Innovative Geometry Control Techniques for Complex Bridge Construction
Atte Mikkonen, SOFiN Consulting Ltd, Espoo, Finland
Georg Pircher, SOFiSTiK AG, Graz, Austria
Contact: [email protected]
Published: The paper was presented at the IABSE congress in San Jose, Costa Rica, in 2024.
Abstract
Complex bridges, including cable-stayed and arc-supported structures, require meticulous planning and control during staged construction to maintain adherence to the original design. Deviations due to erection errors, tolerance effects, or survey discrepancies pose significant challenges.
This study introduces innovative geometry control applications, illustrated by the Thu Thiem 2 bridge in Ho Chi Minh City, Vietnam. Initially, fixed construction plans, including camber and cable stressing forces, were dynamically adjusted in response to real-time deviations and load changes. A critical innovation, the “KINK” feature, was developed to integrate survey data and correct cumulative installation errors, improving the fidelity of the ‘as-built’ analysis and allowing for proactive design modifications.
Our research enhances the precision and efficiency of bridge construction and supports improved collaboration among stakeholders.
Introduction
When constructing bridges, unforeseen challenges are a regular occurrence, necessitating adjustments on a weekly, if not daily, basis. The project timeline often faces delays due to several factors, while the consistency of concrete quality can fluctuate. However, amidst these challenges, one steadfast objective remains: ensuring that the bridge’s appearance aligns with the original design.
Predicting the actual construction sequence is arduous, if not impossible, as outlined by the construction engineering designer. Two key components prove indispensable: precamber and fabrication shape for elements not cast on-site but prefabricated. These elements encompass steel components as well as precast concrete elements. The latter aspect presents an additional hurdle, as the individual geometry of prefabricated elements cannot be altered. This reality poses an even greater challenge for both the contractor and the construction engineering team.
Precamber
Precamber in bridge construction refers to intentionally imparting, typically a slight upward curvature or camber to a bridge girder or beam during fabrication or construction. This curvature is designed to counteract the deflection that will occur when the bridge is subjected of the loads during the construction and over time, typically self-weight, changes in the structural system (in staged construction) and creep and shrinkage. By pre-curving the girder or beam upward before installation, engineers anticipate the downward deflection that will naturally happen. When the bridge is constructed in stages, the precamber of the bridge shall be controlled, and can be adjusted if needed. This technique ensures that, once the bridge is fully loaded, the girder or beam will settle into a level position or maintain a desired upward curve, rather than sagging below the intended level. Precambering helps to maintain the desired profile and structural integrity of the bridge, improving its performance and longevity. It is a customary practice in bridge engineering to ensure that the bridge maintains its intended shape and remains safe and functional throughout its lifespan.
Fabrication shape
Fabrication shape in bridge construction refers to the specific geometric configuration or profile of structural elements such as girders, beams, or trusses during their fabrication process. This process involves shaping steel or concrete into the precise forms required for assembly into a bridge structure. Each structural element of the bridge, whether it is a girder, beam, or truss, has a predetermined shape prior to installation and before any loads are applied.
It is essential to ensure that each component fits together accurately during assembly so that the finished bridge meets the tolerance requirements. It is important to recognize that fabrication shape generates a set of different geometries, which do not fit together as unloaded and does not form a continuous uniform shape.
The already installed part of the structure is loaded typically not only with its self-weight but also some temporary loads and the part to be installed, loaded at least by its own deadload, thus typically temporarily supported during the assembly. At this stage, the components shall fit together (Figure 1).
Geometry control
To ensure a precise implementation of the original design, throughout the construction process, geometry control is typically implemented. It is method to follow if the construction meets the designed geometry. In the case if the tolerances get close to the limits, or if there is a trend to go so, proactive corrective measures can be implemented to realign the construction with the intended geometry. For the Bridges that are built in stages, typically long-span bridges, a slight deviation from the planned construction schedule can lead to significant problems if the precamber is not achieved as intended. A minor error in angle during the initial stages of construction can result in geometry discrepancies of several meters, rendering components incompatible. This highlights the importance of geometry control.
For the construction plans, a staged construction analysis, where all the construction stages are included, is needed (Figure 2). Every action during bridge erection must be carefully and precisely considered. This entails not only accounting for geometry, creep, shrinkage, cable, and tendon stressing, but also the influence of both permanent and live loads. The analysis for the corrective actions shall be based on the actual geometry observed on-site. It is also important to have as realistic as estimate of the load condition at the stage of surveys. In particular cases, the construction components and equipment are weighed for erection control precision.
Based on the survey results, Engineers must also devise strategies for error compensation. Traditionally, remedial measures are planned in such a way that the next phases of construction approach the acupressure plan as much as possible. The challenge is to estimate if the tolerances are due to the misestimate in the material properties, inaccuracies in the loads, or if it is the case of error in construction. Miss interpretation for the corrective action may duplicate the error for the next stages of to the permanent structure. If the analysis is not updated as built and only kept as theoretical, the construction deviations will not be carried over to the next stages. This model will then always represent theoretical construction, not as built. This has often been requested by the designers, that how to include construction errors into analysis for more accurate estimate for the construction analysis.
In the case of the Thu Thiem 2 Bridge project, a collaborative effort with SOFiSTiK development yielded significant advancements, including the introduction of the “fixed camber” and “kink” features. The kink feature empowers designers to adjust segment geometry during analysis upon activation or installation, while preserving the original system geometry and precamber. By keeping fixed camber and system geometry, and incorporating factors such as load variations, material properties, and installation errors, this approach enables accurate as-built modeling within the original system geometry framework. Consequently, engineers can consistently compare construction stages, estimated final outcomes, or intermediate stages with the planned final system geometry, inclusive of any corrective actions implemented during construction. Subsequently, this article explains the method for precamber analysis and expounds upon techniques for conducting more complex as-built analysis.
Linear precamber
The principle of the precamber, in linear way, is explained with the example below [1]. We assume a single span girder loaded by deadload, creep and shrinkage. In a first straight forward analysis we start on a straight formwork. Cast the structure, and the effect of the deadloads and creep until traffic opening, we get a deformation downwards. If we mirror this shape and use it as pre-deformation (precamber) for the formwork, we will end up in a straight shape on traffic opening (Figure 3).
When assuming construction stages, the task is a little bit more complicated, but the same in principle applies. The following description is based on the example of a four-span system as per figure 4. The pre-camber shall give the construction shape to match with a specific target geometry.
Here we set a stage where the bridge is supposed to be handed over for traffic. The example shows a span-by-span erection where concrete is applied on a formwork standing on the ground. The stiffness is activated in advance without dead load and stress-free (first wet concrete).
The construction follows the following steps:
Construction sequence first span and small cantilever (Figure 5):
- stage 1 – the formwork supported on ground, concrete gets filled in and hardening (no dead load) starts.
- stage 2 – the formwork is removed, and the dead load of concrete is activated.
- Stage 3 nothing structural happens on site, for a defined duration the girder is exposed to creep and shrinkage.
Construction sequence for the following spans is the same (Figure 6).
When activating span two again the formwork is supposed to stand on the ground, concrete is filled in and the formwork dismantled before the next span cycle. At the time traffic opening the bridge is not straight and has kinks from one construction block to the next.
After staged construction analysis, all the deformations of the structure for all stages are available and precamber calculation can be performed. As for span one this deformation just must be mirrored and applied as negative precamber to achieve zero displacement on traffic opening. In the same way the construction stage analysis corrects all other deformations, and the displacements are stored.
Thus, the precamber is the inversed geometry as follows in figure 7 for span 1: The correctly applied precamber gives us the wanted geometry for the wanted final stage (open for traffic). It is important to note that a linear precamber as in the explained example, does not change the forces, only the deformations are changed.
Nonlinear precamber
When applying the similar principle on long span and/or cable supported structures several types of non-linearities in the construction and thus in precamber analysis might be needed. A more SOFiSTiKated approach is then required, and the slightly modified approach is described in the following. As the application projects we are looking at in the following, is cable-stayed bridge, we specifically look at this bridge type. The calculation is now not a simple straight forward one stop calculation but requires iterations as the cable force changes depending on the applied geometry. It is essential that the analysis is performed on the displaced and not on an idealized model geometry.
The nonlinear precamber is shown in the following figures following the principle explained for the 4-span bridge. The stages are however calculated geometrically non-linearly. Also newly activated segment, it must be added with its correct stress-free shop form that includes all necessary precamber in the last iteration run. The simplified structural model, shown in figure 8, is erected using two segments and two cables activated sequentially.
When considering that the girder is prefabricated rather than cast in situ, more complexities arise. The analysis must account for both displacement and the internal forces and stresses resulting from construction-induced deformations. To accurately fabricate each segment, it is essential to define the stress-free geometry as the starting point for an iterative analysis (Figure 9). This analysis progresses from the initial, non-precambered geometry to the precambered geometry, achieving the desired final form and structural equilibrium at critical stages, typically at the opening to traffic. This process is synchronized with actual construction stages by automatically estimating the initial geometry. Consequently, the final non-linear construction analysis using stress-free fabrication shapes accurately achieves the intended “perfect” target geometry (in this case, a straight girder).
In real projects, on-site conditions vary over time, necessitating updates to calculations. Once cast, segments cannot be altered; however, adjustments to the precamber and fabrication shapes of upcoming segments can be made to achieve the desired final geometry.
We address deviations by integrating a kink in the construction stage analysis for the next segment, adjusting its orientation to compensate for erection errors, while keeping the predetermined fabrication shape. This approach is proved in the following sections, which also explore how several types of nonlinearities can be included or excluded based on structural requirements.
Thu Thiem 2 Bridge
The Thu Thiem 2 Bridge, inaugurated in April 2022, is a cable-stayed bridge in Ho Chi Minh City, Vietnam, crossing the Saigon River (Figure 10). It spans 850 meters with a deck width of twenty-eight meters and accommodates six lanes of traffic. The bridge’s distinctive feature is its 110-meter high backward-sloping and curved pylon. The main span measures two hundred meters, constructed with a lightweight composite structure of steel and concrete, while the 115-meter back span is made of concrete. The pylon structure is also a composite of steel and concrete, featuring a hollow steel core encased in concrete. The construction of the bridge posed a unique challenge in erecting the main span using the free cantilever method, balanced by the backward-inclined pylon. This required precise engineering to achieve the desired geometry as it reached the pier on the opposite side of the river. Ensuring the planned cable force layout was crucial to balance the loads of the curved pylon.
The challenge for the construction
The analysis for the staged construction of the Thu Thiem 2 Bridge presents a formidable challenge due to its asymmetric span arrangement. The lightweight steel-concrete composite main span is counterbalanced by a heavier, shorter back span made of post-tensioned concrete. Initially, cable forces for the main span stays are defined based on the main span weight. Subsequently, cable forces for the back span are adjusted to eliminate bending moments in the pylon relative to its curved axis. Achieving this equilibrium involves further balancing these cable forces with the weight of the back span, optimized by cable spacing. While this equilibrium is straightforward to solve for the static final stage, where all structural components and dead loads are in place, the challenge lies in orchestrating the construction process to gradually attain this equilibrium. This entails ensuring the safety and stability of the structure throughout each erection step while simultaneously controlling its geometry (Figure 11).
For the main span erection, the back span was entirely constructed on temporary supports and scaffolding. The pylon was built to its possible height before requiring balancing forces from the stay cables for stability. This setup allowed for the initiation of the main span cantilever erection, with the back span on supports providing a solid counterweight. The rest of the pylon was erected parallel to the main span, as advancing it further would have required cable forces from the main span to balance its own deadload. It is crucial to note that after span closure, significant portions of the deadload, such as asphalt layers and concrete balustrades, were absent. Introducing this load to the asymmetric structure created imbalance in cable forces and induced further bending in the pylon. As the equilibrium of forces was consistently decided based on the demands of the main span, restressing of few of the back span cables was required during the stages to maintain stability.
Main span erection sequence
The main span erection process progressed through carefully planned cycles, involving following crucial stages:
- Prefabricated steel segments, weighing between 90 to 103 tons and totaling 109 to 121 tons with auxiliary structures, were lifted from barges using a heavy derrick crane weighing approximately 235 tons.
- The crane maneuvered the segments into position, where they were welded to existing structures.
- Concurrently, concrete deck installation started alongside new stay cable installation. Back stays were installed first, followed by main span stays. Main span cable installation force was adjusted to regulate steel stresses in the girder, in conjunction with the weight of the concrete deck, prior to casting edge beams and stitches to create a composite structure. Back stay force was selected to balance the pylon during erection.
- As the concrete deck was cast, the crane was relocated for subsequent lifting cycles, and the main span cables were restressed. This sequence optimized girder steel stresses and achieved final main span cable lengths during installation cycles, mitigating the need for restressing after span closure.
Secondary steps included partial load introduction, adjustment of temporary loads, and hold points for quality assurance and surveys. Due to heavy lifting, cantilever deformations reached significant magnitudes, with tip deformations approaching one meter (+300 to -600 mm) in a single cycle. Construction inevitably entails tolerance, affecting realized geometry. Despite precise setting of predefined cable forces, there is always minor deviation, affecting segment positioning. Errors in segment placement can accumulate over the span’s length, emphasizing the importance of meticulous adjustments. Additionally, the weight and stiffness of temporary structures, such as the derrick crane, significantly influence construction geometry. Ensuring precise geometry control and adjusting installations, including cable forces, was imperative to guarantee the success of the construction project.
Characteristics of the FE model
The Finite Element Model (FE-model) used for analysis encompassed all main components with precision thought reasonable. Pylon modeling accounted for various weight and stiffness introduction stages, including the lifting and installation of the steel core, subsequent addition of climbing formwork weight, and final inclusion of the weight from the concreted outer casing. Due to the pylon’s inclined and curved nature, load distribution changes resulted in horizontal movement and bending along the pylon leg.
The main span superstructure was represented by beam elements, including two longitudinal main girders and three secondary girders connected by cross beams about every four meters. Cable connections to the cross beams, including cable tubes, facilitated accurate weight distribution, and served as geometry control objects in the analytical model. The deck’s behavior, subjected to heavy equipment loads and wide span, underwent detailed examination. Heavy lifting induced significant uplift force to crane tie-downs, followed by high hogging moments in the deck, leading to tensile stresses and crack analysis considering material nonlinearity (Figure 12).
Cables were modeled using specialized elements accounting for geometric nonlinearity (sagging), which significantly influenced cable stiffness due to small installation forces resulting from missing deadload.
Back span structures and substructures had minimal impact on erection geometry and were simplified in analysis. Combining linear and nonlinear behavior in the model was crucial, with geometric nonlinearity deemed insignificant for the pylon and superstructure, streamlining calculations, and reducing computation time.
Analysis
The analysis comprehensively covered 366 different construction stages, which were crucial for achieving accurate results. Less critical stages and components, such as the activation of piers with aged concrete, were simplified to streamline the process. The effect of concrete creep and shrinkage was integrated into the analysis, aligned with the contractor’s construction schedule, reflecting the actual progression of the structure over time.
An iterative forward analysis approach was employed, targeting specific outcomes such as desired cable forces, optimal steel stresses, and appropriate pylon action forces. This was facilitated by the software’s automation capabilities, which allowed for the automatic definition of new geometries for activated elements aiming to achieve the system geometry at predetermined construction stages (e.g., bridge opening or specific milestones). This iterative procedure was essential to address time-dependent effects and material nonlinearities, such as cable behavior and concrete cracking. Particular attention was paid to the support conditions for the lifted segments, ensuring their geometric compatibility with previously constructed sections (Figure 13).
The heavy lifting loads and the derrick’s weight were recognized to cause significant deformation in the steel construction, particularly at the girder tips, during lifting operations. The support method used during lifting was crucial, as the deformation of a lifted segment depended on how it was supported. Analyzing these conditions was necessary, especially given the heavy loads involved with the composite deck construction, which could not be preemptively simulated or adjusted for in the steel workshop.
This detailed analysis eased a thorough understanding that the final loading conditions and the bridge’s equilibrium were also significantly influenced by the chosen erection methods and the weight of the equipment used.
The outcome of this theoretical simulation was the successful resolution of the geometry and equilibrium for all selected and modeled steps. The early activation of the steel assembly before its deadload became effective allowed for the representation of the structure’s geometry as stress-free. This critical step informs steel fabrication in the workshop, ensuring components are manufactured according to the precise geometries needed to maintain structural integrity and alignment during assembly.
Data exchange for the fabrication
As depicted in Figure 13, the theoretical shape of the steel assembly, including the main girders, exhibits a non-planar form with twisting around their longitudinal axis. This intricate geometry posed significant challenges for workshop fabrication, necessitating simplifications for fabrication. Key elements in the geometry included the start and end points of the girders, crucial for their connection to other assemblies. To facilitate data exchange from analysis to fabrication, a new functionality was implemented to export the deformed geometry from the simulation into a 3D model in IFC format. Unlike other BIM file formats, IFC format is platform-neutral and can be read and edited by any BIM software (Figure 14).
Modelling for shop drawings was carried out using TEKLA software, which directly read these models as a reference, enabling incorporation of fabrication requirements into the shop drawing modelling while maintaining crucial geometry compatibility. The seamless data transfer was facilitated by parametric modelling, ensuring identical geometry for both the analytical model and the physical model used for fabrication. This workflow proved to be highly effective, and segment connections were executed successfully without encountering any challenges.
Erection control
The erection simulation served as the theoretical blueprint for construction, and since it was also used for steel manufacturing, the geometry of these objects remained unchanged and predefined. However, in practice, deviations from the theoretical plan are inevitable to some extent. To address this, an innovative approach was implemented for geometry control analysis. The software-generated theoretical erection analysis was geometrically frozen, allowing for recalculations with updated loads or material properties. This enabled adjustments to applied cable forces or more accurate representation of realized load conditions during erection. Importantly, this method ensured that the analysis could always be performed to completion, providing estimates of the effects of these adjustments on the final construction.
After all lifts and stay stressing, the actual geometry of the construction was surveyed with reasonable accuracy. It became clear that small errors in the steel assembly could accumulate if left uncorrected. However, if errors were attributed to loads rather than installation, the tangential segment installation shall be maintained and not corrected with the geometry.
To analyze reasons for tolerances, a “KINK” functionality was developed for the SOFiSTiK software. This allowed for the activation of the new assembly into a predefined kinked installation angle compared to the theoretical one. The kink, determined by survey results, was incorporated into the model, and maintained throughout, facilitating verification of later surveys and overall construction geometry monitoring (Figure 15).
It became clear that the erected geometry was gradually descending more than initially estimated. Analysis revealed that this discrepancy could be rectified through cable tuning during the longest and most flexible cantilever stages. Additionally, accurately defining restressing lengths during these stages allowed for precise adjustment of the deck elevation to the correct level. The smooth final geometry of the structure and controlled cable forces served as validation for the analysis and method employed.
Conclusions
The introduction of these new methods and functionalities offers powerful tools for engineers to analyze structures as they are built. However, it is crucial to exercise great care when adjusting the analysis. Misinterpreting the reason for an erection error could lead to incorporating the incorrect information into the analysis, potentially resulting in even more inaccurate results. Therefore, meticulous attention to details and thorough understanding of the construction process are essential to ensure the reliability and accuracy of the analysis outcomes.
References
[1]…SOFiSTiK 2024, CSM Construction Stage Manager, software user manual.
