Study of a Phenomenological Model for Elastomeric Bearings

International Journal of Advanced Structural Engineering

The ideal performance of seismic isolating systems during the past earthquakes has proved them to be very useful in protecting structures against earthquakes. The cyclic loading experimental tests are an important part in the process of completing the design of the isolators, yet they are very expensive and time consuming. Using the accurate analytical modeling of hysteresis tests and knowing the limitations and the amount of error of the finite elements model and its effect on designing the isolated structure make it possible to reduce the financial and time expenses involved in designing seismic isolators along with experimental tests. In the present study, the cyclic loading of two different isolating systems, namely, the high damping rubber bearing (HDRB) and lead rubber bearing (LRB) have been modeled and analyzed in ABAQUS and the outcomes were compared with the experimental results attained by other researchers. Regarding the fact that the most important and complicated component of the elastomeric isolating system is rubber, it was modeled using various strain energy functions. Other factors affecting the finite elements models of elastomeric isolators were also studied. After comparing the effective stiffness of the experimental sample with the analytical model of HDRB, the Yeoh function had the best performance in determining the effective stiffness of the isolating system with an error of less than 7%. In studying LRBs, too, three types of bearings with different dimensions and lateral strain values were studied; the polynomial function in shear strain value of 150% had the best performance in estimating effective stiffness and damping with errors of less than 3% and 18%, respectively.

An analytical model for high damping elastomeric isolation bearings is presented in this paper. The model is used to describe mathematically the damping force and restoring force of the rubber material and bearing. Ten parameters to be identiÿed from cyclic loading tests are included in the model. The sensitivity of the ten parameters in a ecting the model is examined. These ten parameters are functions of a number of in uence factors on the elastomer such as the rubber compound, Mullins e ect, scragging e ect, frequency, temperature and axial load. In this study, however, only the Mullins e ect, scragging e ect, frequency and temperature are investigated. Both material tests and shaking table tests were performed to validate the proposed model. Based on the comparison between the experimental and the analytical results, it is found that the proposed analytical model is capable of predicting the shear force-displacement hysteresis very accurately for both rubber material and bearing under cyclic loading reversals. The seismic response time histories of the bearing can also be captured, using the proposed analytical model, with a practically acceptable precision.

Earthquake Engineering & Structural Dynamics, 2009

For the purpose of predicting the large-displacement response of seismically isolated buildings, an analytical model for elastomeric isolation bearings is proposed. The model comprises shear and axial springs and a series of axial springs at the top and bottom boundaries. The properties of elastomeric bearings vary with the imposed vertical load. At large shear deformations, elastomeric bearings exhibit stiffening behavior under low axial stress and buckling under high axial stress. These properties depend on the interaction between the shear and axial forces. The proposed model includes interaction between shear and axial forces, nonlinear hysteresis, and dependence on axial stress. To confirm the validity of the model, analyses are performed for actual static loading tests of lead-rubber isolation bearings. The results of analyses using the new model show very good agreement with the experimental results. Seismic response analyses with the new model are also conducted to demonstrate the behavior of isolated buildings under severe earthquake excitations. The results obtained from the analyses with the new model differ in some cases from those given by existing models. complex aspects of isolation device behavior, such as under large shear deformations or high compressive stresses. Lead-rubber bearings and high-damping rubber bearings are two commonly used types of seismic isolation device. Elastomeric isolation bearings exhibit stiffening or buckling behavior, influenced by the imposed compressive stress at large shear deformations. The change in shear stiffness due to high compressive stress is an important behavior to consider for elastomeric bearings when isolated buildings experience extreme earthquake shaking.

The nuclear accident at Fukushima Daiichi in March 2011 has led the nuclear community to consider the effects of beyond design basis loadings, including extreme earthquakes. Seismic isolation is being considered for new large light water and small modular reactors, and isolation-system designs will have to consider these extreme loadings. The United States Nuclear Regulatory Commission (USNRC) is sponsoring a research project that will quantify the response of low damping rubber (LDR) and leadrubber (LR) bearings under loadings associated with extreme earthquakes. Under design basis loadings, the response of an elastomeric bearing is not expected to deviate from well-established numerical models and bearings are not expected to experience net tension. However, under extended or beyond design basis shaking, elastomer shear strains may exceed 300% in regions of high seismic hazard, bearings may experience net tension, the compression and tension stiffness will be affected by isolator lateral displacement, and the properties of the lead core in LR bearings will degrade due to substantial energy dissipation.

Journal of Structural Engineering, 1999

Elastomeric seismic isolation bearings are subjected to large axial loads and lateral displacements during strong earthquakes. The existing Koh-Kelly model for elastomeric bearings accounts for axial load effects on horizontal stiffness. This linear model is based on small displacements and rotations and predicts stable postcritical behavior or increasing critical load with increasing horizontal displacement; however, unstable postcritical behavior is observed in the bearing test results presented in this study. The analytical model developed in this study, based on the Koh-Kelly model, includes large displacements, large rotations, and nonlinearity of rubber, and it predicts unstable postcritical behavior. The formulation of the analytical model, calibration, and verification using experimental results are presented. It is shown that: (1) the critical load reduces with increasing horizontal displacement; and (2) the horizontal stiffness reduces with increasing horizontal displacement and axial load. It is also shown that the critical load capacity at a horizontal displacement equal to the width of the bearing is not equal to zero, as predicted by the approximate procedure used in design, but higher. FIG. 1. Nonlinear Analytical Model Developed Based on Koh-Kelly Linear Model (K s = Nonlinear Shear Stiffness; K = Nonlinear Rotational Stiffness)

Journal of Mechanics of Materials and Structures, 2007

Seismic isolators are constructed from multiple layers of elastomer (usually natural rubber) reinforced with steel plates; they are, therefore, very stiff in the vertical direction, but soft in the horizontal direction. The buckling of these bearings under compression load is a well-understood phenomenon and has been widely studied. It is therefore unexpected that the buckling analysis for compression predicts that the isolator can buckle in tension at a load close to that for buckling in compression. The linear elastic model that leads to both compression and tension buckling is an extremely simple one, so it might be argued that the tensile buckling may be an artifact of the model itself rather than a property of the isolator. To test the simple theoretical model we have conducted a numerical simulation study using a finite element model of a multilayer elastomeric bearing. We find that the prediction of tensile buckling by the simple linear elastic theory is indeed accurate and not an artifact of the model.

Earthquake Engineering & Structural Dynamics, 2014

The nuclear accident at Fukushima Daiichi in March 2011 has led the nuclear community to consider seismic isolation for new large light water and small modular reactors to withstand the effects of beyond design basis loadings, including extreme earthquakes. The United States Nuclear Regulatory Commission is sponsoring a research project that will quantify the response of low damping rubber (LDR) and lead rubber (LR) bearings under loadings associated with extreme earthquakes. Under design basis loadings, the response of an elastomeric bearing is not expected to deviate from well-established numerical models, and bearings are not expected to experience net tension. However, under extended or beyond design basis shaking, elastomer shear strains may exceed 300% in regions of high seismic hazard, bearings may experience net tension, the compression and tension stiffness will be affected by isolator lateral displacement, and the properties of the lead core in LR bearings will degrade in the short-term because of substantial energy dissipation.

2017

In the last few decades, high damping natural rubber (HDNR) bearings have been extensively employed for seismic isolation of bridges and buildings because of their low horizontal stiffness and high damping capacity, which allows shifting the vibration period of the isolated structure away from where the earthquake input has the highest energy content and at the same time controlling the motion of the system. In HDNR material, filler is added to the natural rubber in order to improve its properties such as stiffness and dissipative capacity. The addition of the filler induces also a stress-softening behavior, known as "Mullins effect". This effect makes the response of HDNR bearings path-history dependent and thus may influence the seismic performance of isolated systems. Published literature has suggested that the initial "virgin" properties of the material are eventually recovered. Accordingly, current seismic codes make the assumption that "Mullins effect" is a reversible phenomenon. The present work aims at studying the consequences of such strain-history dependent behavior on the seismic response of structural systems isolated with HDNR bearings. In particular, the first part of the paper reports a wide experimental campaign carried out on a large number of virgin rubber samples in order to better investigate some aspects of the stress-softening behavior of filled rubber, such as the direction-dependence and the recovery prosperities, and to characterize the stable and transient response under different strain histories. Test results are used to define a model for simulating the behavior of HDNR bearings in shear, which is an advancement in the description of both the stable and the transient behaviors. The proposed model has been used to analyze the seismic response of a simplified isolated structure modeled as a S-DOF (single degree of freedom) system under ground motions with different characteristics and by considering two different conditions for the bearings: one assuming the virgin (or fully recovered) rubber properties and the other assuming the stable (or fully scragged) rubber properties. The obtained results show that, except for the special case of near-fault (NF) ground motions, the differences between the responses are limited although not negligible, whereas for NF records, the assumption of the virgin (or fully recovered) condition significantly reduces the effect of this type of motion on isolated structures.

Earthquake Engineering & Structural Dynamics, 2017

High Damping Natural Rubber (HDNR) bearings are characterized by stiffness and damping capacity that significantly depend on the shear deformation amplitude. More in details, at low deformations stiffness and damping increase, whereas at large deformations the stiffness remarkably increase but the damping capacity decreases. Additionally, this kind of bearings show a loading hysteresis dependence, due to the internal damage of the rubber occurring as the deformation history progresses. This effect, also known as stress-softening, becomes significant for large deformation amplitudes and represents a source of uncertainty, which has recently caused a limitation of the use of this kind of isolators. However, consequences of this nonlinear behaviour of HDNR bearings on the response of isolated structures are not comprehensively investigated, primarily because advanced models have been only recently developed. In this paper some investigations are carried out by using a nonlinear constitutive law recently developed by some of the authors describing the behaviour of a HDNR with significant stress-softening complying with the limits of European code on anti-seismic devices. Analyses are carried out on a multi-degree of freedom system by considering different seismic intensity levels and different response parameters, including floor response spectra. A linear visco-elastic model calibrated at each seismic intensity level is also adopted in the analyses. The obtained results show that some response amplifications happen due to the higher modes of the superstructure, which are underestimated by linear models and may cause damages to non-structural components and equipment.

Applied Sciences, 2021

Elastomeric bearings are commonly used in base-isolation systems to protect the structures from earthquake damages. Their design is usually developed by using nonlinear models where only the effects of shear and compressive loads are considered, but uncertainties still remain about consequences of the tensile loads produced by severe earthquakes like the near-fault ones. The present work aims to highlight the relapses of tension on the response of bearings and superstructure. To this end, three-, seven-and ten-storey r.c. framed buildings are designed in line with the current Italian seismic code, with a base-isolation system constituted of High-Damping-Rubber Bearings (HDRBs) designed for three values of the ratio between the vertical and horizontal stiffnesses. Experimental and analytical results available in literature are used to propose a unified nonlinear model of the HDRBs, including cavitation and post-cavitation of the elastomer. Nonlinear incremental dynamic analyses of the test structures are carried out using a homemade computer code, where other models of HDRBs considering only some nonlinear phenomena are implemented. Near-fault earthquakes with comparable horizontal and vertical components, prevailing horizontal component and prevailing vertical component are considered as seismic input. Numerical results highlight that a precautionary estimation of response parameters of the HDRBs is attained referring to the proposed model, while its effects on the nonlinear response of the superstructure are less conservative.