Temperature reduction during concrete hydration in massive structures

Sandra Lagundžija and Marie Thiam

KTH, Royal Institute of Technology

Fortum

Stockholm

Master of Science Project Stockholm, Sweden 2017

TRITA-BKN. Master Thesis 514, 2017 KTH School of ABE ISSN 1103-4297 SE-100 44 Stockholm ISRN KTH/BKN/EX--514--SE SWEDEN

© Sandra Lagundžija & Marie Thiam, 2017 Royal Institute of Technology (KTH) Department of Civil and Architectural Engineering Division of Concrete Structures

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Abstract Concrete is one of the most used building materials in the world because of its good properties. However, cement which is one of the main components in concrete, produces a high amount of heat during the hydration process. The generated heat leads to temperature rise inside the structure. This temperature rise becomes an issue for massive concrete structures, such as hydropower plants and dams, since natural cooling is no longer sufficient. In combination with restrained boundary conditions, increasing temperatures result in tensile stresses causing thermal cracking of the structure.

Reducing thermal cracking in a restrained massive concrete structure can be done by lowering or controlling the temperature rise. Several methods of cooling can be used to achieve this. These methods may be divided in pre-cooling and post-cooling methods. To pre-cool concrete the cement content can be reduced by replacing it with mineral additions such as limestone, fly ash, silica fume and ground granulated blast furnace slag. Another method is to increase the size of the aggregates or to pre-cool the aggregates. Ice can also be used to reduce the temperature at casting the concrete and reduce the amount of water that is needed in the mix. The main post-cooling method is cooling pipes, with cold water circulating in the pipes to cool the structure.

This master thesis project focuses on comparing the possible methods to reduce the temperature in massive concrete structures. Simulations with the computer program HACON were performed to analyse the effect of these methods.

The results from this study showed that cooling pipes gave the best reduction of the maximum temperature and the maximum temperature gradient by 42 % and 76 %, respectively. However, if cooling pipes were to be avoided, the best result of the studied mineral additions was with a replacement of 30 % fly ash resulting in almost the same reduction in maximum temperature but less than one third of the reduction in the gradient. The reduction obtained with fly ash was not as efficient as cooling pipes; therefore appropriate combinations of different pre-cooling methods were also studied. The results of the combination of fly ash, ice, and larger aggregates showed even better reduction of the maximum temperature reduction compared to cooling pipes.

The results also showed that the obtained temperature reductions were almost independent from the thickness of the structure. This conclusion is however only valid for massive structures, where cases with 1.5 and 3.0 m were analysed.

Further study may be on finding suitable combination of pre-cooling methods to avoid the use of cooling pipes, as well as analysing the cost for the different pre-cooling methods.

Keywords: Massive concrete structures, hydration heat, temperature reduction, crack risk, mineral additions, concrete cooling.

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Sammanfattning Betong är ett av de mest använda byggmaterialen i världen, tack vare dess goda egenskaper. Cement, som är en av huvudkomponenterna i betong, genererar en stor värmeutveckling under hydratationen. Värmeutveckling som genereras leder till temperaturhöjningar i strukturen. Denna temperaturhöjning blir således ett problem för massiva betong-konstruktioner, såsom vattenkraftverk och dammar, på grund av att den naturliga avkylningen inte längre är tillräcklig för att avlägsna värmen. I kombination med yttre och inre tvång resulterar högre temperaturer i dragspänningar som orsakar sprickor i strukturen.

Minskningen av sprickbildning i en fastgjuten massiv betongstruktur kan ske genom att minska eller reglera temperaturhöjningen. För att göra det kan flera kylmetoder användas. Dessa metoder kan delas in i förberedande kylning och efterkylning. Med förberedande kylning kan cementhalten i betong reduceras genom ersättning med mineraltillsatser såsom kalksten, flygaska, silikastoft eller markgranulerad masugnsslagg. En annan metod är att öka ballastens storlek eller att kyla ballasten. Is kan användas både för att minska temperaturen vid gjutning av betong och reducera mängden vatten som behövs i blandningen. Den vanligaste efterkylningsmetoden är användning av kylrör med cirkulerande kallt vatten för att kyla strukturen, dvs. utan att ändra mängden värme som produceras av cementhydratationen.

Denna uppsats ämnar jämföra olika metoder för att reducera temperaturen i massiva betongkonstruktioner. Simuleringar har genomförts med datorprogrammet HACON i syfte att analysera inverkan av olika metoder.

Resultaten från studien visade att kylrör gav den bästa minskningen av den maximala temperaturen och den maximala reduktionen av temperaturgradienten med 42 % respektive 76 %. Om kylrör ska undvikas erhålls det bästa resultatet vid användning av 30 % flygaska, vilket resulterade i en snarlik minskning i maximal temperatur med mindre än en tredjedel av reduktionen av gradienten. Då reduceringen med flygaska inte var lika effektiv som med kylrör har lämpliga kombinationer av olika förberedande kylmetoder studerats. Resultatet av kombinationen med flygaska, is och större ballast visade en ännu effektivare minskning av den maximala temperaturreduceringen jämfört med kylrör.

Vidare visade resultaten även att de erhållna temperaturreduceringarna nästan var oberoende av konstruktionens tjocklek. Denna slutsats kan endast tillämpas för massiva konstruktioner, där fall med en 1.5 och 3.0 m tjock vägg analyserades.

Fortsatta studier kan vara att hitta fler lämpliga kombinationer av förberedande kylmetoder för att undvika användning av kylrör, liksom att analysera kostnaden för de olika förberedande kylmetoderna.

Nyckelord: Massiva betongkonstruktioner, värmeutveckling, temperaturreducering, sprickbildning, mineraltillsatser, kylning av betong.

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Preface This project was carried out in 2017 at the Division of Concrete Structures, Department of Civil and Architectural Engineering at KTH, Royal Institute of Technology in Stockholm, Sweden, in collaboration with Fortum Generation, Sweden.

The research presented was carried out as a part of “Swedish Hydropower Centre – SVC”. SVC has been established by the Swedish Energy Agency, Elforsk and Svenska Kraftnät together with Luleå University of Technology, KTH Royal Institute of Technology, Chalmers University of Technology and Uppsala University. www.svc.nu

We would like to thank all the people we have been in contact with, for all their help and guidance during our master thesis project.

A special thanks to our supervisors at Fortum, Hans Bjerhag and Magnus Svensson, for giving us the opportunity to collaborate and deepen our knowledge about hydropower plants and its massive structures as well as giving us the opportunity to visit two hydropower plants. The support regarding logistics and access to material and tools by Fortum has also been appreciated.

We would like to express our sincere gratitude and thankfulness to our supervisors, Dr. Richard Malm and adj. prof. Erik Nordström, at KTH, Royal Institute of Technology for giving us support and for helping us with our simulations and models in HACON.

Stockholm, June 2017

Sandra Lagundžija & Marie Thiam

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Symbols and Abbreviations BAW Bundesanstalt für Wasserbau

BBK Boverkets handbok om betongkonstruktioner

BKR Boverkets Konstruktionsregler

CSH Calcium silicate hydrates

D Thermal diffusivity

EKS Boverkets Konstruktionsregler

GGBS Ground granulated blast furnace slag

HPC High performance concrete

lh Length of heat diffusion

NSC Normal strength concrete

RIDAS Kraftföretagens riktlinjer för dammsäkerhet

SCC Self-compacting concrete

TC Traditional Concrete

τh Time of hydration

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Table of Contents Abstract ...................................................................................................................................... i  

Sammanfattning ...................................................................................................................... iii  

Preface ....................................................................................................................................... v  

Symbols and Abbreviations ................................................................................................... vii  

1   Introduction ....................................................................................................................... 1  

1.1   Background .................................................................................................................. 1  

1.2   Purpose ........................................................................................................................ 2  

1.3   Limitations ................................................................................................................... 2  

1.4   Structure of the report .................................................................................................. 2  

2   Concrete ............................................................................................................................. 3  

2.1   Cement hydration process ............................................................................................ 3  

2.2   Temperature cracks in concrete ................................................................................... 4  

2.2.1   Internal restraint ................................................................................................... 5  

2.2.2   External restraint .................................................................................................. 5  

2.3   Concrete composition .................................................................................................. 6  

2.4   Definition of massive concrete structures .................................................................... 7  

2.5   Concrete for hydropower plants .................................................................................. 9  

2.6   Regulations and codes ............................................................................................... 10  

2.6.1   RIDAS ................................................................................................................ 10  

2.6.2   Swedish Concrete Standard ................................................................................ 11  

2.7   Methods used to lower the hydration heat ................................................................. 12  

2.7.1   Fillers .................................................................................................................. 12  

2.7.2   Silica fume .......................................................................................................... 14  

2.7.3   Fly ash ................................................................................................................ 16  

2.7.4   Combination of fly ash and silica fume .............................................................. 19  

2.7.5   Slag ..................................................................................................................... 20  

2.7.6   Aggregates .......................................................................................................... 21  

2.7.7   Ice ....................................................................................................................... 22  

2.7.8   Cooling pipes ...................................................................................................... 23  

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2.7.9   Heating ............................................................................................................... 24  

3   Field case studies ............................................................................................................. 27  

3.1   Application of cooling methods at Itaipú .................................................................. 27  

3.1.1   Type of cement used at Itaipú ............................................................................ 29  

3.1.2   Cooling process at Itaipú .................................................................................... 29  

3.2   Other applications of cooling methods ...................................................................... 30  

4   Simulation of a massive wall .......................................................................................... 33  

4.1   Reference model ........................................................................................................ 33  

4.1.1   Assumptions ....................................................................................................... 34  

4.1.2   Geometry ............................................................................................................ 34  

4.1.3   Material .............................................................................................................. 35  

4.1.4   Boundary conditions .......................................................................................... 37  

4.1.5   Calculation of the cross section .......................................................................... 40  

4.1.6   Plane section ....................................................................................................... 41  

4.2   Large aggregates ........................................................................................................ 43  

4.3   Cold aggregates ......................................................................................................... 44  

4.4   Ice .............................................................................................................................. 44  

4.5   Fly ash ........................................................................................................................ 44  

4.6   Silica fume ................................................................................................................. 45  

4.7   Ground granulated blast furnace slag ........................................................................ 46  

4.8   Cooling pipes ............................................................................................................. 47  

4.9   Combination of fly ash, ice and large aggregates ...................................................... 47  

4.10   Combination of ice and large aggregates ............................................................... 47  

4.11   Simulation of a thicker wall ................................................................................... 47  

5   Results and discussion .................................................................................................... 49  

5.1   Results for the temperature simulation ...................................................................... 49  

5.1.1   Reference model ................................................................................................. 49  

5.1.2   Cooling pipes ...................................................................................................... 50  

5.1.3   Comparison for all cases with the reference model ........................................... 52  

5.1.4   Three meter thick wall ........................................................................................ 55  

5.2   Crack risk simulation ................................................................................................. 57  

5.2.1   Reference model ................................................................................................. 57  

5.2.2   Comparison with the reference model ................................................................ 59  

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5.2.3   Three meter thick wall ........................................................................................ 60  

6   Conclusions ...................................................................................................................... 63  

6.1   Further research ......................................................................................................... 64  

References ............................................................................................................................... 65  

Appendix A: Calculation of cement reduction .................................................................... 69  

Appendix B: Hydration heat calculation ............................................................................. 71  

Appendix C: Temperatures and stresses .............................................................................. 73  

Appendix D: Results obtained from HACON ..................................................................... 91  

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1 Introduction

1.1 Background

Concrete is a composite of aggregates, binder and water. It is one of the most used building materials in the world. As a material, it is durable, workable and resistant to attacks such as corrosion, frost and fire. Concrete is especially used when building large structures, for example hydropower plants and dams which are expected to be resilient and thus require high durability. For those constructions, huge amounts of concrete are needed, contributing to significant heat generation during the cement hydration. This hydration heat leads to temperature rise in the structure and in combination with restrained edges, this may cause thermal issues such as cracks which may affect the safety of the structure. For structures which are exposed to water pressure as hydropower plants, thermal cracking may cause leakages and reinforcement corrosion.

In Sweden, a cement called Anläggningscement, which is a type I Portland cement with slow heat generation, is often used for hydropower plant and dam constructions. However, the use of Anläggningscement is not sufficient to prevent cracks and thermal damages in massive structures. This cement has to be combined with measures to reduce the heat generation or to control the temperature rise due to the hydration heat.

To lower the risk of thermal cracking the concrete temperature has to be reduced. Several methods can be applied to reduce the temperature in massive concrete structure. Those methods can be divided in pre-cooling and post-cooling methods. Pre-cooling methods mainly consists in reducing the amount of heat generated by cement with substituting materials or by lowering the concrete temperature at casting. Post-cooling methods are used to lower the temperature of the concrete body while hydrating.

Figure 1-1: Massive concrete dam during construction (Civil engineering dictionary, n.d.)

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1.2 Purpose

The purpose of this master project is to identify and evaluate the different methods available to limit and control the temperature rise during hydration within massive concrete structures. The aim is to identify the potential for reducing heat generation and crack risk during hydration for different types of methods and to find alternatives to conventional cooling pipes. Another aim is to see if the thickness of the structure is affecting the temperature reduction with different methods.

1.3 Limitations

This project will only consider massive concrete structures such as hydropower plants and dams and how to lower the temperature and the crack risk within the structure. Thus no consideration will be taken to the costs, the environmental footprint of the methods or the resilience of the concrete by the different methods.

1.4 Structure of the report

In Chapter 2, the behaviour of concrete at early age as well as the different methods which can be used to lower the temperature of concrete structures are presented.

In Chapter 3, the cooling methods for Itaipú power station in South America has been briefly described to give an example of a project that has been using a cooling plant with cooled aggregates, ice and cooling pipes as a cooling method. Two more cases are also presented.

In Chapter 4, a detailed study of a typical wall that can be found in hydropower plants and dams is presented. The purpose of the simulations is to compare the temperature reduction with different materials replacing a certain amount of cement and to see the relative changes of different measures on the crack risk. The detailed study was performed in HACON 3.

In Chapter 5, the results are presented and discussed.

The conclusions from this study are presented in Chapter 6.

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2 Concrete

2.1 Cement hydration process

Large amounts of concrete are used when building massive structures such as hydropower plants and dams. One primary issue is the heat generated in the concrete due to the cement hydration. As cement is a hydraulic binder, many chemical reactions occur during its hydration with water, resulting in temperature rise within the structure.

Cement is a manufactured product with lime, gypsum, silica and alumina, where the main chemical component is calcium silicate. Calcium silicate is the unique source of strength during the hydration process. In Portland cement, there are approximately 50 % of tricalcium silicate (Ca3SiO5) and 25 % of dicalcium silicate (Ca2SiO4), depending on the type of cement that is used. Both tricalcium and dicalcim silicate generate significant heat while reacting with water. The tricalcium silicate and the dicalcium silicate produce about 173.6 kJ/kg and 58.6 kJ/kg of energy respectively, during the whole hydration process, as seen in the equations below. (MAST, n.d.)

2Ca!SiO! + 7H!O → 3CaO. 2SiO!. 4H!O+ 3Ca(OH)! + 173.6  kJ/kg

2Ca!SiO! + 5H!O → 3CaO. 2SiO!. 4H!O+ Ca(OH)! + 58.6  kJ/kg

The cement hydration takes place in five stages, as illustrated in Figure 2-1. When water is added into the concrete mix, the first stage starts and lasts for about 15 to 30 minutes. However, this duration may vary depending on the cement type and the additives that are used in the concrete mix. Those components may also affect the reaction speed because of their fineness. During this stage, the tricalcium silicate ions are dissolved and react together with the gypsum and the water to form ettringite. Ettringite acts as an obstruction and hinders further tricalcium silicate reactions resulting in a slower reaction. (Ge, 2005)

With a lower level of hydration, the second stage starts. Figure 2-1 shows a quasi-constant hydration rate in the beginning of the second stage. Afterwards the ions concentration increases progressively but still remains low. As a result, this stage is called the dormant period and lasts for about five hours. (Ge, 2005)

During the third stage, hydration heat increases gradually and reaches its peak value. The crystallization of the calcium silicate hydrates starts due to the increased permeability of the layer previously formed by the ettringite. (Ge, 2005)

Once the peak of maximum hydration heat is reached, stage four is entered. The hydration heat starts decreasing progressively due to that the hydrates already formed become a

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protective layer for the part which has not reacted yet. This leads to the reduction of the ions dissolution. (Ge, 2005)

The cement hydration ends when stage five is reached. At this stage, the hydration heat is almost as low as it is during the dormant period. The initial water present in the mixture is almost substituted by formed hydrates during the ions reaction. (Ge, 2005)

Figure 2-1: Schematic illustration of the heat evolution of the cement during the hydration process. Reproduced from Kim (2010).

2.2 Temperature cracks in concrete

When young concrete hardens, the temperature rises inside the structure contributing to temperature differences between the core and surface. This temperature rise in combination with limited movement of the structure due to adjacent parts will result in tensile stresses that may lead to cracks. (Emborg et al., 1997)

During the cement hydration the temperature can increase between 20 °C to 40 °C. This heat is kept in the core of the structure due to relatively low thermal conductivity of concrete. The cooling process of the structure can last for decades if the structure is left to cool without any help. While the core is cooling, deformations such as shrinkage occur. However, the core is not free to move as the surface cools faster and represents a restraining surface. In contrary to the core, the surface cools quite fast and thus this temperature difference between the surface and the core induces stresses which cannot be handled by the concrete at early age. (Casanova, 1980)

Temperature cracks can be located on the surface or they can go through the whole structure. Surface cracks usually appear when the temperature difference is high between the core and the surface in the expansion (warming) phase of the structure. However, they may also occur in the contraction (cooling) phase if the formwork is removed too early in cold weather. Through cracks mostly appear in the contraction phase and are usually correlated to the restraints against other structures or slabs. They may also occur in the expansion phase if the mean temperature within the casted part is large. (Emborg et al., 1997)

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2.2.1 Internal restraint Internal restraints occur when there is a temperature difference between the core and the surface of the structure during the expansion and contraction phase, as seen in Figure 2-2. The temperature at the surface is often cooler than in the core, preventing the inner parts to expand. This results in internal restraint of the structure and the risk of surface cracks arises. Depending on when the cracks occur, they may be permanent. If they occur in the expansion phase, they usually close due to the self-healing properties of concrete. If they occur in the contraction phase they may be permanent. (Blomdahl et al., 2015)

Figure 2-2: Effect of heat generation from cement hydration on mass concrete placement. (Kim, 2010)

2.2.1.1 The expansion phase

The expansion phase occurs in the beginning of the casting and acts until the structure reaches its maximum temperature. During this time the concrete is more plastic with a low elasticity modulus and is expanding due to temperature rise within the structure. As the temperature is rising, the stiffness also gets larger, contributing to compressive stresses in the middle of the structure and tensile stresses close to the surface as seen in Figure 2-2. (Emborg et al., 1997)

2.2.1.2 The contraction phase

The contraction phase follows the expansion phase. This is when the temperature is starting to decrease. However, all the cement paste has not reacted yet and the concrete will still generate heat. The compressive stresses in the core change into tensile stresses and the tensile stresses at the surface change into compressive stresses. (Emborg et al., 1997)

2.2.2 External restraint When a structure is casted against an adjacent structure such as previously casted parts or rock, the adjacent structures cause restraints in the new casted part and prevent it from moving freely, as seen in Figure 2-3. The restraint is largest at the joint between the structures and is decreasing with increasing distance from the joint. With external restraint the risk of through cracks appears, as the structure is not free to move. The through cracks will appear orthogonal to the restraint edge. (Blomdahl et al., 2015)

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Figure 2-3: External restraint on mass concrete. (Kim, 2010)

2.3 Concrete composition

Concrete is a composite material essentially consisting of aggregates, binder and water. The most commonly used binder is Portland cement which itself is a manufactured mixture of several mineral materials. The mixture of water and binder represent a matrix which gives cohesion to the obtained material. The voids between the aggregates are filled with cement paste. This increases the density of the concrete by reducing its porosity. The porosity in concrete is lower with increasing fineness of the binder. (Li, 2011)

In addition to the basic components, chemical or mineral admixtures can be used. They are used to improve the properties of fresh concrete such as the workability, the early age strength in case of fast removal of the formwork or the properties of hardened concrete.

The concrete strength in compression 28 days after casting is used as a mean of characterization because it is easy to measure. It is possible to derive other concrete properties from the compressive strength according to Li (2001). In addition, he mentions that the water cement ratio in concrete is inversely proportional to the compressive strength. Therefore, the smaller the water cement ratio is, the greater the compressive strength is.

Before the advent of admixtures which came to improve given concrete properties in the sixties, it was difficult to achieve high compressive strength due to restrictions regarding the water cement ratio. Thus before that period, the highest strength in compression was typically 30 MPa. (Li, 2011)

Concrete is a quasi-brittle material especially when subjected to tensile forces, as illustrated in Figure 2-4. The resistance of concrete against compression is approximately 10 times higher than its resistance against tension (Nemati, 2015). Brittle materials are to be avoided in construction due to the rapid failure that could occur. Therefore, when constructing concrete

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structures, a high deformation capacity is desired to prevent sudden failures and thus give time to evacuate the premises or to repair the failure before the structure collapses. To achieve a ductile structure, reinforcement bars are added to the parts of the structure subjected to tension, shear or torsion.

Figure 2-4: Failure modes of a (a) brittle, (b) quasi-brittle and (c) ductile material. Reproduced from Li (2011).

2.4 Definition of massive concrete structures

Ulm et al. (2001) defines a characteristic length, lh, to have a measurement scale to specify what a massive structure is. This length is introduced for the heat diffusion in the structure during the hydration process. Calculations have been made both for a normal strength concrete, (NSC), and a high performance concrete, (HPC), having a compressive strength of 25 MPa and 80 MPa respectively. To do so, many assumptions were made. One of them is that the heat diffusion equation was solved considering a one dimensional space and only the positive half of the space (x > 0) was studied for symmetry reasons. The characteristic length of heat diffusion, lh, is calculated with the following equation:

𝑙ℎ = 𝐷𝜏ℎ

where

D is the thermal diffusivity of concrete.

τh is the time of hydration.

In reality, the hydration time τh depends on the hydration degree of cement,  𝜉, and the evolution of the temperature inside the concrete during the casting (Ulm et al., 2001). The hydration degree of the cement represents the ratio of the amount of water needed for cement hydration by the total quantity of concrete poured. It is a kinetic function usually defined by

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performing calorimetric tests. In this case, Ulm et al. (2001) considers adiabatic conditions, which mean that energy is neither gained nor lost. This reflects the behaviour of “infinite massive structures” in so far as the heat is hardly removed from the core of the structure and thus there are almost no heat losses. In the contrary for “thin structures” the heat is evacuated so fast that a nearly constant equilibrium temperature is reached. This case corresponds to isothermal conditions.

In order to have an approximate threshold value for both normal strength concrete and high performance concrete, Ulm et al. (2001) sets the hydration time τh as constant. This is justified by the fact that for both normal strength concrete and high performance concrete, the hydration diffusion length is not varying significantly when the hydration degree,  𝜉, is between 0.1 and 0.5, as illustrated in Figure 2-5. According to Ulm et al. (2001), this range corresponds to the period when there is maximum hydration in adiabatic conditions. This period lasts between 8 and 16 hours.

Figure 2-5: Evolution of the heat diffusion length as a function of the hydration degree (Ulm et al., 2001).

After solving the equations, the results show that when the length is shorter than the characteristic length, lh, the isothermal conditions are applied and the heat is removed by diffusion. Thus, the heat generated is not that harmful when the dimensions do not exceed the characteristic length, lh. When the dimensions are greater than that length, the diffusion process is not sufficient enough to reduce the heat in the structure sufficiently. In those parts of the structure there are adiabatic conditions instead of isothermal ones. The maximum value of the heat hydration length, lh, is 0.2 m and 0.3 m for normal strength concrete and high performance concrete, respectively.

The study has been performed for half the space, (x > 0), of a symmetric structure. Thus if the heat diffusion is possible on both sides of the structure, the obtained length should be multiplied by a factor two. This means that for the whole structure, the hydration length should be 0.4 m and 0.6 m for normal strength concrete and high performance concrete, respectively.

The definition of a massive structure can change from one country to another depending on several factors. Kim (2010) gives three different definitions for Korea, Japan and USA.

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In Korea and Japan, the definitions are more related to given dimensions considering either slabs or restrained walls. The characteristics of the concrete, the building process and environment are also factors to take into account. For the two countries, the limitations for slabs and restrained walls are thicknesses about 0.8 - 1 m in Korea and 0.5 m in Japan, respectively. In addition to these restrictions, architectural rules include any structures having dimensions greater than 1 m in Korea and 0.8 m in Japan. Also, a further criterion in Japan is the temperature difference between the surface and the core which should be less than 25 °C.

The difference in Korea is that any structure having a thickness greater than 1 m is considered as massive. In Japan, those criteria are given by their architecture standard specifications. (Kim, 2010)

In USA, the American Concrete Institute (American Concrete Institute, 1980) defines massive concrete structures as “Any large volume of cast-in-place concrete with dimensions large enough to require that measures be taken to cope with the generation of heat and attendant volume change to minimize cracking.”

2.5 Concrete for hydropower plants

When it comes to massive structures such as hydropower plants, appropriate selections of the concrete components have to be made. As these structures are usually meant to last about 100 years or more, high durability is needed. (Fagerlund, 1989)

In Sweden, low hydration heat cement called Limhamnscement was produced for large structures. This cement type also had good features such as a low alkaline content and good resistance to sulphate attacks. However, its production stopped at the end of 1970’s and has been replaced with construction cement called Anläggningscement. The Anläggningscement is type I Portland cement with moderate hydration heat. It is by far the best cement to use when it comes to casting large structures due to its coarser grains compared to ordinary Portland cement. Therefore the reaction with water is slower, which reduces the heat produced at early age. (Fagerlund, 1989)

Fagerlund (1989) also mentions that a good quality of aggregates is found in Sweden. However, carefulness is needed when it comes to the porosity, the sludge content and the mineral composition of the aggregates. The aggregates porosity should be greater than 0.5 % as a low porosity is a weakness regarding the frost resistance. The pores can easily be filled and saturated with water even during the pouring due to micro cellularity.

With a reduced access to good quality aggregates, the amount of sludge has increased. Moreover, this leads to that the aggregates become contaminated with dust during the crushing process. These impurities represent a weakness for the aggregates and result in lower frost resistance. This is due to that the dust forms a weak porous layer between the aggregates and the cement paste. In several countries, the aggregates are washed before being incorporated to the concrete mixture to remove the dust and thus improve the bond between the components. (Fagerlund, 1989)

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In general, minerals and chemical admixtures can be added to the concrete mix to improve the properties of concrete depending on the demands on the structure. This can e.g. be to obtain a concrete with lower viscosity, a concrete with higher air content or to lower the heat generated inside the core of the concrete structure. Mineral admixtures are waste materials from several industries or fillers used as substitution materials to replace a certain amount of cement. This is done mainly to reduce the heat generated by cement during the hydration process. The most commonly used waste materials are limestone, silica fume, fly ash and ground granulated blast furnace slag. More information about their properties can be found in Section 2.7.

Moreover, chemical admixtures such as air-entraining or water reducing admixtures can be used for the concrete mix. However, according to Fagerlund (1989), the combination of these two types of admixtures leads to a decrease of the concrete frost resistance. To have a good frost resistance, the concrete air-entraining content should be at least 5.5 %. (Fagerlund, 1989)

The use of water reducing admixtures is a mean to reduce the water cement ratio and improve the concrete workability. However, when high compressive strength is wanted for the structure, water reducing admixtures are to be avoided. They increase the concrete fluidity and could lead to aggregates segregation.

Many factors from the surrounding environment should be taken into account to avoid potential damages of concrete structures. These structures may be subjected to attacks such as frost attacks, cracking, erosion, chemical attacks, and corrosion of the reinforcement.

2.6 Regulations and codes

2.6.1 RIDAS In the 1990’s, recommendations and guidelines for dam safety were developed by Swedish power companies and were completed in 1997. This documentation named RIDAS (Kraftföretagens riktlinjer för dammsäkerhet) has been revised a couple of times. (Andersson et al., 2016)

In the guidelines special considerations should be taken to Section 7.3 in RIDAS for concrete dams, as well as to Boverkets handbok om betongkonstruktioner, BBK 04, which is used to fulfil the regulations in Boverkets Konstruktionsregler, BKR. (RIDAS, 2011)

To give the reader a brief insight about regulations that are used in Sweden when it comes to building new hydropower plants as well as restoring old ones, a short introduction for concrete dams is described below. The following information comes from RIDAS, (2011).

The demands on the material properties for concrete in RIDAS are:

● A minimum strength class of C25/30, according to BBK. ● Execution class I, according to BBK. ● Water tightness according to BBK. ● Water cement ratio of maximum 0.55, according to table 5.3.2a in SS 13 70 03. ● Air content, according to table 5.3.2b in SS 13 70 03.

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● Cement quality: Portland cement EN 197-1-CEM I 42.5 N BV LA SR, according to SS-EN 197-1.

In RIDAS it is also mentioned that constructions exposed to water pressure on one side should not have a crack width larger than 0.2 mm. In some cases, if a crack width of 0.2 mm results in unreasonably high amount of reinforcement, the maximum crack width may be set to 0.3 mm instead.

However, the national regulations are not valid anymore and should be replaced by Eurocodes. Since the Eurocode 2 has been introduced for designing concrete structures, it is observed that higher amount of minimum reinforcement is needed in the structures compared to the previous regulations and standards. The new way of designing with a higher amount of minimum reinforcement is particularly seen when it comes to designing thick concrete members. There is an ongoing evaluation on how to apply the Eurocodes for designing dams in Sweden in combination with RIDAS. (Andersson et al., 2016)

The results from the minimum amount of reinforcement made by Andersson et al. (2016), shows that the minimum reinforcement is substantially higher with Eurocode 2, EKS 10, than with old Swedish regulations, as well as with other international standards. Furthermore, they recommend that the minimum reinforcement to limit the crack width should be performed by EKS 10. However, the amount is restricted by the crack width of 0.3 mm calculated according to the German regulation, BAW. If cooling is involved, the minimum reinforcement should be reduced and calculated according to BAW.

2.6.2 Swedish Concrete Standard The Swedish Concrete Standard SS-EN 206:2013+A1:2016 is used for requirements, characteristics, manufacturing and compliance for concrete. Data of interest are for the following materials (Section 5.2.5.2 in SS-EN 206:2013+A1:2016):

● Fly ash ○ k-value is equal to 0.4 for CEM I Portland cement according to EN 197-1. ○ Only 33 % of the cement can be replaced with fly ash. ○ !"#  !"#

!"#"$%≤ 0.33  by    mass  fraction.

● Silica fume ○ The water cement ratio > 0.45. ○ Exposition class is XC4/XF3 ○ k-value is equal to 1.

● Slag ○ k-value is equal to 0.6. ○ !!"#

!"#"$%≤ 1  by  mass  fraction.

The k-value is based on the durability performance of concrete. It is obtained by testing a reference concrete with cement “A” against a test concrete where a part of cement “A” is replaced by an addition in terms of the water/cement ratio and the addition content. (SS-EN 206:2013+A1:2016)

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This data was used to calculation the cement reduction in Appendix A: Calculation of cement reduction.

2.7 Methods used to lower the hydration heat

There are different ways to lower the heat development within concrete. As cement is the main component producing heat, the first measure can be to reduce its amount by replacing it with binders which do not release heat during their reaction. The most common substituting materials are limestone, silica fume, fly ashes, and slag, which are presented in the following Sections 2.7.1, 2.7.2, 2.7.3, 2.7.4 and 2.7.5. In addition to lowering the amount of cement by replacing it with another binder, larger diameter of aggregates can be used to reduce the cement paste needed. Furthermore, those aggregates can be cooled to lower the initial temperature of concrete as explained in Section 2.7.6. Besides working on the materials, superficial cooling can be done by using ice and cooling pipes as explained in Section 2.7.7 and 2.7.8. Even heating can be used to lower the temperature difference see Section 2.7.9. The choice of cooling method depends on many factors which vary from one project to another.

2.7.1 Fillers The most used filler is limestone. It is an inert filler which does not react with the water inside the concrete and will not contribute to the strength of the concrete. There are other fillers such as fly ash, silica fume and slag. These fillers have a certain amount of CaO that is prone to react with water in the presence of an activator. In concrete this activator is normally calcium hydroxide, Ca(OH)2. (Sundblom, 2004)

Poppe and De Schutter (2005) performed an isothermal hydration test and an adiabatic hydration test to evaluate the heat generation with different fillers and cement types. They used two types of fillers in combination with three types of cement. The different fillers are limestone and quartzite, while the different cement types are CEM I 42.5 R, CEM I 52.5 and CEM I 52.5 HSR LA. The different fillers and cement types are tabled out by the authors and can be found in Table 2-1.

Table 2-1: Each material used in the test. Reproduced from Poppe and De Schutter (2005).

CEM I 42.5 R %

CEM I 52.5 %

CEM I 52.5 HSR LA %

Limestone filler %

Quartzite filler %

CaO 61.53 63.95 64.23 – 0.02 SiO2 19.59 20.29 20.80 0.80 99.5 Al2O3 4.99 4.52 3.55 0.17 0.20 Fe2O3 2.98 2.35 3.94 0.10 0.03 MgO 0.78 2.22 2.40 0.50 – K2O 0.87 0.94 0.50 – 0.04 Na2O 0.36 0.20 0.17 – – SO3 3.29 3.35 2.74 – –

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Cl– 0.080 0.015 0.014 0.002 – CaCO3 – – – 98.00 – C3S 58.2 59.0 60.6 – – C2S 12.7 12.6 16.6 – – C3A 8.19 8.01 2.75 – – C4AF 9.1 9.4 13.1 – – Blaine (m2/kg) 281 286 418 526 360

The isothermal hydration test was performed on small cement paste samples, thus removing the influence from aggregates while the adiabatic hydration test was performed on two different self-compacting concretes, (SCC), with the two cement types CEM I 42.5 R and CEM I 52.5. The latter test was also performed on traditional concrete, (TC), with the two cement types to see the different behaviours for the samples with fillers and the one without fillers, as illustrated in Figure 2-6. It is clear that the adiabatic hydration test for the self-compacting concrete have a higher maximum temperature rise than the traditional concrete.

Figure 2-6: Results from the adiabatic hydration test. Reproduced from Poppe and De Schutter (2005).

Furthermore, the results obtained by Poppe and De Schutter shows that both the isothermal and adiabatic hydration test have a second heat peak when limestone is used, as seen in Figure 2-7 and Figure 2-8. This additional peak is not found when quartzite fillers are used, as illustrated in Figure 2-9. Below c/p means cement powder ratio.

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Figure 2-7: Adiabatic test with limestone filler and CEM I 42.5 R. Reproduced from Poppe and De Schutter (2005).

Figure 2-8: Isothermal test with limestone filler and CEM I 42.5 R at 20 °C. Reproduced from Poppe and De Schutter (2005).

Figure 2-9: Isothermal test CEM I 42.5 and quartzite filler at 20 °C. Reproduced from Poppe and De Schutter (2005).

2.7.2 Silica fume Silica fume is a reactive material. According to Langan et al. (2002), the impact of silica fume on the hydration depends on the water cement ratio of the concrete mixture. At low water cement ratio the hydration rate is slower whereas it becomes high as the water cement ratio

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increases. Silica fume delays the cement hydration at low water cement content. It consumes partly the water injected in the mix leading to the formation of a gel hindering the ability of water to be in contact with the cement particles. Therefore, the amount of cement hydrated is lowered which results in a delay in the hydration process. However, as the water cement content increases, the mixture is saturated with water. Consequently, the phenomenon observed differs from the one obtained at low water cement ratio. With an increase of the amount of water, the silica fume does not form bonding barrier on the cement particles which are surrounded by water and thus can react freely. With high water cement ratio, concrete with silica fume reacts faster instead of having a delayed hydration.

Langan et al. (2002) studied the influence of the silica fume on the hydration by comparing the heat evolution of concrete samples containing 10 % silica fume for three different water cement ratios. The results are shown in Figure 2-10, where S0A0 means concrete without silica fume and fly ash (this mixture is taken as reference for the comparisons), and S10A0 means concrete with 10 % silica fume and no fly ash. The three graphs are for a water cement ratio of 0.35, 0.40 and 0.50, respectively. In the beginning of the hydration process, the curves show that silica fume has no direct impact. It starts to affect the hydration approximately two hours after mixing.

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Figure 2-10: Heat evolution of concrete with 10 % silica fume at (a) 0.35, (b) 0.40 and (c) 0.50 water cement ratio (Langan et al., 2002).

2.7.3 Fly ash Fly ash is an inert material mainly used as substitution to some amount of cement. For massive structures, the aim is to reduce the heat generated during the cement hydration. However, it is important to ensure good quality of the fly ash because it may change from one production to another. Therefore, throughout one project, continuous quality control has to be performed so that all concrete mixes have the same features. (Atiş, 2002)

According to ASTM C 618 (2002), fly ashes are divided into two categories: Fly ash F and C. Fly ash F and C contains less than 10 % calcium oxide (CaO) and more than 20 % CaO respectively. Fly ash C has greater cementitious characteristics compared to class F fly ash. (Ge, 2005)

By replacing cement with fly ash, the temperature rise in the concrete will be reduced due to lower ratio of cement that can react with water. Additionally to the cement quantity reduction,

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the pozzolanic properties of fly ash lead the improvements of other concrete characteristics. A study has been performed by Atiş (2002) where different concrete mixtures were compared. In Table 2-2 the different components for each mixture are presented. Concretes M1 and M2 contain 70 % fly ash while M3 and M4 contain 50 % fly ash. (Atiş, 2002)

Table 2-2: Proportions for one cubic meter of concrete mixture. Reproduced from Atiş (2002).

Mix no.

Cement (kg/m3)

Fly ash (kg/m3)

Sand (kg/m3)

Gravel (kg/m3)

Water (kg/m3)

Optimum W/C

Actual W/(FA+C)

SP (l/m3)

M0 400 – 600 1200 220 – 0.55 – M1 120 280 600 1200 112 0.29 0.28 5.6 M2 120 280 600 1200 116 0.29 0.29 – M3 200 200 600 1200 132 0.30 0.33 5.6 M4 200 200 600 1200 120 0.30 0.30 –

The results from Atiş (2002) show that if cement is replaced with 50 % fly ash, a reduction of the peak temperature will go from 55 °C to around 42 °C, as illustrated in Figure 2-11. This is a reduction of 23 % in the peak temperature. Furthermore, the author also mentions that with a moderate amount of 20 - 30 % fly ash, the peak of temperature can approximately be reduced by 10 - 15 %.

Figure 2-11: Replacement with low calcium fly ash of Class F and ordinary Portland cement. (Atiş, 2002)

As for silica fume, the same study has been carried out by Langan et al. (2002) to compare the hydration rate of a concrete containing 20 % fly ash (S0A20) to a concrete containing no fly ash and no silica fume (S0A0) for three different water cement ratios. Figure 2-12 shows the results for a water cement ratio 0.35, 0.40 and 0.50, respectively. It can be concluded that the influence of fly ash on the hydration heat also depends on the water cement ratio of the concrete. Fly ash induces a delay on the hydration process mainly in the second and the third stage i.e. the dormant and the acceleration periods while the first period is accelerated. As the water cement ratio increases, it can be noted that the delay caused by fly ash is more important. With an increase of the water cement ratio, the concentration of the Ca2+ ions is reduced. This causes an elongation of the dormant period. In addition to a lower

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concentration, fly ash reduces the amount of Ca2+ ions contained in the solution. That delays their precipitation and thus the formation of calcium silicate hydrates, CSH. Therefore, as Figure 2-12 shows, fly ash has more impact on the cement hydration at higher water cement ratio.

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Figure 2-12: Heat evolution of concrete with 20 % fly ash at (a) 0.35, (b) 0.40 and (c) 0.50 water cement ratio. (Langan et al., 2002)

In addition to the heat reduction, other properties of concrete are also improved. Testing show that concrete with high fly ash content as replacement to cement is more watertight and less porous, which is an additional advantage especially for dams as there is permanent presence of water. (Atiş, 2002)

As fly ash is finer than cement, it increases the cementitious matrix and thus improves the workability and the fluidity of concrete. Also, concrete with fly ash may have higher compressive strength in the long run thanks to the pozzolanic reaction which occurs later on. (Ge, 2005)

This is also confirmed by Karoriya and Gupta (2016), who replaced cement with 10 %, 20 %, and 30 % of class F fly ash in small test cubes. They found that the workability is better with more fly ash and that the replacement of 10 % fly ash is improving the compressive strength of concrete after 28 days, while the replacement of 20 % and 30 % decreases the strength. However, the strength after seven days was lower due to the slow reaction between fly ash and water. The strength of the concrete is shown first after a longer period, as illustrated in Figure 2-13.

According to Utsi (2008), the compressive strength for concrete with fly ash is higher at 91 days. This may be explained by the fact that fly ash induces a delay in the concrete reaction.

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Figure 2-13: The strength of concrete with different amount of fly ash replacements. (Karoriya and Gupta, 2016)

The price of the residue materials is one other advantage for their utilization. Compared to Portland cement, they are about 50 % cheaper (Ge, 2005). This becomes cost effective mainly with large structures. Their use contributes to having a circular economy as the waste is revalued for building purposes.

2.7.4 Combination of fly ash and silica fume Langan et al. (2002) combined 10 % silica fume and 20 % fly ash in a concrete mixture to see how they both affect the hydration. From previous studies, silica fume delays the hydration at low water cement content while it is accelerated as the water cement ratio increases. Fly ash only retards the hydration. The phenomenon becomes more visible at high water cement ratio. When both fly ash and silica fume are used in the mixture, the hydration is considerably delayed in addition to a decreased heat generation. As the amount of pozzolans increases due to the presence both fly ash and silica fume which reduces the concentration of the Ca2+ ions, the pH of the concrete is lowered. This leads to less calcium hydroxide available to catalyse the reaction of silica fume.

2.7.5 Slag Ground granulated blast furnace slag commonly notated GGBS is a by-product from the iron manufacturing reused in the building industry. It is extensively incorporated to concrete mixture in Europe since approximately 1880. The chemical composition of slag is not unique. It depends on the raw materials used and on the condition of the main product fabrication. (Lewis et al., n.d.)

Slag takes a long time to react with water when it is used alone. However, when it is used in combination with cement, it has good properties both for fresh and hardened concrete. With addition of slag, the amount of cement can be significantly reduced, which the first step of lowering the heat generated during the hydration process. In the first stage of the binder reaction, only the cement reacts with water because the reactive properties of slag are blocked due to its structure. When the cement hydration starts, calcium silicate hydrates (CSH) are

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produced. The sulphates and/or the alkali produced play the role as catalyser for the reaction of slag. While slag commences to react with activation products, the concrete pH becomes higher until it attains a critical value which disturbs the properties of the slag. Once this value is reached, reaction between slag and water is initiated. That leads to the production of slag cementitious products. The two stages below show the reaction between ordinary Portland cement, slag and water. (Lewis et al., n.d.)

• Primary stage:

OPC+Water → C. S.H.+Ca OH !NaOHKOH

(1)

!!"#!!"#$%!!" !" !→!! !,! !!!!!"#$!"#

(2)

• Secondary stage: (i) OPC primary reaction products + ggbs (ii) OPC primary reaction products + ggbs primary reaction products

Figure 2-14 shows the temperature evolution of concrete mixtures having different slag content. Concrete containing 50 % and 70 % slag are compared to a concrete having only Portland cement. As the slag proportion increases, it can be seen that the reaction is delayed and the temperature curves become flatter. With 70 % slag, the maximum temperature is approximately reduced by 10 °C whereas it is only reduced by 4 °C with 50 % of cement replacement as the temperature increases slowly with high slag content. (Lewis et al., n.d.)

Figure 2-14: Temperature evolution depending on the slag content. (Lewis et al., n.d.)

2.7.6 Aggregates Grading curves are used to define the amount of coarse and fine aggregates depending on their diameter. These curves are obtained by performing a sieve analysis of the aggregates. The normal sized aggregates used in Sweden are 0 - 8 mm, 8 - 16 mm and 16 - 32 mm. The larger the aggregates are, the less cement is needed and thus the heat generation is lower. The

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shape of the aggregates will also affect the amount of cement paste needed. If natural aggregates taken from eskers are used, less cement paste will be needed due to the smooth and rounded shape compared to if the aggregates are crushed. Crushed aggregates have more edges and a larger area; it reduce the concrete workability and increases the need of cement paste. The difference between the two types is the properties they give young concrete. (Sundblom, 2004)

Lowering the initial temperature of the concrete is possible by cooling the aggregates in advance (Kim, Yang and Moon, 2015). This can be done either by protecting the aggregates from the sun, sprinkle cold water on the aggregates or to cool with nitrogen (Schackow et al., 2016). However, the amount of water sprinkles on the aggregates affects the initial water cement ratio. Therefore, it has to be taken into account while designing the concrete mix.

Blomdahl et al. (2015), also mention that the temperature expansion and contraction properties differ depending on the aggregates used. These properties are of importance when it comes to the risk of cracks.

Figure 2-15 presents the amount of cement depending on the diameter of the aggregates for three different water cement ratios. The three concretes are formulated to have the same consistency which should be plastic i.e. concrete having a slump between 5 and 9 cm according to the standard SS-EN 206:2013+A1:2016. Independently from the water cement ratio, it can be seen as the aggregate sizes increase, the amount of cement needed is reduced.

Figure 2-15: Evolution of the cement content depending on the aggregates size in concrete for different water cement ratio. (Anon, 1964)

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2.7.7 Ice Pre-cooling with ice can be a good way to lower the temperature inside concrete. To use cold water or ice in the concrete mix is more efficient than to use water with ambient temperature. (Schackow et al., 2016)

The use of ice in large amount to replace water in the concrete mixture contributes to the reduction of concrete casting temperature. This permits to compensate the heat released during the cement hydration and thus limits the concrete temperature rise. This method of cooling concrete is efficient in the way that temperature difference inside the structure is reduced. Therefore, the risk of thermal cracking is lowered. However, it can be expensive to install a facility for ice production only for concrete mixing. In addition, it is important that the concrete factory takes into account the amount of added ice as a part of the initial amount of water that was supposed to be used to keep the water cement ratio constant. This is important to obtain a good quality and watertight structure.

Pre-cooling methods are effective for preventing thermal cracking, according to Takeuchi, Tsuji and Nanni (1993). The use of dry ice to lower the concrete initial temperature is one of the best pre-cooling measures. This is due to that it has a significant latent heat equal to 137 kcal/kg. In addition, small sizes of dry ice i.e. between 1 mm and 2 mm give more efficient cooling than larger ones. Large dry ices have a larger vaporisation time to carbonic acid gas.

Takeuchi, Tsuji and Nanni (1993), performed testing to evaluate the efficiency of dry ice as a concrete cooling method in a batching plant. Results show that this method is reliable with a cooling efficacy between 61 and 70 %. This means that 7 kg of dry ice is needed to reduce the temperature by 1 °C in 1 m3 of concrete. Moreover, the properties of hardened concrete are improved. The compressive strength at 91 days of cooled concrete by means of dry ice is 15 % higher than the uncooled concrete.

2.7.8 Cooling pipes In Sweden, cooling pipes are frequently used to cool concrete. The principle is to lay thin pipes in the structure. When the concrete casting starts, cold water is pumped into these pipes to limit the temperature rise inside the concrete during the hydration.

The construction of the Hoover Dam in the 1930’s is the first case where this method was applied (Qiang, Xie and Zhong, 2015).

According to Qiang, Xie and Zhong (2015), the main criteria affecting the efficiency of a pipe cooling system are:

● The water flow and direction inside the pipes. ● The original temperature of the water. ● The layout and the spacing of the pipes. ● The pipes characteristics such as the diameter, the length and the material. ● The cooling sequences.

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The water flow should be set so that there is a good water exchange in the pipes. During the cooling process, the water is warmed up by absorbing the heat from the concrete hydration. If the flow is not high enough, the water reaches approximately the concrete temperature. Therefore, heat transfers are no longer possible between the water and the concrete. That leads to lower cooling system efficiency. (Charpin et al., 2004)

The choice of the pipe material is very important. The pipes should have low heat resistance. The resistance depends on thermal characteristic and on the pipe dimensions. Thus the material should have high heat conductivity to ease the heat transfer from the concrete to the water through the pipe wall. When it comes to the pipes dimensions, it is better to have many small pipes instead of having few large pipes. The results obtained by using an important quantity of small diameter pipes are better than the results obtained with larger diameter pipes. As the number of pipes increase the surface area in contact with the heating concrete increase. Thus the cooling capacity is higher as well, thanks to more heat absorption. (Charpin et al., 2004)

This method is not easy to handle and includes a lot of risks. One of them is the pipe entrance freezing during winter time due to low ambient temperature. The freezing is hindered by warming the pipes entrance so that water cannot be stocked by ice. To have an efficient cooling system, all the pipes have to be functional and a high level of carefulness is needed.

According to several engineers, this method is way too expensive for the results it gives and many factors have to be taken into account to have good cooling results.

A disadvantage of this method of cooling is that severe cracks may occur in the concrete around the cooling pipes due to a high difference in temperature between the water circulating in the pipes and the concrete. This temperature gradient creates significant tensile stresses which may lead to cracks. However, by reducing the water flow, the stress and thus the crack formation around the pipes can be reduced. The structure will be cooled slowly. Therefore, a balance between having an efficient cooling system and as low stresses as possible near the pipes should be found. (Qian and Gao, 2012)

Although water is primarily used as cooling fluid, air may also be used. However, cooling with air indicates that the diameter for the pipes needs to increase to give an effect. (Hedlund and Groth, 1997) This is due to that the specific heat capacity of water is larger than for air. For example, at 25 °C, the specific heat capacity of water and air are 4.18 and 1.005 kJ/kg.K, respectively. (NIST, n.d.) Thus high amount of air is needed to have efficient cooling. For hydropower plants construction, using air will be much more expensive since the access to cold water is easier.

2.7.9 Heating A way to reduce the temperature differences between an old casted part and a new casted part is preheating. By adding heating cables in the old casted part and heat it up before casting the new part, the risk of cracks and high tensile stresses will be removed. (Jonasson et al., 2001)

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Jonasson et al. (2001) show an example of how a lower temperature (Figure 2-16) and a higher temperature (Figure 2-17) in the already existing part will affect the cooling behaviour. The example is an already cast slab and a wall is about to be added on top of the slab. According to Jonasson et al. (2001), a lower temperature in the slab compared to the new casted wall will lead to compression in the slab caused by the new part. That will generate tensile stresses in the wall and compressive stresses in the slab, giving an unwanted effect on the construction. However, if the slab has a higher temperature than the new casted wall, as illustrated in Figure 2-17, it will be in tension and thus induce compressive stresses in the newly casted wall giving a lower load difference, resulting in a wanted effect.

Figure 2-16: The slab has a lower temperature than the newly cast wall. “1+2” are showing the total load difference, the solid line is representing the average temperature in the wall while the dashed line is representing the average temperature in the slab. (Jonasson et al., 2001)

Figure 2-17: The slab has a higher temperature than the newly cast wall. “1+2” are showing the total load difference, the solid line is representing the average temperature in the wall while the dashed line is representing the average temperature in the slab. (Jonasson et al., 2001)

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3 Field case studies This chapter presents the cooling system of one hydropower station in South America. Different cooling methods were used during its construction, showing how they were combined and applied to a real project. In addition, two other cases are briefly presented.

3.1 Application of cooling methods at Itaipú

Itaipú power station, located in South America between Brazil and Paraguay in the Rio Paraná, is one of the world's largest hydropower plant constructions (Figure 3-1). The entire dam complex is 7 655 m long and comprises 18 generating units of 700 MW each. The main dam is a hollow gravity dam having a length of 1 500 m and a height of 176 m with 12 000 m3 of concrete casted. (Casanova, 1980)

The concrete needed to be cooled to avoid thermal problems induced as high temperature rise due to the hydration heat. To carry out this project, a complete cooling system for the concrete components was placed on site. (Casanova, 1980)

Figure 3-1: Itaipú hydropower plant. (Mallya, 2015)

To cool the concrete for large structures, either pre-cooling or post-cooling can be performed. The choice of method depends mainly on the climate and varies from case to case. Pre-cooling consists in lowering the concrete components temperature before mixing them together. This leads to a lower initial temperature of the concrete and also to a lower

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maximum temperature peak. This is preferable in hot countries where casting temperatures are lower than the ambient temperature.

A pre-study for alternative cooling were performed to compare pre-cooling with post-cooling methods for Itaipú as shown in Figure 3-2. In the figure, the temperature evolution of cooled concrete is compared to the ambient temperature in warm climate. Curve 1 and curve 2 represent the concrete temperature when pre- and post-cooling are used, while curve 3 shows the mean value of the annual ambient temperature in hot climate regions.

When pre-cooling is used, while the concrete temperature increases, it approaches the ambient temperature or slightly higher, as illustrated in Figure 3-2. Consequently, there will not be much temperature difference which reduces the risk of thermal cracking.

With post-cooling, the initial temperature of concrete is not modified, leading to temperature rises up to about 40 °C, as illustrated in Figure 3-2. Afterwards cooling measures such as cooling pipes may be used. In those cases, the access to cold water is usually easy. During the cooling process, the concrete temperature can be lower than the ambient temperature in hot regions. (Casanova, 1980)

Figure 3-2: Evolution of pre-cooled (1), post-cooled (2) concrete temperature and mean annual ambient temperature in hot climate regions (3). (Casanova, 1980)

As South America has warm climate, the pre-cooling methods were applied. Low heat cement with substitutes of fly ash was used for the plant construction. The initial temperature aimed for the concrete was 6 °C. To do so, several cooling measures were combined. The concrete components and their amounts are shown in Table 3-1.

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Table 3-1: Concrete composition. Reproduced from Casanova (1980).

Components Concrete compositions in parts by weight

Mix 1, gravel up to 3/4"Φ, kg/m–3

Mix 2, gravel up to 11/2"Φ, kg/m–3

Mix 3, gravel up to 3"Φ, kg/m–3

Mix 4, gravel up to 6"Φ, kg/m–3

Water 165 140 110 90 Cement 240 200 145 100 Fly ash 60 50 35 30 Natural sand 240 230 210 180 Artificial sand 560 520 490 420 Gravel no. 1 (3/4") 1125 500 300 250 Gravel no. 2 (11/2") 750 360 350 Gravel no. 3 (3") 740 430 Gravel no. 4 (6") 540 Total 2390 2390 2390 2390

3.1.1 Type of cement used at Itaipú Figure 3-3 shows the temperature increase of four concrete mixes using different cement types. The cement used in curves 1, 2, 3 and 4 are; a standard cement, a modified cement, a low-heat cement for dams and a low-heat cement containing substitutes. The used cement to build Itaipú is the latter one presented in curve 4.

Figure 3-3: Temperature evolution of concretes with different cement types. (Casanova, 1980)

3.1.2 Cooling process at Itaipú The concrete temperature could increase by 1 °C between the time of manufacturing and casting, which leads to a maximum casting temperature of 7 °C. Different cooling methods

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were used and not all concrete components tabled in Table 3-1 were cooled depending on their fineness. No cooling measure was applied to the sand. The temperature of cement and fly ash was equal to 40 °C at the end of their own manufacturing process because those materials are the finest. If they are cooled, the risk of freezing may occur and alter the concrete mix.

As illustrated in Figure 3-4, the system is composed by an air cooling part, a cooling tunnel with chilled water in it and cooling water system used subsequently to produce flaked ice. The gravels 3 and 4 in Table 3-1 were first cooled in the tunnel to achieve 8 and 9 °C before being air cooled to -7 and -2 °C. Due to its fineness, gravels 1 and 2 were only cooled in the chilling tunnel. Instead of only using water for the whole concrete mix, it was partly substituted by flaked ice to compensate the heat from uncooled materials.

Figure 3-4: Concrete components cooling system at Itaipú. Reproduced from Casanova (1980).

3.2 Other applications of cooling methods

There are many applications where cooling pipes have been used as a mean to reduce the heat generated from hydration heat. As mentioned previously, massive structures where the natural cooling is not sufficient such as concrete dams, bridges, etc. are typical examples of this. In this section two typical examples where cooling pipes were used are presented.

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The Plattsmouth Bridge built over the Missouri river, Figure 3-5, consists of 19 massive concrete elements. Cooling pipes were used to cool four of those massive elements. (Iowa, 2014)

Cooling pipes were also used for the construction of a Portuguese Arch Dam, as illustrated in Figure 3-6.

Figure 3-5: Plattsmouth Bridge (US-34 Bridge) over the Missouri river. (Library of congress, n.d.)

Figure 3-6: Portuguese Arch Dam. (Blomdahl, 2015)

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4 Simulation of a massive wall The main work of this master project has been to simulate different ways to lower the temperature inside massive structures and to compare them. The simulations have been performed in the computer program HACON 3 which is developed to simulate the temperatures and stresses in hardening concrete.

The simulated case consists of a fictive wall on a rock bed and is restrained on one side, as illustrated in Figure 4-1. This wall can represent a common wall that can be found in many hydropower plants and dams.

The program can only handle two dimensional problems. Therefore, the wall was modelled as a cross section and as a plane section (Figure 4-1).

Figure 4-1: The cross section and plane section of the fictive wall.

4.1 Reference model

The reference model is as shown in Figure 4-1. It consists of a cross section that is 1.5 m thick and 6 m high, and a plane section that is 9 m wide and 6 m high.

In the cross section, the temperature and maturity of the concrete was simulated. The data from the cross section simulation was then imported to the plane section to perform the plane stress simulations.

Below, the input for the reference model is presented, and each step is briefly explained. This reference wall is the guideline to the other simulations to show how the different materials or cooling pipes impact the temperature evolution inside the wall.

34

4.1.1 Assumptions ● Casting occurs during the month of April. ● The mean air temperature for April is 4 °C (SMHI, 2017). ● K40 is used, which corresponds to a concrete strength of C35/45. ● The cement content is 360 kg/m3. ● The water-cement ratio is equal to 0.55 and is predefined in HACON. ● The formwork is made of wood with a thickness of 22 mm. ● The formwork is removed after 5 days. ● The displacement is prescribed in x- and y-direction. Meaning that they are fully

restrained against rock and concrete. ● The wind velocity is set to 5 m/s. ● The simulation is performed for one month, i.e. 720 hours. ● The outlet temperature for the water in the pipes is maximum 4 °C higher than the

inlet temperature. ● Initial temperature of the concrete at casting is 16 °C.

4.1.2 Geometry The structure needs to be modelled twice, one cross section model and one plane section model of the structure. To make a section or a plane model, nodes, curves and surfaces need to be assigned. These are explained for the cross section.

4.1.2.1 Nodes, curves and surfaces

The first step is to place nodes. Nodes 1 to 8 are the outline of the wall while nodes 9 to 14 represent the rock that the wall will be cast on top of (see Figure 4-2). The nodes for the wall are placed every two meters, dividing the height of the structure in three stages. This is made so that the Time of casting (h) in Section 4.1.3 can be adjusted to make a more realistic simulation of the wall.

When the nodes are in place, they are connected by curves. They can either be connected by lines (between two nodes) or by curves (connecting three nodes). These curves are presenting the exterior of the structure and will be used to assign a surface.

The third and last step is to assign a surface to each part. Here it is important to know that a surface is enclosed by four curves. These four curves need to be assigned in a counter clockwise way.

When a surface is defined, it needs to be assigned either 3-, 5- or 8-noded elements. Depending on what part that is assigned a surface, different types of elements are needed. The structure should consist of an 8-noded element, while the soil should have a 3- and 5-noded element. The 3- and 5-noded elements are representing semi-infinite elements and the orientation of them are very important.

35

The 5-noded element is restrained in three directions; see surface 5 in Figure 4-2. The three sides are marked as grey edges. The fourth side should be towards the bottom of the ground, giving surface 5 a spreading of the heat straight down to the ground.

The 3-noded element is restrained in two directions; see surface 4 and 6 in Figure 4-2. Only two sides of the surface are grey and the orientation of the grey sides should be that one of them is towards the ground surface and the other one toward the 5-noded element. This gives a spreading of the heat away from the corner nodes, node 1 and 8 in Figure 4-2, into the ground.

When the right element type is assigned to each surface, the element needs to be given a certain amount of rows and columns for the mesh. The mesh should have as good aspect ratio as possible, i.e. close to 1:1. However, if a too fine mesh is used the simulation will not run nor if there is not the same amount of rows and columns in the connecting surfaces.

Figure 4-2: Final geometry of the wall.

4.1.3 Material After the geometry has been determined, the materials are assigned to the different surfaces. In the beginning all the surfaces are unassigned. There are some predefined materials in HACON 3. For this case the K40 concrete material and the Rock material are used.

36

Figure 4-3: The assigned materials to the structure.

As seen in Figure 4-3, K40 was imported three times. This is because the Time of casting (h) in Edit material, Figure 4-4, had different values for each assigned part. K40 had a time of casting at 0 hours, K401 a time of casting at 2 hours and finally K402 a time of casting at 4 hours as shown in Table 4-1.

Figure 4-4 shows the different property tabs that can be changed. However, the only property tabs that were changed for this purpose are; General and Cement. In General it is the Time of casting (h), Temperature at casting (°C) and Initial maturity time at casting (h) that were changed as shown in Table 4-1, while in Cement it is the Cement content (kg/m3) and Quantity of heat developed at complete hydration (J/kg) that were changed.

37

Figure 4-4: The different properties of the chosen material that can be changed.

Table 4-1: Input that are changed for each material.

Material Time of casting (h)

Temperature at casting (°C)

Initial maturity time at casting (h)

K40 0 16 0.5 K401 2 16 0.5 K402 4 16 0.5

4.1.4 Boundary conditions There are six types of boundary conditions in HACON 3: Temperature, Heatflow, Displacement, Pipeflow, Loading and Spring. For the simulations, Temperature, Displacement and Pipeflow were used.

4.1.4.1 Temperature

The casting of the structure was assumed to be done in the month of April. The mean air temperature in April was set to 4 °C. The simulation of the temperature was monitored for one month (720 hours) and the different boundary conditions for the temperature were; Formwork, Removal of formwork and Exposed surface, as shown in Figure 4-5. The different temperatures at the different boundary conditions are shown in Table 4-2, where the formwork temperature was assumed to be 2 °C lower than the initial casting temperature of 16 °C.

38

Figure 4-5: The boundary conditions for the temperature of the structure.

Table 4-2: Time and temperature for the different boundary conditions.

Boundary conditions Time (h)

Temperature (°C)

Formwork 0 – 120 14 Removal of formwork 120 – 720 4 Exposed surface 0 – 720 4

4.1.4.2 Displacement

In HACON, the restraints can be applied in either x-direction, y-direction or in x- and y-direction. The restraint can be either fully restraint or zero restraint. The displacement restraint was defined at the bottom of the structure against the rock, and was assumed to be fully restraint in both x- and y-direction, as seen in Figure 4-6. To obtain the worst case, the displacement was defined equal to zero in both directions from 0 to 720 hours.

39

Figure 4-6: The displacement is totally restraint in x- and y-direction against rock.

4.1.4.3 Pipeflow

The boundary condition for the pipe flow is modelled in the cross section. However, the pipe flow condition is not a part of the reference model. It is only used in Section 4.8.

The pipes have been attached to the mesh. Therefore a mesh with eight rows and four columns was used, giving a space between the pipes in the vertical direction of 0.5 m and a horizontal distance of 0.375 m. Before assigning the pipes to the mesh, nodes were placed in the mesh corner.

The pipe flow can be described in two ways; Specified pipe flow or Specified output temperature. In this case, the specified pipe flow was used based on recommendations from Nordström (2017). The pipe diameter is 25 mm with a length of 8 m, the cooling starts at zero hours with an inlet temperature of 5 °C and a flow of 0.5 kg/s. The cooling lasted for four days with the same inlet temperature and flow.

The pipes were arranged in three vertical lanes, with the inlet at the bottom of the structure and outlet at the top of the structure, Figure 4-7. The outlet temperature should not be more than 4 °C higher than the inlet temperature of the water. After performing the calculations, the outlet temperature of the water can be obtained in Result type - Pipe - Diagram properties - Output temperature. If the output temperature is higher than 4 °C, the flow needs to be adjusted.

40

Figure 4-7: The pipe arrangement.

4.1.5 Calculation of the cross section The calculation for the cross section is only a temperature and maturity simulation. The general settings for the calculations are shown in Figure 4-8. To have a good time step for the calculation, the total time of simulation was divided into two intervals. The first interval was from 0 - 168 hours from casting, with a Time step of 0.5 hours and a Time increment for the storage of results of 6 hours as shown in Figure 4-8. The second interval was from 168 - 720 hours with a Time step of 1 hour and a Time increment for the storage of result of 12 hours.

The chosen intervals were selected since larger temperature changes occur early in the hardening process. To ensure that the temperature variation is registered, the time step was set to 0.5 hours the first seven days, i.e. two days after the formwork has been removed, and with a time step of 1 hour the remaining analysis. When this is performed, results of temperature and maturity can be evaluated.

41

Figure 4-8: Calculation settings for the temperature and maturity simulation for the cross section.

4.1.6 Plane section The calculations of the plane section were performed in the same manner as for the cross section. However, the difference here was that the geometry for the plane section was defined without any rock in the bottom. The width is 9 m and the height is 6 m, with 8-noded elements, eight rows and eighteen columns. The amount of rows needs to be the same as the amount of rows in the cross section.

The material properties are as in Section 4.1.3 and only the displacement boundary condition was defined as restrained movement at the base and at the right side as shown in Figure 4-9. The temperature and maturity were imported from the cross section to the plane section as shown in Figure 4-10.

The same plane section model can be used regardless if cooling pipes are used or not. The only difference when cooling pipes are used is that the imported temperature distribution and maturity from the cross-sectional model differs.

42

Figure 4-9: The plane section with the boundary conditions for the displacement.

Figure 4-10: The temperature and maturity are imported from an out-file from the cross section.

The analysis of the plane section only differs in the general settings as shown in Figure 4-11 and the time step is same as in Figure 4-8.

43

Figure 4-11: The calculation settings for the plane section.

4.2 Large aggregates

The size of the aggregates reduces the amount of cement in the concrete. Figure 4-12 shows the cement content depending on the maximum nominal size of aggregates for air-entrained and non-air-entrained concrete. In this case, it was assumed that the concrete was air-entrained. It was also assumed that the nominal size of aggregates was 50 mm instead of 25 mm. That corresponds to a cement content of 290 kg/m3 whereas in this case, the nominal size of aggregates is 50 mm corresponding to a cement content of 250 kg/m3 according to

Kosmatka et at. (2003). Therefore, increasing the aggregates size from 25 to 50 mm corresponds to a cement reduction of 14 %, which for the reference case corresponded to a reduction of the cement content from 360 kg/m3 to 310 kg/m3. Only the cement content was changed for this case, otherwise all the parameters were the same as for the reference model.

44

Figure 4-12: Cement conctent depending on the aggregates size. (Kosmatka et al., 2003)

4.3 Cold aggregates

The differences between this case and the reference model were the material properties and the temperature boundary conditions. The temperature of casting was changed and defined equal to 12 °C and in the temperature boundary condition the formwork temperature was assumed to be 10 °C due to colder concrete (i.e. 2 °C lower than the temperature of casting).

4.4 Ice

The differences in this case from the reference model were the material properties and the temperature boundary conditions. The temperature of casting was defined equal to 7 °C and the formwork temperature was assumed to 5 °C in the temperature boundary conditions (i.e. 2 °C lower than the temperature of casting due to colder concrete).

4.5 Fly ash

The difference in this case from the reference model was the material properties where the cement content and the heat generated at complete hydration were changed according to Table 4-3. The fitting parameters defined in Appendix B: Hydration heat calculation, where the calculation of generated heat by weight binder is presented, were kept as in the reference model because they are determined experimentally for each concrete mix.

The amount of fly ash was calculated as being a type II addition with a k-value of 0.4 according to SS-EN 206:2013+A1:2016. The details of the calculations are given in Appendix A: Calculation of cement reduction.

45

Table 4-3: Input data for concrete with 30 % fly ash.

Material Content (%)

Heat reduction (%)

Cement (kg/m3)

Hydration heat (kJ/kg)

Fly ash 30 21 316.8 272.55

By using the equations taken from Utsi (2008), the hydration heat was calculated for several amount of binder replacement by fly ash. Those values were then compared to the heat generated when any cement replacement was made. That lead to the percentage of heat reduction which was plotted against the percentage of fly ash used, see Figure 4-13. The results showed that the heat reduction was perfectly correlated to the percentage of fly ash replacement. Moreover, Utsi (2008) found, as well, a hydration heat reduction of 17 % for 25 % of fly ash content, see Table 4-4.

Table 4-4: Hydration heat reduction depending on the amount of fly ash.

Fly ash content (%) 10 15 20 25 30

Hydration heat reduction (%) 7 10 14 17 21

Figure 4-13: Hydration heat reduction depending on the percentage of binder replacement.

4.6 Silica fume

The difference in this case from the reference model was the material properties as for the model with fly ash. According to Figure 4-14, the hydration heat generated by binder paste without cement replacement and a binder paste with 10 % silica fume is approximately equal to 325 J/g and 290 J/g, respectively. That means that with the binder replacement of 10 % silica fume, the hydration heat is reduced by 11 %.

y  =  0,69x  +  2E-­‐14  R²  =  1  

0  

5  

10  

15  

20  

25  

0   5   10   15   20   25   30   35  

Heat  re

duc*on

 (%)  

Percentage  of  replacement  

46

Figure 4-14: Hydration heat at 3 days of a "pure" cement paste without replacement and of a cement paste with 10 % silica fume replacement. (Zhang, Sun and Liu, 2002)

Table 4-5 presents the data used for the simulations. The amount of silica fume was calculated as being a type II addition with a k-value of 1 according to SS-EN 206:2013+A1:2016. The details of the calculations are given in Appendix A: Calculation of cement reduction.

Table 4-5: Input data for the case with 10 % silica fume.

Material Content (%)

Hydration heat reduction (%)

Cement (kg/m3)

Hydration heat (kJ/kg)

Silica fume 10 11 324.0 307.05

4.7 Ground granulated blast furnace slag

The difference in this case compared to the reference model was the material properties as for the models with fly ash and silica fume.

Gruyaert et al. (2010) tested several mixes with different amount of slag replacement. The heat produced at complete hydration of the binder was measured and compared to the heat produced by Ordinary Portland Cement. The results are shown in Table 4-6. These values of heat generation are obtained under isothermal conditions at 293 K.

Table 4-6: Hydration heat depending on the amount of slag. Reproduced from Gruyaert et al. (2010).

Slag replacement (%) 0 15 30 50 70 85

Heat produced at 14 days (kJ/kg) 411 411 400 363 308 253

Heat produced at complete hydration (kJ/kg) 433 - 406 395 - 243

47

In this simulation, the reduction of hydration found by Gruyaert et al. (2010) for concrete containing slag as shown in Table 4-7 was applied. Therefore, the complete hydration heat was reduced by 6 % for a binder replacement by slag of 30 %. The amount of slag was calculated as being a type II addition with a k-value of 0.6 according to SS-EN 206:2013+A1:2016. The details of the calculations are given in Appendix A: Calculation of cement reduction.

Table 4-7: Input data for 30 % slag.

Material Content (%)

Heat reduction (%)

Cement (kg/m3)

Hydration heat (kJ/kg)

Slag 30 6 295.2 324.3

4.8 Cooling pipes

The same input data as for the reference model were used. The main difference was that a pipe flow condition was added in the boundary conditions as explained in Section 4.1.4.3.

4.9 Combination of fly ash, ice and large aggregates

With fly ash and a nominal aggregate diameter of 50 mm, the cement content was reduced by 12 % and 14 %, respectively. By combining them, the cement content was therefore lowered to 267 kg/m3. The heat generated at complete hydration was kept equal to 272.6 kJ/kg as in the simulation with fly ash. The initial temperature at casting and the formwork temperature were also changed to take into account the use of ice. They were defined equal to 7 °C and 5 °C, respectively.

4.10 Combination of ice and large aggregates

The same input data were used as for the model with large aggregates. Only the concrete temperature at casting and the formwork temperature were changed and defined equal to 7 °C and 5 °C, respectively.

4.11 Simulation of a thicker wall

The thickness of the wall was doubled compared to Chapter 4. This was made to see the effect of some methods depending on the thickness of the structure, as some massive structures could be as thick as 3 to 4 m. The simulations were performed for the reference model, the case with fly ash, cooling pipes and the combined case with fly ash, ice, and large aggregates.

The four cases were chosen to see if similar temperature reductions could be obtained depending on the thickness of the wall. The input data were the same as in Chapter 4, it was only the thickness of the section that was changed to 3 m.

48

The simulation for the cooling pipes was performed by having two identical 1.5 m thick walls next to each other and adding an extra column of cooling pipes in the joint between the two walls. The aim was to see the effect of the same arrangement in a thicker wall as for the 1.5 m thick wall. Other arrangements could be used.

49

5 Results and discussion The results are presented as temperature simulations in Section 5.1 and then as stress and crack risk simulations in Section 5.2. The most important results are presented and discussed in the coming sections, while additional results are presented in Appendix C: Temperatures and stresses and Appendix D: Results obtained from HACON.

5.1 Results for the temperature simulation

5.1.1 Reference model Figure 5-1 shows the maximum temperature for the whole cross section during the analysis and Figure 5-2 shows the temperature distribution in the cross section. The maximum temperature was reached 60 hours after casting and was equal to 46.7 °C.

The temperature follows the same evolution as the heat previously shown in Figure 2-1. The heat evolution is divided into five stages. The first two stages are occurring within the first 5 to 6 hours while the third stage obtain the highest heat evolution and has a second smaller peak in the fourth stage. The same behaviour can be found in Figure 5-1, where the highest temperature was obtained after 60 hours and decreased almost linearly to 132 hours, before decreasing more exponential towards the ambient temperature of 4 °C.

Figure 5-1: Maximum temperature evolution in the cross section for the reference case.

0  

10  

20  

30  

40  

50  

60  

0   100   200   300   400   500   600   700   800  

Tempe

rature  (°C)  

Time  (h)  

Temperature  envelope  

50

Figure 5-2: Maximum temperature in the cross section for the reference case.

Figure 5-3 presents the temperature evolution at the centre and the surface of the cross section. These two nodes were used to evaluate the temperature gradient from the core to the surface of the structure which should be as low as possible to avoid significant stresses and cracks. For the reference model, the maximum temperature gradient was equal to 21.4 °C and was reached at 132 hours after casting which was not necessarily when the maximum temperature was reached in the cross section.

Figure 5-3: Maximum temperature at the centre and the surface of the cross section for the reference case.

5.1.2 Cooling pipes Figure 5-4 and Figure 5-5 show the evolution of the maximum temperature during the hardening process. The maximum temperature was reached 30 hours after casting and was equal to 27.2 °C which represented a reduction of 42 % compared to the reference model.

0  

10  

20  

30  

40  

50  

60  

0   200   400   600   800  

Tempe

rature  (°C)  

Time  (h)  

Reference  model    

Center  

Surface  

51

Only for this case, the shape of temperature curve differed from the reference model. The first peak of temperature was obtained earlier and the second peak was better marked compared to the other models. This second peak was reached at 108 hours which was 12 hours after the cooling stopped.

The aim for this simulation was to get a smooth curve and to not overcool the concrete. More cooling could be used for the simulation, as well as other pipe arrangements. However, the pipe arrangement is limited in HACON due to that the pipes need to be assigned in nodes that are placed in the mesh corners in the structure. If a too fine mesh was used the model would not run and if a too large mesh was used the results might be of poor quality. Therefore, only one case with cooling pipes was simulated with a common spacing between the pipes.

Figure 5-4: Maximum temperature evolution in the cross section due to cooling pipes.

Figure 5-5: Maximum temperature in the cross section due to cooling pipes.

0  

10  

20  

30  

40  

50  

60  

0   100   200   300   400   500   600   700   800  

Tempe

rature  (°C)  

Time  (h)  

Temperature  envelope  

52

5.1.3 Comparison for all cases with the reference model The reduction of the maximum temperature gradient has higher importance than the temperature reduction itself when it comes to surface cracks. However, both will be discussed in this section.

The temperature in the cross section had almost the same evolution for all the models, as illustrated in Figure 5-6. Only the simulation with cooling pipes was showing a different behaviour compared to the other cases. The temperature decreased significantly after the first peak and its second peak when cooling stops was not as important for this method as in the other ones. The second peak for the other cases may be due to that it was the temperature envelope that was presented and vary within the structure.

When ice was used, the peak value of the maximum temperature was delayed. This might be explained by that the casting temperature was low compared to the other models. Thus the temperature in the structure took time to reach its maximum. The second temperature peak was not marked compared to the case with fly ash, making the curve smoother. This indicates a continuous cooling of the wall.

Figure 5-6: Maximum temperature evolution in the cross section for all cases. The second peak is marked for fly ash and cooling pipes.

Figure 5-7 and Figure 5-8 represent the maximum temperature reduction and the maximum temperature gradient reduction of the studied cases compared to the reference model. Cooling pipes were shown to be the best solution with a maximum temperature and a maximum temperature gradient that were 42 % and 76 % lower than the reference model respectively. This result might be an explanation of the common use of cooling pipes in Sweden. However, the simulation did neither take into account the installation of the cooling pipes on site nor did

0  

10  

20  

30  

40  

50  

60  

0   100   200   300   400   500   600   700   800  

Tempe

rature  (°C)  

Time  (h)  

Temperature  envelope   Reference  

Large  aggregates  

Cold  aggregates  

Ice  

Fly  ash  

Silica  fume  

Slag  

Cooling  pipes  

FA  +  Ice  +  Large  aggregates  Ice  +  Large  aggregates  

Second  peak  

53

it considered the risk of cracks around the pipes. The simulation was presenting a perfect case of a cooling pipes system and not the reality, making the result overestimated compared to what might happen in reality.

The effect of the temperature and size of the aggregates was quite similar. The maximum temperature and the gradient reduction was about 10 % compared to the reference model. These cooling measures are to be used in combination with other measures if a significant impact is wanted. It is difficult to use aggregates larger than 50 mm mainly due to limited means for concrete casting on site as the aggregates size affects the concrete pumpability. Moreover, if the aggregates maximum diameter is too large, it may be stuck in the reinforcement and affect the concrete homogeneity. This may have severe consequences regarding the bearing capacity of the structure.

In projects where cooling pipes are not desired, the use of fly ash might be a good way of temperature reduction. According to the results from the simulation, the maximum temperature and the maximum temperature gradient were reduced by 35 % and 22 %, respectively when fly ash was used as replacement of a certain amount of cement. Fly ash was giving the best results after cooling pipes when it was used without any combined measures. In addition, compared to other materials used as cement replacement, there are more data from previous studies about fly ash than for other replacements.

For silica fume and slag, the maximum temperature was reduced by 15 % and 17 % while the gradient was reduced by 14 % and 17 %, respectively compared to the reference model. These mineral additions were showing good result when it came to lowering concrete temperature. Combining these with other methods of heat reduction might give significant result in concrete technology.

Fly ash combined with large aggregates and ice as pre-cooling measures gave better results than the use of cooling pipes when it came to the temperature reduction inside the structure. With this combination the maximum temperature and the maximum temperature gradient were both reduced by 54 % compared to the reference model. However, the maximum temperature gradient was still mostly reduced with the cooling pipes. There was a deviation of 20 % between the two models.

As expected, the combination of ice an large aggregates had a lower impact on the temperature reduction than when fly ash was used as well, as illustrated in Figure 5-7 and Figure 5-8.

Regarding all the uncertainties that exist with a system of cooling pipes, the combination of several pre-cooling methods might be a good alternative to cooling pipes. Further studies should focus on finding optimal combination of pre-cooling measures to avoid post cooling

However, more general research has to be carried out to master the use of the mineral additives such as fly ash, silica fume and slag. It is not only important to know the structure behaviour at early age, but also in the long term perspective to minimize advanced and expensive repairs.

54

Once the heat generation is reduced, the gradient between the core and the surface reflects how the structure is cooled. It is not depending itself on the values of temperature as it is a difference. Significant gradient means that the cooling of the core is taking longer than the cooling of the surface. To make the structure cooling more homogenous, additional measures need to be applied. Those are mainly the execution techniques such as the maximum lifting height, the casting sequences of the different parts, and their arrangement.

Figure 5-7: Percentage of maximum temperature reduction compared to the reference model.

Figure 5-8: Percentage of maximum temperature gradient reduction compared to the reference model.

0  10  20  30  40  50  60  70  80  

Percen

tage  of  red

uc*o

n  (%

)  

Maximum  temperature  

0  10  20  30  40  50  60  70  80  

Percen

tage  of  red

uc*o

n  (%

)  

Temperature  gradient  

55

5.1.4 Three meter thick wall As the wall was thicker, the temperature inside the structure reached a higher maximum temperature as seen in Figure 5-9. For the reference model, the case with fly ash, cooling pipes and the combined cases with fly ash, ice and large aggregates, the maximum temperature was 53.2, 41, 21.1 and 26.6 ℃, respectively.

Figure 5-9: Evolution of the temperature envelope in the cross section for the three cases.

Figure 5-10 and Figure 5-11 present the maximum temperature and the maximum gradient reduction when fly ash was used as part of the binder and when it was combined with ice and large aggregates to lower the heat generation. The peak of temperature was reduced by 23 % when only fly ash was used and by 50 % when it was combined with other methods. Regarding the maximum gradient, the reductions were 25 % and 53 %. The results obtained depending on the thickness of the wall are summarized in Table 5-1.

When fly ash was used in combination with other methods, the obtained reduction for both the maximum temperature and the gradient were quite similar to the result of the 1.5 m thick wall whereas when only fly ash was used, there was a deviation of 12 % for the maximum temperature of the two walls. The fact that the reduction of the gradient remained approximately the same means that these two methods of heat reduction had a quasi-identical effect on the risk of surface cracks independently on the structure thickness.

As for the 1.5 m thick wall, cooling pipes were giving better results with a reduction of the maximum temperature and temperature gradient equal to 60 % and 81 %, respectively.

0  

10  

20  

30  

40  

50  

60  

0   200   400   600   800  

Tempe

rature  (℃

)  

Time  (h)  

Temperature  envelope  

Reference  model  

Fly  ash  

FA  +  Ice  +  Large  aggregates    

Cooling  pipes  

56

Figure 5-10: Maximum temperature reduction compared to the reference model.

Figure 5-11: Temperature gradient reduction compared to the reference model.

Table 5-1: Percentage of reduction of the maximum temperature and the maximum gradient depending on the thickness of the wall.

Thickness of wall (m)

Maximum temperature reduction

(%)

Maximum temperature gradient

reduction (%)

Fly ash 1.5 35 22

3 23 25 FA + Ice + Large aggregates 1.5 54 54

3 50 53

Cooling pipes 1.5 42 76

3 60 81

0  10  20  30  40  50  60  70  80  

Reference   Fly  ash   FA  +  Ice+  Large  aggregates  

Cooling  pipes  

Percen

tage  of  red

uc*o

n  (%

)  Temperature  envelope  (3  m  thick  wall)  

0  10  20  30  40  50  60  70  80  

Reference     Fly  ash   FA  +  Ice  +  Large  aggregates  

Cooling  pipes  

Percen

tage  of  red

uc*o

n  (%

)  

Temperature  gradient  (3  m  thick  wall)  

57

5.2 Crack risk simulation

5.2.1 Reference model Figure 5-12 shows the evolution of the maximum principal stress in the plane section. It was approximately equal to 17.4 MPa which was larger than the tensile strength. The stresses in the plane section were highest in the corners where it was restrained from moving in x- and y-direction, and towards the restrained parts, as illustrated in Figure 5-13.

Figure 5-12: Maximum principal stress evolution in the plane section for the reference case.

Figure 5-13: Maximum principal stress in the plane section for the reference case.

The crack risk was evaluated with the stress-strength ratio. This ratio should be below 100 % to avoid cracking. In Figure 5-14 it can be seen that a part of the restrained edges have been neglected. The neglect of 30 cm from the restrained edges was due to that the wall in reality cannot be fully restrained as assumed in the displacement boundary condition, giving high

0  2  4  6  8  

10  12  14  16  18  

0   100   200   300   400   500   600   700   800  

Maxim

um  prin

cipa

l  stress  (MPa

)  

Time  (h)  

58

stresses in the corners. The stress-strength ratio was about 50 % lower than if the restraint edges were included as seen in Figure 5-15.

Figure 5-14: Distribution of stress-strength ratio in the plane section for the reference model.

For the reference model, the maximum value of this ratio was 243 % which meant that there was a high crack risk in the wall. Even though the value was not lower than 100 %, most cracks were anticipated to appear close to the restraint edges. In reality, the cracks might not be that severe because the real conditions on site are different from the conditions in the program.

Figure 5-15: Stress-strength ratio evolution in the plane section for the reference model.

0  

50  

100  

150  

200  

250  

0   100   200   300   400   500   600   700   800  

Stress-­‐Stren

gth  ra*o

 (%)  

Time  (h)  

59

5.2.2 Comparison with the reference model Discussing the maximum principal stress is the same as discussing the stress-strength ratio. As the crack risk is evaluated with regards to the stress-strength ratio, the focus will be on that part.

Although the values of stress-strength ratio were significant due to the restrain conditions, the difference between the methods used to reduce the temperature in massive concrete structures can still be discussed. The crack risk was not really measured but rather how it could be reduced and which of the methods was the most efficient way to do so.

Figure 5-16 represents the relative gap between the maximum value of the different methods and the reference model. If only one method was used, cooling pipes were giving the best results with a crack risk 57 % lower than the reference model. In addition to that, there was not a significant variation of stress-strength ratio for cooling pipes compared to the other methods, as illustrated in Figure 5-17. After cooling pipes, ice and fly ash were the solutions that gave the best results with a crack risk of 39 % and 23 % lower than the reference, respectively. As the amount of cement was reduced when mineral additions were used, the amount of heat generated during the hydration process decreased. This affected the concrete temperature which was lower than when only cement was used. Therefore, for a highly restrained wall as in these simulations, the tensile stresses were reduced, which made the crack risk less important.

When appropriate combinations were used in the concrete mix such as the combination of fly ash, ice and large aggregates a higher reduction of the crack risk compared to cooling pipes was obtained. The crack risk was reduced by 65 % compared to the reference, and the combination of ice and large aggregates gave a reduction of 49 % compared to the reference model.

The difference between the two combined cases was the content of fly ash. Therefore, these cases showed the influence of fly ash when combined with different pre-cooling methods. If lower amount of fly ash was used, the expected result should be between the two combined cases.

60

Figure 5-16: Comparison of the different methods with the reference model regarding the crack risk.

Figure 5-17: Stress-strength ratio evolution for the different cases.

5.2.3 Three meter thick wall Figure 5-18 shows the stress-strength ratio for the three methods of heat reduction that were applied to a three meter thick wall. This was made to evaluate the crack risk in this wall and to compare it to the crack risk of the thinner wall previously studied.

Compared to the reference model, the crack risk was reduced by 24 % and 64 % for the model with only fly ash and when it was combined with ice and large aggregates as seen in Figure

0  10  20  30  40  50  60  70  80  

Percen

tage  of  red

uc*o

n  (%

)  Stress  -­‐  Strength  ra*o  

0  

50  

100  

150  

200  

250  

0   200   400   600   800  

Stress  -­‐  Strength  ra

*o  (%

)  

Time  (h)  

Stress-­‐Strength  ra*o  

Reference  

Large  aggregates  

Cold  aggregates  

Ice  

Fly  ash  

Silica  fume  

Slag  

Cooling  pipes  

FA+Ice+Large  aggregates  

Ice  +  Large  aggregates  

61

5-19. These results were quasi-identical to the ones obtained for the 1.5 m thick wall with a deviation of 1 %, see Table 5-2. Therefore, the impact of the studied method was not dependent on the thickness of the structure.

A lower reduction of the crack risk was obtained with cooling pipes.

Figure 5-18: Evolution of the stress-strength ratio for the three models for the thicker wall.

Figure 5-19: Crack risk reduction compared to the reference model for the thicker wall.

0  

50  

100  

150  

200  

250  

0   200   400   600   800  

Stress-­‐Stren

gth  ra*o

 (%)  

Time  (h)  

Stress-­‐Strength  ra*o  

Reference  model  

Fly  ash  

FA  +  Ice  +  Large  aggregates  Cooling  pipes  

0  

10  

20  

30  

40  

50  

60  

70  

80  

Reference   Fly  ash   FA+Ice+Large  aggregates  

Cooling  pipes  

Percen

tage  of  red

uc*o

n  (%

)  

Stress  -­‐  Strength  ra*o  (3  m  thick  wall)  

62

Table 5-2: Percentage of reduction for the stress-strength ratio depending on the thickness of the wall.

Thickness of wall (m)

Stress-strength ratio reduction (%)

Fly ash 1.5 23

3 24 FA + Ice + Large aggregates 1.5 65

3 64

Cooling pipes 1.5 57

3 29

63

6 Conclusions The main objective of this master project was to find suitable methods to reduce the temperature in massive concrete structures and thus minimize the risk of cracks. Several methods were compared by means of temperature and stress simulations in HACON.

When the cooling methods were used separately, cooling pipes were the most suitable method in all aspects; maximum temperature reduction, maximum temperature gradient reduction and crack risk. However, one problem with cooling pipes is the amount of pipes used in combination with highly reinforced structures, inducing workability issues.

Between the minerals additions, i.e. fly ash, silica fume, and ground granulated blast furnace slag, fly ash was the most efficient in all aspects and was a good way to reduce the heat generated at early age. Fly ash could be an alternative to cooling pipes when only one cooling method is applied. Moreover, fly ash is already frequently used in several countries as part of the cement content. As fly ash is a pozzolan, its reaction with water is slow, giving a lower concrete strength at early age. Therefore, the strength should be measured at 91 days instead of the usual 28 days to ensure that the effect of fly ash is captured. Better results could be obtained with silica fume and slag if more accurate information regarding their heat development fitting parameters were available.

The combination of pre-cooling methods showed better temperature reduction than when each replacement was used separately. The impact of large and cold aggregates when they were used separately was not that significant and they gave almost the same reduction in all aspects. However, when the large aggregates were combined with ice it showed better results. Furthermore, the combination of fly ash, ice, and large aggregates was another way to reduce the use of cooling pipes. The crack risk was lowered by 20 % compared to cooling pipes. Moreover, this method was more reliable than cooling pipes as there are fewer uncertainties regarding the execution of the structure. Thereby, these pre-cooling methods can be used in combination with cooling pipes to reduce the amount of pipes needed, as well as it can be used without cooling pipes.

When the thickness of the wall was doubled, the obtained results were almost identical in most of the cases simulated for the thicker wall. Cooling pipes showed more differences especially when it came to the crack risk. However, the simulation with cooling pipes was to have a rough estimation of the effect of the thickness. Therefore, the simulated cooling method might be applied independently on the thickness of the wall.

64

6.1 Further research

Further studies can focus on finding more appropriate combinations of pre-cooling methods. The results from the combined cases can be more accurate if more information regarding the mineral addition properties is found.

Cases with different percentage of replacement can be simulated with more advanced computer programs. Further research can be performed in Sweden to evaluate the strength of typical concrete with fly ash at 91 days.

The different methods of temperature reductions can be evaluated in field studies i.e. perform simulations to compare it with measurements on real cases or on large specimens.

Other studies could be to perform a cost analysis regarding the application of the studied methods as the economic aspect is a main part of a project.

When large aggregates are used, the risk of them getting stuck in the pumps and in the reinforcement is high. Therefore, new research regarding different pouring methods can be performed.

65

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Appendix A: Calculation of cement reduction Equations used to calculate the reduction of the cement content in 1 m! of concrete when fly ash, silica fume and slag are used.

The calculations are performed in two steps.

1. Proportions of cement, water and aggregates in the reference concrete recipe.

The equations are taken from Kosmatka, Kerkhoff and Panarese, (2003).

m!"#$% = vct ∙m!"#"$%

where, m!"#"$% – Mass of the cement in the reference recipe.

V – Volume of 1 m! concrete.

vct – water cement ratio.

ρ – Density.

V = Cement+Water+ Aggregates

1 =m!"#"$%

ρ!"#"$%+m!"#$%

ρ!"#$%+m!""#$"!%$&

ρ!""#$"!%$&

m!"#$% = vct ∙m!"#"$%

1 =m!"#"$%

ρ!"#"$%+vct ∙m!"#"$%

ρ!"#$%+m!""#$"!%$&

ρ!""#$"!%$&→

V!""#$"!%$& =m!""#$"!%$&

ρ!""#$"!%$&= 1−m!"#"$%(

1ρ!"#"$%

+vctρ!"#$%

)

Water =vct   ∙  m!"#"$%

ρ!"#$%

2. Amount of addition used to replace the cement content.

The equations are taken from the Swedish Concrete Standard SS-EN 206:2013+A1:2016.

Symbols

A – Quantity of addition (Fly ash, silica fume, slag) by m3 of concrete.

70

C – Quantity of cement by m3 of concrete.

C0 – Quantity of cement of the reference model.

B – Equivalent binder.

k – k-value for the replacement material.

p - Percentage of cement replacement by with fly ash, silica fume or slag.

Assumptions:

- The amount of addition is taken by weight of cement and addition content. - The amount of cement and addition is taken as equal to the amount of cement of the

reference model.

The two unknowns are the quantity of cement and the quantity of addition.

C+ kA = C!"AC!"

= P

→          A = P ∙ C!"

 and        C = C!" − k ∙ A

The reduction of cement is:

Reduction =C! − CC!

71

Appendix B: Hydration heat calculation The following equations are used to calculate the heat generated at complete hydration by weight of binder when fly ash is used as cement replacement. They are taken from Utsi (2008).

Symbols

WB – Heat generated at complete hydration by weight of binder.

W!"! – Heat generated at testing.

W!, κ! and t! – Individual fitting parameters valid for each tested mix.

λ! – Uncoupled parameter.

t! – Equivalent time.

t! – Equivalent time.

FA – Fly ash

B – Equivalent binder

C – Cement content

Wo/C – Water cement ratio

W! =!!"!!

= W! ∙ exp  [−λ![ln 1+ !!!!]!!!   [J/kg]

W! = W!"# ∙ γ! [kJ/kg]

κ! = κ! ∙ γ!

W!"# = 275− 20 ∙ exp −!!!

!.!"

!

[kJ/kg]

γ! = 1− 0.69 ∙FAC    (≥ 0.33)

κ! = 1.65+ 0.35 ∙ exp −w!C0.55

!

72

γ! = 1+ 0.2 ∙ 1− exp −FAC0.8

!

t! = 8+ 2.7 ∙ exp −!!!

!.!"

!"

[h]

73

Appendix C: Temperatures and stresses Results obtained from simulations performed in HACON for each case.

Temperature distribution for a 1.5 m thick wall

Figure 1: Temperature distribution for the reference model.

Figure 2: Temperature distribution for the case study with large aggregates.

74

Figure 3: Temperature distribution for the case study with cold aggregates.

Figure 4: Temperature distribution for the case study with ice.

75

Figure 5: Temperature distribution for the case study with fly ash.

Figure 6: Temperature distribution for the case study with silica fume.

76

Figure 7: Temperature distribution for the case study with slag.

Figure 8: Temperature distribution for the case study with cooling pipes.

77

Figure 9: Temperature distribution for the combined case with fly ash, ice and large aggregates.

Figure 10: Temperature distribution for the combined case with ice and large aggregates.

78

Stress in plane for a 1.5 m wall

Figure 11: Stress in plane for the reference model.

Figure 12: Stress in plane for the case study with large aggregates.

79

Figure 13: Stress in plane for the case study with cold aggregates.

Figure 14: Stress in plane for the case study with ice.

80

Figure 15: Stress in plane for the case study with fly ash.

Figure 16: Stress in plane for the case study with silica fume.

81

Figure 17: Stress in plane for the cases study with slag.

Figure 18: Stress in plane for the case study with cooling pipes.

82

Figure 19: Stress in plane for the combined case with fly ash, ice and large aggregates.

Figure 20: Stress in plane for the combined case with ice and large aggregates.

83

Maximum principal stress for a 1.5 m thick wall

Figure 21: Maximum principal stress for the reference model.

Figure 22: Maximum principal stress for the case study with large aggregates.

84

Figure 23: Maximum principal stress for the case study with cold aggregates.

Figure 24: Maximum principal stress for the case study with ice.

85

Figure 25: Maximum principal stress for the case study with fly ash.

Figure 26: Maximum principal stress for the case study with silica fume.

86

Figure 27: Maximum principal stress for the case study with slag.

Figure 28: Maximum principal stress for the case study with cooling pipes.

87

Figure 29: Maximum principal stress for the combined case with fly ash, ice and large aggregates.

Figure 30: Maximum principal stress for the combined case with ice and large aggregates.

88

Temperature gradient for a 1.5 m thick wall

Figure 31: Temperature gradient for large aggregates (left) and cold aggregates (right).

Figure 32: Temperature gradient for ice (left) and fly ash (right).

Figure 33: Temperature gradient for silica fume (left) and slag (right).

Figure 34: Temperature gradient for combined case with fly ash, ice and large aggregates (left) and combined case with ice and large aggregates (right).

0  10  20  30  40  50  60  

0   200   400   600   800  

Tempe

rature  (°C)  

Time  (h)  

Large  aggregates  

Center  

Surface  

0  10  20  30  40  50  60  

0   200   400   600   800  

Tempe

rature  (°C)  

Time  (h)  

Cold  aggregates  

Center  

Surface  

0  10  20  30  40  50  60  

0   200   400   600   800  

Tempe

rature  (°C)  

Time  (h)  

Ice    

Center  

Surface  

0  10  20  30  40  50  60  

0   200   400   600   800  

Tempe

rature  (°C)  

Time  (h)  

Fly  ash  

Center  

Surface  

0  10  20  30  40  50  60  

0   200   400   600   800  

Tempe

rature  (°C)  

Time  (h)  

Silica  Fume  

Center  

Surface  

0  10  20  30  40  50  60  

0   200   400   600   800  

Tempe

rature  (°C)  

Time  (h)  

Slag  

Center  

Surface  

0  10  20  30  40  50  60  

0   200   400   600   800  

Tempe

rature  (°C)  

Time  (h)  

Combina*on  FA,  ice  and  large  aggregates  

Center  

Surface  

0  10  20  30  40  50  60  

0   200   400   600   800  

Tempe

rature  (°C)  

Time  (h)  

Combina*on  ice  and  large  aggregates  

Center  

Surface  

89

Temperature gradient for a 3 m thick wall

Figure 35: Temperature gradient for the reference model (left) and fly ash (right).

Figure 36: Temperature gradient for cooling pipes (left) and combined case with fly ash, ice and large aggregates (right).

0  10  20  30  40  50  60  

0   200   400   600   800  

Tempe

rature  (°C)  

Time  (h)  

Reference  

Center  

Surface  

0  10  20  30  40  50  60  

0   200   400   600   800  

Tempe

rature  (°C)  

Time  (h)  

Fly  ash  

Center  

Surface  

0  10  20  30  40  50  60  

0   200   400   600   800  

Tempe

rature  (°C)  

Time  (h)  

Cooling  pipes  

Center  

Surface  0  

10  20  30  40  50  60  

0   200   400   600   800  

Tempe

rature  (°C)  

Time  (h)  

Combina*on  FA,  ice  and  large  aggregates  

Center  

Surface  

90

91

Appendix D: Results obtained from HACON The data presented below are used to obtain the graphs presented in the report.

Reference model 1.5 meter thick wall

Temperature Stresses

Time (h)

Max temp. (°C)

Temp. centre (°C)

Temp. surface

(°C)

Temp. gradient

(°C)

Max principal

stress (MPa)

Stress/Strength

6 17.385 16.234 15.711 0.523 0.002 0.061 12 24.921 22.070 19.989 2.081 0.066 4.223 18 32.833 30.441 25.430 5.011 0.239 13.910 24 38.382 36.867 28.933 7.934 0.380 25.266 30 41.855 41.044 30.748 10.296 0.480 32.040 36 44.041 43.643 31.580 12.063 0.529 35.454 42 45.496 45.205 31.879 13.326 0.560 33.660 48 46.298 46.074 31.887 14.187 0.614 33.909 54 46.637 46.468 31.731 14.736 0.655 32.809 60 46.659 46.528 31.479 15.049 0.694 31.532 66 46.448 46.351 31.168 15.183 0.716 33.123 72 46.071 46.003 30.819 15.184 0.731 31.513 78 45.579 45.532 30.447 15.085 0.736 29.790 84 45.000 44.973 30.061 14.912 0.734 28.581 90 44.364 44.349 29.664 14.685 0.729 27.782 96 43.686 43.681 29.263 14.418 0.760 27.115 102 42.983 42.982 28.859 14.123 1.081 26.796 108 42.264 42.264 28.456 13.808 1.406 28.867 114 41.535 41.533 28.054 13.478 1.731 31.851 120 40.800 40.796 27.656 13.140 2.051 35.796 132 39.217 39.212 17.852 21.359 3.715 58.310 144 37.040 37.034 15.701 21.333 4.863 74.712 156 34.432 34.428 14.331 20.097 5.878 88.888 168 31.782 31.780 13.270 18.510 6.786 103.789 180 29.259 29.259 12.369 16.890 7.758 118.819 192 26.919 26.919 11.572 15.347 8.680 132.263 204 24.771 24.771 10.855 13.916 9.516 144.301 216 22.810 22.810 10.206 12.604 10.274 155.079 228 21.024 21.024 9.616 11.407 10.960 164.726 240 19.400 19.400 9.081 10.319 11.581 173.356

92

252 17.926 17.926 8.596 9.330 12.143 181.071 264 16.589 16.589 8.156 8.433 12.650 187.965 276 15.378 15.378 7.757 7.620 13.108 194.122 288 14.281 14.281 7.396 6.885 13.522 199.617 300 13.289 13.289 7.070 6.219 13.895 204.519 312 12.392 12.392 6.775 5.617 14.232 208.891 324 11.582 11.582 6.509 5.074 14.537 212.786 336 10.851 10.851 6.268 4.583 14.812 216.256 348 10.192 10.191 6.051 4.140 15.060 219.346 360 9.597 9.596 5.855 3.741 15.284 222.094 372 9.061 9.059 5.679 3.380 15.487 224.539 384 8.578 8.575 5.519 3.056 15.670 226.712 396 8.143 8.140 5.376 2.764 15.836 228.641 408 7.751 7.748 5.247 2.501 15.986 230.354 420 7.398 7.395 5.131 2.264 16.122 231.874 432 7.081 7.077 5.026 2.051 16.245 233.220 444 6.795 6.791 4.932 1.859 16.357 234.413 456 6.678 6.534 4.847 1.686 16.458 235.469 468 6.608 6.302 4.771 1.531 16.550 236.402 480 6.542 6.094 4.703 1.391 16.634 237.227 492 6.481 5.907 4.641 1.266 16.710 237.955 504 6.424 5.739 4.586 1.153 16.780 238.597 516 6.371 5.587 4.536 1.052 16.843 239.162 528 6.321 5.451 4.491 0.960 16.901 239.661 540 6.274 5.329 4.450 0.878 16.954 240.099 552 6.229 5.219 4.414 0.805 17.002 240.485 564 6.187 5.120 4.381 0.738 17.047 240.824 576 6.147 5.031 4.352 0.679 17.087 241.123 588 6.110 4.950 4.325 0.625 17.125 241.386 600 6.074 4.878 4.302 0.577 17.160 241.618 612 6.039 4.813 4.280 0.533 17.192 241.824 624 6.007 4.755 4.261 0.494 17.222 242.007 636 5.975 4.702 4.243 0.459 17.249 242.169 648 5.946 4.655 4.228 0.427 17.275 242.313 660 5.917 4.612 4.213 0.399 17.299 242.439 672 5.889 4.573 4.201 0.373 17.321 242.544 684 5.863 4.539 4.189 0.350 17.342 242.614 696 5.837 4.507 4.178 0.329 17.361 242.618 708 5.812 4.479 4.169 0.310 17.380 242.460 720 5.788 4.453 4.160 0.293 17.397 241.824

93

Aggregates size 1.5 meter thick wall

Temperature Stresses

Time (h) Max temp. (°C)

Temp. centre (°C)

Temp. surface

(°C)

Temp. gradient

(°C)

Max principal

stress (MPa)

Stress/Strength

6 17.186 16.201 15.684 0.518 0.002 0.054 12 23.458 21.113 19.255 1.857 0.053 3.503 18 29.927 27.968 23.690 4.277 0.191 11.679 24 34.529 33.261 26.562 6.699 0.307 21.490 30 37.479 36.782 28.099 8.683 0.391 27.579 36 39.363 39.025 28.839 10.186 0.449 31.136 42 40.658 40.407 29.135 11.272 0.462 28.819 48 41.395 41.202 29.181 12.021 0.510 29.225 54 41.736 41.589 29.081 12.508 0.617 29.790 60 41.800 41.686 28.893 12.793 0.586 27.169 66 41.661 41.576 28.651 12.925 0.611 26.871 72 41.375 41.315 28.372 12.943 0.621 27.457 78 40.986 40.944 28.071 12.873 0.628 26.043 84 40.518 40.493 27.753 12.740 0.629 25.244 90 39.998 39.984 27.426 12.558 0.627 24.610 96 39.439 39.434 27.092 12.342 0.675 24.079 102 38.856 38.855 26.756 12.099 0.944 23.835 108 38.255 38.255 26.418 11.838 1.216 25.685 114 37.645 37.644 26.080 11.564 1.488 28.228 120 37.028 37.026 25.745 11.281 1.756 31.589 132 35.683 35.679 16.554 19.125 3.246 52.067 144 33.769 33.765 14.574 19.190 4.261 66.761 156 31.439 31.436 13.327 18.109 5.157 79.423 168 29.060 29.058 12.366 16.692 5.958 93.027 180 26.790 26.790 11.553 15.237 6.827 106.405 192 24.683 24.683 10.834 13.848 7.638 118.365 204 22.748 22.748 10.188 12.560 8.375 129.068 216 20.981 20.981 9.603 11.378 9.043 138.648 228 19.372 19.372 9.072 10.299 9.648 147.219 240 17.908 17.908 8.590 9.318 10.196 154.884 252 16.580 16.580 8.153 8.427 10.692 161.735 264 15.375 15.375 7.756 7.619 11.140 167.854 276 14.283 14.283 7.397 6.887 11.545 173.317 288 13.295 13.295 7.071 6.223 11.911 178.192 300 12.401 12.401 6.777 5.623 12.242 182.539 312 11.592 11.592 6.511 5.081 12.540 186.413 324 10.862 10.862 6.271 4.591 12.810 189.864

94

336 10.203 10.202 6.054 4.148 13.054 192.936 348 9.608 9.607 5.858 3.749 13.275 195.669 360 9.072 9.070 5.682 3.389 13.474 198.099 372 8.588 8.586 5.522 3.064 13.655 200.259 384 8.153 8.150 5.379 2.771 13.818 202.175 396 7.760 7.757 5.249 2.507 13.966 203.876 408 7.406 7.403 5.133 2.270 14.099 205.383 420 7.088 7.084 5.028 2.056 14.221 206.718 432 6.801 6.797 4.934 1.864 14.331 207.899 444 6.550 6.539 4.849 1.691 14.431 208.942 456 6.481 6.307 4.772 1.535 14.522 209.863 468 6.417 6.098 4.703 1.395 14.604 210.675 480 6.358 5.910 4.641 1.268 14.680 211.389 492 6.303 5.741 4.586 1.155 14.748 212.017 504 6.251 5.588 4.535 1.053 14.811 212.568 516 6.202 5.452 4.490 0.961 14.868 213.050 528 6.157 5.328 4.450 0.879 14.920 213.472 540 6.114 5.218 4.413 0.805 14.968 213.840 552 6.073 5.118 4.380 0.738 15.012 214.160 564 6.035 5.028 4.351 0.678 15.053 214.439 576 5.999 4.948 4.324 0.624 15.090 214.680 588 5.965 4.875 4.300 0.575 15.124 214.888 600 5.932 4.810 4.278 0.532 15.156 215.068 612 5.901 4.751 4.259 0.492 15.186 215.223 624 5.871 4.698 4.241 0.457 15.213 215.355 636 5.842 4.650 4.225 0.425 15.239 215.468 648 5.815 4.607 4.211 0.396 15.262 215.563 660 5.789 4.568 4.198 0.370 15.284 215.640 672 5.764 4.533 4.186 0.346 15.305 215.699 684 5.739 4.501 4.176 0.325 15.325 215.732 696 5.716 4.472 4.166 0.306 15.343 215.722 708 5.694 4.446 4.157 0.289 15.360 215.622 720 5.672 4.423 4.150 0.273 15.377 215.292

95

Cold aggregates 1.5 meter thick wall

Temperature Stresses

Time (h)

Max temp. (°C)

Temp. centre (°C)

Temp. surface

(°C)

Temp. gradient

(°C)

Max principal

stress (MPa)

Stress/Strength

6 12.532 12.058 11.562 0.496 0.001 0.018 12 17.410 15.329 13.874 1.455 0.019 1.501 18 24.479 22.133 18.430 3.702 0.129 8.004 24 30.584 28.793 22.377 6.416 0.275 17.520 30 34.873 33.755 24.909 8.846 0.387 26.408 36 37.653 37.088 26.312 10.775 0.468 31.817 42 39.565 39.228 27.005 12.223 0.517 34.534 48 40.793 40.541 27.277 13.264 0.541 32.775 54 41.473 41.278 27.301 13.978 0.575 32.264 60 41.754 41.607 27.174 14.433 0.602 30.948 66 41.754 41.642 26.953 14.689 0.617 29.647 72 41.545 41.463 26.672 14.791 0.672 32.267 78 41.186 41.129 26.352 14.777 0.640 29.346 84 40.717 40.680 26.005 14.675 0.640 27.562 90 40.168 40.148 25.641 14.507 0.634 25.693 96 39.564 39.554 25.266 14.288 0.622 24.367 102 38.920 38.917 24.884 14.033 0.609 23.401 108 38.250 38.250 24.498 13.751 0.694 22.608 114 37.562 37.561 24.111 13.450 0.983 22.263 120 36.863 36.861 23.726 13.135 1.276 24.742 132 35.364 35.359 16.112 19.247 2.593 41.526 144 33.400 33.395 14.351 19.043 3.543 55.326 156 31.108 31.103 13.196 17.908 4.393 67.449 168 28.793 28.789 12.283 16.506 5.161 78.793 180 26.587 26.585 11.499 15.086 5.881 91.730 192 24.535 24.535 10.802 13.734 6.663 103.396 204 22.649 22.649 10.171 12.478 7.376 113.871 216 20.922 20.922 9.598 11.324 8.026 123.273 228 19.346 19.346 9.076 10.269 8.615 131.706 240 17.909 17.909 8.602 9.307 9.151 139.265 252 16.602 16.602 8.171 8.432 9.636 146.037 264 15.415 15.415 7.779 7.636 10.076 152.098 276 14.337 14.337 7.423 6.914 10.475 157.521 288 13.359 13.359 7.101 6.258 10.835 162.370 300 12.474 12.474 6.809 5.665 11.162 166.702 312 11.672 11.672 6.545 5.127 11.457 170.572 324 10.946 10.946 6.306 4.641 11.725 174.025

96

336 10.290 10.290 6.089 4.201 11.967 177.105 348 9.698 9.697 5.894 3.803 12.186 179.851 360 9.163 9.162 5.717 3.444 12.384 182.298 372 8.680 8.678 5.558 3.120 12.564 184.476 384 8.244 8.242 5.414 2.828 12.727 186.414 396 7.851 7.849 5.285 2.564 12.875 188.137 408 7.497 7.494 5.168 2.326 13.009 189.668 420 7.177 7.174 5.062 2.112 13.130 191.026 432 6.889 6.886 4.967 1.918 13.241 192.231 444 6.630 6.626 4.881 1.744 13.341 193.298 456 6.481 6.392 4.804 1.588 13.433 194.243 468 6.417 6.181 4.735 1.446 13.516 195.077 480 6.357 5.991 4.672 1.319 13.592 195.814 492 6.302 5.820 4.616 1.205 13.661 196.464 504 6.250 5.666 4.565 1.101 13.724 197.036 516 6.202 5.527 4.519 1.009 13.782 197.538 528 6.156 5.402 4.477 0.925 13.835 197.979 540 6.113 5.290 4.440 0.850 13.884 198.365 552 6.073 5.188 4.407 0.782 13.929 198.702 564 6.035 5.097 4.376 0.721 13.970 198.995 576 5.999 5.015 4.349 0.666 14.008 199.250 588 5.964 4.940 4.324 0.616 14.043 199.471 600 5.931 4.873 4.302 0.571 14.076 199.662 612 5.900 4.813 4.282 0.531 14.106 199.826 624 5.871 4.758 4.264 0.494 14.134 199.967 636 5.842 4.709 4.248 0.462 14.160 200.086 648 5.815 4.665 4.233 0.432 14.184 200.186 660 5.789 4.625 4.219 0.405 14.207 200.269 672 5.764 4.588 4.207 0.381 14.228 200.334 684 5.740 4.555 4.196 0.359 14.248 200.382 696 5.716 4.525 4.186 0.339 14.267 200.409 708 5.694 4.498 4.177 0.321 14.285 200.405 720 5.672 4.474 4.169 0.305 14.302 200.353

97

Ice 1.5 meter thick wall

Temperature Stresses

Time (h)

Max temp. (°C)

Temp. centre (°C)

Temp. surface

(°C)

Temp. gradient

(°C)

Max principal

stress (MPa)

Stress/Strength

6 7.071 7.003 6.516 0.487 0.000 0.077 12 8.804 7.919 7.001 0.918 0.000 0.174 18 13.000 11.393 9.321 2.072 0.000 1.956 24 18.390 16.576 12.583 3.993 0.000 6.687 30 23.483 21.939 15.726 6.213 0.000 15.136 36 27.494 26.408 18.137 8.271 0.000 23.994 42 30.357 29.713 19.731 9.982 0.000 30.047 48 32.339 32.009 20.682 11.327 0.000 33.716 54 33.783 33.532 21.187 12.345 0.000 35.112 60 34.677 34.483 21.398 13.084 0.000 32.833 66 35.160 35.012 21.419 13.593 0.000 32.101 72 35.342 35.229 21.314 13.916 0.000 30.878 78 35.296 35.213 21.124 14.089 0.000 29.117 84 35.079 35.021 20.877 14.144 0.000 27.366 90 34.737 34.698 20.590 14.108 0.000 28.550 96 34.298 34.275 20.276 13.999 0.000 26.666 102 33.790 33.778 19.943 13.835 0.000 24.750 108 33.230 33.226 19.598 13.629 0.033 22.763 114 32.634 32.634 19.244 13.390 0.087 20.792 120 32.013 32.012 18.885 13.128 0.153 19.185 132 30.670 30.665 14.004 16.661 0.622 20.236 144 29.006 29.000 12.736 16.263 1.353 30.131 156 27.129 27.123 11.851 15.271 2.109 39.676 168 25.243 25.238 11.125 14.112 2.825 48.333 180 23.440 23.436 10.488 12.948 3.492 56.749 192 21.753 21.751 9.913 11.838 4.110 65.728 204 20.190 20.190 9.388 10.802 4.678 74.379 216 18.752 18.752 8.908 9.844 5.199 82.187 228 17.432 17.432 8.469 8.964 5.677 89.226 240 16.224 16.224 8.067 8.156 6.113 95.563 252 15.119 15.119 7.700 7.418 6.511 101.264 264 14.110 14.110 7.366 6.744 6.873 106.388 276 13.191 13.191 7.061 6.130 7.203 110.989 288 12.355 12.355 6.784 5.570 7.504 115.117 300 11.594 11.594 6.532 5.062 7.777 118.819 312 10.903 10.903 6.304 4.599 8.025 122.137

98

324 10.276 10.276 6.096 4.180 8.251 125.108 336 9.706 9.706 5.908 3.799 8.457 127.768 348 9.191 9.191 5.737 3.454 8.643 130.147 360 8.724 8.723 5.582 3.141 8.813 132.274 372 8.301 8.300 5.442 2.858 8.968 134.174 384 7.919 7.917 5.316 2.602 9.108 135.870 396 7.573 7.571 5.201 2.370 9.236 137.384 408 7.260 7.258 5.097 2.161 9.353 138.734 420 6.977 6.974 5.003 1.971 9.459 139.936 432 6.721 6.719 4.919 1.800 9.556 141.007 444 6.490 6.487 4.842 1.645 9.645 141.959 456 6.281 6.278 4.773 1.505 9.726 142.805 468 6.192 6.089 4.710 1.379 9.800 143.556 480 6.139 5.919 4.654 1.265 9.868 144.222 492 6.090 5.765 4.602 1.162 9.930 144.812 504 6.044 5.626 4.556 1.069 9.987 145.333 516 6.001 5.500 4.514 0.985 10.040 145.794 528 5.960 5.386 4.477 0.909 10.088 146.200 540 5.922 5.283 4.442 0.841 10.133 146.557 552 5.886 5.191 4.412 0.779 10.174 146.871 564 5.853 5.107 4.384 0.723 10.212 147.146 576 5.820 5.031 4.358 0.672 10.247 147.387 588 5.790 4.962 4.335 0.627 10.280 147.596 600 5.761 4.900 4.315 0.585 10.311 147.777 612 5.734 4.843 4.296 0.548 10.339 147.935 624 5.707 4.792 4.279 0.514 10.366 148.070 636 5.682 4.746 4.263 0.483 10.391 148.185 648 5.658 4.704 4.249 0.455 10.414 148.283 660 5.635 4.666 4.236 0.430 10.436 148.366 672 5.613 4.631 4.224 0.407 10.457 148.434 684 5.591 4.599 4.214 0.386 10.476 148.490 696 5.571 4.571 4.204 0.367 10.494 148.535 708 5.551 4.544 4.195 0.349 10.512 148.570 720 5.532 4.520 4.187 0.333 10.529 148.595

99

Fly ash 1.5 meter thick wall

Temperature Stresses

Time (h)

Max temp. (°C)

Temp. centre (°C)

Temp. surface

(°C)

Temp. gradient

(°C)

Max principal

stress (MPa)

Stress/Strength

6 15.994 16.162 15.651 0.512 0.001 0.046 12 19.080 20.024 18.419 1.605 0.000 2.724 18 23.350 25.233 21.763 3.470 0.000 9.114 24 26.453 29.264 23.932 5.332 0.000 17.363 30 28.340 32.007 25.129 6.878 0.000 22.538 36 29.394 33.802 25.736 8.067 0.000 25.482 42 29.916 34.938 26.002 8.936 0.000 24.756 48 30.099 35.616 26.070 9.546 0.000 23.326 54 30.061 35.969 26.020 9.949 0.000 23.155 60 29.876 36.088 25.895 10.193 0.000 23.609 66 29.593 36.037 25.722 10.315 0.000 22.391 72 29.244 35.862 25.518 10.344 0.013 22.210 78 28.849 35.595 25.292 10.304 0.056 21.698 84 28.425 35.261 25.051 10.210 0.107 21.290 90 27.983 34.877 24.800 10.077 0.172 20.882 96 27.530 34.457 24.543 9.914 0.259 20.577 102 27.073 34.010 24.281 9.729 0.376 20.553 108 26.615 33.546 24.017 9.529 0.528 22.602 114 26.161 33.070 23.753 9.317 0.712 24.706 120 25.712 32.586 23.489 9.097 0.915 27.586 132 23.023 31.512 15.019 16.492 2.317 45.811 144 20.983 29.901 13.241 16.660 3.336 58.556 156 19.237 27.896 12.137 15.759 4.253 69.481 168 17.694 25.833 11.294 14.539 5.083 81.661 180 16.318 23.860 10.584 13.277 5.837 93.124 192 15.085 22.027 9.957 12.069 6.523 103.363 204 13.978 20.342 9.395 10.948 7.146 112.517 216 12.985 18.804 8.885 9.919 7.712 120.704 228 12.094 17.403 8.423 8.980 8.225 128.022 240 11.294 16.129 8.003 8.126 8.689 134.561 252 10.577 14.973 7.622 7.350 9.110 140.401 264 9.934 13.924 7.277 6.647 9.490 145.614 276 9.357 12.974 6.965 6.009 9.835 150.265 288 8.840 12.113 6.681 5.432 10.146 154.411 300 8.376 11.335 6.425 4.910 10.428 158.105 312 7.960 10.631 6.194 4.437 10.682 161.395 324 7.587 9.995 5.985 4.011 10.913 164.323

100

336 7.253 9.421 5.796 3.625 11.121 166.926 348 6.952 8.903 5.625 3.278 11.309 169.240 360 6.683 8.435 5.471 2.964 11.480 171.294 372 6.442 8.014 5.333 2.681 11.635 173.117 384 6.225 7.634 5.208 2.426 11.775 174.732 396 6.030 7.292 5.095 2.197 11.902 176.163 408 5.855 6.983 4.994 1.990 12.017 177.428 420 5.698 6.706 4.902 1.804 12.121 178.546 432 5.558 6.456 4.820 1.636 12.216 179.533 444 5.431 6.231 4.746 1.485 12.303 180.402 456 5.317 6.028 4.679 1.349 12.382 181.166 468 5.215 5.846 4.619 1.227 12.453 181.837 480 5.122 5.682 4.565 1.117 12.519 182.425 492 5.039 5.534 4.516 1.018 12.578 182.938 504 4.965 5.402 4.473 0.929 12.633 183.386 516 4.898 5.282 4.433 0.849 12.683 183.776 528 4.837 5.175 4.398 0.777 12.729 184.113 540 4.782 5.078 4.366 0.712 12.771 184.404 552 4.733 4.991 4.337 0.654 12.810 184.655 564 4.688 4.913 4.311 0.601 12.846 184.869 576 4.648 4.842 4.288 0.554 12.879 185.051 588 4.612 4.778 4.267 0.512 12.910 185.204 600 4.579 4.721 4.248 0.473 12.938 185.333 612 4.549 4.669 4.231 0.439 12.965 185.439 624 4.521 4.623 4.215 0.408 12.989 185.526 636 4.497 4.581 4.201 0.380 13.012 185.595 648 4.474 4.543 4.189 0.354 13.034 185.648 660 4.454 4.509 4.177 0.332 13.054 185.687 672 4.435 4.478 4.167 0.311 13.073 185.710 684 4.419 4.450 4.158 0.292 13.091 185.716 696 4.403 4.425 4.149 0.276 13.107 185.699 708 4.389 4.402 4.142 0.260 13.123 185.640 720 4.376 4.381 4.135 0.247 13.138 185.497

101

Silica fume 1.5 meter thick wall

Temperature Stresses

Time (h)

Max temp. (°C)

Temp. centre (°C)

Temp. surface

(°C)

Temp. gradient

(°C)

Max principal

stress (MPa)

Stress/Strength

6 16.048 16.187 15.672 0.515 0.001 0.051 12 19.720 20.711 18.947 1.764 0.000 3.211 18 24.868 26.948 22.973 3.976 0.000 10.707 24 28.613 31.771 25.582 6.189 0.000 20.079 30 30.862 35.008 26.996 8.012 0.000 25.732 36 32.093 37.091 27.690 9.401 0.000 29.106 42 32.687 38.387 27.979 10.408 0.000 26.232 48 32.880 39.143 28.036 11.108 0.000 27.260 54 32.817 39.521 27.956 11.565 0.000 26.620 60 32.585 39.629 27.793 11.837 0.000 25.315 66 32.241 39.543 27.577 11.966 0.000 25.232 72 31.822 39.316 27.327 11.989 0.000 25.807 78 31.354 38.985 27.054 11.931 0.046 24.420 84 30.854 38.578 26.765 11.813 0.103 23.793 90 30.334 38.116 26.466 11.650 0.173 23.236 96 29.803 37.614 26.161 11.453 0.266 22.783 102 29.269 37.084 25.852 11.232 0.391 22.600 108 28.735 36.535 25.542 10.994 0.557 24.468 114 28.206 35.974 25.231 10.743 0.764 26.833 120 27.684 35.406 24.922 10.483 0.998 30.013 132 24.777 34.159 15.994 18.165 2.530 49.649 144 22.556 32.357 14.089 18.268 3.664 63.624 156 20.649 30.147 12.894 17.253 4.686 75.645 168 18.965 27.884 11.976 15.908 5.611 88.709 180 17.460 25.724 11.200 14.523 6.452 101.384 192 16.111 23.717 10.516 13.201 7.217 112.712 204 14.901 21.873 9.900 11.974 7.912 122.847 216 13.815 20.190 9.342 10.847 8.542 131.916 228 12.840 18.656 8.836 9.820 9.113 140.028 240 11.965 17.262 8.377 8.885 9.630 147.281 252 11.181 15.997 7.960 8.036 10.098 153.762 264 10.477 14.849 7.582 7.266 10.521 159.549 276 9.846 13.808 7.240 6.568 10.904 164.715 288 9.280 12.867 6.930 5.936 11.250 169.324 300 8.773 12.014 6.650 5.365 11.563 173.432 312 8.318 11.244 6.396 4.848 11.845 177.093 324 7.910 10.548 6.167 4.381 12.100 180.353

102

336 7.544 9.920 5.961 3.959 12.331 183.254 348 7.215 9.352 5.774 3.578 12.540 185.834 360 6.921 8.841 5.606 3.235 12.729 188.127 372 6.657 8.379 5.454 2.926 12.900 190.163 384 6.419 7.964 5.317 2.647 13.054 191.970 396 6.207 7.589 5.194 2.395 13.195 193.572 408 6.016 7.252 5.083 2.169 13.322 194.991 420 5.844 6.948 4.983 1.965 13.437 196.246 432 5.690 6.674 4.893 1.782 13.541 197.356 444 5.551 6.428 4.812 1.617 13.636 198.336 456 5.427 6.207 4.739 1.468 13.723 199.199 468 5.315 6.007 4.673 1.334 13.801 199.959 480 5.214 5.828 4.614 1.214 13.873 200.627 492 5.124 5.667 4.561 1.106 13.938 201.213 504 5.042 5.522 4.513 1.009 13.998 201.726 516 4.969 5.391 4.470 0.921 14.053 202.174 528 4.903 5.274 4.431 0.843 14.103 202.564 540 4.843 5.168 4.396 0.772 14.149 202.903 552 4.789 5.073 4.365 0.708 14.191 203.197 564 4.741 4.987 4.337 0.651 14.229 203.451 576 4.697 4.910 4.311 0.599 14.265 203.670 588 4.657 4.841 4.288 0.553 14.298 203.857 600 4.621 4.779 4.267 0.511 14.329 204.017 612 4.589 4.722 4.249 0.473 14.357 204.153 624 4.559 4.672 4.232 0.439 14.384 204.267 636 4.532 4.626 4.217 0.409 14.408 204.362 648 4.508 4.585 4.203 0.381 14.431 204.440 660 4.486 4.547 4.191 0.357 14.452 204.502 672 4.466 4.514 4.180 0.334 14.472 204.545 684 4.447 4.483 4.169 0.314 14.491 204.567 696 4.430 4.456 4.160 0.296 14.509 204.553 708 4.415 4.431 4.152 0.279 14.526 204.471 720 4.401 4.409 4.144 0.264 14.542 204.226

103

Slag 1.5 meter thick wall

Temperature Stresses

Time (h)

Max temp. (°C)

Temp. centre (°C)

Temp. surface

(°C)

Temp. gradient

(°C)

Max principal

stress (MPa)

Stress/Strength

6 17.057 17.057 15.666 1.392 0.001 0.050 12 22.545 22.545 18.791 3.753 0.000 3.066 18 28.131 28.131 22.614 5.517 0.000 10.228 24 32.134 32.134 25.092 7.042 0.000 19.486 30 34.737 34.737 26.442 8.295 0.000 24.815 36 36.416 36.416 27.112 9.304 0.000 28.087 42 37.593 37.593 27.396 10.198 0.000 27.107 48 38.275 38.275 27.457 10.819 0.000 26.240 54 38.607 38.607 27.386 11.221 0.000 25.642 60 38.690 38.690 27.235 11.454 0.000 24.500 66 38.590 38.590 27.033 11.557 0.000 24.397 72 38.356 38.356 26.796 11.560 0.003 25.329 78 38.028 38.028 26.537 11.491 0.049 23.602 84 37.629 37.629 26.263 11.366 0.104 23.054 90 37.180 37.180 25.978 11.201 0.172 22.542 96 36.694 36.694 25.687 11.007 0.262 22.132 102 36.186 36.186 25.392 10.793 0.384 21.985 108 35.660 35.660 25.096 10.565 0.547 23.890 114 35.125 35.125 24.799 10.326 0.746 26.167 120 34.582 34.582 24.503 10.079 0.971 29.255 132 33.388 33.388 15.709 17.679 2.465 48.472 144 31.642 31.642 13.841 17.801 3.564 62.084 156 29.491 29.491 12.673 16.819 4.555 73.783 168 27.286 27.286 11.777 15.509 5.452 86.585 180 25.180 25.180 11.020 14.159 6.267 98.903 192 23.223 23.223 10.353 12.871 7.009 109.912 204 21.427 21.427 9.752 11.674 7.682 119.759 216 19.786 19.786 9.209 10.577 8.294 128.569 228 18.291 18.291 8.716 9.575 8.848 136.448 240 16.932 16.932 8.268 8.664 9.349 143.491 252 15.698 15.698 7.862 7.836 9.803 149.784 264 14.579 14.579 7.494 7.086 10.214 155.403 276 13.565 13.565 7.160 6.405 10.585 160.418 288 12.647 12.647 6.858 5.789 10.921 164.891 300 11.817 11.817 6.584 5.232 11.224 168.878 312 11.066 11.066 6.337 4.728 11.499 172.430 324 10.387 10.387 6.114 4.273 11.747 175.593

104

336 9.775 9.775 5.913 3.863 11.971 178.407 348 9.223 9.223 5.731 3.492 12.174 180.909 360 8.725 8.725 5.567 3.158 12.357 183.132 372 8.276 8.276 5.419 2.857 12.523 185.106 384 7.871 7.871 5.285 2.585 12.674 186.857 396 7.506 7.506 5.165 2.341 12.810 188.409 408 7.177 7.177 5.057 2.120 12.934 189.783 420 6.881 6.881 4.959 1.922 13.046 190.998 432 6.615 6.615 4.872 1.743 13.147 192.072 444 6.416 6.416 4.793 1.623 13.240 193.019 456 6.352 6.352 4.722 1.630 13.324 193.853 468 6.292 6.292 4.657 1.635 13.401 194.587 480 6.237 6.237 4.600 1.637 13.470 195.231 492 6.185 6.185 4.548 1.637 13.534 195.796 504 6.137 6.137 4.501 1.635 13.592 196.289 516 6.091 6.091 4.459 1.632 13.646 196.720 528 6.049 6.049 4.422 1.627 13.694 197.095 540 6.009 6.009 4.388 1.621 13.739 197.420 552 5.971 5.971 4.357 1.614 13.780 197.701 564 5.935 5.935 4.329 1.606 13.818 197.943 576 5.901 5.901 4.304 1.597 13.853 198.150 588 5.869 5.869 4.282 1.587 13.886 198.327 600 5.838 5.838 4.262 1.577 13.916 198.478 612 5.809 5.809 4.244 1.566 13.943 198.604 624 5.781 5.781 4.227 1.554 13.969 198.710 636 5.755 5.755 4.212 1.542 13.993 198.797 648 5.729 5.729 4.199 1.530 14.016 198.867 660 5.705 5.705 4.187 1.518 14.037 198.922 672 5.681 5.681 4.176 1.505 14.057 198.959 684 5.658 5.658 4.166 1.492 14.075 198.975 696 5.637 5.637 4.157 1.479 14.093 198.960 708 5.615 5.615 4.149 1.466 14.109 198.885 720 5.595 5.595 4.142 1.453 14.125 198.675

105

Cooling pipes 1.5 meter thick wall

Temperature Stresses

Time (h)

Max temp. (°C)

Temp. centre (°C)

Temp. surface

(°C)

Temp. gradient

(°C)

Max principal

stress (MPa)

Stress/Strength

6 17.777 16.121 16.895 -0.774 0.002 0.189 12 22.379 18.889 20.674 -1.785 0.031 1.726 18 25.827 23.002 25.066 -2.064 0.102 7.030 24 26.958 24.997 26.917 -1.920 0.123 9.496 30 27.286 24.888 26.728 -1.840 0.105 6.798 36 26.340 23.564 25.481 -1.917 0.136 7.508 42 24.770 21.718 23.813 -2.095 0.494 15.217 48 23.014 19.751 22.066 -2.315 0.946 23.714 54 21.320 17.865 20.404 -2.539 1.613 40.804 60 19.771 16.152 18.901 -2.749 2.074 48.345 66 18.382 14.644 17.581 -2.937 2.472 55.445 72 17.165 13.343 16.443 -3.101 2.834 62.215 78 16.116 12.233 15.474 -3.241 3.149 67.788 84 15.219 11.295 14.655 -3.360 3.419 72.337 90 14.459 10.507 13.968 -3.460 3.680 76.161 96 13.818 9.848 13.393 -3.544 3.885 79.101 102 12.931 9.547 12.487 -2.940 3.747 75.676 108 12.884 10.065 12.423 -2.358 3.613 72.507 114 12.960 10.611 12.541 -1.930 3.498 69.806 120 13.075 11.106 12.703 -1.597 3.391 67.332 132 12.355 11.978 8.107 3.871 3.819 74.181 144 12.464 12.243 7.347 4.896 4.038 77.051 156 12.222 12.044 7.006 5.039 4.233 79.493 168 11.814 11.678 6.792 4.886 4.411 81.688 180 11.356 11.262 6.622 4.640 4.579 83.712 192 10.896 10.838 6.467 4.371 4.737 85.587 204 10.466 10.423 6.319 4.103 4.886 87.323 216 10.054 10.022 6.178 3.844 5.030 88.926 228 9.660 9.640 6.043 3.597 5.174 90.400 240 9.287 9.278 5.915 3.363 5.311 91.753 252 8.936 8.936 5.793 3.142 5.440 92.990 264 8.614 8.614 5.678 2.935 5.562 94.120 276 8.311 8.311 5.570 2.741 5.677 95.148 288 8.029 8.029 5.469 2.560 5.784 96.084 300 7.765 7.765 5.375 2.390 5.885 96.932 312 7.519 7.519 5.287 2.233 5.980 97.701 324 7.291 7.291 5.204 2.086 6.069 98.396

106

336 7.078 7.078 5.128 1.950 6.152 99.024 348 6.882 6.882 5.057 1.824 6.230 99.611 360 6.699 6.699 4.992 1.708 6.302 100.197 372 6.530 6.530 4.931 1.600 6.370 100.727 384 6.374 6.374 4.874 1.500 6.434 101.205 396 6.231 6.230 4.822 1.407 6.494 101.635 408 6.099 6.096 4.774 1.322 6.550 102.022 420 5.978 5.973 4.730 1.243 6.603 102.371 432 5.865 5.859 4.688 1.171 6.652 102.683 444 5.811 5.754 4.650 1.103 6.698 102.964 456 5.774 5.657 4.615 1.042 6.742 103.215 468 5.740 5.567 4.583 0.984 6.783 103.440 480 5.707 5.484 4.552 0.932 6.822 103.640 492 5.676 5.407 4.525 0.883 6.858 103.819 504 5.647 5.336 4.499 0.838 6.893 103.979 516 5.619 5.271 4.475 0.796 6.925 104.120 528 5.592 5.210 4.453 0.757 6.956 104.246 540 5.567 5.154 4.432 0.722 6.985 104.357 552 5.543 5.102 4.413 0.689 7.013 104.456 564 5.520 5.054 4.396 0.658 7.040 104.542 576 5.498 5.009 4.379 0.630 7.065 104.619 588 5.476 4.968 4.364 0.603 7.089 104.685 600 5.456 4.929 4.350 0.579 7.112 104.744 612 5.437 4.893 4.337 0.556 7.134 104.795 624 5.418 4.859 4.325 0.535 7.155 104.838 636 5.400 4.828 4.313 0.515 7.175 104.876 648 5.383 4.799 4.302 0.496 7.194 104.909 660 5.366 4.771 4.292 0.479 7.213 104.936 672 5.350 4.746 4.283 0.463 7.231 104.959 684 5.334 4.722 4.274 0.448 7.248 104.979 696 5.319 4.700 4.266 0.434 7.265 104.995 708 5.304 4.678 4.258 0.421 7.281 105.008 720 5.290 4.659 4.250 0.408 7.297 105.018

107

Combined case with fly ash, ice and large aggregates 1.5 meter thick wall

Temperature Stresses

Time (h)

Max temp. (°C)

Temp. centre (°C)

Temp. surface

(°C)

Temp. gradient

(°C)

Max principal

stress (MPa)

Stress/Strength

6 7.041 7.002 6.515 0.487 0.001 0.093 12 8.014 7.526 6.706 0.820 0.001 0.098 18 10.149 9.360 7.887 1.473 0.011 0.943 24 12.656 11.827 9.411 2.416 0.040 2.978 30 14.991 14.276 10.812 3.464 0.084 6.648 36 16.919 16.381 11.918 4.463 0.129 10.898 42 18.403 18.049 12.715 5.334 0.168 14.347 48 19.507 19.306 13.256 6.050 0.208 16.796 54 20.358 20.218 13.601 6.616 0.249 18.354 60 20.961 20.850 13.803 7.047 0.281 19.163 66 21.351 21.263 13.901 7.362 0.304 19.433 72 21.572 21.504 13.923 7.581 0.279 16.884 78 21.663 21.610 13.890 7.720 0.272 15.677 84 21.650 21.610 13.817 7.794 0.263 14.513 90 21.555 21.528 13.712 7.815 0.255 13.550 96 21.399 21.380 13.585 7.795 0.316 15.275 102 21.193 21.182 13.441 7.742 0.272 12.767 108 20.951 20.945 13.284 7.661 0.268 12.268 114 20.679 20.677 13.117 7.560 0.258 11.850 120 20.385 20.385 12.943 7.441 0.252 11.012 132 19.721 19.720 9.958 9.762 0.575 11.741 144 18.837 18.835 9.219 9.616 0.950 17.001 156 17.799 17.797 8.710 9.087 1.299 22.399 168 16.737 16.735 8.294 8.442 1.622 27.293 180 15.711 15.710 7.927 7.783 1.923 31.699 192 14.743 14.743 7.595 7.148 2.201 36.965 204 13.842 13.842 7.290 6.551 2.457 41.821 216 13.007 13.007 7.010 5.997 2.733 46.209 228 12.237 12.237 6.753 5.484 2.993 50.169 240 11.529 11.529 6.517 5.012 3.232 53.740 252 10.879 10.879 6.300 4.579 3.452 56.957 264 10.284 10.284 6.102 4.182 3.654 59.853 276 9.739 9.739 5.921 3.818 3.840 62.458 288 9.242 9.242 5.756 3.486 4.010 64.801 300 8.788 8.788 5.605 3.183 4.165 66.905 312 8.374 8.374 5.467 2.907 4.308 68.795 324 7.997 7.997 5.342 2.655 4.439 70.492

108

336 7.654 7.654 5.228 2.426 4.559 72.014 348 7.343 7.342 5.124 2.218 4.669 73.379 360 7.060 7.059 5.030 2.028 4.770 74.602 372 6.802 6.801 4.945 1.857 4.862 75.698 384 6.569 6.567 4.867 1.700 4.947 76.680 396 6.357 6.355 4.796 1.559 5.025 77.558 408 6.164 6.163 4.732 1.430 5.097 78.344 420 5.990 5.988 4.674 1.313 5.163 79.047 432 5.831 5.829 4.622 1.208 5.223 79.676 444 5.689 5.685 4.574 1.112 5.280 80.237 456 5.650 5.555 4.530 1.025 5.331 80.738 468 5.613 5.437 4.491 0.946 5.379 81.185 480 5.579 5.329 4.455 0.874 5.424 81.584 492 5.547 5.232 4.423 0.809 5.465 81.940 504 5.517 5.144 4.393 0.750 5.503 82.257 516 5.489 5.063 4.366 0.697 5.539 82.539 528 5.463 4.991 4.342 0.649 5.572 82.790 540 5.438 4.924 4.320 0.605 5.603 83.014 552 5.414 4.864 4.300 0.564 5.632 83.212 564 5.392 4.810 4.281 0.528 5.659 83.388 576 5.370 4.760 4.265 0.495 5.684 83.545 588 5.350 4.714 4.249 0.465 5.708 83.683 600 5.331 4.673 4.236 0.438 5.731 83.806 612 5.313 4.636 4.223 0.413 5.752 83.915 624 5.295 4.601 4.211 0.390 5.772 84.011 636 5.283 4.570 4.201 0.369 5.791 84.096 648 5.275 4.541 4.191 0.350 5.810 84.170 660 5.267 4.515 4.182 0.333 5.827 84.236 672 5.260 4.491 4.174 0.317 5.843 84.294 684 5.252 4.469 4.166 0.302 5.859 84.346 696 5.244 4.449 4.160 0.289 5.874 84.391 708 5.237 4.430 4.153 0.277 5.889 84.430 720 5.230 4.413 4.147 0.266 5.903 84.465

109

Combined case with ice and large aggregates 1.5 meter thick wall

Temperature Stresses

Time (h)

Max temp. (°C)

Temp. centre (°C)

Temp. surface

(°C)

Temp. gradient

(°C)

Max principal

stress (MPa)

Stress/Strength

6 7.061 7.003 6.516 0.487 0.012 0.082 12 8.532 7.785 6.901 0.885 0.001 0.148 18 11.978 10.674 8.816 1.859 0.010 1.576 24 16.279 14.839 11.427 3.412 0.043 5.258 30 20.344 19.104 13.909 5.195 0.103 11.834 36 23.616 22.717 15.843 6.874 0.199 19.103 42 26.024 25.467 17.171 8.296 0.296 24.406 48 27.717 27.437 18.005 9.431 0.380 27.814 54 29.003 28.786 18.484 10.303 0.446 29.770 60 29.831 29.663 18.718 10.945 0.465 28.788 66 30.314 30.184 18.786 11.398 0.471 27.245 72 30.535 30.436 18.742 11.694 0.476 26.053 78 30.559 30.484 18.619 11.865 0.473 24.749 84 30.431 30.378 18.442 11.936 0.476 23.102 90 30.190 30.154 18.227 11.927 0.480 21.488 96 29.862 29.839 17.984 11.856 0.488 22.914 102 29.469 29.457 17.721 11.736 0.467 21.239 108 29.027 29.023 17.444 11.578 0.456 19.628 114 28.551 28.550 17.158 11.391 0.443 18.008 120 28.048 28.048 16.866 11.182 0.428 16.516 132 26.949 26.946 12.633 14.313 0.466 16.710 144 25.559 25.555 11.548 14.008 0.715 24.711 156 23.974 23.970 10.792 13.178 0.959 32.778 168 22.373 22.369 10.172 12.197 1.201 40.111 180 20.837 20.835 9.628 11.207 1.449 46.997 192 19.397 19.395 9.136 10.260 1.688 54.658 204 18.060 18.060 8.686 9.374 1.931 61.984 216 16.828 16.828 8.274 8.554 2.153 68.599 228 15.695 15.695 7.896 7.799 2.356 74.564 240 14.656 14.656 7.551 7.106 2.542 79.938 252 13.706 13.706 7.235 6.471 2.712 84.774 264 12.837 12.837 6.947 5.891 2.867 89.123 276 12.045 12.045 6.684 5.361 3.008 93.031 288 11.323 11.323 6.444 4.878 3.136 96.540 300 10.665 10.665 6.226 4.439 3.252 99.689 312 10.068 10.068 6.028 4.039 3.358 102.512 324 9.524 9.524 5.848 3.676 3.455 105.042

110

336 9.031 9.031 5.685 3.346 3.542 107.307 348 8.584 8.584 5.537 3.047 3.622 109.335 360 8.179 8.178 5.402 2.776 3.695 111.148 372 7.812 7.811 5.280 2.530 3.760 112.769 384 7.479 7.478 5.170 2.308 3.820 114.218 396 7.178 7.176 5.070 2.106 3.875 115.511 408 6.905 6.903 4.980 1.923 3.925 116.664 420 6.658 6.656 4.898 1.758 3.970 117.693 432 6.435 6.433 4.824 1.609 4.011 118.609 444 6.233 6.230 4.757 1.474 4.049 119.424 456 6.050 6.047 4.696 1.352 4.083 120.149 468 6.000 5.882 4.641 1.241 4.115 120.793 480 5.954 5.732 4.591 1.141 4.144 121.365 492 5.910 5.597 4.546 1.051 4.170 121.871 504 5.870 5.475 4.506 0.969 4.194 122.320 516 5.832 5.364 4.469 0.895 4.216 122.717 528 5.796 5.264 4.435 0.828 4.237 123.067 540 5.762 5.173 4.405 0.768 4.256 123.375 552 5.730 5.091 4.378 0.713 4.273 123.646 564 5.700 5.017 4.353 0.664 4.289 123.884 576 5.672 4.949 4.330 0.619 4.304 124.093 588 5.645 4.888 4.310 0.578 4.318 124.275 600 5.619 4.833 4.291 0.541 4.331 124.433 612 5.595 4.783 4.275 0.508 4.343 124.570 624 5.571 4.737 4.259 0.478 4.354 124.689 636 5.549 4.695 4.245 0.450 4.364 124.791 648 5.527 4.658 4.233 0.425 4.374 124.878 660 5.507 4.623 4.221 0.402 4.383 124.952 672 5.487 4.592 4.210 0.382 4.392 125.014 684 5.468 4.564 4.201 0.363 4.400 125.065 696 5.450 4.538 4.192 0.346 4.407 125.108 708 5.432 4.514 4.184 0.330 4.415 125.142 720 5.415 4.492 4.176 0.316 4.422 125.169

111

Reference model 3 meter thick wall

Temperature Stresses

Time (h)

Max temp. (°C)

Temp. centre (°C)

Temp. surface

(°C)

Temp. gradient

(°C)

Max principal

stress (MPa)

Stress/Strength

6 17.386 16.234 15.711 0.523 0.002 0.063 12 24.935 22.076 19.989 2.088 0.068 4.388 18 32.914 30.490 25.431 5.059 0.248 14.512 24 38.642 37.053 28.935 8.118 0.400 27.318 30 42.452 41.515 30.751 10.764 0.513 35.665 36 45.051 44.568 31.586 12.982 0.589 39.225 42 47.108 46.741 31.894 14.847 0.684 40.783 48 48.647 48.349 31.919 16.430 0.778 42.595 54 49.825 49.574 31.791 17.783 0.846 43.292 60 50.737 50.526 31.580 18.946 1.027 49.788 66 51.446 51.271 31.326 19.945 1.011 46.879 72 51.998 51.855 31.050 20.805 1.048 46.768 78 52.423 52.307 30.766 21.541 1.083 46.362 84 52.740 52.650 30.481 22.169 1.118 45.753 90 52.967 52.900 30.200 22.700 1.147 44.958 96 53.120 53.071 29.926 23.145 1.169 44.063 102 53.205 53.172 29.659 23.513 1.185 43.054 108 53.235 53.214 29.401 23.813 1.195 42.520 114 53.214 53.202 29.151 24.051 1.201 42.174 120 53.150 53.144 28.910 24.234 1.204 41.731 132 52.906 52.906 19.022 33.884 1.170 38.479 144 52.530 52.530 17.044 35.487 1.749 38.002 156 52.024 52.024 15.874 36.150 2.426 45.485 168 51.377 51.377 15.039 36.338 3.067 53.022 180 50.586 50.586 14.385 36.201 3.675 60.383 192 49.666 49.666 13.844 35.822 4.255 67.474 204 48.644 48.644 13.379 35.265 4.808 74.267 216 47.545 47.545 12.969 34.577 5.339 80.759 228 46.394 46.394 12.599 33.795 5.848 86.961 240 45.208 45.208 12.260 32.949 6.337 93.208 252 44.008 44.005 11.945 32.060 6.807 100.057 264 42.801 42.794 11.650 31.145 7.260 106.582 276 41.597 41.586 11.370 30.216 7.695 112.787 288 40.402 40.388 11.105 29.284 8.115 118.688 300 39.223 39.205 10.851 28.355 8.565 124.303 312 38.063 38.041 10.607 27.435 9.073 129.645 324 36.925 36.900 10.372 26.528 9.565 134.728

112

336 35.812 35.783 10.146 25.637 10.040 139.726 348 34.725 34.693 9.928 24.765 10.499 144.929 360 33.666 33.631 9.717 23.914 10.943 150.720 372 32.634 32.596 9.513 23.083 11.371 156.292 384 31.632 31.591 9.316 22.275 11.785 161.655 396 30.658 30.615 9.126 21.490 12.185 166.815 408 29.714 29.668 8.941 20.727 12.571 171.780 420 28.798 28.751 8.763 19.987 12.944 176.558 432 27.912 27.862 8.591 19.270 13.303 181.155 444 27.053 27.001 8.425 18.577 13.651 185.580 456 26.223 26.169 8.264 17.905 13.986 189.837 468 25.420 25.365 8.109 17.256 14.310 193.934 480 24.645 24.587 7.960 16.628 14.622 197.876 492 23.898 23.837 7.815 16.022 14.924 201.670 504 23.176 23.112 7.676 15.436 15.215 205.321 516 22.480 22.412 7.541 14.871 15.495 208.834 528 21.808 21.737 7.411 14.325 15.766 212.215 540 21.159 21.085 7.286 13.799 16.028 215.470 552 20.534 20.458 7.166 13.292 16.280 218.602 564 19.931 19.852 7.050 12.803 16.524 221.617 576 19.350 19.269 6.938 12.331 16.759 224.518 588 18.790 18.706 6.830 11.877 16.985 227.312 600 18.250 18.165 6.726 11.439 17.204 230.000 612 17.730 17.643 6.626 11.017 17.415 232.588 624 17.229 17.141 6.530 10.611 17.619 235.080 636 16.747 16.657 6.437 10.220 17.816 237.479 648 16.282 16.191 6.348 9.844 18.005 239.788 660 15.835 15.743 6.262 9.481 18.189 242.012 672 15.406 15.311 6.179 9.132 18.365 244.152 684 14.994 14.896 6.099 8.796 18.536 246.214 696 14.597 14.496 6.023 8.473 18.701 248.198 708 14.215 14.112 5.949 8.162 18.860 250.110 720 13.847 13.742 5.878 7.863 19.013 251.950

113

Fly ash 3 meter thick wall

Temperature Stresses

Time (h)

Max temp. (°C)

Temp. centre (°C)

Temp. surface

(°C)

Temp. gradient

(°C)

Max principal

stress (MPa)

Stress/Strength

6 16.954 16.164 15.651 0.513 0.002 0.048 12 21.830 20.029 18.419 1.610 0.040 2.833 18 26.775 25.270 21.765 3.505 0.146 9.616 24 30.425 29.395 23.934 5.461 0.241 18.844 30 32.967 32.330 25.132 7.198 0.314 25.192 36 34.780 34.427 25.741 8.686 0.406 29.358 42 36.221 35.970 26.013 9.957 0.465 30.166 48 37.350 37.141 26.092 11.049 0.500 29.814 54 38.226 38.052 26.061 11.991 0.548 30.534 60 38.920 38.772 25.964 12.808 0.621 30.457 66 39.469 39.345 25.829 13.516 0.658 30.398 72 39.904 39.802 25.673 14.129 0.729 35.167 78 40.247 40.164 25.506 14.658 0.727 32.890 84 40.512 40.446 25.334 15.112 0.754 32.520 90 40.709 40.661 25.161 15.500 0.776 32.045 96 40.853 40.817 24.989 15.828 0.793 31.468 102 40.946 40.922 24.820 16.102 0.806 31.086 108 40.998 40.983 24.654 16.328 0.816 30.941 114 41.013 41.004 24.493 16.511 0.823 30.721 120 40.996 40.991 24.336 16.655 0.828 30.456 132 40.870 40.869 15.810 25.058 0.971 28.188 144 40.645 40.645 14.152 26.493 1.504 31.453 156 40.317 40.317 13.188 27.128 2.004 37.484 168 39.887 39.887 12.509 27.377 2.473 43.346 180 39.338 39.338 11.984 27.354 2.918 48.952 192 38.681 38.681 11.553 27.128 3.340 54.284 204 37.935 37.935 11.186 26.750 3.744 59.349 216 37.124 37.124 10.864 26.260 4.130 64.163 228 36.266 36.266 10.576 25.691 4.501 68.745 240 35.380 35.379 10.313 25.066 4.857 73.321 252 34.477 34.473 10.070 24.404 5.200 78.338 264 33.567 33.561 9.843 23.718 5.530 83.125 276 32.657 32.648 9.628 23.019 5.849 87.697 288 31.753 31.741 9.425 22.316 6.155 92.068 300 30.860 30.845 9.231 21.614 6.526 96.249 312 29.980 29.963 9.045 20.918 6.893 100.253

114

324 29.117 29.097 8.866 20.231 7.249 104.082 336 28.272 28.249 8.694 19.555 7.593 108.147 348 27.447 27.421 8.528 18.894 7.925 112.546 360 26.642 26.614 8.367 18.247 8.247 116.780 372 25.859 25.829 8.212 17.617 8.557 120.854 384 25.097 25.065 8.062 17.003 8.858 124.774 396 24.357 24.323 7.917 16.406 9.148 128.547 408 23.640 23.603 7.777 15.826 9.429 132.177 420 22.944 22.906 7.642 15.264 9.700 135.671 432 22.269 22.230 7.511 14.719 9.961 139.032 444 21.617 21.576 7.384 14.192 10.214 142.268 456 20.985 20.943 7.262 13.681 10.459 145.381 468 20.375 20.332 7.144 13.188 10.695 148.376 480 19.786 19.740 7.030 12.710 10.923 151.259 492 19.218 19.169 6.920 12.249 11.143 154.033 504 18.669 18.618 6.814 11.804 11.355 156.702 516 18.140 18.085 6.712 11.374 11.561 159.270 528 17.628 17.572 6.613 10.959 11.759 161.742 540 17.135 17.076 6.518 10.559 11.950 164.120 552 16.659 16.598 6.426 10.172 12.135 166.408 564 16.200 16.138 6.337 9.800 12.314 168.610 576 15.758 15.694 6.252 9.441 12.486 170.729 588 15.332 15.266 6.170 9.096 12.652 172.768 600 14.921 14.854 6.091 8.763 12.813 174.730 612 14.525 14.456 6.015 8.442 12.968 176.618 624 14.144 14.074 5.941 8.132 13.118 178.435 636 13.776 13.706 5.871 7.835 13.263 180.183 648 13.423 13.351 5.803 7.548 13.403 181.865 660 13.083 13.009 5.737 7.272 13.538 183.484 672 12.757 12.681 5.674 7.006 13.668 185.043 684 12.443 12.364 5.614 6.751 13.794 186.542 696 12.141 12.060 5.555 6.505 13.916 187.985 708 11.850 11.767 5.499 6.268 14.033 189.374 720 11.570 11.485 5.445 6.040 14.147 190.710

115

Cooling pipes 3 meter thick wall

Temperature Stresses

Time (h)

Max temp. (°C)

Temp. centre (°C)

Temp. surface

(°C)

Temp. gradient

(°C)

Max principal

stress (MPa)

Stress/Strength

6 14.739 15.923 17.020 -1.097 0.001 0.683 12 16.712 18.453 20.721 -2.267 0.007 4.339 18 19.866 22.146 24.966 -2.820 0.043 10.349 24 21.137 23.647 26.631 -2.984 0.072 9.303 30 20.739 23.188 26.272 -3.085 0.053 5.478 36 19.463 21.680 24.893 -3.214 0.138 13.387 42 17.862 19.770 23.137 -3.366 0.284 42.177 48 16.235 17.812 21.339 -3.526 0.426 67.946 54 14.723 15.978 19.659 -3.681 0.628 94.178 60 13.381 14.339 18.165 -3.826 0.795 116.216 66 12.223 12.915 16.871 -3.956 0.962 133.980 72 11.241 11.700 15.771 -4.072 1.064 147.180 78 10.417 10.675 14.848 -4.173 1.167 157.765 84 9.731 9.817 14.078 -4.260 1.257 161.674 90 9.162 9.104 13.440 -4.335 1.330 173.947 96 8.693 8.513 12.912 -4.399 1.394 178.964 102 8.866 8.285 12.073 -3.787 1.372 169.714 108 9.174 8.588 12.033 -3.446 1.348 161.312 114 9.470 8.898 12.162 -3.264 1.327 153.988 120 9.750 9.204 12.326 -3.122 1.309 147.243 132 9.637 9.813 7.809 2.004 1.381 148.382 144 9.653 10.413 7.041 3.372 1.411 145.205 156 9.686 10.983 6.687 4.296 1.436 141.892 168 9.713 11.482 6.485 4.998 1.458 140.620 180 9.728 11.889 6.355 5.534 1.479 140.367 192 9.729 12.204 6.267 5.938 1.499 140.089 204 9.717 12.438 6.202 6.236 1.519 139.783 216 9.691 12.603 6.153 6.450 1.539 139.572 228 9.654 12.711 6.113 6.597 1.558 139.512 240 9.606 12.771 6.079 6.691 1.578 139.617 252 9.549 12.792 6.049 6.743 1.598 139.880 264 9.484 12.782 6.021 6.761 1.617 140.287 276 9.412 12.745 5.994 6.751 1.637 140.820 288 9.334 12.686 5.966 6.720 1.656 141.464 300 9.251 12.609 5.938 6.671 1.676 142.203

116

312 9.164 12.517 5.909 6.608 1.695 143.021 324 9.074 12.412 5.880 6.532 1.714 143.905 336 8.982 12.297 5.850 6.448 1.732 144.845 348 8.887 12.174 5.818 6.355 1.751 145.830 360 8.792 12.043 5.786 6.257 1.769 146.850 372 8.695 11.907 5.754 6.153 1.787 147.899 384 8.598 11.766 5.720 6.046 1.806 148.968 396 8.501 11.621 5.687 5.935 1.825 150.052 408 8.404 11.474 5.653 5.822 1.844 151.146 420 8.308 11.325 5.618 5.707 1.862 152.245 432 8.212 11.175 5.584 5.591 1.880 153.345 444 8.117 11.023 5.550 5.474 1.897 154.443 456 8.023 10.872 5.516 5.357 1.914 155.535 468 7.931 10.721 5.481 5.240 1.931 156.620 480 7.840 10.571 5.448 5.123 1.947 157.695 492 7.751 10.421 5.414 5.007 1.963 158.758 504 7.663 10.273 5.381 4.892 1.979 159.807 516 7.576 10.126 5.348 4.778 1.994 160.841 528 7.492 9.981 5.316 4.665 2.008 161.860 540 7.409 9.838 5.284 4.554 2.023 162.862 552 7.328 9.698 5.253 4.444 2.037 163.846 564 7.248 9.559 5.223 4.336 2.050 164.812 576 7.171 9.423 5.192 4.230 2.064 165.760 588 7.095 9.289 5.163 4.126 2.077 166.688 600 7.021 9.158 5.134 4.024 2.089 167.619 612 6.949 9.030 5.106 3.924 2.102 168.792 624 6.878 8.904 5.078 3.826 2.114 169.941 636 6.809 8.781 5.051 3.730 2.125 171.067 648 6.743 8.661 5.025 3.636 2.137 172.168 660 6.677 8.543 4.999 3.544 2.148 173.245 672 6.614 8.428 4.974 3.454 2.159 174.297 684 6.552 8.316 4.950 3.367 2.169 175.325 696 6.492 8.207 4.926 3.281 2.180 176.329 708 6.433 8.100 4.902 3.198 2.190 177.309 720 6.376 7.996 4.880 3.117 2.200 178.266

117

Combined case with fly ash, ice and large aggregates 3 meter thick wall

Temperature Stresses

Time (h)

Max temp. (°C)

Temp. centre (°C)

Temp. surface

(°C)

Temp. gradient

(°C)

Max principal

stress (MPa)

Stress/Strength

6 7.044 7.003 6.515 0.488 0.000 0.063 12 8.023 7.529 6.706 0.823 0.001 0.105 18 10.189 9.386 7.887 1.499 0.011 1.014 24 12.770 11.911 9.412 2.499 0.043 3.233 30 15.234 14.472 10.814 3.657 0.092 7.374 36 17.354 16.749 11.922 4.827 0.143 12.315 42 19.090 18.654 12.724 5.930 0.190 16.573 48 20.499 20.207 13.272 6.934 0.248 19.854 54 21.654 21.466 13.630 7.836 0.306 22.263 60 22.647 22.489 13.849 8.640 0.356 23.991 66 23.460 23.324 13.971 9.354 0.399 25.132 72 24.124 24.010 14.024 9.986 0.375 22.359 78 24.671 24.573 14.029 10.545 0.394 22.337 84 25.118 25.037 14.000 11.037 0.414 22.507 90 25.483 25.417 13.947 11.469 0.424 22.189 96 25.779 25.725 13.879 11.847 0.435 21.560 102 26.015 25.973 13.799 12.175 0.449 21.058 108 26.200 26.169 13.711 12.458 0.496 23.717 114 26.342 26.319 13.619 12.700 0.495 23.096 120 26.444 26.428 13.523 12.906 0.497 22.638 132 26.551 26.544 10.511 16.034 0.463 20.279 144 26.549 26.547 9.866 16.681 0.446 18.392 156 26.451 26.451 9.465 16.986 0.430 16.725 168 26.270 26.270 9.165 17.105 0.412 15.671 180 26.007 26.007 8.920 17.087 0.460 14.701 192 25.674 25.674 8.711 16.963 0.665 14.730 204 25.285 25.285 8.526 16.759 0.872 16.974 216 24.851 24.851 8.358 16.494 1.077 19.352 228 24.386 24.386 8.203 16.183 1.278 21.775 240 23.897 23.897 8.058 15.838 1.475 24.186 252 23.393 23.392 7.922 15.470 1.667 26.556 264 22.880 22.877 7.792 15.085 1.854 28.866 276 22.362 22.358 7.668 14.690 2.036 31.109 288 21.843 21.836 7.548 14.288 2.214 33.366 300 21.325 21.317 7.432 13.884 2.386 35.856 312 20.811 20.801 7.321 13.480 2.554 38.256 324 20.302 20.291 7.212 13.078 2.717 40.567

118

336 19.801 19.788 7.107 12.681 2.875 42.793 348 19.309 19.294 7.005 12.289 3.028 44.937 360 18.826 18.809 6.906 11.903 3.177 47.000 372 18.353 18.335 6.810 11.524 3.322 48.987 384 17.890 17.871 6.717 11.154 3.463 50.899 396 17.439 17.418 6.626 10.792 3.633 52.824 408 16.999 16.977 6.538 10.438 3.798 55.049 420 16.570 16.547 6.453 10.094 3.958 57.197 432 16.153 16.129 6.370 9.758 4.113 59.269 444 15.747 15.722 6.290 9.432 4.264 61.269 456 15.354 15.327 6.212 9.115 4.410 63.197 468 14.972 14.944 6.137 8.808 4.552 65.058 480 14.602 14.573 6.064 8.509 4.690 66.852 492 14.244 14.213 5.993 8.220 4.823 68.583 504 13.897 13.864 5.925 7.939 4.952 70.252 516 13.561 13.526 5.859 7.667 5.077 71.862 528 13.236 13.200 5.795 7.404 5.199 73.414 540 12.921 12.883 5.734 7.150 5.316 74.911 552 12.617 12.578 5.674 6.904 5.430 76.354 564 12.323 12.282 5.616 6.666 5.541 77.746 576 12.038 11.997 5.561 6.436 5.648 79.088 588 11.764 11.721 5.507 6.214 5.751 80.381 600 11.498 11.454 5.455 5.999 5.851 81.629 612 11.242 11.197 5.405 5.792 5.949 82.832 624 10.994 10.949 5.357 5.592 6.043 83.992 636 10.755 10.709 5.311 5.398 6.134 85.110 648 10.525 10.478 5.266 5.212 6.222 86.188 660 10.303 10.255 5.222 5.032 6.308 87.227 672 10.090 10.039 5.181 4.859 6.391 88.230 684 9.884 9.832 5.140 4.691 6.471 89.196 696 9.685 9.632 5.102 4.530 6.549 90.128 708 9.494 9.439 5.064 4.374 6.624 91.026 720 9.309 9.253 5.028 4.224 6.697 91.892