This thesis explores a suitable method and appropriate input to determine the failure probability of thermal shrinkage cracking in a steel fibre-reinforced underwater concrete floor by examining the factors that influence this failure probability. An underwater concrete (UWC) floor is a common construction type in the Netherlands that is often applied to create building pits under the groundwater table. Usually, these (generally unreinforced) UWC floors only function as a watertight bottom layer of the building pit with only a temporary sealing function. Water tightness and crack prevention are very important aspects of this type of construction. A permanent reinforced structural top floor is frequently used on top of the temporary UWC floor to make a completely watertight construction, which is not the most sustainable and cost-efficient solution. Advances in concrete technology such as fibre-reinforced concrete have made it possible to integrate both the UWC and structural top floor or even use the UWC floor as the permanent structural floor. In these cases, the UWC floor should already function as a watertight barrier and controlling leakage by limiting the crack width becomes even more important. The addition of fibres to concrete may prevent through crack formation in the UWC slab and the possible consequent leakage. An important cause of cracking in UWC floors is thermal shrinkage during the cooling phase of the hardening reaction shortly after casting the UWC floor. Currently, there are no guidelines for the construction of fibre-reinforced concrete (FRC) floors and the prevention or limitation of thermal shrinkage cracking. A CROW-committee "Steel fibre reinforced underwater concrete (SFRUWC) floor as permanent structural floor" has been formed. This committee aims to set up a design recommendation and part of that is addressing the thermal shrinkage cracking problem. There is a lot of uncertainty in geometry, material properties and boundary conditions associated with SFRUWC floor design and construction. Because of this, there is a need for a probabilistic approach to investigate the influence of these uncertainties and tolerances on crack formation in SFRUWC floors during the hardening phase. This research aims to determine a suitable probabilistic method to investigate the failure probability of SFRUWC floors and the parameters that influence this. In order to achieve this, a finite element model was developed that determines the shrinkage cracking behaviour in a part of a UWC floor in a building pit. Before this model could be developed, all the necessary input parameters and design equations were collected from literature and existing guidelines. To set up a model, first the behaviour of UWC floors was studied, followed by the development of a finite element model that includes the hardening behaviour and strength development of young concrete. An important aspect of this finite element model is the use of random fields to introduce spatial variation in the strength properties of the SFRUWC floor, which is a first step to include stochastic variation in the model for the probabilistic analysis. A probabilistic sensitivity study was performed with the finite element model by calculating multiple samples for each set of input parameters. Separate input parameters were varied and the influence on the results was investigated. The parameters that were considered, include the random field properties, material properties and thermal properties. Finally, a full Monte Carlo analysis was performed to give a proof of concept on how to calculate the failure probability regarding thermal shrinkage cracking in SFRUWC floors. In order to prevent leaking cracks and satisfy the crack width criterion, the tension-hardening behaviour of FRC has to be utilised. Tension hardening behaviour will lead to a distributed cracking pattern, consisting of multiple small cracks which can satisfy the crack width criterion as opposed to a single large separation crack which does not satisfy the maximum allowable crack width criterion. It was found that the tensile behaviour of FRC and the use of random fields to model this tensile behaviour were major parameters that influenced the crack width and the occurrence of a distributed crack pattern. An important parameter is the standard deviation of the random field, which influences the difference between the maximum and minimum tensile strength in different locations in the slab. Looking at material behaviour, the main conclusion was that the introduction of a small hardening branch in the tensile material model was the governing influence factor. Both the standard deviation of the random field and the introduction of a hardening branch in the tensile behaviour affect the ratio between the tensile strength of the ordinary concrete and the residual tensile strength of the fibre-reinforced concrete. These two factors in combination with the model that was used, turned out to be dominating the results in such a way that the other input parameters only had a relatively small influence on the crack widths. To determine maximum crack widths in SFRUWC floor it is essential to consider multiple samples with different random fields to find out if only a distributed crack pattern is possible or whether also single localised cracks can occur. The possibility of both these results being able to occur, leads to a large possible error in the maximum crack width. The results of this thesis have shown that the random field parameters remain uncertain and experimental research is needed to determine these correctly. Until then, it is important to investigate how significantly these parameters influence the results. It is recommended to extend this research by improving the model by making it more realistic and finding out if these two factors are still the dominating input parameters.

Nowadays, most of the historical bridges (Amsterdam, 2019) of Amsterdam do not meet the load-bearing criteria of the current design code (Eurocode: 2012). This has several reasons. It comes partly because of the overdue of the maintenance (Amsterdam, 2019) but also because the traffic load for which the bridge has been designed, is lower than the present traffic load (Amsterdam, 2019). The current Eurocode 4 does not guarantee the safety of this type of bridge decks. To guarantee the safety and the remaining service life of the historical bridges in Amsterdam, the municipality has started an investigation on historical steel-concrete-composite-bridge-decks. The focus in this thesis is on historical steel-concrete-composite-bridge-decks (a.k.a. Verbundträger brücken in German) because this type of bridges does not contain shear connectors in their configuration. This leads to the fact that the capacity of the bridge deck is almost not determined in the longitudinal and completely not determined in the transversal direction. The bridge deck in the longitudinal direction satisfies the unity check based on the protocol of the municipality of Amsterdam to check this type of bridges on safety, where they only consider the steel profile to define the capacity of the bridge in this direction. This is very conservative because the concrete is not taken into account during the calculation of the cross-section. In the transverse direction, the bridge deck does not fulfil the necessary unit check limit, because the municipality takes only the shrinkage reinforcement into consideration during their calculations. In addition to this, the state of the bridge decks and relevant research about how the bridge deck is build-up, is investigated. The main conclusion that can be taken from the cross-section of these type of bridge decks is that there is a lot of variation in all the components of the bridge decks. Furthermore, during the investigation of the bridge decks it is decided to choose three typical bridge decks (A, B, C), which will be simulated to gain more insights about the cross-section of these historical bridge decks. The current Eurocode 4, which is implemented to guarantee the safety of the type of cross-section containing steel and concrete, does not provide an answer to calculate the load-bearing capacity of historical steel-concrete-composite-bridge-decks, because of a significant difference between the designed current Eurocode 4 model and the designed cross section of the historical model. The behaviour of the bridge is studied in two directions based on the available literature. In the longitudinal direction, the focus is on the interaction between steel and concrete and how this interaction can be described. In the transverse direction, the aim is to find the relevant failure mechanism and corresponding modelling approach to define the behaviour of the bridge deck in the transverse direction of these bridge decks. The failure mechanisms that were evaluated are: Punching shear failure, compressive membrane action, and failure of concrete strut. The assessment of the aforementioned failure mechanisms is carried out and the most logical model which can be used to validate during the FEA-simulation is the failure of concrete strut which can be modelled by strut and tie model. This model will also be carried out on the other two chosen bridges, next to bridge A on which the in-situ-load-test is done, to validate this model on more than one bridge deck. There was made use of an analytical model based on Eurocode 2, which has been compared the values of the numerical simulations…

In Amsterdam, more than 30 steel-concrete composite bridges were constructed from 1880-1960 without mechanical connectors and transverse reinforcement. Currently, there are no simplified analytical methods to determine the bearing capacity of these bridges. Thus, the bearing capacity is verified using NLFEM or oversimplified analytical calculations. This research proposes an analytical method to determine the bearing capacity of historic steel-concrete-composite bridges without mechanical connectors to avoid time-consuming FEM calculations and offers reasonable results. An experimental and numerical study is performed on data from in situ and laboratory testing of samples from two different bridge decks from these Amsterdam bridges. The tests are accompanied by a numerical model that has been studied and adjusted to a more generalized loading case. This study determined that the exterior composite girders are critical due to their lower lateral stiffness. An analytical model is proposed to examine the behaviour of the exterior composite girder. The model considers a 3-point bending load at midspan between the exterior composite and adjacent girder. The force distribution is described through a compatibility-based strut and tie model (C-STM). The concrete in compression is considered elastic compression struts, only limited by the ultimate load of the model. The concrete in tension is interpreted as a tensile tie, which fails when it exceeds the concrete tensile resistance. Following the failure of the tensile tie, it is assumed that a longitudinal crack propagates between the exterior composite girder and the adjacent girder. Additionally, vertical and lateral stiffness components are included in the model. These account for the flexural stiffness of the exterior and interior composite girder. The vertical stiffness is accounted for as elastic springs, and the lateral stiffness as spring beams. The interior lateral spring beam summarises all the interior composite girders' stiffness, whereas the exterior lateral spring beam only considers the exterior composite girder. Therefore, the configuration assumes that the interior spring beam is significantly stiffer than the exterior. Moreover, the stiffness of the exterior spring beam reduces when the longitudinal cracking occurs, assuming a part of the concrete fails. The C-STM is linked to the cross-section verification of longitudinal shear, biaxial bending and vertical shear resistance in two stages. Stage 1, at the load at longitudinal cracking, determines if the specimen fails at this moment, indicating that there possibly is a brittle failure. Stage 2 is after longitudinal cracking, where the steel-concrete contact perimeters have reduced, and the corresponding resistances accordingly reduce. The failure modes obtained by the analytical model are comparable to the ones observed during the experimental testing. The analytical model showed that the bridges failed due to biaxial bending limited by partial shear interaction. One of the specimens from the testing yielded due to bending but with limited ductility. The other specimen also yielded due to bending with concrete crushing at the top concrete fibre. Further, the bearing capacities obtained from the analytical model are comparable to the failure loads from the experimental and numerical results. The model predicts the failure modes and the bearing capacity and can therefore contribute to the assessment of the historic Amsterdam bridges, helping to reduce the assessment time of the bridges and understand their load-bearing behaviour better. Future work should focus on verifying the method by examining more bridges using FEM.