Bridge engineering seismic design

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BRIDGE
ENGINEERING
Seismic Design

© 2003 by CRC Press LLC

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BRIDGE
ENGINEERING
Seismic Design

EDITED BY

Wai-Fah Chen
Lian Duan

CRC PR E S S
Boca Raton London New York Washington, D.C.

© 2003 by CRC Press LLC

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This material was previously published in Bridge Engineering Handbook, W.K. Chen and L. Duan, Eds., CRC Press, Boca
Raton, FL, 2000.

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Foreword

Among all engineering subjects, bridge engineering is probably the most difficult on which to compose
a handbook because it encompasses various fields of arts and sciences. It not only requires knowledge
and experience in bridge design and construction, but often involves social, economic, and political
activities. Hence, I wish to congratulate the editors and authors for having conceived this thick volume
and devoted the time and energy to complete it in such short order. Not only is it the first handbook of
bridge engineering as far as I know, but it contains a wealth of information not previously available to
bridge engineers. It embraces almost all facets of bridge engineering except the rudimentary analyses and
actual field construction of bridge structures, members, and foundations. Of course, bridge engineering
is such an immense subject that engineers will always have to go beyond a handbook for additional
information and guidance.
I may be somewhat biased in commenting on the background of the two editors, who both came from
China, a country rich in the pioneering and design of ancient bridges and just beginning to catch up
with the modern world in the science and technology of bridge engineering. It is particularly to the
editors’ credit to have convinced and gathered so many internationally recognized bridge engineers to
contribute chapters. At the same time, younger engineers have introduced new design and construction
techniques into the treatise.
This Handbook is divided into four volumes, namely:
•
•
•
•

Superstructure Design
Substructure Design

Seismic Design
Construction and Maintenance

There are 67 chapters, beginning with bridge concepts and aesthestics, two areas only recently emphasized
by bridge engineers. Some unusual features, such as rehabilitation, retrofit, and maintenance of bridges, are
presented in great detail. The section devoted to seismic design includes soil-foundation-structure interaction. Another section describes and compares bridge engineering practices around the world. I am sure
that these special areas will be brought up to date as the future of bridge engineering develops.
I advise each bridge engineer to have a desk copy of this volume with which to survey and examine
both the breadth and depth of bridge engineering.
T. Y. Lin
Professor Emeritus, University of California at Berkeley
Chairman, Lin Tung-Yen China, Inc.

v

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Preface
The Bridge Engineering Handbook is a unique, comprehensive, and state-of-the-art reference work and
resource book covering the major areas of bridge engineering with the theme “Bridge to the Twenty-First
Century”. It has been written with practicing bridge and structural engineers in mind. The ideal reader
will be an M.S.-level structural and bridge engineer with a need for a single reference source to keep
abreast of new developments and the state of the practice, as well as review standard practices.
The areas of bridge engineering include planning, analysis and design, construction, maintenance, and
rehabilitation. To provide engineers a well-organized and user-friendly, easy-to-follow resource, the
Handbook is divided into and printed in four volumes, I: Superstructure Design, II: Substructure Design,
III: Seismic Design, and IV: Construction and Maintenance.

Volume III: Seismic Design provides the geotechnical earthquake considerations, earthquake damage,
dynamic analysis and nonlinear analysis, design philosophies and performance-based design criteria,
seismic design of concrete and steel bridges, seismic isolation and energy dissipation, active control, soilstructure-foundation interactions, and seismic retrofit technology and practice.
The Handbook stresses professional applications and practical solutions. Emphasis has been placed on
ready-to-use materials. It contains many formulas and tables that give immediate answers to questions arising
from practical works. It describes the basic concepts and assumptions, omitting the derivations of formulas
and theories. It covers traditional and new, innovative practices. An overview of the structure, organization,
and content of the book can be seen by examining the table of contents presented at the beginning of the
book, while an in-depth view of a particular subject can be seen by examining the individual table of contents
preceding each chapter. References at the end of each chapter can be consulted for more detailed studies.
The chapters have been written by many internationally known authors in different countries covering
bridge engineering practices, research, and development in North America, Europe, and Pacific Rim
countries. This Handbook may provide a glimpse of the rapid global economy trend in recent years toward
international outsourcing of practice and competition of all dimensions of engineering. In general, the
Handbook is aimed toward the needs of practicing engineers, but materials may be reorganized to
accommodate several bridge courses at the undergraduate and graduate levels. The book may also be
used as a survey of the practice of bridge engineering around the world.
The authors acknowledge with thanks the comments, suggestions, and recommendations during the
development of the Handbook of Fritz Leonhardt, Professor Emeritus, Stuttgart University, Germany;
Shouji Toma, Professor, Horrai-Gakuen University, Japan; Gerard F. Fox, Consulting Engineer; Jackson
L. Durkee, Consulting Engineer; Michael J. Abrahams, Senior Vice President, Parsons Brinckerhoff Quade
& Douglas, Inc.; Ben C. Gerwick Jr., Professor Emeritus, University of California at Berkeley; Gregory F.
Fenves, Professor, University of California at Berkeley; John M. Kulicki, President and Chief Engineer,
Modjeski and Masters; James Chai, Supervising Transportation Engineer, California Department of
Transportation; Jinrong Wang, Senior Bridge Engineer, California Department of Transportation; and
David W. Liu, Principal, Imbsen & Associates, Inc.
Wai-Fah Chen
Lian Duan
vii

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Editors

Wai-Fah Chen is presently Dean of the College of Engineering at the
University of Hawaii. He was a George E. Goodwin Distinguished
Professor of Civil Engineering and Head of the Department of Structural Engineering at Purdue University from 1976 to 1999.
He received his B.S. in civil engineering from the National ChengKung University, Taiwan, in 1959, M.S. in structural engineering from
Lehigh University, Pennsylvania, in 1963, and Ph.D. in solid mechanics from Brown University, Rhode Island, in 1966. He received the
Distinguished Alumnus Award from the National Cheng-Kung University in 1988 and the Distinguished Engineering Alumnus Medal
from Brown University in 1999.
Dr. Chen’s research interests cover several areas, including constitutive modeling of engineering materials, soil and concrete plasticity,
structural connections, and structural stability. He is the recipient of
several national engineering awards, including the Raymond Reese
Research Prize and the Shortridge Hardesty Award, both from the
American Society of Civil Engineers, and the T. R. Higgins Lectureship Award from the American Institute
of Steel Construction. In 1995, he was elected to the U.S. National Academy of Engineering. In 1997, he
was awarded Honorary Membership by the American Society of Civil Engineers. In 1998, he was elected
to the Academia Sinica (National Academy of Science) in Taiwan.
A widely respected author, Dr. Chen authored and coauthored more than 20 engineering books and
500 technical papers. His books include several classical works such as Limit Analysis and Soil Plasticity
(Elsevier, 1975), the two-volume Theory of Beam-Columns (McGraw-Hill, 1976–77), Plasticity in Reinforced Concrete (McGraw-Hill, 1982), and the two-volume Constitutive Equations for Engineering Materials
(Elsevier, 1994). He currently serves on the editorial boards of more than 10 technical journals. He has
been listed in more than 20 Who’s Who publications.
Dr. Chen is the editor-in-chief for the popular 1995 Civil Engineering Handbook, the 1997 Handbook
of Structural Engineering, and the 1999 Bridge Engineering Handbook. He currently serves as the consulting
editor for McGraw-Hill’s Encyclopedia of Science and Technology.

He has been a longtime member of the Executive Committee of the Structural Stability Research
Council and the Specification Committee of the American Institute of Steel Construction. He has been
a consultant for Exxon Production Research on offshore structures, for Skidmore, Owings, and Merrill
in Chicago on tall steel buildings, and for the World Bank on the Chinese University Development
Projects, among many others.
Dr. Chen has taught at Lehigh University, Purdue University, and the University of Hawaii.

ix

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Lian Duan is a Senior Bridge Engineer with the California Department of Transportation, U.S., and Professor of Structural Engineering at Taiyuan University of Technology, China.
He received his B.S. in civil engineering in 1975, M.S. in structural
engineering in 1981 from Taiyuan University of Technology, and
Ph.D. in structural engineering from Purdue University, West Lafayette, Indiana, in 1990. Dr. Duan worked at the Northeastern China
Power Design Institute from 1975 to 1978.
Dr. Duan’s research interests cover areas including inelastic behavior of reinforced concrete and steel structures, structural stability,
and seismic bridge analysis and design. With more than 60 authored
or coauthored papers, chapters, and reports, and his research has
focused on the development of unified interaction equations for steel
beam-columns, flexural stiffness of reinforced concrete members, effective length factors of compression
members, and design of bridge structures.
Dr. Duan is also an esteemed practicing engineer. He has designed numerous building and bridge
structures. He was lead engineer for the development of the seismic retrofit design criteria for the San
Francisco-Oakland Bay Bridge West spans and made significant contributions to the project. He is coeditor of the Structural Engineering Handbook CRCnetBase 2000 (CRC Press, 2000) and the Bridge
Engineering Handbook (CRC Press, 2000), winner of Choice Magazine’s Outstanding Academic Title
Award for 2000. He received the ASCE 2001 Arthur M. Wellington Prize for his paper “Section

Properties for Latticed Members of San Francisco–Oakland Bay Bridge.” He currently serves as Caltrans
Structured Steel Committee Chairman and a member of the Transportation Research Board AC202
Steel Bridge Committee.

x

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Contributors

Mohammed Akkari

Steven Kramer

Charles Scawthorn

California Department of
Transportation
Sacramento, California

University of Washington
Seattle, Washington

Consulting Engineer
Berkeley, California

Fang Li

Keh-Chyuan Tsai

California Department of
Transportation
Sacramento, California

Department of Civil Engineering
National Taiwan University
Taipei, Taiwan
Republic of China

Fadel Alameddine
California Department of
Transportation
Sacramento, California

Brian Maroney
Rambabu Bavirisetty
California Department of
Transportation
Sacramento, California

California Department of
Transportation
Sacramento, California

Wen-Shou Tseng
International Civil Engineering
Consultants, Inc.

Berkeley, California

Jack P. Moehle
Michel Bruneau
Department of Civil Engineering
State University of New York
Buffalo, New York

Department of Civil and
Environmental Engineering
University of California at
Berkeley
Berkeley, California

Chia-Ming Uang
Department of Civil Engineering
University of California at San
Diego
La Jolla, California

Lian Duan
California Department of
Transportation
Sacramento, California

Joseph Penzien

Shigeki Unjoh

International Civil Engineering

Consultants, Inc.
Berkeley, California

Public Works Research Institute
Tsukuba Science City, Japan

Marc O. Eberhard
Department of Civil and
Environmental Engineering
University of Washington
Seattle, Washington

James Roberts

Murugesu
Vinayagamoorthy

California Department of
Transportation
Sacramento, California

California Department of
Transportation
Sacramento, California

Kevin I. Keady

Thomas E. Sardo

Zaiguang Wu

California Department of
Transportation
Sacramento, California

California Department of
Transportation
Sacramento, California

California Department of
Transportation
Sacramento, California

xi

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Yan Xiao

Rihui Zhang

Department of Civil Engineering
University of Southern
California
Los Angeles, California

California Department of

Transportation
Sacramento, California

xii

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Contents

1

Geotechnical Earthquake Considerations Steven Kramer and Charles Scawthorn ....1-1

2

Earthquake Damage to Bridges Jack P. Moehle and Marc O. Eberhard..........................2-1

3

Dynamic Analysis Rambabu Bavirisetty, Murugesu Vinayagamoorthy, and Lian Duan ......3-1

4

Nonlinear Analysis of Bridge Structures Mohammed Akkari and Lian Duan...........4-1

5

Seismic Design Philosophies and Performance-Based Design Criteria

6

Seismic Design of Reinforced Concrete Bridges Yan Xiao ......................................6-1

7

Seismic Design of Steel Bridges Chia-Ming Uang, Keh-Chyuan Tsai,

8

Seismic Retrofit Practice James Roberts and Brian Maroney .............................................8-1

9

Seismic Isolation and Supplemental Energy Dissipation Rihui Zhang...............9-1

10

Soil–Foundation–Structure Interaction Wen-Shou Tseng and Joseph Penzien .........10-1

11

Seismic Retrofit Technology Kevin I. Keady, Fadel Alameddine,

12

Seismic Design Practice in Japan Shigeki Unjoh ..........................................................12-1

13

Active Control in Bridge Engineering Zaiguang Wu .................................................13-1

Lian Duan and Fang Li .......................................................................................................5-1

and Michel Bruneau ............................................................................................................7-1

and Thomas E. Sardo ........................................................................................................11-1

xiii

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1
Geotechnical Earthquake
Considerations
1.1
1.2
1.3

Introduction .................................................................1-1
Seismology ....................................................................1-2
Measurement of Earthquakes......................................1-3
Magnitude • Intensity • Time History • Elastic Response
Spectra • Inelastic Response Spectra

1.4
1.5
1.6

Strong Motion Attenuation and Duration...............1-10
Probabilistic Seismic Hazard Analysis ......................1-12
Site Response ..............................................................1-14
Basic Concepts • Evidence for Local Site Effects •
Methods of Analysis • Site Effects for Different Soil
Conditions

1.7

Earthquake-Induced Settlement ...............................1-21
Settlement of Dry Sands • Settlement of Saturated
Sands

1.8

Steven Kramer
University of Washington

Charles Scawthorn
Consulting Engineer

1.1

Ground Failure ...........................................................1-25
Liquefaction • Liquefaction Susceptibility • Initiation
of Liquefaction • Lateral Spreading • Global Instability
• Retaining Structures

1.9

Soil Improvement.......................................................1-35
Densification Techniques • Drainage Techniques •
Reinforcement Techniques • Grouting/Mixing
Techniques

Introduction

Earthquakes are naturally occurring broad-banded vibratory ground motions that are due to a
number of causes, including tectonic ground motions, volcanism, landslides, rockbursts, and manmade explosions, the most important of which are caused by the fracture and sliding of rock along
tectonic faults within the Earth’s crust. For most earthquakes, shaking and ground failure are the
dominant and most widespread agents of damage. Shaking near the actual earthquake rupture
lasts only during the time when the fault ruptures, a process that takes seconds or at most a few
minutes. The seismic waves generated by the rupture propagate long after the movement on the
fault has stopped, however, spanning the globe in about 20 min. Typically, earthquake ground
motions are powerful enough to cause damage only in the near field (i.e., within a few tens of
kilometers from the causative fault) — in a few instances, long-period motions have caused

1-1

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1-2

Bridge Engineering: Seismic Design

FIGURE 1.1 Fault types.

significant damage at great distances, to selected lightly damped structures, such as in the 1985
Mexico City earthquake, where numerous collapses of mid- and high-rise buildings were due to

a magnitude 8.1 earthquake occurring at a distance of approximately 400 km from Mexico City.

1.2

Seismology

Plate Tectonics: In a global sense, tectonic earthquakes result from motion between a number of
large plates constituting the Earth’s crust or lithosphere (about 15 in total). These plates are driven
by the convective motion of the material in the Earth’s mantle, which in turn is driven by heat
generated at the Earth’s core. Relative plate motion at the fault interface is constrained by friction
and/or asperities (areas of interlocking due to protrusions in the fault surfaces). However, strain
energy accumulates in the plates, eventually overcomes any resistance, and causes slip between the
two sides of the fault. This sudden slip, termed elastic rebound by Reid [49] based on his studies
of regional deformation following the 1906 San Francisco earthquake, releases large amounts of
energy, which constitute the earthquake. The location of initial radiation of seismic waves (i.e., the
first location of dynamic rupture) is termed the hypocenter, while the projection on the surface of
the Earth directly above the hypocenter is termed the epicenter. Other terminology includes nearfield (within one source dimension of the epicenter, where source dimension refers to the length
of faulting), far-field (beyond near-field), and meizoseismal (the area of strong shaking and damage). Energy is radiated over a broad spectrum of frequencies through the Earth, in body waves
and surface waves [4]. Body waves are of two types: P waves (transmitting energy via push–pull
motion) and slower S waves (transmitting energy via shear action at right angles to the direction
of motion). Surface waves are also of two types: horizontally oscillating Love waves (analogous to
S body waves) and vertically oscillating Rayleigh waves.
Faults are typically classified according to their sense of motion, Figure 1.1. Basic terms include
transform or strike slip (relative fault motion occurs in the horizontal plane, parallel to the strike
of the fault), dip-slip (motion at right angles to the strike, up- or down-slip), normal (dip-slip
motion, two sides in tension, move away from each other), reverse (dip-slip, two sides in compression, move toward each other), and thrust (low-angle reverse faulting).
Generally, earthquakes will be concentrated in the vicinity of faults; faults that are moving more
rapidly than others will tend to have higher rates of seismicity, and larger faults are more likely than
others to produce a large event. Many faults are identified on regional geologic maps, and useful
information on fault location and displacement history is available from local and national geologic

surveys in areas of high seismicity. An important development has been the growing recognition
of blind thrust faults, which emerged as a result of the several earthquakes in the 1980s, none of
which was accompanied by surface faulting [61].

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1-3

Geotechnical Earthquake Considerations

1.3

Measurement of Earthquakes

Magnitude
An individual earthquake is a unique release of strain energy — quantification of this energy has
formed the basis for measuring the earthquake event. C.F. Richter [51] was the first to define
earthquake magnitude, as
ML = log A – log Ao

(1.1)

where ML is local magnitude (which Richter defined only for Southern California), A is the maximum trace amplitude in microns recorded on a standard Wood–Anderson short-period torsion
seismometer at a site 100 km from the epicenter, and log Ao is a standard value as a function of
distance, for instruments located at distances other than 100 km and less than 600 km. A number
of other magnitudes have since been defined, the most important of which are surface wave
magnitude MS, body wave magnitude mb, and moment magnitude MW. Magnitude can be related
to the total energy in the expanding wave front generated by an earthquake, and thus to the total
energy release — an empirical relation by Richter is

log 10 Es = 11.8 + 1.5 Ms

(1.2)

where ES is the total energy in ergs. Due to the observation that deep-focus earthquakes commonly
do not register measurable surface waves with periods near 20 s, a body wave magnitude mb was
defined [25], which can be related to MS [16]:
m b = 2.5 + 0.63MS

(1.3)

Body wave magnitudes are more commonly used in eastern North America, due to the deeper
earthquakes there. More recently, seismic moment has been employed to define a moment magnitude MW [26] (also denoted as boldface M), which is finding increased and widespread use:
Log M o = 1.5 M W + 16.0

(1.4)

where seismic moment Mo (dyne-cm) is defined as [33]
Mo = mAu

(1.5)

where µ is the material shear modulus, A is the area of fault plane rupture, and u is the mean
relative displacement between the two sides of the fault (the averaged fault slip). Comparatively,
MW and MS are numerically almost identical up to magnitude 7.5. Figure 1.2 indicates the relationship between moment magnitude and various magnitude scales.
From the foregoing discussion, it can be seen that magnitude and energy are related to fault
rupture length and slip. Slemmons [60] and Bonilla et al. [5] have determined statistical relations
between these parameters, for worldwide and regional data sets, aggregated and segregated by type
of faulting (normal, reverse, strike-slip). Bonilla et al.’s worldwide results for all types of faults are
Ms = 6.04 + 0.708 log10 L

log10 L = – 2.77 + 0.619 Ms

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s = 0.306

(1.6)

s = 0.286

(1.7)


1-4

Bridge Engineering: Seismic Design

FIGURE 1.2 Relationship between moment magnitude and various magnitude scales. (Source: Campbell, K. W.,
Earthquake Spectra, 1(4), 759–804, 1985. With permission.)

Ms = 6.95 + 0.723 log 10d
log10d = –3.58 + 0.5550 Ms

s = 0.323

(1.8)

s = 0.282

(1.9)

which indicates, for example, that for MS = 7, the average fault rupture length is about 36 km (and
the average displacement is about 1.86 m). Conversely, a fault of 100 km length is capable of about
an MS = 7.5* event (see also Wells and Coppersmith [66] for alternative relations).

Intensity
In general, seismic intensity is a metric of the effect, or the strength, of an earthquake hazard at a
specific location. While the term can be generically applied to engineering measures such as peak
ground acceleration, it is usually reserved for qualitative measures of location-specific earthquake
effects, based on observed human behavior and structural damage. Numerous intensity scales were
developed in preinstrumental times — the most common in use today are the Modified Mercalli
(MMI) [68] (Table 1.1), the Rossi–Forel (R-F), the Medvedev-Sponheur-Karnik (MSK-64, 1981),
and the Japan Meteorological Agency (JMA) scales.

Time History
Sensitive strong motion seismometers have been available since the 1930s, and they record actual ground
motions specific to their location, Figure 1.3. Typically, the ground motion records, termed seismographs or time histories, have recorded acceleration (these records are termed accelerograms), for
many years in analog form on photographic film and, more recently, digitally. Analog records required
considerable effort for correction, due to instrumental drift, before they could be used.
Time histories theoretically contain complete information about the motion at the instrumental
location, recording three traces or orthogonal records (two horizontal and one vertical). Time
histories (i.e., the earthquake motion at the site) can differ dramatically in duration, frequency,
content, and amplitude. The maximum amplitude of recorded acceleration is termed the peak
*Note that L = g(MS) should not be inverted to solve for MS = f(L), as a regression for y = f(x) is different from
a regression for x = g(y).

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Geotechnical Earthquake Considerations

TABLE 1.1
I
II
III
IV

V

VI
VII

VIII

IX

X

XI
XII

1-5

Modified Mercalli Intensity Scale of 1931

Not felt except by a very few under especially favorable circumstances
Felt only by a few persons at rest, especially on upper floors of buildings. Delicately suspended objects may swing.
Felt quite noticeably indoors, especially on upper floors of buildings, but many people do not recognize it as an
earthquake; standing automobiles may rock slightly; vibration like passing truck; duration estimated
During the day felt indoors by many, outdoors by few; at night some awakened; dishes, windows, and doors

disturbed; walls make creaking sound; sensation like heavy truck striking building; standing automobiles rock
noticeably
Felt by nearly everyone; many awakened; some dishes, windows, etc., broken; a few instances of cracked plaster;
unstable objects overturned; disturbance of trees, poles, and other tall objects sometimes noticed; pendulum clocks
may stop
Felt by all; many frightened and run outdoors; some heavy furniture moved; a few instances of fallen plaster or
damaged chimneys; damage slight
Everybody runs outdoors; damage negligible in buildings of good design and construction, slight to moderate in
well-built ordinary structures; considerable in poorly built or badly designed structures; some chimneys broken;
noticed by persons driving automobiles
Damage slight in specially designed structures, considerable in ordinary substantial buildings, with partial collapse,
great in poorly built structures; panel walls thrown out of frame structures; fall of chimneys, factory stacks,
columns, monuments, walls; heavy furniture overturned; sand and mud ejected in small amounts; changes in well
water; persons driving automobiles disturbed
Damage considerable in specially designed structures; well-designed frame structures thrown out of plumb; great
in substantial buildings, with partial collapse; buildings shifted off foundations; ground cracked conspicuously;
underground pipes broken
Some well-built wooden structures destroyed; most masonry and frame structures destroyed with foundations;
ground badly cracked; rails bent; landslides considerable from riverbanks and steep slopes; shifted sand and mud;
water splashed over banks
Few, if any, masonry structures remain standing; bridges destroyed; broad fissures in ground; underground pipelines
completely out of service; earth slumps and land slips in soft ground; rails bent greatly
Damage total; waves seen on ground surfaces; lines of sight and level distorted; objects thrown upward into the air

After Wood and Neumann [68].

FIGURE 1.3

Typical earthquake accelerograms. (Courtesy of Darragh et al., 1994.)

ground acceleration, PGA (also termed the ZPA, or zero period acceleration); peak ground velocity
(PGV) and peak ground displacement (PGD) are the maximum respective amplitudes of velocity
and displacement. Acceleration is normally recorded, with velocity and displacement being determined by integration; however, velocity and displacement meters are deployed to a lesser extent.
Acceleration can be expressed in units of cm/s2 (termed gals), but is often also expressed in terms

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1-6

Bridge Engineering: Seismic Design

of the fraction or percent of the acceleration of gravity (980.66 gals, termed 1 g). Velocity is expressed
in cm/s (termed kine). Recent earthquakes — 1994 Northridge, MW 6.7 and 1995 Hanshin (Kobe)
MW 6.9 — have recorded PGAs of about 0.8 g and PGVs of about 100 kine, while almost 2 g was
recorded in the 1992 Cape Mendocino earthquake.

Elastic Response Spectra
If a single-degree-of-freedom (SDOF) mass is subjected to a time history of ground (i.e., base)
motion similar to that shown in Figure 1.3, the mass or elastic structural response can be readily
calculated as a function of time, generating a structural response time history, as shown in
Figure 1.4 for several oscillators with differing natural periods. The response time history can be
calculated by direct integration of Eq. (1.1) in the time domain, or by solution of the Duhamel
integral. However, this is time-consuming, and the elastic response is more typically calculated in
the frequency domain [12].

FIGURE 1.4 Computation of deformation (or displacement) response spectrum. (Source: Chopra, A. K., Dynamics
of Structures, A Primer, Earthquake Engineering Research Institute, Oakland, CA, 1981. With permission.)

© 2003 by CRC Press LLC

1-7

Geotechnical Earthquake Considerations

FIGURE 1.5 Response spectra. (Source: Chopra, A. K., Dynamics of Structures, A Primer, Earthquake Engineering
Research Institute, Oakland, CA, 1981. With permission.)

For design purposes, it is often sufficient to know only the maximum amplitude of the
response time history. If the natural period of the SDOF is varied across a spectrum of
engineering interest (typically, for natural periods from 0.03 to 3 or more seconds, or frequencies of 0.3 to 30+ Hz), then the plot of these maximum amplitudes is termed a response
spectrum. Figure 1.4 illustrates this process, resulting in Sd, the displacement response spectrum,
while Figure 1.5 shows (a) the Sd, displacement response spectrum, (b) Sv, the velocity response
spectrum (also denoted PSV, the pseudo-spectral velocity, “pseudo” to emphasize that this
spectrum is not exactly the same as the relative velocity response spectrum), and (c) Sa, the
acceleration response spectrum. Note that
Sv =

2p
S = vSd
T d

Sa =

2p
2p
Sv = vSv = Ê ˆ Sd = v2 Sd
Ë
T

T¯

(1.10)

and

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2

(1.11)


1-8

Bridge Engineering: Seismic Design

FIGURE 1.6 Response spectra, tripartite plot (El Centro S 0° E component). (Source: Chopra, A. K., Dynamics of
Structures, A Primer, Earthquake Engineering Research Institute, Oakland, CA, 1981. With permission.)

Response spectra form the basis for much modern earthquake engineering structural analysis and
design. They are readily calculated if the ground motion is known. For design purposes, however,
response spectra must be estimated — this process is discussed below. Response spectra may be
plotted in any of several ways, as shown in Figure 1.5 with arithmetic axes, and in Figure 1.6, where
the velocity response spectrum is plotted on tripartite logarithmic axes, which equally enables
reading of displacement and acceleration response. Response spectra are most normally presented
for 5% of critical damping.

Inelastic Response Spectra
While the foregoing discussion has been for elastic response spectra, most structures are not

expected, or even designed, to remain elastic under strong ground motions. Rather, structures are

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Geotechnical Earthquake Considerations

1-9

FIGURE 1.7 Idealized elastic design spectrum, horizontal motion (ZPA = 0.5 g, 5% damping, one sigma cumulative
probability). (Source: Newmark, N. M. and Hall, W. J., Earthquake Spectra and Design, Earthquake Engineering
Research Institute, Oakland, CA, 1982. With permission.)

FIGURE 1.8 Normalized response spectra shapes. (Source: Uniform Building Code, Structural Engineering Design
Provisions, Vol. 2, Intl. Conf. Building Officials, Whittier, 1994. With permission.)

© 2003 by CRC Press LLC


1-10

Bridge Engineering: Seismic Design

FIGURE 1.9 Inelastic response spectra for earthquakes. (Source: Newmark, N. M. and Hall, W. J., Earthquake Spectra
and Design, Earthquake Engineering Research Institute, Oakland, CA, 1982.)

expected to enter the inelastic region — the extent to which they behave inelastically can be defined
by the ductility factor, µ:
m=

um
uy

(1.12)

where um is the actual displacement of the mass under actual ground motions, and uy is the
displacement at yield (i.e., that displacement that defines the extreme of elastic behavior). Inelastic
response spectra can be calculated in the time domain by direct integration, analogous to elastic
response spectra but with the structural stiffness as a nonlinear function of displacement, k = k(u).
If elastoplastic behavior is assumed, then elastic response spectra can be readily modified to reflect
inelastic behavior, on the basis that (1) at low frequencies (<0.3 Hz), displacements are the same,
(2) at high frequencies (>33 Hz), accelerations are equal, and (3) at intermediate frequencies, the
absorbed energy is preserved. Actual construction of inelastic response spectra on this basis is shown
in Figure 1.9, where DVAAo is the elastic spectrum, which is reduced to D¢ and V¢ by the ratio of
1/µ for frequencies less than 2 Hz, and by the ratio of 1/(2µ – 1)⁄ between 2 and 8 Hz. Above 33
Hz, there is no reduction. The result is the inelastic acceleration spectrum (D¢V¢A¢Ao), while A≤Ao¢
is the inelastic displacement spectrum. A specific example, for ZPA = 0.16 g, damping = 5% of
critical, and µ = 3, is shown in Figure 1.10.

1.4

Strong Motion Attenuation and Duration

The rate at which earthquake ground motion decreases with distance, termed attenuation, is a
function of the regional geology and inherent characteristics of the earthquake and its source.
Campbell [10] offers an excellent review of North American relations up to 1985. Initial relationships

© 2003 by CRC Press LLC

1-11

Geotechnical Earthquake Considerations

FIGURE 1.10 Example of inelastic response spectra. (Source: Newmark, N. M. and Hall, W. J., Earthquake Spectra
and Design, Earthquake Engineering Research Institute, Oakland, CA, 1982.)

were for PGA, but regression of the amplitudes of response spectra at various periods is now
common, including consideration of fault type and effects of soil. A currently favored relationship is
Campbell and Bozorgnia [11] (PGA — Worldwide Data)
ln( PGA) = -3.512 + 0.904 M - 1.328 ln

{R

2
s

+ [0.149 exp(0.647 M )]

2

[
]
+ [0.440 - 0.171 ln( R )]S + [0.405 - 0.222 ln( R )]S
+ 1.125 - 0.112 ln( Rs ) - 0.0957 M F
s

where
PGA
M

Rs
F

=
=
=
=

Ssr
=
Shr
=
Ssr = Shr =
e
=

sr

s

hr

}
(1.13)

+e

the geometric mean of the two horizontal components of peak ground acceleration (g)
moment magnitude (Mw)
the closest distance to seismogenic rupture on the fault (km)

0 for strike-slip and normal faulting earthquakes, and 1 for reverse, reverse-oblique, and
thrust faulting earthquakes
1 for soft-rock sites
1 for hard-rock sites
0 for alluvium sites
a random error term with zero mean and standard deviation equal to sln(PGA), the
standard error of estimate of ln(PGA)

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1-12

Bridge Engineering: Seismic Design

FIGURE 1.11 Campbell and Bozorgnia worldwide attenuation relationship showing (for alluvium) the scaling of
peak horizontal acceleration with magnitude and style of faulting. (Source: Campbell, K. W. and Bozorgnia, Y., in
Proc. Fifth U.S. National Conference on Earthquake Engineering, Earthquake Engineering Research Institute, Oakland,
CA, 1994. With permission.)

Regarding the uncertainty, e was estimated as
0.55

if PGA < 0.068

s ln ( PGA) = 0.173 – 0.140 ln(PGA)
0.39

if 0.068 £ PGA £ 0.21
if PGA > 0.21

Figure 1.11 indicates, for alluvium, median values of the attenuation of peak horizontal acceleration
with magnitude and style of faulting. Many other relationships are also employed (e.g., Boore et al.[6]).

1.5

Probabilistic Seismic Hazard Analysis

The probabilistic seismic hazard analysis (PSHA) approach entered general practice with Cornell’s
[13] seminal paper, and basically employs the theorem of total probability to formulate:
P(Y ) =

   p ( Y M, R ) p ( M ) p ( R )
F

M

(1.14)

R

where
Y
= a measure of intensity, such as PGA, response spectral parameters PSV, etc.
p(YÔM, R) = the probability of Y given earthquake magnitude M and distance R (i.e., attenuation)
p(M)
= the probability of a given earthquake magnitude M
p(R)
= the probability of a given distance R
F

= seismic sources, whether discrete, such as faults, or distributed
This process is illustrated in Figure 1.12, where various seismic sources (faults modeled as line
sources and dipping planes, and various distributed or area sources, including a background source

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Geotechnical Earthquake Considerations

1-13

FIGURE 1.12 Elements of seismic hazard analysis — seismotectonic model is composed of seismic sources, whose
seismicity is characterized on the basis of historic seismicity and geologic data, and whose effects are quantified at
the site via strong motion attenuation models.

to account for miscellaneous seismicity) are identified, and their seismicity characterized on the
basis of historic seismicity and/or geologic data. The effects at a specific site are quantified on the
basis of strong ground motion modeling, also termed attenuation. These elements collectively are
the seismotectonic model — their integration results in the seismic hazard.
There is an extensive literature on this subject [42,50] so that only key points will be discussed
here. Summation is indicated, as integration requires closed-form solutions, which are usually
precluded by the empirical form of the attenuation relations. The p(YÔM, R) term represents the
full probabilistic distribution of the attenuation relation — summation must occur over the full
distribution, due to the significant uncertainty in attenuation. The p(M) term is referred to as the
magnitude–frequency relation, which was first characterized by Gutenberg and Richter [24] as
log N(m) = a N – bNm

(1.15)

where N(m) = the number of earthquake events equal to or greater than magnitude m occurring

on a seismic source per unit time, and aN and bN are regional constants ( 10 aN = the total number
of earthquakes with magnitude >0, and bN is the rate of seismicity; bN is typically 1 ± 0.3). The
Gutenberg–Richter relation can be normalized to
F(m) = 1. – exp [– B M (m – M o)]

(1.16)

where F(m) is the cumulative distribution function (CDF) of magnitude, BM is a regional constant,
and Mo is a small enough magnitude such that lesser events can be ignored. Combining this with
a Poisson distribution to model large earthquake occurrence [20] leads to the CDF of earthquake
magnitude per unit time
F(m) = exp [–exp {– a M (m – µM)}]

(1.17)

which has the form of a Gumbel [23] extreme value type I (largest values) distribution (denoted
EXI,L), which is an unbounded distribution (i.e., the variate can assume any value). The parameters

© 2003 by CRC Press LLC


1-14

Bridge Engineering: Seismic Design

aM and µM can be evaluated by a least-squares regression on historical seismicity data, although the
probability of very large earthquakes tends to be overestimated. Several attempts have been made
to account for this (e.g., Cornell and Merz [14]). Yegulalp and Kuo [70] have used Gumbel’s Type
III (largest value, denoted EXIII,L) to successfully account for this deficiency. This distribution
È w - mˆ k ù

F( m) = exp Í-Ê
ú
ÍÎ Ë w - u ¯ úû

(1.18)

has the advantage that w is the largest possible value of the variate (i.e., earthquake magnitude), thus
permitting (when w, u, and k are estimated by regression on historical data) an estimate of the source’s
largest possible magnitude. It can be shown (Yegulalp and Kuo [70]) that estimators of w, u, and k can
be obtained by satisfying Kuhn–Tucker conditions, although, if the data is too incomplete, the EXIII,L
parameters approach those of the EXI,L. Determination of these parameters requires careful analysis of
historical seismicity data (which is highly complex and something of an art [17]), and the merging of
the resulting statistics with estimates of maximum magnitude and seismicity made on the basis of
geologic evidence (i.e., as discussed above, maximum magnitude can be estimated from fault length,
fault displacement data, time since last event, and other evidence, and seismicity can be estimated from
fault slippage rates combined with time since the last event, see Schwartz [55] for an excellent discussion
of these aspects). In a full probabilistic seismic hazard analysis, many of these aspects are treated fully
or partially probabilistically, including the attenuation, magnitude–frequency relation, upper- and
lower-bound magnitudes for each source zone, geographic bounds of source zones, fault rupture length,
and many other aspects. The full treatment requires complex specialized computer codes, which incorporate uncertainty via use of multiple alternative source zonations, attenuation relations, and other
parameters [3,19], often using a logic tree format. A number of codes have been developed using the
public-domain FRISK (Fault RISK) code first developed by McGuire [37].

1.6

Site Response

When seismic waves reach a site, the ground motions they produce are affected by the geometry
and properties of the geologic materials at that site. At most bridge sites, rock will be covered by
some thickness of soil which can markedly influence the nature of the motions transmitted to the

bridge structure as well as the loading on the bridge foundation. The influence of local site conditions
on ground response has been observed in many past earthquakes, but specific provisions for site
effects were not incorporated in codes until 1976.
The manner in which a site responds during an earthquake depends on the near-surface stiffness
gradient and on how the incoming waves are reflected and refracted by the near-surface materials.
The interaction between seismic waves and near-surface materials can be complex, particularly when
surface topography and/or subsurface stratigraphy is complex. Quantification of site response has
generally been accomplished by analytical or empirical methods.

Basic Concepts
The simplest possible case of site response would consist of a uniform layer of viscoelastic soil of
density, r, shear modulus, G, viscosity, h, and thickness, H, resting on rigid bedrock and subjected
to vertically propagating shear waves (Figure 1.13[top]). The response of the layer would be governed
by the wave equation
r

© 2003 by CRC Press LLC

∂ 2u
∂ 2u
∂3u
= G 2 +h 2
2
∂t
∂z
∂z ∂t

(1.19)