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Mechanical models for shear behavior in high damping rubber bearings
Abstract and Figures
High damping rubber bearings have been in use for seismic isolation of buildings worldwide for almost
30 years now. In the present work, a brief introduction to the process leading to their manufacturing is
first given. Next, a series of novel 1D mechanical models for high damping rubber bearings is proposed,
based on the combination of simple and well-known rheological models. These models are calibrated
against a set of harmonic tests at strain amplitudes up to 200%. Extension of the models to bidirectional
horizontal motion and to time-varying vertical loads is the subject of ongoing work
Figures - uploaded by George D. Manolis
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... The hysteretic curve gradually changes from a spindle shape to an S shape, and the energy dissipation capacity increases approximately linearly [15,16]. Markou A. A. et al. [17] conducted shear-strain and frequency correlation tests on HDR bearings with constant compressive stress and shear strains of 120% and 200%, respectively, across frequencies ranging from 0.006 Hz to 0.83 Hz. They indicated that the mechanical properties of HDR bearings may have little relation to frequency. ...
... The test cases were designed to include combinations of different temperatures and compressive stresses. Since the study found that shear frequency has a minor effect on the mechanical properties of HDR, similar to the conclusions of Markou A. A. et al. [17], shear frequency was not considered a factor in this research. A loading frequency of 0.4 Hz was used for all cases. ...
With advancements in seismic isolation and damping technology, high-damping rubber (HDR) bearings are now widely used. However, significant gaps remain in HDR-analysis model research, with few studies integrating multiple factors, the Mullins effect, and stiffness hardening for more accurate practical predictions. This study classifies the effective behavior of HDR and examines the stress–strain relationships of different behavioral types using more appropriate equations. Mathematical models were established based on pseudo-elasticity theory, which is an extension of continuum mechanics. Subsequently, parameter functions were developed through parameter determination tests and regression analysis, leading to the completion of the pseudo-elastic model for HDR. Finally, the model’s effectiveness was validated through validation tests. This study finds that behavior classification effectively examines phenomenological-based HDR stress–strain relationships, as distinct behavioral patterns are not adequately captured by a single approach. Incorporating tests to functionalize material parameters complements theoretical models. Additionally, accurately explaining HDR behavior requires considering the Mullins effect and stiffness hardening, influenced by the coupled effects of temperature, strain amplitude, and compressive stress. Consequently, this HDR pseudo-elastic model offers a comprehensive explanation of HDR behavior, including the Mullins effect and stiffness hardening, under various influencing factors based on clear mechanical principles and explicit computational procedures.
... Natural rubber pads absorbed impact in a Melbourne rail bridge in 1889. Eugene Freyssinet's 1954 patent paved the way for widely used multilayer rubber bearings in earthquake-resistant designs [12]. In 1981, Robinson integrated lead cores into rubber bearings, resulting in the creation of Lead Rubber Bearings (LRBs), aimed at improving energy dissipation [13]. ...
... They also exhibit low shear stiffness but with suitable damping capability at the design displacement level. As displacement amplitudes intensified, HDRBs show a notable increase in stiffness and damping, which is beneficial in restraining movements during major ground motions [12]. When modeling HDRB behavior in seismic isolation systems, it is essential to consider various factors. ...
Civil engineering structures are susceptible to natural calamities such as earthquakes, floods, and strong winds. Base isolation is a proven method for protecting structures during earthquakes. It involves inserting a flexible layer between the foundation and superstructure to isolate the structure from earthquakes, thereby changing the system's dynamic characteristics. The present study compares the dynamic performance of passive base isolators, specifically High Damping Rubber Bearings (HDRBs) and Lead Rubber Bearings (LRBs), under near-fault ground motion conditions to assess their effectiveness in reducing seismic impact on structures. The isolator is first analyzed using a static general approach and validated against existing literature before undergoing dynamic analysis. In this research, the LRB isolation system is analyzed using a dynamic explicit approach in ABAQUS, while the HDRB is analyzed using a dynamic implicit approach. The behavior of these isolators is studied under seismic events such as those from the Imperial Valley, Managua, Loma Prieta, Northridge, and Kocaeli ground motions. The results indicate that LRBs significantly reduce acceleration at the top of the bearing compared to HDRBs. The maximum reductions in response are 68.42% for the Kocaeli earthquake in case of LRBs and 61.80% for the Northridge earthquake in case of HDRBs. The LRB shows a minimum acceleration response reduction of 57.24%, while for HDRB, it is 24.47% for the Imperial Valley records in both cases.
... Hysteresis curves of the lead rubber bearings. (a) At different frequencies and shear strain amplitudes.43 (b) At different temperature.44 ...
Seismic isolation technology has become a crucial element in enhancing the resilience of engineering structures against earthquake-induced forces. This paper provides a comprehensive review of current advancements in seismic isolation technologies, focusing on key categories: rubber isolation, friction isolation, rolling isolation, intelligent isolation, composite isolation, and other types of isolators. Each type is examined in detail, covering materials, device configurations, and structural performance under seismic loads. For example, Beijing Daxing International Airport, the world’s largest single isolated building, uses 1 152 bearings and 160 dampers to enhance seismic resilience. Bridges, such as the Benicia–Martinez Bridge in California, have adopted friction pendulum bearings to improve seismic performance while reducing construction costs. These case studies highlight the practical impact and effectiveness of seismic isolation across diverse engineering structures. The paper also delves into intelligent isolation systems, which incorporate adaptive control strategies to enhance seismic performance, and three-dimensional isolation systems, designed to address both horizontal and vertical seismic forces. The review concludes by discussing the challenges and future directions in the field, such as expanding 3D isolation applications. This review offers valuable insights into the evolution of seismic isolation technologies, advancing the current state of knowledge by providing a critical analysis of their performance, challenges, and future trends, ultimately guiding researchers and engineers toward more resilient structural solutions.
... High Damping Rubber Bearings (HDRB) are the most adopted isolators for construction and retrofitting of crucial infrastructure such as hospitals, bridges, and emergency centers 12 where serviceability of structure during and after a seismic event is essential. The HDRB's are made from elastomeric layers and the steel shims, placed in alternate layers similar kind to NRBs [111,112]. In contrast to LCRB's, the HDRB bearings are more viable in structures with special requirements as they retain grater stiffness before yielding and show better breaking effect when subjected to wind load [113]. ...
In recent decades, the construction of high-rise buildings has accelerated in modern urban areas as a response to the world's expanding population and demand for efficient space utilization. These high- rise buildings are inherently more susceptible to hazards such as strong winds, earthquakes, and human activities, which could jeopardize structural stability. However, when this rapid growth in high-rise construction continues in earthquake-prone regions it highlights the need for cautious design and oversight measures to guarantee the comfort of occupants and overall safety of buildings. So, the necessity to adopt vibration control strategies in structural engineering is therefore becoming more and more clear. As technology is advancing, several control strategies were created and implemented for high-rise buildings around the world. This review article provides a comprehensive overview of base-isolation and inter-storey isolation systems for high-rise buildings, which is accomplished by extracting useful insights from analytical and design features of real-life high-rise buildings equipped with these base isolation and inter-storey isolation systems. In detail the article explores the basic concept and the characteristics of the Base isolation system, and types of isolation bearings used for buildings. The fundamental concepts and benefits of inter-storey isolation system over base isolation. Additionally, the importance of vibration control strategy for buildings, and the different types of vibration control systems were also discussed.
... This friction translates energy into dissipating heat, leading to effective energy management. 10 In rubber-based dampers, the nonrubber segments primarily impart stiffness, while the rubber component contributes to strength and energy dissipation. Historically, enhancements in rubber dampers have come from two principal directions: optimizing structural design, 11 bolstering rubber's innate damping properties, like broadening damping temperature ranges and amplifying the loss factor. ...
Shock-absorbing materials play a vital role in various industrial sectors, including construction and transportation. Among these materials, natural rubber (NR) stands out due to its exceptional elastic and mechanical properties, coupled with its robust crack resistance. Nevertheless, with the rising demand for enhanced damping capacities, there is a need to further optimize the damping performance of NR. One direct approach is to blend it with high-damping rubber. Butyl rubber (IIR) is a prominent member of the high-damping rubber category. Integrating IIR effectively with the NR, however, presents challenges. These challenges arise from IIR’s inherent characteristics, such as its low unsaturation, slower vulcanization rate, and restricted compatibility with NR. Addressing these challenges, our study employed isoprene and isobutene to synthesize a variant of butyl rubber with a higher degree of unsaturation—achieving an unsaturation level between 4 and 6 mol %. Notably, this heightened unsaturation significantly expedited the curing time of IIR and facilitated the concurrent vulcanization of both IIR and NR. Utilizing atomic force microscopy, we observed that the introduction of unsaturated double bonds ameliorated the compatibility between NR and IIR, leading to an interfacial region extending up to 1000 nm. Our tests using a dynamic mechanical analyzer and rubber processing analyzer demonstrated the material’s damping temperature range. Furthermore, there was a noticeable rise in the loss factor (tan δ) at ambient temperature, which remains over 0.1 across both a frequency window of 0.2 to 5 Hz and a strain spectrum of 10 to 200%. This tan δ enhancement ensured the potential of these rubber composites for shock-absorbing applications.
High-damping rubber materials utilized in high-damping rubber isolation bearings are frequently subjected to multiple deformations during the occurrence of earthquakes. Typically, large combined compression–shear deformations of the material could potentially cause compressive shear damage to rubber bearings. During this process, visco-hyperelastic properties of rubber materials will greatly change, which would significantly impact the seismic performance of rubber bearings. Thus, to give out a deep insight into their variations, it is necessary and urgent to develop a high-performance numerical method to investigate this process. This paper proposed a visco-hyperelastic constitutive modeling approach for high-damping rubber materials based on the experimental assessment of combined quasi-static compression–cyclic shear deformation process. Within the thermodynamic framework, the Clausius–Duhem inequality associated with the intrinsic dissipation of the material was firstly derived in accordance with the Lagrangian formulism. Then, stress–strain relations were obtained upon considering the occurrence of entropy production due to viscous dissipation. In the model, Stumpf–Marczak strain energy density function, which satisfies the Baker–Ericksen (B–E) inequality, was harnessed to describe the hyperelasticity of the material. By introducing higher orders of strain and strain rates and taking their couplings into account, a generalized viscous dissipation potential was proposed to capture nonlinear strain and strain rate-sensitivity effects of the material. To identify constitutive parameters, the deformation gradient was particularized for the combined quasi-static compression–cyclic shear deformation process. And, an inverse identification procedure was carried out at different levels of compression stress. The prediction results revealed that the proposed model exhibits remarkable prediction ability and adaptivity for different rubber materials during this process. Several new insights were highlighted on the variations of visco-hyperelastic characteristics of high-damping rubber materials with respect to the compression stress. The accuracy of the model was further validated by design parameters including initial shear modulus, secant shear modulus and equivalent viscous damping factor. This work could provide a fundamental guideline for the optimization and reliability analysis of high-damping rubber isolation bearings used in the field of seismic engineering.
Curved bridges have seen widespread application in complex transportation networks, including interchanges and river crossings. If the displacements caused by an earthquake are too large, curved bridges have a greater risk of suffering serious damage due to the rotation of the superstructure. Since curved bridges are more susceptible to damage during earthquakes due to the effect of curvature, this factor also significantly influences the seismic behaviour of curved bridges. The present investigation has ascertained the impact of the radius of curvature on the seismic response of a bridge. The effect of ground motion characteristics and levels of shaking on the performance of bearings has also been studied. It has also been investigated how the bridge responds to seismic activity for both unidirectional and bidirectional effects. To determine the effect of the radius of curvature on the seismic response of the bridges, a non-isolated and isolated curved bridge with high damping rubber bearings has been considered. Bridges with varying radius of curvature (R= ∞, 315m, 157m, and 105m) have been modelled in the finite element-based software SAP 2000, and their response to three different ground motions has been observed. Isolation bearings in a bridge have been found to be more effective against seismic loads. The performance of an isolated bridge is superior to that of a non-isolated bridge when isolation bearings are installed in all of the piers and abutments. It is observed that a lower radius of curvature increases the deck displacement. It is also observed that bidirectional loading increases the seismic response of the curved bridge significantly relative to unidirectional loading.
This tutorial introduces the CMA Evolution Strategy (ES), where CMA stands for Covariance Matrix Adaptation. The CMA-ES is a stochastic, or randomized, method for real-parameter (continuous domain) optimization of non-linear, non-convex functions. We try to motivate and derive the algorithm from intuitive concepts and from requirements of non-linear, non-convex search in continuous domain.
In 2003-2004 two four-story reinforced concrete buildings belonging to IACP (SR) were seismically retrofitted by hybrid base isolation. The base isolation system for each building, consisted of 12 high-damping rubber bearings (HDRB) and 13 flat lowfriction sliding bearings (LFSB). Within the bearing supply two HDRB were kept for later testing. One of the two bearings was tested at the University of Basilicata on 11th and 12th December 2014. The present report summarizes the results of the tests.
In the present work, we investigate the response of a hybrid base isolation system under earthquake excitation. The physical parameters of the hybrid base isolation system are identified from dynamic tests performed during a parallel project involving two residential buildings in the town of Solarino, Sicily, using the well-established optimization procedure 'covariance matrix adaptation-evolution strategy' as dynamic identification algorithm in the time domain. The base isolation system consists of high damping rubber bearings and low friction sliding bearings. Two separate models are employed for the numerical simulation of the high damping rubber bearing component, namely a bilinear system and a trilinear system, both in parallel with a linear viscous damper. In addition, a linear Coulomb friction model is used to describe the behavior of the low friction sliding bearing system. Analytical solutions are provided, in compact form, for all possible phases of motion of the hybrid base isolation system under earthquake excitation. A series of numerical simulations are carried out to highlight the behavior of the considered hybrid base isolation system under different excitation and site conditions.
multilayer rubber bearings as vibration isolation bearings;multilayer rubber bearings in mechanical and automotive engineering;equipment isolation from vibration via anti-vibration;vibration isolation in concert halls, Benaroya Concert Hall in Seattle;seismic isolation and multilayer rubber bearings;Los Angeles City Hall, a 28-story steel frame building;bearings for Hearst Memorial Mining Building, University of California;base-isolated four-story reinforced concrete building and UNIDO-sponsored program
A fractional derivative Zener (FDZ) model connected in parallel with a linear viscous damper and a Coulomb friction slider is used to numerically simulate the mechanical behavior of a base isolated (BI) building tested under free vibration conditions in Solarino, Sicily. This hybrid BI system comprises high damping rubber bearings in combination with low friction sliding bearings. A comparison study of the present model with previous ones appearing in the literature, namely the bi-linear and the tri-linear models defined in the time domain, is carried out here. Furthermore, the linear viscoelastic solid, namely the classical Zener model, is also implemented and evaluated. The rheological models representing all the above BI systems are analyzed and, for the first time, the rheological formulation for the tri-linear model is presented. The present comparison study shows that the FDZ model is capable of describing the complex nonlinear response of BI systems.
Design Example for a High-Damping Rubber Bearing Design Example for a Lead-Plug Bearing
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