Natural Rubber Bearings Research Articles

Multi-layered solid element for seismic analysis of rubber bearings considering stress continuity based on finite particle method

Rubber bearings are crucial components in seismic isolation systems to mitigate the damaging effects of earthquakes on structures. Rubber bearings generally consist of alternate layers of steel and rubber bonded together. Simplified two-point spring models omit this layered construction and have limitations in adaptability and programmability, while refined multiple solid models lead to substantial computational costs. This study presents an effective and efficient approach to simulate rubber bearings by using multi-layered solid element based on the finite particle method (FPM). The traditional “Zigzag” shape function is extended into the 3D situation to reflect the serrated deformation within the layered construction. Based on the simplified assumption of stress continuity, an iterative approach is presented for the deformation gradient to achieve the force continuity between layers in dynamic nonlinear scenarios. The multi-layered solid models for both natural rubber bearings (NRBs) and lead rubber bearings (LRBs) are proposed based on this element. The errors of the hysteresis curves of rubber bearings are below 3.1 % between the numerical results obtained by using the multi-layered solid model and the experimental results. The computational speedup ratio of the proposed multi-layered solid model is verified to be 19 relative to the refined multiple solid model. The proposed method is applied to a base-isolated frame structure to demonstrate its effectiveness in structural seismic analysis.

Full-scale laboratory investigation on laminated rubber bearings for metro-induced vibration mitigation

The vibration response generated by the operation of a metro system has a profound impact on the physical and mental well-being of urban residents. Vibration control is essential to effectively isolate the multi-band vibration response and structure-borne noise of buildings. Laminated rubber bearings between the foundation and the superstructures serve as a common, cost-effective solution for the seismic isolation of structures and have great potential to be used for metro-induced vibration mitigation. In this study, two types of full-scale laminated rubber bearings (i.e., linear natural rubber bearing and lead rubber bearing) were tested under various compressive stresses, ranging from 5 MPa to 15 MPa, to examine the static and dynamic characteristics of the bearings, including vertical hysteresis curves, vertical static stiffness, time history response, and frequency spectrum. Then, the numerical simulation of a base-isolated building structure equipped with laminated rubber bearings was conducted to evaluate the vertical vibration isolation performance and structure-borne noise isolation capability. It was demonstrated that the laminated rubber bearings have stable vertical bearing capacities and performance in isolating vertical vibrations.

Experimental Study of the Mechanical Properties of Full-Scale Rubber Bearings at 23 °C, 0 °C, and -20 °C.

In this study, the effects of ambient temperature on the horizontal mechanical performance of isolated rubber bearings were investigated using high-speed reciprocating loading methods. A comprehensive series of 54 experimental trials are performed on the full-scale (900 mm-diameter) isolation rubber bearings, encompassing a range of temperatures (-20 °C, 0 °C, and 23 °C), shear pressures (50%, 100%, and 250%), and frequencies (0.20 Hz, 0.25 Hz, and 0.30 Hz). Because the compression-shear tests were conducted at high velocities and pressures (specifically, vertical compressive stress of 15 MPa), the equipment used in these tests was capable of generating substantial inertial and frictional forces. Appropriate correction methodologies for the precise determination of mechanical performance metrics for bearings are presented. Then, a comprehensive investigation of the effects of various loading conditions on the characteristic strength, post-yield stiffness, horizontal equivalent stiffness, and equivalent damping ratio of LRB900 (lead-core rubber bearings 900 mm-diameter) and LNR900 (linear natural rubber bearings 900 mm-diameter) is conducted. The empirical results show a discernible relationship between these characteristics and ambient temperature as the number of loading cycles increases, except for the equivalent damping ratio. Finally, empirical fitting formulations incorporating the influence of ambient temperature are presented for each performance indicator. These formulas are intended to assist designers in performing seismic design analyses by allowing them to take into consideration the effects of ambient temperature comprehensively.

A novel three-dimensional isolation bearing for buildings subject to metro- and earthquake-induced vibrations: Laboratory test and application

The implementation of three-dimensional (3D) isolation technology effectively enhances the structural seismic resilience and mitigates the impact of vibrations induced by metro trains. However, the challenge remains to increase the vertical loading capacity of 3D isolation bearings while reducing their vertical stiffness and guaranteeing excellent stability. The 3D isolation bearing (3DIB) consisting of an improved laminated natural rubber bearing (LNR-400-imp) and spring bearings (SBs) built vertically in series were proposed in this study. Its design principle and working mechanism were introduced, and prototype specimens were designed and manufactured. The 3D mechanical performance of the 3DIB was investigated through horizontal and vertical tests. Furthermore, the earthquake and metro vibration isolation performances of the building installed with the 3DIB were analyzed using a case study. The results demonstrated that the 3DIB exhibited horizontal energy dissipation effect, and had stable vertical performance, higher vertical loading capacity, and lower vertical stiffness attributing to the improved LNR-400-imp and SBs. Specifically, the vertical stiffness of the 3DIB was about 1/14 of that of the traditional LNR-400-tra. The case study demonstrated that the 3DIB had remarkable earthquake and metro vibration isolation effects, behaving huge potentials in enhancing the seismic resilience of structures and mitigating the impact of metro vibrations. This study offers valuable insight and practical guidance for future research on 3DIB in the field of vibration isolation, contributing to the advancement of 3D isolation technology.

A study on performance of natural rubber bearings with time under freeze–thaw cycles

A study on performance of natural rubber bearings with time under freeze–thaw cycles

Experimental and analytical investigations on horizontal behavior of full-scale thick rubber bearings

Thick rubber bearings (TRBs) have been proven to be effective in mitigating both horizontal earthquakes and railway-induced vertical vibration. Due to their low first shape factor, the horizontal properties of TRBs should be carefully examined during isolation design. This study presents experimental and analytical investigations on the horizontal behavior of TRBs with different first and second shape factors (S1 and S2). Eight full-scale thick natural rubber bearings (TNRBs) and lead thick rubber bearings (LTRBs) specimens were designed and tested under shear loading. The effects of geometric parameters and loading conditions were explored. The test results showed that decreasing S1 slightly reduced the horizontal stiffness, whereas the reduction caused by the decrease of S2 was more pronounced. As the applied vertical pressure increased, the horizontal stiffness of both TNRBs and LTRBs reduced, while the yield strength and damping ratio of LTRBs increased. Besides, equations were developed to predict the variations in shear properties of TNRBs and LTRBs under varying shear strains. Then, the test results were used to assess the accuracy of existing formulations for the shear properties of rubber bearings. Accurate equations were determined for the effective stiffness of TNRBs, as well as the yield strength and post-yield stiffness of LTRBs. Moreover, this study validated accurate hysteretic models to predict the cyclic shear behavior of TNRBs and LTRBs.

Full-scale shaking table tests and numerical studies of structural frames with a hybrid isolation system

A typical hybrid isolation system (HIS) incorporating natural-rubber bearings (NRBs) and nonlinear fluid viscous dampers (NFVDs) is proposed for seismic protection of critical equipment in nuclear power industrial buildings (NPIBs) under strong earthquakes. Design procedure with a parametric study towards the HIS considering various stiffness and damping values is first investigated via extensive nonlinear time history analyses. Then a preliminary recommendation for the specific structural demands of the considered system is proposed to direct the seismic design for both member- and system-level tests. Through a suite of full-scale shaking table tests on two typical NPIBs, the efficiency and reliability of the HIS are verified, in comparison to the structure with conventional rubber isolation system (RIS). The shaking table test results exhibit a superior behavior of the HIS in structural dual control strategies, i.e., transient acceleration control in critical equipment and bearing deformation control. Also, the HIS presents stable and resilient performances in both negligible residual bearing deformation and undetectable damage to structural/nonstructural components (containing the seismic isolated devices, i.e., NRBs and NFVDs). Finally, a three-dimensional finite element (FE) structural model and a single-degree-of-freedom (SDOF) system are successively developed to simulate the dynamic responses of the test structures. The well-validated SDOF FE model, serving as a reliable alternative for the isolated NPIBs, can be further utilized to facilitate practical design.

Determination and Prediction of Time-Varying Parameters of Mooney-Rivlin Model of Rubber Material Used in Natural Rubber Bearing under Alternating of Aging and Seawater Erosion.

In this paper, we examined the parameters of the Mooney-Rivlin model based on the effects of alternative aging and sea corrosion tests for natural rubber bearings and rubber materials in seawater. The model parameters for rubber material used in natural rubber bearings were determined using the least-squares method. Meanwhile, the time-varying law formula of the Mooney-Rivlin model parameters of rubber were fitted, and the fitting and calculated values were compared. Both fitting values and calculated values coincide with each other well. Then, the rubber material parameters were predicted based on the calculated results and combined with nonlinear auto-regressive (NAR). The predicted values were compared with both the fitting and calculated values. The average deviations between predicted and fitting values for C10 and C01 were 2.6% and 5.1%, respectively, and average deviations between predicted and calculated values for C10 and C01 were 5.2% and 4.1%. Compared results show that the predicted values are in good agreement with both the fitting and calculated values; meanwhile, the proposed time-varying law formula of the Mooney-Rivlin model parameters of rubber material have been well verified.

Full‐scale shaking table test and numerical analysis of structural frames with SMA cable‐restrained base isolation

AbstractRestrainer is a promising solution for deformation control of isolated systems. The present study comprehensively discusses the behavior, design and potential application of a novel superelastic shape memory alloy (SMA) cable‐restrained laminated natural rubber (SMA‐LNR) bearing. The study commences with a brief introduction of the working principle, and then a quasi‐static test on an individual bearing specimen is presented. A full‐scale shaking table test is subsequently presented, followed by a comprehensive parametric study, leading to preliminary design recommendations. The quasi‐static test shows a two‐stage behavior exhibited by the individual SMA‐LNR bearing, that is, linear flexible behavior at small displacements and restraining stage beyond initial gap. Under dynamic excitations, the SMA cables swayed smoothly with the shear deformation of the bearings, and experienced fracture beyond the maximum considered earthquake (MCE). The restraining effect is strengthened with increasing number of SMA cables, but this is accompanied by an increase in the acceleration response of the superstructure. An earlier engagement of the SMA cables, that is, smaller initial gap, leads to decreases in the bearing deformation. The acceleration responses of the superstructure and the maximum cable strain are not very sensitive to the initial gap. Using an overly small number of SMA cables has limited beneficial effect on bearing deformation control, and may even increase the deformation under certain excitations; therefore, a lower‐bound restraining force offered by SMA cables should be given to ensure an unconditional positive bearing deformation control. Two normalized design parameters and their recommended values are finally proposed to facilitate practical design.

Probabilistic lateral stability and shear failure limit states of bridge natural rubber bearings

This study presents the results of a parametric analysis on a wide range of geometries of bridge natural rubber bearings for the definition of consistent limit states. This range, defined as a matrix depending on the shape factor, slenderness ratio, and device width, ensures maximum homogeneity of the studied population based on values typically found in practice for bridge applications. The effects of typical axial loads are also considered. Numerical analyses are performed on a finite element model previously developed by the authors that is capable of simulating shear failure and buckling limit states. Each specimen undergoes a numerical pushover analysis to obtain the critical shear strain and the type of ultimate limit state achieved. The results of the numerical analyses are first presented to show the influence of the investigated parameters on the type of limit state and the corresponding value of critical deformation. Design charts are constructed for practicing engineers. In addition, this work addresses the framework of performance-based design of bridges, with the objective of defining convenient damage states for the construction of bridge fragility curves. For this purpose, the statistical importance of each studied bearing pad or seismic isolator with respect to the whole population is taken into account to develop probabilistic capacity models. A slenderness threshold is validated for isolators to distinguish between potential limit states.

Seismic Response Analysis of a Large-Span Isolated Structure Equipped with TNRB-DSBs and LRBs

This study focused on comprehensively analyzing the construction, mechanism, and design theory of the Thick Rubber Bearing–Disk Spring Bearing (TNRB-DSB) system, with the aim of evaluating its isolation effect. Mechanical tests were conducted to examine the dynamic characteristics of large-span isolated structures equipped with TNRB-DSBs, and laminated rubber bearings (LRBs), as well as the dynamic responses of non-isolated structures and large-span horizontal isolated structures equipped with natural rubber bearings (NRBs) and LRBs, under various seismic excitations. Finite element software was utilized to compare the behaviors of these structures. The study revealed that the large-span isolated structure equipped with TNRB-DSBs and LRBs had a vertical natural vibration period 1.23 times as long as that of the isolated structure with NRBs and LRBs, and 4.27 times as long as that of the non-isolated structure. The TNRB-DSB system demonstrated good vertical and horizontal isolation capabilities, which compensated for the isolation limitations of other rubber bearings to some extent.

Shaking Table Test for Seismic Isolation Performance of Adjustable Height Seismic Isolation Rubber Bearing

To study the seismic isolation effect of adjustable height seismic isolation rubber bearing, a continuous girder bridge was subjected to a shaking table test study with full bridge scaling to compare the seismic isolation effects of plate rubber bearings, natural rubber bearings (LNR) and adjustable height seismic isolation rubber bearings under different types of seismic waves, loading directions and seismic intensities.The test results show that when the seismic intensity is small, the seismic isolation performance of the three types of bearings is relatively close. But when the seismic intensity is large, the seismic isolation effect of the adjustable height isolation bearing is better than that of the plate rubber bearing and LNR bearing. Adjustable height isolation rubber bearing can significantly reduce the acceleration of the bridge deck plate, shear force and bending moment in the bottom of piers.

Seismic Performance Assessment of Girder Bridges with Composite Rubber Bearings

The objective of this study is to analytically assess the effectiveness of a novel composite rubber bearing (CRB), which is proposed to enhance both the displacement and damping capacities of the laminated natural rubber bearing (LNB), in improving the seismic performance of girder bridges. Four numerical bridge models respectively with the unbonded and bonded LNBs and CRBs (i.e. ULNB, BLNB, UCRB, BCRB) are established based on the bearing restoring force models. Then, incremental dynamic analyses (IDAs) are performed to obtain the fragility functions and the estimated economic costs. The results show that the bearing fragilities of the two CRB bridges are between those of the two LNB ones, but the pier damage is obviously mitigated by the CRBs, leading to the lower system vulnerabilities and economic costs. Allowing bearing sliding can further reduce the damage probability of the piers, but enlarge that of the bearings especially for the collapse limit state.

Seismic performance of a base-isolated flexible liquid storage tank equipped with a novel rate-independent damping device

Conventional base-isolation systems can significantly reduce the hydrodynamic pressure on the walls of large liquid storage tanks, but they have limited or even adverse effects on the sloshing response of liquids because the sloshing period is comparable to the isolation period. In this study, a combined base-isolation system consisting of natural rubber bearings and a novel rate-independent damping device was developed to achieve a simultaneous reduction in the hydrodynamic pressures and sloshing heights of liquid storage tanks. Using an analytical flexible tank model considering higher sloshing modes, the seismic responses of liquid storage tanks equipped with the proposed combined base-isolation system under strong ground motions were investigated. The influence of tank flexibility, higher sloshing modes, and liquid heights on the seismic responses of the controlled storage tank were evaluated quantitatively. The effectiveness of the proposed combined base-isolation system was verified, and its advantages over conventional base-isolation systems were identified. The proposed system can achieve a larger reduction in base shear, overturning moment, and sloshing height than conventional systems without increasing the isolator displacements.

Stability issues for elastomeric bearings: analytical formulations compared to experimental results

During earthquake strong motions, anti-seismic devices are subjected to large horizontal deformations combined to vertical stress due to gravity loads. For elastomeric bearings, the most widespread technology used to this aim, it is necessary to value critical load capacity under this combined effect, to ensure their stability in service. In this paper, elaborations of data from experimental campaign on full-scale rubber bearings (HDRBs) are compared to results form a brief theoretical overview, to evaluate their stability limits. To examine the effect of device geometrical characterization on bearing mechanical behavior, to check instability mode and to evaluate the interaction between vertical pressure and shear deformation, three different types of full-scale devices have been considered (ϕ500, ϕ600, ϕ700). Experimental data refers to “soft” natural rubber bearings, having a shear modulus G= 0.4MPa (at γ=100%), an equivalent damping factor ξ = 10÷15, a primary shape factor S1 varying in the range [19,44 – 22,72] and a secondary shape factor S2 varying in the range [2,8÷3,4]. Data derive from static shear tests, at increasing levels of shear strain (up to γ = 250%) combined to growing compressive stress (from 6 MPa to 20 MPa). Their elaboration has been accompanied by the use of dimensionless factors, in particular the ratio γ/S2, that results an effective design parameter to describe bearing performance. On the base of analytical formulations from literature, the experimental results have been matched with theoretical evaluations of the critical load. The experimental occurrence of buckling instability has been read also in light of design guidelines provided for rubber devices.

Identification and Calibration of Advanced Hysteresis Models for Recycled Rubber–Fiber-Reinforced Bearings

Several studies have investigated the feasibility of reducing the implementation cost of base isolation. In this optic, recycled rubber–fiber-reinforced bearings (RR–FRBs) represent a suitable solution for structures in developing countries. Such devices can be produced using simple manufacturing procedures at a limited cost with respect to conventional isolators. Full-scale tests on RR–FRBs featured energy dissipation values similar to those associated with high-damping natural rubber bearings (HDRBs). Equivalent viscous damping, ranging from 10 to 15%, resulted from testing of RR–FRBs, with poor degradation after cyclic loading. On the other hand, a sensible softening response, associated with the axial–shear interaction, which is much more significant compared to that exhibited by HDRBs, was observed. As a result, the numerical description of the cyclic behavior of the RR–FRBs appears to be more challenging than that of HDRBs. In past studies, simple bilinear hysteresis models were adopted to describe the cyclic behavior of low-cost rubber bearings, thus completely neglecting the P-delta effects which significantly influence the dynamic behavior of such bearings. In this paper, advanced hysteresis numerical models, able to capture the nonlinear response of RR–FRBs, were examined and properly calibrated using a powerful optimization technique, the differential evolution algorithm. Preliminary results of the numerical analyses, performed in OpenSees, were described and compared with those of experimental tests on low-cost rubber bearings. The findings of this study represent the first step of a characterization procedure aimed to provide an accurate representation of the dynamic behavior of these particular bearings. Obviously, additional studies are needed to compare results of response history analyses with those of experimental tests for real structures on RR–FRBs. In this optic, the present paper, along with further studies, could provide a new impulse for the application of low-cost rubber-based devices in current practice.

Shaking Table Test of a Base-Isolated Frame Structure under Near-Fault Ground Motions

A five-story moment frame structural model with a base isolation system was tested on a shaking table. The isolation system comprised both linear natural rubber bearing (LNR) and nonlinear viscous dampers (NLVDs). Seven ground motions were employed: including three far-fault (FF) and four near-fault (NF) earthquake ground motions. The performance of the isolation system was evaluated by measuring the displacement and base shear of the isolation bearings. Furthermore, the axial force and displacement of the NLVDs were measured. The evolution of the fundamental dynamic frequency of the frame during the test was also determined. During strong earthquakes, NF ground motions caused larger story drifts and floor accelerations of the superstructure than FF ground motions. The displacement and base shear of the isolation base was very large when the isolated structure was subjected to Kobe_TAK000 and ChiChi_TCU102/278 pulse-like NF ground motions. Furthermore, the LNR s experienced tension and uplift when the PGA of input earthquake ground motions was larger than 0.80 g. Although the NLVDs performed very well in combination with the LNRs, the severe responses of the isolation bearings were caused by NF ground motion with a pulse period Tp neighboring the fundamental period of the isolated structure.

Probability Distribution Characteristics of Horizontal and Vertical Mechanical Properties of Rubber Bearings.

Rubber bearings are widely used to protect civil structures from destructive earthquakes. The mechanical properties of the bearings are the key technical parameters that determine the seismic isolation performance of isolated structures. To estimate the probability distribution of the mechanical properties related to rubber bearings (including horizontal stiffness, vertical stiffness, post-yield stiffness and yield force) under seismic events. Typical natural rubber bearings (NRBs) and lead-core rubber bearings (LRBs) were designed and fabricated, and the bearings were subjected to repeated load tests using a compression-shear testing machine. The test results of the horizontal and vertical mechanical properties of the bearings in the tests were basically consistent with the design values, and the rubber bearings showed stable mechanical behavior under repeated cyclic loading. The statistical analysis of the test results revealed that the relevant mechanical properties of the NRB and LRB specimens followed a lognormal or general extreme distribution with coefficients of variation mainly ranging from 0.86% to 5.6%. The dispersion of the yield force of LRB was the largest in the repeated tests of many mechanical parameters of typical rubber bearings.

Experimental and analytical investigations on compressive behavior of thick rubber bearings for mitigating subway-induced vibration

When designing over-track buildings, two main problems require attention: the lateral stiffness changes abruptly between superstructures and the podium, and the subway-induced vibration leads to occupant discomfort. As one type of three-dimensional isolators, thick rubber bearings (TRBs) are considered as an effective measure to overcome these problems. However, the extension of the experimental knowledge base concerning the compressive behavior of TRBs is needed to develop analytical methods to precisely predict their vertical stiffness. Also, the effects of geometric parameters and loading conditions on the vertical stiffness of TRBs are required to be examined by experiments. For these purposes, a total of 6 full-scale thick natural rubber bearings (TNRBs) and 4 full-scale lead thick rubber bearings (LTRBs) were designed, and a series of compressive tests were conducted. The geometric parameters included the first and second shape factors (S1 and S2), single-rubber layer thickness, and core configuration (without and with the lead core). Various load amplitudes and vertical pressure were considered. The experimental results showed that the vertical stiffnesses of the TNRBs and LTRBs reduced with the decrease of the S1 and S2, and the lead core had a significant effect on the vertical stiffness of the LTRBs. The change of the load amplitude for the LTRBs and the vertical pressure for the TNRBs also remarkably affected their vertical stiffnesses. Based on the experimental campaign and existing test database, the experimental values of vertical stiffness of TNRBs and LTRBs were compared with current analytical formulations. Finally, analytical methods for determining the vertical stiffnesses of the TNRBs and LTRBs were developed, respectively, which showed good agreement with the test results.

Study on the Stabilities of RTH Tests Using the CDM Method considering Two Kinds of Systematic Errors

Real-time hybrid (RTH) test is a promising test method to investigate seismic responses of structures and is essentially a time history analysis. Therefore, an in-depth understanding of the control algorithm, such as a central difference method (CDM), is important for this method. In this paper, stabilities of the CDM considering two kinds of errors are investigated theoretically and experimentally. It turns out that the convergence criterion of the CDM cannot be changed by constant errors but can be changed by proportional errors. The lowest structural natural period to keep the results stable increases with the increase of the ratio of the displacement error to the interface displacement and the integration time step. At last, the theoretical result of the stability of the CDM considering two kinds of systematic errors are confirmed by the proposed test system with a natural rubber bearing.