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Onderzoek en dataverzameling en -analyse m.b.t. vervormingsmetingen bij afgezonken tunnels. Onderzoek naar het gedrag en de capaciteit van de segmentvoegen/dilatatievoegen van de Kiltunnel.

For the thesis the mortise and tenon joint between the rear post and cross beam in a wooden mitre gate is researched. The joint is an important part of timber lock gates. The force distribution inside the joint and the strength of a tenonned beam are two main focus points.

New and current materials for bridge bearings are subjected to tests, according to the European Standards (NEN-EN 1337). With these tests the materials are not subjected to forces, displacements and rotations that are similar to those in practice. In order to give a critical opinion about the tests, it is necessary to obtain more knowledge about the variable load and movement history of bridge bearings of a concrete bridge, the ‘Dintelhavenbrug’. The load and movement history of bridge bearings of the ‘Dintelhavenbrug’ are analyzed by means of a finite element model. In this model the loads caused by traffic en temperature are considered. The traffic loads follow from a fatigue load model with 12 types of trucks, based on the European Standard for traffic loads (NEN-EN 1991-2) and measurements of traffic on the bridge near ‘Moerdijk’. The temperature loads follow from the European Standards (NEN-EN 1991-1-5). For both types of (static) loadings the forces, displacements, rotations and slide paths, which occurs during the lifetime of the different bridge bearings, are determined for each bearing. These results are compared with the values which are presented in the tests of NEN-EN 1337 Part 2: Sliding elements and NEN-EN 1337 Part 5: Pot bearings.

Today, timber structures are receiving attention more and more. Because of the increasing interest in sustainable construction as well as for other reasons, building industry in Europe is (re)-discovering multi-storey timber structures for construction of mid-rise buildings. In this master’s thesis, an analytical calculation method and modelling approach are presented, to calculate the timber-frame shear-wall racking stiffness. With the research, a specific gap in engineers knowledge is completed, and a contribution is made to the development of multi-storey timber-frame structures in the Dutch context of building engineering.

In this thesis the structural feasibility of a high-rise core composed of precast elements is studied. A core composed of precast elements differs from a cast in situ core in having connections between the precast elements. From preceding research (Falger, 2003) the stiffness reduction due to the horizontal joints and the open vertical joints can be estimated. There is however no literature available on the structural behaviour of precast corner connections. Since corner connections determine the degree in which the flange core walls are activated more research is required on the structural behaviour of precast corner connections. Therefore the focus of this thesis is on the influence of precast corner connections on the lateral deflections of a core.

Due to the increasing demand of transparency in buildings, it is no longer unusual to apply transparent elements into the bearing structure. Glass is a strong but very brittle material, which means safety is rather problematic should it break. Safety is an issue that has to be improved before glass can be considered suitable for structural elements. Earlier studies have shown that reinforcing glass beams will provide reasonable residual load-bearing capacity, which could provide this safety. Glass fibre is suitable as reinforcement material when the transparency is regarded as important. In February 2009 at the Faculty of Architecture at Delft University of Technology, P.C. Louter designed and tested a laminated glass beam with embedded glass fibre rods. The bonding interlayer consisted of SentryGlas foil, developed by DuPont and often applied for lamination in hurricane-resistant windows. The results were promising and the concept showed high potential for further research. The study of this thesis project is focussed on improving the concept of embedding reinforcement in laminated glass beams.

Structural bearings are connections between the substructure and superstructure of the bridge and may allow translations and rotations. They also transmit the external forces, acting on the superstructure, to the foundation. In the past years the traffic loads and intensity on the European traffic system has continuously increased. Bridge bearings are therefore more subjected to the wear. Structural bearings are not only designed and fabricated according to the European standards NENEN 1337, but they are also tested according to these standards. The bearings are however not tested with the forces, translations and rotations which occur in practice. To make a critical judgement regarding these standards, the wear behaviour of a large arch bridge, the first Van Brienenoord Bridge, is analysed. The analysis is performed by means of a linear elastic, finite element model. The bridge model is then subjected to a modified fatigue load model based on the European standards for traffic loads NEN-EN 1991-2 and traffic measurements at the Moerdijk Bridge. Translations and rotation were consequently found along with the simultaneously occurring reaction forces. These results are compared to the qualification tests included in parts 2 (Sliding elements) and 5 (pot bearings) of the European standards for structural bearings.

When analyzing three-dimensional problems with nonlinear finite element analysis (NLFEA) often problems are encountered such as bifurcation and divergence of the solution. In particular, cases subjected to tension softening tend to encourage the emergence of multiple equilibrium paths. In order to overcome these problems the Sequentially Linear Analysis (SLA) method has been developed for three-dimensional solid elements. SLA is an alternative for incremental-iterative solution schemes to model the nonlinear fracture behavior of quasi-brittle materials. It is an attractive method since it avoids the well known convergence and bifurcation problems that are often encountered when using incremental-iterative schemes such as Newton-Raphson. SLA uses a series of linear analyses to model the nonlinear behavior of the structure. By directly specifying a damage increment in each linear analysis, extensive iterations within the load or displacement increment can be avoided. The main objective of this research was to see how the Sequentially Linear Analysis approach could be extended to solid elements, so that it could be used for three-dimensional fracture problems as well. Although three-dimensional geometries such as masonry structures have been analyzed before using SLA, it was always restricted to two-dimensional finite elements only (shell elements). Therefore, first a theoretical constitutive model for three-dimensional stress-strain states has been developed that served as the starting point. Implementation in DIANA was the major second step from which the third and last step could be started: the verification on various fictive and real cases. A single element pull test was used to solve programming errors, whereas the notched beam offered the possibility to check how the newly developed SLA-code would perform for larger models. Both cases showed excellent agreement with the experiment. However, most attention was dedicated to the verification and physical interpretation of a real reinforced concrete slab. The results were critically evaluated, interpreted and compared to results from the experiment and the incremental-iterative Newton-Raphson method. It was concluded that the Sequentially Linear Analysis is able to properly capture the quasi-brittle behavior of the reinforced concrete slab. Especially in comparison to the three-dimensional Newton-Raphson results, SLA turned out to be more robust and accurate.

The increased number of underground infrastructure projects asks for a reliable and efficient assessment of settlement damages to buildings. Currently a three-stage method is in use: the first stage looks into the greenfield deformations, the second stage is a linear elastic 2D method in which greenfield deformations are applied onto a building and the third stage uses finite element methods and 3D models. The goal of this thesis was to improve the second stage by incorporating a non-linear masonry model and a soil-structure interface. A 2D parametric analysis has been performed in which various material and geometrical parameters were varied. The soil model was simplified to a linear-elastic model. The results of the research are twofold. On the one hand there are the results of the parametric analysis showing the effect of incorporating the non-linear masonry model and the soil-structure interface. On the other hand incorporating these two aspects a number of issues came up: the influence of the crack model and convergence criterion, the influence of the building location, the influence of the initial stress and the influence of the participating soil width. For each issue an explanation was sought and the consequences were determined. The results of the parametric analysis showed that including a non-linear material model and a soil-structure interface leads to lower acceptable volume losses. In practice it is generally believed that the current models are already too conservative. The difference between reality and the models must be sought in components that are still missing in the current model.

The tunnel boring process introduces soil settlements. Damage to nearby building could occur if settlements become too large. A reliable damage prediction model is necessary too asses the risks of damage to tunnel induced settlements. A widely used method for damage prediction is the Limiting Tensile Strain Method (LTSM). The LTSM models a masonry building as a weightless, isotropic, linear-elastic, rectangular beam on 2 supports. Although the LTSM is an easy method to use, it has its limitations. For facades for instance the perforation of the wall, which introduces weak spots in the wall and reduces the stiffness, is neglected. In this project the applicability of the LTSM in the case of facades is studied to improve damage predictions in the case of facades. A case study is performed to examine the response of facades in the Daniel Stalpertstraat due to settlements caused by the tunnelling process of the North/Southline. This field data is used to find a calibrated 2D numerical model of the facades. The calibrated numerical model is then subjected to larger settlements to obtain the behaviour of the facades at large settlements. Using linear and nonlinear analyses of the numerical model it is evaluated how accurate and how conservative 4 damage prediction models are. The first two LTSM models were examined: the standard LTSM model with E/G=2.6 and one with E/G=12.5. Based on the findings in the linear analyses also two models based on conventional beam theory were examined for their applicability: portal frame model and Forget-Me-Not model. With linear analyses it is checked how reliable the methods are in terms of strains and deformation under the imposed settlements. With nonlinear analyses the conservativeness of each method in terms of damage is evaluated by comparing the crack with found I the numerical model to the crack width calculated with the damage prediction models. The LTSM with E/G=12.5 gives the best results according to linear numerical analyses results. The LTSM with E/G provided the same curvature and shear distortion as found din the numerical analyses, the strains were approximated with 90%. The Forget-Me-Not model shows the best results according to the nonlinear analyses results. At large settlements this model provides the same results as found in the nonlinear numerical analysis results.

Objective The recently developed material ultra-high performance concrete (UHPC) has compressive strengths of over 150 MPa and a ductile behaviour. It has a higher stiffness and superior durability characteristics in comparison with ordinary concrete. The opportunity emerges to find new optimal structural topologies for this material. The ant system is the first of a family of algorithms that are nowadays all referred to with the term ant colony optimisation (ACO). It is a computational algorithm that is able to solve combinatorial optimisation problems. Its optimisation process is based on the foraging behaviour of ants. ACO is not widely explored for structural design cases. In the city of Apeldoorn a new sports centre called Omnisport is under construction. The centre consists of several halls, one of them containing a cycling and athletics track. The roof of this hall spans an elliptic area of about 120 by 100 metres. This thesis focuses on the creation and evaluation of a structural topology design algorithm, based on the concept of the ant system, for ultra-high performance concrete structures. The algorithm is applied to the design case of the Omnisport sports hall roof. Algorithm A new application for ant colony optimisation is developed in this thesis. Structures are mapped to a binary search space, which forms the link between the structure, ant colony optimisation and the finite element package DIANA. Structures are generated randomly in the first iteration of the routine by assigning material to some elements in a meshed space and leaving others empty. Elements that together form a well-performing structure are more likely to be chosen again in a next iteration. The process is based on a performance that can be any function, and is not necessarily limited to structural information only. In the case considered in the thesis, the UHPC structure is optimised towards a combination of minimum volume, mould surface, pre-stress and the availability of holes for ducts and walking bridges. The algorithm’s multi-objective optimisation process results in a structural topology. Design The algorithm has been applied to the case of the Omnisport hall roof. Based on the results, a preliminary design for the load-bearing structure of the roof in UHPC has been made. A load-bearing structure in this material is found to be possible. The proposed design consists of truss-like supporting elements for the roof. A connection strategy is proposed, member sizes and necessary pre-stress are indicatively determined. Rough cost estimates show that the design is not necessarily more expensive than the current design in steel.

Recent tunnelling projects have received a great amount of media attention due to settlement induced damage. Due to the simplified approach of existing risk assessment methods, a new assessment system is in development, which can account for three-dimensional structural aspects of buildings. The aim of this study is to investigate the influence of the position and geometry of masonry buildings on the development of damage, while undergoing tunnelling induced settlements. In line with previous research, three-dimensional finite element analyses are used as a tool to perform a parametric study. A parametric study consists of an evaluation of the parameters position, aspect-ratio, grouping and orientation. The position parameter is divided into three characteristics: the sagging zone, a combined settlement profile and the hogging zone. The aspect-ratio parameter is also divided into three characteristics: shallow buildings, square buildings and deep buildings. The grouping effect parameter also distinguishes three characteristics: small and large isolated buildings and grouped buildings. The orientation parameter includes seven different increasing angles of the building main axis with respect to the tunnelling axis. The maximum measured crack width in the buildings gives input for a classification of damage, according the system of Burland et al. (1977). An average trend in the damage classification indicates the sensitivity to tunnelling induced settlements of the parameters. Both during and after tunnelling, a position of the building in the combined settlement profile appears to be the most sensitive to differential settlements. Buildings far away from the tunnelling axis generally obtain no more than slight damage. Structures with a low aspect-ratio seem on average to obtain equal amounts of damage as buildings with an aspect-ratio of 1. Structures with a higher aspect-ratio are less affected, both during and after tunnelling. Grouping of the buildings seems to be an influential parameter. Small isolated buildings obtain far less damage than large or grouped buildings. In relation to the numerical analyses, the empirical Limiting Tensile Strain Method (LTSM) seems to overestimate the damage for an isolated small building, but underestimate the damage in large or grouped buildings. For buildings in the sagging zone, a building with a low orientation angle is the least sensitive to differential settlement, while the maximum measured crack width increases by increasing the angle. The difference in maximum crack width can grow to a factor 3. A building in the combined settlement profile or in the hogging zone displays opposite behaviour. Cases with low orientation angles are the most susceptible to damage, while increasing the angle to 90 degrees lowers the maximum measured crack width. The difference in results can grow up to a factor 2.

In the world of structural engineering glass is an innovative material. Compared to other conventional structural materials like concrete, steel and timber, it is especially the transparency property that makes it a valued material. Due to the increasing demand for transparency in contemporary architecture, much more structural components as beams, plates, portals and columns are developed in glass. Besides the transparency property, the brittleness of glass makes it essentially an unsafe structural material as the residual capacity is limited. Therefore, the structural glass column is still in its early phases of development. As architects and clients, in general, do not like columns, they are said to block the view and stand in the way. Engineers need to add columns to buildings to provide support. These conflicting desires can be solved by developing a more attractive column, a glass column. The aim of this research project was to focus on further knowledge and understanding of the structural design aspects specifically related to structural glass columns and, on the basis of these findings, to design a glass column as a structural element in a pavilion. The considered slender columns were assembled from rectangular monolithic flat glass plates into different configurations. An exploratory study to the design aspects of glass columns was performed by doing experiments. One-metre-high glass columns were assembled from glass plates 8 millimetres thick, 100 millimetres wide and 1000 millimetres long and glued with a two-component adhesive based on epoxy resin (Araldite 2000 PLUS 2013) into five different configurations. These columns were compressed by a test bench with felt as the interlayer material to distribute the stresses uniformly over the cross-sectional area. A thorough analysis of the columns and their structural behaviour resulted in four design aspects that should be considered in the design process of a structural glass column: - a difference in the vertical position between the assembled glass plates; - susceptibility to peak stresses at the edges of the glass column; - the stiffness properties of the glue; - imperfections like holes and scratches. A two-dimensional numerical model was developed to study two of the considered design aspects. The effect of a difference in the vertical position between the assembled glass plates (which results in protruding edges) and the stiffness properties of the glue on the stress development in the glass were studied. Another series of experiments was performed to study the effect of several design options on the load bearing capacity of the column. The experiments revealed that, among others, avoiding the chance of uneven loading due to a difference in the vertical position between the glass plates and applying an adhesive with low stiffness results in more uniformly distribution of the stresses over the glass column. Finally, the findings of the experimental and numerical investigations were integrated into the structural design of a glass column for a pavilion. The preliminary design of a pavilion, which consists of ten columns, served as a context for the structural glass columns (each four metres high). Two main aspects were distinguished in the design process of the column: the boundary connection system and the related cross-section. Finally, a safety concept was developed for the monolithic glass column by applying an outer layer of safety glazing around the structural glass column. To conclude, from this research it is found that different design aspects play an important role in the bearing capacity of slender glass columns assembled from rectangular monolithic flat glass plates. On the basis of the experimental and numerical results the most relevant aspects related to designing a structural glass column were listed in the report.

When high strength steels are applicated in dynamically loaded structures, fatigue problems can arise. In most current design codes, the fatigue strength of high strength steels is either not discussed or determined as similar to mild steels. This assumption can be related to the dominance of the crack propagation life during in the total fatigue life when considering welded connections. Weld improvements can increase the length of the crack initiation life and thus increase the total fatigue life and may lead to a difference in fatigue strength between high strength steel and mild steels. This study focuses on the the effects of TIG-dressing on the weld toe geometry and the fatigue strength of TIG-dressed specimens. First a literature study is presented which summarizes earlier researches into the effect of TIG-dressing on fatigue strength and the behaviour of high strength steel in fatigue conditions, both in an as welded situation as after TIG-dressing. The weld toe geometry before and after TIG-dressing is determined. This leads to a extensive data set containing the geometry of the complete weld. The weld toe is then described with the aid of four parameters: weld toe radius, weld toe angle, weld height and undercut. Any influence of the static strength of the material, or any differences between rolled and cast steel are investigated. A comparison is made between the as welded specimens and TIG-dressed specimens. This changed geometry has been coupled to a changed fatigue strength with the aid of the notch stress approach. FEM analyses of the weld toe, based on measured geometries, have been carried out to determine stress concentration factors. Adjustments of the fatigue strength to account for loading mode, thickness, residual stress and mean stress have been derived from literature. A small reduction in residual stress, caused by the TIG-dressing procedure, has also been derived from literature. Fatigue tests have been carried out on 24 specimens ranging from S460 to S1100, made from both cast and rolled steels. The specimens are also adjusted for loading mode, thickness, residual stress and mean stress and compared with the developed model and a larger dataset of comparable as welded specimens. Due to the relatively small number of specimens per steel grade, a reliable quantitative fatigue strength improvement cannot be specified. A extensive qualitative analysis gives insight in the overall trends. From all used plates, hardness measurements are available, which have not been thoroughly analyzed. During the fatigue tests, crack dimensions have been determined during the crack propagation life. These measurements also have not been analyzed. Both data sets are added in annexes and are digitally available at the author or one of the members of the graduation committee.

Considering the recent increase in the use of fiber reinforced polymers in the civil engineering industry in general and in the bridge engineering industry in particular, as well as the recently more and more applied cylindrical truss bridge type, this research focuses on the question whether it is possible to combine fiber reinforced polymers as stand-alone structural material and this bridge type to construct a bridge suitable for heavy traffic as well as bicycle and pedestrian traffic. This research combines an extensive literature study on the use of fiber reinforced polymers for bridge engineering with a theoretical feasibility- and design-study on fiber reinforced polymer cylindrical truss bridges for heavy traffic. During the design study the spatial needs of all bridge users were defined to obtain an initial shape of the bridge. This shape was then optimized in several steps using finite-element-modeling and -analysis, yielding a final shape of the bridge. The behavior of this structure under design loads was then extensively investigated, again using finite element analysis, showing that the bridge could very well meet the self-derived deflection limit for fiber reinforced polymers at relatively low stress levels. Since fiber reinforced materials are a very diverse field of material, with hundreds of different compositions being available, the first result of this study was the choice of a suitable composite for further analysis. For this bridge design very high fiber content (>60%) carbon/epoxy composite was used. The main reason for this choice was the high modulus and -strength of the carbon fibers and the high durability and strength of the epoxy resin. A major reason of the slow implementation of fiber reinforced polymers in the bridge engineering industry are the worries concerning the lack of fire safety of the material. The literature study of this research showed however that it is possible to construct a heavy traffic full-FRP truss bridge, while complying with the known fire safety standards. The virgin FRP material can be adapted by several fire-protection measures; it turned out that a combination of intumescent gel-coating and low volume phosphorous filler systems works best in increasing the fire resistance and thereby providing a fire resistance class of R30 for hydrocarbon fire curve loading. The initial shape of the bridge was optimized in three stages: first several different truss topologies, which were derived with a parametric geometric model, were analyzed and compared using finite element analysis software, yielding the square truss with one diagonal as most efficient topology. In the next steps several grid sizes of this truss as well as several cross section dimensions were compared, again using finite element analysis software. An optimum was found between minimum material usage and minimum deflection, which reduced the material usage of the main load bearing elliptical truss by about 40% compared to the initial variant. The optimized structure was then fitted with the inner bridge deck supporting trusses as well as the cantilever trusses. The elliptical truss bridge performed very well considering the maximum deflections and stresses under Eurocode design loads and load combinations that were derived in finite element modeling software. When comparing the full-FRP bridge design with similar, existing steel structures, the maximum deformations and –stresses were considerably lower for the full-FRP bridge while only weighing about 60% of the steel structure. This research showed that the ‘new’ cylindrical truss bridge type is not only an aesthetically appealing structure but also performs structurally very well when combined with fiber reinforced polymer as structural material. It turned out that fiber reinforced polymers can be used as stand-alone structural material for medium span heavy traffic bridges. Next to that, this research clarified that there is no legitimate structural reason for the fact that fiber reinforced polymers are used relatively scarcely in the civil engineering- and bridge engineering industry compared to traditional building materials such as steel and concrete. Since this research is one of the first researches of its kind, using FRP as stand-alone structural material for a relatively new and complex bridge type, more research is needed in the field of high order connections for fiber reinforced polymer circular hollow sections. Next to that the possibility of the use of differently sized and shaped cross sections for the truss members should be investigated.

Tensairity is a new lightweight structural concept which can be classified as a pneumatic structure. By adding a compression element and cables to an inflated tube a structural system is obtained in which the strut and cables carry the applied load and the air tube transfers forces between both and stabilises the compression element against buckling. The structure combines the favourable features of pneumatics (light, deployable, compact storage and transport volume) with good structural properties and moderate air pressures. Thus, Tensairity is interesting for a wide range of applications, from roof structures to (temporary) bridges and tent structures. Next to beams the Tensairity concept can also be applied to columns and arches. Tensairity research currently focuses on structural improvements which can contribute to the applicability of the concept. One of these improvements is the use of a stiffening membrane strip inside the pneumatic tube. This ‘web’ is ascribed a positive effect on the stabilisation of the compression element. This thesis investigates the stabilising effect of the inflated tube on the compression element in Tensairity, and particularly the effect of the web on this behaviour. The approach is essentially experimental. First the concept of pressure induced stability and the web effect are investigated analytically and experimentally by means of small models. The models appear to display higher buckling loads for increasing pressures, even approaching the theoretical yield load of the compression element. Furthermore, the web improves the buckling load with a factor 2 in practice. Next, full-scale experiments are performed on two 5 m long Tensairity columns, both consisting of three aluminium struts supported and stabilised by an inflated membrane hull: one without and one with internal webs. For different hull pressures the columns are subjected to an axial compressive load. The responses are analysed and compared, also with FE predictions from ANSYS. For both columns the axial stiffness and the buckling load appear to improve for higher pressures in practice, emphasising the stabilising effect of overpressure. The maximum registered buckling load is over 25 kN, which is a promising result. The column with webs performs better than the one without webs: the increase in stiffness and capacity is around 35 % for an average pressure of 150 mbar. In general this improvement is lower than expected from the small models and the FE results, and not sufficient to counteract the drawbacks of the web model regarding applications, like an increased weight and more complicated fabrication. Thus, the application of a web is at this point not an effective contribution to the functioning of a Tensairity column. Yet, in comparison with a conventional truss column of similar dimensions both Tensairity columns display a sound structural behaviour, and they offer clear advantages in terms of deployability and architecture. A Tensairity column would therefore be especially interesting for temporary applications, e.g. acting as a pole in a tent structure.

This thesis focuses on assessing the crack width and durability at the outside of an immersed tunnel in case of fire inside the tunnel. Previous research (for instance Nieman [20]) addressed only the heating phase of a tunnel while also the inevitable cooling phase may have a large influence on the crack width. A user supplied code was written to calculate both the heating and cooling phase and handle the different reversibilities of the material properties. The material model is based on an explicit strain model where some simplifications had been made such as uniaxiality and the omission of the Poisson ratio. This material model is validated on some small models; the tunnel calculations are performed by making use of the geometry of the Wijkertunnel. The results of the tunnel calculations showed good agreement with the results of TNO 2007 [26] for the own weight and pressure loading. During the heating phase the results start to deviate from [26]; partly due to differences in the material model (load induced thermal strains reduces compressive stresses in the walls), partly due to instabilities in the calculation process. The load induced thermal strain decreases the thermal strain under compressive stresses and first time heating. One analysis could follow the complete fire, heating and cooling phase. During the heating and cooling phase the convergence behaviour was poor which is partly due to the complex material behaviour. The material model should be improved to obtain a more stable calculation process. During the cooling phase the tensile stresses increased in the roof and decreased in the walls of the heated tunnel tube as expected. The crack width at the outside of the tunnel is cumulative over a specific area. A lower limit is calculated and a crack width of more than 1 mm is found. This could influence the durability of the tunnel. To support this indication more calculations should be performed. The effect of the load induced thermal strain shows in a decrease of the tensile stresses in vertical direction in the walls and the compressive stresses in the side wall which are present for a longer time. In the mid wall an increase in compressive stress can be seen as a consequence of the net shrinkage which is a consequence of the load induced thermal strain during the cooling phase. It is possible to analyse the crack width during a fire. However more tests need to be performed to get a better understanding about the behaviour of the material properties during heating (high temperatures) and cooling. The code must be validated more thoroughly and only when the deformations of the walls can be explained for sure, a good assessment of the crack width after a heating and cooling phase can be made. In this thesis a foundation is laid for assessing the crack width in immersed tunnels during a heating and cooling phase. No such model existed until now. This model should be perfected, particular with respect to convergence, in order to obtain a more stable calculation and reliable results.