Hot-mix asphalt concrete (HMAC) mixture fatigue characterization constitutes a fundamental component of HMAC pavement structural design and analysis to ensure adequate field fatigue performance. HMAC is a heterogeneous complex composite material of air, binder, and aggregate that behaves in a non-linear elasto-viscoplastic manner, exhibits anisotropic behavior, ages with time, and heals during traffic loading rest periods and changing environmental conditions. Comprehensive HMAC mixture fatigue analysis approaches that take into account this complex nature of HMAC are thus needed to ensure adequate field fatigue performance. In this study, four fatigue analysis approaches; the mechanistic empirical (ME), the calibrated mechanistic with (CMSE) and without (CM) surface energy measurements, and the proposed NCHRP 1-37A 2002 Pavement Design Guide (MEPDG) were comparatively evaluated and utilized to characterize the fatigue resistance of two Texas HMAC mixtures in the laboratory, including investigating the effects of binder oxidative aging. Although the results were comparable, the CMSE/CM approaches exhibited greater flexibility and potential to discretely account for most of the fundamental material properties (including fracture, aging, healing, visco-elasticity, and anisotropy) that affect HMAC pavement fatigue performance. Compared to the other approaches, which are mechanistic-empirically based, the CMSE/CM approaches are based on the fundamental concepts of continuum micromechanics and energy theory.

A l’heure actuelle où la préservation de notre environnement est primordiale, les constructions en béton font intervenir de plus en plus des ciments comprenant des ajouts minéraux, tels que le laitier, les cendres volantes… En effet, la production des ciments composés permet de réduire le dégagement des gaz à effets de serre et de réutiliser des déchets industriels. Les bétons formulés à base de ciment au laitier de haut-fourneau (CEM III) sont également largement utilisés suite à leur bonne résistance aux réactions alcali-silices, à la diffusion des chlorures et aux attaques sulfatiques… Cependant, certains ouvrages construits avec ce type matériau ont présenté au jeune âge des problèmes de fissuration liés à la restriction de leurs déformations différées, telles que le retrait endogène, thermique et de dessiccation. Suite à cette observation, des essais préliminaires ont été réalisés au laboratoire du service BATir de l’Université Libre de Bruxelles. Ils ont mis en avant plusieurs caractéristiques du comportement de ces matériaux : 1. Lors du suivi du retrait restreint à l’aide de l’essai à l’anneau en condition de dessiccation, le béton formulé à base de ciment au laitier de haut-fourneau a fissuré bien avant le béton formulé à base de ciment Portland. 2. Le retrait total en condition libre du béton formulé à base de ciment au laitier de haut-fourneau est nettement supérieur à celui du béton formulé à base de ciment Portland. Cette différence de comportement est principalement due à l’accroissement rapide et plus élevé du retrait endogène des bétons formulés à base de ciment au laitier de haut-fourneau. Au vu de ces résultats expérimentaux, il a semblé intéressant de déterminer quel était l’impact de la déformation endogène des bétons formulés à base de ciments au laitier de haut-fourneau (CEM III) sur leur sensibilité à la fissuration. Afin de répondre à cette question, les déformations différées (retrait endogène, fluage propre en compression et en traction) au jeune âge de trois compositions de béton avec différentes teneurs en laitier (0, 42 et 71%) ont été étudiées expérimentalement en conditions libre et restreinte. Cependant, le suivi du retrait endogène libre et restreint a nécessité le développement de plusieurs dispositifs expérimentaux limitant au maximum les artefacts de mesure, tels que la TSTM (Temperature Stress Testing Machine). De plus, l’interprétation de ces résultats expérimentaux a également nécessité une caractérisation du comportement de ces matériaux à l’échelle macro- et microscopique. Finalement, cette étude a montré que malgré une déformation endogène plus élevée, les bétons formulés à base de ciment au laitier de haut-fourneau fissurent après le béton formulé à base de ciment Portland. Ce comportement est dû à : -l’impact du laitier sur la réaction d’hydratation du matériau cimentaire ; -la présence d’une expansion de la matrice cimentaire des bétons formulés à base de ciment au laitier de haut-fourneau au jeune âge qui retarde l’apparition des contraintes de traction au sein du matériau ; -la plus grande capacité de ces matériaux cimentaires à relaxer les contraintes de traction/ Today, the use of concretes with mineral additions (fly ash, slag) for civil engineering structures is spreading worldwide. Indeed, the production of blended cements is more respectful of the environment than the production of Portland cement, because it allows reducing greenhouse gas emissions and using industrial wastes. Slag cement concretes are also largely used for their good resistance to alkali-silica reactions, sulphate attacks and chloride diffusion. However, some of constructions built with slag cement concretes have exhibited cracking at early age due to their restrained deformations, such as thermal, autogenous and drying shrinkage. Following these observations, a preliminary experimental study was realized in the laboratory of BATir Department at ULB. It revealed several characteristics of the behaviour of slag cement concretes: 1. The study of restrained deformations under drying conditions by means of ring tests showed that the slag cement concretes seem more prone to crack than the Portland cement concretes; 2. The total free shrinkage for slag cement concrete is clearly larger than for Portland cement concrete. This difference of behaviour is mainly due to the fast and large increase in the autogenous deformation of the slag cement concrete. Following these experimental results, the effect of the autogenous deformation on the cracking sensibility of slag cement concretes seemed interesting to investigate. Their deformations (autogenous deformation, compressive and tensile basic creep) have been studied at early age for three concretes characterized by different slag contents (0, 42 and 71%) under free and restrained conditions. For monitoring free and restrained autogenous deformations, several test rigs aimed at limiting artefacts were designed, like the TSTM (Temperature Stress Testing Machine). Moreover, the behaviour of these concretes was also characterized by a study at a macro- and microstructure scale. Finally, this study shows that the slag cement concretes under sealed and fully restrained conditions crack later than the Portland cement concrete, despite the fact that they are characterized by the largest autogenous deformation. This behaviour is due to: - the slag effect on the hydration reaction of cementitious material; - the cement matrix expansion of the slag cement concretes at early age which delays the occurrence of tensile stresses inside the material; - the largest capacity of this concrete to relax tensile stresses.

In this thesis, the focus has been on micro-mechanical mechanisms in polymer-based materials and structures. The first part of the thesis treats length-scale effects on polymer materials. Experiments have showed that the smaller the specimen, the stronger is the material. The length-scale effect was examined experimentally in two different polymers materials, polystyrene and epoxy. First micro-indentations to various depths were made on polystyrene. The experiments showed that length-scale effects in inelastic deformations exist in polystyrene. It was also possible to show a connection between the experimental findings and the molecular length. The second experimental study was performed on glass-sphere filled epoxy, where the damage development for tensile loading was investigated. It could be showed that the debond stresses increased with decreasing sphere diameter. The debonding grew along the interface and eventually these cracks kinked out into the matrix. It was found that the length to diameter ratio of the matrix cracks increased with increasing diameter. The experimental findings may be explained by a length-scale effect in the yield process which depends on the strain gradients. The second part of the thesis treats mechano-sorptive creep in paper, i.e. the acceleration of creep by moisture content changes. Paper can be seen as a polymer based composite that consists of a network of wood fibres, which in its turn are natural polymer composites. A simplified network model for mechano-sorptive creep has been developed. It is assumed that the anisotropic hygroexpansion of the fibres leads to large stresses at the fibre-fibre bonds when the moisture content changes. The resulting stress state will accelerate creep if the fibre material obeys a constitutive law that is non-linear in stress. Fibre kinks are included in order to capture experimental observations of larger mechano-sorptive creep effects in compression than in tension. Furthermore, moisture dependent material parameters and anisotropy are taken into account. Theoretical predictions based on the developed model are compared to experimental results for anisotropic paper both under tensile and compressive loading at varying moisture content. The important features in the experiments are captured by the model. Different kinds of drying conditions have also been examined. / QC 20100910

Probabilistic assessment and life cycle management of engineering components and systems in a nuclear power plant is intended to ensure safe and efficient operation of energy generation over its entire life. The CANDU reactor core consists of 380-480 pressure tubes, which are like miniature pressure vessels that contain natural uranium fuel. Pressure tubes operate under severe temperature and radiation conditions, which result in degradation with ageing. Presence of flaws in a pressure tube makes it vulnerable to delayed hydride cracking (DHC), which may lead to rupture or break-before-leak situation. Therefore, assessment of flaws in the pressure tubes is considered an integral part of a reactor core assessment program. The main objective of the thesis is to develop advanced probabilistic and mechanical stress field models for the assessment of flaws. The flaw assessment models used by the industries are based on deterministic upper/lower bound values for the variables and they ignore uncertainties associated with system parameters. In this thesis, explicit limit state equations are formulated and first order reliability method is employed for reliability computation, which is more efficient than simulation-based methods. A semi-probabilistic approach is adopted to develop an assessment model, which consists of a mechanics-based condition (or equation) involving partial factors that are calibrated to a specified reliability level. This approach is applied to develop models for DHC initiation and leak-before-break assessments. A novel feature of the proposed method is that it bridges the gap between a simple deterministic analysis and complex simulations, and it is amenable to practical applications. The nuclear power plant systems are not easily accessible for inspection and data collection due to exposure to high radiation. For this reason, small samples of pressure tubes are inspected at periodic intervals and small sample of data so collected are used as input to probabilistic analysis. The pressure tube flaw assessment is therefore confounded by large sampling uncertainties. Therefore, determination of adequate sample size is an important issue. In this thesis, a risk informed approach is proposed to define sample size requirement for flaw assessment. Notch-tip stress field is a key factor in any flaw assessment model. Traditionally, linear elastic fracture mechanics (LEFM) and its extension, serves the basis for determination of notch-tip stress field for elastic and elastic-perfectly-plastic material, respectively. However, the LEFM solution is based on small deformation theory and fixed crack geometry, which leads to singular stress and strain field at the crack-tip. The thesis presents new models for notch and crack induced stress fields based on the deformed geometry. In contrast with the classical solution based on small deformation theory, the proposed model uses the Cauchy's stress definition and boundary conditions which are coupled with the deformed geometry. This formulation also incorporates the rotation near the crack-tip, which leads to blunting and displacement of the crack-tip. The solution obtained based on the final deformed configuration yields a non-singular stress field at the crack-tip and a non-linear variation of stress concentration factor for both elastic and elastic-perfectly-plastic material. The proposed stress field formulation approach is applied to formulate an analytical model for estimating the threshold stress intensity factor (KIH) for DHC initiation. The analytical approach provides a relationship between KIH and temperature that is consistent with experimental results.

Probabilistic assessment and life cycle management of engineering components and systems in a nuclear power plant is intended to ensure safe and efficient operation of energy generation over its entire life. The CANDU reactor core consists of 380-480 pressure tubes, which are like miniature pressure vessels that contain natural uranium fuel. Pressure tubes operate under severe temperature and radiation conditions, which result in degradation with ageing. Presence of flaws in a pressure tube makes it vulnerable to delayed hydride cracking (DHC), which may lead to rupture or break-before-leak situation. Therefore, assessment of flaws in the pressure tubes is considered an integral part of a reactor core assessment program. The main objective of the thesis is to develop advanced probabilistic and mechanical stress field models for the assessment of flaws. The flaw assessment models used by the industries are based on deterministic upper/lower bound values for the variables and they ignore uncertainties associated with system parameters. In this thesis, explicit limit state equations are formulated and first order reliability method is employed for reliability computation, which is more efficient than simulation-based methods. A semi-probabilistic approach is adopted to develop an assessment model, which consists of a mechanics-based condition (or equation) involving partial factors that are calibrated to a specified reliability level. This approach is applied to develop models for DHC initiation and leak-before-break assessments. A novel feature of the proposed method is that it bridges the gap between a simple deterministic analysis and complex simulations, and it is amenable to practical applications. The nuclear power plant systems are not easily accessible for inspection and data collection due to exposure to high radiation. For this reason, small samples of pressure tubes are inspected at periodic intervals and small sample of data so collected are used as input to probabilistic analysis. The pressure tube flaw assessment is therefore confounded by large sampling uncertainties. Therefore, determination of adequate sample size is an important issue. In this thesis, a risk informed approach is proposed to define sample size requirement for flaw assessment. Notch-tip stress field is a key factor in any flaw assessment model. Traditionally, linear elastic fracture mechanics (LEFM) and its extension, serves the basis for determination of notch-tip stress field for elastic and elastic-perfectly-plastic material, respectively. However, the LEFM solution is based on small deformation theory and fixed crack geometry, which leads to singular stress and strain field at the crack-tip. The thesis presents new models for notch and crack induced stress fields based on the deformed geometry. In contrast with the classical solution based on small deformation theory, the proposed model uses the Cauchy's stress definition and boundary conditions which are coupled with the deformed geometry. This formulation also incorporates the rotation near the crack-tip, which leads to blunting and displacement of the crack-tip. The solution obtained based on the final deformed configuration yields a non-singular stress field at the crack-tip and a non-linear variation of stress concentration factor for both elastic and elastic-perfectly-plastic material. The proposed stress field formulation approach is applied to formulate an analytical model for estimating the threshold stress intensity factor (KIH) for DHC initiation. The analytical approach provides a relationship between KIH and temperature that is consistent with experimental results.

Hot-mix asphalt concrete (HMAC) mixture fatigue characterization constitutes a fundamental component of HMAC pavement structural design and analysis to ensure adequate field fatigue performance. HMAC is a heterogeneous complex composite material of air, binder, and aggregate that behaves in a non-linear elasto-viscoplastic manner, exhibits anisotropic behavior, ages with time, and heals during traffic loading rest periods and changing environmental conditions. Comprehensive HMAC mixture fatigue analysis approaches that take into account this complex nature of HMAC are thus needed to ensure adequate field fatigue performance. In this study, four fatigue analysis approaches; the mechanistic empirical (ME), the calibrated mechanistic with (CMSE) and without (CM) surface energy measurements, and the proposed NCHRP 1-37A 2002 Pavement Design Guide (MEPDG) were comparatively evaluated and utilized to characterize the fatigue resistance of two Texas HMAC mixtures in the laboratory, including investigating the effects of binder oxidative aging. Although the results were comparable, the CMSE/CM approaches exhibited greater flexibility and potential to discretely account for most of the fundamental material properties (including fracture, aging, healing, visco-elasticity, and anisotropy) that affect HMAC pavement fatigue performance. Compared to the other approaches, which are mechanistic-empirically based, the CMSE/CM approaches are based on the fundamental concepts of continuum micromechanics and energy theory.

This research establishes a physics-based life determination model for the second generation single crystal superalloy PWA 1484 experiencing out-of-phase thermomechanical fatigue (TMF). The life model was developed as a result of a combination of critical mechanical tests, dominant damage characterization and utilization of well-established literature. The resulting life model improves life prediction over currently employed methods and provides for extrapolation into yet unutilized operating regimes. Particularly, the proposed deformation model accounts for the materials' coupled fatigue-environment-microstructure response to TMF loading. Because the proposed model is be based upon the underlying deformation physics, the model is robust enough to be easily modified for other single crystal superalloys having similar microstructure. Future use of this model for turbine life estimation calculations would be based upon the actual deformation experienced by the turbine blade, thereby enabling turbine maintenance scheduling based upon on a "retirement for a cause" life management scheme rather than the currently employed "safe-life" calculations. This advancement has the ability to greatly reduce maintenance costs to the turbine end-user since turbine blades would be removed from service for practical and justifiable reasons. Additionally this work will enable a rethinking of the warranty period, thereby decreasing warranty related replacements. Finally, this research provides a more thorough understanding of the deformation mechanisms present in loading situations that combine fatigue-environment-microstructure effects.

Helicopter rotor system operates in a highly dynamic and unsteady aerodynamic environment leading to severe vibratory loads on the rotor system. Repeated exposure to these severe loading conditions can induce damage in the composite rotor blade which may lead to a catastrophic failure. Therefore, an interest in the structural health monitoring (SHM) of the composite rotor blades has grown markedly in recent years. Two important issues are addressed in this thesis; (1) structural modeling and aeroelastic analysis of the damaged rotor blade and (2) development of a model based rotor health monitoring system. The effect of matrix cracking, the first failure mode in composites, is studied in detail for a circular section beam, box-beam and two-cell airfoil section beam. Later, the effects of further progressive damages such as debonding/delamination and fiber breakage are considered for a two-cell airfoil section beam representing a stiff-inplane helicopter rotor blade. It is found that the stiffness decreases rapidly in the initial phase of matrix cracking but becomes almost constant later as matrix crack saturation is reached. Due to matrix cracking, the bending and torsion stiffness losses at the point of matrix crack saturation are about 6-12 percent and about 25-30 percent, respectively. Due to debonding/delamination, the bending and torsion stiffness losses are about 6-8 percent and about 40-45 percent after matrix crack saturation, respectively. The stiffness loss due to fiber breakage is very rapid and leads to the final failure of the blade. An aeroelastic analysis is performed for the damaged composite rotor in forward flight and the numerically simulated results are used to develop an online health monitoring system. For fault detection, the variations in rotating frequencies, tip bending and torsion response, blade root loads and strains along the blade due to damage are investigated. It is found that peak-to-peak values of blade response and loads provide a good global damage indicator and result in considerable data reduction. Also, the shear strain is a useful indicator to predict local damage. The structural health monitoring system is developed using the physics based models to detect and locate damage from simulated noisy rotor system data. A genetic fuzzy system (GFS) developed for solving the inverse problem of detecting damage from noise contaminated measurements by hybridizing the best features of fuzzy logic and genetic algorithms. Using the changes in structural measurements between the damaged and undamaged blade, a fuzzy system is generated and the rule-base and membership functions optimized by genetic algorithm. The GFS is demonstrated using frequency and mode shape based measurements for various beam type structures such as uniform cantilever beam, tapered beam and non-rotating helicopter blade. The GFS is further demonstrated for predicting the internal state of the composite structures using an example of a composite hollow circular beam with matrix cracking damage mode. Finally, the GFS is applied for online SHM of a rotor in forward flight. It is found that the GFS shows excellent robustness with noisy data, missing measurements and degrades gradually in the presence of faulty sensors/measurements. Furthermore, the GFS can be developed in an automated manner resulting in an optimal solution to the inverse problem of SHM. Finally, the stiffness degradation of the composite rotor blade is correlated to the life consumption of the rotor blade and issues related to damage prognosis are addressed.

In den durchgeführten Versuchsreihen wurden die Wasserabsorption sowie die Gas- und Wasserpermeabilität sowohl an gerissenen als auch rissfreien Prüfkörpern aus textilbewehrtem Beton (TRC) untersucht. Eine deutliche Steigerung der Wasseraufnahme bei Proben mit unbeschichteten Textilien konnte mit Zunahme der Garnfeinheit beobachtet werden. Bei den gerissenen Proben besteht eine ausgeprägte Abhängigkeit der Transportraten von Flüssigkeiten und Gasen zu den relevanten Risscharakteristika (kumulative Risslänge, Rissbreite). Weiterhin sind Selbstheilungseffekte von feinen Rissen infolge einer zyklischen Wasserbeaufschlagung beobachtet worden. Hierbei kam es zu einer deutlichen Reduzierung der Transportraten sowohl für Wasser als auch für Gase. Eine speziell entwickelte Permeabilitätsmesskammer zur Durchführung von In- Situ-Messungen ermöglicht Untersuchungen zum Stofftransport unter axialer Zugbelastung bei verschiedenen Dehnungszuständen.

Die vorliegende Arbeit reflektiert die aktuelle Diskussion von Modellen zur Vorhersage von Rissbreiten und versucht, objektive Vergleichskriterien aufzustellen sowie Folgerungen für mögliche Lösungswege zu ziehen. Am Beginn steht eine ausführliche Auseinandersetzung mit dem Verbundmechanismus zwischen Betonstahl und Beton und den Möglichkeiten der Verbundanalyse. Ausgehend von eigenen Versuchen an kurzen Verbundlängen zur Untersuchung des Verbundverhaltens von Bewehrung in hochfesten Betonen wird in der Arbeit nach Möglichkeiten zur Vorhersage von Gleit- und Sprengbrüchen gesucht. Für Sprengbrüche, also Längsrissbildung, ist ein verbesserter Versuchsaufbau entwickelt worden, der Rückschlüsse auf die Verformungsentwicklung in der potentiellen Sprengbruchfläche und den Aufbau eines Verbundwiderstands unter Belastung ermöglicht. Es stellte sich trotz der Fortschritte in der Versagensanalyse dieser Versuche heraus, dass es wenig sinnvoll ist, die gewonnenen Verbundgesetze direkt auf lange Verbundlängen zur Ermittlung von Rissbreiten anzuwenden. Zur Simulation der mit Bauteilsituationen vergleichbaren langen Verbundlängen wird dagegen eine Hypothese über den Widerstand einer potentiellen Längsbruchfläche verwendet. Dabei wird die mögliche Reaktion von gekoppelten und voneinander abhängigen Betonzugringen um einen Betonstahl, vom Lasteintrag beginnend, sukzessive fortschreitend aufgebaut. Die Aufteilung der Zugringe folgt dabei einer Annahme über die Entwicklung von lokalen Verbundrissen nach Goto. Damit ist die Zugringtheorie von Tepfers auf lange Verbundlängen übertragbar und Simulationen von Zugstäben nahe an Tepfers theoretischen Ansätzen werden so ermöglicht. Die Rechnersimulationen an langen Verbundlängen im Vergleich zur Prognose nach MC 90 wurden für Einzelrissbildung und abgeschlossene Rissbildung an zylindrischen Dehnkörpergeometrien durchgeführt. Zur Verifizierung der zeitabhängigen Einflüsse wie Zwängungen aus Schwinden und Zugkriechen sind einfache Ansätze entwickelt worden. Am Ende dieser Analysen steht eine Neubewertung normativer Ansätze (MC 90/DIN 1045-1 sowie EN 1992-1-1) zur Berechnung einer charakteristischen Rissbreite. Eine Schlüsselstellung nimmt die richtige Prognose des wirksamen Rissabstands in allen Berechnungsmodellen ein. Anhand eines neu zusammengestellten Datensatzes und vorhandener Vergleichsdatensätze wurde die Performance der Modelle untersucht. Anwendungsbereiche, die problematisch erscheinen, konnten eingegrenzt werden. Es war zu folgern, dass die Ansätze für den effektiven Bewehrungsgrad und die Verbundspannung zu verbessern sind. Die daraufhin mit einem additiven Sicherheitselement und einem variablen Mindestwert entwickelte Modellalternative gegenüber den normativen Vorschlägen ist nun zielgerichteter und kann dabei eine effektivere und zuverlässigere Prognose der Rissbreite und damit der konstruktiven Bewehrungslösung liefern. Die Anforderungen an die Performance eines Rechenwertes der Rissbreite wk sind um ein Effektivitätskriterium für den Rissabstand srk ergänzt worden, dessen Vorhersagequalität entscheidend für effiziente und zuverlässige Vorhersagen der Rissbreite ist. Die Zuverlässigkeit des DIN-Ansatzes für Mindestbewehrung im Grenzzustand der Gebrauchstauglichkeit ist ebenfalls geprüft worden. Umfangreiche Zusammenstellungen, Beispiele und Parameterstudien sind im Anhang der Arbeit hinzugefügt, um die theoretischen Ergebnisse zu stützen und Lesern Vergleichsmöglichkeiten zu bieten. Dazu gehören auch zwei Ablaufpläne und Hilfsmittel für einfache Absicherungen, die die zu erwartenden Schwierigkeiten bei der Verwendung des normativen DIN 1045-1 Ansatzes zur Beschränkung auf kleine Rissbreiten ausgleichen können. / The doctoral thesis reflects the recent discussion on the finding of suitable verification models for crack width control. It tries to assemble criteria for the comparison in order to draw conclusions from the outcome. In the very beginning stands a widespread analysis of the bond mechanisms between the reinforcing steel and the concrete. Starting from own testing on short embedment lengths in HPC, opportunities are researched for the prediction of a sliding or splitting failure of the surrounding concrete during bar pull-out. An improved test setup is developed by the Author to verify the splitting failure mechanism that finally leads to longitudinal cover cracking. It enables to obtain better indications for the inner strain development in the later failure plane, showing the development of the bond resistance during loading. Although progress were made in the quality of analysis, it turned out that, a direct implementation of obtained bond laws is less successful to take care of the apparent problem of long embedment lengths. The description of that problem is essential within the crack width verification. Differently, a method is suggested to simulate a probable longitudinal splitting plane and its potential to resist an applied longitudinal load. In that method, the possible reaction of interlinked concrete tension rings around a steel bar is thought to form a growing global resistance with every added resistance ring in a sequential chain that are decreasingly loaded if the distance to the load application increases. The segmentation follows an approximation of the possibly development of local bond cracks acc. to Goto. In this, the application of the tension ring theory from Tepfers were successfully overtaken to the problem of long embedment lengths. It enables for simulations close to the original theory of tensile rings formed by concrete around the reinforcing steel. Comparing the results with MC 90, the simulation of long embedment lengths were performed using imaginary cylindrical test-specimen, enabling the verification of single and stabilized cracking. Simplified methods were developed in order to implement time-dependent influences like restraint from creep and shrinkage.An extensive evaluation of the normative methods (MC 90/ DIN 1045-1 and EN 1992-1-1) for verifications of a characteristic crack width stands at the end of the studies. A key position within the models is held by the realistic prognosis of the accountable crack distance. Using a newly compiled dataset and already existing data for comparison, the performances of current models were verified for predicting crack widths or distances. Complicated fields of its application could be marked and isolated. It was concluded that, the approaches for the determination of the effective reinforcement ratio and the bond stress should be improved. The developed alternative for calculation is assembled with an added safety feature and a variable minimum for the crack distance. It can lead to a more reliable prognosis for crack distances and the depending crack widths in order to design a more efficient reinforcement detailing. The requirements on the performance of a determined characteristic crack width wk are extended by the application of a criteria of effectiveness for the calculated crack distance srk. The reliability of the MC 90 -approach and the DIN-approach for minimum reinforcement has also been checked. Extensive compilations of data, examples and parameter studies are added to the appendix in order to backup the theoretical results and to invite others to compare. Two calculation flow charts and helptools are integrated to ensure the quality of crack width calculations also in cases where smaller crack widths must be verified, using informative and normative methods in MC 90/ DIN 1045-1.