In the energy sector, a transition is made from fossil fuels to sustainable energies. Due to an irregular supply of these sustainable energies, it often occurs that there is a mismatch between supply and demand. Energy storage is a promising technique to overcome this. In this thesis, the aim is to store gravitational energy in concrete spheres which are placed on the seabed. Therefore, this thesis aims to answer whether the most optimal construction method uses 3D Concrete Printing (3DCP) and if so, what the optimal construction method will be using 3DCP. Based on a specific case, five main construction methods are qualitative investigated, from which two are with 3DCP. From an evaluation, it followed that a combination of 3DCP and conventional casting is the most promising method and is therefore selected for more in-depth research. In this construction method, the formwork is made with 3DCP and concrete is cast in the formwork. A prefab bottom and top part are required, because the maximum inclination (nowadays) for printing is limited to 45°. Based on the selected construction method, three different 3DCP-variants are investigated: construction in the dry (1), submerged construction (2) and construction on a pontoon (3). The two main topics that are investigated are the use of 3DCP for the formwork and the suitability of unreinforced concrete for the sphere itself. The possible use of 3DCP is verified based on two failure mechanisms: plastic collapse (results in minimal free height of the formwork) and elastic collapse (results in maximum free height of the formwork). The suitability of unreinforced concrete is verified based on strength requirements. Both in case of construction in the dry and construction on a pontoon, h1 is 0.20 m and h2 is 0.65 m. In case of submerged construction, h1 is 0.25 m and h2 is 0.72 m. The unreinforced wall thickness should not exceed 2.5 m because it is required that the sphere is buoyant. For this wall thickness, a concrete strength class of C60/75 is required for construction in the dry, submerged construction and construction on a pontoon. An evaluation based on feasibility and reliability, combined with the results above, shows that construction in the dry is the most promising method. An adiabatic calculation is made of the temperature increase of the concrete, based on five different cement compositions. It followed that unreinforced concrete will crack. However, in reality, the temperature increase is semi-adiabatic, resulting in lower tensile stresses. It is therefore highly recommended to further investigate this temperature increase in order to verify the suitability of unreinforced concrete. Measures that could be taken to lower the temperature differences are: addition of liquid nitrogen or addition of ice instead of water for the concrete mix. Besides that, it is recommended to investigate the possible use of fibre-reinforced concrete, which could significantly increase the tensile strength of concrete.

Shell is working on mono-diameter drilling (MOD). A MOD well, or MOD well section, has a (nearly) constant diameter over several sections. This is achieved by deploying expandable liners: a liner is lowered into position and is expanded by pulling an over-sized cone through it. This plasticly deforms the pipe, increasing its inner diameter to that of the previous section. MOD eliminates many of the constraints of conventional well design. Greater depths may be reached and zonal isolation may be performed without paying the penalty of reduced production rates. While lowering an expandable assembly (expandable liner and expansion tools) into a well, caution is required. Displacement of the drilling mud causes a pressure drop due to fluid friction and acceleration. The running speed of the assembly into the well is limited by the surge (overpressure) or swab (underpressure) pressure. Pressure must remain within a predefined window to ensure well control. The current understanding of the mechanisms governing surge/swab pressure, as well as the models used to predict it, are deemed insufficient. The effect of unorthodox MOD conditions is unknown. This study is conducted to overcome these obstacles. Firstly, a model is programmed so that transient surge and swab pressures, induced by assembly movement, may be predicted. The drilling mud’s velocity and pressure are described by the water hammer equations, which are solved using the interpolated method of characteristics. One dimensional (1D), unsteady and nonuniform flow of a slightly compressible fluid in a conduit with linearly elastic walls is considered. The annular pressure drop for flow with a moving inner pipe is solved considering both laminar and turbulent flow of a Herschel-Bulkley fluid. Flow over the expansion tools is solved separately and is considered 1D and incompressible. Secondly, the model is validated. The model is first validated under conventional conditions using field measurements presented in literature and performs better than existing models. The validity of the model while dealing with extremely small clearances, as found in MOD applications, is investigated through a full-scale experiment on Shell’s test rig. The surge and swab pressures are generally predictable. Some discrepancies between predictions and measurements are observed and are attributed to the relatively large uncertainty in clearance size and shape, which results from imperfect pipes. The surge/swab pressure’s sensitivity to the size and shape of the pipes means that predictions should be treated with care. The effect of local annular flow restriction over the expansion tools is investigated too. The tools are found to cause acceleration induced transient pressures not predicted by the model. This implies that the 1D and/or incompressible assumption at the interface does not describe the flow adequately. Thirdly, the effect of MOD well design at true well depths and assembly lengths is investigated through a case study. The surge pressure is significant. The pressure drop generated in the narrow annulus between assembly and wellbore is too high to allow significant flow. Instead, all drilling mud is displaced upwards through the drillstring. Swabbing occurs behind the assembly. Circulation while tripping in expandable assemblies is therefore impossible. At these depth and length scales, the effect of fluid compression and borehole expansion becomes significant, causing steady state models to become increasingly inaccurate with depth.

Glass is gaining popularity as a structural material, this is mainly based on its transparent character. But due to its brittle failure behaviour the safety of these structures is an issue. Several concepts are found to guarantee the safety during the development of its structural application. One of these developments is to reinforce glass with other materials, this concept is known from concrete structures. After fracture of the glass (initial failure), the reinforcement will function as a tension element in order for the beam to maintain its integrity. This creates an additional load transfer mechanism, preventing total collapse of the structural system (ultimate failure) if designed properly. The objective of this thesis is to further develop reinforced glass beams. In Chapter 1 this is started by defining an abstract concept called the ideal glass beam. This concept is defined as a glass beam which has increased initial failure resistance, ability to maintain its integrity, freedom in manufacturing and all without disturbing the clean transparency of the glass. For the reason of transparency potential all concepts are fibreglass based. Freedom in manufacturing is realised by the use of fibreglass fabric which can be cut as desired and laminated together with the glass panes, just as is done with fully integrated (GFRP) reinforcement. This results in the three reinforcement concepts; post-tensioned fibreglass reinforcement; fibreglass fabric reinforcement; and transparent fibreglass reinforcement. All these three concepts are not yet or only partially developed and thus require research. However only post-tension and fibreglass fabric are chosen to be elaborated in this thesis. The application of transparent fibreglass is briefly discussed in order to assess its plausibility. Next to these design concepts, some issues exist regarding numerical calculations of glass systems. Most non-linear analysis run into convergence problems. Or computational intensive methods to account for the snap-back constitutive relation. This is due to the relative low fracture energy and high tensile strength with respect to concrete. A new kind of analysing method is in development which uses a series of linear analysis together with a damage model, reducing the material properties at each iteration. This method is called sequential linear analysis (SLA). The stability if this method creates the opportunity to analyse how alterations in design and numerical model influence the performance. These alterations come from differences in modelling approach in previous research, developments in SLA from research in concrete and design possibilities. The design strategy and philosophy of a reinforced glass beams is different from the current design approach, where additional panes are used to prevent ultimate failure. What these differences are and how a reinforced glass beam should be designed is elaborated in Chapter 3. Here the initial and ultimate failure strength capacities are discussed, how their resistance in affected and how they should be designed in order to create a safe system. In Chapter 4 the origin, feasibility and validation of the concepts are elaborated. In order to validate the concepts and numerical method some validation goals are drafted partially consisting on the former mentioned design philosophy. These goals result in desired data requirements which is subsequently used to describe the experiments to acquire this data. Initially only two bending experiments are required, for validation of both post-tension and fibreglass reinforcement. Both are validated using a reference experiment, for post-tension this is a specimen without applied normal force and the fibreglass fabric reinforcement is validated using integrated GFRP strips. In addition to these experiments tensile data of the different reinforcements is obtained to be used as input during numerical modelling. Also pull-out experiments are done for the fibreglass reinforcements to have a more direct comparing approach and to spread the risk of unsuccessful execution of either experiment. In Chapter 5 the experiments are designed based on the former mentioned requirements using analytical calculations. This is done to ensure theoretical feasibility of the experiments and to estimate the behaviour. The post-tensioned design consist of GFRP strips adhered on top and bottom after tensioning in order for them to function as reinforcement. No eccentricity is used te prevent crushing of the glass edges as the tensioning is introduced by head sections on either edge. These steel components function as actuators to introduce the normal force on the glass. The fibreglass fabric beams are designed to have equal ultimate failure resistance as the reference specimen. In the experimental research in Chapter 6 the validation goals are repeated and each experiment is treated. Starting with the tensile experiments, ordinary force displacement experiments are executed on the Fibrolux GFRP strips. These experiments failed at lower values of tensile strength and Youngs’ modulus than expected based on the values given by the manufacturer. This is explained by stress concentrations due to the rectangular geometry and relative low uni-directional (UD) fabric within the composite, according to the manufacturer. The fibreglass composite experiment also failed at a lower resistance than expected. After failure loose fibres are visible implying full saturation is not achieved. Using the theoretical strength of the SentryGlass (SG) it is calculated that approximately 30% of the fibres contributed in the strength resistance. The pull-out experiments are designed as a double pull-out with one lower resistance side which should fail by de-bonding. The difference in resistance can be compared with a reference set which has equal shear resistance to analyse the bonding performance. But due to the same saturation issue as the tensile fibreglass specimen, these fibreglass specimen also failed earlier. Thus making it unable to compare the different reinforcements. The GFRO pull-out specimen did fail properly as is expected from the reference set. Furthermore, the bending experiment using fibreglass fabric reinforcement did perform accordingly. Despite the same internal slipping of the fibreglass, the specimen showed almost sufficient ultimate resistance. After the occurrence of the first crack, the resistance increases again but after some deflection a decrease is observed. This is the consequence of the same internal slip due partial saturation. The final experiment regarding post-tensioning had a fault during the post-tensioning process, resulting in an insufficient posttension force. The experiments did therefore shown no increase in initial failure. Although the post-tension experiment did not succeed, still a GFRP reinforced beam was experimented and a different failure was observed. This different failure mode occurred due to the low stiffness of the reinforcement resulting in high crack opening and earlier failure of the system. The numerical analysis is done in Chapter 7. This chapter contains two parts, first the analysis part and secondly the validation part. During the first part a study is done on different parameter and design considerations. This study is based on an experimental data set from former research, this set is also used on a sequential linear analysis (SLA) and non-linear analysis (NLA) validation and is therefore the ideal case to advance the developments. A reference model is made based on starting points from previous research and each aspect is applied on this reference model to analysis the performance differences. This performance differences are analysed based on four aspects: Resistance, deformation, crack density and amount of cracks. After each analysis a conclusion is made using these performance aspects and is graded with respect to the reference case. Two major objectives in this study is to implement the lacking resistance of the SG interlayer and post-tensioning. For the interlayer, the characteristics of SLA are used to construct an equivalent post-cracked resistance using the reduction branches. The post-tension should be implemented as initial stress/strain conditions but as SLA is still in development this is not yet available. A two solutions are found based on the transformation of the material properties. Both result in the increased initial failure, but only one represents the post-cracked behaviour of a post-tension beam in the correct manner. The numerical models of the reference case and post-tension experiments are validated in the second part of this chapter. Initially the fibreglass fabric experiment were planned to be used as validation, but this is not done. Based on the complex behaviour of the reinforcement, numerical analysis of this experiment does not contributed to the objective. The validation of the numerical analysis is done based on the deviation which represents the difference in ultimate resistance with respect to the experiment. For the reference case the deviation in resistance and deflection to the experiments decreased when the findings are applied to the reference model. However the crack pattern is still an issue as T-shaped crack occurred where V-shaped cracks were expected. Also in the validation of the post-tension experiment this V-crack is not present, but due to the absence of SG the cracking pattern is lot more conform the observations in the experiment. This case not only has small deviations in resistance and deflection, but failed in equal manner as the specimen. All results are summarised and discussed in Chapter 8, from this discussion the conclusions regarding the stated research objectives in the outline are drawn in Chapter 9. In this chapter is concluded that the suitability of GFRP post-tensioning could not be validated due to the fault in the process and the low Young’s modulus resulted in higher crack opening and earlier reaching of ultimate failure. The fibreglass fabric did achieve a fair ultimate failure resistance but as they did not have a higher resistance as the initial fracture they did not pass the validation criteria. This was due to insufficient saturation of fibreglass with SG, causing the fibres to slip on one each other, hence not able to reach their full capacity. The analysis of different aspects using SLA resulted in a development in analysing method. Using a grading system the influences on the performance of each aspect are indicated. Creating insight of the influences of different design and modelling considerations. To finalise some recommendations are in place, as this is only the beginning of a broad subject. Obviously, it is recommended to research the third concept as this could not be included in this thesis, to even further develop the ideal reinforced glass beam. But regarding the post-tensioning, more effective systems are recommended as the initial failure increase in the post-tensioned design was quite low, for example, higher eccentricity and more stable structures. Solutions for higher saturation in the fibreglass fabric to decrease the slip and increase the resistance. Regarding the numerical analysis, implementation of SLA in 3D brick elements and a better more physical correct plasticity model are recommended. Next to these independent subjects reinforced glass in general requires the definition of different failure modes and the prevention of brittle failure modes. Also would it be important to perform force-controlled experiments, possibly in combination with an impact load. Since this is the major reason to apply reinforcements. More recommendations and conclusions are found in Chapter 9. So in conclusion all the independent subjects converge to the contribution in the developments in reinforced glass beams. The freedom and benefits in application of integrated fabric reinforcement are known and more knowledge is obtained regarding design of reinforced glass structures and influences of (in)correct numerical modelling.

Orthotropic bridges are being built for more than half a century. These bridges are prone to high cycle fatigue due to traffic loading. Early onset of fatigue cracking is a serious issue in both old and recently built bridges. To prevent this a number of different cross section have been suggested. Sandwich Panel is one of the suggested alternative that has become more feasible to produce due to advancement in Hybrid Laser Arc Welding (HLAW) technology. One type of sandwich panel with corrugated core was investigated in this thesis. Ease of manufacturing, stronger welds, reduced complexity of welding and improved transverse shear stiffness are some advantages of sandwich panel over conventional orthotropic decks. The aim of this thesis is to apply J-Integral based local approach for fatigue assessment of sandwich panels subjected to lateral loads. J-Integral represents a way to calculate the strain energy release rate and is a measure of crack tip elastic-plastic field. It has already been used successfully to quantify fatigue performance of web core sandwich panels and is therefore used in this thesis. A second aim of this thesis is to justify the use of foam filling in sandwich panels by comparing fatigue performance of empty and foam filled sandwich panels. For validation, bending behaviour of panel was first investigated using Finite Element Analysis (FEA). The model developed for dual stake laser welded panel accurately estimated response parameters (compared to experimental results of Tan et al. [33]) like maximum deflection (2.2% difference), critical stresses in transverse direction (9% difference) for top and bottom face plates etc. For verification of Contour Integral technique of Abaqus/CAE, J-Integral at notch tip of ASTM CT specimen was calculated. Compared with empirical solution the FE estimate showed 16% difference with FE estimate being more conservative. Seven different types of foam were considered as filling in sandwich panels. The foams were of polymeric type - H45, H60, H80, H100, H130, H180, H200, and H250 (Unit weight of foams - 48 to 250 kg/mኽ and Young’s Modulus - 45 to 250 MPa). Based on two stage 3D FEA on empty and foam filled sandwich panels, it was observed that J-Integral value at critical tensile notch decreased consistently as stronger foam fillings were used in the panel (83.8% reduction observed between empty panel and H250 foam filled panel). Cycles to failure for panels were calculated using regression equation derived from existing research on web-core sandwich panel. Between empty and H100 foam filled panel an increase of 171 times was observed in cycles to failure. This increase justifies the use of foam filling.

The orthotropic steel deck (OSD) is a deck system applied regularly in steel bridges all around the world. It consists of a steel deck plate which is stiffened by structural elements placed in two orthogonal directions. The deck plate can be used as an integral part of the structure, causing OSDs to achieve a high material efficiency and therefore low self-weight. However, this structural integration requires a large number of welded connections between the deck plate and stiffening members, which also make the system susceptible to fatigue. The fatigue evaluation of these connections is complex and time-consuming, hindering the manual optimization of orthotropic deck designs. The use of structural optimization could be a solution for this. With parametric optimization, the best possible ratio between structural dimensions may be searched for automatically, while topology optimization could assist in finding new design concepts that could form alternatives to the traditional deck layout. This thesis investigates how these techniques could reduce the self-weight of the design of a case study (the renovated Van Brienenoord bridge) without reducing its fatigue service life. The two methods are treated in separate parts. In the first part, considering parametric optimization, the traditional OSD concept is maintained and the values of seven selected dimensions are adjusted to obtain a design with a minimized weight. A workflow is developed in which an existing mathematical optimization solver (the artificial bee colony algorithm, a metaheuristic) is coupled to a parametric model, finite element program, and fatigue damage calculator. This enables an iterative process in which designs are generated by the solver and then evaluated in the remainder of the workflow. The information gained from the evaluation is returned to the solver and used to search for lighter designs. In the second part, the deck remains a stiffened steel plate, but the location and orientation of stiffeners may be changed. Two possible leads for finding new structural concepts are explored. The first considers a topology optimization using the ground structure method, which can find the optimal orientation and size of stiffeners in a plate. This thesis evaluates the method’s current applicability on steel bridge decks. The second lead interprets the results of a topology optimization from existing literature. This gives a new design concept in which the crossbeams curve directly towards the supports instead of being indirectly connected by main girders. A weight minimization using the workflow of the first part and a study of the force transfer in the deck are performed to assess the new concept’s potential. The first part showed that a 17,4 percent lighter deck structure (280 kg/m2 instead of 339 kg/m2 ) could be obtained for the case study by breaking with the general trend for designing orthotropic steel decks. The optimized design uses smaller and more rectangular troughs than commonly applied, but the largest differences are found in the deck plate thickness and stiffener spacing. For the latter, a value of 300 mm has been in use since the introduction of OSDs in the 1950’s and is present in almost any bridge using an orthotropic steel deck. When fatigue issues started to appear from the 1970’s onward, it was generally decided to increase the deck plate thickness. The results in this thesis strongly suggest that decreasing the stiffener spacing and trough top width is the preferred option when material efficiency is considered. A cost estimation further showed that the price of the optimized design would be comparable to that of the preliminary design that was suggested for the case study. The topology optimization using the ground structure method showed that the optimal placement of stiffeners for a plate-like bridge deck contains two distinctive zones. Between the supports, the traditional longitudinal-transverse orientation is preferred, while the optimal direction of stiffeners in the middle of the bridge segments is arbitrary. The conventional OSD concept could be seen as optimal based on this result, but for definitive conclusions more research is needed towards a non-linear relation between cross-sectional area and resistance in the applied method. The similar support conditions of decks in other bridges make it likely that these conclusions will apply to those cases as well. The optimization of the curved crossbeam concept showed the versatility of the workflow developed in the first part of this thesis, as only minor adaptations in the parametric model were needed for the application on a significantly different design. Despite the successful optimization, the potential of the new design to replace the traditional OSD concept is considered low. In its optimized form, the concept was 9,8 percent heavier and less than half as stiff as the best found result in this thesis’ first part. The comparable support conditions for plate girder bridges in general again suggest similar outcomes for other cases, while a different setup of the optimization would not tackle the fundamental stiffness problem of the design. Further research towards the curved crossbeam concept should therefore stick to the original application of box girder decks.

In light of the global attempts to reduce material use by the construction industry, this research focuses on combining topology optimisation with additive manufacturing of steel. It is investigated whether an automated procedure can be developed to generate reliable strut and tie models for reinforced concrete elements, while satisfying the constraints that apply to 3D-printing using the Wire and Arc Additive Manufacturing(waam) technique. Additive manufacturing offers a fully automated production process where a large freedom in form can be achieved. Topology optimisation concerns with finding a good material distribution within a prescribed domain. A literature review was performed on current developments regarding both subjects. It was found that the waam-technique is very suitable for printing reinforcement designs. Sufficiently large models can be printed, and material properties can be achieved that match the properties of traditional reinforcement steel. This manufacturing process is expected to produce functional structures that can readily be used as reinforcement steel in buildings. Two main manufacturing constraints should be accounted for during design of the model. A minimum member inclination and a minimum member diameter are both expected to be necessary to ensure a smooth printing process. Several different topology optimisation algorithms are discussed in the second part of the literature review, and it is determined which algorithm is most suitable to continue with in the rest of this research. Examples are presented that explain the functionality of three important optimisation schemes: Bi-directional Evolutionary Structural Optimisation(beso, Solid Isotropic Material with Penalisation(simp) and Ground Structure Optimisation(gso). It was found that all three can be used to analyse reinforced concrete. Each algorithm has advantages and disadvantages, so there is no obvious best choice. However, motivated by the easy access to member forces and availability of a very good Python implementation, it is chosen to use gso for the remainder of this research. This Python script was modified to include the constraints that come with an additive manufacturing process. It was found that the minimum member inclination can straightforwardly be included. The new function that was proposed allows the user to specify a minimum inclination, and ensures that no members are generated within the design domain that violate this minimum angle. Experimenting with this new function revealed cases where material use increased significantly when this function was used. This lead to development of an alternative procedure to ensure a printable design. In this alternative procedure, an optimisation without any angle constraint is performed first. Then, in the form of a post-processing script, The complete model is rotated around two separate axes in an attempt to find a suitable printing orientation. The third and final proposition that was done in this part, consists of a post-processing script for the minimum member diameter. Including this minimum diameter in the optimisation would require rigorous changes to the optimisation script. Therefore it was chosen to investigate the performance of this post-processing script first. The case study that was performed in the third part of this research, proved that this post- processing script for member diameter is sufficiently efficient for practical implementation. Together with the ability to slightly suppress the amount of members that are generated in the design domain, the printing constraint for minimum diameter could relatively easily be enforced. A bigger challenge lies within ensuring the minimum member inclination. The 60◦ minimum that was set, proved to be very harsh on the solution space. In the example from the case study, no printable model could be generated without significantly reducing the material efficiency. However, it is argued that this minimum inclination constraint can possibly be relieved by recent developments in additive manufacturing techniques. An example of this could be a rotating printing surface, that has the potential to remove this angle constraint completely. Overall, the experience of combining topology optimisation, additive manufacturing and strut and tie modelling has been predominantly positive throughout this research. The combination of a state of the art manufacturing technique and a more performance driven design process with a labour intensive traditional calculation procedure has shown promising first results. In the example in this research, 30% less material was required to accommodate the tensile forces in the concrete.

Nowadays, Rijkswaterstaat reassesses many older concrete bridges to guarantee their structural safety under the influence of increased traffic loads and stricter standards. Many of these concrete bridges contain open straight-legged stirrups, which are not allowed to take into account for the calculations of the shear resistance according to current standards. This often results in theoretical insufficient shear capacity and critical damage to structures, but this is not observed in reality. This indicates that the open straight-legged stirrups probably do contribute to the shear resistance, where an accurate assessment of this contribution could prevent unnecessary and costly structural safety measures. However, very few shear tests with relevant cross-sectional dimensions are performed and documented in literature, especially tests containing open straight-legged stirrups. The application of Nonlinear Finite Element Analysis (NLFEA) is a useful tool to evaluate and understand the behaviour of structures, but provisions for the implementation of open straight-legged stirrups in concrete structures are lacking. Thus, the goal of this research is to provide a finite element modelling strategy that is able to accurately describe the behaviour of concrete beams with open straight-legged stirrups subjected to shear. The research focusses on describing the behaviour of rectangular concrete beams with open and closed straight-legged stirrups with finite element models using DIANA 10.5 [1]. Schramm [2] has performed multiple shear tests on prestressed concrete beams with several no longer permitted stirrups, including open straight-legged stirrups. He found that open straight-legged stirrups can significantly contribute to the transfer of shear forces [2]. The relevance of the rectangular test beams for comparison with box-girders is validated in this thesis, where the stress distributions in a linear elastic rectangular and box-girder cross-section due to axial forces, bending moments, shear forces and torsion are compared. In the interest of providing a suitable solution strategy, Schramm’s test beams with closed and open straight-legged stirrups are reproduced with 3-dimensional nonlinear finite element models based on the recommendations of the RTD1016-1 [3], where the influence of various modelling considerations is investigated. The concrete is modelled with a smeared total strain-based crack model with the Hordijk tensioning and parabolic compression relations, including confinement and lateral cracking effects. Reinforcements are modelled as embedded truss elements with the Von-Mises plasticity model. To describe the accurate anchorage behaviour of the open straight-legged stirrups, the interaction between the surrounding concrete and the stirrups is described with the Shima bond-slip relation. The finite element model is first calibrated with a beam with closed stirrups, where modelling clamped restraints with supports on both sides of the beam result in a too-stiff response. By allowing a little rotational freedom in the form of boundary springs, the stiffness of the beam is manipulated without changing the overall load-bearing behaviour...

In the construction of subsoil structures, a common challenge is the presence of a high groundwater level in combination with the absence of a naturally impermeable layer or an environment susceptible to settlements due to lowering the groundwater level. To overcome this issue, a building pit with an underwater concrete floor (UCF) can be constructed. The UCF ensures structural rigidity and allows for the building pit to be drained such that a dry and safe subsoil construction site is obtained. The objective of this thesis is to investigate how design efficiency of underwater concrete floors can be improved. In an effort to reduce material usage and achieve cost-effective structures, the following research question was stated: “What is the influence of design parameters and how can parameters be adjusted to improve design efficiency of an underwater concrete floor, and to what extent can the addition of fibre reinforcement contribute to this optimization?” A parametric model was developed to provide insight to the sensitivity of parameters and their impact on design resistance. Furthermore, the model was utilized to examine under what circumstances potential material savings can be obtained by implementing fibre reinforced concrete in UCF’s. This was accomplished through the evaluation and comparison of the minimum required thickness based on bending moment resistance in various scenarios, for both UCF’s and steel fibre reinforced UCF’s (SFUCF). Results obtained with the parametric model established that, in order to enhance the bending moment resistance of an uncracked UCF, increasing the nominal thickness becomes relatively more effective compared to increasing the concrete strength class for higher normal forces. When utilizing a compression arch to obtain bending moment resistance, the implementation of ribbed tensile elements or an increase in nominal thickness are found to be the most suitable methods for increasing resistance. For enhanced shear force resistance, increasing the nominal thickness over the concrete class provides relatively more additional resistance for slender UCF’s. The results found that through the application of ribbed piles, most punching shear force resistance can be obtained. Three use cases for a SFUCF were identified using the parametric model. When centre to centre (c.t.c.) distances larger than 4.4m are applied in combination with a substantial normal force, significant material savings of up to 0.3m thickness are possible, which equates to a reduction of material usage by 30%. For situations where the effective height of the compression arch is small, it was also found that material usage could be reduced by 30%. Perhaps the most significant use case for a SFUCF is when the normal force is close to zero, and additional normal force cannot be obtained through membrane action. In these situations, the application of a SFUCF can make an otherwise near impossible project feasible. As a new design approach, a cost-based optimization tool was developed using the parametric model. An already executed UCF was evaluated using the tool, it was determined that a more cost-effective design could have been achieved, with potential savings of up to 30% in costs.

An exploration into the stability of 3D printed thin-walled concrete elements during manufacturing is presented. The failure mechanisms, material parameters and analysis methods are presented. Self-buckling is the dominant failure mechanism, where the Young's modulus plays an important role. Material experiments to assess the Young's modulus are performed and presented. Predictive analysis methods to evaluate the printability of objects are discussed, where finite element modelling and the mechanistic model of Suiker are compared.

This research studies the experimental and numerical behaviour of a simple beam to column joint using a fin-plate welded to an rectangular hollow core section. The following aspects of the joint are investigated: The resistance of the welded connection. Defining the force distribution inside the joint. Improvement of the design method for resistance of the fin plate connection. Four series of controlled experiments are conducted to test the joints until failure. The series combine a S355 plate with S690/S355 column grade and matching and overmatching weld material. With the data from these experiments and coupon tests, a finite element model is created using DSS Abaqus. Results are validated to accurately follow the force-displacements obtained in the experiments. Key findings from the experiment: The resistance of the welds was found to be much greater than predicted using the nominal values from the Eurocode. The utilization of the nominal design resistance compared to the failure load in experiments was 19% following EN1993-1-8:2005 and 25% with EN1993-1-8:2020. The main reason for this was the high penetration depth and increased weld throat when welding a 3mm weld according to standard procedure, accounting for a 100% increase in resistance. The second reason was that the failure stress was 50% higher than nominal for both the matching and overmatching infused weld material. Insights from the finite element models: It was proven that for certain boundary conditions it is possible to only account for shear transfer through the weld. However it was found that when expanding the Abaqus model to a full building size the boundary conditions change such that also a moment needs to be transferred through the weld and the bolts. The ratio between the stiffness of the beam and the column face determines the magnitude of these moments. The addition to the stress in the start and end of the weld can result in a 75% lower design resistance when comparing to the same weld with only a shear load. The bolt group transfers the moment through horizontal forces, again depending on this ratio. The magnitude of this horizontal force component in the outer bolts can be equal to the vertical component. The following calculation methods were proposed: The moment transfer through the weld from bridging the bolts eccentricity can be reduced according to the stiffness ratio R between the beam and the column face. There are four stiffness factors which influence the force distribution; The column stiffness K_c, the column face stiffness K_cf, the plate bearing stiffness K_p and the beam rotation stiffness K_b. It was found that the governing influence comes from the face stiffness and the beam stiffness. The face stiffness can be calculated by integrating the resistance over the effective length of the column h_p. If there is no yielding in the beam cross-section then the problem can be simplified and welds should be calculated with taking into account the shear force V_ed and the bending moment M_ed which follows directly from the stiffness ratio R.

A series of critical transmission lattice towers failures due to severe ice and wind loads forced German utility companies to reassess the structural stability of their power grid infrastructure. During the structural reassessment process, a problem related to an outdated or even missing documentation of the in-use infrastructure occurred. This issue forced utility companies to gather the data regarding the geometry of the lattice towers on-site, using specialized and labor-intensive geodetic measuring methods. The scale of the required data acquisition endeavor and stability checks to be performed encouraged the use of alternative methods to capture the geometry of the in-situ structures and reconstruct geometric models to be applied during the structural stability checks in a reliable and efficient way. This work presents an innovative method to generate a geometric CAD model using point cloud data captured by a LiDAR scanner. The CAD model can be later implemented for FEA utilized during structural stability assessments. The modeling process defined in this study is fully automatized, enabling to obtain repeatable results and save the time required for manual data processing. For the input point cloud data, two types: Aerial and Terrestrial LiDAR point clouds have been investigated allowing to identify the applicability of both data sets for the proposed method. The model generated with the automatic method proposed in this study is compared in terms of geo-metric discrepancies to an idealized model based on design documentation and a LiDAR point cloud based model manually generated with a commercial software. The two models used for comparison depict a traditional structural engineering approach and a state-of-the-art method within the point cloud processing field accordingly. At the final stage of this work, the automatically generated point cloud based model is used for a non-linear FEA and compared to a FEA response of the idealized mod-el. Results showcase that LiDAR point cloud data is a good source of geometric information to reconstruct a geometric CAD model which can later be implemented in FEA. Obtained results are comparable to the ones of an idealized model based on design documentation in terms of collapse mechanism and ultimate load applied at the failure step. Additionally, the geometrical comparison between the point cloud based models generated with the manual method and the one proposed in this work underline the ad-vantage of the automatic method in terms of permissible level of detail and overall precision of the final geometric model. What is more, the impact of point cloud data usage for FEA modeling is shown. Investigating differences between FEA results of the point cloud based and idealized models allow to showcase the influence of real life imperfections on force redistribution across the analyzed structure and ultimate forces reached by members loaded in compression. The modeling method and analysis results presented in this work can be applied as a set of guidelines for future applications related to point cloud data processing of steel lattice structures used for FEA modeling purposes.

Uncertainties regarding structural safety of reinforced concrete structures may warrant a need for a detailed assessment. A detailed assessment using nonlinear finite element analysis is one of the alternatives which could help in decision-making about maintaining, upgrading or even demolishing and rebuilding of the structure. A reliable assessment should account for the existing damage in the structure, which may cause re-distribution of stresses within the structure, giving rise to unexpected failure modes. The existing approaches in nonlinear finite element analysis which account for the effect of already undergone damage in concrete, pose a number of limitations which either makes structural analysis ambitious or the uncertainty of concrete damage is not effectively accounted for. An alternative approach is adopted in this thesis, which is phenomenological and probabilistic in nature. Existing damage in concrete is conceived as a statistical field, which can be input into a finite element model, such that the existence of damage is taken as the starting point of the structural analysis. Focusing on indications of damage on the surface of concrete, i.e. crack patterns, an exploratory methodology based on image analysis is developed, to account for information obtained from crack pattern observation into nonlinear finite element analysis of reinforced concrete structures. The methodology is implemented on MATLAB and validated on damaged experimental specimens. Results of the computational analyses indicate good efficiency in predicting residual load carrying capacities and failure modes, alongside insightful numerical crack patterns. Through a critical examination of the obtained results and reflection upon the assumptions and simplification made in the methodology, recommendations for future research are provided.

The innovative shear strengthening method using externally bonded CFRP reinforcement to strengthen prestressed concrete I-girders has been investigated in this thesis. These girders potentially have insufficient shear capacity because of the combination of thin webs and insufficient shear reinforcement. Shear failure of these girders should be prevented because they do not warn before the element fails in shear. Shear strengthening using externally bonded CFRP reinforcement seems promising because of low installation costs, negligible increase in weight, no decrease of clear height underneath the bridge and minimising the hinderance. The aim of this thesis is to investigate the feasibility of shear strengthening prestressed concrete I-girders using externally bonded CFRP reinforcement. The shear behaviour of prestressed concrete I-girders strengthened using externally bonded CFRP reinforcement has been investigated with the nonlinear finite element analysis (NLFEA) software DIANA. A three-dimensional finite element model of a 1.0 m high prestressed concrete I-girder with a kinked tendon profile and no shear reinforcement has been made to investigate several parameters and aspects of the CFRP reinforcement. Shear strengthening of prestressed concrete I-girders with vertical CFRP sheets and CFRP anchors is a feasible strengthening method because of the demonstrated potential increase in shear capacity. The externally bonded CFRP reinforcement was especially effective to increase the flexural shear capacity of prestressed concrete I-girders. The numerical analysis showed a promising increase in flexural shear capacity between 40-55% and an increase in ductility of more than 80% compared to the I-girder without CFRP reinforcement

During the early stages of the construction process of a building, the potential impact of design decisions is at its greatest. One of the reasons is the lack of computational tools at these stages. The main objective of this research project was the expansion of StructuralComponents by the development of a parametric real-time computational tool prototype to quickly determine the feasibility of mid-rise buildings designs with rigid frames as stability members. A study of rigid frames behaviour was performed to define a range of applicability of the existing analytical representation and to develop two new methods to analytically represent rigid frames behaviour: a correction method for the shear beam representation and a method based on the Timoshenko beam theory. To allow for vertical connections of different rigid frame geometries, an analytical method to consider a different stiffness along the height was developed. The results showed that the analytical shear beam representation of rigid frames has a reduced range of applicability for parametric purposes. This reduced applicability is due to the combined shear and bending behaviour. The correction method follows from the prediction of the error when using the shear beam representation. In addition to the correction of the shear beam representation, the prediction of the error was defined as a parameter to classify the behaviour of a rigid frame as a shear, flexural or combined type. Both, the applicability range and the correction method are based on analytical and numerical comparisons, as well as the performed validations. The implemented software comprises Maplesoft to get the analytical solutions and Grasshopper with Karamba3D (which contains the finite element solver) to get the numerical solutions. The method based on the Timoshenko beam theory comes from the theoretical derivations of a serial system that takes into account both, bending and shear deformations. It was found that it is more appropriate to analytically represent the general behaviour of rigid frames with the Timoshenko beam theory and by additionally considering a different stiffness calculation for the ground floor. Also, it was shown that the vertical connections of rigid frame geometries can be addressed with the calculation of an analytical solution for each different geometry along the height. Both analytical approaches, the Timoshenko beam representation and the method for vertical connections were implemented in the tool prototype. Such a tool consists of a calculation method to assess the structural performance of a building by the simultaneous structural analysis of every rigid frame subjected to a lateral load. The three main characteristics of the tool prototype are the parametric adaptability, the instantaneous display of results and the stacking “Lego-type” connection between components. The validations in this research project showed that the proposed and implemented methods are suitable for preliminary design stages because the error for the most unfavourable geometric configurations resulted in less than 15 percent. It is recommended to conduct further research and tool development. In so doing, more informed decisions can be made during the preliminary design stages.

On the 17th of October 2021, a concrete grandstand element collapsed at the Goffert stadium in the Netherlands after a crowd jumped on it for 8 seconds. An investigation by an engineering consultancy firm concluded that the design loads in the building code are too low, raising questions about the safety of grandstand elements. Currently, no method to assess the reliability of grandstand elements exists. This thesis presents a state-of-the-art method to determine the reliability of concrete grandstand elements. The reliability is assessed by performing a non-linear dynamical analysis. The element is modelled as a non-linear single-degree-of-freedom system. Excitation signals are synthetically generated by consulting the literature and by analyzing a data set of jumping crowds. A bi-linear force- displacement relationship based on technical drawings of the collapsed grandstand element is adopted and extended by a model uncertainty parameter which accounts for both the non-linearity of the analysis and the uncertainty related to the dynamical basis of the analysis. The reliability is determined through a Monte Carlo simulation: almost 100,000 simulations can be performed per assessment. Out of the 100,000 simulations, 0 failed. This result is not in line with what happened; one failed out of only a few elements. This gives rise to two different investigations. On the one hand, the failure of the Goffert stadium grandstand elements has to be explained. On the other hand, the lifetime reliability of a grandstand element has to be determined. The first assessment indicated that if the element’s resistance conforms to the technical drawings, there is no cause for concern regarding its reliability. Measurements on 23 other grandstand elements in the same stadium showed a high variation in the concrete cover. The collapsed element was, therefore, also likely subjected to a high variation in the concrete cover. To understand the influence of an increased concrete cover on the reliability, two additional analyses were performed, where the post-yielding resistance of the structure was slightly reduced. This resulted in an increase in the probability of failure, which indicates that this parameter plays a crucial role in determining the reliability of grandstand elements. These points combined make it more plausible that the element failed because the concrete cover was larger than intended rather than the design loads being too low, as concluded by the engineering firm. When investigating the lifetime reliability of grandstand elements in general, no collapse is expected after 8 seconds but rather after 30 seconds or even longer durations. Therefore, two additional analyses were performed where signals of longer durations (120 seconds and 300 seconds) excited the system. In these analyses, it is assumed that the resistance of the grandstand element conforms to the technical drawings. Signs of a converged reliability were perceived as 120- and 300-second excitation signals led to a probability of failure of the same order of magnitude, indicating that a steady-state solution is obtained after 120 seconds of jumping. In that case, the lifetime reliability of a grandstand element would be equal to the 120-second reliability. The corresponding reliability passes the lifetime reliability requirements for existing structures in consequence class 2 (for a reference period of 15 years). While the results presented are estimations, and a larger sample size is needed for a converged probability of failure, the proposed method provides a valuable framework for assessing the reliability of grandstand elements. This method can easily be extended to any grandstand element by changing the model parameters, and the true reliability of grandstand elements can be assessed by performing more (1-10 million) simulations.

Existing sophisticated numerical micro- and macro models have already proven to be capable of simulating typical masonry behaviour. However, assessing the global response of masonry buildings using brick-to-brick micro modelling or even simplified macro modelling, in which masonry is regarded as a continuum material, takes such an amount of time that these methods cannot be considered as cost-effective. For the last two decades it has been recognized that, for the global structural behaviour of masonry buildings, simplifications have to be made. The idealization of a masonry wall as an assemblage of numerically integrated (or fibre) beam elements could considerably reduce the computational burden and therefore this study addresses the following research question: To what extent are numerically integrated beam elements applicable for assessing the global response of masonry structures? Whereas existing equivalent frame methods are usually based on lumped plasticity models, the approach discussed here considers the entire member (e.g pier or spandrel) as an inelastic element in which the sectional response is evaluated via a fibre discretization in which each fibre (or integration point over the depth) may follow a material uniaxial nonlinear stress-strain relation. Initially the shear response is kept linear, automatically idealizing the structural response as purely flexural. The proposed model will be hereinafter named FFM (Fibre Flexure Model). Additionally, an extension of the FFM has been proposed, describing the shearing behaviour by means of a structural nodal interface element. Adopting the nodal interface element, placed between two nodes of adjacent beam elements, the axial and bending behaviour is described with the fibre-section discretization and the shear behaviour is modelled via an equivalent Coulomb-type criterion describing the shear force limit. The proposed model will be hereinafter named FF-LSM (Fibre Flexure – Lumped Shear model) because it lumps shearing nonlinearities in one single interface element located in the centre of the structural component, whereas flexural and crushing behaviour is evaluated via smeared crack beam elements. To validate the numerical models, two different types of benchmarks have been investigated, respectively representing the behaviour of either a single structural component (masonry pier) or a composite façade. All numerical models have been subjected to static nonlinear (pushover) analyses and results have been compared with experimental and numerical data through the use of a reference continuum model. First, it has been demonstrated that the FFM, idealizing the structural response as purely flexural, is capable of simulating the rocking failure mode of unreinforced masonry walls, whereas it fails to simulate typical masonry shearing modes such as diagonal cracking and sliding. The use of the model for squat members that are characterized by shear failure leads to significant overpredictions, making the model not applicable for the analysis of masonry structures containing relatively squat structural components, having shear span to depth ratios less than approximately 1. Second, the shortcoming of the FFM regarding the shearing failure mode has been overcome by combining the numerically integrated beam elements with a structural nodal interface element describing the shear behaviour. The FF-LSM including the nodal interface is able to correctly predict the shear capacity of both slender and squat walls, although the observed level of accuracy depends largely on the adopted shear failure criterion. Various shear force criteria (Coulomb friction based) have been considered: the Mann and Muller (1982) criterion, the correction proposed by Magenes and Calvi (1997) and the modification according to Abrams (1992). Generally it was observed that the criteria developed by Abrams (1992) was the most accurate and that especially for a decreasing shear ratio the criterion developed by Magenes and Calvi (1997) appeared to be less precise. Third, analysing a composite façade, with respect to the reference continuum model the FFM and FF-LSM significantly reduce the number of elements, nodes and integration points, consequently minimizing the computational effort and maximizing the computational robustness. In comparison with the corresponding continuum model the computational time decreases by a factor of approximately 10. Despite the limitations of the FFM regarding the shearing failure mode, the model shows an acceptable accuracy in terms of initial stiffness, stiffness reduction and peak strength. Adopting the FF-LSM the numerical model predictions were significantly enhanced and both flexural and shearing failure modes (in piers and spandrels) were detected correctly. Therefore, the result of the investigation has proved to be very promising as with the FF-LSM an acceptable balance between computational cost and accuracy is found, applicable to the global analysis of two dimensional masonry structures constituting slender as well as squat walls. As many problems in engineering practice require solutions in three-dimensional space, a fully three-dimensional extension of the FF-LSM is highly recommended.

The offshore renewable energy market is rapidly growing, particularly in wind and solar sectors. The intermittent nature of these energy sources underscores the necessity for offshore energy storage solutions. Among the techniques being explored, Marine Pumped Hydro-Energy Storage (MPHES) emerges as a promising option. This innovative concept operates similarly to artificial lakes, where water is stored and released to generate electricity. In the MPHES system, a seabed-based reservoir is established, in which water flows, driving turbines to generate electricity. During periods of energy surplus, the system is charged by pumping water out of the reservoir...

The Oscillating Water Column (OWC) device is one of many available technologies for generating electricity from water waves. It is a caisson-like structure, which houses a water column in an enclosed chamber with an inlet at the bottom. Waves enter the device, exciting the water column. The trapped air above is forced out through a turbine, generating electricity. The technology is relatively young compared to other sources of renewable energy, such as solar or wind energy. This makes the produced energy expensive, expressed in the Levelised Cost of Energy (LCOE). Integrating devices into breakwaters already resulted in a large reduction of the costs, as they now can be shared. During the design of such devices, main attention is given to the geometrical design. This should be based on local wave conditions to ensure the largest energy production. Having the eigenperiod match with the incident wave period enhances the resonance effect in the chamber. This research explores the potential to reduce the costs of OWC devices integrated in breakwaters through means of structural optimisation. The structural are built quite robust, leaving the thought there is room for improvement. The device in Civitavecchia, Italy was used as a case study. A new method was adopted to investigate the potential. A numerical model was constructed in STAR-CCM+, including both a fluid domain and a solid domain. The two are one-way coupled, from water to structure. The exerted wave pressures are mapped on the structure directly, resulting in a stress state in the OWC structure. Due to the transient nature of the simulations, all results are available through time. It was found, the main walls shaping the OWC device could be built with 35% less material. Variants of the original geometry were tested as well to see how these influence the results. Furthermore, the structural behaviour was investigated. Clear trends were found in position and timing of governing load combinations in the different walls. One of the most important findings was that the governing load case always was in the direction of the transverse width. The walls were found to behave more like beams in this direction. The bending moments could therefore easily be calculated using standard beam equations and the net horizontal pressure on the wall as load. This leads to the beginning of a new simplified design method where the full numerical structural analysis is not required anymore.

Theshortage in housing and office spaces, combined with the desire of people tolive in densely populated cities results in a lack of space. A proposedsolution can be found in the usage of high-rise buildings. Nowadays there ismore awareness for the environment, thus this research tries to reduce theenvironmental impact of a high-rise building by optimizing the material used inload-bearing structures. This research aims to give designers and engineersmore insight into the added value of structural optimization; in particular forthe material usage in the load-bearing structure of high-rise buildings. Theresearch objective is formulated as follows: What is the optimal topology for a reinforced concrete load-bearingstructure, situated at the perimeter of a high-rise building when optimizingthe material use?  A building isclassified as high-rise building when its roof is 70 m or more above groundlevel and accommodates work and/or living space. In literature the distinctionis made between three sorts of optimization: size, shape and topologyoptimization. Topology optimization has the most freedom, therefore it is morelikely to find a novel structure which minimizes the material use as much aspossible. In specific the Ground Structure Method (GSM) is used. The initialground structure is constructed by creating members between all nodes (fullconnectivity) which are located in the design space. The cross-sectional areasof the bars are the design variables in the optimization. An option is that thevariables turn to zero, thus elements are deleted resulting in less material.The conventional GSM starts with the full connectivity as initial groundstructure, deletes elements and calculates the new load distribution until athreshold is reached. In the end the load-bearing structure will consist ofcolumns, braces and beams, which are located at the perimeter of the floorplan. Literature indicates that (high-rise) buildings which are mainly loadedby horizontal loads would be optimal if they contain arches in the load-bearingstructure, or resemble the so-called Michell truss. However, the influence ofthe vertical load is often not taken into account, therefore this isinvestigated with the help of a parametric study. To compare the results withreality, a case study (Boston & Seattle, Rotterdam) is investigated.   The core of the research is the furtherdevelopment of the optimization code, based on the GSM, written by He et al.,where multiple load cases and demands for the material strengths are implemented.In contrast to deleting elements, the code uses an adaptive ‘member adding’scheme, which is firstly proposed by Gilbert and Tyas. This scheme solvesproblems faster than the conventional GSM, up to 8 times, and is able to solvelarge problems. This code is extended during this research with new functionswhich implement demands for fire, second-order, buildability, flexural bucklingand stiffness. Also it is possible to add self-weight to the optimization. Thestiffness is implemented by adding a constraint to the displacement of the topof the building, wherefore a recursive resizing algorithm is written based onthe article of Chan. Thus the extended code exists of two optimizations, firsta strength optimization and afterwards a stiffness optimization. The code iswritten in Python and for the purpose of post-processing exporting the data toExcel and Abaqus is possible.  With thehelp of the extended code, two design spaces are investigated. One design spaceis smaller, such that the computational time is low and many variations can beexamined during the parametric study on the total vertical to total horizontalload ratio (v/h-ratio). The other is based on a case study for comparison witha realistic situation. The verification of the code shows that the extrafunctions work properly for the investigated problems. If the functionsconcerning the stiffness optimization, inclusion of self-weight, fire,buildability and second-order are used, the extended code becomes unstable andthe computation time increases enormously when optimizing the case study.Therefore it is chosen not to include during obtaining the results. The resultsof the parametric study shows an expected pattern for the load-bearingstructure, for a v/h-ratio below 4. The pattern consist of arches, originatingfrom the Michell truss. The optimization of the case study, subjected to onerealistic load combination, showed no clear pattern for the load-bearingstructure. Post-processing steps, based on engineering judgement, are taken toclarify the solutions, which showed that the columns above the supports shouldbe large in comparison to the other elements and that the arches are the mostoptimal structure. Therefore an “optimized” load-bearing structure consistingof arches is proposed. The analysis of the “optimized” load-bearing structureshows us that most of the elements meet the strength requirements. To find theoptimal solution an iterative process would be needed, because increasing thecross-section of an element will decrease the stress but increase thestiffness, thus attracting more load.   Thedifference between the optimized load-bearing structure and the originalload-bearing structure of the case study is that the optimized uses archesinstead of (punched) structural walls and uses less material (±3%). From thepost-processing of the results it is concluded that increasing the strengthratio (compression to tensile) to 1.0, decreasing the total v/h-ratio orignoring the rigid-diaphragm working of the floor help clarify the results ofthe optimization.   This research extendsthe current literature with extra insights in the use of the Ground StructureMethod in an optimization code. Also, it confirms that the arches (originatingfrom Michel Truss) is an efficient manner to transfer the loads to thesupports. However, more research in the influence of the supports, the designspace and the material type on the clearness of the optimal solution is needed.  The advice for designers and engineersis to see what the possibilities are for arches to use in their load-bearingstructure, because these are efficient in transferring the loads so materialcan be saved. The current version of the code needs to be made more userfriendly, stabler and faster before it is recommended to be used by designersand engineers. The extended code is a first attempt to implement multiple rulesfrom the Eurocode in a optimization code.  

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.