Ground Acceleration
recorded. A range needs to be specified for the magnitude and the PGA in the provided input
boxes. The PGA is always in "g" units and the available range of PGA is shown on the right of
the PGA input boxes.
The user can choose between the Magnitude or PGA by using the radio buttons (see the picture
below).
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For the magnitude, the user has further choices depending upon the type of magnitude one is
interested in. The following magnitude types are available:
- Moment Magnitude (M)
- Local Magnitude (ML)
- Surface Wave Magnitude (MS)
- Other or Unknown Magnitude measure (Other)
- Any of the above mentioned magnitudes (Any)
Again, the type of magnitude is chosen by using the option buttons (shown below).
Distance: This control allows the user to search the records on the basis of distance of the
recording station from the fault. A range needs to be specified for the distance in the input
boxes provided for the purpose. The distance is always in "kilometers".
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For the distance, the user has further choices depending upon the type of distance one is
interested in. The following distance types are available:
- Closest distance (Closest)
- Hypocentral distance (Hypocentral)
- Projected distance on the fault plane (Projection of Fault Plane)
- Any of the above mentioned magnitudes (Any)
The type of distance is chosen by using the option buttons (as shown above).
Site Classification: This control allows the user to search the records on the basis of ASCE-7
Site Classification of the site where the ground motions have been recorded. The available
options are shown below. This classification is based on average shear wave velocity to a
depth of 30m. Following criteria is used to classify a site:
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- Site Class A : Average shear wave velocity > 1500 m/s
- Site Class B : Average shear wave velocity > 750-1500 m/s
- Site Class C : Average shear wave velocity > 360-750 m/s
- Site Class D : Average shear wave velocity < 180-360 m/s
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Data Source: This control allows the user to search the records on the basis of sources that
were used to obtain the raw data. See Section 3.2 for the list of primary data providers.
4.4 Searching for Records in EQTools Environment
Once all the search parameters have been selected by the user, the database search can be
initiated by pressing the “Search” button (as shown below). The database is searched and the
results are displayed in the list on the left as shown below.
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If the search criteria result matches more than 50 records, EQTools recommends narrowing
down the search. This helps in reducing the process time.
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4.5 Viewing the Details of Searched Records
The details of a particular record can be viewed by simply clicking the record in the searched
record list. The record is highlighted, and the details are displayed in the relevant input boxes
where the user made the input for seach parameters. This is shown below.
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The user can view the different magnitudes and distances for a particular record by simply
clicking on the option button of interest as shown below.
In addition, sliders are provided for both windows to view the complete description of the
selected file.
The "RESTORE" button restores the search parameters used by the user in the previous search.
The user can modify or refine the search by changing one or more parameters. Pressing the
"CLEAR" button clears the results of the previous search and prepares the window for a new
search as shown below.
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4.6 Selecting Records for Study
A maximum of 12 searched records can be selected for further study, scaling, or site response
analysis. Horizontal Pair window on the other hand works with only two ground records of a
single earthquake at a time. The records of interest can be transferred to the list of earthquakes
for study by using the arrow keys. The arrow keys can also be used to tranfer records back to
the search list. However, this can be done only if the record being transferred back to list of
searched earthquakes is from the current search. The operations are described next.
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The double arrow key poining towards Earthquake for Study window will transfer all the
records appearing in Component Matching Spectra Criteria. If more than 12 records are
available from the given search parameters, then the double arrow key will transfer the first 12
records. The single arrow key transfers the record components of the selected earthquake
events depending on the option selected from Record Component Groupings. So if Horizontal
Pairs option is selected, which is the default option then single arrow key will put two
horizontal components of the selected event in the Earthquake for Study window.
The
functionality for viewing the details of a particular record, as available for list of searced
earthquakes is also available for the list of earthquakes selected for the study.
Record Component Grouping for Additional Study (shown by yellow elliptical mark) is
provided below Components Matching Search Criteria window. Depending on the option
selected here, records can be called as individual, Horizontal Pairs and Horizontal Pairs and
Vertical. Remember, to keep consistency in selection of records, the program only allows you
to use one option. In case you need to switch to another option to select records, Earthquake for
Study window must be emptied.
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The "Delete Record" button deletes the selected record from the list of selected earthquakes.
The "Clear List" button clears the entire list of selected earthquakes. These buttons are
identified in the screenshot below.
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4.7 Sorting the Searched and Selected Records
The list of searched earthquakes and the selected earthquakes can be simultaneously sorted
based on the following criteria:
-
Alphabetically
-
By Peak Ground Acceleration
-
By Magnitude (i.e. average of maximum and minimum of all available magnitudes)
-
By Distance (i.e. average of minimum and maximum values of all available distances)
The sorting can be done by using the radio option buttons available just above the list of
searched earthquakes (as shown below).
4.8 Saving and Opening Bin of Earthquakes
Saving a Bin of Earthquakes
Unscaled bin of earthquakes for the selected records can be created and saved using the File
→
Save Bin menu command. The user is required to input the name of the bin. This option to
save the bin is not available unless the user has selected at least one (1) record for study.
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Opening a Bin of Earthquakes
Previously saved unscaled/scaled bin of earthquakes can be opened using the File
→
Open Bin
menu command. The user is required to select a previously saved bin. The bin is opened and
the records in the bin are listed in the search list whereby the user can modify the bin by adding
or deleting the records.
Exit the program
Choosing the File
→
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5
Investigating Amplitude and Duration Parameters
5.1 Generating Time History Plots
Using the plotting options available in EQTools environment, you may plot the ground
acceleration, velocity, and displacement time histories for a single record or multiple records
simultaneously. The plots are obtained by clicking on the appropriate plotting button on the
Search Form. The command button for plotting the time histories is shown below.
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5.2 Time History Plots for Single Record
The time history plots of the single recorded ground motion can be generated for any record in
either in the search list or the list of selected earthquakes. To generate the plot, select the
record in the list by clicking it (the record gets highlighted) and then click the Time History
Plot button (shown below). You must make sure that the checkbox "Plot all records for
study" is unchecked for time history plot of a single record.
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The plots generated are of the form shown below.
Ground acceleration, velocity and
displacement are plotted in different windows.
You can change the acceleration, velocity and displacement plot units by clicking the radiostyle option buttons shown below.
After selecting the desired options, the plots are
automatically updated to the selected new units. To restore the plots to default plotting units,
the user just has to press the "Plot All Motions" button. The function of other controls on the
form are described in the section 5.4 (Time History Plot Controls). All other details available
on the form are self explanatory and will not be elaborated upon any further. Print option is not
available with this version of EQTools. Hence the hard copy of plots be obtained by taking the
screen shot.
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5.3 Time History Plots for Multiple Records
The Time History plots for multiple records of ground motion can be generated only for the
records in the list of selected earthquakes. The procedure for generating the plots is same as
with time history plots for a single record except that the checkbox "Plot all records for study"
needs to be checked as shown below.
A sample plot is shown below. A legend, on the right side of the plot, shows the color codes
for the plots in relation to the plotted earthquake record file names. This is shown below.
Unlike the plots for single record where the acceleration, velocity and displacement time
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history plots are shown in different colors, for time history plots of multiple records, all the
three quantities for a particular record are shown in same color. As with the single records, the
plot units for the time histories can be changed by selecting the appropriate radio-type option
buttons on the left. Pressing the “Plot All Motions” button restores the plots to the original
units.
If the user wants to remove any given record from the plot, he/she can uncheck the relevant box
in the list on the right and then press the "Plot Selected Motions" button.
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5.4 Time History Plot Controls
Reading the time history values
By moving the cursor through and inside the time history plot windows for acceleration,
velocity or displacement, the user can get the values of time and the amplitude of the respective
quantities on a real time basis. These values are shown in the boxes above the respective plots
as shown below. This feature is applicable for single as well as multiple time history plots.
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Investigating Amplitude Parameters for Selected Records
Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV) and Peak Ground
Displacement (PGD) are the most commonly used amplitude parameters in engineering
applications. The features in EQTools can be used to directly obtain the values of these
parameters for a single or multiple records.
For a single record, the extreme values are calculated and displayed as shown below.
For multiple records, these values can be obtained by left-clicking the mouse on the file name
in the legend on the right side.
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corresponding values of PGA, PGV and PGD are displayed in the boxes above the plots as
shown below along with cross hairs in the plots identifying the location of maxima.
Changing the Background of Plot Windows
Ground motion records plotted with dark colors may be difficult to see with a dark background.
You can change the background to a light color by using the option buttons shown below.
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5.5 Creating Time History Files
The selected acceleration, velocity and displacement time histories can be saved in the
spreadsheet format by choosing File
→
Create File menu command from the menu bar. Tab
delimited files with .XL1 extensions are created that can be opened and plotted for presentation
using any of the modern spreadsheet programs. MSExcel is recommended for this purpose.
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5.6 Investigating Incremental Velocities
Peak incremental velocity (PIV) is often used for characterizing the damage potential of
earthquake motions in the near-fault region. Incremental velocity represents the area under an
acceleration pulse. EQTools provides the means to visually explore the incremental velocities
associated with a given acceleration time history. The Incremental Velocities (IVs) can be
generated by pressing the "Incremental Velocities" command button on the time history plot
form. This is shown below.
The IVs are plotted for all records as shown below. The default is three positive and three
negative incremental velocities for each record. This can however be changed by the user. The
IVs are calculated and stored in descending order. The IV plots are shown next.
The boxes on top of the plot show the incremental velocities and corresponding time as the
mouse cursor is moved inside the plot window. To choose the number of IVs to be plotted,
input the number in the input boxes on the left and press the "Update" button. The plot units
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can be changed by using the options in the "Units" frame. The legend on the right shows the
color code for the plotted earthquakes.
The statistical data for any record can be seen by selecting the record of interest in the list and
then pressing the "Statistics" button. This will show a bar chart of incremental velocities as
shown next. The incremental velocities for the selected record are shown superimposed on the
acceleration time history, shown as followed:
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To see the statistics for other records, press the "Peak Incr. Velo." button and then choose the
next record followed by the press of the "Statistics" button again. The form in which the
statistical information on the incremental velocities is depicted is shown in the following
screenshot.
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The incremental velocity data can be saved in spreadsheet format by choosing the File
→
Create File command.
5.7 Investigating Incremental Displacements
The investigations for Incremental Displacements (IDs) are accomplished in exactly the same
way as for incremental velocities. Incremental displacements represent the area under the
velocity pulses. The computational tool to investigate the IDs is accessed by pressing the
"Incremental Displacements" command button on the time history plot form. This is shown
below.
All procedures, including printing and saving data, for IDs are same as for IVs.
5.8 Investigating Bracketed Durations
The duration of strong ground motion rather than the duration of entire time history is what is of
interest to engineers. Bracketed duration, which is the time between the first and last exceedance
of some threshold acceleration, is the most commonly used instrumental parameter in this respect
(Bolt, 1969; Page and others, 1972). The threshold acceleration level is usually 0.05g. EQTools
can be used to graphically explore the bracketed duration for time histories for pre-defined or
any user-specified level of threshold acceleration. This feature is accessed by pressing the
"Bracketed Duration" button on the time history plots as shown below.
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The bracketed duration is graphically presented as shown below. The duration is calculated for
pre-defined acceleration levels of 0.01g, 0.02g, 0.03g, 0.04g, 0.05g and 0.10g. The user can
know the bracketed duration for any acceleration level by inputting the level in the input field
"Other" and pressing the "Update" button. The red box in the plot indicates the bounds of the
bracketed duration and threshold acceleration.
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6
Fourier Amplitude Spectrum
6.1 Generating Fourier Amplitude Spectrum using EQTools
The frequency content of selected time histories is calculated and displayed in EQTools by
means of fast Fourier transforms (FFTs). An FFT requires that the number of time-amplitude
data points passed to the routine be a power of 2. This is automatically taken care of in
EQTools. The plot of the resulting amplitude versus frequency is often referred to as a Fourier
Amplitude Spectrum or FAS.
The FAS may be displayed for the entire time interval
represented in the original plot, or for a subset of that plot. The subsets consist of 128, 256, or
512 points of the time-history. In EQTools, the transform is, by default, normalized to have a
maximum value of 1.0. The frequency that has a transform ordinate of 1.0 is the dominant
frequency in the ground motion. The plot is useful in viewing the energy content of a forcing
earthquake at different frequencies. For example, the majority of the energy of the Imperial
Valley Earthquake as measured at Superstition Mountain in May 1940 was focused between 2
and 10 Hertz. An example of this FAS generated in the EQTools environment is shown below.
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The amplitude for each frequency is a complex (imaginary) number that contains both true
amplitude and phase information. The “Fourier Amplitude” plotted by EQTools is the square
root of the sum of the squares of the real and complex portions of the computed amplitude. As
mentioned before, the FFT algorithm used by EQTools requires that the number of points
passed to the routine be a power of two. For the original time-history, a portion of zero
amplitude response is appended to the record to provide the required number of points. For
example, if the input/output record contains 1200 points, the number of points sent to the FFT
routine would be 2048, 1200 points of data and 848 points of zero amplitude data.
The frequency range (maximum recoverable frequency) in a FAS plot is given by:
f range =
0.5
Δt
where Δt is the digitization time step of the original record.
The maximum recoverable
frequency f range is also known as the Nyquist frequency. This is equal to one half of the
sampling frequency. For example, to fully recover a sine wave with a frequency of 1.0 Hz, you
must measure at twice this frequency, or 2.0 Hz. The FFT routine provide amplitudes at n/2
discrete frequencies within this range, where n is the number of points passed to the FFT routine.
Different segments of an earthquake may have different frequency content. The Traveling FFT
provides a method for determining the frequency content of segments of the ground motion (or
computed response) consisting of 128, 256, or 512 contiguous points in the motion. An
example of this screen is show below.
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The FAS of the entire response is shown in the large plot at the upper right of the FAS window,
and to the left of this is a small plot showing the entire time-history. This time-history has a
small traveling window, whose position is controlled from the VCR type controls on the button
bar at the right of the window.
Across the bottom of the form are three smaller FAS plots representing three intervals of 128,
256, or 512 contiguous points from the original record. The user selects the number of points
to use from the “# of Points” frame on the window. Note that the center plot on the bottom of
the window represents the time range shown in the moving window. The plots to the left
(previous) and right (next) represent the windows to the left and right of the traveling (current)
window. The three adjacent windows overlap as shown in the figure below. The smaller the
number of points used in the traveling FAS window, the coarser the resolution in the plot.
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Acceleration (g)
0.150
Next Window
0.075
0.000
-0.075
-0.150
Current Window
Previous Window
0
5
10
15
20
25
30
Time (seconds)
6.2 Fourier Amplitude Spectrum for a Single Record
The FAS plots of the single recorded ground motion can be generated for any record in either
the search list or the list of selected earthquakes. To generate the plot, select the record in the
list by clicking on it (the record gets highlighted), and then click the FAS Plot Button. You
must make sure that the checkbox "Plot all records for study" is unchecked for plotting FFT
of a single record.
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The plots generated are of the form shown below.
6.3 Fourier Amplitude Spectrum for Multiple records
The FFT plots for multiple records of ground motion can be generated only for the records in the list of
selected earthquakes. The procedure for generating the plots is same as for a single record except that
the checkbox "Plot all records for study" needs to be checked as shown below.
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A sample plot is shown next. A legend, on the right side of the plot, shows the color codes for
the plots in relation to the plotted earthquake record file names.
6.4 Fourier Amplitude Spectrum Plot Controls
Following controls are available for studying the FAS for a given ground motion:
Time History for Fourier Amplitude Spectrum Plots
The miniaturized time history plot for the input motion to generate the FAS is depicted in the
window on the left as shown next. The earthquake record can be chosen from the list on the
right of the time history plot. The maximum and minimum values of the input ground motion
quantity are also shown.
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Fourier Amplitude Spectrum Type
The FAS can be generated for ground acceleration, velocity or displacement time histories.
You can select the type of FAS by using the radio option buttons shown below. The plots are
updated instantly to reflect the choice. The time history of the selected input ground motion is
also shown in the window on the top. The default value is the acceleration FAS.
Fourier Amplitude Spectrum Amplitude
The FAS amplitude, by default, is normalized to a value of 1.0.
However, the absolute
amplitude can be set as the option, as shown below.
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Frequency and Amplitude Limits
The FAS amplitude and frequency limits, by default, are set to a predefined value. The values
for the frequency limit range from zero to the Nyquist frequency. The user can change these
values by unchecking the check-boxes and setting user defined limits. This is shown next.
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Reading the Values of Fourier Amplitude Spectrum Frequency and Amplitude
This can be done by moving the mouse inside the Fourier Amplitude window.
The
corresponding frequency and amplitude are shown in the boxes as shown below.
Traveling Fourier Amplitude Spectrum
As discussed earlier, different segments of an earthquake may have different frequency content.
The Traveling FAS provides a method for determining the frequency content of segments of the
ground motion (or computed response) consisting of 128, 256, or 512 contiguous points in the
motion. The input motion and type of FFT can be chosen through the list and option buttons as
stated before. The current position of the travelling window is shown in the time history plot.
The traveling window can be moved forward or backward by using the “Forward”
“Backward”
or
buttons. The traveling FFTs are shown in the three adjacent windows. The
“Beginning” button
moves the traveling window to the beginning of the input ground
motion. An example of this screen is show below.
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Updating the Fourier Amplitude Spectrum Plots
For plotting the multiple records, the selected ground motions can be added or removed from
the plots by unchecking/checking the checkboxes and pressing the "Update" button. This is
shown in the example screen below. The "Update" button is not available while plotting the
FAS for a single record.
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Fourier Amplitude Spectrum Legend
The legend shows the color coding for the plots and the corresponding ground motion data file
name. This is shown below.
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Changing Fourier Amplitude Spectrum Plot Backgrounds
For better visibility, the backgrounds for any of the windows in the FAS plot can be changed
to dark or light using option buttons. This is shown below.
6.5 Exporting the Computed Fourier Amplitude Spectra Data
The FAS data generated using the computational tools in the EQTools environment can be
saved in the spreadsheet format by choosing File
→
Create File menu command from the
menu bar. Tab delimited files with .XL1 extensions are created that can be opened and plotted
for presentation using any of the modern spreadsheet programs.
6.6 Fourier Amplitude Spectrum Analysis Tools
Ground motion during an earthquake is measured by strong motion instruments, which record
the acceleration of the ground. During data acquisition for ground motions, the signal may be
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contaminated by interference, noise or other signals. In addition, poorly mounted recording
equipment can also introduce spurious frequencies in the signal. Filters are frequently used is
seismic signal processing for two general purposes: signal separation and signal restoration. A
filter is just a computation which takes one sequence of numbers (the input signal) and produces
a new sequence of numbers (the filtered output signal). In earthquake engineering, filters are
extensively employed to remove low and high-frequency noise from acceleration time history.
Since the EQTools strong motion database contains instrumental records that have already been
corrected, filtering of frequencies for the records selected from the database is not necessary.
Nevertheless, computational tools are developed and implemented in EQTools environment to
filter frequencies from accelerograms in the frequency domain.
The intention behind
development of these tools was to provide the user with a means to filter frequencies, in
frequency domain, from a ground motion record and explore its implications on time histories
and response spectrum on a real-time basis in a graphical environment.
In addition to filtering frequency content of accelerograms, computational tools are also
available in EQTools that facilitate scaling up or scaling down bands of frequencies in the
frequency domain. These scaling operations can also be performed on bands of time histories.
However, it should be noted that scaling time-bands in the time domain will destroy the causality
inherent in the ground motion record by unrealistically changing the frequency content of the
accelerograms. Scaling of bands of time histories is rarely done in practice. Scaling of entire
time history is a common practice, though. The computational tools in EQTools that facilitate
scaling of bands of time histories are intended only for educational purposes.
The FAS Analysis Tool is a very unique and useful tool. Through this tool, the user can
examine, on a real time basis, what happens to the time history if certain frequencies are filtered
out or scaled up/down. This tool also shows how the frequency content of a time history changes
if a certain range of the time history is scaled up or scaled down. The user can also see, on a real
time basis, the changes in the response spectrum because of the afore-mentioned changes. This
tool is accessed by pressing the “Analyze Record” button on the FAS user-interface. This is
shown ahead.
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The active time history in the FAS plots forms the input for the FAS analysis tool. The
frequency range, amplitude range and other parameters as used in the FAS plots are preserved in
the FFT analysis environment. The opening screen for accessing this tool is also shown below.
The input to be provided by the user is the time range(s) if time history is being filtered/scaled or
the frequency range(s) if the frequency is being filtered/scaled. The option for scaling time
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history or frequency is chosen using radio buttons as shown above. The upper or lower bound
for both the parameters can be input in two ways. First, the user can double-click in the relevant
plot boxes. With every double click, the user is prompted if he would like to use this value. A
series of double-clicks will eventually supply the maximum three ranges of frequencies/time.
The user is also expected to provide the scale factors and the filter type for the chosen ranges.
Square, triangular and sinusoidal filters are available. The figures ahead give the specifications
Gain (or amplitude)
Gain (or amplitude)
for the filters available in EQTools environment:
1
0
fcutoff
1
0
fcutoff
fc
Frequency (Hz.)
Frequency (Hz.)
(b)
Gain (or amplitude)
Gain (or amplitude)
(a)
1
0
f1
f2
fc
1
0
f1
fc
f2
fc
Frequency (Hz.)
Frequency (Hz.)
(d)
(c)
Amplitude response specifications for rectangular filters. (a) Low-pass filter. (b) High-pass filter.
(c) Band-pass filter. (d) Band-stop filter. fc is the Nyquist frequency.
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Gain (or amplitude)
Gain (or amplitude)
1
0
fcutoff
fc
fc
Frequency (Hz.)
(a)
(b)
1
0
f1
0
Frequency (Hz.)
Gain (or amplitude)
Gain (or amplitude)
fcutoff
1
f2
1
0
f2
f1
fc
Frequency (Hz.)
Frequency (Hz.)
(c)
(d)
fc
Amplitude response specifications for triangular filters in the frequency domain. (a) Low-pass
filter. (b) High-pass filter. (c) Band-pass filter. (d) Band-stop filter (called notch-filter if the
frequency band is narrow). fc is the Nyquist frequency
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Gain (or amplitude)
Gain (or amplitude)
1
0
fcutoff
1
0
fcutoff
fc
Frequency (Hz.)
(b)
Gain (or amplitude)
Gain (or amplitude)
(a)
1
0
f1
fc
Frequency (Hz.)
1
0
f1
fc
f2
fc
f2
Frequency (Hz.)
Frequency (Hz.)
(d)
(c)
Amplitude response specifications for sinusoidal filters in the frequency domain. (a) Low-pass
filter. (b) High-pass filter. (c) Band-pass filter. (d) Band-stop filter. fc is the Nyquist frequency
Similarly, the amplitude response specifications for scaling of frequencies or time histories are as
shown below.
Gain (or amplitude)
Gain (or amplitude)
2
s
1
0
f2
f1
1
s
0
f1
fc
f2
fc
Frequency (Hz.)
Frequency (Hz.)
(b)
(a)
Amplitude response specifications for rectangular scaling of frequencies in the frequency
domain. (a) For scale factor > 1.0 (b) For scale factor < 1.0. The user-defined scale factor “s” in
(a) and (b) are the maximum and minimum gains (amplitudes) within the frequency band being
scaled, respectively
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Gain (or amplitude)
Gain (or amplitude)
2
s
1
0
f1
f2
1
s
0
fc
f1
Frequency (Hz.)
f2
fc
Frequency (Hz.)
(a)
(b)
Amplitude response specifications for triangular scaling of frequencies in the frequency domain.
(a) For scale factor > 1.0 (b) For scale factor < 1.0. The user-defined scale factor “s” in (a) and
(b) are the maximum and minimum gains (amplitudes) within the frequency band being scaled,
respectively and correspond to a frequency of 0.5( f1 + f 2 ) .
Gain (or amplitude)
Gain (or amplitude)
2
s
1
0
f1
f2
1
s
0
f2
f1
fc
fc
Frequency (Hz.)
Frequency (Hz.)
(b)
(a)
Amplitude response specifications for sinusoidal scaling of frequencies in the frequency domain.
(a) For scale factor > 1.0 (b) For scale factor < 1.0. The user-defined scale factor “s” in (a) and
(b) are the maximum and minimum gains (amplitudes) within the frequency band being scaled,
respectively and correspond to a frequency of 0.5( f1 + f 2 ) .
Once all the data is input, the analysis is initiated by pressing the "Activate" button. The
filtered/scaled response can be viewed by pressing the "Filtered/Scaled Response" button. The
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view can be restored to original response at anytime by pressing the "Original Response"
button.
The user can toggle between the plots of FAS and Response Spectrum by using the "View
FFT/View RS" button on the bottom left corner. To choose a different range of response
quantities, press the "Deactivate" button, choose different ranges, and re-run the analysis by
pressing "Activate" button. The modified time history, FAS and response spectrum are shown
in red color whereas the original responses are shown in blue color.
A sample analysis result with three ranges of frequency filtering is shown next. The screenshot
at the bottom shows the changes in response spectrum.
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A sample analysis result with scaling of time history in three ranges is shown below:
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7
Elastic Response Spectra and Scaling of Time Histories
7.1 Generating Elastic Response Spectra Using EQTools
Response spectrum is an important tool in the seismic analysis and design of structures and
equipment.
The concept of earthquake response spectrum, introduced by Biot (1941) and
Housner (1941), is widely employed in earthquake engineering as a practical means of
characterizing ground motions and their effects on structures. The response spectrum provides a
convenient means to summarize the peak response of all possible linear single-degree-offreedom (SDOF) systems to a particular component of ground motion. It also provides a
practical approach to apply the knowledge of structural dynamics to the design of structures and
development of lateral force requirements in building codes. A plot of peak values of a response
quantity as a function of the natural vibration period Tn of the system, or a related parameter
such as circular frequency ωn or cyclic frequency f n , is called the response spectrum for that
quantity. The response may be expressed in terms of acceleration, velocity or displacement. The
maximum values of each of these parameters depend only on the natural frequency and the
damping ratio ζ of the SDOF system (for a particular input motion). The maximum values of
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acceleration, velocity, and displacement are referred to as the spectral acceleration ( Sa ), spectral
velocity ( Sv ), and spectral displacement ( Sd ), respectively.
Following the selection of representative ground motion time histories, the computational tools
in the EQTools environment can be used to rapidly generate the elastic response spectra. The
spectra can be generated for upto 12 different time histories simultaneously by pressing the
response spectrum button
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, available on the Search Form as shown below.
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A sample response spectrum plot for eight representative strong ground motions is shown ahead.
7.2 Generating Elastic Response Spectrum for a Single Record
The RS plots of the single recorded ground motion can be generated for any record in either the
search list or the list of selected earthquakes. To generate the plot, select the record in the list
by clicking it (the record gets highlighted) and then click on the Response Spectrum Plot
Button. The user must make sure that the checkbox "Plot all records for study" is unchecked
for plotting RS of a single record.
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The plot generated for a single record is of the form shown below:
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7.3 Generating Elastic Response Spectra for Multiple Records
The RS plots for multiple records of ground motion can be generated only for the records in the
list of selected earthquakes. The procedure for generating the plots is same as for the single
record except that the checkbox "Plot all records for study" needs to be checked as shown
below.
A screenshot of sample response spectrum plot in EQTools environment is shown next. A
legend, on the right side of the plot, shows the color codes for the plots in relation to the plotted
earthquake record file names.
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7.4 Response Spectrum Plot Controls
Following controls are available for studying the Response Spectrum for a single ground
motion or a group of ground motions:
Plot of Spectral Quantities Versus Period/Frequency
The user has the choice of plotting the spectral quantities against time period or frequency.
This choice can be made by clicking the option buttons shown below.
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Damping for Earthquake Spectra
Damping value is considered at two places: to compute response spectra for selected ground
records and to get ASCE-7 design spectrum. For consistency, damping value is set to 5% at
both places.
Response Spectrum Plot Style
The user can choose the plot style for the response spectrum by using the options shown below.
The user has the choice of viewing a tripartite plot, a plot of spectral velocity, spectral
acceleration or the displacement. The average spectrum can be superimposed on the response
spectrum plots by checking the check-box "Plot average spectrum".
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Spectral Coordinates
As the user moves the mouse in the response spectrum window plots, the corresponding
spectral coordinates (period, frequency, acceleration, velocity and displacement) are displayed
dynamically in the boxes shown next.
Response Spectrum Plot Legend
The legend shows the color coding for the plots and the corresponding ground motion data file
name. This is shown below.
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Updating the Response Spectrum Plots
For plotting the multiple records, the selected ground motions can be added or removed from
the plots by unchecking/checking the checkboxes in the list shown below and pressing the
"Update" button. This is shown in the example screen below. The "Update" button is not
available while plotting the response spectrum for a single record.
Changing RS Plot Backgrounds
For better visibility, the backgrounds for the response spectrum plot window can be changed to
dark or light using option buttons. This is shown below.
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7.5 ASCE-7 Design Spectrum
The design response spectrum as per the current ASCE-7 guidelines can be generated and
superimposed on the response spectrum plots by checking the check-box shown below. The
code spectrum is calculated on the basis of predefined parameters. However, the user has the
choice of changing these parameters. A sample plot with code spectrum superimposed is
shown below.
Pressing the "ASCE-7 Parameters" button brings up the code parameters window (shown
next) where the user can change the parameters. Pressing the "Done" button updates the
ASCE-7 Design Spectrum.
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7.6 Scaling of Elastic Response Spectra for Selected Records
The user can access the scaling tools by pressing the "Fit" button in the response spectrum plot
window. This button is available only when the ASCE-7 spectrum is overlaid on the response
spectrum plots as shown following.
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The response spectrum for the selected records can be scaled in various ways. The user can
scale the response spectra to any of the spectral quantities of the design spectrum (i.e.
acceleration, velocity or displacement). This means that the user can chose either the relative
displacement, spectral velocity, or spectral acceleration of the elastic response spectra for the
selected records to fit with the corresponding spectral quantities of the design response
spectrum as per some fitting criteria.
The response spectrum of the selected records can be scaled by different methods to fit the
design response spectrum. The scaling methods are briefly discussed below:
Match at a Point (Simple Uniform Scaling): Scaling of time histories within a “bin” of
earthquakes, termed normalization, by a constant factor to make their response spectrum match
the design spectrum at a single period is most often employed. This simple uniform scaling
procedure preserves the peaks and troughs in the response spectra of the recorded time histories,
allowing the structural response analyses to sample a range of different response spectral shapes.
EQTools can be used to fit the earthquake response spectra to the design spectra for any spectral
quantity for any time period chosen by the user.
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Equal Area Scaling: As mentioned before, since the peak ground acceleration, velocity, and
displacement for various earthquake records differ, the computed responses cannot be averaged
on an absolute basis. One of the most commonly used procedures used is normalizing the
records according to design spectrum intensity where the areas under the spectra between two
periods (or frequencies) are set equal to the area under the design spectrum. Again, any of the
three spectral quantities – acceleration, velocity, or displacement, can be used to fit the data.
EQTools can be used to normalize a bin of earthquakes on this basis. Such bins are allowed to
have a maximum of twelve selected ground motion records. The expected user input is the upper
and lower bound of the fitting region in terms of the time period.
Scaling to Minimize the Square Root of Sum of Squares (SRSS)of Errors: The nonlinear
response of structures is strongly dependent on the phasing of the input ground motion and on
detailed structure of its spectrum. Unlike the case of linear response, which can be obtained by
simple uniform scaling of a single time history matched to a design spectrum, an appropriate
measure of nonlinear response requires the use of multiple time histories having phasing and
response spectral peaks and troughs that are appropriate for the magnitude, distance, site
conditions, and wave propagation characteristics of the region. The purpose behind using a suite
of ground motions is to provide a statistical sample of this variability in phasing and spectra
through a set of time histories that are realistic not only in their average properties but in their
individual characteristics as well. To be consistent with this approach, a scaling procedure is
utilized in which the shape of the response spectra of time histories is not modified. Instead, a
single scale factor is found such that the square root of sum of squares of the error (difference)
between the earthquake response spectrum and the design spectrum between two periods is
minimized. If such a procedure is adopted for scaling all three components of a record, it retains
the ratio between the three components at all periods. EQTools has the provisions to scale the
response spectra on this basis. The expected user input consists of the upper and lower bound of
the fitting region in terms of the time period and the upper and lower bound of the scale factor(s).
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Scaling of Ground Motions as per ASCE-7 Provisions for Two-Dimensional Analyses: The
ground motions are scaled such that the average value of the 5% damped response spectra for the
suite of motions is not less than the design response spectrum for the site for periods ranging
from 0.2 T to 1.5 T seconds where T is the natural time period of the structure in the
fundamental mode of vibration for the direction of response being analyzed. The natural time
period of the structure is expected from the user as input.
Scaling of Ground Motions as per ASCE-7 Provisions for Three-Dimensional Analyses: As per
this procedure, for each pair of horizontal ground motion components, the square root of sum of
squares (SRSS) of the 5% damped response spectrum of the scaled horizontal components shall
be constructed. Each pair of motions shall be scaled such that the average value of the SRSS
spectra from all horizontal component pairs is not less than 1.3 times the 5% damped design
response spectrum for periods ranging from 0.2 T to 1.5 T seconds where T is the natural time
period of the fundamental mode of the structure. This scaling procedure has been implemented
in EQTools in a similar manner as with the scaling for the two-dimensional analysis. Since this
procedure requires pairs of ground motions (i.e. the two orthogonal horizontal components), it is
essential that the searched records are selected in EQTools environment with the option to
include pairs of horizontal components for construction of response spectra.
Following the selected scaling operation is performed, the scaled factors are displayed in the
list on the left. The spectral quantities are displayed in the boxes as the mouse is moved in the
plot window. A sample scaling of records is shown next.
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Pressing the “Done” command button closes the environment for scaling of response spectra.
It also transfers the scale factors to the response spectrum environment where they are
displayed in the list on the right. Once the scale factors are available in the response spectrum
environment, they can be used to scale the time histories by checking the “Apply Scale
Factor(s) to RS Plots” checkbox. Checking this checkbox automatically scales the response
spectra and the details of the scaling are available to the user as shown next:
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7.7 Saving the Scaled Bin of Earthquakes
Once the scaling has been done, the user can save the scaled bin of records by pressing the
"Save Scaled Bin" command button shown below. Alternatively, the user can also save the
scaled bin by using File → Save Scaled Bin menu command. After creating an avi file for
scaled bin of records, EQTools gives an option to create DrainPro data files. This is a default
setting in the program and can be changed by unchecking the ‘Genrerate & Save Nonlin-Pro
Data File’ option shown next in square blue mark.
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7.8 Exporting the Computed Response Spectrum Data
The response spectrum data generated using the computational tools in the EQTools
environment can be saved in the spreadsheet format by choosing File
→
Create File menu
command from the menu bar. Tab delimited files with .XL1 extensions are created that can be
opened and plotted for presentation using any of the modern spreadsheet programs.
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7.9 Generating and Saving DrainPro Data Files
The user can generate and save the data files for scaled records for use with DrainPro program
by checking the "Generate & Save DrainPro Data Files" checkbox before pressing the "Save
Scaled Bin" button.
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8
Ground Motion Attenuation Tools
8.1 Overview of Ground Motion Attenuation Relationships
The evaluation of seismic hazard requires the use of probabilistic distribution of intensity
measures conditioned on the occurrence of an earthquake with a particular magnitude (M) and
a given site-source distance (r). Attenuation relationships define the statistical moments of the
probability density functions (e.g., medians, standard error terms) in terms of parameters such
as M and r. The attenuation relations are derived through regression of empirical data.
The most commonly used ground motion intensity measure is spectral acceleration at a
specified damping level (usually 5%). A number of attenuation relations for this parameter are
available for the generally recognized tectonic regimes. Attenuation relationships are also
available for other intensity measures such as peak horizontal velocity and vertical spectral
acceleration.
EQTools provides the necessary computational tools to visually examine the effect of M and r
on peak ground acceleration, horizontal and vertical spectral acceleration, and peak horizontal
velocity using a number of modern attenuation relationships.
For shallow crustal earthquakes in active tectonic regions, following attenuation relationships
have been implemented in EQTools environment.
Abrahamson and Silva (1997) have derived empirical response spectral attenuation
relationships for both the horizontal and vertical components of ground motion. They have
explicitly included a factor to account for the systematic increase in ground motions recorded at
sites over hanging wall of dipping faults. Non-linear soil response is also explicitly allowed as
a function of the expected peak ground acceleration on rock. Their approach allows a single
functional form to account for attenuation at both soil and rock sites while still allowing for
non-linear site response. An example of peak ground acceleration from this relationship is
shown next.
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Campbell (1997) has also developed empirical attenuation relationships for horizontal and
vertical PGA, PGV, and SA in active tectonic regions. The latest version, implemented in
EQTools, uses a much larger data set (including the 1989 Loma Prieta, 1992 Landers, and 1992
Petrolia eqrthquakes) than earlier versions. The suite of attenuation relationships by Campbell
are designed to be used for estimating ground motions from earthquakes of M > 5 at sites
within 60 km. An example of the spectral acceleration from this relationship is shown next.
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Boore, Joyner, and Fumal (1997) have published equations for estimating horizontal SA and
PGA for shallow earthquakes in North America. These equations, implemented in EQTools,
are an update of their earlier model (Boore et. al., 1994) and now differentiate the response for
strike-slip, reverse-slip, and unspecified faulting. Also, more restrictive ranges of M and rjb
are specified for use with these equations than those given in previous publications. Unlike the
other models, a quantitative measure is used for the site classification based on the average
shear wave velocity in the upper 30 m. An example of the spectral acceleration from this
relationship is shown next.
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Sadigh et al. (1997) have presented attenuation relationships for shallow crustal earthquakes
determined from strong motion data recorded primarily in California. The relationships for
horizontal and vertical PGA and SA are applicable to earthquakes of M 4 to 8+ at distances of
up to 100 km. An example of the spectral acceleration from this relationship is shown next.
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Spudich et. al. (1999) derived a new predictive relationship for PGA and SA using a global data
set of earthquake ground motions recorded in extensional tectonic regimes. In general, their
values of PGA and SA are smaller than those derived by other researchers for active tectonic
regions. An example of the spectral velocity from this relationship is shown next.
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For Cascadia Subduction Zones, the following attenuation relationships have been implemented
in EQTools environment.
Youngs et. al. (1997) have developed attenuation relationships for subduction zone interface and
intraslab earthquakes using data from Alaska, Chile, Cascadia, Japan, Mexico, Peru, and
Soloman Islands. These relationships illustrate that peak ground motions from subduction zone
earthquakes attenuate more slowly than those from shallow crustal earthquakes in tectonically
active regions and that intraslab earthquakes produce larger peak ground motions than interface
earthquakes from the same magnitude and distance. An example of the spectral acceleration
from this relationship is shown next.
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Atkinson and Boore (1997a) provided the preliminary ground motion relationships for the
Cascadia region.
Their Cascadia model does not match earthquakes for large ( M > 7.5 )
earthquakes in other regions. Compared to the recordings from subduction events other than
Cascadia, their model over-predicts near-source ground motions and under-predicts large
distance ( > 100 km.) ground motions. Until further work can be completed on the larger
magnitudes, the Cascadia model is recommended to be used to predict ground motions from
M < 7 earthquakes at all distances and to predict conservative ground motions from large
earthquakes at distances less than 100 km. An example of the spectral velocity from this
relationship is shown next.
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For Stable Continental Region, following attenuation relationships have been implemented in
EQTools environment.
Atkinson and Boore (1997b) used the stochastic point source model to generate a synthetic data
base of strong ground motions.
Empirical recordings from small to moderate size events
recorded by Eastern Canada Telemetered Network (ECTN) and isoseismals from historical
earthquakes were used to constrain some of the parameters in the stochastic point source model.
These relationships illustrate that the use of an empirical source model yields smaller lowfrequency amplitude than the use of theoretical source model. Comparison of these relationships
with those determined for the tectonically active west coast indicates further differences in
amplitudes across the spectrum. Based on these observations, it can be concluded that ground
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motion relationships determined for one tectonic environment cannot be simply scaled for use in
another. An example of the spectral velocity from this relationship is shown next.
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8.2 Ground Motion Attenuation Relationships
A brief description of the development of various attenuation relationships is provided herein.
A more comprehensive description may be found in the Seismological Research Letters, Vol.
68, January/February, 1997.
8.2.1
N. A. Abrahamson and W. Silva Attenuation Relationship
A full description of the development of this attenuation relationship may be found in:
Abrahamson, N. A., and Silva, W. J. (1997), “Empirical Response Spectral Attenuation
Relations for Shallow Crustal Earthquakes,” Seismological Research Letters, Vol. 68(1), 94-127.
Abstract: Using a data base of 655 recordings from 58 earthquakes, empirical response
attenuation relations are derived for the average horizontal and vertical component for shallow
earthquakes in active tectonic regions. A new feature in this model is the inclusion of a factor to
distinguish between ground motions on the hanging wall and footwall of dipping faults. The site
response is explicitly allowed to be non-linear with a dependence on the rock peak acceleration
level.
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Equations:
c1 = 6.4 EQTools V3.0
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EQTools V3.0
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Coefficients for the average horizontal component:
period
0.01
0.03
0.05
0.075
0.1
0.12
0.15
0.17
0.2
0.24
0.3
0.4
0.5
0.75
1
1.5
2
3
4
5
c4
5.6
5.6
5.6
5.5845
5.5
5.3948
5.266
5.1938
5.1
4.9652
4.7999
4.5184
4.3
3.8998
3.7
3.5502
3.5
3.5
3.5
3.5
a1
1.64
1.69
1.87
2.037
2.16
2.2772
2.4065
2.43
2.4057
2.2925
2.114
1.86
1.615
1.1604
0.8279
0.26
-0.15
-0.69
-1.13
-1.46
EQTools V3.0
a3
-1.145
-1.145
-1.145
-1.145
-1.145
-1.145
-1.145
-1.135
-1.115
-1.079
-1.035
-0.988
-0.9515
-0.8852
-0.8383
-0.7721
-0.725
-0.725
-0.725
-0.725
a5
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.61
0.5809
0.5279
0.4904
0.4376
0.4
0.4
0.4
0.4
a6
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.232
0.1977
0.1536
0.1193
0.057
0.0129
-0.0493
-0.0936
-0.156
-0.2
-0.2
a9
0.37
0.37
0.37
0.37
0.37
0.37
0.37
0.37
0.37
0.37
0.37
0.37
0.37
0.331
0.2809
0.2102
0.1599
0.089
0.0389
0
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a10
-0.417
-0.47
-0.62
-0.6281
-0.5977
-0.5914
-0.5766
-0.5218
-0.445
-0.3498
-0.2194
-0.065
0.085
0.32
0.4231
0.5999
0.61
0.63
0.64
0.6641
a11
-0.23
-0.23
-0.2668
-0.28
-0.28
-0.28
-0.28
-0.2647
-0.2448
-0.2225
-0.1952
-0.16
-0.121
-0.0502
0
0.04
0.04
0.04
0.04
0.04
a12
0
0.0143
0.028
0.03
0.028
0.018
0.005
-0.004
-0.0138
-0.0238
-0.036
-0.0518
-0.0635
-0.0862
-0.102
-0.12
-0.14
-0.1726
-0.1956
-0.215
b5
0.7
0.7
0.713
0.728
0.739
0.746
0.754
0.759
0.765
0.772
0.78
0.791
0.799
0.814
0.825
0.84
0.851
0.866
0.877
0.885
b6
0.135
0.135
0.135
0.135
0.135
0.135
0.135
0.135
0.135
0.135
0.135
0.135
0.13
0.123
0.118
0.11
0.105
0.097
0.092
0.087
8/8/2010
Coefficients for the average vertical component:
period
0.01
0.03
0.05
0.075
0.1
0.12
0.15
0.17
0.2
0.24
0.3
0.4
0.5
0.75
1
1.5
2
3
4
5
c4
6
6
6
6
6
6
6
5.72
5.34
4.93
4.42
3.77
3.26
2.5
2.5
2.5
2.5
2.5
2.5
2.5
a1
1.642
2.1
2.62
2.75
2.7
2.48
2.17
1.96
1.688
1.362
0.973
0.591
0.282
-0.253
-0.531
-0.966
-1.294
-1.745
-2.151
-2.447
EQTools V3.0
a3
-1.252
-1.317
-1.37
-1.37
-1.37
-1.299
-1.211
-1.162
-1.099
-1.027
-0.94
-0.878
-0.829
-0.749
-0.74
-0.729
-0.72
-0.72
-0.72
-0.72
a5
0.39
0.432
0.496
0.545
0.58
0.58
0.58
0.58
0.58
0.58
0.58
0.539
0.471
0.348
0.26
0.26
0.26
0.26
0.26
0.26
a6
-0.05
-0.05
-0.05
-0.05
-0.05
-0.017
0.024
0.047
0.076
0.109
0.15
0.15
0.15
0.15
0.15
0.058
-0.008
-0.1
-0.1
-0.1
a9
0.63
0.63
0.63
0.63
0.63
0.63
0.63
0.604
0.571
0.533
0.488
0.428
0.383
0.299
0.24
0.24
0.24
0.24
0.24
0.24
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a10
-0.14
-0.14
-0.14
-0.129
-0.114
-0.104
-0.093
-0.087
-0.078
-0.069
-0.057
-0.043
-0.031
-0.01
0.004
0.025
0.04
0.04
0.04
0.04
a11
-0.22
-0.22
-0.22
-0.22
-0.22
-0.22
-0.22
-0.22
-0.22
-0.22
-0.22
-0.22
-0.22
-0.22
-0.22
-0.22
-0.22
-0.22
-0.22
-0.22
a12
0
0
-0.0002
-0.0007
-0.001
-0.0015
-0.0022
-0.0025
-0.003
-0.0035
-0.0042
-0.005
-0.006
-0.0083
-0.0115
-0.018
-0.024
-0.0434
-0.054
-0.0644
b5
0.76
0.76
0.76
0.76
0.76
0.74
0.72
0.7
0.69
0.69
0.69
0.69
0.69
0.69
0.69
0.69
0.69
0.72
0.75
0.78
b6
0.085
0.085
0.085
0.085
0.085
0.075
0.063
0.056
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
8/8/2010
8.2.2
Kenneth W. Campbell Attenuation Relationship
A full description of the development of this attenuation relationship may be found in:
Campbell, K.W. (1997). Empirical Near-Source Attenuation Relationships for Horizontal and
Vertical Components of Peak Ground Acceleration, Peak Ground Velocity, and Pseudo-Absolute
Acceleration Response Spectra, Seismological Research Letters, 68, January/February, pg. 154179.
Abstract: A consistent set of empirical attenuation relationships is presented for predicting free-
field horizontal and vertical components of peak ground acceleration (PGA), peak ground
velocity (PGV), and 5%-damped pseudo-absolute acceleration response spectra (PSA). The
relationships were derived from attenuation relationships previously developed by the author
from 1990 through 1994. The relationships were combined in such a way as to emphasize the
strengths and minimize the weaknesses of each.
The new attenuation relationships are
considered to be appropriate for predicting free-field amplitudes of horizontal ad vertical
components of strong ground motion from worldwide earthquakes of moment magnitude (M)
greater than or equal to 5 and sites with distances to seismogenic rupture (Rseis) less than or
equal to 60 km in active tectonic regions.
EQTools V3.0
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Equations:
EQTools V3.0
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For generic rock, use: SSR = 1, SHR = 0, and D = 1km.
For generic soil, use: SSR = 0, SHR = 0, and D = 5km.
period
0
0.05
0.075
0.1
0.12
0.15
0.17
0.2
0.24
0.3
0.5
0.75
1
1.5
2
3
4
c1
-3.15
0.05
0.27
0.48
0.576
0.72
0.748
0.79
0.774
0.77
-0.28
-1.08
-1.79
-2.65
-3.28
-4.07
-4.26
c2
0
0
0
0
0
0
0
0
0
0
0.74
1.23
1.59
1.98
2.23
2.39
2.03
EQTools V3.0
c3
0
0
0
0
0
0
0
0
0
0
0.66
0.66
0.66
0.66
0.66
0.66
0.66
c4
0
-0.0011
-0.0024
-0.0024
-0.00184
-0.001
-0.00016
0.0011
0.00302
0.0035
0.0068
0.0077
0.0085
0.0094
0.01
0.0108
0.0112
c5
0.015
0.000055
0.000095
0.000007
-0.0001038
-0.00027
-0.000374
-0.00053
-0.000682
-0.00072
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
Page 105
c6
-0.000995
0.2
0.22
0.14
0.076
-0.02
-0.084
-0.18
-0.356
-0.4
-0.42
-0.44
-0.38
-0.32
-0.36
-0.22
-0.3
c7
c8
0
0
0
0
0
0
0
0
0
0.25
0.37
0.57
0.72
0.83
0.86
1.05
0
0
0
0
0
0
0
0
0
0.62
0.62
0.62
0.62
0.62
0.62
0.62
8/8/2010
8.2.3
David M. Boore, William B. Joyner, and Thomas E. Fumal Attenuation
Relationship
A full description of the development of this attenuation relationship may be found in:
Boore, D.M., W.B. Joyner, and T.E. Fumal (1997).
Equations for Estimating Horizontal
Response Spectra and Peak Acceleration from Western North American Earthquakes: A
Summary of Recent Work, Seismological Research Letters, 68, January/February, pg. 128-153.
Abstract: We summarize our recently published work on estimating horizontal response spectra
and peak acceleration for shallow earthquakes in western North America. Although some of the
sets of coefficients given here for the equations are new, for the convenience of the reader, we
provide tables for estimating random horizontal-component peak acceleration and 5% damped
pseudo-acceleration response spectra in terms of the natural, rather than common, logarithm of
the ground motion parameter. The equations give ground motion in terms of moment magnitude,
distance, and site conditions for strike-slip, reverse-slip, or unspecified faulting mechanisms. Site
conditions are represented by the shear velocity averaged over the upper 30 m, and
recommended values of average shear velocity are given for typical rock and soil sites and for
site categories used in the National Earthquake Hazard Reduction Program's recommended
seismic code provisions. In addition, we stipulate more restrictive ranges of magnitude and
distance for the use of our equations than in our previous publications. Finally, we provide tables
of input parameters that include a few corrections to site classifications and earthquake
magnitude (the corrections make a small enough difference in the ground motion predictions that
we chose not to change the coefficients of the prediction equations).
Equations:
Note: The equations are to be used for M 5.5-7.5 and r no greater than 80 km.
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h is a fictitious depth term from the regression
Regression equation for one standard deviation:
+1σ = ln Y + σ lnY
⇒ σ lnY values are provided in the table below.
Recommended Values Of Average Shear Wave
Velocity* For Use In
the Attenuation Equation
NEHRP Site Class B
1070 m/s
NEHRP Site Class C
520 m/s
NEHRP Site Class D
250 m/s
Soft Rock
620 m/s
Soil (typical)
310 m/s
Shear wave velocity is averaged over top 30 m. Velocities for NEHRP Class E and F sites not
provided due to the wide range of possible velocity values; Table adapted from Boore et
al.,1997.
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EQTools V3.0
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Summary Table
period
0
0.1
0.12
0.15
0.17
0.2
0.24
0.3
0.4
0.5
0.75
1
1.5
2
8.2.4
b1SS
-0.313
1.006
1.109
1.128
1.09
0.999
0.847
0.598
0.212
-0.122
-0.737
-1.133
-1.552
-1.699
b1RS
-0.117
1.087
1.215
1.264
1.242
1.17
1.033
0.803
0.423
0.087
-0.562
-1.009
-1.538
-1.801
b1ALL
-0.242
1.059
1.174
1.204
1.173
1.089
0.941
0.7
0.311
-0.025
-0.661
-1.08
-1.55
-1.743
b2
0.527
0.753
0.721
0.702
0.702
0.711
0.732
0.769
0.831
0.884
0.979
1.036
1.085
1.085
b3
0
-0.226
-0.233
-0.228
-0.221
-0.207
-0.189
-0.161
-0.12
-0.09
-0.046
-0.032
-0.044
-0.085
b5
-0.778
-0.934
-0.939
-0.937
-0.933
-0.924
-0.912
-0.893
-0.867
-0.846
-0.813
-0.798
-0.796
-0.812
bV
-0.371
-0.212
-0.215
-0.238
-0.258
-0.292
-0.338
-0.401
-0.487
-0.553
-0.653
-0.698
-0.704
-0.655
h
5.57
6.27
6.91
7.23
7.21
7.02
6.62
5.94
4.91
4.13
3.07
2.9
3.92
5.85
Va
1396
1112
1452
1820
1977
2118
2178
2133
1954
1782
1507
1406
1479
1795
σln(Y)
0.52
0.479
0.485
0.492
0.497
0.502
0.511
0.522
0.538
0.556
0.587
0.613
0.649
0.672
K. Sadigh, C.-Y. Chang, J.A. Egan, F. Makdisi, and R.R. Youngs Attenuation
Relationship
A full description of the development of this attenuation relationship may be found in:
Sadigh, K., C.-Y. Chang, J.A. Egan, F. Makdisi, and R.R. Youngs (1997). Attenuation
Relationships for Shallow Crustal Earthquakes Based on California Strong Motion Data,
Seismological Research Letters, 68, January/February, pg. 180-189.
Abstract: Attenuation relationships are presented for peak acceleration and response spectral
accelerations from shallow earthquakes. The relationships are based on strong motion data
primarily from California earthquakes. Relationships are presented for strike-slip and reverse
faulting earthquakes, rock and deep soil deposits, earthquakes of moment magnitude M 4 to 8+,
and distances up to 100 km.
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Equations:
EQTools V3.0
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Table for M less than or equal to 6.5
Period
0
0.05
0.075
0.1
0.12
0.15
0.17
0.2
0.24
0.3
0.4
0.5
0.75
1
1.5
2
3
4
5
7.5
EQTools V3.0
c1
-0.624
-0.09
0.1355
0.275
0.348
0.285
0.239
0.153
0.06
-0.057
-0.298
-0.588
-1.208
-1.705
-2.407
-2.945
-3.7
-4.23
-4.714
-5.53
c3
0
0.006
0.006
0.006
0.005
0.002
0
-0.004
-0.011
-0.017
-0.028
-0.04
-0.05
-0.055
-0.065
-0.07
-0.08
-0.1
-0.1
-0.11
Page 111
c4
-2.1
-2.128
-2.131
-2.148
-2.162
-2.13
-2.11
-2.08
-2.053
-2.028
-1.99
-1.945
-1.865
-1.8
-1.725
-1.67
-1.615
-1.57
-1.54
-1.51
c7
0
-0.082
-0.0745
-0.041
-0.014
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8/8/2010
Table for M greater than 6.5
Period
0
0.05
0.075
0.1
0.12
0.15
0.17
0.2
0.24
0.3
0.4
0.5
0.75
1
1.5
2
3
4
5
7.5
c1
-1.274
-0.74
-0.5145
-0.375
-0.302
-0.365
-0.411
-0.497
-0.59
-0.707
-0.948
-1.238
-1.858
-2.355
-3.057
-3.595
-4.35
-4.88
-5.364
-6.18
c3
0
0.006
0.006
0.006
0.005
0.002
0
-0.004
-0.011
-0.017
-0.028
-0.04
-0.05
-0.055
-0.065
-0.07
-0.08
-0.1
-0.1
-0.11
c4
-2.1
-2.128
-2.131
-2.148
-2.162
-2.13
-2.11
-2.08
-2.053
-2.028
-1.99
-1.945
-1.865
-1.8
-1.725
-1.67
-1.61
-1.57
-1.54
-1.51
c7
0
-0.082
-0.0745
-0.041
-0.014
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table for Dispersion Relationships for Horizontal Rock Motion
Period
PGA
0.07
0.10
0.20
0.30
0.40
0.50
0.75
1.00
1.00+
EQTools V3.0
σln(Y)
1.39 - 0.14M; 0.38 for M .ge. 7.21
1.40 - 0.14M; 0.39 for M .ge. 7.21
1.41 - 0.14M; 0.40 for M .ge. 7.21
1.43 - 0.14M; 0.42 for M .ge. 7.21
1.45 - 0.14M; 0.44 for M .ge. 7.21
1.48 - 0.14M; 0.47 for M .ge. 7.21
1.50 - 0.14M; 0.49 for M .ge. 7.21
1.52 - 0.14M; 0.51 for M .ge. 7.21
1.53 - 0.14M; 0.52 for M .ge. 7.21
1.53 - 0.14M; 0.52 for M .ge. 7.21
Page 112
8/8/2010
Table for Deep Soil Sites
Period DSoil
0
0.075
0.1
0.2
0.3
0.4
0.5
0.75
1
1.5
2
3
4
8.2.5
c6 - SS
0
0.4572
0.6395
0.9187
0.9547
0.9251
0.8494
0.701
0.5665
0.3235
0.1001
-0.2801
-0.6274
c6 - RV
0
0.4572
0.6395
0.9187
0.9547
0.9005
0.8285
0.6802
0.5075
0.2215
-0.0526
-0.4905
-0.8907
c7
0
0.005
0.005
-0.004
-0.014
-0.024
-0.033
-0.051
-0.065
-0.09
-0.108
-0.139
-0.16
P. Spudich, J.B. Fletcher, M. Hellweg, J. Boatwright, C. Sullivan, W.B. Joyner, T.C.
Hanks, D.M. Boore, A. McGarr, L.M. Baker, and A.G. Lindh Attenuation
Relationship
A full description of the development of this attenuation relationship may be found in:
Spudich, P., J.B. Fletcher, M. Hellweg, J. Boatwright, C. Sullivan, W.B. Joyner, T.C. Hanks,
D.M. Boore, A. McGarr, L.M. Baker, and A.G. Lindh (1997). SEA96 - A New Predictive
Relation for Earthquake Ground Motions in Extensional Tectonic Regimes, Seismological
Research Letters, 68, January/February, pg. 190-198.
Abstract: We present a new predictive relation for horizontal peak ground acceleration and 5%-
damped pseudo-velocity response spectrum derived from a global set of earthquake ground
motion data recorded in extensional tectonic regimes. We developed our relation based on data
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from extensional regime earthquakes having moment magnitude M > 5.0 recorded at distances
less than 105 km.
Equations:
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Period
pga
0.10
0.12
0.15
0.17
0.20
0.24
0.30
0.40
0.50
0.75
1.00
1.50
2.00
8.2.6
b1
0.156
1.772
1.876
1.964
1.996
2.023
2.035
2.030
2.001
1.971
1.922
1.912
1.964
2.068
b2
0.229
0.327
0.313
0.305
0.305
0.309
0.318
0.334
0.361
0.384
0.425
0.450
0.471
0.471
b3
0.000
-0.098
-0.101
-0.099
-0.096
-0.090
-0.082
-0.070
-0.052
-0.039
-0.020
-0.014
-0.019
-0.037
b5
-0.945
-1.051
-1.035
-1.009
-0.994
-0.972
-0.946
-0.915
-0.879
-0.857
-0.833
-0.837
-0.879
-0.940
b6 h(km) sigma1
0.077 5.57 0.216
0.079 6.27 0.268
0.102 6.91 0.272
0.127 7.23 0.277
0.139 7.21 0.281
0.154 7.02 0.286
0.168 6.62 0.292
0.183 5.94 0.300
0.198 4.91 0.311
0.206 4.13 0.320
0.214 3.07 0.339
0.214 2.90 0.354
0.209 3.92 0.377
0.200 5.85 0.395
sigma2
0.000
0.000
0.000
0.001
0.005
0.012
0.019
0.027
0.038
0.047
0.062
0.073
0.089
0.100
R.R. Youngs, S.-J. Chiou, W.L. Silva, and J.R. Humphrey Attenuation Relationship
A full description of the development of this attenuation relationship may be found in:
Youngs, R.R., S.-J. Chiou, W.L. Silva, and J.R. Humphrey (1997). Strong Ground Motion
Attenuation Relationships for Subduction Zone Earthquakes, Seismological Research Letters, 68,
January/February, pg. 58-73.
Abstract: We present attenuation relationships for peak ground acceleration and response
spectral acceleration for subduction zone interface and intra-slab earthquakes of moment
magnitude M5 and greater for distances of 10 to 500 km. The relationships were developed by
regression analysis using a random effects regression model that addresses criticism of earlier
regression analyses of subduction zone earthquake motions. We find that the rate of attenuation
of peak ground motions from subduction zone earthquakes is lower than that for shallow crustal
earthquakes in active tectonic areas. The difference is significant primarily for very large
earthquakes. The peak motions increase with earthquake depth and intra-slab earthquakes
produce peak motions that are about 50 percent larger than interface earthquakes.
EQTools V3.0
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Equations:
Period
pga
0.075
0.1
0.2
0.3
0.4
0.5
0.75
1
1.5
2
3
EQTools V3.0
c1
0
1.275
1.188
0.722
0.246
-0.115
-0.4
-1.149
-1.736
-2.64
-3.328
-4.511
c2
0
0
-0.0011
-0.0027
-0.0036
-0.0043
-0.0048
-0.0057
-0.0064
-0.0073
-0.008
-0.0089
c3
-2.552
-2.707
-2.655
-2.528
-2.454
-2.401
-2.36
-2.286
-2.234
-2.16
-2.107
-2.033
Page 116
c4
1.45
1.45
1.45
1.45
1.45
1.45
1.45
1.45
1.45
1.5
1.55
1.65
c5
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
8/8/2010
Period
pga
0.075
0.1
0.2
0.3
0.4
0.5
0.75
1
1.5
2
3
8.2.7
c1
0
2.4
2.516
1.549
0.793
0.144
-0.438
-1.704
-2.87
-5.101
-6.433
-6.672
c2
0
-0.0019
-0.0019
-0.0019
-0.002
-0.002
-0.0035
-0.0048
-0.0066
-0.0114
-0.0164
-0.0221
c3
-2.329
-2.697
-2.697
-2.464
-2.327
-2.23
-2.14
-1.952
-1.785
-1.47
-1.29
-1.347
c4
1.45
1.45
1.45
1.45
1.45
1.45
1.45
1.45
1.45
1.5
1.55
1.65
c5
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
Gail M. Atkinson and David M. Boore Attenuation Relationship (1997a)
A full description of the development of this attenuation relationship may be found in:
Atkinson, G.M. and D.M. Boore (1997). Stochastic Point-Source Modeling of Ground Motions
in the Cascadia Region, Seismological Research Letters, 68, January/February, pg. 74-85.
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Abstract: A stochastic model is used to develop preliminary ground motion relations for the
Cascadia region, for rock sites. The model parameters are derived from empirical analyses of
seismographic data from the Cascadia region. The model is based on a Brune point-source
characterized by a stress parameter of 50 bars. The model predictions are compared to ground
motion data from the Cascadia region and to data from large earthquakes in other subduction
zones. The point-source simulations match the observations from moderate events (M<7) in the
Cascadia region. The simulations predict steeper attenuation than observed for very large
subduction events (M>7.5) in other regions; motions are over predicted near the earthquake
source and under predicted at large distances (>100 km). The discrepancy at large magnitudes
suggests further work on modeling finite-fault effects and regional attenuation is warranted. In
the meantime, the preliminary equations are satisfactory for predicting motions from events of
M<7 and provide conservative estimates of motions from larger events at distances less than 100
km.
Equations:
EQTools V3.0
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Period
pga
0.05
0.1
0.125
0.2
0.313
0.5
0.769
1
1.25
2
pgv
8.2.8
c1
0.68
1.47
1.53
1.472
1.273
1.001
0.65
0.232
-0.033
-0.295
-0.912
4.903
c2
0.733
0.733
0.809
0.851
0.929
1.041
1.174
1.322
1.388
1.457
1.565
1.223
c3
0
0
-0.032
-0.044
-0.076
-0.117
-0.165
-0.195
-0.201
-0.201
-0.172
0.000
c4
0.00645
0.00921
0.00829
0.00783
0.00645
0.0053
0.00414
0.00345
0.00299
0.00276
0.00207
0.00253
Atkinson and Boore Attenuation Relationship (1997b)
A full description of the development of this attenuation relationship may be found in:
Atkinson, G.M. and D. M. Boore (1997). Some Comparisons Between Recent Ground Motion
Relations, Seismological Research Letters, 68, January/February, pg. 24-40.
Abstract: We provide an overview of new ground-motion relations for eastern North America
(ENA) developed over the last five years. The empirical-stochastic relations of Atkinson and
Boore (1995) are compared to relations developed by the Electric Power Research Institute
(EPRI, 1993; also Toro et al., 1994) Frankel et al. (1996), and the consensus ENA groundmotion values as reported by SSHAC (1996). The main difference between our relations and
those of EPRI or Frankel is in the low-frequency amplitudes (f<2 Hz, all magnitudes). We
predict lower amplitudes (by more than a factor of two) at 1 Hz, largely due to our use of an
empirical source model rather than a single-corner-frequency Brune source model; the use of an
empirical source model is motivated by the desire to match the ENA ground-motion database as
closely as possible.
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We also compare our new ENA relations to empirical relations for California. The comparison is
complicated by the need to adjust the ENA hard-rock motions to obtain equivalent motions for
typical California soil conditions. Two alternative methods of making this correction lead to
somewhat different conclusions. One possible conclusion is that our ENA predict similar lowfrequency amplitudes to those predicted by Boore et al. (1993, 1994) and Abrahamson and Silva
(1996) for California, but our predicted ENA amplitudes are much higher (factor>2) than
California values at high frequencies. The alternative soil correction leads to the conclusion that
our ENA relations are moderately lower (factor<2) than the California relations at low
frequencies, and moderately higher at high frequencies. Both of these conclusions imply that
ground-motion relations or time series for earthquakes in one region cannot simply be modified
for use in engineering analyses in another region.
Equations:
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Frequency (Hz) Period (sec)
c1
0.5
2
-1.66
0.8
1.25
-0.9
1.0
1
-0.508
1.3
0.7692
-0.094
2.0
0.5
0.62
3.2
0.3125
1.265
5.0
0.2
1.749
7.9
0.1266
2.14
10.0
0.1
2.301
13.0
0.0769
2.463
20.0
0.05
2.762
PGA
PGA
1.841
PGV
PGV
4.697
c2
1.46
1.462
1.428
1.391
1.267
1.094
0.963
0.864
0.829
0.797
0.755
0.686
0.972
c3
-0.039
-0.071
-0.094
-0.118
-0.147
-0.165
-0.148
-0.129
-0.121
-0.113
-0.11
-0.123
-0.086
c4
0.00
0.00
0.00
0.00
0.00
0.00024
0.00105
0.00207
0.00279
0.00352
0.0052
0.00311
0.00
Soil Factor
0.27
0.27
0.27
0.278
0.29
0.263
0.24
0.18
0.15
0.13
-0.03
-0.612
Accelerations for Deep Soil Sites:
⇒ To obtain motions on deep soil profiles overlying rock, use Equation (1) to compute the rock
motions and then multiply the results by the amplification factors provided in the right column of
Table 2.
⇒ For PGA, use factor listed for frequency of 20 Hz; this should provide a conservative estimate
of PGA.
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It is important to distinguish that “soil” here refers to deep deposits of unconsolidated sediments,
typically of Cretaceous age and younger. Typical soil deposits for which the factors above were
derived are in the range of 100’s of m, with shear wave velocities as high as 1000 m/sec. This
definition is different from what would be considered soil by geotechnical engineers that are
typically concerned with near-surface sediments found in the upper 30 m or so. In Charleston,
SC for instance, marl and limestone would be considered soil in the context of the factors
provided above; thus, soil here corresponds to the “soft rock” definition of most engineers, or the
“NEHRP B-C Boundary” classification.
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8.3 Ground Motion Attenuation Plot Controls
To use the old attenuation relationships for plotting ground spectrum plots, the user needs to go
to the Attenuation option on the menu and select Old Relationships option.
Generating ground motion attenuation plots using EQTools involves 2 distinct stages. Stage 1 is
the choice of attenuation relationship and the input as necessary. Stage 2 is choosing the plot
options. The interface for the attenuation relations is as shown next.
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To generate the attenuation plots, follow these steps:
STEP 1: Choose the tectonic regime using the radio buttons on the top left
STEP 2: Choose the attenuation relationship from the list provided. Once a choice is made, the
characteristics of the relationship are displayed in the frame on the top right.
STEP 3: Choose and/or input the site and other parameters. The expected input parameters are
active if and when necessary
STEP 4: Press the "Attenuation" button.
STEP 5: Choose plot options using the radio buttons on the left.
STEP 6: To view attenuation relation coefficients, press the "View Coefficients" button
STEP 7: To view a different attenuation relationship, press the "Reset" button and repeat steps 1
through 6 above
Attenuation relationship coefficients are displayed as shown below.
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9
New Attenuation Relationships
EQTools has been updated to include the new Ground Motion Prediction Equations (GMPE)
developed by PEER group for shallow crustal earthquakes active tectonic region. These new
models are developed on much larger strong ground motion database compared to the data used
to develop old relationships. Hence, these relationships use lot more variables compared to the
previous prediction models. Variables used in these models are stated below:
•
Magnitude (M)
•
Flags for reverse style, normal style, strike style and unspecified style faulting (FRV,FNM)
•
Aftershock flag (FAS)
•
Closest distance to rupture plane (Rrup)
•
Hanging Wall Flag (HW)
•
Average shear velocity in top 30m (Vs30)
•
Rock motion PGA for nonlinear site response (PGA1100)
•
Following parameters are required for scaling hanging wall;
•
Dip down rupture width (W)
•
Dip (δ in degree)
•
Horizontal distance to the surface projection of the rupture (Rjb)
•
Horizontal distance to the edge of the rupture measured perpendicular to strike (Rx)
An overview of new attenuation relationships is as followed:
9.1.1
Abrahamson and Silva (2008)
Data Set: Data set used by Abrahamson and Silva for analysis consist of 2754 recordings from
135 earthquakes compared to 655 records from 58 earthquakes used for analysis of previous
model(1997).
This increased the range of model validity and enabled the developers to
incorporate additional features mentioned in conclusion.
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Model Applicability: It is applicable for magnitude range of 5-8.5 and source to site distance
ranging from 0-200 km.
Attenuation Relationship:
ln
,
,
,
.
,
,
, ,
,
,
,
where:
,
8.5
ln
8.5
ln
This is the base model which is same as the one used in 1997 model.
where:
Function f5 is the site response model. In the previous model, only a linearized relation was
established for site response (shown later), but in the NGA model, developers recognize the nonlinear site response as a function of shear velocity. In the equation below, VLIN is linear scaling
limit below which response becomes nonlinear.
Estimation of VLIN comes from 1-D site
analysis.
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ln
,
ln
ln
ln
where:
Term
is PGA with shear velocity in rock (1100 m/s) and is compute using
following equation:
f
a
@
b
n ln
VLIN
and then substituting this value to calculate total response at zero period and Vs30 as 1100 m/s
in calculation of ln
.
1500 m/s
.
.
.
0.50 sec
.
.
700 m/s
0.50 sec
1 sec
1 sec
2
2 sec
862 m/s
Function f4 is for hanging wall effect. This function was included even in the previous model;
however, the function was inconsistent for some values. The inconsistency was removed by
using five functions to predict the effect of hanging wall instead of two as used in previous
model.
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,
, ,
,
,
,
,
,
where:
1
30
30
0
,
30 km
0.5
,
2
cos
cos
1
cos
,
90
1
,
0
6
6
1
6
7
7
70
20
1
1
70
70
Function f6 is to incorporate the effect of depth to top rapture. Somerville and Patakra studied
this effect in 2006, which proved that large earthquakes tend to rupture on surface, while small or
medium earthquakes occur at depth.
10
10
10 km
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Function f8 incorporates the large displacement effect.
100
0
,
100
100 km
where:
1
5.5
0.5 6.5
0.5
5.5
0.5
6.5
6.5
Function f10 incorporated the effect of soil depth in ground response. Formulation of this effect
is based on study from Silva (2005).
.
,
ln
.
ln
.
.
200
0
.
200
.
200
where:
6.745
ln
.
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180
6.745
1.35 ln
5.394
4.48 ln
180
500
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180
/
500 m/s
500 m/s
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0
1000
ln
min
, 1000
ln
.
ln
min
, 1000
.
ln
.
0
.
0
0.35
0.25 ln
ln
0.35 sec
0.35
2
0.25 ln
ln
1000
0.35
1000
0
1000
/
2 sec
2 sec
2
0.0625
2
2 sec
The spectral acceleration must be adjusted for high periods.
,
where: log
1100
1.25
,
,
.
,
,
0.3
Standard Deviation
where:
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,
,
,
S
ln
,
,
,
,
,
ln
ln
2
,
,
/
,
,
,
ln
,
,
S
ln
,
2
,
,
,
ln
ln
,
/
,
,
ln
,
,
where:
0
ln
,
,
1
ln
5
5
2
5
7
7
5
5
2
,
5
7
7
,
0.3,
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,
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9.1.2
Boore and Atkinson (2008)
This model predicts 5% damped pseudo-absolute acceleration spectra, PGA and PGV. In this
model, developers ignored all the ground motion data generated from aftershocks in order to
avoid different scaling required compared to main shocks.
Relationship: The predicted ground motion parameters are a function of:
T
– Period (sec), use 0 for PGA, -1 for PGV
M
– Moment magnitude
F
– 1 for unspecified, 2 for strike-slip, 3 for normal or 4 for reverse
Rjb
– Joyner-Boore distance (km)
VS30 – Shear wave velocity (m/s) averaged over top 30 m
ln
,
,
,
where:
FM is the magnitude scaling term
U, SS, NS,RS terms are flags for different faults types for general, strike slip, normal
slip and reverse slip respectively.
FD term is for scaling factor that varies with distance and moment.
,
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where:
Next scaling factor is for site consisting of linear (FLIN) and nonlinear (FNL) part.
,
,
where:
ln
FNL
_
0.1
_
0.1
4
0.1
ln
ln
ln
4
ln
4
ln
4
4
4
where:
pga4nl is the predicted PGA in g as given by the general equation for FS = 0 and
=0
ln
ln
ln
ln
0
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3∆
∆ /∆
2∆
∆ /∆
where:
∆
∆
ln
ln
Standard Deviation:
_
√
ε term associated with standard deviation is the measure of deviation of ground motion
from the mean. So if +1 standard deviation is desired for 84 percentile value, ε term
should be substituted as 1.
9.1.3
Campbell and Bozorgnia (2008)
This model is developed for prediction of horizontal component spectrum ordinates for 5%
damped linear elastic response. The equation also gives PGA, PGV and PGD for given
parameters. Model is only valid for magnitude of earthquakes between 4 to 7.5-8.5 (depending
on the fault mechanism) and for distance ranging between 0-200 km. Standard input variables
required are magnitude (M), depth to top of rupture (ZTOT), fault flag for reverse and normal
style; dip angle (δ) closest distance to rupture (RRUP), VS30, depth to VS= 2.5 km/sec (Z2.5).
NGA Ground Motion Model:
ln
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where:
fmag is the magnitude function, which basically incorporates the fact that response increases with
increase in magnitude.
5.5
5.5
5.5
5.5
6.5
6.5
6.5
fdis function expresses the effect of distance and magnitude together on response.
ln
fflt function recognized the effect of different fault styles on response.
,
where:
,
1
1
1
1
0
1
0
30°
150°
150°
flag for reverse fault style
30°
flag for normal fault style
fhang function includes the hanging wall effect in response. This function is divided into 3
components, fhang,M recognizes the influence of magnitude, fhang,Z recognizes the effect of depth
to top of rupture and fhang,δ is to incorporate the influence of dip angle on hanging wall. Total
effect of hanging wall on response is given by;
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,
,
,
,
1
0
,
where:
,
,
,
,
0
2
1
0,
1
0,
1
,
6.0
6.0
6.0
6.5
6.5
0
20
1
90
20
/20 0
/20
ln
20
70
70
ln
ln
ln
ln
1100
1100
1100
where: A1100 is the median estimate of PGA on a reference rock outcrop (VS30 = 1100 m/s) and is
computed using third relation in the bracket using coefficients at T=0 sec.
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1
.
.
0
1
.
1
.
.
1
.
.
3
3
The total response calculated using the set of equations given above gives the median site
response (50 percentile value). + or – one standard deviation (84 and 16 percentile respectively)
can be worked out using equations given below.
Standard Deviation:
if uncertainty of arbitrary horizontal component desired:
where:
2
where:
0
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0.30
and
Developers believe that the model is most reliable for when evaluated for
(i)
M> 4
(ii)
M<8.5 for strike-slip faulting
(iii) M<8.0 for reverse faulting
(iv) M<7.5 for normal faulting
(v)
VS30 = 150-1500 m/s
(vi) ZTOR= 0-15 km
9.1.4
Chiou and Youngs (2008)
This model is developed for estimating horizontal ground motion response for 5% damped
pseudo-acceleration for spectral period 0.1-10 sec caused by shallow crustal earthquake in active
tectonic region. Formulation also provides PGA and PGV for given parameters. Standard input
variables required are magnitude (M), depth to top of rupture (ZTOT), fault flag for reverse and
normal style, dip angle (δ) closest distance to rupture (RRUP), VS30, depth to VS= 2.5 km/sec
(Z2.5), flag for aftershock (AS), horizontal distance to the top of the rupture measured (RX).
ln
ln
min ln
1130
,0
,
1
cosh
ln
1
max 0,
.
cosh 0.15 max 0,
.
15
where:
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ln
4
4
ln
6
cosh
max
ln
ln 1
,0
cosh max
cos
tanh
1
0
1
1
,0
0.001
0
0
1
0
30°
1
0
150°
120°
60°
Standard Deviation:
1
where:
min max
2
2
,5 ,7
min max
0.7
5
,5 ,7
5
1
where:
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1
0
1
0
,
9.1.5
Idriss (2008)
Similar to other GMPE, this model predicts the 5% damped linear elastic response spectrum.
The model is only valid for site conditions where shear wave velocity at 30m depth is between
450-900 m/s and for events between 0-200km distance. Standard input parameters required are:
magnitude (M), fault type (F), closest distance to rupture surface (RRUP) and shear velocity
(VS30).
Attenuation Relationship:
0
450
∆
S
S
900
900
Standard Error:
1.28
0.05 ln
0.08
for M between 5 and 7.5 and T between 0.05 sec and 3 sec.
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9.2 New Ground Motion Attenuation Plot Control
To use new attenuation relationships for plotting ground spectrum plots, the user needs to go to
the Attenuation option on the menu and select New Relationships option.
Selecting New Relationships will open the form as given in the figure below.
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Options provided on this form are explained ahead:
Attenuation Type:
This drop down option shows the entire list of available new attenuation relationships. The user
should remember that only one relationship can be used to generate the attenuation plot at a time.
The open area on the right side is provided for input variables. After the attenuation relation is
selected, the variables necessary for computing spectrum appear. The figure above illustrates an
example with Abrahamson and Silva attenuation relation.
Plot Options:
This control provides following options:
Overlay Earthquake Response Spectra:
Using this option, the user can superimpose the resultant spectrum of ground records selected in
the search tool on the mean attenuation plot. The resultant spectrum can be computed either by
geometric mean (geomean), average, envelope or the square root of sum of squares method using
radio buttons. A list of records, selected from search tool, appear in the window provided below
these combination options. From this list, the records can be selected and unselected at any time.
Show SD Curves:
Using this check box, the user can plot +1 and -1 standard deviation values from the mean
intensity of spectrum. These terms have statistical significance representing 84 percentile and 16
percentile values of intensity respectively for defined parameters.
Overlay ASCE-7 Code Spectra:
This control overlay the ASCE-7 code spectrum on the spectrum computed from attenuation
relation. The code spectrum parameters can be provided by clicking on the “Set ASCE-7
Parameters” key. This would open up a window as shown in figure next.
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Axis Options:
This control defines Magnitude (M) and distance of a site from fault rupture (Rrup). Magnitude
and distance of a site from fault rupture are the two most influential parameters that affect the
spectral shape and intensity. To study their effects, the following controls are provided:
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(i)
Single distance value and a range of magnitudes
(ii)
Single magnitude value and a range of distances
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(iii)
For a specific magnitude and distance pair
Target Spectra Options:
This control creates a spectrum using attenuation relationships, which can be used as a target
spectrum just like ASCE-7 spectrum for scaling ground records. It provides two options:
(i)
Base Spectrum: This option computes a spectrum using selected attenuation
relationship. Magnitude (M) and distance (Rrup) values can be set by clicking on the
Set Parameters key, which will make Target Spectra Options window to pop up.
Other parameters required for the selected attenuation relation can be provided in a
control shown in the subsequent figure.
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(ii)
Conditional Mean Spectrum: The concept conditional mean spectrum is proposed by
Cornell and Baker (2006) and is used to generate a spectrum that satisfies a certain
hazard level for the site under consideration. The following figure illustrates the
input window for three combinations of magnitude, distance and epsilon. These
inputs should typically be taken from the de-aggregation maps provided on USGS
website. The remaining parameters used in the selected attenuation model can be
provided in the control illustrated in the above figure. The combination options
Geomean, Average, Envelope and SRSS are provided to compute the resultant
spectrum to be displayed at the end.
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After all the parameters are set, the response spectrum can be plotted by pressing the Attenuate
key on the right bottom corner. As stated before, these plots can be used as a target spectrum for
scaling ground records. By pressing Save Target user can use the plot as a target spectrum in the
Scaling Form.
Legend:
The legend for the attenuation plot is provided on the right hand bottom corner (above
Attenuation key) as shown in the following figure. Its title is controlled by axis option. For
example, following figure illustrates the legend heading as ‘Magnitude Legend,’ which appears
after selecting the first option which plots multiple spectra for a range of magnitudes with an
increment of 0.5 for a single distance.
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10 Site Response Analysis Using EQTools
10.1 Overview of Site Response Analysis Procedures
Earthquake analysis of building structures, which include site effects, even in an approximate
sense, can lead to more realistic, efficient and safer earthquake resistant designs. Investigations
of major destructive earthquakes (Caracus 1967, Managua 1972, Mexico City 1985) indicate that
perhaps the most important aspect of the response of soil-structure systems is the amplifying
effect that the soil profile can have on the bedrock motions. This consideration is reflected in
many building codes, which modify the lateral design forces based on a knowledge of the
fundamental period of the site.
Site effects can be investigated more thoroughly by
implementing site response analyses procedures. Such analyses do go a long way in improving
the accuracy and reducing the dispersion of ground motion prediction. Extensive research has
been conducted regarding the earthquake response of soil profiles. Several computer programs
are available for evaluating the effect of local soil conditions on the ground surface response.
LAYER, SHAKE, QUAD4, LUSH2, WAVES, etc. are a few of them. WAVES (Wilson and
Hart, 1989), a computer program for computing the dynamic characteristics and seismic response
of horizontally layered soil deposits, is integrated with EQTools to assess the site response.
WAVES was chosen because of its free-field input format and extreme computational efficiency.
Further, this program optionally performs energy balance computations as a means to investigate
the distribution of earthquake energy in the soil profile.
EQTools in tandem with WAVES, can perform the earthquake response analysis of soil deposits
modeled as one-dimensional shear beam finite element systems for a suite of earthquake records
as the base input ground motions. There are options to perform a linear, equivalent linear or
more complex, fully nonlinear analysis. The effect of soil response on the time histories, Fourier
spectrum and the response spectrum are available to be viewed graphically. EQTools can
rapidly carry out the site response analysis for a maximum of ten layer soil model and 12 base
input ground motions.
EQTools can perform any one of the following types of analysis
depending on the user's choice:
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• Linear earthquake response analysis
• Equivalent linear iterative earthquake response analysis
• Nonlinear Earthquake Response Analysis (Constant Time Step)
• Nonlinear Earthquake Response Analysis (variable Time Step)
10.2 Analysis Control Information for Site Response
The analysis control information necessary to be input by the user varies and depends on the
user's choice of the analysis method. Except a few numerical values that need to be provided
by the user, all other required analysis control information in the form of choices to be selected
using ortion buttons. The analysis control information interface is shown below:
Depending upon the user's choice of the time domain procedure for site response, the fields for
expected input values are active and the rest inactive. Hence, the user has a clear idea as to
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what input is necessary. The requisite input data is self explanatory. Once all the data had been
provided, the user presses the "Use for Analysis" command button, whereby the data is saved
for further use in the analysis.
10.3 Base Input Ground Motions
The input for base ground motions to be used in the analysis is provided through the analysis
control information interface, as shown below, by pressing the "Input Acceleration" command
button.
The input of time histories is achieved in two ways. The user can either open a scaled/unscaled
bin of eqrthquakes or he has the choice of using unscaled earthquakes from the active list of
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selected earthquakes on the search query forms. The later option is available only if the search
for is active.
10.4 Geometric and Dynamic Properties of Soil Model
The necessary soil parameters for the analysis again depend on the user's choice of time domain
procedure. Shown below, is the interface for input of soil dynamic properties and geometry of
the soil model for the Equivalent Linear Iterative Earthquake Response Analysis.
As before, the necessary data fields are shown in white. The ones not necessary are grayed out.
Even though the user can input the data in the grayed out fields, this data will be ignored. The
user can also import data from a previously saved file by clicking on the "Import Data"
command button. Once all the data has been input, the user confirms by pressing the "Use for
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Analysis" button. Following this, the user can save the data by pressing the "Save Data"
command button. Once all done, the user can quit this interface by clicking on the "Close"
button.
10.5 Running the Site Response Analysis
Once the analysis control information, earthquake data and soil properties have been provided,
the analysis can be run by pressing the "Compute Response" button as shown below. Please
note that the “Compute Response” command button is not available if any of the three
necessary pieces of information is not provided.
The analysis may take a while depending upon the number of earthquakes and number of soil
layers in the model.
Once the analysis is completed, the interface showing results is
automatically displayed.
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10.6 Interpreting the Site Response Analysis Results
The interface for viewing the analysis results is as shown below:
The desired response quantity can be chosen from the options on the left side. The layer and the
input ground motion for which the response is desired can also be chosen from the drop-down
lists on the left. Original and soil response quantities available are acceleration, velocity and
displacement time histories, their Fourier amplitude spectra and the response spectra. The
response spectra results are ahead. The response spectral quantities can be plotted againgst time
period or the frequency. The response spectra can be viewed for any value of the structural
system damping. Every time the user chooses a new damping value, the user must press the
“Update” button before the modified response spectra are available. Tripartite plots or plots for
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different spectral quantities are available for the response spectra. The force and length units can
be changed any time by using the option buttons in the “Display Units” frame.
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11 Horizontal Pair Window:
This window studies the effect of rotation of the horizontal components of a ground record on
maximum response. This window can handle no more than one pair of ground records at a time.
One of the most important applications of orbit spectrum could be identifying the orientation in
which ground records have maximum energy.
Orbit Spectrum is a locus of maximum response recorded for orthogonal components of a ground
record when rotated at different compass angles from their original orientation for given period
and damping value. For each angle of rotation, a new pair of time histories is computed using
simple mathematical transformation given below.
sin
cos
cos
sin
where X’ and Y’ are new orthogonal components.
Maximum response is calculated by solving the equation of motion numerically for the pair of
time histories of the selected period and damping. Response could be either in acceleration,
velocity or displacement depending on user choice.
Remember, unlike the time history tool, records cannot be selected directly from Component
Matching Search Criteria window.
The following figure illustrates the location of Orbit
Spectrum button.
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A typical interface of the Horizontal Pair form is as shown here.
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Plots and controls provided in this form are explained below.
Time History Plots:
The time history plots are provided in the left hand top corner of the form. Time history plot is a
variation of one of the seismic response quantity (acceleration, velocity or displacement) with
respect to time.
XY Plot:
The XY plot consists of plotting the two orthogonal components on either axis. This plot
represents a two dimensional ground movement viewed from the top.
Polar Plot:
This plot represents the maximum response for the defined damping and period along the radial
direction at every 15 degree increments. The red and the blue contours correspond with the time
history plot to make identification of components easier. The third curve is for geomean
response calculated from the two components and is always plotted in white. The two dotted
lines on the plot along the radial direction represent the original recorded orientation of the
horizontal components.
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RS (Response Spectrum) Plot:
This plot shows the response spectrum for the selected pair of components. Similar to the polar
plot, colors in RS plot are consistent with the time history plot to make the identification of
components easier. By default, the response spectrum is plotted on log-log scale in this form.
Plot Data:
This control enables the user to define desired period, damping and angle of rotation to be
applied on original ground components.
The angle defined in rotate recalculates the time
histories using the transformation shown earlier in this section and changes the XY and RS plots
accordingly.
Period and damping values are specifically needed for the Polar Plot.
For
consistency the damping value is predefined to 5% and cannot be changed.
Plotting ASCE7 Spectra:
The ASCE-7 design spectrum can be generated and superimposed on RS plot by checking the
the ASCE7 option. Parameters can be set by pressing the Parameters key below check box. This
will open up the following window:
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Plot Options:
Four options are provided to calculate the resultant spectrum from the two spectra computed for
individual component. This control is provided with check boxes, thus user can select more than
one option at a time.
Spectral Coordinates:
All plots in this form are digitized, thus the position of the curser on plot displays the coordinates
at that location. Coordinates can be seen in the two boxes provided on right hand top corner of
every plot.
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12 New Scaling Window
This is one of the strongest tools of the program. The scaling procedure involves two steps:
Scale Factor 1 and 2. In Scale Factor 1, the resultant of two components of the same record is
computed and scaled using the procedure chosen by the user while in Scale Factor 2, the
resultant spectrum of all the resultants obtained in the previous step is computed and scaled. The
tool also offers two types of target spectrum on which ground record spectra can be scaled:
ASCE7 design spectrum and Conditional Mean Spectrum as defined by Baker and Cornell
(2006). This tool can handle total 12 ground records (6 pairs of records) at a time. Records are
imported from the Earthquake Records Search Tool. To import the selected records, a scaling
form key is provided on the right hand side as shown.
The Scaling form comes with following controls:
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12.1 Data to Scale:
These set controls provide multiple options of plotting response spectra. Using these radio
buttons, the user can change the display between acceleration, velocity or displacement spectra.
Depending on the selected entity, the control automatically changes the ASCE-7 design
spectrum. However, the user should keep in mind that ONLY acceleration spectrum of the
selected ground records can be used for scaling if Conditional Mean spectrum or a Base
Spectrum is selected as a target spectrum.
The same window also has two more radio buttons: Scale Factor 1 and Scale Factor 2. These
two factors are calculated independently. Thus the selection of the Scale Factor key does not
affect selection of acceleration, velocity or displacement plot. Moreover, during any time in
scaling process, user can switch back and forth between scale factor 1 and 2 to change previously
selected parameters since the program uses temporary memory to save the settings.
12.2 Combination Options:
This control provides four options to combine the pair of ground motion components, which are:
geometric mean, square root of sum of squares, average and envelope. The program uses
selected combination option to compute the resultant spectrum. These options are provided in
both SF1 and SF2 steps. In SF1, using the combination option, the resultant of two components
of the same event is calculated; whereas in SF2, a single resultant is computed from all the
combinations obtained in SF1.
Four combination options mentioned above are defined below:
√
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2
Envelope means locus of maxim values.
12.3 Scaling Options:
Match at a point: As the name suggests, this method scales the ground motions such that the
ground record spectrum matches exactly with the target spectrum at a user defined period value.
The scale factor is calculated by taking the ratio of the ordinate of target spectrum and the
ordinate of ground record spectrum at the period of interest. Usually this period value provided
for scaling is the fundamental period of vibration of the system to be analyzed.
Equal Area Scaling: As mentioned before, since the peak ground acceleration, velocity, and
displacement for various earthquake records differ, the computed responses cannot be averaged
on an absolute basis. One of the most commonly used procedures used is to normalize the
records according to design spectrum intensity where the areas under the spectra between two
periods (or frequencies) are set equal to the area under the design spectrum. Again, any of the
three spectral quantities – acceleration, velocity, or displacement, can be used to fit the data.
EQTools can be used to normalize a bin of earthquakes on this basis. Such bins are allowed to
have a maximum of twelve selected ground motion records. The expected user input is the upper
and lower bound of the fitting region in terms of the time period.
Scaling to Minimize the Square Root of Sum of Squares (SRSS)of Errors: The nonlinear
response of structures is strongly dependent on the phasing of the input ground motion and on
detailed structure of its spectrum. Unlike the case of linear response, which can be obtained by
simple uniform scaling of a single time history matched to a design spectrum, an appropriate
measure of nonlinear response requires the use of multiple time histories having phasing and
response spectral peaks and troughs that are appropriate for the magnitude, distance, site
conditions, and wave propagation characteristics of the region. The purpose behind using a suite
of ground motions is to provide a statistical sample of this variability in phasing and spectra
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through a set of time histories that are realistic not only in their average properties but in their
individual characteristics as well. To be consistent with this approach, a scaling procedure is
utilized in which the shape of the response spectra of time histories is not modified. Instead, a
single scale factor is found such that the square root of sum of squares of the error (difference)
between the earthquake response spectrum and the design spectrum between two periods is
minimized. If such a procedure is adopted for scaling all three components of a record, it retains
the ratio between the three components at all periods. EQTools has the provisions to scale the
response spectra on this basis. The expected user input consists of the upper and lower bound of
the fitting region in terms of the time period and the upper and lower bound of the scale factor(s).
Scaling of Ground Motions as per the Upper Bound Method: The ground motions are scaled
such that the average value of the 5% damped response spectra for the suite of motions is not less
than the design response spectrum for the site for periods ranging from 0.2 T to 1.5 T seconds
where T is the natural time period of the structure in the fundamental mode of vibration for the
direction of response being analyzed. The natural time period of the structure is expected from
the user as input.
12.4 Scaling Criteria:
Selection of scaling option controls the availability of scaling criteria windows for input. There
are total eight windows in this section, with six windows available to input data from the user
depending on choice of Scaling Option. Minimum period and Maximum period in RS options
are blocked from the user to keep consistency in plotting.
Minimum period in RS data: Shows the lowermost period value on X axis used for plotting.
Maximum period in RS data: Shows the higher most period value on X axis used for plotting.
(Note: These two windows are blocked from the user to have consistent plot)
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Lower bound of fitting region: This option becomes available for input when any scaling
approach other than Match at a Point and Do Nothing is selected. It defines the starting point on
response spectrum from which scaling takes place.
Upper bound of fitting region: This option becomes available for input when any scaling
approach other than Match at a Point and Do Nothing is selected. It defines the ending point on
response spectrum where scaling ends.
Matching Period: This option comes into application for single period matching approach, where
ground record spectra are matched with target spectrum at the period value defined in this
window. It is recommended to use fundamental period of the system to be analyzed as matching
period.
Lower bound of scale factor: This input is required for scaling using minimize error option.
Lower bound scale factor defines the lower bound value of the factor that program can apply for
scaling ground records. The default value is set to 0.1 in the program.
Upper bound of scale factor: This input is required for scaling using minimize error option.
Upper bound scale factor defines the higher limit of the factor that program can apply for scaling
ground records. The default value is set to 1.0 in the program.
Increment: This value indicates the increment in scale factor during every iteration. Thus
starting from the lower bound scale factor, program increases the scale factor up to the upper
bound scale factor, with an increment defined by the user here. The default value is set to 0.1 by
the program.
Figure presented next shows the control for scaling criteria.
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12.5 Target Spectrum:
It is a spectrum which acts like a benchmark for scaling selected ground records. Typically,
ASCE-7 code spectrum is used as a target spectrum; however, this program also offers an
additional option of target spectrum using the new attenuation models.
The concept and
construction of conditional mean spectrum is explained in New Attenuation Relationship
chapter. The control to select the target spectrum is shown in the following figure.
(i)
ASCE-7 Spectra: This option generates the current ASCE-7 design spectrum. Option
can be selected by standard radio button shown in following figure. Selection of
ASCE-7 button will automatically unblock the Parameters key, which will enable the
user to input all the parameters required to compute spectral coordinates. Parameters
window is shown in the next figure.
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(ii)
Conditional Mean Spectrum: This is relatively a new concept in probabilistic seismic
design. Conditional mean spectrum is a spectrum representing mean intensity of the
ground motion for certain hazard level.
This spectrum is calculated using new
attenuation models. Further description on this concept and its construction can be
found in the new attenuation relationships chaper.
This option of target spectrum is only made available by the program if the user has
created and saved a target spectrum from the new attenuation relationships form prior
to entering scaling form. After one or more such spectra are constructed and saved,
Attenuation radio key becomes available with a drop down menu as shown in figure.
A drop down menu is provided so that user can construct multiple CMS using one or
more attenuation models and can pick any one for scaling. As soon as the user selects
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a CMS from available option, spectrum appears on screen just like ASCE-7 target
spectrum and further procedure of scaling ground records remains the same.
12.6 Plot Options:
This control provides four options, Geomean, Average, SRSS, and Envelope, to draw the
resultant spectrum. This option does not take any part in calculation of combination defined in
Scale factor 1 and 2 defined before; it just calculates and shows the resultant on the plot. On the
left side these options, the control also provides three options to display the plot: log-Arithmetic
scale, Log-Log scale and Arithmetic-Arithmetic scale.
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Critical Damping:
Damping value is used to compute response spectra of selected ground records. Computation of
response spectra is done using linear piecewise solution. To avoid inconsistency, damping
values for ground record spectra and ASCE-7 spectrum are set to 5%.
Scale Factors:
This window contains a table with a list of selected ground records, their directivity, SF1, SF2
and the final scale factor computed shown as the product of SF1 and SF2. The following figure
illustrates a typical table along with its location in the scaling form.
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On the right hand top corner, coordinates and a legend are provided. The plot is digitized,
displaying the position of the pointer with period and spectral quantities in the respective boxes.
The legend displays all the selected records with their individual components with the
corresponding color used for plotting its spectrum. The last section provides radio buttons for
individual X and Y components of selected ground records. This control is only made available
to the user when Use Ind. Component option is selected during SF1.
12.7 Steps for Scaling
(1) Selected required records from Earthquake Record Search Tool.
(2) Check on Plot all records for study and then click on Scaling Tool key to enter in the
form.
(3) Select the response quantity to be used for scaling.
(4) Select the combination options for SF1 and SF2.
(5) Select the methods of scaling for SF1 and SF2.
(6) Depending on the selected scaling options, provide necessary information in Scaling
Criteria.
(7) Select a target spectrum. If ASCE-7 is selected then provide necessary parameters.
(Note: For Attenuation spectrum, the user will need to define and save a target spectrum
from the new attenuation relationship window prior to entering in this form. If not
selected, close the scaling window, go and save a target spectrum using new attenuation
relationships and come back to the scaling window.)
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(8) Press SF1 to calculate the first scale factor. Note that the plot automatically changes and
shows the resultant spectrum computed using combination option defined in SF1 for each
record (instead of individual components), scaled with the recorded factor in this step.
(9) Press SF2 to calculate the second scale factor. Again the plot will change. In second
step, plot shows scaled resultant spectrum, calculated from the combinations obtained in
SF1, using the combination option defined in SF2.
Note that during any step, user can go back and change the combination options and/or scaling
options and/or scaling criteria and recalculate the scale factors. However, remember to press
Reset key and then click on SF1 and SF2 to computes respective factor.
The procedure can also be described using the following figure.
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12.8 Using Horizontal Pair tool in scaling tool:
In the figure provided previously, a blue elliptical mark shows the Rotate Pair option, which
takes the user to the Horizontal Pair form.
This feature provides additional flexibility by
allowing the user to see which orientation has maximum energy for the selected pair of ground
records. The user can then rotate the pair in that orientation and use the rotated time history and
response spectrum for scaling.
Remember, the Horizontal Pair window can handle only two records (one pair) at a time. Thus if
multiple pairs are selected in scaling window, each pair has to be selected individually and then
rotated using the Rotate Pair option.
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13 References
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