Performance-Based Design of Seismically Isolated Bridges
by
Eric Leonard Anderson
B.S. (California Polytechnic State University) 1987M.S. (University of California, Berkeley) 1996
A dissertation submitted in partial satisfaction of the
requirements for the degree of
Doctor of Philosophyin
Engineering - Civil and Environmental
in the
GRADUATE DIVISION
of the
UNIVERSITY OF CALIFORNIA, BERKELEY
Committee in charge:
Professor Stephen A. Mahin, ChairProfessor Gregory L. Fenves
Professor Ole Hald
Spring 2003
The dissertation of Eric Leonard Anderson is approved:
University of California, Berkeley
Spring 2003
Chair Date
Date
Date
Performance-Based Design of Seismically Isolated Bridges
Copyright 2003
by
Eric Leonard Anderson
Performance-Based Design of Seismically Isolated Bridges
by
Eric Leonard Anderson
B.S. (California Polytechnic State University) 1987M.S. (University of California, Berkeley) 1996
A dissertation submitted in partial satisfaction of the
requirements for the degree of
Doctor of Philosophyin
Engineering - Civil and Environmental
in the
GRADUATE DIVISION
of the
UNIVERSITY OF CALIFORNIA, BERKELEY
Committee in charge:
Professor Stephen A. Mahin, ChairProfessor Gregory L. Fenves
Professor Ole Hald
Spring 2003
The dissertation of Eric Leonard Anderson is approved:
University of California, Berkeley
Spring 2003
Chair Date
Date
Date
Performance-Based Design of Seismically Isolated Bridges
Copyright 2003
by
Eric Leonard Anderson
i
Table of Contents
Section Page
Chapter 1 Introduction 1
1.1 Seismic Protective Systems for Bridges 1
1.2 Commentary on the State of the Art 4
1.3 The Protective Systems Research Program 6
1.3.1 Overall Objectives of the Program 6
1.3.2 Overall Tasks Undertaken 6
1.3.3 Protective system devices considered 7
1.3.4 Test Models 8
1.4 Scope of this Report 9
1.5 Organization of this Report 10
Chapter 2 Preliminary Evaluations 16
2.1 Introduction 16
2.2 AASHTO Guide Specifications 16
2.3 Parametric Seismic Analysis of Idealized Elevated Isolated Bridges19
2.3.1 Introduction 19
2.3.2 Idealized Modeling Assumptions 20
2.3.3 Analytical Models 22
2.3.4 Ground Motion Time-Histories 26
2.3.5 Parametric Studies 27
2.3.5.1 Influence of Substructure or Initial System Flexibility 27
2.3.5.2 Influence of Isolator or Second-Slope Flexibility and Characteristic Strength 31
ii
2.3.5.3 Influence of Substructure Mass 36
2.3.5.4 Influence of Substructure Damping 39
2.3.5.5 Influence of Bi-Directional Ground Motion Input 43
2.3.5.6 Influence of Superstructure Mass Eccentricity 45
2.3.5.7 Influence of Substructure Stiffness Eccentricity 48
2.4 Summary 51
Chapter 3 Testing of a Bridge Deck Model 67
3.1 Introduction 67
3.1.1 Similitude Requirements 68
3.1.2 Design criteria 70
3.1.3 Design Development 72
3.1.4 Final Specimen Design 73
3.1.5 Test Set-Up and Protocol 77
3.2 Earthquake Histories for Testing 85
3.3 Pre-Test Analysis of Bridge Deck Model 102
3.4 Experimental Results for Configuration 1 104
3.5 Experimental Results for Configuration 2 107
3.6 Experimental Results for Configuration 3 108
3.7 Experimental Results for Configuration 4 110
3.8 Experimental Results for Configuration 5 112
3.9 Experimental Results for Configuration 6 114
3.10 Experimental Results for Configuration 7 116
3.11 Experimental Results for Configuration 8 118
3.12 Experimental Results for Configuration 9 120
3.13 Experimental Results for Configuration 10 121
3.14 Experimental Characterization Data for FP Slider Composites 122
iii
Chapter 4 Evaluation of Bridge Model Test Data 127
4.1 Introduction 127
4.2 Influence of Substructure Flexibility 128
4.3 Influence of Isolator Second-Slope Flexibilityand Strength 130
4.4 Influence of Substructure Mass 133
4.5 Influence of Bi-directional Motions 135
4.6 Influence of Substructure Strength 136
4.7 Influence of Superstructure Mass Eccentricity 138
4.8 Influence of Substructure Stiffness Eccentricity 140
4.9 Response of Two-span Isolated Bridge 142
4.9.1 Introduction 142
4.9.2 Characteristic Distribution of Force & Displacement Demands 143
4.9.3 Local Geometric Effects 144
4.10 Substitute System vs. MDOF Response 146
4.11 Influence of Ground Motion 149
4.12 Influence of Vertical Motions on Sliding Systems 154
4.13 Effect of Impact Against Bearing Restraint System 155
4.14 Effect of Bearing Wear on Systems EmployingFP Bearings 157
Chapter 5 Displacement Estimates in Isolated Bridges 214
5.1 Introduction 214
5.1.1 Problem Summary 214
5.2 Analytical Bridge Models 215
5.3 Ground Motion Time-history Suites 216
iv
5.3.1 Suites for Evaluation of the AASHTO Uniform Load Methodand R-factor Provisions 218
5.3.2 Suites for Evaluation of the Effect of Bi-directional Motionson AASHTO Provisions 226
5.3.3 Suites for Parametric Studies of Isolated Bridge Responseand Influence of Substructure Mass and Damping 239
5.4 An Evaluation of the AASHTO Uniform Load Method 250
5.4.1 Introduction 250
5.4.2 AASHTO Uniform Load Method 250
5.4.3 Evaluation Procedure 254
5.4.3.1 Method A: Design Spectrum 254
5.4.3.2 Method B: Specified Ground Motion 255
5.4.4 Isolated Bridge Systems 257
5.4.5 Numerical Analysis Procedure 257
5.4.6 Results 258
5.4.7 Observation summary 269
5.5 Bi-Directional Earthquake Shaking 273
5.5.1 Introduction 273
5.5.2 Isolated Bridge System Models 277
5.5.3 Analytical Procedure and Response Parameters 278
5.5.4 Results 280
5.5.5 Observation Summary 283
5.6 Influence of Substructure Yielding on System Response 288
5.6.1 Introduction 288
5.6.2 System Characterization 290
5.6.3 AASHTO Substructure Component Design Procedures 290
5.6.4 Evaluation Procedure 293
v
5.6.4.1 Response parameters 295
5.6.5 Results 296
5.6.5.1 Displacement and Base Shear Demand 296
5.6.5.2 Substructure Ductility Demand 298
5.6.5.3 Ratio of Peak Response for Systems with and without YieldingSubstructures 299
5.6.5.4 Displacement Distribution Ratios for Systems with and withoutYielding Substructures 301
5.6.5.5 Time-history variations with and without Yielding Substructures:Displacement Redistribution 304
5.6.6 Observation Summary 306
5.7 Parametric Study of Nonlinear Isolated Bridge Response 308
5.7.1 Introduction 308
5.7.2 System Characterization 310
5.7.3 Isolated Bridge Systems 310
5.7.4 Analytical Procedure 311
5.7.5 Results 312
5.7.5.1 Displacement and Base Shear Response 312
5.7.5.2 Isolator and Substructure Displacement Response 319
5.7.5.3 Isolator & Substructure Displacement Distribution Ratios 329
5.7.6 Conclusions 333
5.7.6.1 Total Displacement 334
5.7.6.2 Base Shear 336
5.7.6.3 Isolator Displacements 339
5.7.6.4 Substructure Displacement 340
5.7.6.5 Isolator/Substructure Displacement Ratios 341
5.7.6.6 Earthquake Magnitude and Distance 343
vi
5.7.6.7 Summary 344
5.8 Influence of Substructure Mass and Damping 346
5.8.1 Introduction 346
5.8.2 Isolated Bridge Systems 347
5.8.3 Analytical Procedure and Response Parameters 349
5.8.4 Results: Effect of Substructure Damping 351
5.8.4.1 Total and Isolator Displacement Response 351
5.8.4.2 Substructure Displacement and Base Shear Response 354
5.8.5 Results: Effect of Substructure Mass 358
5.8.5.1 Total Displacement Response 359
5.8.5.2 Isolator Displacement Response 362
5.8.5.3 Substructure Displacement and Base Shear Response 365
5.8.6 Observation Summary 368
5.8.6.1 Effect of Substructure Damping 369
5.8.6.2 Effect of Substructure Mass 371
5.8.6.3 Concluding Remarks 372
Chapter 6 Conclusions and Recommendations 373
6.1 Introduction 373
6.2 Earthquake Simulation Studies 374
6.2.1 Proof-of-concept 374
6.2.2 Sensitivity to characteristics of ground shaking 375
6.2.2.1 Ground motion type: far-field, near-fault, and soft-soil 375
6.2.2.2 Bi-directional motions 377
6.2.2.3 Vertical Motions 378
6.2.3 Effect of System Configuration 378
6.2.3.1 Substructure Flexibility 378
vii
6.2.3.2 Isolator Strength and Flexibility 380
6.2.3.3 Substructure Mass 380
6.2.3.4 Mass Eccentricity 381
6.2.3.5 Stiffness Eccentricity 382
6.2.3.6 Substructure Yielding 384
6.2.4 Characteristic Distribution of Force and Displacement Demands 384
6.2.5 Local Kinematic Effects 385
6.3 Implications for Design Practice 386
6.3.1 Basic AASHTO Design Equation 387
6.3.1.1 Reliability 387
6.3.1.2 Bi-directional Effects 392
6.3.1.3 Equivalent SDF vs. MDF behavior: Influence of Substructure Mass and Damping 396
6.3.1.4 Parametric Study of Nonlinear Isolated Bridge Response 401
6.3.1.5 Substructure Yielding 410
6.3.2 Alternative Methods 413
6.3.2.1 Equivalent Linear Procedures 414
6.3.2.2 Approximate Nonlinear Methods 415
6.3.2.3 Performance-Based Design 416
6.4 Future Research Need 420
6.5 Conclusion 421
Bibliography 422
Appendix A Bridge Deck Specimen Plans 426
Appendix B Pre-test Analysis 448
Appendix C Test Logs 463
Appendix D Test Data Summary Figures 495
viii
Appendix E AASHTO Uniform Load Method 681
Appendix F Bi-directional Motions 702
Appendix G Substructure Yielding 730
Appendix H Parametric Study 769
Appendix I Substructure Mass and Damping 881
1
Abstract
Performance-Based Design of Seismically Isolated Bridges
by
Eric Leonard Anderson
Doctor of Philosophy in Engineering - Civil and Environmental
University of California, Berkeley
Professor Stephen A. Mahin, ChairProfessor Gregory L. Fenves
Professor Ole Hald
The response of simple isolated bridge overcrossings to a variety of multi-dimensional
earthquake inputs was investigated by analysis and experiment. These studies were
undertaken as part of the Protective Systems Research Program at UC Berkeley sponsored
by the California Department of Transportation to establish an understanding of global
and local behavior characteristics, including the effect on response of variations in isolator
properties, pier flexibility, mass and strength, substructure damping, and global mass and
stiffness eccentricity. A versatile 1/4−scale bridge model on flexible piers, enabling one-
or two-span configurations, was tested on an earthquake simulator to validate the findings
of the analytical studies performed. Provisions of the current AASHTO Guide
Specifications for Seismic Isolation Design were also evaluated using the results of the
analytical and experimental investigations. Specifically, the application of the Uniform
Load Method to the design of a broad range of isolated bridge systems was studied. The
2
effect of mass and damping assumptions, bi-directional ground motion inputs, and
substructure strength on these procedures was also evaluated.
Several overriding observations were derived from these investigations. First, these
studies illustrated the considerable overall ability of seismic isolation to provide an
effective means of earthquake resistance in simple bridge overcrossings. The considerable
durability and robustness of these systems under seismic loading was illustrated through
multiple, varied simulations, including multi-dimensional inputs of far-field, near-fault,
and soft-soil ground motions. Secondly, analytical evaluations undertaken were able to
identify sensitivity of the nonlinear behavior of simple isolated bridge types to various
ground motion and structural characteristics. Lastly, these studies established several areas
in the current AASHTO Guide Specifications in need of further development.
• Foremost, it was shown that the Uniform Load Method does not provide uniform reli-ability, pointing to the need for the refinement of current Performance-Based Designprocedures.
• Further, possible improvements to the Guide Specification provisions to more accu-rately account for bi-directional effects were suggested.
• It was also shown that the present R-factor approach may not adequately control duc-tility demands in substructure components.
• Conditions were identified for which the effects of substructure mass and dampingmay require more accurate consideration than presently provided for by typicalapproximate linearized single-degree-of-freedom design procedures.
3
The abstract of Eric Leonard Anderson is approved:
University of California, Berkeley
Spring 2003
Chair Date
Date
Date
1
Abstract
Performance-Based Design of Seismically Isolated Bridges
by
Eric Leonard Anderson
Doctor of Philosophy in Engineering - Civil and Environmental
University of California, Berkeley
Professor Stephen A. Mahin, ChairProfessor Gregory L. Fenves
Professor Ole Hald
The response of simple isolated bridge overcrossings to a variety of multi-dimensional
earthquake inputs was investigated by analysis and experiment. These studies were
undertaken as part of the Protective Systems Research Program at UC Berkeley sponsored
by the California Department of Transportation to establish an understanding of global
and local behavior characteristics, including the effect on response of variations in isolator
properties, pier flexibility, mass and strength, substructure damping, and global mass and
stiffness eccentricity. A versatile 1/4−scale bridge model on flexible piers, enabling one-
or two-span configurations, was tested on an earthquake simulator to validate the findings
of the analytical studies performed. Provisions of the current AASHTO Guide
Specifications for Seismic Isolation Design were also evaluated using the results of the
analytical and experimental investigations. Specifically, the application of the Uniform
Load Method to the design of a broad range of isolated bridge systems was studied. The
2
effect of mass and damping assumptions, bi-directional ground motion inputs, and
substructure strength on these procedures was also evaluated.
Several overriding observations were derived from these investigations. First, these
studies illustrated the considerable overall ability of seismic isolation to provide an
effective means of earthquake resistance in simple bridge overcrossings. The considerable
durability and robustness of these systems under seismic loading was illustrated through
multiple, varied simulations, including multi-dimensional inputs of far-field, near-fault,
and soft-soil ground motions. Secondly, analytical evaluations undertaken were able to
identify sensitivity of the nonlinear behavior of simple isolated bridge types to various
ground motion and structural characteristics. Lastly, these studies established several areas
in the current AASHTO Guide Specifications in need of further development.
• Foremost, it was shown that the Uniform Load Method does not provide uniform reli-ability, pointing to the need for the refinement of current Performance-Based Designprocedures.
• Further, possible improvements to the Guide Specification provisions to more accu-rately account for bi-directional effects were suggested.
• It was also shown that the present R-factor approach may not adequately control duc-tility demands in substructure components.
• Conditions were identified for which the effects of substructure mass and dampingmay require more accurate consideration than presently provided for by typicalapproximate linearized single-degree-of-freedom design procedures.
3
The abstract of Eric Leonard Anderson is approved:
University of California, Berkeley
Spring 2003
Chair Date
Date
Date
1
1 Introduction
1.1 Seismic Protective Systems for Bridges
Various types of bearings are frequently used in bridges at the superstructure support
points. These bearings provide support for superstructure vertical loads, while allowing
thermal and long-term horizontal deformations to develop without transmitting significant
lateral forces into the substructure. The three most widely used types of bridge bearings
are pot, disc, and curved sliding bearings [Stanton et al., 1993]. These bearings are
generally designed to accommodate rotations about any axis. Horizontal translation is
accomodated by sliding along a standard stainless steel-PTFE interface. Examples of pot
and curved sliding bridge bearings are shown in Figure 1-1.
In addition to the above cited benefits of bearings in bridges, such bearings may provide
an ideal method to control forces and accommodate horizontal displacements imposed on
a bridge during an earthquake. During an earthquake, inertial loads acting on the
superstructure can induce large forces in the substructure and relative displacements
between the superstructure and the ground. The displacement variation between the
superstructure and foundation depends on: the characteristics of the ground motion; the
2
mass, stiffness, strength, and energy dissipation characteristics of the substructure; the
mass and flexibility of the superstructure; and the support conditions at the abutments and
foundations. For conventional bridges, piers and abutments are designed to accommodate
this displacement through a ductile mode of behavior. Properly reinforced concrete piers
can be designed to achieve this required displacement ductility. However, large ductile
deformations in these members spalls the concrete, yields the reinforcement in areas of
plastic hinge formation, and results in permanent lateral displacements. After a large
earthquake, damaged piers must be repaired or replaced, and the bridge and roadway may
have to be realigned. Higher mode contributions, support movements, and other
contributions to local stress concentrations may also cause unforeseen damage in
superstructure, substructure, or foundation components. This damage may be difficult to
assess and costly to repair.
As an alternative to conventional bridge design, seismic isolation bearings can be
employed. Such seismic protection devices are intended to control and accommodate
horizontal superstructure displacements without damage to bridge components (or the
bearings themselves) during an earthquake. Seismic protection devices provide engineers
with additional tools to achieve performance requirements for the safety and functionality
of bridges in the event of large earthquakes.
Seismic isolation bearings can accommodate large displacements while limiting force
transmission. Isolation bearings displacing on the order of 20 to 40 in. (500 to 1000 mm)
or more during an earthquake have been designed for bridges located close to major
3
earthquake faults. Representative examples of elastomeric and sliding seismic isolation
bearings are shown in Figure 1-2 and 1-3.
To prevent damage to these bearings and to limit damage to bridge hinges, expansion
joints, and abutments, it is important to control seismic displacement and force demands.
Thus, seismic isolation bearings typically exhibit highly nonlinear behavior, with
considerable hysteresis under cyclic loading. Bearings typically provide between 8 and 30
percent effective damping during seismic excitation, depending on the bearing design and
amount of bearing displacement. This nonlinear behavior, combined with hysteretic,
energy dissipation may effectively control peak superstructure displacements, and
substantially reduce demands on the substructure and superstructure compared to an
elastically designed structure.
Supplemental energy dissipation devices can also be added to seismically isolated and
conventional bridges to increase the total effective damping of the system and further
control response. Representative examples of a supplemental viscous damping device is
shown in Figure 1-4.
Seismic isolation bearings and supplemental dampers are examples of innovative and
practical technologies to enhance the performance of bridges during earthquakes. They
provide a practical method for protecting life and property in the event of a major
earthquake event.
4
1.2 Commentary on the State of the Art
Because of the potential benefits of seismic protective systems, considerable research
related to their use has been completed in the past ten years. An extensive summary of this
history is included in a related work by Whittaker et al. [Whittaker et al., 1998] conducted
as part of the Berkeley-Caltrans Seismic Protective Systems Program. As such, a review
of this literature is not provided herein.
Most studies to date have focused on the behavior of the isolation bearings or energy
dissipation devices themselves. Relatively few studies have addressed the overall
performance of seismically protected bridge systems. Even fewer studies have thoroughly
examined the effects of more than one component of earthquake ground motion on bridge
response.
Through a synthesis and analysis of these previous studies and the observation of
experienced bridge engineers, important issues impeding the application of this
technology to bridges have been identified. Foremost among these, perhaps, is the
potentially large displacement and force demands on seismically isolated bridges located
near major faults. Large amplitude, long duration velocity pulses characteristic of near-
fault ground motions have raised concerns regarding the displacement demands of
relatively weak systems undergoing large displacements. This behavior generally gives
the overall structure the appearance of having a long effective period of vibration. For this
reason, the applicability of seismic isolation for bridges situated on soft soils has also been
questioned. This is because site response effects for large ground motions tend to produce
significant displacements in the long period range. Codification of design guidelines for
5
the application of seismic isolation to bridge systems is also in its relative infancy. Few
seismically isolated bridges have been subjected to large design level earthquakes in the
field, or tested in the laboratorty, to confirm the adequacy of these guidelines. Many of the
concepts and procedures incorporated in these design methodologies have essentially been
adapted from the building code provisions [U.B.C., 1994], and as such, may not
adequately consider the differences in dynamic behavior and performance objectives
between isolated buildings and bridges.
The design of highway bridges with seismic isolation and supplemental damping is
specified in the American Association of State Highway and Transportation Officials
Guide Specifications for Seismic Isolation Design [AASHTO, 1999], referred to in this
report as the Guide Specifications or Guide Spec. The Guide Specifications provide
requirements for analysis of seismically protected bridges, isolation bearing and damper
design, and testing and acceptance of bearings and damper components. The Guide
Specifications incorporate a simplified linearized procedure for bridge design. This is
based on the conceptual equivalence of nonlinear isolated response with that of an
equivalent elastic system undergoing harmonic oscillations. In this respect, this approach
is inherently not entirely realistic. Provisions for more accurate nonlinear time-history
methods are also included in the Guide Specifications, but not required for all systems.
Further, unlike the building code, the Guide Specifications implicitly suggest that some
measure of substructure yielding is also allowed in an isolated bridge system. However, no
guidance is given on how to account for the effect of this substructure yielding into the
procedure.
6
Although the Guide Specifications are a major advance in bridge engineering, it is
apparent that the limited assessment of the response of complete, seismically isolated
bridge systems through analytical studies, laboratory tests or exposure to actual
earthquakes, and the variety of unresolved concerns have impeded the application of
protective systems technology to bridges. As such, research is needed directed towards
developing a better understanding of the response of seismically isolated bridge structures
and the adequacy of currrent design criteria.
1.3 The Protective Systems Research Program
1.3.1 Overall Objectives of the Program
In consideration of these research needs, a series of studies have been undertaken under
the Protective Systems Research Program sponsored by the California Department of
Transportation. A variety of studies were developed as part of this program in order to:
1. Evaluate the effect of bi-directional loading on seismic isolation bearings and developimproved analytical bearing models.
2. Establish an understanding of global and localized response characteristics of simpleseismically protected bridges subjected to various types of seismic input including far-field, near-fault, and soft-soil motions.
3. Validate the efficacy of seismic protective systems for bridges of more complex(realistic) configurations.
4. Assess the applicability of requirements in the AASHTO Guide Specifications forSeismic Isolation Design and recommend improvements based on the results of theresearch.
1.3.2 Overall Tasks Undertaken
Seven major tasks were undertaken to meet the overall objectives of this program. The
tasks were organized to improve knowledge of component behavior and use component
information to understand bridge system performance through integrated experimental
7
and analytical studies. The experimental studies of seismic isolation components and
model testing of seismically protected bridges made extensive use of the earthquake
simulator and bearing test machines at the Pacific Earthquake Engineering Research
Center (PEER), University of California, Berkeley. The major tasks in the research
program were as follows.
1. Experimentally characterize the properties of representative elastomeric and slidingisolation bearings under a wide variety of uni-directional and bi-directionaldisplacement histories and rates.
2. Use the experimental force-displacement data for isolator bearings to develop andcalibrate mathematical models for elastomeric and sliding isolation bearings suitablefor nonlinear response-history analysis of complete bridge systems.
3. Investigate analytically and experimentally the response of a simple, isolated bridgesystem to uni-directional and bi-directional earthquake-history inputs, representingfar-field and near-fault earthquake shaking on different soil types.
4. By experiment and analysis, investigate the effectiveness of fluid viscous dampers onthe earthquake response of simple bridges, including consideration of the effect ofdamper configuration.
5. Use experimentally validated analytical models to examine the effect of substructurestiffness, substructure mass, substructure damping and varying isolation systemproperties on the response of seismically isolated bridge overcrossings subjected tovarious seismic inputs.
6. Use a versatile shaking table model of a more complex bridge with one and two spans,supported on flexible piers, to investigate the effect of mass and stiffness eccentricity,pier flexibility, pier mass and strength, and varying isolator properties on the bridgesystem subjected to one to three components of earthquake ground motionrepresenting far-field, near-fault, and soft-soil earthquake shaking.
7. Evaluate the efficacy and applicability of requirements in the AASHTO GuideSpecifications for Seismic Isolation Design and recommend improvements based onthe results of the research.
1.3.3 Protective system devices considered
Three types of seismic isolation bearings were studied in the overall research program.
These included lead-rubber (LR) and high-damping rubber (HDR) elastomeric bearings
8
and Friction Pendulum (FP) sliding isolation bearings. At the time of writing, LR and FP
seismic isolation bearings have been used in bridge structures in the United States. Lead-
rubber and HDR bearings are composed of alternating layers of elastomer and steel
providing the bearing with sufficient stiffness to carry vertical loads. Energy dissipation is
provided by a central lead core in LR bearings and by a specially formulated elastomer in
the HDR bearing. Photographs of the LR and HDR bearings used in the program are
shown in Figure 1-2. The FP bearing is composed of a high axial load capacity, low-
friction composite coated slider riding on a spherical stainless steel surface. Energy
dissipation is achieved through friction as the articulated slider moves across the stainless
steel surface. An example of an installed FP bearing is shown in Figure 1-3. Detailed
specifications of these test bearings are provided in Chapter 3.
The fluid viscous damper has been the sole type of supplemental damping device used in a
bridge in California to this date. Fluid viscous dampers dissipate seismic energy as heat,
which is generated by the passage of the damper fluid (typically, a silicone oil) past or
through the damper piston. Figure 1-4 shows a typical cross-section through the type of
fluid viscous damper used in this study.
1.3.4 Test Models
In the Protective Systems Research Program, seismically isolated bridge systems were
investigated experimentally with two models on the earthquake simulator. The first model,
referred to as the rigid block model, is shown in Figure 1-5. This model represents a
seismically isolated bridge on rigid pier or abutment supports. The second model, referred
to as the elevated bridge model, is illustrated in Figure 1-6. Experimentation with this
9
latter model allowed testing of one- and two-span bridge configurations. Piers were
designed to provide a range of stiffness and strengths in the longitudinal and transverse
directions of the model. Pier stiffness could also be arranged to provide stiffness
eccentricity along the length of the bridge. Pier components also allowed substructure
mass to be varied. The model allowed dynamic testing with one, two, and three
components of ground motion.
1.4 Scope of this Report
This report addresses several key components of the above outlined Protective Systems
Research Program. The scope of this report relates to aspects of items 2, 3, and 4 of the
defined program objectives as outlined in Section 1.3.1, excluding evaluations related to
the use of supplemental damping devices. Specifically, Task 5, 6 and 7 of the program, as
outlined in Section 1.3.2, are performed herein. Analytical studies related to these tasks
utilize the mathematical models developed and calibrated under program Tasks 1 through
3 (see Section 1.3.2). The specific scope of this report is defined as follows:
1. System Studies
Investigate the response of simple, isolated bridge overcrossings to a variety of earthquake
time-history inputs, by analysis and experiment. Factors considered include the effect of
mass and stiffness eccentricity, pier flexibility, pier mass and strength, substructure
damping and isolator properties.
A scale model of a bridge with one- and two-span configurations on flexible piers was
designed and constructed for testing on the earthquake simulator. These experiments
10
facilitate validation of analytical results and provide proof-of-concept of the efficacy of
seismic isolation for various bridge configurations and ground motion inputs.
2. Design Methodology Studies
The applicability of several requirements in the AASHTO Guide Specifications for
Seismic Isolation Design are evaluated. Specifically, the efficacy of the Uniform Load
Method is investigated as it relates to the design of a broad range of seismically isolated
bridge systems. Also, the effects of bi-directional ground motions and substructure
yielding on the procedures are studied.
An extensive parametric study is performed to investigate the response of simple isolated
bridge overcrossings to a database of recorded earthquake time-history inputs.
Specifically, the effects of varying isolator properties, pier flexibility, pier mass,
substructure damping, and substructure yielding on system displacement and force
response are examined.
3. Conclusions and Recommendations
Overall conclusions of the research findings are identified. Recommendations are
developed for implementation of findings and/or improvement of current design
specifications as indicated by the research results.
1.5 Organization of this Report
Chapter 2 contains a summary of key aspects of current design procedures for seismically
isolated bridges. Various system configurations used for short overcrossings and viaducts
are examined to develop a representative conceptual model of an isolated bridge system.
11
Preliminary analytical evaluations of the effect of basic system variations on isolated
bridge response are presented to help identify key parameters and priorities for subsequent
investigations.
Chapter 3 presents the development and results of the experimental studies undertaken.
Ten configurations of a bridge model are constructed to investigate the effect on system
response of mass and stiffness eccentricity, pier flexibility, mass and strength, and various
isolation system configurations. The models were subjected to various combinations of
one and two components of horizontal ground motion along with vertical ground motion
for earthquakes representing far-field, near-fault, and soft-soil characteristics.
Chapter 4 presents evaluations of the Chapter 3 experimental test results. These
evaluations are organized around the key issues identified in Chapter 2, where applicable.
Chapter 5 presents the results of several related analytical studies. These studies assess the
applicability of several design procedures contained in the AASHTO Guide
Specifications. In particular, the efficacy of the Uniform Load Method and the effects of
bi-directional motions and substructure yielding on the Guide Specifications procedures
are examined. The sensitivity of the response of simple isolated bridge overcrossings to a
database of recorded earthquake time-history inputs is then studied parametrically. The
effect of varying isolator properties, pier flexibility, pier mass, and substructure damping
on system response is also examined.
12
Chapter 6 offers overall conclusions, recommendations, and the needs for further research.
Chapter 6 summarizes the findings of the research in the context of assessing and
recommending improvements where needed to the AASHTO Guide Specifications.
Appendices provide design drawings of the elevated bridge test specimen with photo logs
of construction sequences and model details, result summaries from specimen pre-test
simulation analyses, datalogs for experimental test sequences, earthquake simulation
(shake table) test result summaries, and detailed summaries for each of the analytical
formulations developed in Chapter 5.
a. Pot bearing b. Curved sliding bearing
Figure 1-1 Traditional (non-seismic) bridge bearings
13
a. LR bearing b. HDR bearing
Figure 1-2 Elastomeric seismic isolation bearings
Figure 1-3 Friction pendulum seismic isolation bearing
14
Figure 1-4 Cross-section through a fluid viscous damper (courtesy of Taylor Devices)
Figure 1-5 Rigid-block bridge model on earthquake simulator at the Pacific Earthquake Engineering Research Center, University of California, Berkeley.
15
Figure 1-6 Elevated bridge model with flexible piers on earthquake simulator at the Pa-cific Earthquake Engineering Research Center, University of California, Berkeley.
16
2 Preliminary Evaluations
2.1 Introduction
The preliminary evaluations presented in this chapter provide an overview of design
procedures, standard analysis methodology, and the effects of system configuration on the
response of simple isolated bridge systems. It is the purpose of this chapter to summarize
these issues and effects as a foundation for the more in depth research and evaluation
undertaken in subsequent chapters. This overview outlines many of the critical issues
related to the application of protective systems to simple bridge overcrossings. Many of
these issues, as mentioned in Chapter 1, have impeded the application of this technology
to bridges. As such, these issues constitute key areas of needed evaluation.
2.2 AASHTO Guide Specifications
The AASHTO Guide Specification for Seismic Isolation Design [AASHTO, 1999] was
developed based on information available at the time of its preparation for buildings and
bridges, and adapts essentially the same equivalent linear procedure for isolation design
contained in the building code [U.B.C., 1994]. The dynamic characteristics of isolated
bridges, however, have several fundamental differences from those of isolated buildings.
For example, the flexibility and mass of tall, substructure piers below the isolators in a
bridge may cause significant force or displacement redistributions, altering the
17
effectiveness of the isolation system. Relatively rigid foundations in seismically isolated
buildings limit these concerns. Higher modes contributed by in-plane deck flexibility, or
interactions between several bridge components separated along expansion joints, may
also amplify local component demands in isolated bridge systems, unlike more compact
and regularly shaped buildings. In this respect, it is not certain whether the procedures in
the Guide Specifications adequately consider these and other differences.
The Guide Specifications essentially provide a linearized procedure for isolated bridge
design. The Uniform Load Method prescribed in this document is the linearized procedure
for estimating the design response (i.e., peak forces and deformations) along each of the
orthogonal axes of an isolated bridge. This procedure assumes an equivalence of isolated
response with that of an elastic substitute system oscillating harmonically. The Guide
Specifications stipulates linearized properties based upon the overall isolated system’s
secant stiffness defined at maximum displacement. These properties rely on the
assumption that the isolated system may be represented by an idealized single-degree of
freedom “substitute” system for purposes of determining the global response of the bridge.
For this representation, “equivalent” damping properties are postulated by equating the
energy dissipated per cycle in the isolated bridge system in this state to that of an
“equivalent” linear visco-elastic damping component (oscillating harmonically at the
same maximum amplitude and a harmonic frequency characterized by the system mass
and secant stiffness). Design displacement is then estimated using a smoothed design
spectra modified to account for this “equivalent damping.” Because these linearized
properties are based upon the design response, this method is iterative.
18
Several concerns have been raised about this linearization approach. First of all, it has
been shown that linearized methods based on ideal harmonic response are not as accurate
as those based upon random response [Iwan, W.D., and Gates, N.C., 1979], or for that
matter, as explicit nonlinear methods. Provisions for more accurate time-history methods
are stipulated in the Guide Specifications, but are only required for isolation systems
exhibiting relatively large “effective” damping (in excess of 30 percent of critical). Thus, a
degree of inaccuracy is associated in the current formulation. Further, the idealized single-
degree-of-freedom representation utilized in the formulation makes accounting for
substructure mass or damping difficult, and the Guide Specifications provide no guidance
on how or when to consider these contributions. Simplified methods for accounting for
these effects have been presented [Sheng et al., 1994]. However, a multi-degree-of-
freedom structural representation may be required in certain cases to sufficiently account
for these higher mode contributions to local component responses.
The Guide Specifications stipulate that system response is be determined, utilizing these
simplified procedures and modeling assumptions, separately along each of the specified
orthogonal axes of the isolated bridge system. The Guide Specifications specifies that bi-
directional peak force response may be determined for design utilizing the familiar 100
percent plus 30 percent rule for combination of uni-directional maxima. The reliability of
this procedure, which is based on the results of previous random vibration studies on
reinforced concrete hysteretic systems [e.g., Park et al., 1986], is uncertain for application
to nonlinear isolated bridges. More accurate bi-directional and three-dimensional time-
history methods may be used, as stipulated in the Guide Specifications, but again these are
only required for certain systems.
19
Unlike the building code formulation, there is also an implicit assumption in the
formulation of the Guide Specifications that some measure of substructure yielding will
occur during the seismic response of an isolated bridge. This is inferred from the wording
of the Guide Specifications commentary which states that the lower response modification
factors (R-Factors) utilized for isolation design “ensure, on the average, essentially elastic
substructure behavior in the design-basis earthquake.” This stipulation of essentially
elastic behavior “on average” suggests inelastic substructure behavior will occur for
response above the mean. No further guidance is given, however, on how to incorporate
the effect of this substructure yielding into the procedure.
It is apparent that additional studies are needed to assess and, where necessary, improve
design criteria for seismically isolated bridge systems. It is critical to establish an
understanding of the unique features which effect the dynamic response of simple isolated
bridge overcrossings as a rational basis for this assessment. To this end, several
preliminary analytical studies are presented in the following section to help identify key
parameters to be emphasized through the remainder of this report.
2.3 Parametric Seismic Analysis of Idealized Elevated Isolated Bridges
2.3.1 Introduction
The nonlinear response of simple seismically isolated bridge systems, such as those shown
in Figure 2-1, is sensitive to many factors. These factors include but are not limited to: (1)
the characteristics of the earthquake input; (2) isolation device characteristics; (3)
substructure flexibility; (4) substructure mass; (5) higher modes; (6) system eccentricity;
and (7) substructure yielding.
20
A pilot parametric analysis was undertaken to assess the sensitivity of simple isolated
bridge systems to changes in ground motion characteristics and several of these key
system factors. These studies were performed using nonlinear response-history analysis
procedures and numerical models developed specifically for this undertaking.
2.3.2 Idealized Modeling Assumptions
A typical structural model of an isolated bridge bent responding uni-directionally in its
isolated mode is presented schematically in Figure 2-1. For purposes of design, the Guide
Specifications allow an idealized bilinear force-deformation relationship to be utilized to
characterize isolation bearing hysteresis and total system uni-directional response (for a
isolated bridge responding laterally in its isolated mode along either principal orthogonal
axis), as shown in Figure 2-2(a) and Figure 2-2(b), respectively. With this idealization,
three independent fundamental parameters define the overall bilinear system hysteresis.
These parameters could be chosen as the systems’ first- and second- slope stiffness (K1 &
K2, respectively) and the yield strength (Fy).
Utilizing these definitions (see Figure 2-2), the isolated bridge system properties may be
defined for convenience by the following parameters: the isolator characteristic strength
coefficient,
(1)
the isolator second-slope period,
(2)
CyisoFyMg--------=
Tiso 2π M kd⁄=
21
and the characteristic substructure period,
(3)
For an assumption of rigid-plastic isolation bearings (i.e., infinite ku), variations in the
isolator characteristic strength coefficient, isolator second-slope period, and the
characteristic substructure period effect variations in each of the three fundamental system
hysteretic parameters. In the pilot analytical studies isolation bearings were, for simplicity,
considered rigid-plastic in all cases and response to variations in hysteretic system
properties were examined parametrically by varying the three system properties defined in
Equation 1, 2, and 3 above.
Figure 2-1 Structural idealization of an isolated bridge bent
a. Hysteresis of isolation bearing b. Hysteresis of isolated bridge system
Figure 2-2 Bilinear idealization of an isolation bearing and an isolated bridge system
Tsub 2π M Ksub⁄=
K sub
M
di
d
keff
keff= effective isolator stiffnessKsub= linear substructure stiffnessM = lumped deck massdi = isolator displacementdsub = substructure displacementd = total displacement = di + dsub
ered in these studies assuming a bilin
2-3(b). With this characterization,
system properties (i.e., first- & seco
l t F ) b l t d i
idealized behavior of a subject isola
-1). Parameters are specified to match
e Specifications as shown. The fo
sentation of the subject isolated bri
idge overcrossing
Ksub1 and ku ∞
with rigid abutments and rigid-plastic isolators
spectively. This model is similar to
ch orthogonal axes of the bridge w
onent definitions of the AASHTO Gu
n response of the isolation componen
al bridge model
s
mass, stiffness, anddamping
representation (i.e., K1) may be compu
g components as
= kd and the isolation system defines
of a broad range of full scale (prototy
nstant with a characteristic yield stren
second-slope isolator period of Tiso
e 5 percent damped elastic displacem
represented.
t response data as presented in Figur
ubstructure flexibility representing Ts
e first- and second-slope stiffness of
e substructure becomes more flexible,
on 6) may be computed by combin
on of Equation 5 and the previous sys
ed in Table 2-2 were utilized. The tre
sistent for all ground motions conside
case.
r systems with the most rigid first-sl
ishes, in general, as T1 increases. T
ngth contours as the first-slope per
econds). For example, total displacem
ain considered. Substructure compon
periods of Tsub = 0.05, 1, and 2 seco
With this choice of system propert
ib i ld b d di
flexible substructure in this study,
percent to the total displacement for
ercent for the most flexible and weak
h h d ll i l i ib
olated response of symmetric bri
dies both the simplified single-degree
ridge analytical models were utilized
ions for highway bridges in the U.S.
Spans (ft) Σmpier/Mdeck
142, 100 0.04
124, 152, 124 0.17
70 0
mass becomes larger. These results
somewhat as the substructure becom
ucture becomes more flexible). This i
increasingly insignificant in contribu
ct of substructure mass contributions
rces. These evaluations are necessary
dered (or when they may be reasona
g ratio ζsub which acts on the total sys
with isolation bearings locked, as wo
n compute the viscous damping const
ture damping classically as
ve damping component, csub, assigned
erformed for representative substruc
Analyses were performed on full s
round motion histories selected from
ays greater than unity and tends to
ural components (i.e., Tsub approachin
ity, however, as substructure flexib
or example for this ground motion th
dies. The AASHTO Guide Specificati
each orthogonal axis of an isolated bri
ining uni-directional maxima with
n rule. To evaluate the efficacy of
o uni-directional ground motion inp
e peak total displacement response ve
results show that the 100 percent +
estimate of maximum bi-directio
ricity
y between the bridge superstructure m
his arrangement may be the produc
or unsymmetric skew for example
splacement response (d) for a system
ement response (d0) for the same sys
f these displacements, d/d0, increase
However the d/d0 ratio never excee
torsional response [Bozzo, et al, 19
stiffness and strength properties to a
to align with the center of superstruc
ke simulation studies may also provid
eneralized multi-degree-of-freedom,
d Section 2.3.3). Full scale (prototy
nge of substructure stiffness eccentri
center of mass and substructure cente
ut is limited to a moderate value
fault ground motion. This is an indica
s have on system torsional response e
a bridge of 100 foot span, this rota
), with peak rotation on the order of 0
ectively.
eak bridge deck rotation for an additio
rall isolated system. Balancing the in
blies along the bridge span by pro
o reduce torsional response (compare
ing at all supports). However, the lim
on
iffness eccentricity
can FP 2.0 1.0 DView FN 6.4 1.0 DView FP 6.4 1.0 DJMA FN 3.4 1.0 DJMA FP 3.4 1.0 Do, ivir 45 10 2.01 F
sponse vs. elastic response
0 0.25 0.5 0.75 1 1.25 1.5 1.75 20
2
4
6
8
10
12
14
Tsub
(sec)
Dis
plac
emen
t (in
)d d
i
elastic, 5% damping
3 3.1 3.2 3.3 3.4 3.5 3.66
8
10
12
T2 (sec)
Dis
plac
emen
t (in
)
d elastic: T
2, 15% damping
2 2.5 3 3.5 40
10
20
30
40
T2 (sec)
d (in
)
ope flexibility and characteristic streng
2 2.5 3 3.5 40
0.25
0.5
0.75
1
T2 (sec)
d (in
)
Cyiso
=.04
.08
.12
2 2.5 3 3.5 40
0.25
0.5
0.75
1
T2 (sec)
d (in
)
2 2.5 3 3.5 410
15
20
25
30
35
Tiso
(sec)
d i (in)
ope flexibility and characteristic streng]
2 2.5 3 3.5 40.9999
1
Tiso
(sec)
d i/d
Cyiso
=.04
.08
.12
2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 40.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Tiso
(sec)
d i/d
yiso .06, Tiso 3 sec, [prototype scale
0 0.5 1 1.5 20
5
10
15
20
25
30
Tsub
(sec)
d/d 0
damping ratio = 0.050.10 0.20
0 0.25 0.5 0.75 1 1.25 1.5 1.75 20.7
0.8
0.9
1
1.1
1.2
1.3
Tsub
(sec)
(dm
ax +
0.3
d min
)/d xy
LA01/02 LA21/22 NF01/02 LS17c/18c
n response, Cyiso .06, Tiso 3 sec, [pc/18c]
0 0.25 0.5 0.75 11
1.1
1.2
1.3
T1 (sec)
d/d0
e/L = .05.10
0 0.15 0.3 0.450
0.005
0.01
substructure stiffness eccentricity: e/L
peak
rot
atio
n (r
ad)
0 0.15 0.3 0.450
0.02
0.04
0.06
0.08
substructure stiffness eccentricity: e/L
peak
rot
atio
n (r
ad)
abutment Tiso
= 2 sec
3 sec 4 sec
eccentricity, [prototype scale, NF01]
67
3 Testing of a Bridge Deck Model
3.1 Introduction
The experimental studies in this research were developed to satisfy the program objectives
outlined in Section 1.3.1. Specifically, these studies fulfill program Task 6 in Section
1.3.2, to construct a scale model of a bridge with flexible piers for earthquake testing.
These tests utilized the newly upgraded 3-dimensional capabilities of the earthquake
simulator at the Pacific Earthquake Engineering Research (PEER) center and provided a
first-time opportunity to study the bi-directional and 3-dimensional response of isolated
bridge systems.
The preliminary analytical evaluations of Chapter 2 illustrate the basic sensitivity of the
response of isolated bridge overcrossings to various structural and isolator characteristics.
Based on these evaluations. the specimen tested were developed to confirm these
sensitivities, including the effect of mass and stiffness eccentricity, pier flexibility, pier
mass and strength, and varying isolator properties, on system response.
These simulation tests also subjected various isolated bridge overcrossing configurations
to multiple signals of one to three components of earthquake ground motion. These
earthquake signals were representative of significant far-field, near-fault, and soft-soil
seismic events. In this respect, these studies provide invaluable proof-of-concept
68
verification for the effectiveness and robustness of seismic isolation for simple bridge
types.
3.1.1 Similitude Requirements
Similitude requirements for dynamic structural models have been developed in previous
studies [e.g., Krawinkler, Moncarz, 1982]. These similitude constraints are defined by the
chosen length scale factor, 1r, prescribed for relating model size to the subject prototype
(full-scale) structure (i.e., lr = lm/lp, where lm and lp are the model and prototype length
scale, respectively). With gravity a constant and masses reduced proportionally by the
length factor, ground motion accelerations are held constant in dynamic testing to preserve
force scaling (where F = ma). Similitude requires that prototype and model periods be
related by the square root of the length scale factor (i.e., the time scale factor, tr = 1r1/2),
with frequencies related by its inverse (i.e, the frequency scale factor, ωr = lr-1/2). Ground
motion acceleration time-history records must then be “compressed” by multiplying their
time increment by the time scale factor to preserve similitude. This produces time-history
records for shake table simulations of equal acceleration output (as the original recorded
motion), but of higher frequency. With these constraints applied specimen simulations are
performed, with model and prototype system displacements (i.e., dm and dp, respectively)
related directly by the length scale factor (i.e., the displacement scale factor, dr = dm/dp =
1r) [Krawinkler, Moncarz, 1982].
In Chapter 2, isolated bridge behavior was shown in several cases to vary with system
properties corresponding to “short” and “long” spectral period ranges. The typical
response of these systems was shown in several cases to have unique characteristics in
69
each of these period ranges. To model this behavior experimentally, similitude requires
that the model period, Tm, be related to the prototype system period, Tp, by the time factor
(i.e., tr = 1r1/2) such that
(12)
With this requirement, model stiffnesses (Km) can be selected to produce required model
periods (i.e., Tm), given a model mass (Mm), through the definition of system period as
(13)
A length scale factor of 1/4 (i.e., lr = 1/4) was chosen for model scaling for these studies.
This ratio was selected based upon the load and geometric constraints of the earthquake
simulator which were reached for bridge model weight and length quantities represented
by a typical single-span bridge overcrossing reduced to this size. Ground motion scaling
was performed separately, with length scale factors chosen between 1/2 to 1/5 (i.e., lr
between 1/2 and 1/5) and related time scale factors between and (i.e., tr = 1/ and
1/ , see Equation 12), to produce ground motion simulation records of peak velocity and
displacement within the capacity of the shake table simulator (see Section 3.2 below).
The resulting relationships between model and prototype response produced by tests using
these separate model and ground motion scaling factors may be deduced by applying the
previous similitude relations. For example, for a given model with length scale factor of
trTmTp------- lr
1 2⁄==
Km 4π2MmTm--------=
2 5 2
5
70
lrm, a full-scale prototype system with a period of Tp = Tmlrm-1/2 is represented (see
Equation 12). Applying a different length scale factor of lrg to the ground motion implies
that this same model represents a prototype system with a period of Tp’ = Tmlrg-1/2
subjected to this scaled ground motion record (Equation 12). Combining these provides
Tp’ = Tp(lrm/lrg)1/2. Thus if the ground motion scale is smaller than the model scale (e.g.,
lrg = 1/5 and lrm= 1/4), testing with this ground motion represents the response of a
prototype system with a period, Tp’, larger than the full scale target prototype, Tp. On the
other hand, if the ground motion scale is larger than the model scale (e.g., lrg = 1/2 and
lrm= 1/4), the testing represents the response of a prototype system with a period, Tp’,
smaller than the full scale target prototype, Tp. In this way, the model (with fixed scale,
e.g., lrm = 1/4) may represent systems in different spectral regions of the ground motion
record by varying the chosen scale factor (i.e., lrg) applied to the motion in the given test
sequence. In either case, displacements to the full-scale motion are related to model
displacements in the test sequence by the ground motion scale factor, lrg, as before.
3.1.2 Design criteria
In order to illustrate the effect of basic system variations on the response of the isolated
bridge specimen, component properties were established to accommodate the same
substructure and isolation system variations as those evaluated in Chapter 2. These
properties were established to model systems over the broad spectral range where
preliminary analyses indicated significant variations in response.
71
Bridge size and mass were chosen to produce the largest similitude length scale within the
limits of the shake table physical geometry and vertical load capacity. This implied a ¼-
scale model (i.e., length scale factor, lr = 1/4) with maximum span of 20 feet and a
corresponding bridge deck mass of 65 kips.
Target isolation system properties were determined for the given bridge deck mass. It was
established that model isolation bearings with characteristic periods of Tiso = 1.3 to 1.75
seconds were desired (see Equation 2). These would represent full-scale (prototype)
isolated systems with a rigid-based isolation periods ranging from Tiso = 2.6 to 3.5 seconds
at lr = 1/4. Isolator strengths were selected to be in the typical range of Cyiso = 0.04 to 0.12
(see Equation 1). Several bearing types were to be represented to provide hysteretic
properties covering these ranges, including Lead-rubber (LR), High-damping rubber
(HDR), and Friction Pendulum (FP) bearing types.
Test specimen non-isolated periods of approximately Tsub = 0.025 to 1 seconds were
desired (see Equation 3). These represent prototype (full-scale) non-isolated bridges with
periods ranging from Tsub = 0.05 to 2 seconds at a length scale factor of lr = 1/4 which
covers the range of substructure systems evaluated in Chapter 2. The flexibility of
specimen substructure components was established to target substructure stiffness (Ksub)
to isolator second-slope stiffness (kd) ratios in the range of 2:1 to 7:1. As the AASHTO
Guide Spec presumes some measure of substructure yielding to occur (see Section 2.2), it
was also considered important to study its effect on the response of isolated bridge
systems. Therefore, weaker specimen substructure components designed to yield near
peak response were desired as part of the test specimen arrangement.
72
A versatile specimen which could accommodate these variations in pier flexibility and
isolation bearing properties was required for these studies. In addition, the model had to
accommodate varying pier mass and strength and eccentric arrangements of superstructure
mass and substructure stiffness. The design also needed to be easily alterable during
testing to accommodate these system changes efficiently.
3.1.3 Design Development
In keeping with these requirements, a ¼-scale bridge specimen design was developed with
preliminary consideration given to several alternate systems. Steel columns were
preferred because of the desire to perform many tests on the specimen without damage to
the total substructure. A simple design utilizing standard pipe column sections with
optional cross bracing (added for rigid or eccentric configurations) was first considered.
Standard pipe material (i.e., nominal yield strength, Fy = 46 ksi) proved inadequate to
resist combined effects of axial and flexural loads at pipe lengths required to achieve
target substructure flexibility. A variety of other ideas were then considered, including an
alternative utilizing steel wide-flange, L-frames mounted on 3-dimensional clevis base
pins. For this alternative, prestressed coil spring assemblies were designed to provide
variable rotational base flexibility. These assemblies allowed variations in the lateral
frame stiffness to be achieved by replacing springs of pre-engineered stiffness in the base
connection assembly. Connection detailing, necessary to ensure smooth movement of the
assemblies through the anticipated displacement ranges, proved complicated, however,
causing this alternative to be abandoned in lieu of the simpler final specimen design. Final
specimen design was taken as a combination of these two alternatives, as described in the
next section.
73
3.1.4 Final Specimen Design
Complete construction plans of the test specimen, including as-built photographs, are
included in Appendix A for reference. The final specimen substructure design utilized
steel tube frames mounted on clevis base pins. The clevis pin mounts rotate about two-
orthogonal axes and provide adequate transverse and longitudinal rotation capacity at the
base (with restraint about the vertical axis). Rotational stiffness was provided by thin
tapered plates extending in each orthogonal direction from the base of the steel tube
frames. The wide end of these plates attach to the tube frames near the clevis pins while
their narrow tapered ends attach to a shear pin connection which provides vertical support
only. Tube columns support load cells and isolation bearings, which in turn support a rigid
steel deck frame spanning between pier assemblies. The tube column frames support
vertical gravity load (imposed by the 65 kips of concrete blocks mounted on the bridge
deck frame as mass) and provide lateral stiffness supporting shear loads transmitted from
the bridge deck through the isolation bearings during seismic excitation.
Two tapered plate designs were prepared for the elevated bridge specimen. These two
designs allowed substructure lateral stiffness to be altered by changing the rotational
flexibility at the base of the piers (see Appendix A). Short and long tapered plates
provided the specimen with non-isolated periods of approximately Tsub = 0.67 and 1
seconds, respectively, Adding cross-bracing between the columns provided the specimen
with a non-isolated period of approximately Tsub = 0.25 seconds. Two sets of each size
tapered plates were fabricated from A514 and A36 steel, respectively. The stronger A514
material provided essentially elastic stress levels, while the weaker A36 material allowed
moderately ductile substructure behavior, during the test sequences.
74
Three separate sets of test bearings were designed and fabricated for use in the bridge deck
model tests: 1) high-damping rubber (HDR) bearings supplied by Bridgestone, Inc.; 2)
lead-rubber (LR) bearings supplied by DIS, Inc.; and 3) spherical sliding, or Friction-
pendulum (FP) bearings supplied by Earthquake Protection Systems, Incorporated.
Design details of each are included in Appendix A for reference.
The basic force diplacement properties of these three bearing types (see Figure 3.1) were
intentionally selected to be different in order to cover the ranges of isolation bearing
properties normally seen in practice and to examine behavior in different ranges of
behavior identified in the preliminary evaluations (see Chapter 2). One should not use
these tests to compare the effectiveness of different isolator types, as different designs
could also have resulted in isolators with very similar hysteretic properties. Results from
these tests should be used only for calibration of models, validation of identified trends
and behavior concepts (i.e., how system behavior is effected by changes in the
fundamental hysteretic properties Qd, ku and kd), and the efficacy of isolation in general.
Bearing hysteretic properties established from characterization test data are presented in
Table 3-1 as a reference. Figure 3-1 shows a uni-directional plot comparing the hysteretic
response of the HDR, LR, and FP test bearings illustrating the hysteretic differences in
strength and first- and second-slope stiffness characteristics of these bearing designs.
Characteristic target (rigid-based) isolation periods (i.e., Tiso, see Equation 2) are also
shown in Table 3-1 for each bearing type.
As illustrated in the plans (see Appendix A), this final specimen design is quite versatile.
Lateral substructure stiffness can be distributed uniformly at each span or
75
unsymmetrically (with increasing flexibility along the bridge length) to model bridges
spanning grade changes. Substructure flexibility can also be varied in the longitudinal and
transverse directions to model the cantilever versus frame behavior of a multi-column
bent. For two-span (six-pier) configurations, end piers can be braced longitudinally and
transversely and the central piers left relatively flexible to model bridge overcrossings.
Table 3-1 Summary of bearing mechanical properties from characterization tests
Bearing Type Qd (/W) ku(kips/in) kd (kips/in) Tiso4 (sec)
HDR1 0.015-0.05 4.5-3.5 1.75-1 1.29
LR2 0.05-0.09 15-5 1.6-0.9 1.36
FP3 µ = 0.07 - 0.10 INF R = 30 in.W/R= 0.54 kip/in 1.75
1. Property range over 50-250% shear strain with Tiso at γ = 250%2. Property range over 50-200% shear strain with Tiso at γ = 200%3. FP hysteretic properties based on friction coefficient, µ, and dish radius, R4. Tiso computed for a deck weight of 65 kips applied uniformly to four bearings
Figure 3-1 Comparison of test bearing hysteretic properties
0
0.05
0.1
0.15
0.2
0.25
0 0.5 1 1.5 2
d (in)
F/W
HDRLRFP
76
A column detail also allows additional substructure mass of up to 1.5 kips to be installed
near the 2/3rd height of each column frame. This represents substructure mass proportions
of up to γ = Σ mpier/Mdeck = 10 percent.
For some configurations, the isolators are mounted directly on the shake table. Separate
transition hardware allows FP, LR and HDR isolation bearings to be installed. Bridge deck
mass can also be arranged symmetrically or eccentrically. The mechanical properties of
the bridge specimen substructure are presented in Table 3-2.
Table 3-2 Summary of computed specimen substructure design properties
Frame Configuration
Braced1 Short Plate2 Long Plate3
Tsub 0.25 sec 0.67 sec 1.0 secKsub 26.6 kips/in 4 kips/in 1.8 kips/in
Fy N.A. 8 kips (A514)2.9 kips (A36)
8 kips (A514)2.9 kips (A36)
Cy = Fy/W N.A. 0.5 (A514)0.18 (A36)
0.5 (A514)0.18 (A36)
dy N.A. 1.9 in (A514)0.68 in (A36)
4.0 in (A514)1.44 in (A36)
Ksub/kd (LR) 27:1 4:1 2:1Ksub/kd (FP) 47:1 7:1 3:1
1. Braced pier assembly- see Figure A-1, A-2, & A-7 details, Appendix A2. Pier assembly with short plate - see Figure A-1, A-2, & A-10, Appendix A3. Pier assembly with long plate - see Figure A-1, A-2, & A-10, Appendix ATsub - see Chapter 2, Equation 3Ksub - lateral stiffness at top of pier assemblyFy, Cy - yield strength and yield strength coefficient of pier assemblydy - yield displacement at top of pier assemblyKsub/kd - substructure stiffness to isolator second-slope stiffness ratio
77
3.1.5 Test Set-Up and Protocol
Utilizing the bridge specimen substructure components and isolation test bearings
provided, ten bridge configurations were developed to study various aspects of the
response of isolated bridge overcrossings through earthquake simulation studies. This test
program was developed to examine the global and local response trends of simple and
more complex isolated bridge systems subjected to a variety of earthquake input,
fullfilling objective 2 and 3 of the research program (as outlined in Section 1.3.1). Specific
issues to be examined in the study were outlined in project Task 6 (see Section 1.3.2) and
discussed further in the preliminary evaluations of Chapter 2. These issues include the
effect on isolated bridge response of: (1) the characteristics of the earthquake input
(including fault proximity, site soil effects, and the effect of uni-directional vs. multi-
directional input); (2) isolation system characteristics; (3) substructure flexibility; (4)
substructure mass; (5) higher modes; (6) system eccentricity; and (7) substructure
yielding. The ten bridge specimen configurations developed for these studies are
described in the sections below and schematically illustrated in Figure 3-2 through 3-6.
Configuration 1
This configuration was the standard non-elevated symmetric mass configuration of the
bridge deck model (see Figure 3-2). Table motion in this case represents motion at “rigid”
abutments. In this configuration, load cells were mounted directly on the earthquake
simulator. Isolation bearings were mounted to the top of load cells and connected to the
underside of the steel bridge deck. Concrete blocks were prestressed to the deck frame,
providing 65 kips of weight. Instrumentation for this configuration included: (1) table
78
instrumentation measuring table accelerations and displacements; (2) five degree-of-
freedom load cells measuring x- & y- shear and moment, as well as axial forces, under
each isolation bearing (at quadrant Q1, Q2, Q3 and Q4); (3) linear potentiometers (LP)
measuring bearing, deck, and table displacements; (4) DCDT’s measuring potential
shifting of the concrete mass blocks ; and (5) accelerometers mounted to the bridge deck,
concrete mass, and locally above isolation bearings. Data acquisition in this configuration
is illustrated in Figure 3-7 and detailed descriptions of each instrumentation device are
outlined in Table 3-3.
Configuration 1 was developed to study the response of simple isolated bridge
overcrossings. Variations in isolator characteristic properties (i.e., first- and second- slope
stiffness and strength) were examined in this configuration by replacing bearing types.
The effect of earthquake motion characteristics, including bi-directional and vertical input,
fault-proximity and soil effects, were studied in this and all model configurations. The
effect of idealized near-fault pulse motions were studied solely in this basic configuration
(see Section 3.2 for information regarding earthquake test motions).
Configuration 2
This configuration was similar to Configuration 1, but incorporated an eccentric mass
layout for the bridge deck (see Figure 3-2). This configuration was erected similar to
Configuration 1 with concrete blocks offset to produce superstructure mass eccentricities.
Instrumentation for this configuration was the same as that for Configuration 1 (see Figure
3-7 and Table 3-3).
79
Configuration 2 was developed to study the torsional response of simple isolated bridge
overcrossings. Deck mass was systematically offset to produce superstructure mass
eccentricities of 5 and 10 percent of the longitudinal bridge span. Torsional response of
different isolation systems were also examined in this configuration by replacing bearing
types.
Configuration 3
This configuration was again similar to Configuration 1, but incorporated an unsymmetric
distribution of isolation bearings (see Figure 3-3). This configuration was erected similar
to Configuration 1 with two different isolation bearing types (HDR and LR bearings)
mounted at either end of the bridge span. Instrumentation for this configuration was the
same as that for Configuration 1 (see Figure 3-7 and Table 3-3).
Configuration 3 was developed to study the torsional response of isolated bridge
overcrossings produced by bearing stiffness eccentricity. The installation of HDR and LR
bearings at either end of the deck produced eccentricity in first- and second- slope stiffness
and bearing strength properties. This study was not performed to suggest that different
types of isolators could be installed in a bridge at opposite abutments, but to assess the
effect of these types of variations along a bridge span. The effect of earthquake input
characteristics on this stiffness induced torsional response were also studied in this
configuration.
80
Configuration 4
This was the standard four-pier elevated configuration of the bridge deck model, an
elevated single-span configuration with symmetric substructure stiffness (see Figure 3-3).
In this configuration, substructure pier assemblies were mounted directly to the
earthquake simulator with load cells mounted on top of pier supports. FP isolation
bearings were used exclusively in this configuration attached to the top of load cells and
connected to the underside of the steel bridge deck. Concrete blocks were prestressed to
the deck frame, providing 65 kips of weight. In addition to the same instrumentation
utilized for Configuration 1 through 3 (see Figure 3-7 and Table 3-3), the following
instrumentation was added in this configuration: (1) additional linear potentiometers (LP)
measuring top of pier displacements; (2) additional accelerometers mounted to top of
substructure piers; and (3) linear strain gauges mounted on tapered leaf springs at base of
piers to monitor potential yield conditions. Data acquisition hardware in this configuration
is illustrated in Figure 3-7, 3-8, and 3-9. Detailed descriptions of each instrumentation
device are outlined in Table 3-3 and 3-4.
Configuration 4 was developed to study the response of simple isolated bridge
overcrossings and viaducts. Variations in isolator characteristic strength were examined in
this configuration by replacing FP bearing slider types. The effect of variations in
substructure flexibility were examined by adding or removing bracing or using different
rotational leaf springs at the base of the pier assemblies.
81
Configuration 5
This was an elevated bridge configuration with un-symmetric substructure stiffness,
erected similarly to Configuration 4, with short and long leaf springs inserted at the base
of pier assemblies in the x- and y- directions, respectively (see Figure 3-4).
Instrumentation for this configuration was similar to Configuration 4 as illustrated in
Figure 3-7, 3-8, and 3-9 and outlined in Table 3-3 and 3-4.
Configuration 5 was developed to study the response of simple isolated bridge
overcrossings, with the effect of variations in substructure flexibility in the x- and y-
directions. Variations in isolator characteristic strength were examined in this
configuration by replacing FP bearing slider types as before. The effect of substructure
mass (where γ = Σ mpier/Mdeck) was also studied in this configuration by varying the
number of attached lead weight packets mounted to substructure pier assemblies.
Configuration 6
This configuration is similar to Configuration 5 with additional cross-bracing added to
piers at one end of the specimen (see Figure 3-4). Instrumentation for this configuration
was similar to Configuration 4 and 5 as illustrated in Figure 3-7, 3-8, and 3-9 and outlined
in Table 3-3 and 3-4.
Configuration 6 was developed to study the torsional response of simple isolated bridge
overcrossings having unsymetric substructure conditions. Variation of substructure
flexibility along the span produced by added cross-bracing created the effect of
eccentricity in substructure stiffness in the configuration. Variations in isolator
82
characteristic strength could be examined in this configuration by replacing FP bearing
slider types symmetrically (i.e., replacing all slider types at once) or unsymmetrically (i.e.,
placing weaker FP bearing sliders above braced piers to counteract torsional response).
Configuration 7
This was the standard elevated double-span configuration of the bridge deck model (see
Figure 3-5). In this configuration, six substructure pier assemblies were mounted directly
to the earthquake simulator. Cross-bracing was added to piers in the longitude and
transverse directions at each end of the bridge specimen to simulate stiff abutment
conditions. Center piers were configured with short and long leaf springs inserted at their
base in the x- and y- directions, respectively, simulating a flexible central pier bent. Load
cells were mounted on top of pier supports with FP isolation bearings attached to the top
of load cells and connected to the underside of the steel bridge deck. Concrete blocks and
additional lead packets were prestressed to the deck frame providing 99 kips of weight.
This additional mass was installed to provide the system with an overall yield strength
coefficient (i.e., Cyiso) theoretically equivalent to the four pier specimen (assuming a
constant FP slider µ value). In addition, this larger mass produced nearly equivalent period
characteristics for the six-pier configuration with out cross-bracing as the four pier un-
braced configurations. The instrumentation for this configuration was similar to
Configuration 4 through 6, with the following additions: (1) five degree-of-freedom load
cells under each isolation bearing at pier 5 and 6; (2) linear potentiometers (LP) measuring
top of pier 5 and 6 displacements; (3) accelerometers mounted to locally above isolation
bearings and at top of substructure piers at pier 5 and 6; and (4) linear strain gauges
83
mounted on tapered leaf springs at base of pier 5 and 6. Data acquisition hardware is
illustrated in Figure 3-7, 3-8, and 3-9 and outlined in Table 3-3 and 3-4, as before.
Configuration 7 was developed to study the response of simple double-span isolated
bridge overcrossings. Variations in isolator characteristic strength were examined in this
configuration by replacing FP bearing slider types. These strength variations were
implemented symmetrically (i.e., by replacing all sliders at once) or unsymmetrically (by
placing weaker FP sliders selectively above braced piers or central piers to effect force
distribution).
Configuration 8
This configuration was similar to Configuration 7 with cross-bracing added to piers at
only one end of the specimen and long tapered leaf spring plates installed at the base of
piers in the x- direction at the opposite end (see Figure 3-5). Instrumentation for this
configuration was similar to Configuration 7 as illustrated in Figure 3-7, 3-8, and 3-9 and
outlined in Table 3-3 and 3-4.
Configuration 8 was developed to study the torsional response of simple isolated bridge
overcrossings. Increasing substructure transverse flexibility along the span produced
eccentricity in substructure stiffness. The effect of varying isolator characteristic strength
along the span was examined by replacing FP slider types symmetrically (i.e., replacing
all slider types at once) or unsymmetrically (i.e., placing weaker FP bearing sliders above
braced piers to counteract torsional response).
84
Configuration 9
This configuration was similar to Configuration 7 with weaker (A36) tapered leaf spring
plates inserted at the base of central piers (see Figure 3-6). Instrumentation for this
configuration is similar to Configuration 7 as illustrated in Figure 3-7, 3-8, and 3-8 and
outlined in Table 3-3 and 3-4.
Configuration 9 was developed to study the response of simple double-span isolated
bridge overcrossings with yielding substructure components. A36 leaf spring plates in
central piers were designed to allow ductile response in the lateral force-displacement
characteristics of the central pier assemblies.
Configuration 10
This was a free-standing configuration of substructure pier sub-assemblies (see Figure 3-
6). This configuration utilized the same substructure assemblages as Configuration 9 with
bridge mass and deck, isolation bearings, and load cells removed. Instrumentation for this
configuration consisted of: (1) a linear load cell attached in series with a come-along
winch between tops of pier sub-assemblies to produce an increasing static force, and (2)
linear potentiometers (LP) measuring the displacements at the top of the piers (see Figure
3-6). This configuration was developed to characterize the lateral force-deformation
characteristics of the strong and weak substructure pier sub-assemblies (i.e., those
utilizing A514 and A36 tapered leaf spring base plates, respectively). The piers were
characterized in both their stiff (i.e., short plate) and flexible (i.e., long plate)
configurations (see Table 3-2).
85
Specimen as-built documentation
As a reference, photographs of bridge specimen erection sequences, pier frame
assemblies, and component details are included along with construction plans and
fabrication details in Appendix A.
3.2 Earthquake Histories for Testing
An evaluation of the effect of ground motion input characteristics on the response of the
various configurations of the bridge deck specimen was an essential component in these
simulation studies. The features of seismic demand include: (1) fault proximity (i.e., far-
vs. near- field events); (2) directivity (i.e., fault-normal vs. fault-parallel and forward- vs.
backward-azimuth motions); (3) site specific soil conditions (i.e., rock vs. soil sites); (4)
bi-directional effects; and (5) vertical components of motion. A group of shake table
motions was tailored to consider each of these variations explicitly. In addition, sinusoidal
forcing motions were developed to characterize the friction coefficient of the various FP
bearing slider types provided by the manufacturer. The characteristics of these motions are
described in detail below.
Three representative earthquake time-histories were selected for shake table testing. Basis
recorded time-histories were chosen from the database developed in Phase 2 of the
FEMA/SAC project [SAC, 1997]. The bi-directional ground motion pairs LA13/LA14,
NF01/NF02, and LS17c/LS18c, as listed in Table 2-2, were selected from this database to
represent far-field, near-fault, and soft-soil ground motion types, respectively. These basic
motions were filtered and scaled to produce shake table input motions conforming to the
acceleration, velocity, and displacement limits of the shake table apparatus. The resulting
86
Configuration 1: Non-elevated Symmetric Mass
Configuration 2: Non-elevated Eccentric Mass
Figure 3-2 Test Configurations 1 and 2 for bridge deck model
x
y
(4) FP bearingsor(4) LR bearingsor (4) HDR bearings
C.M.
Deck FrameWdeck = 66 kips
x
y
(4) FPS bearings
C.M.
ey
or(4) LR bearings
Deck FrameWdeck = 66 kips
87
Configuration 3: Non-elevated Eccentric Stiffness
Configuration 4: Elevated Single-span with Symmetric Stiffness
Figure 3-3 Test Configurations 3 and 4 for bridge deck model
x
y
(2) HDR bearings
(2) LR bearings
Deck FrameWdeck = 66 kips
C.M.
x
y
(4) FPS bearings
C.M.
Deck frameWdeck = 66 kips
(4) Substructure piersγ=Σmpier/Mdeck = .05, typical
Stiff rotational springs in x & ydirections, typicalat base of piers
Q1Q2
Q3 Q4
~
88
Configuration 5: Elevated Single-span with Un-symmetric Stiffness
Configuration 6: Elevated Single-span with Eccentric Stiffness
Figure 3-4 Test Configurations 5 and 6 for bridge deck model
x
y
(4) FP bearings
C.M.
Deck frameWdeck = 66 kips
(4) Substructure piers
Stiff rotational springs inx-direction, typ.
Flexible rotational springs iny-direction, typ.
Symmetric pier bracing in x & y direction, optional
γ=Σmpier/Mdeck = .05, typ.~ Single Span Elevated Deck Σmpier/Mdeck = 0.10 condition shown~
x
y
(4) FP bearings
C.M.
Deck frameWdeck = 66 kips
(4) Substructure piersγ=Σmpier/Mdeck = .05, typ.
Stiff rotational springs inx-direction, typ.
Flexible rotational springs iny-direction, typ.
Pier bracing added in x & ydirection, as shown
~
89
Configuration 7: Elevated Double-span
Configuration 8: Elevated Double-span with Eccentric Stiffness
Figure 3-5 Test Configurations 7 and 8 for bridge deck model
(6) FP bearings
Deck frameWdeck = 99 kips
(6) Substructure piersγ=Σmpier/Mdeck = .05, typ.
Stiff rotational springs inx-direction, typ.
Flexible rotational springs iny-direction, typ.
Symmetric pier bracing in x & y direction, typicalat end bays as shown
Q1Q2
Q3 Q4
Pier 5Pier 6
x
y
C.M.
~
(6) FP bearings
(6) Substructure piersγ=Σmpier/Mdeck = .05, typ.
Stiff rotational springs at Q3 & Q4
Flexible rotational springs iny-direction, typ.
Symmetric pier bracing in x & y direction at endshown only
Q1Q2
Q3 Q4
Pier 5Pier 6
x
y
C.M.
Flexible rotational springs at Q1 & Q2,x-direction
Deck frameWdeck = 99 kips
and Pier 5 & 6,x-direction
~
90
Configuration 9: Elevated Double-span with Yielding Piers 5 and 6
Configuration 10: Substructure Static Pullback Tests
Figure 3-6 Test Configurations 9 and 10 for bridge deck model
(6) Substructure piersγ=Σmpier/Mdeck = .05, typ.
Stiff rotational springs inx-direction, typ.
Flexible rotational springs iny-direction, typ.
Symmetric pier bracing in x & y direction, typicalat end bays as shown
Q1Q2
Q3 Q4
Pier 5Pier 6
x
y
C.M.
(6) FP bearings
Deck frameWdeck = 99 kips
Yielding rotationalspring plates inx & y-direction atPiers 5 & 6 only
(A514 - 100ksi)
(A514 - 100ksi nom.)
(A36 - 36ksi nom.)
~
Deck frame and bearings(6) Substructure piers
Stiff rotational springs inx-direction, typ.
Flexible rotational springs iny-direction, typ.
Q1Q2
Q3 Q4
56
x
y Yielding rotationalspring plates inx & y-direction atPiers 5 & 6 only(A36 - 36ksi nom.)
(A514 - 100ksi nom.)
(A514 - 100ksi nom.)
Typical pullback rigging:tension cable and straps,load cell, and come-alongin series at top of pier
removed, typical
91
Figure 3-7 Instrumentation plan for Configurations 1 through 3 of non-elevated bridge deck model
Q
◆ ◆ ◆
◆◆ ◆
◆◆
◆
92
Figure 3-8 Supplementary instrumentation for Configurations 4 through 9 of elevated bridge deck model
93
a. Short plate (a.k.a., stiff spring) b. Long plate (a.k.a., flexible spring)
Figure 3-9 Typical strain gauge layout at pier base rotational leaf springs
Table 3-3 Instrumentation for Configurations 1 thru 3 of non-elevated bridge deck
Channel No. Transducer Response
Quantity Orientation Transducer Location
1 LVDT displacement horizontal table h1o stroke2 LVDT displacement horizontal table h2o stroke3 LVDT displacement horizontal table h3o stroke4 LVDT displacement horizontal table h4o stroke5 DCDT displacement vertical table v1o stroke6 DCDT displacement vertical table v2o stroke7 DCDT displacement vertical table v3o stroke8 DCDT displacement vertical table v4o stroke9 A acceleration horizontal table h1-2 acc.10 A acceleration horizontal table h3-4 acc.11 A acceleration horizontal table h4-1 acc.12 A acceleration horizontal table h2-3 acc.13 A acceleration vertical table 1v acc.14 A acceleration vertical table 2v acc.15 A acceleration vertical table 3v acc.16 A acceleration vertical table 4v acc.17 LC force horiz. shear x load cell - bearing Q118 LC force horiz. shear y load cell - bearing Q119 LC force moment y load cell - bearing Q120 LC force moment x load cell - bearing Q121 LC force axial load cell - bearing Q122 LC force horiz. shear x load cell - bearing Q223 LC force horiz. shear y load cell - bearing Q224 LC force moment y load cell - bearing Q225 LC force moment x load cell - bearing Q2
C L
3”
linear strain gauge (SG),top & bottom of plate
Plan View (N.T.S.)
C L
3” 12”
linear strain gauge (SG),top & bottom of plate
SG, top ofplate only
Plan View (N.T.S.)
94
26 LC force axial load cell - bearing Q227 LC force horiz. shear x load cell - bearing Q328 LC force horiz. shear y load cell - bearing Q329 LC force moment y load cell - bearing Q330 LC force moment x load cell - bearing Q331 LC force axial load cell - bearing Q332 LC force horiz. shear x load cell - bearing Q433 LC force horiz. shear y load cell - bearing Q434 LC force moment y load cell - bearing Q435 LC force moment x load cell - bearing Q436 LC force axial load cell - bearing Q437 A acceleration horiz. y mass - acc138 A acceleration horiz. y mass- acc239 A acceleration horiz. x mass - acc340 A acceleration horiz. x mass - acc441 A acceleration horiz. x mass - acc542 A acceleration horiz. y deck frame - acc643 A acceleration horiz. y deck frame - acc744 A acceleration horiz. x deck frame - acc845 A acceleration horiz. x deck frame - acc946 A acceleration horiz. x deck frame - acc1047 A acceleration horiz. x bearing Q1 - acc1148 A acceleration horiz. y bearing Q1 - acc1249 A acceleration vertical bearing Q1 - acc1350 A acceleration horiz. x bearing Q2 - acc1451 A acceleration horiz. y bearing Q2 - acc1552 A acceleration vertical bearing Q2 - acc1653 A acceleration horiz. x bearing Q3 -acc1754 A acceleration horiz. y bearing Q3 - acc1855 A acceleration vertical bearing Q3 - acc1956 A acceleration horiz. x bearing Q4 - acc2057 A acceleration horiz. y bearing Q4 - acc2158 A acceleration vertical bearing Q4 - acc2259 LP displacement horiz. y deck frame - LP160 LP displacement horiz. y deck frame - LP261 LP displacement horiz. x deck frame - LP362 LP displacement horiz. x deck frame - LP463 LP displacement horiz. x deck frame - LP564 LP displacement horiz. y bearing Q1 - LP665 LP displacement horiz. x bearing Q1 - LP766 LP displacement horiz. y bearing Q2 - LP867 LP displacement horiz. x bearing Q2 - LP968 LP displacement horiz. y bearing Q3 - LP10
Table 3-3 Instrumentation for Configurations 1 thru 3 of non-elevated bridge deck
95
69 LP displacement horiz. x bearing Q3 - LP1170 LP displacement horiz. y bearing Q4 - LP1271 LP displacement horiz. x bearing Q4 - LP1372 LP displacement horiz. y table - LP1473 LP displacement horiz. x table - LP1574 LP displacement horiz. x table - LP16
75 DCDT displacement sloped deck frame to mass - DCDT1
76 DCDT displacement sloped deck frame to mass - DCDT2
77 DCDT displacement sloped deck frame to mass - DCDT3
Table 3-4 Instrumentation for Configurations 4 through 10 of elevated bridge deck
Channel No. Transducer Response
Quantity Orientation Transducer Location
1 thru 58 |Same as Configurations 1 through 3 - non-elevated Bridge Deck, see Table 3-3 above
59 A acceleration horizontal Pier Q1 x - acc2360 A acceleration horizontal Pier Q1 y - acc2461 A acceleration horizontal Pier Q2 x - acc2562 A acceleration horizontal Pier Q2 y - acc2663 A acceleration horizontal Pier Q3 x - acc27
Channel 63 converted to uni-axial force readings for Config. 10 pullback tests, as follows63 LC force horizontal Uni-Axial load cell64 A acceleration horizontal Pier Q3 y - acc2865 A acceleration horizontal Pier Q4 x - acc2966 A acceleration horizontal Pier Q4 y - acc30
67 DCDT displacement sloped deck frame to mass - DCDT1
68 DCDT displacement sloped deck frame to mass - DCDT2
69 DCDT displacement sloped deck frame to mass - DCDT3
70 SG linear strain curvature y Pier Q1 - XOP71 SG linear strain horiz. x Pier Q1 - XFT72 SG linear strain horiz. x Pier Q1 - XTH73 SG linear strain curvature x Pier Q1 - YOP74 SG linear strain horiz. y Pier Q1 - YFT
Table 3-3 Instrumentation for Configurations 1 thru 3 of non-elevated bridge deck
96
75 SG linear strain horiz. y Pier Q1 - YTH76 SG linear strain curvature y Pier Q2- XOP77 SG linear strain horiz. x Pier Q2- XFT78 SG linear strain horiz. x Pier Q2 - XTH79 SG linear strain curvature x Pier Q2 - YOP80 SG linear strain horiz. y Pier Q2 - YFT81 SG linear strain horiz. y Pier Q2 - YTH82 SG linear strain curvature y Pier Q3 - XOP83 SG linear strain horiz. x Pier Q3 - XFT84 SG linear strain horiz. x Pier Q3 - XTH85 SG linear strain curvature x Pier Q3 - YOP86 SG linear strain horiz. y Pier Q3 - YFT87 SG linear strain horiz. y Pier Q3 - YTH88 SG linear strain curvature y Pier Q4- XOP89 SG linear strain horiz. x Pier Q4- XFT90 SG linear strain horiz. x Pier Q4 - XTH91 SG linear strain curvature x Pier Q4 - YOP92 SG linear strain horiz. y Pier Q4 - YFT93 SG linear strain horiz. y Pier Q4 - YTH94 SG curvature curvature y Pier 5 - XOP95 SG linear strain horiz. x Pier 5 - XFT96 SG linear strain horiz. x Pier 5 - XTH97 SG curvature curvature x Pier 5 - YOP98 SG linear strain horiz. y Pier 5 - YFT99 SG linear strain horiz. y Pier 5 - YTH100 SG curvature curvature y Pier 6- XOP101 SG linear strain horiz. x Pier 6- XFT102 SG linear strain horiz. x Pier 6 - XTH103 SG curvature curvature x Pier 6 - YOP104 SG linear strain horiz. y Pier 6 - YFT105 SG linear strain horiz. y Pier 6 - YTH106 LC force horiz. shear x load cell - bearing 5107 LC force horiz. shear y load cell - bearing 5108 LC force moment y load cell - bearing 5109 LC force moment x load cell - bearing 5110 LC force axial load cell - bearing 5111 LC force horiz. shear x load cell - bearing 6112 LC force horiz. shear y load cell - bearing 6113 LC force moment y load cell - bearing 6
Table 3-4 Instrumentation for Configurations 4 through 10 of elevated bridge deck
97
114 LC force moment x load cell - bearing 6115 LC force axial load cell - bearing 6
Channels 116 through 128 skipped129 LP displacement horiz. y deck frame - LP1130 LP displacement horiz. y deck frame - LP2131 LP displacement horiz. x deck frame - LP3132 LP displacement horiz. x deck frame - LP4133 LP displacement horiz. x deck frame - LP5134 LP displacement horiz. y bearing Q1 - LP6135 LP displacement horiz. x bearing Q1 - LP7136 LP displacement horiz. y bearing Q2 - LP8137 LP displacement horiz. x bearing Q2 - LP9138 LP displacement horiz. y bearing Q3 - LP10139 LP displacement horiz. x bearing Q3 - LP11140 LP displacement horiz. y bearing Q4 - LP12141 LP displacement horiz. x bearing Q4 - LP13142 LP displacement horiz. y table - LP14143 LP displacement horiz. x table - LP15144 LP displacement horiz. x table - LP16145 LP displacement horiz. x Pier Q1 - LP17146 LP displacement horiz. x Pier Q1 - LP18147 LP displacement horiz. y Pier Q2 - LP19148 LP displacement horiz. x Pier Q2 - LP20149 LP displacement horiz. y Pier Q3 - LP21150 LP displacement horiz. x Pier Q3 - LP22151 LP displacement horiz. y Pier Q4 - LP23152 LP displacement horiz. x Pier Q4 - LP24153 LP displacement horiz. y bearing 5- LP25154 LP displacement horiz. x bearing 5 - LP26155 LP displacement horiz. y bearing 6 - LP27156 LP displacement horiz. x bearing 6 - LP28157 LP displacement horiz. y Pier 5 - LP29158 LP displacement horiz. x Pier 5 - LP30159 LP displacement horiz. y Pier 6 - LP31160 LP displacement horiz. x Pier 6 - LP32
The following Channels were relocated for Pier 5 & 6 acceleration readingsnote: acc6, acc7, acc8, acc10 to Pier 5x, Pier 5y, Pier 6x, Pier6y respectively
42 A acceleration horiz. x Pier 5 - acc31
Table 3-4 Instrumentation for Configurations 4 through 10 of elevated bridge deck
98
table motions produced are referred to as LA13_14, NF01_02, and LS17c_18c and
utilized associated similitude length scale factors of lr = 1/2, 1/5, and 1/5, respectively, to
enforce conformance with table limits. Each table motion consists of a bi-directional pair
of time-histories oriented orthogonally along the x- and y- axes of the shake table (e.g.,
LA13_14 consists of the scaled x-direction LA13 and y-direction LA14 components). The
scaled near-fault motion (i.e., NF01_02) includes its vertical component as well. Motions
could be run separately, as uni-directional (x- or y-direction) components, or as bi-
directional pairs. In the case of the NF01_02 motion, the vertical component could be
added or omitted from the table time-history. Response spectra for the LA13_14,
NF01_02, and LS17c_18c shake table motions are shown in Figure 3-10 for comparison.
In addition, to study the effect of similitude scaling on the bridge specimen (see Section
3.1.1 discussion) these motions were processed with alternate length scale factors. The
effect of varying similitude length scale (lr) on the response spectra of three of these table
motion components is illustrated in Figure 3-11.
Near-fault ground motions have been shown to place significant demand on structures.
The impulsive and sometimes long-period content of these motions may produce velocity
and displacement demands significantly exceeding the design criteria provided by code
specified spectrum compatible ground motions. These unique earthquake time-histories
may be modeled with sufficient accuracy (for structures responding at or near the peak in
43 A acceleration horix. y Pier 5 - acc3244 A acceleration horiz. x Pier 5 - acc3346 A acceleration horix. y Pier 5 - acc34
Table 3-4 Instrumentation for Configurations 4 through 10 of elevated bridge deck
99
the earthquake’s response spectra) as simple pulse motions [Krawinkler and Alavi, 1998].
On this basis, a suite of bi-directional, pure pulse motions were developed for these
studies with pure cosine and sine waves selected to model fault-normal and fault-parallel
displacement histories, respectively. Figure 3-12 illustrates time-histories for these
simulated motion pairs at their peak displacement amplitude of 5 inches (the limit of the
shake table apparatus). Fault-normal pulse durations of Tp = 1 and 2 seconds were selected
providing a range bracketing characteristic periods (i.e., Tiso) of the test bearings (see
Table 3-1). The duration of associated fault-parallel motions were taken as 2/3, 1, and 3/2
of Tp to evaluate the coupling effect between these orthogonal components. Table 3-5
shows amplitude and duration parameters for the entire suite of idealized pulse motions
developed from these parameters. These synthetic motions are representative of suggested
pulse parameters for actual near-fault earthquake records as recommended in [Krawinkler
and Alavi, 1998] at a similitude length scale factor of lr = 1/4.
To estimate friction coefficients for the various Friction Pendulum slider composites
provided by the manufacturer, a suite of sinusoidal acceleration time-histories were also
developed. These motions were designed to impose a steady-state response of varying
displacement and velocity amplitudes on the test specimen. Results from these tests were
utilized to estimate instantaneous friction values for the different composites. Figure 3-13
illustrates a representative acceleration time-history of these sinusoidal motions. Signal
amplitude and frequencies used to develop the various test motions are in Table 3-6.
100
a. Displacement spectra: LA13_14 b. Total acceleration spectra: LA13_14
c. Displacement spectra: NF01_02 d. Total acceleration spectra: NF01_02
e. Displacement spectra: LS17c_18c f. Total acceleration spectra: LS17c_18c
Figure 3-10 Displacement and total acceleration spectra for LA13_14, NF01_02, and LS17c_18c table motions, ζ=5%
0 0.5 1 1.5 20
5
10
15
T (sec)
D (
in)
la13la14
0 0.5 1 1.5 20
0.5
1
1.5
2
2.5
3
T (sec)
A to
tal (
g)
0 0.5 1 1.5 20
5
10
15
T (sec)
D (
in)
nf01nf02
0 0.5 1 1.5 20
0.5
1
1.5
2
2.5
3
T (sec)
A to
tal (
g)
0 0.5 1 1.5 20
5
10
15
T (sec)
D (
in)
ls17cls18c
0 0.5 1 1.5 20
0.5
1
1.5
2
2.5
3
T (sec)
A to
tal (
g)
101
a. Displacement spectra: LA13 b. Total acceleration spectra: LA13
c. Displacement spectra: NF01 d. Total acceleration spectra: NF01
e. Displacement spectra: LS17c f. Total acceleration spectra: LS17c
Figure 3-11 Response spectra of LA13, NF01, and LS17c table motions with varying length scale, ζ = 5%
0 0.5 1 1.5 20
5
10
15
T (sec)
D (
in)
SF=2SF=4
0 0.5 1 1.5 20
0.5
1
1.5
2
2.5
T (sec)
A to
tal (
g)
0 0.5 1 1.5 20
5
10
15
T (sec)
D (
in)
SF=3SF=5
0 0.5 1 1.5 20
0.5
1
1.5
2
2.5
T (sec)
A to
tal (
g)
0 0.5 1 1.5 20
5
10
15
T (sec)
D (
in)
SF=3SF=5
0 0.5 1 1.5 20
0.5
1
1.5
2
2.5
T (sec)
A to
tal (
g)
102
3.3 Pre-Test Analysis of Bridge Deck Model
An analysis matrix, developed to include all proposed model configurations (see Section
3.1.5), was prepared for pre-test analytical evaluations of the test specimen. Pre-test
analysis assumed properties for specimen substructure components based upon their
design values (see Section 3.1.4). For systems employing FP bearings, nominal friction
coefficients of 0.04, 0.06, 0.09, and 0.12 were considered to bound the range of expected
values. FP bearing stiffness was assumed based upon the design value of the dish radius, R
a. Fault-normal b. Fault-parallel
Figure 3-12 Idealized near-fault pulse displacement histories
Table 3-5 Characteristics of near-fault pulse table motions at full amplitude
Label Fault-orientation Tp (sec) Dgmax (in.) Vgmax (in./sec) Agmax (g)
nfpu
lse1
_
normal 1 5 31.4159 0.5108
parallel 0.667 5 47.1003 1.1483
parallel 1 5 31.4159 0.5108
parallel 1.5 5 20.9440 0.2270
nfpu
lse2
_
normal 2 5 15.7080 0.1277
parallel 1.33 5 23.6210 0.2888
parallel 2 5 15.7080 0.1277
parallel 3 5 10.4720 0.0568
0 0.5 1−5
0
5
time/Tp
Dg (
g)
0 0.5 1−5
0
5
time/Tp
Dg (
in)
103
(see Section 3.1.4). LR bearing properties were averaged from available characterization
test data. Analyses were performed utilizing the generalized multi-degree-of-freedom, bi-
directional bridge model developed previously (see Section 2.3.3). The three earthquake
time-history motions (i.e., LA13_14, NF01_02, and LS17c_18c) and the suite of idealized
near-fault pulse motions (i.e., nfpulse1_ and nfpulse2_, see Table 3-5) were considered
over a range of amplitudes.
Summarized results from these pre-test analyses are included in Appendix B. These
results were examined to establish table motion amplitudes which would likely produce
specimen response near the limits of bearing and component displacement capacities.
Figure 3-13 Representative acceleration time-history of sin signal table motion
Table 3-6 Sin signal characteristics for characterization of FP slider µ values
Ao (g) f (Hz) Do (in) Vo (in/sec)
.130 1.714 0.4331 4.6643
.145 2.285 0.2718 3.9024
.111 2.285 0.20807 2.98740
.097 2.856 0.11639 2.08867
.104 6.000 0.02827 1.0659
0 2 4 6 8 10 12 14−0.15
−0.1
−0.05
0
0.05
0.1
0.15
time (sec)
acc
ele
ratio
n (
g)
104
Trial span settings for test motions were then selected to provide 50% and 100% of these
peak amplitudes. Final peak table span settings were tailored during simulation tests to
produce model response near capacity, with final test sequences run at 50% and 100% of
these final settings.
3.4 Experimental Results for Configuration 1 (Non-elevated, Symmetric Mass)
Table C-1 in Appendix C presents a complete log of shake-table tests performed on the
Configuration 1 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-1 through D-30. For each of the selected tests,
x-y orbit plots of the global displacement and global force, and x- & y-direction bearing
hysteresis (for quadrant 1, a.k.a., Q1) are presented as a summary of the test specimen
response. For uni-directional tests, x-direction displacement and force histories are
presented in lieu of orbits and y-direction bearing hysteresis at quadrant Q1 is omitted.
Selected results are shown only for the maximum table span setting run for each
individual test motion sequence.
The Configuration 1 specimen was tested utilizing the three selected earthquake table
motions and the suite of idealized near fault pulses (see Section 3.2). Tests were performed
at two or more amplitudes (or span settings) and bi-directional motion pairs were run
simultaneously and as separate x- & y-direction inputs. Sinusoidal bearing
characterization tests were also performed to estimate friction coefficients for FP bearing
slider composites.
For earthquake history tests, representative results for both uni-directional and bi-
directional tests are presented in Figures D-1 through D-19. These results are presented for
105
tests with FP, HDR, and LR bearings. Figure D-1 and D-5 illustrate response to the
LA13_14 earthquake table motion. Figure D-1 and D-2 compare response of a system
utilizing FP bearings with type 1 and 2 PTFE slider composite to the x-direction LA13
component. As seen, the FP bearings exhibit broad stable hysteretic response. The type 2
slider composite has a higher friction coefficient (see Section 3.14) resulting in a lower
peak displacement response. Figure D-3 shows the effect of the bi-directional LA13_14
table motion on the FP bearing system. As seen in the displacement orbit (see Figure D-
3(a)), this motion produces response oriented strongly along a 45 degree line to the xy-
axes. This behavior suggests strong coupling in the bearing response, as interaction with
the bearing yield surface is encountered. As expected, the x-direction bearing response at
quadrant Q1 (see Figure D-3(c)) is effected by this coupling, as the force response of the
bearing is reduced (compared to the bearing response without the LA14 component seen
in Figure D-2(c)), particularly in the x- direction induced by the strong coupled response
in the y- direction. Figure D-4 illustrates the response of a HDR bearing system to this
same LA13_14 table motion at a reduced span setting. As seen in the figure, the HDR
bearings exhibit a significant stiffening behavior, particularly in the first cycle excursions
to increasingly larger strain. The result of this behavior is increased force output.
However, reduced displacement response would be expected as a result. Figure D-5
illustrates the response of a system utilizing LR bearings to the LA13 component motion
at the same span setting as the previous test. As seen in the figure, the LR bearings exhibit
broad stable hysteretic response through numerous cycles (see Figure D-5(c)).
Comparisons between bearing characteristics (i.e., Qd, ku and kd) can be made by
106
examining the bearing hysteretic plots shown in these figures (see Table 3-1 and Figure 3-
1).
Figure D-6 through D-13 illustrate response for the FP, HDR, and LR bearing systems to
the LS17c_18c and the NF01_02 table motions. Comparisons between bearing behavior
are similar to the previous test results. The LS17c_18c motion produces relatively regular
harmonic response in the specimen, as noted in the displacement histories of Figure D-
6(a), D-7(a), and D-10(a). This soft-soil motion is rich in long period content (see Figure
3-10) near to the period characteristics of these test bearings, with harmonic response as
the expected result. Bi-directional coupling effects in the LS17c_18c motion are not
significant due to its strong orientation along its x-component. The near-fault NF01_02
motion has an impulsive fault-parallel (x-direction) and fault-normal (y-direction)
component which are inherently strongly coupled. This motion produces strongly coupled
behavior in the specimen as seen in the displacement orbits of Figure D-11 and D-12.
For scaled motion tests, representative results are presented in Figures D-14 through D-19.
These tests were performed utilizing FP bearings with type 1 PTFE composite. As seen in
the plots, the table motions at larger scale factors (i.e., lr) produce specimen response of
larger magnitude and longer period content (compare for example Figure D-14 to Figure
D-15). This difference in specimen behavior is to be expected, as the same motion at a
larger length scale factor produces typically larger spectral response (as seen in Figure 3-
11), particularly in the longer period range representative of the characteristic isolation
periods of the test bearings (see Table 3-1).
107
For near fault pulse tests, representative results are presented in Figures D-20 through D-
28. These tests were performed utilizing FP bearings with type 2 PTFE composite and LR
bearings. As seen in the plots, bearing response to these pure pulse motions are smooth
and cyclic. Bearing response is also strongly influence by coupling behavior induced by
the ground motion signal phasing of fault normal and parallel components. These results
show that fault parallel component pulses with durations of 2/3, 1, and 1.5 times the fault
normal pulse duration (Tp) produce decreasingly smaller coupled response, respectively.
In particular, this is noted in the decreasing bearing response along the direction of the
fault parallel component.
Figures D-29 & D-30 present results of sinusoidal bearing characterization tests for FP
bearings with type 1 and 2 PTFE composite sliders, respectively. Section 3.14 presents a
summary of these and all other FP slider characterization tests.
3.5 Experimental Results for Configuration 2 (Non-elevated, Eccentric Mass)
Table C-2 in Appendix C presents a complete log of shake-table tests performed on the
Configuration 2 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-31 through D-60. For each of the selected tests,
one or two summary figures are presented. The first figure presents three plots of the
global displacement time-history, global force time-history, and the x-direction bearing
hysteresis (for quadrant Q1). For systems with mass eccentricity, the second figure
presents a summary of torsional response including: a comparison of hysteretic response
and displacement time-histories for the East and West ends of the bridge specimen (in the
direction of motion input orthogonal to the direction of mass eccentricity), and a time-
108
history of deck rotation.
The Configuration 2 specimen was tested utilizing the x-direction component of the three
earthquake table motions. Tests were performed at two or more amplitudes (or span
settings) with mass eccentricities in the transverse direction of 0, 5, and 10 percent of the
overall bridge length. Tests were performed utilizing FP bearings (with type 2 PTFE
composite sliders) and LR bearings. Selected results are presented only for tests run at
their maximum amplitude. The figures illustrate the tendency for an increase in system
rotational response and bearing displacements at one end of the span as mass eccentricity
is increased (i.e., e/L increases from 0 to 0.05 to 0.10). This is made apparent by
comparing rotation histories and bearing hysteretic plots at the west and east ends of the
specimen for the same ground motion input with e/L = 0.05 and 0.10. For the case e/L = 0,
negligible system rotation was exhibited, as expected.
3.6 Experimental Results for Configuration 3 (Non-elevated, Eccentric Stiffness)
Table C-3 in Appendix C presents a complete log of shake-table tests performed on
Configuration 3 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-61 through D-66. For each of the selected tests,
two summary figures are presented. The first figure presents the x-direction global
displacement time-history, global force time-history, and bearing hysteresis (for quadrant
Q1). The second figure presents a summary of torsional response including: a comparison
of hysteretic response and displacement time-histories for the East and West ends of the
bridge specimen (in the direction of motion input orthogonal to the direction of stiffness
eccentricity), and a time-history of global deck rotation.
109
The Configuration 3 specimen was tested transversely utilizing the x-direction component
of the three earthquake table motions. Isolation system stiffness eccentricity was provided
by installing LR bearings and HDR bearings on the West and East ends of the bridge,
respectively. Selected results are presented only for tests run at their maximum amplitude.
Test results for this sequence are indicative of the stiffness eccentricity inherent in the
isolation system. Characteristic bearing hysteretic properties are compared in Table 3.1. It
is apparent the LR test bearings have higher initial stiffness (i.e., larger ku) and somewhat
higher characteristic strength (Qu). On the other hand, the HDR test bearings have larger
second-slope stiffness (kd) than the LR bearings at similar peak strains. The HDR bearings
also exhibit scragging effects resulting in increased force output in initial cycles. These
variations produce eccentricity in system strength, and first- and second-slope stiffness,
resulting in torsional behavior. The tendency in the test sequences is for the HDR bearings
(at one end of the span) to exhibit smaller displacement response than the LR bearings (on
the opposite end). This is presumably the result of the larger second-slope stiffness of the
HDR bearings, even though the LR bearings are initially stronger and stiffer. For the first
test cycles to large strain (see Figure D-61 and 62 for the LA13_14 test motion), HDR
bearings exhibited first cycle scragging effects resulting in force output larger than the LR
bearings. In later tests after scragging had occurred and insufficient time had been allotted
between tests to allow recovery in the HDR bearings, LR and HDR bearings exhibited
similar force output (despite the larger displacement response of the LR bearings).
110
3.7 Experimental Results for Configuration 4 (Elevated Single-span with Sym-metric Stiffness)
Table C-4 in Appendix C presents a complete log of shake-table tests performed on the
Configuration 4 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-67 through D-72. For each of the selected tests,
two summary figures are presented. The first figure presents the global displacement and
force orbits and x- & y-direction bearing hysteresis (for quadrant Q1). The second figure
presents a summary of local substructure response including plots of overall, bearing, and
pier hysteretic response in the x- & y-direction (at quadrant Q1).
The Configuration 4 specimen was tested utilizing the three selected earthquake time-
histories. Tests were performed at two or more amplitudes (or span settings) and bi-
directional motion pairs were run simultaneously and as separate x- & y-direction inputs.
Tests were performed utilizing FP bearings with type 4 PTFE composite. Selected results
are presented only for the bi-directional tests run at their maximum table span setting.
Similar to the Configuration 1 specimen test results (see Section 3.4), these results
indicate that response is influenced strongly by ground motion characteristics, including
frequency content and directional orientation. The LA13_14 motion has significantly
higher frequency content (see Section 3.2) and is strongly oriented along a 45 degree axis
to the x-y direction. This results in specimen response with significant coupling in the x-
and y-directions and underlying cycling of higher frequency (see Figure D-67 and D-68).
The LS17c_18c motion contains lower frequency components (see Section 3.2) and is
oriented strongly along the x-direction. This results in specimen response with strong
orientation along the x-direction with little coupled response and low frequency harmonic
111
cycling (see Figure D-69 and D-70). The NF01_02 motion is an impulsive near-fault event
with strong coupled x- and y-components (see Section 3.2). The vertical component
included in this ground motion history also contains significant amplitude accelerations.
This results in similar response to that of the LA13_14 motion, with less underlying high
frequency contribution, and added fluctuations in the bearing friction force component of
the hysteretic response induced by the vertical acceleration contributions (see Figure D-71
and D-72).
In addition, system attributes play an important contribution to the response as well.
Substructure pier response is essentially linear in these tests, with only slight pinching
near the origin, as seen in the hysteretic plots (see Figure D-68, D-70, and D-72 (e) and
(f)). This pinching behavior is discussed further in Section 3.13. On the other hand,
bearing response is essentially bilinear (see Figure D-67, D-69, and D-71 (c) and (d)), with
pinching of varying magnitude. This pinching response may be seen as the result of
several factors: bi-directional coupling in the bearing yield surface, vertical load
fluctuations caused by overturning effects and/or vertical acceleration input (see NF01_02
test results), or vertical load redistributions resulting from kinematic shortening of pier
assemblies. The latter phenomenon is discussed in further detail in subsequent evaluations
in Chapter 4. Finally, it is noted that total specimen displacement response (at the deck
level) is distributed between the isolation bearings and the pier substructure assemblies in
proportion to their flexibilities. Each of these components resist nearly equal force
transmission (varying slightly as the result of substructure mass contributions) with total
displacement response being the sum of the two component displacement contributions in
series.
112
3.8 Experimental Results for Configuration 5 (Elevated Single-span with Un-symmetric Stiffness)
Table C-5 in Appendix C presents a complete log of shake-table tests performed on the
Configuration 5 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-73 through D-98.
The Configuration 5 specimen was tested with and without bracing utilizing the three
earthquake table motions. Tests were performed at two or more amplitudes (or span
settings) and bi-directional motion pairs were run simultaneously and as separate x- and y-
direction inputs. The specimen was also tested with uni-directional components of the
earthquake table motions at alternate length scale factors (i.e., lr), similar to the
Configuration 1 tests (see Section 3.4). The NF01_02 motion was run with and without its
vertical signal. Tests were performed utilizing FP bearings with type 3 and 4 PTFE
composites. Selected results are presented only for tests run at their maximum table span
setting.
For the selected earthquake history tests shown in Figure D-73 through D-92, two
summary figures are presented. The first figure presents the global displacement and force
orbits and x- and y-direction bearing hysteresis (for quadrant Q1). The second figure
presents a summary of local substructure response including plots of overall, bearing, and
pier hysteretic response in the x- and y-direction (at quadrant Q1). The characteristics of
specimen response to the different ground motion histories is similar to the Configuration
4 tests (see Section 3.7 above), with variations in ground motion frequency content and
directionality strongly influencing specimen behavior. For braced specimen tests,
substructure pier response is again nearly linear and notably stiffer than the unbraced
113
condition (compare Figure D-74 (e) and (f) to Figure D-76 (e) and (f)). For the unbraced
specimen, this configuration has larger pier stiffness in the x-direction compared to the y-
direction. This property can be readily observed from the response figures (see, for
example, Figure D-76 (e) and (f) and Section 3.1.4 and 3.1.5). Substructure stiffness
characterizations for these configurations are presented in Section 3.13 below. Foremost,
these results indicate that the effect of increasing substructure flexibility is an increase in
both global and substructure peak displacements. It appears, however, that bearing
displacement response may be somewhat larger, smaller, or relatively unaffected by this
variation (compare for example Figure D-74 to D-76). Further, FP bearing type 3 slider
composite is shown to have a lower friction value than the type 4 PTFE composite (see
Section 3.14 below), resulting in larger global and bearing displacement response when
these sliders are installed (compare Figure D-82 to D-84 (a) and (b)). Finally, it is noted
that bi-directional substructure stiffness is uncoupled in this specimen design. The effect
of this unequal x- and y-direction substructure stiffness (most notably in the unbraced
Configuration 5 specimen) is to skew the systems’ bi-directional yield surface by
producing unequal yield displacements in these directions. This effects the character of
global system hysteretic coupling, which can be seen by comparing Configuration 4 and
Configuration 5 hysteretic response for the same input motion (compare Figures D-72 and
D-86 (a) and (b)).
For uni-directional scaled motion tests in Figure D-93 through D-98, x-direction
displacement and force histories are presented in lieu of orbits, y-direction bearing
hysteresis at quadrant Q1 is omitted, and the plots showing local global, bearing, and pier
response distribution are omitted. The results of these tests are similar to the scaled motion
114
tests of Configuration 1 (see Section 3.4), with the table motions at larger length scale
factors (i.e., lr) producing specimen response of larger magnitude and longer period
content (compare Figure D-94 and D-97). This difference in behavior is similar to before,
as the isolated specimen will experience larger spectral response for the same motion at a
larger length scale (as seen in Figure 3-11).
3.9 Experimental Results for Configuration 6 (Elevated Single-span with Eccen-tric Stiffness)
Table C-6 in Appendix C presents a complete log of shake-table tests performed on the
Configuration 6 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-99 through D-122. For each of the selected
tests, four summary figures are presented. The first figure presents the global
displacement and force orbits and x- and y-direction bearing hysteresis (for quadrant Q1).
The second and third figures present summaries of local substructure response including
plots of overall, bearing, and pier hysteretic response in the x- and y-direction at quadrant
Q1 and Q4, respectively. The fourth figure presents a summary of torsional response
including: a comparison of hysteretic response and displacement time-histories for the
East and West ends of the bridge specimen (in the direction of motion input, orthogonal to
the direction of stiffness eccentricity), and a time-history of global deck rotation.
The Configuration 6 specimen was tested utilizing the three earthquake table motions.
Tests were performed at two or more amplitudes (or span settings) and bi-directional
motion pairs were run simultaneously and as separate x- & y-direction inputs. The
NF01_02 motion was run with and without its vertical signal. Tests were performed
utilizing FP bearings in two configurations. The first slider configuration utilized type 3
115
composite on all four bearings. The second slider configuration utilized type 4 and 3
composite on the East (unbraced) and West (braced) end of the bridge, respectively, in an
effort to counteract the torsional effects of the substructure stiffness eccentricity. Selected
results are presented only for bi-directional tests run at their maximum amplitude.
The torsional response induced by the specimen’s substructure stiffness eccentricity is
apparent from these test results, with global x-direction displacement (orthogonal to
stiffness eccentricity) larger on the unbraced East end relative to the braced West end (see
Figure D-102, D-106, D-110, D-114, D-118, and D-122). On the other hand, global
displacements in the y-direction are similar on the East and West end of the specimen with
displacement compatibility enforced by the longitudinally rigid deck frame (compare, for
example, plot (b) of Figure D-100 vs. D-101 and Figure D-116 vs. D-117). Bearing
displacements in the x-direction are not, however, systematically larger or smaller on the
unbraced end compared to the braced end of the specimen. This implies that shear
response is similar on either end of the specimen span. Torsional response is then mainly
due to kinematic rotation of the substructure about a vertical axis caused by the difference
in displacement between the flexible unbraced piers on the East end relative to the braced
West end piers. Bearing displacements in the y-direction, however, are always larger on
the braced West end of the specimen due to redistribution enforced by displacement
compatibility imposed by the longitudinally rigid deck frame (compare, for example, plots
(c) and (d) of Figure D-100 vs. D-101 and Figure D-116 vs. D-117).
It is also evident from these results that the alternate slider configuration, with lower
friction FP type 3 PTFE sliders installed on the braced end of the specimen and higher
116
friction type 4 sliders installed on the unbraced end, has a tendency to reduce rotational
response due to the underlying substructure stiffness eccentricity. This is illustrated by
comparing torsional response to the same input motion for the system utilizing the
uniform slider configuration and this alternate un-symmetric slider configuration
(compare Figure D-102 vs. D-106, Figure D-110 vs. D-114, and Figure D-118 vs. D-122).
3.10 Experimental Results for Configuration 7 (Elevated Double-span)
Table C-7 in Appendix C presents a complete log of shake-table tests performed on the
Configuration 7 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-123 through D-158. For each of the selected
tests, three summary figures are presented. The first figure presents the global
displacement and force orbits and x- & y-direction bearing hysteresis (for quadrant Q1).
The second and third figures present summaries of local substructure response including
plots of overall, bearing, and pier hysteretic response in the x- & y-direction at quadrant
Q1 and Pier 5, respectively.
The Configuration 7 specimen was tested utilizing the three earthquake table motions.
Tests were performed at two or more amplitudes (or span settings) and bi-directional
motion pairs were run simultaneously and as separate x- & y-direction inputs. The
NF01_02 motion was run with and without its vertical signal. Tests were performed
utilizing FP bearings in four configurations. The first two utilized type 4 and 5 PTFE
composite sliders, respectively, uniformly on all four bearings. The third system utilized
type 4 composite sliders on the East and West braced ends of the span and type 5
composite sliders on the flexible central piers (i.e., Piers 5 and 6) in an effort to reduce
117
shear transfer to these components. The final system utilized type 5 composite sliders on
the East and West braced ends and type 4 composite sliders on the central piers (Piers 5
and 6) in an effort to balance shear forces across all bent lines. Selected results are
presented only for bi-directional tests run at their maximum amplitude.
The effect of ground motion characteristics on specimen response in these tests is similar
to the Configuration 1, 4 and 5 test sequences. As discussed previously, input frequency
content and directionality playing a significant role in determining system dynamic
behavior. See previous discussions in Section 3.4 and 3.7.
The Configuration 7 specimen represents a simple two-span bridge overcrossing, with
relatively rigid end abutments and a flexible central pier bent. It is notable from these
results that this specimen exhibits similar global response as the Configuration 1 and
braced Configuration 5 test specimens when subjected to the same input motion (compare,
for example, Figure D-3, D-73, and D-132 for the LA13_14 input motion). This behavior
would be expected, as each of these configurations has a similar relationship of total mass
to global force-deformation behavior, with Configuration 7 having only the added
complexity of a flexible central pier bent modifying the hysteretic behavior of this
component.
The typical pattern of displacement and force distribution behavior in this specimen can
be seen by comparing hysteretic behavior at the end abutment location (i.e., Q1) to
response at the central pier bent (i.e., Q5) (see for example Figure D-124 and D-125 for
the LA13_14 input motion). The tendency is for bearings at the braced end of the
specimen to contribute nearly all of the total displacement demand at these locations.
118
Larger shear demand is also attracted to the braced abutment ends. The central pier
locations experience similar total displacement demands as end bents, due to displacement
compatibility enforced by the in-plane flexural rigidity of the deck frame. However, the
flexible piers at these locations provide a significant contribution to the total displacement
demand with bearings contributing the remainder. However, kinematic shortening of these
central pier assemblies (which occurs through rigid body rotation of these elements as the
tip of the pier is displaced) effects loss of axial force at these locations. This phenomenon
results in loss of FP bearing stiffness whose friction and pendulum stiffness components
are axial load dependant. This results in a reduction in shear force transmission at these
locations. This behavior is evident by noting the hysteretic pinching which occurs in
bearing response at these locations (see, for example, Figure D-125 and D-128 (c) and
(d)). The implications of this kinematic effect are discussed in further detail subsequently
in Chapter 4.
Bearing characterization tests show that the type 4 and 5 slider composites exhibited
similar friction values during these tests (see Section 3.14). Consequently, it is evident that
due to this similarity the effect of different slider configurations on system response
characteristics was minimal during these test sequences (compare, for example, Figure D-
123, D-126, D-129, and D-132).
3.11 Experimental Results for Configuration 8 (Elevated Double-span with Eccen-tric Stiffness)
Table C-8 in Appendix C presents a complete log of shake-table tests performed on the
Configuration 8 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-159 through D-173. For each of the selected
119
tests, five summary figures are presented. The first figure presents the global displacement
and force orbits and x- & y-direction bearing hysteresis (for quadrant Q1). The second,
third and fourth figures present summaries of local substructure response including plots
of overall, bearing, and pier hysteretic response in the x- & y-direction at quadrant Q1,
Pier 5, and quadrant Q4, respectively. The fifth figure presents a summary of torsional
response including: a comparison of hysteretic response and displacement time-histories
for the East and West ends of the bridge specimen (in the direction of motion input,
orthogonal to the direction of stiffness eccentricity), and a time-history of global deck
rotation.
The Configuration 8 specimen was tested utilizing the three earthquake table motions.
Tests were performed at two or more amplitudes (or span settings) and bi-directional
motion pairs were run simultaneously and as separate x- & y-direction inputs. The
NF01_02 motion was run with and without its vertical signal. Tests were performed
utilizing FP bearings with type 5 composite. Selected results are presented only for bi-
directional tests run at their maximum amplitude.
The pattern of torsional response induced by the specimen’s substructure stiffness
eccentricity is similar to the Configuration 6 test sequences. Global x-direction
displacement (orthogonal to stiffness eccentricity) increases along the span moving from
the braced West end to the unbraced central piers to the unbraced East end (see, for
example, Figure D-160, D-161, D-162 and D-163 for the LA13_14 input motion). As
before, global displacements in the y-direction are similar on the East and West end of the
specimen with displacement compatibility enforced by the longitudinally rigid deck
120
frame. Bearing displacements in the x-direction are similar implying similar shear
response along the specimen span. Torsional response is then mainly due to kinematic
rotation of the substructure about a vertical axis caused by the difference in displacement
between the piers along the span. Bearing displacements in the y-direction, however, are
always larger on the braced end of the specimen due to pier stiffness at this location and
displacement compatibility imposed by the longitudinally rigid deck frame.
3.12 Experimental Results for Configuration 9 (Elevated Double-span with Yield-ing Piers 5 and 6)
Table C-9 in Appendix C presents a complete log of shake-table tests performed on the
Configuration 9 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-174 through D-184. For each of the selected
tests, three summary figures are presented. The first figure presents the global
displacement and force orbits and x- & y-direction bearing hysteresis (for quadrant Q1).
The second and third figures present summaries of local substructure response including
plots of overall, bearing, and pier hysteretic response in the x- & y-direction at quadrant
Q1 and Pier 5, respectively.
The Configuration 9 specimen was tested utilizing the three earthquake table motions.
Tests were performed at two or more amplitudes (or span settings) and bi-directional
motion pairs were run simultaneously and as separate x- & y-direction inputs. The
NF01_02 motion was run with and without its vertical signal. Tests were performed
utilizing FP bearings. Type 5 PTFE composite sliders were utilized on the East and West
braced ends of the specimen while type 4 sliders were utilized on the central piers (i.e.,
Piers 5 and 6). The vertical load was also balanced such that approximately 5/8ths was
121
supported by Piers 5 and 6 (consistent with the loading of a continuous girder span) in an
effort to attract shear forces to this location.
The Configuration 9 specimen configuration is essentially identical to Configuration 7,
with the addition of weaker A36 leaf springs installed in the central piers. Several test
sequences run at increasing span settings were performed on this specimen with limited
yielding occurring in central piers (see, for example, pier hysteresis in Figure D-179 (e)
and (f)) Consequently, pier bracing at the end abutments was removed in an effort to
balance shear behavior across the specimen increasing demands at the yielding central
piers. In this unbraced configuration, span settings were again increased to maximize
ductility demand at the central piers (see pier hysteresis in Figure D-181 and D-184 (e)
and (f)). Peak ductility demand of approximately 1.5-2 were achieved in the final tests
sequence with no apparent reduction in the isolated performance of the system (see Figure
D-182, D-183, and D-184).
3.13 Experimental Results for Configuration 10 (Substructure Static Pullback Tests)
Table C-10 in Appendix C presents a complete log of static pull-back tests performed on
Configuration 10 of the isolated bridge specimen. Selected experimental results from
these tests are presented in Appendix D as Figure D-185. Braced frame stiffness
characterization was computed from dynamic test data (see, for example, Figure D-178 (e)
and (f)). Table 3-7 below tabulates substructure pier assembly properties computed from
these test results.
122
Substructure properties in Table 3-7 determined from these characterization tests can be
compared to the previous computed design values shown in Table 3-2. As seen, a number
of discrepancies between the design and test values are apparent. First of all, stiffness
values are generally lower than computed design values. Actual braced pier stiffness is
slightly less than computed (i.e., 26.7 kips/inch computed vs. 22-24 kips/inch tested). This
reduction is apparently due to friction slip of bolted end connections. In addition, actual
stiffnesses of short and long plate pier assemblies are lower than computed (i.e., 4 kips/
inch computed vs. 2.4-3 kips/inch tested for the short plate assembly and 1.8 kips/inch
computed vs. 1.6-1.7 kips/inch tested for the long plate assembly). These stiffness
reductions are likely due to gapping in the mechanical assemblies which occurred at
movements near the displacement origin. Further, assumed slider elevations were slightly
lower than as-built elevations in design computations. This led to a higher computation of
effective lateral stiffness in design due to the displacement transformation at the lower
assumed slider height. Finally, it is seen that strength values for short and long plate pier
assemblies were higher than computed (i.e, 2.9 kips design value vs. 4 kips tested value).
This effect was certainly the result of material strength above the assumed nominal value
(i.e., 36 ksi for A36 material).
3.14 Experimental characterization data for FP slider composites
A number of tests were performed during the shake table simulation sequences to evaluate
the friction coefficients of the five FP bearing slider composites provided by the
manufacturer. A log of these bearing characterization tests are shown in Table C-1, C-4,
C-5, and C-7 of Appendix C.
123
The shear response, V(u), of a spherical sliding FP bearing responding uni-directionally
can be represented by the following,
(14)
where µ is the friction coefficient of the slider-dish interface, u the uni-directional
displacement, the velocity, N the normal force (possibly varying in time), and R the
bearing radius [Constantinou et al. 1998]. It has been shown that the friction coefficient of
a PTFE slider moving across a stainless steel surface increases with velocity up to a
threshold value [Constantinou et al. 1990] (see Figure 3-14 below). Bearing
characterization tests were performed by applying test signals to the bridge specimen
which produced essentially harmonic bearing response through a range of velocities (see
Figure 3-13 and Table 3-6). Bearing shear response data from these tests were processed
Table 3-7 Substructure pier assembly properties computed from characterization data
Configuration1 Material Ksub (kips/in) α2 yield point 3
(kips)Fy 4
(kips)Tsub
5(sec)
Braced x- 22 0.27
Braced y- 24 0.26
Short Plate A514 2.4-2.6 0.83-0.80
Long Plate A514 1.6-1.7 0.99-1.02
Short Plate A36 2.4-3 .04-.167 4 4.75-5 0.83-0.74
Long Plate A36 1.6-1.7 .23-.25 4 4.6 0.99-1.02
1. see Section 3.1.4
2. strain hardening ratio, see Figure D-185
3. first point of yield onset, see Figure D-185
4. vertex of bilinear idealization, see Figure D-185
5. based upon tributary mass; see Chapter 2, Equation 3
V u( ) µN u·( )sgn NR----u+=
u·
124
to remove the stiffness contribution (i.e., N/R) and then divided by the time varying
normal force to determine the friction coefficient of each slider composite. Mean friction
coefficient results for each of the slider composite types plotted as a function of velocity
are shown in Figure 3-15. Error bars are included in the plots indicating one standard
deviation statistical scatter.
As seen from these results, friction coefficients ranged from lowest to highest for the type
1, 3, 4, 5, and 2 slider composites, respectively. These composite types (in their virgin
condition) exhibited peak average friction coefficient values of approximately 0.05,
0.0575, 0.08, 0.095, and 0.103, respectively. The type 1 slider composite exhibited a
significant increase in friction coefficient after 57 test signals (see Figure 3-15(a)). The
type 4 slider composite exhibited a similar increase in friction response, after 231 tests
were performed (see Figure 3-15(d)). Slider composite type 5, on the other hand, exhibited
a slight reduction in average friction response after 48 tests (see Figure 3-15(e)).
Figure 3-15(f) illustrates the hysteretic friction response of bearings using the type 5 slider
composite subjected to the LS17c table motion time-history. It is apparent from this figure
that higher friction response (approaching 13 percent) is exhibited in the initial
displacement cycle of the bearing. This behavior may indicate an initial “stick”
phenomenon in the slider interface not noted in the previous characterization tests which
were not processed to near zero velocity. As seen in the remaining response, however,
friction of near 10 percent is exhibited during peak displacement cycles. This is consistent
with the bearing characterization data (see Figure 3-15(e) for values of the peak average
friction coefficient plus one standard deviation). As displacement cycles subside in the
125
remaining hysteretic response, friction approaches 8%, consistent with the lower velocity
response for this composite (see Figure 3-15(e)). This is consistent with reported behavior
due to rate effects (see Figure 3-14) [Constantinou et al. 1990].
Figure 3-14 PTFE slider composite behavior as a function of velocity
velocity
fric
tion
coef
ficie
nt
126
a. Type 1 b. Type 2
c. Type 3 d. Type 4
e. Type 5 f. Type 5 friction hysteresis: LS17c
Figure 3-15 Characterization of FP bearing slider composites
0 1 2 3 40.03
0.04
0.05
0.06
0.07
0.08
0.09
velocity (in/sec)
fric
tion
coef
ficie
nt
virgin
after 57 tests
0 1 2 30.06
0.07
0.08
0.09
0.1
0.11
0.12
velocity (in/sec)
fric
tion
coef
ficie
nt
virgin
0 1 2 3 40.045
0.05
0.055
0.06
0.065
0.07
velocity (in/sec)
fric
tion
co
effic
ien
t
virgin
0 1 2 3 40.04
0.06
0.08
0.1
0.12
velocity (in/sec)
fric
tion
coef
ficie
nt
virgin
after 231tests
0 1 2 3 4 5
0.08
0.09
0.1
0.11
velocity (in/sec)
fric
tion
coef
ficie
nt
virgin
after 48tests
−3−2.5−2−1.5−1−0.5 0 0.5 1 1.5 2 2.5 3−0.15
−0.1
−0.05
0
0.05
0.1
0.15
displacement (in)
fric
tion
co
effic
ien
t
67
3 Testing of a Bridge Deck Model
3.1 Introduction
The experimental studies in this research were developed to satisfy the program objectives
outlined in Section 1.3.1. Specifically, these studies fulfill program Task 6 in Section
1.3.2, to construct a scale model of a bridge with flexible piers for earthquake testing.
These tests utilized the newly upgraded 3-dimensional capabilities of the earthquake
simulator at the Pacific Earthquake Engineering Research (PEER) center and provided a
first-time opportunity to study the bi-directional and 3-dimensional response of isolated
bridge systems.
The preliminary analytical evaluations of Chapter 2 illustrate the basic sensitivity of the
response of isolated bridge overcrossings to various structural and isolator characteristics.
Based on these evaluations. the specimen tested were developed to confirm these
sensitivities, including the effect of mass and stiffness eccentricity, pier flexibility, pier
mass and strength, and varying isolator properties, on system response.
These simulation tests also subjected various isolated bridge overcrossing configurations
to multiple signals of one to three components of earthquake ground motion. These
earthquake signals were representative of significant far-field, near-fault, and soft-soil
seismic events. In this respect, these studies provide invaluable proof-of-concept
68
verification for the effectiveness and robustness of seismic isolation for simple bridge
types.
3.1.1 Similitude Requirements
Similitude requirements for dynamic structural models have been developed in previous
studies [e.g., Krawinkler, Moncarz, 1982]. These similitude constraints are defined by the
chosen length scale factor, 1r, prescribed for relating model size to the subject prototype
(full-scale) structure (i.e., lr = lm/lp, where lm and lp are the model and prototype length
scale, respectively). With gravity a constant and masses reduced proportionally by the
length factor, ground motion accelerations are held constant in dynamic testing to preserve
force scaling (where F = ma). Similitude requires that prototype and model periods be
related by the square root of the length scale factor (i.e., the time scale factor, tr = 1r1/2),
with frequencies related by its inverse (i.e, the frequency scale factor, ωr = lr-1/2). Ground
motion acceleration time-history records must then be “compressed” by multiplying their
time increment by the time scale factor to preserve similitude. This produces time-history
records for shake table simulations of equal acceleration output (as the original recorded
motion), but of higher frequency. With these constraints applied specimen simulations are
performed, with model and prototype system displacements (i.e., dm and dp, respectively)
related directly by the length scale factor (i.e., the displacement scale factor, dr = dm/dp =
1r) [Krawinkler, Moncarz, 1982].
In Chapter 2, isolated bridge behavior was shown in several cases to vary with system
properties corresponding to “short” and “long” spectral period ranges. The typical
response of these systems was shown in several cases to have unique characteristics in
69
each of these period ranges. To model this behavior experimentally, similitude requires
that the model period, Tm, be related to the prototype system period, Tp, by the time factor
(i.e., tr = 1r1/2) such that
(12)
With this requirement, model stiffnesses (Km) can be selected to produce required model
periods (i.e., Tm), given a model mass (Mm), through the definition of system period as
(13)
A length scale factor of 1/4 (i.e., lr = 1/4) was chosen for model scaling for these studies.
This ratio was selected based upon the load and geometric constraints of the earthquake
simulator which were reached for bridge model weight and length quantities represented
by a typical single-span bridge overcrossing reduced to this size. Ground motion scaling
was performed separately, with length scale factors chosen between 1/2 to 1/5 (i.e., lr
between 1/2 and 1/5) and related time scale factors between and (i.e., tr = 1/ and
1/ , see Equation 12), to produce ground motion simulation records of peak velocity and
displacement within the capacity of the shake table simulator (see Section 3.2 below).
The resulting relationships between model and prototype response produced by tests using
these separate model and ground motion scaling factors may be deduced by applying the
previous similitude relations. For example, for a given model with length scale factor of
trTmTp------- lr
1 2⁄==
Km 4π2MmTm--------=
2 5 2
5
70
lrm, a full-scale prototype system with a period of Tp = Tmlrm-1/2 is represented (see
Equation 12). Applying a different length scale factor of lrg to the ground motion implies
that this same model represents a prototype system with a period of Tp’ = Tmlrg-1/2
subjected to this scaled ground motion record (Equation 12). Combining these provides
Tp’ = Tp(lrm/lrg)1/2. Thus if the ground motion scale is smaller than the model scale (e.g.,
lrg = 1/5 and lrm= 1/4), testing with this ground motion represents the response of a
prototype system with a period, Tp’, larger than the full scale target prototype, Tp. On the
other hand, if the ground motion scale is larger than the model scale (e.g., lrg = 1/2 and
lrm= 1/4), the testing represents the response of a prototype system with a period, Tp’,
smaller than the full scale target prototype, Tp. In this way, the model (with fixed scale,
e.g., lrm = 1/4) may represent systems in different spectral regions of the ground motion
record by varying the chosen scale factor (i.e., lrg) applied to the motion in the given test
sequence. In either case, displacements to the full-scale motion are related to model
displacements in the test sequence by the ground motion scale factor, lrg, as before.
3.1.2 Design criteria
In order to illustrate the effect of basic system variations on the response of the isolated
bridge specimen, component properties were established to accommodate the same
substructure and isolation system variations as those evaluated in Chapter 2. These
properties were established to model systems over the broad spectral range where
preliminary analyses indicated significant variations in response.
71
Bridge size and mass were chosen to produce the largest similitude length scale within the
limits of the shake table physical geometry and vertical load capacity. This implied a ¼-
scale model (i.e., length scale factor, lr = 1/4) with maximum span of 20 feet and a
corresponding bridge deck mass of 65 kips.
Target isolation system properties were determined for the given bridge deck mass. It was
established that model isolation bearings with characteristic periods of Tiso = 1.3 to 1.75
seconds were desired (see Equation 2). These would represent full-scale (prototype)
isolated systems with a rigid-based isolation periods ranging from Tiso = 2.6 to 3.5 seconds
at lr = 1/4. Isolator strengths were selected to be in the typical range of Cyiso = 0.04 to 0.12
(see Equation 1). Several bearing types were to be represented to provide hysteretic
properties covering these ranges, including Lead-rubber (LR), High-damping rubber
(HDR), and Friction Pendulum (FP) bearing types.
Test specimen non-isolated periods of approximately Tsub = 0.025 to 1 seconds were
desired (see Equation 3). These represent prototype (full-scale) non-isolated bridges with
periods ranging from Tsub = 0.05 to 2 seconds at a length scale factor of lr = 1/4 which
covers the range of substructure systems evaluated in Chapter 2. The flexibility of
specimen substructure components was established to target substructure stiffness (Ksub)
to isolator second-slope stiffness (kd) ratios in the range of 2:1 to 7:1. As the AASHTO
Guide Spec presumes some measure of substructure yielding to occur (see Section 2.2), it
was also considered important to study its effect on the response of isolated bridge
systems. Therefore, weaker specimen substructure components designed to yield near
peak response were desired as part of the test specimen arrangement.
72
A versatile specimen which could accommodate these variations in pier flexibility and
isolation bearing properties was required for these studies. In addition, the model had to
accommodate varying pier mass and strength and eccentric arrangements of superstructure
mass and substructure stiffness. The design also needed to be easily alterable during
testing to accommodate these system changes efficiently.
3.1.3 Design Development
In keeping with these requirements, a ¼-scale bridge specimen design was developed with
preliminary consideration given to several alternate systems. Steel columns were
preferred because of the desire to perform many tests on the specimen without damage to
the total substructure. A simple design utilizing standard pipe column sections with
optional cross bracing (added for rigid or eccentric configurations) was first considered.
Standard pipe material (i.e., nominal yield strength, Fy = 46 ksi) proved inadequate to
resist combined effects of axial and flexural loads at pipe lengths required to achieve
target substructure flexibility. A variety of other ideas were then considered, including an
alternative utilizing steel wide-flange, L-frames mounted on 3-dimensional clevis base
pins. For this alternative, prestressed coil spring assemblies were designed to provide
variable rotational base flexibility. These assemblies allowed variations in the lateral
frame stiffness to be achieved by replacing springs of pre-engineered stiffness in the base
connection assembly. Connection detailing, necessary to ensure smooth movement of the
assemblies through the anticipated displacement ranges, proved complicated, however,
causing this alternative to be abandoned in lieu of the simpler final specimen design. Final
specimen design was taken as a combination of these two alternatives, as described in the
next section.
73
3.1.4 Final Specimen Design
Complete construction plans of the test specimen, including as-built photographs, are
included in Appendix A for reference. The final specimen substructure design utilized
steel tube frames mounted on clevis base pins. The clevis pin mounts rotate about two-
orthogonal axes and provide adequate transverse and longitudinal rotation capacity at the
base (with restraint about the vertical axis). Rotational stiffness was provided by thin
tapered plates extending in each orthogonal direction from the base of the steel tube
frames. The wide end of these plates attach to the tube frames near the clevis pins while
their narrow tapered ends attach to a shear pin connection which provides vertical support
only. Tube columns support load cells and isolation bearings, which in turn support a rigid
steel deck frame spanning between pier assemblies. The tube column frames support
vertical gravity load (imposed by the 65 kips of concrete blocks mounted on the bridge
deck frame as mass) and provide lateral stiffness supporting shear loads transmitted from
the bridge deck through the isolation bearings during seismic excitation.
Two tapered plate designs were prepared for the elevated bridge specimen. These two
designs allowed substructure lateral stiffness to be altered by changing the rotational
flexibility at the base of the piers (see Appendix A). Short and long tapered plates
provided the specimen with non-isolated periods of approximately Tsub = 0.67 and 1
seconds, respectively, Adding cross-bracing between the columns provided the specimen
with a non-isolated period of approximately Tsub = 0.25 seconds. Two sets of each size
tapered plates were fabricated from A514 and A36 steel, respectively. The stronger A514
material provided essentially elastic stress levels, while the weaker A36 material allowed
moderately ductile substructure behavior, during the test sequences.
74
Three separate sets of test bearings were designed and fabricated for use in the bridge deck
model tests: 1) high-damping rubber (HDR) bearings supplied by Bridgestone, Inc.; 2)
lead-rubber (LR) bearings supplied by DIS, Inc.; and 3) spherical sliding, or Friction-
pendulum (FP) bearings supplied by Earthquake Protection Systems, Incorporated.
Design details of each are included in Appendix A for reference.
The basic force diplacement properties of these three bearing types (see Figure 3.1) were
intentionally selected to be different in order to cover the ranges of isolation bearing
properties normally seen in practice and to examine behavior in different ranges of
behavior identified in the preliminary evaluations (see Chapter 2). One should not use
these tests to compare the effectiveness of different isolator types, as different designs
could also have resulted in isolators with very similar hysteretic properties. Results from
these tests should be used only for calibration of models, validation of identified trends
and behavior concepts (i.e., how system behavior is effected by changes in the
fundamental hysteretic properties Qd, ku and kd), and the efficacy of isolation in general.
Bearing hysteretic properties established from characterization test data are presented in
Table 3-1 as a reference. Figure 3-1 shows a uni-directional plot comparing the hysteretic
response of the HDR, LR, and FP test bearings illustrating the hysteretic differences in
strength and first- and second-slope stiffness characteristics of these bearing designs.
Characteristic target (rigid-based) isolation periods (i.e., Tiso, see Equation 2) are also
shown in Table 3-1 for each bearing type.
As illustrated in the plans (see Appendix A), this final specimen design is quite versatile.
Lateral substructure stiffness can be distributed uniformly at each span or
75
unsymmetrically (with increasing flexibility along the bridge length) to model bridges
spanning grade changes. Substructure flexibility can also be varied in the longitudinal and
transverse directions to model the cantilever versus frame behavior of a multi-column
bent. For two-span (six-pier) configurations, end piers can be braced longitudinally and
transversely and the central piers left relatively flexible to model bridge overcrossings.
Table 3-1 Summary of bearing mechanical properties from characterization tests
Bearing Type Qd (/W) ku(kips/in) kd (kips/in) Tiso4 (sec)
HDR1 0.015-0.05 4.5-3.5 1.75-1 1.29
LR2 0.05-0.09 15-5 1.6-0.9 1.36
FP3 µ = 0.07 - 0.10 INF R = 30 in.W/R= 0.54 kip/in 1.75
1. Property range over 50-250% shear strain with Tiso at γ = 250%2. Property range over 50-200% shear strain with Tiso at γ = 200%3. FP hysteretic properties based on friction coefficient, µ, and dish radius, R4. Tiso computed for a deck weight of 65 kips applied uniformly to four bearings
Figure 3-1 Comparison of test bearing hysteretic properties
0
0.05
0.1
0.15
0.2
0.25
0 0.5 1 1.5 2
d (in)
F/W
HDRLRFP
76
A column detail also allows additional substructure mass of up to 1.5 kips to be installed
near the 2/3rd height of each column frame. This represents substructure mass proportions
of up to γ = Σ mpier/Mdeck = 10 percent.
For some configurations, the isolators are mounted directly on the shake table. Separate
transition hardware allows FP, LR and HDR isolation bearings to be installed. Bridge deck
mass can also be arranged symmetrically or eccentrically. The mechanical properties of
the bridge specimen substructure are presented in Table 3-2.
Table 3-2 Summary of computed specimen substructure design properties
Frame Configuration
Braced1 Short Plate2 Long Plate3
Tsub 0.25 sec 0.67 sec 1.0 secKsub 26.6 kips/in 4 kips/in 1.8 kips/in
Fy N.A. 8 kips (A514)2.9 kips (A36)
8 kips (A514)2.9 kips (A36)
Cy = Fy/W N.A. 0.5 (A514)0.18 (A36)
0.5 (A514)0.18 (A36)
dy N.A. 1.9 in (A514)0.68 in (A36)
4.0 in (A514)1.44 in (A36)
Ksub/kd (LR) 27:1 4:1 2:1Ksub/kd (FP) 47:1 7:1 3:1
1. Braced pier assembly- see Figure A-1, A-2, & A-7 details, Appendix A2. Pier assembly with short plate - see Figure A-1, A-2, & A-10, Appendix A3. Pier assembly with long plate - see Figure A-1, A-2, & A-10, Appendix ATsub - see Chapter 2, Equation 3Ksub - lateral stiffness at top of pier assemblyFy, Cy - yield strength and yield strength coefficient of pier assemblydy - yield displacement at top of pier assemblyKsub/kd - substructure stiffness to isolator second-slope stiffness ratio
77
3.1.5 Test Set-Up and Protocol
Utilizing the bridge specimen substructure components and isolation test bearings
provided, ten bridge configurations were developed to study various aspects of the
response of isolated bridge overcrossings through earthquake simulation studies. This test
program was developed to examine the global and local response trends of simple and
more complex isolated bridge systems subjected to a variety of earthquake input,
fullfilling objective 2 and 3 of the research program (as outlined in Section 1.3.1). Specific
issues to be examined in the study were outlined in project Task 6 (see Section 1.3.2) and
discussed further in the preliminary evaluations of Chapter 2. These issues include the
effect on isolated bridge response of: (1) the characteristics of the earthquake input
(including fault proximity, site soil effects, and the effect of uni-directional vs. multi-
directional input); (2) isolation system characteristics; (3) substructure flexibility; (4)
substructure mass; (5) higher modes; (6) system eccentricity; and (7) substructure
yielding. The ten bridge specimen configurations developed for these studies are
described in the sections below and schematically illustrated in Figure 3-2 through 3-6.
Configuration 1
This configuration was the standard non-elevated symmetric mass configuration of the
bridge deck model (see Figure 3-2). Table motion in this case represents motion at “rigid”
abutments. In this configuration, load cells were mounted directly on the earthquake
simulator. Isolation bearings were mounted to the top of load cells and connected to the
underside of the steel bridge deck. Concrete blocks were prestressed to the deck frame,
providing 65 kips of weight. Instrumentation for this configuration included: (1) table
78
instrumentation measuring table accelerations and displacements; (2) five degree-of-
freedom load cells measuring x- & y- shear and moment, as well as axial forces, under
each isolation bearing (at quadrant Q1, Q2, Q3 and Q4); (3) linear potentiometers (LP)
measuring bearing, deck, and table displacements; (4) DCDT’s measuring potential
shifting of the concrete mass blocks ; and (5) accelerometers mounted to the bridge deck,
concrete mass, and locally above isolation bearings. Data acquisition in this configuration
is illustrated in Figure 3-7 and detailed descriptions of each instrumentation device are
outlined in Table 3-3.
Configuration 1 was developed to study the response of simple isolated bridge
overcrossings. Variations in isolator characteristic properties (i.e., first- and second- slope
stiffness and strength) were examined in this configuration by replacing bearing types.
The effect of earthquake motion characteristics, including bi-directional and vertical input,
fault-proximity and soil effects, were studied in this and all model configurations. The
effect of idealized near-fault pulse motions were studied solely in this basic configuration
(see Section 3.2 for information regarding earthquake test motions).
Configuration 2
This configuration was similar to Configuration 1, but incorporated an eccentric mass
layout for the bridge deck (see Figure 3-2). This configuration was erected similar to
Configuration 1 with concrete blocks offset to produce superstructure mass eccentricities.
Instrumentation for this configuration was the same as that for Configuration 1 (see Figure
3-7 and Table 3-3).
79
Configuration 2 was developed to study the torsional response of simple isolated bridge
overcrossings. Deck mass was systematically offset to produce superstructure mass
eccentricities of 5 and 10 percent of the longitudinal bridge span. Torsional response of
different isolation systems were also examined in this configuration by replacing bearing
types.
Configuration 3
This configuration was again similar to Configuration 1, but incorporated an unsymmetric
distribution of isolation bearings (see Figure 3-3). This configuration was erected similar
to Configuration 1 with two different isolation bearing types (HDR and LR bearings)
mounted at either end of the bridge span. Instrumentation for this configuration was the
same as that for Configuration 1 (see Figure 3-7 and Table 3-3).
Configuration 3 was developed to study the torsional response of isolated bridge
overcrossings produced by bearing stiffness eccentricity. The installation of HDR and LR
bearings at either end of the deck produced eccentricity in first- and second- slope stiffness
and bearing strength properties. This study was not performed to suggest that different
types of isolators could be installed in a bridge at opposite abutments, but to assess the
effect of these types of variations along a bridge span. The effect of earthquake input
characteristics on this stiffness induced torsional response were also studied in this
configuration.
80
Configuration 4
This was the standard four-pier elevated configuration of the bridge deck model, an
elevated single-span configuration with symmetric substructure stiffness (see Figure 3-3).
In this configuration, substructure pier assemblies were mounted directly to the
earthquake simulator with load cells mounted on top of pier supports. FP isolation
bearings were used exclusively in this configuration attached to the top of load cells and
connected to the underside of the steel bridge deck. Concrete blocks were prestressed to
the deck frame, providing 65 kips of weight. In addition to the same instrumentation
utilized for Configuration 1 through 3 (see Figure 3-7 and Table 3-3), the following
instrumentation was added in this configuration: (1) additional linear potentiometers (LP)
measuring top of pier displacements; (2) additional accelerometers mounted to top of
substructure piers; and (3) linear strain gauges mounted on tapered leaf springs at base of
piers to monitor potential yield conditions. Data acquisition hardware in this configuration
is illustrated in Figure 3-7, 3-8, and 3-9. Detailed descriptions of each instrumentation
device are outlined in Table 3-3 and 3-4.
Configuration 4 was developed to study the response of simple isolated bridge
overcrossings and viaducts. Variations in isolator characteristic strength were examined in
this configuration by replacing FP bearing slider types. The effect of variations in
substructure flexibility were examined by adding or removing bracing or using different
rotational leaf springs at the base of the pier assemblies.
81
Configuration 5
This was an elevated bridge configuration with un-symmetric substructure stiffness,
erected similarly to Configuration 4, with short and long leaf springs inserted at the base
of pier assemblies in the x- and y- directions, respectively (see Figure 3-4).
Instrumentation for this configuration was similar to Configuration 4 as illustrated in
Figure 3-7, 3-8, and 3-9 and outlined in Table 3-3 and 3-4.
Configuration 5 was developed to study the response of simple isolated bridge
overcrossings, with the effect of variations in substructure flexibility in the x- and y-
directions. Variations in isolator characteristic strength were examined in this
configuration by replacing FP bearing slider types as before. The effect of substructure
mass (where γ = Σ mpier/Mdeck) was also studied in this configuration by varying the
number of attached lead weight packets mounted to substructure pier assemblies.
Configuration 6
This configuration is similar to Configuration 5 with additional cross-bracing added to
piers at one end of the specimen (see Figure 3-4). Instrumentation for this configuration
was similar to Configuration 4 and 5 as illustrated in Figure 3-7, 3-8, and 3-9 and outlined
in Table 3-3 and 3-4.
Configuration 6 was developed to study the torsional response of simple isolated bridge
overcrossings having unsymetric substructure conditions. Variation of substructure
flexibility along the span produced by added cross-bracing created the effect of
eccentricity in substructure stiffness in the configuration. Variations in isolator
82
characteristic strength could be examined in this configuration by replacing FP bearing
slider types symmetrically (i.e., replacing all slider types at once) or unsymmetrically (i.e.,
placing weaker FP bearing sliders above braced piers to counteract torsional response).
Configuration 7
This was the standard elevated double-span configuration of the bridge deck model (see
Figure 3-5). In this configuration, six substructure pier assemblies were mounted directly
to the earthquake simulator. Cross-bracing was added to piers in the longitude and
transverse directions at each end of the bridge specimen to simulate stiff abutment
conditions. Center piers were configured with short and long leaf springs inserted at their
base in the x- and y- directions, respectively, simulating a flexible central pier bent. Load
cells were mounted on top of pier supports with FP isolation bearings attached to the top
of load cells and connected to the underside of the steel bridge deck. Concrete blocks and
additional lead packets were prestressed to the deck frame providing 99 kips of weight.
This additional mass was installed to provide the system with an overall yield strength
coefficient (i.e., Cyiso) theoretically equivalent to the four pier specimen (assuming a
constant FP slider µ value). In addition, this larger mass produced nearly equivalent period
characteristics for the six-pier configuration with out cross-bracing as the four pier un-
braced configurations. The instrumentation for this configuration was similar to
Configuration 4 through 6, with the following additions: (1) five degree-of-freedom load
cells under each isolation bearing at pier 5 and 6; (2) linear potentiometers (LP) measuring
top of pier 5 and 6 displacements; (3) accelerometers mounted to locally above isolation
bearings and at top of substructure piers at pier 5 and 6; and (4) linear strain gauges
83
mounted on tapered leaf springs at base of pier 5 and 6. Data acquisition hardware is
illustrated in Figure 3-7, 3-8, and 3-9 and outlined in Table 3-3 and 3-4, as before.
Configuration 7 was developed to study the response of simple double-span isolated
bridge overcrossings. Variations in isolator characteristic strength were examined in this
configuration by replacing FP bearing slider types. These strength variations were
implemented symmetrically (i.e., by replacing all sliders at once) or unsymmetrically (by
placing weaker FP sliders selectively above braced piers or central piers to effect force
distribution).
Configuration 8
This configuration was similar to Configuration 7 with cross-bracing added to piers at
only one end of the specimen and long tapered leaf spring plates installed at the base of
piers in the x- direction at the opposite end (see Figure 3-5). Instrumentation for this
configuration was similar to Configuration 7 as illustrated in Figure 3-7, 3-8, and 3-9 and
outlined in Table 3-3 and 3-4.
Configuration 8 was developed to study the torsional response of simple isolated bridge
overcrossings. Increasing substructure transverse flexibility along the span produced
eccentricity in substructure stiffness. The effect of varying isolator characteristic strength
along the span was examined by replacing FP slider types symmetrically (i.e., replacing
all slider types at once) or unsymmetrically (i.e., placing weaker FP bearing sliders above
braced piers to counteract torsional response).
84
Configuration 9
This configuration was similar to Configuration 7 with weaker (A36) tapered leaf spring
plates inserted at the base of central piers (see Figure 3-6). Instrumentation for this
configuration is similar to Configuration 7 as illustrated in Figure 3-7, 3-8, and 3-8 and
outlined in Table 3-3 and 3-4.
Configuration 9 was developed to study the response of simple double-span isolated
bridge overcrossings with yielding substructure components. A36 leaf spring plates in
central piers were designed to allow ductile response in the lateral force-displacement
characteristics of the central pier assemblies.
Configuration 10
This was a free-standing configuration of substructure pier sub-assemblies (see Figure 3-
6). This configuration utilized the same substructure assemblages as Configuration 9 with
bridge mass and deck, isolation bearings, and load cells removed. Instrumentation for this
configuration consisted of: (1) a linear load cell attached in series with a come-along
winch between tops of pier sub-assemblies to produce an increasing static force, and (2)
linear potentiometers (LP) measuring the displacements at the top of the piers (see Figure
3-6). This configuration was developed to characterize the lateral force-deformation
characteristics of the strong and weak substructure pier sub-assemblies (i.e., those
utilizing A514 and A36 tapered leaf spring base plates, respectively). The piers were
characterized in both their stiff (i.e., short plate) and flexible (i.e., long plate)
configurations (see Table 3-2).
85
Specimen as-built documentation
As a reference, photographs of bridge specimen erection sequences, pier frame
assemblies, and component details are included along with construction plans and
fabrication details in Appendix A.
3.2 Earthquake Histories for Testing
An evaluation of the effect of ground motion input characteristics on the response of the
various configurations of the bridge deck specimen was an essential component in these
simulation studies. The features of seismic demand include: (1) fault proximity (i.e., far-
vs. near- field events); (2) directivity (i.e., fault-normal vs. fault-parallel and forward- vs.
backward-azimuth motions); (3) site specific soil conditions (i.e., rock vs. soil sites); (4)
bi-directional effects; and (5) vertical components of motion. A group of shake table
motions was tailored to consider each of these variations explicitly. In addition, sinusoidal
forcing motions were developed to characterize the friction coefficient of the various FP
bearing slider types provided by the manufacturer. The characteristics of these motions are
described in detail below.
Three representative earthquake time-histories were selected for shake table testing. Basis
recorded time-histories were chosen from the database developed in Phase 2 of the
FEMA/SAC project [SAC, 1997]. The bi-directional ground motion pairs LA13/LA14,
NF01/NF02, and LS17c/LS18c, as listed in Table 2-2, were selected from this database to
represent far-field, near-fault, and soft-soil ground motion types, respectively. These basic
motions were filtered and scaled to produce shake table input motions conforming to the
acceleration, velocity, and displacement limits of the shake table apparatus. The resulting
86
Configuration 1: Non-elevated Symmetric Mass
Configuration 2: Non-elevated Eccentric Mass
Figure 3-2 Test Configurations 1 and 2 for bridge deck model
x
y
(4) FP bearingsor(4) LR bearingsor (4) HDR bearings
C.M.
Deck FrameWdeck = 66 kips
x
y
(4) FPS bearings
C.M.
ey
or(4) LR bearings
Deck FrameWdeck = 66 kips
87
Configuration 3: Non-elevated Eccentric Stiffness
Configuration 4: Elevated Single-span with Symmetric Stiffness
Figure 3-3 Test Configurations 3 and 4 for bridge deck model
x
y
(2) HDR bearings
(2) LR bearings
Deck FrameWdeck = 66 kips
C.M.
x
y
(4) FPS bearings
C.M.
Deck frameWdeck = 66 kips
(4) Substructure piersγ=Σmpier/Mdeck = .05, typical
Stiff rotational springs in x & ydirections, typicalat base of piers
Q1Q2
Q3 Q4
~
88
Configuration 5: Elevated Single-span with Un-symmetric Stiffness
Configuration 6: Elevated Single-span with Eccentric Stiffness
Figure 3-4 Test Configurations 5 and 6 for bridge deck model
x
y
(4) FP bearings
C.M.
Deck frameWdeck = 66 kips
(4) Substructure piers
Stiff rotational springs inx-direction, typ.
Flexible rotational springs iny-direction, typ.
Symmetric pier bracing in x & y direction, optional
γ=Σmpier/Mdeck = .05, typ.~ Single Span Elevated Deck Σmpier/Mdeck = 0.10 condition shown~
x
y
(4) FP bearings
C.M.
Deck frameWdeck = 66 kips
(4) Substructure piersγ=Σmpier/Mdeck = .05, typ.
Stiff rotational springs inx-direction, typ.
Flexible rotational springs iny-direction, typ.
Pier bracing added in x & ydirection, as shown
~
89
Configuration 7: Elevated Double-span
Configuration 8: Elevated Double-span with Eccentric Stiffness
Figure 3-5 Test Configurations 7 and 8 for bridge deck model
(6) FP bearings
Deck frameWdeck = 99 kips
(6) Substructure piersγ=Σmpier/Mdeck = .05, typ.
Stiff rotational springs inx-direction, typ.
Flexible rotational springs iny-direction, typ.
Symmetric pier bracing in x & y direction, typicalat end bays as shown
Q1Q2
Q3 Q4
Pier 5Pier 6
x
y
C.M.
~
(6) FP bearings
(6) Substructure piersγ=Σmpier/Mdeck = .05, typ.
Stiff rotational springs at Q3 & Q4
Flexible rotational springs iny-direction, typ.
Symmetric pier bracing in x & y direction at endshown only
Q1Q2
Q3 Q4
Pier 5Pier 6
x
y
C.M.
Flexible rotational springs at Q1 & Q2,x-direction
Deck frameWdeck = 99 kips
and Pier 5 & 6,x-direction
~
90
Configuration 9: Elevated Double-span with Yielding Piers 5 and 6
Configuration 10: Substructure Static Pullback Tests
Figure 3-6 Test Configurations 9 and 10 for bridge deck model
(6) Substructure piersγ=Σmpier/Mdeck = .05, typ.
Stiff rotational springs inx-direction, typ.
Flexible rotational springs iny-direction, typ.
Symmetric pier bracing in x & y direction, typicalat end bays as shown
Q1Q2
Q3 Q4
Pier 5Pier 6
x
y
C.M.
(6) FP bearings
Deck frameWdeck = 99 kips
Yielding rotationalspring plates inx & y-direction atPiers 5 & 6 only
(A514 - 100ksi)
(A514 - 100ksi nom.)
(A36 - 36ksi nom.)
~
Deck frame and bearings(6) Substructure piers
Stiff rotational springs inx-direction, typ.
Flexible rotational springs iny-direction, typ.
Q1Q2
Q3 Q4
56
x
y Yielding rotationalspring plates inx & y-direction atPiers 5 & 6 only(A36 - 36ksi nom.)
(A514 - 100ksi nom.)
(A514 - 100ksi nom.)
Typical pullback rigging:tension cable and straps,load cell, and come-alongin series at top of pier
removed, typical
91
Figure 3-7 Instrumentation plan for Configurations 1 through 3 of non-elevated bridge deck model
Q
◆ ◆ ◆
◆◆ ◆
◆◆
◆
92
Figure 3-8 Supplementary instrumentation for Configurations 4 through 9 of elevated bridge deck model
93
a. Short plate (a.k.a., stiff spring) b. Long plate (a.k.a., flexible spring)
Figure 3-9 Typical strain gauge layout at pier base rotational leaf springs
Table 3-3 Instrumentation for Configurations 1 thru 3 of non-elevated bridge deck
Channel No. Transducer Response
Quantity Orientation Transducer Location
1 LVDT displacement horizontal table h1o stroke2 LVDT displacement horizontal table h2o stroke3 LVDT displacement horizontal table h3o stroke4 LVDT displacement horizontal table h4o stroke5 DCDT displacement vertical table v1o stroke6 DCDT displacement vertical table v2o stroke7 DCDT displacement vertical table v3o stroke8 DCDT displacement vertical table v4o stroke9 A acceleration horizontal table h1-2 acc.10 A acceleration horizontal table h3-4 acc.11 A acceleration horizontal table h4-1 acc.12 A acceleration horizontal table h2-3 acc.13 A acceleration vertical table 1v acc.14 A acceleration vertical table 2v acc.15 A acceleration vertical table 3v acc.16 A acceleration vertical table 4v acc.17 LC force horiz. shear x load cell - bearing Q118 LC force horiz. shear y load cell - bearing Q119 LC force moment y load cell - bearing Q120 LC force moment x load cell - bearing Q121 LC force axial load cell - bearing Q122 LC force horiz. shear x load cell - bearing Q223 LC force horiz. shear y load cell - bearing Q224 LC force moment y load cell - bearing Q225 LC force moment x load cell - bearing Q2
C L
3”
linear strain gauge (SG),top & bottom of plate
Plan View (N.T.S.)
C L
3” 12”
linear strain gauge (SG),top & bottom of plate
SG, top ofplate only
Plan View (N.T.S.)
94
26 LC force axial load cell - bearing Q227 LC force horiz. shear x load cell - bearing Q328 LC force horiz. shear y load cell - bearing Q329 LC force moment y load cell - bearing Q330 LC force moment x load cell - bearing Q331 LC force axial load cell - bearing Q332 LC force horiz. shear x load cell - bearing Q433 LC force horiz. shear y load cell - bearing Q434 LC force moment y load cell - bearing Q435 LC force moment x load cell - bearing Q436 LC force axial load cell - bearing Q437 A acceleration horiz. y mass - acc138 A acceleration horiz. y mass- acc239 A acceleration horiz. x mass - acc340 A acceleration horiz. x mass - acc441 A acceleration horiz. x mass - acc542 A acceleration horiz. y deck frame - acc643 A acceleration horiz. y deck frame - acc744 A acceleration horiz. x deck frame - acc845 A acceleration horiz. x deck frame - acc946 A acceleration horiz. x deck frame - acc1047 A acceleration horiz. x bearing Q1 - acc1148 A acceleration horiz. y bearing Q1 - acc1249 A acceleration vertical bearing Q1 - acc1350 A acceleration horiz. x bearing Q2 - acc1451 A acceleration horiz. y bearing Q2 - acc1552 A acceleration vertical bearing Q2 - acc1653 A acceleration horiz. x bearing Q3 -acc1754 A acceleration horiz. y bearing Q3 - acc1855 A acceleration vertical bearing Q3 - acc1956 A acceleration horiz. x bearing Q4 - acc2057 A acceleration horiz. y bearing Q4 - acc2158 A acceleration vertical bearing Q4 - acc2259 LP displacement horiz. y deck frame - LP160 LP displacement horiz. y deck frame - LP261 LP displacement horiz. x deck frame - LP362 LP displacement horiz. x deck frame - LP463 LP displacement horiz. x deck frame - LP564 LP displacement horiz. y bearing Q1 - LP665 LP displacement horiz. x bearing Q1 - LP766 LP displacement horiz. y bearing Q2 - LP867 LP displacement horiz. x bearing Q2 - LP968 LP displacement horiz. y bearing Q3 - LP10
Table 3-3 Instrumentation for Configurations 1 thru 3 of non-elevated bridge deck
95
69 LP displacement horiz. x bearing Q3 - LP1170 LP displacement horiz. y bearing Q4 - LP1271 LP displacement horiz. x bearing Q4 - LP1372 LP displacement horiz. y table - LP1473 LP displacement horiz. x table - LP1574 LP displacement horiz. x table - LP16
75 DCDT displacement sloped deck frame to mass - DCDT1
76 DCDT displacement sloped deck frame to mass - DCDT2
77 DCDT displacement sloped deck frame to mass - DCDT3
Table 3-4 Instrumentation for Configurations 4 through 10 of elevated bridge deck
Channel No. Transducer Response
Quantity Orientation Transducer Location
1 thru 58 |Same as Configurations 1 through 3 - non-elevated Bridge Deck, see Table 3-3 above
59 A acceleration horizontal Pier Q1 x - acc2360 A acceleration horizontal Pier Q1 y - acc2461 A acceleration horizontal Pier Q2 x - acc2562 A acceleration horizontal Pier Q2 y - acc2663 A acceleration horizontal Pier Q3 x - acc27
Channel 63 converted to uni-axial force readings for Config. 10 pullback tests, as follows63 LC force horizontal Uni-Axial load cell64 A acceleration horizontal Pier Q3 y - acc2865 A acceleration horizontal Pier Q4 x - acc2966 A acceleration horizontal Pier Q4 y - acc30
67 DCDT displacement sloped deck frame to mass - DCDT1
68 DCDT displacement sloped deck frame to mass - DCDT2
69 DCDT displacement sloped deck frame to mass - DCDT3
70 SG linear strain curvature y Pier Q1 - XOP71 SG linear strain horiz. x Pier Q1 - XFT72 SG linear strain horiz. x Pier Q1 - XTH73 SG linear strain curvature x Pier Q1 - YOP74 SG linear strain horiz. y Pier Q1 - YFT
Table 3-3 Instrumentation for Configurations 1 thru 3 of non-elevated bridge deck
96
75 SG linear strain horiz. y Pier Q1 - YTH76 SG linear strain curvature y Pier Q2- XOP77 SG linear strain horiz. x Pier Q2- XFT78 SG linear strain horiz. x Pier Q2 - XTH79 SG linear strain curvature x Pier Q2 - YOP80 SG linear strain horiz. y Pier Q2 - YFT81 SG linear strain horiz. y Pier Q2 - YTH82 SG linear strain curvature y Pier Q3 - XOP83 SG linear strain horiz. x Pier Q3 - XFT84 SG linear strain horiz. x Pier Q3 - XTH85 SG linear strain curvature x Pier Q3 - YOP86 SG linear strain horiz. y Pier Q3 - YFT87 SG linear strain horiz. y Pier Q3 - YTH88 SG linear strain curvature y Pier Q4- XOP89 SG linear strain horiz. x Pier Q4- XFT90 SG linear strain horiz. x Pier Q4 - XTH91 SG linear strain curvature x Pier Q4 - YOP92 SG linear strain horiz. y Pier Q4 - YFT93 SG linear strain horiz. y Pier Q4 - YTH94 SG curvature curvature y Pier 5 - XOP95 SG linear strain horiz. x Pier 5 - XFT96 SG linear strain horiz. x Pier 5 - XTH97 SG curvature curvature x Pier 5 - YOP98 SG linear strain horiz. y Pier 5 - YFT99 SG linear strain horiz. y Pier 5 - YTH100 SG curvature curvature y Pier 6- XOP101 SG linear strain horiz. x Pier 6- XFT102 SG linear strain horiz. x Pier 6 - XTH103 SG curvature curvature x Pier 6 - YOP104 SG linear strain horiz. y Pier 6 - YFT105 SG linear strain horiz. y Pier 6 - YTH106 LC force horiz. shear x load cell - bearing 5107 LC force horiz. shear y load cell - bearing 5108 LC force moment y load cell - bearing 5109 LC force moment x load cell - bearing 5110 LC force axial load cell - bearing 5111 LC force horiz. shear x load cell - bearing 6112 LC force horiz. shear y load cell - bearing 6113 LC force moment y load cell - bearing 6
Table 3-4 Instrumentation for Configurations 4 through 10 of elevated bridge deck
97
114 LC force moment x load cell - bearing 6115 LC force axial load cell - bearing 6
Channels 116 through 128 skipped129 LP displacement horiz. y deck frame - LP1130 LP displacement horiz. y deck frame - LP2131 LP displacement horiz. x deck frame - LP3132 LP displacement horiz. x deck frame - LP4133 LP displacement horiz. x deck frame - LP5134 LP displacement horiz. y bearing Q1 - LP6135 LP displacement horiz. x bearing Q1 - LP7136 LP displacement horiz. y bearing Q2 - LP8137 LP displacement horiz. x bearing Q2 - LP9138 LP displacement horiz. y bearing Q3 - LP10139 LP displacement horiz. x bearing Q3 - LP11140 LP displacement horiz. y bearing Q4 - LP12141 LP displacement horiz. x bearing Q4 - LP13142 LP displacement horiz. y table - LP14143 LP displacement horiz. x table - LP15144 LP displacement horiz. x table - LP16145 LP displacement horiz. x Pier Q1 - LP17146 LP displacement horiz. x Pier Q1 - LP18147 LP displacement horiz. y Pier Q2 - LP19148 LP displacement horiz. x Pier Q2 - LP20149 LP displacement horiz. y Pier Q3 - LP21150 LP displacement horiz. x Pier Q3 - LP22151 LP displacement horiz. y Pier Q4 - LP23152 LP displacement horiz. x Pier Q4 - LP24153 LP displacement horiz. y bearing 5- LP25154 LP displacement horiz. x bearing 5 - LP26155 LP displacement horiz. y bearing 6 - LP27156 LP displacement horiz. x bearing 6 - LP28157 LP displacement horiz. y Pier 5 - LP29158 LP displacement horiz. x Pier 5 - LP30159 LP displacement horiz. y Pier 6 - LP31160 LP displacement horiz. x Pier 6 - LP32
The following Channels were relocated for Pier 5 & 6 acceleration readingsnote: acc6, acc7, acc8, acc10 to Pier 5x, Pier 5y, Pier 6x, Pier6y respectively
42 A acceleration horiz. x Pier 5 - acc31
Table 3-4 Instrumentation for Configurations 4 through 10 of elevated bridge deck
98
table motions produced are referred to as LA13_14, NF01_02, and LS17c_18c and
utilized associated similitude length scale factors of lr = 1/2, 1/5, and 1/5, respectively, to
enforce conformance with table limits. Each table motion consists of a bi-directional pair
of time-histories oriented orthogonally along the x- and y- axes of the shake table (e.g.,
LA13_14 consists of the scaled x-direction LA13 and y-direction LA14 components). The
scaled near-fault motion (i.e., NF01_02) includes its vertical component as well. Motions
could be run separately, as uni-directional (x- or y-direction) components, or as bi-
directional pairs. In the case of the NF01_02 motion, the vertical component could be
added or omitted from the table time-history. Response spectra for the LA13_14,
NF01_02, and LS17c_18c shake table motions are shown in Figure 3-10 for comparison.
In addition, to study the effect of similitude scaling on the bridge specimen (see Section
3.1.1 discussion) these motions were processed with alternate length scale factors. The
effect of varying similitude length scale (lr) on the response spectra of three of these table
motion components is illustrated in Figure 3-11.
Near-fault ground motions have been shown to place significant demand on structures.
The impulsive and sometimes long-period content of these motions may produce velocity
and displacement demands significantly exceeding the design criteria provided by code
specified spectrum compatible ground motions. These unique earthquake time-histories
may be modeled with sufficient accuracy (for structures responding at or near the peak in
43 A acceleration horix. y Pier 5 - acc3244 A acceleration horiz. x Pier 5 - acc3346 A acceleration horix. y Pier 5 - acc34
Table 3-4 Instrumentation for Configurations 4 through 10 of elevated bridge deck
99
the earthquake’s response spectra) as simple pulse motions [Krawinkler and Alavi, 1998].
On this basis, a suite of bi-directional, pure pulse motions were developed for these
studies with pure cosine and sine waves selected to model fault-normal and fault-parallel
displacement histories, respectively. Figure 3-12 illustrates time-histories for these
simulated motion pairs at their peak displacement amplitude of 5 inches (the limit of the
shake table apparatus). Fault-normal pulse durations of Tp = 1 and 2 seconds were selected
providing a range bracketing characteristic periods (i.e., Tiso) of the test bearings (see
Table 3-1). The duration of associated fault-parallel motions were taken as 2/3, 1, and 3/2
of Tp to evaluate the coupling effect between these orthogonal components. Table 3-5
shows amplitude and duration parameters for the entire suite of idealized pulse motions
developed from these parameters. These synthetic motions are representative of suggested
pulse parameters for actual near-fault earthquake records as recommended in [Krawinkler
and Alavi, 1998] at a similitude length scale factor of lr = 1/4.
To estimate friction coefficients for the various Friction Pendulum slider composites
provided by the manufacturer, a suite of sinusoidal acceleration time-histories were also
developed. These motions were designed to impose a steady-state response of varying
displacement and velocity amplitudes on the test specimen. Results from these tests were
utilized to estimate instantaneous friction values for the different composites. Figure 3-13
illustrates a representative acceleration time-history of these sinusoidal motions. Signal
amplitude and frequencies used to develop the various test motions are in Table 3-6.
100
a. Displacement spectra: LA13_14 b. Total acceleration spectra: LA13_14
c. Displacement spectra: NF01_02 d. Total acceleration spectra: NF01_02
e. Displacement spectra: LS17c_18c f. Total acceleration spectra: LS17c_18c
Figure 3-10 Displacement and total acceleration spectra for LA13_14, NF01_02, and LS17c_18c table motions, ζ=5%
0 0.5 1 1.5 20
5
10
15
T (sec)
D (
in)
la13la14
0 0.5 1 1.5 20
0.5
1
1.5
2
2.5
3
T (sec)
A to
tal (
g)
0 0.5 1 1.5 20
5
10
15
T (sec)
D (
in)
nf01nf02
0 0.5 1 1.5 20
0.5
1
1.5
2
2.5
3
T (sec)
A to
tal (
g)
0 0.5 1 1.5 20
5
10
15
T (sec)
D (
in)
ls17cls18c
0 0.5 1 1.5 20
0.5
1
1.5
2
2.5
3
T (sec)
A to
tal (
g)
101
a. Displacement spectra: LA13 b. Total acceleration spectra: LA13
c. Displacement spectra: NF01 d. Total acceleration spectra: NF01
e. Displacement spectra: LS17c f. Total acceleration spectra: LS17c
Figure 3-11 Response spectra of LA13, NF01, and LS17c table motions with varying length scale, ζ = 5%
0 0.5 1 1.5 20
5
10
15
T (sec)
D (
in)
SF=2SF=4
0 0.5 1 1.5 20
0.5
1
1.5
2
2.5
T (sec)
A to
tal (
g)
0 0.5 1 1.5 20
5
10
15
T (sec)
D (
in)
SF=3SF=5
0 0.5 1 1.5 20
0.5
1
1.5
2
2.5
T (sec)
A to
tal (
g)
0 0.5 1 1.5 20
5
10
15
T (sec)
D (
in)
SF=3SF=5
0 0.5 1 1.5 20
0.5
1
1.5
2
2.5
T (sec)
A to
tal (
g)
102
3.3 Pre-Test Analysis of Bridge Deck Model
An analysis matrix, developed to include all proposed model configurations (see Section
3.1.5), was prepared for pre-test analytical evaluations of the test specimen. Pre-test
analysis assumed properties for specimen substructure components based upon their
design values (see Section 3.1.4). For systems employing FP bearings, nominal friction
coefficients of 0.04, 0.06, 0.09, and 0.12 were considered to bound the range of expected
values. FP bearing stiffness was assumed based upon the design value of the dish radius, R
a. Fault-normal b. Fault-parallel
Figure 3-12 Idealized near-fault pulse displacement histories
Table 3-5 Characteristics of near-fault pulse table motions at full amplitude
Label Fault-orientation Tp (sec) Dgmax (in.) Vgmax (in./sec) Agmax (g)
nfpu
lse1
_
normal 1 5 31.4159 0.5108
parallel 0.667 5 47.1003 1.1483
parallel 1 5 31.4159 0.5108
parallel 1.5 5 20.9440 0.2270
nfpu
lse2
_
normal 2 5 15.7080 0.1277
parallel 1.33 5 23.6210 0.2888
parallel 2 5 15.7080 0.1277
parallel 3 5 10.4720 0.0568
0 0.5 1−5
0
5
time/Tp
Dg (
g)
0 0.5 1−5
0
5
time/Tp
Dg (
in)
103
(see Section 3.1.4). LR bearing properties were averaged from available characterization
test data. Analyses were performed utilizing the generalized multi-degree-of-freedom, bi-
directional bridge model developed previously (see Section 2.3.3). The three earthquake
time-history motions (i.e., LA13_14, NF01_02, and LS17c_18c) and the suite of idealized
near-fault pulse motions (i.e., nfpulse1_ and nfpulse2_, see Table 3-5) were considered
over a range of amplitudes.
Summarized results from these pre-test analyses are included in Appendix B. These
results were examined to establish table motion amplitudes which would likely produce
specimen response near the limits of bearing and component displacement capacities.
Figure 3-13 Representative acceleration time-history of sin signal table motion
Table 3-6 Sin signal characteristics for characterization of FP slider µ values
Ao (g) f (Hz) Do (in) Vo (in/sec)
.130 1.714 0.4331 4.6643
.145 2.285 0.2718 3.9024
.111 2.285 0.20807 2.98740
.097 2.856 0.11639 2.08867
.104 6.000 0.02827 1.0659
0 2 4 6 8 10 12 14−0.15
−0.1
−0.05
0
0.05
0.1
0.15
time (sec)
acc
ele
ratio
n (
g)
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Trial span settings for test motions were then selected to provide 50% and 100% of these
peak amplitudes. Final peak table span settings were tailored during simulation tests to
produce model response near capacity, with final test sequences run at 50% and 100% of
these final settings.
3.4 Experimental Results for Configuration 1 (Non-elevated, Symmetric Mass)
Table C-1 in Appendix C presents a complete log of shake-table tests performed on the
Configuration 1 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-1 through D-30. For each of the selected tests,
x-y orbit plots of the global displacement and global force, and x- & y-direction bearing
hysteresis (for quadrant 1, a.k.a., Q1) are presented as a summary of the test specimen
response. For uni-directional tests, x-direction displacement and force histories are
presented in lieu of orbits and y-direction bearing hysteresis at quadrant Q1 is omitted.
Selected results are shown only for the maximum table span setting run for each
individual test motion sequence.
The Configuration 1 specimen was tested utilizing the three selected earthquake table
motions and the suite of idealized near fault pulses (see Section 3.2). Tests were performed
at two or more amplitudes (or span settings) and bi-directional motion pairs were run
simultaneously and as separate x- & y-direction inputs. Sinusoidal bearing
characterization tests were also performed to estimate friction coefficients for FP bearing
slider composites.
For earthquake history tests, representative results for both uni-directional and bi-
directional tests are presented in Figures D-1 through D-19. These results are presented for
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tests with FP, HDR, and LR bearings. Figure D-1 and D-5 illustrate response to the
LA13_14 earthquake table motion. Figure D-1 and D-2 compare response of a system
utilizing FP bearings with type 1 and 2 PTFE slider composite to the x-direction LA13
component. As seen, the FP bearings exhibit broad stable hysteretic response. The type 2
slider composite has a higher friction coefficient (see Section 3.14) resulting in a lower
peak displacement response. Figure D-3 shows the effect of the bi-directional LA13_14
table motion on the FP bearing system. As seen in the displacement orbit (see Figure D-
3(a)), this motion produces response oriented strongly along a 45 degree line to the xy-
axes. This behavior suggests strong coupling in the bearing response, as interaction with
the bearing yield surface is encountered. As expected, the x-direction bearing response at
quadrant Q1 (see Figure D-3(c)) is effected by this coupling, as the force response of the
bearing is reduced (compared to the bearing response without the LA14 component seen
in Figure D-2(c)), particularly in the x- direction induced by the strong coupled response
in the y- direction. Figure D-4 illustrates the response of a HDR bearing system to this
same LA13_14 table motion at a reduced span setting. As seen in the figure, the HDR
bearings exhibit a significant stiffening behavior, particularly in the first cycle excursions
to increasingly larger strain. The result of this behavior is increased force output.
However, reduced displacement response would be expected as a result. Figure D-5
illustrates the response of a system utilizing LR bearings to the LA13 component motion
at the same span setting as the previous test. As seen in the figure, the LR bearings exhibit
broad stable hysteretic response through numerous cycles (see Figure D-5(c)).
Comparisons between bearing characteristics (i.e., Qd, ku and kd) can be made by
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examining the bearing hysteretic plots shown in these figures (see Table 3-1 and Figure 3-
1).
Figure D-6 through D-13 illustrate response for the FP, HDR, and LR bearing systems to
the LS17c_18c and the NF01_02 table motions. Comparisons between bearing behavior
are similar to the previous test results. The LS17c_18c motion produces relatively regular
harmonic response in the specimen, as noted in the displacement histories of Figure D-
6(a), D-7(a), and D-10(a). This soft-soil motion is rich in long period content (see Figure
3-10) near to the period characteristics of these test bearings, with harmonic response as
the expected result. Bi-directional coupling effects in the LS17c_18c motion are not
significant due to its strong orientation along its x-component. The near-fault NF01_02
motion has an impulsive fault-parallel (x-direction) and fault-normal (y-direction)
component which are inherently strongly coupled. This motion produces strongly coupled
behavior in the specimen as seen in the displacement orbits of Figure D-11 and D-12.
For scaled motion tests, representative results are presented in Figures D-14 through D-19.
These tests were performed utilizing FP bearings with type 1 PTFE composite. As seen in
the plots, the table motions at larger scale factors (i.e., lr) produce specimen response of
larger magnitude and longer period content (compare for example Figure D-14 to Figure
D-15). This difference in specimen behavior is to be expected, as the same motion at a
larger length scale factor produces typically larger spectral response (as seen in Figure 3-
11), particularly in the longer period range representative of the characteristic isolation
periods of the test bearings (see Table 3-1).
107
For near fault pulse tests, representative results are presented in Figures D-20 through D-
28. These tests were performed utilizing FP bearings with type 2 PTFE composite and LR
bearings. As seen in the plots, bearing response to these pure pulse motions are smooth
and cyclic. Bearing response is also strongly influence by coupling behavior induced by
the ground motion signal phasing of fault normal and parallel components. These results
show that fault parallel component pulses with durations of 2/3, 1, and 1.5 times the fault
normal pulse duration (Tp) produce decreasingly smaller coupled response, respectively.
In particular, this is noted in the decreasing bearing response along the direction of the
fault parallel component.
Figures D-29 & D-30 present results of sinusoidal bearing characterization tests for FP
bearings with type 1 and 2 PTFE composite sliders, respectively. Section 3.14 presents a
summary of these and all other FP slider characterization tests.
3.5 Experimental Results for Configuration 2 (Non-elevated, Eccentric Mass)
Table C-2 in Appendix C presents a complete log of shake-table tests performed on the
Configuration 2 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-31 through D-60. For each of the selected tests,
one or two summary figures are presented. The first figure presents three plots of the
global displacement time-history, global force time-history, and the x-direction bearing
hysteresis (for quadrant Q1). For systems with mass eccentricity, the second figure
presents a summary of torsional response including: a comparison of hysteretic response
and displacement time-histories for the East and West ends of the bridge specimen (in the
direction of motion input orthogonal to the direction of mass eccentricity), and a time-
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history of deck rotation.
The Configuration 2 specimen was tested utilizing the x-direction component of the three
earthquake table motions. Tests were performed at two or more amplitudes (or span
settings) with mass eccentricities in the transverse direction of 0, 5, and 10 percent of the
overall bridge length. Tests were performed utilizing FP bearings (with type 2 PTFE
composite sliders) and LR bearings. Selected results are presented only for tests run at
their maximum amplitude. The figures illustrate the tendency for an increase in system
rotational response and bearing displacements at one end of the span as mass eccentricity
is increased (i.e., e/L increases from 0 to 0.05 to 0.10). This is made apparent by
comparing rotation histories and bearing hysteretic plots at the west and east ends of the
specimen for the same ground motion input with e/L = 0.05 and 0.10. For the case e/L = 0,
negligible system rotation was exhibited, as expected.
3.6 Experimental Results for Configuration 3 (Non-elevated, Eccentric Stiffness)
Table C-3 in Appendix C presents a complete log of shake-table tests performed on
Configuration 3 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-61 through D-66. For each of the selected tests,
two summary figures are presented. The first figure presents the x-direction global
displacement time-history, global force time-history, and bearing hysteresis (for quadrant
Q1). The second figure presents a summary of torsional response including: a comparison
of hysteretic response and displacement time-histories for the East and West ends of the
bridge specimen (in the direction of motion input orthogonal to the direction of stiffness
eccentricity), and a time-history of global deck rotation.
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The Configuration 3 specimen was tested transversely utilizing the x-direction component
of the three earthquake table motions. Isolation system stiffness eccentricity was provided
by installing LR bearings and HDR bearings on the West and East ends of the bridge,
respectively. Selected results are presented only for tests run at their maximum amplitude.
Test results for this sequence are indicative of the stiffness eccentricity inherent in the
isolation system. Characteristic bearing hysteretic properties are compared in Table 3.1. It
is apparent the LR test bearings have higher initial stiffness (i.e., larger ku) and somewhat
higher characteristic strength (Qu). On the other hand, the HDR test bearings have larger
second-slope stiffness (kd) than the LR bearings at similar peak strains. The HDR bearings
also exhibit scragging effects resulting in increased force output in initial cycles. These
variations produce eccentricity in system strength, and first- and second-slope stiffness,
resulting in torsional behavior. The tendency in the test sequences is for the HDR bearings
(at one end of the span) to exhibit smaller displacement response than the LR bearings (on
the opposite end). This is presumably the result of the larger second-slope stiffness of the
HDR bearings, even though the LR bearings are initially stronger and stiffer. For the first
test cycles to large strain (see Figure D-61 and 62 for the LA13_14 test motion), HDR
bearings exhibited first cycle scragging effects resulting in force output larger than the LR
bearings. In later tests after scragging had occurred and insufficient time had been allotted
between tests to allow recovery in the HDR bearings, LR and HDR bearings exhibited
similar force output (despite the larger displacement response of the LR bearings).
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3.7 Experimental Results for Configuration 4 (Elevated Single-span with Sym-metric Stiffness)
Table C-4 in Appendix C presents a complete log of shake-table tests performed on the
Configuration 4 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-67 through D-72. For each of the selected tests,
two summary figures are presented. The first figure presents the global displacement and
force orbits and x- & y-direction bearing hysteresis (for quadrant Q1). The second figure
presents a summary of local substructure response including plots of overall, bearing, and
pier hysteretic response in the x- & y-direction (at quadrant Q1).
The Configuration 4 specimen was tested utilizing the three selected earthquake time-
histories. Tests were performed at two or more amplitudes (or span settings) and bi-
directional motion pairs were run simultaneously and as separate x- & y-direction inputs.
Tests were performed utilizing FP bearings with type 4 PTFE composite. Selected results
are presented only for the bi-directional tests run at their maximum table span setting.
Similar to the Configuration 1 specimen test results (see Section 3.4), these results
indicate that response is influenced strongly by ground motion characteristics, including
frequency content and directional orientation. The LA13_14 motion has significantly
higher frequency content (see Section 3.2) and is strongly oriented along a 45 degree axis
to the x-y direction. This results in specimen response with significant coupling in the x-
and y-directions and underlying cycling of higher frequency (see Figure D-67 and D-68).
The LS17c_18c motion contains lower frequency components (see Section 3.2) and is
oriented strongly along the x-direction. This results in specimen response with strong
orientation along the x-direction with little coupled response and low frequency harmonic
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cycling (see Figure D-69 and D-70). The NF01_02 motion is an impulsive near-fault event
with strong coupled x- and y-components (see Section 3.2). The vertical component
included in this ground motion history also contains significant amplitude accelerations.
This results in similar response to that of the LA13_14 motion, with less underlying high
frequency contribution, and added fluctuations in the bearing friction force component of
the hysteretic response induced by the vertical acceleration contributions (see Figure D-71
and D-72).
In addition, system attributes play an important contribution to the response as well.
Substructure pier response is essentially linear in these tests, with only slight pinching
near the origin, as seen in the hysteretic plots (see Figure D-68, D-70, and D-72 (e) and
(f)). This pinching behavior is discussed further in Section 3.13. On the other hand,
bearing response is essentially bilinear (see Figure D-67, D-69, and D-71 (c) and (d)), with
pinching of varying magnitude. This pinching response may be seen as the result of
several factors: bi-directional coupling in the bearing yield surface, vertical load
fluctuations caused by overturning effects and/or vertical acceleration input (see NF01_02
test results), or vertical load redistributions resulting from kinematic shortening of pier
assemblies. The latter phenomenon is discussed in further detail in subsequent evaluations
in Chapter 4. Finally, it is noted that total specimen displacement response (at the deck
level) is distributed between the isolation bearings and the pier substructure assemblies in
proportion to their flexibilities. Each of these components resist nearly equal force
transmission (varying slightly as the result of substructure mass contributions) with total
displacement response being the sum of the two component displacement contributions in
series.
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3.8 Experimental Results for Configuration 5 (Elevated Single-span with Un-symmetric Stiffness)
Table C-5 in Appendix C presents a complete log of shake-table tests performed on the
Configuration 5 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-73 through D-98.
The Configuration 5 specimen was tested with and without bracing utilizing the three
earthquake table motions. Tests were performed at two or more amplitudes (or span
settings) and bi-directional motion pairs were run simultaneously and as separate x- and y-
direction inputs. The specimen was also tested with uni-directional components of the
earthquake table motions at alternate length scale factors (i.e., lr), similar to the
Configuration 1 tests (see Section 3.4). The NF01_02 motion was run with and without its
vertical signal. Tests were performed utilizing FP bearings with type 3 and 4 PTFE
composites. Selected results are presented only for tests run at their maximum table span
setting.
For the selected earthquake history tests shown in Figure D-73 through D-92, two
summary figures are presented. The first figure presents the global displacement and force
orbits and x- and y-direction bearing hysteresis (for quadrant Q1). The second figure
presents a summary of local substructure response including plots of overall, bearing, and
pier hysteretic response in the x- and y-direction (at quadrant Q1). The characteristics of
specimen response to the different ground motion histories is similar to the Configuration
4 tests (see Section 3.7 above), with variations in ground motion frequency content and
directionality strongly influencing specimen behavior. For braced specimen tests,
substructure pier response is again nearly linear and notably stiffer than the unbraced
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condition (compare Figure D-74 (e) and (f) to Figure D-76 (e) and (f)). For the unbraced
specimen, this configuration has larger pier stiffness in the x-direction compared to the y-
direction. This property can be readily observed from the response figures (see, for
example, Figure D-76 (e) and (f) and Section 3.1.4 and 3.1.5). Substructure stiffness
characterizations for these configurations are presented in Section 3.13 below. Foremost,
these results indicate that the effect of increasing substructure flexibility is an increase in
both global and substructure peak displacements. It appears, however, that bearing
displacement response may be somewhat larger, smaller, or relatively unaffected by this
variation (compare for example Figure D-74 to D-76). Further, FP bearing type 3 slider
composite is shown to have a lower friction value than the type 4 PTFE composite (see
Section 3.14 below), resulting in larger global and bearing displacement response when
these sliders are installed (compare Figure D-82 to D-84 (a) and (b)). Finally, it is noted
that bi-directional substructure stiffness is uncoupled in this specimen design. The effect
of this unequal x- and y-direction substructure stiffness (most notably in the unbraced
Configuration 5 specimen) is to skew the systems’ bi-directional yield surface by
producing unequal yield displacements in these directions. This effects the character of
global system hysteretic coupling, which can be seen by comparing Configuration 4 and
Configuration 5 hysteretic response for the same input motion (compare Figures D-72 and
D-86 (a) and (b)).
For uni-directional scaled motion tests in Figure D-93 through D-98, x-direction
displacement and force histories are presented in lieu of orbits, y-direction bearing
hysteresis at quadrant Q1 is omitted, and the plots showing local global, bearing, and pier
response distribution are omitted. The results of these tests are similar to the scaled motion
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tests of Configuration 1 (see Section 3.4), with the table motions at larger length scale
factors (i.e., lr) producing specimen response of larger magnitude and longer period
content (compare Figure D-94 and D-97). This difference in behavior is similar to before,
as the isolated specimen will experience larger spectral response for the same motion at a
larger length scale (as seen in Figure 3-11).
3.9 Experimental Results for Configuration 6 (Elevated Single-span with Eccen-tric Stiffness)
Table C-6 in Appendix C presents a complete log of shake-table tests performed on the
Configuration 6 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-99 through D-122. For each of the selected
tests, four summary figures are presented. The first figure presents the global
displacement and force orbits and x- and y-direction bearing hysteresis (for quadrant Q1).
The second and third figures present summaries of local substructure response including
plots of overall, bearing, and pier hysteretic response in the x- and y-direction at quadrant
Q1 and Q4, respectively. The fourth figure presents a summary of torsional response
including: a comparison of hysteretic response and displacement time-histories for the
East and West ends of the bridge specimen (in the direction of motion input, orthogonal to
the direction of stiffness eccentricity), and a time-history of global deck rotation.
The Configuration 6 specimen was tested utilizing the three earthquake table motions.
Tests were performed at two or more amplitudes (or span settings) and bi-directional
motion pairs were run simultaneously and as separate x- & y-direction inputs. The
NF01_02 motion was run with and without its vertical signal. Tests were performed
utilizing FP bearings in two configurations. The first slider configuration utilized type 3
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composite on all four bearings. The second slider configuration utilized type 4 and 3
composite on the East (unbraced) and West (braced) end of the bridge, respectively, in an
effort to counteract the torsional effects of the substructure stiffness eccentricity. Selected
results are presented only for bi-directional tests run at their maximum amplitude.
The torsional response induced by the specimen’s substructure stiffness eccentricity is
apparent from these test results, with global x-direction displacement (orthogonal to
stiffness eccentricity) larger on the unbraced East end relative to the braced West end (see
Figure D-102, D-106, D-110, D-114, D-118, and D-122). On the other hand, global
displacements in the y-direction are similar on the East and West end of the specimen with
displacement compatibility enforced by the longitudinally rigid deck frame (compare, for
example, plot (b) of Figure D-100 vs. D-101 and Figure D-116 vs. D-117). Bearing
displacements in the x-direction are not, however, systematically larger or smaller on the
unbraced end compared to the braced end of the specimen. This implies that shear
response is similar on either end of the specimen span. Torsional response is then mainly
due to kinematic rotation of the substructure about a vertical axis caused by the difference
in displacement between the flexible unbraced piers on the East end relative to the braced
West end piers. Bearing displacements in the y-direction, however, are always larger on
the braced West end of the specimen due to redistribution enforced by displacement
compatibility imposed by the longitudinally rigid deck frame (compare, for example, plots
(c) and (d) of Figure D-100 vs. D-101 and Figure D-116 vs. D-117).
It is also evident from these results that the alternate slider configuration, with lower
friction FP type 3 PTFE sliders installed on the braced end of the specimen and higher
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friction type 4 sliders installed on the unbraced end, has a tendency to reduce rotational
response due to the underlying substructure stiffness eccentricity. This is illustrated by
comparing torsional response to the same input motion for the system utilizing the
uniform slider configuration and this alternate un-symmetric slider configuration
(compare Figure D-102 vs. D-106, Figure D-110 vs. D-114, and Figure D-118 vs. D-122).
3.10 Experimental Results for Configuration 7 (Elevated Double-span)
Table C-7 in Appendix C presents a complete log of shake-table tests performed on the
Configuration 7 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-123 through D-158. For each of the selected
tests, three summary figures are presented. The first figure presents the global
displacement and force orbits and x- & y-direction bearing hysteresis (for quadrant Q1).
The second and third figures present summaries of local substructure response including
plots of overall, bearing, and pier hysteretic response in the x- & y-direction at quadrant
Q1 and Pier 5, respectively.
The Configuration 7 specimen was tested utilizing the three earthquake table motions.
Tests were performed at two or more amplitudes (or span settings) and bi-directional
motion pairs were run simultaneously and as separate x- & y-direction inputs. The
NF01_02 motion was run with and without its vertical signal. Tests were performed
utilizing FP bearings in four configurations. The first two utilized type 4 and 5 PTFE
composite sliders, respectively, uniformly on all four bearings. The third system utilized
type 4 composite sliders on the East and West braced ends of the span and type 5
composite sliders on the flexible central piers (i.e., Piers 5 and 6) in an effort to reduce
117
shear transfer to these components. The final system utilized type 5 composite sliders on
the East and West braced ends and type 4 composite sliders on the central piers (Piers 5
and 6) in an effort to balance shear forces across all bent lines. Selected results are
presented only for bi-directional tests run at their maximum amplitude.
The effect of ground motion characteristics on specimen response in these tests is similar
to the Configuration 1, 4 and 5 test sequences. As discussed previously, input frequency
content and directionality playing a significant role in determining system dynamic
behavior. See previous discussions in Section 3.4 and 3.7.
The Configuration 7 specimen represents a simple two-span bridge overcrossing, with
relatively rigid end abutments and a flexible central pier bent. It is notable from these
results that this specimen exhibits similar global response as the Configuration 1 and
braced Configuration 5 test specimens when subjected to the same input motion (compare,
for example, Figure D-3, D-73, and D-132 for the LA13_14 input motion). This behavior
would be expected, as each of these configurations has a similar relationship of total mass
to global force-deformation behavior, with Configuration 7 having only the added
complexity of a flexible central pier bent modifying the hysteretic behavior of this
component.
The typical pattern of displacement and force distribution behavior in this specimen can
be seen by comparing hysteretic behavior at the end abutment location (i.e., Q1) to
response at the central pier bent (i.e., Q5) (see for example Figure D-124 and D-125 for
the LA13_14 input motion). The tendency is for bearings at the braced end of the
specimen to contribute nearly all of the total displacement demand at these locations.
118
Larger shear demand is also attracted to the braced abutment ends. The central pier
locations experience similar total displacement demands as end bents, due to displacement
compatibility enforced by the in-plane flexural rigidity of the deck frame. However, the
flexible piers at these locations provide a significant contribution to the total displacement
demand with bearings contributing the remainder. However, kinematic shortening of these
central pier assemblies (which occurs through rigid body rotation of these elements as the
tip of the pier is displaced) effects loss of axial force at these locations. This phenomenon
results in loss of FP bearing stiffness whose friction and pendulum stiffness components
are axial load dependant. This results in a reduction in shear force transmission at these
locations. This behavior is evident by noting the hysteretic pinching which occurs in
bearing response at these locations (see, for example, Figure D-125 and D-128 (c) and
(d)). The implications of this kinematic effect are discussed in further detail subsequently
in Chapter 4.
Bearing characterization tests show that the type 4 and 5 slider composites exhibited
similar friction values during these tests (see Section 3.14). Consequently, it is evident that
due to this similarity the effect of different slider configurations on system response
characteristics was minimal during these test sequences (compare, for example, Figure D-
123, D-126, D-129, and D-132).
3.11 Experimental Results for Configuration 8 (Elevated Double-span with Eccen-tric Stiffness)
Table C-8 in Appendix C presents a complete log of shake-table tests performed on the
Configuration 8 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-159 through D-173. For each of the selected
119
tests, five summary figures are presented. The first figure presents the global displacement
and force orbits and x- & y-direction bearing hysteresis (for quadrant Q1). The second,
third and fourth figures present summaries of local substructure response including plots
of overall, bearing, and pier hysteretic response in the x- & y-direction at quadrant Q1,
Pier 5, and quadrant Q4, respectively. The fifth figure presents a summary of torsional
response including: a comparison of hysteretic response and displacement time-histories
for the East and West ends of the bridge specimen (in the direction of motion input,
orthogonal to the direction of stiffness eccentricity), and a time-history of global deck
rotation.
The Configuration 8 specimen was tested utilizing the three earthquake table motions.
Tests were performed at two or more amplitudes (or span settings) and bi-directional
motion pairs were run simultaneously and as separate x- & y-direction inputs. The
NF01_02 motion was run with and without its vertical signal. Tests were performed
utilizing FP bearings with type 5 composite. Selected results are presented only for bi-
directional tests run at their maximum amplitude.
The pattern of torsional response induced by the specimen’s substructure stiffness
eccentricity is similar to the Configuration 6 test sequences. Global x-direction
displacement (orthogonal to stiffness eccentricity) increases along the span moving from
the braced West end to the unbraced central piers to the unbraced East end (see, for
example, Figure D-160, D-161, D-162 and D-163 for the LA13_14 input motion). As
before, global displacements in the y-direction are similar on the East and West end of the
specimen with displacement compatibility enforced by the longitudinally rigid deck
120
frame. Bearing displacements in the x-direction are similar implying similar shear
response along the specimen span. Torsional response is then mainly due to kinematic
rotation of the substructure about a vertical axis caused by the difference in displacement
between the piers along the span. Bearing displacements in the y-direction, however, are
always larger on the braced end of the specimen due to pier stiffness at this location and
displacement compatibility imposed by the longitudinally rigid deck frame.
3.12 Experimental Results for Configuration 9 (Elevated Double-span with Yield-ing Piers 5 and 6)
Table C-9 in Appendix C presents a complete log of shake-table tests performed on the
Configuration 9 isolated bridge specimen. Selected experimental results from these tests
are presented in Appendix D as Figures D-174 through D-184. For each of the selected
tests, three summary figures are presented. The first figure presents the global
displacement and force orbits and x- & y-direction bearing hysteresis (for quadrant Q1).
The second and third figures present summaries of local substructure response including
plots of overall, bearing, and pier hysteretic response in the x- & y-direction at quadrant
Q1 and Pier 5, respectively.
The Configuration 9 specimen was tested utilizing the three earthquake table motions.
Tests were performed at two or more amplitudes (or span settings) and bi-directional
motion pairs were run simultaneously and as separate x- & y-direction inputs. The
NF01_02 motion was run with and without its vertical signal. Tests were performed
utilizing FP bearings. Type 5 PTFE composite sliders were utilized on the East and West
braced ends of the specimen while type 4 sliders were utilized on the central piers (i.e.,
Piers 5 and 6). The vertical load was also balanced such that approximately 5/8ths was
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supported by Piers 5 and 6 (consistent with the loading of a continuous girder span) in an
effort to attract shear forces to this location.
The Configuration 9 specimen configuration is essentially identical to Configuration 7,
with the addition of weaker A36 leaf springs installed in the central piers. Several test
sequences run at increasing span settings were performed on this specimen with limited
yielding occurring in central piers (see, for example, pier hysteresis in Figure D-179 (e)
and (f)) Consequently, pier bracing at the end abutments was removed in an effort to
balance shear behavior across the specimen increasing demands at the yielding central
piers. In this unbraced configuration, span settings were again increased to maximize
ductility demand at the central piers (see pier hysteresis in Figure D-181 and D-184 (e)
and (f)). Peak ductility demand of approximately 1.5-2 were achieved in the final tests
sequence with no apparent reduction in the isolated performance of the system (see Figure
D-182, D-183, and D-184).
3.13 Experimental Results for Configuration 10 (Substructure Static Pullback Tests)
Table C-10 in Appendix C presents a complete log of static pull-back tests performed on
Configuration 10 of the isolated bridge specimen. Selected experimental results from
these tests are presented in Appendix D as Figure D-185. Braced frame stiffness
characterization was computed from dynamic test data (see, for example, Figure D-178 (e)
and (f)). Table 3-7 below tabulates substructure pier assembly properties computed from
these test results.
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Substructure properties in Table 3-7 determined from these characterization tests can be
compared to the previous computed design values shown in Table 3-2. As seen, a number
of discrepancies between the design and test values are apparent. First of all, stiffness
values are generally lower than computed design values. Actual braced pier stiffness is
slightly less than computed (i.e., 26.7 kips/inch computed vs. 22-24 kips/inch tested). This
reduction is apparently due to friction slip of bolted end connections. In addition, actual
stiffnesses of short and long plate pier assemblies are lower than computed (i.e., 4 kips/
inch computed vs. 2.4-3 kips/inch tested for the short plate assembly and 1.8 kips/inch
computed vs. 1.6-1.7 kips/inch tested for the long plate assembly). These stiffness
reductions are likely due to gapping in the mechanical assemblies which occurred at
movements near the displacement origin. Further, assumed slider elevations were slightly
lower than as-built elevations in design computations. This led to a higher computation of
effective lateral stiffness in design due to the displacement transformation at the lower
assumed slider height. Finally, it is seen that strength values for short and long plate pier
assemblies were higher than computed (i.e, 2.9 kips design value vs. 4 kips tested value).
This effect was certainly the result of material strength above the assumed nominal value
(i.e., 36 ksi for A36 material).
3.14 Experimental characterization data for FP slider composites
A number of tests were performed during the shake table simulation sequences to evaluate
the friction coefficients of the five FP bearing slider composites provided by the
manufacturer. A log of these bearing characterization tests are shown in Table C-1, C-4,
C-5, and C-7 of Appendix C.
123
The shear response, V(u), of a spherical sliding FP bearing responding uni-directionally
can be represented by the following,
(14)
where µ is the friction coefficient of the slider-dish interface, u the uni-directional
displacement, the velocity, N the normal force (possibly varying in time), and R the
bearing radius [Constantinou et al. 1998]. It has been shown that the friction coefficient of
a PTFE slider moving across a stainless steel surface increases with velocity up to a
threshold value [Constantinou et al. 1990] (see Figure 3-14 below). Bearing
characterization tests were performed by applying test signals to the bridge specimen
which produced essentially harmonic bearing response through a range of velocities (see
Figure 3-13 and Table 3-6). Bearing shear response data from these tests were processed
Table 3-7 Substructure pier assembly properties computed from characterization data
Configuration1 Material Ksub (kips/in) α2 yield point 3
(kips)Fy 4
(kips)Tsub
5(sec)
Braced x- 22 0.27
Braced y- 24 0.26
Short Plate A514 2.4-2.6 0.83-0.80
Long Plate A514 1.6-1.7 0.99-1.02
Short Plate A36 2.4-3 .04-.167 4 4.75-5 0.83-0.74
Long Plate A36 1.6-1.7 .23-.25 4 4.6 0.99-1.02
1. see Section 3.1.4
2. strain hardening ratio, see Figure D-185
3. first point of yield onset, see Figure D-185
4. vertex of bilinear idealization, see Figure D-185
5. based upon tributary mass; see Chapter 2, Equation 3
V u( ) µN u·( )sgn NR----u+=
u·
124
to remove the stiffness contribution (i.e., N/R) and then divided by the time varying
normal force to determine the friction coefficient of each slider composite. Mean friction
coefficient results for each of the slider composite types plotted as a function of velocity
are shown in Figure 3-15. Error bars are included in the plots indicating one standard
deviation statistical scatter.
As seen from these results, friction coefficients ranged from lowest to highest for the type
1, 3, 4, 5, and 2 slider composites, respectively. These composite types (in their virgin
condition) exhibited peak average friction coefficient values of approximately 0.05,
0.0575, 0.08, 0.095, and 0.103, respectively. The type 1 slider composite exhibited a
significant increase in friction coefficient after 57 test signals (see Figure 3-15(a)). The
type 4 slider composite exhibited a similar increase in friction response, after 231 tests
were performed (see Figure 3-15(d)). Slider composite type 5, on the other hand, exhibited
a slight reduction in average friction response after 48 tests (see Figure 3-15(e)).
Figure 3-15(f) illustrates the hysteretic friction response of bearings using the type 5 slider
composite subjected to the LS17c table motion time-history. It is apparent from this figure
that higher friction response (approaching 13 percent) is exhibited in the initial
displacement cycle of the bearing. This behavior may indicate an initial “stick”
phenomenon in the slider interface not noted in the previous characterization tests which
were not processed to near zero velocity. As seen in the remaining response, however,
friction of near 10 percent is exhibited during peak displacement cycles. This is consistent
with the bearing characterization data (see Figure 3-15(e) for values of the peak average
friction coefficient plus one standard deviation). As displacement cycles subside in the
125
remaining hysteretic response, friction approaches 8%, consistent with the lower velocity
response for this composite (see Figure 3-15(e)). This is consistent with reported behavior
due to rate effects (see Figure 3-14) [Constantinou et al. 1990].
Figure 3-14 PTFE slider composite behavior as a function of velocity
velocity
fric
tion
coef
ficie
nt
126
a. Type 1 b. Type 2
c. Type 3 d. Type 4
e. Type 5 f. Type 5 friction hysteresis: LS17c
Figure 3-15 Characterization of FP bearing slider composites
0 1 2 3 40.03
0.04
0.05
0.06
0.07
0.08
0.09
velocity (in/sec)
fric
tion
coef
ficie
nt
virgin
after 57 tests
0 1 2 30.06
0.07
0.08
0.09
0.1
0.11
0.12
velocity (in/sec)
fric
tion
coef
ficie
nt
virgin
0 1 2 3 40.045
0.05
0.055
0.06
0.065
0.07
velocity (in/sec)
fric
tion
co
effic
ien
t
virgin
0 1 2 3 40.04
0.06
0.08
0.1
0.12
velocity (in/sec)
fric
tion
coef
ficie
nt
virgin
after 231tests
0 1 2 3 4 5
0.08
0.09
0.1
0.11
velocity (in/sec)
fric
tion
coef
ficie
nt
virgin
after 48tests
−3−2.5−2−1.5−1−0.5 0 0.5 1 1.5 2 2.5 3−0.15
−0.1
−0.05
0
0.05
0.1
0.15
displacement (in)
fric
tion
co
effic
ien
t
127
4 Evaluation of Bridge Model Test Data
4.1 Introduction
In this chapter, test results reported in Chapter 3 are compared with each other and with
results of simplified analyses. These comparisions are used to assess the basic
observations made for the pilot analytical studies examined in Chapter 2. Results are
presented in this chapter regarding the influence of
1. Substructure flexibility
2. Isolator strength and second-slope flexibility
3. Substructure mass
4. Number of components of horizontal excitation
5. Substructure strength
6. Superstructure mass eccentricity
7. Substructure stiffness eccentricity
8. Type of simplified analytical model used
9. Ground motion characteristics
10. Vertical components of ground motion
11. Displacemenet restraint
12. Bearing wear
128
These comnparisions focus on the particular features incorporated in the test specimens. A
more comprehensive and refined analytical assessment of many of these variables are
considered in Chapter 5.
4.2 Influence of Substructure Flexibility
Configurations 1, 4, and 5 allow comparison of isolated bridge systems having different
substructure flexibility. These configurations were tested with very similar FP bearings.
ALthough two different PTFE slider composites were used, they had similar strength
characteristics. Three earthquake table motions (i.e., LA13_14, NF01_02, and
LS17c_18c) were utilized for these tests. x- and y-direction components were run
individually and together. The specimens tested have substructure periods as shown in
Table 4-1. Based upon the processing criteria used, similitude length scale factors of 2, 5,
and 5 are associated with the LA13_14, NF01_01, and LS17c_18c ground motions,
respectively.
Table 4-1 Nominal substructure properties for bridge model Configuration 1, 4, and 5
Σ Ksub1 Tsub2
Config. PTFE slider3 x-direction y-direction x-direction y-direction
1 type 2 INF4 INF4 0 sec4 0 sec4
55 type 4 96 kip/in 96 kip/in 0.26 sec 0.26 sec
4 type 4 10.4 kip/in 10.4 kip/in 0.8 sec 0.8 sec
5 type 4 10.4 kip/in 6.6 kip/in 0.8 sec 1.0 sec
1. Computed using component stiffness characterized from test data, see Table 3-7.
2. Tsub computed for a deck weight of 65 kips, see Chapter 2, Equation 3.
3. See Appendix C and Figure 3-15
4. Assumed substructure properties for bridge deck mounted directly to simulator.
5. With cross-bracing added at bent frames.
129
The data collected from these test sequences are compared with each other and with the
results of elastic and inelastic analyses to assess the effect of substructure flexibility on the
response of an isolated bridge system. Analyses of isolated bridge systems with
mechanical properties similar to those in the bridge deck specimen were carried out using
recorded table motions. System displacement and acceleration response data taken from
the bridge specimen tests are compared to results from the comparative analyses in
Figures 4-1 through 4-6. The analysis results are presented in terms of spectra computed
for a wide range of substructure periods. The elastic analysis shown corresponds to a
single-degree-of-freedom system with a period corresponding to Tsub and ζ = 5%. A two-
degree-of-freedom nonlinear model is considered for the nonlinear analysis.
As seen in Figures 4-1 through 4-3, peak deck displacements for isolated systems with
very rigid substructures are much larger than those of similar non-isolated elastic systems
(i.e., a system with equal substructure stiffness). Nearly all the displacement in the isolated
system occurring in the isolator component. For isolated systems with relatively large
substructure flexibility, isolator displacement is roughly similar to that of a similar non-
isolated system. For these more flexible systems, total displacement is shared between the
isolation bearings and the substructure component. The proportion of displacement
contributed by the substructure increases as the flexibility of the substructure increases.
Peak deck displacement is thus seen to increase with moderately increasing substructure
flexibility. Peak isolator displacement is constant or increases slightly with substructure
flexibility.
130
As seen in Figures 4-4 through 4-6, measured peak deck acceleration response for these
isolated systems (i.e., Cdeck) is relatively constant over a range of substructure flexibility.
Similar trends are observed from the nonlinear analyses. This might be expected due to the
similar isolator or displacements. On the other hand, computed deck acceleration
undulates greatly for similar elastic systems.
The advantage of isolation is thus not always significant force reduction, but damage
control in substructure elements and more consistent response, that is less sensitivity to
structural characteristics such as stiffness. Damage control is achieved as the isolated
system endures significant displacement demands (taken in a large portion through the
isolation bearings) without yielding or damage to substructure and superstructure
components. Conventional bridges, on the other hand are designed to endure significant
substructure yielding damage in a design basis event.
It should also be noted that the trends seen here compare closely with those reported in
preliminary analyses (see Section 2.3.5.1).
4.3 Influence of Isolator Second-Slope Flexibility and Strength
Several test configurations allow evaluation of the effect of variations in isolation system
properties on system response. Configuration 1 was tested with LR and HDR bearings.
Configuration 1, 4 and 5 were tested with two different strength FP bearings. Each
configuration was tested with both uni-directional components and bi-directional motion
pairs of the three earthquake table motions (i.e., LA13_14, NF01_02, and LS17c_18c) and
several near fault pulse motions (i.e., nfpulse).
131
(a) Model displacement: LA13 (b) Displacement spectra: LA13
(c) Model displacement: NF01 (d) Displacement spectra: NF01
(e) Model displacement: LS17c (f) Displacement spectra: LS17cFigure 4-1 Test data for FP type 2 and 4 vs. nonlinear spectra for Cyiso = 0.09, ground motions at highest span settings.
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
deck isolator
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
deck isolator D elastic, 5% damping
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
132
Mechanical properties of the test bearings were characterized via three sources: the in-
plane test machine, bi-directional pseudo-static shake table testing, and harmonic
characterization tests performed on the bridge specimen [Fenves, 1998]. Characteristic
bearing hysteretic properties taken from these sources are summarized in Table 4-2 (see
also Figure 3-15). Accompanying Figure 4-7 illustrates the hysteretic response of these
three test bearings for the LA13 and LS17c motion sequences applied to Configuration 1.
Isolator displacement and base shear response from the Configuration 1 test sequences are
summarized in Table 4-3 below. These results illustrate the effect of varying isolation
system characteristics on peak response of an isolated bridge with an essentially rigid
substructure (as for Configuration 1). As seen in Table 4-3, displacement response tends to
be sensitive to strength and systematically increases as strength decreases (compare
displacement response for bearings with nearly equal first- and second-slope stiffness
characteristics (i.e., FP type 2 vs. FP type 1 or LR vs. HDR bearings). Base shear
(g) Model displacement: averaged (h) Displacement spectra: averagedFigure 4-1 Test data for FP type 2 and 4 vs. nonlinear spectra for Cyiso = 0.09, ground motions at highest span settings.
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
133
(a) Model displacement: LA14 (b) Displacement spectra: LA14
(c) Model displacement: NF02 (d) Displacement spectra: NF02
(e) Model displacement: LS18c (f) Displacement spectra: LS18cFigure 4-2 Test data for FP type 2 and 4 vs. nonlinear spectra for Cyiso = 0.09, ground motions at highest span settings.
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
deck isolator
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
deck isolator D elastic, 5% damping
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
134
response, on the other hand, consistently increases for bearings with higher second-slope
stiffness (compare FP vs. LR and HDR bearings). This result is indicative of the larger
second-slope stiffness of the LR and HDR bearings compared to the FP bearings, which
produces marked increases in shear response at larger displacements. In addition, the
stiffening behavior of the HDR bearings caused by scragging effects at peak (virgin)
response cycles results in further increases in shear response above those experienced by
the LR bearings (at similar displacement amplitudes). Notably, this force effect (in the
HDR bearings) does not appear to markedly change displacement response. FP bearings,
while experiencing initially higher shear response at low amplitude (due to their larger Qd
values), have markedly lower second-slope stiffness (i.e., kd) and experience relatively
lower shear response at larger amplitudes when compared to the stiffer LR and HDR
bearings. It should be noted, that these effects are indicative of the variation in
characteristic hysteretic properties represented by these three test bearings (i.e., Qd, ku,
and kd) and not necessarily their bearing type (i.e., FP, LR, and HDR). In other words,
(g) Model displacement: averaged (h) Displacement spectra: averagedFigure 4-2 Test data for FP type 2 and 4 vs. nonlinear spectra for Cyiso = 0.09, ground motions at highest span settings.
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
135
(a) Model displacement: LA13_14 (b) Displacement spectra: LA13_14
(c) Model displacement: NF01_02 (d) Displacement spectra: NF01_02
(e) Model displacement: LS17c_18c (f) Displacement spectra: LS17c_18cFigure 4-3 Test data for FP type 2 and 4 vs. nonlinear spectra for Cyiso = 0.09, ground motions at highest span settings.
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
deck isolator
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
deck isolator D elastic, 5% damping
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
136
these bearings could be re-designed such that their hysteretic properties were interchanged
(i.e., FP bearings given higher second-slope stiffness than the LR and HDR bearings, for
example) and the variation in response would be reflective.
Isolator displacement and base shear response from the Configuration 5 test sequences are
summarized in Tables 4-4 and 4-5 below. These results illustrate the effect of varying
isolation system strength on peak response of an isolated bridge having a flexible
substructure (i.e., Tsub = 0.25, 0.8 and 1.0 seconds). As seen in Table 4-4 and 4-5,
displacement response tends to be sensitive to strength and systematically increase as
strength decreases (see the mean displacement ratio in Table 4-4 and Table 4-5). Further,
these results indicate that strength effects displacements more as the substructure becomes
more rigid (compare Table 4-4 mean displacement ratio to Table 4-5). This appears more
apparent for larger amplitude motions. Force response, on the other hand, is less sensitive
(g) Model displacement: averaged (h) Displacement spectra: averagedFigure 4-3 Test data for FP type 2 and 4 vs. nonlinear spectra for Cyiso = 0.09, ground motions at highest span settings.
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
137
(a) Model acceleration: LA13 (b) Deck acceleration spectra: LA13
(c) Model deck acceleration: NF01 (d) Deck acceleration spectra: NF01
(e) Model deck acceleration: LS17c (f) Deck acceleration spectra: LS17cFigure 4-4 Test data for FP type 2 and 4 vs. nonlinear spectra for Cyiso = 0.09, ground motions at highest span settings.
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
isolated deck elastic, 5% damping
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
138
to variations in characteristic isolator strength (see the mean force ratio in Table 4-4 and
Table 4-5).
These results compare closely with those of preliminary analyses reported in Chapter 2
(see Section 2.3.5.2). It was shown there that isolator characteristic strength had a
profound effect on deck and isolator displacements, particularly for systems with the most
rigid substructures (and/or first-slope stiffness). With regard to force response, it was
shown that peak force changes mostly with variations in substructure flexibility and
isolator second-slope flexibility, but insignificantly with isolator strength (for larger
amplitude responses).
4.4 Influence of Substructure Mass
Configuration 5 of the bridge deck model also allowed comparison of an isolated bridge
system incorporating substructures with a range of contributing mass. This configuration
utilized FP bearings with two different strength PTFE slider composites and was tested
(g) Model deck acceleration: averaged (h) Deck acceleration spectra: averagedFigure 4-4 Test data for FP type 2 and 4 vs. nonlinear spectra for Cyiso = 0.09, ground motions at highest span settings.
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
139
(a) Model deck acceleration: LA14 (b) Deck acceleration spectra: LA14
(c) Model deck acceleration: NF02 (d) Deck acceleration spectra: NF02
(e) Model deck acceleration: LS18c (f) Deck acceleration spectra: LS18cFigure 4-5 Test data for FP type 2 and 4 vs. nonlinear spectra for Cyiso = 0.09, ground motions at highest span settings.
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
isolated deck elastic, 5% damping
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
140
with both uni-directional and bi-directional ground motions on the earthquake simulator.
The three earthquake table motions (i.e., LA13_14, NF01_02, and LS17c_18c) were
utilized. The Configuration 5 specimen targeted three nominal substructure mass
proportions, defined as γ = msub/Mdeck (where msub and Mdeck are the total substructure
and deck mass, respectively), equal to approximately 0, 5, and 10 percent. Arrangements
of substructure mass, FP slider composites (see Chapter 3, Section 3.14), and bracing
arrangements used for these test sequences are outlined in Table 4-6 below.
Bridge specimen peak response results from these tests are plotted in Figure 4-8 through
4-11. As seen in the first three of these figures, results indicate the effect of substructure
mass on system response is most prominent on substructure displacement, less so on
isolator displacement, and least so on total deck displacement on average (see Figure 4-8,
4-9, and 4-10 (g) and (h)). In any event, the difference in average response rarely exceeded
10 percent in these tests for a variation of substructure mass of γ = 0 to 10 percent. The
(g) Model deck acceleration: averaged (h) Deck acceleration spectra: averagedFigure 4-5 Test data for FP type 2 and 4 vs. nonlinear spectra for Cyiso = 0.09, ground motions at highest span settings.
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
141
(a) Model deck acceleration: LA13_14 (b) Deck acceleration spectra: LA13_14
(c) Model deck acceleration: NF01_02 (d) Deck acceleration spectra: NF01_02
(e) Model deck acceleration: LS17c_18c (f) Deck acceleration spectra: LS17c_18cFigure 4-6 Test data for FP type 2 and 4 vs. nonlinear spectra for Cyiso = 0.09, ground motions at highest span settings.
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
isolated deck elastic, 5% damping
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
142
tendency is for the average response to increase as the substructure mass ratio, γ,
increases. This implies base shear response is highest for a system with the most
substructure mass (resulting directly from the higher substructure displacement demand),
as expected. On the other hand, Figure 4-11 indicates that the substructure mass ratio has a
(g) Model deck acceleration: averaged (h) Deck acceleration spectra: averaged
Table 4-2 Summary idealized bilinear hysteretic characteristics for test bearings
Bearing Type Qd ku kd Tiso1
FP, type 1 0.81 kips INF2 0.54 kips/in 1.75sec
FP, type 2 1.63 kips INF2 0.54 kips/in 1.75 sec
FP, type 3 0.95 kips INF2 0.54 kips/in 1.75 sec
FP, type 4 1.35 kips INF2 0.54 kips/in 1.75 sec
LR3 1.46 kips 5 kip/in 0.9 kips/in 1.36 sec
HDR4 0.81 kips 3.5 kip/in 1 kips/in 1.29 sec
1. Tiso computed for a deck weight of 65 kips applied uniformly to four bearings.
2. Assumed theoretical initial stiffness for friction device.
3. LR bearing properties at γ = 200%, see Table 3-1.
4. HDR bearing properties at γ = 250%, see Table 3-1.
Figure 4-6 Test data for FP type 2 and 4 vs. nonlinear spectra for Cyiso = 0.09, ground motions at highest span settings.
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Tsub
(sec)
Cdeck
(g
)
143
Table 4-3 Influence of isolation system on Configuration 1 bridge model response
Response Displacement (in.) Base shear (g)
Bearing Type FP,type 1
FP,type 2 LRB HDR FP,
type 1FP,
type 2 LRB HDRH
alf a
mpl
itude
LA13 0.969 2.082 2.052 0.122 0.198 0.237NF01 0.885 1.724 1.733 0.126 0.181 0.190NF02 0.552 0.919 0.114 0.120
NF01_02c 1.361 1.792 0.138 0.198LS17c 0.176 1.448 2.019 0.126 0.161 0.193LS18c 0.063 0.791 0.106 0.105
LS17c_18c 0.247 2.177 0.125 0.197
Full
ampl
itude
NF01 3.500 3.521 0.229 0.423NF02 2.635 2.633 0.193 0.268
NF01_02c 4.560 3.817 0.276 0.497LS17c 2.051 1.729 4.176 0.149 0.161 0.498LS18c 0.662 1.482 0.129 0.163
LS17c_18c 1.672 4.288 0.149 0.480nfpulse1x 6.536 6.001 0.287 0.283
nfpulse0667 2.161 1.469 0.140 0.148nfpulse1_0667 6.862 6.370 0.289 0.290
nfpulse1x 6.496 5.836 0.287 0.285nfpulse1y 0.621 0.121 0.087 0.103
nfpulse1_1 6.389 5.725 0.268 0.269
nfpulse1x 6.372 5.809 0.285 0.286nfpulse15 0.033 0.063 0.059 0.080
nfpulse1_15 6.229 5.749 0.282 0.282nfpulse2_1333 3.696 2.386 4.148 0.216 0.181 0.310
nfpulse2_2 2.497 1.198 3.159 0.164 0.139 0.264
nfpulse2_3 2.605 1.01 3.294 0.172 0.143 0.274
144
relatively insignificant effect on isolator shear force response. Due to the low second-
slope stiffness of these devices, this is to be expected since increased isolator displacement
results in only minor increases in force output.
Table 4-4 Influence of isolation system on response of Configuration 5 bridge deck model, braced, Tsub = 0.25 seconds (nominal)
Response Displacement (in.) Isolator total shear force (kips)
Bearing Type FP, type 3 FP, type 4 ratio FP, type 3 FP, type 4 ratio
Hal
f am
plitu
de
LA13 1.118 0.986 1.134 6.515 8.223 0.792LA14 1.206 1.535 0.786 7.179 9.091 0.790
LA13_14 1.513 2.039 0.742 7.182 9.092 0.790NF01 1.398 1.247 1.121 7.904 8.461 0.934NF02 0.880 0.640 1.375 7.432 7.562 0.983
NF01_02c 1.826 1.659 1.101 7.435 7.566 0.983LS17c 0.484 0.424 1.142 7.702 8.131 0.947LS18c 0.210 0.186 1.134 7.190 7.492 0.960
LS17c_18c 0.415 0.429 0.967 7.191 7.500 0.959
mean = 1.056 1.002
C.O.V. = 0.186 0.083
Full
ampl
itude
LA13 3.363 2.795 1.203 12.434 11.915 1.044LA14 4.442 3.929 1.130 14.820 14.779 1.003
LA13_14 5.001 4.481 1.116 14.836 14.813 1.002NF01 4.314 4.056 1.064 15.784 16.179 0.976NF02 3.355 2.811 1.193 12.666 12.309 1.029
NF01_02c 5.363 5.035 1.065 12.672 12.321 1.028
LS17c 2.325 2.178 1.068 10.510 10.776 0.975
LS18c 0.961 0.898 1.070 7.897 8.574 0.921LS17c_18c 2.401 2.162 1.110 7.899 8.575 0.921
mean = 1.113 0.989
C.O.V. = 0.049 0.045
145
These results compare closely with those of preliminary analyses reported in Section
2.3.5.3. These preliminary analyses indicated that systems with 10 percent or less of the
total mass lumped in the substructure, exhibit approximately 90 percent or more of the
Table 4-5 Influence of isolation system on response of Configuration 5 bridge deck model, Tsub = 0.8 and 1.0 seconds (nominal) in x- and y-direction, respectively.
Response Displacement (in.) Isolator total shear force (kips)
Bearing Type FP, type 3 FP, type 4 ratio FP, type 3 FP, type 4 ratio
Hal
f am
plitu
de
LA13 2.067 2.332 0.886 8.660 9.924 0.873LA14 2.693 2.503 1.076 10.168 10.813 0.940
LA13_14 2.865 2.684 1.067 10.171 10.816 0.940NF01 2.178 2.071 1.051 9.066 10.452 0.867NF02 1.801 1.584 1.137 8.070 8.971 0.900
NF01_02c 2.669 2.595 1.029 8.072 8.971 0.900LS17c 2.0319 2.050 0.991 8.0004 10.191 0.785LS18c 0.582 0.594 0.980 3.222 3.438 0.937
LS17c_18c 2.042 2.137 0.956 3.222 3.438 0.937
mean = 1.019 0.898
C.O.V. = 0.073 0.057
Full
ampl
itude
LA13 4.322 4.048 1.068 12.820 13.119 0.977LA14 6.623 6.454 1.026 16.735 16.870 0.992
LA13_14 6.947 6.701 1.037 16.742 16.875 0.992NF01 5.472 5.218 1.049 15.387 15.652 0.983NF02 5.994 4.679 1.281 15.460 13.535 1.142
NF01_02c 7.945 6.606 1.203 15.472 13.552 1.142
LS17c 3.294 3.513 0.937 11.688 12.781 0.914
LS18c 1.167 1.175 0.993 6.502 6.921 0.939LS17c_18c 3.395 3.410 0.995 6.505 6.922 0.940
mean = 1.065 1.002
C.O.V. = 0.102 0.083
146
(a) FPS, type 2 bearings: LA13 (b) FPS, type 2 bearings: LS17c
(c) LRB bearings: LA13 (d) LRB bearings: LS17c
(e) HDR bearings: LA13 (f) HDR bearings: LS17c
Figure 4-7 Test data for bearing hysteresis, ground motions at highest span settings.
−2 −1 0 1 2−15
−10
−5
0
5
10
15
X − Displ. (in.)
X −
She
ar (
kips
)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
deck isolator D elastic, 5% damping
−2 −1 0 1 2
−10
−5
0
5
10
X − Displ. (in.)
X −
She
ar (
kips
)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
−2 −1 0 1 2−15
−10
−5
0
5
10
15
X − Displ. (in.)
X −
She
ar (
kips
)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
−2 −1 0 1 2
−10
−5
0
5
10
X − Displ. (in.)
X −
She
ar (
kips
)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
−2 −1 0 1 2−15
−10
−5
0
5
10
15
X − Displ. (in.)
X −
She
ar (
kips
)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Tsub
(sec)
Dis
p. (
in)
−2 −1 0 1 2
−10
−5
0
5
10
X − Displ. (in.)
X −
She
ar (
kips
)
147
global deck level peak displacement as a lumped mass (single-degree-of-freedom)
representation of the same system. This test substantiates these previous findings. More
comprehensive studies examining the effect of substructure mass on system response are
developed subsequently in Chapter 5.
4.5 Influence of Bi-directional Motions
Tests on the various configurations of the bridge deck model allowed for the evaluation of
the effect of bi-directional motions on the response of isolated bridge systems. All
configurations were tested using both the uni-directional components of each ground
motion input as well as their bi-directional pairs.
The effect of bi-directional input was evaluated by computing the following two ratios:
(15)
where Uxy is the peak vectored displacement response to the bi-directional pair and Ux and
Uy are the peak displacement responses to the individual uni-directional input of the
ground motion applied separately on the x- and y- direction, respectively; and
Table 4-6 Configuration 5: substructure mass, PTFE slider, and bracing arrangements
γ PTFE slider Cross-bracing x-direction, Tsub y-direction, Tsub
0 type 4 No .75 sec 1 sec
.05 type 4 Yes 0.25 sec .25 sec
.05 type 4 No .75 sec 1 sec
.05 type 3 Yes 0.25 sec .25 sec
.05 type 3 No .75 sec 1 sec
.10 type 4 No .75 sec 1 sec
Uxy mean Ux Uy,( )⁄
148
(a) LA13_14, half amplitude (b) LA13_14, full amplitude
(c) NF01_02, half amplitude (d) NF01_02, full amplitude
(e) LS17c_18c, half amplitude (f) LS17c_18c, full amplitude
Figure 4-8 Total displacement (U), test data for FP type 4, ground motions at half and full amplitude
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
2.5
3
msub
/Mdeck
U (
in) x−direction
y−direction xy−direction
0 0.02 0.04 0.06 0.08 0.10
2
4
6
8
msub
/Mdeck
U (
in)
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
2.5
3
msub
/Mdeck
U (
in)
0 0.02 0.04 0.06 0.08 0.10
2
4
6
8
msub
/Mdeck
U (
in)
x−direction y−direction xy−direction
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
2.5
3
msub
/Mdeck
U (
in)
0 0.02 0.04 0.06 0.08 0.10
2
4
6
8
msub
/Mdeck
U (
in)
149
(16)
where srss(Ux,Uy) is the SRSS (i.e., square root of the sum of the squares) combination of
Ux and Uy.
Results of these ratios are tabulated in Tables 4-7 through 4-11 below for the various
specimen configurations for systems with HDR and FP bearings. Nominal periods T0, T1,
T2, T3, and T4 represent “initial” or non-isolated specimen periods (i.e., Tsub, see Equation
3) for the Configuration 1 through 7 specimen arrangements. Nominal values were
computed utilizing substructure component stiffness characterization data (see Table 3-7).
These results indicate that the bi-directional coefficient ratios appear to generally decrease
as substructure flexibility increases, indicating that the effect of bi-directional input is
most pronounced for systems with the most rigid initial stiffnesses (see Figure 4-12). The
Uxy/mean(Ux,Uy) and Uxy/srss(Ux,Uy) coefficients cover the range of 1.4-1.8 and 0.9-1.2
(g) Mean values, half amplitude (h) Mean values, full amplitude
Figure 4-8 Total displacement (U), test data for FP type 4, ground motions at half and full amplitude
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
2.5
3
msub
/Mdeck
U (
in)
0 0.02 0.04 0.06 0.08 0.10
2
4
6
8
msub
/Mdeck
U (
in)
Uxy srss Ux Uy,( )⁄
150
(a) LA13_14, half amplitude (b) LA13_14, full amplitude
(c) NF01_02, half amplitude (d) NF01_02, full amplitude
(e) LS17c_18c, half amplitude (f) LS17c_18c, full amplitudeFigure 4-9 Isolator displacement (Uiso), test data for FP type 4, ground motions at half and full amplitude.
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
msub
/Mdeck
Uis
o (in
)
x−direction y−direction xy−direction
0 0.02 0.04 0.06 0.08 0.10
1
2
3
4
5
msub
/Mdeck
Uis
o (in
)
x−direction y−direction xy−direction
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
msub
/Mdeck
Uis
o (in
)
0 0.02 0.04 0.06 0.08 0.10
1
2
3
4
5
msub
/Mdeck
Uis
o (in
)
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
msub
/Mdeck
Uis
o (in
)
0 0.02 0.04 0.06 0.08 0.10
1
2
3
4
5
msub
/Mdeck
Uis
o (in
)
151
on average, respectively, for systems with the most rigid substructures. In comparison, if
the peak response Ux and Uy were equal, a value of Uxy/mean(Ux,Uy) = 1.414 and Uxy/
srss(Ux,Uy) = 1.0 would indicate that the peak Ux and Uy displacements were occurring
simultaneously in the bi-directional response, leading to a peak Uxy equal to their vector
sum. Further in-depth studies, carried out to better establish these effects over a broader
range of ground motion inputs and bridge configurations, are presented subsequently in
Chapter 5.
4.6 Influence of Substructure Strength
Configuration 9 of the bridge deck specimen provided for an evaluation of the effect of
yielding substructure components on the response of an isolated bridge system. This
configuration utilized FP bearings with type 5 PTFE composite sliders installed on braced
end piers (abutment ends) and type 4 PTFE composite sliders installed on center, yielding
piers (see Section 3.14 for PTFE slider characterization results). Force-displacement
(g) Mean values, half amplitude (h) Mean values, full amplitudeFigure 4-9 Isolator displacement (Uiso), test data for FP type 4, ground motions at half and full amplitude.
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
msub
/Mdeck
Uis
o (in
)
0 0.02 0.04 0.06 0.08 0.10
1
2
3
4
5
msub
/Mdeck
Uis
o (in
)
152
(a) LA13_14, half amplitude (b) LA13_14, full amplitude
(c) NF01_02, half amplitude (d) NF01_02, full amplitude
(e) LS17c_18c, half amplitude (f) LS17c_18c, full amplitudeFigure 4-10 Substructure displacement (Usub), test data for FP type 4, ground motions at half and full amplitude.
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
msub
/Mdeck
Usu
b (in
)
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
2.5
3
msub
/Mdeck
Usu
b (in
)
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
msub
/Mdeck
Usu
b (in
)
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
2.5
3
msub
/Mdeck
Usu
b (in
)
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
msub
/Mdeck
Usu
b (in
)
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
2.5
3
msub
/Mdeck
Usu
b (in
)
153
characterizations of the high-strength end piers and yielding central piers may be
referenced from Configuration 10 test results (see Section 3.13). Axial load on the
specimen was balanced such that approximately 5/8th’s of the vertical deck weight was
supported on central piers (consistent with the load distribution of a continuous two-span
girder) to attract shear force and induce yielding in central piers. Tests with both uni-
directional and bi-directional inputs of the three earthquake table motions (i.e., LA13_14,
NF01_02, and LS17c_18c) were performed.
Representative results from these tests for global and component hysteretic response are
plotted in Figure 4-13 and 4-14 below. These plots show a pattern of force redistribution
as central piers yield and shear is transferred to outer (non-yielding) end piers. As seen in
these plots, bearing hysteresis at end piers (i.e., quadrant Q1) stiffens near peak negative
displacement indicating increase in load. Meanwhile, pier hysteresis at quadrant Q1
remains essentially linear elastic and pier hysteresis at Pier 5 (a.k.a., Q5) shows plastic
(g) Mean values, half amplitude (h) Mean values, full amplitudeFigure 4-10 Substructure displacement (Usub), test data for FP type 4, ground motions at half and full amplitude.
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
msub
/Mdeck
Usu
b (in
)
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
2.5
3
msub
/Mdeck
Usu
b (in
)
154
(a) LA13_14, half amplitude (b) LA13_14, full amplitude
(c) NF01_02, half amplitude (d) NF01_02, full amplitude
(e) LS17c_18c, half amplitude (f) LS17c_18c, full amplitudeFigure 4-11 Isolator shear force (V), test data for FP type 4, ground motions at half and full amplitude
0 0.02 0.04 0.06 0.08 0.10
2
4
6
8
10
12
msub
/Mdeck
V (
kips
) x−direction y−direction xy−direction
0 0.02 0.04 0.06 0.08 0.10
5
10
15
20
msub
/Mdeck
V (
kips
)
x−direction y−direction xy−direction
0 0.02 0.04 0.06 0.08 0.10
2
4
6
8
10
12
msub
/Mdeck
V (
kips
)
0 0.02 0.04 0.06 0.08 0.10
5
10
15
20
msub
/Mdeck
V (
kips
)
0 0.02 0.04 0.06 0.08 0.10
2
4
6
8
10
12
msub
/Mdeck
V (
kips
)
0 0.02 0.04 0.06 0.08 0.10
5
10
15
20
msub
/Mdeck
V (
kips
)
155
yielding in the negative cycle (indicated by widening of the hysteretic loop). Despite this
yielding behavior, total deck displacement history remains stable as seen in the
accompanying time-histories (see Figure 4-13 and 4-14 (b)). This indicates that isolated
(g) Mean values, half amplitude (h) Mean values, full amplitude
Table 4-7 Uxy/mean(Ux,Uy) coefficients, FP type 2 and 4, ground motions at half and full amplitude
PTFE composite type 2 type 4 type 4 type 4 type 4
Tsub, x-direc-tion 0 sec 0.25 sec 0.75 sec 0.75 sec 0.25 sec
Tsub, y-direc-tion 0 sec 0.25 sec 0.75 sec 1.0 sec 0.25 sec
Hal
f am
plitu
de LA13_14 1.490 1.618 1.056 1.110 1.110NF01_02 1.894 1.758 1.512 1.420 1.609LS17_18c 2.058 1.407 1.473 1.617 1.329Average 1.814 1.594 1.347 1.382 1.349
Full
ampl
itude LA13_14 1.378 1.333 1.236 1.276 1.215
NF01_02 1.486 1.467 1.453 1.335 1.438
LS17_18c 1.399 1.406 1.358 1.455 1.645Average 1.421 1.402 1.349 1.355 1.433
Figure 4-11 Isolator shear force (V), test data for FP type 4, ground motions at half and full amplitude
0 0.02 0.04 0.06 0.08 0.10
2
4
6
8
10
12
msub
/Mdeck
V (
kips
)
0 0.02 0.04 0.06 0.08 0.10
5
10
15
20
msub
/Mdeck
V (
kips
)
156
Table 4-8 Uxy/mean(Ux,Uy) coefficients, FP type 3 and 5, ground motions at half and full amplitude
PTFE composite type 3 type 5 type 5 type 5 type 5
Tsub, x-direc-tion
T0 = 0 sec T1 = 0.25 sec T2 = 0.8 sec T2 = 0.8 sec T4 = 0.30 sec
Tsub, y-direc-tion
T0 = 0 sec T1 = 0.25 sec T2 = 0.8 sec T3 = 1.0 sec T4 = 0.30 sec
Hal
f am
plitu
de LA13_14 1.302 1.204 1.078NF01_02 1.603 1.342LS17_18c 1.194 0.650 1.405Average 1.366 1.065 1.242
Full
ampl
itude LA13_14 1.282 1.269 1.238
NF01_02 1.399 1.386 1.404LS17_18c 1.461 1.522 1.590Average 1.380 1.392 1.411
Table 4-9 Uxy/srss(Ux,Uy) coefficients, FP type 2 and 4, ground motions at half and full amplitude
PTFE composite type 2 type 4 type 4 type 4 type 4
Tsub, x-direc-tion
T0 = 0 sec T1 = 0.25 sec T2 = 0.8 sec T2 = 0.8 sec T4 = 0.30 sec
Tsub, y-direc-tion
T0 = 0 sec T1 = 0.25 sec T2 = 0.8 sec T3 = 1.0 sec T4 = 0.30 sec
Hal
f am
plitu
de LA13_14 1.044 1.118 0.745 0.785 0.785NF01_02 1.305 1.183 1.048 0.995 1.115
LS17_18c 1.317 0.927 0.935 1.001 0.874
Average 1.222 1.076 0.910 0.927 0.925
Full
ampl
itude LA13_14 0.971 0.929 0.869 0.880 0.852
NF01_02 1.041 1.020 1.009 0.943 1.002
LS17_18c 0.903 0.918 0.891 0.921 1.031Average 0.972 0.956 0.923 0.914 0.962
157
performance is maintained, despite the yielding substructure contribution. In this isolated
system, isolation bearings absorb the majority of total displacement demand up to yielding
in the substructure. Beyond this point, central piers yield plastically until peak
displacement is attained. As such, only minor ductility demands are imposed on the
substructure. For a non-isolated system, nearly the entire displacement demand would be
Table 4-10 Uxy/srss(Ux,Uy) coefficients, FP type 3 and 5, ground motions at half-amplitude
PTFE composite type 3 type 5 type 5 type 5 type 5
Tsub, x-direc-tion
T0 = 0 sec T1 = 0.25 sec T2 = 0.8 sec T2 = 0.8 sec T4 = 0.30 sec
Tsub, y-direc-tion
T0 = 0 sec T1 = 0.25 sec T2 = 0.8 sec T3 = 1.0 sec T4 = 0.30 sec
Hal
f am
plitu
de LA13_14 0.920 0.844 0.762NF01_02 1.105 0.944LS17_18c 0.786 0.356 0.951Average 0.937 0.715 0.857
Full
ampl
itude LA13_14 0.898 0.878 0.868
NF01_02 0.982 0.979 0.983LS17_18c 0.954 0.972 0.981Average 0.944 0.943 0.944
Table 4-11 Uxy/mean(Ux,Uy) and Uxy/srss(Ux,Uy) coefficients, HDR, x-direction Tsub = y-direction Tsub = T0 = 0 sec
Uxy/mean(Ux,Uy) Uxy/srss(Ux,Uy)
Amplitude half full half full
Reco
rd
LA13_14 1.392 .979NF01_02 1.351 1.241 .913 .868
LS17_18c 1.550 1.516 1.004 .968
Average 1.431 1.378 .966 .918
158
(a) Uxy/mean(Ux,Uy): LA13_14 (b) Uxy/srss(Ux,Uy): LA13_14
(c) Uxy/mean(Ux,Uy): NF01_02 (d) Uxy/srss(Ux,Uy): NF01_02
(e) Uxy/mean(Ux,Uy): LS17c_18c (f) Uxy/srss(Ux,Uy): LS17c_18cFigure 4-12 Bi-directional coefficients computed from test data, FP type 2 and 4, ground motions at full amplitude.
0 0.2 0.4 0.6 0.81
1.1
1.2
1.3
1.4
1.5
Tsub
(sec)
Uxy
/mea
n(U
x,Uy)
0 0.2 0.4 0.6 0.80.85
0.9
0.95
1
1.05
Tsub
(sec)
Uxy
/srs
s(U
x,Uy)
0 0.2 0.4 0.6 0.81
1.1
1.2
1.3
1.4
1.5
Tsub
(sec)
Uxy
/mea
n(U
x,Uy)
0 0.2 0.4 0.6 0.80.85
0.9
0.95
1
1.05
Tsub
(sec)
Uxy
/srs
s(U
x,Uy)
0 0.2 0.4 0.6 0.81
1.1
1.2
1.3
1.4
1.5
Tsub
(sec)
Uxy
/mea
n(U
x,Uy)
0 0.2 0.4 0.6 0.80.85
0.9
0.95
1
1.05
Tsub
(sec)
Uxy
/srs
s(U
x,Uy)
159
imposed on the substructure elements, inducing significantly larger ductility demands on
these components.
Figure 4-15 illustrates the character of the force redistribution seen in these tests. This
redistribution may be visualized clearly for a static application of lateral force to a
representative isolated, elasto-perfectly-plastic, bridge pier assembly. As shown in the
figure, as load is increased to the level of yielding in the substructure pier, no further load
can be developed in the system at increasing displacement (due to the elastic-perfectly-
plastic pier response). As such, isolator displacement ceases to increase. With moderate
hardening in the yielding substructure component (i.e., α>0), a moderate increase in force
and isolation system displacement would be realized during plastic yielding of the
substructure bent (see Figure 4-15). In a system with additional redundant components (of
higher strength), additional force increases will be developed through redistribution to
these elements. Pseudo-static tests performed by Kawashima, et al [Kawashima and Shoji,
1999] validate this type of redistributive behavior. Under dynamic loading, this behavior
(g) Uxy/mean(Ux,Uy): Mean values (h) Uxy/srss(Ux,Uy): Mean valuesFigure 4-12 Bi-directional coefficients computed from test data, FP type 2 and 4, ground motions at full amplitude.
0 0.2 0.4 0.6 0.81
1.1
1.2
1.3
1.4
1.5
Tsub
(sec)
Uxy
/mea
n(U
x,Uy)
0 0.2 0.4 0.6 0.80.85
0.9
0.95
1
1.05
Tsub
(sec)
Uxy
/srs
s(U
x,Uy)
160
is further complicated by damping, higher mode contributions, axial load redistributions,
and bi-directional interactions. However, as seen in these test results, the nature of this
redistributive mechanism maintains a similar character in the dynamic response as well.
(a) Global system hysteresis (b) Global displacement history
(c) Q1 global hysteresis (d) Q5 global hysteresisFigure 4-13 Configuration 9, Test No. 23, LA13_14, Span Setting [870/0/0]
−6 −4 −2 0 2 4 6
−20
−10
0
10
20
Disp. (in)
She
ar (
kips
)
10 15 20 25
−6
−4
−2
0
2
4
6
time (sec)D
isp.
(in
)
−5 0 5
−4
−2
0
2
4
Disp. (in)
She
ar (
kips
)
−5 0 5
−4
−2
0
2
4
Disp. (in)
She
ar (
kips
)
161
4.7 Influence of Superstructure Mass Eccentricity
Configuration 2 of the bridge deck model allowed the evaluation of the effect of
superstructure mass eccentricity on the response of an isolated bridge overcrossing
(supported on an essentially rigid supporting substructure). This configuration utilized
both FP and LR bearings. Only x- direction uni-directional components of the table
motions (i.e., LA13, NF01, and LS17c) were imposed orthogonal to the direction of mass
(e) Q1 bearing hysteresis (f) Q5 bearing hysteresis
(g) Q1 pier hysteresis (h) Q5 pier hysteresisFigure 4-13 Configuration 9, Test No. 23, LA13_14, Span Setting [870/0/0]
−5 0 5
−4
−2
0
2
4
Disp. (in.)
She
ar (
kips
)
−5 0 5
−4
−2
0
2
4
Disp. (in)
She
ar (
kips
)
−5 0 5
−4
−2
0
2
4
Disp. (in)
She
ar (
kips
)
−5 0 5
−4
−2
0
2
4
Disp. (in.)
She
ar (
kips
)
162
(a) Global system hysteresis (b) Total displacement time-history
(c) Q1 global hysteresis (d) Q5 global hysteresis
(e) Q1 bearing hysteresis (f) Q5 bearing hysteresis
Figure 4-14 Configuration 9, Test No. 24, LA13_14, Span Setting [1000/0/0]
−5 0 5
−20
−10
0
10
20
Disp. (in)
She
ar (
kips
)
5 10 15 20 25−5
0
5
time (sec)
Dis
p. (
in)
−5 0 5−5
0
5
Disp. (in)
She
ar (
kips
)
−5 0 5−5
0
5
Disp. (in)
She
ar (
kips
)
−5 0 5−5
0
5
Disp. (in.)
She
ar (
kips
)
−5 0 5−5
0
5
Disp. (in)
She
ar (
kips
)
163
eccentricity. In order to avoid excessive damage to or permanent displacement of the LR
bearings, displacement amplitudes were limited to half that imposed on the FP bearings.
Table 4-12 below lists results from these tests. Results tabulated are the normalized
isolator displacement ratio, De/Do, a comparative measure between the peak isolator
displacement of a system with and without given mass eccentricity, e (i.e., De and Do,
respectively). These limited test results appear to indicate that torsional contributions to
peak isolator displacement (located at the ends of the deck span) are more prominent for
impulsive and soft-soil type motions than for far-field events (compare NF01 and LS17c
to LA13 results in Table 4-12). Further, the effect of mass eccentricity on peak isolator
response appears to be nonlinear (i.e., isolator displacements at the ends of the span do
not, in general, increase linearly with mass eccentricity).
Previous evaluations by others on isolated systems suggest FP bearings provide a re-
centering mechanism [Bozzo, et al 1989]. The friction force and lateral stiffness of an FP
(g) Q1 pier hysteresis (h) Q5 pier hysteresis
Figure 4-14 Configuration 9, Test No. 24, LA13_14, Span Setting [1000/0/0]
−5 0 5−5
0
5
Disp. (in)
She
ar (
kips
)
−5 0 5−5
0
5
Disp. (in.)
She
ar (
kips
)
164
(a) Isolated bridge deck (b) Idealized dynamic model
(c) Substructure force-displacement (d) Isolator force-displacement
(e) Total system force-displacement response at deck
Figure 4-15 Force redistribution in isolated bridge substructure assembly
di
dsub
d
Substructure bent
Isolation bearings
F
Mdeck
d
kukd
mpier
Csub
dsub
di
KsubαKsub
Qd/(1-kd/ku)Fysub
bent isolator
F
Displ.
Ksub
αKsubα=0
dysubdsub
Fysub
F’
F
Displ.
kd
dyiso di’
Fysub
Qd/(1-kd/ku)
di
F’
ku
α>0
F
K2
Fysub
Qd/(1-kd/ku)
dysub+di
F’
K1
α=oα>0
dsub+di dsub+di’ Displ.
165
bearing is proportional to the applied normal force (see Chapter 3, Equation 14). This
indicates that the center of resistance of an isolated system utilizing FP bearings will
inherently align with the systems center of mass, counteracting torsional response.
Analysis and testing in these previous studies confirmed this behavior [Bozzo et al, 1989].
The tests performed in this report using impulsive motions, however, seem to refute this
generalization. This may be due to the sensitivity of “rigid” structures to strength (see
Section 2.3.5.2 and 4.3 above). The lighter end of the specimen (which has a lower overall
friction force) may tend to displace more than the heavier (i.e., stronger) side producing
the torsional behavior seen here. Comparable results for full intensity motions are not
available for the LR bearings (whose strength is not sensitive to axial applied force) to test
this assumption. In this respect, further analysis and testing is still needed to establish
reliable trends in the response of these eccentric systems.
4.8 Influence of Substructure Stiffness Eccentricity
Configuration 6 and 8 of the bridge deck model allowed the evaluation of the effect of
substructure stiffness eccentricity on the response of an isolated bridge overcrossing.
Configuration 6 (an eccentric version of the Configuration 5 specimen) utilized FP
bearings with two arrangements of PTFE sliders: (1) a symmetric arrangement using type
Table 4-12 Effect of superstructure mass eccentricity on peak isolator displacement: isolator displacement ratio, De/Do
FP bearings (100% motions) LR bearings (50% motions)
Ground Motion e/L =0.05 e/L =0.10 e/L =0.05 e/L =0.10
LA13 1.03 1.18 0.94 1.15
NF01 1.17 1.24 1.21 1.16
LS17c 1.48 1.47 1.34 1.26
166
3 sliders uniformly; and (2) an unsymmetric arrangement arranged to counteract torsional
response (with type 3 sliders on stiffer braced end piers and type 4 sliders on flexible end
piers). Configuration 8 (an eccentric version of the Configuration 7 specimen) utilized FP
type 5 sliders uniformly. Each of these configurations was tested with both uni-directional
components and bi-directional motion pairs of the three earthquake table motions (i.e.,
LA13_14, NF01_02, and LS17c_18c).
Table 4-13 and 4-14 lists results from these tests. Results tabulated are for motion input at
peak amplitudes only. These limited results indicate that peak rotation demand in these
eccentric configurations was not a function of peak displacement amplitude, nor was it
effected significantly by bi-directional input. First of all, stiffness eccentricity in the
supporting substructure is significant in these configurations with the braced and unbraced
ends of the specimen differing in total lateral stiffness by nearly ten times. Prior to
yielding in the isolation bearings, this stiffness eccentricity induces significant torsional
response. After isolation bearings yield, stiffness eccentricity is minimal as the bearings
operate in their isolated mode on either end of the specimen. The rotation response in
these eccentric configurations is therefore due to the tendency of the system to rotate prior
to yielding in the bearings. After bearings have yielded, stiffness eccentricity is nearly
eliminated and rotation demands become insensitive to peak response. Thus, isolated
behavior suppresses torsional behavior to an extent, unlike in a standard bridge where
substructure stiffness eccentricity would impose torsional demands increasing with
response amplitude. Secondly, the orthogonal input motion in these tests imposes loading
on the longitudinal axis of the specimen where the stiffness arrangement is symmetric.
This motion input does not engage lateral-torsional coupling in the system and therefore
167
does not tend to increase rotation demands. Coupling in the yield response of the isolation
bearings imposed by the bi-directional input does not appear to effect peak rotation
significantly either, as torsional response in these systems appears to be more effected by
behavior prior to bearing yield, as just discussed.
Comparing response of the single-span specimen with and without substructure stiffness
eccentricity (i.e., Configuration 5 vs. Configuration 6, see Table 4-13), it was seen for the
case of symmetric bearing strength (i.e., type 3 FP sliders installed uniformly) that
substructure stiffness eccentricity (in the Configuration 6 specimen) tended to increase
isolator response at the ends of the specimen above both the fully braced and unbraced
Configuration 5 arrangements in all instances. This would indicate that torsional rotation
was closely phased with peak response in these test sequences, amplifying local bearing
displacement demands. An unsymmetric configuration utilizing lower and higher strength
PTFE slider composites installed in bearings located above braced and unbraced supports,
respectively, was utilized in the Configuration 6 arrangements successfully to reduce
torsional response. This result was contrary to preliminary analysis in Chapter 2 which
indicated that this type of unsymmetric arrangement of bearing strength would not
significantly reduce torsional response due to substructure stiffness eccentricity (see
Section 2.3.5.4).
Comparing response of the double-span specimen with and without substructure stiffness
eccentricity (i.e., Configuration 7 vs. Configuration 8, see Table 4-14), results indicated
that torsional response tended to increase peak total displacement response above the
Configuration 7 arrangement in all cases. Peak isolator displacement response was not as
168
systematically effected, however (sometimes increasing and sometimes decreasing),
indicating that torsional rotation was not systematically in phase with peak response in
these test sequences.
See also the results of preliminary evaluations in Chapter 2 which showed other notable
response trends due to variations in substructure stiffness eccentricity (see Section
2.3.5.4).
Table 4-13 Comparison of peak response for Configuration 5 and 6
Configuration 5 (e/L = 0) Configuration 6 (e/L = .09)
braced unbraced FP, type 3 FP, type 3 and 4
Record d di d di d di θ (rads) d di θ (rads)
LA13 3.36 3.30 4.32 3.80 4.37 4.42 .0062 4.34 4.32 .0054
NF01 4.31 4.21 5.47 4.73 5.71 5.42 .0062 5.17 4.91 .0044
LS17c 2.33 2.26 3.29 2.75 3.93 3.76 .0089 3.76 3.65 .0064
LA13_14 4.52 3.55 6.66 4.79 5.14 4.80 0.0081 5.05 4.66 0.0036
NF01_02 4.48 4.87 7.27 6.92 5.49 7.42 0.0078 5.17 6.78 0.0051
LS17c_18c 2.40 2.50 3.38 4.11 3.21 4.68 0.0078 3.27 4.56 0.0046
Table 4-14 Comparison of peak response for Configuration 7 and 8
Configuration 7 (e/L = 0) Configuration 8 (e/L = 0.10)
FP, type 5 FP, type 5
Record d di d di θ (rads)
LA13 3.49 3.37 4.01 3.38 0.0100
NF01 4.50 4.52 5.32 4.56 0.0109
LS17c 2.72 2.74 3.13 2.78 0.0119
LA13_14 4.66 3.30 5.37 3.05 0.0103
NF01_02 4.63 4.69 6.10 4.94 0.0110
LS17c_18c 2.76 2.85 3.05 2.75 0.0121
169
4.9 Response of Two-span Isolated Bridge
4.9.1 Introduction
Configuration 7 of the specimen provided for testing of a continuous double-span isolated
bridge overcrossing. This configuration utilized FP bearings with several different
arrangements of PTFE sliders. However, bearing characterization tests show that the type
4 and 5 slider composites used exhibited similar friction values during these tests (see
Section 3.14). Consequently, the effect of different slider configurations on system
response characteristics was minimal. In this configuration, the bridge deck girder
spanned continuously between braced end pier supports (abutments) and central pier
components (see Section 3.1.5). The double-span configuration was tested with both uni-
directional and bi-directional components of the LA13_14, NF01_02, and LS17c_18c
earthquake table motions.
Several noteworthy features in system response were identified from test data. These
features included a characteristic distribution of overall displacement and force demand
between local substructure and isolation bearing components. Also, local kinematic
effects in the response of the specimen’s supporting central bridge piers resulted in
variations in axial load distributions which effected overall response characteristics.
4.9.2 Characteristic distribution of force and displacement demands
Figure 4-16 and 4-17 show typical test sequence results of global and local force and
displacement response of the Configuration 7 specimen. The results in Figures 4-16 and 4-
17 (a) and (b) indicate how displacements at the end and center supports are distributed
between isolator and substructure elements. Part (c) through (h) of these figures illustrate
170
these the local hysteretic response of each isolator at these locations. As seen in the plots,
shear demands tend to concentrate toward the stiffer end (abutment) piers during the time-
history (compare Figure 4-16 (c) to (d), for example). We note that center pier-isolator
assemblies see similar total displacement demands as end pier-isolator assemblies as
displacement compatibility is enforced by the high in-plane stiffness of the bridge deck as
it displaces laterally. Therefore, since the secant stiffness of the central pier-isolator
assemblies at peak displacement is lower than at the end (abutment) pier-isolator
assemblies (for all arrangements of slider compounds used), higher shear demands
concentrate at abutment locations. Further, the displacements in the isolator and pier
components are distributed in relation to the relative flexibilities of these elements at their
respective locations. Therefore, since each location sees nearly equal total displacement
demand, a smaller proportion of the total displacement at center piers is taken in the
isolation bearings with a larger proportion taken in the more flexible center piers
(compared to isolator and pier displacement distribution at stiffer end abutment piers).
4.9.3 Local geometric effects
In the Configuration 7 specimen, end (abutment) piers were braced while center piers
could rotate on the clevis pins at their base (see Chapter 3, Section 3.1.4). During
earthquake testing flexible center piers underwent significant lateral tip displacement
(essentially a rigid body rotation). This rotational behavior caused second-order reduction
of the vertical height of these central piers. On the other hand, the shorter and stiffer
braced end (abutment) piers did not experience this effect nearly as much. because of the
high out of plane stiffness of the specemin deck, shortening in center piers resulted in a
redistribution of axial load between the center and end piers that varied according to
171
(a) Q1, abutment displacement histories (b) Q5, pier displacement histories
(c) Q1 global hysteresis (d) Q5 global hysteresis
(e) Q1, bearing hysteresis (f) Q5, bearing hysteresisFigure 4-16 System displacement and axial load redistribution, Configuration 7, Test No.5, LA13_14, Span Setting [696/0/0]
8 9 10 11 12−5
0
5
time (sec)
Dis
p. (
in)
8 9 10 11 12−5
0
5
time (sec)
Dis
p. (
in)
global bearingpier
−2 0 2
−3
−2
−1
0
1
2
3
Disp. (in)
She
ar (
kips
)
−2 0 2
−3
−2
−1
0
1
2
3
Disp. (in)
She
ar (
kips
)
−2 0 2
−3
−2
−1
0
1
2
3
Disp. (in.)
She
ar (
kips
)
−2 0 2
−3
−2
−1
0
1
2
3
Disp. (in)
She
ar (
kips
)
172
lateral displacement. Representative axial force time-histories are shown in Figure 4-18
illustrating this effect for the LA13 motion (i.e., Test No.5, see also Figure 4-16). Figure 4-
18 (c) shows this variation in axial load by plotting the time-history of total axial load at
end and center piers, respectively, normalized by initial total load (P0). As seen in this
plot, as center piers unload (due to the axial shortening), axial load increases at abutment
piers, illustrating the load redistribution.
Since the slip-force an lateral stiffness of FP bearings are proportional to the supported
axial load (see Chapter 3, Equation 14), the axial force redistribution in these test
sequences causes a significant alteration of the characteristic force-deformation behavior
of the individual FP bearings atop the central piers. This behavior is seen clearly in the
hysteretic plots in Figure 4-16 (e) and (f) for this same test sequence. The hysteresis of
bearings at end piers (see Figure 4-16 (e)) are seen to “fatten” with increased lateral
displacement (due to increase in axial load), while the hysteresis of bearings at central
(g) Q1, substructure hysteresis (h) Q5, substructure hysteresisFigure 4-16 System displacement and axial load redistribution, Configuration 7, Test No.5, LA13_14, Span Setting [696/0/0]
−2 0 2
−3
−2
−1
0
1
2
3
Disp. (in)
She
ar (
kips
)
−2 0 2
−3
−2
−1
0
1
2
3
Disp. (in.)
She
ar (
kips
)
173
(a) Q1, abutment displacement histories (b) Q5, pier displacement histories
(c) Q1 global hysteresis (d) Q5 global hysteresis
(e) Q1, bearing hysteresis (f) Q5, bearing hysteresisFigure 4-17 System displacement and axial load redistribution, Configuration 7, Test No.11, NF01_02, Span Setting [804/0/0]
8 9 10 11 12−5
0
5
time (sec)
Dis
p. (
in)
8 9 10 11 12−5
0
5
time (sec)
Dis
p. (
in)
global bearingpier
−4 −2 0 2 4
−6
−4
−2
0
2
4
6
Disp. (in)
She
ar (
kips
)
−4 −2 0 2 4
−6
−4
−2
0
2
4
6
Disp. (in)
She
ar (
kips
)
−4 −2 0 2 4
−6
−4
−2
0
2
4
6
Disp. (in.)
She
ar (
kips
)
−4 −2 0 2 4
−6
−4
−2
0
2
4
6
Disp. (in)
She
ar (
kips
)
174
piers (see Figure 4-16 (f)) “narrow” and soften with increasing lateral displacement (due
to loss of axial load).
Globally, total axial force (due to gravity) remains constant. Therefore, total bearing slip-
force remains essentially constant and total system strength is unchanged. Locally, the
redistribution of axial force to the end piers tends to increase peak shear demands at these
locations, imposing higher design forces on associated connections and substructure
components.
If bearings at the center and end piers had different friction coefficients, the redistribution
of axial force would increase or reduce overall system strength somewhat. For systems
with small substructure periods, this strength variation could have a significant effect on
peak displacements. Further, redistribution of axial load to the stiffer end piers produces a
system with higher overall stiffness in its isolated mode (i.e., see K3 in Figure 2-3). The
(g) Q1, substructure hysteresis (h) Q5, substructure hysteresisFigure 4-17 System displacement and axial load redistribution, Configuration 7, Test No.11, NF01_02, Span Setting [804/0/0]
−4 −2 0 2 4
−6
−4
−2
0
2
4
6
Disp. (in)
She
ar (
kips
)
−4 −2 0 2 4
−6
−4
−2
0
2
4
6
Disp. (in.)
She
ar (
kips
)
175
effect of this higher might be to increase shear force demand and decrease peak
displacements.
It is important to note that this particular axial load redistribution phenomenon appears to
be more a characteristic of the unique test setup used in this case than that of an actual
bridge. Even for bridges with high out-of-plane stiffness, reinforced concrete piers would
be expected to elongate as they displace laterally due to the opening of flexural cracks. As
a consequence, these two second-order effects may have a tendency to cancel one another
out in an actual bridge. This is an area requiring further investigation.
However, these tests point out that kinematic effects may redistribute axial load acting on
the isolators. These effects may alter the distribution of local forces. These effects are not
typically incorporated in standard design analysis methods nor included in current design
procedures [AASHTO, 1999]. The effect of axial load fluctuations on sliding systems due
to vertical ground motion input is discussed further subsequently in this chapter.
4.10 Substitute system vs. MDOF response
Post test analyses of isolated bridge systems were carried out to compare the response
predicted by two simple, single-degree-of-freedom idealizations with measured response
of the multi-degree-of-freedom bridge specimen. The braced version of Configuration 5
( seconds) with substructure mass of was utilized for this comparison.
This specimen exhibited particularly consistent hysteretic behavior from test and was
therefore considered suitable for comparison with simple, single-degree-of-freedom
models.
Tsub 0.25≈ γ 0.05≈
176
Linear substructure stiffness properties were based upon characterization test data (see
Section 3.13). Friction properties of the FP isolation bearings were selected to closely
match characterization test data as well (see Section 3.14). First-slope bearing stiffness
(ku) was assumed essentially rigid. Second-slope stiffness (kd) was computed based upon
bearing radius of curvature (R) and an imposed normal force taken as the supported deck
weight (where kd = N/R, see Chapter 3, Equation 14). From these mechanical properties,
(a) Axial load history at abutments (b) Axial load history at center piers
(c) Axial load redistribution between center piers and abutments
Figure 4-18 System axial load redistribution, Configuration 7, Test No.5, LA13_14, Span Setting [696/0/0]
3 6 9 12−80
−70
−60
time (sec)
Axi
al (
kip
s)
3 6 9 12−40
−30
−20
time (sec)
Axi
al (
kip
s)
3 6 9 120.6
0.8
1
1.2
time (sec)
Axi
al/P
0 (ki
ps)
abutment pierscenter piers
177
an idealized bilinear system model was developed for transverse and longitudinal isolated
bridge behavior (see Chapter 2, Figure 2-2). For bi-directional response, isolator behavior
was modeled as a bilinear plasticity element utilizing a circular yield function while
substructure flexibility was assumed linear and uncoupled. On the other hand, the
linearized model was only utilized for uni-directional time-history analyses. Linearized
properties were taken as the secant stiffness of the bilinear model at peak displacement
and equivalent viscous damping determined by equating the hysteretic work done by the
bilinear system (assuming symmetric hysteretic response at peak displacement) to that of
a purely viscous damping element (see Chapter 5, Section 5.4.3). Analyses of the
“substitute” bilinear and linear spring-damper systems were carried out utilizing the
ground motion inputs taken from table records of Configuration 5 test sequences.
Nonlinear analysis was performed utilizing standard procedures [Newmark, 1959].
Linearized analysis was performed utilizing standard frequency domain integration and
required an iterative procedure to converge on system spring-damper properties consistent
with computed peak displacement.
Tables 4-15 through 4-17 present force and displacement response results from the
Configuration 5 tests and the substitute system analyses for three earthquake shake table
time-histories. Results presented are the peak total, isolator, and substructure displacement
(d, di, and dsub, respectively) and lateral force response coefficient (Cs). Total
displacement and lateral force response are computed directly from analysis for the SDF
models. Local bearing and substructure response was determined (for the SDF models) by
assuming a static application of peak force applied to the bilinear isolation bearing and
substructure components, respectively (utilizing component mechanical properties from
178
the original SDF model development). This step ignores substructure damping and higher
mode contributions to localized response, dynamic information which is not included in
either of the simplified SDF models.
Tables 4-18 and 4-19 compare substitute system analytical results to test specimen data by
normalizing analysis results by specimen data. Values greater than one in this table imply
the simplified models overestimate specimen response, while values less than one imply
they underestimate them. As seen in these results, the substitute linear SDF model tended
to provide a slightly better estimate in this study of peak displacement responses when
compared to the substitute bilinear system. The linear spring-damper model overestimated
peak total, isolator and substructure displacement response in this study by approximately
3, 1, and 33 percent on average, respectively, compared to the bilinear SDF model which
overestimated these responses by 8, 6, and 50 percent on average, respectively. With
regard to force, however, the bilinear model was more accurate in this study,
overestimating lateral force response by only nearly 4 percent on average, while the linear
model underestimated force by 12 percent on average. Regardless of mean accuracy,
however, the linear SDF model provided larger coefficients of variation on average
predictions compared to the bilinear SDF model in this study. This indicates that errors on
response using the substitute linear model were larger in this study for particular ground
motion records (when compared to the substitute bilinear system), despite being more
accurate on average. The nonlinear analysis procedure does not involve iteration and can
be easily applied to bidirectional input motion.
179
It should be noted that the results of this comparison may be a function of the chosen
mechanical properties utilized to develop the SDF characterizations. Better accuracy of
either SDF model may be possible with better selection of these idealized mechanical
parameters (or a bounding procedure applied to account for their variation). However,
these results do indicate that the bilinear model tends to provide a better prediction of peak
total displacement, isolator displacement, and lateral force response for any particular
ground motion input (having exhibited reasonable average accuracy and lower
coefficients of variation on these response quantities in this study). However, the largest
errors in both of the substitute models occurred on peak substructure displacement
predictions. This indicates that neither substitute SDF model adequately accounts for the
dynamic effect of higher mode response on local substructure demands for an MDOF
isolated bridge system, particularly when these contributions are significant (note: the
Configuration 5 specimen included only a nominal substructure mass of approximately 5
percent of the deck total mass). Bilinear system models may be improved by adding a
substructure degree of freedom to account for these separate mass and damping
contributions (only slightly complicating analytical procedures). Linearized SDF models
may not readily be amenable to this form of improvement. Further in depth evaluations of
these higher mode effects on response predictions and evaluation of the accuracy of
standard linearized analytical procedures are considered in Chapter 5.
Table 4-15 Results from Configuration 5 tests
Table Motion Cyiso d di dsub CsLA13 .0575 3.36 3.30 .07 0.19LA14 .0575 4.44 4.37 0.10 0.23
LA13_14 .0575 5.00 4.93 0.11 0.24
180
4.11 Influence of Ground Motion Characteristics
The three earthquake table motions selected for these comparative studies (i.e., LA13_14,
NF01_02, and LS17c_18c) allowed evaluation of the effect of variations in ground motion
type on the response of simple isolated bridge systems. These ground motions represent
far-field, near-fault and soft-soil motions (i.e., LA13_14, NF01_02, and LS17c_18c,
respectively). Four substructure stiffness values were incorporated in the various bridge
specimen configurations (see Table 4-1). This allowed the evaluation of system response
over a broad range of spectral frequencies. For the given deck mass, corresponding
fundamental (non-isolated) system periods for these four specimen configurations are
shown in Table 4-1 as well. These values are intended to represent full scale bridge
properties at scale factors of lr = 1/2, 1/5, and 1/5 for the LA13_14, NF01_01, and
LS17c_18c table motions, respectively. These configurations were tested with FP bearings
NF01 .0575 4.31 4.21 0.13 0.24NF02 .0575 3.35 3.28 0.10 0.19
NF01_02 .0575 5.36 5.26 0.12 0.27LS17c .0575 2.33 2.26 0.08 0.16LS18c .0575 0.96 0.93 0.06 0.12
LS17c_18c .0575 2.40 2.36 0.07 0.16LA13 .08 2.80 2.75 0.08 0.18LA14 .08 3.93 3.85 0.10 0.23
LA13_14 .08 4.48 4.41 0.11 0.23NF01 .08 4.06 3.95 0.56 0.25NF02 .08 2.81 2.75 0.08 0.19
NF01_02 .08 5.04 4.91 0.13 0.27LS17c .08 2.18 2.12 0.07 0.17LS18c .08 0.90 0.87 0.06 0.13
LS17c_18c .08 2.16 2.10 0.09 0.16
Table 4-15 Results from Configuration 5 tests
181
with two different slider compounds. Each of the uni-directional components and bi-
directional motion pairs of the three earthquake table motions were utilized in the tests.
Figure 4-19 presents 5% damped elastic response spectra for each of the ground motion
table records (i.e., LA13_14, NF01_01, and LS17c_18c at scale factors of lr = 1/2, 1/5,
and 1/5, respectively). Response spectra for both uni-directional components (x- and y-
direction) and bi-directional pairs (xy-direction) are plotted. These spectra present
displacement and total acceleration response for each record superimposed for
comparison. The spectra in Figure 4-19 illustrate the variety of spectral characteristics
contained in this suite of earthquake table motions.
Table 4-16 Results from nonlinear time-history analysis utilizing a bilinear idealization
Table Motion Cyiso d di dsub CsLA13 .0575 3.63 3.51 0.14 0.17LA14 .0575 4.83 4.72 0.17 0.21
LA13_14 .0575 5.58 5.44 0.16 0.23NF01 .0575 4.46 4.31 0.17 0.20NF02 .0575 3.58 3.46 0.13 0.17
NF01_02 .0575 5.55 5.40 0.17 0.23LS17c .0575 2.96 2.86 0.13 0.15LS18c .0575 0.96 0.91 0.07 0.09
LS17c_18c .0575 3.15 3.07 0.11 0.15LA13 .08 2.72 2.60 0.14 0.17LA14 .08 4.06 3.93 0.17 0.21
LA13_14 .08 4.81 4.68 0.16 0.23NF01 .08 3.78 3.64 0.17 0.20NF02 .08 3.12 3.02 0.14 0.18
NF01_02 .08 4.75 4.62 0.17 0.22LS17c .08 2.33 2.23 0.13 0.15LS18c .08 1.07 1.00 0.09 0.11
LS17c_18c .08 2.29 2.22 0.11 0.14
182
Bridge specimen test results to these ground motion inputs indicated that response was
influenced strongly by ground motion characteristics, including frequency content and
directional orientation (see Chapter 3 for more details). Chapter 3, Section 3.4 and 3.7,
discuss details of these response characteristics. For example, the LA13_14 motion has
significant higher frequency content (see Section 3.2) and is strongly oriented along a 45
degree azimuth relative to the x-y axes. This resulted in specimen response with
significant coupling in the x- and y-directions and underlying cycling of higher frequency.
The LS17c_18c motion, on the other hand, is a soft-soil motion with long period content
near the characteristic period of the test bearings (see Section 3.2) and produced relatively
Table 4-17 Results from linearized analysis
Table Motion Cyiso d di dsub CsLA13 .0575 3.47 3.35 0.12 0.17LA14 .0575 5.16 5.01 0.15 0.22
LA13_14 .0575NF01 .0575 4.04 3.90 0.14 0.19NF02 .0575 4.79 4.64 0.14 0.21
NF01_02 .0575LS17c .0575 3.24 3.13 0.12 0.16LS18c .0575 0.73 0.67 0.05 0.08
LS17c_18c .0575LA13 .08 2.54 2.42 0.12 0.16LA14 .08 4.47 4.32 0.15 0.22
LA13_14 .08NF01 .08 3.38 3.24 0.14 0.19NF02 .08 2.47 2.37 0.11 0.16
NF01_02 .08LS17c .08 2.58 2.46 0.12 0.16LS18c .08 0.65 0.58 0.07 0.10
LS17c_18c .08
183
harmonic response in the specimen. The near-fault NF01_02 motion has impulsive,
strongly coupled, fault-normal and fault-parallel components and, therefore, produced
strongly coupled behavior in the specimen.
Further, as seen in Figure 4-19 the peaks in spectral response for the LA13_14, NF01_02,
and LS17c_18c records show unique characteristics. The response of the bridge specimen
was determined by how its fundamental, first-slope period properties correlated with the
“short” and “long” period ranges of these ground motion spectra. To illustrate this point,
Table 4-18 Comparison of bilinear system analyses to test results
Table Motion Cyiso d di dsub CsLA13 .0575 1.078 1.062 1.963 1.065LA14 .0575 1.088 1.081 1.732 1.092
LA13_14 .0575 1.115 1.104 1.523 1.008NF01 .0575 1.034 1.024 1.302 1.042NF02 .0575 1.066 1.054 1.360 1.088
NF01_02 .0575 1.034 1.026 1.443 0.965LS17c .0575 1.275 1.265 1.570 1.187LS18c .0575 1.003 0.986 1.259 1.099
LS17c_18c .0575 1.313 1.299 1.761 1.056LA13 .08 0.972 0.945 1.772 1.161LA14 .08 1.033 1.022 1.754 1.092
LA13_14 .08 1.074 1.061 1.520 1.021NF01 .08 0.932 0.921 0.304 0.988NF02 .08 1.112 1.097 1.839 1.008
NF01_02 .08 0.943 0.941 1.348 0.925LS17c .08 1.070 1.050 1.896 1.126LS18c .08 1.195 1.145 1.594 0.810
LS17c_18c .08 1.059 1.061 1.240 1.040mean 1.078 1.064 1.510 1.043C.O.V. 0.094 0.093 0.249 0.085
184
scaled versions of the x-direction component of each of three earthquake table motions
were processed for shake table simulation studies.
Figure 4-20 presents 5% damped elastic response spectra for each of the scaled ground
motion table records. These spectra present displacement and total acceleration response
for each record at two selected scale factors, superimposed for comparison (i.e., LA13_14
at lr = 1/2 and 1/4, NF01_01 at lr = 1/3 and 1/5, and LS17c_18c at lr = 1/3 and 1/5). As
seen in the figures, acceleration spectra at smaller scale factors (i.e., smaller lr, see Chapter
Table 4-19 Comparison of linearized system analyses to test results
Table Motion Cyiso d di dsub CsLA13 .0575 1.032 1.013 1.700 0.883LA14 .0575 1.161 1.147 1.565 0.983
LA13_14 .0575NF01 .0575 0.937 0.927 1.083 0.772NF02 .0575 1.427 1.414 1.510 1.088
NF01_02 .0575LS17c .0575 1.395 1.384 1.482 0.999LS18c .0575 0.756 0.727 0.939 0.657
LS17c_18c .0575LA13 .08 0.909 0.881 1.522 0.873LA14 .08 1.137 1.121 1.576 0.983
LA13_14 .08NF01 .08 0.834 0.821 0.246 0.755NF02 .08 0.880 0.860 1.375 0.838
NF01_02 .08LS17c .08 1.185 1.161 1.746 0.976LS18c .08 0.722 0.666 1.185 0.751
LS17c_18c .08mean 1.031 1.010 1.328 0.880C.O.V. 0.226 0.238 0.316 0.147
185
3, Section 3.1.1) are shifted toward the longer period range and displacement spectra are
shifted upward. Based on similitude scaling, a structure with a given fixed period will be
in a shorter period spectral range, but have a larger magnitude displacement response, for
a motion processed at a larger length scale factor. On the other hand, the same structure
will be in a longer period spectral range, but have a smaller magnitude displacement
response, to the same motion processed at the smaller length scale factor. Further, for a
given prototype (full-scale) bridge with period Tp, a model of scale lr with period Tm =
trTp (where tr = lr1/2) subjected to an earthquake record processed at the same time scale
(i.e., tr = lr1/2), will exhibit displacement response equal to dm = lrdp, where dp is the
displacement response of the prototype bridge subjected to the full scale earthquake. See
Chapter 3, Section 3.1.1 for further discussion on similitude.
Subsequent analysis of isolated bridge overcrossings were carried out to illustrate this
effect of ground motion scaling on the response of systems incorporating substructures
with a range of stiffnesses bounding those of the bridge deck specimen. These analyses
were performed utilizing the generalized multi-degree-of-freedom bridge model (see
Figure 2-4(c) and Section 2.3.3). These systems incorporated isolation bearings with
similar mechanical characteristics as the FP test bearings. Earthquake ground motions
used for the time-history simulations were taken directly from records of the scaled table
motions used in the test program (i.e., LA13 at lr = 1/2 and 1/4, NF01 at lr = 1/3 and 1/5,
and LS17c at lr = 1/3 and 1/5). Figures 4-21 presents results from these analyses with
response data taken from the bridge specimen tests to the same input motion
superimposed for comparison. As seen in the figure, these analytical results correspond
186
closely to bridge specimen test data. Figure 4-22 presents the same analytical results
carried over a broader range of system periods.
Figure 4-22 illustrates that for isolated systems with very rigid substructures (or shorter
initial elastic periods) peak total displacement is much larger than that of a similar non-
isolated (elastic) system. For systems with greater substructure (or initial) flexibility, total
peak displacement is roughly equal to that of a similar elastic system. This behavior is
characteristic of systems in these “short period” and “long period” (or equal displacement)
ranges of spectral response, as noted earlier in preliminary analytical results (see Chapter
2, Section 2.3.5.1).
The period range defining these “short” and “long” period ranges is a characteristic of the
particular ground motion input. This can be seen clearly as the motion is scaled. For
example, for the LA13 motion the “long period” (equal displacement) range appears to
begin around Tsub = 0.55 seconds for a scale factor of lr = 1/2 (see Figure 4-21 and 4-22
(a)). However, for the same motion at a length scale factor of lr = 1/4, the “long period”
range begins around Tsub = 0.35 (see Figure 4-21 (b)). In comparison, the “long period”
range begins around Tsub = greater than 1 seconds and nearly 0.9 for the NF01 and LS17c
motions at length scale factors of lr = 1/3 and 1/5, respectively. It is apparent most clearly
for the LS17c motion that the “long period” range begins near the peak in the elastic
displacement spectrum (i.e., near 1 and 0.9 seconds for lr = 1/3 and 1/5, respectively, see
Figure 4-21 and 4-22 (e)). For the NF01 motion the “long period” range also begins near
where the elastic displacement spectrum begins “leveling off” (i.e., near 1 and 0.9 seconds
for lr = 1/3 and 1/5, respectively, see Figure 4-22 (d)). On the other hand, for the LA13_14
187
motion the “long period” range begins at a point defined more roughly by where the
acceleration spectrum begins descending (i.e., near 0.55 and 0.35 seconds for lr = 1/2 and
1/4, respectively, see Figure 4-21 and 4-22 (b)).
To illustrate the variation in response characteristics expected for systems in these
different spectral ranges, consider for example an isolated bridge system with a fixed
fundamental (or initial elastic) period of Tsub = 0.4 seconds (and having the same isolation
system properties as those represented in the analytical results presented in Figure 4-21
and 4-22). This isolated system may be in the “short period” range (i.e., exceeding elastic
displacements) for the LA13 motion at lr = 1/4. For the same motion at lr = 1/2, however,
this system would be in the “long period” range (i.e., having nearly equal displacement as
an elastic system). On the other hand, this system would be in the “short period” range for
both the NF01 and LS17c motions at lr = 1/3 and 1/5. Further, an isolated bridge system
with a fixed initial elastic period of Tsub = 1 second (having the same isolation system
characteristics) would be in the “long period” (equal displacements) range for all three
motions at all length scale factors considered. Response characteristics to different ground
motion input can be evaluated similarly. For example, a system with a fixed initial elastic
period of Tsub = 0.8 seconds (an the same isolation system properties) subjected to all three
motions at their smallest length scale factors (i.e., LA13, NF01, and LS17c at lr = 1/2, 1/3,
and 1/3, respectively) would be in the “long period” range for the LA13 motion and the
“short period” range for both the NF01 and LS17c motions (compare Figure 4-21 and 4-
22 (a), (c), and (e)). This illustrates the effect of ground motion spectral characteristics
which dictate system behavior in these general frequency ranges.
188
(a) Displacement spectra: x-direction (b) Total acceleration spectra: x-direction
(c) Displacement spectra: y-direction (d) Total acceleration spectra: y-direction
(e) Displacement spectra: xy-direction (f) Total acceleration spectra: xy-directionFigure 4-19 Comparison of 5% damped elastic response spectra for LA13_14, NF01_02, LS17c_18c ground motions, peak span settings.
0 1 2 3 40
5
10
15
20
Period (sec)
D (
in)
0 1 2 3 40
0.1
0.2
0.3
0.4
Period (sec)
At (
g)
LA13 NF01 LS17c
0 1 2 3 40
5
10
15
20
Period (sec)
D (
in)
0 1 2 3 40
0.1
0.2
0.3
0.4
Period (sec)
At (
g)
LA14 NF02 LS18c
0 1 2 3 40
5
10
15
20
Period (sec)
D (
in)
0 1 2 3 40
0.1
0.2
0.3
0.4
Period (sec)
At (
g)
LA13/14 NF01/02 LS17c/18c
189
(a) Displacement spectra: LA13 (b) Total acceleration spectra: LA13
(c) Displacement spectra: NF01 (d) Total acceleration spectra: NF01
(e) Displacement spectra: LS17c (f) Total acceleration spectra: LS17cFigure 4-20 Comparison of 5% damped elastic response spectra for scaled LA13, NF01, LS17c table motions at two length scale factors, peak span settings.
0 1 2 3 40
2
4
6
8
10
12
14
Period (sec)
D (
in)
0 1 2 3 40
0.1
0.2
0.3
0.4
Period (sec)
At(
g)
lr = 2
lr = 4
0 1 2 3 40
2
4
6
8
10
12
14
Period (sec)
D (
in)
0 1 2 3 40
0.1
0.2
0.3
0.4
Period (sec)
At(
g)
lr = 3
lr = 5
0 1 2 3 40
2
4
6
8
10
12
14
Period (sec)
D (
in)
0 1 2 3 40
0.1
0.2
0.3
0.4
Period (sec)
At(
g)
lr = 3
lr = 5
190
(a) LA13, lr = 1/2 (b) LA13, lr = 1/4
(c) NF01, lr = 1/3 (d) NF01, lr = 1/5
(e) LS17c, lr = 1/3 (f) LS17c, lr = 1/5
Figure 4-21 Comparison of nonlinear spectra for Cyiso = 0.06, test data for FP type 1 and 3, and elastic 5% damped spectra, ground motions at peak span settings.
0 0.2 0.4 0.6 0.8 10
2
4
6
8
Tsub
(sec)
Dis
p. (
in)
isolated system bridge deck model elastic, 5% damping
0 0.2 0.4 0.6 0.8 10
2
4
6
8
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
2
4
6
8
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
2
4
6
8
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
2
4
6
8
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
2
4
6
8
Tsub
(sec)
Dis
p. (
in)
191
(a) LA13, lr = 1/2 (b) LA13, lr = 1/4
(c) NF01, lr = 1/3 (d) NF01, lr = 1/5
(e) LS17c, lr = 1/3 (f) LS17c, lr = 1/5
Figure 4-22 Comparison of nonlinear spectra for Cyiso = 0.06 and elastic 5% damped spectra, ground motions at peak span settings.
0 0.2 0.4 0.6 0.8 10
2
4
6
8
Tsub
(sec)
Dis
p. (
in)
isolated system bridge deck model elastic, 5% damping
0 0.2 0.4 0.6 0.8 10
2
4
6
8
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
2
4
6
8
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
2
4
6
8
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
2
4
6
8
Tsub
(sec)
Dis
p. (
in)
0 0.2 0.4 0.6 0.8 10
2
4
6
8
Tsub
(sec)
Dis
p. (
in)
192
4.12 Influence of Vertical Motions on Sliding Systems
The various configurations of the bridge deck specimen allowed the evaluation of the
influence of vertical motions on the response of a bridge specimen utilizing a sliding
isolation system. All configurations of the specimen incorporating FP bearings were tested
on the earthquake simulator with both uni-directional and bi-directional components of
the NF01_02 table motion with and without its vertical component.
Table 4-20 below presents complete results from these tests. For each of the test
sequences, peak deck, isolator, and substructure displacement and isolator force response
are shown for the same sequence performed with and without vertical input. The trend in
these results is illustrated in Table 4-21, where the ratio of response with vertical input to
the response without vertical input is tabulated for each sequence. A value greater than 1.0
indicates that the response is greater with the vertical signal, while a value less than 1.0
indicates the vertical signal decreased peak response. Mean statistics for the entire group
of tests are presented at the end of the table. The data indicates that the effect of vertical
input motion is small in general and tends to effect isolator and total displacement
response most significantly. Peak isolator and total displacement response were increased
by approximately 9 and 5 percent on average, respectively, by the addition of the vertical
input component. Peak substructure displacement and isolator shear force, on the other
hand, were effected by less than 3 and 1 percent on average, respectively. As noted earlier,
the FP bearing has a characteristic strength and stiffness dependant on the applied axial
force (i.e., Qd = µN and kd = N/R, see Equation 3, Chapter 14). As the axial load fluctuates
with the addition of the vertical signal, the bearing’s strength will vary more than its
stiffness (as 1/R is generally smaller than µ). The effect on deck and isolator
193
displacements (which are sensitive to system strength) would then be expected to be more
pronounced, as shear force response (and consequently substructure displacements and
isolator force response) was shown to be less sensitive to strength variations (see Section
2.3.5.2).
4.13 Effect of impact against bearing restraint system
Due to an error in setting the command signal, Configuration 1, test no. 5 (see Figure 4-
23), resulted FP bearing Q3 impacting against the restrainer ring. Due to the rigid nature
of the substructure in this case, the resulting impact produced a significant shear force
imposed locally on the foundations of this bearing. The effect of this impact on overall
shear force demand and displacement response was, however, less significant.
Figure 4-23 (a), (c), (e), and (g) show hysteretic response of each individual FP bearings in
this test. As seen in Figure 4-23 (e), the FP bearing at quadrant Q3 experienced a
significant increase in shear response as a result of the impact (an approximately 250
percent increase above the shear imposed immediately prior to the impact). In contrast,
Figure 4-23 (b) illustrates that total overall shear response increased less significantly as a
result (by approximately 30 percent). Figure 4-23 (f) illustrates the dramatic spike which
occurs during the shear time-history for the FP bearing at quadrant Q3. In comparison,
Figure 4-23 (h) shows the time-history response of global shear, illustrating how the
impact on total shear is less dramatic. Figure 4-23 (d) shows a time-history of
displacement response at the deck level of the bridge. This time-history illustrates how
insignificant the effect of this impact is on the global isolated response of the specimen.
194
Table 4-20 Response of isolated bridge deck on FP bearings with and without vertical motion input (nominal periods: To = 0 sec, T1 = 0.25 sec, T2 = 0.8 sec, T3 = 1 sec)
RecordTsubx-
Tsuby-
U w/o U w/ V w/o V w/ Uiso w/o Uiso w/ Usub w/o Usub w/
mpier/Mdeck =.05, FP type 3
NF01 T1 T1 4.315 4.276 15.785 16.012 4.136 4.144 0.224 0.206
NF02 T1 T1 3.357 3.706 12.672 12.233 3.284 3.656 0.091 0.101
NF01_02 T1 T1 5.363 5.377 17.299 17.586 5.231 5.248 0.176 0.182
NF01 T2 T3 5.471 5.560 15.387 15.259 4.175 4.280 1.360 1.392
NF02 T2 T3 6.009 6.258 15.472 15.447 3.553 4.004 2.528 2.512
NF01_02 T2 T3 7.945 8.565 19.284 19.280 5.360 5.972 2.875 2.891
mpier/Mdeck = 0.0, FP type 2
NF01 T0 T0 3.501 3.385 14.896 14.630
NF02 T0 T0 2.635 3.060 12.533 12.575
NF01_02 T0 T0 4.560 4.580 17.921 17.996
mpier/Mdeck = 0.0, FP type 4
NF01 T2 T3 5.002 5.060 15.240 15.272 3.561 3.672 1.510 1.512
NF02 T2 T3 4.485 5.052 13.590 14.301 2.407 3.014 2.173 2.272
NF01_02 T2 T3 6.505 6.823 17.334 16.848 4.450 4.52 2.560 2.457
mpier/Mdeck = 0.05, FP type 4
NF01 T1 T1 4.056 4.046 16.180 15.643 3.909 3.923 0.581 0.187
NF02 T1 T1 2.812 3.460 12.321 12.514 2.752= 3.394 0.079 0.092
NF01_02 T1 T1 5.035 5.0018 17.337 17.161 4.873 4.871 0.204 0.173
NF01 T2 T2 5.235 5.374 15.321 15.376 3.933 4.133 1.328 1.292
NF02 T2 T2 3.565 3.957 12.165 12.268 2.409 2.805 1.297 1.331
NF01_02 T2 T2 6.392 6.712 18.412 17.998 4.798 5.148 1.811 1.763
NF01 T2 T3 5.220 5.615 15.652 16.223 3.865 4.292 1.367 1.403
NF02 T2 T3 4.680 5.856 13.552 15.024 2.685 3.695 2.168 2.382
NF01_02 T2 T3 6.606 7.343 18.253 17.784 4.555 4.966 2.578 2.591
mpier/Mdeck = 0.10, FP type 4
195
NF01 T2 T3 5.367 5.426 15.286 15.727 3.879 3.867 1.596 1.589
NF02 T2 T3 5.475 5.650 14.580 13.915 3.435 3.694 2.525 2.360
NF01_02 T2 T3 7.169 7.323 18.290 18.175 4.679 4.834 2.856 2.787
mpier/Mdeck = 0.0, FP type 1
NF01_02S5 T0 T0 3.590 3.502 13.504 13.594
NF01_02S3 T0 T0 5.025 5.036 18.330 17.545
mpier/Mdeck = 0.0, FP type 2
NF01_02S5 T0 T0 2.996 3.012 13.385 13.535
NF01_02S3 T0 T0 4.429 4.439 16.323 15.958
Table 4-21 Effect of vertical motion on peak response of isolated bridge deck on FP bearings (nominal periods: To = 0 sec, T1 = 0.25 sec, T2 = 0.8 sec, T3 = 1 sec)
RecordTsubx-
Tsuby-
U/Uo V/Vo Uiso/Uiso_0 Usub/Usub_0
mpier/Mdeck =.05, FP type 3
NF01 T1 T1 0.991 1.014 1.002 0.920
NF02 T1 T1 1.104 0.965 1.113 1.110
NF01_02 T1 T1 1.003 1.017 1.003 1.034
NF01 T2 T3 1.016 0.992 1.025 1.024
NF02 T2 T3 1.041 0.998 1.127 0.994
NF01_02 T2 T3 1.078 1.000 1.114 1.006
mpier/Mdeck = 0.0, FP type 2
NF01 T0 T0 0.967 0.982
NF02 T0 T0 1.161 1.003
NF01_02 T0 T0 1.004 1.004
mpier/Mdeck = 0.0, FP type 4
NF01 T2 T3 1.012 1.002 1.031 1.001
NF02 T2 T3 1.126 1.052 1.252 1.046
NF01_02 T2 T3 1.049 0.972 1.016 0.960
Table 4-20 Response of isolated bridge deck on FP bearings with and without vertical motion input (nominal periods: To = 0 sec, T1 = 0.25 sec, T2 = 0.8 sec, T3 = 1 sec)
196
The effect is minor presumably because the impact occurs during an instance of low
velocity in the bearing displacement cycle resulting in little change in energy.
mpier/Mdeck = 0.05, FP type 4
NF01 T1 T1 0.998 0.967 1.004 0.322
NF02 T1 T1 1.230 1.016 1.233 1.165
NF01_02 T1 T1 0.993 0.990 1.000 0.848
NF01 T2 T2 1.027 1.004 1.051 0.973
NF02 T2 T2 1.110 1.008 1.164 1.026
NF01_02 T2 T2 1.050 0.978 1.073 0.973
NF01 T2 T3 1.076 1.036 1.110 1.026
NF02 T2 T3 1.251 1.109 1.376 1.099
NF01_02 T2 T3 1.112 0.974 1.090 1.005
mpier/Mdeck = 0.10, FP type 4
NF01 T2 T3 1.011 1.029 0.997 0.996
NF02 T2 T3 1.032 0.954 1.075 0.935
NF01_02 T2 T3 1.021 0.994 1.033 0.976
mpier/Mdeck = 0.0, FP type 1
NF01_02S5 T0 T0 0.975 1.007
NF01_02S3 T0 T0 1.002 0.957
mpier/Mdeck = 0.0, FP type 2
NF01_02S5 T0 T0 1.005 1.011
NF01_02S3 T0 T0 1.002 0.978
Statistical scatter
Mean values 1.052 1.000 1.090 0.973
Standard deviation 0.072 0.032 .099 0.164
Table 4-21 Effect of vertical motion on peak response of isolated bridge deck on FP bearings (nominal periods: To = 0 sec, T1 = 0.25 sec, T2 = 0.8 sec, T3 = 1 sec)
197
This test sequence presents an opportunity to elaborate on the effect of impact on the
behavior of isolated bridge systems. As seen in this sequence, the effect of impact on the
bearing restrainer ring was to increase base shear demands (above that experienced by a
fully isolated system with no restraint). It follows that base shear demand would likely
increase (to a point) as the restraint limit was decreased, given the same earthquake
demand. Assuming the substructure to be designed to its elastic limit (µ=1) for the fully
isolated case, it could be postulated that substructure ductility demand may increase
dramatically as the velocity of the bearing increases upon impact (as would likely be the
case with decreasing restraint limits) as shear in the bearing drives displacement ductility
demand into the yielding substructure component. If substructure components do not yield
(as for systems with significant overstrength), designers would need to consider the effect
of increased local shear demands on connections and weak or brittle elements in the load
path. Thus, designing the substructure to yield at or before contact may be an effective
means of limiting these forces.
Displacement demands imposed on heavy flexible components by these local impacts
may also require special consideration. Simple idealizations which do not account for
higher mode contributions, may not detectthe occurrence of these local impacts. Damage
driven by these increased local force demands may cause premature local damage at
overall system displacements below that considered for behavior with no restraint limit.
More notably, earthquake demands representative of mean (DBE) seismic risk may
overlook the occurrence of impact for events above the mean (which have a 50 percent
likelihood of occurrence).
198
This test sequence points out some special considerations when impact against
displacement restraints occur. However, further analysis and testing is required to provide
a reliable basis for recommending improvements in bearing restraint design requirements.
4.14 Effect of bearing wear on systems employing FP bearings
Data was collected during the Configuration 1 through 9 test sequences to evaluate the
effect of bearing wear on system response. During each test sequence, one table motion
was selected as a basis and run as an initial test, at intervals during the sequence, and at the
conclusion of the sequence. Data collected from these repeated motion tests was evaluated
to determine changes in system response due to supposed “wear” in bearing materials.
Bearing and slider conditions were documented visually at the beginning and completion
of each test sequence to supplement the evaluation.
Table 4-22 shows peak specimen response through these sequences of bearing wear tests.
The number of time-history motions run between subsequent wear tests is denoted as
“History (n)”. Table 4-23 illustrates the effect of bearing wear by normalizing response by
initial test data. Results indicate that bearing wear effects overall system displacement
response only slightly, despite extreme wear in individual sliders. The effect of bearing
wear on shear response was similar, typically. However, an increase of nearly 20 percent
in force did occur during test sequence 9, albeit after 25 large test earthquake signals were
run. In some cases, more than 100 earthquakes were imposed without significant
deterioration in system performance.
199
(a) Q1 bearing hysteresis (b) Global bearing hysteresis
(c) Q2 bearing hysteresis (d) Global displacement history
(e) Q3 bearing hysteresis (f) Q3 shear history
Figure 4-23 Effect of impact against bearing restraint, FP type 1, Config. 1, Test No. 5, LS17c_18c, Span Setting [790/0/0]
−5 0 5−15
−10
−5
0
5
10
15
Disp. (in)
She
ar (
kips
)
−5 0 5−30
−20
−10
0
10
20
30
Disp. (in)
She
ar (
kips
)
−5 0 5−15
−10
−5
0
5
10
15
Disp. (in)
She
ar (
kips
)
4 6 8 10−8
−6
−4
−2
0
2
4
6
8
time (sec)
Dis
p. (
in)
−5 0 5−15
−10
−5
0
5
10
15
Disp. (in)
Sh
ea
r (k
ips)
4 4.5 5 5.5 6−15
−10
−5
0
5
10
15
time (sec)
Sh
ea
r (k
ips)
200
(g) Q4 bearing hysteresis (h) Global shear history
Figure 4-23 Effect of impact against bearing restraint, FP type 1, Config. 1, Test No. 5, LS17c_18c, Span Setting [790/0/0]
−5 0 5−15
−10
−5
0
5
10
15
Disp. (in)
She
ar (
kips
)
4 4.5 5 5.5 6−30
−20
−10
0
10
20
30
time (sec)
She
ar (
kips
)
201
Table 4-22 Peak system response after multiple signals
Sequence History (n) U V Uiso Usub
1
0 6.862 18.753
41 6.672 18.754
55 6.606 18.656
2
0 3.969 14.041
57 4.211 14.928
60 4.256 15.114
3
0 6.372 18.867
35 6.388 19.091
42 6.421 19.077
64 6.476 19.166
115 6.268 18.924
40 3.634 18.761
23 3.682 18.499
50 6.016 16.934 4.500 1.805
18 6.020 17.921 4.445 1.903
60 4.481 15.095 4.407 0.152
28 4.423 15.162 4.328 0.144
70 6.701 18.387 4.097 2.718
24 6.682 18.413 4.279 2.706
80 6.721 18.130 4.199 2.739
30 6.659 17.985 4.165 2.712
90 5.001 15.588 4.932 0.188
25 4.812 18.766 4.735 0.141
100 6.947 17.914 4.452 2.635
27 7.100 18.077 4.559 2.685
110 6.974 17.751 4.559 2.571
16 6.988 17.602 4.448 2.583
120 4.853 23.484
16 5.141 23.741
202
Table 4-23 Effect of bearing wear on peak system response
Sequence History (n) U/U0 V/V0 Uiso/Uiso_0 Usub/Usub
1
0 1.000 1.000
41 0.972 1.000
55 0.963 0.995
2
0 1.000 1.000
57 1.061 1.063
60 1.072 1.076
3
0 1.000 1.000
35 1.003 1.012
42 1.008 1.011
64 1.017 1.016
115 0.984 1.003
40 1.000 1.000
23 1.013 0.986
50 1.000 1.000 1.000 1.000
18 1.001 1.058 0.988 1.054
60 1.000 1.000 1.000 1.000
28 0.987 1.004 0.982 0.944
70 1.000 1.000 1.000 1.000
24 0.997 1.001 1.045 0.995
80 1.000 1.000 1.000 1.000
30 0.991 0.992 0.992 0.990
90 1.000 1.000 1.000 1.000
25 0.962 1.204 0.960 0.747
100 1.000 1.000 1.000 1.000
27 1.022 1.009 1.024 1.019
110 1.000 1.000 1.000 1.000
16 1.002 0.992 0.976 1.005
120 1.000 1.000
16 1.059 1.011
214
5 Displacement Estimates in Isolated Bridges
5.1 Introduction
The dynamic analyses carried out in this chapter are developed to refine and extend the
pilot analyses presented in Chapter 2 and the experimental studies presented in Chapters 3
and 4. This chapter focuses on the program objectives outlined in Section 1.3, specifically
program tasks 3, 5, and 7. The purpose of these tasks is to develop a more comprehensive
understanding of the behavior of simple isolated bridge overcrossings and to evaluate
current design procedures.
5.1.1 Problem Summary
This chapter was developed to systematically evaluate several design issues. Specifically
this chapter
• reviews the numerical models utilized for the subsequent analysis;
• describes the suites of ground motion time-histories used in the analyses;
• presents a systematic evaluation of the reliability of the Uniform Load Method;
• examines the adequacy of the provisions of the AASHTO Guide Specifications related to bi-directional ground motions;
• evaluates the ability of the Guide Specifications R-Factor design approach to control substructure yielding and the effect of this yielding on system response;
215
• describes a comprehensive parametric study of nonlinear isolated bridge response to identify trends related to structural and isolator properties and ground motion charac-teristics that can be used as guidelines to achieve improved performance; and
• evaluates the effect of local substructure mass and damping contributions to assess the adequacy of simplified single and multiple degree-of-freedom idealizations.
Detailed summaries of each analytical segment are included at the conclusion of each
section. Conclusions taken from these evaluations are utilized in Chapter 6 to formulate
overall recommendations for improvements of design procedures.
5.2 Analytical Bridge Models
Three simplified analytical models were utilized for the studies reported in this chapter as
summarized in Table 5-1.
The first two models were developed previously for the pilot analytical studies described
in Chapter 2 (see Section 2.3.3). Each of these models represents deck mass, isolation
system, and substructure properties as lumped components. The first model (Model 1) is a
planar two degree-of-freedom representation with dynamic degrees-of-freedom
representing deck and substructure displacements, respectively (see Figure 2-4(b)). This
model is similar to the simplified single degree-of-freedom model presented in Chapter 2
(see Figure 2-4(a)), but with the ability to incorporate distinct substructure mass and
damping contributions. The second model (Model 2) is a generalized multi-degree-of-
freedom, bi-directional bridge model with dynamic degrees-of-freedom representing deck
and substructure displacements in the x- & y-plane (see Figure 2-4(c)).
The final structural model (Model 3) is a planar single degree-of-freedom model, with the
contribution of a bilinear yielding hysteretic model for the substructure component
216
incorporated. Figure 5-1 presents a general description of this model. The model
represents the overall nonlinear behavior of an idealized isolated bridge responding uni-
directionally with yielding of the substructure and isolator explicitly represented.
Parameters are specified to match the component definitions of the AASHTO Guide
Specification with bilinear hysteretic isolation component behavior (see Chapter 2, Figure
2-2 (a)). Behavior of the substructure is also idealized as bilinear hysteretic, with a
specified yield strength and hardening stiffness ratio defined as shown (see Figure 5-1
(c)). Two internal system degrees of freedom represent the deck and substructure
component, respectively (see Figure 5-1 (b)). Substructure mass and damping
contributions are assumed to be negligible in this case such that overall system force-
deformation response is condensed to a single degree-of-freedom system with lumped
deck mass. This system has a tri-linear hysteresis determined from the mechanical
properties of the bilinear isolation and substructure hysteretic components acting in series
(see Figure 5-1 (d)).
5.3 Ground motion time-history suites
The nonlinear response of an isolated bridge overcrossing is influenced by many factors.
Foremost of these is perhaps the characteristics of the earthquake input. For purposes of
these analytical studies, several suites of ground motion time-history records were
compiled to facilitate evaluation of the effect of input characteristics on system response.
The features of each of these record suites were chosen considering the purpose of each
evaluation being undertaken. Five (5) different suites were utilized for the analytical
evaluations as summarized in Table 5-1. Some of these aggretized sets of records were
217
compiled to represent a uniform hazard of given design basis return interval at sites of a
particular standard soil class (i.e., design basis events representing the design spectra on
average). In other cases, de-aggretized sets of recorded ground motions were compiled to
represent discrete sets (bins) of magnitude and distance pairs for specific soil types. These
were selected to explicitly isolate the effect of earthquake magnitude, distance to fault
rupture and soil characteristics on response. In each case two horizontal components of the
record at each site were available in bi-directional ground motion time-history pairs. In
(a) Isolated bridge deck (b) Idealized dynamic model
(c) Substructure force-displacement (d) System force-displacement
Figure 5-1 Planar single-degree-of-freedom bridge model with yielding substructure
di
dsub
d
Yielding substructure bent
Isolation bearings
Mdeck F
Mdeck
d
kukd
Csub=0
dsub
di
KsubαKsub
Qd/(1-kd/ku)Fysub
bent isolator
mpier = 0
F=CsMg
Dsub
F
Disp.
CysubMg=Fysub
Ksub
αKsub
Fyiso
D
K1=kuKsub/(ku+Ksub)
K2=kdKsub/(kd+Ksub)
F
Disp.
K3= kdαKsubFysub(kd+αKsub)
218
some cases only one component was used, while in others both horizontal components
were considered.
Several synthetic impulsive records were also developed for these studies. These records
were created to represent the fundamental features of near-fault, shock pulses. Detailed
information on each of these ground motion suites is presented in the following sections.
5.3.1 Suites for evaluation of the AASHTO Uniform Load Method and R-factor provi-sions
For purposes of these evaluations, three suites of ground motion records were selected.
These suites were to developed to study the reliability of AASHTO Guide Spec provisions
related the the Uniform Load Method and R-factor approach under both far-field and near-
fault events.
The first suite is an aggretized set of records representing a uniform hazard for seismic
events in the Los Angeles area. This suite contains twenty ground motion records and
consists of ten, bi-directional, ground motion pairs. These records are representative of
Table 5-1 Summary of structural model and ground motion suitesused for analyses segments
Study Section Structural Model Ground Motion Suite
Uniform Load Method 5.4 Model 1Planar 2DOF
Uniform HazardSection 5.3.1
Bi-directional response 5.5 Model 2MDOF
Suite ASection 5.3.2
R-factor approach 5.6Model 3
2DOF w/ yielding substructure
Uniform HazardSection 5.3.1
Global parameter study 5.7 Model 1Planar 2DOF
Suite BSection 5.3.3
Local mass and damping effects 5.8 Model 1
Planar 2DOFSuite B
Section 5.3.3
219
stiff soil sites (NEHRP site type D). They have been amplitude and frequency scaled such
that their mean, 5% damped, elastic spectrum closely matches the USGS target spectrum
corresponding to a probability of exceedence of 10% in 50 years for the Los Angeles area
[SAC, 1997]. This probability of exceedance represents a return interval of 475 years,
approximately equal to the design basis event (i.e., DBE) targeted in the AASHTO
provisions for bridge designs [AASHTO, 1994]. Table 5-2 lists each of the individual
ground motions in this database suite, described as “LA10in50”.
Utilizing an acceleration coefficient of A = 0.4 (representative of a probability of
exceedence of 10 percent in 50 years in the San Fernando region [AASHTO, 1994]) and a
site soil coefficient of Si = 1.5675 (representing approximately AASHTO soil type II), the
ground motion records in this database were linearly scaled such that their mean spectrum
matched the AASHTO design spectrum for this set of parameters with minimum absolute
error, particularly in the constant velocity range (see Figure 5-2 (a)). This set of records
represents a suite of design basis earthquake motions compatible with the AASHTO
design spectrum (i.e., matching the design spectrum on average and the stipulated
probability of exceedance).
The second and third set of records compiled for this study are a set of ten, near-fault
recorded ground motion histories and a set of purely impulsive synthetic records. These
records represent fault-normal and fault-parallel, near-fault ground motion components.
Table 5-3 and 5-4 lists each of the individual ground motion records in the set of near-fault
and synthetic pulse records, described as “Near Fault” and “Impulsive”, respectively.
220
Figure 5-2(b) shows the mean spectra and statistical scatter in the “Near Fault” suite of
motions. Comparing this spectra with the LA10in50 mean spectra in Figure 5-2(a), it can
be seen that the “Near Fault” motions are richer in long period content on average,
suggestive of their more impulsive character. Figure 5-3 shows the ground acceleration,
velocity, and displacement time-histories for the first ten seconds of the NF09 earthquake
record from this suite. The impulsive content of this record is readily apparent,
particularly in the velocity and displacement histories. This characteristic is typical of the
ground motion records in the “Near-Fault” suite.
It has been suggested that near-fault earthquakes may be modeled with sufficient accuracy
(for structures responding at or near the peak in an earthquake’s response spectra) as
simple pulse motions [Krawinkler and Alavi, 1998]. On this basis, pure pulse motions
were developed for these studies with cosine and sine waves selected to model fault-
normal and fault-parallel displacement histories, respectively. Figure 5-2(c) shows the
spectra of this set of motions, titled “Impulsive”. Ground acceleration, velocity, and
displacement histories for these pulse records are shown in Figure 5-4. These records are
characteristic of pure pulse motions with an amplitude of A = 0.4 g and pulse duration of
Tp = 1.0 second. These values produced synthetic records with peak velocity and
displacement characteristics representative of actual near-fault earthquake records
[Krawinkler and Alavi, 1998]. The pulse duration of Tp = 1.0 second also represents the
mid-range of non-isolated bridge systems evaluated in this study (i.e., Tsub = 0 to 2
seconds), allowing an evaluation of isolated response for systems with periods shorter and
longer than the predominant pulse period.
221
Table 5-2 LA10in50 ground motion histories
Record ID Event Year Mag.1 Station Orientation2 R3 (km) Scale4
LA01 Imperial Valley 1940 6.9 El Centro, ivir 45 10 2.01LA02 Imperial Valley 1940 6.9 El Centro, ivir 135 10 2.01LA03 Imperial Valley 1979 6.5 El Centro, Array #5 45 4.1 1.01LA04 Imperial Valley 1979 6.5 El Centro, Array #5 135 4.1 1.01LA05 Imperial Valley 1979 6.5 El Centro, Array #6 45 1.2 0.84LA06 Imperial Valley 1979 6.5 El Centro, Array #6 135 1.2 0.84LA07 Landers 1992 7.3 Barstow 45 36 3.20LA08 Landers 1992 7.3 Barstow 135 36 3.20LA09 Landers 1992 7.3 Yermo 45 25 2.17LA10 Landers 1992 7.3 Yermo 135 25 2.17
LA11 Loma Prieta 1989 7.0 Gilroy, Array #3 45 12.4 1.79LA12 Loma Prieta 1989 7.0 Gilroy, Array #3 135 12.4 1.79LA13 Northridge 1994 6.7 Newhall 45 6.7 1.03LA14 Northridge 1994 6.7 Newhall 135 6.7 1.03LA15 Northridge 1994 6.7 Rinaldi RS 45 7.5 0.79LA16 Northridge 1994 6.7 Rinaldi RS 135 7.5 0.79LA17 Northridge 1994 6.7 Sylmar 45 6.4 0.99LA18 Northridge 1994 6.7 Sylmar 135 6.4 0.99
LA19 North Palm Springs 1986 6.0 dhsp 45 6.7 2.97
LA20 North Palm Springs 1986 6.0 dhsp 135 6.7 2.97
1. Moment magnitude
2. Orientation with respect to fault in degrees
3. Distance from fault
4. Amplitude scale applied to recorded ground motion history [SAC 1997]
222
Table 5-3 Near Fault ground motion histories
Record ID Event Year Mag.1 Station Orientation2 R3 (km)
Soil Type4
NF01 Tabas, Iran 1978 7.4 Tabas N 1.2 DNF02 Tabas, Iran 1978 7.4 Tabas P 1.2 DNF03 Loma Prieta 1989 7.0 Los Gatos N 3.5 DNF04 Loma Prieta 1989 7.0 Los Gatos P 3.5 DNF09 Erzincan, Turkey 1992 6.7 Erzincan N 2.0 DNF10 Erzincan, Turkey 1992 6.7 Erzincan P 2.0 DNF15 Northridge 1994 6.7 Olive View N 6.4 DNF16 Northridge 1994 6.7 Olive View P 6.4 DNF17 Kobe 1995 6.9 Kobe JMA N 3.4 DNF18 Kobe 1995 6.9 Kobe JMA P 3.4 D1. Moment magnitude
2. Orientation with respect to fault; N = normal; P = parallel
3. Distance from fault
4. Soil classification per the 1997 NEHRP Recommended Provisions (FEMA 1997)
Table 5-4 Impulsive ground motion histories
Record ID Event Station Orientation1 Tp2
(sec)A3
(g)V4
(in/s)D5
(in)
FN Cosine Pulse Fault Normal 90 1.0 0.4 24.6 7.8FP Sine Pulse Fault Parallel 0 1.0 0.4 49.2 24.6
1. Orientation with respect to fault in degrees.
2. Pulse duration
3. Peak acceleration amplitude.
4. Peak velocity amplitude.
5. Peak displacement amplitude.
223
a. AASHTO design spectrum and mean spectra of LA10in50 database motions
b. Mean spectra of Near Fault database motions
c. Spectra of Impulsive database motions
Figure 5-2 Psuedo-acceleration spectra for suites of ground motion histories, 5% damping
0 1 2 3 40
1
2
3
4
Period (sec)
Psu
edo−
acce
lera
tion
(g) Mean
AASHTO
maximum
minimum
+−1σ
0 1 2 3 40
1
2
3
4
Period (sec)
Psu
edo−
acce
lera
tion
(g) Mean
maximum
minimum
+−1σ
0 1 2 3 40
0.5
1
1.5
Period (sec)
Psu
edo−
acce
lera
tion
(g) Cosine pulse
Sine pulse
224
a. Ground acceleration time-history
b. Ground velocity time-history
c. Ground displacement time-history
Figure 5-3 Time-histories for NF09 earthquake record (first 10 seconds)
0 1 2 3 4 5 6 7 8 9 10−0.5
0
0.5
Time (sec)
Acc
ele
ratio
n (
g)
0 1 2 3 4 5 6 7 8 9 10−50
0
50
Time (sec)
Vel
ocity
(in
/s)
0 1 2 3 4 5 6 7 8 9 10−20
−10
0
10
20
Time (sec)
Dis
plac
emen
t (in
)
225
a. Cosine pulse, acceleration time-history b. Sine pulse, acceleration time-historyc
c. Cosine pulse, velocity time-history d. Sine pulse, velocity time-history
e. Cosine pulse, displacement time-history f. Sine pulse, displacement time-history
Figure 5-4 Time-histories for Impulsive earthquake records
0 0.5 1 1.5 2−0.5
−0.25
0
0.25
0.5
Time (sec)
Acc
ele
ratio
n (
g)
0 0.5 1 1.5 2−50
−25
0
25
50
Time (sec)
Ve
loci
ty (
in/s
)
0 0.5 1 1.5 2−50
−25
0
25
50
Time (sec)
Ve
loci
ty (
in/s
)
0 0.5 1 1.5 2−30
−15
0
15
30
Time (sec)
Dis
pla
cem
en
t (in
)
0 0.5 1 1.5 2−30
−15
0
15
30
Time (sec)
Dis
pla
cem
en
t (in
)
226
5.3.2 Suites for evaluation of AASHTO provisions related to bi-directional response
Fifty bi-directional pairs of ground motion time-histories, entitled Suite A were selected
for this study. These one-hundred motions were classified into five bins of twenty motions
each (i.e., ten pairs per bin) grouped by magnitude, distance to active fault, and soil type.
This classification provides a de-aggretization of these effects on the ground motion
characteristics. These bin classifications are outlined in Table 5-5. Table 5-6 through Table
5-10 list each of the individual ground motions in Bin 1 through 5, respectively. Bin 1
motions were selected from the ground motion database developed for the SAC Joint
Venture project [SAC, 1997]. Bin 2 through 5 motions were selected from the PEER
Strong Motion Database [PEER, 2000].
For each earthquake event and recording station, a pair of bi-directional ground motion
time histories are listed. For Bin 1, the first (i.e., x-direction) and second (i.e., y-direction)
orthogonal components are oriented normal and parallel, respectively, to the active
earthquake fault. For Bin 2 through 5, the orientation of the recorded bi-directional
components are based upon the orientation of the recording instrument and represent a
somewhat random directivity to the active fault.
Figure 5-5 shows the mean psuedo-acceleration spectrum computed for the set of twenty
histories for each of the Bin 1 through 5 ground motion suites (for a damping ratio of 5%).
Maxima, minima, and +1σ statistics are shown on each plot to illustrate the distribution in
the sets of ground motion data. Note the increase in average amplitude and preponderance
of long period content for motions of increasing magnitude and/or decreasing distance to
the active fault.
227
Figure 5-6 (a) and (b) present the AASHTO psuedo-acceleration and displacement design
spectra, respectively, for selected values of A = 0.4 and Si = 1.5 (parameters representative
of a design basis probability of exceedence of 10% in 50 years in the San Fernando region
and AASHTO soil type II, respectively [AASHTO, 1999]). Figure 5-6 (c) shows a
comparison of the mean spectra of bi-directional bin motions to the spectral shape
represented by the AASHTO psuedo-acceleration design spectrum for three selected
values of A and Si. It is seen in this figure that the mean spectra represented by the Bin 1
through 5 motions fit well to the AASHTO spectral shape, particularly on the descending
branch, or velocity sensitive region. This similarity is important. The AASHTO design
procedures are postulated on the mean response of systems to motions compatible with
this spectral shape (i.e., motions which represent the design basis hazard level and
“match” the spectrum closely on average). It follows that mean response characteristics
for each of these motion bins may be interpreted to apply generally to the design
procedures in the AASHTO Guide Specification.
Figure 5-7 shows a comparison for this suite of records of the mean pseudo-acceleration
spectrum computed for all ground motion histories in a bin to the mean spectra computed
for the first (x-direction) and second (y-direction) component histories in the same bin.
Figure 5-7 (a) shows these results for Bin 1 motions, where the first- and second-
component histories represent fault-normal and fault-parallel components, respectively.
For this plot the effect of directivity on the spectra is readily apparent. This bin, which
represents larger magnitude earthquakes for sites nearer the active fault, the difference
between the “larger”, or fault normal, component and the mean spectrum representing
“average” directivity is very pronounced. This is consistent with trends of near-fault
228
motions discussed in earlier work by Somerville [Somerville, 1997]. Analyses performed
utilizing the Bin 1 motions may then be interpreted as accounting for the effect of fault
directivity explicitly. This same comparison is shown in Figure 5-7 (b) through (e) for Bin
2 through 5 motions. For these bins, bi-directional ground motion pairs are oriented with
random directivity, and the difference between the first- and second-component mean
spectra and the mean spectrum of all motions in the bin is nearly negligible, as expected.
For these ground motion histories, therefore, results will be interpreted to apply generally
to the spectrum representing “average” or random directivity only.
Table 5-5 Ground motion bin classification for Suite A
BIN Name Magnitude R(km) Soil Type Classification1 NF 6.7 - 7.4 < 10 D NEHRP2 LMSR 6.7 - 7.3 10 - 30 A,C USGS3 LMLR 6.7 - 7.3 30 - 60 A,C USGS4 SMSR 5.8 - 6.5 10 - 30 A,C USGS5 SMLR 5.8 - 6.5 30 - 60 A,C USGS
229
Table 5-6 Suite A, Bin 1 ground motion histories: near fault (NF)
Record ID Event Year Mag.1 Station Orientation2 R3 (km)
Soil4Type
NF01 Tabas, Iran 1978 7.4 Tabas N 1.2 DNF02 Tabas, Iran 1978 7.4 Tabas P 1.2 DNF03 Loma Prieta 1989 7.0 Los Gatos N 3.5 DNF04 Loma Prieta 1989 7.0 Los Gatos P 3.5 DNF05 Loma Prieta 1989 7.0 Lex. Dam N 6.3 DNF06 Loma Prieta 1989 7.0 Lex. Dam P 6.3 DNF07 Cape Mendocino 1992 7.1 Petrolia N 8.5 DNF08 Cape Mendocino 1992 7.1 Petrolia P 8.5 DNF09 Erzincan, Turkey 1992 6.7 Erzincan N 2.0 DNF10 Erzincan, Turkey 1992 6.7 Erzincan P 2.0 D
NF11 Landers 1992 7.3 Lucerne N 1.1 DNF12 Landers 1992 7.3 Lucerne P 1.1 DNF13 Northridge 1994 6.7 Rinaldi N 7.5 DNF14 Northridge 1994 6.7 Rinaldi P 7.5 DNF15 Northridge 1994 6.7 Olive View N 6.4 DNF16 Northridge 1994 6.7 Olive View P 6.4 DNF17 Kobe 1995 6.9 Kobe JMA N 3.4 DNF18 Kobe 1995 6.9 Kobe JMA P 3.4 DNF19 Kobe 1995 6.9 Takatori N 4.3 DNF20 Kobe 1995 6.9 Takatori P 4.3 D1. Moment magnitude
2. Orientation with respect to fault; N = normal; P = parallel
3. Distance from fault
4. Soil classification per the 1997 NEHRP Recommended Provisions (FEMA 1997)
230
Table 5-7 Suite A, Bin 2 ground motion histories: large magnitude small distance (LMSR)
Record ID Event Year Mag.1 Station Orientation2 R3 (km) Soil4Type
LP89go1x Loma Prieta 1989 6.9 Gilroy Array #1 0 11.2 A
LP89go1y Loma Prieta 1989 6.9 Gilroy Array #1 90 11.2 A
LP89sgix Loma Prieta 1989 6.9 Hollister: SAGO Vault 270 30.6 A
LP89sgiy Loma Prieta 1989 6.9 Hollister: SAGO Vault 360 30.6 A
NR94lo9x Northridge 1994 6.7 Lake Hughes #9 0 26.8 A
NR94lo9y Northridge 1994 6.7 Lake Hughes #9 90 26.8 A
NR94wonx Northridge 1994 6.7 LA: Wonderland Ave. 95 22.7 A
NR94wony Northridge 1994 6.7 LA: Wonderland Ave. 185 22.7 A
SF71lo9x San Fernando 1971 6.6 Lake Hughes #9 21 23.5 A
SF71lo9y San Fernando 1971 6.6 Lake Hughes #9 291 23.5 A
LP89go2x Loma Prieta 1989 6.9 Gilroy Array #2 0 12.7 C
LP89go2y Loma Prieta 1989 6.9 Gilroy Array #2 90 12.7 C
LN92yerx Landers 1992 7.3 Yermo Fire Station 270 24.9 C
LN92yery Landers 1992 7.3 Yermo Fire Station 360 24.9 C
KB95abnx Kobe 1995 6.9 Abeno 0 23.8 C
KB95abny Kobe 1995 6.9 Abeno 90 23.8 C
IV79he1x Imperial Valley 1979 6.5 El Centro Array #1 140 15.5 C
IV79he1y Imperial Valley 1979 6.5 El Centro Array #1 230 15.5 C
NR94cnpx Northridge 1994 6.7 Canoga Pk: Topanga Can. 106 15.8 C
NR94cnpy Northridge 1994 6.7 Canoga Pk: Topanga Can. 196 15.8 C1. Moment magnitude
2. Orientation with respect to fault in degrees
3. Distance from fault
4. Soil classification per USGS
231
Table 5-8 Suite A, Bin 3 ground motion histories: large magnitude large distance (LMLR)
Record ID Event Year Mag.1 Station Orientation2 R3 (km) Soil4Type
KB95chyx Kobe 1995 6.9 o Chihaya 0 48.7 A
KB95chyy Kobe 1995 6.9 o Chihaya 90 48.7 A
LN9229px Landers 1992 7.3 Twentynine Palms 0 42.2 A
LN9229py Landers 1992 7.3 Twentynine Palms 90 42.2 A
LP89mchx Loma Prieta 1989 6.9 Monterey City Hall 0 44.8 A
LP89mchy Loma Prieta 1989 6.9 Monterey City Hall 90 44.8 A
NR94mtwx Northridge 1994 6.7 Mt. Wilson: CIT Seis Sta. 0 36.1 A
NR94mtwy Northridge 1994 6.7 Mt. Wilson: CIT Seis Sta. 90 36.1 A
NR94grnx Northridge 1994 6.7 San Gabriel: E. Grand Ave. 180 41.7 A
NR94grny Northridge 1994 6.7 San Gabriel: E. Grand Ave. 270 41.7 A
KB95tdox Kobe 1995 6.9 o Tadoka 0 30.5 C
KB95tdoy Kobe 1995 6.9 o Tadoka 90 30.5 C
LN92psax Landers 1992 7.3 Palm Springs Airport 0 37.5 C
LN92psay Landers 1992 7.3 Palm Springs Airport 90 37.5 C
LP89slcx Loma Prieta 1989 6.9 Palo Alto: SLAC Lab 270 36.3 C
LP89slcy Loma Prieta 1989 6.9 Palo Alto: SLAC Lab 360 36.3 C
NR94casx Northridge 1994 6.7 Compton: Castlegate Ave. 0 49.6 C
NR94casy Northridge 1994 6.7 Compton: Castlegate Ave. 90 49.6 C
IV79vctx Imperial Valley 1979 6.5 Victoria 75 54.1 C
IV79vcty Imperial Valley 1979 6.5 Victoria 345 54.1 C1. Moment magnitude
2. Orientation with respect to fault in degrees
3. Distance from fault
4. Soil classification per USGS
232
Table 5-9 Suite A, Bin 4 ground motion histories: small magnitude small distance (SMSR)
Record ID Event Year Mag.1 Station Orientation2 R3 (km) Soil4Type
MH84go1x Morgan Hill 1984 6.2 Gilroy Array #1 230 16.2 A
MH84go1y Morgan Hill 1984 6.2 Gilroy Array #1 320 16.2 A
PS86silx North Palm Springs 1986 6.0 Silent Valley: Poppet F 0 25.8 A
PS86sily North Palm Springs 1986 6.0 Silent Valley: Poppet F 90 25.8 A
WH87wonx Whittier Narrows 1987 6.0 LA: Wonderland
Ave. 75 24.6 A
WH87wony Whittier Narrows 1987 6.0 LA: Wonderland
Ave. 165 24.6 A
WH87mtwx Whittier Narrows 1987 6.0 Mt. Wilson: CIT Seis. Sta. 0 21.2 A
WH87mtwy Whittier Narrows 1987 6.0 Mt. Wilson: CIT Seis. Sta. 90 21.2 A
CL79go1x Coyote Lake 1979 5.7 Gilroy Array #1 230 9.3 A
CL79go1y Coyote Lake 1979 5.7 Gilroy Array #1 320 9.3 A
CL79hvrx Coyote Lake 1979 5.7 Halls Valley 150 31.2 C
CL79hvry Coyote Lake 1979 5.7 Halls Valley 240 31.2 C
IV79cxox Imperial Valley 1979 6.5 Calexico Fire Station 225 10.6 C
IV79cxoy Imperial Valley 1979 6.5 Calexico Fire Station 315 10.6 C
MH84go2x Morgan Hill 1984 6.2 Gilroy Array #2 0 15.1 C
MH84go2y Morgan Hill 1984 6.2 Gilroy Array #2 90 15.1 C
LM80srmx Livermore 1980 5.8 San Ramon Fire Station 70 21.7 C
LM80srmy Livermore 1980 5.8 San Ramon Fire Station 340 21.7 C
WH87buex Whittier Narrows 1987 6.0 Burbank: N. Buena Vista 250 23.7 C
WH87buey Whittier Narrows 1987 6.0 Burbank: N. Buena Vista 340 23.7 C1. Moment magnitude
2. Orientation with respect to fault; N = normal; P = parallel
3. Distance from fault
4. Soil classification per USGS
233
Table 5-10 Suite A, Bin 5 ground motion histories: small magnitude large distance (SMLR)
Record ID Event Year Mag.1 Station Orientation2 R3 (km) Soil4Type
PS86azfx North Palm Springs 1986 6.0 Anza Fire Station 225 46.7 A
PS86azfy North Palm Springs 1986 6.0 Anza Fire Station 315 46.7 A
PS86armx North Palm Springs 1986 6.0 Anza: Red Mountain 270 45.6 A
PS86army North Palm Springs 1986 6.0 Anza: Red Mountain 360 45.6 A
PS86ho2x North Palm Springs 1986 6.0 Winchester Bergman Ran 0 57.6 A
PS86ho2y North Palm Springs 1986 6.0 Winchester Bergman Ran 90 57.6 A
PS86ho1x North Palm Springs 1986 6.0 Murnetz Hot Springs 0 63.3 A
PS86ho1y North Palm Springs 1986 6.0 Murnetz Hot Springs 90 63.3 A
SN71sodx San Fernando 1971 6.6 Upland: San Antonio Dam 15 58.1 B5
SN71sody San Fernando 1971 6.6 Upland: San Antonio Dam 285 58.1 B5
CA83co8x Coalinga 1983 6.4 Parkfield: Cholame 8k1 0 50.7 C
CA83co8y Coalinga 1983 6.4 Parkfield: Cholame 8k1 270 50.7 C
PS86ho6x North Palm Springs 1986 6.0 San Jacinto Valley Cem. 270 39.6 C
PS86ho6y North Palm Springs 1986 6.0 San Jacinto Valley Cem. 360 39.6 C
MH84hchx Morgan Hill 1984 6.2 Hollister City Hall 1 32.5 C
MH84hchy Morgan Hill 1984 6.2 Hollister City Hall 271 32.5 C
WN87cnpx Whittier Narrows 1987 6.0 Canoga Park: Topanga Can. 106 47.4 C
WN87cnpy Whittier Narrows 1987 6.0 Canoga Park: Topanga Can. 196 47.4 C
LM80stpx Livermore 1980 5.8 Tracy: Sew. Treat. Plant 93 37.3 C
LM80stpy Livermore 1980 5.8 Tracy: Sew. Treat. Plant 183 37.3 C1. Moment magnitude
2. Orientation with respect to fault; N = normal; P = parallel
3. Distance from fault
4. Soil classification per USGS
5. Soil classification Type A per Geomatrix
234
a. Bin 1 - NF
b. Bin 2- LMSR
c. Bin 3 - LMLR
Figure 5-5 Mean psuedo-acceleration spectra: Suite A, 5% damping
0 0.5 1 1.5 2 2.5 3 3.5 40
1
2
3
4
Period (sec)
Psu
edo−
acce
lera
tion
(g) mean
max/min
+-1σ, typical
0 0.5 1 1.5 2 2.5 3 3.5 4−0.5
0
0.5
1
1.5
2
2.5
Period (sec)
Psu
edo−
acce
lera
tion
(g) mean
max/min
0 0.5 1 1.5 2 2.5 3 3.5 4−0.5
0
0.5
1
1.5
Period (sec)
Psu
edo−
acce
lera
tion
(g) mean
max/min
235
d. Bin 4 - SMSR
e. Bin 5 - SMLR
Figure 5-5 Mean psuedo-acceleration spectra: Suite A, 5% damping
0 0.5 1 1.5 2 2.5 3 3.5 4−0.5
0
0.5
1
Period (sec)
Psu
edo−
acce
lera
tion
(g) mean
max/min
0 0.5 1 1.5 2 2.5 3 3.5 4−0.2
0
0.2
0.4
0.6
Period (sec)
Psu
edo−
acce
lera
tion
(g) mean
max/min
236
a. AASHTO psuedo-acceleration spectrum b. AASHTO displacement spectrum
c. Mean spectra vs. AASHTO spectral shape
Figure 5-6 AASHTO elastic response spectra with comparison to mean psuedo-accel-eration spectra for Suite A ground motions, 5% damping
0 1 2 3 40
0.2
0.4
0.6
0.8
1
1.2
Period (sec)
Psu
ed
o−
acc
ele
ratio
n (
g)
Ag = 0.4gSi = 1.5, Soil Type II
varies as 1/T
0 1 2 3 40
5
10
15
20
25
Period (sec)
Dis
pla
cem
en
t (in
)
Ag = 0.4gSi = 1.5, Soil Type II
0 0.5 1 1.5 2 2.5 3 3.5 40
0.3
0.6
0.9
1.2
1.5
1.8
Period (sec)
Psu
edo−
acce
lera
tion
(g) AASHTO
BIN motions
varies as 1/T
237
a. Bin 1 - NF
b. Bin 2- LMSR
c. Bin 3 - LMLRFigure 5-7 Mean psuedo-acceleration spectra of Suite A ground motion bins vs. mean of first (x-direction) and second (y-direction) component histories, 5% damping
0 0.5 1 1.5 2 2.5 3 3.5 40
0.5
1
1.5
2
Period (sec)
Psu
edo−
acce
lera
tion
(g) mean of all Bin motions
mean of fault normal components mean of fault parallel components
0 0.5 1 1.5 2 2.5 3 3.5 40
0.2
0.4
0.6
0.8
Period (sec)
Psu
edo−
acce
lera
tion
(g) mean of all Bin motions
mean of first components mean of second components
0 0.5 1 1.5 2 2.5 3 3.5 40
0.1
0.2
0.3
0.4
0.5
Period (sec)
Psu
edo−
acce
lera
tion
(g) mean of all Bin motions
mean of first components mean of second components
238
d. Bin 4 - SMSR
e. Bin 5 - SMLRFigure 5-7 Mean psuedo-acceleration spectra of Suite A ground motion bins vs. mean of first (x-direction) and second (y-direction) component histories, 5% damping
0 0.5 1 1.5 2 2.5 3 3.5 40
0.1
0.2
0.3
0.4
Period (sec)
Psu
edo−
acce
lera
tion
(g) mean of all Bin motions
mean of first components mean of second components
0 0.5 1 1.5 2 2.5 3 3.5 40
0.05
0.1
0.15
0.2
0.25
Period (sec)
Psu
edo−
acce
lera
tion
(g) mean of all Bin motions
mean of first components mean of second components
239
5.3.3 Suites for parametric studies of isolated bridge response and influence of substruc-ture mass and damping
One hundred ground motion time histories, entitled Suite B, were selected for these
studies. These motions were classified into five de-aggretized bins of twenty motions
each. Bins were classified by earthquake magnitude and distance to active fault as
described in Table 5-11. Bin 1 motions for this suite were taken from the ground motion
database developed for the SAC Joint Venture project [SAC, 1997] while Bin 2 through 5
motions were selected from the PEER Strong Motion Database [PEER, 2000].
Table 5-12 through Table 5-16 lists each of the individual ground motions in Bin 1 through
5, respectively. For Bin 1, ground motions are listed sequentially in bi-directional pairs
where the first and second orthogonal components are oriented normal and parallel to the
active fault, respectively. For Bin 2 through 5, only uni-directional components were
selected representing somewhat random fault directivity.
For these studies computational time constraints dictated that only half of the compiled
ground motion records could be used. To facilitate this, every other ground motion record
from each bin was selected for the parametric evaluations (beginning with the first record
of the bin). This implies that for Bin 1 motions, only the “stronger” fault-normal motions
were utilized these studies. Figure 5-8 shows the mean pseudo-acceleration spectrum
computed for the set of ten histories utilized from the Bin 1 through 5 ground motion
suites (for a damping ratio of 5%). Maxima, minima, and +1σ statistics are shown on each
plot to illustrate the distribution in the sets of ground motion data. Figure 5-9 presents a
comparison of these mean spectra. Note the increase in average amplitude and
preponderance of long period content as ground motion magnitude increases and/or
240
distance to the active fault decreases as for the previous de-aggretized, bi-directional bins
(see Figure 5-5).
As for the Suite A motions, Figure 5-10 compares the AASHTO design spectral shape to
the mean spectra of the Suite B motions. It is seen in this figure that the mean spectra
represented by these bins also fit well to the AASHTO spectral shape. This implies, as for
the Suite A motions, that mean response characteristics for each of these motion bins may
be interpreted to apply generally to the AASHTO Guide Spec procedures (see Section 5.3.2
above).
Table 5-11 Ground motion bin classification for Suite B
BIN Name Magnitude R(km) Soil Type Classification1 NF 6.7 - 7.4 < 10 D NEHRP2 LMSR 6.7 - 7.3 10 - 30 D NEHRP3 LMLR 6.7 - 7.3 30 - 60 D NEHRP4 SMSR 5.8 - 6.5 10 - 30 D NEHRP5 SMLR 5.8 - 6.5 30 - 60 D NEHRP
241
Table 5-12 Suite B, Bin 1 ground motion histories: near fault (NF)
Record ID Event Year Mag.1 Station Orientation2 R3 (km)
Soil4Type
NF01 Tabas, Iran 1978 7.4 Tabas N 1.2 DNF02 Tabas, Iran 1978 7.4 Tabas P 1.2 DNF03 Loma Prieta 1989 7.0 Los Gatos N 3.5 DNF04 Loma Prieta 1989 7.0 Los Gatos P 3.5 DNF05 Loma Prieta 1989 7.0 Lex. Dam N 6.3 DNF06 Loma Prieta 1989 7.0 Lex. Dam P 6.3 DNF07 Cape Mendocino 1992 7.1 Petrolia N 8.5 DNF08 Cape Mendocino 1992 7.1 Petrolia P 8.5 DNF09 Erzincan, Turkey 1992 6.7 Erzincan N 2.0 DNF10 Erzincan, Turkey 1992 6.7 Erzincan P 2.0 D
NF11 Landers 1992 7.3 Lucerne N 1.1 DNF12 Landers 1992 7.3 Lucerne P 1.1 DNF13 Northridge 1994 6.7 Rinaldi N 7.5 DNF14 Northridge 1994 6.7 Rinaldi P 7.5 DNF15 Northridge 1994 6.7 Olive View N 6.4 DNF16 Northridge 1994 6.7 Olive View P 6.4 DNF17 Kobe 1995 6.9 Kobe JMA N 3.4 DNF18 Kobe 1995 6.9 Kobe JMA P 3.4 DNF19 Kobe 1995 6.9 Takatori N 4.3 DNF20 Kobe 1995 6.9 Takatori P 4.3 D1. Moment magnitude
2. Orientation with respect to fault; N = normal; P = parallel
3. Distance from fault
4. Soil classification per the 1997 NEHRP Recommended Provisions (FEMA 1997)
242
Table 5-13 Suite B, Bin 2 ground motion histories: large magnitude small distance (LMSR)
Record ID Event Year Mag.1 Station Mechanism2 R3 (km) Soil4Type
IV40elc Imperial Valley 1940 7.0 El Centro Array #9 strike-slip 12.0 DLD92yer Landers 1992 7.3 Yermo Fire Station strike-slip 24.9 D
LP89agw Loma Prieta 1989 6.9 Agnews State Hospital reverse-oblique 28.2 D
LP89cap Loma Prieta 1989 6.9 Capitola reverse-oblique 14.5 D
LP89g03 Loma Prieta 1989 6.9 Gilroy Array #3 reverse-oblique 14.4 D
LP89g04 Loma Prieta 1989 6.9 Gilroy Array #4 reverse-oblique 16.1 D
LP89gmr Loma Prieta 1989 6.9 Gilroy Array #7 reverse-oblique 24.2 D
LP89hch Loma Prieta 1989 6.9 Hollister City Hall reverse-oblique 28.2 D
LP89hda Loma Prieta 1989 6.9 Hollister Diff. Array reverse-oblique 25.8 D
LP89svl Loma Prieta 1989 6.9 Sunnyvale: Colton Ave reverse-oblique 28.8 D
NR94cnp Northridge 1994 6.7 Canoga Park: Topanga Can reverse-slip 15.8 D
NR94far Northridge 1994 6.7 LA - N Faring Rd reverse-slip 23.9 DNR94fle Northridge 1994 6.7 LA - Fletcher Dr reverse-slip 29.5 DNR94glp Northridge 1994 6.7 Glendale - Las Palmas reverse-slip 25.4 DNR94hol Northridge 1994 6.7 Hollywood Store FF reverse-slip 25.5 DNR94stc Northridge 1994 6.7 17645 Saticoy St reverse-slip 13.3 DSF71pel San Fernando 1971 6.6 LA: Hollywood Store Lot reverse-slip 21.2 DSH87bra Superstition Hills 1987 6.7 Brawley strike-slip 18.2 DSH87icc Superstition Hills 1987 6.7 El Centro Imp. Co. Cent strike-slip 13.9 D
SH87wsm Superstition Hills 1987 6.7 Westmorland Fire Station strike-slip 13.3 D1. Moment magnitude
2. Faulting mechanism
3. Distance from fault
4. Soil classification per the 1997 NEHRP Recommended Provisions (FEMA 1997)
243
Table 5-14 Suite B, Bin 3 ground motion histories: large magnitude large distance (LMLR)
Record ID Event Year Mag.1 Station Mechanism2 R3 (km) Soil4Type
BM68elc Borrego Mountain 1968 6.8 El Centro Array #9 strike-slip 46.0 DLD92ind Landers 1992 7.3 Indio: Coachella Canal strike-slip 55.7 DLD92psa Landers 1992 7.3 Palm Springs Airport strike-slip 37.5 D
LP89a2e Loma Prieta 1989 6.9 Hayward Muir Schoolreverse-oblique 57.4 D
LP89fms Loma Prieta 1989 6.9 Freemont: Emerson Ct
reverse-oblique 42.4 D
LP89hvr Loma Prieta 1989 6.9 Halls Valley reverse-oblique 31.6 D
LP89sjw Loma Prieta 1989 6.9 Salinas: John & Work reverse-oblique 32.6 D
LP89slc Loma Prieta 1989 6.9 Palo Alto: SLAC Lab reverse-oblique 36.3 D
NR94ana Northridge 1994 6.7 Anaverde Valley: City R reverse-slip 38.4 DNR94bad Northridge 1994 6.7 Covina: W. Badillo reverse-slip 56.1 DNR94cas Northridge 1994 6.7 Compton: Castlegate St reverse-slip 49.6 DNR94cen Northridge 1994 6.7 LA: Centinela St reverse-slip 30.9 DNR94cmr Northridge 1994 6.7 Camarillo reverse-slip 36.5 DNR94del Northridge 1994 6.7 Lakewood: Del Amo Blvd reverse-slip 59.3 D
NR94dwn Northridge 1994 6.7 Downey: Co Maint Bldg reverse-slip 47.6 DNR94eli Northridge 1994 6.7 Elizabeth Lake reverse-slip 37.2 DNR94jab Northridge 1994 6.7 Bell Gardens: Jaboneria reverse-slip 46.6 DNR94lh1 Northridge 1994 6.7 Lake Hughes #1 reverse-slip 36.3 DNR94loa Northridge 1994 6.7 Lawndale: Osage Ave reverse-slip 42.4 DNR94lv2 Northridge 1994 6.7 Leona Valley #2 # reverse-slip 37.7 D
1. Moment magnitude
2. Faulting mechanism
3. Distance from fault
4. Soil classification per the 1997 NEHRP Recommended Provisions (FEMA 1997)
244
Table 5-15 Suite B, Bin 4 ground motion histories: small magnitude small distance (SMSR)
Record ID Event Year Mag.1 Station Mechanism2 R3 (km) Soil4Type
IV79cal Imperial Valley 1979 6.5 Calipatria Fire Station strike-slip 23.8 DIV79chi Imperial Valley 1979 6.5 Chihuahua strike-slip 28.7 DIV79e01 Imperial Valley 1979 6.5 El Centro Array #1 strike-slip 15.5 DIV79e12 Imperial Valley 1979 6.5 El Centro Array #12 strike-slip 18.2 DIV79e13 Imperial Valley 1979 6.5 El Centro Array #13 strike-slip 21.9 DIV79qkp Imperial Valley 1979 6.5 Cucapah strike-slip 23.6 DIV79wsm Imperial Valley 1979 6.5 Westmorland Fire Station strike-slip 15.1 DLV80kod Livermore 1980 5.8 San Ramon Fire Station strike-slip 21.7 D
LV80srm Livermore 1980 5.8 San Ramon: Eastman Kodak strike-slip 17.6 D
MH84agw Morgan Hill 1984 6.2 Agnews State Hospital strike-slip 29.4 DMH84g02 Morgan Hill 1984 6.2 Gilroy Array #2 strike-slip 15.1 DMH84g03 Morgan Hill 1984 6.2 Gilroy Array #3 strike-slip 14.6 DMH84gmr Morgan Hill 1984 6.2 Gilroy Array #7 strike-slip 14.0 DPM73phn Point Mugu 1973 5.8 Port Hueneme reverse-slip 25.0 DPS86psa N. Palm Springs 1986 6.0 Palm Springs Airport strike-slip 16.6 D
WN87cas Whittier Narrows 1987 6.0 Compton: Castlegate St. reverse 16.9 DWN87cat Whittier Narrows 1987 6.0 Carson: Catskill Ave. reverse 28.1 DWN87flo Whittier Narrows 1987 6.0 Brea: S Flower Ave. reverse 17.9 D
WN87w70 Whittier Narrows 1987 6.0 LA: W 70th St. reverse 16.3 DWN87wat Whittier Narrows 1987 6.0 Carson: Water St. reverse 24.5 D
1. Moment magnitude
2. Faulting mechanism
3. Distance from fault
4. Soil classification per the 1997 NEHRP Recommended Provisions (FEMA 1997)
245
Table 5-16 Suite B, Bin 5 ground motion histories: small magnitude large distance (SMLR)
Record ID Event Year Mag.1 Station Mechanism2 R3 (km) Soil4Type
BO42elc Borrego 1942 6.5 El Centro Array #9 not given 49.0 D
CO83c05 Coalinga 1983 6.4 Parkfield: Cholame 5Wreverse-oblique 47.3 D
CO83c08 Coalinga 1983 6.4 Parkfield: Cholame 8Wreverse-oblique 50.7 D
IV79cc4 Imperial Valley 1979 6.5 Coachella Canal #4 strike-slip 49.3 DIV79cmp Imperial Valley 1979 6.5 Compuertas strike-slip 32.6 DIV79dlt Imperial Valley 1979 6.5 Delta strike-slip 43.6 DIV79nil Imperial Valley 1979 6.5 Niland Fire Station strike-slip 35.9 DIV79pls Imperial Valley 1979 6.5 Plaster City strike-slip 31.7 DIV79vct Imperial Valley 1979 6.5 Victoria strike-slip 54.1 D
LV80stp Livermore 1980 5.8 Tracy: Sewage Treat. Plant strike-slip 37.3 D
MH84cap Morgan Hill 1984 6.2 Capitola strike-slip 38.1 DMH84hch Morgan Hill 1984 6.2 Hollister City Hall strike-slip 32.5 DMH84sjb Morgan Hill 1984 6.2 San Juan Bautista strike-slip 30.3 C
PS86h06 N. Palm Springs 1986 6.0 San Jacinto Valley Ceme-tery strike-slip 39.6 D
PS86ino N. Palm Springs 1986 6.0 Indio strike-slip 39.6 D
WN87bir Whittier Narrows 1987 6.0 Downey - Birchdale # reverse 56.8 D
WN87cts Whittier Narrows 1987 6.0 LA: Century City CC South reverse 31.3 D
WN87har Whittier Narrows 1987 6.0 LB - Harbor Admin FF reverse 34.2 D
WN87sse Whittier Narrows 1987 6.0 Terminal Island: S Seaside reverse 35.7 D
WN87stc Whittier Narrows 1987 6.0 Northridge: Saticoy St. reverse 39.8 D
1. Moment magnitude
2. Faulting mechanism
3. Distance from fault
4. Soil classification per the 1997 NEHRP Recommended Provisions (FEMA 1997)
246
a. Bin 1 - NF (mean spectra of ten selected motions)
b. Bin 2- LMSR (mean spectra of ten selected motions)
c. Bin 3 - LMLR (mean spectra of ten selected motions)
Figure 5-8 Mean pseudo-acceleration spectra: Suite B, 5% damping
0 0.5 1 1.5 2 2.5 3 3.5 4−1
0
1
2
3
4
Period (sec)
Psu
edo−
acce
lera
tion
(g) mean
max/min
+-1σ, typical
0 0.5 1 1.5 2 2.5 3 3.5 4−0.5
0
0.5
1
1.5
Period (sec)
Psu
edo−
acce
lera
tion
(g) mean
max/min
0 0.5 1 1.5 2 2.5 3 3.5 4−0.2
0
0.2
0.4
0.6
Period (sec)
Psu
edo−
acce
lera
tion
(g) mean
max/min
247
d. Bin 4 - SMSR (mean spectra of ten selected motions)
e. Bin 5 - SMLR (mean spectra of ten selected motions)
Figure 5-8 Mean pseudo-acceleration spectra: Suite B, 5% damping
0 0.5 1 1.5 2 2.5 3 3.5 4−0.5
0
0.5
1
1.5
2
Period (sec)
Psu
edo−
acce
lera
tion
(g) mean
max/min
0 0.5 1 1.5 2 2.5 3 3.5 4−0.2
0
0.2
0.4
0.6
0.8
Period (sec)
Psu
edo−
acce
lera
tion
(g) mean
max/min
248
a. Bin 1, 2, and 3 (mean spectra of ten selected motions)
b. Bin 2, 3, 4, and 5 (mean spectra of ten selected motions)
Figure 5-9 Comparison of spectra for Suite B bins of ground motion histories, 5% damping
0 0.5 1 1.5 2 2.5 3 3.5 40
0.2
0.4
0.6
0.8
1
Period (sec)
Psu
edo−
acce
lera
tion
(g) Bin 1
Bin 2Bin 3
0 0.5 1 1.5 2 2.5 3 3.5 40
0.1
0.2
0.3
0.4
Period (sec)
Psu
edo−
acce
lera
tion
(g) Bin 2
Bin 3Bin 4Bin 5
249
a. AASHTO pseudo-acceleration spectrum b. AASHTO displacement spectrum
c. Mean spectra vs. AASHTO spectral shape
Figure 5-10 AASHTO elastic response spectra with comparison to mean pseudo-accel-eration spectra for Suite B ground motions, 5% damping
0 1 2 3 40
0.2
0.4
0.6
0.8
1
1.2
Period (sec)
Psu
ed
o−
acc
ele
ratio
n (
g)
Ag = 0.4gSi = 1.5, Soil Type II
varies as 1/T
0 1 2 3 40
5
10
15
20
25
Period (sec)
Dis
pla
cem
en
t (in
)
Ag = 0.4gSi = 1.5, Soil Type II
0 0.5 1 1.5 2 2.5 3 3.5 40
0.2
0.4
0.6
0.8
Period (sec)
Psu
edo−
acce
lera
tion
(g) AASHTO
BIN motionsvaries as 1/T
250
5.4 An Evaluation of the AASHTO Uniform Load Method
5.4.1 Introduction
The Guide Specifications contain simplified procedures for estimating the design
displacement and force demand imposed on bridges designed to be seismically isolated.
The Uniform Load Method is the linearized single degree-of-freedom procedure for
estimating design response.
The Guide Specifications’ Uniform Load Method is essentially an application of the
“secant stiffness method”. The method establishes that equivalent linear properties for the
subject isolated bridge may be defined by the secant stiffness of the system responding at
its peak displacement. The method determines a design value for peak system
displacement from the ordanates of two smoothed design spectrum (adjusted for
“equivalent damping”) at the systems “secant period” (defined by its mass and “secant
stiffness”). Because the method requires an initial estimate of system properties to initiate,
the method is iterative. The method is assumed to converge to an adequate design
“estimate” of peak average time-history response of an isolated bridge system subjected to
suite of seismic events representative (on average) of the design spectrum.
5.4.2 AASHTO Uniform Load Method
The Uniform Load Method is a unidirectional method prescribed for estimating response
(i.e., forces and deformations) along each of the two orthogonal axes of an isolated bridge
system (generally chosen as the longitudinal and transverse axes). As stipulated in the
Guide Spec, total response is evaluated along each axis of the bridge by either of two
methods: the Single Mode Spectral Method or the Multi-Mode Spectral Method. The
251
Single Mode Spectral Method is focused on here.
A typical structural model of an isolated bridge bent responding uni-directionally in its
transverse isolated mode is presented in Figure 5-11 below. The force-deformation
hysteretic response of typical isolation bearings is generally broad and relatively stable.
The AASHTO Guide Specification allows isolation bearings to be characterized as bilinear
hysteretic for purposes of the design procedures as shown in Figure 5-12 (a). The overall
force-deformation response of the this typical isolated bridge system defined at the level
of the bridge deck defined in the parameters identified in the AASHTO Guide Spec,
neglecting dynamic substructure damping or mass contributions, is presented in Figure 5-
12 (b).
The code prescribes linearized characteristics for the isolated bridge system based upon
secant stiffness properties defined at its maximum displacement. “Effective damping"
properties are postulated by equating the energy dissipated per cycle in the isolated bridge
system to that of an "equivalent" linear visco-elastic damping component (oscillating
Figure 5-11 Structural idealization of an isolated bridge bent
K sub
M
di
d
keff
keff= effective isolator stiffnessKsub= linear substructure stiffnessM = lumped deck massdi = isolator displacementdsub = substructure displacementd = total displacement = di + dsub
(1
xcluding substructure contributions) (
g ratio, where rational first estimates may
), with B established from the code val
of the bridge from Equation (21).
sign spectrum closely on average and
nce). Evaluating the AASHTO Unifo
f records provides a rational basis
ing a reliable estimate of mean respo
ative values imply that the proced
fective system properties varies negligibl
quivalent static force estimates, where
o be deterministic quantities, preclud
ameter α, which represents the isolat
characterized by its idealized hyster
ange from 0 to 1. This captures isolat
Appendix E of this report. Figure
aluation of the AASHTO Uniform Lo
ons. Results plotted are the mean relat
are presented over the entire range
oad Method tended to increasingly ov
bearing properties become more flexi
rigid initial stiffness (i.e., Tsub = 0
the secant method fairly accurately
response on average for these suites
ors tended to increase with increas
re E-2, E-3, and E-4 (a)). As before,
orter characteristic periods (i.e., Tiso
he characteristic period of the isolat
s, the Method A procedure tended
ge, particularly for systems with sho
sults for the LA10in50 ground motio
omputed by Equation 22. Results
res (i.e., Τsub = 0.05 seconds) utiliz
tire range of parameters studied. For
more “nonlinearity” in the system,
nsitivity” of the error to variations
in general as the characteristic isolat
iti l l ti i d l th T
od B evaluation results for the LA10in
for the mean relative error computed
al range of parameters as the Method
(
increased with increasing characteri
o). On the other hand, βeff was redu
ncreasing Tsub), particularly for stron
f β i E ti 18 h i
Teff > 3 seconds and beff > 0.3 occur
e Method B evaluation for this suite
ratios greater than 30% were neglected
nsistent comparison to the Uniform Lo
errors for the Method B procedure.
ariation in results for the Method A
the LA10in50 database ground motio
ge systems determined by the Unifo
enerally accurate or conservative (ov
K2’
K1’K2’
K1
K2>
od” procedure to specific ground mot
re) tended to produce less conservat
study for all suites of ground moti
od” is more accurate on average w
the design setting, despite the mere f
quake events of equal likelihood poss
r” motions would be critical for isolat
for “mean” demand. These systems m
g y j p
). The earthquake demand utilized in
um (see Figure 5-6 (a)), which represe
of exceedence of 10 percent in 50 ye
w t ea t qua e ag tude a d o s
ille, 1997]. Consequently, it follows t
ectrum representing random directiv
ds represented by the mean spectrum
rcent) [AASHTO, 1999]. However, th
of elastic systems, and therefore may
f the bi-directional response of isola
d. 45o displacement path
dy
udinal and transverse axes of the bri
modeling. Five percent of the total m
gree-of-freedom. A damping ratio o
e damping contributions characterized
meters
s was performed utilizing the generali
model developed in these studies (
applied separately. Mean values of th
rectional input on system response.
ws,
motion pairs directly given the aver
motions. This can be seen clearly in
p
and isolation properties. Generally, m
asing system first-slope stiffness (
otions had more effect on systems w
stance from the earthquake fault. Figu
ratio generally decreased
esults were consistent for all ranges
xy x y
Dx Dy,( )
Values for both the Cxy coefficient
systems with the most rigid first-sl
le summarizes these statistical results
each ground motion bin. Ranges un
tudy for the ranges of ground mot
and isolated bridge system parame
of this increase due to bi-directional in
rcent respectively were realized over
This is also consistent with the results
was most pronounced for more ri
t s study d cate t at t s acto
lacement response due to bi-directio
system subjected to a suite of N grou
Dxy/mean(Dx,Dy) computed in this stu
rage value of the Dxy/mean(Dx,Dy) ra
parameters and ground motion reco
e of the D /mean(D D ) ratio ran
s of the design basis ea thquake
without its risks. For a stipulation
imply inelastic substructure behavior
ble motions However since no furt
dures provides sufficient overstrength
er, since the Guide Spec provides that
in lieu of the equivalent linear Unifo
med for certain isolated bridge syste
cte at o was ut ed.
gn Procedures
des general design criteria in Section
vides that the design of components
gy p
nd Q = M in the above design equatio
f flexural strength by dividing by an
redundancy, and ductility. Equation
of spectrum compatible ground motio
erstrength within the design proced
f the overall method. This effect will
d h t i d b li it t
ords. Isolated bridge system parame
he requirement for bounding analy
lastic. Substructure mass and damp
a d da p g co t but o assu ed to
etailed description of this model. Ove
eck is prescribed by a trilinear hystere
isolation and substructure hyster
ch earthquake record (n of N total) we
50” suite. For the case of rigid-pla
period represented by the substruct
al elastic period of the isolated bri
as generally more effected by change
Tiso) than by changes in isolator stren
ploying the most flexible and strong
t t d i th t d f t t
y demand generally increased as isolat
ond-slope stiffness, the system first-sl
co s de ed o t e 0 50 g ou
io D/Do (see Section 5.6.4 above). Th
re yielding had little effect on the to
most substructure hardening (i.e., Tsub
ere computed in this study.
ratio Cb/Cbo (see Section 5.6.4). Th
and isolation system strength decrea
hardening ratio (αsub) tended to incre
pe periods (Tsub <= 0.5 seconds) as s
indicates that the variations in syst
acement contribution from the isolat
contribution in the yielding substruct
average were computed for the majo
b ratio tended to be greatest for syste
s the first-slope period increased. Fo
ratio tended to increase with decreas
th a hardening ratio αsub 0.05. T
ith strength and second-slope flexibi
ively. Figure G-17 shows a time-hist
r the two systems in subplot (a) and
anent offset at the end of the respo
d hysteretic response results to the LA
f the lower shear output of the system
bstructure yielding. As seen in Figure
acement for the system with yield
for the system with a linear ela
ove st e gt t e des g p ov s o
mplied here. Further, the definition
so be at issue here. This may imply lo
in concrete piers, or similar limit s
espect, p ov s o s s ou d qua t y
demands and account for them explic
e incorporated through strength des
velop prior to brittle failure and throu
the response of isolated bridge syste
ustrate the effect of variations in syst
racteristics on peak response measu
Cyiso, Tiso, Tsub, respectively, see Sect
each of the three fundamental syst
em characterization was utilized in th
e AASHTO prescription could be m
o s we e pe o ed ut g t e p a
tion 5.2 and Figure 2-4(b)). Isolat
retic model mimicking the prescrib
Substructure mass was assumed to
x H of this report.
ts for the peak displacement (D (in))
field. For near-fault, fault-normal t
ed slightly with decreasing strength
ss (see Figure H-1 for Bin 1 motions
h l t ill t t th t k b h
0, and 1000 percent for Bin 1, 2, 3, 4,
udy for a variation in initial elastic per
show that peak total displacement w
nd-slope flexibility (i.e., varying Tiso)
ed to motions of larger magnitude
duced significantly with increasing T
ons (i.e., Cyiso = 0.03 subjected to Bi
0 400 percent maximum were realized
hese plots again illustrate that p
g initial system period (i.e., Tsub). A
esponse was more sensitive to variati
l h d f k
5 illustrate in more detail the effect
or systems having fixed isolator seco
t peak base shear was generally redu
ms subjected to far-field and/or sma
ted to ground motions at greater dista
thquake magnitudes (see Figure H-1
for isolated bridge systems subjected
at a given distance range from the act
idge systems with longer initial ela
base shear with decreasing earthqu
stems with a fixed second-slope per
her from the active fault (i.e., Bin 3 an
ely flat along the x-axis of the p
d decrease markedly along the positiv
yiso).
h H-26 present mean contour results
lustrate that substructure displacem
elastic period (i.e., increasing Tsub) fo
cond-slope period (i.e., longer Tiso,
e flexibility for these ground motion
ucture displacement for an increase
ith fixed isolator second-slope flexibil
ent reduced with increasing strength.
ame less effective in reducing isola
d over the long period range. The spec
placement was dependant on the spec
gures H-28 through H-31). The larg
etail the effect of isolator second-sl
ment response for systems having fi
ator displacements were generally l
n substructure displacements.
y p g
e that peak isolator displacement did
increasing initial elastic period. Furth
displacement was generally reduced
f earthquake distance on peak isola
k isolator displacement was reduced
und motions at greater distance from
f magnitudes). This reduction in isola
riod increased.
earthquake magnitude on substruct
mean peak substructure displacement w
ti f ll th k it
ectively) occur concurrently with p
amic assumptions imposed in this stu
utions), it is clear from Equation 44 th
cross the substructure.
strate in more detail the effect of stren
os (Diso/D and Dsub/D) for systems w
ement between the isolation system
bridge may be significantly effected
itial elastic periods. For these syste
reduce the percentage of displacem
more effect on near-fault than far-fi
e H-52 through H-55 for Bin 2 throug
n D /D and D /D shown here (
strated dependencies in the response
of system properties and ground mot
g p g
nce. In this study, a reduction in stren
crease in average total displacement
shortest initial elastic periods conside
m
g
e to variations in isolator second-sl
rger isolator second-slope flexibility
A maximum reduction in average b
hed earlier). For displacement dema
the sensitivity of base shear to variati
ex. However, as increasing strength w
n these studies it is apparent that stron
ess at large displacement amplitude
Displ.
larger δForcen strength
t a e ast c pe od dec eased).
acement increased in general as isola
an due to variations in strength over
tor second-slope flexibility increased
g ca t y as t e t a e ast c pe od
substructure flexibility increased). T
s shown earlier, where since isola
engthened or reduced with increas
os
articipating mass or damping, peak to
olator and substructure displacement
er implies that for these assumptions
ture and base shear response, it was a
structure displacement distribution w
ponse (characteristic of lower magnit
motions) and more sensitive to seco
t uctu e d sp ace e t at o educed)
lt distance. The change in response
ed was dependant on the specific syst
ion.
y g p
ution illustrated a similar, but not
econd-slope stiffness, most sensitive
s, distribution of displacements betw
be effected by varying the second-sl
f a significant effect on total and isola
ective as response amplitude decrea
a linearized method for estimating
ated bridge systems (see Section 5.4
structure approach facilitates simplif
ethod and/or other alternative procedu
ibutions to response.
m substructure components were mode
the substructure degree-of-freedom
f the substructure damping element, c
ue to time constraints, half of the grou
very other record for each bin select
computed, with the difference being t
bridge system with and without a gi
ain computed as D/D0, Diso/Diso 0, D
s for the peak displacement ratio (D/D
) which compare the peak displacem
substructure damping of ζsub = .05 to
ping contributions in a similar mann
and that for Bin 1 motions is due to
r displacement demands (as compared
of strength variations imposed at l
t of substructure damping of ζsub = 0
e was essentially negligible in all ca
y 3% maximum. In the response to ne
amping of ζsub = 0.05 on peak total
0.05) was 40% and 70% on avera
ubjected to Bin 5 ground motions.
ar Response
n 5 motions. For these higher frequen
asing system strength tended to incre
r initial elastic periods and decrease
form sensitivity to either strength
5.7.
so show that the Dsub/Dsub 0 ratios w
ess effected (compare data from Table
ally essentially rigid (i.e., initial ela
mping of ζsub = 0.05 suppressed p
se a maximum of approximately 25%
s are on the order of 5-30%, as sho
997]). Results from Chapter 2 sugges
he D/Do ratios were smallest for stron
smallest for weaker systems (with Tsu
eld) motions were uniformly effected
eriods considered (i e T b = 0 05 t
Do ratio was generally less than unity
sed (i.e., γ = .05 to .10). For Bin 1 (ne
over the entire range of initial ela
. This indicates for these cases that
ve and/or below unity for the mean D
es indicate the most significant variat
.974 1.08 1.11.99 1.11 1.2
1.11 .999 1.18 1.16 1.2
1.04.99 .999 .984 1.06 1.
s in isolator second-slope flexibility (
ratio to increase as Tiso increased wh
e systems were more sensitive to hig
ystems.
ues in Figure I-11 to I-15.
/or below unity for the mean Diso/Dis
es indicate the most significant effect
.873 .919 .839 1.04.947 .86
1.29 1.28 1.42 1.25 1.4
1.38 1.26 1.5 1.51 1.5
o ratios were effected predominantly
early insensitive to system strength (
became more dependant on strength
ure mass ratio increased from γ = .05
stribution is most significant in
ubstructures.
te to these values. These effects
study imply that ignoring higher m
ed with the distribution of substruct
contributions may cause signific
es regarding the relative significance
of these studies are outlined below
nd base shear response is generally m
than peak total and isolator displacem
d generally less effected for systems w
m Table 5-22 through 5-25) For syste
or other ground motion bins, the effec
and isolator displacements became m
flexible (i.e., Tsub >= 0.5 seconds), w
5 to 60 percent for substructure m
these contributions must reasonably
y is needed to establish whether curr
ation or other approximate methods
s to response, without resorting to m
373
6 Conclusions and Recommendations
6.1 Introduction
This report presented the results of a series of experimental and analytical studies
conducted for the California Department of Transportation under the Protective Systems
Research Program at the University of California, Berkeley. This report covers research
developed in order to:
1. Establish an understanding of global and localized response characteristics of simpleseismically protected bridges subjected to various types of seismic input including far-field, near-fault, and soft-soil motions.
2. Evaluate the effect of bi-directional and three-dimensional loading on isolated bridgesystems.
3. Validate the efficacy of seismic protective systems for bridges of simple, but realisticconfigurations.
4. Assess the applicability of requirements in the AASHTO Guide Specifications andrecommend improvements where needed based on the results of this research.
Each of these issues was examined earlier in Chapter 2 through 5 of this report. Reference
each of these chapters directly for more complete information on specific results. In this
concluding chapter, these findings are summarized and used to assess current design
procedures, and develop recommendations for improvement where necessary.
374
With respect to these needs in the current state-of-practice, the results of this study provide
two major conclusions.
• Foremost, earthquake simulation tests of system performance developed under this researchhave provided crucial proof-of-concept for the application of protective systems technology tobridges. These tests and ancilliary analyses have illustrated the efficacy of seismic isolation forsimple single- and double-span overcrossings and more complex bridge segments subjected tomulti-dimensional inputs of far-field, near-fault, and soft-soil ground motions. Key resultsfrom these earthquake simulation studies and analyses are summarized below to illustrate thispoint (see Sections 6.2 and 6.3).
• Secondly, analytical evaluations performed in this research have contributed significantly tothe understanding of the behavior of isolated bridge systems and insight into appropriatedesign approaches. These analytical studies have also established several areas in the currentprovisions of the Guide Specifications in need of further development.
Key analytical results are presented below in detail, along with recommendations for
improvement of code procedures where appropriate (see Sections 6.3).
6.2 Earthquake Simulation Studies
6.2.1 Proof-of-concept
The earthquake simulation studies developed in this project (see Chapter 3) verify the
efficacy of seismic isolation of simple bridge overcrossings. These tests illustrate the
robustness of bridge isolation as a means to mitigate damage during a seismic event.
Numerous input signals representing design basis far-field, near-fault, and soft-soil ground
motion inputs were imposed on the bridge specimens developed for these studies.
Insignificant variation in performance was realized after multiple and repeated tests.
Configurations with significant mass and stiffness eccentricity also showed effective
isolated response to numerous and varied ground motion input. These tests also illustrated
the effect of substructure mass, substructure yielding, vertical motions, and secondary
geometric nonlinearity on the response of these systems. Analytical trends identified in
Chapter 2 showing the effect of basic system variations on response were essentially
375
validated by these experimental simulations. Key results from these simulations are
summarized below.
6.2.2 Sensitivity to characteristics of ground shaking
The effect of variations in ground motion input on the effectiveness of isolated response
was illustrated in these simulation studies. Far-field, near-fault, and soft-soil events were
considered in these studies as well as the effect of multi-dimensional coupling in these
motions (i.e., the correlation of uni-directional, bi-directional, and vertical motion
components).
6.2.2.1 Ground motion type: far-field, near-fault, and soft-soil
Three earthquake table motions (i.e., LA13_14, NF01_02, and LS17c_18c) were selected
for studies of the effect of variations in ground motion type on the response of simple
isolated bridge systems. Four substructure stiffnesses represented by the various bridge
specimen configurations allowed this evaluation to be carried out over a broad range of
spectral frequencies.
Bridge specimen test results to these ground motion inputs indicated that response was
strongly influenced by ground motion characteristics, including frequency content and
directional orientation. The LA13_14 motion had significant higher frequency content and
response was strongly oriented along a 45 degree axis to the x-y direction. This resulted in
specimen response with significant coupling in the x- and y-directions and underlying
cycling of higher frequency. The LS17c_18c motion, on the other hand, was a soft-soil
motion with long period content near the characteristic period of the test bearings and
produced relatively harmonic response in the specimen. The near-fault NF01_02 motion
376
had impulsive, strongly coupled, fault-normal and fault-parallel components and produced
strongly coupled behavior in the specimen.
In general, the response of the bridge specimen could be classified based on the corellation
of its initial elastic period with the ranges of spectral peaks for LA13_14, NF01_02, and
LS17c_18c records. To illustrate this point, versions of the x-direction component of each
of three earthquake table motions were processed at two length scale factors (i.e., lr). In
this way a structure would respond as if it were in a different intensity and spectral
frequency range. This extended the range of structure dynamic characteristics considered
in these studies.
These analytical results indicated that for isolated systems with very rigid substructures
(or shorter initial elastic periods) peak total displacement is much larger than that of a
similar elastic system (i.e., non-isolated bridge with the same mass and initial stiffness
characteristics). For systems with greater substructure (or initial) flexibility, total peak
displacement was roughly equal to that of a similar elastic system. This behavior was
characteristic of systems in these “short period” and “long period” (or equal displacement)
ranges of spectral response (see also preliminary analytical results of Chapter 2). The
period ranges defining these “short” and “long” period ranges was a characteristic of the
particular ground motion input, as seen in the response to the scaled versions of these table
motions (see Chapter 4). For example, the “long period” (equal displacement) range for
the LA13 table motion began around Tsub = 0.55 seconds for a scale factor of lr = 1/2,
while for a length scale factor of lr = 1/4 the “long period” range began around Tsub = 0.35.
To illustrate the variation in response characteristics for systems in these different spectral
377
ranges, consider for example an isolated bridge system with a fixed fundamental (or initial
elastic) period of Tsub = 0.4 seconds. This isolated system may be in the “short period”
range (i.e., exceeding elastic displacements) for the LA13 motion at lr = 1/4. For the same
motion at lr = 1/2, however, this system would be in the “long period” range (i.e., having
nearly equal displacement as an elastic system). Response characteristics to different
ground motion input can be evaluated similarly.
6.2.2.2 Bi-directional motions
The effect of bi-directional input on specimen response was evaluated by computing the
two ratios and from test results. Here Uxy is the
peak displacement response from the bi-directional test while Ux and Uy are the peak
displacement from the x- and y-direction uni-directional tests, respectively. Results of
these ratios for the various specimen configurations indicate that the effect of bi-
directional input is most pronounced for systems with the most rigid initial stiffness (see
Figure 4-12). Values of Uxy/mean(Ux,Uy) and Uxy/srss(Ux,Uy) covered the range of 1.4-1.8
and 0.9-1.2 on average, respectively, for systems with the most rigid substructures (see
Chapter 4). For comparison, values of Uxy/mean(Ux,Uy) = 1.414 and Uxy/srss(Ux,Uy) = 1.0
would indicate that peak Ux and Uy displacements were occurring simultaneously in the
bi-directional response, resulting in peak Uxy displacement equal to their vector sum.
Further in-depth analytical studies on these effects were carried out in Chapter 5.
Uxy mean Ux Uy,( )⁄ Uxy srss Ux Uy,( )⁄
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6.2.2.3 Vertical motions
Experimental tests considered the effect of vertical motions on the response of a bridge
specimen utilizing a sliding isolation system. Test data indicated that vertical input tended
to effect isolator and total displacement response more than substructure displacement and
isolator shear force response. Peak isolator and total displacement response were
increased by approximately 9 and 5 percent on average by the addition of the vertical
input component, while peak substructure displacement and isolator shear force were
effected by less than 3 and 1 percent on average, respectively. The characteristic strength
of FP bearings fluctuate more with axial load variation than their stiffness, since Qd = µN
and kd = N/R and µ is generally an order of magnitude larger than 1/R. Consequently, since
deck and isolator displacements were shown to be more sensitive to system strength than
substructure displacements and isolator forces (see Chapter 2 and 5) the effect on them is
more pronounced.
6.2.3 Effect of system configuration
The effect of variations in basic system properties on isolated response was also studied in
these simulation studies. System variations included substructure mass, strength and
flexibility; isolator strength and flexibility; and global mass and stiffness eccentricity.
6.2.3.1 Substructure flexibility
The various configurations of the bridge deck specimen incorporated substructures with a
range of flexibility. Subsequent analyses on isolated bridge systems with mechanical
properties similar to the bridge deck specimen were also carried out for comparison with
these test results.
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In these experimental and analytical results peak deck displacements for isolated systems
with very rigid substructures were much larger than those of similar non-isolated systems
that are strong enough to remain elastic. Nearly all the displacement in the isolated system
occurs in the isolator component. On the other hand, for isolated systems with relatively
large substructure flexibility total displacement was roughly similar to that of a similar
non-isolated system. For these more flexible systems, total displacement was shared in
varying proportions between the isolation bearings and the substructure component
(dependant upon the characteristics of the ground motion input). Peak deck displacement
was seen to monotonically increase with increasing substructure flexibility. Peak isolator
displacement also increased, but less dramatically, or for certain inputs was roughly
constant for systems varying over the same range of substructure flexibility.
Peak deck acceleration response for these isolated systems was seen to be relatively
constant over a range of substructure flexibility. By comparison, for a similar non-isolated
elastic systems peak acceleration response would undulate dramatically as system
flexibility was varied (dependant again on characteristics of the ground motion input).
The advantage of the isolated system therefore is not significant force reduction, but
damage control and enhanced performance. Performance is enhanced as the isolation
system limits force response and makes it less sensitive to input characteristics. Damage is
controlled as the isolated system endures significant displacement demands (taken in a
large portion through the isolation bearings) without yielding or damage to the
substructure. Conventional bridges, on the other hand, are designed to endure significant
substructure damage in a design basis earthquake event.
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6.2.3.2 Isolator strength and flexibility
The configurations of the bridge deck specimen incorporated isolation system with
different mechanical properties for comparison.
For the isolated bridge specimen with an essentially rigid substructure, results indicated
that displacement response was particularly sensitive to strength and systematically
increased as strength decreased. Base shear response, on the other hand, was particularly
sensitive to isolator second-slope stiffness and consistently increased as bearings second-
slope stiffness increased. In addition, the stiffening behavior of HDR bearings caused by
scragging effects at peak (virgin) response cycles resulted in further increases in shear
response above those experienced by other bearings at similar displacement amplitudes.
Notably this increased force spike in the HDR bearings near peak amplitude did not
appear to markedly change displacement response.
For the isolated bridge specimen with more flexible substructures (i.e., Tsub = 0.25, 0.75
and 1.0 seconds), displacement response was also sensitive to strength and systematically
increased as strength decreased. Strength was seen to have more effect on displacements,
however, as the substructure became more rigid. This was more apparent at larger motion
amplitudes. Force response, on the other hand, was less sensitive to variations in
characteristic isolator strength. Variations in isolator second-slope flexibility were not
evaluated on these specimen configurations.
6.2.3.3 Substructure mass
Varying substructure mass proportions of γ = msub/Mdeck equal to approximately 0, 5, and
10 percent were considered in the simulation studies. Results indicated that the effect of
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variations in substructure mass over this range was most prominent on substructure
displacement (and consequently base shear), less on isolator displacement, and least on
total deck displacement response. However, the difference in average response (to the
three table test motions) as substructure mass was varied from 0 to 10 percent, rarely
exceeded 10 percent. The tendency was for average response to increase as substructure
mass increased. Base shear response was therefore highest for the system with most
substructure mass (resulting directly from the higher substructure displacement demand),
as expected. On the other hand, additional substructure mass had a relatively insignificant
effect on isolator shear force response. This behavior is intuitive, since increased isolator
displacement results in only minor increase in force output due to the low second-slope
stiffness of these devices.
6.2.3.4 Mass eccentricity
Superstructure mass eccentricity of 0, 5, and 10 percent of span length was considered in
these studies for a simple single-span bridge overcrossing. Limited test results indicated
that torsional contributions to peak isolator displacement at the ends of the deck span were
more prominent for impulsive and soft-soil type motions than for far-field events. Further,
isolator displacements at the ends of the deck span did not, in general, increase linearly
with mass eccentricity.
Previous evaluations suggest FP bearings provide a re-centering mechanism to an isolated
system [Bozzo, et al 1989]. The friction force and lateral stiffness of an FP bearing is
proportional to the applied normal force (see Chapter 3, Equation 3). This implies the
center of resistance of an isolated system utilizing FP bearings will inherently align with
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the system’s center of mass, counteracting torsional response. Analysis and testing in
these previous studies confirmed this behavior [Bozzo et al, 1989].
The tests performed in this report using impulsive motions, however, seem to refute this
generalization. This may be due to the sensitivity of “rigid” structures to strength (see
Sections 2.3.5.2 and 4.3). The lighter end of the specimen (having a lower resisting
friction force) may tend to displace more than the heavier (i.e., stronger) side producing
the torsional behavior seen in these studies. Comparable results to test this hypothesis for
full intensity motions utilizing LR bearings (whose strength is not sensitive to axial
applied force) were not possible in these studies. In this respect, further analysis and
testing is still needed to establish reliable trends in the response of systems with eccentric
mass.
6.2.3.5 Stiffness eccentricity
The effect of substructure stiffness eccentricity on isolated response was also evaluated in
these studies. Significant stiffness eccentricity was considered with the braced and
unbraced ends of the specimen differing in total lateral stiffness by an order of magnitude
(i.e., nearly ten times). Configurations utilizing FP bearings with symmetric slider
arrangements and unsymmetric arrangements arranged to counteract torsional response
(with weaker sliders on stiffer braced end piers and stronger sliders on flexible end piers)
were also considered.
These limited results indicated that peak rotation demand in the eccentric configurations
was not a function of peak displacement amplitude nor was it effected significantly by bi-
directional input. Prior to yielding in the isolation bearings, stiffness eccentricity induced
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significant torsional response. However, when bearings operate in their isolated mode on
either end of the specimen overall system stiffness eccentricity is minimized. The rotation
response in these eccentric configurations was therefore due to the tendency of the system
to rotate prior to bearing yield. Post-yield (i.e., in the isolated mode) stiffness eccentricity
is nearly eliminated and rotation demands become insensitive to incremental and peak
displacement response. Isolated behavior in essence suppresses the underlying torsional
behavior, unlike in a standard bridge where substructure stiffness eccentricity would
impose torsional demands increasing with response amplitude.
Further, bi-directional input in these tests imposes an additional orthogonal component of
motion on the longitudinal axis of the specimen. In this direction the stiffness arrangement
was symmetric. Thus, the additional longitudinal component did not engage lateral-
torsional coupling in the system, and results indicated that this additional component did
not tend to increase rotation demands significantly. Coupling in the yield response of the
isolation bearings imposed by the additional longitudinal component did not appear to
effect peak rotation significantly either in these tests. This again indicates that torsional
response in these systems, with substructure stiffness eccentricity, appears to be more
effected by system behavior prior to bearing yield.
Tests results indicated that peak total displacement response was somewhat larger for the
same bridge specimen with added substructure stiffness eccentricity (i.e., one end braced
rigidly). Peak isolator displacement response was not as systematically effected
(sometimes increasing and sometimes decreasing), indicating that torsional rotation was
not consistently in phase with peak response in these test sequences. These limited results
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also indicated an unsymmetric configuration utilizing lower and higher strength FP sliders
installed in bearings located above braced and unbraced supports, respectively, was
effective in reducing torsional response due to underlying substructure stiffness
eccentricity.
6.2.3.6 Substructure yielding
The effect of yielding substructure components on the response of a two-span isolated
bridge specimen illustrated a pattern of force redistribution from central yielding piers to
outer (non-yielding) end piers. Despite this yielding behavior, total deck displacement
history remained stable during the isolated response. In this system, isolation bearings
absorbed the majority of total displacement demand up to yielding in the substructure.
Beyond this point, central piers yielded plastically until peak displacement was attained.
As such, only minor ductility demands were imposed on the substructure. For a
conventional (non-isolated) bridge system, nearly the entire displacement demand would
be imposed on the elements of the substructure, inducing significantly larger ductility
demands on these components.
6.2.4 Characteristic distribution of force and displacement demands
Typical patterns of global and local force and displacement distribution were noted in
these studies. Shear demands tend to concentrate toward stiffer end (abutment) piers.
Center pier-isolator assemblies see similar total displacement demand as end pier-isolator
assemblies enforced by displacement compatibility in relation to the in-plane stiffness of
the bridge deck as it displaces laterally. Since the secant stiffness of the central pier-
isolator assemblies at peak displacement is lower typically than at end (abutment) pier-
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isolator assemblies, higher shear demands concentrate at abutment locations.
Displacement distribution between isolator and pier components are made in relation to
the relative flexibilities of these elements at their respective locations. Since each location
sees nearly equal total displacement demand, a smaller proportion of the total
displacement at center piers is taken in the isolation bearings with a larger proportion
taken in the more flexible center piers. On the other hand, nearly all the displacement
demand is taken by isolation bearings at stiffer end (abutment) piers.
6.2.5 Local kinematic effects
In two-span bridge specimen tests, end (abutment) piers were braced while center piers
could rotate on clevis pins at their base. Consequently, during testing flexible center piers
underwent significant lateral tip displacement and overall rigid body rotation. This
rotational behavior caused second-order axial shortening in the vertical height of these
central piers. Axial shortening in stiffer braced end (abutment) piers was insignificant.
Axial shortening in center piers resulted in redistribution of gravity load to end piers
transmitted by the stiff continuous girder.
Since the slip-force and lateral stiffness of FP bearings are proportional to the supported
axial load (see Chapter 3, Equation 14), the vertical force redistribution in these test
sequences just described caused a significant pinching of the force-deformation behavior
of the FP bearings atop central piers. Globally, total axial force (due to gravity) remained
constant, thus rendering total bearing slip-force and total system strength unchanged.
Locally, however, the redistribution of axial force to end piers, which increased bearing
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strength and stiffness locally, increased shear demand on associated connections and
substructure components at these locations.
This particular phenomenon appeared to be more a characteristic of the unique test setup
in this case then that representative of an actual bridge. However, axial load redistributions
will occur in real bridge structural systems to some extent. These tests highlight the
sensitivity of sliding and FP bearings to fluctuations in axial load, effects that may impose
local force amplifications. The shear stiffness of elastomeric bearings is also effected by
vertical stress variations, and their stability at peak displacement is determined on the
basis of vertical load demands.
The second order kinematic effects causing axial load redistribution in these test
sequences are not typically incorporated in standard design analysis methods nor included
in current design procedures [AASHTO, 1999]. These results highlight the need for
further research in this area. The effect of axial load fluctuations on sliding systems due to
vertical ground motion input was discussed previously, above.
6.3 Implications for Design Practice
Current design practice of isolated bridge systems is embodied in the AASHTO Guide
Specifications for Seismic Isolation Design [AASHTO, 1999]. Results of the preliminary
evaluations presented in Chapter 2, simulation tests presented in Chapter 3 and 4, and the
analytical studies presented in Chapter 5 have indicated several areas where application of
current design procedures is adequate and pinpointed other areas in need of further
consideration. Recommendations for specific improvements are offered below. In some
cases, alternate design methodologies or approaches are suggested. These methodologies
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may effectively mitigate some of the difficulties encountered in the application of the
current Guide Specifications. Further research in some areas is also needed, and several
recommendations for future research are outlined as well.
6.3.1 Basic AASHTO Design Equation
6.3.1.1 Reliability
The guide specifications are based on approximate analytical methods that linearize the
response of inelastic systems. Many general studies of such methods have been under
taken. Most of these linearization methods are based on either harmonic or random
response [Chopra and Goel, 1999]. It has been shown in numerous studies that methods
based on harmonic response considerably overestimate the period shift of the substitute
system, whereas methods derived considering random response give much more realistic
estimates of effective period [Iwan and Gates, 1979b]. Two methods based upon harmonic
response have been widely adapted to the design several types of inelastic structures. The
"substitute structure method" [Shibata and Sozen, 1976] has been popularized by some for
displacement-based design [Gulkan and Sozen, 1974; Shibata and Sozen, 1976; Moehle,
1992; Kowalsky et al., 1995; Wallace, 1995]. The "secant stiffness method" [Jennings,
1968] has been adapted to formulate the "nonlinear static procedure" in the ATC-40
[Applied Technology Council, 1996] and FEMA-274 reports [FEMA, 1997]. For the
design of seismically isolated bridges, the AASHTO Guide Specifications [AASHTO,
1999] utilizes the Uniform Load Method which is an adaption of the "secant stiffness
method".
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Since the Uniform Load Method is based on an assumption of ideal harmonic response,
there is a concern that it may overestimate the shift of the system’s effective period [Iwan
and Gates, 1979b]. In other words, the Uniform Load Method may tend to overestimate
the system’s “effective” flexibility, thereby overestimating displacement response.
Concern has also been raised about the Uniform Load Method’s linear visco-elastic
“equivalent” damping assumption, as this might not be appropriate for response to
strongly impulsive motions (such as those characteristic of near-fault shocks). Dissipation
provided by viscous damping is rendered less effective under impulse excitations.
In these research studies, it was found that the displacements of seismically isolated bridge
systems computed by the Uniform Load Method were generally accurate or conservative
(over-predicted) on average over a broad range of simple isolated bridge structures for a
suite of spectrum compatible ground motions. This suggests that period shift was
generally predicted accurately or over-predicted by the procedure. This is consistent with
previous findings [Iwan and Gates, 1979b]. On the other hand, direct application of the
underlying “secant stiffness method” procedure in these studies using specific ground
motion records tended to still produce conservative, but less conservative, estimates of
peak response on average. This suggests that the “secant method” was more accurate on
average when applied to individual ground motion spectrum directly then when applied to
a smoothed representation of the mean spectrum of a suite of motions (as in the Uniform
Load Method procedure). The level of conservatism is not uniform and some ranges of
structural characteristics produce very conservative results that could have a significant
impact on project costs.
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It was also found that the difference in errors produced by application of the “secant
stiffness method” to far-field, near-fault, and pure pulse type ground motions were
inconclusive in determining whether the harmonic damping assumptions utilized in the
linearization procedure are less conservative for more impulsive ground motion types.
Other structural factors and the relation of ground motion and structural characteristics
were found to be more important as factors in determining the accuracy of the method
than the ground motion characteristics alone.
The basis of the Uniform Load Method on an assumption of linearized behavior suggests it
would necessarily produce more accurate prediction for more “linear” systems. This is
achieved as either kd and ku become equal (i.e., the isolator becomes more “linear”), the
substructure becomes more flexible (i.e., Ksub decreases), or as system strength decreases
(i.e., Qd is reduced). System “linearity” may be evaluated through the parameter αsys (see
Chapter 5, Equation 27), where the system becomes more “linear” as αsys approaches 1.0
(see Chapter 5, Figure 5-13). Strength reduction increases system “linearity” by both
decreasing system “effective damping” and causing system second-slope and secant
stiffness to converge (see Chapter 5, Equation (18) and (26)). Trends in the error between
the peak response computed by the Uniform Load Method and the “exact” response
computed by nonlinear time-history analysis in these studies appear to validate this
prediction. The Uniform Load Method was most accurate for systems with lower strength,
having more flexible substructures, or utilizing more “linear” isolation devices (i.e., kd
approaching ku).
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The results of this study also suggest the inter-relationship between system strength and
first-slope stiffness effects the accuracy in the Uniform Load Method procedure. For more
initially rigid systems (i.e., highest first-slope stiffness), errors in Uniform Load Method
were reduced as system strength reduced consistent with the above discussion (i.e., the
system became more “linear”). However, for more initially flexible systems (i.e., lower
first-slope stiffness) errors were reduced as strength increased. This trend likely resulted
from the tendency for stronger systems to behave more predominantly in their linear first-
slope mode.
The Guide Specifications present limits on the application of the Uniform Load Method
presumably to prohibit usage of its linearized procedure for more nonlinear systems.
Explicit nonlinear analysis is required both for systems with long equivalent periods (i.e.,
Teff > 3 seconds) and for systems which are highly “damped” (i.e., beff >= 0.3, unless B =
1.7 is used). In these studies, these measures did not appear to mitigate error uniformly,
however, with both accurate and inaccurate results alike being discarded by the
application of these limits.
Notably, when the Uniform Load Method was most inaccurate in this study, it tended to
overpredict response on average. However, these results also suggest significant under-
estimation may occur for ground motions with spectra above the mean design spectrum.
Assuming a normal distribution in the statistical scatter, mean-1σ errors as large as 50-75
percent were computed for the suite of twenty motions considered in these studies. These
twenty motions were selected to match the design spectrum closely on average and
possessed the same return interval as the target design spectrum. It is important to note
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that all the earthquake events in this suite are equally as likely to occur within the
representative return interval. Demands from the “larger” motions in the suite would
therefore be critical for isolation systems designed by the Uniform Load Method for
“mean” spectral demand. These systems may be provided with limited overstrength and/or
surplus displacement capacity to resist these larger demands. Similarly, substructure
components designed to remain “essentially elastic” for “mean” design response by the
Uniform Load Method may not possess adequate overstrength or ductility capacity to
resist the level of demand imposed by these larger events. In the end, design based on
“average” spectral intensity masks the risk associated with these larger demands. It may
prove appropriate for the Guide Specifications procedures to rationally account for the
probability of these less numerous, but equally likely, events.
The results of this study showed that the Uniform Load Method had non-uniform
accuracy, suggesting that some systems will be designed more conservatively and some
less conservatively by these procedures. Further, the Guide Specifications limit on
equivalent period and damping (i.e., Teff 3 seconds and beff 0.3) did not resolve this
issue in a consistent fashion. Therefore, while this study has found that the method
appears to provide a level of conservatism on average, alternate displacement-based
design methods may be warranted to achieve more uniform reliability. Measures which
allow rational consideration of the likelihood of risk associated with larger events of
equivalent return period should also be incorporated. A discussion of alternate procedures
which incorporate these features is presented later.
≤ ≤
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6.3.1.2 Bi-directional effects
The AASHTO Guide Specifications define earthquake demand through a smoothed design
spectrum representing a uniform earthquake hazard with a probability of exceedence of
10% in 50 years defined regionally across the nation (see Chapter 5, Figure 5-6 (a)). It is
understood that real ground motions consist of shaking along two horizontal axes and a
vertical axis at a given site. The AASHTO design spectrum represents the uniform hazard
spectrum for expected ground motion records. As such, it represents random or “average”
directivity. With regard to estimating the peak displacement of isolated bridges subjected
to bi-directional inputs, the use of a design spectrum representing random directivity to
estimate response demands poses two distinct difficulties.
First of all, it has been illustrated that the difference between the mean spectrum
representing fault normal or the “larger” orthogonal component of bi-directional ground
motion history pairs and the mean spectrum of all ground motion history pairs
(representing “average” directivity) increases with earthquake magnitude and for sites
located more closely to the active fault [Somerville, 1997]. Consequently, it follows that
design displacement estimates based upon a spectrum representing random directivity
would underestimate mean displacement demands represented by the mean spectrum of
the “larger” (fault normal) orthogonal component of the earthquake record. This
underestimation would be most severe for larger magnitude earthquakes and near-fault
sites.
Secondly, it is not apparent that the peak response of a seismically isolated bridge system
subjected to bi-directional input can be estimated with reasonable accuracy from the
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response of the same system subjected to each of the bi-directional components applied
uni-directionally. The reason for this is twofold. Primarily, phasing within each of the
ground motion components may dictate bi-directional response with peaks occurring more
or less simultaneously producing a maximum vectored displacement much larger than
either of the uni-directional maxima. Next, coupling which occurs in the bi-directional
yield surface of typical seismic isolation systems causes a reduction in resisting force
orthogonal to the direction of initial displacement (see Chapter 5, Figure 5-14). This
coupling effect would presumably cause increases in displacement demand for systems
subjected to bi-directional motions, since displacement along one axes will reduce the
isolation system’s resistance to motion in the orthogonal direction.
Current code procedures provide a method of estimating peak bi-directional force demand
in isolated bridges by combining uni-directional maxima in a combination of 100 to 30
percent (or conversely 30 to 100 percent) [AASHTO, 1999]. However, these procedures
were established from the evaluation of elastic systems, and therefore may not adequately
capture the nonlinear complexities of the bi-directional response of isolated bridge
systems.
An evaluation of the effects of directivity and bi-directional input on the response of
simple seismically isolated bridge systems was undertaken in these studies. It is evident
from the results presented that the effect of bi-directional input on seismically isolated
bridge systems is significant. It was found for all cases considered that on average peak
displacement response due to bi-directional input was considerably larger than peak
response due to uni-directional input applied separately. This disparity was most
394
significant for more rigid structures, employing stronger isolation systems, subjected to
larger magnitude earthquakes, and located nearer to the active fault. For these cases, softer
site-specific soils tended to further increase the bi-directional effect.
These results are consistent with the previous factors which influence the effects of bi-
directional coupling. Firstly, coherent phasing within each of the ground motion
components has been shown to be most significant for near-fault motions (which contain a
more coherent impulsive content than in the far-field) and for soft soils. The results of this
study are consistent with this trend, where it is seen that the bi-directional effect is more
pronounced for these ground motion conditions. Second, coupling in the force-
displacement yield surface of seismic isolation bearings would tend to be more
pronounced for more rigid systems, where interaction with the yield surface would occur
more readily at smaller displacements. In addition, the greatest reduction in resisting force
orthogonal to the direction of initial displacement would occur for the strongest isolation
systems. This is also consistent with the results of these studies, where the bi-directional
effect was most pronounced for systems which were stronger and more initially rigid.
As described previously, the AASHTO Uniform Load Method provides a procedure for
estimating the mean peak displacement response of seismically isolated bridge systems
subjected to a suite of uni-directional spectrum compatible motions representing random
or “average” directivity. If it is assumed that this method provides a reliable estimate of
the mean peak response of an isolated bridge system subjected to a sufficiently large
sampling of spectrum compatible motion pairs, then the results of this study indicate that
the method will significantly underestimate on average the peak displacement response of
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the system when subjected to the same ground motion pairs applied bi-directionally. In
addition, since the difference between the mean spectrum of “larger” (fault-normal)
ground motions and the mean spectrum of all ground motion pairs (representing “average”
or random directivity) increases with closer proximity to the active fault (due to directivity
in the ground motion), the AASHTO Guide Specifications procedures have been shown in
these studies to be increasingly less conservative in accounting for bi-directional effects
with closer fault proximities or soft-soils. The Guide Specifications allow a combination
of 100 percent plus 30 percent of orthogonal maxima to be utilized to account for the
effects of bi-directional input [AASHTO, 1999]. If this procedure is applied a maximum
vectored displacement of only approximately 1.04 would be realized, assuming design
response in each orthogonal direction to be equal. The results of this study indicate that
this factor is inadequate to capture average increases in displacement response due to bi-
directional coupling.
On average, in these studies increases in peak displacement response due to bi-directional
input of ground motion pairs of approximately 25-75 percent above the average response
due to the same pair of ground motions applied separately (i.e., uni-directionally) were
realized for the ranges of ground motion distance, magnitude, site specific soil type, and
isolated bridge system parameters considered (see Chapter 5, Table 5-18). It is therefore
recommended that a revision to code procedures be applied to account for the effects of bi-
directional interactions. For simple bridge overcrossings, substructure stiffness is typically
dictated by essentially rigid abutment conditions. Further, design basis earthquake demand
is nearly equivalent to the Bin 2 motions considered in these studies (see Chapter 5).
Given these general conditions for design, it is recommended that the effects of bi-
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directional motions for simple bridge overcrossings be computed by weighting design
displacements as follows
(50)
where dbi is the peak bi-directional displacement in any vectored direction, Cxy is a bi-
directional weighting factor, and dx and dy are the uni-directional design displacements
computed by Guide Specifications procedures in each orthogonal direction of the bridge,
respectively. It is recommended that a factor of Cxy= 1.5 be used for the weakest and most
initially flexible isolation systems (where bi-directional interactions would be least) and
Cxy= 1.7 be used for the strongest and more initially rigid isolation systems (where bi-
directional interactions would be greatest). For near-fault and softer site specific soil
conditions these factors should be increased by an additional 5%.
6.3.1.3 Equivalent SDF vs. MDF behavior: Influence of Substructure Mass and Damping
The linearized substitute structure procedure employed in the AASHTO Uniform Load
Method is a conceptually appealing approach which facilitates analysis. However, it has
limitations with regard to the incorporation of substructure mass and damping
contributions. These contributions make the determination of “equivalent” single-mode
“effective stiffness” and “effective damping” properties difficult. The Guide
Specifications allows a Multi-Mode Spectral Method to be utilized to incorporate the
effects of non-isolated higher modes which may potentially capture substructure mass
effects. Alternative damping procedures for accounting for substructure contributions
have also been suggested by others [Sheng et al., 1994]. Ignoring these contributions is
dbi Cxydx dy+
2-----------------
=
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also a practical simplification. However, possible loss of accuracy in the methodology
may result. To this end an evaluation of the effects of substructure mass and damping
contributions on the response of simple seismically isolated bridge systems was
undertaken in these studies. These results suggest that substructure mass and damping
contributions play different roles in effecting total, isolator, and substructure response.
The magnitude of these influences may determine when these contributions can be
neglected in the design process without significant loss of accuracy, or on the other hand,
when ignoring these contributions may cause significant underestimation of peak
response.
The results of these studies illustrated that for isolated bridge systems with essentially
rigid substructures the effect of adding substructure damping of 5 percent of critical (i.e.,
ζsub = 0.05, see Chapter 5, Equation 49) on peak total and isolator displacement response
was negligible in all cases (suppressing average response by less than approximately 3
percent maximum). For these systems (i.e., simple bridge overcrossings with essentially
“rigid” abutments), these substructure damping contributions could be reasonably
neglected. For response to near-fault motions (i.e., Bin 1), the effect of 5 percent
substructure damping on peak total and isolator displacement response was minor even for
systems with the most flexible substructures, with a peak reduction in average response of
approximately 10 percent maximum. For far-field and lower magnitude earthquakes (i.e.,
Bin 2 through 5), the effect of 5 percent substructure damping on peak total and isolator
displacement response became increasingly more significant with increasing substructure
flexibility. For these motions the addition of 5 percent substructure damping produced
maximum reductions in average peak total and isolator displacement of 40 and 70 percent,
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respectively, for the most flexible substructures considered (i.e., Tsub = 2 seconds). In all
cases, the addition of substructure damping caused reductions in average peak total and
isolator displacement response. Ignoring these contributions would be considered a
conservative simplification (as they result in reductions in computed average peak
displacement). For systems with more flexible substructures which may benefit
significantly from these reductions, this simplification may be perhaps considered overly
conservative.
These results also indicated that for systems with stiffer substructures the addition of 5
percent substructure damping had more effect on average peak substructure displacement
and base shear response than on peak total and isolator displacement. On the other hand,
for systems with more flexible substructures the opposite was true. For systems with
essentially rigid substructures (i.e., Tsub = 0.05 seconds), 5 percent substructure damping
reduced average peak substructure displacement and base shear response by
approximately 25 percent maximum in these studies (compared to 3 percent for total peak
and isolator displacement response). For systems with the most flexible substructures
considered (i.e., Tsub = 2 seconds), 5 percent substructure damping reduced average peak
substructure displacement and base shear response by approximately 30 percent
maximum (compared to 40 and 70 percent for total and isolator displacement,
respectively). While these reductions in substructure displacement and base shear
response may be considered significant, ignoring these reductions would again be
considered a conservative simplification in the design process. Particularly, since it is the
performance goal in an isolated bridge to limit substructure damage, considering higher
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force demands for these components (by ignoring substructure damping contributions)
will contribute to this result.
The effect of typical substructure mass contributions of 5 and 10 percent of the total
system mass (i.e., γ = .05 to .10, see Chapter 5, Equation 48) were examined in these
studies as well. Results indicated for systems with essentially rigid substructures that 5
and 10 percent substructure mass contributions reduced average peak total and isolator
displacement response approximately 8 and 16 percent maximum, respectively. For
response to near-field, motions (i.e., Bin 1), 5 and 10 percent substructure mass
contributions had only a minor effect on peak total and isolator displacement response for
all ranges of substructure flexibility considered (with response varying by approximately
10 percent maximum). For these cases, ignoring substructure mass contributions may be
considered a reasonable simplification (as they result in reductions or otherwise minor
variations in total and isolator response). For other ground motion conditions (i.e., Bins 2
through 5), the effect of substructure mass contributions up to 10 percent on peak total and
isolator displacements became more significant as substructure flexibility increased, with
average response increased by approximately 15 to 60 percent over the range of isolation
system parameters considered. For these cases, ignoring substructure mass distribution
may result in significant underestimation in computed response, particularly for systems
with more flexible substructures.
The results of this study showed that substructure mass contributions always increased
average peak response of the substructure. For systems which were initially essentially
rigid (i.e., Tsub = 0.05 seconds), substructure mass contributions of 5 and 10 percent
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increased peak substructure response approximately 50 and 90 percent maximum,
respectively. For systems with the most flexible substructures (i.e., Tsub = 2 seconds), 5
and 10 percent substructure mass contributions increased average peak substructure
response approximately 10 and 25 percent maximum, respectively. Systems with
intermediate substructure flexibilities, showed increases in response between these values.
These effects are significant, and ignoring these substructure mass contributions would
likely cause considerable underestimation of average peak substructure response (i.e.,
displacement and base shear).
These results are useful in establishing the significance of substructure mass and damping
contributions to the global response of simple isolated bridge systems. Conditions in
which these contributions may be reasonably ignored without significant loss of accuracy
have been identified in the discussions above. Ignoring these contributions in these cases
is a practical simplification. For cases where more accurate consideration of substructure
damping is warranted, alternative equivalent damping procedures which seek to account
for these contributions are available. Many of these methods have been examined by
others [Sheng et al., 1994]. Strain-energy proportional methods for determining these
effects have also been presented [Kawashima et al., 1994]. For cases where more accurate
consideration of substructure mass contributions are warranted, the Guide Specifications
allows the Multi-Mode Spectral Method to be utilized to account for these higher mode
effects. Further study is needed to establish whether this procedure is adequate in
compensating for these contributions. More accurate modeling discretization and explicit
time-history analysis may be required in some cases to account for these higher modes.
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6.3.1.4 Parametric Study of Nonlinear Isolated Bridge Response
Due to the underlying difficulties with current linearized Guide Specifications procedures,
and the need to understand the trend in nonlinear displacement and force response of
isolated bridges for purposes of design, a systematic evaluation of the nonlinear response
of seismically isolated bridge systems was undertaken in these studies. This parametric
evaluation was developed to establish the specific effects of pertinent design variables on
the response of isolated bridge systems. These fundamental variations include mechanical
properties of the isolation system and substructural components as well as variations in
features of the earthquake ground motion input.
For purposes of this study, a bilinear simplification was utilized to characterize isolation
bearing hysteresis and total system uni-directional force-deformation response (see
Chapter 2, Figure 2-2 (a) & (b)). Three independent parameters (eg., the first- & second-
slope stiffness, K1 & K2 respectively, and the system yield strength, Fy) define this
bilinear system. An evaluation of the influence of these hysteretic parameters on system
response was used to understand the explicit nonlinear behavior of simple isolated bridge
systems.
Total Displacement. - These studies illustrated that total displacement response was very
sensitive to variations in the initial elastic period of the isolated bridge system. Total
displacement response increased as much as tenfold on average in these studies for an
increase in initial first-slope elastic period from 0.05 to 2 seconds for systems with fixed
strength and isolator second-slope flexibility.
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Total displacement response was also found to be more sensitive to variations in system
strength than isolator second-slope flexibility over the range of properties considered (i.e.,
strength coefficeients from 3 to 12 percent and bearing characteristic isolation periods
from 2 to 6 seconds). In this respect, increased strength resulted in decreased total
displacement for systems with shorter initial elastic periods and increased total
displacement for systems with longer initial elastic periods. The spectral region at which
strength had negligible effect on average total displacement became centered at
progressively longer periods for ground motions of increasing magnitude and decreasing
fault distance.
Similar dependency on strength had been reported previously in the nonlinear response of
single-degree-of-freedom bilinear oscillators subjected to earthquake and shock inputs
[Newmark, et al. 1975]. For these inputs imposed on systems with initial elastic periods
less than the predominant pulse period, displacement increases dramatically as strength is
reduced. For systems with initial elastic periods near the predominant pulse period,
however, displacement decreases with reduced strength. This behavior was illustrated
earlier in Chapter 5, Figure 5-16. The total displacement response seen in these studies
mimics this reported behavior.
Base Shear. - These studies illustrate that base shear response was less sensitive than total
displacement to variations in initial elastic period. Maximum decreases in mean base shear
of 50 percent occurred in these studies for an increase in initial elastic period of 0.05 to 2
seconds over the range of isolation system parameters and ground motion inputs
considered.
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Generally, base shear decreased as strength was reduced and/or isolator second-slope
flexibility was increased. However, base shear was more sensitive to strength for low
amplitude response (characteristic of Bin 3, 4, and 5 motions) and more sensitive to
isolator second-slope flexibility for large amplitude response (characteristic of Bin 1
motions) in these studies. For system response in the intermediate range of amplitudes
(characteristic of Bin 2 motions), weaker systems with higher isolator second-slope
stiffness had base shear response more sensitive to variations in isolator second-slope
flexibility while stronger and/or systems with larger isolator second-slope flexibility had
base shear response more sensitive to strength.
This trend in base shear behavior may be explained by considering fundamental system
response at varying displacement amplitude ranges. For lower magnitude and/or far-field
motions in this study (characteristic of Bin 3, 4, and 5 motions), total displacement
response was relatively small. As shown earlier for small amplitude displacement
response (see Chapter 5, Figure 5-17 (a)), variations in system second-slope stiffness have
a relatively minor effect on overall force output (and on displacement response as well, as
discussed previously above). Comparatively, an increase in system strength, although
perhaps reducing overall displacement, will also produce a significant increase in overall
force output. On the other hand, for near-fault, fault-normal motions in this study (i.e., Bin
1 motions), total displacement demands were relatively large. As shown earlier for this
type of large amplitude response (see Chapter 5, Figure 5-17 (b)), variation in system
strength, although perhaps effecting overall displacements dramatically, does not have a
relatively large impact on force output compared to the effect of system second-slope
flexibility imposed over this larger displacement demand (understanding that
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displacements are not significantly effected by variation in second-slope flexibility, as
established earlier). For displacement demands intermediate to these cases, as for Bin 2
motions, the sensitivity of base shear to variations in strength and isolator flexibility is
more complex. However, as increasing strength was seen to reduce displacement response
generally in these studies, it is apparent that stronger systems subjected to these motions
will have displacement demands toward the smaller amplitude range with base shear
response showing sensitivity as shown in Chapter 5, Figure 5-17 (a). Weaker systems
subjected to these motions, on the other hand, will have displacement demands toward the
larger amplitude range with base shear response showing sensitivity as illustrated in
Chapter 5, Figure 5-17 (b). However, for systems with the largest second-slope flexibility
(i.e., larger Tiso) response is nearly elastic perfectly-plastic. These systems will have force
output necessarily more sensitive to changes in strength as shown earlier in Chapter 5,
Figure 5-17 (c).
Isolator Displacements. - These studies illustrate that isolator displacements were more
sensitive in general to system strength than isolator second-slope flexibility, similar to
total displacement response. Further, increased isolator strength decreased isolator
displacements consistently on average in these studies. For example for a strength increase
from 3 to 12 percent, maximum reductions in isolator displacement of 80 percent in
isolator displacement occurred for systems with the shortest initial elastic periods in these
studies.
These results also illustrated that isolator displacement increased in general as isolator
second-slope flexibility increased, but less so than due to variations in strength over the
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range considered. Sensitivity to changes in isolator second-slope flexibility was greatest
for weaker, stiffer isolation bearings and for systems with longer initial elastic periods.
On the other hand, unlike total displacement response isolator displacements did not
increase or decrease in general with increasing initial elastic period. For far-field motions,
average isolator displacement response in this study increased by approximately 100
percent but also decreased by as much or more as initial elastic period increased from 0.05
to 2 seconds for specific isolation system parameters over the range of properties
considered. For near-fault motions, isolator displacement in this study reduced nearly 40
percent maximum with increasing initial elastic period for systems with the weakest and
most flexible isolation systems considered, but in general remained relatively constant.
Substructure Displacement. - For these studies, isolation systems were considered rigid
plastic such that initial system flexibility was attributed entirely to the substructure
component. These studies illustrated that substructure displacement was dependant upon
its stiffness. Substructure displacement response increased significantly as the initial
elastic period of the isolated bridge system increased (i.e., as substructure flexibility
increased), similar to total displacement response. Since isolator displacement response
was seen to neither consistently increase or reduce with increasing substructure flexibility,
it is implied that increase in total displacement is largely the result of increasing
substructure displacement as the substructure is made more flexible.
Furthermore, these studies illustrated that substructure displacement showed sensitivity to
strength for low amplitude response and to second-slope isolator flexibility for large
amplitude response similar to base shear. Similarly for intermediate amplitude response,
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substructure displacement was most sensitive to strength when employing the strongest
and most flexible isolation systems and most sensitive to isolator second-slope flexibility
when employing the weakest and stiffest isolation systems.
Finally, these studies illustrated that displacement of flexible substructures was the most
sensitive to variations in isolation system properties. In general, substructure displacement
response was reduced by reducing strength and/or increasing isolator second-slope
flexibility.
Isolator and Substructure Displacement Ratios. - These studies illustrated that in general
the ratio Diso/D decreased (and inversely Dsub/D increased) on average as substructure
flexibility increased (i.e., increasing initial elastic period) for all isolation system
parameters and ground motion inputs considered. In addition, isolator and substructure
displacement distribution illustrated the same sensitivity to strength and isolator second-
slope flexibility as base shear and substructure displacement response (for a system with a
fixed substructure stiffness). With this in mind, these studies illustrated that reduced
strength increased the isolator’s contribution to total displacement and reduced it for the
substructure (i.e., increased Diso/D and decreased Dsub/D) for a system with fixed initial
stiffness. Increasing isolator second-slope flexibility caused a similar redistribution.
Earthquake Magnitude and Distance. - These studies illustrated for all cases of system
parameters considered that larger earthquake magnitude and/or nearer fault distance
increased total displacement, isolator displacement, substructure displacement, and base
shear response on average over the suites of ground motion records utilized in these
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studies. In addition, the isolator displacement ratio was increased (and the substructure
displacement ratio reduced) for larger earthquake magnitude and/or nearer fault distance.
Further, as system response amplitude increased at larger earthquake magnitude and/or
nearer fault distance the sensitivity of base shear, substructure displacement, and
substructure to isolator displacement distribution changed from strength to isolator
second-slope flexibility. Increasing response amplitude did not effect appreciably the
sensitivity of total and isolator displacement to strength, however.
Summary. - Performance objectives in an isolated bridge system typically include control
of force and displacement demands. The results of these studies are useful in establishing
the causal links in ground motion and system characteristics effecting these performance
measures.
Total and substructure displacement response were shown in these studies to be
particularly sensitive to initial elastic system stiffness. On the other hand, base shear
response was shown to be relatively insensitive to this variation. In addition, isolator and
total displacement response was shown to be more sensitive to strength and relatively
insensitive to variations in isolator second-slope flexibility. Further, base shear and
substructure displacement response illustrated a dependency on strength and isolator
second-slope flexibility in relation to the amplitude of response (i.e., more sensitive to
strength for low amplitudes and more sensitive to second-slope flexibility for the large
amplitude response). Isolator and substructure displacement distribution illustrated a
similar, but not as dramatic, dependency on strength and isolator second-slope stiffness,
most sensitive for flexible substructures.
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Taking these dependencies into consideration, response may be tailored to meet specific
performance objectives and design situations. Practical limits of isolation system
mechanical properties and substructure component proportioning must be considered in
this respect, as well as the potential seismic environment for the proposed application.
Reduction in total and/or substructure displacements for an isolated bridge system may be
most effected by an increase in initial elastic system (or substructure) stiffness. These
studies indicate that this will have a minor effect on total base shear and likely a minor
effect on isolator displacement (although in the far-field, a likely reduction in this as well).
Isolator displacements are best reduced by adding strength, although adding initial elastic
stiffness may also provide a significant reduction in these displacements (although may
also perhaps produce an undesirable increase).
Base shear (and substructure displacements) can best be reduced for lower amplitude
response (i.e., in the far-field) by reducing strength, anticipating an associated increase in
total and isolator displacements. Reducing base shear (and substructure displacements) by
adding isolator second-slope flexibility is also an option, although most effective for
larger amplitude response (i.e., in the near-field). Further, since total and isolator
displacements are relatively insensitive to this variation, this latter method is promising
for reducing base shear without producing an over-compensation in displacement
response.
For systems with relatively flexible substructures, distribution of displacements between
the isolator and substructure component can be effected by varying the second-slope
flexibility of the isolation system (without fear of a significant effect on total and isolator
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displacements). This method becomes less effective as response amplitude decreases.
Varying isolator second-slope flexibility should be executed with discretion, as this
measure may either unduly increase base shear response or produce large residual
displacements which may require post-earthquake recentering.
In addition, for systems with relatively flexible substructures displacement distribution
between the isolator and substructure can also be effected by strength. This measure
becomes less effective as response amplitude increases. Also, re-distributing
displacements in this manner will also effect isolator and total displacements significantly,
requiring this measure to be balanced with other performance objectives.
The understanding of these trends in the nonlinear behavior of isolated bridges is key to
removing the dependence on linearized assumptions which cloud current design
procedures and provide limited guidance to designers. Nonlinear spectra of the types
produced in this study produced from a large statistical sample could also be adapted
directly for use as a design methodology. This would provide a measure of rationality in
the procedure and would allow uncertainty to be statistically quantified in the design
method. Falling short of this, utilization of the understanding of explicit nonlinear
behavior developed here in conjunction with current linearized design procedures will
assist designers in proportioning simple isolated bridge systems to meet desired
performance.
Finally, current Guide Specifications procedures require consideration of variations in
isolation device properties in the design procedure. This is instituted by requiring
component properties to be multiplied by λ factors which have been empirically
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formulated from test results to bound mechanical properties. Results of the parametric
studies undertaken in this research lend further clarity to these measures. These results
indicate that variations in certain properties may produce negligible variation in system
response and thus their consideration is irrelevant in the bounding analyses. On the other
hand, particular variations significantly effect system response (e.g., strength). In these
cases, any additional rational measures aimed at considering lower and upper bounds in
these properties are certainly well justified.
6.3.1.5 Substructure yielding
The formulation of the AASHTO Guide Specifications suggests that some measure of
substructure yielding may occur. This is implied by stipulating the use of force reduction
factors which eliminate overstrength in the demand-capacity equations for substructure
design for the case of an isolated bridge (see Chapter 5, Section 5.1.1). The Guide
Specifications commentary states that these lower R-Factors (in the range of 1.5 to 2.5) are
formulated such that their “ductility based portion is near unity and the remainder
accounts for material overstrength and structural redundancy” and design by these
provisions “ensure, on average, essentially elastic substructure behavior in the design-
bases earthquake”. The Guide Specifications commentary further states that response
calculated by the prescribed procedures “represent an average value, which may be
exceeded given the inherent variability in the characteristics of the design basis
earthquake” [AASHTO, 1999]. However, since no further guidance is given in the Guide
Specifications on how to assess or provide for this yielding behavior, the formulation
implies that yielding of substructural components will not adversely effect the
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performance of the isolation system nor inflict ductility demands on substructure
components beyond their inherent limits.
On this basis, studies were performed to evaluate the efficacy of this new code
formulation in its ability to meet these stated performance objectives (i.e., ensure elastic
behavior on average). The results of these studies indicate that significant yielding of
substructure components may occur for isolated bridge systems designed optimally to
these current AASHTO design provisions. Most notably, substructure ductility demands
greater than 1.0 on average were computed in these studies in all cases (and in many cases
much greater than 1.0). This appears to refute the claim that the provisions in the Guide
Specifications “ensures essentially elastic substructure response on average” [AASHTO,
1999]. Either way, it appears columns in isolated bridge systems designed by Guide
Specifications provisions will require a measure of ductile capacity (since ductility
demands are at least implied by the commentary for response above the mean). However,
since a significant portion of the overall displacement demand occurs in the bearings for
an isolated bridge system, ductility demands in the columns of isolated bridges will still be
substantially smaller than in a comparable non-isolated system.
Further research is needed to establish whether the AASHTO detailing provisions provide
sufficient nominal ductility capacity in their component design specifications to meet the
demands implied by this study. The definition of “essentially elastic substructure
response” may also be at issue here. This definition may imply local strain demands to the
level of surface spalling in concrete piers, or similar limit state definitions, which would
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be produced at a level of global ductility demand larger than unity. Further research is
needed to address these ancillary issues.
The results of these studies also indicate that the presence of substructure yielding in
systems designed optimally to the AASHTO Guide Specifications had negligible effect on
overall total and isolator displacement demands, but instead caused a redistribution of
displacement between the isolation system and the yielding substructure component. This
effect may limit displacement demands on isolation devices and in turn drive displacement
ductility demands into the substructure. Further, when substructure yielding is explicitly
allowed, shears are reduced - a desirable effect which will limit forces on foundations,
connections, and brittle components. However, the effects of isolator overstrength due to
variations in isolator material properties, contamination, aging, scragging, or path effects;
impact on displacement restraint systems; and system vs. component overstrength
relations may result in increases in force output and produce larger substructure ductility
demands on systems designed without their consideration. These additional factors must
be considered in any rational design procedure.
Finally, if the intentions of the AASHTO provisions are to ensure elastic substructure
response on average, then it is implied that ductile response will be allowed for 50 percent
of “design basis” ground motions. In this respect, provisions should quantify the
magnitude and risk associated with these implied demands and account for them explicitly
in component design procedures. Given a determination of these substructure ductility
demands, strength design procedures may then be utilized to ensure ductile mechanisms
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develop prior to brittle failure and that proper detailing requirements are supplied to
provide sufficient plastic rotation, local strain, and/or inelastic buckling capacity.
Barring a more detailed procedure, a general procedure for estimating substructure
ductility demands in simple bridge overcrossings may be postulated as follows:
1. Since total displacements were shown in these studies to be generally conserved,substructure and isolator displacement demands may be estimated for simple isolatedbridge overcrossings given that
(50)at peak response. This simplification may be considered appropriate for bridgeovercrossings since the effect of substructure mass and damping contributions onisolator and substructure displacements was shown in these studies to be essentiallynegligible for all but the most flexible substructures.
2. Isolator and substructure component nonlinear force-deformation relations may thenbe established though test results, mechanical relationships, or as for column bentsthrough standard moment-curvature analysis procedures.
3. Demands for isolator and substructure elements may then be established to satisfy theabove relation assuming force compatibility for these components at computeddisplacements.
4. As a final step, ductility demands for substructure components may be evaluatedthrough the established force-deformation relations from the previous step.
6.3.2 Alternative Methods
Displacement based design methods are currently utilized as standard practice. These
procedures focus on establishing displacement demands (and associated forces) for the
purpose of system design. Examples of these are incorporated in the ATC-40 [Applied
Technology Council, 1996] and FEMA-274/356 [FEMA, 1997] building codes. The
AASHTO Guide Specifications for Seismic Isolation Design (or Guide Spec) [AASHTO,
1999] also incorporates displacement based procedures for the design of isolated bridges.
Diso Dsub+ D≈
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Displacement based methodologies can be loosely characterized into equivalent linear and
approximate nonlinear procedures. More recently performance-based design (PBD)
methodologies have been undergoing development as well. PBD methods go beyond
earlier approximate procedures and seek to rationally quantify the likelihood of specific
limit or loss state outcomes given the conditional probability of system response in a given
seismic environment. A summary of equivalent linear, approximate nonlinear, and PBD
procedures are presented below.
6.3.2.1 Equivalent Linear Procedures
Equivalent linear analytical methods for estimating response of inelastic systems include
methods based on either harmonic or random response [Chopra and Goel, 1999].
Currently, two methods based upon harmonic response have been adapted to the design of
inelastic structures. The "substitute structure method" [Shibata and Sozen, 1976] has been
popularized by some for displacement-based design [Gulkan and Sozen, 1974; Shibata
and Sozen, 1976; Moehle, 1992; Kowalsky et al., 1995; Wallace, 1995]. The "secant
stiffness method" [Jennings, 1968] has been adapted to formulate the "nonlinear static
procedure" in the ATC-40 [Applied Technology Council, 1996] and FEMA-274/356
reports [FEMA, 1997]. For the design of seismically isolated bridges, the AASHTO Guide
Specifications [AASHTO, 1999] has adopted the Uniform Load Method which is
essentially an adaption of the "secant stiffness method".
It has been shown that methods based on harmonic response considerably overestimate
the period shift of the substitute system, whereas methods derived considering random
response give much more realistic estimates of effective period [Iwan and Gates, 1979b].
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Further, it was shown in these studies that the Uniform Load Method utilized in the
AASHTO Guide Specifications does not produce results of uniform reliability. Results of
these studies indicate that this method may produce slightly over-conservative designs for
certain system characteristics and slightly under-conservative designs in other cases (see
Chapter 5, Section 5.4).
6.3.2.2 Approximate Nonlinear Methods
Approximate nonlinear methods have been pioneered by numerous authors. Earlier
techniques focused on establishing system strength capacity necessary to limit global
ductility demands [Newmark, 1975]. These techniques focused on establishing strength
reduction factors which permit estimation of inelastic strength demands from elastic
strength demands. A comprehensive review of various investigations of strength reduction
factors carried out over the last thirty years has been performed by others [Bertrero, 1994].
Recently nonlinear displacement based procedures have been formulated as well. These
methods focus on establishing inelastic displacement ratios defined as the ratio of the
maximum lateral inelastic displacement demand of a structure with given strength to the
maximum lateral elastic displacement demand for a system with similar first-slope
stiffness properties [Miranda, 2000]. Researchers have reviewed several of these new
procedures and compared advantages and disadvantages of each method [Miranda, 2002].
Approximate nonlinear displacement based procedures have also been formulated for
standard practice. Examples of these are incorporated in the ATC-40 [Applied Technology
Council, 1996] and FEMA-274/356 [FEMA, 1997] building codes.
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While both forced-based and displacement-based approximate nonlinear methods are
useful, and explicitly recognize the nonlinear behavior of real structural systems subjected
to earthquake overloads, their formulation has been predominately developed for building
structures which inherently have a limited upper bound on ductility. Isolated systems
characteristically respond with displacement ductilities significantly greater than those
imposed on non-isolated building systems. Therefore, currently available approximate
nonlinear procedures have limited use for design of isolated bridges without significant
reformulation to consider larger nonlinear displacement amplitudes.
6.3.2.3 Performance-Based Design
Performance based design (PBD) methods seek to enable accurate probabilistic
quantitative evaluation of structural performance. These methods integrate consideration
of random variations in input and system characteristics and evaluate their effect on
nonlinear response to discern statistical bounds on likely outcomes.
Probabilistic models. - The development of PBD methods has focused initially on the
formulation of probabilistic models of system performance. Recently a comprehensive
Bayesian methodology for developing probabilistic capacity and demand models for
structural components and systems has been formulated [Der Kiureghian, Mosalam, et al,
2002]. These probabilistic models are similar to deterministic capacity and demand
procedures commonly used in practice, but apply additional correction terms to account
for inherent systematic and random errors. These models provide means to gain insight
into the underlying behavioral phenomena and to select ground motion parameters that are
most relevant to the seismic demands. The models take into account information gained
417
from engineering principles, laboratory test or field data, and engineering experience and
judgment [Der Kiureghian, Mosalam, et al, 2002].
PEER methodology. - The Pacific Earthquake Engineering Research Center (PEER) is
engaged in developing a complete probability-based framework for performance-based
design. This formulation is both rational and adaptable to a variety of applications. The
methodology comprises several models including a seismic demand model. The PEER
Center is not alone in this endeavor. Both FEMA (the Federal Emergency Management
Agency) and ASCE (the American Society of Civil Engineers) have developed the
FEMA/ASCE 356 prestandard. This document addresses performance in terms of facility
operability, occupiability, life safety, and resistance to collapse, under four discrete levels
of seismic excitation. PEER's methodology seeks to address economic performance as
well as operability and safety, and to express performance in probabilistic terms such as
distributions on repair costs and loss-of-use on an annualized or lifetime basis.
PEER's performance based design methodology is illustrated schematically in Figure 6-1
below. This PBD formulation seeks to quantify the likelihood of specific limit or loss state
outcomes rationally conditional on system response in a given earthquake hazard
environment. The methodology incorporates hazard analysis and structural analysis, both
familiar aspects of current design practice. The PEER methodology also adds two new
features, damage and loss analysis. Damage analysis is the explicit, probabilistic
calculation of physical damage (eg., which bars have buckled, which beams have spalling,
etc.) for a given level of global demand. Loss analysis is the explicit, probabilistic
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calculation of performance in terms of economic loss and loss of use for a given level of
damage.
PEER's performance-based methodology is currently in development. It is being evaluated
in the PEER testbed project, which seeks to demonstrate and exercise the methodology on
six real facilities: two buildings, two bridges, a campus of buildings, and a network of
highway bridges. In conjunction with this, engineering practitioners are comparing the
PEER methodology with current practice (such as the ASCE/FEMA prestandard and other
approach), to identify strengths and areas of needed development [Deierlein, 2001].
Bridge design parameter sensitivity. - Currently researchers are utilizing the development
of recent probability-based PBD framework to develop probabilistic demand models for
highway bridge overpasses [Stojadinovic, 2002]. This framework seeks to develop
demand models which relate ground motion intensity measures (IM), such as peak
Figure 6-1 PEER PBD Analysis Methodology [Deierlein, 2001]
419
spectral acceleration, to bridge demand parameters (DP), such as displacement ductility.
These models are used to assess response sensitivity to variations in bridge design
parameters, such as column height and diameter. Relations for each design parameter give
bridge designers the ability to evaluate the effect of their design choices on structural
performance [Stojadinovic, 2002].
Conclusion. - Performance based design methods are the current trend in design of
systems for earthquake performance. These methods seek to enable accurate probabilistic
quantitative evaluation of system performance and quantify decision making parameters
in terms of damage and loss. These methods integrate the consideration of variability in
ground motion input, system mechanical characteristics, and nonlinear response. These
methods are rational and adaptable and may be readily formulated for use in the design of
isolated bridge systems.
Performance-based formulations also seek to remove the dependence on approximate
equivalent linear and nonlinear procedures. There focus is to determine response based
upon accurate probabilistic distributions, and establish sensitivity for each design
parameter giving designers the ability to evaluate the effect of their design choices on
structural performance. This formulation is similar to the evaluations performed in these
studies, where earthquake hazard was defined by a suite of deaggretized motions,
nonlinear response determined explicitly through time-history analyses to these inputs,
and response presented statistically for each bridge system-input variation to illustrate
sensitivity. This PBD approach provides statistical quantification of the likelihood of
specific performance limit outcomes given system response to a given seismic
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environment. The performance-based methodology removes the reliance on approximate
methods which cannot inherently provide the rational measure of reliability essential to
defining risk. In this respect, PBD procedures represent the next step in the development
of design procedures for earthquake resistant systems.
6.4 Future Research Need
Through the research presented in this paper, developed under the Coordinated Protective
Systems Program for the California Department of Transportation, much insight has been
gained regarding the application of these technologies to bridge systems. In particular, as
outlined in the program objectives (see Chapter 1, Section 1.3), this research has improved
knowledge in the following areas:
1. Understanding the effects of bi-directional loading on seismic isolation bearings and indeveloping improved analytical bearing models.
2. Understanding global and local response characteristics of simple seismicallyprotected bridges subjected to various types of seismic input including far-field, near-fault, and soft-soil motions.
3. The efficacy of seismic protective systems for simple and more complex (realistic)bridge configurations.
4. The efficacy of requirements in the AASHTO Guide Specifications for SeismicIsolation Design.
Results and conclusions presented in the preceding six chapters highlight this
understanding. In conjunction with this research, however, areas of future research need
have also been identified. Further development in these areas is deemed critical to assist
the application of protective systems to bridge structures to gain broad acceptance and use.
These research areas include:
1. Effect of deck flexibility and overturning on global and local isolated response.
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2. Effect of abutment pounding on energy dissipation and isolated response.
3. Effect of bridge joints.
4. Effect of bridge skew.
5. Kinematic effects on axial load distribution.
6. Effect of random variations in isolation system characteristics.
7. Performance-based design procedures.
8. Performance hybrid systems incorporating isolators and supplemental energydissipation devices.
These areas of research are logical extensions of the studies already performed under
Phase I of the Protective Systems Research Program presented in this report.
6.5 Conclusion
The devastating consequences of a major seismic event was illustrated during the Loma-
Prieta, Kobe, Northridge and more recent earthquakes. Protective systems provide a
practical method for protecting life and property in the event of a major earthquake. The
studies performed in this research have illustrated the general ability of protective systems
to provide an effective means of earthquake resistance in simple bridge systems. The
considerable durability and robustness of these systems were illustrated through multiple
and varied simulations. Given this validation, broad acceptance of this technology in
bridge applications should be considered a priority in zones of high seismic risk. To this
end, support of new and existing protective systems applications is essential, as well as
support for continuing research efforts and the current trend of development of
performance based design procedures.
422
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