Thesis EQTools
Thesis EQTools
Thesis EQTools
Riaz Syed
MASTER OF SCIENCE
in
Civil Engineering
by
Riaz Syed
(ABSTRACT)
One of the most difficult tasks towards designing earthquake resistant structures is the
determination of critical earthquakes. Conceptually, these are the ground motions that
would induce the critical response in the structures being designed. The quantification of
this concept, however, is not easy. Unlike the linear response of a structure, which can
often be obtained by using a single spectrally modified ground acceleration history, the
nonlinear response is strongly dependent on the phasing of ground motion and the
detailed shape of its spectrum. This necessitates the use of a suite (bin) of ground
acceleration 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. Further, these suites of records may have to be scaled to
match the design spectrum over a period range of interest, rotated into strike-normal and
strike-parallel directions for near-fault effects, and modified for local site conditions
before they can be input into time-domain nonlinear analysis of structures. The
generation of these acceleration histories is cumbersome and daunting. This is especially
so due to the sheer magnitude of the data processing involved.
Abstract ii
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. The
various computational tools developed in EQTools facilitate the identification of severity
and damage potential of more than 700 components of recorded earthquake ground
motions. The application also includes computational tools to estimate the ground motion
parameters for different geographical and tectonic environments, and perform one-
dimensional linear/nonlinear site response analysis as a means to predict ground surface
motions at sites where soft soils overlay the bedrock.
While EQTools may be used for professional practice or academic research, the
fundamental purpose behind the development of the software is to make available a
classroom/laboratory tool that provides a visual basis for learning the principles behind
the selection of ground motion 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.
Abstract iii
ACKNOWLEDGEMENTS
The author would like to thank Dr. Finley A. Charney for serving as the authors major
advisor, as well as for the ideas, guidance, and advice offered to him throughout the
research work. His insight and experience in computing and earthquake engineering have
been of tremendous help in the authors quest for learning. Gratitude is also extended to
Dr. Raymond H. Plaut and Dr. James R. Martin for reviewing this thesis, offering ideas
and suggestions, and serving on the authors committee. The author would also like to
thank Ann Crate and Lindy Cranwell for their support and help during his graduate work
The author is grateful to his parents for their constant encouragement, moral support, and
love. It is to them that this thesis is dedicated.
Acknowledgements iv
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ........................................................................................................................ iv
LIST OF FIGURES.................................................................................................................................... vii
LIST OF TABLES....................................................................................................................................... xi
CHAPTER 1: INTRODUCTION ............................................................................................................... 1
1.1 PURPOSE AND SCOPE ............................................................................................................................ 6
1.2 ORGANIZATION OF TEXT ...................................................................................................................... 6
CHAPTER 2: EARTHQUAKE GROUND MOTIONS............................................................................ 9
2.1 STRONG GROUND MOTION DATABASE ................................................................................................. 9
2.2 SEISMOLOGICAL SEARCH PARAMETERS ............................................................................................. 13
2.2.1 Earthquake Magnitude ............................................................................................................... 14
2.2.2 Peak Ground Acceleration ......................................................................................................... 16
2.2.3 Distance ..................................................................................................................................... 17
2.2.4 Zone of Recording ..................................................................................................................... 18
2.2.5 Fault Mechanism........................................................................................................................ 19
2.2.6 Record Component .................................................................................................................... 21
2.2.7 Site Classification ...................................................................................................................... 21
2.2.8 Miscellaneous Search Parameters .............................................................................................. 22
2.3 ROTATION OF HORIZONTAL COMPONENTS OF GROUND MOTION HISTORIES ..................................... 23
CHAPTER 3: GROUND MOTIONS - AMPLITUDE AND DURATION PARAMETERS............... 29
3.1 AMPLITUDE PARAMETERS .................................................................................................................. 29
3.1.1 Peak Ground Acceleration ......................................................................................................... 30
3.1.2 Peak Ground Velocity................................................................................................................ 33
3.1.3 Peak Ground Displacement........................................................................................................ 33
3.2 INCREMENTAL VELOCITIES AND INCREMENTAL DISPLACEMENTS ...................................................... 33
3.3 STRONG GROUND MOTION DURATION ............................................................................................... 36
CHAPTER 4: GROUND MOTIONS - FREQUENCY CONTENT ...................................................... 39
4.1 FOURIER AMPLITUDE SPECTRUM........................................................................................................ 39
4.2 FILTERING/SCALING FREQUENCIES AND TIME HISTORIES .................................................................. 48
4.2.1 Filtering Frequencies and Time Histories .................................................................................. 48
4.2.2 Scaling Frequencies and Time Histories.................................................................................... 55
CHAPTER 5: GROUND MOTIONS RESPONSE SPECTRUM AND MODIFICATION OF
ACCELEROGRAMS................................................................................................................................. 60
5.1 RESPONSE SPECTRUM CONCEPT ......................................................................................................... 60
5.2 DEFORMATION, PSEUDO-VELOCITY, AND PSEUDO-ACCELERATION RESPONSE SPECTRA .................. 62
5.2.1 Deformation Response Spectrum............................................................................................... 62
5.2.2 Pseudo-Velocity Response Spectrum ........................................................................................ 63
5.2.3 Pseudo-Acceleration Response Spectrum.................................................................................. 64
5.2.4 Combined Deformation-Velocity-Acceleration Spectrum......................................................... 65
5.3 RESPONSE SPECTRUM CHARACTERISTICS ........................................................................................... 67
5.4 FACTORS INFLUENCING RESPONSE SPECTRA ...................................................................................... 72
5.4.1 Magnitude .................................................................................................................................. 72
5.4.2 Distance ..................................................................................................................................... 73
5.4.3 Source Characteristics................................................................................................................ 74
5.4.4 Duration ..................................................................................................................................... 75
5.4.5 SITE GEOLOGY ................................................................................................................................ 75
5.5 EARTHQUAKE DESIGN RESPONSE SPECTRA ........................................................................................ 76
5.6 NORMALIZATION AND SCALING OF GROUND MOTION RECORDS ....................................................... 84
5.6.1 Simple Uniform Scaling............................................................................................................. 84
5.6.2 Equal Area Scaling .................................................................................................................... 86
Table of Contents v
5.6.3 Scaling to Minimize the Square Root of Sum of Squares of Errors........................................... 87
5.6.4 Scaling of Ground Motions for Two-Dimensional Analysis as per NEHRP Provisions ........... 88
5.6.5 Scaling of Ground Motions for Three-Dimensional Analysis as per NEHRP Provisions ......... 89
CHAPTER 6: ESTIMATION OF GROUND MOTION PARAMETERS - ATTENUATION
RELATIONSHIPS ..................................................................................................................................... 93
6.1 OVERVIEW .......................................................................................................................................... 93
6.2 GENERAL FORMULATION OF ATTENUATION RELATIONSHIPS ............................................................. 95
6.3 ATTENUATION RELATIONSHIPS FOR DIFFERENT TECTONIC ENVIRONMENTS...................................... 97
6.3.1 Shallow Earthquakes in Active Tectonic Regions ..................................................................... 97
6.3.2 Subduction Zones....................................................................................................................... 99
6.3.3 Stable Continental Regions........................................................................................................ 99
6.4 HORIZONTAL SPECTRAL ACCELERATION ......................................................................................... 100
6.4.1 Regression Procedures ............................................................................................................. 100
6.4.2 Factors Affecting Attenuation.................................................................................................. 104
6.4.2.1 Effect of Magnitude and Distance......................................................................................... 105
6.4.2.2 Effect of Fault Mechanism.................................................................................................... 105
6.4.2.3 Effect of Site Condition ........................................................................................................ 107
6.4.2.4 Ground Motion Variations across Different Tectonic Regimes............................................ 109
6.5 OTHER GROUND MOTION PARAMETERS ........................................................................................... 110
6.5.1 Peak Horizontal Velocity ......................................................................................................... 110
6.5.2 Vertical Spectral Acceleration ................................................................................................. 110
CHAPTER 7: GROUND RESPONSE ANALYSIS .............................................................................. 112
7.1 INTRODUCTION ................................................................................................................................. 112
7.2 ONE-DIMENSIONAL SOIL RESPONSE ANALYSIS PROCEDURES .......................................................... 114
7.3 INTEGRATION OF WAVES IN EQTOOLS ENVIRONMENT .................................................................. 115
7.4 APPLICATION OF TIME DOMAIN PROCEDURES .................................................................................. 117
CHAPTER 8: CONCLUSIONS AND FUTURE DIRECTIONS ......................................................... 122
8.1 CONCLUSIONS................................................................................................................................... 122
8.2 FUTURE DIRECTIONS ........................................................................................................................ 123
REFERENCES ......................................................................................................................................... 127
APPENDIX A ........................................................................................................................................... 137
STRONG GROUND MOTION RECORDS IN EQTOOLS DATABASE............................................ 137
APPENDIX B............................................................................................................................................ 156
DATA FORMAT FOR STRONG MOTION TIME HISTORY FILES ................................................. 156
APPENDIX C ........................................................................................................................................... 159
GROUND MOTION ATTENUATION RELATIONSHIPS AND REGRESSION COEFFICIENTS .. 159
APPENDIX D ........................................................................................................................................... 184
TIME DOMAIN NUMERICAL PROCEDURES FOR SITE RESPONSE ANALYSIS....................... 184
APPENDIX E............................................................................................................................................ 218
EQTOOLS USERS GUIDE ................................................................................................................. 218
APPENDIX F............................................................................................................................................ 345
GROUP EXERCISES USING EQTOOLS............................................................................................ 345
VITA.......................................................................................................................................................... 371
Table of Contents vi
LIST OF FIGURES
Figure 1.1 Flowchart showing the elements of the probabilistic hazard methodology in the context of
performance-based seismic design criteria methodology. .................................................................... 3
Figure 2.1 Various measures of site-to-source distances for the recorded ground motions in the EQTools
database............................................................................................................................................... 18
Figure 2.2 Types of fault mechanisms (a) Strike-slip faulting (b) Normal faulting (c) Reverse faulting.... 20
Figure 2.3 Strong motion recording of the longitudinal (180o), transverse (90o) and vertical (up) of the 1999
Kocaeli earthquake at Yarimca, Turkey.............................................................................................. 24
Figure 2.4 Schematic orientation of the rupture directivity pulse and fault displacement (fling step) for
strike-slip and dip-slip faulting. .......................................................................................................... 25
Figure 2.5 Schematic representation of transformation of horizontal components into strike-normal and
strike-parallel components. ................................................................................................................. 26
Figure 2.6 As-recorded and transformed ground acceleration histories for the Anza (Horse Cany)
earthquake of 1980, recorded at the Rancho De Anza recording station. The strike of the fault used
for the transformation is 20 degrees.................................................................................................... 28
Figure 3.1: Corrected accelerogram and integrated velocity and displacement time histories for the N-S
component of Cape Mendocino Earthquake of April 25, 1992, recorded at 89156 Petrolia recording
station.................................................................................................................................................. 30
Figure 3.2: Amplitude parameters for the horizontal components of ground motions as recorded at 5047
Rancho De Anza recording station during Anza (Horse Cany) earthquake of February 25, 1980. .... 32
Figure 3.3 Pictorial representation of incremental velocities and incremental displacements for the E-W
horizontal component recorded at 16 LGPC Station during Loma Prieta earthquake of October 18,
1989. ................................................................................................................................................... 35
Figure 3.4 Statistical representation of incremental velocities for the S45E component of recording at
Superstition Mtn Camera during the 1979 Imperial Valley earthquake.............................................. 36
Figure 3.5 Bracketed duration for NS horizontal component recorded at the 24 Lucerne Station during
Landers earthquake of June 28, 1992. The threshold acceleration level is 0.05g ............................... 38
Figure 4.1 Normalized Fourier amplitude spectrum of acceleration time history for the S70E component,
recorded at 57212 Coyote Lake Dam (SW abutment) during the Coyote Lake earthquake of August
06, 1979. ............................................................................................................................................. 45
Figure 4.2 Normalized Fourier amplitude spectra of acceleration time history for Gilroy Array #1(rock) and
Gilroy Array #2(soil) strong motion records, recorded during the Coyote Lake earthquake of August
6, 1979. ............................................................................................................................................... 46
Figure 4.3 Fourier amplitude spectra of acceleration time history for the N45E component of Imperial
Valley earthquake motion, recorded at 289 Superstition Mtn. Camera station during the event in
1979. The corner and cutoff frequency parameters are illustrated. ..................................................... 47
Figure 4.4 Traveling Fourier amplitude spectrum for a 512-point segment of the original acceleration time
history for the N45E component of 1979 Imperial Valley earthquake, recorded at 286 Superstition
Mtn. Camera recording station. Windows identify the pertinent segments of the record. .................. 48
Figure 4.5 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. ................................... 50
Figure 4.6 Low-pass filtered response for NS horizontal component of Bishop (Rnd. Valley) earthquake of
1984 recorded at McGee Creek Station. The response obtained using a rectangular filter with
fcutoff = 10.0Hz. (a) Original Fourier amplitude spectrum. (b) Filtered Fourier amplitude spectrum.
(c) Original and filtered acceleration time histories. (d) Original and filtered, 5% damped, response
spectrum.............................................................................................................................................. 52
Figure 4.7 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 ................................................................... 53
Figure 4.8 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.... 53
List of Figures ix
Figure D. 7 Summary of the algorithm TSTEPS for integrating dynamic equilibrium equations for a tri-
diagonal system using Newmark-Wilson scheme (adapted, Hart and Wilson, 1989)....................... 196
Figure D.8 Definition of equivalent shear modulus and equivalent shear damping for a single hysteretic
cycle (after Hart and Wilson, 1989).................................................................................................. 197
Figure D.9 Strain dependent dynamic properties for soil (after Hart and Wilson, 1989)......................... 198
Figure D.10 Summary of algorithm ITERAT for equivalent linear earthquake response analysis (adapted,
Hart and Wilson, 1989)..................................................................................................................... 200
Figure D.11 Schematic of Newton iteration (after Hart and Wilson, 1989) ............................................. 203
Figure D.12 Summary of the algorithm WALK to perform nonlinear earthquake response analysis of soil
profiles implementing the combination iteration and event-to-event strategy with CAA integration
method (adapted from Hart and Wilson, 1989)................................................................................. 206
Figure D.13 Variation of internal forces for a linear system using CAA method (a) inertial forces
constant; (b) damping forces linear variation; and (c) static forces quadratic variation.............. 208
Figure D.14 Schematic for determination of effective shear stress over time step (after Hart and Wilson,
1989) ................................................................................................................................................. 208
Figure D.15 Summary of algorithm AUTO for linear or nonlinear earthquake response analysis of soil
profiles implementing iteration and event-to-event strategy including automatic time step control
(adapted from Hart and Wilson, 1989). ............................................................................................ 210
Figure D.1 Mathematical model of the soil profile (a) Idealized soil profile; (b) Finite element mesh; and
(c) Lumped mass model (adapted, Hart and Wilson, 1989).............................................................. 184
Figure D.2 Soil layer element shape functions (adapted, Hart and Wilson, 1989)................................... 185
Figure D.3 Equivalent modal damping (adapted, Hart and Wilson, 1989)................................................ 189
Figure D.4 Damping with control in two modes (after Hart and Wilson, 1989). ...................................... 189
Figure D.5 Time domain shape functions for Constant Average Acceleration method (a) acceleration
constant; (b) Velocity linear variation; and (c) displacement quadratic variation....................... 195
Figure D.6 Time domain shape functions for Linear Acceleration method (a) acceleration linear
variation; (b) Velocity quadratic variation; and (c) displacement cubic variation. ..................... 195
Figure D. 7 Summary of the algorithm TSTEPS for integrating dynamic equilibrium equations for a tri-
diagonal system using Newmark-Wilson scheme (adapted, Hart and Wilson, 1989)....................... 196
Figure D.8 Definition of equivalent shear modulus and equivalent shear damping for a single hysteretic
cycle (after Hart and Wilson, 1989).................................................................................................. 197
Figure D.9 Strain dependent dynamic properties for soil (after Hart and Wilson, 1989)......................... 198
Figure D.10 Summary of algorithm ITERAT for equivalent linear earthquake response analysis (adapted,
Hart and Wilson, 1989)..................................................................................................................... 200
Figure D.11 Schematic of Newton iteration (after Hart and Wilson, 1989) ............................................. 203
Figure D.12 Summary of the algorithm WALK to perform nonlinear earthquake response analysis of soil
profiles implementing the combination iteration and event-to-event strategy with CAA integration
method (adapted from Hart and Wilson, 1989)................................................................................. 206
Figure D.13 Variation of internal forces for a linear system using CAA method (a) inertial forces
constant; (b) damping forces linear variation; and (c) static forces quadratic variation.............. 208
Figure D.14 Schematic for determination of effective shear stress over time step (after Hart and Wilson,
1989) ................................................................................................................................................. 208
Figure D.15 Summary of algorithm AUTO for linear or nonlinear earthquake response analysis of soil
profiles implementing iteration and event-to-event strategy including automatic time step control
(adapted from Hart and Wilson, 1989). ............................................................................................ 210
Figure D1.1 Ramberg-Osgood Hysteresis Model (after Hart and Wilson, 1989)...................................... 214
List of Figures x
LIST OF TABLES
Table 6.1 Summary information of attenuation models implemented in EQTools environment .............. 102
Table A- 1 Characteristics of strong ground motions in EQTools database recorded within the continental
United States ..................................................................................................................................... 140
Table A- 2 Characteristics of strong ground motions in EQTools database recorded outside the continental
United States ..................................................................................................................................... 153
Table C-1: Coefficients for Regression and Standard Errors for the Average Horizontal Components;
Abrahamson and Silva (1997)........................................................................................................... 163
Table C-2: Coefficients for Regression and Standard Errors for the Average Vertical Components;
Abrahamson and Silva (1997)........................................................................................................... 164
Table C-3: Regression Coefficients for Horizontal Spectral Acceleration SAH ; Campbell (1997) ......... 169
Table C-4: Regression Coefficients for Vertical Spectral Acceleration SAV ; Campbell (1997) .............. 170
Table C-5: Recommended values of average shear velocity for use with Boore, Joyner and Fumal
attenuation relationship (1997) ......................................................................................................... 172
Table C-6: Smoothed coefficients for estimating pseudo-acceleration response spectra (g) for the random
horizontal component at 5% damping. The entries for zero period are the coefficients for peak
horizontal acceleration. ..................................................................................................................... 173
Table C-7 : Attenuation Relations of Horizontal Response Spectral Accelerations (5% Damping) for Rock
Sites; Sadigh et al. (1997) ................................................................................................................. 175
Table C-8 : Dispersion Relationships for Horizontal Rock Motion; Sadigh et al. (1997) .......................... 176
Table C-9: Attenuation Relations of Horizontal Response Spectral Accelerations (5% Damping) for Deep
Soil Sites; Sadigh et al. (1997).......................................................................................................... 176
Table C-10: Smoothed Coefficients for Regression Relation SEA99, for Geometric Mean PGA and 5%
damped PSV; Spudich et al. (1999) .................................................................................................. 178
Table C-11: Regression Coefficients for Horizontal Response Spectral Acceleration (5% damping) for
Subduction Zones; Youngs et al. (1997)........................................................................................... 180
Table C-12: Cascadia 50-bar Point Source Model Coefficients for median Horizontal Components on Rock
Sites; Atkinson and Boore (1997a) ................................................................................................... 182
Table C-13: Regression Coefficients for Quadratic Equations; Atkinson and Boore (1997b) ................... 183
Table F-1 : List of preliminary ground motions obtained through the EQTools database search. ............ 333
Table F-2 : Amplitude and duration measures for the preliminary earthquakes......................................... 337
Table F-3 : Scale factors as computed by EQTools for the records in the bin of earthquakes. .................. 343
List of Tables xi
Chapter 1: Introduction
This thesis presents the concepts behind the development of suites of ground motions for
input into time-domain nonlinear analysis of structures within a performance-based
seismic design (PBSD), a subset of performance-based seismic engineering (PBSE).
These concepts have then been used to develop software computational tools (hereinafter
called EQTools) for systematic assembly, characterization, evaluation, and modification
of strong ground motions.
Ground motions are a basic mechanism by which earthquakes damage structures of all
types. During the course of designing earthquake resistant structures, one of the most
important decisions the design engineers must make is the selection of the design
earthquake(s). Conceptually, these should be ground motions, selected from all possible
ground motions at a given site, which will induce critical response in the structure and
thereby result in the highest damage potential. The quantification of this concept,
however, is not easy. Unlike the case of linear response of a structure which can often be
obtained by a single spectrally modified ground acceleration history (GAH), the
nonlinear response of structures is strongly dependent on the phase of the design ground
motion and the detailed shape of its spectrum. Accordingly, an appropriate estimation of
nonlinear response requires multiple realistic acceleration 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 of providing
multiple acceleration histories is to provide a statistical sample of the variability in
phasing and spectra through a set of GAHs that are realistic not only in their average
properties but also in their individual characteristics. Probabilistic seismic hazard analysis
(PSHA) produces estimates of ground intensity measures for specified annual
probabilities of exceedance and these intensity measures, then, form the basis for
selecting the existing ground motion records and specifying the suites of acceleration
histories for input into time-domain nonlinear analysis of structures.
Introduction 1
PBSD is based on the probabilistic specification of strong ground motions. In PBSD,
each performance objective is associated with a specified annual probability of
exceedance, with increasingly undesirable performance characteristics caused by
increasing levels of strong ground motion having decreasing annual probability of
exceedance. PSHA takes into account the ground motions from the full range of
earthquake magnitudes that can occur on each fault that can possibly affect the site. The
PSHA produces intensity measures (or other response spectral ordinates) for each of the
annual probabilities that are specified for performance-based design. Figure 1.1 illustrates
elements of the probabilistic ground motion hazard methodology in the context of a
complete program for establishing engineering seismic design criteria for a site of
significant engineering importance. The PSHA methodology aggregates ground motion
contributions from earthquake magnitudes and distances of significance to a site of
engineering interest and, as such, the PSHA results are not representative of a single
earthquake. However, engineering applications generally require empirical or synthetic
earthquake acceleration histories as input for dynamic analyses of structures. Hence, it is
necessary to estimate the most likely earthquake magnitude and/or the most likely source-
site distance at the site. The same could be said for other intensity measures obtained as
engineering end results of PSHA. These quantities may then be used for selecting
existing ground motion records (recorded in earthquakes of similar magnitude at similar
source-site distance) or simulating ground motions for response analyses. A procedure
called deaggregation has been developed to examine the dependence of PSHA results on
the distance and magnitude. Considerable attention has recently been focused on PSHA
deaggregation (Stepp et al., 1993; Cramer et al., 1996; Chapman, 1995; McGuire, 1995;
Bazzurro and Cornell, 1999; Harmsen et al., 1999) and no attempt is made to review it
here as the deaggregation procedures are beyond the scope of this research.
The ground motions produced by earthquakes can be quite complicated and the
evaluation of effects of earthquakes at a particular site requires objective and quantitative
ways of describing strong ground motion. Typical ground motion records, such as the
GAHs, ground velocity histories (GVH), and ground displacement histories (GDH),
Introduction 2
Historical & Macroseismic
Instrumental Geology and Intensity & Strong
Earthquake Catalog Tectonics Motion Records
SEISMOTECTONIC MODEL
LOGIC TREE
DEAGGREGATION
Natural Period of Design Earthquakes Return Period of
Structure Bedrock Time Histories Design Event
SITE RESPONSE
Site-Specific
Geotechnical Data Soil Amplification Seismic Design
Site-Specific Time Histories Criteria
Figure 1.1 Flowchart showing the elements of the probabilistic hazard methodology in the context of
performance-based seismic design criteria methodology.
Introduction 3
contain a tremendous amount of information. To express all this information accurately
(i.e., to reproduce each of the three ground histories exactly), every variation of these
quantities over the time of occurrence must be addressed. This large amount of
information makes precise description of a ground motion rather cumbersome. For
engineering purposes, however, it is not necessary to reproduce the ground history
exactly to adequately describe the ground motion. It is necessary and sufficient to be able
to describe the characteristics of the ground motion that are of engineering significance
and to identify a number of ground motion parameters that reflect those characteristics. In
this regard, the amplitude, frequency content, and the duration of motion are of primary
significance. In practice, it is usually necessary to use more than one of these parameters
to characterize a particular ground motion adequately. Of course, the ground motion itself
should conform to the magnitude, distance, and other parameters as dictated by
deaggregation of PSHA.
The response spectrum provides a convenient means to summarize the peak response of
all possible linear single-degree-of-freedom systems with a specified level of viscous
damping. With the gradual accumulation of strong ground motion recordings since 1934,
the elastic response spectrum is now widely employed as a practical means of
characterizing the effect of ground motions on structures. Design ground motions are
often expressed in terms of design spectra that are usually determined by smoothing,
averaging, or enveloping the response spectra of multiple motions. The use of design
response spectra (generally quite smooth) implicitly recognizes the uncertainty with
which soil and structural properties are known by avoiding sharp fluctuations in spectral
accelerations with small changes in structural period. Typically, the spectral amplitudes
of the identified suitable records do not match with those of the design spectrum within
the period range (or at a specific period) of interest, and scaling of the instrumented or
simulated ground motion records is required before using them in dynamic analyses.
Introduction 4
at the site by an earthquake of a particular size and at a particular distance must be
determined by some means. For this purpose, predictive relationships derived through
regression analyses of recorded strong motion databases are employed. Of these
relationships, the ones that are used to estimate parameters that decrease with increasing
distance are often referred to as attenuation relationships. Two of the most commonly
estimated ground motion intensity measures using attenuation relationships are the peak
ground acceleration and the spectral acceleration at a specified damping level (usually
5%). A number of attenuation relations are available for these parameters and are
discussed later. A brief review of attenuation relations for other intensity measures, such
as peak horizontal velocity and vertical spectral acceleration, is also presented. All the
discussed attenuation relationships have been implemented in EQTools.
Earthquake analyses of building structures which include site effects (i.e., the influence
of local soil conditions on strong ground motions and the consequent effect on the
response of the structure), even if it is in an approximate sense, can lead to more realistic
and safer earthquake resistant designs. Perhaps the most important consideration is the
amplifying effect that soft soils at a site can have on earthquake motions. Site effects can
be investigated more thoroughly by implementing site response analysis procedures.
Various simplified time-domain procedures, introduced by Hart and Wilson (1989), are
reviewed and implemented.
The generation of suites of ground histories from the available recorded strong ground
motions using the procedures described above is cumbersome and time consuming. This
is especially so due to the sheer magnitude of data processing involved. The need for this
research and development was motivated by the fact that no programs are available that
provide the means to automate, in an integrated environment, the process of selection,
characterization, evaluation, and modification of ground motion ground histories within a
PBSD framework. The work under this research is limited to development of
computational tools necessary to develop the suite of ground histories following the
PHSA deaggregation (see Figure 1.1) and for estimation of ground motions using
attenuation relations.
Introduction 5
1.1 Purpose and Scope
The scope of this work is the development and documentation of integrated software-
based 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.
While EQTools may be used for professional practice or academic research, the
fundamental purpose behind the development of the software is to make available an
integrated classroom/laboratory tool that provides a visual basis for learning the
principles behind the selection of ground 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.
The text in this thesis is organized into eight chapters and six appendices. Chapters 1
through 8 describe the technical basis and the overall process of development of various
computational tools in EQTools. Supplemental information and the users guide are
Introduction 6
available in appendices. The users guide, included as Appendix E, gives specific
instructions on the use of various features available in EQTools.
Chapter 1 serves as an introduction and outlines the research objectives of this work.
Chapter 2 discusses the architecture of the EQTools strong ground motion database and
the available trace parameters that may be used to search this database for recorded
ground histories. It also discusses the technical basis of rotating the horizontal
components of the record.
Chapter 3 deals with the instrumental ground motion parameters that are often used for
characterizing the important characteristics of strong ground motion in compact,
quantitative form. It also discusses the means available in EQTools to investigate these
parameters.
In Chapter 4, the frequency content parameters of accelerograms are dealt with. Further,
the scaling/filtering of frequencies associated with the accelerograms and its effect on
ground histories is discussed along with the features available in EQTools to accomplish
this.
Chapter 5 deals with the response spectra, an important tool for seismic analysis and
design of structures and equipment. It also elaborates on the concepts behind various
types of scaling of earthquake response spectra and the implementation of these concepts
in EQTools.
Chapter 6 reviews the available methods for estimation of ground motion parameters
(attenuation relations) and their implementation in EQTools.
Chapter 7 deals with the site response analysis. It discusses the implementation and
integration of time domain numerical procedures in the EQTools environment for site
response analysis. These time domain procedures employed to compute site response in
Introduction 7
EQTools were introduced and developed by Hart and Wilson (1989). With the intention
of providing an easy reference to the engineering basis behind the time domain
procedures, relevant portions of their work have been reproduced in Appendix D.
A summary of work under this research and its major conclusions are presented in
Chapter 8. This chapter also discusses the various models and methods that may be added
to EQTools in the future to better meet the ground motion characterization needs for
contemporary performance-based earthquake-risk management.
Appendix E contains the EQTools Users Guide that comprehensively discusses the
various tools developed in the environment and the graphical interface resources
available to use these tools. Appendix F gives a short exercise with the intention of
familiarizing the user with the steps involved in solving practical problems using
EQTools.
Introduction 8
Chapter 2: Earthquake Ground Motions
Earthquake strong motion records are useful for engineering applications where dynamic
analyses are contemplated. Whether it is to investigate local ductility demands in ductile
structures, or to evaluate the response of base isolated structures, or to carry out complex
soil-structure interaction evaluations, time stepping analysis is likely to be needed and
reliable and realistic ground histories are required for the purpose. However, there is a
fundamental problem: design codes are based around design response spectra which are
quite unlike those of the motions recorded in any real earthquake. There is a good reason
for this: design spectra usually represent the smoothed envelope of a range of possible
events which might affect a certain site, and it is one of the strengths of response
spectrum analysis that it can, in one shot, reasonably address the maximum response of
lightly damped, linear elastic systems to this range of possibilities. But when other
conditions apply the presence of geometric or material nonlinearities, for example the
usefulness of response spectrum analysis begins to break down and direct time history
based methods are required. The answer to the question of how to select ground histories
that are reliable for the purpose required, while still satisfying code provisions without
undue conservatism, is therefore an important but complex one. With the introduction of
performance-based design specifications in recent seismic codes and regulations,
designers of earthquake resistant structures are going to need strong ground motion
records increasingly. As mentioned in the previous chapter, the ground motion histories
that are used to represent an intensity measure corresponding to a particular hazard level
(or return period) should reflect the magnitude, distance, site conditions, and other
parameters that control the ground motion characteristics. Hence the foremost
requirement in the above context is the access to recorded ground motions for various
magnitudes, distances, site condition, and other intensity measures and characteristics.
In the EQTools environment, the access to recorded 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
The EQTools strong motion database currently contains 755 records of engineering
interest from tectonically active regions around the world. Three orthogonal components
are available for each recording in the database. The records are categorized into those
recorded within the continental United States and those recorded outside of the
continental United States. The contents of the database utilize publicly available
processed data from the Pacific Earthquake Engineering Research Center (PEER),
Berkeley. Appendix A gives a comprehensive list of ground motion records in the
database along with the important characteristics of the motion. For engineering
applications, only the strong motion part of the accelerograms is of interest, and hence the
database contains only those records that have a peak ground acceleration of more than or
equal to 0.05g.
Instrumentally recorded GAHs are usually corrected to remove the errors associated with
digitization and to establish the zero acceleration line (baseline correction) before
computing the GVHs and GDHs through integration. As mentioned above, the EQTools
database utilizes uniformly processed data from PEER, Berkeley. The processing
procedures employed for correcting the accelerograms are available at the PEER
website and are reproduced below. This information can be accessed at
http://peer.berkeley.edu/smcat/process.html.
Strong motion data processing has two major objectives to make the data useful
for engineering analysis: (1) correction for the response of the strong motion
instrument itself, and (2) reduction of random noise in the recorded signals. The
processing concentrates on extending both the high- and low-frequency ranges of
the useable signal in the records. More recent data, particularly from digital
recorders, do not benefit from additional processing and are entered unaltered
into the database after review.
To achieve these objectives, the flowchart identifies the important steps in the
processing of records in the PEER Strong Motion Database. The processing
begins with Volume 1 or 2 data from the strong motion data provider. In some
cases, only film records (such as SMA-1) are available so a digitizing step is
necessary, which introduces considerable noise over a wide frequency range.
The instrument response is deconvolved in the Fourier domain accounting for the
amplitude and phase of the instrument. Noise is reduced through the use of causal
Butterworth filters at both high- and low-pass frequencies to produce a frequency
range over which the earthquake ground motion in the recorded signal
significantly exceeds the noise level. The LP and HP filter frequencies are
selected individually for each component of a record based on an assessment of
the Fourier amplitude spectrum and the integrated displacement time history
D(t).
Since the Butterworth filter has a significant reduction (0.707) at the LP and HP
frequencies, the useable bandwidth of the records for the purpose of engineering
analysis is within 1/1.25 of the LP frequency and and 1.25 of the HP frequency.
Volume 2 data
from provider.
De-glitch if necessary.
Select new
HP filter.
Review
Fourier D(t) acceptable?
Spectrum.
Processing procedure for PEER strong motion database (Source: Pacific Engineering)
The processing of the strong motion records in the PEER database is in general
different than the processing done by the agency that collected the data. Although
the processed records may be different, the differences should be small within the
frequency passband common to both processing procedures.
The searched records are displayed as a preliminary list of all the records in the database
that satisfy the search criteria. The user can then graphically examine the records one by
one for amplitude parameters, frequency contents, etc. and transfer the records of interest
to a final list. These records can then be used for scaling and site response analyses.
The following section describes the various parameters available in EQTools to facilitate
the strong ground motion database search for the purpose of assembling the recorded
ground motion histories that comply with the parameters obtained through PSHA.
Different earthquake magnitudes have been defined, the more common being the Richter
magnitude (local magnitude) M L , the surface wave magnitude M s , and the moment
accelerations, velocities, and displacements. These magnitude scales are briefly discussed
in the following paragraphs.
Local magnitude M L (Richter, 1935) is defined as the logarithm to base ten of the
maximum seismic wave trace amplitude (i.e., trace amplitude of seismograph) in micro-
meters, recorded on a Wood-Anderson seismograph located at a distance of 100
kilometers from the earthquake epicenter (see Figure 2.1 for definition of epicenter).
Since the fundamental period of vibration of the Wood-Anderson seismograph is 0.8
second, it selectively amplifies those seismic waves with a period ranging approximately
from 0.5 to 1.5 seconds (Naeim, 2001). The natural period of many building structures is
within this range and so the local magnitude is of great value to engineers. Even though
M L is a well known magnitude, it is not always the most appropriate scale for
description of earthquake size because it does not distinguish between different types of
waves.
this reason, this magnitude is independent of the instrument used to record the
acceleration.
Both the previously described magnitude scales are based on various instrumental
measurements of ground motion characteristics. These ground motion characteristics do
not necessarily increase proportionally with the increase in the total amount of energy
released during an earthquake. In other words, it can not be assumed that the bigger the
size of an earthquake, the higher would be the ground motion characteristics. A
comparison of the San Francisco earthquake of 1906 and the Chilean earthquake of 1960
elucidates this point (Boore, 1977). Both earthquakes had a magnitude M s of 8.3 but the
rupture area for the San Francisco earthquake was only about 3% of the rupture area
during the Chilean earthquake. Obviously the latter was a much larger event than the
former. It has been observed that for large earthquakes, the instrumented ground motion
characteristics become less sensitive to the size of the event than for the smaller
earthquakes (Kramer, 1996). This phenomenon is referred to as magnitude saturation.
Richter magnitudes saturate at magnitudes of 6 to 7, whereas the surface wave
magnitudes saturate at about 8 (Kramer, 1996). Clearly, to be able to describe a very
large-sized earthquake, it is desirable to have a magnitude scale that does not saturate.
Hanks and Kanamori (1979) devised a scale, called moment magnitude scale M W , based
The EQTools ground motion database can be searched with any of the above magnitudes
as the basis in itself or in combination with other search parameters. Some records in the
database contain magnitude information that does not identify the type of magnitude. The
records can be searched on the basis of such unknown magnitude types as well through
an option. A range of magnitudes can be prescribed for the search. Further, the largest of
all available magnitudes for the records is also available as a search parameter,
irrespective of the magnitude type. This is achieved by selecting the option provided for
this purpose.
One of the fundamental engineering end results of PSHA is the amplitude of some
ground motion parameter that is associated with a particular return period. This
probabilistic format of relating ground motion amplitude to a specific return period in
now a common practice in a number of seismic design codes and recommended practices,
including those of the National Earthquake Hazard Reduction Program (NEHRP), the
International Building Code (IBC), the National Fire Protection Association (NFPA), the
American Petroleum Institute (API), and the International Standards Organization (ISO),
among others. Additionally, the ground motion attenuation relations also estimate the
ground motion parameters in some form or other.
Peak ground acceleration (PGA) is the most commonly used parameter in this context.
The seismic hazard at a site for a given return period is often expressed as PGA. The
PGA thus obtained forms the basis for assembling the recorded ground motions for
engineering analyses. Either PGA or magnitude of the earthquake (as discussed in the
previous section) is available in EQTools as a search parameter. Like the magnitude, the
2.2.3 Distance
As has been said earlier, the PSHA results are deaggregated to determine magnitudes and
distances that contribute to the calculated hazard at a given return period and at a
structural period of interest (typically, the fundamental period of the structure). Much of
the energy released by rupture along a fault takes the form of stress waves and as these
waves travel away from the source of the earthquake, they spread out and are absorbed to
various degrees by the materials they travel through. As a result, the specific energy
(energy per unit volume) decreases with increasing distance from the source. The
characteristics of stress waves, being dependent on the specific energy, will also be
strongly related to distance. Hence, source-site distance is an essential parameter while
searching and assembling the representative recorded GAHs for engineering purposes.
The distance between the source of an earthquake and the site under consideration can be
interpreted in different ways. Figure 2.1 illustrates the definition of source-site distances
as available in the EQTools database for searching the records with distance as the search
criterion. In the figure, R1 is the closest distance from the site to the projection of fault
rupture on the ground. R2 is the closest distance from the site to the zone of rupture (not
including the sediment deposits overlying the bed rock). R3 is the distance from the site
to the hypocenter (point at which rupture begins and the first seismic waves originate).
The ground motion records in the EQTools database can be searched with any of the
aforementioned distances. There are several records in the database where the distance is
known but its type is unknown. An option is available in the EQTools environment to
include such records in the search.
Surface projection R2
Epicenter
R3
Hypocenter
Figure 2.1 Various measures of site-to-source distances for the recorded ground motions in the
EQTools database.
Ground motions close to the fault rupture (near-fault motions) can be radically different
from those recorded further away from the fault. The near-fault zone is generally
assumed to be within a distance of 20-60 kilometers from the earthquake source (Stewart
et al., 2001). Within this zone, ground motions are strongly influenced by fault
mechanism, the direction of rupture propagation relative to the site, and possible
permanent ground displacements resulting from the fault slip. These factors result in
effects termed rupture-directivity and fling-step (Stewart et al., 2001). These effects
have a significant influence on the ground motion characteristics in terms as the
amplitude, duration, and horizontal ground displacements. The sites lying in the direction
of earthquake rupture propagation will experience shorter strong motion durations than
those lying away from the direction of propagation (Reiter, 1990). As per Faccioli (1997),
during the Northridge earthquake of 1994, the fault rupture propagated away from
downtown Los Angeles and hence caused moderate damage. In contrast, the direction of
In view of the foregoing, the estimation of ground motions close to an active fault should
account for the characteristics of near-fault ground motions. This can be done by
assembling those GAHs that have been actually recorded very close to the ruptured faults
or those that were recorded within the near-fault zone (distance of recording station from
the ruptured fault between 20-60 kilometers). EQTools includes the zone of recording as
a search parameter. All records with distances less than or equal to 20 kilometers are
defined as near-fault in the database. In addition, several records are available (and
included in the database) that have been actually recorded very close to the earthquake
source. However, very few such records are available. The distance parameter can be
used alone or in combination with other parameters to search the database.
Several studies have concluded that the fault mechanisms play an important role in
determining ground motion amplitudes because of their relation to the state of stress at
the source. Many investigators believe that large ground motions are associated with
reverse and thrust faults, whereas smaller ground motions result from normal and strike-
slip faults. A study by McGarr (1984, 1986) concluded that ground accelerations from
reverse faults should be greater than those from normal faults, with strike-slip faults
having intermediate accelerations. Campbell (1987) found that the PGA in reverse-slip
earthquakes is larger by 40%-60% than those in strike-slip earthquakes. The fault
mechanism has been included in EQTools as a search parameter. Ground motions can be
searched on the basis of the following earthquake mechanisms:
SS = Strike Slip
N = Normal
RN = Reverse Normal
RO = Reverse-Oblique
NO = Normal-Oblique
Unknown
(a)
(b)
(c)
Figure 2.2 Types of fault mechanisms (a) Strike-slip faulting (b) Normal faulting (c) Reverse faulting
Soil conditions greatly influence the ground motion and its attenuation. Hence, the GAHs
that are used to represent an intensity measure corresponding to a particular hazard level
(or return period) should reflect the site conditions that control the ground motion
characteristics. Ideally, for performance-based design, one should select ground motion
histories that have been recorded on soil conditions that closely match the soil conditions
at the site. However, getting a soil match is usually an unobtainable ideal. Even with
perfect knowledge, it might be difficult to decide whether the soil match is good-
enough and, in practice, only a small percentage of records in the database have even
rudimentary information on the precise local soil conditions at the recording stations. The
ideal solution is to base the choice of records on ones with appropriate magnitude and
The majority of the earthquake records in the EQTools database have been originally
recorded by the United States Geological Survey (USGS) and for a large percentage of
these records, the site conditions at the recording station have been well-documented. The
USGS has its own site classification system whereby the site is designated a letter, based
on the average shear wave velocity Vs to a depth of 30m. This classifications system has
been included, wherever available, as part of the information for earthquake events in the
EQTools database. The soil conditions, as classified by USGS, are:
Site classification is included as a search parameter. The default value for this parameter
is USGS site class B. The database can be searched either solely on the basis of this
parameter or in combination with other available search parameters.
To provide additional flexibility in searching the ground motion record available in the
EQTools database, certain miscellaneous parameters are available as search criteria. The
information on geographical location of the recording is available in the database. Based
on this, the user can extract strong ground motions recorded either within the continental
United States or outside of the continental United States. A comprehensive list of
earthquakes under these two categories is available in Appendix A.
The EQTools database can also be searched for a particular earthquake event. During the
run-time, the user is presented with a list of earthquakes available in the database
whereby the choice can be made for any earthquake event of interest.
An earthquake occurs when elastic strain energy that has gradually been accumulated
across a fault over a period of time is suddenly released by the failure of the rock along
the fault. This phenomenon, often described as elastic rebound (Reid, 1911), generates
dynamic, strong ground motions lasting for a few seconds to a few minutes, and also a
static deformation of the ground. The static deformation of the ground consists of a
discontinuity in displacement on the fault itself if the fault is inside the ground, or if there
is a surface faulting, the static displacements are discontinuous across the fault at the
ground surface. Strong near-fault ground motion recorded on digital accelerographs in
recent earthquakes, including the 1985 Michoacan, 1999 Chi-Chi, Taiwan, and 1999
Koceali, Turkey earthquakes contain both dynamic ground motions and static ground
displacements. Figure 2.3 shows the strong motion recording of the strike-slip Kocaeli
earthquake at Yarimca, Turkey. The static displacement of the ground is about 1.0
meters in the east-west direction, parallel to the strike of the fault. The large dynamic
ground pulse for this recording is oriented north-south, in the fault normal direction. The
static ground displacement is coincident with the largest dynamic ground velocities, as
shown in the figure, and occurs over a time interval of several seconds. It is therefore
necessary to treat the dynamic and static components of the seismic load as coincident
loads.
The propagation of fault rupture towards a site at a velocity close to the shear wave
velocity causes most of the seismic energy from the rupture to arrive in a single large
pulse of motion that occurs at the beginning of the record (Archuleta and Hartzell, 1981;
Somerville et al., 1997). The radiation pattern of the shear dislocation of the fault causes
this large pulse of motion to be oriented in the direction perpendicular to the fault plane,
Fling Step
Fault
Directivity Pulse
Directivity Pulse
Fling Step
Fault
Figure 2.4 Schematic orientation of the rupture directivity pulse and fault displacement (fling
step) for strike-slip and dip-slip faulting.
pulse is oriented in the direction normal to the fault dip, and has components both in the
vertical direction and the horizontal strike normal direction. The static ground
displacement is oriented in the direction parallel to the fault dip, and has components in
both the vertical direction and the horizontal strike normal direction.
Figures 2.3 and 2.4 demonstrate that near-fault ground velocities and displacements have
orientations that are controlled by the geometry of the fault, specifically by the strike, dip,
and direction of slip on the fault. Consequently, it is necessary to treat them as vector,
rather than scalar, quantities. The simplest method of treating them as vector quantities is
to partition then into strike-normal and strike-parallel components. The dynamic and
The rotation of the two recorded components North ( N ) and East ( E ) into strike-parallel
and strike-normal components SP and SN is accomplished using the following
transformations:
SP = N cos + E sin ; SN = N sin + E cos
where is the strike of the fault measured clockwise from the North. If the recording
orientation is not North and East but rotated clockwise by the angle , then would be
reduced by . This is illustrated in Figure 2.5 below.
N
N cos
N sin
E sin
Fault
E cos
In the EQTools environment, for obvious reasons, the option to transform the recorded
ground motions is available only if pairs or all three components of the ground motion
are searched and selected. Once the ground motion histories are transformed, they are
available in this form for further characterization and/or analysis.
0.00
-0.15
0 2 4 6 8 10
Time (seconds)
0.15
Horizontal, S45E
Acceleration (g)
0.00
-0.15
0 2 4 6 8 10
Time (seconds)
0.15
Strike-Normal
Acceleration (g)
0.00
-0.15
0 2 4 6 8 10
Time (second)
0.15
Strike-Parallel
Acceleration (g)
0.00
-0.15
0 2 4 6 8 10
Time (seconds)
Figure 2.6 As-recorded and transformed ground acceleration histories for the Anza (Horse Cany)
earthquake of 1980, recorded at the Rancho De Anza recording station. The strike of the fault used
for the transformation is 20 degrees.
The most widely used method of describing a ground motion is with a time history. The
motion parameters may be acceleration, velocity, or displacement, or all three may be
displayed together as shown in Figure 3.1. Typically, only one of these quantities is
measured and the others are computed from it by integration/differentiation. The GAH
shows a significant proportion of relatively high frequencies. Integration produces a
smoothing or filtering effect and, therefore, the GVH shows substantially less high
frequency motion than the acceleration time history. The GDH, obtained by integration of
GVH, is dominated by relatively low frequency motion. EQTools generates the time
histories on-screen for single or multiple records selected through the database search.
All the amplitude parameters discussed in the following text can be investigated for the
assembled ground motion records using the features available in EQTools. EQTools also
has provisions to print and store the processed ground motion histories.
0.4
0.0
-0.4
-0.8
0 10 20 30
Time (seconds)
60
Velocity (cm/s)
30
-30
-60
0 10 20 30
Time (seconds)
25.0
Displacement (cm)
12.5
0.0
-12.5
-25.0
0 10 20 30
Time (Seconds)
Figure 3.1: Corrected accelerogram and integrated velocity and displacement time histories for the
N-S component of Cape Mendocino Earthquake of April 25, 1992, recorded at 89156 Petrolia
recording station.
One of the most widely employed measure of the amplitude of a particular ground motion
is the peak horizontal acceleration (PHA). The PHA for a given component of motion is
Unlike the horizontal accelerations, vertical accelerations have received less attention in
earthquake engineering. This is mainly because the margins of safety against static
vertical forces in structures usually provide adequate resistance to dynamic forces
induced by the vertical accelerations during earthquakes. For engineering purposes, the
peak vertical acceleration (PVA) is often assumed to be two-thirds of the PHA (Newmark
and Hall, 1982). The ratio of PHV to PHA, however, has been found to be highly variable
but generally found to be greater than two-thirds near the source of moderate to large
earthquakes and less than two-thirds at larger distances (Campbell, 1985; Abrahamson
and Litehiser, 1989). Peak vertical accelerations can be very large; a PVA of 1.74g was
measured between the Imperial and Brawley faults in the 1979 Imperial Valley
earthquake (Kramer, 1996). In the EQTools ground motion database, time histories are
available for two horizontal and one vertical component for each recording and,
therefore, the PVA can be readily found in addition to PHA for the selected records.
Ground motions with high peak accelerations are usually more destructive than motions
with lower peak accelerations. However, very high peak accelerations that last for a very
short duration may cause little damage to many types of structure (Kramer, 1996).
Although peak acceleration is a very useful parameter, it provides no information on the
frequency content or duration of motion. Consequently, it must be supplemented by
additional information to characterize a ground motion accurately. Figure 3.2 shows the
0.10
PHA = 0.092 at 3.425 sec.
Acceleration (g)
0.00
-0.05
-0.10
0 2 4 6 8 10
Time (seconds)
8.0
PHV = -5.950 cm/s at 3.555 sec.
PHV = +6.693 cm/s at 3.585 sec.
Velocity (cm/s)
4.0
0.0
-4.0
-8.0
0 2 4 6 8 10
Time (seconds)
0.9
PHD = 0.454 cm at 3.445 sec.
Displacement (cm)
0.0
-0.3
-0.6
0 2 4 6 8 10
Time (seconds)
Figure 3.2: Amplitude parameters for the horizontal components of ground motions as recorded at
5047 Rancho De Anza recording station during Anza (Horse Cany) earthquake of February 25, 1980.
The peak horizontal velocity (PHV) is another useful parameter for characterization of
ground motion amplitude. Since the velocity is less sensitive to the higher-frequency
components of ground motion as illustrated in Figure 3.1, the PHV is more likely than
PHA to characterize ground motion amplitude accurately at intermediate frequencies. For
structures or facilities that are sensitive to loading in this intermediate-frequency range
(e.g., tall or flexible buildings, bridges, etc.), the PHV may provide a much more accurate
indication of the potential for damage than the PHA (Trifunac and Todorovska, 1997;
Boatright et al., 2001). PHV has been normalized by soil shear wave velocity for use as a
measure of shear strain in soil (Trifunac and Todorovska, 1996). PHV has also been
correlated to earthquake intensity (e.g., Trifunac and Brady, 1975a; Krinitzky and Chang,
1987). EQTools has provisions to investigate this parameter for records as illustrated in
Figure 3.2.
As mentioned earlier, the PHA parameter is most often associated with the severity of a
recorded ground motion. However, this parameter alone is not sufficient to characterize a
ground motion, since large values of peak ground acceleration alone can seldom initiate
either resonance in the elastic range or be responsible for large scale damage in the
inelastic range. For instance, large recorded peak acceleration may be associated with a
180
Peak Incremental Velocity = 151.6 cm/s
Incremental Velocity (cm/s)
120
60
-60
-120
Acceleration time history not to scale
-180
0 5 10 15 20 25
Time (seconds)
80
Incremental Displacement (cm)
40
-40
Time (seconds)
Figure 3.3 Pictorial representation of incremental velocities and incremental displacements for the E-
W horizontal component recorded at 16 LGPC Station during Loma Prieta earthquake of October
18, 1989.
The incremental velocities (or incremental displacements) are displayed as vertical bars
at the end of each acceleration (or velocity) pulse. The length of the bar is proportional to
the magnitude of the incremental velocity (or incremental displacement). The distribution
of these parameters across various ranges is also available to be viewed as a histogram as
9.5 - 10.0
9.0 - 9.5
8.0 - 8.5
6.5 - 7.0
6.0 - 6.5
Incremental Velocity Range (cm/s)
5.5 - 6.0
5.0 - 5.5
4.5 - 5.0
4.0 - 4.5
3.5 - 4.0
3.0 - 3.5
2.5 - 3.0
2.0 - 2.5
1.5 - 2.0
1.0 - 1.5
0.5 - 1.0
0.0 - 0.5
Figure 3.4 Statistical representation of incremental velocities for the S45E component of recording at
Superstition Mtn Camera during the 1979 Imperial Valley earthquake.
The duration of strong motion can have a strong influence on earthquake damage. The
degradation of strength and stiffness of certain types of structures is sensitive to the
number of load or stress reversals that occur during an earthquake. A motion of short
duration may not produce enough load reversals for damaging response to build up in a
structure, even if the amplitude parameters of the motion are high. On the other hand, a
motion with moderate amplitude and long duration can produce enough load reversals to
cause substantial damage. The duration of strong ground motion is related to the time
required for release of energy by rupture along the fault. As the length, or area, of fault
rupture increases, the time required for rupture increases. As a result, the duration of
strong ground motion increases with increasing earthquake magnitude.
interval between the 5% and the 95% contribution is selected as the duration of strong
motion. A third procedure suggested by McCann and Shah (1979) is based on the average
energy arrival rate. The duration is obtained by examining the cumulative root mean
square acceleration ( rms ) of the accelerogram. A search is performed on the rate of
change of the cumulative rms to determine the two cut-off times. The final cut-off time
is obtained when the rate of change of cumulative rms acceleration becomes negative
and remains so for the remainder of the record. The initial time is obtained in a similar
manner except that the search is performed starting from the tail-end of the record. Power
spectral density concepts can also be used to define the duration of strong ground motion
(Vanmarcke and Lai, 1977).
The purpose of the intended application dictates the selection of a procedure for
computing the duration of strong ground motion. Since bracketed duration implicitly
reflects the strength of shaking, it is most commonly used for computing elastic and
inelastic response and assessing damage to structures. Computational tools have been
implemented in EQTools to calculate the bracketed duration of ground motion records for
pre-defined or user-specified threshold acceleration. The pre-defined values available are
0.01g, 0.02g, 0.03g, 0.04g, 0.05g, and 0.1g. Figure 3.5 shows the form in which EQTools
0.8
Bracketed duration for threshold acceleration of 0.05g = 33.3 seconds
0.4
Acceleration (g)
0.0
-0.4
-0.8
0 10 20 30 40 50
Time (seconds)
Figure 3.5 Bracketed duration for NS horizontal component recorded at the 24 Lucerne Station
during Landers earthquake of June 28, 1992. The threshold acceleration level is 0.05g
The frequency content of ground motion can be examined by transforming the motion
from the time domain to the frequency domain through a Fourier transform. The Fourier
Amplitude Spectrum, which is based on this transformation, directly depicts the
frequency dependent characteristics of the recorded motion and, hence, may be used to
characterize the frequency content.
A physical process can be described either in the time domain, by the values of some
quantity x as a function of time t , e.g., x(t ) , or else in the frequency domain, where the
process is specified by giving its amplitude X (generally a complex number indicating
phase as well) as a function of frequency f , that is X ( f ) , with < f < . For many
purposes, it is useful to consider x(t ) and X ( f ) as being two different representations of
the same function. The transformation from one representation to the other is achieved by
means of the Fourier transform equations,
= 2 f X ( ) = [ X ( f ) ] f = / 2 (4.1.2)
1
fc (4.1.4)
2t
On the basis of the sampling theorem, it can be assumed that the Fourier transform for a
set of discrete samples is equal to zero outside of the frequency range f c and fc . The
Nyquist frequency, therefore, represents the maximum recoverable frequency through
Fourier transforms from a discrete time series for a variable.
For cases where the function x(t ) is not continuous, the Fourier transforms are obtained
by summation rather than integration. Suppose there are N consecutive sampled values
n N N
fn = , n= ,........., (4.1.6)
N t 2 2
The extreme values of n in (4.1.6) correspond exactly to the lower and upper limits of
the Nyquist critical frequency range. The integral in (4.1.1) is then approximated by a
discrete sum:
N 1 N 1
X ( fn ) = x(t )e 2 if n t dt xk e 2 if n tk t = t xk e2 ikn / N (4.1.7)
k =0 k =0
Here equations (4.1.5) and (4.1.6) have been used in the final equality. The final
summation in equation (4.1.7) is called the discrete Fourier transform (DFT) of the N
points xk . In terms of the angular frequency , equation (4.1.7) takes the form:
N 1
X (n ) = t xk ein tk (4.1.8)
k =0
The DFT can also be inverted: that is, a set of data spaced at equal frequency intervals,
, can be expressed as a function of time, using the inverse discrete Fourier transform
(IDFT):
or
1 N 1
x(tn ) = [ X k cos k tn + iX k sin k tn ]
N k =0
(4.1.11)
The Fourier amplitude spectrum FS ( ) is defined as the square root of the sum of the
squares of the real and imaginary parts of the discrete Fourier transform. Thus
2 2
N 1 N 1
FS (n ) = t xk cos ntk + t xk sin ntk (4.1.12)
k = 0 k = 0
As a means to characterize the frequency content, the above concepts have been
employed in EQTools to generate and display the Fourier response spectrum of
acceleration, velocity, and displacement time histories for single or multiple earthquake
records obtained through the database search. Obtaining a DFT using the procedure
discussed above, even for modest values of N, is extremely labor intensive. Since n takes
on N different values, the summation operation will be performed N times. The time
needed for N points from 2N 2 to N log 2 N . In the EQTools environment, the discrete
Fourier transform is computed using a FFT by means of the Danielson-Lanczos Lemma
or bit reversal method. This method is briefly described in the following text. Danielson
and Lanczos (1942) showed that a discrete Fourier transform of length N (where N is
even) can be rewritten as the sum of two discrete Fourier transforms each of length N / 2 .
One of the two is formed from the even-numbered points of the original N , the other
= X ne + W n X no (4.1.13)
X ne denotes the nth component of the Fourier transform of length N / 2 formed from
other words, X nee and X neo can be defined to be the discrete Fourier transforms of the
points which are respectively even-even and even-odd on the successive subdivisions of
the data. With the restriction that N is a power of 2, the Danielson-Lanczos Lemma can
be continuously applied until the data is subdivided all the way down to a transform of
length 1, the total number of such transforms being log 2 N . The Fourier transform of
length one is just an identity operation that copies its one input number into its one output
number. In other words, for every pattern of log 2 N evens and odds, there is a one-point
To find out which value of k corresponds to which pattern of evens and odds, the pattern
of evens and odds is reversed, then letting e = 0 and o = 1 , the value of k (in binary) is
obtained. This is the basis of FFT as implemented in EQTools.
As mentioned earlier, for the FFT algorithm to work correctly in the EQTools
environment, the number of data points passed to the routine must be a power of 2. If the
length of the data set (i.e., acceleration, velocity, or displacement time histories) is not a
power of 2, then the data is padded with zeros up to the next power of 2. This padding
data points, the number of data points passed to the FFT algorithm would be 8192 ( 213 ),
6000 points of original data and 2192 points of zero variable value data. The frequency
range displayed in the Fourier amplitude spectrum is equal to the Nyquist frequency, fc .
This means that if the digitization time step of the original record t is, say, 0.005
seconds, then the maximum frequency for which the Fourier amplitudes are calculated
and displayed is 100 Hz (i.e., 0.5 / 0.005 ).
The Fourier amplitude spectrum of a strong ground motion shows how the amplitude of
the motion is distributed with respect to frequency (or period). It expresses the frequency
content of a motion very clearly. On the basis of the previous discussion, the Fourier
amplitude spectrum of an accelerogram FS ( f ) is defined as
2 2
T T
FS ( f ) = a (t ) sin(2 ft )dt + a (t ) cos(2 ft )dt (4.1.15)
0 0
The Fourier amplitude spectrum may be narrow or broad. A narrow spectrum implies that
the motion has a dominant frequency (or period). Such a spectrum indicates that the input
time history is almost sinusoidal. A broad spectrum, on the other hand, corresponds to a
motion that contains a variety of frequencies and hence indicates a jagged and very
1.2
Normalized Fourier amplitude (g-second)
1.0
0.8
0.6
0.4
0.2
0.0
0 10 20 30 40
Frequency (Hertz)
Figure 4.1 Normalized Fourier amplitude spectrum of acceleration time history for the S70E
component, recorded at 57212 Coyote Lake Dam (SW abutment) during the Coyote Lake
earthquake of August 06, 1979.
low frequencies (or high periods) while the reverse is observed for the Anza (Horse
Cany) record. A close examination of ground motion records can reveal the difference in
frequency content, but the difference is explicitly and quantitatively illustrated by the
Fourier amplitude spectrum.
When the Fourier amplitude spectra of actual earthquake motions are plotted on
logarithmic scales, their characteristic shapes can be readily seen. As illustrated in Figure
4.3, Fourier acceleration amplitudes tend to be dominant over an intermediate range of
frequency f max on the high side, signifying lowest and highest frequencies with
significant energy content, respectively. The corner frequency can be shown theoretically
(Brune, 1970, 1971) to be inversely proportional to the cube root of the seismic moment.
Normalized Fourier amplitude
1.2
N21W Component, 130 LB-Terminal Island, Borrego Mtn., 1968
0.8
0.4
0.0
0 2 4 6 8 10
Frequency (Hz.)
Normalized Fourier amplitude
1.2
N45W Component, 5160 Anza Fire Station, Anza (Horse Cany), 1980
0.8
0.4
0.0
0 5 10 15 20 25 30
Frequency (Hz)
Figure 4.2 Normalized Fourier amplitude spectra of acceleration time history for Gilroy Array
#1(rock) and Gilroy Array #2(soil) strong motion records, recorded during the Coyote Lake
earthquake of August 6, 1979.
This indicates that large earthquakes produce greater low-frequency motions than do
smaller earthquakes. The cutoff frequency is not well understood; it has been
characterized both as a near-site effect (Hanks and McGuire, 1981; Hanks, 1982) and a
source effect (Papageorgiou and Aki, 1983) and is usually assumed to be constant for a
given geographic region. The data generated by EQTools can be used to plot the Fourier
amplitude spectrum on logarithmic scales using any of the various spread sheet programs
available.
1
Fourier amplitude (g-sec)
0.1
0.01
fco fmax
0.001
0.01 0.1 1 10 100
Frequency (Hertz)
Figure 4.3 Fourier amplitude spectra of acceleration time history for the N45E component of
Imperial Valley earthquake motion, recorded at 289 Superstition Mtn. Camera station during the
event in 1979. The corner and cutoff frequency parameters are illustrated.
0.000
-0.150
0 5 10 15 20 25 30
Time (seconds)
Figure 4.4 Traveling Fourier amplitude spectrum for a 512-point segment of the original acceleration
time history for the N45E component of 1979 Imperial Valley earthquake, recorded at 286
Superstition Mtn. Camera recording station. Windows identify the pertinent segments of the record.
Filtering a signal x(t ) in the frequency domain consists of obtaining the DFT X ( f ) of
x(t ) and identifying the spectral band or frequency range that captures the phenomenon
of interest. Values X u ( f ) in the selected frequency band are retained, and the other
values in X ( f ) are rejected and replaced with zeros. The following three classical
types of filters are available in EQTools to carry out frequency filtering of acceleration,
velocity, and displacement time histories in the frequency domain:
a) Low-pass Filter: These filters keep frequency component below the cutoff frequency
fc utoff while frequency components above the cutoff frequency are rejected. Low-
The modified array Yu is then transformed back to the time domain by inverse FFT to get
the representative time history.
Depending upon the form of the function used to eliminate or retain the pass-band of
frequencies, three types of filters are available in EQTools: rectangular, triangular, and
sinusoidal. Rectangular filters have a step frequency response that has sharp boundaries
at the edges of the pass-band (or stop band). Figure 4.5 shows the specifications for the
rectangular filter as employed in EQTools. In this figure, f1 and f 2 represent the lower
and the upper bound of the pass-band (or stop-band, respectively).
Gain (or amplitude)
Gain (or amplitude)
1 1
0 0
fcutoff fc fcutoff fc
Frequency (Hz.) Frequency (Hz.)
(a) (b)
1
Gain (or amplitude)
1
Gain (or amplitude)
0 0
f1 f2 fc f1 f2 fc
Frequency (Hz.) Frequency (Hz.)
(c) (d)
Figure 4.5 Amplitude response specifications for rectangular filters. (a) Low-pass filter. (b) High-pass
filter. (c) Band-pass filter. (d) Band-stop filter. f c is the Nyquist frequency.
Sharp boundaries show excessive ringing, and hence smoothly varying band pass filters
are preferred. Triangular and sinusoidal filters are available in EQTools to effect smooth
variation in filtering the frequency content in a pass-band. Figure 4.7 shows the
specifications for a triangular filter as implemented in EQTools. For a low-pass triangular
filter, the gain (or amplitude) is linearly reduced from 1.0 at the cut-off frequency fcutoff
to zero at the Nyquist frequency, fc . Similarly, for a high-pass triangular filter, the gain
is increased linearly from zero at the zero frequency to 1.0 at the cut-off frequency. For a
triangular band-pass filter, the gain is increased from zero at the lower frequency of the
band f1 to 1.0 at the mid-frequency of the pass-band i.e. ( f1 + f 2 ) / 2 and then to zero
again at the higher frequency of the pass-band f 2 . For a band-cut triangular filter, the
variation, as used for a band-pass filter, is simply inverted. In the sinusoidal filter, instead
of linear variation, a sine-variation is used in a similar manner as for triangular filters.
Figure 4.8 shows the specifications for a sinusoidal filter. Figure 4.9 shows the filtered
amplitude spectrum, time history, and response spectrum for the EW horizontal
component of the Bishop (Rnd Valley) earthquake of 1984, recorded at the McGee Creek
recording station. A band-pass triangular filter was used with the lower bound of pass-
band f1 = 8.0 Hz and the upper bound f 2 = 35.0 Hz.
All the above filters can also be applied with ease to the ground motion time histories.
Even though time-band filtering of ground motion records is rarely done in practice, the
provisions to accomplish this are available in EQTools to interactively assess, from an
educational point of view, the effects of these operations on frequency content and
various spectra.
6 6
4 4
2 2
0 0
0 20 40 60 80 100 0 2 4 6 8 10
0.00
-0.15
0 1 2 3 4 5 6 7
Time (seconds)
(c)
100
10
Pseudo-Velocity (cm/s)
0.1
0.01
0.001 0.01 0.1 1 10 100
0 0
fcutoff fc fcutoff fc
Frequency (Hz.) Frequency (Hz.)
(a) (b)
0 0
f1 f2 fc f1 f2 fc
Frequency (Hz.) Frequency (Hz.)
(c) (d)
Figure 4.7 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
Gain (or amplitude)
Gain (or amplitude)
1 1
0 0
fcutoff fc fcutoff fc
Frequency (Hz.) Frequency (Hz.)
(a) (b)
1
Gain (or amplitude)
1
Gain (or amplitude)
0 0
f1 f2 fc f1 f2 fc
Frequency (Hz.) Frequency (Hz.)
(c) (d)
Figure 4.8 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
2 2
1 1
0 0
0 20 40 60 80 100 0 20 40 60 80 100
0.0
0 1 2 3 4 5 6 7
Time (seconds)
(c)
10
Original RS (5% Damped)
Filtered RS (5% Damped)
Pseudo-Velocity (cm/s)
0.1
0.01
0.001 0.01 0.1 1 10 100
Figure 4.9 Band-pass filtered response for EW horizontal component of Bishop (Rnd. Valley)
earthquake of 1984 recorded at McGee Creek Station. The response obtained using a triangular
filter with f1 = 8.0 Hz. and f 2 = 35.0 Hz. (a) Original Fourier amplitude spectrum. (b) Filtered
Fourier amplitude spectrum. (c) Original and filtered acceleration time histories. (d) Original and
filtered, 5% damped, response spectrum.
As has been described earlier, the representation of a time domain signal in the frequency
domain is a group of amplitudes of sine and cosine waves. For an N point time domain
signal contained in x(t ) , the frequency domain of this signal, called X ( f ) , consists of
two arrays, each of ( N / 2 + 1) samples. These are called the real part of X ( f ) written as,
say, Re X ( f ) and the imaginary part written as Im X ( f ) . The values in Re X ( f ) are
the amplitudes of cosine waves, while the values in Im X ( f ) are the amplitudes of the
sine waves. Just as the time domain runs from x(0) to x( N 1) , the frequency domain
signals run from Re X (0) to Re X ( N / 2) , and from Im X (0) to Im X ( N / 2). That is, N
points in the time domain correspond to ( N / 2 + 1) points in the frequency domain. The
frequency domain can alternatively be expressed in polar form. In this notation, Re X ( f )
and Im X ( f ) are replaced with two other arrays, called the magnitude of X ( f ) and the
phase of X ( f ) . The former is denoted as, say, MagX ( f ) and the latter as PhaseX ( f ) .
The magnitude and phase are a pair-for-pair replacement for the real and imaginary parts.
For example, MagX (0) and PhaseX (0) are calculated using only Re X (0) and
Im X (0) . Likewise, MagX (6) and PhaseX (6) are calculated using only Re X (6) and
Im X (6) , and so forth.
M
B
A
M = ( A2 + B 2 )1/ 2
= arctan( B / A)
Figure 4. 10 Rectangular-to-polar conversion. The addition of a cosine and sine wave (of the same
frequency) follow the same conversion equations as do simple vectors.
In the polar notation, MagX ( f ) holds the amplitude of the cosine wave ( M in equation
4.2.1), while PhaseX ( f ) holds the phase angle of the cosine wave ( in equation 4.2.1).
Keeping in view the above concepts, the following equations convert the frequency
domain from rectangular to polar notation:
1/ 2 Im X ( f )
MagX ( f ) = Re X ( f ) 2 + Im X ( f )2 and, PhaseX ( f ) = arctan (4.2.2)
Re X ( f )
Similarly, the frequency domain is converted from polar to rectangular coordinates using:
As with the filters, three types of scaling options are available: rectangular, triangular,
and sinusoidal. Figure 4.11 illustrates the specifications for rectangular scaling of
frequency bands for scale factors greater than and less than 1.0, respectively. The scale
factor s within the frequency bands being scaled is a constant value for this type of filter.
Figure 4.12 depicts the specifications for triangular scaling of frequency bands. Here, the
scale factor s , specified by the user, is the maximum (or minimum) gain in the user
defined frequency-band for scale factor greater (or less) than 1.0 and corresponds to the
frequency 0.5( f1 + f 2 ) . On either side of this frequency, the scale factor varies linearly
from a value of s to 1.0. Figure 4.13 details the specifications for sinusoidal scaling
where the variation of the scale factor on either side of the average frequency, i.e.,
0.5( f1 + f 2 ) , in the selected band is approximated by a sinusoidal variation. Figure 4.14
shows the scaled amplitude spectrum, time history, and response spectrum for the NS
horizontal component of the Loma Prieta earthquake of 1989, recorded at Gilroy Array
#3 recording station. Sinusoidal scaling was used for a frequency band with f1 = 1.0 Hz
Scaling of time history over a time-band is straightforward and involves simple scaling of
amplitude values in the time-band of interest. Again, rectangular, triangular, or sinusoidal
scaling can be applied.
s
1
s
0
0
f1 f2 fc f1 f2 fc
Frequency (Hz.) Frequency (Hz.)
(a) (b)
Figure 4.11 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.
2
s
Gain (or amplitude)
1
Gain (or amplitude)
1 s
0
0
f1 f2 fc f1 f2 fc
Frequency (Hz.) Frequency (Hz.)
(a) (b)
Figure 4.12 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 ) .
2
1
Gain (or amplitude)
Gain (or amplitude)
1
s
0
0
f1 f2 fc f1 f2 fc
Frequency (Hz.) Frequency (Hz.)
(a) (b)
Figure 4.13 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 ) .
30 30
20 20
10 10
0 0
0 5 10 15 20 0 5 10 15 20
0.2
0.0
-0.2
-0.4
-0.6
0 2 4 6 8 10 12 14 16 18
Time (seconds)
(c)
100
Pseudo-Velocity (cm/s)
10
0.1
0.001 0.01 0.1 1 10 100
Figure 4.14 Scaled response for the NS horizontal component of Loma Prieta earthquake of 1989,
recorded at Gilroy Array #3 station. The response obtained using a sinusoidal scaling with
f1 = 1.0 Hz. , f 2 = 10.0 Hz. and a scale factor of 0.3 (a) Original Fourier amplitude spectrum. (b)
Scaled Fourier amplitude spectrum. (c) Original and scaled acceleration time histories. (d) Original
and scaled, 5% damped, response spectrum.
Response spectrum is an important tool in the seismic analysis and design of structures.
The concept of earthquake response spectrum, introduced by Biot (1941, 1942) 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-of-freedom (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 n 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
of the SDOF system (for a particular input motion). The maximum values of acceleration,
velocity, and displacement are referred to as the spectral acceleration ( Sa ), spectral
where u&&(t ) , u& (t ) , and u (t ) are respectively the spectral absolute acceleration, spectral
relative velocity, and spectral relative displacement response of the SDOF system
subjected to a ground acceleration u&&g (t ) . The total acceleration response is obtained by
summing up the absolute acceleration and the applied ground acceleration. Thus,
For a given natural vibration period Tn and damping ratio of an SDOF system, the
and of the SDOF system. These steps are repeated for a range of Tn and covering
all possible systems of engineering interest, which finally gives the complete response
spectrum. A plot of Sd against Tn (or f n ) for fixed is called a deformation response
spectrum. A similar plot for Sv is the relative velocity response spectrum, and for Sa is
the acceleration response spectrum.
As mentioned before, the deformation spectrum provides all the information necessary to
compute the peak values of deformation and internal forces. Two related spectra, the
pseudo-velocity and pseudo-acceleration response spectra, are, however, usually
developed as well because of their usefulness in studying characteristics of response
spectra, constructing design spectra, and relating structural dynamics results to building
codes. The implementation of these spectra in EQTools is discussed in the following
sections.
The procedure to determine the deformation spectrum has been discussed before. The
deformation spectrum for the Loma Prieta ground motion, developed using EQTools, is
shown in Figure 5.1. For each SDOF system with a given natural time period Tn and
damping , the peak value of deformation is determined from the deformation history.
Usually, the peak occurs during ground shaking. However, for lightly damped systems
with very long periods, the peak response may occur during the free vibration phase after
the ground shaking has stopped (Chopra, 2000). Repeating such computations for a range
of values of Tn while keeping constant at 5% provides the deformation response
spectrum shown in Figure 5.1.
30
Sd (centimeters)
20
10
0
0 1 2 3 4 5 6
Period (sec)
Figure 5.1 Deformation response spectrum ( = 5% ) for 1989 Loma Prieta ground motion (N00E
horizontal component, recorded at Saratoga-Aloha Ave Station)
PSV for an SDOF system with natural frequency n (or natural period Tn ) is related to
2
PSV = n Sd = Sd (5.2.1)
Tn
The quantity PSV has units of velocity and is related to the peak value of strain energy
ESo stored in the system during an earthquake by the equation
m( PSV ) 2
ESo = (5.2.2)
2
120
Pseudo-Velocity (cm/s)
90
60
30
0
0 1 2 3 4 5 6
Period (sec)
Figure 5.2 Pseudo-velocity response spectrum ( = 5% ) for 1989 Loma Prieta ground motion (N00E
horizontal component, recorded at Saratoga-Aloha Ave Station)
Another parameter often computed in the context of response spectrum is called peak
pseudo-acceleration (PSA). Again, the term pseudo is used to avoid confusion with the
true peak acceleration u&&(t ) max . PSA for an SDOF system with natural frequency n (or
2
2 2
PSA = n Sd = Sd (5.2.3)
Tn
The quantity PSA has units of acceleration and is related to the peak value of base shear
Vbo (or peak value of the equivalent static force f so ) as:
PSA
Vbo = f So = m( PSA) = w (5.2.4)
g
where m and w are the mass and weight of the structure, respectively, and g is the
acceleration due to gravity. The quantity ( PSA / g ) may be interpreted as the base shear
1.5
Pseudo-Acceleration (g)
1.0
0.5
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Period (sec)
Figure 5.3 Pseudo-acceleration response spectrum ( = 5% ) for 1989 Loma Prieta ground motion
(N00E horizontal component, recorded at Saratoga-Aloha Ave Station)
PSA sloping at +45 and 45 , respectively to the Tn -axis are also logarithmic scales
but not identical to the vertical and horizontal scales.
The response spectrum computational tools available in the EQTools environment can
easily be used to generate, plot, and print the tripartite plots for a single record or a group
of records. The period is limited to 10 seconds, as structures with a period longer than
this are rarely encountered in seismic analysis and design. Figure 5.4 shows the tripartite
plot of spectrum curves for = 0, 2, 5, 10 and 20% over the period range of 0.01 to 10
seconds for the north-south component of 1989 Loma Prieta ground motion recorded at
the Saratoga-Aloha Avenue station. This plot has been generated using the results from
EQTools.
10
.0
100
Pseudo-velocity (cm/s)
1.cc
ce
0
0
1.
xe
)
m
(c
n
io
at
m
0.
10
or
1
ef
D
Ps
eu
01
do
0.
-a
cc
lee
ra
t io
0.
01
00
(g
.0
)
1
1
0.01 0.1 1 10
Period (sec)
Figure 5.4 Combined deformation-velocity-acceleration spectrum for 1989 Loma Prieta ground
motion (N00E horizontal component, recorded at Saratoga-Aloha Ave Station), plotted as a tripartite
plot; = 0, 2, 5, 10 and 20 %.
The parameters PSV and PSA have certain characteristics that are of practical interest
(Newmark and Hall, 1982). The pseudo-velocity PSV is close to the maximum relative
velocity Sv at high frequencies (frequencies greater than 5 Hz), approximately equal for
intermediate frequencies (frequencies between 0.5 Hz To 5 Hz), but different for low
frequencies (frequencies smaller than 0.5 Hz). In a recent study (Sadek et al., 2000),
based on a statistical analysis of 40 damped SDOF structures with period range of 0.1 to
40 sec subjected to 72 accelerograms, it was found that the maximum relative velocity Sv
is equal to the pseudo-velocity PSV for periods in the neighborhood of 0.5 sec (frequency
of 2 Hz). For periods shorter than 0.5 sec, Sv is smaller than PSV, while for periods
longer than 0.5 sec, Sv is larger and increases as the period and damping ratio increase. A
Sv
= avT bv (5.3.1)
PSV
where,
T is the natural period, and is the damping ratio. The relationship between Sv and
PSV is presented in Figure 5.5.
4.0
Damping=0.02
3.5 Damping=0.05
Damping=0.10
Damping=0.20
3.0 Damping=0.30
Damping=0.40
Damping=0.50
Mean (Sv / PSV) ratio
2.5
2.0
1.5
1.0
0.5
0.0
0 2 4 6 8 10
Period (sec)
Figure 5.5 Mean ratio of maximum relative velocity to pseudo-velocity for SDOF structures with
different damping ratios.
Sa
= 1 + aaT ba (5.3.2)
PSA
where,
T is the natural period, and is the damping ratio. The relationship between Sa and
PSA is presented in Figure 5.6.
5.0
Damping=0.02
4.5 Damping=0.05
Damping=0.10
Damping=0.20
4.0
Damping=0.30
Damping=0.40
3.5 Damping=0.50
Mean (Sa / PSV) ratio
3.0
2.5
2.0
1.5
1.0
0.5
0 2 4 6 8 10
Period (sec)
Figure 5.6 Mean ratio of maximum absolute acceleration to pseudo-acceleration for SDOF structures
with different damping ratios.
10
10
.0
17.5 cm/s
1
10
Pseudo-velocity (cm/s)
g
1.
9.
6
0
15
0
cm
0.
cc
1
ce
0.
xe
0.
1
)
m
(c
n
io
01
at
Ps
0.
1
m
eu
or
ef
do
D
-a
cc
lee
1
00
ra
tio
0.
n
0.
(g
00
)
1
0.1
0.01 0.1 1 10
Figure 5.7 Response spectra for 2, 5, 10, 20% damping for S21E component of 1952 Kern County
earthquake recorded at Taft Lincoln School station. The peak ground motions are also shown.
With the availability of a large number of recorded earthquake ground motions since
1971, several statistical studies (Mohraz et al., 1972; Hall et al., 1975; Mohraz, 1976)
were carried out to determine the average peak ground velocity and displacement for a
given acceleration. These studies recommended that two ratios, peak velocity to peak
acceleration, v / a , and peak acceleration-displacement product to the square of the peak
while a larger ad / v 2 ratio results in a flat spectrum in the velocity region. Response
spectra may shift towards high or low frequency regions according to the frequency
content of the ground motion.
5.4.1 Magnitude
The specification of peak ground acceleration at a site, in the past, did not account for the
effect of magnitude on spectra, and so the spectral shapes and amplifications were
obtained independent of the earthquake magnitude. Earthquake magnitudes, however,
influence spectral amplification to a certain extent. A study by Mohraz (1978) on the
influence of earthquake magnitude on response amplifications for alluvium shows larger
acceleration amplifications for records with magnitudes between 6 and 7 than those with
magnitudes between 5 and 6. Figure 5.8 shows the effect of magnitude on acceleration
amplification for USGS site class D. It can be seen from the figure that higher
magnitudes result in higher spectral ordinates. This consideration can be taken into
account in the EQTools environment by assembling bins of earthquake records with
different magnitudes through the database search.
6
Magnitude between 5 & 6
Acceleration Amplification
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Period (seconds)
Figure 5.8 Effect of earthquake magnitude on spectral shapes.. The ground motion records are from
USGS Site Class D.
5.4.2 Distance
The effect of distance on the shapes and amplitudes of the earthquake spectra has been
considered in recent studies. Using the data from the Loma Prieta earthquake of October
17, 1989, Mohraz (1992) divided the records into three groups: near-field (distance less
than 20 km), mid-field (distance between 20 to 50 km), and far-field (distance greater
than 50 km). This study concluded that for sites on rock, the amplifications for the near-
field are substantially smaller than those for mid- or far-field for periods longer than
about 0.5 seconds. For shorter periods, the amplification for the near-field is larger. The
effect of distance is less pronounced for records on alluvium. EQTools has provisions
whereby ground motion records can be searched on the basis of distances. This feature
can be used for selecting and assembling records having spectral shapes appropriate for
the distance of a given site. Figure 5.9 shows a plot of acceleration amplification for rock
sites for the above mentioned zones of recording. These plots have been created using the
data generated through EQTools.
5% Damping
4 Rock Near-Field
Acceleration Amplification
Rock Mid-Field
Rock Far-Field
3
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Period (seconds)
Figure 5.9 Acceleration amplification for 5% damping for different distances for sites on rock.
5.4.4 Duration
Before the 1971 San Fernando earthquake, the number of available strong motion records
was insufficient to study the influence of different parameters on response spectra.
Consequently, most design spectra were based on records on alluvium soil and did not
refer to any specific soil condition. Studies by Hayashi et al. (1972) and Kuribayashi
(1971) on the effects of soil conditions on Japanese earthquakes had shown that soil
The 1971 San Fernando earthquake provided a large database to study the influence of
many earthquake parameters, including soil condition, on earthquake ground motion and
response spectra. Two independent studies, one by Seed, Ugas, and Lysmer (1976), and
the other by Mohraz (1976), considered the influence of soil condition on response
spectra. The study by Seed et al. (1976) showed that soil conditions affect the spectra to a
significant degree and indicated that for periods greater than approximately 0.4 to 0.5
second, the normalized spectral ordinates (amplifications) for rock are substantially lower
than those for soft to medium clay and for deep cohesionless soil. The study by Mohraz
(1976) indicated that the acceleration amplification for alluvial soils extends over a larger
period range than the amplification for rock soil or alluvial soil underlain by rock. At
short periods, the spectral ordinates are lower than those for other soil categories,
whereas for intermediate and long periods they are higher.
The EQTools database can be searched for the recorded ground motions on the basis of
the soil conditions at a given site. As mentioned before, the site class for the records in
the database is identified through USGS site classification. Spectra, compatible with the
site conditions, can then be generated using the computational tools discussed before.
While response spectra for a specified earthquake record may be used to obtain the
response of a structure to an earthquake ground motion with similar characteristics, they
cannot be used for design. The design spectrum should satisfy certain requirements
because it is intended for the design of new structures, or the seismic safety evaluation of
existing structures, to resist future earthquakes. The jaggedness in the response spectrum
is characteristic of that one excitation. The response spectrum for another ground motion
recorded at the same site during a different earthquake is also jagged, but the peaks and
valleys are not necessarily at the same periods. Similarly, it is not possible to predict the
jagged response spectrum in all its details for a ground motion that may occur in the
Since the peak ground acceleration, velocity, and displacement for various earthquake
records differ, the computed response cannot be averaged on an absolute basis. Various
procedures are used to normalize response spectra before averaging is carried out.
Among these procedures, two have been most commonly used: 1) normalization
according to spectrum intensity (Housner, 1952) where the areas under the spectra
between two given frequencies or periods are set equal to each other, and 2)
normalization to peak ground motion where the spectral ordinates are divided by peak
ground acceleration, velocity, or displacement for the corresponding region of the
spectrum. Normalization to other parameters such as effective peak acceleration (peak
acceleration that remains after filtering out accelerations above 8 to 9 Hz) has also been
suggested and used in development of design spectra for seismic codes (Benjamin and
Associates, 1988).
PSV(g)
Figure 5.10 Design spectrum defined as the envelope of design spectra for earthquakes originating
on two different faults.
Various procedures have been developed over the years for constructing the design
spectrum. The first of these was developed by Housner (1970) where the spectrum was
A new procedure for constructing design spectra was recommended in the 1991 NEHRP
provisions by obtaining the spectral acceleration ordinates at periods of 0.3 and 1.0 sec
from the spectral maps. These provisions have been constantly updated, and the latest
generalized procedures to determine the spectra for a given site are available in the
NEHRP (2000) recommended provisions. The design response spectra are constructed in
the EQTools environment using these provisions. These procedures are based on the
maximum considered earthquake ground motion in terms of mapped values of the
spectral response acceleration at short periods, S S , and at one second, S1 , for Site Class
B sites. These parameters may be directly obtained from maximum considered
earthquake ground motion maps developed jointly by the Building Seismic Safety
Council (BSSC) and United States Geological Survey (USGS) in 1997. These maps are
available for 10%, 5%, and 2% probabilities of exceedance in 50 years.
In order to obtain acceleration response parameters that are appropriate for sites with
other characteristics, S S and S1 values are modified with the use of two coefficients, Fa
and Fv , which respectively scale the S S and S1 values determined for firm rock sites to
appropriate values for other site conditions. The maximum considered earthquake
spectral response accelerations adjusted for Site Class effects are designated,
respectively, S MS and S M 1 , for short period and 1 second period response. In order to
account for over-strength, structural design as per NEHRP (2000) provisions is
performed for earthquake demands that are 2/3 of the maximum considered earthquake
response spectra. Two additional parameters, S DS and S D1 , are used to define the
acceleration response spectrum for this design level event. These are taken, respectively,
as 2/3 of the maximum considered earthquake values S MS and S M 1 , and completely
define a design response spectrum for sites of any characteristics.
period regions respectively, as per the procedures in FEMA-273 (1997). SRa and SRv
are, respectively, the modification factors for constant acceleration and constant velocity
regions. These factors are shown graphically in Figure 5.11.
1.4
1.0
Modification factor
0.8
0.6
0.4
0.2
0 10 20 30 40 50 60
Figure 5.11 Modification factors for modifying maximum considered earthquake spectral response
accelerations for damping ratios other than 5%.
The general procedure for constructing the design response spectrum as per NEHRP
(2000) provisions for sites where site-specific procedures are not used is given below.
Figure 5.12 illustrates the notations used in the procedure.
1. For periods less than or equal to T0 , the design spectral response acceleration, Sa ,
shall be taken as:
SD1 Sa=SD1/T
T0 Ts 1.0
Period, T
Figure 5.12 Illustration of parameters for constructing the design response spectrum as per NEHRP
(2000) guidelines.
S
S a = 0.6 DS T + 0.4S DS SRa (5.5.1)
T0
2. For periods greater than or equal to T0 and less than or equal to TS , the design
3. For periods greater than TS , the design spectral response acceleration, Sa , shall be
taken as:
S D1
Sa = SRv . (5.5.2)
T
TS = S D1 / S DS .
The above procedures are implemented in EQTools to generate the design response
spectra automatically. The values of S S , S1 , the damping ratio, and the site classification
are the only expected input parameters. Figure 5.13 shows the design response spectrum
for S S and S1 values of 1.2g and 0.48g respectively, for different damping ratios. These
plots were created by the computational tools available in EQTools.
1.0
0.8 5% Damping
Spectral Response Acceleration (g)
10% Damping
20% Damping
0.6
0.4
0.2
0.0
0 1 2 3 4 5 6
Period (seconds)
Figure 5.13 Design response spectra developed as per the NEHRP (2000) provisions for S S =1.2g and
S1 =0.48g and different damping ratios.
The scaling of ground-motion records is one of the most common issues seismologists
and engineers face while carrying out nonlinear dynamic analysis of a structure. As
previously mentioned, a common application of the design earthquake parameters
resulting from a PSHA deaggregation is the identification of suitable earthquake records
to be used is dynamic engineering analyses and design. The defined magnitude and
distance parameters from the deaggregation serve as a guide in the selection of three-
component (two horizontal and one vertical) empirical earthquake time series from
appropriate recording stations of historical earthquakes. The design earthquake
parameters are only a general guide, however, with other factors such as site class,
earthquake mechanism, and representative spectral shape also have a bearing on the
record selection. All of these parameters cannot usually be completely satisfied in the
record search. Typically, the spectral amplitudes of the identified suitable records do not
match the design spectrum within the period band of engineering interest, and scaling of
empirical records is required. The scaling is commonly, but not always, performed on
some average of the spectra of the two horizontal components of the motion. There are a
number of scaling methods that can be applied, including a simple uniform scaling at the
structures lowest frequency, normalization according to spectral intensity (Housner,
1952), among others. The scale factors thus obtained may then be applied to the recorded
time histories to obtain empirical motions that are representative of expected earthquake
ground motions at the site. Various normalization and scaling procedures implemented in
the EQTools environment are briefly discussed in the following sections.
0.8
NEHRP Design Spectrum
Chalfant Valley, 1986 (Unscaled)
Holliester, 1961 (Unscaled)
0.6
Pseudo-acceleration (g)
0.4
0.2
0.0
0 1 2 3 4 5 6
Period (seconds)
Figure 5.14 Unscaled acceleration response spectrum of ground motion records. The design
spectrum is for Site Class B with S s = 1.0g and S1 = 0.4g.
1.5
0.5
0.0
0 1 2 3 4 5 6
Period (seconds)
Figure 5.15 Simple uniform scaling of records shown in Figure 5.14. The acceleration response
spectra have been scaled to match the design spectrum at a period of 1.0 seconds. The design
spectrum is for Site Class B with S s = 1.0g and S1 = 0.4g. Numbers in parentheses indicate the scale
factors.
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 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. Figure 5.15
shows the spectrum plots where the response spectrum from the 1979 Imperial Valley
earthquake record has been scaled to have an area equal to that of the design spectrum
between the time periods of 0.1 second and 5.0 seconds.
0.8
0.6
0.4
0.2
0.0
0 1 2 3 4 5 6
Period (seconds)
Figure 5.16 Equal-Area scaling of acceleration response spectrum between periods of 0.4 sec and 2.0
sec for a record from 1979 Imperial Valley earthquake. The design spectrum is for Site Class B with
S s = 1.0g and S1 = 0.4g. Numbers in parentheses indicate the scale factors.
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.
1.0
Period Range NEHRP Design Spectrum
Kern County, 1952 (Unscaled)
0.8
Kern County, 1952 (Scaled, 1.40)
Pseudo-acceleration (g)
0.6
0.4
0.2
0.0
0 1 2 3 4 5 6
Period (seconds)
Figure 5.17 SRSS scaling of the acceleration response spectrum between periods of 0.3 sec and 2.0
sec. for a record from the 1952 Kern County earthquake. The design spectrum is for Site Class B
with S s = 1.0g and S1 = 0.4g. Numbers in parentheses indicate the scale factors.
The above scaling procedure can be accomplished in the EQTools environment for a
suite of ground motions containing up to a maximum of twelve records. The
appropriateness of the record(s) can be ensured through a refined search of the database
and further characterization of these searched records using the available tools. Figures
5.18 and 5.19, respectively, show the unscaled and scaled (as per NEHRP provisions for
2-dimensional analysis) response spectra for a natural time period T of 1.0 second in the
fundamental mode. The ground motion selection parameters are: Local Magnitude = 7.0,
Closest Distance = 85-95 km, and the fault mechanism is strike-slip. In this example,
acceleration response spectra have been scaled.
0.4
0.2
0.0
0 1 2 3 4 5 6
Period (seconds)
Figure 5.18 Unscaled acceleration response spectrum of 1995 Kobe earthquake ground motion
records. The design spectrum is for Site Class B with S s = 1.0g and S1 = 0.4g.
3.0
NEHRP Design Spectrum
2.5 Scaled spectrum of earthquake component records (Kobe, 1995)
Average of the scaled earthquake response spectra
Pseudo-acceleration (g)
2.0
1.5
1.0
0.0
0 1 2 3 4 5 6
Period (seconds)
Figure 5.19 Scaling of acceleration spectra for the records shown in Figure 5.18 using NEHRP 2000
provisions for two-dimensional analysis of a structure with a natural period of 1.0 second in the
fundamental mode. The design spectrum is for Site Class B with S s = 1.0g and S1 = 0.4g.
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 the EQTools environment with the option to include pairs of
horizontal components for construction of response spectra. This option is unavailable if
the user fails to select pairs of ground motions from the searched records. Figures 5.20
and 5.21, respectively, show the unscaled and scaled (as per NEHRP provisions for 3-
dimensional scaling) response spectra for a natural time period T of 1.5 second in the
fundamental mode. The ground motion selection parameters are: Local Magnitude = 6.0
to 8.0, Closest Distance = 90-100 km, and the fault mechanism is strike-slip. In this
example, again, the acceleration response spectra have been scaled.
0.4
0.2
0.0
0 1 2 3 4 5 6
Period (seconds)
Figure 5.20 Unscaled acceleration response spectrum of 1995 Kobe and 1992 Landers earthquake
ground motion records. The design spectrum is for Site Class B with S s = 1.0g and S1 = 0.4g.
1.6
NEHRP Design Spectrum
1.4
Scaled spectra for horizontal component pair, Kobe 1995
Scaled spectra for horizontal component pair, Landers 1992
1.2
Pseudo-acceleration (g)
1.0
0.8
0.6
0.4
Scale factor = 1.987
0.2
0.0
0 1 2 3 4 5 6
Period (seconds)
Figure 5.21 Scaling of acceleration spectra for the records shown in Figure 5.20 using NEHRP 2000
provisions for three-dimensional analysis of a structure with a natural period of 1.5 second in the
fundamental mode. The design spectrum is for Site Class B with S s = 1.0g and S1 = 0.4g.
6.1 Overview
The evaluation of seismic hazard requires the use of probabilistic distribution of intensity
measures (IMs) subject to the condition of occurrence of an earthquake with a particular
magnitude ( m ) at a given source-site distance ( r ). The probability density function
(PDF) for a single IM is written as f ( IM | m, r ) , and is usually log-normal (i.e., the
logarithms of the parameters are approximately normally distributed). Attenuation
relationships define the statistical moments of these PDFs (e.g., median, standard
deviation) in terms of m , r , and other seismological parameters, and are derived through
regression of empirical data (Stewart et al., 2001). The most commonly estimated ground
motion parameters are horizontal and vertical peak ground acceleration (PGA), peak
ground velocity (PGV), and 5% damped spectral acceleration (SA) for a given site.
(the Joyner-Boore distance); rrup , the closest distance to the rupture surface; rseis , the
closest distance to the seismogenic rupture surface (assumes that near-surface rupture in
sediments is non-seismogenic (Marone and Scholz, 1988)); and rhypo , the hypocentral
distance. The seismogenic depth is the depth to the top of crust excluding the sediment
deposits. These different distance measures arerjbshown graphically in Figure 6.1.
rrup
rseis Seismogenic
Depth
rhypo
Hypocenter
Vertical Faults
rjb=0 rjb
rrup
rseis
Seismogenic
rhypo Depth rrup & rseis
rhypo
Hypocenter
Hypocenter
Dipping Faults
Figure 6.1 Site-to-source distance measure for ground motion attenuation models.
The functional form of the attenuation relationship is usually selected to reflect the
mechanics of the ground motion process as closely as possible. This minimizes the
number of empirical coefficients and allows greater confidence in application of the
attenuation relationship to conditions (magnitudes and distances) that are poorly
represented in the database. Common forms of attenuation relationships are based on the
following observations (Kramer, 1996):
Combining these observations, a typical attenuation relationship may have the form
(Kramer, 1996):
ln
{ IM = C1 + C2 m + C3mC4 + C5 ln[r + C6e(C7 m) ] + C8r + f ( F ) + f ( HW ) + f ( S ) (6.2.2)
144 42444 3 123 1424 3 { 1444 424444 3
1 2 3 4 5 6
and ln IM = C9
where the numbers inside the squares indicate the observations associated with each term.
Some attenuation relationships utilize all these terms (and some have even more) and
others do not. The ln IM term describes the uncertainty in the value of the ground
motion parameter given by the attenuation relationship. It represents a statistical estimate
of the standard deviation of ln IM at the magnitude and distance of interest. Historically,
most ln IM values have been constant, but several recent attenuation relationships
When using any attenuation relationship, it is very important to be fully aware of how
parameters such as m and r are defined and to use them in a consistent manner. It is also
important to recognize that different attenuation relationships are usually obtained from
different data sets. To make reasonable predictions of ground motion parameters, an
attenuation relationship based on data that are consistent with the conditions relevant to
the prediction is required.
Abrahamson and Silva (1997) have derived empirical response spectral attenuation
relationships for both the horizontal and vertical components of ground motion. They
Campbell (1997) has also developed empirical attenuation relationships for horizontal
and vertical PGA, PGV , and SA in active tectonic regions. The 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 moment magnitude, M > 5 at sites within 60 km.
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 r jb are specified for use with these equations than those given in
previous publications. Unlike the other models, this model uses a site classification based
on the average shear wave velocity in the upper 30 m.
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
moment magnitude, M from 4 to 8+ at distances ranging from 0 to 100 km.
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.
There are few strong motion recordings from subduction zone earthquakes in the United
States, so most attenuation models for subduction zone events are primarily based on
recordings from Japan and South America. Most subduction zone events are recorded at
large distances because the events tend to be deep or offshore. The exception is the
recordings of the 1985 Michoacan earthquake from the Guerrero array, which has
distances as small as 13 km. The sparse data within 30 km leads to large uncertainty in
the extrapolation of these models to short distances (Abrahamson and Shedlock, 1997).
Youngs et al. (1997) have developed attenuation relationships for subduction zone
interface (events that occur due to interaction between adjacent tectonic plates) and
intraslab (events that occur within a tectonic plate) earthquakes using data from Alaska,
Chile, Cascadia, Japan, Mexico, Peru, and Solomon 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 with the
same magnitude and distance.
Atkinson and Boore (1997a) provided the preliminary ground motion relationships for
the Cascadia region. Their Cascadia model does not match observations 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 (Abrahamson and Shedlock,
1997). Until further work can be completed on the larger magnitudes, the Cascadia model
is recommended to be used to predict ground motions from the moment magnitude,
M < 7 earthquakes at all distances and to predict conservative ground motions from
large earthquakes at distances less than 100 km.
Due to low seismicity rates in stable continental regions, there are very few strong motion
data available for this tectonic regime. As a result, attenuation relationships for this
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 the 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 low-frequency amplitude than the use of a
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 motion
relationships determined for one tectonic environment cannot be simply scaled for use in
another.
Table 6.1 gives summary information of all the attenuation relationships that have been
implemented in EQTools. Appendix C gives the details of mathematical models and
regression coefficients for various attenuation relationships.
Earthquake ground motions have been recorded by seismographs since the late nineteenth
century (Bolt, 1993). Major initiatives to instrument seismically active regions around the
world were undertaken in the twentieth century, and these instruments have provided a
large inventory of recordings. Data from this inventory have been used to develop
attenuation relationships, which are either fully empirical or rely on empirical data to
calibrate theoretical models (Stewart et al., 2001).
Despite the large ground motion inventory, the strong motion data set remains poorly
sampled for the development of attenuation relations. For example, Figure 6.2, which
8.0
7.5
7.0
Magnitude
6.5
6.0
5.5
5.0
0.1 1 10 100 1000
Figure 6.2 Inventory of strong ground motion recordings in EQTools database; February 1937
Humbolt Bay, United States earthquake to November 1999 Duzce, Turkey, earthquake.
The horizontal lines of dots are in most cases single events that were well recorded.
According to Stewart et al. (2001), there are sampling problems with the inventory and
the data from sparsely and well-recorded events should be weighted relative to each other
in the regression analysis. To elaborate upon these aspects, the relevant section from the
reference is presented:
First sampling problem is that there are only 82 recordings of large magnitude
earthquakes ( m > 7 ) at close distance ( r < 20 km), and 59 of these are from
Subduction Zone
Atkinson and Boore (1995, 1997b) PGA, SA, PGV simulation 4 7.25 10 500 rhypo Rock only -
1
PGA = Peak Ground Acceleration; SA = 5% damped spectral acceleration; PGV = Peak Ground Velocity; PSV = 5% damped pseudo-velocity.
2
RE = random effects; WLS = weighted least square
3
r = site-source distance; rseis = seismogenic depth distance; r jb = surface projection distance; rhypo = hypocenter distance
4
S = rock/soil; S sr , Shr = soft rock, hard rock factors; Db = depth to basement rock; Vs = shear wave velocity
5
F = style of faulting factor; HW = hanging wall factor; Zt = subduction zone source factor; h = focal depth
The second sampling problem is associated with the fact that the data set is
dominated by a few well-recorded events. For example, the data set in Figure 6.1
contains approximately 1800 recordings, but 1055 of these are from only eight
earthquakes (m6.6 1971 San Fernando, Califormia; m6.5 1979 Imperial Valley,
California; m6.4 1983 Coalinga, California; m7.3 1992 Landers, California;
m6.7 1994 Northridge, California; m7.6 1999 Chi Chi, Taiwan). While these well-
recorded events allow for robust quantification of intra-event aleatory variability
of ground motion (random variability within an event), this clustering of data in a
few events is not sufficient to unambiguously evaluate inter-event aleatory
variability (random variability across events). In other words, if inter-event
variability were negligible, attenuation relations could be developed by weighting
each data point equally, where as if intra-event variability were negligible, the
collective data from each event would be weighted equally. As neither source of
variability is small, an important question is how data from sparsely and well-
recorded events should be weighted relative to each other in the regression
analysis.
Joyner and Boore (1981) proposed a two-step regression procedure in which all
data points are weighted equally to derive the shape of functions describing the
Using the data generated through EQTools, an illustration of the effect of m and r on
spectral acceleration is provided in Figure 6.3, which shows median values of peak
horizontal acceleration (PHA) and 3.0 second spectral acceleration (SA) for a strike-slip
focal mechanism and rock site condition using the Abrahamson and Silva (1997)
attenuation relationship. It can be deduced from the figure that the PHA attenuates more
rapidly with distance than long-period spectral acceleration, and that long-period spectral
acceleration is more sensitive to magnitude. Figure 6.3 shows that the PHA increases
with an increase in magnitude, although the amount of this increase is larger at large
1 1
Peak Horizontal Acceleration (g)
m8
0.1 0.1 m8
m7
m7
m6
0.01 m5 0.01 m6
m5
0.001 0.001
0.1 1 10 100 0.1 1 10 100
Figure 6.3 Attenuation of PHA and 3.0 second spectral acceleration for strike-slip focal mechanism
and rock/shallow site condition; Abrahamson and Silva (1997) attenuation relationship.
distances than at short distances. At short distances, the limited available data suggest a
saturation of high-frequency ground motion parameters such as PHA. This effect has
also been found in some simulation exercises (Anderson, 2000).
Significant differences are observed between reverse earthquake motions and strike-slip,
which are discussed below. Observations from the Northridge earthquake and other
reverse events indicate that median ground motions from these earthquakes are higher
than those from strike-slip events (e.g., Campbell, 1982; Somerville et al., 1996). This
trend is present on both the footwall and hanging wall sides of reverse faults (see Figure
Foot Wall
Top of fault
rupture
Hanging Wall
Bottom of fault
rupture
Figure 6.4 Definition of footwall and hanging wall. After Abrahamson and Somerville (1996)
0.1 0.1
0.01 0.01
Strike Slip
Strike Slip
Reverse/Thrust
Reverse/Thrust
0.001 0.001
0.1 1 10 100 0.1 1 10 100
Figure 6.5 Effect of focal mechanism on attenuation of PHA and 3.0 s spectral acceleration;
Abrahamson and Silva (1997) attenuation relationship.
0.001 0.001
0.1 1 10 100 0.1 1 10 100
Figure 6.6 Effect of fault mechanism and hanging wall effect on attenuation of PHA and 3.0 s
spectral acceleration; Abrahamson and Silva (1997) attenuation relationship.
The effect of geological and local soil conditions underlying the recording location can
significantly influence the characteristics of recorded ground motion. To partially account
for this effect, parameter S and a site term, f(S), are generally included in regression
equations for median spectral acceleration (e.g., Equation 6.2.2).
time), as the site parameter. Campbell (1997) uses three parameters, S sr and Shr for local
S sr = 0 and Shr =1 for hard rock. Parameter Db is taken as the depth to Cretaceous or
Analytical forms of site correction factors f(S) vary from simple constants to more
complex functions that attempt to account for nonlinearity in the local ground response.
Boore et al. relationships take f(S) as the product of a period-dependent constant and 30-
m Vs . Campbell relationships incorporate distance rseis into the site term to allow for the
soil nonlinearity. Abrahamson and Silva use the median peak acceleration on rock
predicted by their attenuation relation as an input parameter to the site term. The value of
the site term decreases as the rock acceleration increases, thus incorporating nonlinearity.
Sadigh et al. do not use a site term, but perform the full regression separately for rock and
soil sites.
Figure 6.7 presents the analyses for rock and soil site conditions to illustrate the effect of
site response in the Abrahamson and Silva attenuation relation. For PHA, deamplification
0.1 0.1
0.01 0.01
Rock Rock
Soil Soil
0.001 0.001
0.1 1 10 100 0.1 1 10 100
Figure 6.7 Effect of site condition on attenuation of PHA and 3.0 s spectral acceleration;
Abrahamson and Silva (1997) attenuation relationship.
The Youngs et al. and Atkinson models were developed using procedures most
comparable to those for active tectonic regions, and thus allow direct comparisons of
ground motion attenuation characteristics. A comparison of the Youngs et al. and
Abrahamson and Silva attenuation models is made in Figure 6.8, which shows that PHA
and long-period spectral acceleration from inter-plate subduction zone events are smaller
at close distance, but attenuate more slowly with distance, than ground motions from
active regions. Intra-slab events produce larger amplitude ground motions more
comparable at close distance to those from active regions, but which still attenuate
relatively slowly with distance (Stewart et al., 2001).
1 1 m = 5, 6, 7
Peak Horizontal Acceleration (g)
0.1 0.1
m = 5, 6, 7
0.001 0.001
0.1 1 10 100 0.1 1 10 100
Figure 6.8 Variation of attenuation of PHA and 3.0s spectral acceleration between active tectonic
regions and subduction zones (rock site condition). Median accelerations shown for strike-slip
earthquakes in active regions and interpolate earthquakes in subduction zones with focal depth =
20km; Abrahamson and Silva (1997) and Youngs et al. (1997) attenuation relations.
Very little strong motion data are available for stable continental regions, and as a result,
attenuation relationships are generally based on simulated ground motions instead of
recordings. Regression analyses utilizing these simulated motions are used to develop
A number of ground motion parameters other than spectral acceleration and PHA can
significantly affect the nonlinear response and performance of structures. The
identification of such critical parameters for building and bridge structures is the focus of
many ongoing studies. The identification of these parameters may include peak velocity,
pseudo-velocity, and vertical ground motion parameters (for long-span structures).
Attenuation relations for peak horizontal velocity (PHV) have been developed for active
tectonic regions by Campbell (1997, 2000, 2001), for the Cascadia subduction zone by
Atkinson and Boore (1997a), and for eastern North America by Atkinson and Boore
(1997b). Attenuation of PHV follows trends similar to mid-period spectral acceleration
(i.e., Sa at T 1 sec). Specific regression equations used by these investigators (and
implemented in EQTools) and the corresponding regression coefficients are available in
Appendix C.
7.1 Introduction
Evaluation of ground response is one of the most important and frequently encountered
problems in earthquake engineering. Investigations of major destructive earthquakes
(Caracus 1967, Managua 1972, Mexico City 1985) indicate that perhaps the single most
important aspect of the response of a soil system is the amplifying effect that the soft soil
deposits can have on the bedrock motion (Seed et al., 1970a, 1970b; Schnabel, 1971;
Espinosa and Algermissen, 1972; Johnson, 1975; Borg, 1986). In cases where the
dominant period of the bedrock motion approximately matches the fundamental period of
the site, severe amplification of the earthquake waves can be expected at the ground
surface as compared to the waves at the bedrock.. If, in addition, the fundamental
structural period matches the fundamental site period, potentially damaging resonant
motions can occur. In view of this, earthquake analyses of building structures which
include site effects, even if they are in an approximate sense, can lead to more realistic
and safer earthquake resistant designs. This consideration is reflected in many building
codes, which modify the lateral design forces based on knowledge of the fundamental
period of the site.
A complete ground response analysis, ideally, would need modeling of the rupture
mechanism at the source of an earthquake, and the propagation of stress waves through
the earth to the top of the bedrock beneath a particular site. Then the analysis would
determine how the ground surface motion is influenced by the soils that lie above the
bedrock. According to Kramer (1996), the mechanism of fault rupture, in reality, is so
complicated and the nature of energy transmission between the source and the site so
uncertain that this approach is not practical for common engineering applications. In
practice, empirical methods based on the characteristics of recorded earthquakes are used
to develop predictive relationships of the types discussed in Chapter 6. These predictive
relationships are often used in conjunction with a seismic hazard analysis to predict
bedrock motion characteristics at the site. The problem of ground response analysis then
The fact that the local site conditions can significantly influence the extent of earthquake
damage has been recognized for many years. Seismologists and engineers have worked
towards the development of quantitative procedures for predicting the influence of local
soil conditions on strong ground motion. Over the years, a number of techniques have
been developed for ground response analysis. The techniques are often classified on the
basis of the dimensionality of problems they can address, although many of the two- and
three-dimensional techniques are relatively straightforward extensions of corresponding
one-dimensional techniques.
When a fault ruptures below the earths surface, body waves travel away from the source
in all directions. As they reach the boundaries between different geological materials,
they are reflected and refracted. By the time the rays reach the ground surface, multiple
refractions have often bent them to a nearly vertical direction (Figure 7.1). One-
dimensional ground response analyses are based on the assumption that all boundaries are
horizontal and that the response of a soil deposit is predominantly caused by SH-waves
(horizontal plane movement) propagating vertically from the underlying bedrock. For
one-dimensional ground response analysis, the soil and bedrock surface are assumed to
extend indefinitely in the horizontal direction. Procedures based on this assumption have
been shown to predict ground response that is in reasonable agreement with measured
response in many cases.
Computational tools have been implemented in EQTools that can perform linear and non-
linear analyses to predict the response of a one-dimensional site model. The
methodology, algorithms, and FORTRAN subroutines developed by Hart and Wilson
(1989) have been employed to develop these computational tools. The FORTRAN
subroutines are available in the site response analysis program WAVES. This program,
Site
Fault
Surficial layers
Path
Source
Figure 7.1 Refraction process that produces nearly vertical wave propagation near the ground
surface.
Site response analysis can be performed either in the frequency domain or in the time
domain. Irrespective of the analysis procedure implemented, one of the most important
considerations is the discretization of the site into an appropriate mathematical model.
Frequency domain procedures obtain the response of the soil model by assuming that the
input and output motions are the summation of harmonic motions that are related through
transfer functions. The time domain procedures, on the other hand, obtain the response of
the soil model by numerically solving the dynamic equilibrium equations through step-
by-step integration.
As mentioned before, WAVES has been integrated with EQTools to perform site
response analysis procedures with the user-specified soil profile and the searched and
selected records through EQTools database as the base input ground motions. Several
other computer programs are available for evaluating the effect of local soil conditions on
the ground surface response, but WAVES was chosen for this work because its free-field
input format eased the integration into the EQTools environment. Additionally, WAVES
is extremely computationally efficient and it can perform energy balance computations as
a means to investigate the distribution of earthquake energy in the soil profile. WAVES
can compute the mode shapes and vibration periods of the finite element site model and
can also conduct linear or iterative, equivalent linear site response analysis using direct
step-by-step time domain integration. Time domain procedures, as implemented in
WAVES, can result in slightly more efficient numerical solutions than similar frequency
domain based procedures with the added advantage of being able to perform nonlinear
site response analysis using various solution strategies.
EQTools, in tandem with WAVES, can be used to perform a linear, equivalent linear, or
more complex nonlinear site response analysis. The input data for use with WAVES is
generated through an interactive interface designed as part of the EQTools environment.
Some minor changes were necessary to the FORTRAN subroutines of WAVES to enable
The first step in the site response analysis is the determination of dynamic properties of
the soil deposits. These include the mass, stiffness, and damping of the soil elements. Site
bore logs and geophysical tests together with the empirical relationships (Hardin and
Drnevich, 1972; Idriss et al., 1976; Seed and Idriss, 1972) developed for various soil
types can be utilized to determine the mass properties and the strain-dependent shear
moduli and damping ratio of soil layers. These and the geometric properties of the layers
in the soil profile can be input interactively in the EQTools environment. Appendices D
and E provide further details on these aspects.
The procedures for assembling design ground motions have been discussed previously.
The ground motions searched from the EQTools database, and selected on the basis of
these procedures, form the base input ground motions for analysis with WAVES. Once
all the necessary analysis control information, dynamic and geometric properties of soil
layers, and the base input ground motion data are available, EQTools generates the data
files for use with WAVES to perform the site response analysis. The analysis and other
necessary processing are performed in the background. Analysis is done progressively for
each earthquake in a systematic manner.
As the analysis progresses, EQTools imports the layer response acceleration histories by
reading the output files generated by waves sequentially. Once the response acceleration
histories are available for each layer and each base input ground motion, the
computational tools in EQTools generate the response velocity and displacement for each
layer by integration. The velocity and displacement histories are base-line corrected to
establish the zero baselines. The ground motion histories of the layer response can then
The site response analysis results have been validated by the developers. Hence, for the
purpose of this work, as a demonstration of time domain site response analysis, the
computational tools in EQTools are utilized to investigate the seismic response of a
horizontally layered soil profile. In this section, the soil profile and the corresponding
finite element discretization are discussed and some of the analysis results are presented.
The soil profile selected for analysis (shown in Figure 7.2) represents the subsurface
conditions at an arbitrary site. The subdivision of layer elements should be carefully
chosen to ensure spatial convergence (i.e., to ensure that further mesh subdivision will
not affect the solution). A general rule of thumb is to select the maximum layer thickness
such that 8 elements fit within the wave length of the important seismic waves
propagating vertically through the site; effectively approximating a full sine wave with 8
equal lengths, straight line segments (Hart and Wilson, 1989). For example, if the
average shear wave velocity of a site is assumed to be 50 m/s (164 ft/s) and the
fundamental period of the site is 2.0 seconds, the corresponding harmonic wavelength is
100 m (328 ft), resulting in a maximum layer thickness of 100/8 = 12.5 m (41 ft).
For the purpose of site response analysis, it is necessary to select input motions which can
be considered as representative of the motions developed at the base rock level of the
SCT site. As discussed in Chapter 5, base input motions are typically obtained by scaling
the amplitude and/or frequency of previously recorded earthquake accelerograms to
reflect site variables such as distance from the causative fault and earthquake magnitude.
For this analysis, horizontal components of motions recorded at a rock location, namely
5051 Parachute Test Site, during the 1979 Imperial Valley earthquake are assumed to be
16.4 ft 211 94 1 1
23.0 ft
75.9 78 2 2
45.5 ft
213.9 83 1 1
58.6 ft 206.1 76 2 1
61.9 ft
3285.8 108 1 1
78.3 ft 640.9 88 2 1
82.1 ft
Figure 7.2 Example soil profile considered for the site response analysis
The first and second mode shapes of the site, which correspond to vibration periods of
1.21 and 0.36 seconds, respectively, are shown in Figure 7.4. With the above discussed
soil profile and the base input ground motions, a linear earthquake response analysis of
the site based on the initial dynamic soil properties was conducted using EQTools. The
results are presented in Figures 7.5 and 7.6. Figure 7.5 shows a comparison of the
pseudo-acceleration response spectra for the base input motion and the site ground
response for the N45W component. A similar comparison for the S45W component is
shown in Figure 7.6.
0.3
0.2
0.1
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Period (seconds)
Figure 7.3 Pseudo-acceleration response spectra for the N45W and S45W components of the 1979
Imperial Valley earthquake recorded at the 5051 Parachute Test Site.
Mode 1 Mode 2
T=1.21 seconds T=0.36 seconds
Figure 7.4 Example Soil Profile Mode shapes for modes 1 and 2.
The site response results presented herein are the ground responses to the base input
motions (i.e., the response of the topmost layer in the soil profile). In the EQTools
environment, the response can be examined for any layer and any base input ground
motion graphically. This feature is useful from practical considerations, as the founding
level of majority of the structures is at some depth from the ground
1.2
0.8
0.6
0.4
0.2
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Period (seconds)
Figure 7.5 Pseudo-acceleration response spectrum from linear site response analysis (using N45W
component as input motion)
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Period (seconds)
Figure 7.6 Pseudo-acceleration response spectrum from linear site response analysis (using S45W
component as input motion)
8.1 Conclusions
The preceding chapters have presented contemporary concepts and procedures for
characterization, evaluation, and modification of strong ground motions within a
performance-based seismic design framework. These concepts are used to develop
analytical tools, termed EQTools, in an integrated and interactive environment. EQTools
has been created with the objective of providing engineers, researchers, and students with
facilitated access to powerful and state-of-the-art computational tools in the field of
engineering seismology and earthquake engineering within a performance-based design
framework. EQTools constitutes an easy and efficient way to process strong-motion
data, featuring a user-friendly visual interface and the capability of deriving a number of
strong-motion parameters often required by structural engineers, seismologists, and
geotechnical earthquake engineers. In addition to this, EQTools also provides the
necessary means to investigate frequency content of accelerograms, carry out high-pass,
low-pass, band-pass, and band-stop filtering using three different digital filter types,
generate and scale elastic response spectra, and perform linear or nonlinear site response
analysis.
By virtue of the fact that EQTools makes available various processes by which ground
motions are evaluated for performance-based design applications under one unique
framework, not only does it standardize the procedures but it also minimizes the
possibility of inconsistencies in evaluation of ground motions. Recognizing the fact that
earthquake engineering is a broad, multidisciplinary field, EQTools draws from
seismology, geotechnical engineering, structural engineering, risk analysis, and other
technical disciplines. In that respect, EQTools is a common platform and is
complementary to almost all the procedures employed in earthquake engineering. Hence,
EQTools is intended to enhance the research capabilities and efficiency of researchers
working in any of the aforementioned disciplines. Additionally, EQTools is a working
EQTools has a tremendous educational value by virtue of the fact that it provides a visual
basis for learning the principles behind the selection of ground motion 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), provides a complete environment for learning the concepts of
earthquake engineering, particularly as related to structural dynamics, damping, ductility,
and energy dissipation.
There is scope for improving the functionality and usefulness of EQTools by developing
and implementing additional features and methods in its environment. This section
discusses, in general, the models and methods that are recommended to be added to
EQTools to better meet the ground motion characterization needs for contemporary
performance-based earthquake-risk management.
EQTools, in its current state, is based on the premise that the engineering end results of
seismic hazard analysis are available beforehand as input for assembling ground motion
records. Seismic hazards may be analyzed deterministically, as when a particular
earthquake scenario is assumed, or probabilistically, in which uncertainties in earthquake
size, location, and time of occurrence are explicitly considered. Seismic hazard is a
critical part of the development of design ground motions and, as such, it will be
worthwhile to develop and implement tools to achieve this in the EQTools environment.
Available data resources are inadequate to constrain models for a number of important
problems such as ground motions from very large earthquakes, near-fault ground
motions, and basin effects, as well as ground motions in intra-plate regions. Ground
As discussed in Chapters 2 and 3, the duration of strong ground motions that form the
input into time-domain nonlinear analyses of structures can significantly influence the
response of the structure. Currently, in the EQTools environment, the capability to search
the ground motions on the basis of duration parameters is not available. One of the
duration measures (bracketed duration) can, however, be investigated once the searched
records are available. Various strong motion duration measures can be computed for the
records in the database and made available as search parameters in the EQTools
environment as part of the future work.
As mentioned in Chapter 2, the EQTools database is a stand-alone database that has 755
records at the time of this writing. Even though the database is updatable, the fact
remains that the stand-alone nature of the database is a limitation since it restricts the
access to only those ground motions that are available in the database. There are a
plethora of sources that provide access to raw or corrected accelerograms over the World
Wide Web. The accelerograms are available in various data formats but a majority of
them follow one of the few standard formats. The capabilities of EQTools can be
tremendously enhanced by enabling its environment to access and possibly search for
ground motion records over the internet and automatically update its database. This
exercise will require great effort but it is perceived to be worthwhile.
EQTools currently has provisions to generate only the elastic response spectra. The
maximum restoring force in the SDOF system, which represents the base shear in the
code formulations, is the product of mass and the spectral acceleration. Economic
constraints limit this level of design force only to structures that are extremely important
Finally, with the intention of enabling the engineering research and student community to
remotely access the EQTools environment, it is strongly recommended that EQTools be
deployed over the World Wide Web. This exercise, however, will require extensive re-
modeling of the EQTools architecture.
Abrahamson, N. A., and Somerville, P. G., Effect of the Hanging Wall and Footwall on
Ground Motions Recorded during the Northridge Earthquake, Bulletin of the
Seismological Society of America, Vol. 86, S93-S99, 1996.
Allahabadi, R., DRAIN-2DX Seismic Response and Damage Assessment for Two-
Dimensional Structures, Ph. D. Dissertation, University of California, Berkeley, 1987.
Atkinson, G. M., and Boore, D. M., Stochastic Point Source Modeling of Ground
Motions in the Cascadia Region, Seismological Research Letters, Vol. 68(1), 74-85,
1997a.
Atkinson, G. M., and Boore, D. M., Some Comparisons Between Recent Ground
Motion Relations, Seismological Research Letters, Vol. 68(1), 24-40, 1997b.
Archuleta, R. J., and Hartzell, S. H., Effects of Fault Finiteness on Near-Source Ground
Motion, Bulletin of the Seismological Society of America, Vol. 71, 939-957, 1981.
Bathe, K. J., and Wilson, E. L., Numerical Techniques for the Solution of Soil-Structure
Interaction Problems in the Time Domain, Earthquake Engineering Research Center,
Report No. EERC 83-04, University of California, Berkeley, 1983.
Bazzuro, P., and Cornell, C. A., Disaggregation of Seismic Hazard, Bulletin of the
Seismological Society of America, Vol. 89, 501-520, 1999.
References 127
Bender, B., Incorporating Acceleration Variability into Seismic Hazard Analysis,
Bulletin of the Seismological Society of America, Vol. 74, 1451-1462, 1984.
Bolt, B. A., Duration of Strong Motion, Proceedings of the 4th World Conference on
Earthquake Engineering, Santiago, Chile, 1304-1315, 1969.
Boore, D. M., Joyner, W. B., and Fumal, T. E., Equations for Estimating Horizontal
Response Spectra and Peak Acceleration from Western North American Earthquakes: A
Summary of Recent Work, Seismological Research Letters, Vol. 68(1), 128-153, 1997.
Borg, S. F., The 19 September 1985 Mexican Earthquake Rational Analysis of the
Anomalous Central Mexico City Behavior, Technical Report COE-86-1, Stevens
Institute of Technology, 1986.
Brune, J. N., Tectonic Stress and the Spectra of Seismic Shear Waves from
Earthquakes, Journal of Geophysical Research, Vol. 75, 4997-5009, 1970.
Brune, J. N., Correction, Journal of Geophysical Research, Vol. 76, 5002, 1971.
References 128
Chapman, M. C., A Probabilistic Approach to Ground-Motion Selection for Engineering
Design, Bulletin of the Seismological Society of America, Vol. 85, 937-942, 1995.
Charney, F. A., NONLIN: A Computer Program for Nonlinear Dynamic Time History
Analysis of Single- and Multi-Degree of Freedom Systems, Federal Emergency
Management Agency, 2003.
Clough, R. W., and Penzien, J., Dynamics of Structures, Volume 2, McGraw Hill, New
York, N.Y., 1993
Cooley, P. M., and Tuckey, J. W., An Algorithm for the Machine Computation of
Complex Fourier Series, Mathematics of Computations, Vol. 19, No. 4, 297-301, 1965.
Crammer, C. H., and Petersen, M. D., Predominant Seismic Source Distance and
Magnitude Maps for Los Angeles, Orange and Ventura Counties, California, Bulletin of
the Seismological Society of America, Vol. 86, 1645-1649, 1996.
Crouse, C. B. and McGuire, J. W., Site Response Studies for Purpose of Revising
NEHRP Seismic Provisions, Earthquake Spectra, Vol. 12, No. 3, 407-439, 1996.
Faccioli, E., Estimating Ground Motions for Risk Assessment, Proceedings of the U.S.-
Italian Workshop on Seismic Evaluation and Retrofit, Edited by D. P. Abrams and G. M.
Calvi, Technical Report NCEER-97-0003, National Center for Earthquake Engineering
Research, Buffalo, New York, 1-16, 1997.
Gutenberg, B., and Richter, C. F., On Seismic Waves (third paper), Gerlands Bietraege
zur Geophysik, Vol. 47, 73-131, 1936.
References 129
Hall, W. J., Mohraz B., and Newmark, N. M., Statistical Studies of Vertical and
Horizontal Earthquake Spectra, Nathan M. Newmark Consulting Engineering Services,
Urbana, Illinois, 1975.
Hanks, T. C., and Kanamori, H., A Moment Magnitude Scale, Journal of Geophysical
Research, Vol. 84, 2348-2350, 1979.
Hanks, T. C., and McGuire, R. K., The Character of High-Frequency Strong Ground
Motion, Bulletin of the Seismological Society of America, Vol. 71, 2071-2095, 1981.
Hanks, T. C., fmax, Bulletin of the Seismological Society of America, Vol. 72, 1867-
1879, 1982.
Hardin, B. O. and Drenovich, V. P., Shear Modulus and Damping in Soils: Design
Equation and Curves, Journal of the Soil Mechanics and Foundations Division, ASCE,
Vol. 98, No. SM7, 1972.
Harmsen, S., Perkins, D., and Frankel, A., Disaggregation of Probabilistic Ground
Motions in the Central and Eastern United States,Bulletin of the Seismological Society of
America, Vol. 89, 1-13, 1999.
Hart, J. D., An Introduction to WAVES A New Computer Program for Evaluating the
Earthquake Response of Horizontally Layered Soil Deposits, Individual Research
Report, Department of Civil Engineering, University of California, Berkeley, 1987.
Hart, J. D., and Wilson, E. L., Simplified Earthquake Analysis of Buildings Including
Site Effects, Report No. UCB/SEMM-89/23, University of California, Berkeley, 1989.
Hayashi, S., Tsuchida, H., and Kurata, E., Average Response Spectra for Various
Subsoil Conditions, Third Joint Meeting, U.S. Japan Panel on Wind and Seismic
Effects, UJNR, Tokyo, 1971.
References 130
Hughes, T. J. R., Stability, Convergence and Growth and Decay of Energy of the
Average Acceleration Method in Nonlinear Structural Dynamics, Computers and
Structures, Vol. 6, 313-324, 1976.
Idriss, I. M., Dorby, R., and Singh, R. D., Nonlinear Behaviour of Soft Clays During
Cyclic Loading, Journal of the Geotechnical Engineering Division, ASCE, No. GT12,
1972.
Iwan, W. D., On a Class of Model for Yielding Behavior of Continuous and Composite
Systems, Journal of Applied Mechanics, ASME, Vol. 34, 612-617, 1967.
Johnson, J. A., Site and Source effects on Ground Motion in Managua, Nicaragua,
Report No. UCLA-Eng-7536, University of California, Los Angeles, 1975.
Kramer, S. L., Geotechnical Earthquake Engineering, Prentice Hall, Upper Saddle River,
New Jersey, 1996.
Kuribayashi, E., Iwasaki, T., Iida, Y., and Tuji, K., Effects of Seismic and Subsoil
Conditions on Earthquake Response Spectra, Proceedings of the International
Conference on Microzonation, Seattle, Wash., 499-512, 1972.
Lysmer, J., Udaka, T., Seed, H. B., and Hwang, R., LUSH A computer Program for
Complex Response Analysis of Soil Structure Systems, Earthquake Engineering
Research Center, Report No. EERC 7-74, University of California, Berkeley, 1974.
Marone, C., and Scholz, C. H., The Depth of Seismic Faulting and the Upper Transition
from Stable Slip Regimes, Geophysics Research Letters, Vol. 15, 621-624, 1988.
References 131
McGarr, A., Scaling of Ground Motion Parameters, State of Stress, and Focal Depth,
Journal of Geophysical Research, Vol. 89, 6969-6979, 1984.
McGuire, R. K., PSHA and Design Earthquakes: Closing the Loop, Bulletin of the
Seismological Society of America, Vol. 85, 1275-1284, 1995.
Mohraz, B., Influences of the Magnitude of the Earthquake and the Duration of Strong
Motion on Earthquake Response Spectra, Proceedings of the Central American
Conference on Earthquake Engineering, San Salvador, El Salvador, 1978.
Mohraz, B., Recent Studies of Earthquake Ground Motion and Amplification, Proc.
10th World Conference on Earthquake Engineering, Madrid, Spain, 6695-6704, 1992.
Mohraz, B., Hall, W. J., and Newmark, N. M., A Study of Vertical and Horizontal Earthquake
Spectra, Nathan M. Newmark Consulting Engineering Services, Urbana, Illinois, AEC Report
WASH-1255, 1972.
Murphy, J. R., and OBrien, L. J., The Correction of Peak Ground Acceleration
Amplitude with Seismic Intensity and Other Physical Parameters, Bulletin of the
Seismological Society of America, Vol. 67, 877-915, 1977.
Naeim, F., Seismic Design Handbook, 2nd ed., Kluwer Academic Publishers, New York,
NY, 2001.
Naeim, F., and Anderson, J.C., Classification and Evaluation of Earthquake Records for
Design, A report to EERI and FEMA, Report No. 93-08, Department of Civil
Engineering, University of Southern California, July 1993.
NEHRP Recommended Provisions for the Development of Seismic Regulations for New
Buildings, 1985 Edition, Building Seismic Safety Council, Washington, D.C., 1985.
NEHRP Recommended Provisions for the Development of Seismic Regulations for New
Buildings, 1988 Edition, Building Seismic Safety Council, Washington, D.C., 1988.
References 132
NEHRP Recommended Provisions for the Development of Seismic Regulations for New
Buildings, 1991 Edition, Building Seismic Safety Council, Washington, D.C., 1991.
NEHRP Recommended Provisions for the Development of Seismic Regulations for New
Buildings, 2000 Edition, Building Seismic Safety Council, Washington, D.C., 2000.
Newmark, N. M. and Hall, W. J., Procedures and Criteria for Earthquake Resistant
Design, Building Practices for Disaster Mitigation, National Bureau of Standards, U.S.
Department of Commerce, Building Research Series 46, 209-236, 1973.
Newmark, N. M. and Hall, W. J., Earthquake Spectra and Design, EERI Monograph,
Earthquake Engineering Research Institute, Berkeley, California, 103, 1982.
Page, R. A., Boore, D. M., Houner, W. B., and Caulter, H. W., Ground Motion Values
for Use in the Seismic Design of the Trans-Alaska Pipeline System, USGS Circular 672,
U. S. Geological Survey, Reston, Virginia, 1972.
Papageorgiou, A. S., and Aki, K., Earthquake Spectra and Design, EERI Monograph,
Earthquake Engineering Research Institute, Berkeley, California, 103, 1982.
Peng, M. H., Elghadamsi, F. E., and Mohraz, B., A Simplified Procedure for
Constructing Probabilistic Response Spectra, Earthquake Spectra, Vol. 5, No. 2, 393-
408, 1989.
Reiter, L., Earthquake Hazard Analysis: Issues and Insights, Columbia University Press,
New York, 1990.
Sadigh, K., Chang, C.Y., Egan, J. A,, Makdisi, F., and Youngs, R. R., Attenuation
Relations for Shallow Crustal Earthquakes Based on California Strong Motion Data,
Seismological Research Letters, Vol. 68(1), 180-189, 1997.
Sadek, F., Mohraz, B., and Riley, M. A., Linear Procedures for Structures with
Velocity-Dependent Dampers, Journal of Structural Engineering, Vol. 128, No. 8, 887-
895, 2000.
References 133
Schnabel, P. B., Lysmer, J., and Seed, H. B., SHAKE A Computer Program for
Earthquake Response Analysis of Horizontally Layered Sites, EERC Report No.
UCB/EERC-72-12, University of California, Berkeley, 1972.
Seed, H. B., Idriss, I. M., and Dezfulian, H., Relationship Between Soil Conditions and
Building Damage in the Caracas Earthquake of July 29, 1972, Earthquake Engineering
Research Center, Report No. EERC 70-2, University of California, Berkeley, 1970.
Seed, H. B., and Idriss, I. M., Soil Moduli and Damping Factors in Dynamic Response
Analysis, Earthquake Engineering Research Center, Report No. EERC 701-0, University
of California, Berkeley, 1970.
Seed, H. B., Romo, M. P., Sun, J., Jaime, A., and Lysmer, J., Relationship Between Soil
Conditions and Earthquake Ground Motions in Mexico City in the Earthquake of Sept.
19, 1985, Earthquake Engineering Research Center, Report No. UCB/EERC-87/15,
University of California, Berkeley, 1987.
Seed, H. B., Ugas, C., and Lysmer, J., Site-Dependent Spectra for Earthquake-
Resistance Design, Bulletin of Seismological Society of America, Vol. 66(1), 221-243,
1976.
Singh, J. P., Earthquake Ground Motions: Implications for Designing Structures and
Reconciling Structural Damage, Earthquake Spectra, Vol. 1(2), 239-270, 1985.
Shome, N., Cornell, C. A., Bazzuro, P., and Carballo, E. J., Earthquakes, Records, and
Nonlinear Responses, Earthquake Spectra, 14, 469-500, 1998.
Somerville, P. G., Smith, N. F., Graves, R. W., and Abrahamson, N. A., Modification of
Empirical Strong Ground Motion Attenuation Relations to Include the Amplitude and
Duration Effects of Rupture Directivity, Seismological Research Letters, Vol. 68, 199-
222, 1997.
Somerville, P. G., Smith, N., Punyamurthula, S., and Sun, J., Development of Ground
Motion Time Histories for Phase 2 of the FEMA/SAC Steel Project, Background
Document Report No. SAC/BD-97/04, SAC Steel Project, 1997.
Spudich, P., Joyner, W. B., Lindh, A. G., Boore, D. M., Margaris, B. M., and Fletcher, J.
B., SEA99: A Revised Ground Motion Prediction Relation for Use in Extensional
Tectonic Regimes, Bulletin of the Seismological Society of America, Vol. 88(5), 1156-
1170, 1999.
References 134
Stepp, J. C., Silva, W. J., McGuire, R. K., and Sewell, R. W., Determination of
Earthquake Design Loads for a High Level Nuclear Waste Repository Facility, in
Proceedings of the Natural Phenomena Hazards Mitigation Conference, Vol. 2, 651-657,
1993.
Streeter, V. L., Wylie, E. B., Benjamin, E., and Richart, F. E., Soil Motion
Computations by Characteristic Method, Journal of the Geotechnical Engineering
Division, ASCE, Vol. 100, No. GT3, 1974
Stewart, J. P., Chiou, Shyh-Jeng, Bray, J. D., Graves, R. W., Somerville, P. G., and
Abrahamson, N. A., Ground Motion Evaluation Procedures for Performance-based
Design, PEER Report 2001/09, University of California, Berkeley, 2001.
Trifunac, M. D., and Brady, A. G., On the Correlation of Seismic Intensity with Peaks
of Recorded Ground Motion, Bulletin of the Seismological Society of America, Vol. 65,
139-162, 1975a.
Trifunac, M. D., and Brady, A. G., A Study of the Duration of Strong Earthquake
Ground Motion, Bulletin of the Seismological Society of America, Vol. 65, 581-626,
1975b.
Trifunac, M. D., and Todorovska, M. I., Nonlinear Soil Response 1994 Northridge,
California earthquake, Journal of Geotechnical and Geoenvironmental Engineering,
ASCE, Vol. 122(9), 725-735, 1996.
Vanmarcke, E. H., and Lai, S. P., Strong Motion Duration of Earthquakes, Report R77-
16, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1977.
References 135
Wilson, E. L., A Computer Program for the Dynamic Stress Analysis of Underground
Structures, Report No. UC SESM 68-1, Department of Civil Engineering, University of
California, Berkeley, 1968.
Youngs, R. R., Chiou S.J., Silva, W. J., and Humphrey, J. R., Strong Ground Motion
Attenuation Relationships for Subduction Zone Earthquakes, Seismological Research
Letters, Vol. 68(1), 58-73, 1997.
References 136
APPENDIX A
STRONG GROUND MOTION RECORDS IN EQTOOLS DATABASE
The EQTools Strong Motion Database contains 755 uniformly processed records from 72
earthquakes events from tectonically active regions around the world. Tables A-1 and A-
2 give the list of records from the continental United States and outside of the continental
United States respectively. Various characteristics relevant to structural design
applications are also presented in these tables.
The following notations and nomenclature are applicable to the earthquake data presented
in the tables.
Event Specifics
The earthquake event is specified by the event name, the year of occurrence, and the
name of the station where the data was recorded. This information is presented in the first
three columns of the table.
Component
For each recording, three components are available one vertical and two orthogonal
horizontal components. The horizontal components are specified as per the recording
orientation. For example, 045 means the horizontal component was recorded in a
direction 45 degree from the true north. This information is contained in colum four of
the table.
Earthquake Mechanisms
Wherever available, the fault mechanism has been presented as per the following
abbreviations:
SS = Strike Slip
N = Normal
RN = Reverse Normal
Appendix A 137
RO = Reverse Oblique
NO = Normal Oblique
Blank = Unknown fault mechanism
Earthquake Magnitudes
The following nomenclature applies to the magnitude information presented in the tables:
M w = Moment magnitude
M l = Local magnitude
M s = Surface wave magnitude
Other = Other or unknown magnitude measure
Distance Measures
The distance (in km) of recording stations from the fault location are presented as per the
following notations:
Site Classification
One-letter site codes are presented as per the USGS site classification on the basis of
average shear wave velocity Vs to a depth of 30.0m. The site codes are as follows:
Duration of Shaking
Appendix A 138
Ground Motion Parameters
Appendix A 139
Table A- 1 Characteristics of strong ground motions in EQTools database recorded within the continental United States
Appendix A 140
Table A-1 Characteristics of strong ground motions in EQTools database recorded within the continental United States
Appendix A 141
Table A-1 Characteristics of strong ground motions in EQTools database recorded within the continental United States
Appendix A 142
Table A-1 Characteristics of strong ground motions in EQTools database recorded within the continental United States
Appendix A 143
Table A-1 Characteristics of strong ground motions in EQTools database recorded within the continental United States
Appendix A 144
Table A-1 Characteristics of strong ground motions in EQTools database recorded within the continental United States
Appendix A 145
Table A-1 Characteristics of strong ground motions in EQTools database recorded within the continental United States
Appendix A 146
Table A-1 Characteristics of strong ground motions in EQTools database recorded within the continental United States
Appendix A 147
Table A-1 Characteristics of strong ground motions in EQTools database recorded within the continental United States
Appendix A 148
Table A-1 Characteristics of strong ground motions in EQTools database recorded within the continental United States
Appendix A 149
Table A-1 Characteristics of strong ground motions in EQTools database recorded within the continental United States
Appendix A 150
Table A-1 Characteristics of strong ground motions in EQTools database recorded within the continental United States
Appendix A 151
Table A-1 Characteristics of strong ground motions in EQTools database recorded within the continental United States
Appendix A 152
Table A- 2 Characteristics of strong ground motions in EQTools database recorded outside the continental United States
Appendix A 153
Table A-2 Characteristics of strong ground motions in EQTools database recorded outside the continental United States
Appendix A 154
Table A-2 Characteristics of strong ground motions in EQTools database recorded outside the continental United States
Appendix A 155
APPENDIX B
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 a 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. The contents of the database utilize publicly available processed
data from Pacific Earthquake Engineering Research Center (PEER), Berkeley. PEER has
separate files for acceleration, velocity and displacement time histories. However, 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.
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 required to provide the number of time-series values
indicated in the value given in the fourth header line.
Appendix B 156
Velocity Data Block
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 required to provide the number of time-
series values indicated in the value given in the fourth header line of the velocity data
block.
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 required to provide the number of time-
series values indicated in the value given in the fourth header line of the displacement
data block.
Appendix B 157
A partial listing of the file IMPVSUPH135.ACC is given below. The lines with . in
column 1 indicate data that was eliminated from the record for brevity.
Appendix B 158
APPENDIX C
GROUND MOTION ATTENUATION RELATIONSHIPS AND
REGRESSION COEFFICIENTS
Background
Regression Model
Using a database of 655 recordings from 58 earthquakes, empirical response spectral
attenuation relations have been derived for the average horizontal and vertical
components. 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. This site
response is explicitly allowed to be non-linear with a dependence on the rock peak
acceleration level. The general functional form of the model is:
where
Sa ( g ) = Spectral acceleration in units of g
M = Moment magnitude
Appendix C 159
rrup = Closest distance to the rupture plane in kilometers
for M c1
for M > c1
where R = rrup 2 + c4 2
Style-of-Faulting Factor
The functional form that allows for a magnitude and period dependence of the style-of-
faulting is given by:
a5 .............................M 5.8
(a a )
f3 ( M ) = a5 + 6 5 ..........5.8 < M < c1
(c1 5.8)
a6 ............................M c1
hanging wall effect is taken from Somerville and Abrahamson (1995) and is modeled as
separable in magnitude and distance so that
Appendix C 160
f 4 ( M , rrup ) = f HW ( M ) f HW (rrup )
where
0...............................M 5.5
f HW ( M ) = M 5.5....................5.5 M 6.5
1...............................M 6.5
and
0........................................rrup < 4
r 4
a9 rup .........................4 < rrup < 8
4
f HW (rrup ) = a9 ......................................8 < rrup < 18
a 1 rrup 18 ..............18 < r < 24
9 7
rup
0.......................................rrup > 25
Site response
The functional form that accommodates non-linear soil response follows the approach
used by Youngs (1993) in which soil amplification is a function of the expected peak
acceleration on rock. The non-linear site response is modeled by:
where PGArock is the expected peak acceleration on rock in gs (as predicted by the
median attenuation relation with S = 0).
Standard Error
In these relations, both the inter-event ( ) and intra-event ( ) standard errors are
allowed to be magnitude dependent and are modeled as follows:
Appendix C 161
b1................................M 5.0
( M ) = b1 b2 ( M 5)............5.0 < M < 7.0
b 2b ......................M 7.0
1 2
and
b3 ................................M 5.0
( M ) = b3 b4 ( M 5)............5.0 < M < 7.0
b3 2b4 ......................M 7.0
The total standard error is then computed by adding the variance of the two terms. The
total standard error was then smoothed and fit to the form
b5 ................................M 5.0
total ( M ) = b5 b6 ( M 5)............5.0 < M < 7.0
b 2b ......................M 7.0
5 6
Tables C-1 and C-2 give the coefficients for regression and standard errors for the
average horizontal and vertical components of the spectral accelerations respectively.
Appendix C 162
Table C-1: Coefficients for Regression and Standard Errors for the Average Horizontal Components; Abrahamson and Silva (1997)
Coefficients for
Regression Coefficients for Average Horizontal Component
Standard Errors
Appendix C 163
Table C-2: Coefficients for Regression and Standard Errors for the Average Vertical Components; Abrahamson and Silva (1997)
Coefficients for
Regression Coefficients for Average Vertical Component
Standard Errors
Appendix C 164
1.2 Kenneth W. Campbell Attenuation Relationships (1997)
where
AH ( g ) = Mean horizontal component of peak ground acceleration in units of g
M = Moment magnitude
Rseis = Closest distance to the seismogenic rupture surface in kilometers
F = Style-of-faulting factor (0 for strike-slip, 1 otherwise)
S SR = Soft rock soil factor (1 for soft rock, 0 otherwise)
Appendix C 165
S HR = Hard rock soil factor (1 for hard rock, 0 otherwise)
0.15S SR 0.30 S SR
Appendix C 166
The horizontal component of the 5% damped pseudo-absolute acceleration response
spectra, SAH (in units of g), is given by the following expression:
+ c7 tanh(c8 D)(1 S HR ) + f SA ( D) +
where
f SA ( D) = 0 when D 1 km
The standard errors of estimate of ln VH and ln( SAH ) are given by the following
expressions:
for VH : H = 2 + 0.062
acceleration ( SAV ) were developed by taking the ratio of the vertical to the mean
horizontal components from the 1990 study and multiplying this ratio by the values of
AH , VH , or SAH from the recommended horizontal attenuation relationships. The
resulting expressions are:
Appendix C 167
ln(VV ) = ln VH 2.15 + 0.07 M 1.24 ln [ Rseis + 0.00394 exp(1.17 M ) ]
ln( SAV ) = ln( SAH ) + c1 0.10 M + c2 tanh [ 0.71( M 4.7) ] + c3 tanh [ 0.66( M 4.7)]
The standard errors of estimate for ln( AV ) , ln VV , and ln( SAV ) are given by:
for AV : V = 2 + 0.362
for VV : V = H 2 + 0.302
Tables C-3 and C-4 present the regression coefficients for 5% damped horizontal and
vertical spectral accelerations.
Appendix C 168
Table C-3: Regression Coefficients for Horizontal Spectral Acceleration SAH ; Campbell (1997)
Period(s) c1 c2 c3 c4 c5 c6 c7 c8
Appendix C 169
Table C-4: Regression Coefficients for Vertical Spectral Acceleration SAV ; Campbell (1997)
Period(s) c1 c2 c3 c4
0.050 -1.32 0 0 0
0.075 -1.21 0 0 0
0.100 -1.29 0 0 0
0.150 -1.57 0 0 0
0.200 -1.73 0 0 0
0.300 -1.98 0 0 0
0.500 -2.03 0.46 -0.74 0
0.750 -1.79 0.67 -1.23 0
1.000 -1.82 1.13 -1.59 0.18
1.500 -1.81 1.52 -1.98 0.57
2.000 -1.65 1.65 -2.23 0.61
3.000 -1.31 1.28 -2.39 1.07
4.000 -1.35 1.15 -2.03 1.26
Appendix C 170
1.3 David M. Moore, William B. Joyner, and Thomas E. Fumal Attenuation
Relationships (1997)
This attenuation relationship is applicable for estimating horizontal response spectra and
peak acceleration for shallow earthquakes in western North America. Coefficients are
provided 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 (NEHRP) recommended seismic code
provisions. The ground motion estimation expression is given as follows:
VS
ln Y = b1 + b2 ( M 6) + b3 ( M 6)2 + b5 ln r + bV ln ; r = r jb 2 + h 2
VA
where
Y = Ground motion parameter (peak horizontal acceleration or pseudo
acceleration response in g).
M = Moment magnitude
r jb = Closest horizontal distance to the vertical projection of the rupture.
Appendix C 171
Table C-5: Recommended values of average shear velocity for use with Boore,
Joyner and Fumal attenuation relationship (1997)
The mean plus one sigma value of natural logarithm of the ground-motion value in
attenuation equation is ln Y + ln Y where ln Y is the square root of the overall variance
of the regression given by:
ln Y 2 = r 2 + e 2
e 2 represents the correction needed to give the variance corresponding to the randomly-
oriented horizontal component.
Table C-6 gives the regression coefficients to be used with this attenuation relationship.
Appendix C 172
Table C-6: Smoothed coefficients for estimating pseudo-acceleration response spectra (g)
for the random horizontal component at 5% damping. The entries for zero period are the
coefficients for peak horizontal acceleration.
0.00 -0.313 -0.117 -0.242 0.527 0 -0.778 -0.371 5.57 1396 0.520
0.10 1.006 1.087 1.059 0.753 -0.226 -0.934 -0.212 6.27 1112 0.479
0.12 1.109 1.215 1.174 0.721 -0.233 -0.939 -0.215 6.91 1452 0.485
0.15 1.128 1.264 1.204 0.702 -0.228 -0.937 -0.238 7.23 1820 0.492
0.17 1.090 1.242 1.173 0.702 -0.221 -0.933 -0.258 7.21 1977 0.497
0.20 0.999 1.170 1.089 0.711 -0.207 -0.924 -0.292 7.02 2118 0.502
0.24 0.847 1.033 0.941 0.732 -0.189 -0.912 -0.338 6.62 2178 0.511
0.30 0.598 0.803 0.700 0.769 -0.161 -0.893 -0.401 5.94 2133 0.522
0.40 0.212 0.423 0.311 0.831 -0.120 -0.867 -0.487 4.91 1954 0.538
0.50 -0.122 0.087 -0.025 0.884 -0.090 -0.846 -0.553 4.13 1782 0.556
0.75 -0.737 -0.562 -0.661 0.979 -0.046 -0.813 -0.653 3.07 1507 0.587
1.00 -1.133 -1.009 -1.080 1.036 -0.032 -0.798 -0.698 2.90 1406 0.613
1.50 -1.552 -1.538 -1.550 1.085 -0.044 -0.796 -0.704 3.92 1479 0.649
2.00 -1.699 -1.801 -1.743 1.085 -0.085 -0.812 -0.655 5.85 1795 0.672
Note: This relation is applicable for M 5.5 7.5 and distance no greater than 80 kilometers.
Appendix C 173
1.4 K. Sadigh, C. Y. Chang, J. A. Egan, F. Makdisi, and R. R. Youngs attenuation
relationship (1997)
Attenuation relationships are developed 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.
Historically, there are typically more data for peak acceleration than for response spectral
acceleration, and the set of digitized and processed accelerograms tends to be the larger
amplitude recordings from any individual earthquake. Therefore, the process used to
develop attenuation relationships consists of two stages. First, attenuation relations are
developed for PGA by regression analyses using the general form:
( )
ln( PGA) = C1 + C2 M + C3 ln rrup + C4 eC5M + C6 Z t
where,
M = Moment magnitude
rrup = Closest distance to the rupture surface.
Zt = Indicator variable taking the value 1 for reverse events and 0 for strike
slip events.
Different coefficients are developed for events larger and smaller than M 6.5 to
account for near-field saturation effects. In the second stage of the analysis, relationships
for apectral amplification (SA/PGA) are fit to the response spectral ordinate data
normalized by the PGA of the recordings. The form of the relation is:
(
ln( SA / PGA) = C7 + C8 (8.5 M ) 2.5 + C9 ln rrup + C4eC5M )
The final attenuation models for SA are obtained by combining the above two models.
The resulting parameters were then smoothed to produce attenuation relationships that
predict smooth response spectra over the full range of magnitudes ( M 4 to 8+) and
Appendix C 174
distances ( rrup 0 to 100 km). Tables C-7 and C-9 give the attenuation relations and the
(
ln( SA / PGA) = C1 + C2 M + C3 (8.5M ) 2.5 + C4 ln rrup + exp(C5 + C6 M ) + C7 ln rrup + 2 ) ( )
Period(s) C1 C2 C3 C4 C5 C6 C7
For M 6.5
PGA -0.624 1.0 0.000 -2.100 1.29649 0.25 0.0
0.050 -0.090 1.0 0.006 -2.128 1.29649 0.25 -0.0820
0.075 0.136 1.0 0.006 -2.131 1.29649 0.25 -0.0745
0.100 0.275 1.0 0.006 -2.148 1.29649 0.25 -0.0410
0.120 0.348 1.0 0.005 -2.162 1.29649 0.25 -0.0140
0.150 0.285 1.0 0.002 -2.130 1.29649 0.25 0.0
0.170 0.239 1.0 0.000 -2.110 1.29649 0.25 0.0
0.200 0.153 1.0 -0.004 -2.080 1.29649 0.25 0.0
0.240 0.060 1.0 -0.011 -2.053 1.29649 0.25 0.0
0.300 -0.057 1.0 -0.017 -2.028 1.29649 0.25 0.0
0.400 -0.298 1.0 -0.028 -1.990 1.29649 0.25 0.0
0.500 -0.588 1.0 -0.040 -1.945 1.29649 0.25 0.0
0.750 -1.208 1.0 -0.050 -1.865 1.29649 0.25 0.0
1.000 -1.705 1.0 -0.055 -1.800 1.29649 0.25 0.0
1.500 -2.407 1.0 -0.065 -1.725 1.29649 0.25 0.0
2.000 -2.945 1.0 -0.070 -1.670 1.29649 0.25 0.0
3.000 -3.700 1.0 -0.080 -1.615 1.29649 0.25 0.0
4.000 -4.230 1.0 -0.100 -1.570 1.29649 0.25 0.0
5.000 -4.714 1.0 -0.100 -1.540 1.29649 0.25 0.0
7.500 -5.530 1.0 -0.110 -1.510 1.29649 0.25 0.0
For M > 6.5
PGA -1.274 1.1 0.000 -2.100 -0.48451 0.524 0.0
0.050 -0.740 1.1 0.006 -2.128 -0.48451 0.524 -0.0820
0.075 -0.515 1.1 0.006 -2.131 -0.48451 0.524 -0.0745
0.100 -0.375 1.1 0.006 -2.148 -0.48451 0.524 -0.0410
0.120 -0.302 1.1 0.005 -2.162 -0.48451 0.524 -0.0140
0.150 -0.365 1.1 0.002 -2.130 -0.48451 0.524 0.0
0.170 -0.411 1.1 0.000 -2.110 -0.48451 0.524 0.0
0.200 -0.497 1.1 -0.004 -2.080 -0.48451 0.524 0.0
0.240 -0.590 1.1 -0.011 -2.053 -0.48451 0.524 0.0
0.300 -0.707 1.1 -0.017 -2.028 -0.48451 0.524 0.0
.0.400 -0.948 1.1 -0.028 -1.990 -0.48451 0.524 0.0
0.500 -1.238 1.1 -0.040 -1.945 -0.48451 0.524 0.0
0.750 -1.858 1.1 -0.050 -1.865 -0.48451 0.524 0.0
1.000 -2.355 1.1 -0.055 -1.800 -0.48451 0.524 0.0
1.500 -3.057 1.1 -0.065 -1.725 -0.48451 0.524 0.0
2.000 -3.595 1.1 -0.070 -1.670 -0.48451 0.524 0.0
3.000 -4.350 1.1 -0.080 -1.610 -0.48451 0.524 0.0
4.000 -4.880 1.1 -0.100 -1.570 -0.48451 0.524 0.0
5.000 -5.364 1.1 -0.100 -1.540 -0.48451 0.524 0.0
7.500 -6.180 1.1 -0.110 -1.510 -0.48451 0.524 0.0
Note: Relationships for reverse/thrust faulting are obtained by multiplying the above strike-slip amplitudes by 1.2.
Appendix C 175
Table C-8 : Dispersion Relationships for Horizontal Rock Motion; Sadigh et al. (1997)
Period (second) ln Y
PGA 1.39 0.14 M ; 0.38 for M 7.21
0.07 1.40 0.14 M ; 0.39 for M 7.21
0.10 1.41 0.14 M ; 0.40 for M 7.21
0.20 1.43 0.14 M ; 0.42 for M 7.21
0.30 1.45 0.14 M ; 0.44 for M 7.21
0.40 1.48 0.14 M ; 0.47 for M 7.21
0.50 1.50 0.14 M ; 0.49 for M 7.21
0.75 1.52 0.14 M ; 0.51 for M 7.21
1.00 1.53 0.14 M ; 0.52 for M 7.21
> 1.00 1.53 0.14 M ; 0.52 for M 7.21
( )
ln( SA / PGA) = C1 + C2 M C3 ln rrup + C4eC5M + C6 + C7 (8.5 M ) 2.5
where, C1 = -2.17 for strike-slip, -1.92 for reverse and thrust earthquakes
C2 = 1.0
C3 = 1.70
C4 = 2.1863, C5 = 0.32 for M 6.5
C4 = 0.3825, C5 = 0.5882 for M > 6.5
rrup = closest distance to rupture surface
Appendix C 176
1.5 P. Spudich, W. B. Joyner, A. G. Lindh, D. M. Boore, B. M. Margaris, and J. B.
Fletcher Attenuation Relationship (1999)
log10 (Y ) = b1 + b2 ( M 6) + b3 ( M 6) 2 + b5 log10 D + b6 ; D = r jb 2 + h 2
where,
M = Moment magnitude
r jb = Closest horizontal distance to the vertical projection of rupture surface.
b1, b2 ,............., b6 and h are regression coefficients that depend on period. Table C-10
gives the smoothed coefficients for regression relation SEA99, for geometric mean
horizontal peak ground acceleration and 5% damped pseudo-velocity. The standard
deviation of log10 (Y ) is given by:
log Y = 12 + 22
The terms 1 and 2 are the standard deviation of record-to-record variation and
Appendix C 177
Table C-10: Smoothed Coefficients for Regression Relation SEA99, for Geometric
Mean PGA and 5% damped PSV; Spudich et al. (1999)
Appendix C 178
2.0 Attenuation Relationships for Subduction Zone Earthquakes
These relationships predict the peak ground acceleration and response spectral
acceleration for subduction zone interface and intraslab earthquakes of moment
magnitude M=5 and greater and 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. 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 intraslab earthquakes produce peak motions that are about 50 percent larger than
interface earthquakes.
The attenuation models for rock site and soil site are given by the expressions:
( )
ln(Y ) = 0.2418 + 1.414M + C1 + C2 (10 M )3 + C3 ln rrup + 1.7818e0.554 M + 0.00607 H + 0.3846ZT
( )
ln(Y ) = 0.6687 + 1.438M + C1 + C2 (10 M )3 + C3 ln rrup + 1.097e0.617 M + 0.00648 H + 0.3643ZT
where
Y = Spectral acceleration in units of g.
M = Moment magnitude
rrup = Closest horizontal distance to the rupture surface.
The standard deviation is = C4 + C5 M . Table C-11 lists the regression coefficients for
rock and soil sites.
Appendix C 179
Table C-11: Regression Coefficients for Horizontal Response Spectral Acceleration (5%
damping) for Subduction Zones; Youngs et al. (1997)
For Rock
( )
ln(Y ) = 0.2418 + 1.414M + C1 + C2 (10 M )3 + C3 ln rrup + 1.7818e0.554 M + 0.00607 H + 0.3846 ZT
Standard Deviation, = C4 + C5 M
* *
Periods(sec) C1 C2 C3 C4 C5
PGA 0.000 0 -2.552 1.45 -0.1
0.075 1.275 0 -2.707 1.45 -0.1
0.100 1.188 -0.0011 -2.655 1.45 -0.1
0.200 0.722 -0.0027 -2.528 1.45 -0.1
0.300 0.246 -0.0036 -2.454 1.45 -0.1
0.400 -0.115 -0.0043 -2.401 1.45 -0.1
0.500 -0.400 -0.0048 -2.360 1.45 -0.1
0.750 -1.149 -0.0057 -2.286 1.45 -0.1
1.000 -1.736 -0.0064 -2.234 1.45 -0.1
1.500 -2.640 -0.0073 -2.160 1.50 -0.1
2.000 -3.328 -0.0080 -2.107 1.55 -0.1
3.000 -4.511 -0.0089 -2.033 1.65 -0.1
For Soil
( )
ln(Y ) = 0.6687 + 1.438M + C1 + C2 (10 M )3 + C3 ln rrup + 1.097e0.617 M + 0.00648 H + 0.3643ZT
Standard Deviation, = C4 + C5 M
* *
Periods(sec) C1 C2 C3 C4 C5
PGA 0.000 0 -2.329 1.45 -0.1
0.075 2.400 -0.0019 -2.697 1.45 -0.1
0.100 2.516 -0.0019 -2.697 1.45 -0.1
0.200 1.549 -0.0019 -2.464 1.45 -0.1
0.300 0.793 -0.0020 -2.327 1.45 -0.1
0.400 0.144 -0.0020 -2.230 1.45 -0.1
0.500 -0.438 -0.0035 -2.140 1.45 -0.1
0.750 -1.704 -0.0048 -1.952 1.45 -0.1
1.000 -2.870 -0.0066 -1.785 1.45 -0.1
1.500 -5.101 -0.0114 -1.470 1.50 -0.1
2.000 -6.433 -0.0164 -1.290 1.55 -0.1
3.000 -6.672 -0.0221 -1.347 1.65 -0.1
*
Standard deviation for magnitudes greater than M 8 set equal to the value for M 8.
Appendix C 180
2.2 Gail M. Atkinson, and David M. Boore Attenuation Relationships (1997a)
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. Upon comparison of
predicted ground motions 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 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. These relations predict the median horizontal peak
ground acceleration, peak ground velocity, and the spectral accelerations on rock sites in
the Cascadia region. The general form of the model is given by:
where,
Y = PGA (g), PGV(cm/s) or Spectral Acceleration (g)
M = Moment magnitude
rhypo = Hypocentral distance in kilometers
Table C-12 gives the regression coefficients for Cascadia 50-bar point source attenuation
model.
Appendix C 181
Table C-12: Cascadia 50-bar Point Source Model Coefficients for median
Horizontal Components on Rock Sites; Atkinson and Boore (1997a)
Appendix C 182
3.0 Attenuation Relationships for Stable Continental Region Earthquakes
A stochastic model is used to develop preliminary ground motion relations for the sites in
stable continental regions in eastern and central North America. The attenuation model
comprises simple quadratic equations that approximate the estimates for the purpose of
seismic hazard calculation. The quadratic equations were obtained by regression of a
subset of simulated ground-motion data. The subset includes all distance ( rhypo 500
km) for large events ( M > 6.5 ) but only near distances ( rhypo 25 km) for small events.
This constrains the attenuation to match the relatively slow decay of motions that is
applicable for large earthquakes. The coefficients of the quadratic prediction equations
are listed in Table C-13.
Table C-13: Regression Coefficients for Quadratic Equations; Atkinson and Boore (1997b)
SA, PGA in g, PGV in cm/s. SA is the pseudo-acceleration (5% damped) for the
random horizontal component on rock.
Period (sec) c1 c2 c3 c4
0.0500 2.762 0.755 -0.110 0.0052
0.0769 2.463 0.797 -0.113 0.0035
0.1000 2.301 0.829 -0.121 0.0028
0.1266 2.140 0.864 -0.129 0.0021
0.2000 1.749 0.963 -0.148 0.0011
0.3125 1.265 1.094 -0.165 0.0002
0.5000 0.620 1.267 -0.147 0.0000
0.7692 -0.094 1.391 -0.118 0.0000
1.0000 -0.508 1.428 -0.094 0.0000
1.2500 -0.900 1.462 -0.071 0.0000
2.0000 -1.660 1.460 -0.039 0.0000
PGA 1.841 0.686 -0.123 0.0031
PGV 4.697 0.972 -0.086 0.0000
Appendix C 183
APPENDIX D
TIME DOMAIN NUMERICAL PROCEDURES FOR SITE RESPONSE
ANALYSIS
D.1 Dynamic Properties and Equilibrium Equation for the Finite Element
Formulation of Soil Deposits
In order to model a horizontally layered soil deposit, it must be first discretized into an
equivalent shear beam finite element system. Figure D.1 shows a horizontally stratified
soil deposit, the corresponding finite element discretization, and a physically analogous
lumped mass system. Before the details of the numerical procedures are discussed, the
u1 u1
h1 G1 1 1
u2 u2
h2 G2 2 2
u3 u3
h3 G3 3 3
(a) (b) (c )
Figure D.1 Mathematical model of the soil profile (a) Idealized soil profile; (b) Finite element mesh;
and (c) Lumped mass model (adapted, Hart and Wilson, 1989)
Appendix D 184
dynamic property matrices and the equilibrium equations of the finite element system
(which are common to all of the analysis methods) must be developed.
Element Shape Functions: Utilizing the finite element formulations, each layer or sub-
layer of the soil profile is replaced by an element of unit cross sectional area (Figure D.2)
for which the shape functions N ( z ) are assumed to be linear for unit values of the nodal
displacements ui and u j :
z
ui = 1, u j = 0 : Ni ( z ) = 1
H
z
ui = 0, u j = 1 : N j ( z ) =
H
where z is the element coordinate and H is the element thickness. This displacement
pattern corresponds to pure shear deformation. Once the element shape functions have
been established, the displacements within an element can be interpolated based on nodal
displacements:
z z ui
u ( z ) = 1 u = Nu (D.1.1)
H H j
Y Y Y
uj = 0 uj =1
uj
G, ,
H
z
ui X ui = 0
X ui = 1
X
N ( z ) = (1 z / H ) N ( z) = ( z / H )
Figure D.2 Soil layer element shape functions (adapted, Hart and Wilson, 1989)
Appendix D 185
The shear strain within each element can likewise be computed from the nodal
displacements:
du ( z ) 1 1 ui dN
= = = u = Bu (D.1.2)
dz H H u j dy
where B is the strain-displacement matrix.
where G is the element shear modulus. The layer element stiffness matrices are added
into the global stiffness matrix using direct stiffness assembly:
# layers
K= kl (D.1.4)
l =1
with a half-bandwidth of two which enables the use of an extremely efficient numerical
solution scheme.
Element and Global Mass Matrices: It is possible to formally develop the layer element
mass matrix using the principle of virtual displacements. However, such an approach
would result in a matrix with the same coupling properties as the stiffness matrix. If a
physical lumped mass approximation is used, the element mass is diagonal, resulting in a
slight reduction in accuracy and a considerable savings in computer storage and time. In
this formulation, one half of the element mass is lumped at each node to obtain:
H 1 0
ml = (D.1.5)
2 0 1
Appendix D 186
where is the mass density of the layer element. The global mass matrix of the system
is generated by assembling the mass matrices of each layer element:
# layers
M= ml (D.1.6)
l =1
Element and Global Damping Matrices: Since the exact nature of damping forces on
an underdamped system is not well understood, and since the effect of these forces on the
transient response is generally small, a simplifying assumption regarding the nature of
these forces is justified. For most structural engineering applications, it is common to
assume that the damping matrix is a linear combination of the mass and the stiffness
matrices (proportional damping). Application of this assumption at the element level
results in the following form of the layer element damping matrix:
cl = l ml + l kl (D.1.7)
It is customary to determine the constants and for each element based on the
knowledge of the element damping ratio, , and the frequencies of the system. This is
because most of the experimental information regarding damping has been related to the
frequencies and mode shapes of the vibrating system. Two approaches for determining
the constants and are commonly employed: the first uses a single control frequency
and the second uses two control frequencies.
The determination of and based on the knowledge of the damping ratio and a
single vibration frequency is termed equivalent modal damping (Wilson, 1968). It can
be shown that the modal damping ratio i for the i th mode is given in terms of constants
and by:
i
i = + (D.1.8)
2i 2
where i is the frequency of the i th mode. For given values of and , the frequency
Appendix D 187
1/ 2
*
= (D.1.9)
If the minimum damping ratio * and the frequency * are given, the damping
coefficients and are calculated from the following equations:
= * * (D.1.10)
*
= (D.1.11)
*
The modal damping expression can now be rewritten as:
* i *
i = +
* 2
(D.1.12)
i
or in terms of period as:
Ti T * *
i = * + (D.1.13)
T Ti 2
Determination of and based on the knowledge of the damping ratio * and two
frequencies is termed damping with two mode control. Assuming that the damping ratio
is the same in modes i and j yields the following expressions for and :
2 *i j
= (D.1.14)
(i + j )
2 *
= (D.1.15)
(i + j )
Appendix D 188
1.0
1 T T* *
= +
2 T * T
0.8
Minimum Damping = 2.5%
Minimum Damping = 5.0%
Minimum Damping = 10.0%
0.6
Damping Ratio
0.4
0.2
0.0
0.01 0.1 1
(T / T * )
Figure D.3 Equivalent modal damping (adapted, Hart and Wilson, 1989)
This relationship between damping ratio and frequency is shown in Figure D.4. From the
figure, it can be seen that for frequencies i and j , the damping ratio is less than * ,
while for frequencies outside of this range, larger damping ratios are obtained.
Damping Ratio
i j
Circular Frequency
Figure D.4 Damping with control in two modes (after Hart and Wilson, 1989).
Appendix D 189
Once the element damping matrices have been determined, the global damping matrix
can be assembled as:
# layers
C= cl (D.1.16)
l =1
C is also a tri-diagonal matrix with a half-bandwidth of two. Because each soil layer
element in the finite element mesh can have a different damping ratio, the global
damping matrix assembled from the proportional element damping matrix is, in general,
non-proportional.
Dynamic Equilibrium Equations: Using the finite element formulation, the soil profile
is first discretized into layer elements, each of which is completely defined by a thickness
h , shear modulus G , mass density , and damping ratio . The element property
matrices are then assembled into the global property matrices, which can then be used in
the dynamic equilibrium equations for the site model:
1 = Unity vector
u&&g (t )
The discrete finite element formulation permits the expression of the dynamic
equilibrium of soil profile as a set of ordinary differential equations rather than the partial
Appendix D 190
differential equations required to describe the continuous profile model. The dynamic
equilibrium equations can be solved numerically by discretizing them in the time domain
with exact solution U (t ) , U& (t ) , and U&& (t ) approximated by U t , U& t , and U&&t ,
respectively.
Frequency domain procedures obtain the response of the site model by assuming that the
input and output ground motions are the summation of harmonic motions which are
related through a frequency domain transfer function. For the ground response problem,
transfer functions can be used to express various response parameters, such as
displacement, velocity, acceleration, shear stress, and shear strain, to an input motion
parameter such as bedrock acceleration. Frequency domain procedures involve
manipulation of complex numbers, and the mathematical aspects of the transfer function
approach and related complex analyses have been developed and implemented by
Schnabel et al. (1972), Seed et al. (1974), and Wolf (1985). A qualitative discussion of
these procedures is discussed in the following sections.
In the most basic form, the method of complex analysis assumes that the earthquake
loading, expressed here as a vector R (t ) , is a harmonic function of frequency ;
R (t ) = R ( )eit (D.2.1)
where the amplitude vector R( ) may be complex. This assumption implies that the
response (which may be a vector) is also harmonic. Hence,
U (t ) = U ( )eit (D.2.2)
where the response amplitude vector U ( ) is also, in general, complex. The amplitudes
of the harmonic input and output are related through frequency domain equations of
motion:
I ( )U ( ) = R( ) (D.2.3)
where I ( ) is the complex stiffness or impedance matrix of the finite element model,
which includes the resistance due to inertial, viscous, and static forces. The response
Appendix D 191
amplitude U ( ) can be obtained as a function of using the complex frequency
response function H ( ) :
U ( ) = H ( ) R ( ) (D.2.4)
The complex frequency response function is also called the compliance matrix or the
complex flexibility matrix and is equal to the inverse of the complex stiffness matrix:
1
H ( ) = I ( ) (D.2.5)
Once the vector of response amplitudes is determined, it can be used to generate the time
history of the response vector U (t ) .
Frequency domain analysis relies on the use of Fourier transformation and inverse
Fourier transformation to move from time domain to the frequency domain and back (see
Chapter 4). The essential operations in the procedure for estimating the site response in
the frequency domain are as follows:
- On the basis of mass, stiffness, and damping matrices of the site model, obtain the
impedance matrix of the system, I ( ) .
1
H ( ) = I ( ) (D.2.7)
- Obtain the response amplitudes from the Fourier transform of the earthquake load
vector and the compliance matrix:
U ( ) = H ( ) R ( ) (D.2.8)
- Transform the response amplitude vector to the time domain using the inverse
Fourier transform:
Appendix D 192
it
U (t ) = U ( )e d (D.2.9)
The frequency domain procedures rely on the principle of superposition and hence this
approach can only be applied to analysis of linear systems. True nonlinear site response
can be approximated, however, using time domain procedures.
This section briefly presents various time domain numerical procedures, as implemented
in EQTools, for the earthquake response analysis of soil deposits modeled as one-
dimensional shear beam element systems.
For linear systems, the solution of dynamic equilibrium equations can be obtained either
by the mode superposition method or by the direct integration method. Since the standard
mode superposition method is applicable only to proportionally damped systems, direct
integration techniques are used in EQTools to obtain the solution. The basic idea behind
direct integration is to begin with the known initial conditions of motion and to move
ahead in time computing solution states at discrete time intervals. Various references are
available that discuss the stability and the computational errors involved in different
numerical integration schemes (Bathe and Wilson, 1976; Hughes, 1976; Chopra, 2000).
1
U t +t = U t + tU& t + t 2 U&&t + t 2 U&&t +t (D.3.2)
2
U& t +t = U& t + t (1 )U&&t + t U&&t +t (D.3.3)
Appendix D 193
These equations constitute three vector equations for determining three vector unknowns;
U t +t , U& t +t , and U&&t +t . Value of < 1/ 2 will introduce positive numerical damping in
the solution while values > 1/ 2 introduce negative numerical damping (which in effect
adds spurious energy to the system). For = 1/ 2 , no numerical damping is introduced to
the solution. These observations, coupled with the fact that second order accuracy is
achieved if and only if = 1/ 2 , essentially forces the selection of = 1/ 2 . The
parameter controls the assumed shape functions of the nodal accelerations across the time
interval t . The most common selections of and are:
assumes a constant acceleration vector with a value of 1/ 2(U&&t + U&&t +t ) over the time
step. This assumption results in a linear variation in velocity and quadratic variation
in displacement over time step (Figure D.5).
variation of acceleration vector between U&&t and U&&t +t over time step. This
assumption results in a quadratic variation in velocity and cubic variation in
displacement over time step (Figure D.6).
The Wilson- method (Bathe and Wilson, 1976) is a modification of the linear
acceleration method. The technique includes satisfying equilibrium at a time t + t and
then interpolating (based on linear acceleration) to calculate the state of motion at a time
t + t for use as initial condition for the next time step. An unconditionally stable
method with large damping in the higher modes is produced with = 1.4 .
Appendix D 194
u&& u& u
u&&t +t u&t +t ut +t
u&&t u&t ut
t t t
t t + t t t + t t t + t
(a) (b ) (c )
Figure D.5 Time domain shape functions for Constant Average Acceleration method (a) acceleration
constant; (b) Velocity linear variation; and (c) displacement quadratic variation.
u&& u& u
u&&t +t u&t +t ut +t
u&&t u&t ut
t t t
t t + t t t + t t t + t
(a ) (b ) (c )
Figure D.6 Time domain shape functions for Linear Acceleration method (a) acceleration linear
variation; (b) Velocity quadratic variation; and (c) displacement cubic variation.
Appendix D 195
Assemble global matrices : K , M and C
Update maxima
Yes
Is t < duration?
No
Stop
Figure D. 7 Summary of the algorithm TSTEPS for integrating dynamic equilibrium equations for
a tri-diagonal system using Newmark-Wilson scheme (adapted, Hart and Wilson, 1989)
1 1 1
Note 1: = t ; a0 = ; a1 = ; a2 = ; a3 = 1 ; a4 = 1 ; a5 = 2 ; a6 = t (1 ) ;
( 2 ) ( ) ( ) 2 2
1
a7 = t ; a8 = t 2 ; a0 = t 2
2
1
Note 2: U&&t + = a0 (U t + U t ) a2U& t a3U&&t ; U&&t +t = U&&t + (U&&t + U&&t ) ; U& t +t = U& t + a6U&&t + a7U&&t +T ;
U t +t = U t + tU& t + a8U&&t + a9U&&t +t
Appendix D 196
D.3.2 Equivalent Linear Earthquake Response Analysis
Since it is known that soils can exhibit nonlinear behavior, even at small strain
amplitudes, it is important to appropriately account for the effects of nonlinearity on the
earthquake response of a soil profile. In many cases, the use of an equivalent linear site
model has been found to provide a satisfactory means of evaluating the nonlinear seismic
response characteristics of a soil profile (Schnabel et al., 1972). The procedure involves
performing a linear analysis using strain-compatible dynamic stiffness and damping
properties selected to qualitatively represent the effects of nonlinear behavior in each
layer.
For a single hysteretic strain cycle in a given layer, equivalent linear dynamic properties
can be determined graphically as shown in Figure D.8. The equivalent shear modulus,
Geq , is the slope of the line connecting the two unloading points, while the equivalent
Geq
C
O D
W = area of loop
W = areas (OAD + OBC )
1 W
eq =
B 2 W
Figure D.8 Definition of equivalent shear modulus and equivalent shear damping for a single
hysteretic cycle (after Hart and Wilson, 1989)
hysteretic layer to that dissipated in the viscous layer over the cycle (Jacobsen, 1960). For
multiple hysteresis cycles in a given layer, the equivalent linear properties can be
Appendix D 197
obtained by using the average of the properties for each cycle, or equivalently by using a
graphical approach on the hysteresis cycle corresponding to the average or effective
strain developed during the cycling. Empirical observations indicate that for cyclic shear
strain histories, the ratio of effective strain to maximum strain is between 0.5 and 0.7
(Schnabel, 1972). Relationships between equivalent linear dynamic properties and
effective strains have been established for various soil types (Hardin and Drnevich, 1972;
Idriss et al., 1976; Seed and Idriss, 1970). The trends observed in typical soil types are
that the shear modulus and damping ratio decrease and increase, respectively, with
increasing effective strain values (Figure D.9).
G
Gmax
1.0
eff
max
1.0
eff
Figure D.9 Strain dependent dynamic properties for soil (after Hart and Wilson, 1989)
Appendix D 198
The fundamental idea behind the application of equivalent linear analysis to the
earthquake response of soil profiles is that after some iteration to obtain strain compatible
dynamic properties, a qualitative representation of the true nonlinear response of the
profile can be obtained. The steps involved in the analysis are as follows:
assumed to be between 0.55 and 0.65 (Schnabel, 1972) with the larger value
appropriate for giving more uniform strain histories.
- Using the effective strains, update the shear modulus and damping ratio for each
layer using the strain dependent curves (Figure 7.10).
The above steps are repeated until the difference between the modulus and damping used
and the strain compatible modulus and damping ratio are less than some acceptable
difference for each layer. A FORTRAN subroutine, ITERAT, has been developed for use
in equivalent linear iterative response analysis of soil profiles. The algorithm is
summarized in Figure D.10.
Appendix D 199
Form global mass matrix, M
STEP 1
Call the algorithm for integrating dynamic equilibrium equations for a tri-diagonal
system using Newmark-Wilson scheme.
STEP 5
STEP 4
No
STEP 5
Stop
Figure D.10 Summary of algorithm ITERAT for equivalent linear earthquake response analysis
(adapted, Hart and Wilson, 1989)
Appendix D 200
D.3.3 Nonlinear Earthquake Response Analysis
During cyclic loading, the stress-strain behavior of soils is nonlinear and hysteretic, hence
the earthquake response of soil profiles may be influenced significantly by nonlinear
effects. The discrete finite element site model can be used to approximate the nonlinear
response of soil profiles by implementing soil layer elements whose nonlinear hysteretic
properties are representative of soil behavior. Appendix D discusses the Ramberg-
Osgood hysteresis model which has been used in EQTools to represent the constitutive
relationship of soil layer elements. The discrete finite element site model is extended to
the nonlinear earthquake analysis of soil profiles.
The instantaneous dynamic equilibrium equations of the finite element site model can be
expressed in vector form as:
RI + RD + RS = RE (D.3.4)
where
RI = Vector of inertial resisting force
RD = CU& (D.3.6)
RS = KU (D.3.7)
For a linear system, equilibrium can be satisfied at discrete time intervals using step-by-
step integration, as discussed in Section D.3.1. In the analysis of the system whose
elements have nonlinear stress-strain behavior, the global stiffness matrix becomes a
function of the time varying nodal displacements and the element constitutive
relationships, i.e., K = K (U ) . In such systems, the static resisting force vector can no
Appendix D 201
longer be determined as above. Rather, it must be determined indirectly from the nodal
displacements using the element constitutive relationships:
RS = R( S ) (D.3.8)
The application of step-by-step integration to systems with nonlinear stiffness properties
results in a loss of equilibrium at the end of each time step. The instantaneous unbalance
can be expressed as:
RU = RE RI RD RS (U ) (D.3.9)
If the unbalanced forces are allowed to accumulate over successive time steps, substantial
errors can be introduced into the solution. Hence it is apparent that the step-by-step
solution strategy must be appropriately modified to account for equilibrium errors in
order to ensure accurate solutions. Several methods have been developed to deal with the
loss of equilibrium at a time step for nonlinear dynamic analysis (Allahabadi, 1987;
Ghose, 1974; Golafshani, 1981) but the choice of solution strategy is largely problem
dependent and must be selected with judgment. Because the Ramberg-Osgood hysteresis
model (see Figure D1.1) provides a continuous stress-strain relationship for a given
branch of the hysteresis loop but is discontinuous between branches (at unloadings), a
solution strategy which implements tangent stiffness iteration within a branch and an
event-to-event scheme between the branches is employed.
Iteration Strategy: To correct the equilibrium errors at the end of a time step, a Newton
type iteration scheme has been selected. This is because the element constitutive model
(Ramberg-Osgood) provides a continuous relationship between stress and strain on a
given branch of the hysteresis loop. Within a branch, the Ramberg-Osgood function is
well behaved and the tangent stiffness is continuously defined; these conditions are
critical for convergence with the Newton method. The essential features of the iteration to
satisfy equilibrium can be investigated by considering the relationship between dynamic
load and displacement for a SDOF system. Figure D.11 shows the dynamic load versus
displacement in the R-U plane. The steps corresponding to Figure D.11 are as follows:
Appendix D 202
1. An equilibrium state has been obtained at time t . The state is defined by the
instantaneous displacement, velocity, acceleration, static resisting force, and
R* = K *U (D.3.10)
then calculating the tentative acceleration, velocity, and displacement based on
the numerical integration scheme.
3. The static resisting force and the tangent stiffness corresponding to the tentative
displacement ( U tent ) are obtained from the constitutive relationship:
RS = RS (U tent ) (D.3.11)
K * = K * (U tent ) (D.3.12)
R
Ru (2)
Ru (1)
RE
equilibrium state
at time = t + t
equilibrium state
at time = t
Figure D.11 Schematic of Newton iteration (after Hart and Wilson, 1989)
4. The unbalance between the dynamic load RE and the tentative internal resisting
Appendix D 203
RU = RE MU&&tent CU& tent RS (U tent ) (D.3.13)
5. If the unbalance is unacceptably large, the solution is advanced to a new tentative
state by solving the following pseudo static equation for the incremental
displacement:
RU = K *U (D.3.14)
6. Steps 3, 4, and 5 are then continued until the unbalanced force is smaller than the
acceptable level, at which point the tentative state becomes the equilibrium state
at time t + t .
The number of iterations within a given time step depends on the degree of nonlinearity
and the step size, but for earthquake analysis of moderately nonlinear soil profiles, only a
few iterations should provide acceptable accuracy.
The Ramberg-Osgood model satisfies the Masing criterion (Iwan, 1967) which dictates
that the unloading and reloading branches of the hysteresis loop are the same backbone
curve with both stress and strain scales expanded by a factor of two and the origin
translated. One consequence of this stipulation is that the unloading stiffness is equal to
the initial stiffness. Physically, element unloading occurs when the element strain rate has
a zero crossing, or in discrete time, when two subsequent strain increments are of
opposite sign. The method used to capture unloading events within the step-by-step
integration scheme is as follows:
1. At the beginning of the time step, the incremental shear strains are determined
from the incremental displacements using the strain-displacement transformation:
= BU (D.3.15)
Appendix D 204
2. The strain increment of each layer element is compared to the corresponding
strain increment from the previous step. If the strain increments are of opposite
sign, then unloading has occurred in the selected layer element during the time
step. The shear modulus of each unloading element is set to the unloading shear
modulus.
3. If unloading occurred, the global stiffness matrix is reformed based on the
updated shear moduli and the time step is restarted.
This type of event-to-event scheme was developed by Ghose (1974). This procedure is
not exact because it assumes that unloading occurs at time t when in reality, unloading
occurs somewhere between times t and t + t . However, for the small time steps
encountered in earthquake response analysis, the errors generated by this method are not
expected to be significant.
Automatic Time Step Control: The idea behind most step-by-step integration
techniques is to satisfy the dynamic equilibrium equations of the finite element system at
discrete time intervals. As the integration time step is reduced, the discretization errors
tend to zero and the numerical solution approaches the exact solution. Hence, the
appropriate selection of the integration time step is critical for generating accurate
numerical solutions. It is common for an analyst to select an integration time step,
perform the dynamic analysis, then rerun the analysis with a smaller time step until only
small differences exist between subsequent solutions. Although this technique does
ensure that
Appendix D 205
Form global matrices: K , M and C
A
Set initial conditions: U 0 , U& 0 and U&&0
Stop
A
Figure D.12 Summary of the algorithm WALK to perform nonlinear earthquake response analysis of soil profiles implementing the combination iteration and event-to-
event strategy with CAA integration method (adapted from Hart and Wilson, 1989)
Appendix D 206
the numerical solution will not change with further decrease in the time step, it wastes a
tremendous amount of computational time and effort. Therefore, a more efficient
procedure is desired. A procedure (Allahabadi, 1987) has been implemented in EQTools
in which the accuracy of the numerical solution is controlled by increasing or decreasing
the integration time step as the analysis progresses based on a measure of the mean
equilibrium error over a time step. This procedure represents an attempt to balance the
tradeoff between solution accuracy and computational efficiency for the earthquake
response analysis of soil profiles.
Within a given time step, if the vectors of the inertia forces, damping forces, static forces,
and external loads varied linearly with time, the equilibrium errors would be zero at all
times. If the CAA method is applied to a linear system, the variation of the dynamic force
vectors over the time step is shown in Figure D.13. By considering the time average of
the difference between the assumed force variations and a linear variation over the time
step, a measure of the mean equilibrium error over the step can be computed. Because the
inertial and damping forces are constant and linear, respectively, over the time step, the
time average of the difference between these distributions and a linear distribution
integrates to zero (see Figure D.13). However, the error due to static forces varies
quadratically and has a nonzero mean value given by:
t
Em = K U& (D.3.16)
12
For a nonlinear system which utilizes an iteration strategy, the stiffness matrix K may
vary over the time step and this equation for mean static error is no longer valid.
However, by using an effective stiffness matrix, K eff , based on the element states at the
beginning and end of the time step (see Figure D.14), the mean equilibrium error of the
system can be approximated by replacing K with K eff .
Appendix D 207
MU&& CU& KU
MU&&t +t CU& t +t KU t +t
mean error
t
CU& t = K U&
MU&&t KU t 12
t t t
t t + t t t + t t t + t
(a) (b ) (c )
Figure D.13 Variation of internal forces for a linear system using CAA method (a) inertial forces
constant; (b) damping forces linear variation; and (c) static forces quadratic variation
In order to perform earthquake response analysis with automatic step size control, a
tolerance for the mean equilibrium error over the time step is specified. If the norm of the
mean equilibrium error vector exceeds the tolerance, then the time step is halved and the
step is repeated with the new time step. If the error norm is less than the tolerance for a
user-specified number of time steps (implying that t is unnecessarily small), then the
time step is doubled and the step is repeated. It should be borne in mind that the
maximum time step cannot exceed the time step of the input earthquake acceleration if
the loading is to be properly discretized. Methods for determining appropriate tolerances
t +t
Geff
t t +t
Figure D.14 Schematic for determination of effective shear stress over time step (after Hart and
Wilson, 1989)
Appendix D 208
on the mean equilibrium error have been developed (Allahabadi, 1987) or may be
developed with experience and by comparison with the results of constant time step
analyses.
Appendix D 209
Form global matrices: K , M and C A
Set initial conditions: U 0 , U& 0 and U&&0 Calculate resisting force, RS and update shear moduli, G :
Rs = Rs (U tent ) ; G = G ( tent )
Compute dynamic portion of dynamic Reform stiffness based on current shear moduli, G :
stiffness matrix, D : D = a1M + a4C K = K (G )
Form dynamic stiffness, K * : K * = K + D Form effective stiffness for time step control:
increase time step: t = 2t
K eff = K eff (Geff )
Set change flag, ichange =1
* *
Solve for incremental displacement vector, U : K U = R Start step counter, icount = 1
Calculate mean equilibrium error vector over time step:
Compute layer strain increments, : = BU Reduce time step: t = t / 2 E = (t /12) K eff U&
Set change flag, ichange =1
Start step counter, icount = 1
E tolerance
Unloading Yes Reform K based on unloading E > tolerance Compare icount < nmax
occurred? shear moduli; K = K (G )
E and
No
Update tentative state of motion
E tolerance and icount = nmax
Iter = 0 Iter = 1
U&&tent = U&&t + a1U a2U& t a3U&& U&&tent = U&&tent + a1U Unset change flag, ichange = 0
U& tent = U& tent + a4 U Increment step counter,
U& tent = U& t + a4U a5U& t icount=icount+1
U tent = U tent + U Yes Is t < duration?
Perform energy balance
No
A
Update maxima
Stop
Go to STEP 3
Figure D.15 Summary of algorithm AUTO for linear or nonlinear earthquake response analysis of soil profiles implementing iteration and event-to-event strategy
including automatic time step control (adapted from Hart and Wilson, 1989).
Appendix D 210
APPENDIX D1
The Ramberg-Osgood hysteresis model (Ramberg and Osgood, 1943) was developed to
model the stress-strain relationships of steel using three control parameters. Jennings
(1963) modified the relationship by adding a fourth control parameter. The model
calculates strains or deformations as an explicit function of stress or forces. As shown in
Figure D1.1, the relationship is defined by two functions, one for loading on the primary
curve and one for unloading:
Loading:
( 1)
d f f
= 1 + (D1.1)
dc fc fc
Unloading:
( 1)
d d0 f f 0 f f0
= 1+ (D1.2)
2d c 2 fc 2 fc
where:
f = current force
d = current deformation
f c = control force
dc = control deformation
Appendix D1 211
Figure D1.1 shows the range of nonlinearity that can be obtained by varying the
parameter . = 1 will produce a linear-elastic primary curve, while = will produce
an elasto-plastic primary curve.
In the state determination phase of a nonlinear analysis, the function of the hysteresis
model is to return the state of an element after an increment of strain or deformation is
imposed. The element state essentially consists of the internal stress or resisting force and
the tangent modulus. In order to implement the Ramberg-Osgood model into a
displacement method of analysis, it must be modified to obtain the stress or force as a
function of strain or deformation. This is accomplished by applying a Newton-Raphson
iteration scheme to the one-to-one correspondence between force and deformation given
by the Ramberg-Osgood functions.
The most important aspect of the practical use of the Ramberg-Osgood model is the
proper selection of the four control parameters: f c , dc , , . The control force and control
Gmax = Vs 2
For relatively small values of , the tangent modulus is equal to f c / dc only for a very
limited range of deformation, while for relatively large values, the tangent modulus is
equal to f c / dc for a much larger range of deformations. Once a value of the control
Appendix D1 212
deformation dc is selected, the control force f c is computed based on the above
relationships.
Techniques for determining the parameters and for various materials have been
developed by many researchers (Streeter et al., 1974; Richart, 1975; Idris et al., 1976;
Singh et al., 1978). The basic approach to determine the parameters requires knowledge
of the force-deformation relationship of the material. A plot is made of the log of the
departure from linearity of the deformation versus the applied force. Examination of the
primary loading curve relationship indicates that the departure from linearity is given by:
f
log( ) + log c
dc
Thus, and are the intercept and the slope of the straight line which best fits the data
of the semi-logarithmic plot. In one investigation (Singh et al., 1978) the hyperbolic
modulus and damping curves proposed for soils by Hardin and Drenovich (1972) were
best fit by using:
f c = 0.8 f max
= 1.0
= 3.0
When measured stress-strain data for a given material is unavailable, results from other
investigations can be used. Experiments performed on various soil samples indicate that
the approximate ranges
1.0 < < 4.0 0.3 < < 3.0
may be appropriate (Richart, 1943; Streeter et al., 1974; Singh et al., 1978). In any case,
the ideal selection of the Ramberg-Osgood parameters requires at least the basic
information on the soil properties and the application of engineering judgment.
Appendix D1 213
f
d0 , f0
Loading:
( 1)
d f f
= 1+
dc fc fc
d
d0 , f0
Unoading:
( 1)
d d0 f f 0 f f0
= 1+
2d c 2 fc 2 fc
f
fc =1
1< <
1 =
1+ d
1
dc
Figure D1.1 Ramberg-Osgood Hysteresis Model (after Hart and Wilson, 1989)
Appendix D1 214
APPENDIX D2
[ dU ]T MU&&t + CU& + KU = 0
where U&&t is the vector of total nodal accelerations. Making the substitution
dU = dU t 1du g into the first term of the above equation and rearranging terms results
Each of these scalar differential energy terms can be expressed in the general form:
dE = [ dU ] R = RT dU
T
E = RT dU
Appendix D2 215
Physically, this integral represents the area under the force-displacement curve for each
component of the R and U vectors. Integrating each differential energy term would
yield the energy balance for the system. Because the inertia forces are linear in
acceleration, the damping forces are linear in velocity and the static forces are linear in
displacement (for linear systems), the external load required for equilibrium is obviously
a complex function of displacement, velocity and acceleration. These observations
indicate that the energy integrals as expressed above are, in general, quite difficult to
evaluate.
Step-by-step integration schemes do not generally satisfy energy balance, even for linear
systems (Allahabadi, 1987). However, for integration schemes which satisfy equilibrium
at discrete time intervals, pseudo-work expressions can be developed as
approximations to the actual energy quantities. The incremental pseudo-work or energy
approximations are expressed in the general form:
E = [ U ] Rave = [ Rave ] U
T T
where Rave is defined by the values of R at the beginning and end of the time step, i.e.,
1
Rave = ( Rt + Rt +t )
2
The pseudowork terms represent trapezoidal approximations to the area under the
force-displacement curves for each component of the various R and U vectors. The
evolution of the energy distribution in the finite element model is approximated by the
summation of the incremental pseudowork terms over all the time steps:
E E
It should be noted that for numerical integration using small time steps, the pseudo-
work equations provide reasonable approximations to the actual energy balance
equations. EQTools can optionally compute the time history of the pseudo-work
Appendix D2 216
approximations of the earthquake energy balance of the soil profile modeled as one-
dimensional shear beam elements.
Appendix D2 217
APPENDIX E
Appendix E 218
vpi&su
eqtools 2.0
Computational Tools for Characterization, Evaluation, and Modification of
Strong Ground Motions within Performance-Based Seismic Design
Framework.
Users Guide
http://www.cee.vt.edu
Appendix E 219
The department of Civil Engineering at Virginia Polytechnic Institute and State University (VPI&SU) owns
both the EQTools software program and its documentation. Both the program and documentation are
copyrighted with all rights reserved by VPI&SU. No part of this publication may be produced, transmitted,
transcribed, stored in a retrieval system, or translated into any language in any form without the written
permission from, Department of Civil and Environmental Engineering, VPI&SU.
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.
Copyright 2003 Virginia Polytechnic Institute & State University. All rights reserved.
Microsoft, Windows, and the Windows logo are registered trademarks of Microsoft Corp. Windows NT is a
trademark of Microsoft Corp.
Other brand names and product names referred to are trademarks or registered trademarks of their
respective owners.
November, 2003
Appendix E 220
Contents
ABOUT THE USERS GUIDE................................................................................................................ 223
1: WELCOME TO EQTOOLS............................................................................................................... 224
What is EQTools?.................................................................................................................................. 224
Application Design and Concepts.......................................................................................................... 225
System Requirements ............................................................................................................................ 225
Installing EQTools................................................................................................................................. 226
Technical Support.................................................................................................................................. 227
Acknowledgements................................................................................................................................ 227
2: STRONG GROUND MOTION DATABASE.................................................................................... 229
About the Strong Ground Motion Database .......................................................................................... 229
Sources of Ground Motion Records ...................................................................................................... 229
Adding Records to the Database............................................................................................................ 230
File Naming Convention for Time History Files ................................................................................... 233
Data Format for Strong Motion Time History Files .............................................................................. 233
3: GROUND MOTION DATABASE SEARCH TOOLS ..................................................................... 236
Main Program Window ......................................................................................................................... 236
EQTools Database Search Engine ......................................................................................................... 237
Database Search Parameters .................................................................................................................. 237
Searching for Records in EQTools Environment .................................................................................. 244
Viewing the Details of Searched Records ............................................................................................. 245
Selecting Records for Study .................................................................................................................. 247
Sorting the Searched and Selected Records........................................................................................... 248
Rotation of Horizontal Components of Time Histories ......................................................................... 249
Saving, Opening, and Printing Bin of Earthquakes ............................................................................... 249
A Final Word on Record Search and Selection ..................................................................................... 252
4: INVESTIGATING AMPLITUDE AND DURATION PARAMETERS......................................... 253
Generating Time History Plots .............................................................................................................. 253
Time History Plots for Single Record.................................................................................................... 254
Time History Plots for Multiple Records............................................................................................... 257
Time History Plot Controls.................................................................................................................... 259
Creating Time History Files .................................................................................................................. 263
Investigating Incremental Velocities ..................................................................................................... 264
Investigating Incremental Displacements .............................................................................................. 266
Investigating Bracketed Durations......................................................................................................... 267
5: FOURIER AMPLITUDE SPECTRUM............................................................................................. 268
Generating Fourier Amplitude Spectrum using EQTools...................................................................... 268
Fourier Amplitude Spectrum for a Single Record ................................................................................. 270
Fourier Amplitude Spectrum for Multiple records ................................................................................ 271
Fourier Amplitude Spectrum Plot Controls ........................................................................................... 272
Exporting the Computed Fourier Amplitude Spectra Data.................................................................... 277
Fourier Amplitude Spectrum Analysis Tools ........................................................................................ 278
6: ELASTIC RESPONSE SPECTRA AND SCALING OF TIME HISTORIES ............................... 285
Generating Elastic Response Spectra Using EQTools........................................................................... 285
Generating Elastic Response Spectrum for a Single Record ................................................................. 286
Generating Elastic Response Spectra for Multiple Records .................................................................. 287
Response Spectrum Plot Controls.......................................................................................................... 288
Appendix E 221
NEHRP Design Spectrum...................................................................................................................... 292
Scaling of Elastic Response Spectra for Selected Records.................................................................... 293
Saving the Scaled Bin of Earthquakes ................................................................................................... 296
Exporting the Computed Response Spectrum Data and Printing .......................................................... 297
Generating and Saving DrainPro Data Files .......................................................................................... 297
7: GROUND MOTION ATTENUATION TOOLS............................................................................... 298
Overview of Ground Motion Attenuation Relationships ....................................................................... 298
Ground Motion Attenuation Relationships ............................................................................................ 304
Ground Motion Attenuation Plot Controls ............................................................................................ 313
Exporting the Computed Attenuation Data and Printing ....................................................................... 314
8: SITE RESPONSE ANALYSIS USING EQTOOLS.......................................................................... 315
OVERVIEW OF SITE RESPONSE ANALYSIS PROCEDURES ......................................................................... 315
ANALYSIS CONTROL INFORMATION FOR SITE RESPONSE ....................................................................... 316
BASE INPUT GROUND MOTIONS ............................................................................................................. 317
GEOMETRIC AND DYNAMIC PROPERTIES OF SOIL MODEL ...................................................................... 318
RUNNING THE SITE RESPONSE ANALYSIS ............................................................................................... 319
INTERPRETING THE SITE RESPONSE ANALYSIS RESULTS ........................................................................ 320
REFERENCES ......................................................................................................................................... 322
APPENDIX A .......................................................................................................................................... 325
List of Strong Ground Motions in EQTools Database.......................................................................... 325
INDEX ....................................................................................................................................................... 326
Appendix E 222
About the Users Guide
This Users Guide contains an introduction to EQTools features and environment,
including resources available in the application for getting more out of EQTools.
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.
Appendix E 223
1: Welcome to EQTools
What is EQTools?
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 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 so 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 available an
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
1
EQTools, Copyright 2003, Virginia Polytechnic Institute and State University, Blacksburg, Virginia.
2
Windows is a trademark of Microsoft Corporation, Redmond, Washington
Appendix E 224
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.
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 Microsofts Visual Basic 6.0, Enterprise
Edition.
System Requirements
For best results, your system's video should be set to 1024 by 768 resolution,
displaying not less than 256 simultaneous colors. 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 1.10, the following are recommended or required:
Appendix E 225
Mouse or compatible pointing device
At least 200MB of disk space
Installing EQTools
Note This installation of EQTools 2.0 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 EQTools CD. The installation
procedure given below will work for both Windows NT V4.0 and Windows 95(or later
versions).
4. Follow the setup instructions on the screen. EQTools and associated compressed
files are expanded and placed in the newly created C:\Program
Files\EQTools20 directory by default. You can change a different directory
name during the setup process.
You can run EQTools from the Start button on the Taskbar, highlighting Programs, and
then clicking on the EQTools 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.
Appendix E 226
COMDLG32.OCX, IGTHREED40.OCX, IGRESIZER40.OCX, RICHTX32.OCX,
VSVIEW20.OCX, VSVIEW60.OCX, VSFLEXG3.OCX, VSFLEX6.OCX,
VSPRINT8.OCX
Do not delete or move these files. If any or all of these files are accidentally deleted from
the C:\WINDOWS\SYSTEM32 directory, you will have to run SETUP again to replace
them.
Technical Support
To obtain a copy of EQTools software, the EQTools Users Guide or for technical
support or questions relating to EQTools 2.0, the following persons may be contacted:
Riaz Syed
Department of Civil Engineering
Virginia Polytechnic Institute and State University
309J Patton Hall
Blacksburg, VA 24060
Telephone: (540) 231-3974
Fax: (540) 231-7532
e-mail: rsyed@vt.edu
Acknowledgements
Appendix E 227
entirely by the developer. Funding was provided through a grant from the Federal
Emergency Management Agency (FEMA).
EQTools 2.0 was written in Microsoft Visual Basic Enterprise Edition, Version 6.0. The
files MHPFST.VBX and MHRUN400.DLL are part of the IOTech VisuaLab-GUI
system.
Appendix E 228
2: Strong Ground Motion Database
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 755 records of engineering
interest from tectonically active regions. Three orthogonal components are available for
each recording in the database. 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. Appendix-A gives a comprehensive list
of earthquakes that contribute to the ground motion records in the database along with the
important characteristics of the event. 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 2000 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:\PROGRAMFILES\EQTOOLS20
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.
Appendix E 229
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
USGS United States Geological Survey
VADVA VA Department of Veterans Affairs
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:
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
Appendix E 230
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 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 MaxMagAnyneeds to be
calculated by the user)
Field Directivity - Whether near-field record or not. This filed has following
possible entries:
- Near Field (Distance <= 20 Km)
- Near Field (Classified)
- Far Field
Appendix E 231
Field DistClose - Closest distance to the fault (in Kilometers)
Type "999999999" if not known
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 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 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
Appendix E 232
File Naming Convention for Time History Files
The strong motion data files in the database contain the acceleration, velocity and
displacement records at a constant time step. 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. 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.
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 a 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),
Berkeley. PEER has separate files for acceleration, velocity and displacement time
histories. However, 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
respectively, in that order.
Appendix E 233
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.
A partial listing of the file IMPVSUPH135.ACC is given below. The lines with . in
column 1 indicate data that was eliminated from the record for brevity.
Appendix E 234
Example Acceleration Record for Imperial Valley Earthquake:
Appendix E 235
3: Ground Motion Database Search Tools
After EQTools is started, the main EQTools window automatically appears. This
windows is shown below.
The EQTools main window consists of a title bar and a menu bar. This window is always
open, and serves as a "container" for all other windows used by the 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 and version.
The search query form, the main entry into the program environment is accessed by the
following option:
Appendix E 236
EQTools Database Search Engine
The search query form in EQTools environment is accessed by File Search Database
for Records. This action brings up the following window. Through the inputs in this
window the user can search the database for ground motion records by various
parameters or a combinations of the parameters.
The user can search the database by 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 is
"Any".
Appendix E 237
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 value is "Any".
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 non-dominant orthogonal horizontal components. The available options for
these parameters are shown below. The default value is "Horizontal" component.
Appendix E 238
Mechanism : This parameter lets the user search a record on the basis of mechanism of
the fault causing the earthquake. The available options for these parameters are shown
below. The default value is "Strike-Slip" component.
Record Field: 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:
Magnitude or Peak Ground Acceleration (PGA) : This control allows the user to
search the records on the basis of 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.
Appendix E 239
The user can choose between the Magnitude or PGA by using the radio buttons (see the
picture below).
For the magnitude, the user has further choices he/she can make depending upon the
type of magnitude one is interested in. The following magnitude types are available:
Appendix E 240
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".
For the distance, the user has further choices he/she can make depending upon the type
of distance one is interested in. The following distance types are available:
The type of distance is chosen by using the option buttons (as shown above).
Appendix E 241
Site Classification: This control allows the user to search the records on the basis of
USGS Site Classification (1997) of the site where the ground motions have been
recorded. The available options are shown below. Thi classification is based on average
shear wave velocity to a depth of 30m. Following criteria is used to classify a site:
Appendix E 242
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 2 for the list of primary data
providers.
Appendix E 243
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.
Appendix E 244
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.
In addition, the PGA (in "g" units) and the duration of the selected earthquake is shown
in bold on to of the list (see below).
Appendix E 245
The user can view the different magnitudes and distances for a particular record by
simply clicking on the option button of his/her interest. This is shown below.
In addition, hovering the mouse cursor on a record in the list also displays the pertinent
details in a pop-up box.
The "RESTORE" button restores the search parameters used by the user in the previous
search. The user can modify or refine his search by changing one or more parameters.
Pressing the "CLEAR" button clears the results of previous search and prepares the
window for a new search. See below.
Appendix E 246
Selecting Records for Study
A maximum of 12 searched records can be selected for further study, scaling, or site
response analysis. 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 shown below.
The user has the choice to select either the individual records, pairs of horizontal
components or all three recorded components for a given earthquake event. This can be
achieved by selected appropriate radio buttons available on the left under the list of
searched records. This is shown above. The user should note that depending upon what
option is selected for "Record Components", the operation for removing records from
the list of earthquakes for study would remove individual, pairs or all three components
from the list.
Appendix E 247
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.
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.
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).
Appendix E 248
Rotation of Horizontal Components of Time Histories
There are large differences between the strike-normal and strike-parallel components of
ground motion. These differences may have an important impact on the response of
structures, as indicated by the preferred failure orientations of structure in both the 1994
Northridge and 1995 Kobe earthquakes (north and north-west respectively). To enable
analyses of these effects, EQTools has features to rotate the horizontal components of
the time histories into strike-normal and strike-parallel components.
The rotation of two recorded components North (N) and East (E) into strike-normal and
strike-parallel components SP and SN is accomplished by using the following
equations:
where, is the strike of the fault measured clockwise from North. If the recording
orientation is not North and East but rotated clockwise by the angle , then would be
reduced by . The transformation of records is accomplished by checking the box
"Transform Horizontal Components" as shown below.
The user is prompted to input the strike of the fault (in degrees) as shown above. It is
mandatory for transformation that pairs of horizontal components or all three recorded
components are selected for study. If individual records are selected, the transformation
option is not available for obvious reasons.
If the records have been transformed, then the description of records is shown in blue
color. Once transformed, all other subsequent calculations are performed with the
transformed time histories.
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.
Appendix E 249
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.
All pertinent details of the records in the list of selected earthquakes can be printed (viz.
name, recodring station, magnitude, distance from fault, etc.) by choosing the File
Print Record Details menu command.
Appendix E 250
Choosing the File Exit menu command closes EQTools program.
Appendix E 251
A Final Word on Record Search and Selection
The group of command buttons shown below are used for further processing of the
selected ground motions. The functionality of these command is discussed in the
following sections.
Appendix E 252
4: Investigating Amplitude and Duration Parameters
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.
Appendix E 253
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.
Appendix E 254
The plots generated are of the form shown below. Ground acceleration, velocity and
displacement are plotted in different windows.
You can convert the acceleration, velocity and displacement plot units by clicking the
radio-style option buttons shown below. After selecting the desired options, the plots are
automatically update to the selected new units. To restore the plots to default plotting
units, the user just has to press the "Original Plots" button. The function of other
controls on the form are described in the section on Time History Plot Controls. All
other details available on the form are self explanatory and will not be elaborated upon
any further. To obtain a hard copy of the plots, press the "Print Plots" button.
Alternatively, the hard copy of time histories can be obtained by File Print Plot
menu command.
Appendix E 255
Appendix E 256
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 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-stype option buttons on the left. Pressing the Original
Plots button restores the plots to the original units. Also, to obtain a hard copy of the
plots, "Print Plots" button may be pressed or the File Print Plot menu command
may be used.
Appendix E 257
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 "Update Plots" button.
Appendix E 258
Time History Plot Controls
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.
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.
Appendix E 259
For multiple records, these values can be obtained by left-clicking the mouse on the file
name in the legend on the right side. The selected record is highlighted in white and the
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.
Appendix E 260
Zooming the plots
Plotting multiple ground motion records simultaneously may affect the visibility of
records in the plot winodows. To get oevr this issue, zooming capabilities have been
provided where you may zoom the plots by rubberbanding in the acceleration, velocity
or displacement plot windows to see the plots better. Rubberbanding is done by clicking
the left mouse button in the plot window and drawing a rubberband window covering
the area you wish to zoom. Upon releasing the mouse button, all the plot is zoomed with
respect to the time (i.e. x-axis) and the response quantity (i.e. y-axis). This is shown
below. Zooming can be done separately in any of the three plot windows.
The resulting plots after above zooming (rubberbanding) operation are shown below.
The plots can be individually restored to depict over full recorded time by pressing the
"RESTORE" button in the left bottom corner of each plot window. This button is
available whenever any plot window is in the zoomed mode. Alternatively, all three
plots cam be restored to full recorded time by pressing the "Original Plots" button.
Appendix E 261
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.
Appendix E 262
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. Full color plots can also be printed by pressing the
"Print Plots" command or alternatively choosing File Print Plots menu command
as shown below.
Appendix E 263
Investigating Incremental Velocities
Peak incremental velocity (PIV) is often 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 3 positive and 3
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
below.
The boxes on top of the plot show the incremental velocities and corresponding time as
you move the mouse cursor 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 can be changed by using the options in the "Units" frame. The legend on
the right shows the color code for the plotted earthquakes.
Appendix E 264
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 below. The incremental velocities for the selected record is shown
superposed on the acceleration time history as shown below:
To see the statistics for other records, press the "Peak Incr. Velo." button and then
choose the next record followed by the press of "Statistics" button again. The form in
which the statistical information on the incremental velocities is depicted is shown in
the following screenshot.
Appendix E 265
The incremental velocity data can be saved in spreadsheet format by choosing the File
Create File command. Hard copies of the plots can also be obtained by pressing the
Print command button.
All procedures, including printing and saving data, for IDs are same as for IVs.
Appendix E 266
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 exceedances 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.
Appendix E 267
5: Fourier Amplitude Spectrum
Generating Fourier Amplitude Spectrum using EQTools
The frequency content of selected time histories is calculated and displayed by 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 an 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 FAS generated in EQTools environment is shown below.
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
Appendix E 268
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:
0.5
f range = frange = (0.5/dt)
t
where t 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.
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.
Appendix E 269
Across the bottom of the form are three smaller FAS plots representing three intervals
of wither 128, 256, or 512 contiguous points from the original record. You select the
number of points to use from the No. 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. Note that 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.
0.150
0.000
-0.150
0 5 10 15 20 25 30
Time (seconds)
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 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.
Appendix E 270
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.
Appendix E 271
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.
Following controls are available for studying the FAS for a given ground motion:
The miniaturized time history plot for the input motion to generate the FAS is depicted in
the window on the left. This is shown below. 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.
Appendix E 272
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.
The FAS amplitude, by default, is normalized to a value of 1.0. However, you can see
the absolute amplitude by setting the option accordingly as shown below.
Appendix E 273
Frequency and Amplitude Limits
The FAS amplitude and frequency, by default, are set to a predefined value. The
predefined value for the frequency ranges from zero to the Nyquist frequency. You can
change these values by unchecking the check-boxes and setting your own limits. This is
shown below.
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.
Appendix E 274
Travelling Fourier Amplitude Spectrum
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.
Appendix E 275
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.
Appendix E 276
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.
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. Full
color plots can also be printed by pressing the "Print" command or alternatively by
choosing File Print Plots menu command as shown below.
Appendix E 277
Fourier Amplitude Spectrum Analysis Tools
The FAS Analysis Tool is a very unique and useful tool. Through this tool, you can
examine, on a real time basis, what happens to the time history if certain frequencies are
filtered out or scaled up/down. On the other hand, how does the frequency content of a
time history change if certain range of time history is scaled up or scaled down. You 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.
Appendix E 278
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 is
preserved in the FFT analysis environment. The opening screen for accessing this tool is
as 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 history or frequency is chosen using radio buttons as shown
above. The upper or lower bound for both the parameters can be input in 2 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 3 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 for the filters
available in EQTools environment:
Appendix E 279
Gain (or amplitude)
1
0 0
fcutoff fc fcutoff fc
Frequency (Hz.) Frequency (Hz.)
(a) (b)
0 0
f1 f2 fc f1 f2 fc
Frequency (Hz.) Frequency (Hz.)
(c) (d)
Amplitude response specifications for rectangular filters. (a) Low-pass filter. (b) High-pass filter. (c) Band-
pass filter. (d) Band-stop filter. f c is the Nyquist frequency.
Gain (or amplitude)
Gain (or amplitude)
1 1
0 0
fcutoff fc fcutoff fc
Frequency (Hz.) Frequency (Hz.)
(a) (b)
1
Gain (or amplitude)
1
Gain (or amplitude)
0 0
f1 f2 fc f1 f2 fc
Frequency (Hz.) Frequency (Hz.)
(c) (d)
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
Appendix E 280
Gain (or amplitude)
Gain (or amplitude)
1 1
0 0
fcutoff fc fcutoff fc
Frequency (Hz.) Frequency (Hz.)
(a) (b)
0 0
f1 f2 fc f1 f2 fc
Frequency (Hz.) Frequency (Hz.)
(c) (d)
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. f c is the Nyquist frequency
2
Gain (or amplitude)
1
Gain (or amplitude)
s
1
s
0
0
f1 f2 fc f1 f2 fc
Frequency (Hz.) Frequency (Hz.)
(a) (b)
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
Appendix E 281
2
s
Gain (or amplitude)
1
0
0
f1 f2 fc f1 f2 fc
Frequency (Hz.) 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 ) .
2
Gain (or amplitude) 1
Gain (or amplitude)
1
s
0
0
f1 f2 fc f1 f2 fc
Frequency (Hz.) Frequency (Hz.)
(a) (b)
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 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 where as the original responses are shown in blue color.
Appendix E 282
A sample analysis result with three ranges of frequency filtering is shown below. The
screenshot at the bottom shows the changes in response spectrum. The user can zoom the
time history by rubber-banding.
Appendix E 283
A sample analysis result with scaling of time history in three ranges is shown below:
Appendix E 284
6: Elastic Response Spectra and Scaling of Time
Histories
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 (1932)
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-of-freedom (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 n 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 the natural frequency and the damping ratio of the SDOF
system (for a particular input motion). The maximum values of 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 , available on the Search Form as shown
below.
Appendix E 285
A sample response spectrum plot for eight representative strong ground motions is shown
ahead.
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 the Response
Spectrum Plot Button. You must make sure that the chechbox "Plot all records for
study" is unchecked for plotting RS of a single record.
Appendix E 286
The plot generated for a single record is of the form shown below:
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.
Appendix E 287
A screenshot of sample response spectrum plot in EQTools environment 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.
Following controls are available for studying the Response Spectrum for a single
ground motion or a group of ground motions:
You have the choice of plotting the spectral quantities against time period or frequency.
This choice can be made by clicking the option buttons shown below.
Appendix E 288
Damping for Earthquake Spectra
You can set the damping value for which the response spectra are to be generated. You
must press the "Update" button to generate plots with the changed damping. Please note
that the damping value for the spectra should be the same as the damping for NEHRP
spectra for the purpose of scaling. If the two damping values are not the same, a
warning message is generated. If you still decide to proceed with the plots, the NEHRP
damping is displayed in red color to remind you that the the damping values are
different. These aspects are shown in the sample below.
You can chose the plot style for the response spectrum by using the options shown
below. You have 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".
Appendix E 289
Spectral Coordinates
As you move 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 below.
The legend shows the color coding for the plots and the corresponding ground motion
data file name. This is shown below.
Appendix E 290
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.
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.
Appendix E 291
NEHRP Design Spectrum
The design response spectrum as per NEHRP 2000 guidelines can be generated ans
superimposed on the response spectrum plots by checking the check-box shown below.
The code spectrum is calculated on the basis of a predefined parameters. However, you
have the choice of changing these parameters. A sample plot with code spectrum
superimposed is shown below.
Pressing the "NEHRP Parameters" button brings up the code parameters window
(shown below) where you can change the parameters. Pressing the "Done" button
updates the NEHRPDesign Spectrum.
Appendix E 292
Scaling of Elastic Response Spectra for Selected Records
You can access the scaling tools by pressing the "Fit" button in the response spectrum
plot window. This button is available only when the NEHRP spectrum is overlaid on the
response spectrum plots as shown below.
The response spectrum for the selected records can be scaled in various ways. You can
scale the response spectra to any of the spectral quantities of the design spectrum i.e.
acceleration, velocity or displacement. This means that you can chose eithe 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:
Appendix E 293
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 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).
Appendix E 294
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.
Folllowing the selected scaling operation is performed, the scled 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 below.
Pressing the Done command button closes the environment for scaling of response
spectra. It also transfers the scale factors to the response spectrum environment whereby
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 scling are available to the
user as shown below:
Appendix E 295
Saving the Scaled Bin of Earthquakes
Once the scaling has been done, you can save the scaled bin of records by pressing the
"Save Scaled Bin" command button shown below. Alternatively, you can also save the
scaled bin by using File Save Scale Bin menu command.
Appendix E 296
Exporting the Computed Response Spectrum Data and Printing
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. Full color plots can also be printed by pressing the "Print"
command or alternatively by choosing File Print Plots menu command. as shown
below.
You 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.
Appendix E 297
7: Ground Motion Attenuation Tools
Overview of Ground Motion Attenuation Relationships
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.
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.
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
Appendix E 298
faulting. Also, more restrictive ranges of M and r jb 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.
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 upto 100 km.
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.
Appendix E 299
Campbell Attenuation Relationship (1997): Spectral Acceleration
Appendix E 300
Sadigh, Chang & Egan Attenuation Relationship (1997): Spectral Acceleration
Appendix E 301
For Cascadia Subduction Zones, following attenuation relationships have been
implemented in EQTools environment. The screen shots for these relationships are
presented ahead:
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 zones 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.
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.
Appendix E 302
Atkinson and Boore Attenuation Relationship (1997a): Spectral Acceleration
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 low-frequency 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 motion
relationships determined for one tectonic environment cannot be simply scaled for
use in another.
Appendix E 303
Atkinson and Boore Attenuation Relationship (1997b): Peak Ground Velocity
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.
Appendix E 304
Kenneth W. Campbell Attenuation Relationship
Appendix E 305
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.
Appendix E 306
David M. Boore, William B. Joyner, and Thomas E. Fumal Attenuation Relationship
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 and in
keeping with the style of this homepage, tables are provided 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.
Equations:
Note: The equations are to used for M 5.5-7.5 and r no greater than 80 km.
Appendix E 307
K. Sadigh, C.-Y. Chang, J.A. Egan, F. Makdisi, and R.R. Youngs Attenuation
Relationship
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.
Appendix E 308
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
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. Relations developed based on data from
extensional regime earthquakes having moment magnitude M > 5.0 recorded at distances
less than 105 km.
Appendix E 309
R.R. Youngs, S.-J. Chiou, W.L. Silva, and J.R. Humphrey Attenuation Relationship
Attenuation relationships for peak ground acceleration and response spectral acceleration
for subduction zone interface and intraslab earthquakes of moment magnitude M 5 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. 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 intraslab earthquakes
produce peak motions that are about 50 percent larger than interface earthquakes.
Appendix E 310
Gail M. Atkinson and David M. Boore Attenuation Relationship (1997a)
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 overpredicted near the earthquake source and underpredicted 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
A new ground-motion relations for eastern North America (ENA) developed over the last
six 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 ground-motion 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). It predicts lower
amplitudes (by more than a factor of two) at 1 Hz, largely due to use of an empirical
source model rather than a single-corner-frequency Brune source model; the use of an
Appendix E 311
empirical source model is motivated by the desire to match the ENA ground-motion
database as closely as possible
Appendix E 312
Ground Motion Attenuation Plot Controls
Generating ground motion attenuation plots uning 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 below.
STEP 1: Choose the tectonic regime using the radio buttons on the top left
STEP2: 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.
STEP3: Choose and/or input the site and other parameters. The expected input
parameters are active if and when necessary
Appendix E 313
STEP5: Choose plot options using the radio buttons on the left.
STEP6: To view attenuation relation coefficients, press the "View Coefficients" button
STEP6: To view a different attenuation relationship, press the "Reset" button and repeat
steps 1 through 6 above
The data generated using attenuation relationship 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. Full color plots can also be printed by choosing File Print
Plots menu command from the menu bar
Appendix E 314
8: Site Response Analysis Using EQTools
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:
Appendix E 315
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 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.
Appendix E 316
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 selected earthquakes on the search query forms. The later option
is available only if the serch for is active.
Appendix E 317
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 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.
Appendix E 318
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 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.
Appendix E 319
Interpreting the Site Response Analysis Results
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 you choose a new
damping value, you must press the Update button before the modified response spectra
are available. Tripartite plots or plots for 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.
Appendix E 320
Appendix E 321
References
Abrahamson, N. A., and Litehiser, J. J., Attenuation of Vertical Peak Acceleration,
Bulletin of the Seismological Society of America, Vol. 79, 549-580, 1989.
Atkinson, G. M., and Boore, D. M., Stochastic Point Source Modeling of Ground
Motions in the Cascadia Region, Seismological Research Letters, Vol. 68(1), 74-85,
1997a.
Atkinson, G. M., and Boore, D. M., Some Comparisons Between Recent Ground
Motion Relations, , Seismological Research Letters, Vol. 68(1), 24-40, 1997b.
Bolt, B. A., Duration of Strong Motion, Proceedings of the 4th World Conference on
Earthquake Engineering, Santiago, Chile, 1304-1315, 1969.
Boore, D. M., Joyner, W. B., and Fumal, T. E., Equations for Estimating Horizontal
Response Spectra and Peak Acceleration from Western North American Earthquakes: A
Summary of Recent Work, Seismological Research Letters, Vol. 68(1), 128-153, 1997.
Charney, F. A., NONLIN: A Computer Program for Nonlinear Dynamic Time History
Analysis of Single- and Multi-Degree of Freedom Systems, Federal Emergency
Management Agency, 2003.
Appendix E 322
Clough, Ray, W., and Penzien, J., Dynamics of Structures, Volume 2, McGraw Hill, New
York, N.Y., 1993
Hart, J. D., An Introduction to WAVES A New Computer Program for Evaluating the
Earthquake Response of Horizontally Layered Soil Deposits, Individual Research
Report, Department of Civil Engineering, University of California, Berkeley, 1987.
NEHRP Recommended Provisions for the Development of Seismic Regulations for New
Buildings, 1985 Edition, Building Seismic Safety Council, Washington, D.C., 1985.
NEHRP Recommended Provisions for the Development of Seismic Regulations for New
Buildings, 1988 Edition, Building Seismic Safety Council, Washington, D.C., 1988.
NEHRP Recommended Provisions for the Development of Seismic Regulations for New
Buildings, 1991 Edition, Building Seismic Safety Council, Washington, D.C., 1991.
NEHRP Recommended Provisions for the Development of Seismic Regulations for New
Buildings, 1994 Edition, Building Seismic Safety Council, Washington, D.C., 1994.
NEHRP Recommended Provisions for the Development of Seismic Regulations for New
Buildings, 1997 Edition, Building Seismic Safety Council, Washington, D.C., 1997.
NEHRP Recommended Provisions for the Development of Seismic Regulations for New
Buildings, 2000 Edition, Building Seismic Safety Council, Washington, D.C., 2000.
Page, R. A., Boore, D. M., Houner, W. B., and Caulter, H. W., Ground Motion Values
for Use in the Seismic Design of the Trans-Alaska Pipeline System, USGS Circular 672,
U. S. Geological Survey, Reston, Virginia, 1972.
Sadigh, K., Chang, C. Y., Egan, J. A,, Makdisi, F., and Youngs, R. R., Attenuation
Relations for Shallow Crustal Earthquakes Based on California Strong Motion Data,
Seismological Research Letters, Vol. 68(1), 180-189, 1997.
Somerville, P. G., Smith, N. F., Graves, R. W., and Abrahamson, N. A., Modification of
Empirical Strong Ground Motion Attenuation Relations to Include the Amplitude and
Duration Effects of Rupture Directivity, Seismological Research Letters, Vol. 68, 199-
222, 1997.
Appendix E 323
Spudich, P., Joyner, W. B., Lindg, A. G., Boore, D. M., Margaris, B. M., and Fletcher, J.
B., SEA99: A Revised Ground Motion Prediction Relation for Use in Extensional
Tectonic Regimes, Bulletin of Seismological Society of America, Vol. 88(5), 1156-1170,
1999.
Youngs, R. R., Chiou S. J., Silva, W. J., and Humphrey, J. R., Strong Ground Motion
Attenuation Relationships for Subduction Zone Earthquakes, Seismological Research
Letters, Vol. 68(1), 58-73, 1997.
Appendix E 324
Appendix A
Appendix E 325
Index
.
.XL1 3
A
acceleration 7, 8, 11, 12, 13, 32, 34, 36, 37, 39, 42, 43, 44, 46, 53, 59, 67, 73, 77, 82, 83, 91, 92, 93, 95, 96, 97, 108
amplitude 7, 37, 47, 48, 53, 54, 60, 63, 89, 108
Amplitude 32, 37, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 62, 63, 64, 112
Analysis 59, 60, 103, 104, 106, 107, 110
Attenuation 82, 84, 85, 86, 87, 88, 89, 90, 91, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 110, 112
Attenuation Relationships 82, 90, 112
B
background 41
bin 2
Bin 29, 30, 80, 82
bracketed 46
Bracketed 46
C
Cascadia 87, 98, 110
characterization 2
Component 9, 18
Computational tools 2
control 2, 17, 20, 21, 22, 23, 104, 106
Create 42, 45, 58, 81, 102
critical earth 2
D
damping 3
Damping 72
database 7, 8, 9, 11, 12, 16, 17, 19, 23, 59, 99
Database 1, 7, 9, 15, 16, 17, 113
default 5, 8, 11, 17, 18, 19, 34, 43, 47, 53, 54
Design Spectrum 75
displacement 11, 12, 13, 32, 34, 36, 37, 39, 42, 53, 67, 73, 77, 108
distance 7, 10, 11, 21, 22, 30, 78, 82, 87, 94
ductility 3
duration 7, 25, 46
Duration 11, 32, 46, 110, 112, 113
Dynamic 105, 110
Appendix E 326
E
earthquake 2, 3, 7, 9, 10, 11, 12, 18, 19, 25, 27, 36, 43, 47, 48, 52, 55, 59, 67, 71, 77, 78, 82, 83, 96, 97, 98, 103, 106
earthquakes 7, 18, 27, 28, 29, 30, 33, 35, 44, 50, 51, 69, 70, 77, 78, 83, 87, 89, 90, 92, 93, 95, 96, 97, 98, 103, 105,
107
Elastic 67, 69, 70, 76
empirical 82, 83, 89, 90, 92, 98, 99
energy dissipation 3
EQTools 1, 2, 3, 4, 5, 6, 7, 9, 12, 15, 16, 23, 29, 31, 32, 37, 43, 46, 47, 48, 58, 59, 61, 67, 68, 71, 77, 78, 79, 81, 82,
83, 87, 89, 100, 102, 103, 113
Equal Area 77
Equivalent linear 103
F
far field 19
Far Field 10
FAS 47, 48, 49, 50, 52, 53, 54, 55, 56, 58, 60, 64
FFT 47, 48, 50, 51, 55, 60, 64
field 9, 10, 11, 19, 46, 92, 103
File 1, 12, 15, 16, 29, 30, 31, 35, 36, 42, 45, 58, 80, 81, 102
Filtered 64
Fourier 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 103, 108
Frequency 54, 71
G
Geometric 105
ground motion 2, 8, 9, 16, 29, 33, 35, 39, 46, 47, 48, 50, 51, 52, 53, 55, 57, 59, 67, 68, 69, 70, 71, 74, 78, 82, 83, 87,
89, 92, 94, 96, 98, 100, 103, 108
I
incremental 43, 44, 45, 46
Incremental 43, 46
input 3
installation 4
integrated 2
interface 60, 87, 97, 101, 104, 105, 106, 107
intraslab 87, 97
IOTech VisuaLab-GUI system 6
L
LAYER 103
legend 36, 38, 44, 52, 57, 71, 74
linear 3
Linear 103, 106
location 7, 13, 38
LUSH2 103
M
magnitude 2, 7, 10, 20, 21, 30, 78, 82, 87, 92, 94, 95, 96, 97
Appendix E 327
mechanism 9, 19
Microsoft Access 8, 9
Microsoft Windows 2, 3
model 83, 87, 89, 90, 97, 98, 99, 103, 106, 107
multiple 12, 32, 35, 36, 37, 38, 39, 51, 56, 70, 74, 78
N
near fault 2
Near Field 10
NEHRP 72, 75, 76, 78, 111
NONLIN 3
nonlinear 2, 3
Nonlinear 103, 104, 110
O
Opening 29, 30
Orientation 9
Original 34, 36, 40, 64, 108
P
Peak Ground Acceleration 20, 28, 37, 84, 110
Peak ground displacement 11
Peak ground velocity 11
PEER 7, 8, 12, 14
performance-based 2
PGA 9, 11, 20, 25, 37, 38, 83, 92, 113
plots 3, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 46, 49, 50, 51, 52, 53, 56, 57, 58, 60, 64, 69, 70, 71, 72, 73, 74, 75,
76, 81, 100, 101, 102, 108
point-source 98
print 5, 7
Printing 29, 30, 81, 102
Q
QUAD4 103
R
regression 82, 97
resolution 3
Response Spectra 67, 70, 76, 110
response spectrum 59, 60, 64, 65, 67, 68, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 96, 103
Response Spectrum 64, 69, 71, 72, 73, 74, 81
RESTORE 26, 40
rotation 29
Rotation 29
rupture 92
Appendix E 328
S
Saving 29, 80, 82
Scale Factor 80
scaled 2
Scaled 64, 80, 82
Scaling 59, 67, 76, 77, 78
SHAKE 103
site conditions 2, 7, 78, 94
Sorting 28
source 2, 7, 13, 82, 87, 89, 98, 99
spectral 2, 68, 71, 73, 77, 78, 79, 82, 83, 95, 97, 108
Spectral 71, 73, 85, 86, 87, 88, 89, 110
spectrum 2
spreadsheet 3
SRSS 78, 79
Strike-Slip 10, 19
strong motion 7, 8, 12, 13, 59, 83, 95
structural dynamics 3
suite 2
T
tectonic regions 83, 84, 90, 92
time histories 2, 3, 7, 11, 12, 29, 32, 35, 36, 42, 46, 47, 53, 59, 63, 68, 77, 78, 80, 103, 105, 108
time history 2, 11, 12, 13, 33, 36, 37, 43, 44, 46, 52, 53, 55, 59, 60, 61, 64, 65, 66, 78
U
uninstallation 4
units 11, 13, 20, 25, 34, 36, 43, 108
Update 36, 43, 46, 56, 72, 74, 108
Updating 56, 74
V
velocity 11, 12, 13, 22, 32, 34, 36, 37, 39, 42, 43, 45, 46, 53, 67, 73, 77, 82, 83, 92, 94, 96, 108
version 3, 4, 15, 83
View 64, 102
W
WAVES 103, 111
window 15, 16, 26, 39, 40, 43, 49, 52, 53, 54, 55, 73, 74, 76, 79
Windows 95 4
Windows 98 3
Windows NT 3
WordPad 3
Z
zooming 39, 40
Appendix E 329
APPENDIX F
Appendix F 330
Group Exercise 1
Development of Ground Motions for Topical Investigation of Structural Response
Problem Statement: Investigations are to be carried out for a 6-story office building,
located in Seattle, Washington, to quantify the capacity of structural elements and
systems and the demands imposed on these systems through structural response to strong
ground motions. The structure resists the lateral loads through steel moment resisting
frames. The approximate fundamental period of vibration for the building is 0.91 second.
For this investigation, a suite of ten strong ground motions is to be developed for a
probability of occurrence of 2% in 50 years. The structure is situated on NEHRP Site
Class C materials.
Quantify the parameters for EQTools database search for appropriate records
Fault Mechanism: Ideally, the records should come from various fault
mechanisms. Hence, set this parameter to Any
Zone of Recording: Choose Any. If the site is known to be located in the near-
fault region, you should choose Near-Fault for this parameter.
Appendix F 331
Quantify the parameters for EQTools database search for appropriate records
(contd)
Site Class: NEHRP site class C represents soft rock conditions. The corresponding
USGS site class is B. So, use the site class B as the search parameter.
Perform the search of the EQTools database by pressing the Search command button.
After performing the search, the Searched Earthquake list on the left side of the
EQTools environment should show 26 records, as shown below.
Appendix F 332
The magnitude, distance, site conditions, and other parameters for each of these records
can be viewed by clicking on the record of interest. These parameters are tabulated below
for the earthquakes available through the search.
Table F-1 : List of preliminary ground motions obtained through the EQTools database search.
Earthquake Name Year Recording Station Degree Fault Mw R
Mechanism (km)
Cape Mendocino, USA 1992 89509 Eureka-Myrtle & West 090 Reverse Normal 7.1 44.6
Cape Mendocino, USA 1992 89486 Fortuna-Fortuna Boulevard 000 Reverse Normal 7.1 44.6
Cape Mendocino, USA 1992 89486 Fortuna-Fortuna Boulevard 090 Reverse Normal 7.1 44.6
Cape Mendocino, USA 1992 89509 Rio Dell Overpass - FF 270 Reverse Normal 7.1 44.6
Cape Mendocino, USA 1992 89509 Rio Dell Overpass - FF 360 Reverse Normal 7.1 44.6
Cape Mendocino, USA 1992 89530 Shelter Cove Airport 000 Reverse Normal 7.1 44.6
Cape Mendocino, USA 1992 89530 Shelter Cove Airport 090 Reverse Normal 7.1 44.6
Cape Mendocino, USA 1992 89509 Eureka-Myrtle & West 000 Reverse Normal 7.1 44.6
Chi-Chi, Taiwan 1999 TCU084 000 Reverse Normal 7.6 10.39
Chi-Chi, Taiwan 1999 TCU084 090 Reverse Normal 7.6 10.39
Imperial Valley, USA 1979 6604 Cerro Prieto 237 Strike Slip 6.5 26.5
Imperial Valley, USA 1979 286 Superstition Mtn Camera 045 Strike Slip 6.5 26.0
Imperial Valley, USA 1979 6604 Cerro Prieto 147 Strike Slip 6.5 26.5
Imperial Valley, USA 1979 5051 Parachute Test Site 225 Strike Slip 6.5 14.2
Imperial Valley, USA 1979 5051 Parachute Test Site 315 Strike Slip 6.5 14.2
Imperial Valley, USA 1979 286 Superstition Mtn Camera 135 Strike Slip 6.5 26.0
Kern County, USA 1952 1095 Taft Lincoln School 021 Reverse Oblique 7.4 41.0
Kern County, USA 1952 1095 Taft Lincoln School 111 Reverse Oblique 7.4 41.0
Koceali, Turkey 1999 Arcelik 000 Strike Slip 7.4 17.0
Koceali, Turkey 1999 Arcelik 090 Strike Slip 7.4 17.0
Landers, USA 1992 24577 Fort Irwin 000 Strike Slip 7.3 64.2
Landers, USA 1992 24577 Fort Irwin 090 Strike Slip 7.3 64.2
Loma Prieta, USA 1989 58065 Saratoga-Aloha Ave. 000 Reverse Oblique 6.9 13.0
Loma Prieta, USA 1989 58065 Saratoga-Aloha Ave. 090 Reverse Oblique 6.9 13.0
Northridge, USA 1994 24538 Santa Monica City Hall 360 Reverse Normal 6.7 27.6
Northridge, USA 1994 24538 Santa Monica City Hall 360 Reverse Normal 6.7 27.6
Mw = Moment Magnitude; R = Closest Distance
Please note that you can also examine the peak ground acceleration and the duration for
any record by clicking the record of interest in the list of searched earthquakes.
This completes the step for assembling the preliminary records for our purposes.
The next step is to identify the severity and damage potential of the preliminary records
by investigating their amplitude and duration parameters.
Appendix F 333
STEP 2: AMPLITUDE AND DURATION PARAMETERS OF THE RECORDS
Amplitude and duration parameters are fundamentally instrumental values obtained either
directly or with some simple calculations from the digitized and corrected versions of the
instrument records. The peak values of ground acceleration, velocity, and displacement
need to be investigated for each record. In addition to that, the incremental velocities are
also to be explored. Finally, the bracketed duration is investigated for a threshold
acceleration level of 0.05g.
The amplitude parameters are examined by selecting a record from the searched
earthquakes and pressing the time history button . Peak values of ground
acceleration, velocity and displacement are displayed as shown below.
You can print the ground motion histories or save the time history data in spread sheet
format at any time by using the File > Print Plots or File > Create File commands
respectively.
Appendix F 334
Investigate the incremental velocities.
Appendix F 335
Investigate the bracketed duration for threshold acceleration of 0.05g.
The bracketed durations for the records are investigated by pressing the
command button available on the ground motion history
plot forms. The threshold acceleration is specified by using the radio buttons. The
default value of threshold acceleration is 0.01g. The bracketed duration for a
record is displayed as shown below.
Once al the amplitude and duration parameters have been investigated for preliminary
records, the next step is to identify the severity and damage potential of these ground
motions using one or more of these parameters.
The aforementioned parameters, available through EQTools for the searched records, are
tabulated ahead.
Appendix F 336
Table F-2 : Amplitude and duration measures for the preliminary earthquakes.
Incremental
PGA PGV PGD Bracketed
Earthquake Name Degree Velocity
(g) (cm/s) (cm) Duration (s)
Factor
Cape Mendocino, USA 090 0.178 28.3 11.4 8.4 13.7
Cape Mendocino, USA 000 0.116 30.0 27.6 12.5 17.1
Cape Mendocino, USA 090 0.114 21.7 12.8 6.4 16.0
Cape Mendocino, USA 270 0.244 44.0 22.0 16.8 14.9
Cape Mendocino, USA 360 0.549 42.1 18.6 15.6 16.9
Cape Mendocino, USA 000 0.229 6.60 6.40 18.4 11.3
Cape Mendocino, USA 090 0.189 6.70 0.60 18.3 9.4
Cape Mendocino, USA 000 0.154 20.2 5.90 4.7 9.7
Chi-Chi, Taiwan 000 0..417 45.6 21.3 35.5 16.4
Chi-Chi, Taiwan 090 0.465 114.7 31.4 34.5 23.7
Imperial Valley, USA 237 0.157 18.6 8.00 31.3 8.8
Imperial Valley, USA 045 0.109 5.20 2.20 4.7 6.1
Imperial Valley, USA 147 0.169 11.6 4.30 24.3 8.9
Imperial Valley, USA 225 0.111 17.8 12.3 7.7 12.1
Imperial Valley, USA 315 0.204 16.1 9.90 5.4 11.5
Imperial Valley, USA 135 0.195 8.80 2.80 4.3 9.4
Kern County, USA 021 0.156 15.3 9.20 17.3 7.8
Kern County, USA 111 0.155 17.5 9.00 17.2 7.7
Koceali, Turkey 000 0.219 17.7 13.6 6.0 15.8
Koceali, Turkey 090 0.150 39.5 35.6 5.9 30.4
Landers, USA 000 0.114 9.70 3.70 8.1 15.9
Landers, USA 090 0.112 16.4 21.8 5.7 15.9
Loma Prieta, USA 000 0.512 41.2 16.2 12.2 22.9
Loma Prieta, USA 090 0.324 42.6 27.5 11.3 16.6
Northridge, USA 360 0.370 25.2 7.20 12.9 13.0
Northridge, USA 360 0.883 41.7 15.1 13.6 17.4
The fundamental period of vibration of the structure is 0.91 seconds (i.e., a frequency of
1.09 Hz), as given in the problem statement. This falls into an intermediate frequency
range of vibration and hence PGV is would provide a much more accurate indication of
the potential for damage than the PGV. This parameter alone, however, is not sufficient
to characterize the ground motion. The degradation of strength and stiffness of the
structure depends on the number of stress reversals that occur during an earthquake.
Hence, in addition to PGV, we will also use bracketed duration to choose the records
from the preliminary list. With relative moderate acceleration amplitude, serious
structural damage can occur if the pulse duration is long relative to the period of the
structure. In other words, a large area under the acceleration pulse (termed incremental
Appendix F 337
velocity) would make the ground motion more damaging. A low value of incremental
velocity factor signifies an earthquake with more damage potential. So, we will use the
incremental velocity as well to select the records. Ten records are identified and selected
on the basis of the aforementioned parameters. These records have been highlighted in
the table presented before.
Once the suitable records have been identified, they are assembled as a specific
magnitude-distance bin of earthquakes.
Appendix F 338
STEP 4: ELASTIC RESPONSE SPECTRUM FOR SELECTED RECORDS
Once the bin of earthquakes has been created for a specific magnitude and distance, the
next step is the generation of elastic response spectrum.
The elastic response spectra for all the records in the bin are generated by pressing
the command button. You must ensure that the checkbox named Plot all
records for study is checked before pressing the above command button. Once this
button is pressed, response spectra are generated for all the earthquakes in the bin
for a default damping of 5% critical and displayed as a tripartite plot. In this
exercise, we will generate the response spectra for damping of 5% critical. The
generated response spectra are shown below.
You can see the plots for spectral quantities separately by choosing appropriate options.
Also, you can generate the spectra for different damping ration by supplying the new
damping value and then pressing the command button. Note that the scale
factors for each ground motion are 1.0. This is because the response spectra have not
been scaled as yet. The next step is to generate the design response spectrum.
Appendix F 339
STEP 5: GENERATING THE ELASTIC DESIGN RESPONSE SPECTRUM
Once the bin of earthquakes has been created for a specific magnitude and distance, the
next step is the generation of elastic design response spectrum for 5% critical damping
(same as used for earthquake response spectra). This spectrum is generated as per
NEHRP guidelines. The expected inputs are the short period and one second mapped
spectral acceleration parameters ( S s and S1 , respectively) and the Site Class. The
structure is situated in Seattle. We use the maximum considered ground motion maps
developed by the Building Seismic Safety Council and the USGS to get the acceleration
parameters for 2% in 50 years hazard.
Access the environment for generating the NEHRP design spectrum by pressing
Appendix F 340
The design response spectrum is viewed together with the earthquake elastic response
spectra by checking the checkbox named Overlay NEHRP Spectrum. This is shown
below.
Once the design response spectrum and the earthquake response spectra are available, the
next step is to scale the earthquake response spectra using EQToolss autoscaling
capability to determine the scale factors for each ground motion.
where the Target Spectral Acceleration for a system with damping and period T
comes from the design (NEHRP) response spectrum, and the Computed Spectral
Acceleration is the maximum computed pseudo-acceleration for a linear single-degree-
of-freedom system with damping and period T subjected to the unscaled ground
motion. For our exercise, we are using a system damping of 5% critical. We will scale the
Appendix F 341
response spectra to match the NEHRP design spectrum at the structures fundamental
period of vibration (i.e., T = 0.91 second.)
With the NEHRP design spectrum overlaid on the earthquake response spectra, access
the environment for scaling by pressing the button on the response
spectrum plot form. Enter the period as 0.91 seconds and then press the
command button. The scale factors are automatically calculated for each earthquake
and displayed for the target period of 0.91 second. This is shown below.
Please note that the scale factors for some ground motions may be unrealistically large
depending upon the nature of the response spectra for those records. In order to remain
realistic for design purposes, amplitude scaling of not more than a factor of 2.0 is
recommended to be used. EQTools does not modify the scale factors per this guideline. It
displays the as-computed scale factors.
Appendix F 342
The scale factors as calculated by EQToolss scaling tools for various target periods
including for T = 0.91 sec, are shown in the table below.
Table F-3 : Scale factors as computed by EQTools for the records in the bin of earthquakes.
T=0s
T=0.2s T=0.91s T=1.0s
Ground Motion Acc=0.502g
Acc=1.080g Acc=0.533g Acc=0.485g
(PGA)
CAPMRIO270.ACC 1.302 1.530 1.045 0.902
CAPMSHL090.ACC 2.201 1.175 19.996 19.564
CAPMSHL000.ACC 2.664 2.153 21.786 19.030
CHICU084000.ACC 1.203 1.515 0.500 0.563
CHICU084090.ACC 0.434 0.662 0.159 0.190
IMPVCPEH237.ACC 3.201 2.139 1.799 1.649
IMPVCPEH147.ACC 2.969 2.791 4.229 5.055
KERNTAF021.ACC 3.220 3.008 2.163 2.732
LOMASTGA090.ACC 1.547 0.948 1.494 1.410
NORTSTMO360.ACC 1.360 1.351 1.731 1.423
You can view the scaled response spectrum by checking the checkbox named Apply
scale factor(s) to RS plots. The EQTools screenshot below shows this. The scale factors
are shown in the frame on the right of the response spectrum environment.
Appendix F 343
STEP 7: SAVING THE SCALED BIN OF EARTHQUAKES
The scaled bin of earthquakes can be saved by using the File > Save Scaled Bin from the
main menu. The earthquake information and the scale factors are saved on the hard-disk.
Such saved bins can again be imported into the EQTools environment.
Appendix F 344
Group Exercise 2
Filtering and Scaling Frequencies of Accelerograms
Problem Statement: This exercise is designed to familiarize the user with the
computational tools and features available in EQTools to filter and/or scale the
frequencies of accelerograms.
In this exercise, we will generate the Fourier amplitude spectrum (FAS) for any arbitrary
record accessible through the EQTools database search. We will then explore the effect
of scaling and/or filtering frequencies on the ground motion history and the response
spectrum.
Generate the Fourier amplitude spectrum for a given record accessible through the
EQTools database search
Perform the EQTools database search using any search parameters. For the purpose
of this exercise, a search is performed with the following parameters.
All other parameters are set to Any. Initiate the search by pressing the
command button. The search results are available in the frame on
the left of the search form.
Select the ground motion recorded at the 5049 Borrego Air Ranch station during the
1980 Anza (Horse Cany) earthquake (third record in the list). Generate the Fourier
Appendix F 345
STEP 2: THE ENVIRONMENT FOR FREQUENCY FILTERING
Press the command button on the form for FAS plots and you are
taken to the environment where you can filter or scale frequencies. Filtering and
scaling can be applied to the ground motion history as well. The opening screen
shows the FAS plot at the bottom and the plot of the ground motion history on the
top. The pertinent details of the records are displayed in the frame on the left. The
screenshot of this window is shown ahead.
Appendix F 346
STEP 3: FILTERING FREQUENCIES
In the EQTools environment, you can perform low-pass, high-pass, band-pass, and band-
stop filtering of frequencies. Three types of filters are available for you to apply. These
are the rectangular, triangular and the sinusoidal filters.
We will apply a square low-pass filter to the FAS with a cut-off frequency of 2.0
Hz. Choose the option Filter/Scale Acceleration FFT Spectrum in the frame
called Input Options for Filtering/Scaling. Enter a value of 2.0 in the first row of
the Low field in the frame titled Filtering/Scaling Parameters. In the High
field, enter a value of 20.0. In the first row of the Scale Factor field, enter 0.
Then press the command button followed by the
command button. The filtered FAS and the consequently
modified ground acceleration history are displayed as shown below.
Appendix F 347
To view the response spectrum, press the command button. The original
and modified response spectra are displayed as shown below.
Appendix F 348
Perform high-pass filtering of frequencies.
We will now apply a square high-pass filter to the FAS with a cut-off frequency of
10 Hz. Press the command button. Enter a value of 0.01 in the first
row of the Low field in the frame titled Filtering/Scaling Parameters. In the
High field, enter a value of 10.0. In the first row of the Scale Factor field,
enter 0. Then press the command button followed by the
command button. The filtered FAS and the consequently
modified ground acceleration history are displayed as shown below. The original
response spectrum and the response spectrum modified because of the filtering are
also shown below.
Appendix F 349
Perform band-pass filtering of frequencies with the filter applied to 3 bands of
frequencies.
We will now apply a square band-pass filter to the FAS. The frequencies in the
ranges 2.0-4.0 Hz and 6.0-16.0 Hz are retained and the remaining ranges of
frequencies are completely filtered out. Press the command button.
Enter a value of 0.01 and 2.0 in the first row, 4.0 and 6.0 in the second row, and
16.0 and 20.0 in the third row. Enter the scale factor as 0 for all the ranges. Then
press the command button followed by the
command button. The filtered FAS and the consequently modified ground
acceleration history are displayed as shown below. The original response spectrum
and the response spectrum modified because of the filtering are also shown ahead.
Appendix F 350
Appendix F 351
The band-stop filtering can be carried out in a similar way. The frequencies can also be
scaled up or down in a similar manner by specifying the desired scale factor.
All the filters (and scaling) can also be applied to filter ranges of ground motion history.
This provision, however, is only for educational purpose as in practice, ranges of ground
motion histories are never scaled or filtered.
Appendix F 352
Group Exercise 3
Attenuation Relationships
Problem Statement: This exercise is designed to familiarize the user with the
computational tools and features available in EQTools to estimate the ground motion
parameters for different tectonic regimes using the appropriate attenuation relationships.
In this exercise, we will estimate the peak horizontal ground acceleration (PGA), peak
horizontal ground velocity(PGV), and the horizontal spectral accelerations (SA) for soft
rock sites in the active tectonic region (e.g., western North America). We will assume the
fault mechanism to be strike slip type and the depth of basement rock to be 3.0 km. The
ground motion parameters will be estimated for a range of magnitudes and at various
distances from the source. Horizontal spectral accelerations will be estimated for a
period of vibration of 2.0 seconds.
On the main menu, click on Attenuation. This gives you the access to the
environment for estimation of ground motion parameters. We will use Campbell
Attenuation Relationships (1997) for the purpose of this exercise.
In the list under the frame named Attenuation Relationship, choose the
Campbell (1997) relationship by clicking on it. The expected input parameters are
contained within the frame titled Site and Other Parameters. Provide the inputs
as follows:
- Choose Strike Slip for the fault type from the drop down list.
- Choose Soft Rock Site for the site classification from the drop down list.
- Input the depth of basement rock as 3.0 in the field provided.
- make sure the option Horizontal is selected under the Component frame.
Once all the input has been provided, the parameters are estimated by pressing the
command button. Following this, choose the option PGA
under the frame titled Ground Motion/Response Amplitude. This displays the
PGA for a range of magnitudes as shown below. The PGA is plotted against
distance on a log-log scale for various magnitudes. This is shown below.
Appendix F 353
To view the peak horizontal ground velocity, choose the PGV option. The estimated
values for PGV are displayed as shown below.
Appendix F 354
To view the estimates for the 2.0 sec spectral acceleration, choose the option named
Plot against distance (km) under the frame Plot Options. Then, from the drop
down list, choose the period of 2.0 seconds. The plots are automatically updated to
show the 2.0 sec horizontal spectral acceleration for a range of magnitudes. The
spectral accelerations are plotted against distance on a log-log scale. The display is
shown below.
You can save the data generated in a format compatible with the spreadsheet programs.
The date is generated for various distances, magnitudes and periods.
Appendix F 355
VITA
Riaz Syed was born on October, 15 1967, at Agra, India. This the place where the famous
Taj Mahal is situated. He graduated from Thapar Institute of Engineering and
Technology, Patiala, India in May, 1989 with a Bachelor of Science degree in Civil
Engineering. Following that, he enrolled for graduate studies in Structural Engineering at
the same school and graduated in December, 1990 with a Post-Graduate Diploma.
He started his professional career in February, 1991 with GILCON Project Services (I)
Pvt. Ltd., New Delhi, India as a Junior Design Consultant where he was assigned to carry
out detailed analysis and design of reinforced and prestressed concrete bridges. His stint
at GILCON ended after one year when he joined Consulting Engineering Services (I) Pvt.
Ltd. (CES), New Delhi, India in May, 1992 as Assistant Engineer. During the course of
his work, he was involved in analysis and design of various types of structures at the
national and international level, ranging from long span bridges to building with
complicated structural systems. He was also involved in site supervision for the
construction of post-tensioned box girder bridges and flyovers. He rose to the level of
Engineer within two years of work at CES. In October, 1995 he left CES and joined
Malaysian Japanese Aiport Consortium (MJAC), Kuala Lumpur, Malaysia to work on the
now-world renowned Kuala Lumpur International Airport, Sepang, Malaysia as Senior
Structural Engineer. On this project, his primary responsibilities covered design &
construction monitoring, project coordination and management, and post construction
services. Following the completion of this project, he worked on several other turnkey
infrastructure and commercial building projects. In August, 2001, he enrolled with the
Department of Civil Engineering at Virginia Polytechnic Institute and State University
(VPI&SU), Blacksburg, Virginia to pursue formal graduate studies related to earthquake
engineering. The author is currently completing the requirements for the Master of
Science degree in Civil Engineering at VPI&SU.
Vita 356