A study on experimental shear behavior of fiber-reinforced elastomeric isolators with various fiber layouts, elastomers and aging conditions

Engineering Structures 52 (2013) 422–433

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A study on experimental shear behavior of fiber-reinforced elastomeric isolators with various fiber layouts, elastomers and aging conditions Gaetano Russo, Margherita Pauletta ⇑, Andrea Cortesia Department of Civil Engineering and Architecture, University of Udine, Viale delle Scienze 206, 33100 Udine, Italy

a r t i c l e

i n f o

Article history: Received 30 August 2012 Revised 20 February 2013 Accepted 28 February 2013 Available online 10 April 2013 Keywords: Seismic isolator Carbon fiber Elastomer Unbonded application Experimental test Shear deformation Horizontal stiffness Geometrical model

a b s t r a c t Fiber-reinforced elastomeric isolators are innovative devices for seismic isolation that employ fibers, rather than steel, as reinforcement material. Their light weight and low cost could help to widen the application of seismic isolation, to housing for example, and to buildings in highly seismic areas of the developing world. Experimental studies available in the literature have already demonstrated the suitability of fiber-reinforcing isolators to protect buildings from earthquake. Theoretical analyses have been carried out to describe the isolator behavior under compression and bending. However, no treatment of its behavior under compression and shear has been performed yet. This because of objective difficulties due to the non-linearity both of the geometry and the properties of these materials. The present paper proposes a simplified geometric model to describe the isolator’s deformed configuration under compression and shear, based on the observation of its experimental behavior. The results of compression and shear tests carried out on 17 pairs of fiber-reinforced isolators are reported. The specimens have different characteristics as regards rubber typology (neoprene and low and high damping neoprene), reinforcement (bi-directional or quadri-directional carbon fiber fabrics), shape factor, and aging (unaged and aged specimens). On the basis of the proposed model, an expression for the equivalent linear horizontal stiffness of fiber-reinforced isolators is proposed. This expression predicts well the experimental results. The predictions are more uniform and accurate than those obtained from the stiffness expression of traditional isolators, which is commonly used in the literature also for fiber-reinforced isolators. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Traditional elastomeric isolators are made by alternating layers of elastomeric material (5–20 mm thick) and thin reinforcing steel plates (2–3 mm thick), bonded together by means of a bonding compound and a vulcanization process. These isolators are delimited at the top and at the bottom by two 25–30 mm thick steel endplates, which anchor the isolator to the super- and sub-structure. The axial and bending stiffnesses of both end-plates and thin steel plates are some orders of magnitude greater than the stiffness of the elastomer layers. This implies that when the isolator is subjected to horizontal seismic loads, deformation takes place only in the elastomer layers and is assimilable to a pure shear deformation. When the horizontal deformation is large, high traction stresses develop between the steel plates and the elastomer layers. Such traction stresses have to be borne by the bonding between the steel and the elastomer. Unlike traditional isolators, fiber-reinforced isolators, the subject of this research, have reinforcing layers made of carbon-fiber ⇑ Corresponding author. Tel.: +39 0432 558065; fax: +39 0432 558052. E-mail addresses: [email protected] (G. Russo), margherita.pauletta@uniu d.it (M. Pauletta), [email protected] (A. Cortesia). 0141-0296/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engstruct.2013.02.034

fabrics and are not anchored to the structure, i.e., have no steel end-plates. The manufacturing cost of fiber reinforced isolators is greater than that of traditional ones, due to the major cost of the fibers. Anyhow, the costs connected with the labor involved in preparing the steel reinforcement (cutting, sandblasting, cleaning with acid, and coating with bonding compound) are eliminated. Moreover the absence of end-plates for the anchorage to the structure and the substitution of the steel reinforcements with fiber ones reduces the isolator’s weight. Hence, being fiber-reinforced isolators much lighter than the traditional ones and also less voluminous, transportation and installation are simpler and the relevant costs are lower than those for traditional isolators. It results that the overall cost of a fiber-reinforced isolator is a little lower than a traditional one. Due to both the use of deformable reinforcing layers and the absence of anchoring to the structure, the deformed configuration of the fiber-reinforced isolators under horizontal loads deeply differs from the configuration of traditional isolators. In particular, fiberreinforced isolators show a rollover deformation, such as the one represented in Fig. 1, with portions of the isolator (delimited by the dotted lines in Fig. 1) detaching from the structure [1–9]. These portions are then substantially unstressed [8,10], hence no traction develops between the reinforcements and the elastomer. For this

G. Russo et al. / Engineering Structures 52 (2013) 422–433

Fig. 1. Deformation of (a) traditional steel reinforced isolator anchored to the structure, (b) fiber-reinforced elastomeric isolator not anchored to the structure.

reason, it is not necessary to treat the fibers with bonding compound and the process of vulcanization is alone sufficient to efficiently bond together the fibers and the elastomer. Although theoretical and experimental studies [1–13] have been carried out on fiber-reinforced isolators not anchored to the structure, there is still a lack of a description of the behavior of such isolators under horizontal loads. A theoretical treatment presents objective difficulties, due to the nonlinearity both of the geometry and the properties of the materials. In fact, the isolators are subjected to large shear deformations, hence a definition of the problem in the finite deformation field should be performed. Moreover the elastomer shows a nonlinear viscous behavior, while the fibers possess high traction stiffness, but negligible compression and bending stiffness. Considering that the two materials have radically different characteristics, it is not possible to define a continuum equivalent material for the isolator, to be used in the analysis in the finite deformation field. Finally, even if it was possible to define the problem in the finite deformation field, it is not sure that a closed form solution could be found for this problem. Given the complexity of the problem and the necessity to reach a solution for the practical design and use of fiber-reinforced isolators, this paper proposes a simplified geometric model for the isolator’s deformed configuration under horizontal loads, deduced from the observation of its experimental behavior. On the basis of this model, an expression for the equivalent linear horizontal stiffness of fiber-reinforced isolators is also proposed, which predicts the experimental results more uniformly and accurately than the stiffness expression used for traditional isolators. The proposed expression can be used in the linear modeling of isolators in programs of structural calculus. 2. Specimen characteristics The isolator prototypes subjected to experimental tests were built by ILPEA Industries according to the typology and methods of production specified in two patents held by the University of Udine [14,15]. With reference to Fig. 2, a seismic isolator, according to this patent, is formed by n layers or sheets of elastomer material, positioned one on top of the other, and n  1 relative reinforcement elements, consisting of sheets of fabric with a carbon fiber base. The sheets of fabric are disposed alternating between one layer of elastomer and the other, so that the isolator is delimited, at the bottom and at the top, by layers of elastomer. The carbon fiber fabrics are of the same type of those currently used for the restoration or strengthening of concrete or masonry structures. The isolator is produced using a mold of the desired shape, for the isolators presented in this paper, this is a square shape, into which the layers alternating with the reinforcement elements are inserted one on top of the other as described. The layers and the reinforcement elements stacked in the mold are subjected to a pre-determined compression at a temperature and pressure able to cause them to be glued together by means of vulcanization, so as to be held together and to constitute substantially a single body (Fig. 2). The first distinctive features of such an isolator, compared

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to similar ones described in the literature [16,17], is that the reinforcing elements, made by carbon-fiber fabrics, are not saturated in any polymer matrix before being stacked in the mold, but are bonded to the elastomer layers by means of the vulcanization process alone. Another distinctive feature from those used in [16] is that the carbon-fiber fabrics are not subjected to pretensioning before being stacked in the mold. These two features make the described isolator cheaper than the similar fiber reinforced ones. Several specimens were tested within the research described in this paper; their side lengths a and b, single rubber layer thickness t, number of elastomer layers n, total thickness of rubber te, total thickness of the isolator H, and shape factor S (given by the ratio between the loaded and the free areas of a single rubber layer, i.e., l2/[4lt]) are summarized in Table 1 in columns (2)–(8) under the line labeled ‘‘Authors.’’ Some of the tested specimens had a layer of rubber of thickness equal to 5 mm, coating all the lateral (unloaded) surfaces. Others had two consecutive sides covered, because they were obtained by cutting larger specimens which were covered on all sides, in four equal portions. These characteristics are specified in Table 2 in column (2). As elastomer material, three different types of rubber were used to build the isolators: neoprene (Shore A, durometer hardness 60 ± 5, G = 0.9 MPa), low damping neoprene (Shore A, durometer hardness 60 ± 5, G = 1.15 MPa), and high damping natural rubber (Shore A, Durometer hardness 54.5 ± 5, shear modulus G = 0.8 MPa), respectively named MA, MB, and MC rubber in the following (Table 2, column (3)). As carbon fiber fabrics, two types were used (Fig. 2c): bi-directional and quadri-directional ones, called in the following bd and qd fabrics, respectively (Table 2, column (4)). The bd fabric had fibers along two principal directions, at 0° and 90°, and qd fabric had fibers along four directions, at 0°, 45°, 90° and 135°. The fibers were not immersed in a matrix. The superficial density was 200 g/m2 for bd fabric and 380 kg/m2 for qd fabric and the thicknesses were 0.112 mm and 0.212 mm, respectively. The Young’s modulus was 230,000 MPa and the ultimate fabric strength was 3500 MPa for both fabrics. The specimens having the suffix aged were subjected to a process of aging, before being subjected to the other tests, consisting in leaving the specimens in an oven at a temperature of 70 °C for 21 days. This is the standard aging process prescribed by the Italian Code [18], but the representing age for the treated specimens is not specified by this Code. The specimens that are the exact unaged counterparts of pair of aged specimens B1aged–B2aged, QB1aged–QB2 aged and QB1aged-QB2aged are A1–A2, QA1–QA2 and BA1–BA2, respectively. 3. Test setup The tests were performed in the Laboratory of Materials and Structures of the University of Udine. All the specimens were tested in compression and compression with shear. Both tests were performed to assess the suitability of the studied devices for the isolating function. A compression test was performed to measure the vertical (axial) displacement of the specimens under a compressive stress, which would have been applied during the shear test. The tests under compression with shear, which will be called shear tests hereafter, were performed to analyze the relative deformed configuration of the isolators and the correlation between the real horizontal stiffness of the isolators and such deformed configuration. 3.1. Compression test setup Fig. 3 shows the setup for the compression test: an isolator prototype was placed between two concrete blocks, which reproduced

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Fig. 2. Representation of (a) isolator component parts, (b) whole isolator and (c) close-up view of fiber fabric layouts.

the sub- and super-structure. The compressive stress was applied quasi-statically (loading rate of 0.01 mm/s) under displacement control by the 500 kN hydraulic actuator of the MTS machine (Fig. 3a). Three cycles of loading–unloading were performed for each specimen, with a maximum value of compressive stress equal to 12 MPa for specimens MOD1, MOD2, C, and D; 6 MPa for specimens A1, A2, B1 aged, and B2 aged; and 8 MPa for the other specimens. Four inductive transducers were vertically positioned on the lateral surfaces of the concrete blocks (Fig. 3b), to measure the vertical (axial) displacement of the specimens, which was calculated by taking the average of the transducers’ readings. 3.2. Shear test setup Fig. 4a shows the setup for the shear test: two specimens were vertically oriented and simultaneously subjected to the test, to obtain a symmetrical setup. Every specimen was positioned on contact with two of the three concrete blocks that simulated the sub- and super-structure (Fig. 4b). These blocks had been preliminarily roughened and cleaned, to assure adequate bond conditions, and, between each test and the following one, were cleaned to assure the same bond conditions for every test. Compressive stress rV was applied to the isolators by means of two horizontal hydraulic jacks acting on the two lateral concrete

blocks (Fig. 4b). The average compressive stress applied by the jacks was held at a constant value equal to 6 MPa, under load control, when the isolator was displaced. The concrete blocks, being placed upon sliding supports made by smooth steel bars, were able to move horizontally, to allow the compressive strains to be applied to the isolators. Vertical (shear) displacements were applied to the specimens by the central concrete block connected to the vertical 300 kN hydraulic actuator of an INSTRON machine. This actuator was operated under displacement control and the maximum displacement allowed by the machine was ±50 mm. Four potentiometric transducers were vertically positioned on contact with the central concrete block, one for each corner, to record the vertical relative displacement, which was calculated by taking the average of the transducers’ readings. As regards the loading rate, it has to be said that, when an isolating device is tested, to obtain reliable results, the used frequency should be equal to the inverse of the design isolating period [19]. To investigate the influence of loading rate on the specimen behavior, tests under different loading rates had already been carried out by the authors on specimens BB1aged–BB2aged made with high damping natural rubber. The results of these test are reported in [20], where the above specimens were called B1 and B2. The carried out tests were not cyclic, but were characterized only

Table 1 Specimens considered for the experimental comparison. (1) Specimen name

(3) b (mm)

(4) t (mm)

(5) n

(6) te (mm)

90 85 82 79 77.5 76 74.5 73 71 120 120 240 240 240 240 240 240

90 85 82 79 77.5 76 74.5 73 71 120 120 240 240 240 240 240 240

2.8 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 3 3 2.5 2.5 2.5 2.5 2.5 2.5

15 16 16 16 16 16 16 16 16 16 16 20 20 20 20 20 20

42 40 40 40 40 40 40 40 40 48 48 50 50 50 50 50 50

183 183 735 735 190 190 750 750 190 190 740 740 190 190 390 183 183 377 377 183 183 377 377

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33

99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99

Kelly and Takhirov [2] DRB1(0°) 735 DRB1(0°) 735 DRB1(90°) 183 DRB1(90°) 183 DRB2(0°) 750 DRB2(0°) 750 DRB2(90°) 190 DRB2(90°) 190 DRB3(0°) 740 DRB3(0°) 740 DRB3(90°) 190 DRB3(90°) 190 DRB4(0°) 365 DRB4(0°) 365 DRB5(90°) 190 DRB6(0°) 377 DRB6(0°) 377 DRB6(90°) 183 DRB6(90°) 183 DRB7(0°) 377 DRB7(0°) 377 DRB7(90°) 183 DRB7(90°) 183

(7) H (mm) 43.68 41.99 41.99 41.99 41.99 41.99 41.99 41.99 41.99 51.18 51.18 52.02 52.02 54.03 54.03 52.02 52.02 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105

(8) S

(9) A (mm2)

(10) Gnom (MPa)

(11) P (kN)

(12) uV (mm)

(13) Kh,ave(c = 0.5) (N/mm)

(14) Kh,ave(c = 1) (N/mm)

(15) Kh,ave(c = 1.5) (N/mm)

(16) Kh (N/mm)

(17) Kh,equiv(c = 0.5) (N/mm)

(18) Kh,equiv(c = 1) (N/mm)

(19) Kh,equiv(c = 1.5) (N/mm) – – – – – – – – – – – – – – – – – 1118.1 1120.5 – – 1185.9 1188.5 – – 1169.2 1171.2 – – – – – – – – – – – – –

8.0 8.5 8.2 7.9 7.8 7.6 7.5 7.3 7.1 10.0 10.0 23.0 23.0 23.0 23.0 23.0 23.0

8100 7225 6724 6241 6006 5776 5550 5329 5041 14400 14400 57600 57600 57600 57600 57600 57600

0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 1.15 1.15 0.80 0.80 0.80 0.80

48.6 43.4 40.3 37.4 36.0 34.7 33.3 32.0 30.2 86.4 86.4 345.6 345.6 345.6 345.6 345.6 345.6

2.104 1.732 1.714 1.838 2.589 2.238 2.277 1.970 2.584 1.692 1.885 1.560 1.627 1.430 1.615 1.513 1.663

– – – – – – – – – – – 1389.4 1565.8 1064.2 1178.0 937.2 1088.0

126.0 107.3 100.4 82.7 91.6 81.5 73.4 66.5 63.4 205.5 220.0 1107.0 1250.5 730.9 834.7 672.7 790.0

– – – – – – – – – – – – – – – – –

173.6 162.6 151.3 140.4 135.1 130.0 124.9 119.9 113.4 270.0 270.0 1324.8 1324.8 921.6 921.6 921.6 921.6

– – – – – – – – – – 1220.9 1403.2 849.9 975.7 849.7 975.8

138.2 112.9 103.4 94.0 87.6 84.2 79.9 76.6 69.9 201.3 200.5 1151.9 1323.9 801.9 920.5 801.7 920.6

24.4 24.4 24.4 24.4 25.3 25.3 25.3 25.3 25.2 25.2 25.2 25.2 20.8 20.8 21.3 20.5 20.5 20.5 20.5 20.5 20.5 20.5 20.5

134505 134505 134505 134505 142500 142500 142500 142500 140600 140600 140600 140600 69350 69350 74100 68991 68991 68991 68991 68991 68991 68991 68991

0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90

233.6 467.3 233.6 467.3 233.6 467.3 233.6 467.3 233.6 467.3 233.6 467.3 253.7 507.3 253.7 60.1 120.2 60.1 120.2 60.1 120.2 60.1 120.2

1.337 1.835 1.337 1.835 1.169 1.650 1.169 1.650 1.272 1.662 1.272 1.662 1.809 2.385 2.002 0.700 1.040 0.700 1.040 0.690 1.000 0.690 1.000

– – – – – – – – – – – – – – – – – – – – – – –

1408.6 1354.3 856.7 839.2 1180.8 1189.6 763.9 788.4 977.6 949.6 1263.2 1291.2 604.4 569.4 425.7 485.3 502.8 373.2 378.4 518.6 527.3 381.9 387.2

1228.1 1173.8 – – 1066.9 1052.9 – – 651.7 695.5 – – – – – – – – – – – – –

1228.2 1228.2 1228.2 1228.2 1301.2 1301.2 1301.2 1301.2 1283.9 1283.9 1283.9 1283.9 633.3 633.3 676.6 630.0 630.0 630.0 630.0 630.0 630.0 630.0 630.0

1200.8 1203.2 1118.1 1127.7 1271.8 1274.4 1185.2 1195.2 1255.1 1257.1 1171.7 1179.5 607.2 609.6 624.8 598.7 600.9 565.6 570.2 598.7 600.7 565.5 569.7

1159.4 1161.8 952.0 961.6 1228.9 1231.4 1015.7 1025.7 1212.1 1214.1 1004.4 1012.3 564.2 566.7 536.7 557.4 559.6 480.4 484.9 557.3 559.3 480.3 484.5

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Authors T1aged, T2aged R085 R082 R079 R077.5 R076 R074.5 R073 R071 MOD1,MOD2 C, D A1, A2 B1aged, B2aged QA1, QA2 QB1aged, QB2aged BA1, BA2 BB1aged, BB2aged

(2) a (mm)

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Table 2 Tested specimens.

4. Experimental results

(1) Specimen name

(2) Covered Sides

(3) Rubber

(4) Fabric

(5) KV (N/mm)

(6) ne %

T1aged, T2aged R085 R082 R079 R077.5 R076 R074.5 R073 R071 MOD1,MOD2 C, D A1, A2 B1aged, B2aged QA1, QA2 QB1aged, QB2aged BA1, BA2 BB1aged, BB2aged

0 0 0 0 0 0 0 0 0 0 2 4 4 4 4 4 4

MA MA MA MA MA MA MA MA MA MA MA MB MB MC MC MC MC

bd bd bd bd bd bd bd bd bd qd qd bd bd qd qd bd bd

29,077 30,840 25,960 22,980 15,500 16,110 15,710 16,520 12,660 98,333 70,939 458,015 374,075 517,885 428,655 361,910 378,990

16.88 18.99 16.61 21.73 19.20 18.50 22.10 24.41 25.72 12.38 10.57 7.50 6.52 15.06 14.97 15.38 12.34

by a loading branch up to displacement of 90 mm. The used loading rates were 70 and 100 mm/s. Such tests pointed out an increase in the secant horizontal stiffness of the 9% for an increase in the loading rate of 43%. Within this research work, the authors also carried out shear tests under different loading rates on specimens MOD1 – MOD2 made with neoprene. These were cyclic tests and the frequencies 0.25 Hz and 0.35 Hz were used. From the tests it was observed that the average horizontal stiffness and the damping ratio at the frequency of 0.35 Hz were 7.5% and 6.8% respectively greater than the corresponding values measured at 0.25 Hz. Tests of other authors [4] on specimens made with soft compound of natural gum rubber showed that the influence of the loading rate on the horizontal stiffness was negligible, while the equivalent viscous damping was slightly overestimated when the loading rate was low. From the above observations it was concluded that the influence of loading rate involves variations in the parameters investigated in this study lower than 9%. Hence the tests were performed by applying a only loading rate equal to the maximum one allowed by the testing machine. Three fully reversed dynamic sinusoidal cycles at a loading rate of 0.35 Hz were utilized. For all the shear tests, the maximum applied shear strain c, which was calculated as the ratio between the maximum applied displacement dmax and the total rubber thickness te of the specimens, was equal to 1 or 0.5.

4.1. Compression test results The load-vertical displacement diagram reported in Fig. 5 represents the behavior of specimen QA1 under compression test. A similar behavior was obtained also for all the other specimens. The following conclusions, valid for all the tested specimens, can be drawn from Fig. 5. The specimens had loading curves in the first cycle with a low initial slope, which means a low initial vertical stiffness. This was due to the fact that the reinforcing elements, made by carbon fiber fabrics, had not been pre-tensioned during the building process of the isolators. The fiber fabrics needed the rubber to be deformed in order to be put under tension and to exert their containing action to further elastomer deformations. After the fibers had been reorganized and put in tension, the curves of the first cycle showed a higher slope, i.e., a higher vertical stiffness. This behavior is a peculiarity of fiber-reinforced isolators without pre-tensioning of fibers, and is in agreement with the observations of other authors [2,4]. Within one cycle, the loading curve was different from the unloading one. This behavior also was due to the absence of pretensioning of the carbon fiber fabric. Indeed, during the unloading stage, the fibers behaved like relaxed ‘‘cables,’’ hence the whole isolator behavior was governed only by the elastomer, which has viscous-elastic properties. Due to the reorganization of the carbon fiber fabric configuration and the viscous-elastic properties of rubber, a vertical residual displacement was recorded at the end of the first cycle unloading stage. Then, the second cycle began from this deformed configuration. Anyway, the residual displacements recorded at the end of the second and third cycles were very close to those at the end of the first cycle, because, during these cycles, the maximum load attained in the first one was not exceeded: hence, according to the Mullins effect [21], the rubber had already become stable. At the end of the compression test, leaving the specimens without load, it was observed that the residual displacement occurring at the first cycle was recovered. It can be said that the isolators showed an elastic behavior with non-instantaneous recover. Table 2, column (5), shows the values of the compression stiffness of the specimens, KV. This was calculated as the average between the values of compression stiffness of two identical specimens, for the specimens reported in pairs in Table 2, and as a single value, for the specimens reported alone. The KV value of each specimen was estimated at the first cycle according to [18] by means of the following expression

Fig. 3. Compression test: (a) test setup, and (b) instrumentation.

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Fig. 4. Shear test: (a) test setup, and (b) detail.

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Fig. 5. Compression test results for specimen QA2.

KV ¼

rV  r0:3V uV  u0:3V

ð1Þ

where rV is the design compressive stress, assumed equal to 6 MPa, r0.3V is 30% of rV, uV is the measured vertical displacement of the isolator at pressure rV, and u0.3V is the measured vertical displacement at pressure r0.3V. When the isolator was provided with rubber cover on its sides, the effective work area in the vertical direction, necessary to calculate rV, was the area in plan of the fiber fabrics alone. From the obtained values of the vertical stiffness KV (column (5) in Table 2) the following observations can be made: – KV strongly depends, as is known, on the shape factor S, and it increases as S increases. – Quadri-directional carbon fiber fabrics yielded higher values of vertical stiffness. In particular, for S = 23, specimens QA1 and QA2, made with high damping natural rubber and quadri-directional fabrics (qd), had a KV value of 517885 N/mm, which was 43% higher than 361910 N/mm attained by specimens BA1 and BA2 equal to QA1 and QA2 except for the fabrics, which were bi-directional. Having a greater vertical stiffness makes the isolator less sensitive to vertical displacements. – For specimens with high damping natural rubber the KV variation due to aging is lower than 5% when bi-directional fiber fabrics are used (specimens BB1aged–BB2aged versus BA1–BA2), while it is equal to 17.2% with quadri-directional fiber fabrics (specimens QB1aged–QB2aged versus QA1–QA2). For specimens with low damping natural rubber and bi-directional fiber fabrics, the KV variation is equal to 18.3% (specimens B1aged– B2-aged versus A1–A2). The compression tests, besides studying the specimen behavior under compression, were used to obtain the vertical (axial) displacement of the specimens uV at a compressive stress of 6 MPa, which is the stress applied during the shear test. The values of uV were measured at the first cycle and are reported in column (12) of Table 1.

4.2. Shear test results At the application of a horizontal load, the tested fiber-reinforced isolators exhibited rollover deformation (Fig. 6), due to their boundary conditions at the contact surfaces, where no mechanical or chemical bonding was realized. This deformation was in accordance to the deformation already observed by other researchers [1–11] on similar specimens.

The behavior of all the tested specimens was qualitatively similar, hence the considerations, reported in the following, are valid in general. The relative load–displacement diagrams were like the one showed in Fig. 7, recorded in the test on the pair of specimens QA1 and QA2. The only differences regard the values of horizontal stiffness (slope of the curves) and damping ratio (area bounded by the cycles). From this figure it can be observed that the specimen rollover deformation was stable, because, within one cycle of loading, all the specimens had curves with increasing resisting force at an increase of the applied shear deformation. No zero or negative tangent horizontal stiffness (softening branch), i.e., no decrease in the specimen resisting force, was recorded. No damage was visible after the cyclic tests were completed. In Fig. 7, a reduction of the maximum resisting force can be observed from the first cycle to the third. The reduction was higher between the first and second cycle, while it was negligible between the second and the third ones, according to the Mullins effect. Analogously to the force, also the dissipated energy, represented by the area within one cycle, was higher at the first cycle and slightly lower at the following two. The two mechanical properties of interest in studying the shear behavior of the isolator prototypes were the average horizontal stiffness and the equivalent viscous damping ratio. The average horizontal stiffness was derived, on the basis of the experimental results, using the three cycles to which the isolator was subjected. The values computed for c = 0.5 and c = 1 are reported in columns (13) and (14) of Table 1, respectively. The horizontal stiffness was calculated (Table 1, column (16)) also according to the expression usually used for steel reinforced isolators anchored to the structure

GA te

Kh ¼

ð2Þ

where G is the nominal shear modulus, provided by the rubber supplier (Table 1, column (10)), and A (Table 1, column (9)) is the cross-sectional area of the isolator in plan, including any side rubber coating, if present. The equivalent viscous damping ratio was calculated only for c = 1 (Table 2, column (6)), according to [22] as follows

ne ¼

Wd 4p  W s

ð3Þ

where Wd is the dissipated energy (area within the hysteresis loop) and Ws is the restored (elastic) calculated as

Ws ¼

1 2  K h;eff  dmax;av e 2

ð4Þ

in which Kh,eff is the effective horizontal stiffness [19]

K h;eff ¼

F max  F min dmax  dmin

ð5Þ

with Fmax, Fmin, dmax and dmin the maximum and minimum values of the horizontal force and displacement, respectively, and dmax,ave = (dmax + |dmin|)/2. Each ne value, reported in column (6) of Table 2 for c = 1, was calculated as the average of the three values obtained from each loading cycle. When more than one test was performed at c = 1, the average of ne determined for each test as previously described was taken. 4.2.1. Results concerning the horizontal average stiffness Kh,ave On the basis of the values obtained from experiment, the following observations, regarding the average stiffness Kh,ave, can be made.

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(a)

429

(b)

Fig. 6. Specimens under shear strain: (a) d = 40%te and (b) d = 120%te.

values of Kh,ave corresponding both to c = 0.5 and c = 1. Hence this equation, commonly used for conventional isolators, is not suitable for fiber-reinforced isolators in unbonded applications. 4.2.2. Results concerning the damping ratio ne Regarding the damping ratio ne the following observations can be made.

Fig. 7. Shear test results for the pair of specimens QA1 and QA2.

– A decrease in Kh,ave occurred with the increase of maximum imposed shear deformation. In particular, considering the shear deformations of 0.5 and 1, the decrease ranged from 20.1%, for specimens B1aged–B2aged, to 31.3% for specimens QA1–QA2. – For the same applied shear deformation, the average stiffness of unaged specimens increased with the increase of the shape factor S. In particular, for c = 1, Kh,ave ranged from 63.4 N/mm for S = 7.1 (specimens R071) to a maximum of 1107 N/mm for S = 23 (specimens A1–A2). – High damping natural rubber yielded lower values of average stiffness. In particular, for S = 23 and c = 1, unaged specimens BA1 and BA2 made with high damping rubber (MC) and bidirectional fiber reinforcement (bd) had a Kh,ave value of 672.7 N/mm, which was 39 % lower than the 1107 N/mm attained by specimens A1–A2, identical to BA1–BA2 except for the rubber, made by low damping neoprene (MB). – As expected for elastomeric devices, the process of aging produced an increase in the values Kh,ave of pairs of identical isolators (B1aged–B2aged versus A1–A2, QB1aged–QB2aged versus QA1–QA2, and BB1aged–BB2aged versus BA1–BA2). For c = 1, the variations of Kh,ave ranged from 13% for specimens B1aged– B2aged versus A1–A2 to 17.4% for specimens BB1aged–BB2aged versus BA1–BA2, with 15% being the average variation. – Specimens reinforced with bi-directional fiber fabrics (bd) had values of Kh,ave lower than specimens reinforced with quadridirectional fabrics (qd). In particular, considering specimens made with high damping natural rubber, the difference was 8.7% for unaged specimens (BA1–BA2 versus QA1–QA2) and 5.7% for aged ones (BB1aged–BB2aged versus QB1aged– QB2aged). The values of the horizontal stiffness, calculated by means of Eq. (2), reported in Table 1, column 16, cannot approximate the correct

– The damping ratio decreases with an increase of the shape factor. Specimens made with neoprene (MA) showed ne values ranging from 25.72%, for specimens R071 with S = 7.1, to 10.57%, for specimens C–D with S = 10, with 18.83% being the average value. – By considering specimens having a shape factor comparable with those usually employed in practice (S = 23), the lowest values of ne were observed for specimens made with low damping neoprene (MB), whose average was 7.01%. While, as expected, the highest values of ne, were exhibited by specimens made with high damping natural rubber (MC), which showed an average damping ratio equal to 14.44. This value is comparable with that of conventional steel reinforced isolators. – Specimens made with quadri-directional carbon fiber fabrics showed greater dissipation properties than specimens made with bi-directional ones. In particular, by considering specimens having the same shape factor (S = 23) and rubber typology (MC), the average ne value of specimens with quadri-directional fabrics was 8.35% greater than the average value of specimens with bi-directional fabrics. This is probably due to the greater amount of fibers present in the quadri-directional fabrics. Not all the fibers are glued to the rubber, in particular the interior ones, hence these fibers crawl over one another while the isolator is cyclically subjected to shear deformation. This friction creates energy dissipation and the dissipation is the greater, the larger is the number of fiber fabrics involved. Greater dissipation properties are positive, because further reduce the acceleration transferred from the isolator to the structure. – Process of aging produced decrease of the damping ratio. The decrease was more pronounced for isolator with bi-directional carbon fiber fabrics (13% for isolators B1aged–B2-aged versus A1–A2 and 20% for BB1aged–BB2aged versus BA1–BA2), while it was almost negligible (0.6%) for specimens with quadridirectional carbon fiber fabrics (QB1aged–QB2aged versus QA1–QB1). 5. Model for the isolator’s deformed configuration under horizontal loads The rollover deformation performed by the specimens subjected to the shear test is analyzed herein by making reference to Fig. 8.

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The isolator is initially subjected to compressive stresses only (step 0 in Fig. 8), which cause a vertical displacement uV. As a consequence, the isolator’s undeformed height H reduces to h, the height of the compressed isolator. When a horizontal displacement d is applied to the isolator, the deformed configuration becomes one of those shown at steps 1, 2 or 3. Such configurations are simplified representations of the real ones, because the isolator vertical surfaces (AB and FG in Fig. 8) experience curvilinear shaped deformations. This is demonstrated in Fig. 6 where the grid drawn on the isolator shows clearly how the isolator deforms. However, according to other authors [8], the curvilinear deformed configuration is here approximated by an equivalent planar one, in performing the analysis of the isolator deformation. For the geometry and the load pattern, the isolator shows point symmetry (or rotational symmetry of order two) with respect to the center of the Cartesian axes x–y fixed in the center of gravity of the compressed isolator (see axes at step 0 in Fig. 8). Hence the considerations made in the following for the left portion of the deformed isolator in Fig. 8 (steps 1–3) hold also for the point symmetric right portion. When the applied displacement is small, as is the one in Fig. 8 – step 1, no detachment from the concrete supports occurs and the isolator undergoes the same shear deformation as conventional isolators anchored to a structure. Such deformation remains until the horizontal displacement d is smaller than a limit value, d0 at step 2 in Fig. 8, beyond which the isolator begins to detach from the concrete blocks. When the applied displacement exceeds d0 (see Fig. 8 – step 3) the isolator performs a rollover deformation, i.e., the bottom left edge A begins to detach (roll-off) from the bottom support. At increasing applied displacements, a progressive detachment of the isolator’s bottom portion occurs, and its length s progressively increases. Simultaneously a progressive rotation of the lateral isolator surface (AB in Fig. 8) occurs around the edge B, which remains on contact with the top concrete block. The values of d0 and s can be determined by means of the following geometrical considerations. It appears reasonable to assume that the isolator begins to detach from the support (point A at step 2) when the lateral surface AB has recovered the initial length H. It follows that the displacement d0 can be obtained by applying the Pythagorean theorem to the triangle BEA

d0 ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 H2  h

ð6Þ

With reference to step 3, the stresses in the isolator portion ABD3 detached from the supports are zero [8], hence the length s of arc AD3 is equal to the distance of the detachment point D3 from the position of the isolator edge A at rest (point O), hence

s ¼ d  d0

ð7Þ

Hence, to know the length of isolator portion which has detached from the structure, it is sufficient to know the applied horizontal displacement d and the vertical displacement uV under the applied pressure. The isolator rollover deformation evolves until the lateral surface, represented by side AB, is all in contact with the top support (step 4). The picture in Fig. 9 shows as an example one of the tested isolators at a displacement of 200%te with the lateral surfaces nearly in contact with the supports. 6. Proposed expression for the equivalent linear horizontal stiffness The nominal shear modulus of rubber G is the parameter which characterizes the isolator behavior under horizontal displace-

ments. Such a parameter is normally provided by the rubber suppliers and is determined by performing pure shear tests on rubber. Since steel reinforced isolators anchored to the structure perform nearly pure shear deformations under horizontal displacements, the shear modulus of conventional isolators can be assumed, with good approximation, equal to the rubber shear modulus. However it has been experimentally observed that the modulus G depends on the displacement applied to the isolator, in fact it is well known that G is high and nonlinearly decreasing for small displacements (c < 40%), lower and almost constant for greater displacements (50% < c < 150%), and it increases again for c > 150%. In this regard, the national codes usually assume as the isolator modulus G the value obtained for an applied shear deformation c equal to 1. The corresponding equivalent horizontal stiffness of a conventional isolator is usually expressed by Eq. (2). On the basis of the experimental results obtained in this research it is already clear that Eq. (2) is not able to correctly predict the horizontal stiffness of fiber-reinforced isolators in unbonded applications. Such an expression is good for conventional isolators, which perform pure shear deformation for all their rubber volume. In contrast, fiber-reinforced isolators perform a nonlinear deformation, with the detached portions approximately unstressed, and the portion remaining in contact performing nearly a pure shear deformation. This can be clearly seen in Fig. 6, where most of the grid meshes belonging to the contact portion show a rhomboidal shape, typical of pure shear deformation. The isolator portion in contact with the concrete blocks and subjected to pure shear has a base equal to the contact area. The contact area, Ac, is equal to the product of the isolator side length in the direction perpendicular to the applied load, b in Fig. 2, and the side length, a, minus the detached portion, s, in the direction parallel to the applied load

Ac ¼ b  ða  sÞ

ð8Þ

where s is provided by Eq. (7). Hence the value of the isolator base area to be used in Eq. (2) should be Ac, instead of A. Nevertheless, Ac value varies at varying of the applied displacement, hence it is necessary to identify an average value Ac,ave, which should be used in Kh expression. This value can be the average between the contact area at displacement equal to zero (d = 0) and the contact area at the maximum displacement (d = dmax) reached by the isolator

Ac;av e ¼

Ac ðd ¼ 0Þ þ Ac ðd ¼ dmax Þ 2

ð9Þ

Hence the proposed expression for the equivalent linear horizontal stiffness is

K h;equiv ¼

G  Ac;av e te

ð10Þ

6.1. Experimental validation of the proposed expression To asses the reliability of the proposed expression, the horizontal stiffnesses of all the isolators tested in this research and of fiber-reinforced isolators tested by other authors [2] have been calculated by means of Eq. (10) and compared with the values obtained from Eq. (5) by using the experimental results. Table 1, in columns (2)–(10), shows the characteristics of the specimens tested by other authors under the lines labeled Kelly and Takhirov. The tests were performed under the values of vertical load P specified in column (11) and the vertical displacements uV performed by the specimens under such load are listed in column (12). Kelly and Takhirov’s specimens [2] were made with natural rubber compound layers interleaved with fiber layers. The long sides

G. Russo et al. / Engineering Structures 52 (2013) 422–433

431

Fig. 8. Deformed patterns of isolator.

of the isolators were in the east–west direction. The imposed shear deformation was in the east–west direction when the number in the brackets close to the specimen name (column (1)) is equal to 0°, but in the north–south direction when it is equal to 90°. The

nominal rubber shear modulus given by the manufacturer of the isolators was 0.69 MPa, but the authors, after having carried out the tests, observed that this value was too small, and, on the basis of the obtained results, stated that a more appropriate value for the

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reinforced isolators anchored to a structure, the proposed one is more accurate (AVG = 1.08 versus AVG = 1.31) and reliable (COV = 0.18 versus COV = 0.24). In Fig. 10 all the ratios, Kh/Kh,ave represented by open triangles and Kh,equiv/Kh,ave by filled circles, are plotted versus the applied compressive stress rV. 7. Conclusions On the basis of the test results on carbon fiber-reinforced isolators in unbonded application and the experimental comparison between the proposed expression for the horizontal stiffness and the traditional expression, the following conclusions can be drawn:

d=200% te Fig. 9. Specimen subjected to d = 200%te.

Fig. 10. Ratios of calculated to measured horizontal stiffness versus applied compressive stress.

shear modulus was 0.904 MPa. This G value has been used herein for the stiffness evaluation of Kelly and Takhirov’s specimens. The horizontal stiffness of traditional isolators and fiber-reinforced ones remains almost constant in the range of shear deformation equal to 0.5  1.5. Accordingly, the values of Kh,ave were calculated for c = 0.5, c = 1 and c = 1.5, when the corresponding forces and displacement values were available and are reported in columns (13), (14) and (15) of Table 1. The values of the horizontal stiffness Kh calculated according to Eq. (2) are reported in column (16). It has to be noticed that, Eq. (2) yields a unique value of stiffness independently of the applied shear strain. The values of stiffness obtained from the proposed expression (Eq. (10)) are shown in columns (17), (18) and (19), for c = 0.5, c = 1 and c = 1.5, respectively. To take account of the experimental results obtained in this research for aged specimens, the equivalent horizontal stiffness (Eq. (10)) of these specimens has been multiplied by an amplification factor of 1.15, being the measured average increase in stiffness of aged isolators equal to 15%. The ratios Kh/Kh,ave and Kh,equiv/Kh,ave have been calculated for all the considered experimental results using the values in column (16) for Kh, (17)–(19) for Kh,equiv, and (13)–(15) for Kh,ave. The average AVG, the standard deviation, and the coefficient of variation COV of the ratios Kh/Kh,ave were 1.31, 0.31, and 0.24, respectively, while, for Kh,equiv/Kh,ave, they were 1.08, 0.2, and 0.18, respectively. From the values obtained it is apparent that the expression proposed for calculating the equivalent horizontal stiffness of fiberreinforced isolators in unbonded applications (Eq. (10)) predicts well the real behavior of these isolators. Moreover, in comparison with the general expression (Eq. (2)) used for conventional steel-

– Fiber-reinforced isolators subjected to shear force deform nonlinearly, with the detached portions approximately unstressed, and the portion remaining in contact performing a nearly pure shear deformation. – By increasing the maximum imposed shear strain, the area of the isolator surfaces in contact with the concrete blocks decreases and, as a consequence, the isolator average horizontal stiffness also decreases. – For the same applied shear deformation, the average horizontal stiffness of unaged specimens increases with the increasing of the shape factor. – The process of aging produces an increase in the average horizontal stiffness and reduction of the damping ratio. – Specimens reinforced with bi-directional carbon fiber fabrics have lower average horizontal stiffness than specimens reinforced with quadri-directional fabrics. – The damping ratio increases with the decrease of the shape factor. – Fiber-reinforced isolators made with high damping natural rubber have an average damping ratio comparable with that of conventional steel reinforced isolators. – Specimens made with quadri-directional carbon fiber fabrics are vertically stiffer and more dissipative under horizontal loads than specimens made with bi-directional fabrics. – The proposed model allows geometrically describing the deformed configuration of the isolators under shear. – The proposed expression for the equivalent horizontal stiffness takes the reduction of the isolator contact area at increasing shear strain adequately into account. – This expression is more accurate and reliable than the expression used for steel-reinforced isolators in predicting the real horizontal stiffness of fiber-reinforced isolators in unbonded applications.

Acknowledgements The research has been partially funded by Italian Department of Civil Protection (within the framework of Executive Projects DPCReLUIS 2005–2008 and 2010–2013), whose support is greatly appreciated. The authors also want to acknowledge the ILPEA Industries of Pordenone (Italy), which built the specimens, the BASF Chemical Company of Treviso (Italy), which provided the carbon fiber fabric, and Eng. Guido Tognan, who collaborated in the arrangement of the test setup. References [1] Kelly JM, Takhirov SM. Analytical and experimental study of fiber-reinforced elastomeric isolators. PEER Report 2001/11, Univ. of California, Berkeley; 2001. p. 49. [2] Kelly JM, Takhirov SM. Analytical and experimental study of fiber-reinforced strip isolators. PEER Report 2002/11, Univ. of California, Berkeley; 2002. p. 106.

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