This paper will also report on the methodology of various strengthening concepts that were developed and tested using these models.

Transcription

1 Computer Models Developed for the Strengthening of the Approach Viaducts of the Westgate Bridge Grahme, Bridge Engineer, Sinclair Knight Merz Martin Pircher, Technical Director, ABES Pty Ltd Craig Allen, Executive Engineer, Sinclair Knight Merz 1. Synopsis For the purpose of planning and optimising the strengthening works on the concrete bridge components of the Westgate Bridge in Melbourne, various detailed analyses and checks using numerical models have been performed. The concrete bridge components encompass the Eastern and Western Approach Viaducts, Anchorage Abutments and the Minor Spans on the eastern and western sides. Computer models were developed to incorporate the various stages of these bridges during their life time and checks were performed in accordance with ABDC 1 and AS design codes in order to establish the structural adequacy of the bridge. In addition, a Bridge Specific Assessment of Live Load (BSALL) incorporating local traffic Weigh in Motion (WIM) data was developed for the project. The numerical 3-dimensional finite element models developed included global models of the sub- and super-structure with localised sections modelled in greater detail. A comprehensive representation of the 4 th dimension of time, and the associated effects considering the history of the bridge, integrating the construction sequence and all previous strengthening measures was also included. This paper will also report on the methodology of various strengthening concepts that were developed and tested using these models. 2. Introduction The West Gate Bridge in Melbourne is one of Australia s most iconic and important links in the national transportation network. The 2.6 km structure is comprised of an 850m long cable stayed steel box girder central portion with segmental pre-stressed concrete box girder approach viaducts of 670m on the western side and 870m on the eastern. Minor approach spans constructed with steel girder and composite concrete deck link the viaducts to the West Gate Freeway over local roads and railway lines on the east and west sides. The focus of this paper is the modelling work carried out on the concrete viaducts, minor spans and piers. This forms part of the current work being undertaken as part of the West Gate Bridge Strengthening Alliance including VicRoads, Flint & Neill, SKM and John Holland. The assessment was carried out using the structural design software SOFiSTiK. SOFiSTiK is a 3-dimensional Finite Elements program that allows for the consideration of staged construction and time-dependent effects. Analysis and design of pre-stressed concrete as well as steel and composite structures is possible with this software Computer Models... Westgate Bridge 1

2 package. The structural analysis performed was to provide the necessary forces and stresses resulting form various lane and loading configurations to ensure that the bridge is strengthened within the allowable limits as specified in the bridge specific design criteria developed in January Modelling 3.1 General Global models of the individual structures were created using predominantly beam elements. Within these models selected portions were modelled with much greater detail using shell elements in order to examine local effects. All models were created taking into consideration the actual 3D geometry of the structure, the support conditions, all the stages of prestressing and where applicable, the temporary supports used during construction. Time could be seen as a fourth dimension that was introduced into the model. The original construction sequence was modelled including all modifications up to present day, taking into consideration concrete creep and shrinkage and steel relaxation. All strengthening options including their time-dependent effects were also modelled. Material properties were set according to the bridge specific design criteria developed in January 2008 which included measured values where applicable. The cross-section properties including the component, composite and shear lag properties were computed and taken into account at the relevant times during the construction and final stages. Loading models were created for all permanent and transient effects and various traffic loading models were considered as outlined in the design criteria. Primary and secondary effects of the prestressing were calculated and utilised in appropriate calculations. Service Limit State (SLS) and Ultimate Limit State (ULS) design envelopes were generated and design checks performed in accordance with AS5100 and ABDC. Time dependent effects of differential settlement were also included in the analysis. Additionally, a 2D SOFiSTiK model of the cross-section was created in order to investigate wind action on the main girder of the approach viaducts. For this investigation a computational fluid dynamics (CFD) code using the Vortex Particle Method was used. 3.2 Concrete Viaducts A detailed assessment was conducted in order to determine the actual construction scheme adopted. This included review of the original design, as-built drawings and construction photographs, plus interviews with construction managers. A thorough stepby-step process was then undertaken to replicate the actual erection process taking into account the section geometry and construction loading on the appropriate section properties active at that time. This was a challenging aspect since the viaducts consist of several pre-cast sections erected and prestressed at different stages. Computer Models... Westgate Bridge 2

3 The first stage in the construction process was casting and temporary support of the pinned piers. Spine girder segments were then lifted into position using a steel assembly gantry. These segments typically extended from the inflection point of the previous span erection to the inflection point of the next span in the construction process. A 100mm stitch pour was cast between each segment followed by stressing of the bottom flange tendons and draped web tendons. The typical geometry of the precast spine segment showing tendon locations can be seen in Figure 1. Figure 1: Typical spine girder unit. The assembly gantry was then advanced to the next span. Temporary supports were placed under the forward most unit of the spine girder and the next span was constructed in the same manner, as seen in Figure 2. Top flange tendons two spans behind the advancing gantry were then stressed. Pre-cast cantilevers were positioned transverse to the spine girder and tensioned. Pre-cast deck units were then placed on the cantilevers and an in-situ deck was cast to form the composite deck section as shown in Figure 3. A view of the complete model of the eastern viaduct is shown in Figure 4 and a view of the bridge from underneath is shown in Figure 5. Structure input and the input of permanent loads was performed using the SOFiSTiK pre-processor which is based on an AutoCAD kernel. Other loading conditions and analysis and design specifications were input using a mixture of graphic dialogues and script language. Computer Models... Westgate Bridge 3

4 Figure 2: Span by span construction (circa 1970 and SOFiSTiK model duplication) Figure 3: Placement of pre-cast sections, transverse cantilevers and deck slab. Figure 4. Model of the approach viaduct on eastern side. Computer Models... Westgate Bridge 4

5 Figure 5. Underside of the completed bridge photographic view and detailed model. 3.3 Minor Spans The minor spans were designed and constructed as composite bridges with longitudinal steel I-sections and concrete deck slabs. Detailed computer models were set up taking into consideration the time lines and construction sequence (Figure 6). The sections were modelled to account for the strains due to self-weight of the steel girders and the weight of the wet concrete during construction prior to the formation of the cured composite state. As with the approach viaducts, various traffic loading models were considered in order to ensure that the bridges are adequate to carry the required traffic loading. Figure 6. Model of the Minor Spans. Computer Models... Westgate Bridge 5

6 Wind Analysis A CFD model of the cross-section was built in order to investigate the wind loading on the bridge using an input in SOFiSTiK called crosswind. Wind effects due to lateral wind applied at different angles (Figure 7) were investigated. The results of these analyses were compared to the static wind loading as defined in the AS5100 and AS design codes. Figure 7. Wind velocity field around cross-section at -10 deg attack angle. 4. Analysis/Results 4.1 Concrete Viaducts The viaducts were modelled and analysed as both a complete longitudinal series of beam elements over their entire lengths (Figure 4) and also using localized beam and plate elements (Figure 5). In the longitudinal models loading considered the construction sequencing, self-weight, post-tensioning, superimposed dead loads, live loading (including traffic loading and transient loads such as wind, temperature and settlement) and long-term effects of creep and shrinkage. Analysis of the structures for traffic loading considered several approaches. The structures were initially analysed for current loading conditions according to ABDC and AS5100 loading requirements on 8-lane configurations to create a baseline understanding of the existing stress state. This approach then shifted to the BSALL loading to be run over the 8-lane configuration and the proposed 10-lane final configuration after strengthening. Once all inputs were detailed and checked, output plots and tables were created to determine strengthening options. Analysis for SLS stresses was able to take advantage Computer Models... Westgate Bridge 6

7 of the pre-stressing forces and effective section properties to provide plots of maximum and minimum compression and tension in the extreme fibres of the section as seen in Figure 8. These were oriented along the layout of the bridge profile to provide quick reference to areas of interest and targeted strengthening works (Figure 9). The ULS forces were output in a similar fashion, but used the gross section properties and provided utilisation factors instead of stresses. Figure 8. Effective (dark) and gross cross-section in longitudinal direction. Figure 9. SLS stresses along the bottom fibre of the western viaduct. Development of strengthening options using additional longitudinal post tensioning was carried out following the same logic as for the original construction. In regions of noncompliance, such as tension in the bottom fibre of the spine girder at SLS, additional external web tendons were provided to alleviate this tension (Figure 10). The detailed model allowed for design optimisation by varying the number of strands per tendon as well as modifying the vertical offsets to maximise eccentricities (Figure 11). Plots were automatically updated and results presented in a manner than enabled easy comparisons. The long-term behaviour of the strengthening was also considered in this optimisation process. Figure 10. PT stress diagrams. Computer Models... Westgate Bridge 7

8 Figure D representation of PT layout. The localised transverse models allowed for a detailed examination of the individual elements in the viaducts. Local wheel and axle loads in various locations and combinations were considered to determine the most extreme behaviour of the deck, cantilevers, and spine girder webs and flanges (Figure 12). Combinations were also made to examine global system behaviour by using engineering processes combing percentages of global and local forces. These models were also used to examine the effects of temporary construction loading including temporary barriers and access gantries.. Figure 12. Local wheel loading of a deck section. Minor Spans The minor spans were modelled and subjected to loading using a similar approach to what was performed on the concrete viaducts (Figure 13). Design loading envelopes were created to compare against section capacities and plotted along the associated members to view areas of interest. Additional capacity checks were also performed using design spreadsheets and grillage software to verify the results from Sofistik. Computer Models... Westgate Bridge 8

9 Figure 13. Lane loading including UDL and point loads. Piers Detailed 3D models of the piers were used to ensure the capacity under the BSALL traffic loading for the 10-lane configuration was not exceeded. Non-linear concrete behaviour and second order effects were taken into account for these checks (Figure 14). Figure 14. Typical pier model Wind Loading Wind loading in accordance with AS5100 and AS1170 was used for the detailed modelling work. A CFD model was however set up to investigate loading conditions on the deck at SLS and ULS wind velocities and to compare these loadings to those used. It was found that the inclination angle of the wind had a strong influence on the resulting loading. However, in general it could be confirmed that the CFD model produced less conservative values. Computer Models... Westgate Bridge 9

10 5. Conclusions The use of SOFiSTiK software allowed for a full three-dimensional analysis of the concrete bridges including various loading configurations and associated demands. The ability to add the fourth dimension of time allowed for a detailed examination of the various losses in the structures and the changing stress states over time. The use of in-depth construction stage analysis procedures allowed for an appropriate stress state to be included in the assessment as various casting and tendon stressing stages were carried out. Having these models in place allowed for testing and optimisation of various strengthening options. Once the modelling process was finalised, examination of the bridges at the service and ultimate limit states was simplified with the various strengthening configurations and loading options proposed. At the conclusion of the Alliance works the models will remain with the client, VicRoads, for continued maintenance and revisions if it is determined additional works are ever required. 6. REFERENCES 1 AustRoads Australian Bridge Design Code (1996). 2 AS 5100 Bridge Design Australian Standard (2004). 3 AS/NZS 1170 Structural Design Actions (2002). 4 EN 1317 Part 2 Road Restraint Systems British Standard (1978). 5 British Concrete Society Technical Report No Euro Code FIB Technical Report Bulletin SOFiSTiK Software Handbook, Version 23, Nürnberg, Germany (2008). 8 S. Taylor, R. Percy, C. Allen, West Gate Bridge Strengthening, Proceedings: AustRoads Conference 2009, Auckland (2009). Computer Models... Westgate Bridge 10