Die vorliegende Arbeit befaßt sich mit der experimentellen Analyse des Tragverhaltens von Hochleistungsbeton unter mehraxialer Beanspruchung. Dabei wurden sowohl die zwei und die dreiaxiale Drucktragfähigkeit als auch das Verhalten unter zweiaxialer kombinierter Druck Zug Beanspruchung untersucht. Für die Analyse kamen jeweils drei Betonfestigkeitsklassen zum Einsatz, C 55/67, C 70/85 und C 90/105. Innerhalb der durchgeführten Versuchsreihen wurden sowohl die jeweiligen Bruchlasten als auch die Spannungs Dehnungs Beziehungen ermittelt. Die Ergebnisse dieser Untersuchungen wurden mit denen verglichen, die an Normalbeton gewonnen wurden. Aus diesem Vergleich wurden Schlußfolgerungen für den Einsatz von Hochleistungsbetonen abgeleitet. Zur mathematischen Beschreibung des Tragverhaltens von Hochleistungsbeton wurden für die untersuchten Beanspruchungsregime Näherungsfunktionen angegeben. / The subject of this paper is the experimental analysis of the behavior of High Performance Concrete under multiaxial loading. Thereby the behavior under bi- and triaxial compression as well as the behavior under combined compression-tension stresses were examined. Three concrete grades were examined, C 55/67, C 70/85 and C 90/105. Within the test series, the ultimate loads and the stress-strain-relationships were determined. The results of the examinations were compared to the results which are already known for normal strength concrete. From these comparisons conclusions for the usage of high performance concrete were made. For the examined states of stress mathematical approximations are specified.

The autogenous shrinkage due to self-desiccation of high- and ultra-high performance concretes with very low water-cement ratio in case of restraint leads to considerable stresses starting from very early age. The resultant risk of cracking presently cannot be adequately investigated. Parameters that are particularly difficult to capture experimentally are the concrete temperature and the viscoelasticity. The primary objective of this work was to assess as precise as possible the autogenous shrinkage cracking propensity of representative concretes at strong restraint and constant room temperature. Test methods needed to be chosen and enhanced in a way that preferably allowed for the efficient and precise investigation of all relevant factors in the future. Ideally, a method suitable for a complete empirical modeling was provided. First the methodological requirements and the advantages and disadvantages of existing test methods were discussed. Based on this, optimized test methods were proposed. Their suitability was verified using the example of ultra-high strength concrete. The choice of concrete compositions considered the essential measures for reducing shrinkage (internal curing, shrinkage-reducing admixtures, reduction of the fraction of Portland cement in the binder). The autogenous shrinkage was measured with the shrinkage cone method. This new test method was validated by investigations of the repeatability and reproducibility and proved efficient and precise. It allows for measurements under non-isothermal conditions; no established test method exists for that purpose to date. The autogenous shrinkage of the ultra-high strength concretes at the age of 24 h, investigated under quasi-isothermal conditions (20 °C), was between 0,25 mm/m and 0,70 mm/m. It was particularly low when a shrinkage-reducing admixture was added and when superabsorbent polymers were used. The stresses due to restraint were determined with the restrained ring test. A large part of the stresses to be expected according to Hooke’s Law were eliminated by creep and relaxation. The relaxation capacity being very pronounced at very early age was the main reason that no visible cracking occurred, not even with the concretes with high autogenous shrinkage. The development of the autogenous shrinkage cracking propensity was described as ratio of restraint stress and splitting tensile strength. By means of modified ring tests, used to determine the maximum tensile stress, it could be shown that the ratio of stress to strength is an appropriate failure criterion. However, the cracking propensity can be calculated correctly only if the strongly age-dependent ratio of uniaxial to splitting tensile strength is accounted for. Besides, it needs to be considered that at very early age a plastic stress redistribution may occur in restrained ring tests. The reference concrete showed a high cracking propensity of up to 0.68. The fact that shrinkage-reducing measures led to significantly lower values reveals their relevance for the safe application of ultra-high strength concrete. However, the investigations carried out here at 20 °C do not allow for a final assessment of the cracking propensity under typical on-site conditions. To empirically model the autogenous shrinkage cracking propensity as a function of temperature and stress level in the future, an analytical stress solution for non-isothermal restrained ring tests and a new approach for investigating the residual stress and relaxation capacity by means of non-passive restrained ring tests was suggested.:1 Introduction 2 Autogenous shrinkage 5 2.1 Shrinkage and hydration 5 2.2 Definitions and research approaches 10 2.3 Metrological issues 14 2.3.1 Multitude of test methods 14 2.3.2 Time-zero 16 2.3.3 Other metrological issues 18 2.4 Corrugated tube method 19 2.5 Influencing parameters 21 2.5.1 Concrete composition 21 2.5.2 Temperature 23 2.5.3 Specific countermeasures 25 2.6 Summary and conclusions with respect to the own work 25 3 Concretes used in the own investigations 27 3.1 Preliminary remarks 27 3.2 Concrete compositions 27 3.3 Constituents 28 3.3.1 Cement 28 3.3.2 Ground-granulated blast furnace slag 28 3.3.3 Silica fume 28 3.3.4 Admixtures 29 3.3.5 Aggregates 29 3.4 Mixing 29 3.5 Basic properties 30 3.5.1 Compressive strength 30 3.5.2 Splitting tensile strength 31 3.5.3 Modulus of elasticity 33 3.5.4 Analysis of mechanical properties 35 3.5.5 Coefficient of thermal expansion 38 3.5.6 Isothermal calorimetry 39 3.6 Summary 39 4 Shrinkage cone method for measuring autogenous shrinkage 41 4.1 Introduction 41 4.2 Setup and measurement procedure 41 4.3 Temperature control 44 4.4 Precision under quasi-isothermal conditions 47 4.4.1 Repeatability 47 4.4.2 Reproducibility 49 4.4.3 Shrinkage cone method vs. corrugated tube method 49 4.5 Autogenous shrinkage of the investigated concretes at 20 °C 54 4.6 Tests under non-isothermal conditions 55 4.7 Summary 56 5 Stress and cracks due to restrained autogenous shrinkage 58 5.1 Introduction 58 5.2 Degree of restraint 58 5.3 Formation of cracks 60 5.4 Very early age and importance of stress relaxation 63 5.5 Creep and cracking - further methodological aspects 65 5.6 Autogenous shrinkage cracking propensity 69 5.7 Role of temperature history 70 5.8 Further state of knowledge 72 5.8.1 Preliminary remarks on test methods 72 5.8.2 Quantitative investigations under restraint conditions 73 5.8.3 A full-scale model for assessing the cracking risk at very early age 77 5.9 Summary 78 6 Investigation of the autogenous shrinkage cracking propensity 80 6.1 Introduction 80 6.2 Suitability of temperature-stress testing machines 80 6.2.1 Development, setup and use 80 6.2.2 Results of round robin tests 83 6.3 Restrained ring test - methodological foundations 86 6.3.1 Setup and use 86 6.3.2 Evaluation of restrained ring tests 90 6.3.3 Use of temperature changes for the investigation of creep and relaxation 96 6.4 Own investigations with the restrained ring test 97 6.4.1 Setup 97 6.4.2 Compensation of disturbing temperature effects 99 6.4.3 Repeatability 100 6.4.4 Measured steel ring strains 101 6.4.5 Simple stress analysis 102 6.4.6 Autogenous shrinkage cracking propensity - further analysis 106 6.4.7 Thermal stress component 116 6.4.8 Period of maximum cracking propensity 118 6.4.9 Restraint stress versus autogenous shrinkage 119 6.4.10 Cracking propensity versus autogenous shrinkage 120 6.4.11 Further considerations on creep 121 6.5 Summary 126 7 Summary, conclusions and outlook 128 7.1 Summary and conclusions 128 7.2 Outlook 130 8 Literature 131 9 Annex 159 / Das durch Selbstaustrocknung verursachte autogene Schwinden von besonders leistungsfähigen Betonen mit sehr niedrigem Wasserzementwert führt bei Dehnungsbehinderung bereits in sehr frühem Alter zu erheblichen Zwangsspannungen. Die Gefahr der Rissbildung, die sich daraus ergibt, lässt sich bislang nur unzureichend untersuchen. Experimentell besonders schwer zu erfassende Faktoren sind die Betontemperatur und die Viskoelastizität. Das vorrangige Ziel der Arbeit war die möglichst genaue Ermittlung der autogenen Schwindrissneigung repräsentativer Betone bei starker Dehnungsbehinderung und konstanter Raumtemperatur. Dabei waren die Prüfverfahren möglichst so zu wählen und weiterzuentwickeln, dass sich zukünftig alle relevanten Faktoren effizient und genau untersuchen lassen. Im Idealfall sollte eine Methode entstehen, die eine vollständige empirische Modellierung erlaubt. Zunächst wurden die methodischen Anforderungen und die Vor- und Nachteile existierender Prüfverfahren diskutiert. Darauf aufbauend wurden optimierte Verfahren vorgeschlagen. Ihre Eignung wurde an ultrahochfestem Beton überprüft. Bei der Auswahl der Betone wurden die wesentlichen Maßnahmen zur Schwindreduzierung berücksichtigt (innere Nachbehandlung, schwindreduzierende Zusatzmittel, Verringerung des Portlandzementanteils am Bindemittel). Das autogene Schwinden wurde mit dem Schwindkegelverfahren gemessen. Das neue Verfahren wurde durch Untersuchungen zur Wiederhol- und Vergleichsgenauigkeit validiert und erwies sich als effizient und genau. Es ermöglicht Messungen unter nicht-isothermen Bedingungen; hierfür existiert bisher kein etabliertes Verfahren. Das autogene Schwinden der untersuchten ultrahochfesten Betone unter quasi-isothermen Bedingungen (20 °C) betrug im Alter von 24 h zwischen 0,25 mm/m und 0,70 mm/m. Besonders gering war es bei Zugabe eines schwindreduzierenden Zusatzmittels bzw. Verwendung superabsorbierender Polymere. Mit dem Ring-Test wurden die bei Dehnungsbehinderung entstehenden Spannungen ermittelt. Ein großer Teil der gemäß Hooke’schem Gesetz zu erwartenden Spannungen wurde durch Kriechen und Relaxation abgebaut. Die im sehr frühen Alter stark ausgeprägte Relaxationsfähigkeit war der wesentliche Grund dafür, dass es selbst bei Betonen mit hohem autogenen Schwinden zu keiner erkennbaren Rissbildung kam. Die Entwicklung der autogenen Schwindrissneigung wurde als Verhältnis von Zwangsspannung und Spaltzugfestigkeit beschrieben. Durch modifizierte Ring-Tests, mit deren Hilfe die maximale Zugspannung ermittelt wurde, konnte gezeigt werden, dass das Verhältnis von Spannung und Festigkeit als Versagenskriterium geeignet ist. Die Rissneigung lässt sich aber nur dann korrekt berechnen, wenn das stark altersabhängige Verhältnis von einaxialer Zugfestigkeit und Spaltzugfestigkeit berücksichtigt wird. Außerdem ist zu beachten, dass es im sehr frühen Alter zu einer plastischen Spannungsumlagerung in Ring-Tests kommen kann. Der Referenzbeton wies eine hohe Rissneigung von bis zu 0,68 auf. Dass die schwindreduzierenden Maßnahmen zu deutlich geringeren Werten führten, zeigt deren Bedeutung für den sicheren Einsatz von ultrahochfestem Beton. Die hier bei 20 °C durchgeführten Untersuchungen erlauben allerdings keine abschließende Bewertung der Rissneigung unter baustellentypischen Bedingungen. Um die autogene Schwindrissneigung zukünftig als Funktion der Temperatur und des Lastniveaus empirisch modellieren zu können, wurden eine analytische Spannungslösung für nicht-isotherme Ring-Tests und ein neuer Ansatz zur Untersuchung der Resttrag- und Relaxationsfähigkeit mit Hilfe nicht-passiver Ring-Tests vorgeschlagen.:1 Introduction 2 Autogenous shrinkage 5 2.1 Shrinkage and hydration 5 2.2 Definitions and research approaches 10 2.3 Metrological issues 14 2.3.1 Multitude of test methods 14 2.3.2 Time-zero 16 2.3.3 Other metrological issues 18 2.4 Corrugated tube method 19 2.5 Influencing parameters 21 2.5.1 Concrete composition 21 2.5.2 Temperature 23 2.5.3 Specific countermeasures 25 2.6 Summary and conclusions with respect to the own work 25 3 Concretes used in the own investigations 27 3.1 Preliminary remarks 27 3.2 Concrete compositions 27 3.3 Constituents 28 3.3.1 Cement 28 3.3.2 Ground-granulated blast furnace slag 28 3.3.3 Silica fume 28 3.3.4 Admixtures 29 3.3.5 Aggregates 29 3.4 Mixing 29 3.5 Basic properties 30 3.5.1 Compressive strength 30 3.5.2 Splitting tensile strength 31 3.5.3 Modulus of elasticity 33 3.5.4 Analysis of mechanical properties 35 3.5.5 Coefficient of thermal expansion 38 3.5.6 Isothermal calorimetry 39 3.6 Summary 39 4 Shrinkage cone method for measuring autogenous shrinkage 41 4.1 Introduction 41 4.2 Setup and measurement procedure 41 4.3 Temperature control 44 4.4 Precision under quasi-isothermal conditions 47 4.4.1 Repeatability 47 4.4.2 Reproducibility 49 4.4.3 Shrinkage cone method vs. corrugated tube method 49 4.5 Autogenous shrinkage of the investigated concretes at 20 °C 54 4.6 Tests under non-isothermal conditions 55 4.7 Summary 56 5 Stress and cracks due to restrained autogenous shrinkage 58 5.1 Introduction 58 5.2 Degree of restraint 58 5.3 Formation of cracks 60 5.4 Very early age and importance of stress relaxation 63 5.5 Creep and cracking - further methodological aspects 65 5.6 Autogenous shrinkage cracking propensity 69 5.7 Role of temperature history 70 5.8 Further state of knowledge 72 5.8.1 Preliminary remarks on test methods 72 5.8.2 Quantitative investigations under restraint conditions 73 5.8.3 A full-scale model for assessing the cracking risk at very early age 77 5.9 Summary 78 6 Investigation of the autogenous shrinkage cracking propensity 80 6.1 Introduction 80 6.2 Suitability of temperature-stress testing machines 80 6.2.1 Development, setup and use 80 6.2.2 Results of round robin tests 83 6.3 Restrained ring test - methodological foundations 86 6.3.1 Setup and use 86 6.3.2 Evaluation of restrained ring tests 90 6.3.3 Use of temperature changes for the investigation of creep and relaxation 96 6.4 Own investigations with the restrained ring test 97 6.4.1 Setup 97 6.4.2 Compensation of disturbing temperature effects 99 6.4.3 Repeatability 100 6.4.4 Measured steel ring strains 101 6.4.5 Simple stress analysis 102 6.4.6 Autogenous shrinkage cracking propensity - further analysis 106 6.4.7 Thermal stress component 116 6.4.8 Period of maximum cracking propensity 118 6.4.9 Restraint stress versus autogenous shrinkage 119 6.4.10 Cracking propensity versus autogenous shrinkage 120 6.4.11 Further considerations on creep 121 6.5 Summary 126 7 Summary, conclusions and outlook 128 7.1 Summary and conclusions 128 7.2 Outlook 130 8 Literature 131 9 Annex 159

<p dir="ltr">Reinforced concrete elements are vulnerable to sliding against each other when shear forces are transmitted between them. Shear-friction is the mechanism by which shear is transferred between concrete surfaces. It develops by aggregate interlock between the concrete interfaces while reinforcement crossing the shear interface or normal force due to external loads contributes to the shear resistance. Current design provisions used in the United States (ACI 318-19, AASHTO LRFD (2020), and the PCI Design Handbook (2017)) include design expression for shear-friction capacity. However, the value of the reinforcement yield strength input into the expressions is limited to a maximum of 60 ksi. Furthermore, the concrete strength is not incorporated into the primary design expressions. These limits cause the potential contribution of high-strength reinforcement and high-strength concrete in shear-friction applications from being considered. Therefore, a research program was developed to investigate the possibility of improving current shear-friction design practice and addressing these current limits.</p><p dir="ltr">Specifically, an experimental program was conducted to evaluate the influence of high-strength reinforcement and high-strength concrete on shear-friction strength. In addition, a statistical analysis was performed using a comprehensive shear-frication database comprised of past tests available in the literature. The experimental program consisted of two phases. Phase I included 24 push-off specimens to study the influence of the yield strength of the interface reinforcement (Grade 60 and Grade 100) and the number and size of interface reinforcing bars (6-No.4 and 4-No. 5 bars) with three different interface conditions (rough, smooth, and shear-key). Phase II included 20 push-off specimens with rough interfaces to investigate the influence of the yield strength of the interface reinforcement (Grade 60 and Grade 100) and concrete strength (target strengths of 4000 psi and 8000 psi). The influence of these two variables was observed over a range of reinforcement ratios (ρ = 0.55%, 0.83%, 1.11%, and 1.38%).</p><p dir="ltr">The test results showed that the overall shear-friction strength was the greatest for rough interface specimens, followed by specimens detailed with shear keys. The smooth interface specimens had the lowest strengths. The results of both phases of the experimental program indicated that the use of high-strength reinforcement did not improve shear-friction capacity.</p><p dir="ltr">Furthermore, the results from the Phase II tests showed that increasing the concrete compressive strength led to increased shear-friction capacity. The test results from the experimental program were analyzed and compared with current design provisions, which demonstrated room for improvement of current design practice.</p><p dir="ltr">Following the experimental program, a comprehensive shear-friction database was analyzed, and multilinear regression was used to create a model to predict shear-friction strength. Factors were then applied to the model to provide acceptable design expressions for shear-friction strength (less than 5% unconservative estimates). The database was used to evaluate the factored model and current design provisions.</p><p dir="ltr">The research outcomes, especially the expressions for shear-friction strength that were developed and that include consideration of the concrete compression strength, along with the shear-friction tests demonstrating the lack of strength gain with the use of Grade 100 reinforcement, provide valuable information for the concrete community to help direct efforts toward improving current shear-friction design practice.</p>