thermal-mechanical coupled behavior of elasto- …
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THERMAL-MECHANICAL COUPLED BEHAVIOR OF ELASTO-MERIC ISOLATION BEARINGS UNDER CYCLIC LOADINGS
Masaru KIKUCHI1 and Ken ISHII2
ABSTRACT In this paper, the authors focus on the thermal-mechanical coupled behavior of elastomeric isolation bearings under cyclic loading. In Japan, long-period and long-duration ground motions have been a great concern since the 2011 Tohoku Earthquake. Such motions induce excessive and numerous cyclic deformations in elastomeric isolation bearings. Elastomeric isolation bearings with hysteretic damping absorb seismic input energy and convert it into heat energy. Therefore, a large number of cyclic deformations might cause the performance of the bearings to deteriorate due to internal heat generation. Because of this, the authors have developed a numerical analysis model considering the thermal-mechanical coupled behavior of elastomeric isolation bearings with hysteretic damping. An analysis model is constructed by combining a seismic response analysis and thermal conductivity analysis. Three types of elastomeric isolation bearings are examined: high-damping rubber, lead-rubber, and tin-rubber bearings. First, the developed model is briefly presented. The model is customized according the mechanical properties of each type of bearing. Second, the model is verified by simulating cyclic loading tests of these bearings. Finally, seismic response analyses using the model are conducted to evaluate the dynamic behavior of a seismically isolated building. The authors conclude that characteristic change due to cyclic deformation of the bearings should be considered in order to accurately predict the response of a seismically isolated building under long-period and long-duration ground motions. Keywords: seismic isolation; elastomeric isolation bearing; cyclic loading; thermal conductivity analysis; seismic response analysis 1. INTRODUCTION Seismic isolation is the most effective technology for protecting structures from being damaged by earthquakes. This protection is achieved by introducing a type of flexible support, usually at the foundation level, that moves the period of the structure away from the predominant period of the ground motions (Naeim et al. 1999). Therefore, seismically isolated buildings can be understood as long-period structures. The most commonly used type of seismic isolation device is now elastomeric isolation bearings in Japan. Some types of the bearings have hysteretic damping performance inside of them, thus eliminate the need for separate dampers. Long-period and long-duration ground motions have been a great concern in Japan since the 2011 Tohoku Earthquake, when ground motions lasting more than 5 minutes were observed across a wide area of Japan. Previous research has predicted that very large subduction earthquakes in the Nankai and Tokai regions of Japan will produce similar long-duration, strong ground shaking with long-period characteristics, so the possible impacts of these events have become a major concern in the Japanese earthquake engineering community. Such ground motions might induce excessive and numerous cyclic deformations in elastomeric isolation bearings. In particular, a large number of cyclic deformations will cause the performance of seismic isolation devices to deteriorate due to fatigue or internal heat generation (Kalpakidis et al. 2009a and 2009b, Kochiyama et al. 2009). Since April 2017, the Japanese Ministry of Land, Infrastructure, Transport and Tourism (MLIT) has obliged structural
1Professor, Faculty of Eng., Hokkaido Univ., Sapporo, Japan, [email protected] 2Research Fellow, Faculty of Eng., Hokkaido Univ., Sapporo, Japan, [email protected]
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engineers to consider how the long-period earthquake ground motion caused by an earthquake in the Nankai Trough would impact the design of a seismically isolated building constructed in that area. To contribute to strengthening seismically isolated buildings against earthquakes, this research is focused on the thermal-mechanical coupled behavior of elastomeric isolation bearings under cyclic loading. Elastomeric isolation bearings with hysteretic damping absorb seismic input energy and convert it into heat energy. However, this heat generation degrades the damping performance of the bearings. Thus, this degradation needs to be suppressed to improve the performance of the bearings under a large number of cyclic loadings induced by a long-duration earthquake. A theory for predicting the temperature of lead plugs and strength reduction was proposed (Kalpakidis et al. 2009a and 2009b). The theory was verified by comparing its results with experimental results. The theory was based on a simplified assumption of the heat conduction in a round cross-section lead-rubber bearing. It is useful in predicting the cyclic behavior of lead-rubber bearings. Recently, the authors also developed a numerical analysis model that considers the thermal-mechanical coupled behavior of elastomeric isolation bearings with hysteretic damping. The model is applicable to various types of elastomeric isolation bearings. It is also applicable to square cross-section lead-rubber bearings equipped with multiple lead plugs. The model was constructed by combining a seismic response analysis and thermal conductivity analysis. The seismic response analysis uses nonlinear hysteresis models specialized for elastomeric isolation bearings. The thermal conductivity analysis employs a finite volume method. Both the thermal and mechanical procedures are performed interactively by updating their parameters at each time step increment. The model presented here was implemented in the OpenSees program (McKenna et al. 2006). In this paper, three types of elastomeric isolation bearings are examined: high-damping rubber bearings (HDRBs), lead-rubber bearings (LRBs), and tin-rubber bearings (SnRBs). These are the major types of seismic isolation devices used in Japan. 2. NUMERICAL ANALYSIS MODEL FOR THERMAL-MECHANICAL COUPLED
BEHAVIOR 2.1 Analysis Flow As mentioned, the numerical analysis model consists of a thermal conductivity analysis and seismic response analysis. Both analyses are performed interactively by updating their parameters at each time step increment. Figure 1 shows a flowchart of the thermal-mechanical coupled analysis.
Figure 1. Flowchart of thermal-mechanical coupled analysis
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First, the mechanical properties of the bearing are updated by using the temperature obtained at the previous analysis step. Then, seismic response analysis is conducted at a certain time step by using the updated mechanical properties of the bearing. Accordingly, an energy increment absorbed by an elastomeric isolation bearing, E, is calculated at the end of the time increment in the seismic response analysis. Seismic response analysis employs the Newmark-beta method as a time integration method (Newmark, 1959). Next, E is distributed to heat generation parts in an elastomeric isolation bearing, and thermal conductivity analysis is conducted. For numerical analysis stability, a time increment for the thermal conductivity analysis is preferably divided into from one fifth to one tenth of the time increment for seismic response analysis. Accordingly, the temperature of the heat generation parts for the next analysis step is obtained. This procedure is repeated by the end of the input ground motion. 2.1 Seismic Response Analysis The latest nonlinear hysteresis models optimized according to the type of elastomeric isolation bearing are used in the seismic response analysis for seismically isolated buildings. The deformation-history integral model for the HDRB (Kato et al. 2015), Kikuchi-Aiken model for the LRB (Kikuchi et al. 1997 and 2010), and bilinear model for the SnRB are employed. The authors made some modifications to these models so that the change in mechanical properties due to temperature rise could be considered. As shown in Figure 2, these hysteresis models are used to evaluate the restoring force of elastomeric isolation bearings by combining elastic and hysteretic components separately. The influence of temperature on the restoring force, F, is expressed using Equation 1. F = ce(T) Fe + ch(T) Fh (1) where Fe and Fh are the elastic and hysteretic components of the restoring force at standard temperature (usually at 20°C), respectively, and ce and ch are the coefficients for each restoring force component at temperature T (°C) in the elastomeric isolation bearing.
Figure 2. Concept of hysteresis models for elastomeric isolation bearings ce and ch were identified in the preliminary experimental and analytical studies as follows. HDRB: ce(T) =0.6359 + (10.6359) exp(− (T−20) ∕ 32.16)) (2) ch(T) =0.5892 + (10.5892) exp(− (T−20) ∕ 30.99)) (3) LRB: ce(T) =1.0 (4) ch(T) =1.0 − ∕ ∕ (5)
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SnRB: ce(T) =1.0 (6) ch(T) =1.0−0.00872T+0.0000278T 2 (T ≤100 °C), 0.724−0.00315 T (T >100 °C) (7) 2.3 Thermal Conductivity Analysis A finite volume method is used for the thermal conductivity analysis. Figure 3 shows axisymmetric two-dimensional models for typical cylindrical round cross-section elastomeric isolation bearings. In consideration of symmetry in the height direction, only the upper half of the bearings is modeled. The rubber part and inner steel plate part are modeled by separate cells. Heat is generated in the entire rubber part in the HDRB. Therefore, the effect of radiation at the surface of cover rubber is considered for the HDRB. As for the LRB and the SnRB, heat is generated only in the lead or tin plug inserted in the center of the bearing. The effect of radiation can be neglected for the LRB and SnRB. The material constants used for this analysis are summarized in Table 1. In addition, a square-section LRB equipped with multiple lead plugs will be examined to eliminate the degrading of the damping performance of LRB in Chapter 4. The two-dimensional model is not applicable to the square LRB due to its geometrical shape. The modeling method for the square LRB will be also described later. (a) HDRB (b) LRB and SnRB
Figure 3. Axisymmetric models for thermal conductivity analysis
Table 1. Material constants for thermal conductivity analysis
(a) HDRB Material Thermal conductivity
[W/(m･K)] Density [g/cm3]
Specific heat capacity [J/(g･K)]
High-damping rubber 0.310 1.15 1.45
Cover rubber 0.289 1.15 1.88
Steel 59 7.86 0.473
(a) LRB and SnRB
Material Thermal conductivity [W/(m･K)]
Density [g/cm3]
Specific heat capacity [J/(g･K)]
Lead 35.2 11.33 0.130
Tin 64 7.30 0.230
Rubber 0.13 1.04 1.90
Steel 59 7.86 0.473
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3. SIMULATION ANALYSES OF INDIVIDUAL BEARING CYCLIC LOADING TESTS Simulation analyses of individual bearing loading tests were conducted to verify the numerical analysis method described in Chapter 2. Experimental results were obtained from the tests conducted by using the test facilities owned by the manufacturers. Note that the test program and conditions for these three types of elastomeric isolation bearings were not the same. Therefore, the performances obtained from these tests should not be compared with each other. 3.1 High-Damping Rubber Bearing (HDRB) A low-shear modulus 225-mm-diameter scaled HDRB was tested. The compound of this HDRB is called “X0.4S” by the manufacturer. A sinusoidal cyclic horizontal loading test was carried out under the condition of a constant vertical pressure of 11 MPa, loading frequency of 0.33 Hz, and shear strain amplitude of 200 percent. Figure 4 shows the experimental and analytical results. Deterioration of the shear force in the hysteresis loops was observed. The temperature at the side surface of the bearing rose from 18 °C to 40 °C during 75 cyclic loadings. The analysis results showed good agreement with the experimental test results. The degradation of the shear force and the change in temperature were predicted well by the analysis.
Figure 4. Experimental and analytical results of HDRB
3.2 Lead-Rubber Bearing (LRB) A 500-mm-diameter LRB was tested (Wake et al. 2017). Assuming that the LRB was installed in a concrete structure, 12.7-mm-thick heat insulators were installed on the outer ends of the top and bottom flange plates. A sinusoidal cyclic horizontal loading test was carried out under the condition of a constant vertical pressure of 2.5 MPa, loading frequency of 0.25 Hz, and shear strain amplitude of 200 percent. The number of horizontal loading cycles was 35. The vertical pressure was less than the design pressure of 15 MPa due to the performance of the test facilities. Thermocouple sensors were inserted into the lead plug and laminated rubber part. Figure 5 shows the experimental and analytical results. The temperature at the center of the lead plug reached 223 °C at the end of the 35 cyclic loadings. However, the temperature at the laminated rubber part did not rise. This fact shows that the generated heat did not easily diffuse from the lead plug to the outer laminated rubber part within the duration time of the earthquake. The analysis results showed good agreement with the experimental test results. The analysis predicted the degradation of the shear force in the hysteresis loops well. The change in measured temperatures at the lead plug and laminated
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Figure 5. Experimental and analytical results of LRB
3.3 Tin-Rubber Bearing (SnRB) A 700-mm-diameter SnRB was tested. A sinusoidal cyclic horizontal loading test was carried out under the condition of a constant vertical pressure of 15 MPa, loading frequency of 0.2 Hz, and shear strain amplitude of 100 percent. The number of horizontal loading cycles was 100. A thermocouple sensor was inserted into the top of the tin plug. Figure 6 shows the experimental and analytical results of the tests. The time histories of temperature are shown for 600 seconds, although the duration time of the cyclic loadings was 500 seconds. The temperature at the top of the tin plug rose up to 90 °C by the end of the 100 cyclic loadings and thereafter decreased shortly. Deterioration of the shear force due to cyclic loading was seen. The numerical model accurately reproduced the experimental results of the force-displacement relationship and change in temperature of the tin plug.
Figure 6. Experimental and analytical results of SnRB
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4. SEISMIC RESPONSE ANALYSES OF ISOLATED BUILDING A series of seismic response analyses using the proposed numerical models was conducted to investigate the influence of long-period, long-duration earthquakes on the dynamic response of seismically isolated buildings. The analyses involved comparing the response values obtained when the degradation of the yielding force of the elastomeric isolation bearings due to heat generation was and was not taken into consideration. 4.1 Building Model A 15-story reinforced concrete building model was used for the seismic response analyses. The model was characterized as a typical seismically isolated condominium designed after the 1995 Kobe earthquake in Japan (Architectural Institute of Japan, 2016). The superstructure consisted of six bays by one bay in the plan, with each bay measuring 6.5 m by 12.0 m. One isolation bearing was placed at each section of the bays for a total of 14 seismic isolation bearings. The structure was modeled as a 16-node MDOF system, as shown in Figure 7. The analysis dealt with only the X-direction of the building. The total mass of the superstructure was 11,443 tons. The superstructure was assumed to be elastic. The fundamental period was 1.23 seconds when the base of the superstructure was fixed. A damping ratio of 3% was defined for the fundamental period of the fixed-base structure.
Figure 7. Building model 4.2 Seismic Isolation Bearing Model Figure 8 shows the elastomeric isolation bearings used for the seismic response analysis. Three types of cylindrical round cross-section elastomeric isolation bearings discussed in the previous chapter, the HDRBs, LRBs, and SnRBs, were considered. The diameters of these bearings range from 1000 mm to 1200 mm. These diameters were determined from the compressive stresses recommended by their manufacturer. In addition, square cross-section LRBs equipped with multiple lead plugs were examined to see if they improved the ability to eliminate the effect of heat generation on the mechanical properties. They provided another advantage, that is, a compact design with a smaller footprint that was one size smaller as compared with the circular type of the same specifications. The size of the cross section of the square LRBs was 1000 mm by 1000 mm. The number of lead plugs was four. The diameter of the plugs was determined to be 110 mm so that the total cross-section area of the plugs was the same as that of a single-plug LRB. The authors focused on the advantage of using multiple lead plugs to improve the heat diffusion over a single lead plug. In total, four types of elastomeric isolation bearings were examined in the seismic response analyses. The configurations of these bearings are summarized as the four cases in Figure 8. Note that the three-dimensional thermal conductivity analysis model was necessary only for the square cross-section LRBs with multiple lead
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plugs in Case 4. In consideration of the symmetry of the geometrical shape, 1/8 of the square LRB was modeled as shown in Figure 8.
Figure 8. Elastomeric isolation bearings used for seismic response analyses 4.3 Ground Motions The ground motions used in the seismic response analyses were provided by MLIT in Japan. The motions had been developed for the purpose of reviewing the design of long period structures such as high-rise buildings or seismically isolated buildings against a Nankai Trough mega earthquake (Building Research Institute, Japan, 2017). These ground motions are called “Kiseisoku-ha” in Japanese. Two of them were selected for the seismic response analyses, as shown in Figure 9. “CH1” is the ground motion for the design of the buildings in the Chukyo area, and OS1 is for the Osaka area. The duration time of both ground motions exceeded 500 seconds, although the peak accelerations were not very large. Figure 10 shows the pseudo velocity response spectra of a 5% damped system. Both ground motions had flat spectral characteristics in the long-period region.
Figure 9. Acceleration time history of input ground motions
Figure 10. Response spectra of input ground motions
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4.4 Analysis Results The distributions of the maximum response accelerations and displacements along the height of the structure, force-deformation relationship, and time history of the temperature of the isolation bearings are shown in Figures 11-14. The response values of the isolated buildings equipped with HDRBs when considering heat generation and when not were almost similar. This fact shows that the HDRBs were least influenced by temperature. The temperature of the rubber rose only 5 °C. Since the HDRB generates heat throughout the entirety of the rubber, the temperature does not easily rise in the bearing. In contrast, the behaviors of the SnRBs shown in Figure 12 and the single plug LRBs shown in Figure
Figure 11. Seismic response analysis results of HDRBs (Case 1)
Figure 12. Seismic response analysis results of SnRBs (Case 2)
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13 were considerably influenced by the temperature changing. The response displacements at the isolation story of the isolated building equipped with the single plug LRBs had more than twice the difference due to whether heat was considered or not. Significant degradation can be seen in the hysteresis loops of the SnRBs under the earthquake ground motion of CH1. The temperature of the tin plug rose to near the melting point of tin (232 °C). The temperature of the single-typed lead plug also rose (328 °C) under the earthquake ground motion of CH1. These facts suggest that the heat generated in the plugs accumulated around the plugs and that it was difficult for it to diffuse outside in the plug-inserted type elastomeric isolation bearings such as the LRBs and SnRBs.
Figure 13. Seismic response analysis results of LRBs equipped with single plug (Case 3)
Figure 14. Seismic response analysis results of square LRBs equipped with multiple plugs (Case 4)
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The improvement from using multiple plugs can be clearly seen in the comparison of Cases 3 and 4. The peak temperature of the lead plug of Case 4 was less than 200 °C. The maximum displacement at the isolation story significantly decreased from 68 cm in Case 3 to 52 cm in Case 4. The seismic response analyses conducted in this paper show that high-damping rubber bearings or elastomeric isolation bearings equipped with multiple plugs are possible solutions to eliminate the deterioration in shear force in isolation devices due to long-duration earthquake ground motions. 5. CONCLUSION The probability of very large subduction earthquakes in the Nankai regions of Japan has become one of the major concerns in the Japanese earthquake engineering community. Previous research has predicted that these events will produce long-duration, strong ground shaking with long-period characteristics. Thus, this research was focused on the thermal-mechanical coupled behavior of elastomeric isolation bearings under cyclic loading in seismically isolated buildings. The bearings with hysteretic damping absorb seismic input energy and convert it into heat energy. The heat generation possibly degrades the damping performance of the bearings when they suffer from a large number of cyclic loadings induced by a long-duration earthquake. This degradation needs to be suppressed to improve the performance of the bearings. In this paper, the authors presented a numerical analysis model considering the thermal-mechanical coupled behavior of the bearings with hysteretic damping. The model was constructed by combining a thermal conductivity analysis and seismic response analysis. Three types of bearings were examined: high-damping rubber, lead-rubber, and tin-rubber bearings. Furthermore, two types of structures for the lead-rubber bearing equipped with a single lead plug and multiple lead plugs were examined. These seismic isolation bearings have been the major types of seismic isolation devices used in Japan. The validity of the proposed model was demonstrated with analyses of the loading tests of these bearings. The model captured the mechanical behaviors of these bearings under a large number of cycling loadings well. Seismic response analyses of an isolated building under long-duration earthquake ground motions were conducted. The response analysis results showed that the heat generation in the lead-rubber and tin-rubber bearings significantly affected the dynamic behavior of the seismically isolated building. It turned out that the diffusion of heat was important to suppress the performance deterioration due to heat generation. The high-damping rubber bearings and lead-rubber bearings with multiple plugs improved the ability to eliminate the effect of heat generation on the mechanical properties. Both types of bearings have a structure that diffuses generated heat effectively. The authors conclude that characteristic change due to the cyclic deformation of elastomeric isolation bearings should be considered in order to accurately predict the behavior of an isolated building under long-period, long-duration ground motions. The model presented in the paper was implemented in the OpenSees program. It can be an effective numerical tool for the design of seismically isolated structures. 6. ACKNOWLEDGMENTS In this research, the work for the lead-rubber bearings was supported by the Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (A), 15H02274, 2017, and the work for the tin-rubber bearings was supported by the Collaborative Research Project of Materials and Structures Laboratory, Tokyo Institute of Technology. The test data for the high-damping rubber bearings were provided by the Bridgestone Corporation, Japan. The test data for the lead-rubber bearings were provided by the Oiles Corporation, Japan. The test data for the tin-rubber bearings were provided by the Aseismic Devices Co., Ltd., Showa Cable System Co., Ltd., and Sumitomo Metal Mining Siporex Co., Ltd., Japan. Assistance in the numerical analyses was provided by Mr. Yohei Kuroshima, Mr. Masamori Kato, and Ms. Shiori Honda at Hokkaido University, Japan. The authors would like to express their thanks for all of the financial support, contributions, and assistance.
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