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The approach spans of the West Gate Bridge are currently being retrofitted with innovative materials in the form of carbon fibre polymer laminates and fabrics. This is to account for the planned increase of operational traffic lanes from 4 to 5 each way.
Related works from literature is discussed on various aspects of the structural assessment and modelling work carried out on the concrete viaducts and minor spans of the West Gate Bridge. This was done with the purpose of gaining a better understanding on the application of Finite Elements program on bridges. A literature review was also done on the carbon fibre polymer technology.
Background & recent structural assessment
Models were developed for both the steel and concrete sections of the West Gate Bridge by the West Gate Bridge Strengthening Alliance in year 2009 in order to assess the present capacity of the bridge and to develop an effective strengthening option to attain the desired loading criteria (Taylor, Percy & Allen 2009). According to Williams et al. (2009), the structural adequacy of the bridge was established with computer models which included various stages of the bridges during their life time.
Moreover, Service Limit State (SLS) and Ultimate Limit State (ULS) design envelopes were generated and various checks were performed with accordance to the Austroads Bridge Design Code (ABDC) and AS 5100 design codes. According to Rombach and Specker (n.d.), SLS includes full prestressing (minimum compressive stress of 1 MPA) and the shear transfer in the joints. ULS considers the opening of the joints and the load transfer in the joints.
Taylor et al. (2009) also demonstrated the usage of Bridge Specific Assessment of Live Load (BSALL) and how data of actual vehicles that travel over the West Gate Bridge was applied in the analysis, local traffic Weigh in Motion (WIM) data was developed for the West Gate Bridge strengthening project.
In this literature review, computer models developed on the concrete bridge components (Eastern and Western Approach Viaducts and the minor spans for the strengthening of the West Gate Bridge will be critically analysed.
Modelling is the making an idealization of a real structure. Rombach (2004) sees the majority of finite element method errors come from the modelling. Thus, Biggs et al. (2000) has employed several finite element strategies which include several assumptions to simplify the model development without any loss in the accuracy of the representation. Finite element strategies used by Biggs are shown in .
Table . Finite element strategies.
Component of Bridges
Finite Element Representations
Reinforced concrete deck
Shell elements and rebar elements
Simple supports of multipoint constraints
Surface pressure loads
Accordingly, Williams et al. (2009) suggested that global models of the individual structures of West Gate Bridge were created using primarily beam elements. Selected portions were modelled using detailed shell elements in order to observe local effects. Considering the actual 3D geometry of the structure, the effects of the support conditions, stages of prestressing and the temporary supports used during construction are analysed.
Moreover, Williams et al. (2009) introduced the time element into the construction sequence of the model by including time-dependent effects of the strengthening. Such effects include the creep and shrinkage of the concrete and steel relaxation.
Biggs et al (2000) identified that the complexity of the material is the major factor which limits the capabilities of the finite element method. Similarly, Rombach (2004) stated that (Finite Element Method) FEM is usually based on a linear-elastic material behaviour with limited redistribution of member forces. In relevance to the West Gate Bridge, the material properties of the viaducts were set according to the bridge specific design criteria developed in January 2008 with measured values (Williams, Pircher, & Allen 2009). This could be done by taking into account the section properties of the components such as the shear lag properties during computation.
Additionally, loading models which consists of pressure loads applied to deck elements were created for all permanent and transient effects and various traffic loading models were considered (Williams, Pircher & Allen 2009). Study done by Biggs et al. (2000) stated that the load magnitudes corresponded to the tire loads of a standard AASHTO-type, multiaxle truck, and the load locations in relation to the tire footprints. Rombach (2004) believes that this may lead to an increase of the actual area under load in the calculation of slabs under concentrated loads.
Williams et al. (2009) has performed a detailed assessment on the WGB prior to modelling. It is to verify the implemented construction scheme through review of the original design, as-built drawings, construction photographs, and interviews with construction managers. As time has been included as a fourth dimension in the mode, the original construction staging, the time dependent effects (creep and shrinkage), the section geometry and construction loading on the suitable section properties has been simulated into the model. This was a challenging task since the viaducts consist of several pre-cast sections erected and prestressed at different phases. However, according to Taylor et al. (2009), the Alliance has provided a set of 'as built' drawings to illustrate the completion of the drawing sets and cross reference them with on-site measurements and observations. Thus, the obtained records are deemed accurate.
Williams et al. (2011) on his paper on 'Carbon fibre retrofitting of the West Gate Bridge' described that the approach viaducts consists of three cell precast concrete box segments which were originally assembled span-by-span to form a central spine. The typical geometry of the precast spine segment showing tendon locations can be seen in .
Figure . Typical spine girder unit.
Temporary supports were positioned under the first unit of the spine girder and the next span was constructed in the same technique. Precast transverse cantilevers stick out at right angles from the spine to hold the remaining width of the deck as shown in . These were erected and post-tensioned to the central spine in order to carry a concrete slab constructed from precast panels and insitu concrete.
Figure . Placement of pre-cast sections, transverse cantilevers and deck slab.
A view of the complete model of the eastern viaduct is shown in and a view of the bridge from underneath is shown in .
SOFiSTiK pre-processor (based on an AutoCAD kernel) was used to perform structure input and the effect of permanent loads of the WGB (Williams, Pircher & Allen 2009). Taylor et al. (2009) sees SOFiSTiK as a finite element analysis and design package which allows for the integration of construction stage analysis, full 3D prestressed geometry definition including un-bonded tendons and time dependent effects due to creep and shrinkage. Additional loading conditions and analysis were evaluated in the model with a combination of graphical user interface and script language of SOFiSTiK. Rombach (2004) sees that the design of a bridge is usually done separately for the transverse and longitudinal directions. Accordingly, Taylor et al. (2009) has presented both independent longitudinal analysis models and the transverse models for the concrete viaducts. The models and their verifications are detailed in the following sections.
Figure . Model of the approach viaduct on eastern side.
Figure . Underside of the completed bridge - photographic view and detailed model.
As discussed in Section , the original construction process consisted of a span by span sequence. Detailed three-dimensional line models were developed for the assessment of the longitudinal behaviour of the Western and Eastern (as shown in ). According to Rombach (2004), the bridge is modelled as an ordinary beam in a longitudinal model with a rigid cross-section with no distortions due to bending or shear. It is then used to estimate the longitudinal, shear and torsion reinforcements, the relevant support forces, the stresses, and the deflection of the bridge.
In the context of WGB, the model for the concrete viaducts were integrated with the latest external prestressing strengthening works alongside with the corresponding time dependent effects to provide the ability to assess the effect of the recent strengthening (Taylor, Percy & Allen 2009).
Figure . Longitudinal Sofistik model.
In this model, Taylors et al. (2009) have also performed the influence lines evaluation for live load application and super-positioning. The results were then confirmed against simplified SpaceGass models and close accuracy was found. From the longitudinal mode, significant results obtained included the extreme fibre tensile and compressive stress evaluations considering shear lag effects. The ultimate flexural, shear and torsional resistance were also obtained.
Rombach (2004) analyzed the transverse behavior of a bridge by modeling the truss element of a '1 meter' wide section of the bridge. The variable depth of the beams and the inclination of the axis of gravity are taken into account. Similarly, transverse analysis models by Taylor et al. (2009) consist of a combination of plate and beam elements (see ). Plate elements were used to model the spine while beam elements were used to model the cantilever beams. These models typically simulated the original construction sequence and included the time dependent effects due to creep and shrinkage.
This modelling by Taylor et al. (2009) was also undertaken using Sofistik. It allowed for the combining of beam and plate elements with the integration of construction stage analysis, the 3D prestressed geometry and including the time dependent behaviour of concrete as well.
Figure . Local Sofistik model.
The aim of these analyses was to estimate the transverse flexure of the spine and the capacity of the precast cantilever. Besides forces and moments, the fibre tensile and compressive stress, ultimate flexural capacity of the precast cantilever beam were analysed precisely. The results of the assessment were generally in line with what was expected after the results were verified against simplified hand calculations and SpaceGass models
The minor spans were designed and constructed as composite bridges with longitudinal steel I-sections and concrete deck slabs (Williams, Pircher & Allen 2009). Detailed computer models were generated by considering the time lines and construction sequence (). The sections were modelled in consideration for the strains due to self-weight of the steel girders and the weight of the wet concrete during construction prior to the curing of 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 . Model of the Minor Spans.
Taylor et al. (2009) stated that models of WGB were wind tunnel tested at the time of its design in 1973. However since some of the strengthening options and proposed upgrades will alter the cross sectional profile of the bridge, it was considered essential to re-evaluate the bridge's aerodynamic stability. Thus, Williams et al. (2009) have re-evaluated the wind analysis of the WGB. A computational fluid dynamics (CFD) model of the cross-section was built in order to study the wind loading on the bridge using an input in SOFiSTiK called crossWind. Wind effects due to lateral wind applied at different angles (see ) were examined. The results of these analyses were compared to the static wind loading as defined in the AS5100 and AS1170 design codes.
Figure . Wind velocity field around cross-section at -10 deg attack angle.
It is the nature of long span bridges with aerodynamic sections that relatively small changes in certain sensitive locations along the bridge can have a distinct effect on the bridge' behaviour.
ANalysis of structural assessment
This section will review the technical analysis and results obtained from the finite element models used to evaluate some of the important characteristics of the bridge behaviour.
The viaducts were modelled and analysed as both a complete longitudinal series of beam elements over their entire lengths and also using localized beam and plate elements.
Williams et al. (2009) considered several approaches in analysis of the structures for traffic loading. Similarly, Rombach (2004) agrees that various load cases have to be considered in the design of a bridge structure. The loadings have to be combined in the most unfavourable manner. The relevant positioning of the traffic loads such as acle loads can be considered in two different ways. Firstly, one can 'drive' the traffic loads by the computer over the bridge in all different lanes. This results in enormous number of load cases and a major computational effort. The engineer has to know in advance which parts of the structure should be loaded to get the greatest member force. The structures were firstly analysed for current loading conditions according to ABDC and AS5100 loading requirements on 8-lane configurations. It is to create a baseline understanding of the existing stress state. This approach then modified 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 alternatives. According to Williams et al. (2009), analysis for SLS stresses was able to provide plots of maximum and minimum compression and tension in the extreme fibres of the section as seen in . These were oriented along the layout of the bridge profile to provide quick reference to areas of interest and targeted strengthening works (). Similiarly, The ULS forces used the gross section properties and provided utilisation factors instead of stresses.
Figure . Effective (dark) and gross cross-section in longitudinal direction.
Figure . SLS stresses along the bottom fibre of the western viaduct.
Rombach and Specker (n.d.) have identified the critical sections under the ultimate loads as shown in .
Table . Critical sections.
Mid of span
Greatest bending moment
First joint after support
Great shear force but prestress force not uniformly distributed in cross-section
High concentrated loads due to anchorage of tendons
High concentrated loads due to tendons
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 improve this tension ().
Figure . PT stress diagrams.
Rombach and Specker (n.d.) proposed that the deformation characteristics and bearing capacity of segmental bridges are subjected to the opening of the joints, the local contact between the tendons and the concrete at the anchorages and deviators. According to their findings, real joint can only transfer normal and shear forces under compression. As the normal stress becomes positive due to bending, the joint contact is broken and no force is transmitted. Therefore, a simple non-linear stress-strain relationship is used for concrete according to ideal plastic model for the tendons. Similarly, Megally et al. (2002) stated that contact elements at the interfaces allowed the compression forces to develop at the joints, but eliminated tension forces. In reality, the epoxy between the segments does carry some tension until either the epoxy or the adjacent concrete breaks. The post-tensioning strand was modelled using link elements which resisted only axial force and provided the tension component necessary to resist the moments created by the loadings.
Megally et al. (2002) also proposed that FEM used a linear-elastic constitutive model for the concrete and did not account for any plastic deformations of the concrete or for crushing of the concrete. Besides, the research also suggested that the loading on finite element model was terminated when the opening of the centre joint reached a point where the contact area was smaller than the contact elements. A complete concrete constitutive model would have to be created, and the computational requirements would increase considerably.
By considering the assumptions and imitation of FEM by previous research in this particular field, modelling by Williams et al. (2009) has allowed for design optimisation by varying the number of strands per tendon as well as modifying the vertical offsets to maximise eccentricities (). Plots were automatically updated and results presented in a manner that enabled easy comparisons. The long-term behaviour of the strengthening was also considered in this optimisation process.
However, analysis by Williams et al. (2009) has failed to address the principal behaviour of the bridge under normal bending. Research by Rombach and Specker (n.d.) shows that when the bridge structure is under full compression, segmental bridge behaves linear elastic like a monolithic one. Joints start to open and the deflections exhibit a non-linear growth as the stiffness decreases. Failure occurred when tendons start to yield and the neutral axis is shifted into the top slab, causing the concrete to crush.
Figure . 3-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 . Local wheel loading of a deck section.
Combinations were also made to examine global system behaviour by using engineering processes combining 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. Rombach (2004) believes that an interpolation of the values of different support conditions (fully or partially restraint at the web supports) and the location of the single loads is required. However, such analysis is more time-consuming than and FE analysis.
According to Tang (2000), the transverse analysis has assumed four series of finite-element test runs under different conditions. Test A assumed that minor cracks exist in the overlay. Test B was analysed under the condition of zero cracking and perfect bonding. One major longitudinal crack existing in the overlay was assumed for Test C. Test D examined the effects of temperature gradients only.
The minor spans were modelled and subjected to loading using a similar approach to what was performed on the concrete viaducts (). 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.
Figure . Lane loading including UDL and point loads.
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 . Typical pier model.
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.