PROOF TESTING IN SUPPORT OF SEIMIC BRIDGE DESIGN: EXAMPLE OF THE SAN FRANCISCO-OAKLAND EAST BAY SAFETY PROJECT Frieder SEIBLE 1 Alessandro DAZIO 2 1 Eric and Johanna Reissner Professor of Structural Engineering; Dean, Jacobs School of Engineering 2 Post Graduate Researcher Department of Structural Engineering, University of California at San Diego 9500 Gilman Drive, La Jolla, CA 92093-0085, USA Keywords: San Francisco-Oakland Bay Bridge, large scale proof tests, numerical simulations, capac- ity design, seismic bridge design, self-anchored suspension bridge. SUMMARY The replacement of the East Span of the San Francisco-Oakland Bay Bridge is of significant social and economical importance for the State of California. The new multi-billion dollar bridge is designed to accommodate the very high traffic volume crossing the Bay, and as a lifeline structure has to offer full functionality almost immediately after a major earthquake. To fulfill these stringent performance requirements, capacity design was adopted and the seismic behavior of the bridge was systematically investigated by means of state-of-the-art transient non-linear finite element computations and large scale or full scale proof/validation tests under controlled laboratory conditions. The paper describes the structural system of the new bridge, presents the seismic design philoso- phy, and discusses the proof-tests of key structural bridge components performed at the University of California, San Diego, to validate the design of the bridge. 1 INTRODUCTION 1.1 Background The San Francisco-Oakland Bay Bridge (SFOBB), pictured in Figure 1a, carries 10 lanes of Inter- state traffic on two decks with more than 280,000 vehicles each day. This aging structure was first opened to the public in 1936 and was designed according to elastic theory to resist approximately 0.10g horizontal acceleration [1, 2]. Fig. 1. West and East Spans of the existing San Francisco-Oakland Bay Bridge (a) and collapse of one span of the East Bay Bridge during the 1989 Loma Prieta Earthquake (b).
Transcript
PROOF TESTING IN SUPPORT OF SEIMIC BRIDGE DESIGN: EXAMPLE OF THE SAN FRANCISCO-OAKLAND EAST BAY SAFETY
PROJECT
Frieder SEIBLE1 Alessandro DAZIO2 1 Eric and Johanna Reissner Professor of Structural Engineering; Dean, Jacobs School of
Engineering 2 Post Graduate Researcher Department of Structural Engineering, University of California at San Diego 9500 Gilman Drive, La Jolla, CA 92093-0085, USA Keywords: San Francisco-Oakland Bay Bridge, large scale proof tests, numerical simulations, capac-ity design, seismic bridge design, self-anchored suspension bridge. SUMMARY The replacement of the East Span of the San Francisco-Oakland Bay Bridge is of significant social and economical importance for the State of California. The new multi-billion dollar bridge is designed to accommodate the very high traffic volume crossing the Bay, and as a lifeline structure has to offer full functionality almost immediately after a major earthquake. To fulfill these stringent performance requirements, capacity design was adopted and the seismic behavior of the bridge was systematically investigated by means of state-of-the-art transient non-linear finite element computations and large scale or full scale proof/validation tests under controlled laboratory conditions.
The paper describes the structural system of the new bridge, presents the seismic design philoso-phy, and discusses the proof-tests of key structural bridge components performed at the University of California, San Diego, to validate the design of the bridge. 1 INTRODUCTION 1.1 Background
The San Francisco-Oakland Bay Bridge (SFOBB), pictured in Figure 1a, carries 10 lanes of Inter-state traffic on two decks with more than 280,000 vehicles each day. This aging structure was first opened to the public in 1936 and was designed according to elastic theory to resist approximately 0.10g horizontal acceleration [1, 2].
Fig. 1. West and East Spans of the existing San Francisco-Oakland Bay Bridge (a) and collapse of one span of the East Bay Bridge during the 1989 Loma Prieta Earthquake (b).
At 5:04 p.m. on October 17, 1989, both spans of the double deck roadway above Pier E9 experi-enced partial collapse under the seismic motions from the Loma Prieta Earthquake, see Figure 1b. The damage suffered during the earthquake cost a human life and closed the bridge for 30 days, re-sulting in millions of dollars per day in economic losses to the Bay Area.
The Loma Prieta earthquake had a moment magnitude of 7.1 with its epicenter nearly 100 kilome-ters southwest of the bridge. This earthquake comprised a relatively minor threat to the bridge com-pared to the probable threat of a larger earthquake on either the San Andreas or the Hayward faults, both situated within 12 to 25km from the bridge.
Following the Loma Prieta earthquake, Caltrans (California Department of Transportation) started a multi-year seismic vulnerability assessment and retrofit project of all major bridges in California, in-cluding the SFOBB East Bay Span [3]. First, a retrofit of the East Span Steel Truss structure was evaluated. However, due to the high cost and the questionable reliability in term of performance of the retrofit and due to its difficult implementation under full traffic, a replacement structure was determined to provide a seismically more reliable alternative, resulting in the SFOBB East Span Replacement Pro-ject. This bridge replacement project is the largest bridge project in California's history (estimated at close to $3 billion) with the main objective to establish seismic safety and reliability as quickly as pos-sible without interruption of traffic across the Bay. 1.2 The New East Span Seismicity Safety Project
The design of the new East Bay bridge was strongly defined by a set of recommendations pre-pared by an Engineering and Design Advisory Panel (EDAP), a panel of worldwide recognized experts in bridge design, assembled to guide Caltrans in the development of designs of the East Span. Among other recommendations, the following had a major impact on the design of the new bridge (from [1]):
• The new East Span and the existing West Span retrofit should be designed to provide post- earthquake “lifeline service”;
• The new East Span should have a cable-supported main span with a single vertical tower with single or multiple legs in the transverse direction and single or multiple planes of supporting cables;
• The new East Span should not be double decked; • The cable or suspension tower on the East Span should not be taller than the suspension
towers on the existing West Span. Following these and other recommendations Caltrans selected and contracted with the joint ven-
ture of T.Y. Lin International / Moffatt & Nichol to develop 30 percent designs for two alternative bridges: one with a cable-stayed main span [1, 4] and one with a self-anchored suspended main span [1, 5]. After careful evaluation of all aspects and mainly due to a better assimilation with the other existing suspension bridges in the San Francisco Bay, the alternative of the self-anchored suspension bridge shown in Figure 2 was chosen.
Fig. 2. Rendering of the new East Span of the San Francisco-Oakland Bay Bridge at night [courtesy of T.Y.Lin International].
The new bridge, shown in Figures 2 and 3, consists of four distinct structures: (1) the Oakland
landing or touchdown structures (2) a segmental concrete box girder crossing called the Skyway, (3) a Self-Anchored Suspension (SAS) signature span, and (4) a series of multi-cell post-tensioned con-crete box girder bridges providing the transition to the tunnel on Yerba Buena Island [5]. The new
bridge will feature parallel roadways and will be built next to the existing bridge, which will be disman-tled after the new bridge is opened to traffic. This paper focuses only on the seismic safety aspects of two of the four segments of the new SFOBB East Span Bridge, namely the Skyway and the SAS bridges. In the following, brief descriptions of the elements governing key seismic response aspects are provided; a complete description of the different bridge systems can be found in [1, 6 and 7].
The Skyway consists of two parallel segmental precast concrete viaducts with a typical span of 160m, grouped in frame units of three or four piers per frame, separated by expansion joints. The haunched single cell box girder cross-section has a depth of 5.5m at midspan (9.9m at the pier) and features two vertical webs spaced 8.5m apart. The total deck width of 25m is reached using over-hangs of 8.3m on each side. The deck is post-tensioned in the longitudinal and in the transverse direc-tions while the webs are post-tensioned longitudinally and vertically. The cast-in-place hollow rectan-gular reinforced concrete piers of the Skyway rely on highly-confined corner elements for inelastic de-formation capacity and on connecting structural walls for stiffness and strength (Figure 6b). The Sky-way piers imitate the main span tower in geometry and architectural treatment through cover concrete articulation, helping to maintain a consistent visual theme throughout the entire bridge [2]. The Skyway piers have heights ranging from 36m at Pier E3 to 14m at Pier E16 with monolithic connections to the superstructure and to the foundations.
Main Span Skyway StructuresYBI Transition
Structures
Total length: 3.9 km (2.4 miles)
OaklandTouchdown
2100 m (6900 ft.)
Existing Bridge
620 m (2030 ft.) 660 m (2160 ft.) 500 m (1640 ft.)
Expansion Joint ”K”
Expansion Joint ”A”Expansion Joint ”B”
Expansion Joint ”C”
Expansion Joint ”D”
Expansion Joint ”E”New Bridge
W2 E2 E9 E15Pier1
Fig. 3. Schematic representation of the new East Span of the San Francisco-Oakland Bay Bridge.
The signature span (or main span) of the New San Francisco-Oakland Bay Bridge is the world’s largest self-anchored suspension (SAS) bridge. The SAS bridge consists of a 385m front span and a 180m back span. The single tower is 160m tall and is made up of four steel shafts (tapered stiffened box members) connected with intermittent shear links along its height. The tower pile cap is positioned at water level supported by thirteen 2.5m diameter CISS concrete piles. The permanent shell termi-nates 30m below the pile cap with a CIDH pile continuing to a depth of approximately 75m below the water line and into the bedrock of the Franciscan Formation. The 0.78m diameter main cable is an-chored to the deck at the east bent (Pier E2) and looped around the west bent (Pier W2) through de-viation saddles. At Pier E2 the cable is parallel to the deck inducing a horizontal compressive force in the deck only. On the other side, at Pier W2, the inclined main cable induces a horizontal compressive force into the deck and a vertical tensile force that has to be carried by the pier. The uplift at W2, due to the self-weight of the front span, is balanced by the self-weight of the massive cap beam of Pier W2. The additional seismic uplift is resisted by a tie-down system consisting of 28 tendons (each with 61-15mm diameter strands) anchored in the cap beam and in the foundation blocks. Finally, uplift is resisted by the weight of the foundation blocks encased in the bedrock and by eight 2.5m diameter CIDH concrete piles.
Pier W2 consists of a north and south pier fixed at the base and tied together at the top by a stiff cap beam. Each pier is made up of four 3.5m diameter circular concrete columns, with pentagonal shaped architectural concrete to ensure visual consistency with the other piers of the bridge. The col-umns are fixed to the foundation block and to the cap beam and are not interconnected (Figure 10a).
Pier E2 consists of a north and south pier fixed to the foundation at the base and tied together at the top by a stiff cap beam, and is similar in design to the Skyway piers.
The superstructure of the self-anchored suspension bridge consists of two 25m wide dual, hollow orthotropic steel boxes, accommodating five lanes of traffic and two shoulder lanes each. The super-structure is under a permanent compression load of 200MN per each girder, corresponding to about 30% of the nominal yield strength of the longitudinal girders, to balance the cable tension forces. The box girders are connected by crossbeams spaced 30m apart. The crossbeams carry the transverse load between the suspenders and ensure that the dual boxes act compositely during wind and seismic loads. The suspenders are splayed to the exterior side of the box girder and are spaced 10m apart. 2 SESMIC DESIGN PHILOSOPHY 2.1 Performance Limit States
The seismic risk to the new bridge comes mainly from the Hayward Fault located 12km away, ca-pable to generate a 7.5 Richter magnitude earthquake, and from the San Andreas Fault located 25km away, capable to generate an 8.1 Richter magnitude earthquake. The bridge is designed to resists two levels of earthquake, namely (1) the Safety Evaluation Earthquake (SEE), addressing an approxi-mately 1500year event on either fault, and (2) a Functional Evaluation Earthquake (FEE) correspond-ing to a shorter return period (~450year) event.
The FEE performance criteria requires full service almost immediately following the earthquake with only minimal damage to the structure. Minimal damage implies essentially elastic performance, and is characterized by minor inelastic response, narrow cracking in concrete, no apparent permanent deformations and only limited damage to expansions joints that can temporarily be bridged with steel plates.
After the SEE event the lifeline bridge needs to provide service with no more than repairable dam-age to the structure. Repairable damage is damage that can be repaired with a minimum risk, such as minimal damage to superstructure and tower shafts, limited damage to piers (including yielding of rein-forcement and spalling of concrete cover) and tower shear links, small permanent deformations, not interfering with serviceability of the bridge, and damage to expansions joints that can temporarily be bridged with steel plates. To ensure the ability of the bridge to carry traffic across expansion joints af-ter the SEE event the allowable average permanent deformation is limited to 300mm. 2.2 General Seismic Design Concept
The bridge design philosophy is aimed at providing an inherent toughness in the pier-foundation system, to define a clear sequence of yielding damage in overload conditions, and to avoid inspection or repair at inaccessible locations.
These requirements and the high seismicity in the Bay Area required state-of-the-art capacity de-sign of the new bridge, allowing plastic deformation in clearly designated structural components that were specially designed for this purpose. For example, in the Skyway, plastic hinges are allowed to form at the top and bottom of all concrete piers protecting the foundations and the superstructure against overload. In the SAS bridge, shear hinges are allowed to form in the steel shear links connect-ing the four steel shafts of the main tower, protecting the tower legs against yielding (Figure 4). The shear links were designed to be replaceable after a seismic event. Expansion joints reduce the con-straints between the four distinct structures of the bridge and within the Skyway (Figure 3).
Fig. 4. Seismic response mechanism of the East Bay Bridge.
To implement this design philosophy and to meet the expected performance, the bridge was de-
signed based on capacity design principles for limited-ductility structures but implementing detailing and proportioning requirements for full-ductility structures. This delivers a structure with excellent ser-viceability characteristics and with a high degree of inherent safety and reliability. To demonstrate that all performance requirements can be safely met by the proposed design, components in the bridge that were expected to see any inelastic action under the SEE, had to be proof tested at large or full scale to clearly establish all performance limit states. 2.3 Proof Test Program
The design of the bridge was carried out based on nonlinear time-history analyses with multiple support input. The ground motions used for the analyses were specially developed for this project, taking source-to-site effects, near source effects, as well as site-specific geological and geotechnical characteristics into account.
Local element capacities were established from first principles using section analyses or through detailed non-linear finite element modeling. As outlined above, the performance limit states (capacities at predetermined damage/performance levels) for all components with expected inelastic actions or plastic hinges, see Figure 5, needed to be verified by means of full or large scale proof-testing.
Fig. 5. Rendering of the new East Span of the San Francisco-Oakland Bay Bridge and of the key structural components tested in the Charles Lee Powell Structural Research Laboratories at the
University of California, San Diego [original rendering courtesy of T.Y.Lin International].
This proof-testing program was conducted at the Charles Lee Powell Structural Research Labora-tories at the University of California, San Diego. In the framework of this program, two steel shear links at 100% scale were tested by McDaniel et al. in [8], two concrete piers of the Skyway at 25% scale were tested by Hines et al. in [2] and the results of the test on a 25% scale model of the West Anchor Pier W2, tested by Dazio and Seible, are presented in [9]. To round up the investigation, two steel shear links at 50% scale were tested by Dusicka et al. at the University of Nevada at Reno [10]. The latter tests complemented the full-scale shear link tests performed in San Diego, since proper bound-ary conditions for the link in the form of half-scale tower leg sections were introduced.
In addition to all inelastic bridge components, two additional bridge elements were tested despite the fact that they are expected to remain elastic during the SEE event, namely the epoxy bonded segment-to-segment joints in the Skyway superstructure to determine the effects of possible joint opening under the SEE, and different SAS bridge orthotropic steel deck sections to establish their lo-cal buckling characteristics.
Two segmental box girder sections of the Skyway at approximately 20% scale, were tested by Megally et al. in [11] to investigate different design philosophies for the segment-to-segment construc-tion joint in order to optimize the erection procedure of the Skyway, yet ensuring satisfactory seismic performance. Two panels of the SAS bridge steel box girder were tested at 45% scale by Chou et al. in [12] to investigate the ability of the deck to sustain seismic induced compressive stresses near yielding, without buckling. These proof-of-concept tests for the SFOBB East Bay Bridge are discussed in the following. 3 PROOF TESTS AND KEY FINDINGS In the following sections the proof tests performed at the University of California, San Diego in support of the design of the of the new East Span of the San Francisco-Oakland Bay Bridge are briefly presen-tend. Due to space limitation only highlights of the tests are presented, giving an overview of the per-formed investigations. For a detailed understanding of the tests and the test results, the relevant re-search reports have to be consulted [2, 8, 9, 11, 12, 13, 14]. 3.1 Skyway Pier Tests
To validate the performance of the Skyway piers, two 25% scale models of a representative (ge-neric) pier of the Skyway were tested. The generic quarter scale pier had the cross section of Pier E15 end the height of Pier E9 (Figure 3) and was selected to provide design and analysis model validation for the architectural concrete performance, the plastic hinge length, the shear force transfer, and the overall deformation capacity [15]. 3.1.1 Test Setup and Loading History
The two test units were nearly identical, however they were tested using two different loading his-tories. The first unit was tested in the bridge longitudinal direction only, hence the designation as Lon-gitudinal Pier Test (LPT), while the second unit was tested using a rigorous bi-directional loading his-tory, i.e. Diagonal Pier Test (DPT).
a) Detail
b) Test Unit Section
c) d)
-0.2 -0.1 0.0 0.1 0.2T ransverse drift [m ]
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Fig. 6. Skyway Pier Test Unit and relevant loading history.
The setup for the DPT is pictured in Figure 6a. In the bridge longitudinal direction the pier is re-strained by the foundation and by the girder. In the test these boundary conditions were simulated by locating the line of action of the longitudinal actuators at pier mid-height using a steel loading frame
and by preventing any rotation of the top of the pier using vertical actuators connected to the loading frame. In the bridge transverse direction the pier behaves mainly as a cantilever restrained by the foundation only; the actuators used in the test to simulate this condition are shown in the upper right corner of Figure 6a. An axial load of about 0.10 Agfc’ was applied to the test unit to simulate the action of superstructure self-weight. The cross section of the test units is pictured in Figure 6b.
For the DPT a special loading history was developed. Figure 6c shows the drift of Pier E9 under one set of input motions to the SEE design level. In this displacement history the pier shows tenden-cies to deform along the bridge principal and diagonal axes and in a sweeping motion from one princi-pal axis to the other. Based on this observation and due to the importance to investigate the perform-ance of the pier in the principal and diagonal directions, the loading history of Figure 6d was proposed. This loading history determined first the ideal yield displacements ∆yL, ∆yT and ∆yD in the longitudinal, transverse and diagonal directions of the bridge, respectively. In displacement control, the column was then cycled once according to a butterfly-wings pattern, beginning in the longitudinal direction, transi-tioning (from A to C in Figure 6d) to the transverse direction, and then (from D to F) back to the longi-tudinal direction. Subsequently, the test unit was cycled once in the other diagonal direction, in a pat-tern that resembled the body of the butterfly (Positions G and H). After these two cycles, the dis-placement ductility demand was increased. The loading history used to test the LPT corresponds to a simple cyclic displacement along the AF axis on Figure 6d.
The number of cycles was of major importance. A loading history significantly more severe than a real earthquake would lead to an overly conservative and prohibitively expensive design, while a less demanding loading history would raise questions concerning the safety of the design. In the frame-work of these proof tests, the severity of a loading history was estimated considering the Displacement Ductility (DD, µ∆), the Number of Plastic Excursions (NPE), and the Sum of Normalized Plastic Defor-mation Ranges (SNPDR) that it imposed to structures. The SNPDR is the sum of the ratios between the plastic range ∆P,i of the ith excursion and the nominal yield displacement of the structure ∆y. The NPE and SNPDR for the LPT and DPT loading histories were determined using the “rain flow” count-ing method and are pictured in Figure 7. During time-history computations at the SEE event level, Pier E9 and E5 underwent only minor plastic deformations in the longitudinal direction. Assuming rigid foundations, Pier E5 reached a DD of 2.7, and Pier E9 of 1.6. Corresponding values in terms of NPE and SNPDR are plotted in Figure 7. As expected, in order to fulfill the design criteria, the SEE event was able to produce only moderate plastic deformations in the skyway piers, see Figure 7. To investi-gate the behavior of the Skyway under larger plastic deformations, inelastic Single Degree of Freedom (SDOF) systems, having the same elastic period as the Skyway, were employed. In the bridge longi-tudinal direction a SDOF system with a period of 1.5 seconds was chosen while in the transverse di-rection the SDOF system had a period of 2.0 seconds. The results of this investigation are also plotted in Figure 7. From Figure 7 it can be concluded that the LPT and DPT loading histories are able to dis-place the test unit to a ductility bigger than the SEE and that considering the same displacement ductility, the chosen LPT and DPT loading histories are generally more severe than a real time history both in terms of NPE and SNPDR. Only at low ductility the real time histories showed a slightly higher amount of NPE, but this was deemed not to be significant.
0 1 2 3 4 5 6 7 8D isplacem ent ductility [-]
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xcursions
a) SFOBB Skyway Pier TestsLP T long. loading history
D P T long. loading history
D P T trans. loading history
Long. S D O F T =1.5s
T rans. S D O F T =2.0s
= P ier E 5 under S E E event (long)
= P ier E 9 under S E E event (long.)
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Long. S D O F T =1.5s
T rans. S D O F T = 2.0s
= P ier E 5 under S E E event (long.)
= P ier E 9 under S E E event (long.)
Fig. 7. Dependence of Number of Plastic Excursions (NPE) and Sum of Normalized Plastic Deformation Ranges (SNPDR) on Displacement Ductility (DD) for different loading histories
of the Skyway piers.
3.1.2 Test Results The Longitudinal Pier Test (LPT) experienced premature damage with spalling of the cover con-
crete occurring as early as displacement ductility 1. This displacement level corresponds roughly to the displacements expected during the FEE event. Therefore, the observed damage was inconsistent with the performance requirements stated in Section 2.1. The main cause of the premature spalling was the shape of the architectural concrete with sharp corners protruding outside the concrete core, experiencing large compressive strains already at low ductility levels. In response to this early spalling, isolation gaps (25mm in the test and 100mm in the prototype) for the architectural concrete were pro-vided at both the top and the bottom of the Diagonal Pier Test (DPT), see Figure 6b. Furthermore the reinforcement of the architectural concrete corners was improved.
The hysteretic behavior of the DPT is pictured in Figure 8. Similar to the LPT, the DPT showed primarily flexural response and outperformed the displacements allowed by the SEE strain criteria by more than a factor of two, validating the design of the Skyway piers. Failure occurred, as expected, in a progressive and ductile fashion by tensile fracture of longitudinal bars, following bar buckling during the previous compressive loading cycle. The first bar fractured at loading position H, see Figure 6d, during cycling at ductility 6. During the following cycles at ductility 8 about 30% of the bars fractured and the global failure criteria of 20% loss in strength was first reached in the transverse direction at position D. The different load positions at ductility 6 are indicated in Figure 8 with capital letters allow-ing a better interpretation of the hysteretic response. The most distinctive characteristic of this re-sponse is the drop in load capacity after a diagonal sweep (Load positions A,B,C or D,E,F). The ca-pacity drop is most significant for the positive excursions in the transverse (B to C) direction and the negative excursions in the longitudinal direction (E to F), where the test unit was cycled from a diago-nal displacement to a displacement in a principal direction. While the component of displacement in the principal direction increased, the load decreased significantly, indicating that some of the steel that had been loaded in the diagonal direction probably unloaded on the way to the displacement in the principal direction. This reflects the fact that under cyclic loading, steel can offer either a large tensile resistance, a greatly reduced tensile resistance, or even compressive resistance at the same strain level. Therefore an appropriate constitutive model for the reinforcement steel is mandatory for the suc-cessful prediction of the test unit behavior by means of finite elements as shown in Figure 8.
-400 -300 -200 -100 0 100 200 300 400Longitudinal displacem ent [m m ]
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-Fy
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F E m odelE xperim entS E E strain lim its
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b) SFOBB - DPTTransverse direction
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Fig. 8. DPT and FE model hysteretic behavior. Longitudinal (a) and transverse direction (b).
Figure 9a shows the top of LPT and Figure 9b the top of DPT at the end of the test. In the DPT the isolation gaps can be clearly seen. The top of the pier is strained only when the pier is loaded in longi-tudinal direction, therefore the top of both piers were subjected to nearly the same action. While LPT experienced significant spalling, DPT shows only minor damage, validating the effectiveness of the isolation gaps.
Fig. 9. Damage to top of column at end of test. Comparison between LPT (a) and DPT (b).
3.2 Pier W2 Test The design of Pier W2, the only pier of the bridge founded on rock, was extremely challenging be-
cause the pier had to be strong enough to guarantee the anchorage of the Main Span but not too stiff to attract too much force during seismic events. Furthermore, Pier W2 also features architectural treat-ment in the form of hexagonal concrete sections to ensure its harmonious visual integration within the whole project. Pier W2, consisting of eight circular columns fixed top and bottom is shown in Figure 10a. About 65% of the overturning moment in the bridge longitudinal direction at the base of the pier are transferred by bending of each single column while the remaining 35% are transferred by frame action between the columns. The stiffness of Pier W2 is strongly influenced by the bending and axial stiffness of each column and by the interaction between the columns. All these parameters are difficult to estimate especially with the pier undergoing inelastic deformations. No pier of this size had been built using this structural system, leaving the designers without any experimental validation for their design. Considering that the seismic behavior of Pier W2 strongly affects the dynamic behavior of the entire SAS bridge, its detailed analytical, numerical and experimental assessment was mandatory.
c)b)a)
Fig. 10. Isometric view of the prototype Pier W2 (a), cross-section of the prototype south pier (b) and 25% scale Pier W2 Test Unit (c).
3.2.1 Test Setup
The seismic behavior of Pier W2, shown in Figure 10a, was extensively investigated, mainly using the global finite element model of the Main Span pictured in Figure 17a. The nonlinear time history analyses showed that:
• The 8 columns of Pier W2 behave mostly in double bending when the pier is loaded in the transverse direction and, due to the length (70m) of the stiff cap beam connecting the columns, only a slight variation of the axial load in each column occurs. Contrary to this, when the pier is loaded in the longitudinal direction, a frame action between the front and the back columns occurs leading to a substantial variation of the axial load in each column, with the tension column of the frame reaching a net positive tensile force.
• The rotation of the cap beam in the bridge longitudinal direction is partially restrained by the SAS bridge superstructure and bending action is imposed from the SAS bridge superstructure to the pier. When the largest seismic drift occurs, the location of the inflection point of the pier is located between approximately 30 and 40m above the foundation block.
• The total axial load in the pier varies during the seismic event; however, the resultant is always in compression and there is a poor correlation between total axial load and longitudinal seismic drift.
• The maximum seismic drift in the bridge longitudinal direction during SEE is approximately 1.1m. This corresponds to a displacement ductility of less than two.
Based on these findings a test setup to establish the behavior of Pier W2 in the critical bridge lon-gitudinal direction was proposed. To capture the correct frame action a test setup consisting of two columns was selected (Figure 10b). To match laboratory constraints, a 25% model scale was chosen. The inflection point was kept constant and the steel loading frame pictured in Figure 10c was used to ensure its location within the range identified by the FE analyses. A constant axial load of 0.045 Agfc’ was applied to the test unit, corresponding to the axial load due to dead load. 3.2.2 Test Predictions and Results
The structural system with correct framing action for Pier W2 makes the analytical performance prediction challenging. Therefore, major effort was devoted to the development of analytical models to predict the behavior of Pier W2. Four different analytical models were developed: a Plastic Mechanism Model (PMM, Figure 11a) that can be solved in closed form when the unknown moments Mp1 and Mp2 are expressed as functions of the axial loads N1 and N2, using the moment axial load interaction dia-gram of the columns cross-sections; A Matrix Analysis Model (MAM, Figure 11b) where the stiffness matrix of the Pier W2 frame is assembled taking into account rotational springs at the end of the col-umns. The axial and bending stiffnesses of the members 1) and 2) are assumed to be constant. The bending stiffness of the cracked members EIcr and the stiffness k of the rotational springs are taken from moment-curvature relationships calculated using the axial loads obtained from the PMM. The axial stiffness of the cracked members EAcr is calculated as EAcr=(EIcr/EIg)EAg. Where EIg and EAg are the properties of the gross sections; The Beam Element Model (BEM, Figure 11c) uses two-node Ber-noulli beam fiber elements and simplified uniaxial cyclic constitutive laws for reinforcing steel and con-crete [16]; The Solid Element Model (SEM, Figure 11d) is an ABAQUS [17] model where the concrete is modeled with solid elements and each reinforcement bar is represented as a subelement within the concrete continuum elements. For both steel and concrete the state-of-the-art “ANACAP-U” material model are used [18].
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Figure 12 compares the force deflection curves of the test unit calculated by means of the analyti-
cal models pictured in Figure 11, showing a good agreement between the results. The nominal yield displacement of the test unit corresponding to a displacement ductility 1 was estimated to be 150mm, indicating that the MAM would predict failure of the test unit at a ductility of just 4.4, while the SEM stopped converging at about ductility 5.3. Both values seemed to be relatively low compared to previ-
ous tests performed, where at least a displacement ductility of 6 could be reached prior to failure. In the case of the MAM, the failure was triggered by reaching an ultimate confined compressive strain of 0.018 at the extreme concrete fiber. The convergence of the SEM was problematic when the test unit reached large displacements, and minor modification of the mesh in the plastic hinge region led to very different ultimate displacements. With finer discretization, the ultimate displacement was lower because stress concentrations induced locally very high strains at the integration point level in the strongly non-linear concrete material model, disrupting the convergence of the model. Therefore, the ultimate displacement predicted by the SEM has to be interpreted cautiously. The results of the predic-tion of the behavior of the Pier W2 Test Unit show again the importance of the assumed strain limit states: a problem still not fully solved. A thorough discussion of this problem is presented by Hines in [14]. However, it has to be noted that all the predictions clearly outperformed the maximum displace-ment demand of 0.27m expected during the SEE event.
The excellent hysteretic behavior of Pier W2 Test Unit is shown in Figure 13a. The FEE event is expected to displace Pier W2 up to ductility 1. At this displacement the test unit showed a maximum crack width of 0.4mm. The cracks closed after unloading and no spalling of the concrete cover was observed. At ductility 2, at displacements 10% larger than the ones expected during the SEE, the test unit showed a maximum crack width of 1.5mm and a residual crack width after unloading of 0.6mm. Only minor spalling of the cover architectural concrete occurred. The residual deformation after unloading was 100mm, corresponding to 400mm in the prototype structure. This value does not con-form to the performance requirement listed in Section 2.1. However, this value was obtained for the stand-alone Pier W2. Time-history analyses performed by the designers show that when the entire Main Span is considered, the permanent displacements are less than the required 300mm. The test unit failed during the second cycle at ductility 6 due to tensile fracture of previously buckled longitudi-nal reinforcing bars. This occurred at a drift of 7.7% (Figure 13a), which in the prototype would corre-spond to a displacement of 3.6m, more than three times the expected displacement during the SEE event, demonstrating the excellent performance of Pier W2. This assessment of the hysteretic behav-ior of Pier W2 confirms that large permanent deformations are possibly the biggest drawback of con-ventional ductile reinforced concrete structures. Therefore the development of new structural systems with reduced permanent deformations after an earthquake should be investigated.
M atrix A nalysis M odelB eam E lem ent M odelS olid E lem ent M odel
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Blind predictions of the hysteretic behavior computed with the Solid Element and the Beam Ele-ment Models are compared against experimental evidence in Figure 13a. Both predictions are able to capture strength, stiffness, stiffness degradation and residual displacement of the unit. This implies that the interaction between the bending moment and the varying axial loads in the columns due to frame action was properly accounted for. As expected, shear deformations were negligible, therefore the BEM was able to accurately predict the behavior of the test unit. However it was not possible to accurately predict the failure of the test unit because, to date, no reliable failure criteria are available for the kind of failure experienced by Pier W2 Test Unit.
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Fig. 13. Pier W2 test: Experimental and numerical hysteretic behavior of the test unit (a) and picture of the test unit at ductility 1 x +6 (b). Top displacement: 900mm. Drift: 7.7%.
3.3 Main Tower Shear Link Tests
The Main Tower of the SAS bridge uses an innovative structural system to ensure adequate seis-mic performance at both the FEE and SEE level. The single tower is comprised of four vertical steel box shafts. The shafts are interconnected in the bridge longitudinal and transverse directions by steel shear links creating a frame action between the shafts. At the FEE level, both the shafts and the shear links remain elastic and the added stiffness, due to the links, plays an important role in the control of the displacements. At the SEE level the links are designed to yield in shear. The yielding of the links softens the stiffness of the tower and dissipates hysteretic energy, reducing the seismic forces acting on the bridge. Furthermore, it protects the shafts from yielding, which is a major advantage consider-ing their high axial load and the difficulty to repair them. The bolted connections between the links and the tower shafts are designed according to capacity design principles to remain elastic while the links are yielding. This allows the links to be easily replaced after a major seismic event. The strategic loca-tion of the links and the fine-tuning of their stiffness provides the designers with flexibility to tailor the structural response to meet the performance requirements.
The concentration of all inelastic deformations in replaceable sacrificial elements (links) improves both performance and maintainability of the structure with stringent performance criteria for the links. The links need to be able to withstand the high shear deformation ductility demand expected during the SEE event without loss in strength. The link-shaft connections should allow the replacement of the links after they have undergone large inelastic deformations, and the links should have a predictable overstrength to allow the capacity design of shafts and connections.
In order to answer these questions, two shear links at 100% scale were tested at the University of California, San Diego (UCSD) [8] and two shear links at 50% scale comprising part of the tower shafts were tested at the University of Nevada, Reno (UNR) [10]. 3.3.1 Test Setup
The setup to test the shear links at UCSD is shown in Figure 14a. The four pin portal loading frame was stabilized by the shear link at mid-height. The longitudinal displacement of the top of the frame by means of two 2MN servo-hydraulic actuators induced a shearing and bending action into the links, similar to the one expected in the prototype. The shape of the loading frame columns was differ-ent compared to the tower shaft, however the bolted connection was the same as in the prototype. Two types of links with different aspect ratios exists. The slender Type 1 Shear Link connects the tower shafts in the bridge transverse direction while the shorter Type 3 Shear Link connects the tower shafts in the longitudinal direction. 3.3.2 Test Results
The hysteretic behavior of the Shear Link Type 3 is shown in Figure 14b. The link experienced a brittle web failure after reaching an average shear deformation of 0.069 radians, thus easily outper-forming the SEE event demand of 0.03 to 0.04 radians. Up to that point the link showed a very stable hysteretic behavior with a significant increase in strength. The overstrength of the link defined as the ratio between the maximum shear strength Vp and the nominal shear strength Vy was 1.94. This value is significantly larger than the overstrength factor of 1.25, normally suggested by design codes, poten-tially jeopardizing the capacity design of the connections. However, in the case of the SFOBB SAS
bridge, due to the conservative design, the connections remained elastic and the link could be easily removed from the loading frame following the test.
Fig. 14. Overall view of the test setup with Type 1 Shear Link (a). Shear force vs. average shear deformation in the deformable region of Type 3 Shear Link (b).
The brittle failure of the links, caused by the diagonal crack across the web surface and shown in
Figure 15a, generated a significant drop in load carrying capacity. The diagonal crack initiated at ear-lier stages of the test at the highly restrained intersection of the 28mm thick web with the 45mm thick flange and the 28mm thick stiffener (Figure 15b).
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Fig. 15. Brittle failure of Type 3 Shear Link (a), close up view of fracture origin (b). ABAQUS FE model of the same shear link (c) and detail of the transverse stiffener weld modeling (d).
In order to improve the performance of the link, different solutions were investigated to alleviate
stress concentrations which led to the cracking at the toe of the intermediate stiffener fillet weld. To
this purpose a finite element model of the link was assembled using the program ABAQUS (Figure 15c). Particular care was devoted to the modeling of the web/flange/stiffener intersection zone as shown in Figure 15d. For this parametric study, the variations of the stress concentration patterns be-tween the different solutions rather than the absolute value of the stresses were of primary interest. The analyses showed that the most straightforward and effective solution was to terminate the web/stiffener fillet weld further away from the web/flange/stiffener intersection, corresponding to an increase of the distance z in Figure 15d. Consequently, the weld configuration of the links was redes-igned and the distance z was increased from 0.5tw to 1.5tw and to 2.5 tw in the Type 1 and Type 3 links, respectively (tw = web thickness). Furthermore the end of the stiffener/web fillet weld was ta-pered. This configuration was implemented in the links tested at the University of Nevada, Reno (UNR), where a significant improvement of the performance of the links was demonstrated by almost doubling their shear deformation capacity [10].
As expected, slippage of the bolted link connection occurred during testing, increasing the flexibil-ity of the shear link/tower shaft assemblage. The increase in rotation of Type 3 Shear Link due to flange splice slippage is pictured in Figure 16a and is of the same order of magnitude as the deforma-tion occurring in the deformable region of the link (Figure 14b). The hysteretic behavior of the deform-able region and of the connection region are significantly different, the latter showing less energy dis-sipation capacity. To properly assess the behavior of the shear link/tower shaft assemblage theoretical hysteresis rules were developed to model the flexibility of the connection region (Figure 16b).
Fig. 16. Increased rotation in connection region of Type 3 Shear Link due to flange splice slippage. Rotation measured during testing (a) and relevant analytical hysteretic model (b).
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Based on the results of the tests, macro finite elements, simulating the behavior of the deformable
and connection regions of the shear links, could be calibrated and implemented in the “Ruaumoko 3D” [19] model of the SAS bridge pictured in Figure 17a, allowing the investigation of the global behavior of the bridge. In a parameter study, the influence of different ground motions, the tower link stiffness,
the tower link location, and the hysteretic behavior of the links was investigated. As an example of the results of these analyses, Figure 17b shows the formation of plastic hinges along the tower shaft as a function of the location of the shear links: links located at tower mid-height proved to be the most ef-fective completely preventing the formation of plastic hinges. A comprehensive set of general recom-mendations for the design of future cable-supported bridges featuring shear link main towers based on the results of this analyses was developed by McDaniel in [13]. 3.4 Orthotropic Deck Compression Test
The axial load in the longitudinal girders due to dead load and initial cable stressing forces corre-sponds to about 30% of their nominal centric yield force. During the SEE the axial load can rise to 40% of the nominal centric yield force. This increase is not enough to cause global buckling of the Main Span. However, due to the bending moment acting on the girder, the axial stress in the deck or in the soffit of the girder can reach values close to yield, potentially inducing local buckling. While a numerical investigation performed with the ABAQUS FE model [17] of the Main Span, shown in Figure 18a, proved that local yielding or buckling of the deck would only insignificantly affect the safety against global buckling, local buckling is not compatible with the performance criteria adopted for the bridge. Therefore, the design had to ensure that all sections are able to reach yield before buckling. One possibility to reach this goal was to use oversized ribs, increasing the total weight of the super-structure, and leading to even bigger seismic forces that would affect the design of the entire bridge. Finally the decision to design the lightest possible section and to investigate its stability using large scale testing was taken.
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Fig. 18. First global buckling mode of the SFOBB SAS bridge (a). Cross-section of one SAS bridge steel box girder (b) and Orthotropic Deck Specimens at 45% scale (c and d).
3.4.1 Test Setup
In order to prevent warping of the cross section shown in Figure 18b, the girder is stiffened by transverse diaphragms, or floor-beams, located every 5m along the bridge longitudinal direction. The floor-beams define the boundary conditions for local buckling of the deck. The post-buckling behavior of the orthotropic plates of the deck and the soffit were also of interest. Figures 18c and 18d show the test specimens for the local buckling tests.
The setup for the Orthotropic Deck Compression Test is shown in Figure 19a. The specimen is vertical with a pinned support at the top and at the bottom, simulating the boundary conditions pro-vided by the first and the third floor-beams. A further support at mid-height consisting of a blade plate provided a horizontal support, simulating the action of the second floor-beam. The axial load was ap-plied with a loading beam to amplify the capacity of the actuators using the lever principle. The test was monotonic and in displacement control. This, combined with the high stiffness of the test setup, allowed the loading of the specimens in the post-buckling domain in a fully controlled way.
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Fig. 19. Global view of the Orthotropic Deck Compression Test Setup (a) and post-buckling deformed shape of Specimen Type 2 (b).
Two specimens were tested: Specimen Type 1 modeled the girder deck orthotropic plate while
Specimen Type 2 modeled the soffit. To fit within laboratory constraints the specimens were at 45% scale. Recognizing the importance of initial imperfections and initial stresses on the stability of slender member, both specimens were built using the same construction, quality control and quality assurance procedures that will be used to build the prototype. 3.4.2 Test Results
The tests validated the design of both the deck and the soffit of the girder. Specimen Type 1 failed gradually in double curvature buckling of the deck and rib plates after reaching a peak strength 34% higher than the Safety Evaluation Earthquake (SEE) demand. Specimen Type 2, shown in Figure 19b, failed gradually in double curvature, local torsional buckling of the ribs and local buckling of the girder plate after reaching a peak strength 20% higher than the SEE demand. The peak strengths of both specimens exceed the nominal yield capacity of the section. However, due to the initial residual stresses and geometric imperfections of the specimens, the ultimate strength was 7% and 5% lower than the actual yield capacity. Furthermore, the results of the tests were compared with predictions based on four different design codes. Table 1 gives a brief summary of this comparison: the Japanese code JRA 2002 provided the best predictions for peak strength and failure mode of both specimens.
Table 1. Orthotropic Deck Specimen behavior: Comparison between actual test and code provisions.
Numerical simulations of both tests were performed using finite element models of the specimens
developed with ABAQUS [17]. Analyses were conducted in displacement control, taking into account material and geometric nonlinearities. Each model started out with a perfect specimen geometry and was successively refined taking into account initial imperfections measured on the actual specimen prior to testing (Figure 20a) and initial residual stresses assumed based on state-of-the-art assump-tions (Figure 20b). Figure 20c shows that, provided initial deformations and residual stresses were taken into account, an excellent agreement between the results of Specimen Type 1 Test and its nu-merical prediction in term of both peak strength and post-buckling behavior could be reached. Similar results could be obtained for Specimen Type 2.
Code Specimen Type 1 Specimen Type 2 Test Buckling after yielding Buckling after yielding AASHTO-LRFD: Bridge Design Specifications (1998) Buckling at 94% of yielding Buckling at 94% of yielding FHWA-TS-80 (1980) Buckling at 70% of yielding Buckling at 84% of yielding British Standard BS 5400: Steel, Concrete and Composite Bridges (1982)
Buckling after yielding Buckling after yielding
Japan Road Association (JRA): Specification for Highway Bridges (2002)
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Fig. 20. Orthotropic Deck Specimen Type 1: measured initial imperfections (a), assumed initial stresses (b) and comparison between experimental evidence and numerical predictions (c).
3.5 Skyway Precast Segmental Girder Tests
The superstructure of the Skyway consists of parallel precast segmental girders and while the de-sign of the bridge according to capacity design principles confines inelastic deformations to the piers of the skyway protecting the foundation and the superstructure against overloading, possible joint opening between the segments during the SEE event has to be taken into account. Therefore, the compatibility of the damage resulting from joint opening with the performance requirements listed in Section 2.1 had to be investigated. A further objective of investigation was the connection between joints. Caltrans requires in high seismic regions to provide partial continuity of reinforcement at seg-ment-to-segment joints. Two different options to provide continuity of the deck reinforcement were tested. In the first case continuity was provided by a cast-in-place (CIP) deck closure joint with lapped mild reinforcement as shown in Figure 22b. In a second case the continuity was provided with “un-stressed” auxiliary bonded tendons located in the deck slab as shown in Figure 22c. The auxiliary ten-dons are stressed to only about 40% of the ultimate capacity (to eliminate slack) protecting them from yielding in case of joint opening in order to ensure an almost perfect closing of the joint upon unload-ing. The solution with the CIP deck closure joint was expected to provide more energy dissipation ca-pacity, which is of minor importance since no inelastic deformations of the superstructure are expected to occur under the design earthquake. On the other hand the solution with the auxiliary tendons allows a full precast erection procedure, saving time and money, and it was expected to result in minor per-manent top joint opening due to the clamping effect of the tendons. For comparison purposes a third girder with no deck reinforcement continuity was tested (Figure 22a).
In the following section a brief overview of the test results pertaining to the SFOBB seismic safety project is given. A more comprehensive discussion of the results of all tests performed on the seismic performance of superstructure segment-to-segment joints is presented by Megally and Seible in [20].
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3.5.1 Test Setup The setup used to test the models of the skyway precast segmental girders under high bending
moment and low shear (4 point bending test) is pictured in Figure 21a. During a first stage of the test the equivalent of the dead load of the prototype superstructure were applied defining the reference load level of the girder. Afterwards, the equivalent of seismic loads was applied by vertical cycling of the four servo-hydraulic actuators following a cyclic loading history with incremental increasing target displacements at midspan [11]. 3.5.2 Test Results
Figure 22 shows the three girders at failure under downward loading while the corresponding hys-teretic responses are depicted in Figure 23 (Note: downward deflections are positive). The Test Unit, 100INT without any reinforcement continuity in the deck slab, failed due to rupture of the bottom ten-don at a mid-span vertical deflection of 122mm (L/80). Test Unit 100INTCIP, with mild reinforcement continuity and closure concrete pour in the deck slab, failed due to crushing of the compression zone at 150mm (L/65) deflection; this compression failure was initiated by the buckling of the lapped mild steel reinforcement of the CIP deck closure joint. Test Unit 100INTAUX, with “un-stressed” continuity tendons in the deck, failed due to rupture of the bottom tendon at a mid-span vertical deflection of 168mm (L/58). The strength under upward loading of a superstructure with CIP deck joint or with “un-stressed” auxiliary continuity tendons is similar, as long as the same mechanical continuity reinforce-ment content is provided. In the tests, Test Unit 100INTCIP showed a slightly higher upward strength because of a slightly higher reinforcement content. All three sections clearly outperformed any defor-mation capacity requirement in both downward and upward directions, even under seismic events sig-nificantly stronger than the SEE.
Fig. 22. Different sections and behavior at failure of the three Skyway Precast Segmental Girders. a) Test Unit 100INT, b) Test Unit 100INTCIP, c) Test Unit 100INTAUX
Nonlinear time-history analyses of the Skyway performed by the designers indicated that during
the SEE event the maximum stress reached in the main tendon is 83% of the ultimate stress (fpu=1,862MPa). Considering the stress-strain relationship of the tendons, this stress is reached at a strain of 8,100 microstrains, which is less than the nominal yield occurring at 10,500 microstrains. In all three test units a strain of 8,100 microstrains in the tendons was reached at a downward displace-ment of 20 to 25mm, after unloading the joints completely closed, fulfilling the performance require-
ment at SEE level. In the case of the SFOBB Skyway both continuity solutions are expected to deliver a similar performance, however, due to the clear construction advantages, the solution with the auxil-iary tendons will be implemented.
Finite elements simulation of the Test Units 100INT and 100INTCIP were performed with ABAQUS in conjunction with the state-of-the-art ANACAP-U [18] steel and concrete material models using the 3D brick model pictured in Figure 21b. The results of numerical predictions performed for the Test Units 100INT and 100INTCIP are plotted in Figure 23 on top of the experimental results. The prediction of the Test Units 100INT is in excellent agreement with the experimental results even cap-turing the ultimate displacement and the failure mechanism. In the prediction of the behavior of the Test Units 100INTCIP the monotonic analysis results were able to more closely match the actual ex-periment than the cyclic analysis. The discrepancies in the cyclic analysis were mainly due to the in-ability of the model to capture buckling of the deck reinforcement bars and to accurately model the hysteretic mild steel behavior. Based on steel coupon tests performed in the framework of the Shear Link and Skyway Pier Tests, the ANACAP-U material models were revised by refining the constitutive laws describing the Bauschinger Effect and the hardening of the steel, improving the quality of the predictions like in the case of Pier W2 test (Figure 13a).
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Fig. 23. Hysteretic behavior of the Test Units 100INT (a), 100INTCIP (b) and 100INTAUX (c). Comparison between experimental evidence and numerical predictions.
4 Conclusions The large scale tests on all structural elements of the new East Span of the San Francisco-Oakland Bay Bridge with expected inelastic performance characteristics proved that the design fully meets all performance requirements. The large or full scale tests were able to identify performance issues, re-sulting in design improvements and considerable cost savings. Alternative detailing and construction procedures were validated, leading to a more economic construction of the new bridge.
Analytical and numerical models developed to assess the seismic behavior of the Bay Bridge were calibrated against experimental results. These models are now available for the final assessment of the new SFOBB East Span and other future bridges. ACKNOWLEDGEMENTS The research presented in this paper was funded by the California Department of Transportation (Cal-trans) under Contract No. 59A0189.
Dr. Eric M. Hines - Structural Engineer at LeMessurier Consultants, Cambridge MA - was in charge of the Skyway Pier Tests. Prof. Cole C. McDaniel - Assistant Professor of Structural Engineer-ing at Washington State University, Pullman WA - was in charge of the Main Tower Shear Link Tests. Prof. Chung-Che Chou - Assistant Professor of Structural Engineering at the National Chiao Tung University, Taiwan - was in charge of the Orthotropic Deck Compression Tests. Dr. Sami H. Megally, Assistant Project Scientist at the University of California San Diego, was in charge of the Precast Segmental Girder Tests. Prof. Chia-Ming Uang, Professor of Structural Engineering at the University of California San Diego, served as Co-PI for the steel structures tests.
All of the large scale tests presented in this paper were conducted in the Charles Lee Powell Structural Research Laboratories at the University of California, San Diego, where the expertise of the laboratory staff was essential.
Mr. Rafael Manzanarez, Dr. Marwan Nader, Dr. John Sun and Dr. Sajid Abbas of T.Y. Lin Interna-tional provided critical input and support during the analysis of the prototype structures and during the design of the tests.
Dr. Robert Dowell of Dowell-Holombo Engineering, Inc. and Mr. Daniel Parker of ANATECH Cor-poration prepared independent finite element predictions of several tests and provided invaluable input on many numerical issues. REFERENCES [1] Caltrans: “SFOBB East Span Seismic safety project - 30% Type Selection”. May 29, 1998. [2] Hines E.M., Dazio A., Chou C.C., Seible F.: “Structural Testing of the San Francisco-Oakland
Bay Bridge East Span Skyway Piers”. Research Report SSRP-2002/01. Department of Structural Engineering. University of California San Diego, 2002.
[3] Seible F.: “Long Span Bridges in California - Seismic Design and Retrofit Issues”. Proceedings of the XII World Conference in Earthquake Engineering. Auckland 2000.
[4] Goodyear D., Sun J.: “New Developments in Cable-Stayed Bridge Design, San Francisco”. Structural Engineering International, 1/2003.
[5] Tang M.-C., Manzanarez R., Nader M., Abbas S., Baker G.: “Replacing the East Bay Bridge”. Civil Engineering, September 2000.
[6] Joint Venture T.Y. Lin International & Moffatt and Nichol: “The San Francisco-Oakland Bay Bridge East Span Seismic Safety Project. Skyway Structures: 100% Submittal”. November 17, 2000.
[7] Joint Venture T.Y. Lin International & Moffatt and Nichol: “The San Francisco-Oakland Bay Bridge East Span Seismic Safety Project. Main Span Structures: 85% Submittal”.May 31, 2000.
[8] McDaniel C.C., Uang, C.M, Seible F.: “Cyclic Testing of Suspension Tower Shear Links of the San Francisco-Oakland Bay Bridge”. Research Report SSRP-2002/12. Department of Structural Engineering. University of California San Diego, 2001.
[9] Dazio A, Seible F.: “Structural Testing of the San Francisco-Oakland Bay Bridge East Spans Pier W2”. Research Report SSRP 2002/11. Department of Structural Engineering. University of California San Diego, 2002.
[10] Dusicka P., Itani A.M., Buckle I.G.: “Cyclic Behavior of Shear links and Tower Shafts Assembly of San Francisco-Oakland Bay Bridge Tower”. Report No. CCEER 02-06. Center for Civil Engineering Earthquake Research. University of Nevada, Reno, 2002.
[11] Megally S.H., Garg M., Seible F., Dowell R.K.: “Seismic Performance of Precast Segmental Bridge Superstructures”. Research Report SSRP-2001/24. Department of Structural Engineering. University of California San Diego, 2001.
[12] Chou C.C., Uang, C.M., Seible F.: “Compression Testing of Orthotropic Steel Deck for the New San Francisco-Oakland Bay Bridge”. Research Report SSRP-2002/12. Department of Structural Engineering. University of California San Diego, 2002.
[13] McDaniel C.C.: “Influence of Inelastic Tower Links on the Seismic Response of Cable Supported Bridges”. Ph.D. Thesis. Department of Structural Engineering. University of California San Diego, 2002.
[14] Hines E.M.: “Seismic Performance of Hollow Rectangular Reinforced Concrete Bridge Piers with Confined Corner Elements”. Ph.D. Thesis. Department of Structural Engineering. University of California San Diego, 2002.
[15] Hines E.M., Seible F.: “Seismic Performance Limits of the Skyway Piers for the New East Bay Spans of the San Francisco-Oakland Bay Bridge”. Proceedings of the FIB 2003 Symposium Concrete Structures in Seismic Regions. Athens May 6-9, 2003.
[16] Dazio A.: “Entwurf und Bemessung von Tragwandgebäuden unter Erdbebeneinwirkung (Design and Detailing of RC-Wall Buildings under Seismic Action)”. Diss. ETH Nr. 13739. Zurich, 2000.
[17] Hibbit, Karlson & Sorensen: “ABAQUS Version 5.8: User’s Manual”. Hibbit, Karlson & Sorensen, Inc., Pawtucket, Rhode Island, 1997
[18] ANATECH Corporation: “ANACAP-U Version 2.5: User’s Manual”. ANATECH Corporation, San Diego, 1997.
[19] Carr A.J.: “Ruaumoko 3D: User’s Manual”. Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Christchurch, April 2001.
[20] Megally S.H., Seible F.: “Precast Segmental Bridges: Seismic Performance of Superstructure Segment-to-Segment Joints”. Proceedings of the FIB 2003 Symposium Concrete Structures in Seismic Regions. Athens May 6-9, 2003.
