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Seismic Response of Bearings for Quasi-Isolated Bridges – Testing and Component Modeling J. S. Steelman 1 , L. A. Fahnestock 2 , J. M. LaFave 3 , J. F. Hajjar 4 , E. T. Filipov 1 , and D.A. Foutch 5 1 Graduate Research Assistant, Dept. of Civil and Environmental Engr., University of Illinois at Urbana-Champaign, 205 N. Mathews Ave. Urbana, IL61801; email: [email protected] , [email protected] 2 Assistant Professor, Dept. of Civil and Environmental Engr., University of Illinois at Urbana-Champaign, 205 N. Mathews Ave. Urbana, IL 61801; PH (217) 265-0211; email: [email protected] 3 Associate Professor, Dept. of Civil and Environmental Engr., University of Illinois at Urbana-Champaign, 205 N. Mathews Ave. Urbana, IL 61801; PH (217) 333-8064; email: [email protected] 4 Professor and Chair, Dept. of Civil and Environmental Engr., Northeastern University, 360 Huntington Avenue, Boston, MA 02115; PH (617) 373-3242; email: [email protected] 5 Professor Emeritus, Dept. of Civil and Environmental Engr., University of Illinois at Urbana-Champaign, 205 N. Mathews Ave. Urbana, IL 61801; PH (217) 333-6359; email: [email protected] ABSTRACT In areas of moderate seismicity, such as Mid-America, there is interest in developing alternate bridge design and construction methodologies to the typical approaches that are employed in high-seismic regions. One such method is to design so that various bearing components will exceed their ultimate capacities during a major seismic event in a specific sequence, leading to a global bridge structure response similar to a seismically-isolated system. Because the bridge would typically exhibit a stiff response, only developing an isolated response during major earthquakes, the bridge superstructure response may be described as quasi-isolated. This paper presents results for elastomeric bearing components obtained for an experimental program performed to investigate and characterize various bearing types that are being used for quasi-isolated designs. The elastomeric bearings investigated displayed approximately linear elastic response before sliding with a friction coefficient in the range of 0.3 – 0.45, at a shear strain in the range of 150 – 250%. The experiments also investigated the response of anchored retainer brackets used to prevent transverse motion for service loads and small earthquakes to characterize the combined effects of shear and overturning up to and including rupture of the concrete anchor. The test data indicate that the required horizontal force delivered by a bearing to a retainer to cause a failure of the anchor is slightly higher than the ultimate pure tensile strength of the anchor. 164 Structures Congress 2011 © ASCE 2011

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Page 1: Seismic Response of Bearings for Quasi-Isolated Bridges - Testing and Component Modelingjfhajjar/home/Steelman et al. -- Bridge... · 2011-07-16 · Seismic Response of Bearings for

Seismic Response of Bearings for Quasi-Isolated Bridges – Testing and Component Modeling

J. S. Steelman1, L. A. Fahnestock2, J. M. LaFave3, J. F. Hajjar4, E. T. Filipov1, and

D.A. Foutch5

1Graduate Research Assistant, Dept. of Civil and Environmental Engr., University of Illinois at Urbana-Champaign, 205 N. Mathews Ave. Urbana, IL61801; email: [email protected], [email protected] 2Assistant Professor, Dept. of Civil and Environmental Engr., University of Illinois at Urbana-Champaign, 205 N. Mathews Ave. Urbana, IL 61801; PH (217) 265-0211; email: [email protected] 3Associate Professor, Dept. of Civil and Environmental Engr., University of Illinois at Urbana-Champaign, 205 N. Mathews Ave. Urbana, IL 61801; PH (217) 333-8064; email: [email protected] 4Professor and Chair, Dept. of Civil and Environmental Engr., Northeastern University, 360 Huntington Avenue, Boston, MA 02115; PH (617) 373-3242; email: [email protected] 5Professor Emeritus, Dept. of Civil and Environmental Engr., University of Illinois at Urbana-Champaign, 205 N. Mathews Ave. Urbana, IL 61801; PH (217) 333-6359; email: [email protected] ABSTRACT

In areas of moderate seismicity, such as Mid-America, there is interest in developing alternate bridge design and construction methodologies to the typical approaches that are employed in high-seismic regions. One such method is to design so that various bearing components will exceed their ultimate capacities during a major seismic event in a specific sequence, leading to a global bridge structure response similar to a seismically-isolated system. Because the bridge would typically exhibit a stiff response, only developing an isolated response during major earthquakes, the bridge superstructure response may be described as quasi-isolated. This paper presents results for elastomeric bearing components obtained for an experimental program performed to investigate and characterize various bearing types that are being used for quasi-isolated designs. The elastomeric bearings investigated displayed approximately linear elastic response before sliding with a friction coefficient in the range of 0.3 – 0.45, at a shear strain in the range of 150 – 250%. The experiments also investigated the response of anchored retainer brackets used to prevent transverse motion for service loads and small earthquakes to characterize the combined effects of shear and overturning up to and including rupture of the concrete anchor. The test data indicate that the required horizontal force delivered by a bearing to a retainer to cause a failure of the anchor is slightly higher than the ultimate pure tensile strength of the anchor.

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INTRODUCTION Seismic isolation has been implemented as an effective means of earthquake damage mitigation in structural engineering, with some of the earliest patents dating back to the turn of the 20th century, and increasing frequency from the 1970s onward (Buckle and Mayes, 1990). Isolation systems have typically been used in high-seismic areas, such as the west coast of the United States, Japan, and New Zealand, where additional design and construction costs are justifiable in light of the seismic hazard. For bridges outside of high-seismic areas, however, commonly employed components to permit thermal displacements of superstructures inherently possess properties suitable for isolation systems. Consequently, a quasi-isolated design that relies on thermal expansion devices to also provide seismic energy dissipation can be an appealing alternative within the suite of earthquake protection design options, providing the benefits of reduced force demands, as long as the structural system is designed to account for the associated increased displacements of an isolated response. The Illinois Center for Transportation (ICT), working in conjunction with the Illinois Department of Transportation (IDOT), is currently investigating the behavior of bridge systems to calibrate and refine IDOT’s Earthquake Resisting System (ERS) methodology. The IDOT ERS philosophy relies on prescribed sequential “fusing” (i.e., exceeding ultimate capacity) of specific components, arranged by levels ranging from 1 to 3 (Tobias et al., 2008). The dual use of thermal expansion components for seismic energy dissipation is a key feature of the IDOT ERS. Level 1 requirements are intended to provide a force capacity threshold to ensure elastic response to service loads and small to moderate earthquakes, and Level 2 requirements address displacement demands following Level 1 fusing. IDOT bridges commonly employ elastomeric bearings to permit thermal deformations of the superstructure. The experimental program includes tests of two types of elastomeric bearings: steel-reinforced elastomer only (IDOT Type I), and steel-reinforced elastomer combined with a flat Teflon sliding surface (IDOT Type II). Both types of elastomer bearings include stiffened L-shaped retainer brackets to restrain transverse motion of the superstructure. The first tests of the experimental program focused on the response of the components of Type I bearings and individual retainer response. EXPERIMENTAL TESTING SETUP The experimental tests were performed at the Newmark Structural Engineering Laboratory at the University of Illinois, using a testing apparatus shown in Figure 1, designed to realistically reflect field conditions for the typical, full-scale bridge bearing specimens.

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Figure 1. Testing Setup Elevation

The primary objective of the testing program was to simulate large lateral deformations of elastomeric bearings that may occur due to seismic excitation. Based on preliminary analyses of full bridges in conjunction with a review of literature documenting previous tests of elastomeric bearings (Stanton and Roeder, 1982; Roeder et al., 1987; Kulak and Hughes, 1992; Mori et al., 1999), a target of 400% shear strain was selected for the testing program. The largest bearings included in the testing program were comprised of 5 layers of 5/8” (15.9 mm) elastomer layers, for an equivalent rubber thickness of 3.125” (79.4 mm), and an associated 400% shear strain of 12.5” (317.5 mm). A 30” (762 mm)-stroke, 220 kip (980 kN) capacity actuator was employed to provide the required 25” (635 mm) horizontal displacement capacity for fully reversed cyclic tests. The vertical loading and support was designed to capture the lateral response realistically. Vertical loading was imposed on the bearings using a pair of 100 kip (445 kN) capacity actuators reacting against a steel frame secured to the laboratory strong floor with pretensioned anchors. The use of a pair of actuators allowed the vertical load to be maintained at a specified target of simulated gravity load, regardless of the lateral displacement of the bearing. Concrete pads were cast to simulate typical bridge substructures, including a brushed finish as specified by IDOT (IDOT, 2007), to ensure that the frictional response of elastomers bearing on concrete was captured realistically. A concrete pad is secured to the strong floor during a test by using pretensioned anchors around the perimeter of the pad. The experimental results presented in this paper are for specimens and parameters listed in Table 1. Dimensions of test specimens conformed to standards used by IDOT, and full details for the test specimens may be found in the IDOT Bridge Manual (IDOT, 2009). The specimens in Table 1 represent only a portion of the

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complete testing program. The complete program also includes tests of 13c bearings, Type II 7c bearings, and fixed bearings, with tests performed on bearings oriented to simulate both longitudinal and transverse loading for all types of bearings.

Table 1. Partial Test Matrix

Test Specimen ProtocolVertical

Load (MPa)1 Type I 7c #1 Monotonic 3.452 Type I 7c #1 Monotonic 3.453 Type I 7c #1 Monotonic 3.454 Type I 7c #1 Monotonic 3.455 Type I 7c #1 Monotonic 2.596 Type I 7c #1 Monotonic 1.387 Type I 7c #1 Monotonic 3.458 Type I 7c #2 Cyclic 1.389 Type I 7c #3 Cyclic 3.45

10 Type I 7c #2 Cyclic 5.5211 Retainer Monotonic N/A

ELASTOMERIC BEARING EXPERIMENTS Displacements of Type I and Type II bearings include both shear deformations in the elastomers, and frictional sliding, so deformations are referred to using “equivalent shear strain” for convenience. For the Type I bearings, sliding occurs at the elastomer-concrete interface. The first experiments imposed horizontal displacements simulating deformations parallel to a bridge span. Images captured at the initiation of lateral displacement and incipient sliding are shown in Figure 2.

(a) Initiation of Lateral Displacement (b) Incipient Sliding Figure 2. Still Captures of Test Specimen #1 during Test #1

The bearing shown in Figure 2 is a typical Type I 7c bearing, composed of a steel top plate bonded to a block of steel-reinforced elastomer during vulcanization. The top steel plate measures 8” x 14” in plan, and 1-1/2” thick (203 x 356 x 38.1 mm), and the reinforced elastomer is composed of 5 layers of elastomer, each measuring 7” x

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12” x 3/8” (178 x 305 x 9.53 mm), with each layer separated by a 3/32” (2.38 mm) thick steel shim. With 5 layers of 3/8” elastomer, the equivalent rubber thickness of the bearing is 1.875” (47.6 mm), corresponding to a maximum displacement during tests of 7.5” (190.5 mm). The steel top plate is tapped with four holes so that the plate can be bolted to the bottom flange of a steel girder in the field, which was simulated with a built-up steel plate fixture for the experiments. Lines were drawn on the sides of the elastomer so that deformations could be more easily seen. Horizontal lines correspond to locations of internal steel shims, and vertical lines were added to construct a grid of approximately square spaces. Steel studs were welded to the top plate, and needles were inserted into the elastomer so that string potentiometer lines could be attached and used to record displacements of the specimen. Elastomeric bearings used by IDOT are designed based on vertical load limitations of 1.38 to 5.52 MPa (200 to 800 psi). Based on discussions with an internal technical review panel assembled within IDOT, a typical simulated gravity load was set at 3.45 MPa (500 psi). Initial tests to identify fundamental constitutive response were performed by imposing monotonic horizontal shear deformations from rest up to 400% equivalent shear strain. Data from the initial tests is shown in Figure 3 through Figure 5. All tests in Figure 3 were performed with a common simulated gravity load of 3.45 MPa (500 psi). All loading was removed from test specimens for approximately 1 day between tests so that the elastomer could recover from any scragging that may have developed in a previous test. In the case of these tests, however, deterioration of the bearing elastomer was not limited to hyperelastic material response. When the elastomer is ground against the surface of the concrete, portions of the elastomer are permanently removed by abrasion, in particular at the leading edge of the elastomer base in the direction of motion. The bearing edge appeared chamfered at a roughly 45º angle after the first test. The mechanism appeared to stabilize in the succeeding tests however, based on the difference in lateral force versus displacement evident between Test 1 and Tests 2 and 3. Large deformations of elastomers reported in the literature typically consider bearings with different construction details (e.g., use of both top and bottom plates to secure bearing to super- and substructures) and material properties (high damping versus low damping elastomers). Consequently, one of the primary points of interest for these bearing experiments was to establish the response of bearings that have not been specifically designed for seismic effects when subjected to deformations larger than typical non-seismic limitations of 50 – 70% shear strain. In general, elastomers are expected to stiffen significantly when subjected to large deformations, regardless of whether the elastomeric material would be classified as high-damping or low-damping. For the tests represented in Figure 3 through Figure 5, a material softening branch was not observed, and a stiffening branch appeared to be precluded by the initiation of sliding.

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Figure 3. Successive Monotonic Tests of Type I bearing, all tests with 3.45 MPa

(500 psi) simulated gravity load

To investigate the response of the bearing when subjected to varying gravity load cases, a series of monotonic tests were performed in the opposite direction from the first three tests. Tests were performed successively, with the typical delay between tests to allow for scragging recovery, in a sequence of 3.45, 2.59, 1.38, and 3.45 MPa (500, 375, 200, and 500 psi). As would be expected, the slip load of the bearings decreases as the applied vertical load decreases, and so the lower vertical load also results in less shear deformation, and a larger proportion of sliding for the imposed monotonic displacement, as seen in Figure 4. The variation in slip load is not, however, linearly scaled with imposed vertical load. Whether due to a reduced curling of the elastomer base with the lower gravity load, or differences at a microscopic level of interaction at the interface of the elastomer and roughened concrete, the data shown in Figure 5 indicate that the coefficient of friction is correlated inversely with the applied vertical load. At a load of 3.45 MPa, based on Figure 3 and Figure 5, the coefficient of friction for sliding is approximately 0.3 – 0.35, and slightly higher at 2.59 MPa, tending to fall at or slightly above 0.35. When the vertical load is decreased further, to 1.38 MPa, the coefficient of friction increases to approximately 0.45.

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Figure 4. Successive Monotonic Tests of Type I bearing, varying simulated

gravity load, load versus displacement

Figure 5. Successive Monotonic Tests of Type I bearing, varying simulated

gravity load, horizontal to vertical load ratio versus shear strain

To investigate the cyclic response of Type I bearings, tests were also performed with cyclic loading protocols as follows: seven fully reversed cycles @ 25% and 50% equivalent shear strain, three fully reversed cycles @ 100%, 200%, 300%, and 400% equivalent shear strain. Tests were also performed for several levels of simulated gravity load. The first test, using a new bearing, was conducted with a simulated gravity load of 1.38 MPa (200 psi), and provided the data shown in Figure 6. The next test, also using a new bearing, was conducted with a simulated load of 3.45 MPa (500 psi), and generated the data shown in Figure 7. Finally, the bearing that had

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been tested with a 1.38 MPa simulated gravity load was retested with the maximum permissible simulated gravity load of 5.52 MPa, shown in Figure 8.

Figure 6. Cyclic Tests of Type I bearing, 1.38 MPa simulated gravity load

Figure 7. Cyclic Tests of Type I bearing, 3.45 MPa simulated gravity load

The three sets of test data reflect results similar to the monotonic tests for similar testing parameters. For example, the slip coefficient for the bearing subjected to the lightest simulated gravity load was significantly higher than for the tests at higher gravity loads, similar to Figure 5. The values ranged from approximately 0.4 – 0.5 at 1.38 MPa, to approximately 0.2 – 0.25 at 5.52 MPa. Other aspects of the response can only be observed in the cyclic tests, rather than the monotonic, such as the apparent degradation of bearings with successive cycles. Rather than being

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consistent across all results, however, the influence of the cyclic degradation appears to be correlated to the testing parameters.

Figure 8. Cyclic Tests of Type I bearing, 5.52 MPa simulated gravity load

The data in Figure 6 show a continuous degradation in slip force with increasing cycles, suggesting that the degradation is tied to the bearing’s travel on an abrasive surface. For the other two cases, however, in Figure 7 and Figure 8, degradation does occur on successive cycles, so long as the maximum displacement does not increase. When the maximum displacement increases for a new stage of the loading protocol, however, the frictional resistance increases at the maximum and minimum limits of displacement. This suggests that the degradation is partially influenced by abrasion of the elastomer base, but also by the condition of the concrete surface, so that “clean” surfaces which the bearing is traveling over for the first time possess greater frictional resistance than locations where the bearing has already deposited portions of elastomer by previous abrasions. Regardless of the source of these variations, the effect appears to be minor overall. For large deformations, there is a stable response of linear elastic loading followed by frictional slip, with no visible damage other than minor abrasion of the elastomer base for gravity load up to 3.45 MPa. The test with 5.52 MPa was terminated prematurely for reasons other than the condition of the testing specimen. However, upon inspection following the test, the bearing had been deformed and ground against the concrete so severely that the edge of the lowest internal shim was visible. RETAINER BRACKET EXPERIMENTS To resist lateral translations of the bridge superstructure under service conditions and small seismic events, IDOT uses a standard detail for a stiffened L bracket, with a single holddown anchor installed into the concrete substructure. Figure 9 shows the

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first tested retainer bracket mounted in the testing setup, prior to the test, and dismounted after the test is performed. Displacements were measured during the test with a combination of four string potentiometers and two LVDTs mounted with brackets to the sides of the retainer. Visible damage was limited to the threaded anchor and the concrete near the embedded anchor.

(a) Installed and Instrumented Prior to Test (b) Dismounted After Test

Figure 9. Still Captures of Retainer #1

A schematic view of the test setup prior to the start of the test is shown in Figure 10. The anchor is installed to an embedment of 9 inches (230 mm). The top plate of a Type I bearing was simulated by using the steel fixture of the testing frame to push against the face of the retainer.

Figure 10. Schematic of Retainer Test Setup, Prior to Test

The contact height of the steel fixture caused the retainer to rotate as well as slide, as shown in Figure 11, and inducing the loading shown on the free-body diagram in Figure 12.

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Figure 11. Schematic of Retainer Test at Incipient Failure of Anchor

Figure 12. Free-Body Diagram of Reactions on Retainer at Incipient Anchor

Failure

(a) Mounted, at Incipient Failure (b) Face of Retainer After Test Figure 13. Still Captures of Retainer #1 Overturning Effects

As the retainer began to rotate, the toe of the retainer was driven into the concrete, as seen in Figure 13(a). An oval in the lower left of the image has been drawn to highlight the concrete being crushed at the toe of the retainer. The gap opening at the top of the retainer due to rotation is also indicated on the right-hand side of the image. Simultaneously, the retainer was developing a vertical load, at the contact location of the steel fixture, also contributing to the prevention of retainer rotation, and relieved by intermittent slips of the steel fixture along the vertical face of the retainer. This effect was evidenced by jumps in the vertical load recorded during the experiment,

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combined with the scraping of paint where the steel fixture slipped against the retainer, shown in Figure 13(b). The maximum horizontal force recorded during the retainer test was 29.6 kips (132 kN), using a 3/4” (19 mm) threaded anchor to the concrete test pad. Anchor material was specified as ASTM F1554, Grade 36, however, random selection of three anchor samples for tension tests indicated that the material was likely rejected Grade 55 material. Ultimate strengths obtained from the three tension test specimens were 84.7, 73.9, and 73.5 ksi (584, 510, and 507 MPa). Dividing the maximum horizontal force by the effective area of the threaded anchor (per ASTM F1554), the resulting stress is 88.5 ksi (610 MPa), slightly higher than the average ultimate strength of the tension test specimens. The typical IDOT design procedure for the retainer used in this test would have estimated the “fuse” capacity to be 9.5 kips (42.3 kN) for Grade 36 material, or 11.9 kips (52.9 kN), even if Grade 55 had been assumed. These values are determined by accounting for tension demands on the concrete anchor with a reduced resistance factor. The current design approach neglects shear resistance at the toe and induced vertical load on the bearing plate on the retainer face. With respect to the overarching design strategy, this test indicated that the force required to transition to a quasi-isolated response would be approximately 3 times greater than expected, regardless of material strength assumed, indicating that the calculation methodology to estimate fuse strength of retainers should be calibrated for future versions of the IDOT ERS to prevent the development of unexpectedly high lateral forces in the structural system. COMPUTATIONAL MODELING Computational modeling is in development using Abaqus (2010), which will use the experimental data for calibration. The computational models will then be used to consider variations in parameters beyond those tested, such as material strength of various components, to investigate the associated effects on the bearing response. Preliminary models of elastomeric bearings are 2D plain strain models, with quad elements used for elastomeric material and the steel top plate, and beam elements used to model the thin internal steel shims. The Yeoh (1993) model was selected to capture the hyperelastic response of the elastomer. The top steel plate and internal shims are tied rigidly to the surrounding elastomer elements, and both the base and sides of the elastomer are modeled with hard contact and friction slip interactions relative to the rigid part representing the concrete test pad. Images showing the bearing with 3.45 MPa gravity load applied at the start and at the end of a monotonic displacement are shown in Figure 14 and Figure 15.

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Figure 14. Type I 7c Bearing Model, Gravity Load Only

Figure 15. Type I 7c Bearing Model, Displaced to 400% Equivalent Shear Strain

(a) Initial Condition (b) Incipient Failure of Anchor Figure 16. Computational Retainer Model

The preliminary retainer model includes a damage evolution model with element removal for the steel, to capture the degradation and rupture of the concrete anchor. The bottom and side of the retainer are modeled with contact interactions to permit contact and separation of the bearing top steel plate on the side, and the concrete surface on the bottom, using both hard contact for normal interactions and friction sliding for tangential interactions. Screen captures of the initial condition and

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incipient failure of the anchor from the retainer model in Abaqus are shown in Figure 16, above. CONCLUSIONS The experimental testing program has generated data indicating that typical Type I bearings used by IDOT, incorporating low damping elastomers, can generally be characterized with linear elastic response for light to moderate loads, even at large displacement demands on the order of 250% shear strain, because the elastomer is permitted to slide on the concrete substructure, thereby precluding a stiffening branch. A stiffening branch may, however, begin to appear in the constitutive response for very large gravity loads. Furthermore, repeated monotonic tests on a single bearing, along with cyclic tests incorporating multiple reversed cycles up to 400% equivalent shear strain, indicate that the bearings are remarkably resilient. Scragging and deterioration effects appear minor in most cases. The bottom surface of the elastomer is visibly worn and roughened by being dragged across concrete through multiple cycles of large displacements, but the visible abrasions appear to have only a minor influence on force-displacement response. Furthermore, delamination was not observed externally, and the only visible damage extending to the internal shims was for the case of the highest tested vertical load. Characterization of retainer response can be relatively complex. The retainer is subject to overturning resistance at the toe, as well as an induced vertical load at the bearing plate. The orientations and magnitudes of the loads are therefore somewhat difficult to predict, and the fuse capacity of the sacrificial retainer during a major seismic event may be significantly underestimated by current design techniques in use by IDOT. The data indicate that for the retainer tested, the shear resistance is equivalent to slightly more than the full ultimate capacity of the concrete anchor. The data presented in this paper are representative of only an initial set of experiments. The completed experimental program will also include experiments of larger, 13c Type I bearings, Type II 7c bearings, and fixed bearings. All bearing types and sizes are tested for loading in both longitudinal and transverse orientations. The complete set of experiments will be used to calibrate a suite of computational models, and the parametric variations of the computational models will be used to formulate appropriate models to capture the response characteristics of quasi-isolated full bridge structures in global bridge models. ACKNOWLEDGMENTS

This article is based on the results of ICT R27-70, Calibration and Refinement of Illinois’ Earthquake Resisting System Bridge Design Methodology. ICT R27-70 was conducted in cooperation with the Illinois Center for Transportation (ICT); IDOT; Division of Highways; and the U.S. Department of Transportation, Federal Highway

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Administration (FHWA). The contents of this article reflect the view of the authors, who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the ICT, IDOT, or FHWA. The authors would like to thank the members of the project Technical Review Panel, chaired by D. H. Tobias, for their valuable assistance with this research. REFERENCES Abaqus FEA (2010). SIMULIA website, Dassault Systèmes, Vélizy-Villacoublay,

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Performance---A World View.” Earthquake Spectra, EERI, 6(2), 161-201. Illinois Department of Transportation (IDOT). (2009). Bridge Manual, Springfield,

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Road and Bridge Construction, Springfield, Illinois. Kulak, R. F, and Hughes, T. H. (1992). “Mechanical Tests for Validation of Seismic

Isolation Elastomer Constitutive Models,” DOE Facilities Programs, Systems Interaction, and Active/Inactive Damping, Eds. C.-W. Lin et al., ASME Publication PVP Vol. 229, 41-46.

Mori, A., Moss, P. J., Cooke, N., and Carr, A. J. (1999). “The Behavior of Bearings Used for Seismic Isolation under Shear and Axial Load,” Earthquake Spectra, EERI, 15(2), 199-224.

Roeder, C. W., Stanton, J. F., and Taylor, A. W. (1987). Performance of Elastomeric Bearings. National Cooperative Highway Research Program 298. Washington, D.C: Transportation Research Board.

Stanton, J. F., and Roeder, C. W. (1982). Elastomeric Bearings Design, Construction, and Materials. National Cooperative Highway Research Program 248. Washington, D.C: Transportation Research Board, National Research Council.

Tobias, D. H., Anderson, R. E., Hodel, C. E., Kramer, W. M., Wahab, R. M., and Chaput , R. J. (2008). “Overview of Earthquake Resisting System Design and Retrofit Strategy for Bridges in Illinois.” Practice Periodical on Structural Design and Construction, ASCE, 13(3), 147-158.

Yeoh, O. H. (1993). “Some Forms of the Strain Energy Function for Rubber.” Rubber Chemistry and Technology, American Chemical Society, Vol. 66, 754-771.

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