This thesis emphasizes the critical importance of crack control in designing and constructing reinforced concrete (RC) structures. Cracks in such structures can significantly reduce strength and durability, pose safety risks, and lead to high repair costs. Existing codes and standards offer varying approaches, resulting in inconsistent results in designing for serviceability limit state (SLS). The evolution of modern reinforced concrete, incorporating additives like superplasticizers and silica fume, requires an update to crack control models based on outdated conceptions. The thesis aims to compare crack width calculations, understand bond stress in contemporary concrete models, and enhance crack control models. The study covers crack development, mathematical aspects of crack design, laboratory testing, and analysis of RC specimens. The findings aim to offer valuable recommendations and improve crack control measures, contributing to a more robust database and aiding the development of effective global model codes and standards for crack control in RC structures.:1. Introduction 2. General knowledge of cracks in RC structures 2.1. Cause of crack formation 2.1.1. Crack during the hardening process 2.1.1.1. Plastic shrinkage cracks 2.1.1.2. Plastic settlement cracks 2.1.2. Crack of hardened concrete 2.1.2.1. Drying shrinkage cracks 2.1.2.2. Thermal cracks 2.1.2.3. Crack due to chemical reaction 2.1.3. Crack due to external loads 2.2. Crack development in an axially loaded member 3. Crack width calculations 3.1. Design formula according to EN:1992 3.1.1. Calculating crack width 3.1.2. Calculating minimum reinforcement 3.1.3. Detailing of reinforcement 3.2. Design formula according to fib Model Code 3.2.1. Crack width calculation per fib Model Code 1990 3.2.2. Crack width calculation per fib Model Code 2010 3.3. Design formula in other codes and standards 3.3.1. Crack width calculation in American standard (ACI) 3.3.2. Crack width calculation in British standard (BS) 3.3.3. Crack width calculation in Vietnamese standard (TCVN) 3.3.4. Summary and example of crack width calculations a. Crack control per EN 1992-1-1 b. Crack control per Model Code 1990 c. Crack control per Model Code 2010 d. Crack control per ACI e. Crack control per BS f. Crack control per TCVN 4. Pull-out experiments 4.1. Experimental basis 4.2. Experiment setup 4.2.1. Test machine 4.2.2. Test cubes 5. Results and Discussion 5.1. Failure modes and bond-slip curves 5.2. The bond-slip functions 6. Conclusion 7. References

In marine environments and where de-icing salts are applied, the degradation of reinforced concrete structures due to chloride induced corrosion of the reinforcement is a major problem. The expansive nature of the corrosion process results in cracking of the concrete and eventually spalling. In order to select suitable remedial measures it is necessary to make an assessment of the residual strength and the residual life. In order to investigate the effect of corrosion on bond strength of the reinforcement, specimens comprising square prismatic sections containing steel reinforcement in the four corners have been subjected to a wet-dry cycle and corrosion has been accelerated by polarising the bars. The research has studied the change of bond strength with level of corrosion for 12 mm and 16 mm bars with concrete cover of 1 and 3 times the bar size. The bond strength is assessed by means of pull out tests and the corresponding extent of corrosion has been assessed in terms of the mass loss. Observations and measurements of the form of the corrosion (pit dimensions and loss of bar diameter) are also presented. The relationship between bond strength and surface crack width has been investigated. Results show that the surface crack width may be a good indicator of residual bond strength. In addition, the influence on bond strength of concrete compressive strength, reinforcement cover, bar position and bar size on the change of bond strength has been explored. It should be noted that all conclusions drawn in this project are based on tests on specimens without shear reinforcement (unconfined) and that accelerated corrosion (by impressed current) has been adopted. Consequently, care should be exercised in applying these results directly to structures in the field. Additional research is needed to assess the influence of impressed current on crack patterns and the effect of shear reinforcement.

This paper presents results of an experimental investigation to study the structural performance and deformability of a concrete bridge deck reinforced with corrosion resistant reinforcing (CRR) bars, i.e., bars that exhibit improved corrosion resistance when embedded in concrete as compared to traditional black steel. Flexural tests of one-way slabs were conducted to simulate negative transverse flexure over a bridge girder as assumed in the commonly employed strip design method. The bar types studied were Grade 60 (uncoated), epoxy-coated reinforcing (ECR, Grade 60), Enduramet 32 stainless steel, 2304 stainless steel, MMFX2, and glass fiber reinforced polymer (GFRP). The experimental program was designed to evaluate how a one-to-one replacement of the Grade 60 with CRR, a reduction of concrete top clear cover, and a reduction in bar quantities in the bridge deck top mat influences flexural performance at service and ultimate limit states. Moment-curvature predictions from the computer-based sectional analysis program Response 2000 were consistent with the tested results, demonstrating its viability for use with high strength and non-metallic bar without a defined yield plateau.    Deformability of the concrete slab-strip specimens was defined with ultimate-to-service level ratios of midspan deflection and curvature. The MMFX2 and Enduramet 32 one-to-one replacement specimens had deformability consistent with the Grade 60 controls, demonstrating that bridge deck slabs employing high strength reinforcement without a defined yield plateau can still provide sufficient ductility at an ultimate limit state. A reduction in bar quantity and cover provided acceptable levels of ductility for the 2304 specimens and MMFX2 reinforced slabs. / Master of Science

<p>After only two years of service, extensive cracking was found in the webs of two light-rail commuter line bridges in Stockholm, the Gröndal and Alvik bridges. Due to this incident it was found necessary to study the means available for analysing shear cracking in concrete structures subjected to in-plane stresses. The aim of this PhD project is to study shear cracking with these two bridges as reference. In this thesis, the first part aims to study the possibility of using finite element analysis as a tool for predicting shear cracking for plane state stresses. The second part is concerning how the shear cracks are treated in the concrete design standards.</p><p>Shear cracking in reinforced beams has been studied with non-linear finite element analyses. In these analyses the shear cracking behaviour was compared to experiments conducted to analyse the shear failure behaviour. Finite element analyses were performed with two different FE programs Abaqus and Atena. The material model used in Atena is a smeared crack model based on damage and fracture theory with either fixed or rotated crack direction. The material model used in Abaqus is based on plasticity and damage theory. The fixed crack model in Atena and the model in Abaqus gave good results for all studied beams. For the two studied deep beams with flanges the results from the rotated crack model were almost the same as obtained with the fixed crack model. The rotated crack model in Atena gave though for some beams a rather poor estimation of the behaviour.</p><p>The calculation of crack widths of shear cracks has been studied for the long-term load case in the serviceability state for the Gröndal and Alvik bridges, with the means available in the design standards. The methods based on the crack direction corresponding to the principal stress and do not include the effect of aggregate interlocking seems to be too conservative. Two of the studied methods included the effect of aggregate interlocking, it was made either by introducing stresses in the crack plane or implicitly by changing the direction of the crack so that it no longer coincide with the direction of principal stress. For calculations based on probable load conditions, these methods gave estimations of the crack widths that were close to the ones observed at the bridges. Continuous measurements of cracks at the Gröndal and the Alvik bridges have also been included. Monitoring revealed that the strengthening work with post-tensioned tendons has, so far, been successful. It also revealed that the crack width variations after strengthening are mainly temperature dependent where the daily temperature variation creates movements ten times greater than those from a passing light-rail vehicle. Monitoring a crack between the top flange and the webs on the Gröndal Bridge showed that the top flange was moving in a longitudinal direction relative to the web until the strengthening was completed. The crack widths in the sections strengthened solely by carbon fibre laminates seem to increase due to long-term effects.</p>

Reinforcement of concrete flexural components has been traditionally provided by steel rebar; however, durability concerns and life maintenance costs of this product have powered the emergence of fibre reinforced polymers (FRP) as reinforcement in concrete. FRP products hold tremendous promise but their application can be constrained due to design challenges resulting from a reduced modulus of elasticity. The ability to meet serviceability behavior, such as crack width and deflection, is commonly the limiting factor for design. Therefore, the area of FRP reinforcement provided is often greater than the amount required for strength alone and this has significant impacts on the project economics. The bond dependent coefficient (kb) of FRP is required for serviceability design purposes in order to account for the bonding capability of FRP to concrete. The values of this coefficient reported in experimental studies are highly variable, resulting in unreliable crack response predictions. Therefore, a more consistent interpretation and calculation must be found for the bond dependent coefficient due to its critical importance in design. The bond dependent coefficient, as well as physical parameters which influence crack width in GFRP reinforced concrete, were investigated experimentally in this study using a total of 33 specimens. The test procedure was taken from a procedure being developed by the American Concrete Institute (ACI) Committee 440 and was evaluated and modified as required during testing. Phase I testing was used to investigate and determine the physical parameters which had the most significant influence on cracking behaviour and bonding capability. Using significant findings from Phase I, Phase II testing was structured to focus on the interpretation of the bond dependent coefficient and the statistical variation in a set of 5 identical test specimens. Current design equations, as recommended by ACI 440.1R-06 and CHBDC CAN/CSA-S6-06, were used for the calculation of the bond dependent coefficient for all specimens. Interpretation of the bond dependent coefficient was considered using the stress-level approach and newly developed slope approach. Results of the study indicated that the high variability of kb was likely due to its interpretation. Current design equations force a zero intercept, neglecting the fact that concrete does not crack immediately upon loading. In addition, clear definitions of service stress and maximum crack width are ambiguous, further complicating the calculation of the bond dependent coefficient. This resulted in a range of kb values for a given beam despite the fact that kb is inherently a material property of the bar. The behaviour of specimens following load cycling was also very different than the initial loading cycle and consequently, kb was also significantly different. As structures in the field will be subjected to continual loading and unloading, the effect of cyclic loading becomes a consideration in the calculation of kb.

The strive for a time-efficient construction process naturally put focus on the possibility of reducing the time of waiting between stages of construction, thereby minimizing the construction cost. If recently placed concrete, cast or sprayed, is exposed to impact vibrations at an early age while still in the process of hardening, damage that threatens the function of the hard concrete may occur. A waiting time when the concrete remains undisturbed, or a safe distance to the vibration source, is therefore needed. However, there is little, or no, fully proven knowledge of the length of this distance or time and there are no established guidelines for practical use. Therefore, conservative vibration limits are used for young and hardening concrete exposed to vibrations from e.g. blasting. As a first step in the dynamic analysis of a structure, the dynamic loads should always be identified and characterized. Here it is concluded that impact-type loads are the most dangerous of possible dynamic loads on young and hardening concrete. Shotcrete (sprayed concrete) on hard rock exposed to blasting and cast laboratory specimens subjected to direct mechanical impact loads have been investigated using finite element models based on the same analysis principles. Stress wave propagation is described in the same way whether it is through hard rock towards a shotcrete lining or through an element of young concrete. However, the failure modes differ for the two cases where shotcrete usually is damaged through loss of bond, partly or over larger sections that may result in shotcrete downfall. Cracking in shotcrete due to vibrations only is unusual and has not been observed during previous in situ tests. The study of shotcrete is included to demonstrate the need of specialized guidelines for cases other than for mass concrete, i.e. structural elements or concrete volumes with large dimensions in all directions. Within this project, work on evaluating and proposing analytical models are made in several steps, first with a focus on describing the behaviour of shotcrete on hard rock. It is demonstrated that wave propagation through rock towards shotcrete can be described using two-dimensional elastic finite element models in a dynamic analysis. The models must include the material properties of the rock and the accuracy of these parameters will greatly affect the results. It is possible to follow the propagation of stress waves through the rock mass, from the centre of blasting to the reflection at the shotcrete-rock interface. It is acceptable to use elastic material formulations until the strains are outside the elastic range, which thus indicates imminent material failure. The higher complexity of this type of model, compared with mechanical models using mass and spring elements, makes it possible to analyse more sophisticated geometries. Comparisons are made between numerical results and measurements from experiments in mining tunnels with ejected rock mass and shotcrete bond failure, and with measurements made during blasting for tunnel construction where rock and shotcrete remained intact. The calculated results are in good correspondence with the in situ observations and measurements, and with previous numerical modelling results. Examples of preliminary recommendations for practical use are given and it is demonstrated how the developed models and suggested analytical technique can be used for further detailed investigations. The modelling concept has also been used for analysis of impact loaded beams and concrete prisms modelled with 3D solid elements. As a first analysis step, an elastic material model was used to validate laboratory experiments with hammer-loaded concrete beams. The laboratory beam remained un-cracked during the experiments, and thus it was possible to achieve a good agreement using a linear elastic material model for fully hardened concrete. The model was further developed to enable modelling of cracked specimens. For verification of the numerical results, earlier laboratory experiments with hammer impacted smaller prisms of young concrete were chosen. A comparison between results showed that the laboratory tests can be reproduced numerically and those free vibration modes and natural frequencies of the test prisms contributed to the strain concentrations that gave cracking at high loads. Furthermore, it was investigated how a test prism modified with notches at the middle section would behave during laboratory testing. Calculated results showed that all cracking would be concentrated to one crack with a width equal to the sum of the multiple cracks that develop in un-notched prisms. In laboratory testing, the modified prism will provide a more reliable indication of when the critical load level is reached. This project has been interdisciplinary, combining structural dynamics, finite element modelling, concrete material technology, construction technology and rock support technology. It is a continuation from previous investigations of the effect on young shotcrete from blasting vibrations but this perspective has been widened to also include young, cast concrete. The outcome is a recommendation for how dynamic analysis of young concrete, cast and sprayed, can be carried out with an accurate description of the effect from impact-type loads. The type of numerical models presented and evaluated will provide an important tool for the work towards guidelines for practical use in civil engineering and concrete construction work. Some recommendations on safe distances and concrete ages are given, for newly cast concrete elements or mass concrete and for newly sprayed shotcrete on hard rock. / <p>QC 20150529</p>

No description available.

Transverse cracking in bridge decks has been found to be a rising problem for slab-on-girder bridges. In response to the concern, this research examined the influence of structural parameters and developed an analytical truss model, based on finite element modelling responses, for predicting the condition of long term cracking. Crack widths predicted using the truss model are very similar to that measured in a recent survey of Ontario highway overpass bridges. The approach to control cracking in deck slabs through structural design decisions enables engineers to provide high cracking resistance at locations of the bridge deck that are most likely to crack. Recommendations were made, based on the findings obtained from two sets of parametric studies, to help ensure transverse cracking in bridge decks is properly controlled for typical slab-on-girder bridges designed using the empirical design method specified in the current Canadian Highway Bridge Design Code.

Transverse cracking in bridge decks has been found to be a rising problem for slab-on-girder bridges. In response to the concern, this research examined the influence of structural parameters and developed an analytical truss model, based on finite element modelling responses, for predicting the condition of long term cracking. Crack widths predicted using the truss model are very similar to that measured in a recent survey of Ontario highway overpass bridges. The approach to control cracking in deck slabs through structural design decisions enables engineers to provide high cracking resistance at locations of the bridge deck that are most likely to crack. Recommendations were made, based on the findings obtained from two sets of parametric studies, to help ensure transverse cracking in bridge decks is properly controlled for typical slab-on-girder bridges designed using the empirical design method specified in the current Canadian Highway Bridge Design Code.

In this thesis, the possibility to numerically describing the behaviour that signifies shear type cracking in concrete is studied. Different means for describing cracking are evaluated where both methods proposed in design codes based on experiments and advanced finite element analyses with a non-linear material description are evaluated. It is shown that there is a large difference in the estimation of the crack width based on the calculation methods in design codes. The large difference occurs due to several of these methods do not account for shear friction in the crack face. The finite element method is an important tool for analysing the non-linear behaviour caused by cracking. It is especially of importance when combined with experimental investigations for evaluating load bearing capacity or establishing the structural health. It is shown that non-linear continuum material models can successfully be used to accurately describe the shear type cracking in concrete. A method based on plasticity and damage theory was shown to provide accurate estimations of the behaviour. The methods based on fracture mechanics with or without inclusion of damage theory, overestimated the stiffness after crack initiation considerably. The rotated crack approach of these methods gave less accurate descriptions of the crack pattern and underestimated the crack widths. After verification of the material model, realistic finite element models based on plasticity and damage theory are developed to analyse the cause for cracking in two large concrete structures. The Storfinnforsen hydropower buttress dam is evaluated where the seasonal temperature variation in combination with the water pressure have resulted in cracking. With the numerical model the cause for cracking can be explained and the crack pattern found in-situ is accurately simulated. The model is verified against measurements of variation in crest displacement and crack width with close agreement. The construction process of a balanced cantilever bridge, Gröndal Bridge, is numerically simulated and a rational explanation of the cause for cracking is presented. It is shown that large stresses and micro-cracks develop in the webs during construction, especially after tensioning the continuing tendons in the bottom flange. Further loads from temperature variation cause cracking in the webs that is in close agreement with the cracking found in-situ. The effect of strengthening performed on this bridge is also evaluated where the vertical Dywidag tendons so far seem to have been successful in stopping further crack propagation. / QC 20100730