A test program was developed to investigate the cyclic behavior of elastomeric bearings. ... damping are determined from hysteretic data for the bearings, and used to ... particular reference to scragging, stiffness recovery, age hardening, ...
CYCLIC BEHAVIOR OF HIGH-DAMPING RUBBER BEARINGS Troy A. Morgan1, Andrew S. Whittaker2, and Andrew C. Thompson3
Fifth World Congress on Joints, Bearings and Seismic Systems for Concrete Structures ABSTRACT In the design of bridges supported by isolation systems, it is crucial to evaluate the behavior of the isolator so that a reliable prediction of maximum seismic response can be made. The performance of high-damping rubber (HDR) bearings was investigated with funding from the California Department of Transportation though a series of uni-directional, bi-directional, and earthquake simulation studies for a variety of bearing types. The results of these tests show behavior that is heavily dependent on strain history, path history, age, and strain rate of the isolator. This behavior leads to difficulty in creating robust mathematical models for HDR bearings, which may lead to inaccurate estimations of forces in the super- and sub-structure and displacements in the isolators. Key results from the experimental program are presented. INTRODUCTION Serviceability of transportation systems is of vital importance following major seismic events, and considerable effort has been made to construct systems to mitigate earthquake risk in bridges. One class of these protective systems that has been implemented recently is that of seismic isolation. Isolation of a structure is accomplished through the design of a flexible system between the foundation and the base of the superstructure. The use of seismic isolation lengthens the fundamental period of the structure, decoupling its motion with that of the ground. Methods of isolation include the use of elastomeric bearings, sliding bearings, and hybrid systems to provide the necessary flexibility in the structure. The objectives of the research described in this report are two-fold: (i) to characterize the behavior of high-damping rubber seismic isolation bearings, and (ii) investigate the impact of these characteristics on the response of seismically isolated structures. To investigate the impact of component-level behavioral characteristics on the seismic response of isolated structures, several experimental programs were conducted. The first of these experimental programs was designed to characterize the uni-directional hysteretic behavior of a variety of elastomeric bearings. Of primary importance in these tests was the evaluation of the stiffness and damping properties of each bearing, and the effects of scragging, age hardening, stiffness recovery, strain rate, strain-history, and path-history on the hysteretic behavior of these bearings. Lead-rubber bearings and various highdamping rubber bearings were tested.
1
Structural Designer, Forell/Elsesser Engineers, Inc., San Francisco, CA, USA Associate Professor, Department of Civil, Structural, and Environmental Engineering, State University of New York, Buffalo, NY, USA 3 Engineer, Advanced Technology Group, Ove Arup and Partners, London, UK 2
In addition to these uni-directional bearing tests, the bi-directional behavior of these bearings was also investigated. Of particular interest is the influence of large strain cycles in one direction on the material properties in the orthogonal direction. The bi-directional testing program was also used to develop mathematical models of bearings and to characterize path-history effects. EXPERIMENTAL PROGRAM The testing program included both uni-directional and bi-directional horizontal cyclic testing capabilities. Uni-directional tests were carried out in the Single Bearing Test Machine (SBTM) at the Structural Research Laboratory building at PEER. This test frame is depicted in Figure 1, and is capable of testing a single small-to-moderate scale bearing. This machine can apply displacement or load control to a bearing vertically and horizontally (along one axis). Horizontal Actuator Loading Beam Load Cell Test Bearing Load Cells Stiffened Pedestal
Load Cell
Vertical Actuators
Figure 1 – Schematic of Single Bearing Test Machine
The top of the bearing is bolted to a stiff steel beam, which is controlled by one horizontal actuator, and two vertical actuators. The majority of tests were horizontal cyclic tests, which are described here. The horizontal actuator imposes a lateral displacement on the bearing corresponding to an input signal, while the vertical actuators act under force control, sustaining a prescribed vertical load on the bearing during each test to simulate gravity. The bottom of the bearing is supported by a steel plate, which rests on four load cells. Each load cell is capable of measuring axial force, and two components each of both shear and moment. These load cells are bolted to a rigid steel frame, which is post-tensioned to the laboratory testing floor. The bearing test machine has a peak axial load output of 300 kips while simultaneously imposing displacements of ± 6 inches at a maximum velocity of 25 inches/second. A test program was developed to investigate the cyclic behavior of elastomeric bearings. In each test, the bearing was subjected to an input displacement signal defined by varying levels of shear strain, number of cycles at each shear strain, frequency of the signal, and a constant axial pressure. These tests were developed specifically to investigate the effects of strain history, strain rate, scragging, recovery, and age hardening on effective stiffness and equivalent viscous damping for a variety of elastomeric bearings. New bearings, recently tested bearings, and bearings first tested up to 15 years ago were included in these experiments. The bearings that had been tested prior to this test program were useful for studies on recovery and age hardening. The bearings in this test program also represent a wide variety of manufacturer type, effective modulus, and equivalent damping. All of the bearings tested in this program were reduced scale bearings. The horizontal displacement signals used were harmonic, defined by an amplitude corresponding to shear strain and a forcing frequency. Typical signals involve five cycles at each shear strain, for varying levels of shear strains. The investigation of strain history effects requires a variation in shear-strain sequence.
In characterizing elastomeric bearings, design values for effective stiffness and equivalent viscous damping are determined from hysteretic data for the bearings, and used to approximate maximum earthquake response. This is often undertaken using response-spectrum analysis, where effective stiffness yields an isolated period, which, when combined with a value for percent-critical viscous damping, can be used to determine the maximum displacement. Therefore, calculated quantities for effective stiffness and equivalent viscous damping are necessary in determining design forces and displacements in the structure. For high-damping rubber bearings, these values of stiffness and damping can vary depending upon strainhistory used in the cyclic tests. That is, the stiffness and damping calculated for a bearing which undergoes a displacement sequence of [150%, 100%, 50%, 25%] shear strain may not be equivalent to the same bearing undergoing a displacement sequence of [25%, 50%, 100%, 150%] shear strain. The frequency of the sinusoidal input signal was also varied to examine the importance of strain rate on the peak force output of the bearing. These tests were run with axial pressures corresponding to commonly accepted design values. The bi-directional displacement-controlled testing used an isolated rigid block subjected to specified planar displacement histories. The rigid-block model is supported on four isolators, and rests on the earthquake simulator platform at EERC. A plan and elevation of the rigid block supported by four bearings is shown in Huang et. al [7]. To produce reasonable levels of axial pressure on each bearing, the rigid block supports concrete and lead weights totaling 65 kips, or a vertical load on each bearing of approximately 16.25 kips. Four struts braced the rigid frame against reaction buttresses located around the simulator platform. With the struts fixing the frame to the buttresses, the simulator platform was moved under displacement-control according to specified bi-directional horizontal displacement orbits. Figure 2 shows the model with struts attached.
Figure 2 – Picture of displacement-controlled rigid-block test setup
The displacement orbits (histories) for bi-directional testing were selected to facilitate the development of accurate mathematical models for isolation components, and for the investigation of path-history effects. These displacement histories were simple but had to be capable of illustrating bi-directional interaction effects, if any, present in seismic isolation bearings. The four displacement orbits selected for testing of elastomeric bearings are shown in Figure 3. All four displacement orbits start at the origin. The figure-8 orbit is defined by sine functions in the lateral and longitudinal directions; the frequency in the longitudinal direction is twice that in the lateral direction. Varying levels of maximum displacement (and therefore shear strain in the elastomeric bearings) in the two directions for the four orbits were used to evaluate the path-dependent and strain-dependent behavior present in the bearings. These path- and
strain-history displacement tests were run at a very slow frequency of approximately 0.01 Hz so as not to introduce strain-rate (velocity) effects. To investigate strain-rate (velocity) effects, the figure-8 orbit was run at a frequency of approximately 0.5 Hz, and the data compared with the slow test (0.01 Hz.). In order to eliminate scragging effects of the high-damping rubber isolators, the bearings were first displaced to 250% shear strain in each direction.
ORBIT 1
ORBIT 2
ORBIT 3
ORBIT 4
Figure 3 – Displacement-controlled orbits for bi-directional testing for elastomeric bearings.
RESULTS OF BEARING CHARACTERIZATION A series of uni-directional and bi-directional experiments were developed to investigate the characteristics of high-damping rubber (HDR) bearings. The results of these experiments are discussed below, with particular reference to scragging, stiffness recovery, age hardening, temperature, strain-history, and pathhistory. Such characterization is needed to a) develop robust mathematical models of HDR bearings, and b) understand the behavior of bridges isolated on HDR bearings. Scragging and Recovery Filled elastomers such as those used in high-damping rubber bearings exhibit a phenomenon known as scragging. Scragging represents the change in strength and stiffness from the first half-cycle of loading of a virgin bearing to subsequent cycles of loading. Properties calculated from first half-cycle (or first cycle) data are often termed unscragged or virgin properties, while those calculated from subsequent cycles are termed scragged properties. Scragging is the cyclic reduction of the bulk modulus of elastomers at moderate to high shear strains. Mullins [12] showed that most of this reduction occurred during the first cycle of deformation to a given level of strain, and that subsequent cycling to that strain level produced incrementally smaller reductions in modulus. Such stabilization in the hysteresis can be seen in Figure 4 in fourth and fifth cycles of loading.
10
8 First Cycle 6
4
Force (kips)
2
0
-2
-4
-6
-8
-10 -5
-4
-3
-2
-1
0
1
2
3
4
5
Displacement (inches)
Figure 4 – Force-displacement relation for a high-damping rubber bearing
The percentage reduction in effective modulus with cycling depends on the formulation of the elastomer compound, the vulcanization profile used to fabricate the isolator, and strain history. Filler materials such as carbon black, synthetic elastomers, oils, and resins are routinely added to natural rubber to reduce the modulus and/or increase the damping of the HDR bearing. Mullins observed that the addition of filler materials increased the percentage reduction in effective modulus. To substantiate this observation for modern high-damping elastomers, data from both previously conducted component tests and the this test program were analyzed to provide improved estimates of the likely degree of scragging, and the relationship between the scragging factor, λscrag, defined as the ratio between first and third cycle effective shear modulus, and equivalent viscous damping. Figure 5 presents the relation between the scragging factor and the third-cycle effective shear modulus at 100-percent shear strain for 45 high-damping rubber bearings. Third-cycle effective shear modulus was chosen for the abscissa because it is often used to characterize the stiffness of HDR bearings. The 45 bearings were fabricated by six manufacturers using a total of 12 different compounds. Some of the data points are those of virgin bearings. The damping ratio, βeq, was calculated using the effective shear stiffness at the maximum shear strain as defined in the AASHTO Guide Specification [1]. 2.50
5% < damping < 9% 9% < damping < 13%
Scragging factor
2.00
13% < damping < 17%
1.50
1.00
0.50 0
50
100
150
200
250
300
350
400
Third-cycle effective modulus at 100% shear strain (psi)
Figure 5 – Values of the scragging factor for high-damping elastomeric bearings
Production seismic isolators are often scragged as part of the manufacturer’s quality control practices. Such scragging always involves unidirectional shearing of the isolator to a strain level that is typically less than the maximum design strain. Two questions arise from this practice. First, does scragging along one axis scrag the bearing along all axes? Second, are the virgin (pre-scragged) properties recovered over time? Bi-directional tests of two types of seismic isolation bearings were conducted to study the effect of scragging along orthogonal axes. This test involved one fully reversed cycle to 250-percent shear strain followed by one fully reversed cycle to 250-percent shear strain in the orthogonal direction. The results of these tests indicate that scragging along one axis significantly influences response on the perpendicular axis. Data from the cruciform-orbit tests of another low-modulus, high-damping elastomeric bearing from a different manufacturer support this observation, but the degree of interaction appears to be compound-dependent. If the effective modulus of an elastomer recovers with time following repeated cycling, design of a seismic isolation system incorporating such elastomers should explicitly account for unscragged properties and the consequent increase in the force output of the isolators if displacements are preserved. Mullins observed that rubber, which showed softening over numerous cycles of stretching exhibited recovery toward its initial stress-strain properties over time. He also observed that stiffness recovery was accelerated and more complete at higher temperatures. Kulak et. al. [10] reported recovery data from large strain tests of high-modulus, high-damping elastomers and concluded that elastomers do recover stiffness, and that scragging of a bearing before installation is not important. Data from the Berkeley test program and elsewhere [6] support this observation although the degree and rate of recovery appear to vary as a function of elastomer compound, manufacturing process, and frequency of testing (an increase in strain rate will raise the temperature and accelerate recovery.) Data from tests of four high-damping elastomeric bearings were analyzed (one high-modulus and two low-modulus compounds). For one highmodulus and one low-modulus compound, 100-percent recovery was observed in a five-year period; more than 65 percent of the recovery in the low-modulus compound was observed in the first 12-month period. For the remaining low-modulus compound, 60-percent recovery was observed in one month. None of these bearings were axially loaded between tests. Age Hardening Long term changes in the mechanical properties of elastomer compounds can result from hardening due to continued vulcanization of the elastomer and degradation of the elastomer due to exposure to oxygen and ozone. Protection against ozone and oxygen degradation can be achieved by including various waxes and chemical anti-oxidants in the rubber matrix [15]. Although bulk components are generally not significantly affected by such degradation, elastomeric bearings are normally fabricated with a layer of cover rubber that includes these anti-oxidants to protect the core of the bearing from significant infiltration by oxygen and ozone. Age hardening due to continued vulcanization of the elastomer can lead to an increase over time in effective shear modulus. The percentage increase in effective modulus will vary depending on a number of factors including completeness of the initial vulcanization and temperature [16]. In this study, uni-directional cyclic tests were run on a variety of bearings that were previously tested at Berkeley. Each of these bearings was cycled using identical strain histories to those used previously so that changes in effective modulus could be detected independent of strain-history effects (described below). These bearings were first tested in late 1994 and early 1995 by Clark, Aiken and Kelly [2], and re-tested in June 1999 by the authors, using the same test protocol as that used previously. Effective moduli for each of these tests at various strain levels are shown below. The moduli are reported for thirdcycle data and therefore do not include scragging or recovery effects.
It appears that HDR compounds do experience increases in effective stiffness over time. This increase appears to be uniform across all levels of shear strain. Percent increase in effective shear modulus ranges from 10% to 32%, but does not show a strong dependence on the level of shear strain. This increase in stiffness, while quantifiable for 5-year aging studies, cannot be linearly extrapolated to estimate increases in stiffness over longer periods of time. This is due in part to the nature of age hardening in filled elastomers, whereby the continued vulcanization of the rubber matrix occurs more rapidly in the first few years after the rubber is compounded, but slows over time. For this reason, the effective modulus is expected to reach a limiting value, which can only be evaluated by longer-term aging studies. Strain Rate Prototype tests of elastomer bearings for bridges and buildings are typically undertaken at pseudo-static rates because of test machine limitations. Manufacturers often supplement prototype test data with data from dynamic tests of moderate-scale bearings to increase the rated damping of prototype bearings. Although the increase in damping is considered beneficial, the corresponding increase in effective modulus is typically considered detrimental, especially for low-modulus compounds. Figure 6 illustrates the effect of strain rate on effective modulus and damping ratio for five high-damping elastomer compounds supplied by four manufacturers. Values for effective modulus and damping ratio were calculated using the procedures set forth in the AASHTO Guide Specification [1] using response data from maximum shear strain cycles that ranged in amplitude from 150 to 250 percent. The velocity factors were calculated as the ratio of effective modulus (damping ratio) at high and low strain rates. Because some of the experimental data presented in Figure 6 were prepared for other test programs, the high and low strain rates are not unique. However, the low velocity (strain rate) tests were conducted at frequencies between 0.01 Hz and 0.1 Hz, where rate effects are not expected to be significant, and the high velocity tests were conducted at realistic frequencies for the similitude scale of the tested isolator. The increase in damping and effective stiffness ranged between 10% and 28%, and 7% and 19%, respectively. 1.40
1.35
Damping ratio
1.30
Velocity (strain rate) factor
Effective Stiffness 1.25
1.20
1.15
1.10
1.05
1.00 0.0
50.0
100.0
150.0
200.0
250.0
Third cycle effective modulus at 100% shear strain (psi)
Figure 6 – Effect of strain rate on response of high-damping rubber bearings
Strain History Cyclic unidirectional tests at different levels of shear strain are typically used to characterize the hysteretic response of elastomeric bearings. Data from these tests such as effective stiffness, equivalent viscous damping, zero-displacement force intercept, and second-slope stiffness are used for several purposes. First, the data are used to construct mathematical models of seismic isolation bearings. Second, the data are used to judge whether prototype bearings meet the requirements of a project-specific specification for the supply of seismic isolation bearings. Ideally the response of elastomeric bearings would be independent of strain history, that is, values of the descriptors listed in the previous paragraph at a given level of shear strain would be not be dependent on the loading or strain-history protocol. Property dependence on strain history would make development of robust mathematical models and evaluation of prototype test data most difficult. The study of strain-history response of high-damping elastomeric bearings was undertaken by comparing the hysteretic response of three bearings using different loading protocols. The three bearings tested were a low-modulus Bridgestone bearing, a high-modulus Bridgestone bearing, and a low-modulus Rubber Consultants bearing. Figure 7 presents sample data from 100-percent shear strain. Third-cycle data are presented to substantially eliminate scragging effects from the data sets. In Figure 7, two hysteresis loops are shown: one with increasing levels of shear strain starting at strain levels of 5 or 10 percent, the other with decreasing levels of shear strain starting at a shear strain of 250 percent. The data in each figure were generated using the same axial (face) pressure and the two test sequences were executed one after the other. The data of Figure 8 show significant differences in response indicating substantial strain-history effects. 4 5%, 25%, 50%, 75%, 100% 3
250%, 150%, 100%, 50%, 25% 2
Shear (kips)
1
0
-1
-2
-3
-4 -2
-1.5
-1
-0.5 0 0.5 Displacement (inches)
1
1.5
2
Figure 7 – Third cycle hysteresis loops at 100% shear strain for a high-modulus HDR bearing tested with different strain histories
The strain histories for three bearings tested demonstrate appreciable differences between the effective moduli are evident at all levels of shear strain for each bearing. Differences of 60% to 70% in effective modulus at were observed at all levels of shear strain due to differences in load history. Calculated values of Energy Dissipated per Cycle do not appear to be very sensitive to strain history, but appreciable differences in effective stiffness demonstrate variability in calculated equivalent viscous damping at all levels of shear strain for each bearing.
CONCLUSIONS The behavior of high-damping rubber bearings is significantly different from that of isotropic elasto-plastic systems. Numerous models have been proposed for HDR bearings, none of which fully capture the complicated behavior of these elastomeric compounds. In the design of isolated structures using HDR bearings, it is unconservative to use simple models for behavior that ignore the effects identified in this report. The key conclusions of this study are: 1. The scragging factors listed in the AASHTO Guide specifications for high-damping rubber bearings should be increased to 2.0 for low-modulus bearings and 1.5 for high-modulus bearings. 2. For the purpose of design of a HDR seismic isolation system, full recovery of virgin (unscragged) properties of the isolators must be assumed in the absence of independently generated test data. 3. Rate or velocity effects can substantially increase the stiffness and damping of HDR bearings. Both increases should be included in the calculation of design displacements and design forces in isolated structures. 4. HDR bearings exhibit substantial strain-history effects. Such effects make the development of robust mathematical models most difficult and lead to erroneous estimates of design forces and displacements. More work is needed to characterize such effects. Engineers should consider such effects carefully when choosing values of effective stiffness and damping for design. ACKNOWLEDGEMENTS The research presented in this report was funded by the California Department of Transportation under Contract 59A169. The support of Dorie Mellon and Li-Hong Sheng of Caltrans is appreciated. Thanks are due to Prof. Stephen Mahin and Prof. Gregory Fenves for their input throughout the project, and graduate students Wei-Hsi Huang and Gilbert Mosqueda for contributing extensively to the studies described here. The invaluable assistance of the EERC laboratory staff is also greatly appreciated. REFERENCES [1] [2]
[3]
AASHTO. 1999. Guide Specifications for Seismic Isolation Design. Washington D.C.: American Association of State Highway and Transportation Officials (AASHTO) Clark, P.W., Aiken, I.D., and J.M. Kelly. 1995. Testing of Reduced-Scale Seismic Isolation Bearings for the Advanced Liquid Metal Reactor. Report to Westinghouse Hanford Corporation. Berkeley, Calif.: Earthquake Engineering Research Center, University of California. Clark, P.W., I. D. Aiken, and J. M. Kelly. 1997. Experimental Studies of the Ultimate Behavior of Seismically Isolated Structures, Report UCB/EERC-97/18. Berkeley, Calif.: Earthquake Engineering Research Center, University of California.
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