SEISMIC PERFORMANCE LIMITS OF THE SKYWAY PIERS FOR THE NEW EAST BAY SPANS OF THE SAN FRANCISCO-OAKLAND BAY BRIDGE

Transcription

1 SEISMIC PERFORMANCE LIMITS OF THE SKYWAY PIERS FOR THE NEW EAST BAY SPANS OF THE SAN FRANCISCO-OAKLAND BAY BRIDGE Eric M. HINES Frieder SEIBLE Ph.D., Structural Engineer, LeMessurier Consultants, 675 Massachusetts Ave., Cambridge, MA, 9, Ph.D., P.E., Dean, Irwin and Joan Jacobs School of Engineering, Eric and Johanna Reissner Professor of Structural Engineering and Alied Mechanics, University of California, San Diego, Mail Code 4, La Jolla, CA, 99, Keywords: SFOBB, skyway ier, sread of lasticity, erformance limit, flexural strain INTRODUCTION The exerimental evaluation of a bridge ier's seismic erformance requires the relationshi between measured caacity and calculated demand to be clearly defined. Efforts to correlate caacity and demand with increasing recision have received much attention as ``erformance-based earthquake engineering" (PBEE) []. The new San Francisco-Oakland Bay Bridge (SFOBB) East Bay Sans were designed according to erformance-based criteria both for a functional evaluation earthquake (FEE) and for a safety evaluation earthquake (SEE) []. Key structural comonents of the new SFOBB were recently tested at the University of California, San Diego (UCSD) in order to rove that their inelastic deformation caacity exceeds the exected demand from a 5 year earthquake on either the San Andreas or the Hayward Faults. In order to ``rove" that the comonents satisfied life safety erformance requirements, the test units' measured dislacements were required to exceed dislacement levels corresonding to assumed flexural strain limits. Functionality was evaluated rimarily based on visual observations. The aer introduces two large-scale structural tests of the SFOBB Skyway Piers and comares their results to the SFOBB erformance limits. It discusses the assumtions undergirding such comarisons and highlights the ambiguities inherent in such assumtions. The aer then focuses on the exerimental flexure-shear behavior of the iers' lastic hinge regions and rooses alternative assessments for strain limits and the sread of lasticity. Finally, the aer comares the exerimental sread of lasticity with values that were assessed analytically, demonstrating the accuracy of the roosed method for most levels of dislacement and curvature ductility. TESTING PROGRAM Two nearly identical /4 scale Skyway Piers were subjected to fully reversed cyclic loading []. The first test unit, known as the Longitudinal Pier Test (LPT), was loaded only in the bridge longitudinal direction. The second test unit, known as the Diagonal Pier Test (DPT), was loaded in the bridge longitudinal direction, in the bridge transverse direction and in different combinations of these directions. The rototye ier, ictured in Fig., is tyical for a majority of the iers suorting the Skyway. Fig. shows an isometric view of the ¼ scale test setus for both tests. The Skyway Pier roof tests were conducted both to verify immediately the safety of the existing Skyway design and to sharen the fundamental understanding of bridge ier behavior under seismic loads. Different aroaches to the lastic hinge length are aroriate to suit these different uroses. Therefore, the aer aroaches the relationshi between flexural strains and ier dislacements from three different oints of view. The first aroach is based on the actual Skyway Pier design assumtions and bears significance only for the East Bay Bridge Skyway Piers. Fig. comares results from this aroach to the LPT test hysteresis. The second aroach assumes that the caacity strain limits assumed by the designers reresent the real strains in the Skyway Piers at their full caacity. The third aroach assumes neither strain limits nor lastic hinge length and calculates both based on the assumtion of a linear distribution of curvatures in the lastic hinge region [4].

2 Transverse Longitudinal E5E deck 59 (9'-4") E9E height E5E section 8 (9'-") A A L 55 (7") T 85 (5") E5E ileca 65 ('-4") Section A-A Fig.. East Bay Skyway Pier detail: re-cast box girder, hollow rectangular ier with highly-confined corner elements, battered cast-in-steel-shell iles. Transverse loading Vertical loading load stub 54 (6") column 7 (76") Longitudinal loading Vertical loading footing 7 (54") (No PT rods shown.) North West (a) East West South South North (b) East Fig.. Longitudinal Pier Test (LPT) setu (a). Diagonal Pier Test (DPT) setu (b).

3 Actuator force [kn] Drift ratio / L (%) F' y FEE ε s =. Dislacement ductility ratio µ SEE ε c =. (/ ε cu ) Caacity limit ε c =.5 (/ ε cu ) Test caacity 8 Multile 6 bar fractures 4 (kis) To dislacement [mm] (in.) Fig.. LPT: Theoretical and exerimental force-deflections behaviors comared. Transverse Longitudinal V T M L V L B D H + B D H H = L V T V L M T M L Fig. 4. SFOBB Skyway Pier moment diagrams and deflections in the bridge transverse and longitudinal directions.

4 STRAIN LIMITS Strain-based erformance limits according to the SFOBB Design Criteria [] are given in Table. According to these criteria, the ultimate confined concrete strain caacity, ε cu, is calculated as.4ρsfyε su ε cu =.4 + () f ' cc where ρ s = the volumetric confinement ratio, f y = the yield stress of the confining reinforcement, ε su = the confining reinforcement strain at eak stress, and f cc = the confined concrete strength, calculated according to [5]. Furthermore, ε su =. for confinement bars and ε su =.9 for longitudinal bars. Table. SFOBB Skyway strain-based erformance limits. Level ε c ε s () () () FEE.4. SEE / ε cu / ε su The SFOBB design team defined the relationshi between curvature and deflection for the Skyway Piers in a memo to the UCSD research team. This memo assumed that allowable ultimate curvatures were based on / of the ultimate material strains listed above. The memo also assumed that L =.8L + 9 () d b where L = the column shear san, and d b = the longitudinal bar diameter [6]. The memo secified the following equations for dislacement, corresonding to Fig. 4. For > y : Longitudinal: H φy D = + D φy 6 ( φ ) L ( H L ) () Transverse: ( H + B / ) D φy D = + ( φd φy ) L ( H + BD / L / ) (4) The UCSD research team assumed that shear deformations were to be neglected in the calculation of test unit strains based on the test unit dislacements. Furthermore, the UCSD research team assumed y and φ y to be the ideal yield dislacement and curvature. 4 PLASTIC HINGE LENGTH The Skyway Design Criteria assumed strain limit states generally acceted to be conservative with regard to the flexural deformation of the Skyway Piers. The lastic hinge length secified according to Eq. () was not, however calibrated based on columns with geometry and reinforcement of the Skyway Piers, and therefore did not necessarily aly to the Skyway Piers. In order to comare the dislacement caacity of the LPT with the demand limits laced on a tyical Skyway Pier, both the lastic hinge length and the base curvature of the test unit must be calculated

5 according to the same method used for designing the Skyway Piers. This necessity imlies that neither the concet of an exerimental lastic hinge length nor the concet of an exerimental base curvature for the Skyway Pier Test Units bears any ractical significance for the design of the Skyway. In this case, the total ier dislacement measured from a realistic roof test is enough to check the safety of the design. Fig. makes this comarison between test unit dislacements and the limits on allowable redicted Skyway Pier dislacements. Alternatively, assuming a theoretical base curvature that corresonds to the strain limits assumed by the designers, the average ultimate exerimental test unit dislacement can be used to calculate an exerimental lastic hinge length. If the lastic hinge length is calibrated to reflect actual test unit behavior, then the dislacement level associated with the assumed failure strains must corresond to the dislacement of the test unit at failure. For this urose, the caacity strain limit refers to the strains at the highest level of dislacement reached by the test unit before longitudinal bar fracture. The designers assumed the limiting caacity strain to be / ε su = / (.) =.5 for the bridge longitudinal direction and / ε su = / (.9) =.6 for the bridge transverse direction. It is imortant to consider, however, the consequences of basing calculations for the lastic hinge length on strain limits that are / of the assumed ultimate strain. While the reduction factor of / was assumed to ensure greater safety in the design of the Skyway Piers, the lastic hinge length is used exlicitly as a tool to redict ultimate dislacements. Exerimental lastic hinge lengths that are derived based on / ultimate strains corresond exactly to the limits secified by the designers. Exerimental lastic hinge lengths that are derived based on ultimate strains ensure, however, that the designers' assumed / strain limits are conservative. Additionally, exerimental lastic hinge length values deend heavily on exerimental values for ultimate dislacement. Exerimental ultimate dislacements corresonded to dislacement ductility levels ranging between µ = 6 and µ = 8. Therefore, deending on how the test units were loaded and the relationshi between the first longitudinal bar fracture and column failure, the true value of exerimental ultimate dislacement can vary by as much as %. Table. Proerties necessary for calculating L according to assumed strain limits. φ y L L (ATC-) u φ u L Test ε u [µrad/mm] [mm] [mm] [mm] [µrad/mm] [mm] () () () (4) (5) (6) (7) (8) ε c = LPT ε c = DPT(L) DPT(T) ε c = ε c = ε s = ε s = Table gives the lastic hinge lengths (Column (8)) calculated according to both the ultimate strain limits and the / ultimate strain limits (Column (6)). Both versions of exerimental lastic hinge length are given in accordance with average ultimate dislacements rior to first bar fracture (Column (5)). This dislacement level corresonded to the nominal level µ = 6 and is labeled ``test caacity" in Fig.. The values of L were solved according to Eqs. () and (4). Column () lists the shear san values as L. For the bridge longitudinal direction L = H/, assuming zero rotation of the load stub, and for the bridge transverse direction L = H + B D /. The exerimental lastic hinge length values in Column (8) corresonding to ultimate strain limits show remarkable similarity to the lastic hinge length values calculated according Eq. () in Column (4). The accuracy of Eq. () loses some of its credibility, however, if one takes into account the fact that Eqs. () and () were calibrated to yield results that are conservative by aroximately 5% [7]. Furthermore, Eq. () gives little hysical insight into the sread of lasticity in the Skyway Piers.

6 5 PLASTIC HINGE REGION FLEXURE-SHEAR MECHANISM True flexural deformation mechanisms have long been recognized as rohibitively comlex for the creation of a consistent and lasting theory of flexural deformation. ``Flexural deformation" itself is a misnomer, since the comlexity is due in art to the fact that lastic flexural deformations in reinforced concrete are almost always couled with the shear behavior of the lastic hinge region--namely the fanning crack attern. Therefore, the term ``flexure-shear deformation" is assumed to be a more accurate descrition of the henomenon. If strain enetration and tension shift could be described urely in terms of sreading lasticity, they could be accounted for with a fair amount of rigor. The action of tension shift is, however, intimately linked to a concentration of comression strains at the oint of maximum moment. This comlicates the notion of base curvature and increases the difficulty of basing calculations for flexural deformation on actual strain levels at he column base. Fig. 5 shows measured tensile and comressive strain distributions along the DPT column height in each rincile direction. This figure reinforces the notion that while the tensile strains sread u the column height, the comression strains remain concentrated near the base. Fig. 6 shows that such behavior was also recorded rior to yield in both rincial directions. The concentration of comression strains at the base of the column varies according to column geometry, reinforcement, material roerties and axial load. Columns subjected to higher shear stresses were likely to exhibit a higher concentration of comression strains at their base, since the flexure-shear crack angles were generally steeer and forced more comression struts to radiate directly out of the comression toe at the base of the column. Taller columns subjected to lower shear stresses exhibited only artial concentration of comression strains at their base due to their less inclined flexure-shear crack angles [4]. 7 DPT (L) 64 DPT(T) Height above footing, h [m] 5 4 ε y Average lastic strain rofiles µ = µ = µ = µ = 4 µ = (in.) ε y h/h h/d Strain Strain. Fig. 5. DPT average lastic strain rofiles in the longitudinal (L) and transverse (T) directions.

7 7 DPT (L) 64 DPT(T) Height above footing, h [m] 5 4 ε y (in.) ε y h/h h/d Strain -... Strain. Fig. 6. DPT average elastic rofiles in the longitudinal and transverse directions. If increased shear force and broader fanning of comression struts out of the comression toe increases the concentration of comression strains at the column base, then strain limit states should also deend on the level of shear alied to a column and the manner in which this shear is transferred within the member. While this knowledge may be alicable in setting u a sectrum of strain limits that varies according to alied shear, it is not yet ossible to aly it to the rediction of actual strain limit states. In addition to the concentration of comression strains at the column base resulting from tension shift, the confinement rovided to the comression toe at the column base by the footing is not understood in detail. Furthermore, strain enetration occurring on the tension side of the column creates a discontinuity in the section lane at the column base if the same level of strain enetration is not assumed to occur on the comression side. In light of this discussion of actual flexure-shear deformations in a column's lastic hinge region, it aears more ractical to characterize a column's flexure-shear deformations based on a simlified moment curvature aroach. Historically, this has been the same conclusion reached by many other researchers, whose work was discussed thoroughly in [8]. Comrehensive assessment of exerimental curvature rofiles allows one to calculate exerimental values for L that reflect the true sread of lasticity. The exerimental curvature rofiles, shown for the DPT in Figs. 9 and, consistently indicate further sread of lasticity with increasing deformation demand. If lastic curvature rofiles are assumed to have a linear distribution, a least squares line can be fitted to the lastic curvatures in order to determine both the base curvature and the height of the lastic hinge region, L r. The exerimental lastic hinge length can then be calculated based on the two different exressions given in Eq. (5). φ L = L Lr = + L s (5) where = the lastic dislacement, φ = the lastic base curvature, and L s is defined according to [7] as L =.d f [MPa] (6) s b y

8 If the exerimental value of L is calculated based on and φ in the first exression of Eq. (5), then the exerimental value of L s can be calculated for comarison with Eq. (6). If no satisfactory value of φ can be determined (because, for instance, the lastic curvature distribution covers fewer than three gage levels above the base gages), a value of L s can be calculated according to Eq. (6) in order to determine L and hence φ. While the two exressions for determining L given in Eq. (5) are not entirely redundant, they allow one to maximize the value of the available test data by roviding two different aroaches to characterizing the lastic hinge length. The DPT base curvatures (at h = ) in Figs. 9 and were calculated according to Eq. (5). See [4] for further discussion of these and other exerimental base curvatures. 6 LONGITUDINAL BAR BUCKLING Longitudinal bar buckling offers a more convincing exlanation of the hoo fracture mechanism than ure dilation of the confined concrete. Observations of the SFOBB Skyway Pier Tests suorted the idea that longitudinal bars often buckle rior to hoo fracture and force a small section of an individual hoo to bow outward. This section of hoo reaches its fracture strain caacity well before the dilation strains of the concrete itself aroach a level that would cause the hoos to fracture. Fig. 7. Photos of longitudinal bar buckling for the DPT (to) and Test A (bottom). In the Skyway Pier tests and suorting tests, when hoos did not fracture, the test units eventually reached their flexural caacity by buckling and subsequent fracture of the longitudinal bars. The longitudinal bars were observed either to buckle over several hoos (see the uer art of Fig. 7), in between two hoos (see the lower art of Fig. 7), or sideways within the core, deending on the strength

9 and sacing of the longitudinal bars and the hoos. Longitudinal bars were also observed to buckle between two hoos and force the hoos u and down to either side of the buckled length, thereby creating a longer sace over which to buckle. The longitudinal bar failure mechanism deends, therefore, not only on the strength and sacing of the longitudinal bars and hoos, but also on arbitrary factors such as the orientation of the longitudinal bar ribs, the actual sacing of the hoos, and the constitution of the core concrete immediately surrounding the buckling bars. It is well known that once the hoos have yielded, their ability to restrain bar buckling and exansion of the core concrete is greatly diminished. With no elastic reserves to restrain bar buckling, even the slightest eccentricity in a longitudinal bar may allow P- moments to buckle the bar inelastically and ush it outward against sirals that have already lost their elastic stiffness. If this haens, once a buckled bar has ushed a siral ast its yield oint, the siral is unlikely to restrain the longitudinal bar at all. Furthermore, yield of the sirals has often been observed to occur at low ductility levels, when ε c <.. It is roosed that a strain limit state associated with a buckled bar deends rimarily on the geometry of the buckled bar itself. The comressive strains become critical when a bar buckled under such a strain level has exerienced sufficient stress concentrations to fracture on the next ull cycle. Although these thoughts on bar buckling are inconclusive, it is still ossible to assess exerimental strain limit states of columns directly from column tests, rather than relying simly on data from uniaxial comonent tests. From the data reorted for the Skyway Pier tests and eight other suorting large scale structural tests [8], it is recommended to limit εc + ε s φ u =.5 (7) D' where D = the distance between the extreme fiber confined concrete comressive strain, ε c, and the extreme fiber longitudinal steel strain, ε s, in order to estimate the curvatures associated with the onset of bar buckling and fracture. Tyically, this onset of buckling and fracture corresonds to µ = 6, whereas µ = 8 is reached either at or beyond fracture of the longitudinal bars. These assumtions aly only to cases where the exerimental sread of lasticity is evaluated according to the method resented here. With a satisfactory definition of strain limits, the ultimate curvature can be derived for a given concrete cross section. This ultimate curvature is commonly assumed to be distributed over a given lastic hinge length, roducing a lastic rotation. If this lastic rotation is assumed to be concentrated at the base of a column, then it can be multilied by the column length in order to find the lastic dislacement. The following section outlines this rocess, exlaining in detail the assumtions used for calculating dislacements based on curvatures. 7 SPREAD OF PLASTICITY An aroach to assessing the sread of lasticity in reinforced concrete members based on the actual mechanics of the lastic hinge region are discussed in detail under searate cover [9]. This aroach is summarized below with reference to Fig. 8 and its results are comared to the exerimental results introduced reviously.

10 V P d P L A L r = jdcotθ T yav θ V+V s cr jd A C V-( V s+vcr) Fig. 8. Free body diagram for assessing the sread of lasticity. Assuming T yav to be the flexural tensile force resultant at the highest oint in the lastic hinge region reached by inclined cracks emanating from the column base, and assuming T to be the flexural tensile force resultant acting at the column base, moment equilibrium about the flexural comressive force resultant, C, in Fig. 8 gives ( T T ) jd = ( V V ) jd cotθ yav s + cr (8) Assuming that all transverse steel in the lastic hinge region has yielded, and assuming that V cr can be aroximated according to an average, uniformly distributed load, f t w, the sread of lasticity can be aroximated as L r ( T Tyav ) jd = jd cotθ = (9) ( A f / s) + f t v yv w where A v = the area of transverse steel at a given level, f yv = the yield stress of the transverse steel, and s = the sacing between the transverse bars. Based on moment-curvature analysis, Eq. (5), Eq.(7), Eq. (9), and equations for elastic dislacement and shear dislacement introduced in [9], dislacement can be calculated for all inelastic levels of curvature ductility as M M + s = ' + y φ φ' y L L () M' y M' y f

11 Height above footing, h [m] 5 4 φ y Average lastic curvature rofiles SFOBB Test DPT(L) (Hines et al. ) µ = µ = µ = µ = 4 µ = 6 h/l h/d Plastic hinge region length, L r SFOBB Test DPT(L) (Hines et al. ) Exeriment Theory (in.) Curvature ductility, µ φ = φ / φ y Curvature ductility, µ φ = φ / φ y Fig. 9. DPT(L) average lastic curvature distributions and sread of lasticity. Height above footing, h [m] φ y SFOBB Test LPT (Hines et al. ) µ = µ = µ = µ = 4 µ = 6 h/l..5 h/d SFOBB Test LPT (Hines et al. ) Exeriment Theory (in.) Height above footing, h [m] Average lastic curvature rofiles Plastic hinge region length, L r. 7 SFOBB Test DPT(T) SFOBB Test DPT(T) 6 (Hines et al. ) (Hines et al. ) φ y h/l Curvature ductility, µ φ = φ / φ y Curvature ductility, µ φ = φ / φ y Fig.. LPT and DPT(T) average lastic curvature distributions and sread of lasticity. Figs. 9 and comare Eq. (9) to some of the SFOBB Skyway Pier exerimental results, showing that the equation adequately redicts the sread of lasticity at most levels of curvature ductility, µ φ, for both test units with the excetion of the DPT(L) at the base of the ier. In this case, the sread of lasticity in the bridge longitudinal direction was influenced by the higher sread of lasticity in the bridge transverse direction (see Fig. ). Both the exeriment and the theory show the lasticity sreading further with increasing curvature ductility. They also both show the lasticity sreading raidly between µ = and µ h/d (in.)

12 = and then slowing down for higher levels of dislacement ductility. Note that while all exerimental and analytical data is reorted according to curvature ductility exerimental data was collected at levels of dislacement ductility, µ, secified in round numbers. 8 CONCLUSIONS Large-scale structural roof-of-concet tests for the SFOBB East Bay Skyway Piers successfully demonstrated the iers' ability to withstand flexural dislacement demands believed to corresond to a 5 year earthquake. Attemts to comare the iers' dislacement caacities to their assumed demands raised many questions concerning the correct alication of so-called erformance limits in seismic design and evaluation. On one level, the dislacements of the test units could be comared directly with assumed ier dislacement demands, since the test units were scale models of the iers themselves. On another level, the contribution of the test units' behavior to general understanding of reinforced concrete bridge iers required more accurately defined flexural strains and lastic hinge lengths. A new method for calculating the lastic hinge length based on the actual sread of lasticity roved to reflect adequately the sread of lasticity in the Skyway Piers for nearly all levels of curvature and dislacement ductility. ACKNOWLEDGEMENTS Funding for this work was rovided by the California Deartment of Transortation (Caltrans). The authors would like to acknowledge Dr. Andrew Budek, Dr. Alessandro Dazio, Dr. Jay Holombo, and Dr. Christoher Latham for their hel in designing and conducting the SFOBB Skyway Pier Tests. REFERENCES [] Hose, Y.D., Seible, F., Hines, E.M.: Alication of the Performance Evaluation Database to the San Francisco-Oakland Bay Bridge East Bay Skyway. Proceedings of the Seventh U.S. National Conference on Earthquake Engineering, Boston, Massachusetts, July. [] T.Y. Lin International / Moffat & Nichol Engineers, a joint venture: San Francisco-Oakland Bay Bridge East San Seismic Safety Project: Design Criteria, Draft: , Revision 6, San Francisco, California, 999. [] Hines, E.M., Dazio, A., Seible, F.: Structural Testing of the San Francisco-Oakland Bay Bridge East San Skyway Piers, Structural Systems Research Project SSRP /, University of California, San Diego, La Jolla, California,. [4] Hines, E.M., Seible, F.: Exerimental Sread of Plasticity in Reinforced Concrete Bridge Piers, Structural Systems Research Project SSRP /8, University of California, San Diego, La Jolla, California,. [5] Mander, J.B., Priestley, M.J.N., Park, R.: Theoretical Stress-Strain Model for Confined Concrete, ASCE Journal of Structural Engineering, 4(8):84 86, August 988. [6] ATC-: Imroved Seismic Design Criteria for California Bridges, Alied Technology Council, Redwood City, California, 996. [7] Priestley, M.J.N., Seible, F., Calvi, G.M.: Seismic Design and Retrofit of Bridges, Wiley, New York, 996. [8] Hines, E.M.: Seismic Performance of Hollow Rectangular Reinforced Concrete Bridge Piers with Confined Corner Elements, Ph.D. Dissertation, University of California, San Diego,. [9] Hines, E.M., Seible, F., Restreo, J.I.: Force-Dislacement Characterization of Hollow Rectangular Bridge Piers, ACI Structural Journal, submitted for ublication,.