Fiber-reinforced elastomeric isolators: A review

Soil Dynamics and Earthquake Engineering 125 (2019) 105621

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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn

Fiber-reinforced elastomeric isolators: A review Niel C. Van Engelen

T

Department of Civil and Environmental Engineering, University of Windsor, Windsor, Ontario, Canada

ARTICLE INFO

ABSTRACT

Keywords: Fiber-reinforced Seismic isolation Elastomeric isolator Vibration isolation Base isolation Rubber

The concept of seismic isolation is well established. Provisions for seismic isolation are gradually being included in building and design codes around the world. Consequently, the quantity of base isolated structures continues to grow globally with favorable performance observed after every significant seismic event. The growth in seismic isolation technology has led to the development of numerous innovative and unique base isolation devices. Although many different types of devices exist, most can be classified as either an elastomeric or sliding isolator. Within the elastomeric classification, steel-reinforced elastomeric isolators are the most common. Fiberreinforced elastomeric isolators (FREIs) have been proposed as a type of reinforced elastomeric isolators that have distinct performance characteristics. The original intent of FREIs centered on developing a low-cost device appropriate for wide-spread application, particularly in developing countries where the devastation of earthquakes is often more severe. For this reason, the concept has gained significant attention within the research community. This review summarizes the development and current state-of-knowledge of FREIs.

1. Introduction At the time of the comprehensive review and bibliography on base isolation by Ref. [1] in 1986, the concept had not yet been widely accepted by the engineering community and remained largely untested by strong ground motions. In the past several decades, base isolated structures have become a common feature in many areas with high seismic hazards and continues to be an active area of research. The favorable performance of base isolated structures in notable seismic events, such as the L'Aquila (Italy, 2009), Maule (Chile, 2010), Canterbury (New Zealand, 2010, 2011), Tohoku (Japan, 2011), and Lushan (China 2013) earthquakes, have encouraged increased application of the technology [2]. As of early 2017, all base isolated structures subjected to severe ground motions have exhibited excellent behavior [2]. Provisions for seismic isolation have been included in numerous building and design codes around the world to facilitate further application (e.g. Refs. [3,4]). The interest in seismic isolation has led to the development of numerous unique and innovative devices although most applications use elastomeric or sliding isolators. Elastomers have been used for seismic isolation applications since 1969 [5]. Elastomers are ideal for base isolation due to the low shear modulus, near incompressibility and ability to accommodate large recoverable strains at relatively low stress levels. Modern elastomeric isolation devices are composed of alternating horizontal layers of reinforcement and vulcanized elastomer. The reinforcement enhances the compression characteristics of the isolator allowing the composite

device to develop the necessary strength and stability to support the overlaying structure. Traditionally, steel shims are the reinforcement of choice. Steel-reinforced elastomeric isolators (SREIs) are widely used in base isolation applications and as bridge bearings. The use of fiber-glass as an alternative to steel reinforcement was considered as early as 1974 for elastomeric bridge bearings [6]. Fiberglass was selected “in hopes of finding a reinforcing fabric stiffer and more creep resistant than polyester” [6] which at the time was widely used. Through a series of experimental tests, the study concluded the fiber-glass performed similar to the steel-reinforcement [6]. In 1999, Ref. [7] proposed that the steel reinforcement used in seismic isolators could be replaced with a similar volume of lighter fiber reinforcement. The proposal was a progression of an earlier study that investigated reducing the thickness of the steel reinforcement and suggested using fiber reinforcement [8]. In both cases, the primary intention was to reduce the production and installation cost of SREIs, which at the time, and to some extent to this day, were barriers to widespread application of base isolation technology. Earlier investigations (e.g. Refs. [6,9]) had been conducted to develop a glass fiber-reinforced bearing, although Ref. [7] proposed and popularized the concept of fiber-reinforced elastomeric isolators (FREIs) for seismic isolation applications. It was believed that the use of fiber reinforcement could result in a less laborintensive manufacturing process by manufacturing larger pads and subsequently cutting it to individual isolators of the desired size. Reference [7] provided early analytical and experimental evidence for the viability of the concept and is often cited as the leading study on FREIs.

E-mail address: [email protected]. https://doi.org/10.1016/j.soildyn.2019.03.035 Received 8 January 2019; Received in revised form 25 March 2019; Accepted 25 March 2019 0267-7261/ © 2019 Elsevier Ltd. All rights reserved.

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FREIs are at a relatively early stage in development and application, although, most of the concepts and knowledge applicable to SREIs is transferable to FREIs (with some refinement). Due to the similarities between SREIs and FREIs, there is a tendency to compare the two types. A direct comparison between a SREI and FREI, however, is difficult to achieve primarily due to the difference in reinforcement thickness and mechanical properties. This review provides a comprehensive overview of the state-of-knowledge of FREIs for critical design properties, experimental programs, as well as analytical and numerical modeling. The list of references is non-exhaustive and some valuable contributions to the field may have been overlooked. Conference publications are generally excluded unless a significant contribution unpublished in other sources was made. The emphasis is on contributions directly investigating FREIs.

Fig. 1. Lateral bulging and reinforcement extension of a fiber-reinforced elastomeric pad under a uniform compression load.

reinforcement, horizontal planes remain plane and parallel, the lateral bulging of the elastomer follows a parabolic profile, the extension of the reinforcement is uniform through the layer, the elastomer and reinforcement are linear elastic, the normal stresses within the elastomer are dominated by the internal hydrostatic pressure, and the shear stresses in the horizontal plane are negligible. Some research has been conducted to release several of these assumptions [15–17], although the pressure solution is generally considered to be valid for elastomeric pads with a shape factor of about 5 or greater. Fig. 1 illustrates the assumed displacement of an elastomeric pad bonded to flexible reinforcement, where Δ is the vertical deflection, u0 is the amplitude of the lateral bulging, u1 is the extension of the reinforcement, t is the thickness of the elastomeric layer and tf is the thickness of the reinforcement. Several experimental (i.e. circular [18] and rectangular [19]) and finite element investigations (i.e. infinite strip [20–23], circular [12,24] and rectangular [13]) have been in good agreement with the respective analytical solutions. In most cases, the compression modulus can be expressed as a function of a dimensionless parameter, λ, which has the general form:

2. Vertical properties 2.1. Vertical stiffness Obtaining an adequately high vertical compression stiffness is an important consideration in the design of an isolation system. Intuitively, the isolator must support the vertical compressive load of the structure without excessive deformations or failure. A high vertical stiffness is also necessary to suppress potential rocking modes introduced by the isolation system [5], ideally resulting in similar (or improved) vertical performance as a conventional fixed-base structure. In most applications, the isolation system is effective only in the horizontal direction. The primary function of the reinforcement is to restrain the lateral bulging of the elastomeric layers that occurs due to a compressive load. The restraint of the elastomeric layers vertically stiffens the isolator while leaving the horizontal stiffness relatively unchanged. Therefore, by virtue of the reinforcement, it is possible to obtain a device for which the vertical stiffness is several orders of magnitude greater than the lateral stiffness. In addition to the material properties of the elastomer and reinforcement, the vertical stiffness is a function of the geometry of the isolator and the shape factor, defined as the ratio of the loaded area to unloaded area free to deform laterally for a single layer of elastomer. The vertical deflection of an elastomeric isolator under an applied load occurs because of lateral bulging and volumetric strain. The dependency on lateral bulging and bulk compressibility is largely a function of the shape factor of the isolator. When a vertical load is applied, tensile stress develops in the reinforcement and shear stress develops in the elastomeric layers as the elastomer displaces laterally through Poisson's effect. For low shape factors (i.e. relatively thick layers of elastomer), the elastomeric layers are largely unrestrained by the reinforcement and the elastomer deforms significantly due to lateral bulging. As the shape factor increases, representative of thinner layers of elastomer if the loaded area is held constant, the reinforcement restrains the lateral bulging and reduces deformation. In the limit as the shape factor approaches infinity, rigid reinforcement fully confines the elastomer and, consequently, the compression modulus of the isolator approaches the bulk modulus of the elastomer. From an analytical perspective, the primary difference between a SREI and a FREI is that steel reinforcement can be assumed rigid, whereas the extensibility and flexibility of fiber reinforcement must be considered. The extensibility of the reinforcement can be viewed as having a similar global effect as lateral bulging. The extensibility of the reinforcement allows a volume of elastomer to displace laterally under the vertical load. Therefore, an increase in reinforcement stiffness increases the vertical stiffness due to increased lateral bulging restraint on the elastomeric layers. Closed-form analytical solutions for the compression modulus have been developed based on the assumptions of the pressure solution for most basic elastomeric pad geometries (e.g. infinite strip [10], circular [11,12], rectangular [13,14] and annular [11]). The pressure solution assumes that the elastomer is perfectly bonded to the

= cGS 2

1 t +e K Ef t f

(1)

where G and K are the shear and bulk modulus of the elastomer, respectively, S is the shape factor of the elastomeric layer, Ef is the effective elastic modulus of the reinforcement and c and e are geometry specific coefficients. Note that Ef is representative of the properties of the fiber reinforcement as a composite bonded to the elastomer, not the elastic modulus of the individual fibers. Thus, Ef can be changed by increasing or decreasing the density or type of fibers. The sensitivity of the compression modulus, Ec, to λ is illustrated in Fig. 2a for an infinite strip pad. For all pad geometries, Ec converges to Ke as λ approaches infinity where:

Ke =

1 t +e K Ef t f

1

(2)

Equation (2) indicates that the compression modulus is equally sensitive to changes in K or Ef corrected by the thickness ratio and e. Inclusion of the extensibility of the reinforcement (from an otherwise assumed infinite value) has the effect of reducing Ke and therefore reducing the maximum theoretical compression modulus. The bulk modulus of elastomers is a difficult property to measure and control, but the effective elastic modulus of the reinforcement and reinforcement thickness ratio are parameters that can more readily be controlled by designers. Thus, the use of fiber reinforcement has the potential to offer increased control over the vertical properties in addition to the pad geometry. Fig. 2b shows Ec normalized by the compression modulus assuming an incompressible elastomer and inextensible reinforcement, Ec . Neglecting compressibility and extensibility may be appropriate for small shape factors and high values of Ke/G but otherwise may introduce significant error. Similar trends exist for all other basic elastomeric pad geometries [25]. 2

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Fig. 2. Compression modulus of an infinite strip pad (a) convergence to Ke with increasing λ and (b) sensitivity to Ke/G as a function of S.

2.2. Multiple layers of elastomer and boundary conditions

attributed to the manufacturing of the specimen which resulted in nonplanar reinforcement layers at the ends of the isolator.

Most closed-form analytical solutions consider only a single layer of elastomer [10–14]. The compression modulus of an isolator can be derived by treating the individual layers as springs in a series. The thickness of the elastomeric layers is typically identical with the potential exception of the exterior layers in contact with, or bonded to, the supports or steel end-plates. If the elastomeric layers have the same thickness and boundary conditions, the relationship between Ec and the vertical stiffness, kv, is:

kv =

Ec A tr

3. Lateral properties 3.1. Lateral stiffness In elastomeric isolators it is common to assume that the shear deformation is concentrated entirely in the elastomeric layers. While the reinforcement restrains the lateral bulging of the layers due to the vertical load, the elastomer is otherwise able to deform freely under horizontal shear mostly independent of the layer design [21,33]. Thus, the lateral stiffness, kH, neglecting non-linearity associated with the material properties or geometric and stability effects is:

(3)

where tr is the total thickness of the elastomeric layers (i.e. EcA for each layer is equal to EcA for the isolator). As discussed in the subsequent Lateral properties section, isolators can be placed bonded or unbonded between the upper and lower supports. If there is no slip at the interface between the unbonded FREI and the supports, an unbonded FREI is identical to a bonded FREI with respect to the vertical properties at zero lateral displacement [16,26]. Otherwise, the vertical stiffness of an unbonded FREI becomes a function of the friction between the elastomer and supports. An increase in friction decreases slip and consequently increases the vertical stiffness. In the limits, a layer that experiences no slip (i.e. bonded) will have a vertical stiffness that is four times greater than an identical layer with zero friction. Therefore, in unbonded FREIs with few elastomeric layers, the vertical stiffness may be sensitive to slip at the boundaries. This sensitivity decreases as the number of elastomeric layers increases and the overall properties of the isolator are less sensitive to individual layers [16,17].

kH =

GA tr

(4)

An important distinction must be made with respect to the boundary conditions of the isolator. In SREIs, it is common to use large steel end-plates to mechanically fasten the isolator to the upper and lower supports. Although also possible for FREIs, often the isolator is investigated unbonded between the upper and lower supports. In this case, the transfer of lateral forces is entirely dependent on friction. The unbonded application aligns well with the original light-weight, lowcost intention of FREIs. The significant weight of the end-plates and related costs associated with manufacturing and installation can be eliminated. The friction between the elastomer and concrete (or steel) supports has generally been found to be adequate to prevent slip, although slip may occur if the vertical compressive stress is low or the lateral load is high [34]. The unbonded application is also favorable since it prevents the development of large tensile stresses in the end sections, identified in Fig. 3a, in bonded applications [35–37] which otherwise may result in failure. The lower tensile stress demand reduces the bond requirements between the elastomer and reinforcement. This occurs because of the combined unbonded application and lack of flexural rigidity of the fiber reinforcement. In unbonded FREIs, this is the unique rollover deformation that occurs with lateral displacement. Rollover occurs as the top and bottom horizontal layers of elastomer lose contact with the upper and lower supports and begin to rotate with lateral displacement (Fig. 3b). This phenomenon was identified in the 1974 experimental program in Ref. [6]. The rotation of the rollover sections continues until the initially vertical faces of the isolator contact the supports, denoted as full rollover (Fig. 3c). Full rollover represents a distinct change in the lateral response of an unbonded FREI, although displacements exceeding full rollover (Fig. 3d) can be achieved. Occurrence of rollover is a function of the flexural rigidity of the reinforcement [38] and has been observed in SREIs with thin reinforcing plates [39] and steel mesh [40,41].

2.3. Run-in effect FREIs may exhibit a run-in effect where the vertical stiffness is developed as a function of the vertical displacement. The initial lack of straightness of the fibers results in larger vertical displacements under uniform compression until the tension in the reinforcement pulls the fibers taut. An analytical study based on an infinite strip pad has identified that the theoretical stiffness is expected to be effectively achieved before all the fibers are pulled taut (i.e. the theoretical stiffness is rapidly asymptotically approached) [27]. To minimize the run-in effect, the fiber reinforcement can be bonded to the elastomer under a nominal load to increase the initial straightness of the fibers [28]. Numerous experimental programs [7,10,19,23,28–32] have identified that the vertical stiffness increases as vertical load increases (nonlinearly, at a decreasing rate). This is often postulated to be due to the straightening of the fibers. Run-in may significantly increase the total deflection of the isolator and should be considered in the design process. Run-in was also observed in Ref. [32] where it was partially 3

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Fig. 3. Lateral displacement of (a) a bonded FREI, (b) an unbonded FREI showing rollover, (c) an unbonded FREI at full rollover and (d) an unbonded FREI at a displacement exceeding full rollover.

3.2. Full rollover displacement Full rollover (i.e. the transition between softening and stiffening) is an important consideration. By assuming that the elastomer is incompressible and that the length of the surface that has lost contact with the supports is equal to the lateral displacement, a simple estimate of the theoretical full rollover strain, γf, for infinite strip and rectangular isolators can be derived [39] as: f

=

5h 3 tr

(5)

where h is the total height of the isolator. Equation (5) has not been verified through in-depth experimental studies or finite element analysis. However, in the experience of the author, it has generally been found to give a satisfactory approximation of full rollover for rectangular isolators and has good agreement with the other available analytical model predicting full rollover [38]. Neglecting reinforcement (i.e. h = tr), from Eq. (5), full rollover occurs at a shear strain of 1.67. Correcting for the reinforcement ratio, full rollover occurs approximately at a shear strain of 1.75–2.00, depending on the isolator design. Numerous experimental programs have tested unbonded FREIs up to or exceeding a shear strain of 2.50 [19,28,30,45,49,52,53]. These studies indicate that significant displacement capacity can be satisfactorily achieved after full rollover. The stiffening response does not occur instantaneously with full rollover; all experimental programs that exceed full rollover have shown a smooth transition between the softening and stiffening regime [19,28,30,45,49,52,53]. Finite element studies that consider displacements exceeding full rollover generally predict a more abrupt change in tangential stiffness than observed experimentally [51,55,73]. Some studies [49,60,74] distinguish between initial contact of the initially vertical face of the isolator and full contact (i.e. full rollover). Initial contact occurs as the elastomeric layers closer to the point of rotation contact the supports due to lateral bulging and other non-linearities. Although initial contact is attributed to some level of stiffening [49,60,74], full rollover is generally considered from a design and analysis perspective due to the significant change in tangential stiffness. Currently, there is no method available (aside from finite element analysis) to predict the initial contact of the elastomeric layers.

Fig. 4. Typical normalized lateral force-displacement hysteretic response of an unbonded FREI (adapted from Ref. [72]).

Rollover and full rollover are the source of a softening and stiffening (or hardening) response, respectively. This lateral response is similar to the triple friction pendulum [42], sliding systems with variable curvature [43], or elastomeric isolators with strain-induced crystallization [44]. Devices exhibiting this softening and stiffening response are described as adaptive devices since the response can be tailored to the hazard level. The softening increases the efficiency of the isolation system by shifting the fundamental period further out of the critical high-energy range of a typical earthquake event. Whereas, the stiffening regime is believed to behave as a self-restraint mechanism against excessive displacements at events that meet or exceed the maximum considered earthquake [42,44,45]. The softening and stiffening behavior of unbonded FREIs, exemplified in Fig. 4, has been observed in numerous experimental programs for square [28,46–49], circular [50], and rectangular [19,45,51–54] isolator geometries. For square pads, a similar, albeit less pronounced, relationship is observed at 45° angles from the principle axis [28,37,46,47] and at other angles based on finite element analysis [36,55]. Experimental programs on unbonded FREIs with displacements that do not exceed full rollover have also observed significant softening in square [30,34,37,55–62], rectangular [10,57,63,64] and circular isolator geometries [32,57,65]. Numerous experimental programs considering FREIs in bonded applications have also been conducted [18,31,48,66–71] where significant softening due to rollover is not observed; although, Ref. [31] observed rollover behavior after failure of the bond between the steel end-plates and elastomer occurred. A finite element investigation conducted by Ref. [55] observed no significant coupling under bidirectional loading of a square FREI not exceeding full rollover and concluded that unbonded FREIs can be evaluated based on unidirectional loading for the specimens and displacements considered.

3.3. Analytical models The resistance to lateral displacement of the rollover sections is less than an equivalent area in simple shear. Thus, as the isolator is displaced laterally, rollover has the effect of reducing the lateral stiffness 4

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of the isolator. If the size of the rollover section is assumed to be directly proportional to the lateral displacement, u, the lateral stiffness of a rectangular isolator is [39]:

kH (u) =

3.4. Lateral stability The reduction in lateral stiffness due to rollover is primarily a function of the width-to-total height aspect ratio, R, in the direction of loading. It is otherwise largely independent of other material or geometric properties, assuming the reinforcement remains flexible in bending [38,60]. From Eqs. (5) and (6) with r = 1, it can be shown that lateral instability (i.e. negative tangential stiffness) will occur before full rollover if R ≤ 3.33. However, the contribution of the rollover sections is not insignificant and lower aspect ratios can be used while retaining lateral stability. Studies that comment on lateral stability up to and exceeding full rollover suggest that R ≥ 2.5 is required [38,47,76]. Lateral stability under quasi-static tests have been observed with aspect ratios as low as about 2.0, but limited to a maximum shear strain of about 1.5 (i.e. less than full rollover) [60]. As R increases, the area that experiences rollover remains constant, whereas the area of the central section (in simple shear) increases. Thus, an increase in R decreases the overall softening observed [21,38]. To appreciate the benefits of the adaptive characteristics, an aspect ratio of 2.5–3.0 is desirable (i.e. maximum softening while retaining lateral stability). At an aspect ratio of 2.5–5.0 a 40–60% reduction in the initial stiffness can be achieved. By an aspect ratio of 5.0–10.0, the softening characteristics become largely insignificant [21]. Aspect ratios below 2.5 are permitted provided the displacement demands are not expected to result in lateral instability. Experimental investigations [37,58] and shake table studies [81–84] have been conducted on such isolators. These isolators are more susceptible to roll-out under the applied load, which is otherwise prevented by full rollover in unbonded FREIs with R ≥ 2.5.

GA eff (6)

tr

where Aeff is the effective area of the central section, identified in Fig. 3, defined as

Aeff (u) = b (a

ru)

(7)

a and b are the width and length of the rectangular isolators, respectively, and r is a coefficient that varies depending on the analytical model considered. Equation (6) with r = 1 in Eq. (7) represents a lower bound prediction of the lateral stiffness of an unbonded FREI by neglecting any contribution from the rollover sections. The expression predicts a parabolic force-displacement relationship that reaches a maximum at u = a/2. Any displacements beyond this point would be considered laterally unstable as the tangential stiffness becomes negative. Variations of Eq. (7) have also been proposed where r = 3/4 or r (u,h) to account for the lateral resistance contribution of the rollover sections (i.e. the effective area of the central section is assumed to be larger) [75–77]. Reference [78] proposed Eq. (6) (with r = 1) for unbonded FREIs and Eq. (4) for bonded FREIs but accounted for the nonlinear properties of the elastomer (i.e. G is a function of shear strain) and the influence of the vertical load on the lateral properties. This model, with the inclusion of r(u,h) [76], were combined in Ref. [79] to account for the influence of the vertical load and rollover on the lateral properties of unbonded FREIs. Reference [56] proposed an equivalent linear stiffness determined from an average area in simple shear (i.e. Aeff is constant). It was proposed that the vertical deformation of the isolator, which reduces the total height, delays the loss of contact between the isolator and the upper and lower supports. The region of the isolator in contact with the supports was assumed to behave in simple shear, and, as with Eq. (6) with r = 1, the rollover sections were assumed to be stress free. The average area of the central section was determined from two points: the area at zero horizontal displacement and at full rollover. It should be noted that the model requires a vertical deflection (determined at zero lateral displacement) and a full rollover displacement to determine the average area of the central section. In Ref. [56], these parameters were determined from experimental results. The model in Ref. [56] was applied in Ref. [60] to predict lateral instability based on an iterative procedure. Reference [50] adapted the methodology of Refs. [56,79] to develop a model for a circular isolator. Reference [38] developed an analytical model based on a cantilever representation of the rollover sections using large deflection theory. The proposed model modified and expanded on work by Refs. [39,80]. This model predicts full rollover and the horizontal force-displacement relationship up to and exceeding full rollover based on an iterative procedure. It is currently the only model available that predicts full rollover and the post-full rollover response of unbonded FREIs, although full rollover is also accounted for in the model by Ref. [77] which relies on finite element modeling. All the available analytical models are similar in that the central section of the isolator that does not experience rollover is the primary source of lateral resistance. The majority of the analytical models aim to represent the rollover sections by correcting the effective area of the central section [39,50,56,75–77,79]. These models are simplified representations of a complex problem but do provide designers with insight to the expected force-displacement relationship without the need for experimental testing or finite element analysis. Note the vertical load is an important parameter in determining the lateral stiffness as discussed in the Buckling properties section and should be considered for a more developed model.

3.5. Energy dissipation The curvature of the initially horizontal planes that occurs in the rollover sections with increasing lateral displacement is believed to produce friction damping as the individual fibers move over one another [7]. Additional energy dissipation due to internal friction could be highly advantageous, reducing the required supplementary damping or additional damping to be obtained from the elastomer through compound additives. Numerous experimental studies have observed increased equivalent viscous damping in FREIs, bonded and unbonded, either relative to a similar SREI design [48,66–70,85], in comparison to the inherent damping of the elastomer [7,28,31,46,48,58,65], or in FREIs with a higher fiber density [56]. However, some experimental investigations have concluded that the fiber reinforcement does not significantly contribute to the damping [18,57,59,69]. It is evident that the energy dissipation capabilities of FREIs are not yet reliably predictable and dependent on the isolator design and loading. The lateral energy dissipation is expected to increase with an increase in the applied vertical compressive load attributed to an increase in internal friction in the elastomer at the molecular level as well as increased friction in the fibers [28,30,48,49,69]. Experimental testing often observes damping values between 10 and 15% of critical; although, results vary significantly between studies for different isolator designs and elastomeric compounds and values in excess of 30% of critical have been reported [32]. In general, the equivalent viscous damping has been observed to decrease with increasing lateral displacement [18,19,28,31,32,45–48,53,69,85]. 4. Rotational properties 4.1. Bending stiffness Similar to SREIs, the bending stiffness of FREIs is often expressed in terms of an effective bending modulus. Following the assumptions of the pressure solution, adjusting for applied rotation, closed-form analytical solutions have been developed for infinite strip [10], and 5

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rectangular [13,86] pad geometries. To date, no analytical solution for a circular or annular pad including the effects of compressibility and extensibility has been derived. Solutions including compressibility [87] or extensibility [88–90], exclusively, are available for circular pads, and considering only compressibility for annular pads [33]. Good agreement between the pressure solution and finite element analysis conducted on infinite strip [20] and rectangular [13,23] pad geometry has been observed. Experimental studies on rectangular unbonded FREIs subjected to rotation were conducted in Refs. [23,64]. It was found that, for the isolators considered, rotations up to 0.03 rad did not have a significant effect on the vertical or lateral stiffness. The bending modulus exhibits similar limits as the compression modulus, approaching the elastic modulus of the elastomer as S approaches 0, or the bulk modulus as S approaches infinity assuming the reinforcement is rigid. Inclusion of the extensibility of the reinforcement determines that the bending modulus will approach Ke (Eq. (2)) as S approaches infinity. Note that Ke may vary between the compression modulus and bending modulus for the same pad geometry (i.e. e depends on the geometry and loading). Thus, including the extensibility of the reinforcement acts to decrease the effective bending modulus, similar to the compression modulus. The closed-form analytical solutions for the bending modulus do not reflect the loss of rigidity experienced by the fiber reinforcement in compression. Due to the near incompressibility of the elastomer, the inward bulging that may occur under an applied rotation (see Fig. 5) could introduce a compressive force into the fiber reinforcement. This was analytically investigated for an infinite strip pad in Ref. [91]. The conditions for compression to develop in the reinforcement is analogous to lift-off, discussed in the subsequent section, where the tensile stress due to the applied rotation overcomes the hydrostatic compressive stress due to the applied axial vertical compressive load. Finite element investigations have identified that the tension-only reinforcement may buckle under a compressive stress [20], although it is believed that the reinforcement would return to the original state if the magnitude of the rotation was reduced or removed.

is three times greater than the characteristic rotation [86]. In circular pads, lift-off will be initiated at double the characteristic rotation. In rectangular pads, lift-off will occur between 1.5 and 3 times the characteristic rotation depending on the length-to-width aspect ratio and λ [86]. If compressibility and extensibility is included, the magnitude of rotation required to initiate lift-off decreases, converging to the characteristic rotation as λ approaches infinity for infinite strip, rectangular and circular pad geometries [86]. Lift-off significantly reduces the rotational stiffness of the isolator [20,86]. From an analytical perspective, the area of the isolator that has lost contact with the supports is assumed to be stress free, similar to rollover. The instantaneous properties are based on a reduced effective isolator. An example of the moment-rotation relationship of an infinite strip pad is shown in Fig. 6b (λ ≈ 0). The moment, M, has been normalized by the lift-off initiating moment, M0. For isolators with rigid reinforcement and an incompressible elastomer, Ref. [92] found that lift-off did not have a significant impact on the shear stresses. Due to this observation, previous no lift-off requirements in the AASHTO LRFD Bridge Design Specification [93] have been removed. No corrections are made for lift-off. However, other standards, such as the Canadian Highway Bridge Design Code (CSA S6-14) [94], maintain a no lift-off requirement. 5. Buckling properties Elastomeric isolators can be viewed as short columns supporting the weight of the structure and are therefore also susceptible to buckling instability. The isolator is often idealized as a continuous composite system that acts as a beam, extending from Refs. [8,95–97]. The analytical solutions developed in Refs. [98,99] for the buckling load of SREIs at zero horizontal displacement assumed that the steel reinforcement was flexible and extensible, thus making it appropriate for FREIs as well. The solution determined the horizontal stiffness accounting for stability, shear, bending and warping effects. The buckling load was established by equating the horizontal stiffness to zero. This analytical solution represents the most comprehensive solution available for FREIs, but it is limited to zero horizontal displacement. From Refs. [98,99], the lateral stiffness is expected to decrease with increasing vertical load, approaching zero as the vertical load approaches the critical buckling load. Accounting for lateral displacement, the analytical investigation by Ref. [100] on the stability of an infinite strip unbonded FREIs ignored the rollover sections. The assumption is believed to provide a lower estimate of the actual buckling characteristics of an unbonded FREI. The ‘tension-only’ nature of the fiber reinforcement may also reduce the stability in comparison to an equivalent SREI, as shown analytically in Ref. [91]. Experimental investigations considering the sensitivity of the lateral response of FREIs to vertical loads have somewhat conflicting conclusions. Studies have observed increasing [18,34], decreasing [23,30,32,48,49,64], and negligible [28,69,70] change in the lateral stiffness with an increase in the applied vertical load for a range of isolator designs and average vertical stress. Table 1 provides the values of S, the applied average vertical compressive stress, σc, the second shape factor (S2, ratio of the length or diameter to tr) and the observed trend in the experimental studies. The shape factor and second shape factor are both critical properties in analytically determining the buckling capacity of a reinforced elastomeric isolator. In general, investigations that considered a large range and relatively high values of σc observe a decrease in lateral stiffness with increasing vertical load. This result is expected based on the analytical solution [98,99]. It is evident that other factors, such as friction and non-linearity of the elastomer, may contribute to an observed increase in lateral stiffness [18,34]. The analytical solutions also indicate that isolators with a lower S are expected to be more sensitive to the vertical load. This is also reflected in experimental results found in the references provided in Table 1.

4.2. Lift-off Some level of rotation is expected in all elastomeric isolator applications due to construction tolerances. In addition to the development of shear stress in the elastomer, rotations can also introduce tensile stress in the elastomer of bonded isolators or result in lift-off of unbonded isolators. Lift-off, or the loss of contact between the exterior elastomer layers and supports due to rotation, occurs in situations where the level of rotation overcomes the applied compressive stress. Lift-off is initiated at rotations greater than the characteristic rotation, defined as the rotation, θ, at which the rotational strain is equal to the compressive strain, εc, at the extreme edge of an elastomeric pad (i.e. at b or a for rectangular isolators):

b = t

c

(8)

The relationship between εc and the lift-off initiating rotation, θ0, is illustrated in Fig. 6a for an infinite strip pad. If incompressibility and inextensibility is assumed, lift-off will occur when the applied rotation

Fig. 5. Buckling of tension-only reinforcement in bonded FREIs due to inward lateral bulging (adapted from Ref. [20]). 6

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Fig. 6. The (a) strain ratio required to initiate lift-off and (b) normalized moment-rotation relationship accounting for lift-off for an infinite strip pad (λ ≈ 0) [86].

elastomeric isolators often consider only uniform compression or pure bending. While investigating the impact of reducing steel reinforcement thickness, Ref. [8] identified that warping effects (i.e. plane sections do not remain plane after deformation) may have a significant effect on the buckling capacity. In addition to being extensible, fiber reinforcement has no appreciable flexural rigidity and hence is susceptible to warping effects. Following Ref. [8], Refs. [98,99] derived an analytical solution for the buckling load of a reinforced elastomeric isolator including warping effects. Reference [15] investigated warping effects in greater detail for an infinite strip isolator, releasing numerous assumptions associated with the pressure solution. Warping may significantly impact the buckling capacity and the stresses and strains that develop within the elastomer, yet, beyond Refs. [8,15,98,99], warping remains largely uninvestigated for other pad geometries.

Table 1 Values of S, σc and S2 used to determine the observed trend in lateral stiffness with increasing σc. Trend

Ref.

S

σc (MPa)

S2

Decrease

[23] [30] [48]

5.5 12 8.7, 20.5

4.4 4.4 3.0, 4.3, 4.7

[64] [32] [49]

6 8.7, 20.5 11

2, 4, 6, 8, 10 3, 5, 7, 10, 12, 15 3.9, 5.8, 7.7, 11.6, 15.4 2, 6, 10 3.9, 7.7, 11.6 1.6 to 18.4

3.4, 4.2, 7.7 3.2, 4.2, 4.7 3.7

[69]

3, 6

3.4, 3.5, 3.6

[70] [28]

14.5, 22.4, 39.8 5.8, 11.7 11

1, 2, 3 0.8, 1.6, 2.4

2.7, 2.9, 3.3, 3.8, 5.8 3.7

[34] [18]

23 8.8, 17.5

0.15 to 8 3.45, 6.90

4.8 3.1, 3.8

Negligible

Increase

8. Shear strain demands Standards and codes covering the design of elastomeric bearings [93,94,101–105] place limitations on the maximum shear strain (or axial strain) in the elastomer due to compression, γc, rotation, γr, and imposed lateral displacements from all sources, individually and/or in combination. If shear strain due to warping is expected to be significant it should also be considered. The development of these shear strains is illustrated in Fig. 7. Existing equations for quantifying the maximum shear strain due to compression and rotation in design guidelines may be somewhat restrictive, being applicable for limited pad geometries and often ignoring the compressibility of the elastomer and extensibility of the reinforcement. Analytical solutions are available for most basic pad geometries based on the pressure solution including these effects [25,106]. It has been shown that neglecting compressibility and extensibility can lead to significant error in comparison to the analytical solutions [25,106], particularly with large shape factors (or values of λ), for which the assumption of incompressibility or

6. Vertical and lateral combined loading The vertical stiffness of unbonded FREIs as a function of lateral displacement has been investigated experimentally for rectangular isolators [19] and with finite element analysis for infinite strip isolators [22]. In Ref. [19] it was observed that the vertical stiffness remained nearly constant with a lateral offset despite the reduction in loaded area (although the vertical displacement increased with lateral displacement). In Ref. [19], it was postulated that Ef increased due to straightening of the fibers, consequently increasing the restraint on the elastomeric layers and therefore increasing the effective compression modulus. Thus, despite the reduction in area due to the lateral offset, the vertical stiffness remained nearly constant. These experimental observations contradict the conclusions of a finite element investigation by Ref. [22], which observed decreasing vertical stiffness with increasing lateral displacement (as well as increased vertical displacement with lateral displacement). Note that the finite element investigation assumed that the reinforcement was linear elastic (i.e. fiber straightness non-linearity was not represented). This assumption is typically made in finite element investigations on FREIs, as discussed in the Finite element analysis section. The fact that a decreasing vertical stiffness was observed in the finite element investigation, which neglects non-linearity of the fiber reinforcement, reinforces the postulate of the experimental study. Further investigation in this area is required; regardless, both investigations observed an increase in vertical displacement with lateral displacement. 7. Warping properties

Fig. 7. Development of shear strains in elastomeric pads due to applied lateral displacements, compression and rotation.

Studies on the compression and bending properties of reinforced 7

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inextensibility becomes less appropriate. The need to accommodate shear strains caused by compression and rotation can be challenging for designers due to the opposing trends as a function of shape factor: c

r

c GS

S2

=f( )

9.2. Finite element analysis The development of local stresses and strains within the elastomeric and fiber-reinforcement layers has been investigated utilizing two-dimensional and three-dimensional finite element analysis (FEA). The FEA models may be difficult to develop due to the large strains and deformations expected in the elastomer (in particular for unbonded models). Reference [120] discusses different FEA techniques for FREIs. The elastomeric material has been modelled with a hyperelastic Neo-Hookean model [12,20–22,24,35,51,52,58,64,73,113], Mooney-Rivlin [121,122], JamesGreen-Simpson model [53], Ogden model [55,113], Yeoh model [36,77,112,118] and a combination of the hyperelastic and viscoelastic models (e.g. Mooney-Rivlin Prony [109,123] and Odgen Prony [37]). The fiber reinforcement has been modelled as a linear elastic isotropic or orthotropic material with membrane, shell, rebar, or truss elements [12,13,20–22,24,35,36,51–53,64,73,100,113,118,121,123]. The boundary conditions are rigid surfaces that are glued to the elastomer in bonded applications, or that have a contact surface defined with Coulomb friction [12,20,21,35,37,55,58,64,77]. The coefficient of friction is selected to be sufficiently high to prevent slip. The contributions and observations from these studies are presented and discussed in the appropriate sections. By modeling the reinforcement as a linear-elastic material the run-in effect cannot be observed in finite element analysis. In general, the vertical, lateral and rotational stiffness is constant, barring any nonlinearities from the material models or geometric considerations due to large amplitude loading (e.g. rollover, lift-off).

(9)

where f is a function dependent on the bearing geometry and applied loading (i.e. compression or rotation). Increasing the shape factor vertically stiffens the bearing and reduces the vertical compression strain, which is proportional to γc; however, it also increases the rotational stiffness, resulting in an increased value of γr for the same level of rotation. Refs. [25,106] provides or derives the analytical solutions for the maximum shear strain due to compression and rotation for various pad geometries. The study also proposes simplified expressions including compressibility and extensibility appropriate for use in design guidelines. 9. Modeling FREIs 9.1. Numerical models for time history analysis Various approaches have been pursued to model FREIs numerically for non-linear time history analysis. Several different models have been used including displacement and rate sensitive functions for stiffness and damping [47,107], bi-linear and tri-linear models [62,68,74,107–110], Takeda-Elastic model [61], a combination of hysteretic and sliding elements [111], non-linear springs with viscous damping [36,75,112,113], pivot-elastic model [114,115], variations of the Bouc-Wen model [45,62,116,117], 12 degree-of-freedom beam element [118] and a phenomenological model [119]. These FREI models have been used to investigate the response of base isolated buildings [36,45,68,75,107,110–112,114,115,117,118,120], bridges [61,109], a liquid storage tank [113], and non-structural components and systems [45] to seismic events. The response of a base isolated building with a tuned liquid damper subjected to wind loads has also been considered [116]. These studies have all recognized the expected benefits of a base isolation system with FREIs in comparison to a conventional fixed-base structure. Displacements that do not exceed full rollover can be satisfactorily represented by any of the above models. The numerical models can be calibrated based on experimental results or finite element analysis. For larger displacements exceeding full rollover, modifications can be made to the existing models to capture the softening and stiffening characteristics. For example, in lieu of the traditional Bouc-Wen model, which contains a yield and post-yield stiffness, a fifth order polynomial can be used for the restoring force, F [45]:

F = a1 u + a2 u u + a3 u3 + a4 u u3 + a5 u5 + Bz

10. FREI variations Numerous unique variations of FREIs have been proposed with the purpose of cost savings, controlling or enhancing selected performance characteristics, or to address potential limitations. The ability to cut a FREI to the desired size from a larger pad determines that modifications can easily be made to the isolator geometry. The following is a brief outline of materials and modifications in geometry that have been considered or proposed in the literature. 10.1. Materials used in FREIs Numerous studies have compared SREIs and FREIs directly [6,18,32,48,57,69]; however, the number or thickness of the elastomeric layers is often adjusted to maintain the same height, or the two isolators are otherwise dissimilar. The number and thickness of the reinforcement layers can have significant influence on the properties of an isolator. Thus, studies comparing the two types of isolators should be reviewed to identify the differences in isolator design and the potential impact on the conclusions. Unlike steel reinforcement, the mechanical properties of fiber reinforcement can vary considerably by the type of fiber. Reinforcement layer design can also vary based on the weave, density and thickness. Thus, the geometry of an isolator can remain relatively unchanged while properties (e.g. compression and bending modulus) can vary with a change in fiber reinforcement. Table 2 shows the different combinations of fiber-reinforcement and elastomer that have been considered in experimental investigations. Within these investigations, additional variations can be found with respect to the weave, density, and thickness of the fiber reinforcement used. Carbon fiber has thus far been the primary reinforcement of choice.

(10)

with the hysteretic parameter, z, defined as:

z=

u {A Y

[ sgn(zu) + ] z n }

(11)

where B, Y, A, β, γ, ai (i = 1:5) and n are quantities that control the shape of the hysteresis and sgn is the sign function. The parameters in Eqs. (10) and (11) can be determined through regression techniques on experimental data. A viscous damping component could also be included to Eq. (10). Note that some of the physical interpretations of the parameters with a traditional Bouc-Wen model have been lost (i.e. yield displacement, yield and post-yield stiffness). Variations of Eqs. (10) and (11) have been proposed in Refs. [116,117]. It is worth noting that in Ref. [107] a bilinear model provided better predictions of the peak values observed in a shake table investigation than a displacement and rate sensitive model with 10 fitted parameters. Although this is not expected to always be true, it is a reminder that increased complexity does not necessarily guarantee increased accuracy.

10.2. Modified rectangular (strip) FREIs In Ref. [7] it was believed that it would be possible to manufacture FREIs in long rectangular strips. In addition to cost savings in the manufacturing process, strip isolators provide uniform support along shear walls, reducing the requirements of the rigid diaphragm used to transfer loads to smaller square or circular isolators. Time history 8

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Table 2 Summary of elastomer and fiber-reinforcement types considered in experimental programs. Elastomer

Unspecified elastomer Neoprene Natural Rubber Recycled Rubber Other

Fiber Reinforcement Kevlar

Carbon

Glass

Other

[7,65]

[29,31,34,37,50,55,66–69,74,83–85,110,113,123] [28,45,46,49,51–53,56,60,124] [10,18,19,23,32,47,57] [58,59,62,81,82] [56,71,108,125]

[63,67,85,113,122] [6] [32]

[30,50,66,67]

Fig. 8. Potential modified rectangular FREI geometry [52,53].

analyses conducted in Ref. [114] confirmed the viability of using rectangular strip isolators on a masonry shear wall structure. In an effort to reduce the lateral stiffness of the large strip isolators, thereby increasing the overall efficiency of the isolation system, Refs. [52,53] proposed modifying the loaded surface of the rectangular FREI by removing a portion of the area either from the interior or exterior of the isolator, as shown in Fig. 8. This concept was investigated experimentally and with finite element analysis for the vertical and lateral directions. It was found that the vertical and lateral stiffness was highly sensitive to the interior modifications and, to a lesser extent, exterior modifications. Other critical parameters, such as the maximum shear strain due to compression, was also significantly impacted. The studies demonstrated that the concept has merit, but more research is required to develop a better understanding of the sensitivity of the critical properties due to the modifications.

stiffening can be increased. Accelerating full rollover was found to provide a self-restraint mechanism at the expense of an increased response (e.g. acceleration) of the investigated structure for the ground motions considered. 10.4. Partially bonded FREIs Two potential disadvantages with the unbonded application of FREIs is the possibility of slip under certain loading conditions and the inability to resist any uplift forces. Slip has been observed in experimental programs [10,34] and, as expected, is more probable in circumstances with a low applied vertical compressive stress [34]. In order to address these potential disadvantages, it was proposed that an unbonded FREI could be partially bonded to the upper and lower supports [51], thereby creating a hybrid between an unbonded and fully bonded isolator. It has been demonstrated experimentally and with finite element analysis that a significant area (e.g. the central section identified in Fig. 3c) of the isolator can be bonded without significantly altering the lateral or vertical properties of the isolator. The beneficial softening and stiffening adaptive characteristics of unbonded FREIs are retained while alleviating concerns over the potential for slip and introducing some level of uplift resistance. The concept does require the re-introduction of steel-end plates for bonding but, depending on the application, the benefits may outweigh the additional cost. The application of partially bonded FREIs as bridge bearings, aging effects, and temperature sensitivity has also been investigated [125].

10.3. FREIs with modified support or end geometry The beneficial rollover characteristics of unbonded FREIs is primarily a function of the geometry of the bearing. From Eq. (5), full rollover is a function of the total thickness of the elastomeric layers and total height of the bearing (assuming the reinforcement is flexible). Equation (5) assumes that the supports are parallel to the isolator plane and that the faces of the isolator are a plane perpendicular to the supports. Reference [126] proposed that the lateral response of an unbonded FREI could be modified by either altering the end geometry (i.e. the initially vertical faces) of the isolator, or by modifying the support geometry that the faces contact at full rollover. In Ref. [126], a preliminary experimental program was conducted by modifying the initially vertical faces of the isolator to a wedge shape. The concept was further validated in Ref. [45] which investigated the use of modified support geometry, illustrated in Fig. 9, to accelerate or delay full rollover and stiffen or soften the post-full rollover response of the isolator. It was shown that modifying the support geometry did not have any impact on the softening characteristics of an unbonded FREI. However, by delaying full rollover, the displacement capacity of the device before

11. Application and discussion The design of a base isolated structure with FREIs has been completed in numerous investigations [46,75,83,84] based on the requirements in ASCE/SEI 7-10 [127]. Design algorithms for the sizing of unbonded FREIs as well as for preventing sliding and overturning of the superstructure have been proposed in Ref. [75]. Optimization of the isolator design for a particular structure has been investigated in Ref. [109]. Numerous shake table studies [81–84,124] and numerical

Fig. 9. Examples of modified support geometry that will (a) accelerate full rollover and increase stiffening or (b) delay full rollover and decrease stiffening [72]. 9

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investigations [36,45,47,61,68,74,75,84,107–115,117] have demonstrated that FREIs exhibit the expected benefits of a base isolation system in comparison to a conventional fixed-base structure. A two-story prototype masonry building located in Tawang, India, has the distinction of being the first structure to be seismically isolated with unbonded FREIs (to the author's best knowledge) [74]. The residential structure is well aligned with the intended application of FREIs in developing countries as initially proposed by Ref. [7]. The building has reinforced concrete floors and basement beams that support the isolators. The building is supported by 14 (5–310 mm and 9–250 mm) square unbonded FREIs (S = 12.5 and 15.5, respectively). Each bearing is designed to support an average vertical stress of 5.6 MPa. In Ref. [74] significant experimental testing and numerical modeling was conducted to demonstrate the improved performance of the isolation system in comparison to a conventional fixed-base structure. It is postulated that with adequate prototype testing and development, as is commonly required in building codes and standards related to elastomeric bearings [3,4,93,94,101–105], FREIs can currently be satisfactorily applied to structures as they have been in Tawang, India. However, the current common practice of customized isolator design, manufacturing and prototype testing for every application is not conducive to widespread low-cost application of base isolation technology. For this to be realized, it is envisioned that a catalogue of devices will be developed such that an appropriate device can be quickly selected based on simple design constraints. Manufacturing of a large volume of standardized designs will allow economies of scale to be realized and reduce the need for prototype testing. For such a catalogue to be developed, consensus is required in the research community on the limitations and constraints to be applied to FREIs through the development of appropriate design guidelines and standards. In the opinion of the author, development of such a guideline or standard is the primary challenge for FREI research moving forward. Within this scope, all critical areas of isolator design, as discussed herein, are relevant and worthy of additional research. Current guidelines and standards on elastomeric bearings have almost exclusively been developed based on steel reinforcement [93,94,101–105]. To the author's best knowledge, none currently account for the extensibility of the reinforcement. AASHTO LRFD Bridge Design Specification [93] provides guidelines for the design of fiberglass reinforced elastomeric bearings based on the 1974 study by Ref. [6]. These requirements, referred to as Method A, cover numerous types of elastomeric bearings and are restrictive compared to the requirements of Method B which is exclusive for SREIs. CSA S6-14 [94] allows “other reinforcement capable of withstanding the expected stresses and deformations” to be considered, but otherwise only outlines equations appropriate for low shape factor SREIs. Moreover, the bulk compressibility of the elastomer is also typically neglected or accounted for in a limited capacity at the engineer's discretion. Limitations for use of the equations, based on the shape factor, and recommended corrections for bulk compressibility, when available, are provided in the commentary or appendix of the standard [93,102–105]. Note that neglecting the compressibility is acceptable for low shape factors, common in bridge bearings, but can otherwise lead to significant error.

development of FREIs was primarily to reduce the cost of isolation devices. Although the potential for cost savings is well appreciated in the literature, a detailed study demonstrating and quantifying the potential savings has not been completed. It is believed that this is largely reflective of the fact that FREIs are not currently manufactured in large quantities, nor has the concept of cutting smaller isolators from larger pads been realized on a large scale (although this is commonly done when manufacturing specimens for research). It is believed that increased application of FREIs will encourage manufacturers to enter the market, which will assist in determining accurate cost estimates and allow the potential benefits of manufacturing larger pads to be realized. Acknowledgments This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References [1] Kelly JM. Aseismic base isolation: review and bibliography. Soil Dynam Earthq Eng 1986;5:202–16. [2] Clemente P, Martelli A. Anti-seismic systems: worldwide application and conditions for their correct use. Proc. 16th world conf. Earthq. Eng., Santiago, Chile. 2017. [3] National Research Council Canada. National Building Code of Canada 2015. Ottawa, Canada. 2015. [4] American Society of Civil Engineers (ASCE). Minimum design loads for buildings and other structures ASCE/SEI 7-16. Reston. 2017. [5] Naeim F, Kelly JM. Design of seismically isolated structures: from theory to practice. John Wiley & Sons; 1999. [6] Crozier W, Stoker J, Martin V, Nordlin E. A laboratory evaluation of full size elastomeric bridge bearing pads (CA-DOT-TL-6574-1-74-26). Sacramento, CA: Highway Research Report; 1974. [7] Kelly JM. Analysis of fiber-reinforced elastomeric isolators. J Seismol Earthq Eng 1999;2:19–34. [8] Kelly JM. The influence of plate flexibility on the buckling load of elastomeric isolators Rep No UCB/EERC-94/03 Berkeley: Earthquake Engineering Research Center; 1994. [9] Muniandy K, Pond TJ, Lim CL. Light weight natural rubber bearings. Proc. Int. Rubber technol. Conf., Kuala Lumpur, Malaysia. 1993. p. 303–27. [10] Kelly JM, Takhirov SM. Analytical and experimental study of fiber-reinforced strip isolators Rep No PEER 2002/11 Berkeley: Pacific Earthquake Engineering Research Center, Univ California; 2002. [11] Pinarbasi S, Okay F. Compression of hollow-circular fiber-reinforced rubber bearings. Struct EngMech 2011;38:361–84. [12] Kelly JM, Calabrese A. Analysis of fiber-reinforced elastomeric isolators including stretching of reinforcement and compressibility of elastomer. Ing Sismica 2013;30:5–16. [13] Angeli P, Russo G, Paschini A. Carbon fiber-reinforced rectangular isolators with compressible elastomer: analytical solution for compression and bending. Int J Solids Struct 2013;5:3519–27. https://doi.org/10.1016/j.ijsolstr.2013.06.016. [14] Kelly JM, Van Engelen NC. Fiber-reinforced elastomeric bearings for vibration isolation. J Vib Acoust 2016;138. https://doi.org/10.1115/1.4031755. [15] Pinarbasi S, Mengi Y. Elastic layers bonded to flexible reinforcements. Int J Solids Struct 2008;45:794–820. https://doi.org/10.1016/j.ijsolstr.2007.08.029. [16] Tsai H-C. Compression stiffness of infinite-strip bearings of laminated elastic material interleaving with flexible reinforcements. Int J Solids Struct 2004;41:6647–60. https://doi.org/10.1016/j.ijsolstr.2004.06.005. [17] Tsai H-C. Compression stiffness of circular bearings of laminated elastic material interleaving with flexible reinforcements. Int J Solids Struct 2006;43:3484–97. https://doi.org/10.1016/j.ijsolstr.2005.05.012. [18] Naghshineh AK, Akyüz U, Caner A. Comparison of fundamental properties of new types of fiber-mesh-reinforced seismic isolators with conventional isolators. Earthq Eng Struct Dyn 2014;43:301–16. https://doi.org/10.1002/eqe.2345. [19] Al-Anany YM, Van Engelen NC, Tait MJ. Vertical and lateral behavior of unbonded fiber-reinforced elastomeric isolators. J Compos Constr 2017;21:4017019. https:// doi.org/10.1061/(ASCE)CC.1943-5614.0000794. [20] Al-Anany YM, Tait MJ. A numerical study on the compressive and rotational behavior of fiber reinforced elastomeric isolators (FREI). Compos Struct 2015;133:1249–66. https://doi.org/10.1016/j.compstruct.2015.07.042. [21] Toopchi-Nezhad H, Tait MJ, Drysdale RG. Influence of thickness of individual elastomer layers (first shape factor) on the response of unbonded fiber-reinforced elastomeric bearings. J Compos Mater 2013;47:3433–50. https://doi.org/10. 1177/0021998312466686. [22] Osgooei PM, Konstantinidis D, Tait MJ. Variation of the vertical stiffness of stripshaped fiber-reinforced elastomeric isolators under lateral loading. Compos Struct 2016;144:177–84. https://doi.org/10.1016/j.compstruct.2016.01.089. [23] Al-Anany YM, Tait MJ. Experimental assessment of utilizing fiber reinforced elastomeric isolators as bearings for bridge applications. Compos B Eng 2017;114:373–85. https://doi.org/10.1016/j.compositesb.2017.01.060.

12. Conclusions The concept of FREIs is promising. Since 1999, FREIs have been investigated extensively experimentally, analytically, and numerically, with all studies reporting favorable findings. If structures isolated with FREIs, such as in Tawang, India, exhibit satisfactory behavior during strong ground motions, it is expected that the number of structures utilizing FREIs will increase rapidly. The primary challenge for researchers moving forward is to develop a comprehensive design guideline or standard for FREIs. Within this aim, research is required within all areas discussed in this paper to reach a consensus. It is interesting to note that the original impetus for the 10

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N.C. Van Engelen [24] Osgooei PM, Tait MJ, Konstantinidis D. Three-dimensional finite element analysis of circular fiber-reinforced elastomeric bearings under compression. Compos Struct 2014;108:191–204. https://doi.org/10.1016/j.compstruct.2013.09.008. [25] Van Engelen NC, Tait MJ, Konstantinidis D. Development of design code oriented formulas for elastomeric bearings including bulk compressibility and reinforcement extensibility. J Eng Mech 2016;142:4016024. https://doi.org/10.1061/ (ASCE)EM.1943-7889.0001015. [26] Konstantinidis D, Moghadam SR. Compression of unbonded rubber layers taking into account bulk compressibility and contact slip at the supports. Int J Solids Struct 2016;87:206–21. https://doi.org/10.1016/j.ijsolstr.2016.02.008. [27] Kelly JM. Analysis of the run-in effect in fiber-reinforced isolators under vertical load analysis of the run-in effect in fiber-reinforced isolators under vertical load. J Mech Mater Struct 2008;3:1383–401. https://doi.org/10.2140/jomms.2008.3. 1383. [28] Toopchi-Nezhad H, Drysdale RG, Tait MJ. Parametric study on the response of stable unbonded-fiber reinforced elastomeric isolators (SU-FREIs). J Compos Mater 2009;43:1569–87. https://doi.org/10.1177/0021998308106322. [29] Moon BY, Kang GJ, Kang BS, Kim GS, Kelly JM. Mechanical properties of seismic isolation system with fiber-reinforced bearing of strip type. Int Appl Mech 2003;39:1231–9. https://doi.org/10.1023/B:INAM.0000010377.92594.3c. [30] Tan P, Xu K, Wang B, Chang CM, Liu H, Zhou FL. Development and performance evaluation of an innovative low-cost seismic isolator. Sci China Technol Sci 2014;57:2050–61. https://doi.org/10.1007/s11431-014-5662-6. [31] Hedayati Dezfuli F, Alam MS. Performance of carbon fiber-reinforced elastomeric isolators manufactured in a simplified process: experimental investigations. Struct Contr Health Monit 2014;21:1347–59. https://doi.org/10.1002/stc.1653. [32] Ruano PC, Strauss A. An experimental study on unbonded circular fiber reinforced elastomeric bearings. Eng Struct 2018;177:72–84. https://doi.org/10.1016/j. engstruct.2018.09.062. [33] Kelly JM, Konstantinidis D. Mechanics of rubber bearings for seismic and vibration isolation. Chichester: John Wiley & Sons; 2011. [34] Russo G, Pauletta M. Sliding instability of fiber-reinforced elastomeric isolators in unbonded applications. Eng Struct 2013;48:70–80. https://doi.org/10.1016/j. engstruct.2012.08.031. [35] Toopchi-Nezhad H, Tait MJ, Drysdale RG. Bonded versus unbonded strip fiber reinforced elastomeric isolators: finite element analysis. Compos Struct 2011;93:850–9. https://doi.org/10.1016/j.compstruct.2010.07.009. [36] Habieb AB, Milani G, Tavio T. Two-step advanced numerical approach for the design of low-cost unbonded fiber reinforced elastomeric seismic isolation systems in new masonry buildings. Eng Fail Anal 2018;90:380–96. https://doi.org/10. 1016/j.engfailanal.2018.04.002. [37] Das A, Dutta A, Deb SK. Performance of fiber-reinforced elastomeric base isolators under cyclic excitation. Struct Contr Health Monit 2015;22:197–220. https://doi. org/10.1002/stc.1668. [38] Van Engelen NC, Tait MJ, Konstantinidis D. Model of the shear behavior of unbonded fiber-reinforced elastomeric isolators. J Struct Eng 2015;141:4014169. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001120. [39] Kelly JM, Konstantinidis D. Low-cost seismic isolators for housing in highlyseismic developing countries, Proceedings of the 10th world conference on seismic isolation, energy dissipation, and active vibration control of structures, Turkey. 2007. [40] Li H, Tian S, Dang X, Yuan W, Wei K. Performance of steel mesh reinforced elastomeric isolation bearing: experimental study. Constr Build Mater 2016;121:60–8. https://doi.org/10.1016/j.conbuildmat.2016.05.143. [41] Mishra HK, Igarashi A, Matsushima H. Finite element analysis and experimental verification of the scrap tire rubber pad isolator. Bull Earthq Eng 2013;11:687–707. https://doi.org/10.1007/s10518-012-9393-4. [42] Fenz DM, Constantinou MC. Spherical sliding isolation bearings with adaptive behavior: theory. Earthq Eng Struct Dyn 2008;37:163–83. https://doi.org/10. 1002/eqe.751. [43] Tsai CS, Chiang TC, Chen BJ. Finite element formulations and theoretical study for variable curvature friction pendulum system. Eng Struct 2003;25:1719–30. https://doi.org/10.1016/S0141-0296(03)00151-2. [44] Yang TY, Konstantinidis D, Kelly JM. The influence of isolator hysteresis on equipment performance in seismic isolated buildings. Earthq Spectra 2010;26:275–93. https://doi.org/10.1193/1.3276901. [45] Van Engelen NC, Konstantinidis D, Tait MJ. Structural and nonstructural performance of a seismically isolated building using stable unbonded fiber-reinforced elastomeric isolators. Earthq Eng Struct Dyn 2016;45:421–39. https://doi.org/10. 1002/eqe.2665. [46] Toopchi-Nezhad H, Tait MJ, Drysdale RG. Lateral response evaluation of fiberreinforced neoprene seismic isolators utilized in an unbonded application. J Struct Eng 2008;134:1627–37. https://doi.org/10.1061/(ASCE)0733-9445(2008) 134:10(1627). [47] Toopchi-Nezhad H, Tait MJ, Drysdale RG. Testing and modeling of square carbon fiber-reinforced elastomeric seismic isolators. Struct Contr Health Monit 2008;15:876–900. https://doi.org/10.1002/stc.225. [48] Strauss A, Apostolidi E, Zimmermann T, Gerhaher U, Dritsos S. Experimental investigations of fiber and steel reinforced elastomeric bearings: shear modulus and damping coefficient. Eng Struct 2014;75:402–13. https://doi.org/10.1016/j. engstruct.2014.06.008. [49] de Raaf MGP, Tait MJ, Toopchi-Nezhad H. Stability of fiber-reinforced elastomeric bearings in an unbonded application. J Compos Mater 2011;45:1873–84. https:// doi.org/10.1177/0021998310388319. [50] Losanno D, Sierra IEM, Spizzuoco M, Thomson P. Experimental assessment and analytical modeling of novel fiber-reinforced isolators in unbounded

[51] [52]

[53]

[54] [55] [56]

[57] [58] [59] [60] [61] [62]

[63] [64] [65] [66] [67] [68] [69]

[70] [71] [72]

[73]

[74] [75] [76]

11

configuration. Compos Struct 2019;212:66–82. https://doi.org/10.1016/j. compstruct.2019.01.026. Van Engelen NC, Osgooei PM, Tait MJ, Konstantinidis D. Partially bonded fiberreinforced elastomeric isolators (PB-FREIs). Struct Contr Health Monit 2015;22:417–32. https://doi.org/10.1002/stc.1682. Van Engelen NC, Osgooei PM, Tait MJ, Konstantinidis D. Experimental and finite element study on the compression properties of modified rectangular fiber-reinforced elastomeric isolators. Eng Struct 2014;74:52–64. https://doi.org/10. 1016/j.engstruct.2014.04.046. Osgooei PM, Van Engelen NC, Konstantinidis D, Tait MJ. Experimental and finite element study on the lateral response of modified rectangular fiber-reinforced elastomeric isolators (MR-FREIs). Eng Struct 2015;85:293–303. https://doi.org/ 10.1016/j.engstruct.2014.11.037. Kelly JM. Seismic isolation systems for developing countries. Earthq Spectra 2002;18:385–406. https://doi.org/10.1193/1.1503339. Ngo TV, Deb SK, Dutta A. Effect of horizontal loading direction on performance of prototype square unbonded fibre reinforced elastomeric isolator. Struct Contr Health Monit 2018;25. https://doi.org/10.1002/stc.2112. Russo G, Pauletta M, Cortesia A. A study on experimental shear behavior of fiberreinforced elastomeric isolators with various fiber layouts, elastomers and aging conditions. Eng Struct 2013;52:422–33. https://doi.org/10.1016/j.engstruct. 2013.02.034. Naghshineh AK, Akyüz U, Caner A. Lateral response comparison of unbonded elastomeric bearings reinforced with carbon fiber mesh and steel. Shock Vib 2015. https://doi.org/10.1155/2015/208045. Spizzuoco M, Calabrese A, Serino G. Innovative low-cost recycled rubber-fiber reinforced isolator: experimental tests and Finite Element Analyses. Eng Struct 2014;76:99–111. https://doi.org/10.1016/j.engstruct.2014.07.001. Calabrese A, Serino G, Strano S, Terzo M. Experimental investigation of a low-cost elastomeric anti-seismic device using recycled rubber. Meccanica 2015;50:2201–18. https://doi.org/10.1007/s11012-015-0155-7. Pauletta M, Cortesia A, Russo G. Roll-out instability of small size fiber-reinforced elastomeric isolators in unbonded applications. Eng Struct 2015;102:358–68. https://doi.org/10.1016/j.engstruct.2015.08.019. Al-Anany YM, Moustafa MA, Tait MJ. Modeling and evaluation of a seismically isolated bridge using unbonded fiber-reinforced elastomeric isolators. Earthq Spectra 2018;34:145–68. https://doi.org/10.1193/072416EQS118M. Calabrese A, Spizzuoco M, Strano S, Terzo M. Hysteresis models for response history analyses of recycled rubber–fiber reinforced bearings (RR-FRBs) base isolated buildings. Eng Struct 2019;178:635–44. https://doi.org/10.1016/j. engstruct.2018.10.057. Zhang H, Peng TB, Li JZ, Li W. Experimental study of FRP rubber bearing. Adv Mater Res 2011;168–170:1621–4https://doi.org/10.4028/www.scientific.net/ AMR.168-170.1621. Al-Anany YM, Tait MJ. Fiber reinforced elastomeric isolators for the seismic isolation of bridges. Compos Struct 2017;160:300–11. https://doi.org/10.1016/j. compstruct.2016.10.008. Kelly JM, Takhirov SM. Analytical and experimental study of fiber-reinforced elastomeric isolators Rep No PEER 2001/11 Berkeley: Pacific Earthquake Engineering Research Center, Univ California; 2001. Bakhshi A, Jafari MH, Valadoost Tabrizi V. Study on dynamic and mechanical characteristics of carbon fiber- and polyamide fiber-reinforced seismic isolators. Mater Struct 2014;47:447–57. https://doi.org/10.1617/s11527-013-0071-z. Moon BY, Kang GJ, Kang BS, Kelly JM. Design and manufacturing of fiber reinforced elastomeric isolator for seismic isolation. J Mater Process Technol 2002;130–131:145–50. https://doi.org/10.1016/S0924-0136(02)00713-6. Kang GJ, Kang BS. Dynamic analysis of fiber-reinforced elastomeric isolation structures. J Mech Sci Technol 2009;23:1132–41. https://doi.org/10.1007/ s12206-008-1214-y. Ashkezari GD, Aghakouchak AA, Kokabi M. Design, manufacturing and evaluation of the performance of steel like fiber reinforced elastomeric seismic isolators. J Mater Process Technol 2008;197:140–50. https://doi.org/10.1016/j.jmatprotec. 2007.06.023. Hedayati Dezfuli F, Alam MS. Experiment-based sensitivity analysis of scaled carbon-fiber-reinforced elastomeric isolators in bonded applications. Fibers 2016;4. https://doi.org/10.3390/fib4010004. Khanlari S, Ashkezari GD, Kokabi M, Kashani MR. Fiber-reinforced nanocomposite seismic isolators: design and manufacturing. Polym Compos 2009;16:299–306. https://doi.org/10.1002/pc.20803. Van Engelen NC, Konstantinidis D, Tait MJ. Structural and nonstructural performance of a seismically isolated building using stable unbonded fiber-reinforced elastomeric isolators. Earthq Eng Struct Dyn 2016;45:421–39. https://doi.org/10. 1002/eqe.2665. Osgooei PM, Tait MJ, Konstantinidis D. Finite element analysis of unbonded square fiber-reinforced elastomeric isolators (FREIs) under lateral loading in different directions. Compos Struct 2014;113:164–73. https://doi.org/10.1016/j. compstruct.2014.02.033. Ngo TV, Deb SK, Dutta A. Mitigation of seismic vulnerability of prototype low-rise masonry building using U-FREIs. J Perform Constr Facil 2018;32:4017136. https://doi.org/10.1061/(ASCE)CF.1943-5509.0001136. Ehsani B, Toopchi-Nezhad H. Systematic design of unbonded fiber reinforced elastomeric isolators. Eng Struct 2017;132:383–98. https://doi.org/10.1016/j. engstruct.2016.11.036. Toopchi-Nezhad H. Horizontal stiffness solutions for unbonded fiber reinforced elastomeric bearings. Struct Eng Mech 2014;49:395–410. https://doi.org/10. 12989/sem.2014.49.3.395.

Soil Dynamics and Earthquake Engineering 125 (2019) 105621

N.C. Van Engelen

[104] BSI. Structural bearings - Part 3: elastomeric bearings BS EN 1337-3:2005. London: The British Standards Institution; 2005. [105] BSI. Anti-seismic devices BS EN 15129:2018. London: The British Standards Institution; 2018. [106] Van Engelen NC, Konstantinidis D, Tait MJ. Shear strain demands in elastomeric bearings subjected to rotation. J Eng Mech 2017;143:4017005. https://doi.org/ 10.1061/(ASCE)EM.1943-7889.0001194. [107] Toopchi-Nezhad H, Tait MJ, Drysdale RG. Simplified analysis of a low-rise building seismically isolated with stable unbonded fiber reinforced elastomeric isolators. Can J Civ Eng 2009;36:1182–94. https://doi.org/10.1139/L09-056. [108] Pauletta M, Cortesia A, Pitacco I, Russo G. A new bi-linear constitutive shear relationship for Unbonded Fiber-Reinforced Elastomeric Isolators (U-FREIs). Compos Struct 2017;168:725–38. https://doi.org/10.1016/j.compstruct.2017.02. 065. [109] Hedayati Dezfuli F, Alam MS. Multi-criteria optimization and seismic performance assessment of carbon FRP-based elastomeric isolator. Eng Struct 2013;49:525–40. https://doi.org/10.1016/j.engstruct.2012.10.028. [110] Kang BS, Li L, Ku TW. Dynamic response characteristics of seismic isolation systems for building structures. J Mech Sci Technol 2009;23:2179–92. https://doi. org/10.1007/s12206-009-0437-x. [111] Pauletta M, Di Luca D, Russo E, Fumo C. Seismic rehabilitation of cultural heritage masonry buildings with unbonded fiber reinforced elastomeric isolators (U-FREIs) – a case of study. J Cult Herit 2018;32:84–97. https://doi.org/10.1016/j.culher. 2017.09.015. [112] Habieb AB, Milani G, Tavio T, Milani F. Seismic performance of a masonry building isolated with low-cost rubber isolators. WIT Trans Built Environ 2017;172:71–82. https://doi.org/10.2495/ERES170071. [113] Mordini A, Strauss A. An innovative earthquake isolation system using fibre reinforced rubber bearings. Eng Struct 2008;30:2739–51. https://doi.org/10.1016/ j.engstruct.2008.03.010. [114] Osgooei PM, Tait MJ, Konstantinidis D. Seismic isolation of a shear wall structure using rectangular fiber-reinforced elastomeric isolators. J Struct Eng 2016;142:4015116. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001376. [115] Osgooei PM, Tait MJ, Konstantinidis D. Non-iterative computational model for fiber-reinforced elastomeric isolators. Eng Struct 2017;137:245–55. https://doi. org/10.1016/j.engstruct.2017.01.056. [116] Love JS, Tait MJ, Toopchi-Nezhad H. A hybrid structural control system using a tuned liquid damper to reduce the wind induced motion of a base isolated structure. Eng Struct 2011;33:738–46. https://doi.org/10.1016/j.engstruct.2010.11. 027. [117] Manzoori A, Toopchi-Nezhad H. Application of an extended bouc-wen model in seismic response prediction of unbonded fiber-reinforced isolators. J Earthq Eng 2017;21:87–104. https://doi.org/10.1080/13632469.2016.1138166. [118] Habieb AB, Valente M, Milani G. Base seismic isolation of a historical masonry church using fiber reinforced elastomeric isolators. Soil Dynam Earthq Eng 2019;120:127–45. https://doi.org/10.1016/j.soildyn.2019.01.022. [119] Vaiana N, Sessa S, Marmo F, Rosati L. An accurate and computationally efficient uniaxial phenomenological model for steel and fiber reinforced elastomeric bearings. Compos Struct 2019;211:196–212. https://doi.org/10.1016/j. compstruct.2018.12.017. [120] Gerhaher U, Strauss A, Bergmeister K. Effektivität eines Erdbebenisolationssystems für Hochbauten mittels faserbewehrter Elastomerlager. Bautechnik 2009;86:14–21. https://doi.org/10.1002/bate.200910002. [121] Zhang H, Li J, Peng T. Development and mechanical performance of a new kind of bridge seismic isolator for low seismic regions. Shock Vib 2013;20:725–35. https://doi.org/10.3233/SAV-130780. [122] Peng T, Tang W, Zeng Z, Zhao Y. Compression modulus and vertical vibration isolation efficiency of FRP rubber isolators. Mater Res Innovat 2015;19. https:// doi.org/10.1179/1432891714Z.0000000001188. S5-754-S5-759. [123] Hedayati Dezfuli F, Alam MS. Sensitivity analysis of carbon fiber-reinforced elastomeric isolators based on experimental tests and finite element simulations. Bull Earthq Eng 2014;12:1025–43. https://doi.org/10.1007/s10518-013-9556-y. [124] Toopchi-Nezhad H, Tait MJ, Drysdale RG. Shake table study on an ordinary lowrise building seismically isolated with SU-FREIs (stable unbonded-fiber reinforced elastomeric isolators). Earthq Eng Struct Dyn 2009;38:1335–57. https://doi.org/ 10.1002/eqe.923. [125] Toopchi-Nezhad H, Ghotb MR, Al-Anany YM, Tait MJ. Partially bonded fiber reinforced elastomeric bearings: feasibility, effectiveness, aging effects, and low temperature response. Eng Struct 2019;179:120–8. https://doi.org/10.1016/j. engstruct.2018.10.043. [126] Tait MJ, Toopchi-Nezhad H, Drysdale RG. Influence of end geometry on fiber reinforced elastomeric isolator bearings. Proceedings of the 14th World Conference on Earthquake Engineering. 2008. [127] American Society of Civil Engineers (ASCE). Minimum design loads for buildings and other structures ASCE/SEI 7-10. Reston, VA. 2013..

[77] Habieb AB, Valente M, Milani G. Implementation of a simple novel Abaqus user element to predict the behavior of unbonded fiber reinforced elastomeric isolators in macro-scale computations. Bull Earthq Eng 2019:2741–66. https://doi.org/10. 1007/s10518-018-00544-6. [78] Gerharer U, Strauss A, Bergmeister K. Verbesserte Bemessungsrichtlinien für Bewehrte Elastomerlager. Bautechnik 2011;88:451–8. https://doi.org/10.1002/ bate.201101475. [79] Ngo TV, Dutta A, Deb SK. Evaluation of horizontal stiffness of fibre-reinforced elastomeric isolators. Earthq Eng Struct Dyn 2017;46:1747–67. https://doi.org/ 10.1002/eqe.2879. [80] Peng TB, Zhang H, Li JZ, Li WX. Pilot study on the horizontal shear behavior of FRP rubber isolators. J Vib Shock 2009;28:127–30. [81] Calabrese A, Spizzuoco M, Serino G, Della Corte G, Maddaloni G. Shaking table investigation of a novel, low-cost, base isolation technology using recycled rubber. Struct Contr Health Monit 2015;22:107–22. https://doi.org/10.1002/stc.1663. [82] Calabrese A, Strano S, Terzo M. Real-time hybrid simulations vs shaking table tests: case study of a fibre-reinforced bearings isolated building under seismic loading. Struct Contr Health Monit 2015;22:535–56. https://doi.org/10.1002/stc. 1687. [83] Das A, Deb SK, Dutta A. Shake table testing of un-reinforced brick masonry building test model isolated by U-FREI. Earthq Eng Struct Dyn 2016;45:253–72. https://doi.org/10.1002/eqe.2626. [84] Das A, Deb SK, Dutta A. Comparison of numerical and experimental seismic responses of FREI-supported un-reinforced brick masonry model building. J Earthq Eng 2016;20:1239–62. https://doi.org/10.1080/13632469.2016.1140098. [85] Kang BS, Kang GJ, Moon BY. Hole and lead plug effect on fiber reinforced elastomeric isolator for seismic isolation. J Mater Process Technol 2003;140:592–7. https://doi.org/10.1016/S0924-0136(03)00798-2. [86] Van Engelen NC. Rotation in rectangular and circular reinforced elastomeric bearings resulting in lift-off. Int J Solids Struct 2019. https://doi.org/10.1016/j. ijsolstr.2019.03.021. [87] Chalhoub MS, Kelly JM. Effect of bulk compressibility on the stiffness of cylindrical base isolation bearings. Int J Solids Struct 1990;26:743–60. https://doi.org/ 10.1016/0020-7683(90)90004-F. [88] Tsai H-C, Kelly JM. Stiffness analysis of fiber-reinforced elastomeric isolators. Rep No PEER 2001/05. Berkeley: Pacific Earthquake Engineering Research Center, Univ California; 2001. [89] Tsai H-C, Kelly JM. Bending stiffness of fiber-reinforced circular seismic isolators. J Eng Mech 2002;128:1150–7. https://doi.org/10.1061/(ASCE)0733-9399(2002) 128:11(1150). [90] Tsai H-C. Tilting analysis of circular elastic layers interleaving with flexible reinforcements. Int J Solids Struct 2007;44:6318–29. https://doi.org/10.1016/j. ijsolstr.2007.02.028. [91] Tsai H-C. Deformation analysis of infinite-strip bearings of laminated elastic material interleaving with tension-only reinforcements. Int J Solids Struct 2008;45:2836–49. https://doi.org/10.1016/j.ijsolstr.2008.01.003. [92] Stanton JF, Roeder CW, Mackenzie-Helnwein P, White C, Kuester C, Craig B. NCHRP report 596: Rotation limits for elastomeric bearings. Seattle, WA: Transportation Research Board; 2008. [93] AASHTO. AASHTO LRFD bridge design specifications. 8th ed. Washington D.C.: American Association of State Highway and Transportation Officials; 2017. [94] Canadian Standards Association. CSA S6-14 Canadian highway bridge design code. Mississauga, Canada: Canadian Standards Association; 2014. [95] Haringx JA. On highly compressible helical spring and rubber rods, and their application for vibration-free mountings—part III. Philips Research Report 1948;4:206–20. [96] Gent AN. Elastic stability of rubber compression springs. J Mech Eng Sci 1964;6:318–26. https://doi.org/10.1243/JMES_JOUR_1964_006_046_02. [97] Gent AN, Meinecke EA. Compression, bending, and shear of bonded rubber blocks. Polym Eng Sci 1970;10:48–53. [98] Tsai H-C, Kelly JM. Buckling load of seismic isolators affected by flexibility of reinforcement. Int J Solids Struct 2005;42:255–69. https://doi.org/10.1016/j. ijsolstr.2004.07.020. [99] Tsai H-C, Kelly JM. Buckling of short beams with warping effect included. Int J Solids Struct 2005;42:239–53. https://doi.org/10.1016/j.ijsolstr.2004.07.021. [100] Kelly JM, Marsico MR. Stability and post-buckling behavior in nonbolted elastomeric isolators. Seism Isol Prot Syst 2010;1:41–54. [101] AASHTO. Guide specification for seismic isolation design. 4th ed. Washington D.C.: American Association of State Highway and Transportation Officials; 2014. [102] ISO. Elastomeric seismic-protection isolators - Part 2: applications for bridges specifications ISO 22762-2:2018. Geneva: International Organization for Standardization; 2018. [103] ISO. Elastomeric seismic-proetction isolators - Part 3: applications for buildings specifications ISO 22762-3:2018. Geneva: International Organization for Standardization; 2018.

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