EERC 2004-01 March 2004 Experimental and

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Technical Report Documentation Page 1. Report No.

2. Government Accession No.

3. Recipient's Catalog No.

UCB/EERC 2004-01 4. Title and Subtitle

5. Report Date

Experimental and Analytical Studies of the Friction Pendulum System for the Seismic Protection of Simple Bridges.

March 2004 6. Performing Organization Code

UCB/ENG-9374 7. Author(s)

8. Performing Organization Report No.

Gilberto Mosqueda, Andrew S. Whittaker, Gregory L. Fenves, and Stephen A. Mahin 9. Performing Organization Name and Address

UCB/EERC 2004-01 10. Work Unit No. (TRAIS)

Earthquake Engineering Research Center University of California, Berkeley 1301 South 46th Street Richmond, CA 94804

11. Contract or Grant No.

Contract No. 59 A 169

12. Sponsoring Agency Name and Address

13. Type of Report and Period Covered

Research Report August 1994-December 2000

California Department of Transportation Engineering Service Center 1801 30th Street MS#9 Sacramento, CA 95816

14. Sponsoring Agency Code

California Department of Transportation

15. Supplementary Notes

16. Abstract

Experimental and analytical studies were conducted to examine the behavior of sliding bearings to multiple components of excitation. In the experimental studies, a 7 ft. by 10 ft. rigid frame model isolated with Friction PendulumTM bearings, representing a scaled model of an isolated bridge, was subjected to displacement-controlled orbits and earthquake simulations. The displacement test data were used to characterize the bearings to bi-directional orbits and calibrate mathematical models suitable for representing Friction Pendulum bearings. The earthquake test data were compared with analytical simulations to evaluate the efficacy of the calibrated models. Models based on plasticity and linear viscoelastic theory were evaluated in the analytical studies. The results show that for a bidirectional earthquake analysis, coupling of friction in the two orthogonal components should be accounted for to correctly predict bearing displacements. Modeling of the vertical load on the bearings is also necessary for accurate prediction of bearing forces. Tri-directional simulations conducted on the earthquake simulator platform showed that vertical acceleration has a small effect on the displacement response of a bridge isolated with Friction Pendulum bearings.

17. Key Word

18. Distribution Statement

seismic isolation, friction, bearings, shaking table, experiments, bidirectional loading, modeling 19. Security Classif. (of this report)

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20. Security Classif. (of this page)

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21. No. of Pages

110

22. Price

Experimental and Analytical Studies of the Friction Pendulum System for the Seismic Protection of Simple Bridges

By

Gilberto Mosqueda Andrew S. Whittaker Gregory L. Fenves and Stephen A. Mahin

A Report on Research Conducted Under Grant No. 59A169 from the California Department of Transportation

Earthquake Engineering Research Center University of California, Berkeley March 2004

UCB/EERC 2004-01

Abstract Experimental and analytical studies were conducted to examine the behavior of sliding bearings to multiple components of excitation. In the experimental studies, a 7 ft. by 10 ft. rigid frame model isolated with Friction PendulumTM bearings, representing a scaled model of an isolated bridge, was subjected to displacement-controlled orbits and earthquake simulations. The displacement test data were used to characterize the bearings to bi-directional orbits and calibrate mathematical models suitable for representing Friction Pendulum bearings. The earthquake test data were compared with analytical simulations to evaluate the efficacy of the calibrated models. Models based on plasticity and linear viscoelastic theory were evaluated in the analytical studies. The results show that for a bi-directional earthquake analysis, coupling of friction in the two orthogonal components should be accounted for to correctly predict bearing displacements. Modeling of the vertical load on the bearings is also necessary for accurate prediction of bearing forces. Tri-directional simulations conducted on the earthquake simulator platform showed that vertical acceleration has a small effect on the displacement response of a bridge isolated with Friction Pendulum bearings.

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Acknowledgements This research was supported by the California Department of Transportation (Caltrans) under Contract No. 59A169. This support is gratefully acknowledged. Caltrans engineers Tom Post, Dorie Mellon, Roberto Lacalle, and Li-Hong Sheng worked closely with the project team. Earthquake Protective Systems provided the bearings used in this study. The mathematical models and calibration procedures were developed by Dr. Wei-Hsi Huang. Mr. Troy Morgan and EERC Laboratory Manager Don Clyde provided extensive support of the experimental program.

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Table of Contents

CHAPTER 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 1.2 1.3 1.4

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Caltrans/Berkeley Protective Systems Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Objectives of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Organization of Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 4 5 5

CHAPTER 2. Friction Pendulum Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Formulation of Model for Friction Pendulum Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Bi-Directional Plasticity Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.1 Modified Plasticity Model for Friction Pendulum Bearings . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.2 Bi-directional Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 Rotation of Friction Pendulum Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

CHAPTER 3. Experimental Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Test Specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Facilities and Procedures for Bi-directional Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Description of Rigid Block Model and Test Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Test Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Facilities and Procedures for Bi-directional Earthquake Simulations . . . . . . . . . . . . . . . . . . . . . 3.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Selection of Earthquake Histories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Test Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19 20 20 21 23 27 27 27 30

CHAPTER 4. Results and Analysis of Displacement-Controlled Tests . . . . . . . . . . . . . . 43 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Characterization of Bearings from Bi-Directional Displacement-Controlled Tests . . . . . . . . . . 4.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Influence of Test Setup on Friction Pendulum Bearing Behavior . . . . . . . . . . . . . . . . . . . 4.2.3 Breakaway or Static Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Stick-Slip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Velocity Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.6 Pressure Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.7 Load History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.8 Path History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Calibration of Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Comparison of Models with Displacement Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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43 43 43 44 48 51 52 54 56 58 59 63 70

CHAPTER 5. Results and Analysis of Earthquake Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5.2 Typical Response of Friction Pendulum Bearings to Earthquake Excitation . . . . . . . . . . . . . . . 71 5.2.1 Combination of Horizontal Ground Motion Components . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.2.2 Effect of Vertical Ground Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.3 Response Analysis of Rigid Block Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.3.1 Selection of Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.3.2 Comparisons of Experimental Response with Mathematical Models . . . . . . . . . . . . . . . . 86 5.3.2.1 LA21/22 (1995 Kobe, JMA Station): . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.3.2.2 LS17C/18C (1994 Northridge, Olive View, simulated soft soil site): . . . . . . . . . . . 91 5.3.3 Evaluation of Mathematical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.3.4 Modeling of Axial Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.4 Recommendations for Modeling FP Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

CHAPTER 6. Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.2 Conclusion and Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

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List of Figures Figure 1-2 Friction Pendulum bearing........................................................................................................2 Figure 1-1 Lead-rubber bearing in a deformed state. ................................................................................. 2 Figure 1-3 Viscous damper (courtesy of Taylor Devices) .......................................................................... 3 Figure 2-1 Pendular trajectory of structure isolated with Friction Pendulum bearings..............................8 Figure 2-2 Forces acting on the articulated slider in FP bearings .............................................................. 9 Figure 2-3 Elastic and hysteretic resisting force components of plasticity model ................................... 10 Figure 2-4 Interaction surface for bi-directional uncoupled and coupled plasticity model...................... 14 Figure 2-5 Examples of response of coupled and uncoupled plasticity model with typical parameters for a FP bearings ................................................................................................................... 15 Figure 2-6 Rotation of FP bearings .......................................................................................................... 16 Figure 2-7 Rotated spherical surface of FP bearing ................................................................................. 17 Figure 2-8 Effect of concave dish rotation on FP bearing hysteresis .......................................................18 Figure 3-1 EPS Friction Pendulum bearing.............................................................................................. 20 Figure 3-2 FP bearing with concave plate raised to show the sliding surface.......................................... 21 Figure 3-3 Plan and elevations of the rigid block model with struts attached.......................................... 22 Figure 3-4 Rigid block model with struts attached................................................................................... 22 Figure 3-5 Instrumentation of rigid block model for bi-directional testing..............................................24 Figure 3-6 Orbits for the bi-directional displacement-controlled tests..................................................... 28 Figure 3-7 Scaled input motion LA13, 1994 Northridge, Newhall; length scale = 2, amplitude scale = 100% (Table 3-4)....................................................................................... 32 Figure 3-8 Scaled input motion LA14, 1994 Northridge, Newhall; length scale = 2, amplitude scale = 100% (Table 3-4)....................................................................................... 33 Figure 3-9 Scaled input motion LA21, 1995 Kobe, JMA Station; length scale = 5, amplitude scale = 100% (Table 3-4)....................................................................................... 34 Figure 3-10 Scaled input motion LA22, 1995 Kobe, JMA Station; length scale = 5, amplitude scale = 100% (Table 3-4)....................................................................................... 35 Figure 3-11 Scaled input motion LS01E, 1940 El Centro; length scale = 3, amplitude scale = 100% (Table 3-4)....................................................................................... 36 Figure 3-12 Scaled input motion LS02E, 1940 El Centro; length scale = 3, amplitude scale = 100% (Table 3-4)....................................................................................... 37 Figure 3-13 Scaled input motion LS17C, 1994 Northridge, Sylmar; length scale = 5, amplitude scale = 100% (Table 3-4)....................................................................................... 38 Figure 3-14 Scaled input motion LS18C, 1994 Northridge, Sylmar; length scale = 5, amplitude scale = 100% (Table 3-4)....................................................................................... 39 Figure 3-15 Scaled input motion NF01, 1978 Tabas; length scale = 5, amplitude scale = 100% (Table 3-4)....................................................................................... 40 Figure 3-16 Scaled input motion NF02, 1978 Tabas; length scale = 5, amplitude scale = 100% (Table 3-4)....................................................................................... 41 Figure 4-1 Axial load variations in bearings supporting the rigid block model.......................................45 Figure 4-2 Typical response of rigid block model supported on FP bearings .......................................... 46 Figure 4-3 Influence of axial load variations on the response of FP bearing 3 ........................................ 47 Figure 4-4 Typical variation of friction coefficient with sliding velocity (adapted from Constantinou et al. 1999)....................................................................................................................................... 49 Figure 4-5 Earthquake testing of a virgin slider showing apparent breakaway friction........................... 50 Figure 4-6 Test setup for measuring friction (adapted from Rabinowicz 1995) ...................................... 51 Figure 4-7 Stick-slip in FP bearings ......................................................................................................... 52 Figure 4-8 Velocity dependence of the coefficient of friction for one FP composite............................... 53

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Figure 4-9 Pressure dependence of the coefficient of friction..................................................................56 Figure 4-10 Reduction in the coefficient of friction with repeated cycling ............................................. 57 Figure 4-11 Path-dependent response of FP bearings: box Orbit 2 and hourglass Orbit 3 ...................... 60 Figure 4-12 Path-dependent response of FP bearings: box Orbit 2 and figure-8 Orbit 4......................... 61 Figure 4-13 Effect of path offset on response of FP bearings ..................................................................62 Figure 4-14 FP Bearing No. 4: Experimental data compared with coupled and uncoupled plasticity model for Orbit 2 ....................................................................................................65 Figure 4-15 FP Bearing No. 4: Experimental data compared with coupled and uncoupled plasticity model for Orbit 3 ....................................................................................................66 Figure 4-16 FP Bearing No. 4: Experimental data compared with coupled and uncoupled plasticity model for Orbit 4 ....................................................................................................67 Figure 4-17 FP Bearing No. 4: Experimental data compared with coupled and uncoupled plasticity model for Orbit 7 ....................................................................................................68 Figure 4-18 Examples of response of plasticity model with typical parameters for an FP bearings around a sharp corner for displacement increments of (a) 0.05 in. and (b) 0.005 in. ............69 Figure 5-1 Experimental response of rigid block model in X-direction for bi-directional test (l) NF01/02-100% .................................................................................................................. 72 Figure 5-2 Experimental response of rigid block model in the Y-direction for bi-directional test (l) NF01/02-100% .................................................................................................................. 73 Figure 5-3 Acceleration response spectra (5% damping) of recorded earthquake simulator acceleration for uni-directional tests (j) LA21(X)-100%, (k) LA22(Y)-100%, bi-directional test (h) LA21/22-100% and tri-directional test (i) LA21/22V-100% .............. 74 Figure 5-4 Experimental response of rigid block model Bearing 3 for uni-directional tests (j) LA21(X)-100%, (k) LA22 (Y)-100% and bi-directional test (h) LA21/22-100%............76 Figure 5-5 Experimental response of rigid block model Bearing 3 for uni-directional tests (j) LA21(X)-100%, (k) LA22(Y)-100% and bi-directional test (h) LA21/22-100%............. 77 Figure 5-6 Experimental response of rigid block model Bearing 3 for uni-directional tests (n) NF01(X)-100%, (o) NF02(Y)-100% and bi-directional test (l) NF01/02-100% ............. 78 Figure 5-7 Experimental displacement histories of rigid block model Bearing 3 for bi-directional test (l) NF01/02-100% and tri-directional test (m) NF01/02/V-100% ................................... 80 Figure 5-8 Experimental response of rigid block model Bearing 3 for bi-directional test (l) NF01/02-100% and tri-directional test (m) NF01/02/V-100%.......................................... 81 Figure 5-9 Experimental response of rigid block model Bearing 3 for bi-directional test (l) NF01/02-100% and tri-directional test (m) NF01/02/V-100%.......................................... 82 Figure 5-10 Experimental response histories of rigid block model Bearing 3 and earthquake simulator for bi-directional test (l) NF01/02-100% ............................................................... 83 Figure 5-11 Experimental response histories of rigid block model Bearing 3 and earthquake simulator for tri-directional test (l) NF01/02/V-100% ........................................................... 84 Figure 5-12 Linearized viscous model parameters................................................................................... 87 Figure 5-13 FP Bearing 3: experimental response of rigid block model, (h) LA21/22-100% ................. 88 Figure 5-14 FP Bearing 3: simulated response of rigid block model using coupled plasticity model with varying axial load, (h) LA21/22-100% ............................................................... 89 Figure 5-15 FP Bearing 3: simulated response of rigid block model using coupled plasticity model with constant axial load, (h)LA21/22-100% ............................................................... 90 Figure 5-16 FP Bearing 3: simulated response of rigid block model using uncoupled plasticity model with varying axial load, (h) LA21/22-100% ............................................................... 91 Figure 5-17 FP Bearing 3: simulated response of rigid block model using uncoupled plasticity model with constant axial load, (h)LA21/22-100% ............................................................... 92 Figure 5-18 FP Bearing 3: simulated response of rigid block model using linearized viscous model, (h)LA21/22-100% ......................................................................................................93

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Figure 5-19 FP Bearing 3: experimental response of rigid block model, (r) LS17C/18C-50% ............... 94 Figure 5-20 FP Bearing 3: simulated response of rigid block model using coupled plasticity model with varying axial load, (r) LS17C/18C-50% ............................................................. 95 Figure 5-21 FP Bearing 3: simulated response of rigid block model using coupled plasticity model with constant axial load, (r) LS17C/18C-50% ............................................................ 96 Figure 5-22 FP Bearing 3: simulated response of rigid block model using uncoupled plasticity model with varying axial load, (r) LS17C/18C-50% ............................................................. 97 Figure 5-23 FP Bearing 3: simulated response of rigid block model using uncoupled plasticity model with constant axial load, (r) LS17C/18C-50% ............................................................ 98 Figure 5-24 FP Bearing 3: simulated response of rigid block model using linearized viscous model, (r) LS17C/18C-50% ................................................................................................... 99 Figure 5-25 Summary of maximum displacements of FP Bearing 3 for experimental data and mathematical models; CP = Coupled Plasticity, UP = Uncoupled Plasticity....................... 101 Figure 5-26 Summary of maximum force of FP Bearing 3 for experimental data and mathematical models; CP = Coupled Plasticity, UP = Uncoupled Plasticity....................... 102 Figure 5-27 Summary of dissipated energy of FP Bearing 3 for experimental data and mathematical models; CP = Coupled Plasticity, UP = Uncoupled Plasticity....................... 103 Figure 5-28 FP Bearing 3: simulated response of rigid block model using coupled plasticity model with varying axial load as measured experimentally, (h) LA21/22-100%................ 104

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List of Tables Table 3-1 Table 3-2 Table 3-3 Table 3-4 Table 3-5 Table 4-1

Instrumentation list for rigid-block model displacement-controlled tests............................. 25 Datalog of displacement-history tests of Friction Pendulum bearings.................................. 29 Earthquake records selected for simulator testing ................................................................. 30 Scale factors and filters applied to the SAC motions for use in the testing program ............30 Earthquake simulator tests of rigid block model with FP bearings.......................................31 Calibrated best-fit values of friction coefficient (percent) using the coupled plasticity model for Friction-Pendulum Bearings..................................................................................64 Table 5-1 Evaluation of 30%-combination rule for bi-directional response of rigid block model........ 79 Table 5-2 Calibrated coefficient of friction used in the earthquake analysis......................................... 85

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1 Introduction 1.1

Overview Recent earthquakes have shown that bridges in critical routes should remain at least

operational to emergency traffic after a major event (Kawashima 2000). Damage to bridges may increase the response time of emergency teams following a major earthquakes, hampering rescue efforts. Additionally, at a time when resources are limited, the repair of bridges is time consuming and expensive. Conventional bridge design focuses on providing sufficient strength and ductility to meet seismic performance requirements. Ductile design of reinforced concrete piers can achieve the required displacement demands at the expense of concrete spalling and yielding of reinforcement. After a large earthquake, damaged columns must be repaired or replaced. Recently developed technologies for the design of earthquake resistant bridges, including seismic isolation, have the potential for improving seismic performance without the structural damage associated with ductile construction. Seismic isolation of bridges increases the flexibility between the piers and deck to control the transfer of forces and minimize interaction between the superstructure and substructure. Seismic isolation of a structure is typically achieved through a combination of elastomeric bearings, sliding bearings and damping devices. Elastomeric bearings consist of alternating layers of steel and rubber to provide horizontal flexibility while maintaining sufficient vertical stiffness. Inherent damping can be included in elastomeric bearings by inserting a lead core into the bearing or by adding filler material, such as carbon black, to the rubber matrix. These two types of damped bearings are known as lead-rubber bearings and high-damping rubber bearings, respectively. A photograph of a lead-rubber bearing in a deformed state is shown in Figure 1-1.

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Figure 1-1

Lead-rubber bearing in a deformed state.

Sliding bearings include a sliding surface that dissipates energy by means of friction and a restoring force device to minimize residual displacements. One innovative sliding bearing that compactly combines these two characteristics is the Friction PendulumTM (FP) bearing (Zayas et al. 1987) that is shown in Figure 1-2. Other types of sliding isolation systems consist of a flat sliding surface coupled with rubber bearings, helical springs, or other types of restoring force devices.

Self lubricating composite liner

Articulated slider

Stainless steel concave surface

Figure 1-2

Housing plate

Friction Pendulum bearing

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Concave plate

An isolated bridge located on stiff soil subjected to earthquake excitation will respond with reduced accelerations at the expense of increased relative displacements of the bearings and superstructure. Although seismic isolation bearings can be designed for a large displacement capacity, the displacements must also be accommodated by expansion joints. Additional damping mechanisms, such as the viscous damper shown in Figure 1-3, may be added to the isolation system to further increase the dissipation of energy and reduce displacements. Other types of devices based on friction or yielding of metals can be added to enhance energy dissipation in the isolation system.

Figure 1-3

Viscous damper (courtesy of Taylor Devices)

The effectiveness of a seismic isolation system is dependent on the properties of the isolation devices. The properties are selected based on models of the structure and the isolation hardware. Accurate bearings models are important to this process. In an earthquake analysis, these models are used to estimate the displacements demands on bearings; the bearing resisting forces determine the design forces for the piers. Seismic isolation bearings are commonly modeled by bridge engineers as either uncoupled bilinear or equivalent linear springs. The spring models are based on uni-directional laboratory test data because information on the bi-directional response is limited. For example, to model FP bearings, the are numerous uni-directional experimental studies on the behavior of PTFE-stainless steel interfaces, an interface similar to that used in FP bearings (Mokha et al. 1990, Constantinou et al. 1990, Bondonet and Filiatrault 1997, Constantinou et al. 1999). Experimental studies on the bi-directional behavior of flat Teflon sliders are limited to one important study conducted by Mokha et al. (1993). Since earthquakes can have strong motions in

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both horizontal directions, it is important to evaluate bearing characteristics and models under two components of excitation (Mosqueda et al. 2003). 1.2

Caltrans/Berkeley Protective Systems Project To extend current knowledge of seismic isolation systems for bridges, the California

Department of Transportation (Caltrans) sponsored the Protective Systems (PROSYS) Research Project at the University of California, Berkeley. The goal of PROSYS was to understand the behavior of seismic isolation hardware under a wide range of conditions, including bi-directional excitation and different hardware configurations. Tasks were organized to improve knowledge of component behavior and use the component information to better understand bridge system behavior. The research program integrated experimental and analytical studies of isolation hardware and bridges. The experimental studies made extensive use of the earthquake simulator and bearing test machine at the Earthquake Engineering Research Center, University of California, Berkeley. The major tasks in the research program were: 1. Experimentally characterize elastomeric and sliding isolation bearings under unidirectional and bi-directional displacement histories. 2. Using the experimental data, develop and calibrate mathematical models for elastomeric and sliding isolation bearings suitable for nonlinear response-history analysis of bridge systems. 3. Characterize the response of a simple, isolated bridge system to uni-directional, bidirectional and tri-directional earthquake excitation by experimentation and analysis. 4. Investigate the effectiveness of supplemental viscous dampers on the earthquake response of simple bridges by experimentation and analysis, including the effects of damper configuration on the earthquake response. 5. Construct a scale model of a bridge with two or three bents for experimentation on the earthquake simulator to investigate the effect of mass and stiffness eccentricity, pier flexibility, pier strength, and varying isolator properties on the bridge system.

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Three types of seismic isolation bearings and one type of supplemental energy dissipation device were investigated in PROSYS: (1) lead-rubber bearings, (2) high-damping rubber bearings, (3) FP bearings, and (4) fluid viscous dampers. To date, the fluid viscous damper is the only type of supplemental damping device that has been used in bridges in California. 1.3

Objectives of Research The scope of this report is limited to the experimental and analytical studies conducted on

FP Bearings from Tasks 1 through 3 in the previous section. The model used in the experimental studies was a rigid frame supported by four bearings on the earthquake simulator platform. The experimental testing program included bi-directional displacement controlled orbits and earthquake simulations. The displacement controlled tests served to model and characterize the bearings under bi-directional motions. The data from the earthquake tests were used to test the efficacy of the calibrated models. Tri-directional earthquake tests were also conducted on the rigid frame model to observe the effects of vertical ground acceleration on FP bearings. The bi-directional test data allows for detailed studies of path-history effects and a reexamination of design parameters such as static friction, dynamic friction, rate effects, and load history effects. The importances of these parameters, bi-directional coupling, and the bearing normal load in modeling the seismic response of bridges isolated with FP bearings are evaluated. In the analytical studies, the bi-directional plasticity model with time-dependent parameters is used to model the bearings. In addition to the non-linear models, the equivalent linear viscous model recommended for analysis in the Guide Specifications (AASHTO 1999) is also evaluated. 1.4

Organization of Report This report is divided into six chapters and a list of references. The following chapter

introduces the FP bearing and derives a mathematical formulation to model its behavior. It is shown that the derived mathematical model can be represented numerically using a bi-directional coupled plasticity model. Chapter 3 describes the testing equipment, lists the instrumentation used to measure the response of the model, and identifies the procedures for selecting both the displacement orbits and earthquake tests. Chapter 4 provides a summary of results for the displacement tests used to characterize the bearings and procedures to calibrate the analytical models. The key tests results from the earthquake tests are provided in Chapter 5, including a

5

validation of several analytical models by comparing them to the experimental response of the rigid block model. Conclusions are presented in Chapter 6. A list of references follows Chapter 6.

6

2

Friction Pendulum Bearings

2.1

Introduction The Friction Pendulum (FP) bearing is a sliding bearing that consists of an articulated

slider moving on a concave spherical surface. The components of the bearing, as illustrated in Figure 1-2, are the concave plate, the housing plate and the articulated slider. A stainless steel overlay with a mirror finish is placed on the concave plate to achieve the target friction coefficient and reduce the likelihood of corrosion. The semi-spherical articulated slider and the semispherical contact surface in the housing plate are each lined with a polymeric composite similar to PTFE. The composite liner in the semi-spherical contact surface allows for rotation between the housing plate and concave plate with minimal resistance. FP bearings impose a pendular trajectory on the supported structure subjected to horizontal motion as show in Figure 2-1. The uplift of the displaced structure serves as a restoring gravity force. Similar to a pendulum, the period of the isolated structure is independent of the structural mass. Neglecting the effects of friction, the period of a rigid structure isolated with FP bearings is dependent only on the radius and is given by T = 2π R --g

(2-1)

where R is the radius of the concave sliding surface and g is the gravitational constant. FP bearings have a separate mechanism for flexibility and energy dissipation. The design stiffness or period of the structure is obtained by selecting the radius of curvature of the sliding surface. Separately, the required energy dissipation specified in the design can be met by properly selecting the contact pressure between the slider and the stainless steel overlay, the composite liner of the slider, and the finish of the concave surface to attain the desirable friction coefficient.

7

Trajectory of supported structure

Friction Pendulum bearings

Figure 2-1

Pendular trajectory of structure isolated with Friction Pendulum bearings

The separation of the flexibility and damping components allows for a simplified design. Furthermore, for bridge applications, the high initial stiffness provided by the friction interface reduces vibrations of the supported deck under service loads such as braking traffic and wind. This chapter introduces mathematical models of FP bearings. The equations describing the lateral force resistance of FP bearings are derived from physical relations in Section 2.2. In Section 2.3, the bi-directional plasticity model and its applications to FP bearings are introduced. Finally, some practical modeling aspects of FP bearings pertinent to bridge applications are discussed in Section 2.4 2.2

Formulation of Model for Friction Pendulum Bearings The equilibrium equations for FP bearings are derived below for uni-directional motion,

and then extended to bi-directional motion. The approximations required to arrive at the simplified equations for small displacement theory are noted. The formulation describing the force resistance of a FP bearing is developed by balancing the forces acting on the articulated slider that is shown hatched in Figure 2-2. The figure depicts a FP bearing with radius, R , and applied weight, W , subjected to a lateral force, F , at displacement, u . The reactions at the sliding surface are the normal force, N , and the friction force, f . The force balance of the slider in the vertical and horizontal directions produce the following relations: F = N sin θ + f cos θ

(2-2)

W = N cos θ + f sin θ

(2-3)

8

θ Spherical sliding surface

W

R

F

u P0 Figure 2-2

N

f

Forces acting on the articulated slider in FP bearings

where the angle θ satisfies 2

2

u R –u sin θ = --- and cos θ = --------------------R R

(2-4)

The friction coefficient is usually prescribed as a function of several factors, the most influential being velocity and pressure. For now, it is assumed that the friction may be modeled as Coulomb friction and f is set equal to µN , where µ is a constant coefficient of friction. Substituting for sin θ using Equation 2-4 and combining Equation 2-2 and Equation 2-3 gives: N · W 1 F = ---- u + µN sgn ( u ) cos θ = ⎛⎝ ----- u + µW cos θ⎞⎠ ⎛⎝ ---------------------------------⎞⎠ R R cos θ + µ sin θ

(2-5)

·· where the signum function, sgn( ⋅ ), is used to determine the correct sign of the friction force. Typically, FP bearings have a displacement capacity less than 20 percent of R . For u ⁄ R < 0.2, the minimum value of cos θ and the maximum value of sin θ are 0.98 and 0.20, respectively. Considering a coefficient of friction of 0.1 and a positive or negative friction force, Equation 2-5 may be simplified within a 5 percent error to obtain W · F = ----- u + µW sgn ( u ) R

(2-6)

Equation 2-6 is usually written in terms of N in the literature, where it is assumed that N ≈ W because cos θ is approximately equal to 1.0 and the vertical axial load on the bearings, W , is specified. The same substitution is made here.

9

T

Extending the displacement and force to bi-directional motion by letting U = U x U y , F = Fx Fy

T

, and aligning the friction force resultant in the same direction as the

instantaneous velocity (Rabinowicz 1995), Equation 2-6 can be expressed as: Fx Fy

· Ux N 1 - Ux ---------= + µN · R U U U· y y

(2-7)

The resisting force in Equation 2-7 is composed of two components: a pendulum component ( ( N ⁄ R )u ) and a friction force component ( µN ). The pendulum force is directed towards the center of the bearing; the friction force acts in the direction opposite to the instantaneous velocity. 2.3

Bi-Directional Plasticity Model A simple non-linear model to capture the behavior of FP bearings is the rate-independent

plasticity model (Huang 2002). For this model, the bi-directional restoring force is given by F = K 2 U + Fp

(2-8)

where K 2 is the post-yield hardening stiffness and F p is the hysteretic force. The contribution of the elastic and hysteretic force components to the total resisting force of the plasticity model is shown schematically in Figure 2-3. F

F

F

K1-K2

K2 U

Elastic force Figure 2-3

K2

QD

QD +

K1 U

Hysteretic force

=

U

Plasticity model

Elastic and hysteretic resisting force components of plasticity model

The hysteretic component, F p , is modeled as elastic-perfectly plastic with initial stiffness, K 1 – K 2 , and yield force, Q D . The plastic force is given by

10

Fp = ( K1 – K2 ) ⋅ ( U – Up )

(2-9)

where U p is the plastic displacement. For bi-directional motion, FP bearings exhibit isotropic behavior and a circular yield condition is proposed. The yield surface satisfies the condition Φ ( Fp ) = F p – QD ≤ 0

(2-10)

where the change in plastic deformation, U· p , is zero for Φ ( F p ) < 0 . For Φ ( F p ) = 0 , an associative plastic flow rule with slip rate γ ≥ 0 is assumed as follows: ∂Φ ( F p ) Fp U· p = γ ⋅ ------------------- = γ ⋅ ----------∂F p Fp

(2-11)

The loading/unloading conditions are described by the Kuhn-Tucker complimentary conditions γ ≥ 0, Φ ( F p ) ≤ 0,

γ ⋅ Φ ( Fp ) = 0

(2-12)

and the consistency requirement · γ ⋅ Φ ( Fp ) = 0

(2-13)

Using the conditions set forth in Equation 2-8 to Equation 2-13, the return-mapping algorithm for plasticity (Simo and Hughes 1998) is used to compute the resisting force F . 2.3.1

Modified Plasticity Model for Friction Pendulum Bearings The form of Equation 2-7 parallels Equation 2-8 in that it has separate elastic and plastic

force components. By setting N K 2 = ---R

(2-14)

· 1 - Ux Fp = µN -------U· U· y

(2-15)

and

the plasticity model can be used instead of Equation 2-7 to model FP bearings. Assuming a constant normal force N, the restoring pendulum force behaves as an elastic spring of stiffness

11

N ⁄ R , and the friction force can be modeled as a hysteretic component with a very large initial stiffness, K 1 , and Q D = µN

(2-16)

The initial stiffness of the friction force results from small deformations of the composite material at the sliding surface. The amount of deformation is dependent on the thickness of the slider, and is usually on the order of 0.01 in. (Scheller and Constantinou 1999). An approximation for the plasticity model parameter K 1 is given by Q µN K 1 = ------D- = ------UY UY

(2-17)

where U Y is the yield displacement. The value recommended for K 1 is an approximation. However, the resisting force of the plasticity model will not be significantly affected by variations in K 1 within a range of values two orders of magnitude greater than K 2 and Q D . Using the parameters K 1 , K 2 and Q D defined in Equations 2-14, 2-16 and 2-17, the coupled plasticity model can be used to model the force-deformation behavior in an FP bearing. The parameter K 2 can be obtained from the bearing radius and K 1 can be approximated as noted above. It is only necessary to calibrate the plasticity model for one parameter, namely the friction coefficient, to obtain Q D . In modeling FP bearings for bi-directional motion, the restoring pendulum force is properly represented as two orthogonal elastic springs with stiffness K 2 . The friction force, on the other hand, is in the direction of instantaneous velocity (see Equation 2-7) and its magnitude is independent of displacement. A coupled plasticity model with a circular yield surface provides the correct magnitude for the plastic force, F p , but it is not obvious that the plastic force is colinear with the instantaneous velocity. In the plasticity model, however, the hysteretic force is controlled by the incremental plastic displacements ∆U p = ∆U px ∆U py

T

(2-18)

The bi-directional friction force is given by ∆U px 1 ∆t ∆U px ⁄ ∆t 1F p = µN --------------= µN --------------≈ µN -------∆U p ∆U ∆U p ∆U ⁄ ∆t U· py py

12

U· x U· y

(2-19)

where the instantaneous velocities are approximately represented by the incremental plastic displacements over the time step ∆t . The plastic displacements correspond to sliding in the bearing and do not account for deformation in the composite material. It can be concluded that the magnitude and direction of the friction force are properly represented by a coupled plasticity model. The bi-directional Bouc-Wen model generalized by Park et al. (1986) is a smoothed plasticity model and it can represent the behavior of FP bearings according to: Z N F = ---- U + µN x R Zy

(2-20)

where the Z parameters satisfy an evolutionary differential equation. Such a model is used in SAP 2000 (Computers and Structures 1997) and 3-D BASIS (Tsopelas et al. 1994). The differences between the Bouc-Wen and plasticity models are small when the two-dimensional evolutionary equation for Z is properly formulated (Huang 2002). For larger values of K 1 , the differences between the Bouc-Wen and plasticity models are negligible. One important characteristic in modeling sliding bearings is that the resisting lateral force is proportional to the normal load, N , on the bearing. It is necessary to modify the plasticity model to account for changes in axial load throughout the analysis by making N a function of time. One simple method to account for axial load effects is to update the parameters K 2 and Q D at each time step as part of the iterative solution scheme. It is possible, however, that the convergence rate may be reduced because of the lack of a consistent tangent stiffness matrix. 2.3.2

Bi-directional Coupling For the bi-directional plasticity model, a coupled interaction surface is proposed. The bi-

directional uncoupled model can be considered as two independent, uni-directional models oriented along the coordinate axis, each having a behavior that is independent of the other. In this case, the yield force will remain constant along each direction, forming a square shape interaction surface as shown in Figure 2-4. Note that for a force path along the 45 degree direction, the yield force will be greater by factor of

2 when compared to a path along one of the coordinate axes.

13

This behavior is inconsistent with the isotropic behavior of the friction force, which is independent of the direction of sliding. In a coupled model, the magnitude of the yield force remains constant regardless of the force path with respect to the orientation of the coordinate axis. The resulting yield interaction surface for the coupled model is circular in shape as shown in Figure 2-4. The difference between a coupled and uncoupled model will be greatest if the response path is primarily oriented along the 45-degree direction. The uncoupled model could attain a higher yield force and more hysteretic energy dissipation, which can lead to unconservative displacement estimates. If the predominant response of the bearing is oriented along the X or Y directions, then the two models are likely to provide similar results. Fy

Fy

Fx

Fx

Uncoupled model Figure 2-4

Coupled model

Interaction surface for bi-directional uncoupled and coupled plasticity model

Figure 2-5 illustrate the response of the coupled and uncoupled plasticity models to three displacement orbits; Orbit 2: square, Orbit 3: hourglass and Orbit 4: figure-8. (See Section 3.3.2 for more information on these orbits.) The direction of travel for the orbits are noted by the arrows in Figure 2-5a. The parameters used in the plasticity model are: K 1 =150 kip/in., K 2 =0.5 kip/in. and Q D =1.2 kip. These values are representative of the small-scale FP bearings used in the experimental program described in Chapter 3. Note that the uncoupled model overestimates the resultant force along the trajectories of the three different orbits with the exception of the lowerleft and lower-right locations of the force locus for Orbit 4. At these locations, the displacement reversal in the X-direction combined with the high initial stiffness cause a complete force reversal in the X-direction for the uncoupled model.

14

Deformation in Y (in)

5

Legend

0

Orbit 2 Orbit 3 Orbit 4

−5 −5

0 Deformation in X (in) (a) displacement orbits

5

4 Resisting force in Y (kip)

Resisting force in Y (kip)

4

2

0

−2

−4 −4

−2 0 2 Resisting force in X (kip)

0

−2

−4 −4

4

(b) uncoupled FP bearing Figure 2-5

2

−2 0 2 Resisting force in X (kip)

4

(c) coupled FP bearing

Examples of response of coupled and uncoupled plasticity model with typical parameters for a FP bearings ( K 1 =150 kip/in., K 2 =0.5 kip/in. and Q D =1.2 kip)

Figure 2-5 shows that there is a substantial difference in behavior between the coupled and uncoupled models. More discussion on comparisons between coupled and uncoupled models will be presented in Chapter 4 for the displacement-controlled tests and Chapter 5 for the rigid block earthquake tests.

15

2.4

Rotation of Friction Pendulum Bearings In bridge applications, bearings can be installed out-of-level or atop flexible piers as

shown in Figure 2-6. In both cases, the concave dish rotates with respect to the housing plate and can affect the behavior of FP bearings. The semi-spherical socket connection for the articulated slider in a FP bearing allows for relative rotation between the concave dish and housing plate without any moment transfer. The rotation is limited only by the geometry of the bearing, namely, the gap between the concave and housing plate. This rotation capacity makes FP bearings most suitable for bridge applications where rotations may be imposed on the bearings by the piers. Although FP bearings are free to rotate up to a certain limit, the resisting shear force may be modified as a result of the rotation. Rotations of the spherical surface (concave dish) will result in a shift of the equilibrium position of the bearing, since the slider tends towards the surface location tangent to the horizontal (Figure 2-7). The friction force is virtually unaffected by a small change in angle. -F

a. out-of-level Figure 2-6

b. flexible pier

Rotation of FP bearings

The effects of rotation on an FP bearing are dependent upon the center of rotation. For example, a rotated concave dish has a larger impact on the response than a rotated housing plate. A counterclockwise rotation, α , about the center point of the spherical surface, P0, in Figure 2-7 will shift the static equilibrium position of the bearing from P0 to Pr a distance of u r = –R sin α or – R α if a small angle approximation is used. In Figure 2-7, u continues to be the displacement of the slider relative to the center of the spherical surface. The angle θ r now satisfies the relationship

16

A

Ar

θr W

α

Original surface location

R F ur

f

Rotated surface Pr Figure 2-7

u N

P0

Rotated spherical surface of FP bearing 2

2

u–u R + –( u – u r ) sin θ r = -------------r and cos θ r = ---------------------------------------R R

(2-21)

Considering rotations of the spherical surface, the resisting force for a given displacement is given by N F = ---- ( u – u r ) + µN R

(2-22)

The net effect of a fixed bearing rotation is to increase or decrease the effective displacement of the bearing (the distance from the slider to the surface point tangent to the horizontal). The hysteresis translates vertically a distance of NRα for a counterclockwise rotation α in radians, as shown in Figure 2-8. The direction of the restoring gravity force and friction force are also slightly affected. No change in second slope stiffness results for an out-of-level rotation of an FP bearing A rotated housing plate will have a smaller impact on the response of FP bearings. In this situation, the effective bearing displacement will be modified by u r = h sin α , where h is the height of the bearing and is much less than R . Consider now a concave dish installed atop a flexible pier that can be modeled as a cantilever as shown in Figure 2-6b. Such a pier will displace laterally and rotate due to the shear

17

F

F

NR α u

u Unrotated

Unrotated Rotated

Rotated

(a) Out-of-level counterclockwise rotation Figure 2-8

(b) Rotation atop flexible column

Effect of concave dish rotation on FP bearing hysteresis

forces imposed by the FP bearing. Assume that the pier responds elastically and the rotation, α , at the top of the pier is proportional to the bearing resisting force, F , such that α = – λF and u r = – R sin ( –λ F ) ≈ RλF

(2-23)

The negative α implies that a positive force will produce a negative rotation in the counterclockwise direction. Substituting Equation 2-23 into Equation 2-22, it is seen that pier rotations proportional to bearing forces have the effect of decreasing the effective normal load on the bearing for positive λ such that N 1 F = ----------------- ⎛⎝ --- u + µ sgn ( u· )⎞⎠ 1 + λN R

(2-24)

The second slope stiffness and the width of the hysteresis loop will both be reduced for bearing installed atop flexible piers, as shown in Figure 2-8(b). These results indicate that FP bearings are sensitive to rotations of the concave surface. To minimize the effects of rotations, the housing plate should be installed to the part of the structure that is likely to experience the largest rotation. For installation in bridges, it is recommended to attach the concave plate to the superstructure were rotations will typically be smaller than those atop flexible piers. This orientation is also preferred because P-delta moments will not be transferred to the piers and the likelihood of debris collecting on the sliding surface is minimized.

18

3 Experimental Program 3.1

Introduction A series of displacement-controlled and earthquake simulation experiments were carried

out to investigate the characteristics of Friction Pendulum (FP) bearings. The experimental model used for the displacement-controlled and the earthquake testing program was a rigid frame supporting lead and concrete weights. With an appropriate length scale factor, the testing frame represented a bridge with rigid superstructure and rigid substructure. This simple model was selected to focus modeling efforts on the bearings and not on the entire bridge structure. Although uni-directional displacement testing of seismic isolation bearings has been routine for more than a decade, the bi-directional testing that is presented in this chapter is new. This testing program was developed and undertaken to extend current information on seismic isolation bearings and to characterize and validate mathematical models under bi-directional excitation. The objectives of the earthquake testing program were to examine the bi–directional earthquake response of the isolated frame, evaluate the effects of different types of ground motions, including near–fault ground motions, and evaluate analytical models developed from the displacement tests. Ground motions were selected to represent different source types, soil types, intensities, and durations Detailed specifications of the FP bearings used in this study are provided in Section 3.2. The research program and procedures used to characterize the response of the bearings to bidirectional displacement histories are presented in Section 3.3. The earthquake testing program and the selection of ground motions are described in Section 3.4.

19

3.2

Test Specimens The FP bearings used in this study were manufactured by Earthquake Protection Systems

in Vallejo, California. The housing plate and concave plate of the bearings were fabricated from ASTM A36 steel. A stainless steel overlay was placed on each concave plate to achieve the target friction coefficient and reduce the likelihood of corrosion. The semi-spherical articulated slider and the semi-spherical contact surface in the housing plate were each lined with a high-load, lowfriction, self-lubricating polymeric composite with mechanical properties similar to those of polythetrafluoroethylene (PTFE). Detailed measurements of the FP bearings used in this study are given in Figure 3-1. The radius of the concave surface and stainless steel overlay was 30 in. The diameter of the articulated slider was 1.44 in. and the displacement capacity of the bearings was ± 7 in. A photograph of the FP bearing is shown in Figure 3-2.

Ø0.5625 in. hole with Ø1.125 in., 0.5 in. deep countesink

Ø0.5 in. - 13 UNC threaded hole 1 in. deep min.

Ø20.5 in.

Ø16.5 in.

0.50 in.

8.00 in.

2.00 in.

3.50 in. 5.00 in.

R30 in.

Ø1.44 in. 0.50 in. 22.00 in.

Figure 3-1

3.3

EPS Friction Pendulum bearing

Facilities and Procedures for Bi-directional Characterization Small-scale FP bearings were tested under bi-directional displacement histories using the

earthquake simulator at the Earthquake Engineering Research Center, which is headquartered at the University of California, Berkeley. The test setup consisted of four bearings installed under a

20

Figure 3-2

FP bearing with concave plate raised to show the sliding surface

rigid frame that was modified for the experimental program. The two limitations to this approach were (a) that the maximum axial load on the frame was limited to the maximum payload of the simulator (approximately 125 kips), and (b) the maximum horizontal displacement in the two orthogonal directions was limited to the ± 5 in. displacement capacity of the simulator. 3.3.1 Description of Rigid Block Model and Test Setup A plan and elevation of the rigid block frame, supported by four bearings, is shown in Figure 3-3. The frame was loaded with concrete and lead weights totaling approximately 65 kips, to produce a target vertical load on each bearing of 16.25 kips. A five-component load cell was located under each bearing to measure the axial load, shear, and moment response. The complete set-up, including the frame, the isolators, the reaction blocks, and the struts is referred to as the rigid block model. Four tube-steel struts braced the rigid frame against the reaction blocks located on two sides of the simulator platform. Each reaction block was designed to resist a maximum horizontal force of 75 kips at 26 in. above the simulator platform. With the struts locking the frame to the rigid buttresses, the simulator platform was moved to achieve the requisite displacement orbits. A

21

Struts

Bearing Load Cell

ation Longitudinal Elevation

Bearing Load Cell

Transverse Elevation Earthquake Simulator Platform

Plan View Figure 3-3

Plan and elevations of the rigid block model with struts attached

Figure 3-4

Rigid block model with struts attached

photograph of the rigid block model during the bi-directional displacement history tests (i.e., struts installed) is shown in Figure 3-4. Seventy-three transducers measured the response of the rigid block model during the bidirectional characterization tests. Table 3-1 lists the channel number, instrument type, response

22

quantity, instrument orientation, and location of each transducer. Figure 3-5 is a plan view of the rigid block model showing the location of selected transducers, the global X-Y-Z coordinate system, and the four bearings denoted as bearings 1 through 4. The number in parenthesis for each transducer shown in Figure 3-5 corresponds to the channel numbers listed in Table 3-1. 3.3.2 Test Protocol The displacement orbits for the bi-directional static and dynamic testing were selected to meet a number of objectives with the goal of providing information to parameterize the bidirectional behavior of sliding isolation bearings. The seven displacement-controlled orbits are shown in Figure 3-6. Orbit 1 (the cruciform orbit) was used exclusively for the elastomeric bearings to study scragging effects, and is not further discussed. Orbits 2 and 3 were used to study bi-directional path-history effects. Orbit 4 was used for static and dynamic testing by running the cyclic test at different frequencies. The figure-8 displacement history of Orbit 4 was defined by two sine functions in the X- and Y-directions with the loading frequency in the Y-direction equal to twice the frequency in the X-direction. Orbit 5 was used to characterize the FP bearing in a manner similar to that typically used in uni-directional tests. Changes in bearing hysteresis due to an offset from the bearing center were examined using Orbit 6. Orbits 5 and 6 consisted of uni-directional sinusoidal displacement histories. The resisting force characteristics of FP bearings subjected to a constant velocity were evaluated using the circular Orbit 7. One objective of the FP bearing testing program was to characterize their bi-directional behavior at different velocities. Uni-directional tests using Orbit 5 at peak velocities of 1, 2, 5, and 20 in./sec. were used to examine the velocity dependence of the friction coefficient. These tests were followed by the offset Orbit 6 tests at peak velocities of 2, 5 and 20 in./sec. Orbits 2 and 3 were run at slow rates while Orbits 4 and 7 were run at peak velocities ranging from 2 to 20 in./ sec. to evaluate the bi-directional path-dependence and rate effects of FP bearings. Table 3-2 lists the testing sequence for the FP bearings with a nominal friction coefficient of 0.09.

23

38'-5"

denotes length of wire

dcdt2(71)

dcdt1(70)

to pot13

Simulator platform

72"

Buttress pot2(40)

Bearing 1

85.5"

81.25"

acc13(66)

63.75"

63.5"

103.5"

pot1(39) pot9(47)

103"

acc1(54) X acc3(56) Z acc2(55) Y

acc8(61) Y acc9(62) Z acc15(68) acc7(60) X

acc11(64) Y acc12(65) Z acc10(63) X

111.25"

acc14(67) acc4(57) X acc6(59) Z acc5(58) Y

111.75"

38'-8"

99"

60.25"

102.5"

111.25"

pot14(52)

66"

dcdt3(72) pot4(41)

55.75"

Bearing 2

Struts

57"

85.75

pot3(42)

38'-7"

pot15(53) 103.25"

pot5(43)

dcdt4(73)

103.5"

67.75"

63.5"

63.25"

acc16(69)

pot10(48) pot7(45)

pot6(44)

pot13(51)

57"

Bearing 4

pot8(46)

70.5"

Y

Z

147"

57"

146.5"

81"

Bearing 3

Instrumentation Key

pot12(50)

X

pot11(49)

CONTROL ROOM

accN(CN) potN(CN) dcdtN(CN)

Note: The simulator platform transducers (Channels 3-18) and load cells (Channels 19-38) are not shown; acc = accelerometer; dcdt = direct-current displacement transducer; pot = linear potentiometer; N = transducer number; CN = channel number

Figure 3-5

Instrumentation of rigid block model for bi-directional testing

24

Table 3-1

Instrumentation list for rigid-block model displacement-controlled tests

Channel

Transducer

Response Quantity

Orientation

Transducer Location

1

-

date

-

-

2

-

time

-

-

3

LVDT

displacement

X

simulator platform

4

LVDT

displacement

Y

simulator platform

5

LVDT

displacement

X

simulator platform

6

LVDT

displacement

Y

simulator platform

7

LVDT

displacement

Z

simulator platform

8

LVDT

displacement

Z

simulator platform

9

LVDT

displacement

Z

simulator platform

10

LVDT

displacement

Z

simulator platform

11

ACC

acceleration

X

simulator platform

12

ACC

acceleration

X

simulator platform

13

ACC

acceleration

Y

simulator platform

14

ACC

acceleration

Y

simulator platform

15

ACC

acceleration

Z

simulator platform

16

ACC

acceleration

Z

simulator platform

17

ACC

acceleration

Z

simulator platform

18

ACC

acceleration

Z

simulator platform

19

load cell

shear force

-X

bearing 1

20

load cell

shear force

Y

bearing 1

21

load cell

moment

X

bearing 1

22

load cell

moment

Y

bearing 1

23

load cell

force

Z

bearing 1

24

load cell

shear force

X

bearing 2

25

load cell

shear force

Y

bearing 2

26

load cell

moment

X

bearing 2

27

load cell

moment

Y

bearing 2

28

load cell

force

Z

bearing 2

29

load cell

shear force

-X

bearing 3

1. ACC = accelerometer; DCDT = direct-current displacement transducer; LVDT = linear-variable differential transformer; POT = linear potentiometer; the numbered transducers are shown in Figure 3-5. 2. -N indicates negative N polarity; see Figure 3-5 for details.

25

Table 3-1

Instrumentation list for rigid-block model displacement-controlled tests

Channel

Transducer

Response Quantity

Orientation

Transducer Location

30

load cell

shear force

Y

bearing 3

31

load cell

moment

X

bearing 3

32

load cell

moment

Y

bearing 3

33

load cell

force

Z

bearing 3

34

load cell

shear force

-X

bearing 4

35

load cell

shear force

Y

bearing 4

36

load cell

moment

X

bearing 4

37

load cell

moment

Y

bearing 4

38

load cell

force

Z

bearing 4

39

POT1

displacement

-X

bearing 1

40

POT2

displacement

-Y

bearing 1

41

POT3

displacement

X

bearing 2

42

POT4

displacement

-Y

bearing 2

43

POT5

displacement

X

bearing 3

44

POT6

displacement

Y

bearing 3

45

POT7

displacement

-X

bearing 4

46

POT8

displacement

Y

bearing 4

47

POT9

displacement

X

model

48

POT10

displacement

X

model

49

POT11

displacement

Y

model

50

POT12

displacement

Y

model

51

POT13

displacement

-X

simulator platform

52

POT14

displacement

-Y

simulator platform

53

POT15

displacement

-Y

simulator platform

54

ACC1

acceleration

-X

bearing 1

55

ACC2

acceleration

-Y

bearing 1

56

ACC3

acceleration

Z

bearing 1

57

ACC4

acceleration

X

bearing 2

58

ACC5

acceleration

-Y

bearing 2

1. ACC = accelerometer; DCDT = direct-current displacement transducer; LVDT = linear-variable differential transformer; POT = linear potentiometer; the numbered transducers are shown in Figure 3-5. 2. -N indicates negative N polarity; see Figure 3-5 for details.

26

Table 3-1

Instrumentation list for rigid-block model displacement-controlled tests

Channel

Transducer

Response Quantity

Orientation

Transducer Location

59

ACC6

acceleration

Z

bearing 2

60

ACC7

acceleration

X

bearing 3

61

ACC8

acceleration

Y

bearing 3

62

ACC9

acceleration

Z

bearing 3

63

ACC10

acceleration

-X

bearing 4

64

ACC11

acceleration

Y

bearing 4

65

ACC12

acceleration

Z

bearing 4

66

ACC13

acceleration

Y

model

67

ACC14

acceleration

X

model

68

ACC15

acceleration

X

model

69

ACC16

acceleration

Y

model

70

DCDT1

displacement

Y

struts

71

DCDT2

displacement

Y

struts

72

DCDT3

displacement

X

struts

73

DCDT4

displacement

X

struts

1. ACC = accelerometer; DCDT = direct-current displacement transducer; LVDT = linear-variable differential transformer; POT = linear potentiometer; the numbered transducers are shown in Figure 3-5. 2. -N indicates negative N polarity; see Figure 3-5 for details.

3.4

Facilities and Procedures for Bi-directional Earthquake Simulations

3.4.1 Introduction The experimental setup used for the bi-directional displacement tests was used for dynamic earthquake testing by removing the struts. For the earthquake tests, the instrumentation list was identical to Table 3-1 with the removal of the four DCDT’s located on the struts (Channels 70-73). 3.4.2 Selection of Earthquake Histories The earthquake records were selected to include motions representing different source types, soil types, intensities, and durations with a limited number of records. A suite of records from the FEMA/SAC project (SAC 1997) were considered and the selected records are listed in Table 3-3. The selection was based on the records, scaled in length and amplitude, satisfying the 27

Y

Y

X

Orbit 1: cruciform

X

Orbit 3: hourglass

Y

X

Orbit 5: uni-directional

Y

X

Orbit 2: box

Y

Figure 3-6

Y

X

Orbit 4: figure-8

Y

X

X

Orbit 6: offset uni-directional

Orbit 7: circular

Orbits for the bi-directional displacement-controlled tests

limitation of the earthquake simulator (peak displacement = ± 5 in. and peak velocity = ± 23 in./ sec.) and similitude laws to properly represent the scaled prototype bridge. Table 3-3 lists information on the source from which the ground motions were derived and the scaling factors applied by FEMA/SAC. Among the records selected, there were two soft soil records and three near-fault ground motions. In addition, the primary direction of the selected earthquakes also varies; LS17C/18C was oriented along the X-direction; LA13/14 and LA21/22 were oriented in the 45-degree direction; strong bi-directional effects were evident in LS01E/02E and NF01/02. Table 3-4 lists the scale factors appropriate for the tested model and the filters applied to the FEMA/SAC motions to satisfy the physical limitations of the earthquake simulator. Figures 37 through 3-16 present the acceleration history, acceleration response spectrum and displacement response spectrum for each component of the records listed in Table 3-4. Spectra are provided for damping ratios of 5%, 10%, 20%, and 30%, which are representative of the linearized isolated frame model. The records, as shown in the figures, are scaled and filtered with the parameters specified in Table 3-4. These signals served as the reference input for the earthquake simulator.

28

Table 3-2

Datalog of displacement-history tests of Friction Pendulum bearings 1

X-disp2 (in.)

Y-disp 2 (in.)

X-vel3 (in./sec.)

Y-vel3 (in./sec.)

Cycles

Log No.

(a)ORBIT5Y-01

5

0

5

0

1

3

991111185851

(b)ORBIT5Y-02

5

0

5

0

2

3

991111192107

(c)ORBIT5Y-05

5

0

5

0

5

3

991111193536

(d)ORBIT5Y-20

5

0

5

0

20

3

991111194302

(e)ORBIT5X-01

5

5

0

1

0

3

991111200154

(f)ORBIT5X-02

5

5

0

2

0

3

991111202111

(g)ORBIT5X-05

5

5

0

5

0

3

991111202504

(h)ORBIT5X-20

5

5

0

20

0

3

991111203003

(i)ORBIT6X-02

6

5

2.5

2

0

3

991111203631

(j)ORBIT6X-05

6

5

2.5

5

0

3

991111204035

(k)ORBIT6X-20

6

5

2.5

20

0

3

991111204418

(l)ORBIT6X-02

6

2.5

5

2

0

3

991111204733

(m)ORBIT6X-05

6

2.5

5

5

0

3

991111205114

(n)ORBIT6X-20

6

2.5

5

20

0

3

991111205343

(o)ORBIT3-01

3

5

5

-

-

3

991111205722

(p)ORBIT2-01

2

5

5

-

-

3

991111210855

(q)ORBIT7-02

7

2.5

2.5

2

2

3

991111211931

(r)ORBIT7-05

7

5

5

5

5

3

991111212309

(s)ORBIT4-04

4

2.5

2.5

4

2

3

991111212645

(t)ORBIT4-10

4

5

5

10

5

3

991111212943

(u)ORBIT4-20

4

5

5

20

10

3

991111213246

Test Label

Orbit

1. See Figure 3-6 for information on orbits. 2. X-disp = maximum displacement amplitude in the x-direction; Y-disp = maximum displacement amplitude in the y-direction; all displacement cycles are symmetric. 3. X-vel = maximum velocity in the x-direction; Y-vel = maximum velocity in the y-direction.

Figures 3-7 through 3-16 identify the ordinate of the rigid block model isolated with FP bearings for the displacement and acceleration spectra. From these records, it appears that the soft soil records (LS02 and LS17) and a near-fault record (NF02) are the most demanding on the isolated rigid block model. Note, however, that these are linear spectra whereas the behavior of the isolation bearings is highly non-linear.

29

Table 3-3

Earthquake records selected for simulator testing Source

SAC ID

Description3

Amplitude Factor4

Soil Type5

Record

Mag.1

R2(km)

LA13/LA14

1994 Northridge, Newhall

6.7

6.7

NF - FA

1.03

SD

LA21/LA22

1995 Kobe

6.9

3.4

NF - FA

1.15

SD

LS01E/LS02E

1940 El Centro

6.9

10

FF

2.01

SF

LS17C/LS18C

1994 Northridge, Sylmar

6.7

6.4

0.99

SE

NF01/NF02

1978 Tabas

7.4

1.2

1.00

SD

NF

1. Mag. = magnitude of original record. 2. Distance from fault. 3. Description of original record; NF = Near Field; FF = Far Field; FA = Forward Azimuth. 4. Amplitude factor applied to match USGS target spectrum. 5. The original records were modified to be representative to the targeted soil type based on NEHRP.

Table 3-4

Scale factors and filters applied to the SAC motions for use in the testing program

SAC ID

Record

Length Scale1

Filter2

PGA3 (g) X-dir.

Y-dir.

LA13/LA14

Newhall, 1994 Northridge

2

[0.1,0.15,12 15]

0.619

0.541

LA21/LA22

1995 Kobe

5

[0.05,0.10,12,15]

1.243

0.926

LS01E/LS02E

1940 El Centro

3

[0.05,0.10,12,15]

0.401

0.725

LS17C/LS18C

1994 Northridge, Sylmar

5

[0.05,0.10,12,15]

0.332

0.424

NF01/NF02

1978 Tabas

5

[0.05,0.10,12,15]

0.796

0.630

1. A length scale of 5 corresponds to a time scale factor of

5.

2. Low pass - high pass trapezoidal window filter parameters [low cut, low corner, high corner, high cut]. 3. PGA of record after filtering and scaling, the odd numbered record is considered to be in the X-direction and the even numbered record is oriented along the Y-direction.

3.4.3 Test Protocol The rigid block model isolated with FP bearings was subjected to the five earthquake records at a range of amplitudes. Four test were conducted using the earthquake sets LA21/22 and NF01/02: (i) X component only, (ii) Y component only, (iii) X and Y component simultaneously, (iv) X, Y, and vertical component simultaneously. The earthquake tests with corresponding labels, length scale factors and amplitude factors are listed in Table 3-5.

30

Table 3-5

Earthquake simulator tests of rigid block model with FP bearings

Test Label

Record

Length Scale

Amplitude Factor

Span Setting1

Log No.

(a) LA21/22-25%

LA21/22

5

25%

[135,121,0]

991115191348

(b) NF01/02-25%

NF01/02

5

25%

[201,250,0]

991115192019

(c) LA21/22-50%

LA21/22

5

50%

[269,242,0]

991115192507

(d) NF01/02-50%

NF01/02

5

50%

[402,500,0]

991115192730

(e) LA13/14-50%

LA13/14

2

50%

[348,488,0]

991115193200

(f) LS17C/18C-25%

LS17C/18C

5

25%

[198,062,0]

991115193511

(g) LS01E/02E-50%

LS01E/02E

3

50%

[222,392,0]

991115193921

(h) LA21/22-100%

LA21/22

5

100%

[538,484,0]

991115194313

(i) LA21/22V2-100%

LA21/22

5

100%

[538,484,579]

991115195113

(j) LA21(X)-100%

LA21/22

5

100%

[538,0,0]

991115195506

(k) LA22(Y)-100%

LA21/22

5

100%

[0,484,0]

991115195720

(l) NF01/02-100%

NF01/02

5

100%

[804,1000,0]

991115200028

(m) NF01/02V 2-100%

NF01/02

5

100%

[804,1000,830]

991115200520

(n) NF01(X)-100%

NF01/02

5

100%

[804,0,0]

991115200927

(o) NF02(Y)-100%

NF01/02

5

100%

[0,1000,0]

991115201230

(p) LA13/14-100%

LA13/14

2

100%

[696,976,0]

991115201559

(r) LS17C/18C-50%

LS17C/18C

5

50%

[395,123,0]

991115201911

1. Earthquake simulator span settings listed as [X-direction, Y-direction, Z-direction]. A span setting of 1000 corresponds to a displacement of 5 inches in the X- and Y-directions, and 2 inches in the Z-direction. 2. Includes vertical ground motion component.

31

1.5

Acceleration (g)

1 0.5 0 −0.5 −1 −1.5

0

5

10 15 Time (seconds) a. acceleration history

20

25

Acceleration (g)

4 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

3 2 1 FP 0

0

0.5

1

1.5 2 Period (seconds) b. acceleration response spectrum

2.5

3

Displacement (inches)

20 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

15 10 FP 5 0

0

Figure 3-7

0.5

1

1.5 2 Period (seconds) c. displacement response spectrum

2.5

3

Scaled input motion LA13, 1994 Northridge, Newhall; length scale = 2, amplitude scale = 100% (Table 3-4)

32

1.5

Acceleration (g)

1 0.5 0 −0.5 −1 −1.5

0

5

10 15 Time (seconds) a. acceleration history

20

25

Acceleration (g)

4 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

3 2 1 FP 0

0

0.5

1

1.5 2 Period (seconds) b. acceleration response spectrum

2.5

3

Displacement (inches)

20 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

15 10 FP 5 0

Figure 3-8

0

0.5

1

1.5 2 Period (seconds) c. displacement response spectrum

2.5

3

Scaled input motion LA14, 1994 Northridge, Newhall; length scale = 2, amplitude scale = 100% (Table 3-4)

33

1.5

Acceleration (g)

1 0.5 0 −0.5 −1 −1.5

0

5

10 15 Time (seconds) a. acceleration history

20

25

Acceleration (g)

4 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

3 2 1 FP 0

0

0.5

1

1.5 2 Period (seconds) b. acceleration response spectrum

2.5

3

Displacement (inches)

20 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

15 10 FP 5 0

Figure 3-9

0

0.5

1

1.5 2 Period (seconds) c. displacement response spectrum

2.5

3

Scaled input motion LA21, 1995 Kobe, JMA Station; length scale = 5, amplitude scale = 100% (Table 3-4)

34

1.5

Acceleration (g)

1 0.5 0 −0.5 −1 −1.5

0

5

10 15 Time (seconds) a. acceleration history

20

25

Acceleration (g)

4 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

3 2 1 FP 0

0

0.5

1

1.5 2 Period (seconds) b. acceleration response spectrum

2.5

3

Displacement (inches)

20 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

15 10 FP 5 0

0

Figure 3-10

0.5

1

1.5 2 Period (seconds) c. displacement response spectrum

2.5

3

Scaled input motion LA22, 1995 Kobe, JMA Station; length scale = 5, amplitude scale = 100% (Table 3-4)

35

1.5

Acceleration (g)

1 0.5 0 −0.5 −1 −1.5

0

5

10 15 Time (seconds) a. acceleration history

20

25

Acceleration (g)

4 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

3 2 1 FP 0

0

0.5

1

1.5 2 Period (seconds) b. acceleration response spectrum

2.5

3

Displacement (inches)

20 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

15 10 FP 5 0

0

Figure 3-11

0.5

1

1.5 2 Period (seconds) c. displacement response spectrum

2.5

3

Scaled input motion LS01E, 1940 El Centro; length scale = 3, amplitude scale = 100% (Table 3-4)

36

1.5

Acceleration (g)

1 0.5 0 −0.5 −1 −1.5

0

5

10 15 Time (seconds) a. acceleration history

20

25

Acceleration (g)

4 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

3 2 1 FP 0

0

0.5

1

1.5 2 Period (seconds) b. acceleration response spectrum

2.5

3

Displacement (inches)

20 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

15 FP

10 5 0

0

Figure 3-12

0.5

1

1.5 2 Period (seconds) c. displacement response spectrum

2.5

3

Scaled input motion LS02E, 1940 El Centro; length scale = 3, amplitude scale = 100% (Table 3-4)

37

1.5

Acceleration (g)

1 0.5 0 −0.5 −1 −1.5

0

5

10 15 Time (seconds) a. acceleration history

20

25

Acceleration (g)

4 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

3 2 1 FP 0

0

0.5

1

1.5 2 Period (seconds) b. acceleration response spectrum

2.5

3

Displacement (inches)

20 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

15 FP 10 5 0

0

Figure 3-13

0.5

1

1.5 2 Period (seconds) c. displacement response spectrum

2.5

3

Scaled input motion LS17C, 1994 Northridge, Sylmar; length scale = 5, amplitude scale = 100% (Table 3-4)

38

1.5

Acceleration (g)

1 0.5 0 −0.5 −1 −1.5

0

5

10 15 Time (seconds) a. acceleration history

20

25

Acceleration (g)

4 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

3 2 1 FP 0

0

0.5

1

1.5 2 Period (seconds) b. acceleration response spectrum

2.5

3

Displacement (inches)

20 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

15 10 5 FP 0

0

Figure 3-14

0.5

1

1.5 2 Period (seconds) c. displacement response spectrum

2.5

3

Scaled input motion LS18C, 1994 Northridge, Sylmar; length scale = 5, amplitude scale = 100% (Table 3-4)

39

1.5

Acceleration (g)

1 0.5 0 −0.5 −1 −1.5

0

5

10 15 Time (seconds) a. acceleration history

20

25

Acceleration (g)

4 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

3 2 1 FP 0

0

0.5

1

1.5 2 Period (seconds) b. acceleration response spectrum

2.5

3

Displacement (inches)

20 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

15 10 FP 5 0

0

Figure 3-15

0.5

1

1.5 2 Period (seconds) c. displacement response spectrum

2.5

3

Scaled input motion NF01, 1978 Tabas; length scale = 5, amplitude scale = 100% (Table 3-4)

40

1.5

Acceleration (g)

1 0.5 0 −0.5 −1 −1.5

0

5

10 15 Time (seconds) a. acceleration history

20

25

Acceleration (g)

4 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

3 2 1 FP 0

0

0.5

1

1.5 2 Period (seconds) b. acceleration response spectrum

2.5

3

Displacement (inches)

20 ξ = 0.05 ξ = 0.10 ξ = 0.20 ξ = 0.30

15 FP 10 5 0

0

Figure 3-16

0.5

1

1.5 2 Period (seconds) c. displacement response spectrum

2.5

3

Scaled input motion NF02, 1978 Tabas; length scale = 5, amplitude scale = 100% (Table 3-4)

41

42

4 Results and Analysis of DisplacementControlled Tests 4.1

Introduction

For the design and analysis of seismically isolated bridges, bearings are typically modeled using two uncoupled linear or bilinear (nonlinear) springs. However, it was not known prior to this study whether such models could adequately capture the response of seismic isolation bearings subjected to uni-directional horizontal, bi-directional horizontal, or tri-directional earthquake shaking. The purpose of the displacement-controlled tests was to characterize the behavior of Friction Pendulum (FP) bearings from bi-directional test data and develop mathematical models to predict their behavior. The data resulting from these tests is first examined in Section 4.2 to characterize the bearings, with a particular emphasis on breakaway friction, stick-slip, velocity dependence, pressure dependence, load history and path history effects. Following the characterization, practical models are proposed that capture the behavior of FP bearings. The procedures used to calibrate the models are discussed in Section 4.3 and these models are then compared to the experimental displacement tests data in Section 4.4. 4.2

Characterization of Bearings from Bi-Directional Displacement-Controlled Tests

4.2.1 Introduction Numerous experimental studies (including Mokha et al. 1990, Constantinou et al. 1990, Bondonet and Filiatrault 1997, and Constantinou et al. 1999) have been conducted on the behavior of PTFE-stainless steel interfaces, an interface similar to that used in FP bearings. Mokha et al. (1990) showed that the friction force at the sliding interface is dependent on several

43

factors, of which the most influential are composite type, sliding velocity, and pressure. The behavior of sliding bearings is also dependent on the materials used, such as the composite or PTFE, and roughness of the stainless steel surface. Studies have shown that modifications to the properties of the composite and the sliding surface affect the magnitude of the friction force, but generally the overall interface characteristics remain unchanged. (Mokha et al. 1990). Some of the factors that influence the behavior of FP sliding bearings are discussed in this section. In particular, issues related to friction such as breakaway and stick-slip behavior, and the velocity and pressure dependence of the friction coefficient are examined. The bi-directional response of FP bearings is examined using the rigid block model experimental data. Previous studies have investigated the bi-directional behavior of a flat sliding surface (Mokha et al. 1993) but not the behavior of FP bearings. It should be noted at the outset that the behavior of sliding bearings, in particular the friction coefficient and changes in response due to frictional heating, depends on the size of the slider and the procedures used to bond the composite to the face of the slider. For example, the confinement provided to the composite on a small diameter slider, such as that used in these experiments, will be different from that provided in full-size FP bearings for bridges. The values obtained in this experimental program for the breakaway (static) and dynamic coefficients of friction should not be used for the design of isolated bridges: data from full-scale testing must be used. Nonetheless, the trends reported below from the tests of small- to moderate-scale FP bearings are likely to apply for full-scale bridge bearings. 4.2.2 Influence of Test Setup on Friction Pendulum Bearing Behavior The rigid block model provided a constant axial (gravity) load on all four bearings but the axial load on individual bearings changed continuously over the course of the displacementhistory tests. It proved difficult to achieve an equal distribution of axial load on all four FP bearings with such a stiff steel frame. Minor changes (e.g., 0.1 in.) in the vertical alignment of the rigid block model led to significant changes, and in some cases complete unloading, of one or more of the four FP bearings. Overturning forces also had a significant effect on the bearing axial forces. Figure 4-1 is a drawing of the rigid block model test fixture showing the location of the center of mass and the horizontal struts that attached the frame to the buttresses. The axial forces in the struts produced overturning forces on the four-bearing isolation system as shown in the

44

L+x

L-x

x

x W

V

h Load Cells V 2 W ( L − x) Vh − 2L 2L

Figure 4-1

V 2 W ( L − x) Vh + 2L 2L

Axial load variations in bearings supporting the rigid block model

figure. Large bearing displacements under the relatively small rigid block model also produced significant second-order effects: a 5 in. displacement of the rigid block model redistributed the gravity load to 58 percent of the total load on two bearings and 42 percent on the two remaining bearings. The typical behavior of the rigid block model supported by FP bearings under a unidirectional (Orbit 5) displacement-controlled test is shown in Figure 4-2; the target peak velocity of this test was 5 in./sec. The base shear force (sum of the resisting forces in the four bearings) versus displacement is shown in Figure 4-2b. The hysteretic behavior is representative of a bilinear system, which is the expected behavior for FP bearings with a constant normal load. Parts c through f of Figure 4-2 show the resisting force-deformation loops for each individual bearing during the same test. These four loops show significant departures from the bilinear loop shape of Figure 4-2b. The individual resisting force-deformation plots have a curved shape, as if the bearing were stiffening in one direction and softening in the other. This behavior is explained below by focusing on Bearing 3. Figure 4-3 provides additional information on the response of this FP bearing.

45

20

Total resisting force in X (kip)

Deformation in X (in.)

6 4 2 0 −2 −4 −6

0

5

10

15

20

25

10

0

−10

−20 −6

30

Time (sec.) a. input displacement history Orbit 5 Resisting force in X (kip)

Resisting force in X (kip)

2 0 −2 −4 −4

−2

0

2

4

4

6

2 0 −2 −4 −6 −6

6

−4

−2

0

2

4

6

4

6

Deformation in X (in.) d. hysteresis for Bearing1 6

Resisting force in X (kip)

6

Resisting force in X (kip)

2

4

Deformation in X (in.) c. hysteresis for Bearing 2

4 2 0 −2 −4 −4

−2

0

2

4

4 2 0 −2 −4 −6 −6

6

Deformation in X (in.) e. hysteresis for Bearing 3 Figure 4-2

0

6

4

−6 −6

−2

Deformation in X (in.) b. hysteresis for isolated rigid block

6

−6 −6

−4

−4

−2

0

2

Deformation in X (in.) f. hysteresis for Bearing 4

Typical response of rigid block model supported on FP bearings

46

6

4

4

Velocity in X (in./sec.)

Deformation in X (in.)

6

2 0 −2 −4 −6

0

5

10

15

20

25

2 0 −2 −4 −6

30

0

5

10

Time (sec.) a. input displacement history Orbit 5

15

20

25

30

4

6

Time (sec.) b. velocity history

Normal load (kip)

−12

−14

−16

−18

−20

0

5

10

15

20

25

30

Time (sec.) c. normal load history 0.4

Resisting force/normal load

Resisting force in X (kip)

6 4 2 0 −2 −4 −6 −6

−4

−2

0

2

4

0

−0.2

−0.4 −6

6

Deformation in X (in.) d. bearing hysteresis Figure 4-3

0.2

−4

−2

0

2

Deformation in X (in.) e. normalized hysteresis

Influence of axial load variations on the response of FP bearing 3

47

For the displacement tests, the axial load history was well correlated with the displacement history. A positive displacement in Bearing 3 reduced the normal load (from the static value of approximately 16 kips to a minimum of approximately 12 kips) on the bearing and negative displacements increased the normal load (to a maximum of approximately 20 kips). The resulting hysteresis in Figure 4-3d shows softening for positive displacements and stiffening for negative displacements. Additionally, the width of the hysteresis loop increases with increased axial load (negative displacements). This behavior shows the direct influence of the axial load on the resisting force response of the bearing. Neglecting variations in the friction coefficient, the resisting force is proportional to the normal load on the bearing per Equation 2-7. If the bearing resisting force is normalized by the normal load, the resulting hysteresis, presented in Figure 4-3e, is bilinear as expected. The second-slope stiffness of this normalized hysteresis is the inverse of the radius of curvature of the concave sliding surface. Note from Figure 4-3d that the yield displacement in these FP bearings is approximately 0.01 in., which corresponds to the yield deformation in the composite material. 4.2.3 Breakaway or Static Friction Certain materials used for sliding interfaces require a larger force to initiate sliding than to continue sliding. Such a force at the onset of sliding is related to the breakaway or static coefficient of friction through the normal force on the interface. PTFE is a material that exhibits a breakaway coefficient of friction that is greater than the dynamic coefficient of friction for small velocities. This phenomenon is observed at surfaces that have either never slipped relative to one another or only after relative motion between the surfaces has stopped for a sufficiently long interval of time (Mokha et al. 1991). Breakaway friction effects are not evident at sudden stops in motion such as displacement reversals. Mokha et al. (1990) report that the magnitude of the breakaway coefficient of friction for PTFE materials is typically less than the maximum friction coefficient attained at high velocities, as shown in Figure 4-4. For FP bearings using a composite liner with the properties of Figure 4-4, the breakaway coefficient of friction will never dictate the maximum force output of the bearing, even if the radius of curvature is very large. The breakaway friction force at a PTFE-stainless steel interface is due primarily to an increase in the true contact area at the interface and the resultant transfer of a very thin film of PTFE to the stainless steel surface (Constantinou et al. 1999). Because PTFE exhibits viscoelastic

48

Coefficient of friction

fmax Breakaway coefficient

Increasing normal load and increasing temperature

fmin

Sliding velocity

Figure 4-4

Typical variation of friction coefficient with sliding velocity (adapted from Constantinou et al. 1999)

behavior, this increase in the true contact area occurs while the surfaces are at rest (dwell) for a relatively short period of time (from minutes to a few hours). An increase in the dwell time beyond a few hours has no further effect on the breakaway or static friction. Experiments conducted by Mokha et al. (1991) reported no difference in the breakaway coefficient of friction for identical unfilled Teflon sliders for dwell times of 30 minutes and 594 days. Breakaway friction is also more evident for sliding on a clean surface than on a surface over which sliding has already occurred because sliding transfers a thin layer of PTFE to the stainless steel surface (Constantinou et al. 1999). The breakaway friction that is observed in many experiments involving sliding surfaces is a consequence of inertial effects in the test fixture (Rabinowicz 1995, Constantinou et al. 1999). At the initiation of sliding and at displacement reversals, inertial forces develop in the test fixture. These forces are measured by the load cells and often misinterpreted as breakaway friction forces. The data gathered from the current research program show little or no evidence of breakaway friction because most tests were not conducted with new sliders on clean stainless steel surfaces. One example of breakaway friction can be seen in Figure 4-5 which shows the

49

response of one of four virgin sliders to small-amplitude earthquake shaking of the rigid block model. The maximum displacement of the bearing was less than 10 percent of the 7-in. displacement capacity and the maximum sliding velocity was 5 in./sec., which is greater than the velocity at which the maximum dynamic coefficient of friction is realized. The maximum resisting force in the bearing occurred at the onset of sliding, but it includes inertial effects in the load cell. For reference, this breakaway force of approximately 2 kips is less than 40 percent of maximum force output of this bearing (for a normal load of 16 kips). Note also the residual or permanent offset of approximately 0.1 in., which was typically observed following tests involving low to moderate earthquake excitation of the FP bearings. 2

Resisting force in X (kip)

1.5 1 0.5 0 −0.5 −1 −1.5 −2

−0.5 −0.4 −0.3 −0.2 −0.1

0

0.1

0.2

0.3

0.4

0.5

Deformation in X (in.) Figure 4-5

Earthquake testing of a virgin slider showing apparent breakaway friction

In bridges, FP and other sliding bearings will be constantly subjected to movement induced by traffic loadings and thermal expansion. Such continual movement under non-seismic loads will mitigate or eliminate the breakway effect on the seismic response of the bridge.

50

4.2.4 Stick-Slip Fluctuations in the friction force at times other than the initiation of sliding are often described as stick-slip behavior, but it is questionable whether the source of the stick-slip behavior is an intrinsic property of friction or due to inertial effects and finite stiffness in the test fixture. Rabinowicz (1995) noted that a sudden change in the direction of friction force could result in oscillations of a test mechanism with finite stiffness that in turn produce measured force oscillations by the load cell. A typical experimental apparatus for measuring friction (Rabinowicz 1995) can be modeled as a slider controlled by a stiff spring as shown in Figure 4-6, where the spring represents the stiffness of the load cell and supporting frame. A sudden change in the direction of the friction force will produce inertial forces in the spring that are measured as force fluctuations by the strain gages in the load cells.

normal force

spring support

slider flat surface friction force

Figure 4-6

Test setup for measuring friction (adapted from Rabinowicz 1995)

Figure 4-7 compares the hysteresis of one bearing subjected to 3 cycles of uni-directional sinusoidal displacement at peak velocities of 2 in./sec. and 20 in./sec. This bearing had been tested previously so that breakaway friction effects had been eliminated. The maximum resisting force for both tests are approximately the same, but the hysteresis loop for the test conducted at 2 in./sec. is much smoother than the loop for the 20 in./sec. test. The test at 20 in./sec. exhibits “stick-slip” motion with force fluctuations at the start of the test (breakaway) and immediately after displacement reversals. Parts c and d of this figure present the relationships between the normalized resisting force (measured resisting force divided by coexisting normal load) and the displacement. Some of the apparent stick-slip oscillations are not evident in the normalized resisting force loops, which indicate that variations in the axial force contributed to the observed

51

6

Resisting force in X (kip)

Resisting force in X (kip)

6 4 2 0 −2 −4 −6 −6

−4

−2

0

2

4

4 2 0 −2 −4 −6 −6

6

Deformation in X (in.) a. hysteresis loop for 2 in./sec. test

Resisting force/normal load

Resisting force/normal load

0

2

4

6

0.3

0.2 0.1 0 −0.1 −0.2 −4

−2

0

2

4

6

0.2 0.1 0 −0.1 −0.2 −6

Deformation in X (in.) c. normalized hysteresis loop for 2 in./sec. test Figure 4-7

−2

Deformation in X (in.) b. hysteresis loop for 20 in./sec. test

0.3

−6

−4

−4

−2

0

2

4

6

Deformation in X (in.) d. normalized hysteresis loop for 20 in./sec. test

Stick-slip in FP bearings

stick-slip. Further, the fact that stick-slip is only apparent in the normalized hysteresis loops for the high velocity test leads to the conclusion that the observed stick-slip is primarily due to inertial effects in the test fixture and is not an intrinsic property of the interface materials. 4.2.5 Velocity Dependence Figure 4-4 from Constantinou et al. (1999) shows the typical relationship between friction force and velocity for PTFE or PTFE-like materials sliding on a stainless steel surface. A detailed presentation on the velocity dependence of such interfaces is presented by Constantinou et al. (1999) and is not repeated here.

52

The dynamic coefficients of friction for the different composites used in this experimental program were established using data from the uni-directional sinusoidal displacement-history tests (Orbit 5). Sample data are presented in Figure 4-8 for one of the composites. Friction values were determined using resisting force and axial load data at the instant at which the target velocity was reached. Data associated with the initial breakaway half-cycle were not used to calculate the friction coefficients. Figure 4-8 shows a slight increase in the coefficient of friction as the velocity increases from 2 to 5 in./sec.; at a velocity of 20 in./sec. the friction coefficient is slightly less than the value at 5 in./sec. Also included in this figure is a friction-velocity relationship that was developed using the experimental data fitted to the model of Constantinou et al. (1990) µ = f max – ( fmax – f min ) e

–a v

(4-1)

where fmax and fmin are the coefficients of friction at high and low velocities, respectively, as indicated in Figure 4-4, a is a constant that describes the rate of the transition from low to high velocities, and v is the magnitude of the velocity vector. 0.12

Coefficient of friction

0.1

0.08 Bearing 3, Y−direction Bearing 4, Y−direction Constantinou (1990)

0.06

0.04

0.02

0

0

2

4

6

8

10

12

14

16

18

Velocity (in./sec.) Figure 4-8

Velocity dependence of the coefficient of friction for one FP composite

53

20

The 1990 Constantinou model assumes that the coefficient of friction increases with velocity and tends to an asymptotic value. However, a modest reduction in the coefficient at high velocities was measured in both the current experimental program and in the work of Bondonet and Filiatrault (1997), who reported a reduction in the coefficient at velocities exceeding 10 in./ sec. This observation can be attributed to frictional heating. An increase in the temperature of the sliding interface will reduce the coefficient of friction (Constantinou et al. 1999), but the percentage reduction will be a function of the type and thickness of the composite liner on the articulated slider. The uni-directional tests of the FP bearings using the Berkeley simulator made use of sinusoidal displacement signals that were preceded by a transition displacement history to accommodate the initial conditions of the sinusoidal signal. Much more high-velocity travel was required to achieve the target velocity of 20 in./sec. than was required to reach the target velocity of 5 in./sec. The frictional heating associated with this significantly greater travel distance and velocity likely contributed to the reduction in the coefficient of friction. Of importance to bridge engineers is the velocity beyond which the friction coefficient remains essentially constant, that is, the velocity at which f max is achieved. Mokha et al. (1990) reported that the threshold velocity is approximately 5 in./sec. for unfilled PTFE using flat sliders with diameters of 5 in. and 10 in. More recent studies using full-scale FP bearings and composites designed for building applications suggest that the transition velocity is approximately 1 in./sec. For the sliders used in the Berkeley study, fmax was achieved at velocities as low as approximately 1 in./sec. For Bearing 3 in Figure 4-8, there is virtually no increase in the coefficient of friction for velocities greater than 1 in./sec. Such a result is desirable because the constant friction model can be used instead of Equation 4-1 to describe the response of FP bearings. It was not the intent of this research program to develop relations between friction and velocity because of the reduced scale of the test bearings. Nonetheless, the data presented above illustrate trends that are supported by other FP bearing experimental programs. 4.2.6 Pressure Dependence Previous experimental data clearly show that the friction coefficient is reduced with increasing contact pressure. Constantinou et al. (1999) proposed an explanation for this behavior of PTFE-stainless steel interfaces using information on Teflon presented by Bowden and Tabor

54

(1964), Tabor (1991) and Rabinowicz (1995). Constantinou et al. states that the resisting force, F, at the sliding interface is given by F = sA n = ( s0 + α p ) An

(4-2)

where An is the nominal contact area that is approximately equal to the real contact area after sufficient dwell time due to the viscoelastic nature of PTFE, and s is the shear strength at the interface that is a linear function (Tabor 1981) of the actual pressure p . If the coefficient of friction is defined as the shear force divided by the normal load then ( s0 + α p ) A n s F - = ----0 + α µ = ---- = ---------------------------N N p

(4-3)

This relation states that the friction coefficient is a linear function of the inverse of the actual pressure. To account for pressure effects, f max in Equation 4-1 varies by (Tsopelas and Constantinou 1996) fmax = f maxo – ∆ f ⋅ tanh ( α p )

(4-4)

where fmaxo , ∆ f and α are parameters calibrated from experimental data. During the large amplitude displacement-history tests, the axial load typically varied by ± 5 kips from the target value of 16.25 kips and resulted in contact pressures fluctuating between

approximately 7000 psi and 13000 psi. The maximum pressure occurred at the peak displacements as can be seen by comparing the axial load history with the displacement history in Figures 4-3a and 4-3c. Normalizing the resisting force in an FP bearing by the normal load gives F1 --= --- u + µ N R

(4-5)

The width of the hysteresis loop that plots normalized resisting force versus displacement is 2 µ . Figure 4-9 presents Figure 4-3e at a larger scale and identifies the normal load and friction coefficient at the maximum and minimum displacements. This figure shows that the friction coefficient increases with decreasing pressure ( µ =0.106 for N=13 kips and µ =0.088 for N=19 kips). Despite these changes in individual bearing hysteresis, it must be noted that the total gravity load on the rigid block model did not change and that the global friction coefficient for the isolation system remained constant.

55

0.4

Resisting force/normal load

0.3 0.2

0.213 (N=13 kips)

0.1 0 −0.1

0.176 (N=19 kips)

−0.2 −0.3 −0.4 −6

−4

−2

0

2

4

6

Deformation in X (in.) Figure 4-9

Pressure dependence of the coefficient of friction

4.2.7 Load History The mechanism by which sliding bearings displace is much different from elastomeric bearings. In elastomeric bearings, the bulk of the rubber deforms whereas in sliding bearings deformations are limited to the PTFE or composite liner at the sliding surface. Once the yield deformation of the composite liner is reached, which is of the order of 0.01 in. for PTFE, the composite liner is fully deformed and deformation in the liner will be the same regardless of whether the bearing displacement is 0.05 in. or 5 in. from sliding. For this reason, FP bearings are not expected to exhibit load-history effects. However, the hysteresis of FP bearings will change if frictional heating substantially increases the temperature at the sliding surface. Figure 4-10 shows the change in friction coefficients over 3 cycles of sinusoidal loading. One value of the friction coefficient is plotted for each half cycle. The data show a modest decrease in the friction coefficient with repeated cycling. The four tests were conducted consecutively in the order of increasing velocity with a time interval of about 5 minutes between each test. The coefficients of friction at the start of the 2, 5, and 20 in./sec., tests are greater than the values at the end of the preceding tests due to cooling of

56

the composite and liner between tests and the consequent increase in the coefficient of friction. The reduction in friction is not a result of wear on the slider. The data from these uni-directional tests overestimate the variations in the coefficient of friction expected in full-size bridge bearings due to earthquake shaking because the slider in the bridge bearing will traverse a chaotic bidirectional orbit rather than a uni-directional path for which the temperature rise and change in friction coefficient will be maximized. 0.12 Velocity = 1 in./sec. Velocity = 2 in./sec. Velocity = 5 in./sec. Velocity = 20 in./sec.

Coefficient of friction

0.11

0.1

0.09

0.08

0.07

0.06

0

0.5

1

1.5

2

2.5

3

Cycles Figure 4-10

Reduction in the coefficient of friction with repeated cycling

FP bearings shed a very thin layer of composite material onto the stainless steel surface during sliding and wear of the slider is inevitable. If the wear is sufficiently large, the performance of the bearing and the FP isolation system will be affected. For bridge applications in which FP bearings are subjected to substantial travel due to thermal cycling of the superstructure, a thicker composite is used to mitigate the effects of wear. The composites that were bonded to the sliders in the rigid block model tests of the FP bearings were subjected to the equivalent of tens of maximum capable earthquakes. Although the wear of the composite was noticeable by visual inspection, the changes in bearing hysteresis were negligible.

57

4.2.8 Path History The FP bearings were subjected to a series of bi-directional displacement orbits to study their path -history dependence. Information on these orbits is presented in Figure 3-6. The bi-directional response of the FP bearings was studied by comparing the force responses for different orbits. Sample data are presented in Figures 4-11 (Orbits 2 and 3) and 4-12 (Orbits 2 and 4). The box orbit (Orbit 2) was selected as the basis for comparison since it contains a number of peak displacement points common to the other orbits. To eliminate effects due to variations in axial load on individual isolators, the force orbits are plotted for the isolated rigid block rather than individual bearings. There is clear evidence of path-dependent behaviors for the orbits, particularly at the sharp corners of the box and hourglass displacement orbits. Consider first the force orbit of Figure 4-11 and the displacement point (-5,-5) in. The forces in the X and Y directions are identical because both orbits approach this point along the same path. However, since the displacement orbits depart in different directions, the forces follow different paths. Consider now the displacement point (+5,+5) in. The forces in the X and Y directions are different because this point is approached from different directions (from (+5,-5) for Orbit 2 and from (-5,-5) for Orbit 3) and as a result the direction of the friction force is different. Nonetheless, the friction force acts in the direction of the instantaneous velocity (incremental displacement), which is predictable behavior. Figure 4-12 shows the displacement and forces for Orbits 2 and 4. The abrupt changes in resisting force that accompany the sharp displacement-orbit changes in Orbit 2 are not evident in Orbit 4. Also, because the maximum displacements of the figure-8 orbit (Orbit 4) slightly exceed the target values, the resisting force at the nominally common points and directions of approach (e.g., 0, -5) differ slightly. The main objective of the offset uni-directional test (Orbit 6) was to study geometrical path dependence. By cycling the FP bearing on an offset uni-directional path, the bearing is effectively traveling along a smaller radius of curvature. An offset of 5 in. for the FP bearing used in this study changes the effective radius from 30 in. to 29.6 in. This change should have a negligible effect on the hysteretic response of the bearing. The data of Figure 4-13 confirm this hypothesis. The solid lines in this figure correspond to a ± 5 in. uni-directional test with no offset.

58

The dotted lines correspond to a ± 2.5 in. uni-directional test with a 5 in. offset. As expected, there is no discernible difference between the responses for displacements less than ± 2.5 in. In summary, the measured pendulum force is linear and proportional to the lateral displacement, and always acts toward the center of the bearing. As such, it exhibits no path dependence. The friction force acts in the direction of the instantaneous velocity and is path dependent. 4.3

Calibration of Models

In the characterization of the FP bearings, it was shown that the friction coefficient is dependent on several factors such as velocity, pressure, and temperatures. One important question, however, is the effect these characteristics will have in modeling structures subjected to earthquake excitation. From a practical standpoint, a model that considers all of the above factors appears cumbersome because all of the necessary parameters have to be calibrated. Instead, a much simpler approach is taken by assuming the coefficient of friction to remain constant. This simplified model is validated in the following chapter by comparison with experimental results from the earthquake tests. A method to calibrate model parameters for elastomeric bearings was developed by Huang (2002) as part of the PROSYS project. This method was adopted for the current study on FP bearings. The calibrated friction coefficient was determined by the minimization of a residual function corresponding to the difference in response between the experimental data and analytical models for a given displacement history. A simple residual function can be defined as the absolute sum of the force difference at each recorded displacement point. However, since the displacement increments in experimental data may not be equally spaced, a residual function normalized by the length of displacement path is defined as follows: T Fe – Fm (model parameters) d U Normalized residual = -------------------------------------------------------------------------------------------





(4-6)

d UT d U

where Fe is the resisting force of a bearing from experimental data, and Fm is the analytical resisting force. The numerator on the right-hand side of Equation 4-6 represents the absolute value of work done in a bearing for a given displacement history. The denominator represents the

59

6

Deformation in Y (in.)

4

2

0

−2

−4

−6 −6

−4

−2

0

2

4

6

Deformation in X (in.) a. displacement orbit 20

Total resisting force in Y (kip)

15 10 5 0 −5 −10 −15 −20 −20

−15

−10

−5

0

5

10

15

20

Total resisting force in X (kip) b. force orbit for isolated rigid block Figure 4-11

Path-dependent response of FP bearings: box Orbit 2 and hourglass Orbit 3

60

6

Deformation in Y (in.)

4

2

0

−2

−4

−6 −6

−4

−2

0

2

4

6

Deformation in X (in.) a. displacement orbit 20

Total resisting force in Y (kip)

15 10 5 0 −5 −10 −15 −20 −20

−15

−10

−5

0

5

10

15

20

Total resisting force in X (kip) b. force orbit for isolated rigid block Figure 4-12

Path-dependent response of FP bearings: box Orbit 2 and figure-8 Orbit 4

61

6

Deformation in Y (in.)

4

2

0

−2

−4

−6 −6

−4

−2

0

2

4

6

4

6

Deformation in X (in.) a. displacement orbit 20

Total resisting force in X (kip)

15 10 5 0 −5 −10 −15 −20 −6

−4

−2

0

2

Deformation in X (in.) b. hysteresis for isolated rigid block Figure 4-13

Effect of path offset on response of FP bearings

62

length of this displacement path. The normalized residual of Equation 4-6 can be used to compare fits between different displacement histories because of the normalization by path length. The downhill simplex method (Nelder and Mead 1965) was used to minimize the residual function of Equation 4-6 in terms of the friction coefficient. This method was selected because it is efficient and does not require the gradient of the residual function with respect to the model parameters. Moreover, the software package Matlab (MathWorks 1996) includes a subroutine for minimizing functions based on this method. Only one initial value is needed for the subroutine, with the other starting points being automatically generated. The calibrated friction coefficient for the plasticity model considering the effects of axial load were determined for all tests and are listed in Table 4-1. For the test using the unidirectional Orbit 5, the friction coefficient changes very little as the peak sliding velocity is increased. This trend supports the use of a constant friction coefficient model. 4.4

Comparison of Models with Displacement Data

Using the calibrated friction coefficient determined in the previous section, the plasticity model was compared to the experimental results from the displacement tests. Figures 4-14 through 4-17 illustrate the response of FP bearing 4 to Orbits 2, 3, 4, and 7 (see Figure 3-6) with peak displacements of 5 in. in both the X and Y directions. Comparing the experimental results with the coupled plasticity model resisting force indicates that the model effectively captures the behavior of FP bearings. The change in width of the hysteresis loops results from changes in axial load due to overturning forces and this behavior is also modeled. It is apparent from these figures that the peak forces produced by the coupled plasticity model are about 20 percent less than the peak forces from the experimental data. A possible reason for this difference is that the response predicted for the FP bearings made use of the axial force data from the five component load cells; data found not to be 100-percent reliable. The force output from the coupled plasticity model also differed from the experimental data at sharp turning points such as the corners in Orbits 2 and 3. For example, at the upper left corner of the force orbit in Figure 4-14a, the experimental data has a linear transition as the plastic force changes from the (-X) direction to the (-Y) direction. In Figure 4-14b, the coupled plasticity model produces a more rounded transition at this same corner. This inconsistency is not surprising

63

Table 4-1

Calibrated best-fit values of friction coefficient (percent) using the coupled plasticity model for Friction-Pendulum Bearings

Test Label

Orbit1

(a)ORBIT5Y-01 (b)ORBIT5Y-02 (c)ORBIT5Y-05 (d)ORBIT5Y-20 (e)ORBIT5X-01 (f)ORBIT5X-02 (g)ORBIT5X-05 (h)ORBIT5X-20 (i)ORBIT6X-02 (j)ORBIT6X-05 (k)ORBIT6X-20 (l)ORBIT6X-02 (m)ORBIT6X-05 (n)ORBIT6X-20 (o)ORBIT3-01 (p)ORBIT2-01 (q)ORBIT7-02 (r)ORBIT7-05 (s)ORBIT4-04 (t)ORBIT4-10 (u)ORBIT4-20

5y 5y 5y 5y 5x 5x 5x 5x 6x 6x 6x 6x 6x 6x 3 2 7 7 4 4 4

X-disp2 (in.) 0 0 0 0 5 5 5 5 5 5 5 2.5 2.5 2.5 5 5 2.5 5 2.5 5 5

Y-disp2 (in.) 5 5 5 5 0 0 0 0 2.5 2.5 2.5 5 5 5 5 5 2.5 5 2.5 5 5

X-vel3 (in./sec.) 0 0 0 0 1 2 5 20 2 5 20 2 5 20 2 5 4 10 20

Y-vel3 Bearing4 Bearing Bearing Bearing (in./sec.) 1 2 3 4 1 7.51 8.09 10.04 9.31 2 8.15 8.00 10.52 9.74 5 8.26 7.90 9.98 9.94 20 7.41 7.35 8.79 9.27 0 8.20 8.47 11.50 9.90 0 8.27 8.47 10.67 9.74 0 8.21 8.52 10.39 10.10 0 7.34 7.69 9.24 9.34 8.87 8.60 10.24 10.40 8.63 8.38 10.96 10.32 8.52 8.44 9.64 10.87 8.40 8.29 11.04 9.36 8.51 8.32 9.68 9.34 7.88 7.98 8.48 9.02 7.06 7.49 9.63 9.10 7.05 8.00 9.38 8.65 2 9.05 8.51 11.11 11.08 5 9.60 8.80 10.98 11.78 2 9.20 8.66 11.36 10.99 5 8.77 8.81 10.96 11.44 10 8.53 8.46 10.48 10.95

1. See Figure 3-6 for information on orbits; x denotes cycling in the X-direction and y denotes cycling in the Ydirection. 2. X-disp = maximum displacement amplitude in the X-direction; Y-disp = maximum displacement amplitude in the Y-direction. 3. X-vel = maximum velocity in the X-direction; Y-vel = maximum velocity in the Y-direction. 4. For location of bearing, see Figure 3-5; coefficient of friction is given in percent.

since the plasticity model provides an approximation of the friction-force direction, which may not be very accurate when there is a sudden change in direction. This difference in behavior could also be attributed to the filtered experimental displacement data. The experimental force and displacement data presented in Figures 4-14 through 4-17 was filtered or smoothed by replacing each data point by the average of the neighboring four points. This same smoothing function was applied on the experimental displacement data used as input to the plasticity model. Filtering of the experimental displacement data was necessary since small noise levels on the order of the yield displacement were amplified

64

−5

5

0

−5 −5 0 5 Deformation in X (in)

5

0

−5 −5 0 5 Deformation in X (in)

Figure 4-14

5

−5 −5 0 5 Resisting force in X (kip)

0

−5

−5 0 5 Deformation in Y (in) (b) coupled plasticity model Resisting force in Y (kip)

Resisting force in X (kip)

−5 0 5 Deformation in Y (in) (a) experimental data Resisting force in Y (kip)

Resisting force in X (kip)

−5 0 5 Deformation in X (in)

0

Resisting force in Y (kip)

−5

0

5

5

Resisting force in Y (kip)

0

5

Resisting force in Y (kip)

Resisting force in Y (kip)

Resisting force in X (kip)

5

0

−5

−5 0 5 Deformation in Y (in) (c) uncoupled plasticity model

5

0

−5 −5 0 5 Resisting force in X (kip)

5

0

−5 −5 0 5 Resisting force in X (kip)

FP Bearing No. 4: Experimental data compared with coupled and uncoupled plasticity model for Orbit 2

by the high initial stiffness used in the FP bearing model. The yield displacement = 0.01 in.; noise levels of this magnitude resulted in additional forces of ± QD in the model. Filtering the displacement data also modified the transition at the corners, making them rounded instead of

65

0

−5

5

0

−5

5

0

−5 −5 0 5 Deformation in X (in)

Figure 4-15

0

−5 −5 0 5 Resisting force in X (kip)

5

0

−5

−5 0 5 Deformation in Y (in) (b) coupled plasticity model Resisting force in Y (kip)

−5 0 5 Deformation in X (in)

Resisting force in X (kip)

−5 0 5 Deformation in Y (in) (a) experimental data Resisting force in Y (kip)

Resisting force in X (kip)

−5 0 5 Deformation in X (in)

5

Resisting force in Y (kip)

−5

5

Resisting force in Y (kip)

0

Resisting force in Y (kip)

Resisting force in Y (kip)

Resisting force in X (kip)

5

5

0

−5

−5 0 5 Deformation in Y (in) (c) uncoupled plasticity model

5

0

−5 −5 0 5 Resisting force in X (kip)

5

0

−5 −5 0 5 Resisting force in X (kip)

FP Bearing No. 4: Experimental data compared with coupled and uncoupled plasticity model for Orbit 3

maintaining a sharp 90-degree turn. Rounded corners in the displacement input are likely responsible for the rounded force transition in the coupled plasticity model. The sensitivity of the plasticity model to a 90 degree change in direction is further investigated in Figure 4-18. Figure 4-18a shows the displacement orbit with a displacement

66

−2

6 4 2 0 −2 −4

−5 0 5 Deformation in X (in)

6 4 2 0 −2 −4

0 −2 −4

−5 0 5 Deformation in X (in)

−5 0 5 Deformation in Y (in) (a) experimental data

4 2 0 −2 −4 −4 −2 0 2 4 6 Resisting force in X (kip)

6 4 2 0 −2 −4

−5 0 5 Deformation in Y (in) (b) coupled plasticity model Resisting force in Y (kip)

Resisting force in X (kip)

−5 0 5 Deformation in X (in)

2

Resisting force in Y (kip)

−4

Resisting force in Y (kip)

0

4

6

Resisting force in Y (kip)

2

6

Resisting force in Y (kip)

Resisting force in Y (kip)

4

Resisting force in X (kip)

Resisting force in X (kip)

6

6 4 2 0 −2 −4

−5 0 5 Deformation in Y (in)

6 4 2 0 −2 −4 −4 −2 0 2 4 6 Resisting force in X (kip)

6 4 2 0 −2 −4 −4 −2 0 2 4 6 Resisting force in X (kip)

(c) uncoupled plasticity model Figure 4-16

FP Bearing No. 4: Experimental data compared with coupled and uncoupled plasticity model for Orbit 4

increment of 0.05 in. and the resulting plasticity model forces for two different displacement histories. Both curves in the figure are for the same original displacement data, but one displacement set was smoothed in a similar fashion as the experimental displacement data. Smoothing resulted in a rounded displacement transition at the corner as can be seen from the data

67

−5

5

0

−5

5

0

−5 −5 0 5 Deformation in X (in)

Figure 4-17

5

−5 0 5 Resisting force in X (kip)

0

−5

−5 0 5 Deformation in Y (in) (b) coupled plasticity model Resisting force in Y (kip)

Resisting force in X (kip)

−5 0 5 Deformation in X (in)

−5

−5 0 5 Deformation in Y (in) (a) experimental data Resisting force in Y (kip)

Resisting force in X (kip)

−5 0 5 Deformation in X (in)

0

Resisting force in Y (kip)

−5

0

5

5

0

−5

−5 0 5 Deformation in Y (in) (c) uncoupled plasticity model

5

0

−5 −5 0 5 Resisting force in X (kip)

Resisting force in Y (kip)

0

5

Resisting force in Y (kip)

Resisting force in Y (kip)

Resisting force in X (kip)

5

5

0

−5 −5 0 5 Resisting force in X (kip)

FP Bearing No. 4: Experimental data compared with coupled and uncoupled plasticity model for Orbit 7

set marked with ‘+’. The resulting forces for the two displacement sets are shown in the diagram on the right, where the unfiltered data provides a linear transition similar to the experimental results. Note that there are essentially no data points within the transition zone for the unfiltered case. In Figure 4-18b, the same procedure is repeated for displacement increments of 0.005 in.,

68

which is half of the assumed yield displacement. In this case, both, the smoothed and unfiltered displacements provide rounded force transitions at the corners. The plasticity model is not able to reproduce the experimental results at corners because: (a) the input displacement data is filtered and/or (b) the experimental data is not sampled at a sufficiently fast rate to adequately capture the force transition. 4 Resisting force in Y (kip)

Deformation in Y (in)

5.1

5

4.9

4.8

4.7 4.7

3.5

3

2.5

2

4.8 4.9 5 Deformation in X (in)

1

1.5 2 2.5 Resisting force in X (kip)

3

(a) displacement increment ∆u = 0.05

4 Resisting force in Y (kip)

Deformation in Y (in)

5.1

5

4.9

4.8

4.7 4.7

3.5

3

2.5

2

4.8 4.9 5 Deformation in X (in)

1

1.5 2 2.5 Resisting force in X (kip)

3

(b) displacement increment ∆u = 0.005 in. Figure 4-18

Examples of response of plasticity model with typical parameters for an FP bearings ( K 1 =150 kip/in., K2 =0.5 kip/in., QD =1.2 kip, and U Y = 0.01 in.) around a sharp corner for displacement increments of (a) 0.05 in. and (b) 0.005 in.

69

Also included in Figures 4-14 through 4-17 are the computed results for the uncoupled plasticity model, which poorly captures the path of the friction force. The uncoupled model is affected by noise in the displacement data. While the bearing deforms in the X-direction with a fixed displacement in the Y-direction, the uncoupled model computes large force fluctuations in the Y-direction. Along this path segment, the plasticity model amplifies noise in the presumed constant Y-displacement data by the large initial stiffness K1 . Noise in the displacement history as little as 0.01 in. (0.2% of peak displacements) results in a differential force output of ± QD ≈ ± 1.5 kip. These force fluctuations are not computed by the coupled plasticity model

because the dominant displacement increment is in the direction of sliding. The larger displacement increment controls the direction of the plastic force. 4.5

Summary

In the characterization of FP bearings, it was shown that the difficulties in modeling bearings are attributed to friction. Key parameters that influence the friction coefficient were identified, but a model capturing all of these characteristics appears tedious. Instead a constant friction model was proposed and verified to adequately capture the behavior of FP bearings. The importance of considering coupling for bi-directional models was also noted.

70

5 Results and Analysis of Earthquake Tests 5.1

Introduction

This chapter presents the results of an extensive experimental investigation of a seismically isolated bridge model using the earthquake simulator. The same rigid block frame described in Section 3.2 was used in these experiments. For earthquake testing, the struts were removed and the model was tested dynamically on the simulator. The rigid block model represented a small-scale bridge with rigid superstructure and rigid substructure excited by up to three components of ground motion. The objectives of this phase of the experimental program were to examine the bi–directional earthquake response of a simple bridge system with seismic isolation bearings, evaluate the effects of different types of ground motions, including vertical acceleration, and evaluate the mathematical models for Friction Pendulum (FP) bearings. The sequence of earthquake tests are listed in Table 3-5. 5.2

Typical Response of Friction Pendulum Bearings to Earthquake Excitation

An example of the response of the four FP bearings to the bi-directional earthquake test (l) NF01/02-100% is presented in Figures 5-1 and 5-2 for the X- and Y-directions, respectively. The hysteresis plots show that the maximum displacement occurs during a large pulse in the positive X-direction to approximately 4 in. The X-direction response clearly shows the overturning effect. For Bearings 1 and 4 located on the positive X side of the rigid frame, the additional axial load on the bearings increases the resisting force during the large positive X displacement excursion. In contrast, Bearings 2 and 4 on the negative X side experience a decrease in axial load from overturning, which reduce the bearing resisting force to a shallow slope for the large displacement excursion. In the Y-direction, shown in Figure 5-2, the displacements are less than in the X-

71

4 Resisting force in X (kip)

Resisting force in X (kip)

4 2 0 −2 −4

2 0 −2 −4

−4

−2 0 2 Deformation in X (in.)

4

−4

a. X-hysteresis of FP Bearing 1

4 Resisting force in X (kip)

Resisting force in X (kip)

4

b. X-hysteresis of FP Bearing 2

4 2 0 −2 −4

2 0 −2 −4

−4

−2 0 2 Deformation in X (in.)

4

−4

c. X-hysteresis of FP Bearing 3 Figure 5-1

−2 0 2 Deformation in X (in.)

−2 0 2 Deformation in X (in.)

4

d. X-hysteresis of FP Bearing 4

Experimental response of rigid block model in X-direction for bi-directional test (l) NF01/02-100%

direction, with the maximum displacement of 2.3 in. in the positive Y-direction at the same time the maximum X-direction displacement occurs. For this test, the rigid block model recentered at the end of the earthquake excitation. 5.2.1 Combination of Horizontal Ground Motion Components A series of tests were conducted with the FP bearings to evaluate the contributions of the horizontal ground motion components using the LA21/22 and NF01/02 records. For each record

72

4 Resisting force in Y (kip)

Resisting force in Y (kip)

4 2 0 −2 −4

2 0 −2 −4

−4

−2 0 2 Deformation in Y (in.)

4

−4

a. Y-hysteresis of FP Bearing 1

4 Resisting force in Y (kip)

Resisting force in Y (kip)

4

b. Y-hysteresis of FP Bearing 2

4 2 0 −2 −4

2 0 −2 −4

−4

−2 0 2 Deformation in Y (in.)

4

−4

c. Y-hysteresis of FP Bearing 3 Figure 5-2

−2 0 2 Deformation in Y (in.)

−2 0 2 Deformation in Y (in.)

4

d. Y-hysteresis of FP Bearing 4

Experimental response of rigid block model in the Y-direction for bi-directional test (l) NF01/02-100%

four tests were conducted: (i) X component only, (ii) Y component only, (iii) X and Y components simultaneously, and (iv) X, Y, and vertical components simultaneously. Before comparing the response of the rigid block model with different ground motion components, it is necessary to verify that the motion of the simulator platform was not affected by the number of ground motion components specified in the command signals. To investigate crosscoupling in the simulator, the response spectra computed from the measured horizontal table acceleration for the uni-directional, bi-directional, and tri-directional tests are shown in Figure 5-3

73

Acceleration in X (g)

4 (h)LA21/22−100% (i)LA21/22/V−100% (j)LA21(X)−100%

3 2 1 0

0

0.5

1

1.5 Period (sec.)

2

2.5

3

a. acceleration response spectra in X-direction

Acceleration in Y (g)

4 (h)LA21/22−100% (i)LA21/22/V−100% (k)LA22(Y)−100%

3 2 1 0

0

0.5

1

1.5 Period (sec.)

2

2.5

3

b. acceleration response spectra in Y-direction Figure 5-3

Acceleration response spectra (5% damping) of recorded earthquake simulator acceleration for uni-directional tests (j) LA21(X)-100%, (k) LA22(Y)-100%, bidirectional test (h) LA21/22-100% and tri-directional test (i) LA21/22V-100%

for LA21/22. These plots show that the spectra of the table motion in two horizontal directions are not affected by cross-coupling for vibration periods greater than 0.5 seconds, which includes the isolated rigid block model. The low cross-coupling of the earthquake simulator allows for an unbiased comparison of the experimental response between the tests with different ground motion components. A similar comparison of the response spectra corresponding to the measured table motions from the NF01/02 set of ground motions support these observations. The effect of horizontal ground motion components on the response of the rigid block model is first examined using the LA21/22 ground motion. Figure 5-4 shows the displacement

74

response of FP Bearing 3 subjected to combinations of horizontal ground motion components: bidirectional test (h)LA21/22-100%, and the two corresponding uni-directional tests (j)LA21(X)100% and (k)LA22(Y)-100%. Comparison of the displacement histories in Figures 5-4a and 5-4b shows that the displacements in one direction is primarily due to the ground motion component in that direction. The orthogonal ground motion component produces in-phase response and generally increases the peak displacement compared with the uni-directional case. Figure 5-4c shows the displacement orbit of the bi-directional test, (h)LA21/22-100%, superimposed on a bounding box formed by the maximum displacements from the individual uni-directional tests, (j)LA21(X)-100% and (k)LA22(Y)-100%. A similar bounding box is applied on the force orbit in Figure 5-4d, showing that the uni-directional tests provide an upper bound for the maximum resisting force in the bearing. Figure 5-5 compares the force-displacement relationships in FP Bearing 3 for the uni-directional and bi-directional tests. There are more fluctuations in the bearing force and the width of the hysteresis loop is smaller for the bi-directional test. This behavior is expected because under bi-directional motion, the resisting force is influenced by the varying axial loads in addition to coupling of the friction force. The friction force is not necessarily oriented in the direction of motion considered in the plot since there exists an orthogonal velocity component in the bi-directional case. The experimental behavior of the rigid block model subjected to the NF01/02 ground motions in Figure 5-6 is similar to that observed for LA21/22. The figure shows similar trends although the orthogonal ground motion component results in a somewhat larger increase in displacement in the Y-direction, compared with the uni-directional test in Figure 5-6b. The AASHTO Guide Specifications requirement for combining maximum bearing displacement and forces due to two components of horizontal ground motion is the same as the AASHTO Standard Specifications requirement. The maximum response is the greatest combination of the uni-directional response in one direction plus 30% of the uni-directional response in the second direction. The so-called 30%-combination rule is a simplification of the square-root-sum-of-the-squares (SRSS) combination of a response quantity to multiple components of ground motion (Clough and Penzien, 1993). The experimental data was used to evaluate the 30%-combination rule. Table 5-1 shows the maximum displacements and forces from the bi-directional tests for LA21/22 and NF01/02 and the estimated maximum responses using the 30%-combination rule of the uni-directional

75

Deformation in X (in.)

4

(h)LA21/22−100% (j)LA21(X)−100%

2 0 −2 −4

Deformation in Y (in.)

0

2

4

6

8 Time (sec.) a. displacements in X

10

4

12

14

(h)LA21/22−100% (k)LA22(Y)−100%

2 0 −2 −4 0

2

4

6

8 Time (sec.) b. displacements in Y

2 0 −2 −4 −4

14

2 0 −2 −4

−2 0 2 Deformation in X (in.)

4

−4

c. displacement orbit of (h) LA21/22-100% Figure 5-4

12

4 Resisting force in Y (kip)

Deformation in Y (in.)

4

10

−2 0 2 4 Resisting force in X (kip)

d. force orbit of (h) LA21/22-100%

Experimental response of rigid block model Bearing 3 for uni-directional tests (j) LA21(X)-100%, (k) LA22 (Y)-100% and bi-directional test (h) LA21/22-100%

76

4 Resisting force in Y (kip)

Resisting force in X (kip)

4 2 0 −2 −4 −2 0 2 Deformation in X (in.)

4

−2

−4

a. X- hysteresis of (h) LA21/22-100%

−2 0 2 Deformation in Y (in.)

4

b. Y- hysteresis of (h) LA21/22-100%

4 Resisting force in Y (kip)

4 Resisting force in X (kip)

0

−4

−4

2 0 −2 −4

2 0 −2 −4

−4

−2 0 2 Deformation in X (in.)

4

−4

c. X- hysteresis of (j) LA21(X)-100% Figure 5-5

2

−2 0 2 Deformation in Y (in.)

4

d. Y- hysteresis of (k) LA22(Y)-100%

Experimental response of rigid block model Bearing 3 for uni-directional tests (j) LA21(X)-100%, (k) LA22(Y)-100% and bi-directional test (h) LA21/22-100%

tests. For these tests, the 30%-combination rule estimates the maximum displacement with less than 5 percent error and is conservative for the maximum bearing force. The maximum resisting forces are overestimated by 15 percent. Recent studies by Warn (2003) indicate that this rule is likely unconservative for earthquake sets with horizontal components that produce similar displacement demands.

77

Deformation in X (in.)

4

(l)NF01/02−100% (n)NF01(X)−100%

2 0 −2 −4 0

2

4

6

8

10

12

14

Time (sec.)

Deformation in Y (in.)

a. displacements in X

4

(l)NF01/02−100% (o)NF02(Y)−100%

2 0 −2 −4 0

2

4

6

8 Time (sec.) b. displacements in Y

2 0 −2 −4 −4

14

2 0 −2 −4

−2 0 2 Deformation in X (in.)

4

−4

c. displacement orbit of (l) NF01/02-100% Figure 5-6

12

4 Resisting force in Y (kip)

Deformation in Y (in.)

4

10

−2 0 2 4 Resisting force in X (kip)

d. force orbit of (l) NF01/02-100%

Experimental response of rigid block model Bearing 3 for uni-directional tests (n) NF01(X)-100%, (o) NF02(Y)-100% and bi-directional test (l) NF01/02-100%

78

Table 5-1

Evaluation of 30%-combination rule for bi-directional response of rigid block model Maximum Displacement (in.)

Maximum Force (kip)

Tests Bi-directional

30%-rule

Bi-directional

30%-rule

(h,j,k) LA21/LA22

4.54

4.50

15.90

18.59

(l,n,o) NF01/NF02

4.66

4.52

17.97

20.74

5.2.2 Effect of Vertical Ground Motion One issue that has been raised about the response of bridges with FP bearings is the effect of vertical ground motion because vertical acceleration affects the normal pressure on the bearings, changing the pendulum force and the friction force. To a smaller extent, the friction coefficient is dependent on the pressure on the articulated slider. To examine the effect of vertical ground motion, additional tests of the rigid block model were conducted with the LA21/22 and NF01/02 ground motion records. A comparison of displacements for (l)NF01/02-100% and (i)NF01/02/V-100% in Figure 5-7 show that the rigid block response was very similar without and with the vertical ground motion component, respectively. There is a minor difference in the rotation of the rigid frame between the two tests in Figure 5-7c, likely caused by changes in the friction and pendulum force with the vertical acceleration. The displacement and force orbits in Figure 5-8 and the hysteresis loops in Figure 5-9 confirm that the vertical ground motion component had a minor effect on the response for this ground motion. Results from the tri-directional tests (i)LA21/22/V-100% support these conclusions. There is, however, an interesting feature in the force response of Bearing 3 in the Xdirection during NF01/02 that was not observed for the LA21/22 set of ground motions. In Figure 5-9, there is a sharp peak in the resisting force at the maximum negative displacement for both tests as the rigid block model reverses direction, but the maximum force is greater for the tridirectional case. Figures 5-10 and 5-11 show the axial force and vertical acceleration histories for the cases without and with vertical ground motion component, respectively. The negative peak in the resisting force occurs at 6 sec. in both tests. For the case without the vertical ground motion component the vertical load on Bearing 3 increased because of overturning to approximately 23 kip. When the test was repeated with the vertical ground motion component included, the vertical force on the bearing increased to approximately 27 kip because, at the same instance, the vertical

79

Deformation in X (g)

4

(l)NF01/02−100% (m)NF01/02/V−100%

2 0 −2 −4 0

2

4

6

8 Time (sec.) a. displacement in X

10

Deformation in Y (g)

4

12

14

(l)NF01/02−100% (m)NF01/02/V−100%

2 0 −2 −4

Frame rotation (10−3 rad.)

0

2

4

6

8 Time (sec.) b. displacement in Y

10

4

12

14

(l)NF01/02−100% (m)NF01/02/V−100%

2 0 −2 −4 0

Figure 5-7

2

4

6

8 Time (sec.) c. rotation of rigid frame

10

12

14

Experimental displacement histories of rigid block model Bearing 3 for bi-directional test (l) NF01/02-100% and tri-directional test (m) NF01/02/V-100%

80

4 Resisting force in Y (kip)

Deformation in Y (in.)

4 2 0 −2 −4 −4

2 0 −2 −4

−2 0 2 Deformation in X (in.)

4

−4

a. displacement orbit of (l) NF01/02-100%

b. force orbit of (l) NF01/02-100%

4 Resisting force in Y (kip)

Deformation in Y (in.)

4 2 0 −2 −4 −4

2 0 −2 −4

−2 0 2 Deformation in X (in.)

4

−4

c. displacement orbit of (m) NF01/02V-100% Figure 5-8

−2 0 2 4 Resisting force in X (kip)

−2 0 2 4 Resisting force in X (kip)

d. force orbit of (m) NF01/02V-100%

Experimental response of rigid block model Bearing 3 for bi-directional test (l) NF01/02-100% and tri-directional test (m) NF01/02/V-100%

ground motion component has a positive acceleration peak. The increased vertical load increases the resisting force and causes the spike shown in Figure 5-9c. 5.3

Response Analysis of Rigid Block Model

Three mathematical models were studied for the purpose of evaluating the earthquake response of the rigid block model with FP bearings: (1) the coupled plasticity model, (2) the uncoupled plasticity model, and (3) the linear viscoelastic model (Huang et al. 2000). The first

81

4 Resisting force in Y (kip)

Resisting force in X (kip)

4 2 0 −2 −4 −2 0 2 Deformation in X (in.)

4

−2

−4

a. X-hysteresis of (l) NF01/02-100%

−2 0 2 Deformation in Y (in.)

4

b. Y-hysteresis of (l) NF01/02-100%

4 Resisting force in Y (kip)

4 Resisting force in X (kip)

0

−4

−4

2 0 −2 −4

2 0 −2 −4

−4

−2 0 2 Deformation in X (in.)

4

−4

c. X-hysteresis of (m) NF01/02V-100% Figure 5-9

2

−2 0 2 Deformation in Y (in.)

4

d. Y-hysteresis of (m) NF01/02V-100%

Experimental response of rigid block model Bearing 3 for bi-directional test (l) NF01/02-100% and tri-directional test (m) NF01/02/V-100%

two models were applied with (a) constant axial load and (b) varying axial load. The constant axial load model (a) adopted an axial load equal to the force measured by the load cell prior to testing. The varying axial load history (b) was calculated as the sum of (a) plus a varying component due to overturning forces computed from the acceleration of the rigid block and the P∆ effect that resulted from bearing displacements (See Section 4.2.2). The five models are:

1. Coupled plasticity model with varying axial load. The parameters, K2 , and QD , are dependent on the time-varying axial load on the bearing (See Section 2.3.1).

82

Resisting force in X (kip)

4 2 0 −2 −4 0

2

4

6

8 Time (sec.) a. resisting force in X

10

12

14

Axial force (kips)

−5 −10 −15 −20 −25

Vertical table acceleration (g)

−30

0

2

4

0

2

4

6

8 Time (sec.) b. bearing axial load

10

12

14

8 10 Time (sec.) c. vertical acceleration of earthquake simulator

12

14

0.3 0.2 0.1 0 −0.1 −0.2

Figure 5-10

6

Experimental response histories of rigid block model Bearing 3 and earthquake simulator for bi-directional test (l) NF01/02-100%

83

Resisting force in X (kip)

4 2 0 −2 −4 0

2

4

6

8 Time (sec.) a. resisting force in X

10

12

14

Axial force (kips)

−5 −10 −15 −20 −25

Vertical acceleration (g)

−30

0

2

4

0

2

4

6

8 Time (sec.) b. bearing axial load

10

12

14

8 10 Time (sec.) c. vertical acceleration of earthquake simulator

12

14

0.3 0.2 0.1 0 −0.1 −0.2

Figure 5-11

6

Experimental response histories of rigid block model Bearing 3 and earthquake simulator for tri-directional test (l) NF01/02/V-100%

84

2. Coupled plasticity model with constant axial load. The three parameters, K1 , K2 , and QD , are constant, independent of the axial load. 3. Uncoupled plasticity model with varying axial load. This model is similar to the coupled model with axial load dependence, but the uni-directional models in the X- and Ydirections are uncoupled, implying a square interaction surface. 4. Uncoupled plasticity model with constant axial load. In this model the parameters of the uncoupled model are independent of the axial load. 5. Linearized viscous model. The values of effective stiffness and damping ratio, Keff and β , are computed based on the maximum displacement. Since the parameters depend on the maximum displacement, iteration is required. 5.3.1 Selection of Model Parameters From the calibrations of the models using displacement-controlled test data in Section 4.3, the friction coefficient for the FP bearings listed in Table 5-2 were obtained. A constant coefficient of friction for each bearing was assumed for the simulations, neglecting dependence on velocity and pressure. Table 5-2

Calibrated coefficient of friction used in the earthquake analysis Bearing

Coefficient of friction, µ

1

0.079

2

0.081

3

0.100

4

0.097

The plasticity model parameters are based on a strength of QD = µ N , where µ is the friction coefficient in Table 5-2 and N is the vertical load on each bearing as measured by the load cell prior to testing. The second slope stiffness due to the pendulum effect, K2 = N ⁄ R , where R = 30 in. is the radius of the spherical dish. The first slope is rather arbitrary for the rigidplastic behavior; it is estimated as K1 = QD ⁄ U Y , where U Y = 0.01 in. The linearized viscous model parameters, Keff and β , are dependent on the maximum displacement, which requires iteration in the analysis. For this study, the parameters were

85

computed directly from the plasticity model parameters. The effective stiffness, given as the ratio of maximum force to maximum displacement u 0 , is given as QD + u 0 K2 µN N - = ------- + ---Keff ( u 0 ) = ------------------------u0 R u0

(5-1)

To compute the effective damping, the system response is assumed to be harmonic with frequency equal to the natural vibration frequency of the isolated system. The hysteretic energy dissipated by one fully reversed cycle of loading in the plasticity model is equated to the energy dissipated by the linear system to obtain 1 2QD 1 2µN β ( u 0 ) = --- ------------------------= --- -------------------------π K eff ( u 0 ) u 0 π Keff ( u 0 ) u 0

(5-2)

The linearized viscous model parameters for the FP bearings are plotted as a function of maximum displacements in Figure 5-12. 5.3.2 Comparisons of Experimental Response with Mathematical Models Using the five calibrated mathematical models for FP bearings presented earlier, the simulated response of the rigid block was compared with the experimental results. A detailed comparison is presented for tests (h)LA21/22-100% and (r)LS17C/18C in Table 3-5. The experimentally measured maximum resisting force, maximum displacement, and dissipated energy are compared with the simulated responses for all the bi-directional tests in Table 3-5. 5.3.2.1 LA21/22 (1995 Kobe, JMA Station): Figure 5-13 shows the experimental response of FP Bearing 3 for the rigid block model subjected to LA21/22 with a length scale of 5 and amplitude scale of 100%. The displacement orbit is predominantly along the 45-degree direction due to the orientation of the input motion. At the center of the force orbit, there is a circular region of radius QD , the friction force, that forms as a result of small oscillations around the center of the bearing. The non-smooth nature of the force orbit is typical of friction behavior because of the rapidly changing direction of the friction force, particularly at small displacements. The bearing hysteresis in both the X- and Y- directions shows a high degree of bi-directional interaction and sensitivity to axial load, as discussed previously in Section 5.2.

86

5

Keff (kip/in.)

4 3 2 1 0

0

1

2

3 4 5 Maximum displacement (in.)

6

7

6

7

a. effective stiffness, K eff

60 50

β (%)

40 30 20 10 0

0

1

2

3 4 5 Maximum displacement (in.)

b. effective viscous damping, β Figure 5-12

Linearized viscous model parameters with µ = 0.1 and N=16 kip

Figure 5-14 shows the simulated response of FP Bearing 3 using the coupled plasticity model with varying axial load. Comparing the simulated response to the experimental data of Figure 5-13, the mathematical model captures the displacement orbit, even at small displacements. The force orbit for the simulation shows the circular region of radius QD , similar to the experimental results in Figure 5-13b. The simulated force orbit beyond the friction force is less accurate, particularly in regards to the details at the peak resisting forces in the X- and Ydirections. Further insight into the simulated results can be seen by comparing the hysteresis loops in Figures 5-13c,d and 5-14c,d. Although the general character of the hysteresis loops is

87

4 Resisting force in Y (kip)

Deformation in Y (in.)

4 2

0

−2

2 0 −2 −4

−4 −4

−2 0 2 Deformation in X (in.)

4

−4

a. displacement orbit

b. force orbit

4 Resisting force in Y (kip)

Resisting force in X (kip)

4 2 0 −2 −4 −4

2 0 −2 −4

−2 0 2 Deformation in X (in.)

4

−4

c. hysteresis, X-direction Figure 5-13

−2 0 2 4 Resisting force in X (kip)

−2 0 2 Deformation in Y (in.)

4

d. hysteresis, Y-direction

FP Bearing 3: experimental response of rigid block model, (h) LA21/22-100%

represented by the model, the experimentally measured resisting force has more oscillations than are predicted by the mathematical model. Figure 5-15 shows the simulated response using the coupled plasticity model with constant axial load on the bearings. The simulated global response of the rigid frame is similar to the response with varying axial load because the overturning effects cancel when summing the resisting forces over the four bearings. For an individual bearing, FP Bearing 3 in this case, the force orbit is significantly different in Figure 5-15b from those shown in Figures 5-13b and 5-14b because of the effect of varying axial load on the bearing. An increase in compressive axial load

88

4 Resisting force in Y (kip)

Deformation in Y (in.)

4 2

0

−2

2 0 −2 −4

−4 −4

−2 0 2 Deformation in X (in.)

4

−4

a. displacement orbit

b. force orbit

4 Resisting force in Y (kip)

Resisting force in X (kip)

4 2 0 −2 −4 −4

2 0 −2 −4

−2 0 2 Deformation in X (in.)

4

−4

c. hysteresis, X-direction Figure 5-14

−2 0 2 4 Resisting force in X (kip)

−2 0 2 Deformation in Y (in.)

4

d. hysteresis, Y-direction

FP Bearing 3: simulated response of rigid block model using coupled plasticity model with varying axial load, (h) LA21/22-100%

produces a larger resisting force, hence the maximum resisting force is underestimated if the varying axial load on a bearing is not considered. This is confirmed by comparing Figures 5-13c and 5-15c, where in the range of negative displacements, the model with constant axial load produces a peak force that is 50% less than the experimental results. Additional discussion on the effects of axial load is provided in Section 5.3.4. The uncoupled models with and without varying axial load are presented in Figures 5-16 and 5-17, respectively. Both of these models provide a poor representation of the displacement

89

4 Resisting force in Y (kip)

Deformation in Y (in.)

4 2

0

−2

2 0 −2 −4

−4 −4

−2 0 2 Deformation in X (in.)

4

−4

−2 0 2 4 Resisting force in X (kip)

a. displacement orbit

b. force orbit

4 Resisting force in Y (kip)

Resisting force in X (kip)

4 2 0 −2 −4 −4

0 −2 −4

−2 0 2 Deformation in X (in.)

4

−4

c. hysteresis, X-direction Figure 5-15

2

−2 0 2 Deformation in Y (in.)

4

d. hysteresis, Y-direction

FP Bearing 3: simulated response of rigid block model using coupled plasticity model with constant axial load, (h)LA21/22-100%

orbit when compared to the experimental data, emphasizing the importance of bi-directional coupling. In Figures 5-16b and 5-17b, the square region formed at the center of the force orbit by the uncoupled models is a result of the implied square yield surface. Similar to the other uncoupled models, the linearized viscous model in Figure 5-18 predicts poorly the bearing forces and displacements. The hysteresis loops for the viscous model appears to be stiffer than the plasticity model (Figure 5-17). The large linear stiffness, Keff as compared to K2 in the plasticity model is due to the relatively large value of QD .

90

4 Resisting force in Y (kip)

Deformation in Y (in.)

4 2

0

−2

2 0 −2 −4

−4 −4

−2 0 2 Deformation in X (in.)

4

−4

a. displacement orbit

b. force orbit

4 Resisting force in Y (kip)

Resisting force in X (kip)

4 2 0 −2 −4 −4

2 0 −2 −4

−2 0 2 Deformation in X (in.)

4

−4

c. hysteresis, X-direction Figure 5-16

−2 0 2 4 Resisting force in X (kip)

−2 0 2 Deformation in Y (in.)

4

d. hysteresis, Y-direction

FP Bearing 3: simulated response of rigid block model using uncoupled plasticity model with varying axial load, (h) LA21/22-100%

5.3.2.2 LS17C/18C (1994 Northridge, Olive View, simulated soft soil site): The experimental response of FP Bearing 3 to LS17C/18C with a length scale of 5 and amplitude scale of 50% is presented in Figure 5-19. The displacement response of the rigid block is oriented primarily along the X-direction with maximum displacements less than 2 inches. Due to the dominant X-direction orientation of the earthquake history, there is little bi-directional interaction.

91

4 Resisting force in Y (kip)

Deformation in Y (in.)

4 2

0

−2

2 0 −2 −4

−4 −4

−2 0 2 Deformation in X (in.)

4

−4

a. displacement orbit

b. force orbit

4 Resisting force in Y (kip)

Resisting force in X (kip)

4 2 0 −2 −4 −4

2 0 −2 −4

−2 0 2 Deformation in X (in.)

4

−4

c. hysteresis, X-direction Figure 5-17

−2 0 2 4 Resisting force in X (kip)

−2 0 2 Deformation in Y (in.)

4

d. hysteresis, Y-direction

FP Bearing 3: simulated response of rigid block model using uncoupled plasticity model with constant axial load, (h)LA21/22-100%

The simulated response of the coupled plasticity with varying axial load (Figure 5-20) and the coupled plasticity model with constant axial load (Figure 5-21) are similar because the relatively small displacements result in small overturning forces. The two uncoupled models, shown in Figure 5-22 and Figure 5-23, are also similar to the coupled models because of the orientation of the ground motion. Even though coupling is not important for representing the maximum displacement and forces in the predominant X-direction, the uncoupled models poorly

92

4 Resisting force in Y (kip)

Deformation in Y (in.)

4 2

0

−2

2 0 −2 −4

−4 −4

−2 0 2 Deformation in X (in.)

4

−4

a. displacement orbit

b. force orbit

4 Resisting force in Y (kip)

Resisting force in X (kip)

4 2 0 −2 −4 −4

2 0 −2 −4

−2 0 2 Deformation in X (in.)

4

−4

c. hysteresis, X-direction Figure 5-18

−2 0 2 4 Resisting force in X (kip)

−2 0 2 Deformation in Y (in.)

4

d. hysteresis, Y-direction

FP Bearing 3: simulated response of rigid block model using linearized viscous model, (h)LA21/22-100%

capture the response in the Y-direction. As with other earthquake records, the linearized viscous model shown in Figure 5-24 does not adequately capture the earthquake response of FP bearings. 5.3.3 Evaluation of Mathematical Models Comparisons of earthquake simulator test data for the test series and the five mathematical models are summarized in Figures 5-25, 5-26 and 5-27 for the maximum displacement, maximum resisting force, and dissipated energy, respectively. The abscissa labels in these figures correspond

93

3 Resisting force in Y (kip)

Deformation in Y (in.)

2 1 0 −1 −2 −2

−1 0 1 Deformation in X (in.)

2 1 0 −1 −2 −3 −3

2

a. displacement orbit

3 Resisting force in Y (kip)

Resisting force in X (kip)

3

b. force orbit

3 2 1 0 −1 −2 −3

2 1 0 −1 −2 −3

−2

−1 0 1 Deformation in X (in.)

2

−2

c. hysteresis, X-direction Figure 5-19

−2 −1 0 1 2 Resisting force in X (kip)

−1 0 1 Deformation in Y (in.)

2

d. hysteresis, Y-direction

FP Bearing 3: experimental response of rigid block model, (r) LS17C/18C-50%

to the eleven bi-directional earthquake tests listed in Table 3-5. The simulated response is compared with the experimental response by the relative error of the peak responses defined as ve – vs ε = --------------------ve

(5-3)

where ε is the relative error, ve is the value from the experiments, and vs is the value from the simulation. Both figures include the mean, x , and standard deviation, s , of the relative error as defined in Equation 5-3 for the five models.

94

3 Resisting force in Y (kip)

Deformation in Y (in.)

2 1 0 −1 −2 −2

−1 0 1 Deformation in X (in.)

2 1 0 −1 −2 −3 −3

2

a. displacement orbit

3 Resisting force in Y (kip)

Resisting force in X (kip)

3

b. force orbit

3 2 1 0 −1 −2 −3

2 1 0 −1 −2 −3

−2

−1 0 1 Deformation in X (in.)

2

−2

c. hysteresis, X-direction Figure 5-20

−2 −1 0 1 2 Resisting force in X (kip)

−1 0 1 Deformation in Y (in.)

2

d. hysteresis, Y-direction

FP Bearing 3: simulated response of rigid block model using coupled plasticity model with varying axial load, (r) LS17C/18C-50%

In general, the mathematical models under-estimate the maximum measured displacement of the bearings as shown in Figure 5-25. However, the uncoupled models under-estimate the maximum displacements more than the coupled models. The uncoupled models also overestimate the maximum resisting forces as compared with the coupled models. Of the five models, the coupled plasticity model with varying axial load provides the best estimate of the maximum displacement, resisting force, and energy dissipation. Although assuming constant axial load on the bearing has a small effect on simulating the maximum displacements, the error in the maximum resisting force in individual bearings is significant. The

95

3 Resisting force in Y (kip)

Deformation in Y (in.)

2 1 0 −1 −2 −2

−1 0 1 Deformation in X (in.)

2 1 0 −1 −2 −3 −3

2

a. displacement orbit

3 Resisting force in Y (kip)

Resisting force in X (kip)

3

b. force orbit

3 2 1 0 −1 −2 −3

2 1 0 −1 −2 −3

−2

−1 0 1 Deformation in X (in.)

2

−2

c. hysteresis, X-direction

Figure 5-21

−2 −1 0 1 2 Resisting force in X (kip)

−1 0 1 Deformation in Y (in.)

2

d. hysteresis, Y-direction

FP Bearing 3: simulated response of rigid block model using coupled plasticity model with constant axial load, (r) LS17C/18C-50%

linearized viscous model provides the poorest simulation, in addition the significant drawback that iteration is required to determine the effective stiffness and damping. 5.3.4 Modeling of Axial Loads The global system response of the rigid block, including displacements and the total resisting force of the four bearings, is relatively independent of assumptions about axial load on the bearings because the overturning forces cancel. In the simulation of the response of the rigid block model, the plasticity models with varying and constant axial load give nearly the same

96

3 Resisting force in Y (kip)

Deformation in Y (in.)

2 1 0 −1 −2 −2

−1 0 1 Deformation in X (in.)

2 1 0 −1 −2 −3 −3

2

a. displacement orbit

3 Resisting force in Y (kip)

Resisting force in X (kip)

3

b. force orbit

3 2 1 0 −1 −2 −3

2 1 0 −1 −2 −3

−2

−1 0 1 Deformation in X (in.)

2

−2

c. hysteresis, X-direction Figure 5-22

−2 −1 0 1 2 Resisting force in X (kip)

−1 0 1 Deformation in Y (in.)

2

d. hysteresis, Y-direction

FP Bearing 3: simulated response of rigid block model using uncoupled plasticity model with varying axial load, (r) LS17C/18C-50%

displacement orbit for Bearing 3 (see Figures 5-14 and 5-15 and Figures 5-20 and 5-21). This same conclusion might not hold for irregular bridges in which rotation of the superstructure about a vertical axis (torsion) could have a greater influence on local bearing response. For an individual bearing the axial load is an important factor in determining the resisting force. The data presented in Figure 5-26 show that the plasticity models with varying axial load consistently produce larger peak forces than models with constant axial load because an increase in bearing compression load produces a larger resisting force from friction and the pendulum effect.

97

3 Resisting force in Y (kip)

Deformation in Y (in.)

2 1 0 −1 −2 −2

−1 0 1 Deformation in X (in.)

2 1 0 −1 −2 −3 −3

2

a. displacement orbit

3 Resisting force in Y (kip)

Resisting force in X (kip)

3

b. force orbit

3 2 1 0 −1 −2 −3

2 1 0 −1 −2 −3

−2

−1 0 1 Deformation in X (in.)

2

−2

c. hysteresis, X-direction Figure 5-23

−2 −1 0 1 2 Resisting force in X (kip)

−1 0 1 Deformation in Y (in.)

2

d. hysteresis, Y-direction

FP Bearing 3: simulated response of rigid block model using uncoupled plasticity model with constant axial load, (r) LS17C/18C-50%

In the comparisons between the simulated and experimental responses, the models with varying axial load included the overturning forces and P-∆ effects on the bearing axial loads. This is an idealization of the actual axial load, because the dynamics of the rigid block and the earthquake simulator platform introduce additional vertical forces on the bearings. Since the coupled plasticity model with varying axial load gives the best simulation of the experimental results, it is used for an additional examination of the effect of vertical forces. Revisiting Figures 5-13 and 5-14, the experimental hysteresis loops have more fluctuations in resisting force when compared to the simulated response. To further investigate the

98

3 Resisting force in Y (kip)

Deformation in Y (in.)

2 1 0 −1 −2 −2

−1 0 1 Deformation in X (in.)

2 1 0 −1 −2 −3 −3

2

a. displacement orbit

3 Resisting force in Y (kip)

Resisting force in X (kip)

3

b. force orbit

3 2 1 0 −1 −2 −3

2 1 0 −1 −2 −3

−2

−1 0 1 Deformation in X (in.)

2

−2

c. hysteresis, X-direction Figure 5-24

−2 −1 0 1 2 Resisting force in X (kip)

−1 0 1 Deformation in Y (in.)

2

d. hysteresis, Y-direction

FP Bearing 3: simulated response of rigid block model using linearized viscous model, (r) LS17C/18C-50%

effect of bearing axial loads on the simulated response, the coupled plasticity model analysis was repeated for the LA21/22 ground motion with the bearing axial load measured by the load cells during the test. The measured axial load on the FP bearing includes the static component, the overturning and P-∆ component, the vertical vibration of the frame, and the small vertical acceleration of the simulator platform that results from control error. The results of the plasticity model with measured axial load is shown in Figure 5-28. Comparing Figure 5-28 with Figures 513 and 5-14 it is clear that the varying axial load in the bearing caused the oscillations in the experimentally measured hysteresis loops. The plasticity model with measured axial load is able

99

to capture the high frequency oscillations in the bearing forces well, although maximum displacements are still underestimated by approximately 9 percent. 5.4

Recommendations for Modeling FP Bearings

The evaluation of the mathematical models clearly demonstrate that the bi-directional plasticity model with varying axial load provides a good simulation of FP bearings within approximately 10% on average. For proper simulation of the resisting forces of FP bearings it is essential that the axial load variation and coupling be included in the model. Equivalent viscoelastic models should not be used for the analysis of FP-isolated structures.

100

Maximum displacement (in.)

Figure 5-25

0 5% )

0.5

5% L

1

0% )

1.5

50

%

0% 8

% /1

2

% /2

2

1

1/

/2

0

/2

Summary of maximum displacements of FP Bearing 3 for experimental data and mathematical models; CP = Coupled Plasticity, UP = Uncoupled Plasticity

(e)

2

0% S

2.5

%

3

x : mean of absolute relative errors for model s : standard deviation of absolute relative errors for model

8C −

3.5

25 S

4

L

00 N

4.5

)L

2− 2

A2 1

(a)

0% (p

Experimental CP with varying axial load (x=8.2%, s=8.4%) CP with constant axial load (x=8.1%, s=8.8%) UP with vayring axial load (x=13.2%, s=9.5%) UP with constant axial load (x=13.5%, s=9.2%) Linearized Viscous (x=31.3%, s=35.9%)

)L

2− 2 1/ NF 0

(b

0% (h

4− 5 3/

LA 1

2− 5

A2 1 (c)

02 − NF 0

(d

4− 1 A1 3

5

/1 17 C (f) L

E− 5 /0 01 E (g )L

2− 1 A2 1

−1 0 /0 F0 1 (l)

00 LS (q )

c− 5 /1 17 c

101

Figure 5-26

25

%

2

5%

50

% 1/

2

1/

5%

)

2

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Seismic coefficient 0% 8 14

2

22

Summary of maximum force of FP Bearing 3 for experimental data and mathematical models; CP = Coupled Plasticity, UP = Uncoupled Plasticity

(c)

2− 5 1/

LA 2

0 0% )

1

1 3/ LA 1

(e)

4− 5 S

2

8 /1

3

A

x : mean of absolute relative errors for model s : standard deviation of absolute relative errors for model

0% (h

4

0% N

5

A

Experimental CP with varying axial load (x=8.5%, s=5.3%) CP with constant axial load (x=17.6%, s=6.9%) UP with varying axial load (x=29.5%, s=13.4%) UP with constant axial load (x=10.7%, s=5.8%) Linearized Viscous (x=48.3%, s=30.2%)

0% (p

6

LS

Maximum resisting force (kip)

(a)

0% (q )

2− 2

1/

LA 2

02 −

NF 0

(b

02 − NF 0

(d

0% 17 C (f) L

C− 2 S (g )L

E− 5 /0 01 E

−1 0 21 / )L

−1 0 /0 F0 1 (l)

−1 0 13 / )L

c− 5 /1 17 c

102

5% (c)

Dissipated energy (kip−in.)

Figure 5-27

22 − 1/

8c −

50

% 0% % 0

2

3/

0

%

0

%

1/

Summary of dissipated energy of FP Bearing 3 for experimental data and mathematical models; CP = Coupled Plasticity, UP = Uncoupled Plasticity

LA 2

0 50 )

10

0% (e)

20

% S

30

8 /1

40

02 1E /

50

5%

70 x : mean of absolute relative errors for model s : standard deviation of absolute relative errors for model 60

0% )L

80

E− 5 (h

Experimental CP with varying axial load (x=8.5%, s=3.3%) CP with constant axial load (x=8.2%, s=3.9%) UP with vayring axial load (x=9.7%, s=6.2%) UP with constant axial load (x=9.3%, s=6.0%) Linearized Viscous (x=38.3%, s=25.4%)

0% (l)

90

(a)

14 − LA 1

−1 0 /2 A2 1

22 −

LA 2

25 ) (b

4 /1 A1 3

2− 2 1/

NF 0

C− 2 S0 (g )L

2− 1 1/ NF 0

2− 5 1/

NF 0 (d

50 17 C (f) L

00 )L (p

−1 0 L (q )

100

c/1 S1 7

103

4 Resisting force in Y (kip)

Deformation in Y (in.)

4 2

0

−2

2 0 −2 −4

−4 −4

−2 0 2 Deformation in X (in.)

4

−4

a. displacement orbit

b. force orbit

4 Resisting force in Y (kip)

Resisting force in X (kip)

4 2 0 −2 −4 −4

2 0 −2 −4

−2 0 2 Deformation in X (in.)

4

−4

c. hysteresis, X-direction Figure 5-28

−2 0 2 4 Resisting force in X (kip)

−2 0 2 Deformation in Y (in.)

4

d. hysteresis, Y-direction

FP Bearing 3: simulated response of rigid block model using coupled plasticity model with varying axial load as measured experimentally, (h) LA21/22-100%

104

6

Summary and Conclusions

6.1

Summary The selection of the properties of a seismic isolation system is dependent on the models

used for the isolators, which reinforces the need for robust mathematical models of the bearings. This report examined, through analytical and experimental studies, the efficacy of the plasticity model and the linear viscous model in representing the bi-directional behavior of Friction Pendulum (FP) bearings. The analytical and experimental testing program of a seismically isolated bridge model consisted of two phases. The first phase examined the behavior of the bearings under imposed bidirectional displacement histories and the second phase examined the seismic response of a simple bridge system to multiple components of excitation. A key contribution from these tests is experimental data to study the bi-directional response of FP bearings. Prior to these studies, tests on FP bearings had been conducted with only one component of horizontal loading. The bidirectional displacement tests provided data to characterize and develop mathematical models for seismic isolation bearings. Supplemental information was obtained from these tests on the behavior of friction, including characteristics that are well supported by previous research from uni-directional tests. The earthquake tests served to investigate the influence of varying axial load and the coupling of friction on bearing response during actual earthquake loading. The experimental data and analysis presented showed that the restoring pendulum force component of the bearings can be physically modeled by linear springs with sufficient accuracy. On the other hand, the friction component exhibits path-dependent behaviors that also depend on velocity, pressure, and temperature. In this study, the variation of the friction coefficient encountered in the experimental testing is low and a Coulomb friction model provides a good

105

approximation. The use of the coupled plasticity model with constant friction was verified by a comparison with experimental simulations of a rigid block model isolated with FP bearings. 6.2

Conclusion and Recommendations

The conclusions derived from the characterization of the FP bearings, and observations from the earthquake tests of a simple bridge model are listed below. These conclusions might not hold for bridges with flexible diaphragms or flexible substructures. 1. Stick-slip behavior is likely due to inertial effects in the tests fixture since it is only apparent in high velocity tests. Breakaway friction was only observed on virgin sliders and is of little concern in the earthquake response of bridges isolated with sliding bearings. 2. The sliding coefficient of friction for the composite tested in this program was essentially constant for sliding velocities exceeding 1 in./sec. The value of the coefficient of friction was observed to drop slightly at high velocities, most likely due to frictional heating. For the purposes of modeling FP seismic isolation bearings, a constant value of sliding friction can be assumed for analysis and design. 3. The experimental response of the FP bearings to bi-directional horizontal earthquake shaking showed strong coupling of the response in the two orthogonal directions. The coupling is a result of the friction force being colinear with the instantaneous velocity. The experimental results suggest that considering only one component of excitation typically provides a reasonable upper bound of the maximum resisting forces but underestimates the bearing displacements. 4. Vertical earthquake shaking had a small effect on the global response of the isolated rigid frame model, but led to substantial variations in forces developed in individual isolators, especially when the amplitude of the vertical shaking was large at the time of the maximum horizontal displacement in the isolation system. 5. Of the five mathematical models evaluated in this research program, the plasticity model with a circular yield surface and consideration of dynamic axial load variations provided the best correlation with measured responses and the linearized viscous model provided the worst correlation with measure responses. The linearized viscous model is not

106

recommended for highly nonlinear isolators such as FP bearings. Based on this study, uncoupled plasticity models typically underestimated peak displacements by 13% and overestimated maximum bearing forces by 30%. Uncoupled plasticity models should not be used for analysis if a coupled plasticity model is available. 6. Variations in bearing axial forces due to the effects of horizontal and vertical earthquake shaking have little effect on the displacement response of the isolation system but can have a significant impact on the local forces on individual bearings. The maximum lateral and vertical forces on individual isolators could be underestimated if variations in bearing axial forces are ignored.

107

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References AASHTO. (1999). Guide specifications for seismic isolation design. American Association of State Highway and Transportation Officials (AASHTO). Bondonet, G, and Fliatrault A. (1997). “Frictional response of PTFE sliding bearings at high frequencies.” Journal of Bridge Engineering, ASCE, 2(4): 139-148. Computers and Structures (1997). SAP2000 Analysis Reference, Vol. 1 Constantinou, M.C., Mokha A., and Reinhorn A.M. (1990). “Teflon bearings in base isolation. II: Modeling.” Journal of Structural Engineering, ASCE, 116(2): 455-474. Constantinou, M.C., Tsopelas P., Kasalanati A., and Wolff E.D. (1999). “Property modification factors for seismic isolation bearings”. Report MCEER-99-0012, Multidisciplinary Center for Earthquake Engineering Research, State University of New York. Clough, F.W. and Penzien J. (1993). Dynamics of Structures, McGraw-Hill, New York. Fenves, G.L., Whittaker, A.S., Huang, W.-H., Clark, P.W., and Mahin S.A. (1998). “Analysis and testing of seismically isolated bridges under bi-axial excitation.” Proceedings, 5th Caltrans Seismic Research Workshop, California Department of Transportation Huang, W.-H. (2002). “Bi-directional testing, modeling, and system response of seismically isolated bridges. P.h.D. Dissertation, Department of Civil and Environmental Engineering, University of California, Berkeley. Huang W.-H., Fenves G.L., Whittaker, A.S., and Mahin, S.A. (2000). “Characterization of seismic isolation bearings for Bridges from Bi-directional Testing.” Proceedings, 12th World Conference on Earthquake Engineering, New Zealand Kawashima, K. (2000). “Seismic design and retrofit of bridges.” Proceedings, 12th World Conference on Earthquake Engineering, New Zealand Lubliner, J. (1990). Plasticity Theory, Macmillan, New York.

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Mokha, A., Constantinou, M.C., and Reinhorn, A. M. (1990). “Teflon bearings in base isolation. I: Testing.” Journal of Structural Engineering, ASCE, 116(2): 438-454. Mokha, A., Constantinou, M.C., and Reinhorn, A.M. (1991). “Further results on frictional properties of teflon bearings.” Journal of Structural Engineering, ASCE, 117(2): 622-626. Mokha, A., Constantinou, M.C., and Reinhorn, A. M. (1993). “Verification of friction model of teflon bearings under triaxial load.” Journal of Structural Engineering, ASCE, 119(1): 240261. Mosqueda, G. Whittaker, A.S., and Fenves, G.L. (2003). ‘Characterization and modeling of friction pendulum bearings subjected to multiple components of excitation.” Journal of Structural Engineering, ASCE, 130(3): 433-442. Park, Y.J., Wen, Y.K., and Ang, A.H.-S. (1986). “Random vibration of hysteretic systems under bi-directional ground motions.” Earthquake Engineering and Structural Dynamics, 14:543557 Rabinowicz, E. (1995). Friction and Wear of Materials. Wiley, New York. SAC (1997). “Suites of earthquake ground motions for analysis of steel moment frame structure.” Report SAC/BD-97/03, Woodward-Clyde Federal Services, SAC Steel Project. Scheller, J. and Constantinou M.C. (1999). “Response history analysis of structures with seismic isolation and energy dissipation systems: Verification examples for program SAP2000.” Report MCEER-99-0002, Multidisciplinary Center for Earthquake Research, State University of New York at Buffalo. Tsopelas, P.C., Constantinou, M.C. Reinhorn, A.M. (1994). “3D-BASIS-ME: Computer program for nonlinear dynamic analysis of seismically isolated single and multiple structures and liquid storage tanks.” Report NCEER-94-0010, National Center for Earthquake Engineering Research. State University of New York at Buffalo. Warn, G. (2003). “Performance estimates in seismically isolated bridges.” M.S. Thesis. Department of Civil, Structural, and Environmental Engineering, State University of New York at Buffalo. Zayas V., Low S., and Mahin S.A. (1987). “The FPS earthquake resisting system.” Report UCB/ EERC-87/01, Earthquake Engineering Research Center, University of California at Berkeley.

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