The theoretical part describes the properties of fine-grained admixtures and the ways how these admixtures modify concrete properties. There are also described ways to assemble grain curves in the range 0-1000 m. The practical part describes the properties of all the concrete components used for the tests. From the admixtures and cement, the individual grain curves were compiled. Curves were assembled in the first stage manually by using MS Excel. Subsequently, a simple program was developed based on the knowledge of composing grain curves, which automatically compiles the grain curve according to the given limits. The maximum cement replacement was set at 25% by weight. The physical and mechanical properties of the graded curves thus established were first verified on mortar mixtures where the workability, bulk density and strength were verified at the age 7, 28 and 90 days. In addition, the porosity of cement cement with mercury porosimetry has been verified for selected recipes. The acquired knowledge was subsequently applied to the concrete in the laboratory. Here the maximum cement compensation was set at 30%. In particular, concrete consistency over time, air content in the concrete and compresive strength of concrete at the age 3, 7, 28 and 90 days were verified. Verification was also carried out in practice on the optimization of self-compacting concrete. Mechanical properties have been retained for optimized recipe but there were financial savings and CO2 emissions reductions compare with the original recipe.

This thesis addresses numerical simulations of self-compacting concrete (SCC) castings and suggests a novel modelling approach that treats reinforcement zones in a formwork as porous media. As a relatively new field in concrete technology, numerical simulations of fresh concrete flow can be a promising aid to optimise casting processes and to avoid on-site casting incidents by predicting the flow behaviour of concrete during the casting process. The simulations of fresh concrete flow generally involve complex mathematical modelling and time-consuming computations. In case of a casting prediction, the simulation time is additionally significantly increased because each reinforcement bar occurring in succession has to be considered one by one. This is particularly problematic when simulating SCC casting, since this type of concrete is typically used for heavily reinforced structural members. However, the wide use of numerical tools for casting prediction in practice is possible only if the tools are user-friendly and simulations are time-saving. In order to shorten simulation time and to come closer to a practical tool for casting prediction, instead to model steel bars one by one, this thesis suggests to model zones with arrays of steel bars as porous media. Consequently, one models the flow of SCC through a reinforcement zone as a free-surface flow of a non-Newtonian fluid, propagating through the medium. By defining characteristic parameters of the porous medium, the influence on the flow and the changed (apparent) behaviour of concrete in the porous matrix can be predicted. This enables modelling of any reinforcement network as a porous zone and thus significantly simplifies and fastens simulations of reinforced components’ castings. Within the thesis, a computational model for SCC flow through reinforced sections was developed. This model couples a fluid dynamics model for fresh concrete and the macroscopic approach for the influence of the porous medium (formed by the rebars) on the flow. The model is implemented into a Computational Fluid Dynamics software and validated on numerical and experimental studies, among which is a large-scale laboratory casting of a highly reinforced beam. The apparent rheology of concrete within the arrays of steel bars is studied and a methodology to determine unknown input parameters for the porous medium is suggested. Normative tables defining characteristic porous medium parameters as a function of the topology of the rebar zone for different reinforcement cases are generated. Finally, the major contribution of this work is the resulting numerical package, consisting of the numerical solver and the parameter library. The thesis concludes on the ability of the porous medium analogy technique to reliably predict the concrete casting behaviour, while being significantly easier to use and far less time consuming than existing tools. / Die Arbeit behandelt die numerische Modellierung des Fließverhaltens von selbst-verdichtendem Beton (SVB) in bewehrten Schalungselementen. Die numerische Simulation des Fließens von Frischbeton kann eine vielversprechende Unterstützung bei der Optimierung von Befüllvorgängen sein, indem diese bereits im Vorfeld vorhergesagt werden. Die Simulation des Fließens von Frischbeton verwendet komplizierte mathematische Modelle und zeitintensive Rechenoperationen. Darüber hinaus wird die Simulationszeit für die Vorhersage des Füllvorgangs zusätzlich deutlich verlängert, weil aufeinanderfolgende Bewehrungsstäbe einzeln zu berücksichtigen sind. Das ist insbesondere für die Simulation von SVB ein entscheidendes Problemfeld, da SVB oft gerade für hochbewehrte Bauteile verwendet wird. Dennoch ist ein weitreichender Einsatz von numerischen Hilfsmitteln bei der Vorhersage von Füllprozessen nur denkbar, wenn die Anwenderfreundlichkeit und eine Zeitersparnis gewährleistet werden können. Um die Simulationszeit zu verkürzen und näher an eine anwenderfreundliche Lösung für die Vorhersage von Füllprozessen zu kommen, wird als Alternative zur einzelnen Modellierung aller Stahlstäbe in dieser Arbeit vorgeschlagen, Zonen mit Bewehrungsstäben als poröse Medien zu modellieren. Infolgedessen wird das Fließen von SVB durch bewehrte Zonen als Strömung eines nicht-Newton’schen Fluides durch ein poröses Medium betrachtet. Durch die Definition charakteristischer Parameter des porösen Mediums kann das veränderte Verhalten des Betons in der porösen Matrix vorhegesagt werden. Dies ermöglicht die Modellierung beliebiger Bewehrungszonen und vereinfacht und beschleunigt folglich die numerische Simulation bewehrter Bauteile. Im Rahmen der Arbeit wird ein Rechenmodell für das Fließverhalten von SVB durch bewehrte Schalungszonen entwickelt. Das Modell verkoppelt das Strömungsverhalten von Beton mit dem makroskopischen Ansatz für den Einfluss von porösen Medien, welche in diesem Fall die Bewehrungsstäbe ersetzen. Das entwickelte Modell wird in eine CFD-Software implementiert und anhand mehrerer numerischer und experimenteller Studien validiert, darunter auch ein maßstabsgetreues Fließexperiment eines hochbewehrten Balkens. Darüber hinaus wird die scheinbare Rheologie des Betons innerhalb der Anordnung der Stahlstäbe untersucht und daraus eine Methode zur Bestimmung unbekannter Parameter für das poröse Medium vorgeschlagen. Es werden hierfür auch normative Tabellen generiert, die die charakteristischen Eigenschaften der porösen Medien für unterschiedliche Bewehrungsanordnungen abbilden. Zuletzt ist der Hauptbeitrag dieser Arbeit das resultierende Numerikpaket, bestehend aus dem numerischen Solver einschließlich des implementierten Modells sowie der Parameterbibliothek. Im Abschluss werden die Verlässlichkeit der Vorhersage von Füllvorgängen durch die Analogie zu porösen Medien erörtert sowie Schlussfolgerungen zur deutlichen Ersparnis an Aufwand und Zeit gegenüber herkömmlichen Methoden vorgenommen.

Gegenstand der Arbeit ist die Entwicklung eines numerischen Stoffgesetzes, welches die materialspezifischen Besonderheiten Selbstverdichtender Betone in jungem Alter erfasst. Durch das erhöhte Schwindmaß eines Selbstverdichtenden Betons innerhalb der ersten zwölf Stunden können Dehnungszustände hervorgerufen werden, welche zu Schädigungen führen, die von den einschlägigen Normen bisher noch nicht erfasst wurden. Im Zuge des Forschungsprojektes „Selbstverdichtender Beton im Untertagebau“ konnten Erkenntnisse über das materialspezifische Verhalten bei konstanten Umgebungsbedingungen erlangt werden. Diese Ergebnisse wurden mit übertägig gewonnen Daten verglichen, um eine klare Abgrenzung zu einem normalen Rüttelbeton zu ziehen. Im weiteren Verlauf wurden die Ergebnisse zur Kalibrierung einer numerischen Simulation herangezogen. Damit kann nun, in Abhängigkeit der relativen Luftfeuchtigkeit und der Bauteilgröße, das Dehnungsverhalten eines SVB in jungem Alter realitätsnah beschrieben werden.:Inhaltsverzeichnis Vorwort II Kurzfassung III Abstract IV 1. Einleitung 1 1.1 Problemstellung 1 1.2 Stand der Erkenntnis 4 1.3 Zielsetzung 8 2. Mechanische Eigenschaften Selbstverdichtender Betone 12 2.1 Rheologische Grundlagen 12 2.1.1 Mischungszusammensetzung für den Einsatz Untertage 12 2.1.2 Kinetik des Erstarrens 17 2.1.3 Frisch- und Festbetoneigenschaften 20 2.1.4 Mischungsentwurf 22 2.2 Feuchte- und Wärmetransport 24 2.2.1 Hydratationsverhalten 24 2.2.2 Feuchtetransport und Speicherung 28 2.2.3 Numerische Umsetzung der Feuchte- Wärmekopplung 32 2.2.4 Finite Element Formulierung und Umsetzung mit Abaqus 35 2.3 Mathematische Formulierung 40 2.3.1 Thermische Leitfähigkeit 40 2.3.2 Hygrische Leitfähigkeit 42 2.3.2.1 Hygrische Transportvorgänge bei Änderung der Umgebungsfeuchte 43 2.3.2.2 Hygrische Transportvorgänge anhand von Temperaturveränderungen 46 2.4 Lastunabhängige Verformungen von Beton 47 2.4.1 Temperatureffekte 47 2.4.2 Feuchteffekte 49 3. Experimentelle Untersuchungen 51 3.1 Ergebnisse der Laborversuche 51 3.1.1 Zug- und Druckfestigkeiten 51 3.1.2 Hydratationsverhalten 55 3.1.3 Feuchtemessungen an Schwindrinnen 57 3.1.4 Schwindverhalten aus Laborversuchen 62 3.2 Untersuchungen am Großversuchsstand 65 3.2.1 Einrichtung des Versuchsstandes 65 3.2.2 Fördertechnologie 68 3.2.3 Schalungsdrücke 69 3.2.4 Hydratationsverhalten und Lastunabhängige Verformungen 70 3.3 Versuchsergebnisse am Großversuchsstand 70 3.3.1 Hydratation und Wärmefreisetzung 70 3.3.2 Schalungsdrücke 74 3.3.3 Schwind- und Temperaturdehnungen 76 3.3.3.1 Schwindrinnen 76 3.3.3.2 Tunnelbauwerk 78 3.4 Rissbildung am Bauwerk 80 3.4.1 Übersicht zu gängigen Risskonzepten 80 3.4.2 Methodenvalidierung der Risskriterien 83 4. Numerische Berechnungen 87 4.1 Numerische Grundlagen 87 4.1.1 Zwangsspannungen infolge Hydratation 87 4.1.1.1 Instationäre Wärmeleitungsprobleme 89 4.1.1.2 Berechnung von Verschiebungsfeldern 90 4.1.2 Thermisch-hygrische Dehnungen 92 4.2 Numerische Detailuntersuchungen und Modellparameter 94 4.2.1 Konstruktive Details des Modells 95 4.2.2 Bewehrungselemente 97 4.2.3 Ermittlung der benötigten Parameter 99 4.3 Vergleichsberechnungen 103 4.3.1 Hydratationswärmeentwicklung 103 4.3.2 Thermisch-hygrische Kopplung 106 4.4 Berechnungsergebnisse 109 4.4.1 Schwindrinne 110 4.4.1.1 Temperaturentwicklung und Trocknungsverhalten 110 4.4.1.2 Schwinddehnungen 113 4.4.1.3 Längenänderungen infolge unterschiedlicher Umgebungsfeuchten 117 4.4.2 Untertägiges Tunnelbauwerk 119 4.4.2.1 Temperaturentwicklung und Trocknungsverhalten bei hohen Luftfeuchtigkeiten 119 4.4.2.2 Spannungsentwicklung infolge Zwang 122 4.4.3 Rissbildung in jungem Alter 126 4.4.3.1 Kritischer Hauptspannungsraum und mögliche Rissbreiten 126 4.4.3.2 Beanspruchungen der Bewehrung 131 4.4.4 Abhängigkeiten der Dehnungsverteilung und Rissbreite von Selbstverdichtenden Betonen in jungem Alter 134 5. Zusammenfassung und Ausblick 139 Literaturverzeichnis 143 Abkürzungsverzeichnis 151 Abbildungsverzeichnis 152 Tabellenverzeichnis 156 Anhangsverzeichnis 157

Idag är intresset för högpresterande betong (HPB) växande runt om världen då fördelarna är många, eftersom slankare, tätare, starkare och lättare konstruktioner kan tillverkas.   Detta examensarbete handlar om materialförsök och modellering för en typ av HPB som ska användas i husbyggnation. Arbetet inleddes med materialförsök i färskt tillstånd, där god gjutbarhet och konsistens eftersträvades. Utgångspunkten var från ett grundrecept med två olika ballastsorter (slaggballast med flygaska och krossballast från asfaltindustrin med silikastoft), vilka namngavs till pilotförsök 1 och pilotförsök 2. Vidare valdes pilotförsök 1 att provas i hårdnat tillstånd då det visades att det var mer ekonomiskt lönsam eftersom ballasten inte behövde siktas, lägre vct tillhandhölls och att flygaskan som användes i pilotförsök 1 är billigare än silikastoft som användes i pilotförsök 2. Resultaten efter 28 dygn för de materialförsök som utfördes i hårdnat tillstånd var: Tryckhållfasthet; 141,9 MPa Draghållfasthet; 7,0 MPa Böjdraghållfasthet; 10,0 MPa Elasticitetsmodul; 46,4 GPa Krympning efter 56 dygn; 0,5 ‰ Samtliga försök utfördes enligt svenska standarder (SS).   Dessutom vidareutvecklas och förbättrades ett redan arkitektoniskt gestaltat Attefallshus ur ett konstruktions- och hållbarhets perspektiv, där fokus låg på transport- och produktionsförutsättningar. Det resulterade i att horisontella avstyvningar tillades i väggelementen för att öka styvheten och minska risken för brott under transport och produktion. Huset är tänkt att produceras med prefabriceringsteknik. Avslutningsvis modellerades ett oarmerat väggelement i FE-programmet Abaqus under linjärt elastiskt tillstånd. Vid modelleringen användes de materialparametrar som erhölls från materialförsöken.  Det resulterade i att deformationer, spänningar samt knäcknings- och bucklingsanalys kunde redas ut. Väggelementen i huset klarar normenliga laster enligt modelleringen. / Nowadays the interest for high-performance concrete (HPC) is growing around the world as the benefits are many, for example slender, denser, stronger and lighter structures can be manufactured.   This thesis is about material and design experiments for a type of HPC to be used in building construction. The work began with materials experiments in the fresh state, where good workability and consistency were tried to be obtained. The starting point was from a basic recipe with two different aggregate types (slag aggregates with fly ash and crushed aggregates from the asphalt industry with silica fume), which were named as the pilot test 1 and the pilot test 2. Furthermore pilot test 1 was elected to be tested in hardened state as it turned out to be more economically profitable, had a lower vct, and that the flyash was cheaper than the silica fume used in the pilot test 2. The results after 28 days when the materials experiments were carried out in the hardened state were: Compressive strength; 141,9 MPa Tensile strength; 7,0 MPa Flexural strength; 10,0 MPa Modulus of elasticity; 46,4 GPa Shrinkage after 56 days; 0,5 ‰ All experiments were performed according to Swedish standards SS.   Moreover, an existing architecturally portrayed Attefallshus was further developed and improved from a design and a strength perspective that mainly focused on transport and production. It resulted in the horizontal stiffeners to be installed in the wall elements to increase rigidity and reduce the risk of breakage during shipment and production. The house is intended to be built with prefabrication technology. Finally the unreinforced wall elements were modeled in the FE program ABAQUS under linear elastic condition. During modeling the material parameters obtained from material tests were used in the model. Consequently, strain, stress and buckling analysis could be made. The wall sections in the house met the norm loads according to the model.

As a response to the ever denser cities, skyscrapers have become yet more popular and are growing more and taller than ever. A new efficient structural system for skyscrapers has been proposed by Tyréns AB, called the Tubed Mega Frame. This structural system consists of hollow concrete tubes at the perimeter of the building. Since this structural system has not yet been used in any skyscraper several aspects have still not been studied or investigated. An important aspect having an impact on the system’s competitiveness compared to traditional structural systems is how a skyscraper using this new structural system could be built. This thesis treats the construction methodology of Tubed Mega Frame structures. The construction methodology of a prototype building is evaluated to connect the findings to a plausible real project. Building very tall concrete structures sets a lot of demands on the concrete used and having an effective construction is essential. The elastic modulus of the concrete has been identified as one of the most important concrete properties why this topic has been studied. Comparisons of the formulas of different codes for estimating the elastic modulus have been made to see what elasticity can be achieved. Concrete recipes that have been used in already built skyscrapers have been reviewed to see what elastic moduli are feasible to reach and expect. Pumping concrete to high levels sets demands on the concretes flowability and self-compacting concrete is necessary to use. Ways of improving the concrete properties are also studied. All studies show that the Tubed Mega Frame structural system would be possible to construct with today’s concrete and pumping technology even though improvements can be expected from future development in concrete technology. As most skyscrapers that are built today, a Tubed Mega Frame structure would preferably be built with a self-climbing formwork system rising one level at a time. From a review of available construction methodologies, the thesis shows that these systems would be applicable on a Tubed Mega Frame structure with minor adaptions of the systems. The floor cycle time, i.e. the time it takes to complete an entire floor before proceeding to the next level, has a significant importance in determining the construction time of a skyscraper. For this reason a floor cycle with all activities related to the structural system and their sequences have been developed for the prototype building. By determining all the relations that are between activities and using productivities for estimating their durations it has been possible to evaluate the time it would take to complete a standard floor. By the use of Microsoft Project the duration of a stated average floor cycle has been estimated to a little more than 4 days. / Som en reaktion på att allt fler människor bor i städer har skyskrapor kommit att växa sig allt fler och högre. Traditionellt har skyskrapor oftast utnyttjat någon form av kärna som stomsystem vilken upptar stor yta av våningsplanen. Som en möjlig metod att göra skyskrapors stomsystem effektivare har Tyréns utvecklat det nya stomsystemet Tubed Mega Frame. Då detta bärande system ännu inte har använts i någon skyskrapa är det ett flertal aspekter som inte har blivit studerade och undersökta. En viktig aspekt som är av stor vikt för systemets konkurrenskraft gentemot mer traditionella system är hur det skulle gå till att bygga en skyskrapa som använder detta nya stomsystem. Det här examensarbetet behandlar byggnationsmetodiken för Tubed Mega Frame. Byggnationen av en prototypbyggnad som använder detta system utvärderades för att koppla resultaten till en möjlig verklig byggnad. Att bygga väldigt höga konstruktioner i betong ställer stora krav på betongen som används, och att ha en effektiv byggnation är också av stor vikt. Betongens elasticitetsmodul har identifierats som en av de viktigaste egenskaperna för betongen och därför har detta område studerats djupare. En jämförelse av hur olika normer beräknar elasticitetsmodulen har gjorts och vilka elasticitetsmoduler det ger. De betongsammansättningar som har använts i tidigare skyskrapebyggande har studerats för att se vilka elasticitetsmoduler som kan förväntas. Att pumpa betong till höga höjder ställer stora krav på betongens pumpbarhet. För att göra detta möjligt är det nödvändigt att använda självkompakterande betong. Vilka olika sätt som finns tillgängliga för att styra betongens egenskaper har också studerats. Undersökningarna visar på att det skulle kunna vara möjligt att med dagens betong och pumpteknologi bygga en skyskrapa som använder Tubed Mega Frame som bärande system. Med framtida framsteg inom betongteknologi kan man även förvänta att bättre lämpad teknik kommer att utvecklas. En skyskrapa med stomsystemet Tubed Mega Frame skulle liksom de flesta av dagens skyskrapor lämpligtvis byggas med hjälp av självklättrande formsystem, och därigenom bygga en våning i taget. Studier av teknik och byggnationsmetoder som finns tillgängliga idag har visat på att dagens teknik skulle vara möjliga att applicera på Tubed Mega Frame med endast mindre justeringar. Det som har ett stort inflytande på byggtiden av en skyskrapa är våningscykeltiden, d.v.s. den tid det tar att bygga en våning innan det är möjligt att fortsätta på nästa. Av denna anledning har en våningscykel med alla relevanta moment som ingår blivit bestämd och utvärderad för prototypbyggnaden. Genom att ha klargjort alla relationer mellan olika aktiviteter och den tid de tar att utföra har det varit möjligt att utvärdera den tid en hel våningscykel skulle ta. Med hjälp av Microsoft Project har en våningscykel för en våning som bedömts som representativ för hela prototypbyggnaden kommit att ta drygt fyra dygn.

This study aims at examining capacity building for Foundation Phase Mathematics teachers in curriculum differentiation in Limpopo Province. Proceeding within the framework of inclusive education, it takes as its point of departure two issues which are collectively critical for learner performance in Mathematics, namely, teacher capacity and differentiated instruction. The study revolves around the view that for improved learner achievement in Mathematics, particularly in lower grades, instructional practices aimed at supporting learners should be differentiated; and, that for this to be possible, teachers should be equipped with the capacity needed to carry out curriculum differentiation. This view emerges from the convergence of three problems which constitute the motivation for conducting this study. The first problem is poor learner achievement in Mathematics in South Africa, which is a subject dominating the public media and scientific discourse. The second problem is a documented general lack among teachers of appropriate knowledge, skills and attitudes needed for modification and adaptation of curriculum to the differentiated needs of learners. The last problem is the changing curriculum policy context in which teachers work as represented by the current national curriculum policy taking place against the backdrop of the broader South African education transformation agenda, geared towards inclusion. Underlying these problems is the recognition of curriculum as constituting one of the barriers to inclusive education.Based on an assumption that poor performance of learners in the Foundation Phase Mathematics is due to teachers’ inability to differentiate curriculum and their lack of the necessary capacity, this study adopts a qualitative research design and follows a qualitative approach to examine the problem. Data was collected by means of interviews, observations and document analysis. Twelve Mathematics teachers from three purposively selected schools and one curriculumadvisor from one circuit participated in the study. Data were analysed by means ofBraun and Clarke’s method of thematic analysis. The results present the challenges that Foundation Phase Mathematics teachers face, which include inability to respond to learner diversity and inadequate training in curriculum differentiation. / Inclusive Education / M. Ed. (Inclusive Education)

This study aims at examining capacity building for Foundation Phase Mathematics teachers in curriculum differentiation in Limpopo Province. Proceeding within the framework of inclusive education, it takes as its point of departure two issues which are collectively critical for learner performance in Mathematics, namely, teacher capacity and differentiated instruction. The study revolves around the view that for improved learner achievement in Mathematics, particularly in lower grades, instructional practices aimed at supporting learners should be differentiated; and, that for this to be possible, teachers should be equipped with the capacity needed to carry out curriculum differentiation. This view emerges from the convergence of three problems which constitute the motivation for conducting this study. The first problem is poor learner achievement in Mathematics in South Africa, which is a subject dominating the public media and scientific discourse. The second problem is a documented general lack among teachers of appropriate knowledge, skills and attitudes needed for modification and adaptation of curriculum to the differentiated needs of learners. The last problem is the changing curriculum policy context in which teachers work as represented by the current national curriculum policy taking place against the backdrop of the broader South African education transformation agenda, geared towards inclusion. Underlying these problems is the recognition of curriculum as constituting one of the barriers to inclusive education.Based on an assumption that poor performance of learners in the Foundation Phase Mathematics is due to teachers’ inability to differentiate curriculum and their lack of the necessary capacity, this study adopts a qualitative research design and follows a qualitative approach to examine the problem. Data was collected by means of interviews, observations and document analysis. Twelve Mathematics teachers from three purposively selected schools and one curriculumadvisor from one circuit participated in the study. Data were analysed by means ofBraun and Clarke’s method of thematic analysis. The results present the challenges that Foundation Phase Mathematics teachers face, which include inability to respond to learner diversity and inadequate training in curriculum differentiation. / Inclusive Education / M. Ed. (Inclusive Education)