Realistic Seismic Behavior of the Main Tower of the New SAS Bay Bridge and Its Base Anchors

Transcription

1 Realistic Seismic Behavior of the Main Tower of the New SAS Bay Bridge and Its Base Anchors Abolhassan Astaneh-Asl, Ph.D., P.E., Professor Xin Qian, Doctoral Graduate Student Maryam Tabbakhha, Ph.D., Lecturer University of California Berkeley, Berkeley Abstract The new, 2013 East Spans of San Francisco-Oakland Bay Bridge is a Self-Anchored-Suspension (SAS) bridge with a single tower. The bridge is located between two active seismic faults, the Hayward, and San Andreas faults. The main tower of the bridge is a steel tower made of four shafts, each shaft made of a 5-sided hollow steel box-section. The four shafts are connected to each other by I-shaped steel horizontal shear links at various levels along the height. The tower is connected to its footing by high-strength ASTM A354 BD, 3-, or 4-inch diameter, hot-dip-galvanized anchor rods. A few months before the bridge opened to traffic, 32 of the 96, 3-inch diameter, A354 BD hot dip galvanized anchor rods connecting the shear keys to the top of the Pier E2 on the east end of the SAS Bay Bridge fractured after tightening. In 2013, two out of 424, 3-inch diameter, A354 hot-dipgalvanized anchor rods connecting the single tower to the pile cap were fractured. This paper presents the results of two inter-related studies of pushover analysis of the main tower of the new SAS Bay Bridge. One study focused on the pushover behavior of the tower itself with anchor rods at the base of the tower in place, while for the second pushover analyses, it was assumed that, as is likely during the 150-years design life of the bridge, all hydrogen-embrittled A354 BD anchor rods connecting the tower to the pile cap have fractured and cannot resist tension. Using the general-purpose finite element analysis software ANSYS R15.0 and construction drawings, detailed nonlinear finite element analysis models of the SAS Bay Bridge tower, with and without the anchor rods connecting it to the pile cap were built. Realistic nonlinear pushover analyses of the tower with gravity load present were performed. The results indicated that when the tower with the anchor rods in place as designed, contrary to the claims of the designers, the inelasticity was not limited to the shear links connecting the four tower shafts to each other. Instead, the two tower shafts on the tension side experienced yielding, and worse, the two shafts on the compression side of the tower developed severe local buckling relatively early in the inelastic range of the behavior. The local buckling of the shafts resulted in a drop of the strength and stiffness, which in turn resulted in much smaller ductility than what the designers have assumed. Also, the results of pushover analysis of the tower with all hydrogen-embrittled anchor rods fractured indicated that, again contrary to the claims of the designers that the anchor rods are not needed, if the anchor rods are not present, the tower uplifts on the tension side resulting in severe local buckling of the compression side of the tower base as well as crushing of the concrete in the pile cap. Introduction to the New SAS Bay Bridge The new East Span of San Francisco-Oakland Bay Bridge is a Self-Anchored-Suspension (SAS) bridge with a single tower. In a self-anchored suspension bridge, the main suspension cables, instead of being connected to the anchor blocks embedded in the ground as is the case for traditional suspension bridges, are connected to the deck itself. As a result, the horizontal component of the typically very large tension forces in the main cables, create quite large axial compression in the deck of the bridge. This large compression force is one of the main reasons why prior to the construction of the new Bay Bridge, there were only two selfanchored modern bridges built, one in Japan, connecting a man-made island to the mainland and the other in S. Korea, a non-seismic zone, connecting an airport to a parking lot. Gimsing and Georgakis in their definitive book on Cable Supported Bridges: Concept and Design state that: A number of self-anchored suspension bridges were constructed mainly in Europe before World 1

2 War II but in the post-war period, it became evident that with the complications during construction the self-anchored suspension system was inferior to both the earth anchored suspension system and the selfanchored cable-stayed system. The number of self anchored suspension bridges constructed in recent years is therefore small and they have only been chosen in cases where the increased construction costs has been disregarded, (Gimsing and Georgakis, 2011). In addition to the higher cost of construction of the selfanchored suspension bridges, due to the presence of an axial load on the deck, is the cost of building and removing the temporary bridge that is needed in this case. The temporary bridge is needed to support the deck during construction and only after completion of the deck the main cable can be connected to the deck and the temporary bridge be removed. Figure 3 shows the elevation of the main tower. The 512ft (156m) tower (at the cable intersecting point) consists of four shafts, each shaft being a pentagonal steel hollow box with vertical stiffeners and horizontal diaphragms, Figure 4. The steel used in the tower shaft is ASTM A709 Gr. 50 steel with a minimum specified yield strength of 50 ksi (345 MPa) and an ultimate strength of 65 ksi (448 MPa). As is standard, the shafts have horizontal stiffeners every 9.9ft (3m). I-shaped shear links connect the shafts to each other along the height of the tower and by a saddle at the top. The main cable is a single cable connecting the top of the tower to the orthotropic steel deck and passes through the saddle. Figures 1 and 2, show the overall structure and main components of the new SAS Bay Bridge. The bridge opened to traffic in 2013 and is located between two active seismic faults, which are the Hayward and San Andreas faults. According to the United States Geological Survey (USGS, 2017), there is a 63% probability of occurrence of an earthquake with a magnitude 6.7 or greater in the greater San Francisco Bay Area during a 30-year period from 2007 to Figure 3. Elevation View of the Main Tower ELEVATION PLAN Figure 1. Elevation and Plan Views of the New SAS Bay Bridge CROSS SECTION Figure 2. Typical Cross Section of the New SAS Bay Bridge Figure 4. Typical Cross Section of the Tower (Astaneh-Asl and Qian, 2016) 2

3 Figure 5 shows the plan view of the main tower base plate and anchor rods as well as shear dowels on it. For clarity, only ¼ of the double symmetric base plate is shown. Note that the base plate is made of 14 separate base plate, four doughnut-shaped plates under the tower leg and 10, almost rectangular plates, under the shear walls at the base of the tower. The shear walls at the base of the tower connect the four tower shafts to each other. The base plate is made of ASTM A709 Gr. 50 steel with minimum specified yield strength of 50 ksi (345MPa) and an ultimate strength of 65 ksi (448 MPa). Figure 5. Plan View of ¼ of the Base Plate of the Main Tower (Astaneh-Asl, Tabbakhha, and Qian, 2016) The anchor rods shown in Figure 5 are 3-in (75mm) and 4-in (100mm) diameter ASTM A354 BD hot-dip galvanized threaded rods. The 6-in (150mm) diameter ASTM A633 shear dowels, are to resist only the shear, while the anchor rods resist only axial tension. The material of the anchor rods is SAE 4140 steel with a minimum yield strength of 115 ksi (793 MPa) and a minimum ultimate strength of 140 ksi (965 MPa) (ASTM 2011.) The use of A354 BD zinc-coated hot-dip galvanized anchor rods in this key traffic corridor was a major engineering flawed decision. Almost all bridge design specifications and codes throughout the world prohibit the use of hot-dip galvanized high strength A490 bolts and A354 BD threaded rods since such hot dip galvanizing results in the introduction of hydrogen into the material causing hydrogenembrittlement and likely fracture of the embrittled bolts or threaded rods. The AASHTO, "LRFD Bridge Design Specification has following provisions on the bolts and threaded rods: AASHTO M 253 (AASHTO A490) bolts and ASTM A354 Grade BD, bolts, studs, and other externally threaded fasteners, ASTM F1554 Grade 105 (with Fu = 150 ksi) anchor bolts and ASTM A722 bars shall not be galvanized. No cleaning process shall be used that will introduce hydrogen into steel. (AASHTO, 2016) The A354 BD threaded rods used in the new SAS Bay Bridge, were hot dip galvanized, and as expected, exhibited undesirable behavior a few months before the opening of the bridge in 2013 after tightening of the 3-inch diameter threaded rods connecting the shear keys at the east end of the deck to the top of the pier E2, thirty-two of the threaded rods fractured. Since the rods were embedded in the concrete, there was no way to remove and replace the fractured rods. More than $40 million was spent to construct saddles over the base of the shear keys to transfer shear from the shear keys to the top of the pier. The other rods, including the anchor rods at the base of the main tower, which was also made of A354 BD steel and hot-dip galvanized, never were tightened to the required level of 70% of their ultimate strength and the bridge opened with most of the threaded rods tightened to not more than 55% of their ultimate strength out of fear of them also fracturing if tightened to the required level of 70% of ultimate strength. In 2013, it was discovered that two out of the 424 anchor rods connecting the tower to the pile cap was fractured. Caltrans stated that one fracture was due to hydrogen embrittlement of the A354 BD anchor rod and the other was due to thread stripping, the latter introduced a new problem to the anchor rods. The fracture of the rest of the anchor rods due to hydrogen embrittlement is likely to occur during the service life of the bridge as all 424 rods were hydrogen embrittled (Chung, 2014). As mentioned earlier, the expected fracture of the anchor rods at the base of the tower, and possible threadstripping of those that have not fractured yet are the reasons for conducting the pushover analysis of the tower without the hydrogen-embrittled anchor rods. The elevation view of the pile cap supporting the tower is shown in Figure 6. The pile cap consists of a concrete-steel composite box. The piles are concrete filled steel piles embedded in the bedrock of the Yerba Buena Island. ELEVATION Figure 6. Elevation of the Pile Cap/Pile Footing Supporting the Tower of the New SAS Bay Bridge (Astaneh-Asl, Tabbakhha, and Qian, 2016) 3

4 2017 SEAOC CONVENTION PROCEEDINGS Figure 7 shows the plan view of the pile cap supporting the tower. the tower skirt at the base of the tower, were not included in the model. The impact of the decks on the tower shafts were not included, considering the gap between the main tower and the bridge decks; see Figures 1 and 4 earlier. PLAN Figure 7. Plan View of the Pile Cap/Pile Footing Supporting the Tower (Astaneh-Asl, Tabbakhha, and Qian, 2016) Objectives of the Study The main objective of the research was to establish the stiffness, strength, buckling behavior, and ductility of the asbuilt main tower of the SAS Bay Bridge under two scenarios: with full good quality anchor rods connecting the tower to the pile cap as design intended, and without any anchor rods assuming that the hydrogen-embrittled anchor rods have all fractured at some point during the 150 years of design life of the bridge. Finite Element Modeling The general-purpose finite element software ANSYS R15.0 was used to establish pushover behavior of the main tower. As shown in Figure 8, all components of the main tower, except the vertical stiffeners of the tower shaft, were modeled with the SHELL181 element. This is a 4-node shell element that is suitable for linear, large deflection, and large-strain nonlinear applications. The BEAM188 element of ANSYS, which is a 2-noded linear, quadratic, or cubic 3D beam element based on Timoshenko beam theory, was used to model the vertical stiffeners of the tower shafts. The tower shaft stiffeners were attached to the tower shaft plates with bonded contact (ANSYS, 2013). The geometric features of the tower were modeled in detail based on the construction drawings (Caltrans, 1999). All critical structural components of the main tower including all three types of shear links, vertical stiffeners of the tower shafts, and horizontal diaphragms inside the tower shafts were modeled. Non-structural and architectural features, e.g. 4 Figure 8. Finite Element Models of the SAS Bay Bridge Tower with Details of the Cross Sections Two types of steel material properties were used in the modeling of the tower structure. Almost all components of the main tower and the tower base plate were ASTM A709

5 Gr. 50 with a minimum specified yield stress of 50 ksi (345MPa). The connection plates of the shear links to the tower shafts were modeled with Gr.70 steel with a minimum specified yield stress of 70 ksi (485MPa). Bi-linear kinematic hardening material model was considered for the steel with an elastic modulus of 29,000 ksi (200 GPa), Poisson ratio of 0.3, and strain hardening ratio of 1%. Point D : a point where the pushover strength has dropped to 85% of the maximum strength at Point U. Point D is commonly used as the point of maximum displacement in calculating the ductility of a system. The ductility of a system is defined as this displacement U in at 85% maximum strength divided by the displacement at yield point, U y. The concrete used in this analysis to model the pile cap and the piles has an elastic modulus of 4,350 ksi (30 GPa), Poisson ratio of 0.18 and compressive strength of f c =5.073 ksi (35 MPa) which was obtained from the construction drawings (Caltrans, 1999) as the specified values. The concrete inside the steel box was modeled as confined concrete. Pushover of the tower was achieved by nonlinear large deflection multi-step static analysis including both material and geometric nonlinearities. Gravity prestress forces included the self-weight of the tower itself as well as the vertical components of the cable forces acting on the saddle. The cable forces were obtained from gravity analysis of the whole bridge model in SAP2000. Incremental horizontal displacements were applied after gravity pre-stressing step using the displacement controlled iteration algorithm. The horizontal displacements were applied at the centroid of cable saddle grooves. This research project considered pushover analyses in five different directions - longitudinal (0ᵒ), transverse (90ᵒ), and 30ᵒ, 45ᵒ, and 60ᵒ from the longitudinal axis of the bridge; see Figure 8(a). A. Pushover of the Tower with Anchor Rods The pushover of the tower, assuming all anchor rods connecting the tower to the pile-cap are present was conducted in the transverse and longitudinal directions as well as along the 30, 45, and 60 degrees angles, Figure 8(a). The results of a pushover in transverse and longitudinal directions, with all anchor rods in place, are shown in Figure 9. Results of Pushover Analysis Due to the similar characteristics of the pushover curves, three critical points are defined for convenience of discussion in the rest of the paper. The three points are: Point Y : the yield point. For large and complex structures, such as the main tower of the SAS Bay Bridge, local yielding occurs at relatively small displacements due primarily to stress concentrations; such small local yielding cannot be considered as the yield point of the tower. For pushover curves without an obvious strain hardening branch as the ones to be presented in this paper, the yield point can be defined as the point where the displacement of the structure deviates from the initial stiffness line with an amount equal to 10% of the elastic displacement. For more information for the definition of this 10% deviation rule for yield point, see reference (Astaneh-Asl and Qian, 2016) Figure 9. Transverse and Longitudinal Pushover Curves for the Tower With Full Anchor Rods A.1. Pushover of the Tower with Anchor Rods in the Transverse Direction It can be seen that the pushover behavior of the tower with anchor rods in place in the transverse direction of the bridge is more critical than the longitudinal direction in terms of ductility. The pushover curves indicated that the tower yielded gradually and then the lateral load resistance dropped relatively quickly after the applied pushover force reached its maximum value. Considering the transverse pushover curve shown in Figure 9, the ductility of the tower in the transverse direction is approximately U in /U y =5.4m/1.7m = 3.2. Point U : the point where maximum push-over strength is reached. It was found that at the yield point (Point Y), the top seven and middle three pairs of shear links yielded first, while all 5

6 other parts of the tower remained essentially elastic. Then, all the shear links, except the four at the bottom of the tower, gradually started to yield as the displacement increased before reaching Point U. At this stage, the upper shear links continued to experience larger rotation. It was found that the rotation of the shear link at 357.6ft (109m) from the base reached the ultimate rotation capacity of 0.09 radians at a tower tip displacement of 15.75ft (4.8m). Although the fracture of the material was not included in the model, it is expected that some shear link fractures could happen before the tower reaches its maximum strength in the transverse direction. separate tower shafts: the four tower shafts tend to deform independently (the mechanism by which the shear links work), while the rigid grillage is trying to hold them together and remain flat. Figure 10 shows the local buckling of the tower shaft and yielding at the grillage/tower shaft interface at Point D. More discussions on the transverse direction pushover can be found in reference (Astaneh-Asl and Qian, 2016). A.2. Pushover of the Tower with Anchor Rods in the Longitudinal Direction The pushover curve in the longitudinal direction was shown earlier in Figure 9. The longitudinal pushover curve has a shape similar to that of the curve for the transverse pushover curve and follows the same sequence of events. In this case, the top and middle shear links yielded first, followed by the yielding of the shear links throughout the tower and yielding of the tower shaft plates. Lastly, the tower experienced a drop of strength primarily due to yielding and local buckling of the tower shafts. However, the pushover curve in the longitudinal direction had a smaller initial stiffness and a lower ultimate strength. Figure 10. Von Mises Stress Distributions of the Tower Shaft at Point D (Transverse Pushover With All Anchor Rods In Place) From Point Y to U, some yielding of the tower shafts also occurred. Such yielding of tower shaft plates occurred at the mid-height portion of the tower where there is a slight change of the slope of the tower shaft. The connection interface between the tower grillage directly below the saddle also yielded. After passing Point U, the strength of the tower dropped relatively fast, and local buckling of the yielded mid-height portions of the tower shafts became more pronounced (the local buckling of the tower structure is essentially the overall buckling of the stiffened vertical shaft plates between the horizontal diaphragms). During this stage, from Point U to Point D, larger regions of the tower grillage-totower shaft interface yielded. The yielding is likely to be due to the difference in rigidity of the grillage and the four As shown in Figure 11, in the longitudinal pushover, the yielding of the tower shaft skin plates was more uniformly distributed along the height of the tower, instead of relatively concentrated at the mid-height of the tower which was the case for the transverse pushover. More importantly, probably due to the more gradually changed tower shaft profile in this direction and the more uniform distribution of stresses, the buckling of the shaft plates did not occur in the mid-height but occurred at the base of the tower, Figure 11(c). This has resulted in a smoother and slower decrease of the strength and a correspondingly higher ductility. The ductility in the longitudinal direction is about 6.5/1.7=4.1. A.3. Pushover of the Tower with Anchor Rods in the 30, 45, and 60-Degrees Directions As mentioned earlier, in order to establish stiffness, strength, and ductility of the main tower in various directions, the pushover analysis was done pushing the saddle at the top of the tower horizontally, where the pushover direction made angles of 0, 30, 45, 60, and 90 degrees with the longitudinal (i.e. East-West) direction of the bridge. By plotting the results of the pushover analyses when the tower is pushed in various directions, typical capacity-envelope curves such as those shown in Figure 12 are obtained. The horizontal and vertical axes in Figure 12 are the longitudinal and transverse base shear. They can also be the transverse and longitudinal displacements. The displacements are usually normalized by dividing them by the displacement of the Point D, where the 6

7 2017 SEAOC CONVENTION PROCEEDINGS strength has reached its maximum and dropped to the 85% of the maximum strength. Earlier we mentioned that this Point D is where the ductility is measured. tower. When a time history analysis of the bridge is done, the base shear demand of the tower from the time-history analysis, such as those shown in Figure 12, can be superimposed on these capacity curves and performance of the tower can be assessed. Figure 12. Typical Base Shear Capacity Curves for the Tower when Pushed Over in Various Directions The capacity envelopes shown in Figure 13 were created assuming the behavior of the tower is doubly symmetric since the prestress of the tower due to gravity load was found to have minimal influence on the shape of the capacity envelope. The very little difference of the resulting pushover curves was observed comparing the case with applied displacement in the positive and in negative X-direction, the latter being opposite of the pre-stress direction of gravity. This validated the assumption of the symmetric behavior of the tower. It was observed that, when rotated from the bridge longitudinal direction to the transverse direction, the tower had progressively higher initial elastic stiffness and larger maximum strength while saw a faster strength degradation. Figure 11. Von Mises Stress Distributions of the Tower Shaft at Different Stages (Longitudinal Pushover With All Anchor Rods in Place) The use of curves in Figure 12 is that these curves represent the capacity side of the equation for the base shear of the The capacity envelope curves shown in Figure 13 indicated that the 10% yielding base shears (Point Y) for the longitudinal and transverse directions, (i.e. the 0, and 90degree pushovers) are smaller than the base shear when the tower is pushed over in other directions, making the 10% yield capacity curve to have an 8-shape. Beyond 10% yielding, both the largest ultimate strength (Point U) and the 85% ultimate strength (Point D) occur in the transverse direction. On the contrary, the tower tip displacement at Point U is larger for angles closer to the longitudinal direction. 7

8 Base Shear in Transverse Direction 45 The Circle is for 10 MN Figure 15 shows pushover behavior of the main tower without any anchor rods under pushover displacement in the longitudinal (dashed line) and transverse (solid line) directions. In these pushover cases, it was assumed that all hydrogen-embrittled anchor rods at the base of the tower have fractured and no longer existed to resist tension. Base Shear in Longitudinal Direction Figure 13. Base Shear Capacity Curves for the Tower (Pushovers With All Anchor Rods in Place) Figure 14 shows the displacement ductility envelope for the tower when the top of the tower is pushed over horizontally under various angles. In general, the ductility (U in /U y ) in all directions exceeds 2.0, with the highest ductility being 4.1 in the longitudinal direction. The ductility in the transverse direction is about 3.2. Comparatively, 45 and 60 degrees seem to be weak in terms of ductility, but this is mainly due to their relatively large yielding displacements. Ductility In Transverse Direction The Circle is for Ductility of 3. Ductility in Longitudinal Direction Figure 14. Tower Tip Displacement Ductility Curves (Longitudinal Pushover With All Anchor Rods in Place) B. Pushover of the Tower without Anchor Rods Figure 15. Transverse and Longitudinal Pushover Curves for the Tower Without Anchor Rods B.1. Pushover of the Tower without Anchor Rods in the Transverse Direction As Figure 15 shows, the tower under transverse pushover behaved elastically from the start of the pushover (i.e. the origin) to the point of 10% yielding. During this initial phase of the pushover, since there were no anchor rods to connect its base to the pile cap, the tension side of the tower base uplifted and the compression side of the base of the tower yielded at Point Y. As the tower reached its maximum strength at Point U, the compression side of the base of the tower had significant yielding and severe local buckling appeared at the compression side of the base of the tower just above the base plate. Pushing the top of the tower beyond Point U resulted in very severe local buckling at the base of the tower. The pushover ductility of the tower without anchor rods in the transverse direction was measured as 2.5. Pushover Behavior of the Tower-Similar to the pushover of the tower with the anchor rods, in this case also, the top of the tower was pushed in the horizontal direction while the gravity load was present. The equivalent Von-Mises stresses in the tower at Point D during the pushover in the transverse direction are shown in Figure 16. 8

9 2017 SEAOC CONVENTION PROCEEDINGS The behavior of the Base Plate - Figure 17 shows the equivalent Von-Mises stresses on the bottom surface of the tower base plate when the tower reaches its maximum strength (i.e. Point U in Figure 15 given earlier). At this point, some areas of the base plate had yielded. Such yielding of the base plate during the pushover is in violation of the Performance Criteria for this bridge, which allows only yielding of the shear links while the rest of the tower remains elastic. Figure 16. Von Mises Stresses in the Tower Shafts at Point D Where Ductility is Measured (Transverse Pushover of the Tower Without Anchor Rods) It is observed that at yield point, two out of seven pairs of shear links at the top portion of the tower yielded, while the other parts mainly remained elastic. High stresses were generated on the compression side of the tower in the middle portion and at the base of the tower. At Point U, where the maximum strength was reached, shear links in the upper part, as well as in the middle part of the tower had yielded in shear. There was also yielding and some local buckling in the compression side of the tower in the middle portion. However, the compression side of the tower at the base showed severe yielding and local buckling when the maximum strength was reached at Point U. After reaching the maximum strength, pushover strength of the tower dropped relatively fast due to local buckling in several areas of the tower base and corner stiffeners. At Point D, where ductility is measured, more yielding of the shear links at the top and middle portions of the tower occurred, Figure 16. Moreover, the base of the tower showed widespread yielding and severe local buckling on the compression side. For more information about the model see Astaneh-Asl, Tabbakhha, and Qian (2016). Figure 17. Equivalent (i.e. Von Mises) Stresses on the Bottom Surface of the Base Plate at Point U (Transverse Pushover of the Tower Without Anchor Rods) (AstanehAsl, Tabbakhha, and Qian, 2016) Stresses on the Pile Cap - The vertical pressures that the bottom surface of the base plate exerted on the top of the pile cap at Point U during the pushover are shown in Figure 18. Figure 18. Crushing of the Concrete under the Base Plate at Point U (Transverse Pushover of the Tower Without Anchor Rods) (Astaneh-Asl, Tabbakhha, and Qian, 2016) 9

10 2017 SEAOC CONVENTION PROCEEDINGS Since the concrete under the base plate is confined, the maximum compression strength on it can reach 1.7f'c, where f c is the specified compressive strength of the concrete measured using cylinder specimens. Therefore, in Figure 18, the red corresponds to the locations with pressure on the concrete exceeding 1.7f'c, which indicated compressive crushing of concrete under the base plate. B.2. Pushover of the Tower without Anchor Rods in the Longitudinal Direction Figure 15 earlier showed the pushover curve in the longitudinal direction for the tower without anchor rods (the dashed line). The general shape of the pushover curve in the longitudinal direction is similar to the curve for the transverse direction pushover and exhibits similar events as well. The ductility of the system under longitudinal pushover was measured as 2.8 which is 12% greater than the ductility of the system under the transverse pushover, which was 2.5.) Tower Behavior under Pushover Figure 19 shows von Mises stresses in the tower as it is pushed in the longitudinal direction. Note that in this case, no anchor rods connect the base of the tower to the pile cap. As shown in Figure 19(a) at the yield point of the tower, the shear links at the top and middle part of the tower yielded first. By increasing the displacement at the point of maximum strength, i.e. Point U, more shear links yielded and some yielding was also observed at the shear plate at the base of the tower, Figure 19(b). At Point D, where the strength is dropped to 85% of the maximum strength more shear links have yielded and the shear plates at the base of the tower have yielded more, Figure 19(c). Some parts of the base of the tower shafts also showed yielding. Unlike the response of the tower under transverse pushover, yielding was more concentrated at the intersection of the shear plates means the location of the welds. As observed in Figure 15, the behavior of the tower under longitudinal loads is smoother than the transverse one. The tower did not exhibit the severe local buckling that occurred during the pushover in the transverse direction. Base Plate Behavior under Pushover The von Mises stresses at the bottom of the tower base plate at the maximum strength point (i.e. Point U) is shown in Figure 20. As the figure indicates, unlike the transverse pushover case discussed earlier, in this case, no yielding of the base plate was observed. Two middle corners at the right side of the base plate, which were under compression, developed larger stresses than the other areas of the base plate. 10 Figure 19. Von Mises Stress Distributions in the Tower Shafts at Different Stages (Longitudinal Pushover Without Anchor Rods)

11 Figure 20. Von Mises Stresses at the Bottom Surface of the Base Plate at Maximum Pushover Force (Point U) (Longitudinal Pushover Without Anchor Rods) Stresses on the Pile Cap Figure 21 shows the pressure at the bottom of the base place, namely the top of the pile cap at Point U. As explained earlier, the compressive strength of the confined concrete here is 60 MPa. The figure shows that the concrete was crushed at the two middle corners of the righthand side of the pile cap. Figure 22. Comparison of Transverse Pushover Curves for Towers With and Without Anchor Rods (Astaneh-Asl, Tabbakhha, and Qian, 2016) Curve OYUD in Figure 22 is the pushover of the tower with anchor rods in the transverse direction. Curve OY U D is the pushover curve for the tower without any anchor rods. The initial elastic stiffness for both curves are almost identical, which means, before significant yielding or uplift of base plates, under dynamic loading during the earthquakes, the tower with O or without anchor rods connecting it to the pile cap will be subjected to almost the same seismic inertia forces. However, comparing the pushover force at Points Y and Y, the tower without the anchor rods will yield the shear links at about 70% of the force that will yield the tower with the anchor rods. The reason for the early yielding of the shear links when the tower does not have anchor rods is due to the fact that, when there are no anchor rods at the base of the tower, the tension side of the base of the tower uplifts to some extent and the gravity load in the uplifted legs need to be transferred to the compression side of the tower through the shear links. Figure 21. Crushing of the Concrete under the Base Plate (Longitudinal Pushover Without Anchor Rods) Discussion of Results Comparison of Pushover Curves in the Transverse Direction for the Tower with and without Anchor Rods Figure 22 compares the transverse pushover behavior of the tower with and without anchor rods connecting it to the pile cap (Astaneh-Asl, Tabbakhha, and Qian, 2016.) As for the maximum pushover strength, comparing Points U and U in Figure 22, the tower without the anchor rods reaches its maximum and drops the load at about 63% of what the tower with anchor rods could take. In other words, the maximum base shear strength of the tower without the anchor rods is only 63% of the strength of the tower if the anchor rods were performing as they were designed and not fractured due to hydrogen embrittlement. To compare ductility of these two cases of the tower with and without anchor rods, we need to compare the ratio of displacements at D and Y to the ratio of displacements at D and Y. This process indicates that ductility of the tower without the anchor rods is reduced to 2.5 compared to 3.2 for the case with the anchor rods. 11

12 Comparison of Pushover Curves in the Longitudinal Direction for the Tower with and without Anchor Rods Figure 23 compares the longitudinal pushover behavior of the main tower with and without anchor rods connecting it to the pile cap. Similar to the transverse direction pushover, for the longitudinal pushover both curves exhibit the same initial elastic stiffness, which again means in both cases of the tower with and without anchor rods will behave in a similar way under dynamic loading as long as the tower remains elastic. The yield strength of the tower without anchor rods is approximately 75%, and the ultimate strength is about 62% of those for the tower with full anchor rods. In addition to the significant decrease of lateral load resistance, the ductility of the tower without any anchor rods also reduces from 4.1 to 2.8, a 30% drop. Figure 23. Comparison of Longitudinal Pushover Curves for Towers With and Without Anchor Rods The comparison of pushover curves in both transverse and longitudinal directions for the tower with and without anchor rods indicate that the bridge tower might perform satisfactorily during small and probably medium earthquakes that create the displacements at the top of the tower not to exceed about three feet (one meter). However, if the horizontal displacement of the top of the tower exceeds the 3- feet limit, the tower with deficient anchor rods is likely to yield early, offer only about 60% of the design capacities. Comparison of Pushover Curves using Shell Elements vs Beam Elements Figure 24 compares the transverse pushover curves of the model used by the authors in this study, where shell elements were used to model steel plates, and the model used by the designers (Nader and Maroney, 2007) which had the tower shafts and the shear keys modeled as beam elements. In both models, it was assumed that the anchor rods are present and the base of the tower is fixed to the pile cap. Figure 24. Comparison of Pushover Curves by the Designers (Nader and Maroney, 2007) using Simplistic Beam Elements to the Curves by the Authors (Astaneh- Asl and Qian, 2016) using Realistic Shell Elements As Figure 24 shows, the use of beam elements instead of modeling the shafts using shell elements has resulted in underestimation of the stiffness and ultimate strength and overestimation of the ductility. The consequence of underestimating stiffness and strength is that the inertia forces generated in the structure during a seismic event will be significantly larger than the inertia forces established by the time-history analysis of the structure predicted by the designers using beam element based model. In other words, by modeling the tower shafts using simplistic beam elements, the bridge has been designed for smaller seismic forces than it may experience when subjected to the same seven design earthquakes ground motions established by Fugro-Earth Mechanics (2001) and used by the designers in the design of the SAS Bay Bridge. In addition, as Figure 24 also shows, since the bridge design team has used beam elements in their pushover analysis, yielding of the tower occurs under much smaller forces than it would if the tower was realistically modeled using shell elements for steel plates. This unrealistic early yielding resulted in an incorrect ductility of about 5.5 for the tower by the bridge design team, compared to the realistic value of 3.2, resulting from a pushover analysis of the tower modeled using shell elements. The reason for low ductility of the tower, predicted by more realistic pushover by the authors using shell elements to model the steel plates is that only shell elements can predict local buckling which occurred in this case. The designers of the SAS Bay Bridge by using beam elements for the tower shafts have completely ignored the possibility of local buckling of the plates in the tower shafts and have obtained a pushover capacity curve that is incorrect and might have designed the bridge for using incorrect and less than actual 12

13 forces, and incorrect ductility, much less than the actual ductility of the tower. Design Considerations In addition to the above comparisons, the analysis results summarized herein also posed a question on the effectiveness of using a shear-link coupling system as a seismic fuse in the tower of the SAS Bay Bridge. Unlike eccentrically braced frames in buildings, where the frames on either side of the shear link are connected to each other only by shear links, in the case of tower of the SAS Bay Bridge, the tower shafts connected to each other not only by the shear links but also by a massive cable saddle and its supporting grillage system. The yielding of the shear links depends on the relative displacement of the tower shafts in the vertical direction. However, with a rigid saddle and its supporting grillage restraining the top of the tower shafts, such a yielding mechanism is disrupted, resulting in relatively large axial forces generated in the shafts as well as large stresses generated in the grillage. The results also showed that the change of the slope of the tower shafts at about mid-height results in stress concentration at that location and contributes to initiating local yielding and local buckling at that location relatively early in the pushover. It seems this has not been considered in design by designers since their simplistic beam element based model of the tower could not predict local buckling. It is important to note that the Performance Criteria established for the SAS Bay Bridge and given to the Design Team to satisfy in the design states that the inelasticity in the tower should be limited only to yielding of the shear links and all other components of the tower need to remain elastic (Nader, Manzanarez, and Maroney, 2000). Considering the extensive yielding and local buckling of the tower, that is not included in the designers analysis, the designers claim that the inelasticity in the tower will be limited to only yielding of the shear keys, while the tower shafts essentially remain elastic (Nader, Manzanarez, and Maroney, 2000) seems not a valid claim. Suggestions for Retrofit of the Main Tower One of the most important findings of this study is that premature local buckling of the tower shafts could occur during a strong seismic event. From the publications by the lead members of the design team, it appears that using the beam elements for the tower shafts, the local buckling failure mode is not considered in the design and analysis of the SAS Bay Bridge. The main reason for premature local buckling of the tower plates is that the vertical stiffeners used in the tower are not sufficiently stiff and strong to prevent inelastic local buckling of the plates in the tower shafts. The vertical stiffeners in the tower shafts are flat plates instead of stiffer geometries such as T, or U, which are more effective in stiffening steel plates and thus preventing local buckling. Such stiffeners are used in most steel bridges, including in the orthotropic deck of the SAS Bay Bridge itself. Qian and Astaneh-Asl (2016) have studied the effects of various geometries and locations of the vertical stiffeners in steel bridge towers and piers. Equally spaced flat plate stiffeners, used in the tower of the SAS Bay Bridge, were found to be the least effective stiffeners in preventing local buckling of plates. In order to prevent local buckling of the tower shafts of the SAS Bay Bridge, which can result in the progressive collapse of the entire signature span, a retrofit scheme is proposed as shown in Figure 25 (Astaneh-Asl and Qian, 2016). Here, bolted T sections or welded pipes and channels are added to the vertical stiffeners over about threefourths of the height of the tower where local buckling of the tower shaft plates are likely to occur. If a welded option is selected, the traffic on the bridge needs to be reduced or halted during welding. However, to avoid welding in the field, the pipe and the channel in Options 2 and 3, can be shop-welded to a plate and the plate field-bolted to the vertical stiffeners. Retrofit Option 1: Add Bolted WT-Section Existing Flat Plate Stiffeners Retrofit Option 2: Add Welded Pipe Shear Links Connecting Tower Shafts Retrofit Option 3: Add Welded Channels Shaft Vertical Stiffeners Figure 25. Three Suggested Bolted or Welded Retrofit Solutions for the Tower Shafts to Prevent Local Buckling (Astaneh-Asl and Qian, 2016) Suggested Retrofit to Mitigate the Seismic Risk Posed by the Brittle Tower Anchor Rods The problem of SAS Bay Bridge anchor rods is directly related to the following aspects: 13

14 (a) the design decision to use ASTM A354 BD hot-dip galvanized anchor rods in a very corrosive offshore environment; (b) the failure during construction in leaving the anchor rods in the open environment unprotected for more than two years; (c) embedding the anchor rods in the pile cap concrete inside sleeves and not filling the sleeves with grout. The lack of protective grout resulted in the seawater seeping into the pile cap to collect around the anchor rods and caused further stress corrosion in them. In this paper, it was shown that not having the anchor rods can result in an undesirable behavior of the main tower. To mitigate the problem, the following is a summary of proposed retrofit measures: 1. The tower needs to be retrofitted to prevent yielding and local buckling of the tower legs. The problem of the local buckling of the tower legs is also an issue even when anchor rods have no problem as discussed earlier and in Astaneh-Asl and Qian (2016) in greater details. Hence, the vertical stiffeners inside the tower legs need to be strengthened by adding stiffening material to them as shown in Figure 24; 2. The Partial Joint Penetration Welds (PJP) connecting the tower legs to the base plate need to be strengthened to develop the yield strength of the tower shaft plates; 3. Many of the existing 3-inch (7.6 cm) diameter unacceptable brittle A354 BD anchor rods that are not above the piles can be replaced, albeit at very high cost, with 3.5-inch (8.9 cm) ductile upset A354 BC anchor rods. To do so will require boring through the existing anchor rods through the entire 19.7 ft (6m) depth of the composite pile cap, attaching a steel reaction frame to the bottom of the pile cap, and installing the new A354 BC upset anchor rods connecting the tower base plate on top of the pile cap to the new steel structure at the bottom of the pile cap; 4. Water sealed caisson around the pile cap needs to be constructed to prevent seawater from reaching pile cap. The seawater currently is causing not only corrosion of the anchor rods but corrosion of the steel plate box of the composite pile cap. This latter problem is not part of this paper but also needs to be solved. So, this retrofit step can protect the pile cap as well. Summary and Conclusions In this study, a detailed nonlinear finite element model of the SAS Bay Bridge tower was built based on the construction drawings using the general-purpose finite element software ANSYS 15.0v. Nonlinear static pushover analyses were performed to establish stiffness, strength, buckling behavior, and ductility of the tower with and without any anchor rods connecting the base of the tower to the top of the pile cap. The effects of the failure of the anchor rod on the pushover behavior of the main tower of the new SAS Bay Bridge was evaluated. Based on the results of realistic pushover of the SAS Bay Bridge tower with and without anchor rods, using shell elements for the plates, the following observations were made and conclusions reached: 1. This study shows that the pushover strength and ductility of the tower without anchor rods connecting it to the pile cap is only about 60% and 80% of that for the case with the anchor rods respectively. 2. There is a need for seismic retrofit of the tower itself to prevent local buckling of the tower shafts during strong seismic events. The shafts of the tower can buckle locally during relatively early stages of the pushover. Such local buckling of the tower legs can lead to the collapse of the tower, which in turn will result in the collapse of the entire SAS span as well as the adjacent spans that are supported on or supporting the SAS span deck. The main reason for local buckling of the SAS Bay Bridge tower shaft is the inadequacy of the vertical stiffeners in the tower shafts. The stiffeners, which currently are flat plates, need to be retrofitted by adding preferably bolted T section to them or welded or bolted pipes or channel sections as discussed in the paper. 3. The design team has not considered local buckling failure mode in their analysis and design of the tower since the design team has modeled the tower shafts as beam elements. As a result, they have established a pushover ductility of 5.5 for the tower. Considering local buckling failure mode, this study shows that the actual ductility of the tower, depending on the direction of pushover is from 2.5 for a 45-degree angle push to 4.1 for a push in the longitudinal direction. The use of such a large and incorrect value of ductility for the tower by the design team is of serious concern with regard to the seismic safety of the bridge. 4. The 424, 3-inch and 4-inch diameter hot-dip galvanized anchor rods are hydrogen-embrittled and are very likely to fracture during the 150 years design life of the bridge. 14

15 Already two of the anchor rods have fractured, one due to hydrogen-embrittlement and one due to thread stripping. The design team has stated that the anchor rods are not needed during the service life or during a future earthquake. This study shows that this statement is not true. The pushover strength of the tower without the anchor rods is only about 60% of the strength of the tower with the anchor rods. There is an urgent need to replace the existing hydrogen- embrittled anchor rods connecting the tower to pile caps before the next strong earthquake occurs in northern California, which has a probability of occurrence of 67% over the next 30 years. The paper suggests replacing those anchor rods that are not above the piles with 3.5-inch diameter A354 BC upset anchor rods. These new anchor rods would pass through the pile cap and be connected to a steel framing under the pile cap. 5. The Performance Criteria for this lifeline bridge states that the bridge should be designed to be opened to traffic almost immediately after a major earthquake, with limited damages in specifically designated areas, among which for the tower is the yielding of the shear links only. However, as the study shows, this requirement of the Performance Criteria is far from satisfied and during a major earthquake, the tower is to develop severe yielding and local buckling of the tower shafts and the grid that supports the saddle on top of the tower. The extensive damage to the tower poses a serious hazard to the stability of the entire span. Even without major collapse issue, the downtime may not be as short as what the bridge is designed for. Acknowledgement This study was part of a larger project on Investigation of Seismic Performance of the New Self-Anchored Suspension (SAS) Bay Bridge East Spans at the University of California Berkeley, USA, with Prof. Abolhassan Astaneh-Asl as the Principal Investigator. The project was not funded and was done through the volunteer efforts of the authors. The authors would like to express their sincere appreciation for the tremendous technical support provided by Dr. Metin Ozen, President, and the analysts at the Ozen Engineering Inc. on the use of the powerful ANSYS nonlinear structural analysis software featured in this project. Special thanks are due to Casey Heydari for his input in the use of ANSYS. References AASHTO (2016). AASHTO LRFD Bridge Design Specifications, Customary U.S. Units, 7th Edition, with 2015 and 2016 Interim Revisions, American Association of State Highway and Transportation Officials, Washington D.C. ANSYS, Inc. (2013). ANSYS Mechanical APDL Theory Reference, Release 15. ANSYS Inc., Canonsburg, PA. Astaneh-Asl, A., Tabbakhha, M., Qian X. (2016). The Effects of Failure of Anchor Rods on the Performance of the Tower of the New Bay Bridge, International Journal of Modern Engineering, Vol. 17, No.1, pp (A public access copy is here: IJME%20fall%202016%20 v17%20n1%20(pdw-2).pdf#page=39 ) Astaneh-Asl, A., and Qian, X. (2016). Pushover Analysis of the New Self-Anchored Suspension Bay Bridge Tower, International Journal of Engineering Research and Innovation, Vol.8, No.2, pp (A public access copy is here: Archives/issues/fall2016/X IJERI%20fall%202016%20v8 %20n2%20(PDW-2).pdf#page=64 ) ASTM (2011). Standard Specification for Quenched and Tempered Alloy Steel Bolts, Studs, and Other Externally Threaded Fasteners, ASTM Standard A354-11, American Society for Testing and Material. Caltrans (1999). Project Plans for Construction on State Highway in San Francisco County in San Francisco from 0.6km to 1.3km East of the Yerba Buena Tunnel East Portal. Engineering Drawings, The State of California, Department of Transportation, Sacramento. Chung, Y. (2014) Corrosion on the New Eastern Span of the San Francisco-Oakland Bay Bridge, Material Performance, NACE International, Vol. P53, No.1, p. 58. Fugro-Earth Mechanics (2001). Ground Motion Report, San Francisco-Oakland Bay Bridge East Span Seismic Safety Project. A Report Prepared for the California, Department of Transportation, Earth Mechanics Inc. and Fugro, a Joint Venture, March, 160 pp. Nader, M., Manzanarez, R., and Maroney, B. (2000). Seismic Design Strategy of the New East Bay Bridge Suspension Span. Proceedings of the 12th World Conference on Earthquake Engineering. Paper No. 0911, Auckland, New Zealand. Nader, M., and Maroney, B. (2007). One-of-a-Kind Design: The New San Francisco-Oakland Bay Bridge Self-Anchored Suspension Span. Structure Magazine, October. Qian, X., and Astaneh-Asl A. (2016). Behavior and Seismic Design of Stiffeners for Steel Bridge Tower Legs and Piers, Proceedings of the World Congress on Civil, Structural, and Env. Engineering (CSEE 16), Prague, Czech Republic. USGS (2017) Bay Area Earthquake Probabilities, Website of the USGS, Retrieved on August 1 st, 2017, from 15