The focus of this research is on the control of random cracking in concrete paving by using sawcut notch locations in the early stages of construction. This is a major concern in concrete pavement construction. This research also addresses a probabilistic approach to determine the optimum time and depth of sawcutting for newly constructed portland cement concrete pavements. Variability in climate conditions and material characteristics during the hardening process affects the potential of cracking at any sawcut depth. Several factors affecting the probability of crack initiation are material strength parameters, method and quality of curing, slab/subbase stiffness, the amount and depth of steel reinforcement, friction between the slab and the subbase, and concrete shrinkage. Other factors relevant to concrete mixture characteristics such as cement content and type of coarse aggregate affect development of early aged stresses caused by shrinkage and thermally induced contraction. A probabilistic analysis of the factors that affect crack control using sawcut notches is presented in relation to different weather conditions (concrete placement temperature) at the time of construction, and concrete mixture characteristics such as fly ash replacement (FA) and cement factor (CF). Both of these significantly affect sawcut timing and depth requirement. The determination of crack initiation is based on fracture mechanics. Estimation of the time of cracking is based on predicted tensile strength and stress in the concrete at the bottom of the sawcut notch to assess the feasibility of crack control in the early stages of construction.

The focus of this research is on the control of random cracking in concrete paving by using sawcut notch locations in the early stages of construction. This is a major concern in concrete pavement construction. This research also addresses a probabilistic approach to determine the optimum time and depth of sawcutting for newly constructed portland cement concrete pavements. Variability in climate conditions and material characteristics during the hardening process affects the potential of cracking at any sawcut depth. Several factors affecting the probability of crack initiation are material strength parameters, method and quality of curing, slab/subbase stiffness, the amount and depth of steel reinforcement, friction between the slab and the subbase, and concrete shrinkage. Other factors relevant to concrete mixture characteristics such as cement content and type of coarse aggregate affect development of early aged stresses caused by shrinkage and thermally induced contraction. A probabilistic analysis of the factors that affect crack control using sawcut notches is presented in relation to different weather conditions (concrete placement temperature) at the time of construction, and concrete mixture characteristics such as fly ash replacement (FA) and cement factor (CF). Both of these significantly affect sawcut timing and depth requirement. The determination of crack initiation is based on fracture mechanics. Estimation of the time of cracking is based on predicted tensile strength and stress in the concrete at the bottom of the sawcut notch to assess the feasibility of crack control in the early stages of construction.

In prestressed precast segmental concrete bridges, conventional longitudinal reinforcement serves only as shrinkage crack controllers. The presence of this reinforcement, however, has restricted the ability to reduce the cross-section of the segments when high strength concrete is used because of the minimum dimensions required to accomodate the reinforcement. Research on fibre reinforced concrete (FRC) indicated that the addition of steel fibres to concrete significantly improved the tensile behaviour and the crack control characteristics of the concrete. This research investigates the feasibility of fibres to replace the conventional shrinkage reinforcement, allowing for the design of thinner and lighter structures with comparable or better crack control characteristics. Extensive work was conducted to investigate the effectiveness of hooked-end steel fibres to control cracks. Seven types of material tests were performed: uniaxial tension test, cylinder compression test, modulus of rupture test, splitting test, free and autogenous shrinkage test, and restrained shrinkage test. In addition, ten 890×890×70 mm concrete panels were tested under in-plane pure-shear loading using the Panel Element Tester. The parameters of study were the fibre volume content (0.5%, 1.0%, and 1.5%), the concrete compressive strength (50 and 80 MPa), and the fibre geometry and tensile strength. In addition to the experimental study, a model was developed to investigate the behaviour of a 1D restrained FRC member subjected to shrinkage. The experimental results indicated that the addition of fibres significantly improved the behaviour of the concrete, particularly the crack control characteristics, the post-peak compressive response, the post-cracking tensile response, the toughness, and the ductility of the concrete. The results also indicated that steel fibres were as effective as conventional reinforcement in controlling shrinkage cracking, provided that sufficient fibre volume content was added to the concrete. For example, in order to achieve a maximum crack width of 0.35 mm, a minimum fibre content of 0.9% and 1.1% should be provided for 50 MPa FRC containing high aspect ratio fibres and low aspect ratio fibres, respectively. In addition, the results indicated the importance of fibre content and fibre aspect ratio on the effectiveness of fibre reinforcement.

In prestressed precast segmental concrete bridges, conventional longitudinal reinforcement serves only as shrinkage crack controllers. The presence of this reinforcement, however, has restricted the ability to reduce the cross-section of the segments when high strength concrete is used because of the minimum dimensions required to accomodate the reinforcement. Research on fibre reinforced concrete (FRC) indicated that the addition of steel fibres to concrete significantly improved the tensile behaviour and the crack control characteristics of the concrete. This research investigates the feasibility of fibres to replace the conventional shrinkage reinforcement, allowing for the design of thinner and lighter structures with comparable or better crack control characteristics. Extensive work was conducted to investigate the effectiveness of hooked-end steel fibres to control cracks. Seven types of material tests were performed: uniaxial tension test, cylinder compression test, modulus of rupture test, splitting test, free and autogenous shrinkage test, and restrained shrinkage test. In addition, ten 890×890×70 mm concrete panels were tested under in-plane pure-shear loading using the Panel Element Tester. The parameters of study were the fibre volume content (0.5%, 1.0%, and 1.5%), the concrete compressive strength (50 and 80 MPa), and the fibre geometry and tensile strength. In addition to the experimental study, a model was developed to investigate the behaviour of a 1D restrained FRC member subjected to shrinkage. The experimental results indicated that the addition of fibres significantly improved the behaviour of the concrete, particularly the crack control characteristics, the post-peak compressive response, the post-cracking tensile response, the toughness, and the ductility of the concrete. The results also indicated that steel fibres were as effective as conventional reinforcement in controlling shrinkage cracking, provided that sufficient fibre volume content was added to the concrete. For example, in order to achieve a maximum crack width of 0.35 mm, a minimum fibre content of 0.9% and 1.1% should be provided for 50 MPa FRC containing high aspect ratio fibres and low aspect ratio fibres, respectively. In addition, the results indicated the importance of fibre content and fibre aspect ratio on the effectiveness of fibre reinforcement.

The finite element method (FEM) is commonly used to design the reinforcement in concrete slabs. In order to simplify the analysis and to be able to utilize the superposition principle for evaluating the effect of load combinations, a linear analysis is generally adopted although concrete slabs normally have a pronounced non-linear response. This type of simplification in the modeling procedure will generally lead to unrealistic concentrations of cross-sectional moments and shear forces. Concrete cracks already at service loads, which leads to redistribution of moments and forces. The moment- and force-peaks, obtained through linear finite element analysis, can be redistributed to achieve a distribution more similar to what is seen in reality. The topic of redistribution is however poorly documented and design codes, such as the Eurocode for concrete structures, do not give descriptions of how to perform this in practice. In 2012, guidelines for finite element analysis for the design of reinforced concrete slabs were published in a joint effort between KTH Royal Institute of Technology, Chalmers University of Technology and ELU consulting engineers, which was financially supported by the Swedish Transport Administration. These guidelines aim to include the non-linear response of reinforced concrete into a linear analysis. In this thesis, the guidelines mentioned above are followed to obtain reinforcement plans based on crack control, for a fictitious case study bridge by means of a 3D finite element model. New models were then constructed for non-linear analyses, where the reinforcement plans were implemented into the models by means of both shell elements as well as a mixture of shell and solid elements. The results from the non-linear analyses have been compared to the assumptions given in the guidelines. The results from the non-linear analyses indicate that the recommendations given in the aforementioned guidelines are indeed reasonable when considering crack width control. The shell models yield crack widths equal to approximately half the design value. The solid models, however, yielded cracks widths that were 15 - 20$\%$ lower than the design value. The results show that many factors attribute to the structural behavior during cracking, most noticeably the fracture energy, a parameter not featured in the Eurocode for concrete structures. Some limitations of the models used in this thesis are mentioned as well as areas for further improvement.

Precast, prestressed concrete panels (PCPs) have been widely used in Texas as stay-in-place formwork in bridge deck construction. Although PCPs are widely popular and extensively used, Texas is experiencing problems with collinear cracks (cracks along the strands) in panels. One reason for the formation of collinear cracks is thought to be the required level of initial prestress. Currently, PCPs are designed assuming a 45-ksi, lump-sum prestress loss. If the prestress losses are demonstrated to be lower than this value, this could justify the use of a lower initial prestress, probably resulting in fewer collinear cracks. For this purpose, 20 precast, prestressed panels were cast at two different plants. Half of those 20 panels were fabricated with the current TxDOT-required prestress of 16.1 kips per strand, and the other half were fabricated with a lower prestress of 14.4 kips per strand based on initially observed prestress losses of 25 ksi or less. Thirteen of those panels were instrumented with strain gages and monitored over their life time. Observed losses stabilized after five months, and are found to be about 24.4 ksi. Even with the reduced initial prestress, the remaining prestress in all panels exceeds the value now assumed by TxDOT for design. / text

Cracks in the concrete slab of continuous composite bridges are common due to the tensile stresses at the supports. These bridges are allowed to crack as long as the cracking is controlled and not exceeding the design crack width (according to Bro 94 the crack should be injected if they are bigger than 0.2 mm). The Ångermanälven Bridge (railway bridge part of the Bothnia line project) was designed with big edge beams of width 1.2 m, 40 % of the total area of the concrete deck cross-section. During the final inspection cracks larger than the design crack width (0.3 mm according to Bro 94) were observed over the supports.In this thesis the design and the construction procedure of the bridge is studied to clarify the causes of the cracking in the edge beam. The objectives of this thesis were addressed through a literature study of the different types of cracks and the Swedish bridge codes. The expected crack width was calculate according to the same code, using a 2-D FEM model for the moment calculation, and compared with the crack width measured at the bridge.The result of the calculations shows that tensile stress due to ballast and only restraining moment due to shrinkage is not big enough to cause the measured crack width. Shrinkage force and temperature variation effects may have contributed to the concrete cracking in the edge beams. The large cross-section area of the edge beams indicates that it should be designed as part of the slab, taking that into consideration, 1.1 % reinforcement ratio in the edge beams is believed to limit the crack width to the code limits (0.3 mm).

Efter introduktionen av Eurokoderna har mängden minimiarmering i betongkonstruktioner ökat. Denna ökning beror på skillnader i metoderna som nu används för att beräkna mängden minimiarmering i olika typer av betongkonstruktioner och de som användes tidigare då BKR var den gällande normen. Minimiarmering används i betongkonstruktioner för att omfördela tvångsdeformationer. I detta arbete undersöks om mängden minimiarmering kan minskas utan att dess huvudsakliga funktion går förlorad. I arbetet har ett antal metoder för att beräkna minimiarmering jämförts för att se hur stora skillnaderna i armeringsmängd blir, varför dessa uppkommer och vilka för- och nackdelar som finns med metoderna. De undersökta metoderna inkluderar den som anges i Eurokod 2, förändringar som gjorts i den tyska nationella bilagan till Eurokod 2 och ett förslag till ändring som presenterats av Hallgren i ett preliminärt arbete.   Resultaten bygger på simuleringar utförda i FEM-programmet Atena där olika typfall undersökts. I typfallen har betongens hållfasthetsklass, tvärsnittsdimension, armeringsdimension, täckande betongskikt och vidhäftningsförutsättning varierats. Armeringsmängden varierades för att motsvara den mängd som krävs vid beräkning enligt de tidigare nämnda metoderna. I alla undersökta fall antas tvärsnittet vara utsatt för ren dragbelastning, vilket är fallet vid krympning. Resultaten från de numeriska simuleringarna visade att en större armeringsmängd ger minskade sprickbredder och ökade möjligheter att omfördela tvångsdeformationer till nya sprickor. Bildandet av nya sprickor sker också vid en mindre krympning. Skillnaderna jämfört med om en mindre armeringsmängd används blir dock i de flesta fall små och mängden armering kan reduceras utan att minimiarmeringens sprickfördelande funktion äventyras. Resultaten från de numeriska simuleringarna användes också för att ta fram ett alternativ som ger en mindre mängd minimiarmering utan att armeringens huvudsakliga funktion försvinner. I detta arbete föreslås en förändring rörande koefficienten k i Eurokod. Förändringen av värdet på koefficienten k gör att mängden erforderlig minimiarmering minskar betydligt vid beräkningar, speciellt för tvärsnitt med en större tvärsnittshöjd. Fler numeriska simuleringar utfördes och det kunde säkerställas att en armeringsmängd motsvarande den som ges med den föreslagna ändringen fungerar för alla undersökta typfall. Endast en liten ökning av sprickbredderna sker.   En undersökning av sprickproblematiken under betongens hållfasthetstillväxtfas har gjorts, och resultaten visar att problem med sprickbildning inte beror på den autogena krympningen eller på uttorkningskrympningen. Endast en liten andel av denna krympning hinner uppnås under de första veckorna, samtidigt som hållfasthetstillväxten sker relativt snabbt. Problem med sprickbildning under denna tidsperiod beror istället på andra faktorer såsom en stor värmeutveckling i betongen, en ojämn uttorkning eller en ojämn temperaturfördelning över tvärsnittet i kombination med tvång. Efter den värmeutveckling som skett i betongen under det första dygnet efter gjutning påbörjas en avsvalningsfas. Under denna kan sprickbildning uppstå i betongen, och denna sprickbildning finns kvar när uttorkningskrympningen senare fortskrider. En jämförelse har även gjorts mellan handberäkningar av karaktäristiska sprickbredder enligt Betongföreningens handbok till Eurokod 2 och sprickbredder utlästa ur resultaten från de numeriska simuleringarna. Resultaten visar att metoden överlag fungerar bra, men att vissa justeringar skulle kunna göras för att anpassa den till mindre värden på betongens krympning. / After the introduction of the Eurocodes, the minimum amount of reinforcement for crack control in concrete structures has increased. This is due to differences in themethods for calculating the minimum amount of reinforcement used in the Eurocodes and in BKR, a standard which was used in Sweden before the Eurocodes. Minimum reinforcement for crack control is used in concrete structures to redistribute the tensile stresses caused by restraint during the shrinkage. This thesis examines if the amount of minimum reinforcement can be reduced without compromising the main functions of the reinforcement. In this thesis a number of methods for calculating the minimum reinforcement has been compared to see how large the differences in the amount of reinforcement are, why they occur and what are the advantages and disadvantages of the different methods. The different methods revised in this thesis are the method in Eurocode 2, the changes made in the German National Annex to the Eurocode 2 method and a method proposed by Hallgren in a preliminary work.   The results are based on simulations performed in the FEM-application Atena where different scenarios were examined. In the investigated scenarios, the strength classes of the concrete, the cross-sectional dimensions, the size of the reinforcement bars, the size of the concrete cover and the bond strength has been varied. The amount of reinforcement in each case has been varied to correspond to the required minimum amount according to the different methods for calculating minimum reinforcement. In all investigated cases, the cross section is assumed to be exposed to pure tensile load, which is the case for shrinkage. The results of the simulations showed that a larger amount of reinforcement reduces the width of the cracks, that a larger amount of small cracks are formed, and that new cracks are formed earlier at a lower shrinkage value. The differences are however in most cases small compared to when a lower amount of reinforcement is used. In other words, a lower amount of reinforcement could be used without compromising the main functions of the minimum reinforcement. The results from the simulations have also been used to obtain an alternative method for calculating the minimum reinforcement that gives a lower amount of reinforcement without compromising the main functions. The proposed change in Eurocode is a modification in the value of the coefficient k. By changing the value of the coefficient k, the amount of required minimum reinforcement is decreased significantly, especially for large crosssection heights. More numerical simulations were performed to ensure that the reinforcement amount according to the proposed change works for all scenarios considered in this thesis. The results showed that the reinforcement were capable of redistributing the tensile stresses caused by restraint. Only a small increase in the crack widths could be observed.   An investigation was conducted to find an explanation to why cracks occur during the first weeks after casting of the concrete. The results show that the problem with cracks occurring during this period is neither due to the autogenous shrinkage nor the drying shrinkage. Only a small share of those types of shrinkage are achieved during the first weeks, and at the same time the concrete strength growth is relatively fast. Instead, the problems with cracks seem to be caused by other factors, such as a large heat development in the concrete during the first day, uneven drying shrinkage or an uneven temperature distribution over the cross section in combination with restraint. Cracks can develop during the first days after casting of the concrete due to the shrinkage that occur when the concrete cools off after the large heat development the first day. These cracks remain when the drying shrinkage continues. A comparison was also made between hand calculations of the characteristic crack widths according to “Betongföreningens handbok till Eurokod 2” and the crack widths read out of the results from the numerical simulations. The results showed that the method generally works well, but some minor adjustments could be made to adapt the method to smaller values of concrete shrinkage.