REPORT NO. UCB/EERC-89/13 NOVEMBER 1989

EARTHQUAKE ENGINEERING RESEARCH CENTER

MECHANICS Of lOW SHAPE FACTOR ElASTOMERIC SEISMIC ISOlATION BEARINGS

by

IAN D. AIKEN JAMES M. KELLY FREDERICK F. TAJIRIAN

Report to the Rockwell International Corporation

COLLEGE OF ENGINEERING

UNIVERSITY OF CALIFORNIA AT BERKELEY

MECHANICS OF LOW SHAPE FACTOR ELASTOMERIC

SEISMIC ISOLATION BEARINGS

by

Ian D. Aiken Earthquake Engineering Research Center

James M. Kelly Earthquake Engineering Research Center

Frederick E Tajirian Bechtel National, Inc

Report to Sponsor: Rockwell International Corporation

Report No. UCB/EERC-89/13 Earthquake Engineering Research Center

College of Engineering University of California at Berkeley

November, 1989

ABSTRACT

This report presents the results of an experimental and analytical study of low shape factor

(LSF) elastomeric seismic isolation bearings. The test bearings were of a design developed for a seismic isolation application to provide horizontal and vertical isolation. This dual requirement led to a

bearing design with a shape factor smaller than usual for bearings designed to provide horizontal iso-

lation only.

The experimental phase of the project involved the dynamic testing of a range of LSF bearings, subjected to a variety of test conditions. The bearings were all of one basic design, but varied in the elastomer from which they were manufactured and the details of the end-plate connections. Connec-

tions used were of the doweled-type, currently the preferred shear connection for seismic isolation

bearings, and the bolted type, which has yet to see common use in the United States. Bearings were

manufactured from both a filled, high-damping, natural rubber compound and an ordinary unfilled,

natural rubber compound.

An extensive series of tests was undertaken to investigate the performance characteristics of the

different types of bearings. One particular objective of the test program was to evaluate the merit of the standard cyclic shear test (with constant axial load) as a representative test for more generalized loading conditions. A large number of tests was performed to study the behavior of the LSF bearings

when subjected to cyclic vertical loading. Buckling tests and shear and tension failure tests were also conducted.

On the basis of the test results a number of comparisons were made of the different bearings.

The influences of axial load and shear strain on the bearing characteristics of shear stiffness, vertical

stiffness, and damping behavior were investigated, with particular emphasis on evaluating the conse-

quences of a low shape factor. Comparisons of the bolted and doweled connections, and the filled

and unfilled elastomers were also made.

Design equations for elastomeric bearings were reviewed for their particular suitability to LSF

bearings. A previously developed analytical model for the prediction of bearing behavior was

reviewed and extended for application to LSF bearings. The suitability of the model was evaluated in

light of the experimental results.

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ACKNOWLEDGEMENTS

The research reported herein was supported by grant no. R84PNZ88418060 from Rockwell

International Corporation, and was conducted at the Earthquake Simulator Laboratory of the Earth-

quake Engineering Research Center of the University of California at Berkeley, Professor James

Kelly was the principal investigator for this project.

The authors would like to express their thanks to Messrs. D. Clyde, W. Neighbour, J. McNab,

and L Van A~ten of the Earthquake Simulator Laboratory for their assistance during the experimental

phase of the project. Thanks also are due to Dr. Beverley Bolt for invaluable advice and assistance during the preparation of the report.

ABSTRACT ... H

ACKNOWLEDGMENTS

TABLE OF CONTENTS

LIST OF TABLES HHH

LIST OF FIGURES .H.

1. INTRODUCTION ..... .

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Table of Contents

1.1 Base !solation Overview HHHHoHHHH ................. ..

1.2 Interest in Low Shape Factor Bearings HH .... H.H H .......... H ..... H ................ H ... H ... H.H ...... .

II

iii

Vii

ix

1

1

2

1.3 Objectives and Scope of Studies .H.H .......................................... H.................................... 4

1.4 Literature Review .............................................................................................................. .

1.5 Summary .......................................................... H ................................................................... ..

5

8

2. BEARING DESIGN PARAMETERS . "H" H .... H " .. ..... H .. H ..... H .. H .... H..... 9

2.1 Introduction H ...... H.H ............................... ..

2.2 Shear Stiffness .... H ............ H ... H .............. H

2.3 Compression Stiffness H .... H ................................................................... H ........ H .. H .. H .. HH

2.4 Stability - Buckling Load .

3. DESIGN OF LSF BEARINGS

3.1 Introduction H.

3.2 Description of SAFR Plant ............................................................................................ ..

3.3 Dynamic Analysis .............................................................................................................. .

3.4 SAFR Bearing Design

9

9

10

13

15

15

15

15

16

3.5 Test Bearing Designs

3.6 Comments on Design

4. TESTS OF LSF BEARINGS

4.2 Description of Test Facility ...

4.3 Description of Tests

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4.4 Rate Effects ................................................................ ..

5. TEST RESULTS .............. ..

5.1 Introduction ......................................... ..

5.2 Shear Tests ................... .

5.3 Vertical Tests .................................................................... .

5.4 Combined Loading Tests ...................... .

5.5 Failure Mode Tests ............................... .

5.6 Buckling Tests

5.7 Vertical Test Results and Design Equations

6. A.N ANALYTICAL MODEL FOR THE BEHAVIOR OF

LSF BEARINGS . ......... .. ..

6.1 Introduction .............. ..

6.2 A Two-Spring Physical Model for Elastomcric

Bearing Behavior ......... ..

6.3 Nonlinear Two-Spring Model

7. SUMMARY AND CONCLUSIONS

7.1 Summary ............................ .

7.2 Conclusions ...... .

.... ,, ......

16

17

19

19

19

21

25

-n

27

27

37

40

41

46

47

49

49

50

51

53

53

53

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REFERENCES ..... 57

TABLES............................ ............ ........ . ................ .. . ........ ...................... 63

FIGURES ................................................................................................................................................... 89

APPENDIX A: Haringx Theory of Bearing Stability ....

APPENDIX B: Two-Spring Model for Elastomeric Bearings ....................................... .

163

169

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List of Tables

Table 301 Dimensions and Design Properties of the Prototype and

Reduced-Scale LSF Bearings ,0,,,, Oo 00o0,000hOOOOOOhhhoo OOOOOO,OhooooooohOO>OOOhooooooooOOO>Oooooooooo,oo

401 Channel List for LSF Bearing Tests 42 Notation Adopted for Test Bearings 43 Test List: Load Case 1 4A Test List: Load Case 2 45 Test List: Load Case 3 00000000000000, 406 Test List: Load Case 4 407 Test List: Load Case 5 000000 00000 408 Test List: Load Case 6 409 Shear Failure Tests 0,000000 4010 HB2 Vertical Failure Tests ooO 4011 Characteristics of Test Signals 0 ooooooooooo,ooo,OooO OOoO,OOoOhoO>OOOO OOOOoohoo,o,OO,OOOOOohooooo,oOOoOooooooooo,o,ooHOoOooooo,oooo>o

501 52 53

Shear Hysteresis Loop Parameters, HD1 Bearing Shear Hysteresis Loop Parameters, HB1 Bearing Shear Hysteresis Loop Parameters, LD Bearing Oohoho OHHOOOoOooo

SA Shear Hystcoresis Loop Parameters, LB Bearing 0 55 Wct- ya Dependence ooO oooooo,,,,,o,OOOOOOOOoO 506 Vertical Stiffness Results: Load Cases 1 and 2 507 Load Case 3 Test Results: HD1 and HB1 Bearings 5B Load Case 3 Test Results: HD1 and HB1 Bearings 509 Hysteresis Loop Parameters: Load Case 6 0000 SolO Compression Stiffness: Theory and Experiment 0

page

63

64 65 66 67 68 70 74 75 76 77

78

79 80 81 82 83 84 85 86 87 88

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List of Figures

Figure 3.1 Cross-Section of SAFR Plant 3.2 3.3 3.4

Horizontal Spectral Responses, Isolated and Unisolated Conditions Vertical Spectral Responses, Isolated and Unisolatcd Conditions Prototype SAFR Bearing Design ......................................... .

3.5 Test Bearing Design: Doweled Connections .. 3.6 Test Bearing Design: Bolted Connections

4.1 Schematic Diagram of Test Facility ........ .. 4.2 Single Bearing Test Machine .................. . 4.3 Single Bearing Test Machine ....... . 4.4 Test Machine Instrumentation ...

5.1 5.2 5.3

5.4

5.5

Typical Shear Force vs. Displacement Loop, HB1 Bearing .................................................................. . Typical Shear Force vs. Displacement Loop, LD Bearing ..................................................................... .. Example of Nonlinear Hysteresis Behavior, LD Bearing ......................................... , .. ., .................. ., .... .,. Definitions of Kh,. and~ on Typical Hysterests Loop, HB1 Bearing ............ , .... , .............................. .. Shear Modulus vs. Shear Strain, Unfilled and Filled Elastomers

5.6 Hysteresis Loops for Cyclic Shear Test, Constant Strain

page

89 90 90 91 92 93

94 95 96 97

98 99

100 101 102

and Variable Axial Load, HD1 Bearing ... ., .. , .............. , .. , ........ , .......... ., ....... .,.,.................... 103 5.7 Kh,ff vs. Axial Load, HD 1 Bearing .. ., ... , .... ., ............... ,., ............................. ., ............................... , ........ .. 107 5,8 Hysteresis Loops for Cyclic Shear Tests, Constant Strain

and Variable Axial Load, HB1 Bearing ................... , ............ ., .... , ..... ,,................................. 108 5.9 Hysteresis Loops for Cyclic Shear Tests, Constant Axial

Load and Variable Strain, HD1 Bearing ............. , ................... , ...................................... , .. . 5.10 Hysteresis Loops for Cyclic Shear Tests, Comtant Axial

Load and Variable Strain, HB1 Bearing 5.11 LD Bearing at Approximately 200% Shear Strain 5.12 5.13 5.14

Dissipated Area vs. Axial Load, HB 1 Bearing "Normalized" Wd vs. Axial Load, HB1 Bearing Hysteresis Loops for Cyclic Shear Tests, Constant Strain

and Variable Axial Load, LD Bearing , ................ ., .. .,.,, .................... ., ................. ., ........... .. 5.15 Hysteresis Loops for Cyclic Shear Tests, Constant Strain

and Variable Axial Load, LB Bearing . 5.16 Kh vs, Axial Load, W Bearing ............ , ...

'" 5.17 K, vs. Axial Load, LD Bearing .............. , .. .. 5.18 Kh vs. Axial Load, LB Bearing ................. ..

'"

112

114 116 117 117

118

122 126

126 127

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5.19 Hysteresis Loops for Cyclic Shear Tests, Constant Axial Load and Variable Strain, LD Bearing ................................................... .

5.20 Hysteresis Loops for Cyclic Shear Tests, Constant Axial Load and Variable Strain, LB Bearing ....

5.21 Monotonic Vertical Loading, HD 1 Bearing ......... . .......................... . 5.22 Monotonic Vertical Loading, HB1 Bearing .............................................. . 5.23 Monotonic Vertical Loading, LD Bearing .................................. ., ................ . 5.24 Monotonic Vertical Loading, LB Bearing .......................................... . 5.25 Cyclic Vertical Loading about Initial Load, HD 1 Bearing ... ., .................... . 5.26 Cyclic Vertical Loading about Initial Load, HB1 Bearing . 5.27 Cyclic Vertical Loading about Initial Load, LD Bearing 5.28 Cyclic Vertical Loading about Initial Load, LB Bearing 5.29 Cyclic/Monotonic Vertical Stiffness Ratio vs. Axial

Prestrain, High Damping Bearings 5.30 Cyclic/Monotonic Vertical Stiffness Ratio vs. Axial

Prestrain, Low Damping Bearings ............................................. . 5.31 Typical Cyclic Vertical Hysteresis Loop, HB1 Bearing ....................................... ., ... ., ..

128

130 132 133 134 135 136 137 138 139

140

141 142

5.32 K,"' vs. Horiwntal Displacement Offset .................................................................................................. 143 5.33 l; vs. Horizontal Displacement Offset ....................................................................................................... 145 5.34 Shear Hysteresis Loop for HB1 Bearing, Standard Test with Shear

Strain Amplitude = 100% and Axial Load = 31.8 12.8 kips ... 5.35 Shear Force--Displacement Relationships for

Incremental Strain Tests to Failure, HB1 Bearing ............................................................. . 5.36 LB Bearing at Approximately 330% Shear Strain

During Shear Failure Test .................................................................................................. . 5.37 Shear Force--Displacement Relationships for

Incremental Strain Tests to Failure, LB Bearing 5.38 Shear Force-Displacement Relationships for

Incremental Strain Tests to Failure, HB2 Bearing ... 5.39 HB2 Bearing at Approximately 260% Shear Strain

During Shear Failure Test ..................... . 5.40 Overturning (Roll-Out) Condition in a Doweled Bearing .................. . 5.41 Shear Force-Displacement Relationships for Incremental

Strain Tests to Failure, LD Bearing, Axial Load = 31.8 kips 5.42 LD Bearing at Approximately 250% Shear Strain During

Shear Failure Test ................................................... . 5.43 Shear Force--Displacement Relationships for Incremental

Strain Tests to Failure, LD Bearing, Axial Load = 15.9 kips 5.44 Tension-Compression Axial Load Cycles, HB1 Bearing ..... . 5.45 Half-Cycle Tensile Load vs. Axial Displacement Failure Tcsl>,

HB1 Bearing ..................................................................... . 5.46 HB1 Bearing Undeformed Configuration .............................................. .

147

148

149

150

151

152 152

153

154

155 156

157 158

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5.47 HB1 Bearing During Tensile Failure Test ................................................................................................ 158 5.48 Axial Load vs. Horizontal Displacement for HD Bearing Buckling Test .............................................. 159

6.1 A Two-Spring Physical Model for an Elastomeric Bearing ..................................................................... 160 6.2 Force-Deformation Relationship of Non-linear Two-Spring Model 161

Al Haringx's Column for Modeling an Elastomeric Bearing Subjected to End Loads ............ .... .......... ..... .. ... .. .. ... .. ................. ........................................... 162

A2 Equilibrium and Kinematics at an Arbitrary Section of a Haringx Column .... .. ........................ ............ 162

CHAPTER 1

INTRODUCTION

1.1 Base Isolation Overview

Base isolation is a seismic design concept which reduces the level of ground motion that a struc-

ture experiences during an earthquake by moving the period of the structure away from the predom-

inant period of the ground motion. This is achieved by introducing a flexible connection, usually at

the foundation level, between the structure and the ground.

Many techniques have been proposed since the turn of the century to achieve the "flexible foun-

dation" goal (1], but so far only a very limited number have actually been implemented. Among the techniques that have gained acceptance, the most common is the elastomeric bearing-based system.

This approach uses elastomeric bearings, which consist of multiple bonded layers of elastomer and

steel shims, to simultaneously carry the gravity load of the isolated structure and provide the horizon-

tal flexibility necessary to reduce the level of seismic forces transmitted to the superstructure. Other

systems that have been utilized in practice include elastomeric bearing-slider bearing systems, elas-

tomeric bearings coupled with devices to provide additional energy dissipation (these devices which are many and varied, include lead extrusion dampers, lead inserts in the bearings themselves, lead

flexural dampers, flexural and torsional mild steel dampers, hydraulic viscous dampers, and friction

dampers [2-4]) and sleeved-pile systems to provide horizontal flexibility, coupled with mechanical energy dissipating devices [5].

The number of base isolation applications has grown considerably over the last decade [6]. The list of buildings and other structures incorporating base isolation is now extensive (approximately 122 structures worldwide at the end of 1988 [7,8]) but applications in the U.S. are still limited. At the time of writing, there were 7 buildings, 8 bridges, and 4 pieces of heavy equipment that incorporated base

isolation either complete or under construction in the U.S. In addition, a number of other projects were at the feasibility stage.

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The elastomeric bearing systems that have been implemented can be separated into two types:

those which include additional devices to supplement the overall damping of the isolation system, and

those which have no extrinsic devices which add to the system damping. The latter can be of the

lead-rubber type, in which elastomeric bearings contain a lead-plug insert to supplement damping, or

of the filled type, in which a filler material is added to the rubber to enhance the damping and stiffness properties of the compound.

Shape factor is a dimensionless ratio that provides a measure of the "relative size" of a layer of

elastomer (Section 2.3), and it is commonly used to characterize layers of elastomer in bearings. High values of shape factor correspond to thin layers of material (that have high vertical stiffness), and low values correspond to thick layers (with low vertical stiffness). Thus, a bearing that is designed to pro-vide horizontal isolation only and which is intended to be stiff vertically will have high shape factor

layers, while a bearing which is designed for both horizontal and vertical isolation will have layers

with a low shape factor. ln this report, bearings that are designed to provide both horizontal and vert-

ical isolation are referred to in terms of the shape factor of their elastomer layers and are denoted as

low shape factor or LSF bearings.

1.2 Interest in Low Slrnpe Factor Bearings

A number of recent isolation research programs in the U.S. and Japan have focused on the

development of LSF bearings to provide horizontal and vertical isolation protection to several different

types of structures.

In Japan, interest in LSF bearings has been mainly for the development of isolation systems that

can protect buildings from earthquake loadings (horizontal isolation) as well as vibration isolation (vertical and horizontal isolation). Two different isolation concepts (SAFR and PRISM, see Section L4) [9] for the protection of advanced liquid metal reactors (LMRs) have received considerable atten-tion in the U.S. The SAFR concept has as its basis the horizontal and vertical isolation of a modular

type LMR plant The design requires bearings of appropriately low stiffness in the vertical direction

(Le., of low shape factor) as well as the usual low horizontal stiffness property. The SAFR research and development program was the origin of the bearings for the current study.

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As well as possessing low vertical stiffness as a consequence of the vertical isolation an addi-

tional feature is necessary - namely, bolting of the bearings to the superstructure and to the founda-

tion., Seismic jsoJation bea."rings .have more usually featured do\veled, shear -connect:h::ms, but in the light of the increased vertical displacements (and the, albeit unlikely, possibility of vertical tension loads on the bearing) bolting is likely to be necessary to maintain the integrity of the bearing end-plate connections. This leads to a further distinctive aspect of this study: the evaluation of the behavior of

bolted elastomeric bearings compared with similar doweled bearings.

For a number of years it has been known that the damping of an elastomeric hearing is

influenced by axial load if the load is near that which causes buckling of the bearing [10,11]. Recent work by Koh and Kelly has shown that the increase in the damping ratio under high axial loads is due

both to an increase in energy dissipated per cycle and to a reduction in bearing horizontal stiffness

[12]. This research program provides a further opportunity to investigate this phenomenon.

The failure mode of doweled, elastomeric bearings is weil-understood (for most axial loads, "roll-out" or lateral instability represents failure) and it is possible to predict such failure. Bearings with boiled connections, and particularly those of low aspect ratio (that is, squat bearings with a low value of height to width ratio) are not susceptible to roll-out and there is an obvious need to verify experimentally the failure modes of such bearings when subjected to large strain lateral loadings. Bolt-ing of the end-plates raises the additional question of the tensile strength of elastomeric bearings and

the experimental program included tests to answer this question.

Bearings which are much wider than they are tall (i.e., of low aspect ratio) introduce the possi-bility of taking advantage of another desirable physical characteristic of natural rubber. At large

strains, natural rubber undergoes a strain-induced crystallization [11,13] which is evidenced by an increase in material stiffness and, consequently, in the stiffness of the bearing as a whole. If this

stiffening effect were able to be utilized, the behavior of elastomeric bearings under extreme loadings

could be enhanced by this inherent reserve of stiffness. For bearings to operate safely at these high

levels of strain several things are necessary: in particular, that the bearings be of low aspect ratio (so that geometric instability under lateral deformation is avoided), and that the end-plate connections be bolted to ensure that the bearing-superstructure and bearing-foundation connections are maintained

even under the most extreme loadings. The viability of making use of the physical characteristic of

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high-strain stiffening as a valid design approach must be verified by experiment, and this is an addi-

tional motive for the current study.

1.3 Objectives and Scope of Studies

1.3.1 Objectives

The principle objectives of the studies reported herein were to conduct a series of experimental tests on a set of LSF bearings to evaluate the influence of shape factor on the perfom1ance characteris-

tics of elastomeric seismic isolation bearings and to endeavor to develop a mechm1ical model suitable

for predicting the behavior of LSF bearings when subjected to static and dymunic loads.

The design of the test bearings was extended to allow two further aspects of elastomeric bear-

ings to be studied. These aspects were response comparisons of bearings with bolted end-plate con-

nections and bearings with doweled connections; and comparisons of bearings made from two

different natural rubber compounds: a filled (high-damping), natural rubber and a conventional

unfilled, natural rubber.

1.3.2 Scope

To achieve the objectives outlined above, an extensive series of experimental tests was con-ducted. The following tests and studies were undertaken:

e A review of current analytical and experimental information on the behavior of elastomcric

seismic isolation bearings.

'" A series of tests to ascertain the vertical stiffness properties of the bearings, and also the

influence of lateral displacement on vertical stiffness.

A series of tests to determine the dynamic properties of shear stiffness and damping as

influenced by the vertical loading and the shear strain applied to the bearings.

A series of tests to investigate the modes of failure of doweled bearings subjected to shear and compression loads, bolted bearings subjected to shear and compression loads and bolted bear-ings subjected to tension loads. Tests to evaluate the buckling loads of the bearings were also conducted.

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The evaluation of the suitability of existing design equations to accurately predict the parameters

necessary for the design of LSF bearings.

The development of an -analytical model (or the extension of a suitable existing -m"odel)- to-predict the behavior of LSF bearings to static and dynamic loadings.

The evaluation of the test results regarding the suitability of LSF bearings to provide vertical

and horizontal seismic isolation for structures in regions of seismic risk

1.4 Literature Review

Interest in the general concept of base isolation has grown significantly since the early 1970's,

and a large proportion of the experimental research effort since that time has been devoted to the

study of elastomeric bearings and elastomeric bearing-based isolation systems. Substantial early efforts

were made in several countries, in particular, in New Zealand, the U.S., France. In the 1980's Japan

has made significant contributions to the field.

New Zealand

Research in New Zealand has tended to focus on lead-rubber bearings, which are natural rubber

bearings that incorporate a lead-plug insert to enhance the damping behavior of the bearing unit [14]. These bearings arc typically combined with ordinary natural rubber bearings for buildings, or slider

bearings for bridges to provide a complete isolation system. Extensive testing has been performed to

investigate the dynamic behavior of these bearings [15-17].

France

Base isolation research in France has emphasized the development of systems suitable for the

seismic protection of Pressurized Water Reactor (PWR) nuclear power plants. A system using neoprene bearings (additionally with a sliding frictional interface in regions of higher seismic risk) has been developed and implemented in six plants, four in France and two in South Africa [18-20]. The bearings used in this system, however, differ significantly from most other types of elastomeric base

isolation bearings. Typically, they consist of only a few layers of neoprene. This means that the

overall thickness of elastomer is much less than that for more usual isolation bearings. As a result,

the bearings are only able to sustain small lateral deformations for moderate shear strains in the

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neoprene, compared with deformations that are 5 to 10 times greater for most other types of isolation

bearings. In zones of high seismicity, because of the limited shear strain capacity of the bearings,

sliding plates- are placed bef!,veen the top of the bearings and the uppe-r foundation to limit the

neoprene shear strains.

U.S A.

Substantial research devoted to elastomeric, seismic isolation bearings has taken place in the

U.S.A. A joint project between the Earthquake Engineering Research Center (EERC) of the University of California at Berkeley and the Malaysian Rubber Producers' Research Association (MRPRA) led to the development of isolation bearings utilizing carbon black-filled natural rubber, with properties well

suited to base isolation applications. The carbon black filler enhances the material damping charac-

teristics and produces a nonlinear shear modulus-shear strain relationship. The modulus is high at

small strains and decreases nonlinearly as the deformation increases. This is a particularly desirable

characteristic, as it allows bearings to provide high stiffness to the isolation system for wind and low-

level earthquake loads while having a (preferable) lower stiffness under large seismic excitations. Further, the modulus is largely independent of strain in the 50--100% range and this permits simple,

but accurate, preliminary design calculations [21,22].

Performance evaluation of a large number of different types of bearings has taken place over the

last few years in conjunction with earthquake simulator studies of base isolated structures [23-28]. Using results from tests of bearings designed for earthquake simulator testing of a base isolated,

bridge-deck model [29], Koh and Kelly evaluated the effects of axial load on the behavior of elas-tomeric isolation bearings [12]. This study led to the development of a simplified mechanical model

for the behavior of such bearings, which is able to accurately predict the effects of axial load on the

fundamental bearing properties of damping, and horizontal and vertical stiffness [30]. Results are available for tests performed on high-damping, natural rubber bearings used in the first base isolated

structure in the U.S. - the Foothill Communities Law and Justice Center located in Rancho

Cucamonga, San Bernardino County, California [31].

Interest in the possibility of applying base isolation to the seismic protection of LMR nuclear

power plants has heightened considerably in both the U.S. and Japan in recent years. In the U.S., two

advanced modular, compact concepts have emerged: the Power Reactor Inherently Safe Module

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(PRISM) developed by a team led by General Electric Company, and the Sodium Advanced Fast Reactor (SAFR) developed by a team led by Rockwell International Corporation. Department of Energy funding of the SAFR project stopped in 1989 when the PRISM concept was selected as the U.S. reference design. PRISM [32] uses high-damping, elastomeric bearings to provide horizontal protection of only the reactor module, whereas SAFR [33] employs low shape factor, elastomeric bearings to achieve horizontal and vertical isolation of the entire reactor building [9]. Tests have been conducted at EERC on 1/2-scale PRISM bearings [34,35]. Recently, real time tests of 1/4-scale PRISM bearings were performed, and in the near future real time tests of full-scale PRISM bearings

are planned.

Japan

The pace of isolation research in Japan has accelerated dramatically in the 1980's with the

growth of interest in isolation for nuclear power plants. Extensive tests have been conducted on

numerous different types of isolation bearings and these different systems have found their way into

more than 34 buildings [8].

Kajima Corporation has constructed a research laboratory building on LSF bearings, completed in 1987 [36]. The isolation system, which provides both horizontal and vertical isolation, consists of eighteen laminated rubber bearings, fourteen hysteretic dampers (cantilever steel rods), and a number of oil (viscous) dampers. The elastomer compound used for the bearings did not provide sufficient damping for earthquake loading and so the hysteretic dampers and oil dampers were included to

enhance the horizontal and vertical damping, respectively, of the isolation system. The LSF bearings

are intended to provide a degree of vertical isolation and to filter out micro-tremors caused by external

ground-transmitted vibrations. Fail-safe blocks which limit ultimate system displacements are incor-

porated to provide secondary protection against primary system failure. The horizontal frequency of

the building is 0.5 Hz and the vertical frequency at the design weight is 5 Hz. The LSF bearings have

a shape factor of 5.2 and consist of four rubber layers (each 1.9 inches thick) and four steel shim plates (each 0.2 inch thick). Bolted type connections are used. The bearings are supported on steel boxes that allow for adjustments to compensate for creep effects, which for LSF bearings are expected to be larger than for conventional bearings. Analysis, vibration testing, and recorded earthquake data

have demonstrated that the isolation system can reduce earthquake peak accelerations by a factor of 4

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to 5. Forced vibration tests showed that more than 20 dB of vibration reduction can be attained at fre-

quencies over 10 Hz.

Ohbayaslii Corp(Jratiori has constructed a one story, reinforced concrete test structure, 19.7 ft by 29.5 ft in plan, supported on four high-dampirrg rubber bearings which are soft vertically [37]. Several tests and earthquake observations have demonstrated that the isolation system is effective in reducing

the effects of micro-vibrations as well as earthquake motions.

Bolted bearing connections have become a common feature of LSF as well as conventional iso-

lation bearings designed in Japan. The use of this detail in the U.S. or N.Z., however, has not yet

reached acceptance. Recent tests have been performed by Fujita and Shiojiri [38,39] to evaluate the failure modes of high-damping rubber, lead-rubber, and ordinary rubber bearings. These tests demon-

strated that Japanese bearings are capable of accommodating shear strains in excess of 450 % prior to

failure.

1.5 Summary

The growth of interest in base isolation as a seismic design strategy has substantially increased

experimental studies of elastomeric bearings worldwide. The scope and number of tests performed has

grown markedly, but to date no experimental tests of LSF bearings designed specifically to provide

seismic isolation in both the horizontal and vertical directions have been reported. Bolted bearing

connections are not employed in the U.S., and will not be until the influence of this detail on material

and bearing behavior has been thoroughly investigated by experiment.

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CHAPTER 2 BEARING DESIGN PARAMETERS

2.1 Introduction

The design of elastomeric bearings for seismic isolation applications requires the determination

of three important bearing properties. These properties are:

(i) the horizontal stiffness of the bearings, so that a specific horizontal natural frequency can be designed for;

(ii) the vertical stiffness of the bearings, so the designer can ensure that no undesirable vertical or rocking modes will occur, and that the predominant vertical frequency is controlled; and

(iii) the stability of the bearings under combined vertical load and lateral displacement This com-bined loading condition must be checked to ensure that a reasonable factor of safety exists

against instability caused by extreme loading.

ln this chapter the various different analytical and empirical relationships currently used for the

determination of these elastomeric bearing design parameters are reviewed and discussed.

2.2 Shear Stiffness

The usual equation used to calculate the shear siiffness of a bearing is

(2.1)

where

As = shear area of bearing

T, = total rubber thickness

= nt, for n rubber layers each of thickness t

and G is the shear modulus of the elastomer. The equation assumes that lateral deformation of bear-

ings is a result of shear deformation; that is, that flexural deformation is negligible in comparison.

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For nonlinear material behavior, it should be noted that the value used for G is important.

Z.3 Compression Stiffifess-

The equation generally used to calculate the compression stiffness of a bearing is

where

A - shim area of bearing

Ec - bearL'1g compression modulus

Ec A K =--v T

'

(2.2)

and T, is as defined for Eq. 2.1. Ec can be evaluated using a number of different equations. The

equations for Ec that are applicable to bearings of low shape factor are outlined below.

Method 1 by Gent & Lindley (1959)

The commonly used equation for the compression stiffness of rubber blocks, derived by Gent

and Lindley in 1959 [ 40], is

E c Eo (1 + 2k5 2 ) (2.3)

where

0 - Young's modulus

k =material modifying factor (determined by experiment, [11])

S = shape factor.

The shape factor S (first defined by Keys in 1937 [41]) for a rubber layer is the ratio of the loaded area of the layer to the total force-free area. It is used in most equations for the compression

stiffness of rubber blocks. Specifically,

s = one loaded area total force -free area

D 41

for a circular bearing, diameter D

- 11 -

where t = the thickness of one rubber layer.

Young's modulus E 0 is defined as the modulus in the region of zero strain (usually y < 10% is con-

Experimental studies have led to relations between E 0, 0 and rubber hardness [11,42], which

were utilized irr the design calculations for the LSF bearings. Hardness tests for rubber involve

measuring the penetration of the rubber by a specially shaped indentor under a specified load. It is

essentially a measurement of a reversible elastic deformation and is therefore related to the Young's

modulus of the rubber. This contrasts with the various metal hardness tests which consist of measur-

ing an irreversible plastic indentation. Tests for rubber hardness differ from those for metal in another

respect the readings from the different types of tests (International Rubber Hardness Degrees (!RHD), British Standard Hardness Degrees (0 BS) and the Shore Durometer A Scale) are all approxi-mately the same, so that equations based on hardness are generally applicable.

Variations of this method (Eq. 2.3) depend on the value used for Young's modulus, E 0. These

are:

(i) E 0 = 30 ,

and 0 is obtained either from material tests or empirical data. This value assumes that Poisson's

ratio, v = 0.5; that is, that the material is incompressible.

(ii) 0 = 40 ,

and 0 is obtained either from material tests or empirical data. According to [13], for harder

rubbers containing a fair proportion of non-rubber constituents, thixotropic and other effects

increase E 0 to about 40 . Therefore, for the case of a high-damping rubber with a substantial

amount of carbon black filler we would expect 4G to be a better estimate for E 1P and 30 to be

more suitable for unfilled, low-damping rubbers.

Method 2 by Derham

Research by Derham [43] has suggested that when S > 3 it is reasonable to use

E, = 5.6 OS 2 (2.4)

and that 0 should be obtained from material tests or empirical data. The LSF test bearings are

- 12 -

actually outside the recommended range of application for this equation (for the LSF bearings S ~ 2.5, see Table 3,1 and Section 3,3) but for purposes of interest it will be evaluated,

Method 3 by Rocard (1937)

This derivation [ 44 J is based on equating the stored energy with the work done on deformation of an incompressible material, The exact solution obtained by Rocard involves an infinite series and

is not easy to evaluate, The equation can be evaluated for the two limiting cases of very small and

very large shape factors, giving a practical equation for the compression modulus:

(2.5)

where k 1 = 4,8 and k 2 ~ 4, The values of k 1 and k 2 depend on what function is chosen for the varia-

tion between small and large shape factor,

Method 4

Derham has studied Rocard 's equation (Eq, 2,5) and found that closer agreement to experiment is obtained if the values k 1 = 9 and k 2 = 4 are used instead of those originally recommended by

Rocard [43], Derham further modified Eq, 25 to express E, in terms of hardness instead of G, obtaining

(2,6)

where H is the rubber hardness,

There are several further equations for E, that take into account compressibility effects by

including the bulk modulus of the elastomer, However, compressibility only becomes significant when

the shape factor is high, and in the case of the LSF bearings these equations would not provide any

significant improvement over those already presented, For this reason, these equations are not be dis-

cussed here, (For discussion of compressibility effects see [ 40,45 ]),

- 13 -

2.4 Stability - Buckling Load

The stability condition of bearings must also be considered. The lateral stiffness of a multilayer

compression and shear some flexural bending of the bearing takes place. This bending causes some

tilting of the internal shims and thus the faces of the individual elements of elastomer are no longer

parallel, so that the behavior of the layers is changed.

The theory for this deformation was first developed by Haringx [46] and subsequently applied to

rubber bearings by Gent [47]. The Haringx theory as it applies to elastomeric bearings is developed in Appendix A. The buckling load of a bearing, taking into account the shear and flexural stiffnesses,

is expressed in Eq. A.17 as

where Ps; GA.,

Ps 2

; 'tLE!eff z2

(A.l7)

Most isolation bearings are quite squat, with I z R. This leads to a reasonable approximation

for Per , given by

(A.19)

3.1 Introduction

- 15 -

CHAPTER3 DESIGN OF LSF BEARINGS

This chapter describes the SAFR plant, the SAFR bearing design, and the reduced-scale designs

selected for testing. A summary of the bearing parameters is presented and some aspects of the

designs are discussed.

3.2 Description of the SAFR Plant

The SAFR plant is a compact. advanced, nuclear power plant concept which employs a 450

MWe pool type Liquid Metal Reactor (LMR) as its basic module [9,33]. The reactor assembly module is a standardized, shop-fabricated unit that can be shipped to the plant site by barge for installation.

Several passive features have been incorporated in the design to improve safety. The reactor vessel

and steam generator arc housed in a building with plan dimensions of 124 ft by 82 ft. The total

weight of the reactor building and its contents is 29,000 tons. The seismic design basis for SAFR is a

safe shutdown earthquake (SSE) with a maximum horizontal and vertical acceleration of 0.3g anchored to the NRC Regulatory Guide 1.60 design response spectra. This is expected to cover 85

percent of potential U.S. nuclear sites, excluding high seismic zones such as California. It was decided

to seismically isolate the standardized SAFR reactor building to enhance seismic margins and to per-

mit siting in regions of high seismicity. The selected system employs low shape factor (LSF) elas-tomeric bearings under the reactor building to provide isolation in both the horizontal and vertical

directions (Fig. 3.1).

3.3 Dynamic Analysis

Dynamic time history analyses were performed to evaluate the response of the SAFR reactor

with and without isolation. A comparison of the horizontal and vertical response spectra of the reactor

supports is shown in Figs. 3.2 and 3.3. It can be seen that there are substantial reductions of horizon-

tal acceleration for all resonant frequencies of the internal equipment. In the vertical direction, the

- 16 -

response is amplified in the range of the vertical isolation frequencies, but at frequencies greater than

4 Hz, which is the range of vertical frequencies of most components, fhe response is reduced. The

tal direction. In general, a large arnount of rocking may result in buildings supported on LSF bearings.

The SAFR building, however, has a sufficiently low center of gravity and a wide base to limit rocking

to acceptable levels.

3.4 SAFR Bearing Design

The SAFR bearings are 42 inches in diameter and have an overall height of 16.75 inches (Fig. 3.4). The bearings consist of three 4 inch rubber layers separated by two 1/8 inch steel shims and with 2 inch thick end-plates. An external rubber cover layer (2 inches fhick) is provided for protec tion. The design horizontal frequency is 0.5 Hz and the vertical frequency is approximately 3 Hz. For

a carried mass of about 290 tons per bearing, the compressive stress on each bearing is approximately

416 psi. The elastomer used for the bearings is a filled, high-damping natural rubber. Tests are

required to verify the suitability of existing design formulas (as presented in Chapter 2) for the design of LSF bearings and to evaluate the behavior of bearings with bolted connections.

3.5 Test Bearing Designs

The full-scale bearings for the SAFR reactor module are large by current standards so the test

bearings needed to be of a reduced scale in order to be of a reasonable size and stiffness for testing

using fhe existing facilities at EERC

It was felt that a bearing of 10 inches diameter would be a reasonable size for testing and this

led to a test bearing design corresponding to 1/4-scale. The test bearings were designed with both

bolted and doweled end-plate connections" One further design variable was added: to evaluate bear-

ings manufactured from two different rubber compounds, a filled, high-damping natural rubber, and an

ordinary unfilled, natural rubber. The design properties and dimensions of the prototype and reduced-

scale SAFR bearings are presented in Table 3"1.

- 17 -

Doweled Bearing Design

The doweled bearings are of 10 inches overall diameter and 5.25 inches in height. The end-

_________________________ -----_:pla!es--a.re--1--in.,..h---thick, urith f"'"'"-1-~ete.:-} 7/8 ineh deep dovvd holes Oif a- 6 htdt diameter in

each end-plate. The bearings consist of three 1 inch thick rubber layers, separated by two 9 inch

diameter, 12 gauge steel shims. The external cover layer is 0.5 inch thick. To preserve the vertical and

horizontal frequencies of the prototype bearing the vertical load was selected to be 31.8 kips. The

doweled bearing design is shown in Fig. 3.5.

The elastomer for the test bearings was compounded by LTV Energy Products Co. of Arlington,

Texas. The bearings were manufactured by the Structural Bearings Division of Fluorocarbon, Athens,

Texas. The high-damping rubber was of a formulation designated 243-62 by the compounder and had

a Duromctcr hardness of 62, with a shear modulus of approximately 130 psi at 50 % shear strain.

The unfilled rubber was of a formulation designated 247-55 by the compounder, with a shear modulus

of approximately 120 psi at 50 % shear strain. The elongation-at-break (EB) of the high-damping material was 562 %, and 662 % for the unfilled rubber.

Bolted Bearing Design

The design of the bolted bearings differed only from that of the doweled bearings in the end-

plate detail. End plates of 18 inches diameter and 1 inch thickness, with eight 1 inch diameter bolt

holes on a 14 inch center were provided in this design. The bolted bearing design is shown in Fig.

3.6.

3.6 Comments on Design

The general design methodology for elastomeric bearings for seismic isolation represents several

significant departures from the design requirements for elastomeric bearings used for vibration isola-

tion or to accommodate service loads in bridge structures. In particular, slenderness, rated load, and

lateral displacement criteria are substantially different from those currently used for bridge bearings.

Further discussion of these aspects is offered by Stanton and Roeder in [ 48] and Kelly eta!. in [49].

In the context of current practice in the field of seismic isolation bearing design, the LSF bear-

ings of this test program are of particular interest for two main reasons:

- 18 -

The relatively thick rubber layers - necessary to achieve the desired vertical isolation -

represent a much lower shape factor than typical for current isolation bearing designs. This

---- ---ilOOld havc-Un..p!icaticar~ __ ings.

" The use of oversize end plates to facilitate bolting of the bearings is a detail not currently

employed in the U.S. (although it is used in Japan), but could prove to be advantageous in the future. It is an aspect of isolation bearing design that warrants investigation.

- 19 -

CHAPTER 4 TESTS OF LSF BEARINGS

4.1 Introduction

This chapter presents a description of the types of tests performed on the LSF bearings and an

outline of the complete test program. The facilities at EERC for the testing of single isolator bearings

are also described.

4.2 Description of Test Facility

This section presents a brief description of the test setup, instrumentation layout, and the control

and data acquisition systems used. Fig. 4.1 shows an overall schematic diagram of the facility and the

various stages of testing and data analysis.

4.2.1 Test Setup

All of the tests of the LSF bearings were performed in a test machine capable of subjecting sin-gle bearings to simultaneous generalized horizontal and vertical dynamic loadings. Fig. 4.2 shows the

details of fhe test machine and Fig. 4.3 is a general view of the machine with a test bearing in place.

The test machine consists of two rigid reaction frames supporting one horizontal actuator and

two vertical actuators. The test bearing is mounted on a force transducer which measures shear force,

axial force and bending moment. The force transducer is located on a braced pedestal which is

attached to a base block. The base block consists of a concrete block and a wide flange steel beam to

provide anchorage to the test floor. Loads arc applied to the test bearing by a beam; vertical loads by

two vertical actuators to simulate gravity loads on the bearings, and the horizontal loads by a horizon-

tal actuator which acts along the longitudinal axis of the load beam.

The rigid pedestal is placed between rhe transducer and the test floor to maximize the length of

the vertical actuators so that the change in the vertical load component due to horizontal displacements

during testing is not significant. Two lateral struts are connected to opposite ends of the load beam to

stabilize fhe setup in the transverse direction. For constant axial loads applied to fhe test bearing the

- 20 -

vertical actuators are under force control, which means that the vertical load is maintained constant

and is independent of the horizontal displacements of the load beam. In addition, the differential dis-

_.. .. _ ... - .... ~ ....... ~ .... -f~~pA; .... betweeP..-the-b!J.o. ..... e:cticaLartJrators is ... maintain.e.dlli .... &G:X.~suring thatJhe load beam is kept horizontal.

Control of the hydraulic system is performed by an MTS 443 Controller. The hydraulic actuator

can develop a maximum dynamic load of 76.2 kips at a hydraulic pressure of 3000 psi. The maximum

travel of the horizontal actuator is 6 inches (i.e., 12 inch stroke). Maximum piston velocity is 30.3 in!s and the servo-valve on the actuator has a flow capacity of 200 gpm. If displacements in excess

of the 6 inch limit are required the setup can be modified to obtain a maximum displacement of 10

inches for loading in one horizontal direction only. A maximum load of 300 kips can be applied by

the two vertical actuators, each with a servo-valve capacity of 25 gpm.

Signal control is performed by an IBM-AT 286 personal computer. Control signals for both

components of loading can be completely general in nature.

4.2.2 Instrumentation

A total of 14 channels of data was recorded for the tests of the LSF bearings. The attributes

(response component, units and channel name) for each of the channels arc presented in Table 4.1 and their spatial orientation is indicated in Fig. 4.4. A brief description of the components that were meas-

ured follows.

The loads applied by the hydraulic actuators were measured by prccalibrated load cells. The

compression load on the bearing is calculated by summation of the measured forces in the two vertical

actuators. Shear force, axial force and bending moment are measured by a force transducer located

underneath the bearing. A linear variable differential transformer (LVDT) built into the horizontal actuator measures the horizontal displacement of the load beam (this being the lateral displacement of the bearing). Linear potentiometers attached to both of the vertical actuators provide feedback signals for the control of the vertical load. Four direct current differential transformers (DCDTs) measure the vertical displacements of the load beam near the corners of the top of the bearing. To observe any

shortening of the pedestal assemblage and other components below the test bearing, two DCDTs were

connected between the base block and the bottom bearing plate (situated between the bearing and the

- 21 -

force transducer).

4 2 3 Data "'-cquisitia aa HBI> LD, and LB bearings. Failure tests were performed on the HBI> HBz, and LD

- 22 -

bearings. The HD2 bearing was used for the buckling load tests.

Testing of isolation bearings has in recent years had as a basis the so-called standard cyclic

shear test, which is a displacement-controlled, sinusoidal, lateral shear test performed under a state of

constant compression load. This test, while widely believed to produce bearing behavior which is

representative of behavior under more complicated and less uniform loading conditions, has yet to be

shown to be conclusively acceptable as a test procedure from which to draw generalized conclusions

regarding behavior under many different types of loading. One of the objectives of the study was to subject bearings to a number of non-standard loading conditions and to evaluate the behavior of the bearings in terms of the standard cyclic shear test procedure.

With this in mind, the following loading conditions were chosen:

(1) monotonic vertical load

(2) cyclic vertical load about an initial vertical load (no horizontal displacement permitted)

(3) cyclic vertical load about initial vertical load with constant horizontal displacement offset

( 4) cyclic horizontal displacement with constant vertical load

(5) cyclic horizontal displacement about an initial horizontal displacement offset with constant verti-cal load

(6) simultaneous, cyclic horizontal and vertical excitations.

Each of load cases ( 4), (5) and (6) consisted of tests performed at increasing increments of shear strain and a range of vertical loads. With these three different load cases the aim was to be able to

draw some conclusions regarding the suitability of the standard tests to reveal the overall behavior of

the bearing in cases of more complicated, non-standard loading.

The complete list of tests is presented in Tables 4.3-4.10. The tests are presented separately for

each load case, and are characterized in terms of shear strain, vertical load, displacement offset and

the test signal used. The specific characteristics of the test signals used to apply the different load

cases are detailed in Table 4.1 L The various combinations of loading required a total of 13 test sig-

nals. Each of the six different load cases is described in more detail in the following section.

- 23 .

Description of Load Cases

Load Case 1 : Monotonic vertical load

This load case consisted of monotonic vertical load applied to the bearing with no horizontal dis-

placement permitted. This test allowed observation of the vertical stiffness under monotonic loading

conditions. Load cycles to peak loads of 15.9, 31.8, 47.7, and 63.6 kips were performed. These

loads correspond to 50, 100, 150, and 200% of the design vertical load, and peak pressures of 250,

500, 750, and 1000 psi, respectively. The complete list of tests performed for this load case is

presented in Table 4.3.

Load Case 2 : Cyclic vertical load abour initial vertical load (no horizontal displacement permitted)

The bearing was subjected to an initial vertical load and then the vertical load was cycled about the initial load with no horizontal displacement allowed. These observations revealed the cyclic

loading-unloading vertical stiffness properties of the bearings. Initial vertical loads of 15.9, 3L8,

47.7, and 63.6 kips were applied with a vertical load cycle of 10 kips for all tests. The complete

list of tests performed for this load case is presented in Table 4.4.

Load Case 3 : Cyclic vertical load about initial vertical load with constant horizontal displacement

offset

This load case provided another loading variation for evaluation of vertical stiffness properties.

In this instance the test was constructed so as to reveal any influence of horizontal displacement offset

on the vertical stiffness of the bearings. An initial vertical load of 3L8 kips was used for all of these

tests. Horizontal displacement offsets of 0, 0.75, 1.50, 2.25, and 3.00 inches and cyclic vertical load

amplitudes of 6.4, 12.8, and 25.6 kips were applied. The complete list of tests performed for this

load case is presented in Table 4.5.

Load Case 4 : Cyclic horizontal displacement with constant vertical load

This load case has become the standard test for elastomeric seismic isolation bearings. Axial

loads of 15.9, 31.8, 47.7, and 63.6 kips and shear strain amplitudes of 10, 25, 50, 75, 100, 125, 150,

- 24 -

and 160% were used for these tests. The complete list of tests performed for this load case is

presented in Table 4.6.

Load Case 5 Cyclic horizontal displacement about initial horizontal displacement offset with con-stant vertical load

An initial displacement was imposed on the bearing and then the standard test (load case 4) was conducted to achieve sinusoidal displacement excitation with constant vertical load about a constant

horizontal displacement offset position. An axial load of 31.8 kips was used for all of these tests. An

offset displacement of 1.5 inches (50% shear strain) and cyclic strain amplitudes of 50% and 100% were used. The complete list of tests performed for this load case is presented in Table 4.7.

Load Case 6 : Simultaneous cyclic horizontal and vertical loading

The basis for these tests was to investigate the effect of horizontal and vertical excitations of the

bearing occurring simultaneously, representing quasi-resonant loading conditions. The bearings were

subjected to 5 cycles of vertical excitation for every cycle of horizontal excitation. This relationship between loading rates represents approximately the ratio of the vertical frequency to the horizontal fre-

quency for the test bearings under their design loading (Table 4.1). An initial axial load of 31.8 kips was used for all of these tests. Shear strain amplitudes of 50% and 100% and cyclic axial load ampli-

tudes of 6.4 and 12.8 kips were used. The complete list of tests performed for this load case is

presented in Table 4.8.

4.3.2 Failure Tests

Failure tests were conducted on the bearings to determine their modes of failure in shear and

tension. One doweled bearing was tested to failure in shear (for doweled bearings, failure in shear actually corresponds to a geometric instability phenomenon, termed "roll-out"), two bolted bearings were used for tension tests to failure, and a third bolted bearing was used for shear failure tests. The

failure tests performed are listed in Tables 4.9 and 4.10.

- 25 -

4.3.3 Buckling Tests

Buckling tests were conducted on the HD2 doweled bearing. These consisted of applying a

onoton;coJ!y increasing-

5.1 Introduction

- 27 -

CHAPTER 5 TEST RESULTS

This chapter presents the results for the tests of the LSF bearings. Results for the standard and

non-standard tests, buckling tests and failure mode tests are presented and discussed. Results are com-

pared with predictions by design equations for vertical stiffness, bukling load and roll-out displace-

ment.

5.2 Shear Tests

Standard cyclic shear tests of a total of four bearings were performed for a shear strain range of

10%-160%, with axial loads varying from 15.9 kips to 63.6 kips (202 psi to 808 psi). The complete list of these tests is presented in Table 4.6, and the tests have been previously described in Section

4.3.1. Typically, each test consisted of 5 cycles of sinusoidal displacement loading applied under con-

stant axial load conditions. The testing sequence consisted of applying a constant axial load to the

bearing and performing tests at increasing shear strain amplitude, changing the axial load setting and

repeating the sequence of increasing strain tests, and so on. The tests were performed in the order

listed in Table 4.6.

Typical shear force-displacement hysteresis loops for the standard tests on the four bearings are

presented in Figs. 5.1 and 5.2 as examples of the results obtained from these tests. Because of the

large number of tests performed (166) individual hysteresis loops arc not presented for every test.

5.2.1 Analysis of Hysteresis Loops

The hysteresis loops obtained for the szandard shear tests were analyzed to obtain a number of

different performance parameters for the LSF bearings.

Depending on the loading conditions (axial load and shear strain) and the type of bearing under investigation, the bearing stiffness as revealed by the test hysteresis loops was in some instances

highly nonlinear. Fig. 5.3 illustrates an example of this nonlinear behavior. The hysteresis loop

- 28 -

represents the 150% shear strain test of the LD bearing under an axial load of 63.6 kips. It is clear

that the bearing undergoes a substantial change of stiffness from the small strain to the large strain

determined for all of the standard shear tests.

A simple calculation of stiffness based on values of peak force and peak displacement is defined

as

(5.1)

where Fmax Frnin, dmax and drnin are the maximum and minimum values of shear force and displace-

men!, respectively. This stiffness is interpreted as the "effective" or overall stiffness of the bearing

during the test. In the case of highly nonlinear stiffness behavior (Fig. 5.3), however, Kh is not a '"

good measure of the total behavior of the bearing. For this reason, a second stiffness, K:. was defined as the slope of the tangent to the hysteresis loop at zero displacement Fig. 5.4 shows the definition of

Kt.," and K: in terms of a typical hysteresis loop. K, was calculated as

Fo+ - Fo--------

do+- do-(5.2)

where do+, and d0- are the first positive and negative displacement data points on either side of d = 0, and F0+ , F0- are the corresponding force values.

The hysteresis loops were also analyzed to obtain the equivalent viscous damping ratio of the

bearings for each test. A hysteresis loop is a plot of force against displacemen~ and the area con-

tained within such a loop represents the energy dissipated by the bearing.

The equivalent viscous damping ratio exhibited by the bearings is evaluated in the usual (structural engineering) fashion [52]

(5.3)

where W d = dissipated energy (hysteresis loop area)

W, = stored (clastic) energy

- 29 -

These bearing characteristics (Kh,rr K. and !;) were determined for all of the standard tests on each of the HD1, HBh LD, and LB bearings. These results, as well as the actual vertical load on the

--~---OO&r.ffig,-~1""'k- displac'ffle-t,{--aifai!Wd~1fle--er:espomliffg--pealf. s!lem stram for -etteb--test4l'fe---------- --------

presented in Tables 5.1-5.4 for the four test bearings. As mentioned above, each test consisted of 5

cycles of loading. The analyses of the loops were performed for the middle three cycles of loading,

i.e., cycles 2, 3, and 4, with the first and last cycles not considered for analysis. The parameters

presented in Tables 5.1-5.4 represent averaged values for these three cycles of response.

In the subsequent sections the influence of bearing axial load and peak shear strain on these cal-

culated bearing parameters is investigated. Section 5.2.3 presents the results obtained from a study of

the high-damping bearing parameters, and Section 5.2.4 presents a similar study of the low-damping

bearings.

5.2.2 Material Shear Modulus

The shear modulus G for the filled and unfilled elastomers was determined from coupon tests of

the materials. These tests consisted of sinusoidal shear tests of small material samples performed

under conditions of no axial load. The shear modulus-shear strain relationships for the unfilled and

filled elastomers are presented in Figs. 5.5a and 5.5b, respectively, The nonlinearity of G with shear

strain is apparent from the figures. The filled rubber (243-62) has a much larger G in the low strain range than does the unfilled rubber (247-55) hut at large strains G for both materials is about the

same. For sbear strains in excess of 50-75% G for the filled rubber can be regarded as almost con-

slant

5.2.3 Observations of Behavior: High-Damping Bearings

The bearing parameters Kh " K,, and s were evaluated from the hysteresis loops for all of the "'

standard cyclic shear tests using the relationships described in Section 5.2.1. This section discusses

the trends in these parameters for the high-damping (HD1 and HB1) bearings, with respect to both bearing axial load and shear strain.

Before evaluating the data obtained from analyses of the hysteresis loops several observations

regarding the consistency of the results must be drawn. The detailed behavior of the bearings (in par-ticular, those manufactured from the high-damping, filled rubber compound) was not entirely

- 30 -

independent of the loading history of the bearing. That is, scragging as a result of prior tests

influenced the observed results (to some extent) for any given test. Thus, the results obtained are

that the apparent stiffness degradation is not a permanent effect, but rather a short-term phenomenon

from which the bearings do recoveL Fletcher and Gent found that the dynamic modulus of filled

natural rubber decreases after cycles of large amplitude deformation [53,54]. They observed that the

modulus subsequently increases with time, reaching its original value after 24 hours at room tempera-

ture. Further work has suggested that this recovery time may be less [55,56]. Their results indicate

that filled, high-damping rubbers will show small short-term decreases in stiffness for repeated large

amplitude deformation cycles, but will recover to their original stiffness after a short time. Nonethe-

less, this fact compounds the difficulty in making definitive statements regarding the effects of single

factors on the behavior of the LSF bearings.

(a) Shear Stiffness

Hysteresis loops for the HD 1 bearing plotted for constant values of peak shear strain (25-175%) and overlaid for the four test axial loads of 15.9, 31.8, 47.7, and 63.6 kips applied to the bear-ing are presented in Fig. 5.6. The general trend apparent from these loops is that increasing axial load

leads to a gradual reduction in bearing stiffness up to about 125% strain (Figs. 5.6a--c), beyond which point the bearing exhibits a marked increase in stiffness (for constant strain) with increasing axial load (Figs. 5.6f and 5.6g). This is evident in Fig. 5. 7, which shows Kh as a function of axial

'"

load for the HD1 bearing, plotted for curves of constant strain. The two lower curves correspond to

strains of 25, 50, 75, and 100% and show a decrease in Kh with increasing axial load while the '"

upper curves, for strains of 125, 150, and 175%, increase with increasing P.

The phenomenon of increasing stiffness for high axial loads and strains in excess of 100% is

caused by two separate factors. The first of these is the strain-induced stiffening property of natural

rubber which is due to crystallization at high shear strains. This crystallization is not accompanied by

a brittle transition, as is commonly associated with materials that crystallize, but is primarily a

stiffening and toughening phenomenon. This material nonlinearity is accentuated by the presence of

the carbon black filler, which has the effect of increasing the "effective strain" occurring in the elas-

tomer. The filler causes constrictions in the elastomer-filler matrix and these in turn cause increased

- 31 -

local strains in the materiaL Qualitatively, the effect the filler has on the shear modulus at high strains can be regarded as one of strain amplification. At the microscopic level of behavior in the compound,

-~~-------J.l:te __ dc.sktipliQll._oUhis.~LiJLc.ompl icate d .. {13J._.:r:he.. add; !ion a! shear~-~ilh ''Grtica! --------------~ load on the bearing is the second factor contributing to the nonlinear stiffness behavior. The compres-

sion strains corresponding to the (higher) axial loads, 47.7 and 63.6 kips, are of the order of 13-16%. Axial load on the bearing has the effect of compressing the elastomer-filler matrix, which in

turn causes localized strain-amplifications and magnifies the strain nonlinearity of the filled material.

The maximum shear strain induced in a layer of elastomer by a compression load (derived from a strain energy approach) is

(5.4)

where S shape factor

Ec = compression strain,

Eq. (5.4) indicates that for an

- 32 -

The tangent stiffness, K,, showed a slight decrease with increasing axial load (at constant strain) and decreased with increasing strain for constant axial load conditions. These K, trends were observed

Figs. 5.9 and 5.10 present overlaid hysteresis loops for tests of the HD1 and HB1 bearings under

constant axial load and increasing shear strain amplitude. The effect of scragging on the stiffness of

the bearings is evident in these plots. Fig. 5.10b, for example, shows hysteresis loops for the HB1

bearing under 31.8 kips axial load and at shear strain cycles of 10-160%. This sequence of tests is

tabulated in Table 4.6b. With reference to the table, it can be seen that the tests up to 100% were the

first shear tests conducted on the bearing, and that the high strain shear cycles (125, 150, and 160%) were not performed until the later stages of the HB1 tests. The consequence of this sequence is evi-

dent in Fig. 5.10b. The inner three loops (10, 25, and 50%) show an initial "settling-in" of the bear-ing - as expected for the very first test cycles of a bearing - and then at 75% and 100% the loops

follow a well-defined, nonlinear envelope. The three tests at large strains, however, show a clear

change in stiffness, and do not follow the envelope pre-described by the smaller strain tests. This

stiffness reduction is a direct consequence of the substantial work performed on the bearing

(represented by tests 890320.21 - 890321.26, 18 tests, Table 4.6c) between the 100% and 125% shear strain cycles. As described above, the stiffness returns to its original value after a recovery

period.

(b) Damping Behavior

The equivalent viscous damping ratio, !; (Eq. 5.3), was calculated for all of the cyclic shear tests of the HD1 and HB1 bearings. The results are listed in Tables 5.1 and 5.2.

It is known that for highly nonlinear systems or for systems that do not behave according to

viscous theory the calculation represented by Eq. 5.3 is not a good measure of the damping behavior

of such systems. For this reason, the variation of damping with respect to axial load P and peak shear

strain was not investigated in terms of !; but rather in terms of the dissipated energy, determined from

the area of the hysteresis loops.

If a system has ideal viscous damping, then the damping it exhibits is independent of displace-

ment and is a function only of the rate of loading. Eq. 5.3 can be rewritten as

- 33 -

(5.5)

------~-- _w h_e~e __ dl!lllK_i~t!J_e_~~i_!11u_ll1_iii1p()_se_d_~isJll_ac_r:ll1S.'lLii!'_d_f_m;a_i~Jll_ElCtti_ng_m~!l!ll.!!LfQL'~-Thll_'h __ W4.---~~ ~-has a linear displacement dependence, since s is, by definition, independent of displacement Alterna-tively, if !he system under consideration behaves according to ideal linear viscoelastic theory, then it

can be shown that

(5.6)

where

G" ~ loss modulus of the viscoelastic material

Yo ~ cyclic strain amplitude

V = volume of elastomer _

ln this case, W d has a strain-squared dependence.

To investigate the nature of the strain-dependence of the damping of !he LSF bearings the fol-

lowing relationship was studied. We assume that

wd = constant (5"7)

that is, that W d is a function of the strain raised to some power rJ.. We wish to find the value of a that

satisfies Eq. 5"7 for the experimental data. We note here that if: (1) a= 0, the system behaves accord-ing to viscous damping theory; (2) a ~ 1, the damping is a linear function of displacement (hys-teretic), and (3) a~ 2, then the damping behavior obeys viscoelastic theory. Then, from Eq. 5.7,

!n(Wd) ~ o. ln(y) +constant, (5.8)

which is of the general form y ~ ax + b.

The experimental data were evaluated to find the form of Eq. 5.8, and specifically the value of

o.. For the range of axial loads used in the tests it was found that a varied over the range

1.4s o. s 2"0 (Table 55). It was found that a was larger for the low-damping than for the high-damping bearings, and larger for the doweled than for the bolted bearings. These results indicate that

the behavior of !he filled and unfilled LSF bearings docs not agree fully with either viscous or

- 34 -

viscoelastic theory.

Fig. 5.12 is a plot of Wd against axial load (curves of constant strain) for the HB1 bearing. Fig. ~-----5.Tns-preseiifeoio-il!ustrafe-ilie-'t'"=aepeiidence-onne-energy-arssipatron.1nng:-s:n,-w.J-rnvnreuoy---

{' is plotted against axial load for curves of constant strain amplitude (25-160% ), where a = 1.54 is the mean value of a found for the HB1 bearing. It can be seen that the unique curves for each strain

amplitude in Fig. 5.12 have collapsed to a single straight-line in Fig. 5.13. This line shows an almost

linear increase in the energy dissipation capability of the bearing with increasing axial load.

While values of l; have been calculated and tabulated in Tables 5.1 and 5.2, for the reasons dis-

cussed above the investigation of specific trends in l; -- the equivalent viscous damping ratio - as a

function of axial load or strain have not been pursued.

In previous tests of doweled, clastomcric bearings performed at EERC it bas been observed that

the geometric distortions of the bearings at large strains have caused flexural bending of the bearing

end plates which contributed to the damping behavior of the bearings. This phenomenon did not occur

with the LSF bearings, primarily because of the low shape factor (and thus the low vertical stiffness). Fig. 5.11 is a view of the LD bearing at approximately 250% shear strain and under 31.8 kips axial

load. The bearing has undergone considerable lateral distortion, but it is seen that the end plates have

rotated without any apparent flexural deformation. That they did not deform in flexure can be attri-

buted to their (1 inch) thickness in relation to the soft vertical stiffness of the bearing, which allowed the gross shape deformations of the bearing at large strains to be accommodated by compression and

shear of the rubber layers. From these observations it was concluded that end plate bending was a

negligible component of the damping behavior of the doweled LSF bearings at large strains.

5.2.4 Observations of Behavior: Low Damping Bearings

(a) Shear Stiffness

Hysteresis loops for the LD bearing tested at constant shear strain amplitudes (25-160%) and overlaid for the four axial loads (15.9-63.6 kips) are presented in Fig. 5.14. A similar sequence of plots for the LB bearing is given in Fig. 5.15. The influence of axial load on the behavior of the LD

bearing is illustrated in Figs. 5.14c and 5.14d, which arc for tests at 75 and 100% shear strain. The

bearing shows a consistent reduction in stiffness for each increment of axial load. It is also evident

- 35 -

that as the axial load increases, the size of the hysteresis loops also increases. The implications of this

on the damping of the bearing are discussed in the next section.

It can be seen that there is a general reduction in Kh with increasing P, and for a given P, ~ ~ff eff decreases with increasing shear strain amplitude. Similar curves are plotted for K. against P in Fig. 5.17. It is interesting to observe that at very large strains and high axial loads (47.7 and 63.6 kips) K. tends to zero, and at 150% and 160% is actually negative for the 63.6 kip axial load. These results

suggest a very unusual state in the bearing, which can be explained if the behavior is considered to be

viscoelastic. The elastic component of the bearing shear resistance mechanism has become negative,

but the viscous component remains positive and is opposed to this negative stiffness and the applied

loading which, incidentally, docs not become negative.

Two differences between the sequences of constant strain tests at different axial loads for the LB

bearing (Fig. 5.15) and those for the LD bearing (Fig. 5.14) are apparent: (1) the decrease in stiffness for increased axial load is not as substantial for the LB bearing as for the LD bearing, and (2) the increase in area of the hysteresis loops at high strains is dearly not as marked for the LB bearing as

for the LD bearing (for example, compare Fig. 5.15f and 5.15g with Fig. 5.14f and 5.14g, respec-lively). In fact, the LB bearing shows a significant Kh,,,-P independence. This can be seen in Fig,

5.18, which shows constant strain curves of Kh . against P for the LB bearing. ~ decreases as ~ .

strain increases (for constant P), but the constant strain relationships are quite linear (and independent of P). The variation of K, with P is similar to that shown in Fig. 5.17 for the LD bearing, but does not reach negative values for the extreme strain and high P loading conditions.

Figs. 5.19 and 5.20 present the overlaid hysteresis loops for tests of the LD and LB bearings

under conditions of constant axial load and increments of increasing shear strain. As was observed

for the high-damping bearings, these plots reveal that the behavior is dependent to an extent on the

loading history of the bearings. Fig. 5.19b shows the sequence of increasing strain tests of the LD

bearing at 31.8 kips axial load. Referring to Table 4.6b, it can be seen that (as for the high-damping bearings) the 31.8 kip axial load tests up to 100% shear strain were performed at the outset of the series, but that the 31.8 kip sequence was not concluded until the bearing had undergone many further

tests. This load history dependence is reflected in the figure, where the first five tests (up to 100%

- 36 -

shear strain, 3 inches displacement) follow essentially the same loading envelope, but the final tests at 125% and 150% show a clear deviation from the smaller strain loading envelope. A similar trend is

apparenrfonl'fe-rest-sequenceS

- 37 -

of this phenomenon.

Tests to investigate the effects of load rate on the LSF bearings were performed for vertical and

horizontal loading conditions. The horizontal tests (load case 4) listed in Tables 4.6a-----d were at fre-quencies of O.Dl Hz (signal rkw3), 0.5 Hz (signal rkw4), and 1.0 Hz (signal rkw5). The vertical tests (load case 3) listed in Tables 4.5a and 4.5b were conducted at frequencies of 0.01 Hz (signal rkwlO) and 0.5 Hz (signal rkw6).

Results for the horizontal tests are presented in Tables 5.1-5.4. The horizontal tests revealed

small differences in the stiffness and damping characteristics with changing rate, but these were so

small that other bearing nonlinearitics masked any rate-related trends. The slight differences between

the slow- and the fast-rate rests were more noticeable for the vertical tests than for the horizontal tests.

The variable-rate, vertical tests were the very first tests to which the bearings were subjected. This fact was significant, because initial tests of any bearing reflect a "settling-in", which stablizes after a

number of load cycles. 1bis settling-in appeared to be more significant than the effects related to the

rate of loading. The high-damping bearings (HD1 and HB1) did exhibit some creep tendency at 0.01 Hz, caused by the filler in the elastomer. However, creep was only evident for the first test and was

much reduced for subsequent tests.

5.3 Vertical Tests

5.3.1 Load Case 1 : Monotonic Verrical Load

Half-cycle excursions of monotonic compression loading to peak loads of 15.9, 31.8, 47.7, and

63.6 kips were applied to each of the four types of bearings. The axial load-displacement relation-

ships for these 4-test sequences are shown in Figs" 5.21-5.24 for the HD1, HB1, LD, and LB bear-

ings, respectively.

A comparison of the loading curves obtained for the HD1 and HB1 bearings shows that the two

bearings possess almost exactly the same vertical stiff.'less characteristics, and as expected, the end-

plate connection detail had no influence on the vertical stiffness. A similar comparison of the LD and

LB curves shows even closer agreement between the vertical stiffness of the two types of unfilled,

low-damping bearings. The results for the low-damping (LD and LB) and high-damping (HD1 and

- 38 -

HB1) bearings do, however, show some differences. The vertical stiffness of the high-damping bear-

ings is clearly nonlinear with respect to vertical displacement, unlike the !ow-da.'Ilping bearings. This

-lS duelO!heracrmannred nmlrrarmbbers pussess greater ~-te!'ldenei:es~mmlle&-

5.3.3 Load Case 3

- 39 -

Cyclic vertical load about initial vertical load with constant horizontal dis-

placement offset ---~~~-~--~-~faa&=- cornpr ise

- 40 -

of the cyclic vertical loading. An interesting result is that the "low"-damping bearings actually exhi-

bited more damping in the vertical direction than did the high-damping bearings. This is in contrast

Witb~the aampmg behaViofsllowney-tile-rwrr

- 41 -

in Section 4.3.1.

A comparison between the behavior of the HB1 bearing subjected to combined loading and to ~----------"Shear-feadfflg-ooly-iY~-i:ty--RgY.--5c34-and-5o:Y5o'fhe-figores present lOO'!irstreru stt ain hysteresis

loops at axial loads of 31.8 kips constant load and 31.8 12.8 kips load, respectively. The

differences between the horizontal response for the two load cases is not significant, and this was

further indicated by analysis of the stiffness and damping parameters for the combined loading hys-

teresis loops. These results are presented in Table 5.9, and a comparison with the results obtained

from the shear-only tests (Tables 5.1-5.4) showed the the effect of simultaneous vertical and hor-izontal loading did not significant! y alter the response of the LSF bearings from that observed for

loading in one direction only.

5.5 Failure Mode Tests

5.5.1 Introduction

Tests were performed on four LSF bearings to investigate different modes of failure of elas-

tomeric bearings. Shear tests on the LD, LB, and HB2 bearings, and a tension test to failure on the

fiD1 bearing were conducted. Results for these tests are presented in the following section.

5.5.2 Shear Failure Tests

(a) LB Bearing

A sequence of large strain tests (Table 4.9, tests 890322.56-890322.61) were performed on the LB bearing. The objective of these tests was to impose lateral displacements on a bolted bearing sufficient to cause failure and to investigate the nature of this failure.

Because of the large displacements required to induce failure strains in the LSF test bearings the

test machine was reconfigured for the series of failure tests to perrnit maximum displacements of

approximately 10 inches by offsetting the horizontal actuator with a spacer-block. !n this

configuration, it was possible to apply only half-cycles of loading to the bearing.

An initial loading cycle to 50% strain was performed to determine the stiffness of the bearing

prior to any degradation. Subsequent tests corresponding to peak shear strains of 200, 225, 225, 328,

- 42 -

and 344% were conducted. A photograph of the LB bearing at approximately 330% shear strain is

shown in Fig. 5.36. The force-displacement plots for the sequence of LB shear failure tests are shown

---,sup1llirnposeU-:iirflg:~5:37:-'fhe-fust-evidenee--crf+.rt!ttre-was-seen-dming~tl!e-~%--,~her~--at ---~

approximately 9.5 inches (320% strain) an obvious change in stiffness occurred. This coincided with clearly visible rupture of the bottom layer of elastomer in the bearing. It is interesting to note that the

subsequent 344% strain test (the most extreme envelope in Fig. 5.37) revealed only a small loss of stiffness beyond about 4 inches of displacemen~ with the bearing still capable of carrying loads in

excess of that at which significant damage to the bearing had first occurred. The bearing continued to

accommodate lateral deformation to approximately 9 inches before total failure occurred. At this stage,

however, the bottom layer of elastomer was almost completely torn through.

An additional feature of these results warr