pca temperature

PCA R&D Serial No. 3030

Predicting Temperature Rise and Thermal Cracking in Concrete

by Michael Edward Robbins

©Graduate Thesis by Michael Edward Robbins 2007 All rights reserved

PREDICTING THE EARLY AGE TEMPERATURE RESPONSE OF CONCRETE USING ISOTHERMAL

CALORIMETRY

by

Michael Edward Robbins

A thesis submitted in conformity with the requirements

for the degree of Master of Applied Science

Department of Civil Engineering

University of Toronto

© Copyright by Michael E. Robbins 2007

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Predicting the Early Age Temperature Response of Concrete using Isothermal Calorimetry

Michael Edward Robbins, M.A.Sc. Department of Civil Engineering

University of Toronto

Supervisor: R.D. Hooton Convocation: March 2007

A simplified thermal simulation tool was developed for predicting the temperature rise due to hydration

within concrete elements including those that contain slag or fly ash. The purpose of the program is to

perform a rough thermal analysis without requiring detailed technical inputs. The simulation is designed to

perform its analysis on a 2-D section through the element using a finite difference method, taking into

account surface convection and conduction to adjacent materials, as well as solar radiation. An

experimental program involving isothermal heat-conduction calorimeter testing was used to help populate

the model with data for cementing materials commonly available in Ontario, including several Portland

cements and a number of blast-furnace slags and fly ashes at various replacement levels. To verify the

simulation results, results from the simulation will be compared to the results of two different field trials

involving mass concretes with high levels of SCM replacement.

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Acknowledgements

I would like to express my thanks to my thesis advisor, Professor R.D. Hooton. Thank you for your advice,

support and direction during this thesis project. Thanks also to NSERC and the Portland Cement

Association for their generous financial support.

I would also like to thank Terry Ramlochan and Shervan Khanna for their input and assistance during the

isothermal testing program. Additionally, thanks to Ursula Nytko and the rest of the Concrete Materials

Group for their encouragement and support. Thanks also to Nathan Hess for his on-site training and to

Paul Sandberg and Gary Knight who provided invaluable insight and experience that led to the

development of the calorimetry testing methods that were used in this project.

I would also like to thank the industry representatives that supplied samples and information for this study.

Thanks to Jim Whiting and Tom Whelend of Essroc Italcementi Group; John Blair, Dwight Steeves Doug

Anderson and Brent Burnell of Lafarge North America; Dennis Baker and Chris McColl of St. Lawrence

Cement and Nick Paupoff of St. Mary’s Cement. Special thanks go to Robert Munroe of Lafarge North

America for his help and input which was invaluable in developing the initial concept for this thesis project

and the thermal simulation program.

I would also like to extend thanks to everyone involved in the two case studies that were used for

validation of the thermal simulation results. Thanks to Dennis Mitchell and John A. Bickley for the Innocon

1 m3 field trial and to Phil Trunk, Dennis Baker and Chris McColl of St. Lawrence Cement and John

Goffredo of Kenaidan regarding the St. Lawrence VRM project. Thanks also to Sal Fasullo and his team

from Davroc Testing Laboratories.

Finally, I would like to extend my deepest gratitude to Jenny. Thank you for your unconditional patience,

encouragement and love. Without your help none of this would have been possible.

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Table of Contents

List of Tables ................................................................................................................................................vi List of Figures .............................................................................................................................................. vii Chapter 1: Introduction ............................................................................................................................. 1

1.1 Problem Statement ................................................................................................................. 2 1.2 Project Goals and Objectives ................................................................................................. 2 1.3 Applications for the Simulation ............................................................................................... 4

1.3.1 Hot Weather Concreting ......................................................................................................... 4 1.3.2 Cold Weather Concreting........................................................................................................ 5

1.4 Scope...................................................................................................................................... 8 Chapter 2: Literature Review.................................................................................................................... 9

2.1 Understanding the Hydration of Portland Cement Concrete ................................................ 10 2.1.1 Reaction Stages.................................................................................................................... 11 2.1.2 Factors Influencing Hydration ............................................................................................... 13 2.1.3 Total Heat of Hydration ......................................................................................................... 20

2.2 Determining the Rate of Hydration ....................................................................................... 22 2.2.1 Quantifying the Degree of Hydration .................................................................................... 23 2.2.2 Equivalent Age Maturity Method........................................................................................... 28 2.2.3 Determination of the Apparent Activation Energy................................................................. 29

2.3 Calorimetry Methods............................................................................................................. 31 2.3.1 Isothermal Heat-Conduction Calorimetry.............................................................................. 32 2.3.2 Other Calorimetry Methods................................................................................................... 37 2.3.3 Relations between the Calorimetry Methods........................................................................ 39

2.4 Modeling Concepts ............................................................................................................... 40 2.4.1 Modeling the Heat Generation and Associated Internal Temperatures................................ 41 2.4.2 Specific Heat and Thermal Conductivity of Hardening Concrete ......................................... 42 2.4.3 Coefficient of Thermal Expansion of Concrete ..................................................................... 43 2.4.4 Boundary Conditions and Environment ................................................................................ 44

2.5 Determining the Cracking Potential ...................................................................................... 49 2.5.1 Description of the Thermal Cracking Mechanism................................................................. 49

2.6 Summary............................................................................................................................... 52 Chapter 3: Development of the Thermal Simulation............................................................................... 53

3.1 Problem Outline .................................................................................................................... 53 3.1.1 Design Goals ........................................................................................................................ 55

3.2 Calculating the Associated Internal Heat Rise...................................................................... 57 3.2.1 Finite-Difference Methods..................................................................................................... 58 3.2.2 Finite-Element Methods........................................................................................................ 61

3.3 Design and Implementation of the Thermal Simulation Program ......................................... 61 3.3.1 Assumptions and Limitations ................................................................................................ 62 3.3.2 Solution Method .................................................................................................................... 66

3.4 Summary............................................................................................................................... 70 Chapter 4: Test Methods ........................................................................................................................ 71

4.1 Purpose of the Testing Program........................................................................................... 71 4.2 Method Development............................................................................................................ 71 4.3 Final Mixing Procedure ......................................................................................................... 73 4.4 Materials ............................................................................................................................... 74 4.5 Paste Mix Parameters........................................................................................................... 75 4.6 Isothermal Calorimetry Method............................................................................................. 75 4.7 Summary............................................................................................................................... 76

Chapter 5: Experimental Results and Case Studies .............................................................................. 77 5.1 Isothermal Calorimetry Results............................................................................................. 77

5.1.1 Neat Portland Cements (Type GU)....................................................................................... 77

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5.1.2 GU Cements with Ground-Granulated Blast-furnace Slag ................................................... 88 5.1.3 GU Cements with Fly Ash..................................................................................................... 92 5.1.4 Using the TAM Air Results as Thermal Simulation Inputs .................................................. 101

5.2 Field Testing and Verification ............................................................................................. 104 5.2.1 Innocon 1 m3 Test Cubes.................................................................................................... 104 5.2.2 St. Lawrence Cement VRM Foundation Mass Concrete Pour ........................................... 111

5.3 Summary............................................................................................................................. 119 Chapter 6: Conclusions and Recommendation .................................................................................... 120

6.1 TAM Air Isothermal Calorimetry Results............................................................................. 120 6.2 Using TAM Air Results as Hydration Model Inputs............................................................. 122 6.3 Success of the Thermal Simulation Program ..................................................................... 123 6.4 Recommendations for Future Testing ................................................................................ 124

References ............................................................................................................................................... 126 Appendix A: Material Information ............................................................................................................. 130 Appendix B: Isothermal Calorimetry Results ............................................................................................ 132 Appendix C: ASTM Draft Test Method for Measurement of Heat of Hydration of Cement with Heat

Conduction Calorimetry ..................................................................................................................... 156 Appendix D: Excerpt from “Factors Influencing the Early-Age Cracking of High Performance Concrete,” a

Literature Review Project by M.E. Robbins ....................................................................................... 177

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List of Tables

Table 1-1: Permissible concrete temperatures at placing (CSA A23.1 Table 14) ........................................ 6 Table 1-2: Maximum permissible temperature differential between concrete surface and

ambient (wind up to 25 km/h) (CSA A23.1 Table 21).............................................................................. 6 Table 2-1: Range of cement properties used for calibration of the hydration model

(Schindler, 2002) ................................................................................................................................... 28 Table 2-2: Range of mixture proportions and SCM properties used for the calibration of

the hydration model (Schindler, 2002) .................................................................................................. 28 Table 2-3: Typical values of concrete wet density and thermal conductivity as a function

of aggregate type (Neville, 1995) .......................................................................................................... 43 Table 2-4: Material properties for supporting layers and formwork involved in conductive

heat flow (Schindler, 2002; Janna, 2000; Guyer, 1999) ........................................................................ 46 Table 2-5: Thermal conductivities and conductance values for common surface coverings

and form materials (Schindler, 2002; Guyer, 1999; Hutcheon and Handegord, 1995) ......................... 48 Table 3-1: Range of cement properties used for calibration of the hydration model

(Schindler, 2002) ................................................................................................................................... 66 Table 3-2: Range of mixture proportions and SCM properties used for the calibration of

the hydration model (Schindler, 2002) .................................................................................................. 66 Table 4-1: Testing program summary, materials supplied by Essroc Italcementi Group........................... 74 Table 4-2: Testing program summary, materials supplied by Lafarge North America ............................... 74 Table 4-3: Testing program summary, materials supplied by St. Lawrence Cement Inc. .......................... 74 Table 4-4: Testing program summary, materials supplied by St. Marys Cement Group............................ 74 Table 5-1: Summary of the peak hydration rates and peak times for the six GU cements,

based on isothermal calorimetry at 23°C ............................................................................................. 79 Table 5-2: Summary of isothermal calorimetry results for the six neat GU cements,

measured at 23°C.................................................................................................................................. 80 Table 5-3: Degree of hydration at 72 and 168 hours for the six neat GU cements, based

on isothermal calorimetry at 23°C ........................................................................................................ 83 Table 5-4: Calculated versus theoretical values for the apparent activation energy,

calculated from isothermal calorimetry results at three temperatures................................................... 86 Table 5-5: Effect of partial GGBS replacement on the peak hydration rate and peak time

at various levels of replacement; tested at 23°C................................................................................... 90 Table 5-6: Effect of partial GGBS replacement on the peak hydration rate and peak time

at various levels of replacement; tested at 23°C................................................................................... 92 Table 5-7: Effect of partial fly ash replacement on the peak hydration rate and peak time

at various levels of replacement; tested at 23°C................................................................................... 95 Table 5-8: Effect of partial GGBS replacement on the peak hydration rate and peak time

at various levels of replacement; tested at 23°C................................................................................... 99 Table 5-9: Hydration curve parameters calculated from isothermal heat-conduction

calorimetry data; tests performed for 7 days at 23°C.......................................................................... 102 Table 5-10: Hydration curve parameters calculated using Schindler and Folliard’s

hydration model, based on the cement chemistries............................................................................ 102 Table 5-11: Mix designs and hydration parameters for the two concretes under

consideration from the Innocon 1 m3 field tests................................................................................... 107 Table 5-12: Mix design information and hydration parameters for the St. Lawrence VRM

Foundation pour .................................................................................................................................. 115

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List of Figures

Figure 1-1: Graphical determination of the safe stripping time for insulated formwork (CSA A23.1) ...................................................................................................................................................... 7

Figure 2-1: Reaction stages during cement hydration process (Schindler, 2002)...................................... 12 Figure 2-2: Influence of C3S content on heat evolution, C3A content approximately

constant (Neville, 1995)......................................................................................................................... 14 Figure 2-3: Influence of C3A content on heat evolution, C3S content approximately

constant (Neville, 1995)......................................................................................................................... 15 Figure 2-4: Development of the heat of hydration for different cement types (cured at

21°C, w/c 0.4) (Neville, 1995)................................................................................................................ 15 Figure 2-5: Influence of varying levels of GGBS replacement on the heat development of

concrete paste; measured at 23°C........................................................................................................ 17 Figure 2-6: Influence of varying levels of fly ash replacement on the heat development of

concrete paste; measured at 23°C........................................................................................................ 18 Figure 2-7: Influence of water-cement ratio on the heat evolution of concrete (Schindler,

2002) ..................................................................................................................................................... 19 Figure 2-8: Rate of hydration of the various cement components (Neville, 1995) ..................................... 23 Figure 2-9: Influence of water-cement ratio on the ultimate degree of hydration (Schindler,

2002) ..................................................................................................................................................... 24 Figure 2-10: Effect of change in hydration time parameter on the degree of hydration

development (Schindler, 2002) ............................................................................................................. 26 Figure 2-11: Effect of change in hydration slope parameter on the degree of hydration

development (Schindler, 2002) ............................................................................................................. 26 Figure 2-12: Effect of change in hydration slope parameter on the degree of hydration

development (Schindler, 2002) ............................................................................................................. 27 Figure 2-13: Cutaway diagram of the TAM Air calorimeter (Thermometric AB. 2004)............................... 33 Figure 2-14: Cutaway diagram of one channel in the TAM Air calorimeter (Thermometric

AB, 2004)............................................................................................................................................... 34 Figure 2-15: Relationship between the various calorimetry methods (Wadso, 2003)................................ 39 Figure 2-16: Influence of aggregate type on the linear coefficient of thermal expansion of

concrete (Neville, 1995) ........................................................................................................................ 44 Figure 2-17: Heat transfer mechanisms between a concrete element and its environment

(Guyer, 1999) ........................................................................................................................................ 45 Figure 2-18: Development of early-age concrete thermal stresses and strength

(Schindler, 2002) ................................................................................................................................... 50 Figure 3-1: Decision tree for the thermal simulation program (adapted from Schindler,

2002) ..................................................................................................................................................... 54 Figure 3-2: Software development considerations (Guyer, 1999).............................................................. 56 Figure 3-3: Sketches of the four different cases available within the thermal simulation

program; all cases are discretized using a body-centred grid............................................................... 63 Figure 4-1: Influence of ampoule type on the TAM Air results ................................................................... 73 Figure 5-1: Plot of the rate of hydration (power) vs. time curves for the six neat GU

cements; measured at 23°C.................................................................................................................. 78 Figure 5-2: Detail of the main hydration peak of the neat GU cements, power vs. time;

measured at 23°C.................................................................................................................................. 78 Figure 5-3: Plot of the heat evolved (energy) vs. time for the six neat GU cements;

measured at 23°C.................................................................................................................................. 82 Figure 5-4: Plot of the degree of hydration vs. time for the six neat GU cements;

measured at 23°C.................................................................................................................................. 82

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Figure 5-5: Plot of the power vs. time for the Essroc GU (Picton) cement; measured at 10, 23 and 35°C........................................................................................................................................... 84

Figure 5-6: Plot of the degree of hydration vs. time for the Essroc GU (Picton) cement; measured at 10, 23 and 35°C................................................................................................................ 86

Figure 5-7: Plot of the degree of hydration vs. effective time for the Essroc GU (Picton) cement; effective time calculated using the experimental value for Ea; measured at 10, 23 and 35°C........................................................................................................................................... 88

Figure 5-8: Plot of power vs. time for the Lafarge GU (Bath) cement with varying levels of partial replacement with Stoney Creek GGBS (class S); measured at 23°C........................................ 89

Figure 5-9: Plot of the total heat evolved vs. time for the Lafarge GU (Bath) cement with varying levels of partial replacement with Stoney Creek GGBS; measured at 23°C ............................ 91

Figure 5-10: Plot of the degree of hydration vs. time for the Lafarge GU (Bath) cement with varying levels of partial replacement with Stoney Creek GGBS (class S); measured at 23°C.................................................................................................................................. 91

Figure 5-11: Plot of power vs. time for the St. Marys GU (St. Marys) with varying levels of partial replacement with Baldwin fly ash (class CH); measured at 23°C .............................................. 93

Figure 5-12: Plot of power vs. time for the Lafarge GU (Woodstock) cement with varying levels of partial replacement with Atikokan fly ash (class CI); measured at 23°C................................. 94

Figure 5-13: Plot of power vs. time for the Lafarge GU (Woodstock) cement with varying levels of partial replacement with Hatfield fly ash (class F); measured at 23°C.................................... 94

Figure 5-14: Plot of the total heat evolved vs. time for the St. Marys GU (St. Marys) with varying levels of partial replacement with Baldwin fly ash (class CH); measured at 23°C....................................................................................................................................................... 96

Figure 5-15: Plot of the total heat evolved vs. time for the Lafarge GU (Woodstock) cement with varying levels of partial replacement with Atikokan fly ash (class CI); measured at 23°C.................................................................................................................................. 96

Figure 5-16: Plot of the total heat evolved vs. time for the Lafarge GU (Woodstock) cement with varying levels of partial replacement with Hatfield fly ash (class F); measured at 23°C.................................................................................................................................. 97

Figure 5-17: Plot of the degree of hydration vs. time for the St. Marys GU (St. Marys) cement with varying levels of partial replacement with Baldwin fly ash (class CH); measured at 23°C.................................................................................................................................. 98

Figure 5-18: Plot of the degree of hydration vs. time for the Lafarge GU (Woodstock) cement with varying levels of partial replacement with Atikokan fly ash (class CI); measured at 23°C.................................................................................................................................. 98

Figure 5-19: Plot of the degree of hydration vs. time for the Lafarge GU (Woodstock) cement with varying levels of partial replacement with Hatfield fly ash (class F); measured at 23°C.................................................................................................................................. 99

Figure 5-20: Plot of the power vs. time for the Essroc GU (Picton) cement; simulated curves produced using hydration parameters based on isothermal calorimetry data; measured and simulated at 10, 23 and 35°C ...................................................................................... 103

Figure 5-21: Plot of the degree of hydration vs. time for the Essroc GU (Picton) cement; simulated curves produced using hydration parameters based on isothermal calorimetry data; measured and simulated at 10, 23 and 35°C .......................................................... 103

Figure 5-22: Section through the centre of the Innocon 1 m3 field test setup, including thermocouple locations and formwork details (typical); all dimensions in millimetres ........................ 105

Figure 5-23: Plot of power vs. time for the Innocon 1 m3 reference and slag-cement pastes, based on the concrete mix designs used in the field trials; measured at 23°C ...................... 108

Figure 5-24: Plot of the degree of hydration vs. time for the Innocon 1 m3 reference and slag-cement pastes, based on the concrete mix designs used in the field trials; measured at 23°C................................................................................................................................ 108

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Figure 5-25: Comparison of the measured and predicted temperatures for Cube 1, made with Mix 1 (Reference concrete).......................................................................................................... 109

Figure 5-26: Comparison of the measured and predicted temperatures for Cube 2, made with Mix 2 (Slag-concrete)................................................................................................................... 110

Figure 5-27: Plan view of the St. Lawrence VRM foundation, including thermocouple locations; all dimensions in millimetres ............................................................................................... 112

Figure 5-28: Section through the centre of the St. Lawrence VRM foundation, from west to east along line A, including thermocouple locations; all dimensions in millimetres ............................ 113

Figure 5-29: Plot of the power vs. time for the St. Lawrence VRM foundation reference and slag-cement pastes, based on the concrete mix design used in the field trial; measured at 23 and 35°C.................................................................................................................... 117

Figure 5-30: Plot of the degree of hydration vs. time for the St. Lawrence VRM foundation reference and slag-cement pastes, based on the concrete mix design used in the field trial; measured at 23 and 35°C............................................................................................................ 117

Figure 5-31: Comparison of the measured and predicted temperatures for the St. Lawrence VRM foundation for location T1 (centre of the element) ..................................................... 118

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Chapter 1: Introduction

Concrete is the mainstay construction material used for engineered structures in Canada (Cement

Association of Canada, 2006). The creative use and application of this durable material has earned the

Canadian cement industry a world class reputation for innovation, performance and research. This is

partly due to Canada’s harsh climate, which poses several distinct challenges to engineers and concrete

suppliers. The extremely high seasonal temperature variation of approximately 40-50°C (Environment

Canada, 2006) requires certain accommodations in order to meet performance goals. In addition,

Canada’s cold winter climate combined with the liberal use of de-icing chemicals has been responsible for

the severe deterioration of many concrete structures. This has led to the current prevalence of various

high performance concrete (HPC) mixtures – including many that utilize supplementary cementing

materials (SCMs) – in today’s construction industry. These high performance mixes involve high quality

ingredients, optimized mix designs, and are produced to meet the highest industry standards (Kosmatka

et. al., 1995). These HPC mixes almost always provide higher strengths than normal concretes (often in

excess of 80 MPa), and are used where high strength, durability or other performance requirements (such

as abrasion resistance, permeability, high early strength) are called for.

However, there are a variety of design complications that arise from the increasing use of high

performance concretes. For one, these mixtures must be subjected to very stringent curing practices in

order to develop the desired properties. These mixes are also typically dependent on high doses of

chemical admixtures in order to achieve the workability required for placement, which can lead to issues

such as slump loss, or the potential for the unwanted addition of water by construction crews (in order to

save on the high cost of these admixtures). Thirdly, these HPC mixes are particularly at risk of developing

early age cracks due to the high amounts of heat that they generate as a part of the hydration process.

These thermally induced stresses, which were once a concern only to the designers of mass concrete

dams, are arguably one of the most critical and controllable mechanisms resulting in early age cracking of

today’s HPC structures. This thermal cracking is of particular concern for HPC structures, including

concrete pavements, roller compacted concretes, and mass concrete elements and foundations, because

of the high levels of heat development in these structures that result from the demand for high

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strength at early ages. This can induce thermal gradients in the structure which may be transformed into

internal tensile stresses that can lead to the formation of cracks in the structure. If uncontrolled, these

cracks can severely impact the long term durability and performance of the structure. In some

applications, such as bridge decks and concrete highways, the occurrence of thermal cracks in a section

of the structure may require its complete replacement at high cost to the contractor.

1.1 Problem Statement

The key problem that this thesis project seeks to address is the need for an accurate prediction of a

concrete structure’s internal temperature rise in advance of construction. This prediction should be based

on the knowledge of the materials involved, and the placing and curing conditions the element will be

subject to. Finally, this model should be of use to a wide variety of users, regardless of their technical

background.

1.2 Project Goals and Objectives

The goal of this project is to create a simplified thermal simulation that can be used to help predict heat

rise within concrete elements. This model will be based on a theoretical model developed by Dr. Anton

Schindler, Gottlieb Assistant Professor at Auburn University, during his Ph.D. dissertation (2002) at the

University of Texas at Austin; this model was further refined in a series of papers co-authored by Dr. Kevin

Folliard (2004, 2005). A testing program will accompany this theoretical model in order to provide

additional calibration data, as well as real world verification of the results. This program relies on

isothermal heat-conduction calorimetry performed using a Thermometric TAM Air eight channel

instrument.

It should be noted that there are several software solutions available to perform this analysis, including a

program called Concrete Works developed by Dr. Schindler and his team. However, many of these

solutions require an advanced knowledge of the various principles involved in the analysis. These

solutions also typically require a complex set of input parameters, which can be overwhelming to many

end-users. The aim of this project is to develop a simplified simulation that provides a reasonable

estimate of what can be expected given a set of straight-forward inputs, which can help users to decide

whether or not they should be concerned about the potential for thermal cracking in their structure. If there

is cause for concern, the simulation can be used to scout out possible solutions, though it is highly

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recommended that the end user perform a more detailed thermal analysis, to supplement the findings of

this simulation. The goal here is not to replace the existing solutions, but to add a simple tool that can help

end-users determine when they should be consulting these more detailed applications.

The thermal simulation was developed in Microsoft Excel using Visual Basic for Applications (VBA). There

were four major design goals specified for the development of the thermal simulation. These goals were

generated to help guide the development, and to set limits on the scope of the project. These goals were

as follows:

1. The simulation must provide estimates of the maximum internal concrete temperature

that are suitable for use in determining whether or not a more complete thermal

analysis is required.

2. The simulation must have a simplified set of inputs, based on known material

properties rather than unusual cement chemistry parameters.

3. The user must have the ability to override any and all of the inputs that are supplied by

the program itself for situations where better input data is available.

4. The simulation should provide some aid in the interpreting of the results, including

some general recommendations regarding the performance of the element being

analyzed.

Another key aspect in the development of the simulation is a consideration of the end user that will be

using the software. Based on several discussions with Lafarge’s Robert Munroe, two key end users were

identified:

1. Consulting engineers, who would use the project to perform a rough check of the

suitability of a particular mix design with regards to thermal cracking issues for a given

element.

2. Ready mix concrete and cement company technical service representatives, who

would use the simulation to demonstrate the effectiveness of mixes incorporating

SCMs for mitigating thermal cracking issues.

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These four goals and the knowledge of the potential end users will be referred back to throughout the

simulation’s development, which is outlined in detail in Chapter 3. These four goals will also be used as

evaluation criteria in examining whether or not the final simulation has met the goals of this thesis project.

1.3 Applications for the Simulation

According to clause 7.4.1.2 of the CSA A23.1 code, “(f)reshly deposited concrete shall be protected from

freezing, abnormally high temperatures or temperature differentials, premature drying, and moisture loss

for the period of time necessary to develop the desired properties of the concrete.” This simulation will be

geared to address the first three concerns presented in that clause, namely the minimum and maximum

temperatures reached for a given set of placing conditions, as well as the determination of the maximum

internal temperature differential acting on the concrete. The following two sections will outline these three

concerns in more detail.

1.3.1 Hot Weather Concreting

The CSA A23.1 standard defines hot weather concreting as any placing period where the ambient air

temperature is at or above 27°C (Clause 7.4.2.4.1). The placing temperature is a very important factor

that determines how quickly the hydration will initially occur, and it provides a base temperature on top of

which the heat rise from hydration will be added [Neville, 1995; Bush et al., 1995]. Allowable concrete

placing temperatures range between 20-35°C depending on the thickness of the element being placed –

the thicker the element, the lower the allowed temperature. This is to ensure that extremely high

temperatures are not reached within the concrete during the curing period, as this is one of the major

concerns regarding concreting in hot conditions. Other factors, such as evaporation of water from the

surface causing plastic shrinkage cracking and crazing, can also be of concern, but this is beyond the

scope of this simulation.

Failure to control the placing temperature can lead to a variety of concerns, including an increased water

demand and rate of slump loss, accelerated setting due to increased rate of hydration and a reduction in

the long-term strength of the concrete. This accelerated rate of hydration is particularly troublesome as it

can further aggravate the problem. This happens because the higher rate of hydration will release more

heat in a smaller amount of time, which leads to even higher internal concrete temperatures.

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There are a variety of approaches that are commonly employed to help deal with the increased

temperatures that can cause problems when concreting. In some cases, the cement content of the mix

can be reduced so that hydration energy doesn’t exacerbate the problem. Another common approach is to

control the placing temperature of the concrete. This can be done by chilling the aggregates, or the mix

water, or by adding ice as a partial replacement for the mix water, or even by injecting liquid nitrogen. The

placing temperature (or the amount of water or ice required for a given temperature) can be calculated

using the following formula, available from a variety of sources (Neville, 1995; Kosmatka et. al. 1995)

wca

wwccaa

WWWWTWTWT

T++++

=)(22.0)(22.0

Equation 1-1

In this formula, T denotes the temperature (in °C or °F) and W denotes the mass of the ingredient

(aggregates, concrete and water) per unit volume of concrete. It should be noted that it is not always

possible to control the placing temperature using chilled water or ice shavings, particularly in concretes

with a low water content. In these cases it may be required to use liquid nitrogen, though this can be

expensive to do for small volumes of concrete, as it requires highly specialized equipment. Finally, it may

be necessary to help cool some concrete elements from the inside, using cooling pipes. These pipes are

used to circulate cool water, which can be useful when dealing with extremely large mass concrete

elements. Regardless of the method employed, it is often necessary to protect the concrete element from

direct sunlight, as this can also contribute a significant amount to thermal rise within the element.

The thermal simulation will be useful for predicting the effectiveness of a reduced placement temperature,

or a reduction in the cement content, in dealing with concreting in hot weather. The simulation can also be

used to evaluate the effectiveness of replacing a portion of the cement with supplementary cementing

materials, such as ground granulated slag or fly ash. However, the simulation will not be able to predict

the heat rise in complex situations, such as if there are cooling pipes within the element, as this is beyond

the scope of the project.

1.3.2 Cold Weather Concreting

Concreting in cold weather is another situation where special steps may be required to protect the

concrete from freezing or cracking. CSA A23.1 requires that protective steps be taken if the air

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temperature is at or below 5°C, or when there is a reasonable probability that it will drop below this point

within 24 hours of placing (Clause 7.4.2.5.1). The code also specifies a minimum concrete temperature of

5 or 10°C, depending on the dimensions of the element being cast (Clause 7.4.2.5.2), as shown in Table

1-1. The code requires that the concrete be adequately protected from the cold, by means of heated

enclosures, coverings, insulation, or a combination of the three. Furthermore, the element is to be

protected in such a way that thermal differentials upon removal of the protective measures are limited to a

maximum of 20°C for all structural components made from high-performance concrete (Clause

7.4.2.5.3.3) and mass concrete elements (Clause 7.4.2.3). Other elements have a maximum thermal

differential that is based on their thickness and aspect ratio, as given in Table 1-2.

Table 1-1: Permissible concrete temperatures at placing (CSA A23.1 Table 14) Temperatures, °C Thickness of section, m Minimum Maximum* < 0.3 10 35 0.3 – 1 10 30 1 – 2 5 25 > 2 5 20 * In no case shall the placing temperature for high-performance concrete exceed 25°C

Table 1-2: Maximum permissible temperature differential between concrete surface and ambient (wind up to 25 km/h) (CSA A23.1 Table 21)

Maximum permissible temperature differential, °C Length-to-height ratio of structural elements*

Thickness of concrete, m 0† 3 5 7 20 or more < 0.3 29 22 19 17 12 0.6 22 18 16 15 12 0.9 18 16 15 14 12 1.2 17 15 14 13 12 > 1.5 16 14 13 13 12 * Length shall be the longer restrained dimension and the height shall be considered the unrestrained dimension. † Very high, narrow structural elements such as columns.

As with hot weather concreting, the temperature at placement is controlled by altering the temperature of

the various components used in the mix. The easiest component to heat is the water, though a limit of 60 –

80°C is recommended to minimize the potential for flash set of the concrete (Neville, 1995). The

aggregate itself can also be heated for cold weather mixes; this is preferably done by passing steam

through heating coils, as using steam directly can result in a variable moisture content in the aggregate. It

is particularly important to prevent any ice from being introduced to the mix with the aggregate, since the

heat required to melt it would further chill the concrete mix (Neville, 1995).

7

Common practice in cold weather is to use insulated forms to limit the heat loss of the concrete during

curing. This is done to minimize thermal gradients on the surface of the concrete by slowing the rate of

cooling of the entire element. Best practice requires that this formwork (as well as the sub-grade, if

applicable) be heated prior to casting, in order to prevent cooling upon placement (Neville, 1995). ACI

306R-88 details various types of insulation that are commonly used for this purpose.

The most important consideration when using insulated forms is to remove the forms in a manner that

avoids a sudden change in temperature at the surface of the concrete (Neville, 1995), particularly along

the edges and at the corners of the element (CSA A23.1). This typically requires the forms to be left on

the surface of the element longer than is required from strength requirements alone. The safe stripping

time can then be determined by a variety of methods, including the nomograph provided in CSA A23.1,

which is shown in Figure 1-1.

Figure 1-1: Graphical determination of the safe stripping time for insulated formwork (CSA A23.1)

8

1.4 Scope

A variety of materials were examined in order to develop and calibrate the thermal simulation. In order to

keep the number of samples required for the testing program to a manageable level, this project focused

on materials that are commonly available in the Ontario market.

A total of six CSA Type GU (formerly Type 10) cements were tested along with eight SCMs (four slag

cements and four fly ashes), at replacement levels of 10 and 20%, and in some cases 50%. In addition,

four of the neat GU cements were tested at three temperatures – 10, 23 and 35°C – to facilitate calculation

of the apparent activation energy.

Secondly, this thesis project focused on the early age thermal reaction of the concrete. In order to limit the

scope of the paper to allow for concise discussion, early-age has been taken to mean the period of time

between the initial set of the concrete and 28 days. A more precise definition would be based upon the

degree of hydration of the cement (Han, 1996), or the cement’s maturity, but for simplicity’s sake the

definition given above will be adhered to in this paper.

In terms of the thermal simulation, this project will focus on delivering a two-dimensional temperature

analysis of the concrete elements under consideration. This decision was made to simplify the problem for

the end user, by introducing a set of pre-determined geometry types. While this approach will limit the

application of this simulation somewhat, it will still remain useful for the types of elements that were

originally of interest.

Finally, this thesis project will rely on internal temperature differentials that are generated within the

concrete element during hydration as the prime indicator of a potential for thermal cracking at early ages.

While there are a variety of different factors that directly influence this early-age cracking potential, such

as the zero stress temperature, the concrete strength, and the degree of restraint, a detailed stress

analysis is beyond the scope of this thesis project. As such this thesis project will focus on obtaining an

accurate prediction of the internal response of the element.

9

Chapter 2: Literature Review

Thermal stresses developed at early age have been a major cause for the early age cracking of concrete

since the beginning of the 20th century, and it continues to be a problem today (Lange and Altoubat,

2003). This potential for cracking has generated a lot of research on the topic over the years. The first

attempts to predict hydration temperatures in concrete were performed by Yoshida, dating back to 1921.

In the 1950s, Rastrup proposed one of the first hydration models that incorporated the influence of

temperature and degree of hydration in his hydration model.

The first attempts to estimate the magnitude of induced thermal stresses for comparison with the

increasing tensile strength of concrete at early ages were made in the late 1960s. However, these

predictions found that there were two key obstacles yet to be overcome. Firstly, the results of thermal

stress calculations were dependent on the stiffness of the concrete as it transformed from a semi-liquid to

a solid, and secondly, the restraint stresses could not be determined with conventional methods, which

therefore meant that no data were available to verify the stress calculations. (Springenschmid, 1998)

More recently, there have been a large number of papers on the topic of predicting heat rise and thermal

cracking potential in concrete elements. Several of these papers have focused on the effects that

supplementary cementing materials have on the hydration of concrete, which is an issue that has

previously not been covered in depth. Other papers have outlined hydration models that can be used to

perform detailed thermal analyses of concrete elements, including several computer based approaches.

There has also been much discussion on the temperature sensitivity of cementitious systems, as well as a

host of papers on the growing use of calorimetry as a tool for hydration analysis.

In general there are three things that one needs to know to be able to predict the heat rise within concrete

elements. They are 1) an understanding of the total heat of hydration evolved by the element, and the rate

at which this occurs, 2) knowledge of the strength development of the concrete mix, and 3) knowledge of

the physical arrangement and dimensions of the element, including the boundary conditions. Of course

this is something of an oversimplification, and each of these three elements is far more complex than

10

these simple descriptions imply, but these elements do serve as a method for organizing discussion on

the topic.

2.1 Understanding the Hydration of Portland Cement Concrete

Cement hydration is a complex set of exothermic reactions that occurs when cement and water are mixed

together. This reaction can liberate relatively large amounts of energy – up to 500 Joules per gram of

cement – which can cause high thermal gradients given that concrete is a relatively poor conductor

(Neville, 1995). This is particularly true when conditions act to dramatically cool the surface of the

concrete element under consideration.

There are two main cementitious reactions of interest that occur when cement hydrates. These two

reactions involve a reaction between water and the dicalcium silicates and the tricalcium silicates to form

calcium silicate hydrates (CSH) and hydrated lime, as shown in the following two simplified equations:

( )22 OHCaHSCWaterSC +−−→+ Reaction 1

( )23 OHCaHSCWaterSC +−−→+ Reaction 2

The reaction product of these reactions is the formation of calcium silicate hydrates (C-S-H), which can

account for about 50 to 60% of the volume of the hydrated paste. This C-S-H paste controls the strength

and durability of the concrete paste. The exact chemical composition of the C-S-H paste will vary

according to a number of factors, including time, as well as the presence of other compounds within the

cement and the ratio of calcium to silica present in the cement (Neville, 1995). For the purposes of this

thesis, it is assumed that the precise composition of the gel is not of crucial importance.

A secondary product, calcium hydroxide (Ca(OH)2) is also formed during these reactions. This compound

is less dense than the C-S-H, and contributes essentially nothing to the strength of the paste. However, in

the presence of fly ash, this calcium hydroxide will react to produce additional C-S-H paste, which results

in a denser concrete. This reaction occurs much more slowly than the dicalcium silicate and tricalcium

silicate reactions however.

11

( ) HSCWaterOHCaAshFly −−→++ 2 Reaction 3

There are also secondary reactions that take place involving the tricalcium aluminate (C3A) and the

tetracalcium aluminoferrite (C4AF). These phases are present not because they are important for the

strength development of the cement, but because they act as a catalyst for the formation of the calcium

silicates during the cement production process (Neville, 1995). The tricalcium aluminate reactions are of

the most interest, because if uncontrolled they can lead to flash set, an immediate stiffening of the paste

which occurs due to a lack of gypsum in the cement. These reactions are as follows:

EttringiteWaterGypsumAC →++3 Reaction 4

This reaction will proceed until the supply of gypsum in the cement is exhausted, at which point the

ettringite will become unstable. At this point, the C3A will continue to react with the ettringite to produce

monosulfate, a stable product.

eMonosulfatWaterEttringiteAC →++3 Reaction 5

If there is still C3A remaining once all of the ettringite is converted to monosulfate, the C3A will react with

water to produce calcium aluminate hydrate (C-A-H).

HACWaterAC −−→+3 Reaction 6

2.1.1 Reaction Stages

For a typical concrete, all of these reactions proceed in a particular order, which is often divided into five

stages for discussion (D’Aloia, 2003; Mindess et al., 1981). These five stages are shown in Figure 2-1,

which shows both the rate of heat evolution and degree of hydration, both as a function of time. Of

particular interest is stage three, which is the most important stage in terms of the heat release and

temperature development.

12

Figure 2-1: Reaction stages during cement hydration process (Schindler, 2002)

Stage one occurs immediately after water is added to the cementitious materials. This stage involves very

rapid heat evolution, accompanied by a large but brief spike in the rate of heat evolution. This heat is the

result of the C3A reaction with gypsum (Reaction 4). As the gypsum present is consumed, the rate of

ettringite production slows, leading up to the dormant period. Although the C2S and C3S will also begin to

react during this stage, their contribution to the heat evolution is minimal.

This stage can have a very measurable effect on the temperature of the concrete, but due to the rapid

nature of the reactions, the stage will occur in the batch mixer or ready mix truck. As a result, this stage

mainly impacts the placement temperature of the concrete (Schindler, 2002).

Stage two, typically called the dormant or induction period, is a time of relatively low reaction. Throughout

this stage the concrete remains plastic and workable; it is during this stage that the concrete is handled

and placed. The concentration of calcium and hydroxide ions build throughout this stage, and when a

13

critical value is reached, the reaction of C3S and C3A proceed at a rapid rate, signalling the onset of stage

three. At normal placing temperatures, this stage generally lasts between one to three hours.

Stage three is typically known as the acceleration stage. The C3S reaction will begin to accelerate, leading

to the maximum hydration rate achieved during the hydration process. The C3A will also begin to react

again, producing additional ettringite; this reaction will continue until all of the gypsum is consumed, at

which point Reactions 5 and 6 will take over. The final set of the concrete will occur shortly after the onset

of this stage, and this is followed by a period of rapid strength development, though at this point the

concrete is unable to sustain any real load without risk of damaging the very young C-S-H matrix.

Depending on the mix, this stage can last for three to twelve hours, or longer.

Stage four, called the deceleration stage, is a period of ongoing strength gain. By this point, the majority of

the C3S and C3A have reacted, which leaves the much slower C2S reaction – in addition to any reactions

due to fly ash or slag, if applicable - to continue building strength at a relatively slow rate. This stage can

last from four to 150 hours or longer.

Finally, stage five indicates the onset of a steady state condition within the concrete matrix. Most of the

material that will hydrate has reacted by this point, leaving the slow pozzolanic reactions which will

continue to produce C-S-H from the calcium hydroxide (Schindler, 2002). There will be some additional

strength gain during this phase, and the concrete will continue to develop certain resistances to outside

attack.

2.1.2 Factors Influencing Hydration

There are a large number of factors that can influence concrete hydration. They include (though this list is

not exhaustive): the curing temperature and exposure history; the temperature of the fresh concrete at the

time of placing; the type and amount of cement used; the presence of supplementary cementing

materials; the water-cement ratio of the concrete; and finally, the use of chemical admixtures, particularly

accelerators and retarders.

Of these factors, only a few can be manipulated to provide solutions when faced with the potential for

thermally induced cracking. These include the cement type chosen for the mix design, the presence of

14

supplementary cementing materials, and the water-cement ratio of the mix. As mentioned in Section 1.3.1

the placing temperature can also be controlled somewhat, either through the addition of ice chips to the

mix water or chilling the aggregate, or by chilling the concrete itself with liquid nitrogen. The other factors

are typically fixed for a particular situation, which means that potential thermal issues are often dealt with

by making changes to the mix design itself.

2.1.2.1 Cement Type

The cement type plays a critical role in the amount of heat evolved during hydration. The different calcium

compounds each produce a different amount of heat when they hydrate, and varying the cement

composition will have an effect on the total heat of hydration (see Section 2.1.3). Roughly two thirds of the

total heat of hydration will be produced as a result of C3S hydration for typical Type GU cements. This is

due in part to the high C3S in modern cements, which is a result of the construction industry’s demand for

high early strengths. The second highest contribution to the total heat of hydration will be from the C3A.

The influence of C3S and C3A content on the heat evolution is shown in Figures 2-2 and 2-3, respectively.

Figure 2-4 illustrates the typical heat of hydration development for the different cement types. Therefore, it

stands to reason that to reduce heat from hydration one should specify cement that is low in C3S and C3A,

in favour of a higher C2S concentration.

Figure 2-2: Influence of C3S content on heat evolution, C3A content approximately constant (Neville, 1995)

15

Figure 2-3: Influence of C3A content on heat evolution, C3S content approximately constant (Neville, 1995)

Figure 2-4: Development of the heat of hydration for different cement types (cured at 21°C, w/c 0.4) (Neville, 1995)

In the Canadian Cementitious Materials Compendium (CSA A3000-03), there are two cement

designations that specifically address this need: MH, or moderate heat cement (formerly Type 20) and LH

or low heat (formerly known as Type 40). These two designations both limit the maximum amount of C3S

and C3A in the cement. However, neither of these cements are widely available in the Ontario market;

here it is more common to specify blended cements that meet the requirements of CSA A3000-03 (i.e. a

MHb or LHb cement; see Section 2.1.2.2).

16

Cement’s fineness can also play a role in the amount of heat it produces. Typically measured in terms of

its specific surface area, fineness is a measure of the available particle surface area that is available for

reaction; the greater this surface area, the faster the reaction. Increasing the fineness of the cement (or

the SCM for that matter) also causes a higher temperature rise, since an increased rate of hydration

within the cement causes heat to be generated more quickly, while the rate of heat loss to the

environment remains more or less constant (Bush et al., 1995). Type GU (general use, formerly Type 10)

cements will typically have a fineness measuring between 380-410 m2/kg, while Type HE (high early

strength, formerly Type 30) and silica fume blends can have a fineness value exceeding 600 m2/kg. In

fact, some HE cements are produced from the same clinker as a company’s GU cement, simply by

increasing the fineness of the finished product. It is interesting to note that while an increased fineness will

speed up the hydration at early ages, there will be little change in the total heat of hydration at very late

ages (Mindess and Young, 1981).

2.1.2.2 Use of Supplementary Cementing Materials

Supplementary cementing materials such as ground granulated blast-furnace slag and fly ash are

commonly used to replace a portion of the Portland cement used in making concrete. This is often done

for economical reasons – both of the supplementary materials are cheaper than Portland cement – but

these binary mixes have certain advantages compared to concretes made from neat Portland cement.

The fly ash produces a pozzolanic reaction that consumes calcium hydroxide and produces C-S-H paste.

Slag cement differs from fly ash in that it is a hydraulic cement, though its reaction may be partially

pozzolanic; its chemical composition is similar to that of cement, though it tends to have a higher silica

and alumina content than Portland cement. However, like Portland cement, slag is a hydraulic cement,

and its reaction will proceed even if there is no cement present (unlike fly ash). Both of these additional

chemical reactions help to produce a denser paste matrix, which increases a concrete’s resistance to

certain forms of deterioration, particularly those that rely on the ingress of a fluid (such as chloride attack,

sulphate attack, etc.).

17

In addition to improving certain properties of a mix design, SCMs can be used to help control the heat of

hydration. Research done by Douglas et al. (1990) has shown that replacing some of the Portland cement

with slag or fly ash can have a marked reduction in the heat produced during hydration. This decrease in

the heat of hydration is generally linear with replacement, though the reduction may increase slightly as

higher replacement levels are used (Douglas et al., 1990). Figure 2-5 illustrates this reduction in heat

development for various replacement levels of ground-granulated blast-furnace slag, and Figure 2-6

illustrates the reduction due to fly ash replacement. This reduction in total heat is due mainly to the fact

that the reactions that occur as a result of the SCMs tend to produce less heat, particularly at early ages.

This reduction in the total heat of hydration has a further beneficial effect, as the rate of Portland cement

hydration is slowed due to the lower temperatures that result from this reduction in heat production.

0.00

1.00

2.00

3.00

4.00

5.00

0 12 24 36 48 60 72Time [h]

Pow

er [

mW

/gm

at]

St. Lawrence GU (Mississauga)

St. Lawrence GU (Mississauga) + 10% Grancem GGBS (S)



Figure 2-5: Influence of varying levels of GGBS replacement on the heat development of concrete paste; measured at

23°C

18

0.00

1.00

2.00

3.00

4.00

5.00

0 12 24 36 48 60 72Time [h]

Pow

er [

mW

/gm

at]

Lafarge GU (Woodstock)

Lafarge GU (Woodstock) + 10% Atikokan Fly Ash (CI)



Figure 2-6: Influence of varying levels of fly ash replacement on the heat development of concrete paste; measured at

23°C

As mentioned in Section 2.1.1.1, binary mixes are commonly produced to meet certain low heat

requirements. CSA A3000-03 defines performance criteria in terms of the seven day heat of hydration that

can be used to characterize these binary mixes as MHb or LHb cements. These blends can be used

interchangeably with Portland cements of Type MH or LH respectively, and are available from several

different manufacturers in the Ontario market under a variety of trade names.

The use of supplementary cementing materials can be greatly effective in producing concretes that have

low hydration heats (Bush et al., 1995; Douglas et al., 1990). The use of SCMs doesn’t simply reduce the

amount of heat produced, it also generally delays the time to maximum temperature rise, resulting in a

rise in temperature within the concrete that is less severe than in a normal Portland cement mixture, but

that lasts longer (Douglas et al., 1990). Douglas et al. concluded from their research that while a slag

replacement of 50% provides the most acceptable compromise in terms of lowering the heat of hydration

of the concrete while retaining most of the compressive strength, fly ash is better overall at lowering the

19

amount of heat generated, and as such is better suited to use where the ultimate strength is not of as

much concern.

2.1.2.3 Water-Cement Ratio

The water-cement ratio (w/c) – also known as the water to cementitious materials ratio (w/cm) in blended

systems - provides information regarding the amount of water available for hydration relative to the

cementitious material present in the mix. This water cement ratio is of key importance to the strength

development of the concrete, as it controls how much of the available cementitious materials will hydrate,

as well as the ultimate degree of hydration that can be attained by the mix (Neville, 1995). The influence

of varying the water-cement ratio on the heat evolution for various concretes is shown in Figure 2-7.

The ultimate degree of hydration will directly affect the amount of heat that is released during hydration,

and as such it must be accounted for in any model developed for the prediction of the heat of hydration for

different concrete mixes (Schindler, 2002). Refer to Section 2.2.1 for a discussion of how the water-

cement ratio of a concrete affects the ultimate degree of hydration, and hence the heat generation.

Figure 2-7: Influence of water-cement ratio on the heat evolution of concrete (Schindler, 2002)

20

2.1.3 Total Heat of Hydration

The heat of hydration is the quantity of heat produced by the complete hydration of the material at a given

temperature, and is normally measured in joules per gram of material (J/gmat). Strictly speaking, this heat

of hydration accounts for both the chemical heat of reactions, and the heat of adsorption of water in the

gel layers of the calcium silicate hydrate (C-S-H) matrix, the latter of which accounting for approximately

one quarter of the total heat of hydration (Neville, 1995). Bogue (1955) observed that for normal Portland

cements, approximately one half of the total heat of hydration is evolved between one and three days,

about 75% in seven days, and about 83-91% in six months. The chemical composition of the cement

dictates the precise values, but the above approximation holds true for a wide range of commonly used

cements.

The total heat of hydration of a cement is very nearly the sum of the heats of hydration of the individual

compounds – that is, the various calcium compounds, namely C2S, C3S, C3A and C4AF - when hydrated

separately. It follows then that given the compound - or Bogue - composition of a cement, its heat of

hydration can be calculated with a fair degree of accuracy using the following formula (Neville, 1995):

AFCACSCSCcem ppppH4323

3020062136 +++= Equation 2-2a

AFCACSCSCcem ppppH4323

126840260570 +++= Equation 2-2b

This formula yields the total heat of hydration, measured in calories per gram of material (Equation 2-2a)

or Joules per gram (Equation 2-2b), with pi representing the mass ratio of the i-th component. It may be

noted that there is no relation between the heat of hydration and the cementing properties of the individual

compounds.

Variations of this formula have been published by many different authors, and in each there will some

difference in the precise numerical values representing the specific heat of the various components.

However, these differences are generally quite minimal, and in general any of the versions of this formula

will produce good results.

21

A slightly more comprehensive version of this approach that accounts for the presence of free lime,

sulphur and magnesium oxides is presented by Schindler and Folliard (2005):

MgOFreeCaOSOAFCACSCSCcem pppppppH 850118662442086626050034323

++++++=

Equation 2-3

If there are supplementary cementing materials present in the mix design, these also have to be

accounted for in the total heat of hydration calculation, as shown in the following equation (Schindler and

Folliard, 2005). The reduction in the total heat of hydration is due to the dilution of the Portland cement

with a cementitious material that produces less heat; the total heat of a blended cement system can be

calculated using Equation 2-4:

FlyAshFlyAshGGBSGGBScemcemu pHpHpHH ⋅+⋅+⋅= Equation 2-4

The values for HGGBS and HFlyAsh will vary from material to material based on the composition and

fineness, so the best way to determine these input values is to do so experimentally. However, this is not

always possible, and in these cases theoretical or assumed values must be used. Several values for

specific materials are presented in the literature, with values for HGGBS ranging from 355 and 461 J/g and

values for HFA ranging from 150 to 210 J/g depending on the class of the ash. Schindler and Folliard

recommend using a value of HGGBS equal to 461 J/g, and a value for HFlyAsh equal to CaOFAp⋅1800 (J/g)

(Schindler and Folliard, 2003).

It should also be noted that the compound or Bogue composition is most often calculated using the

chemical composition measured in terms of oxides. This is done because is it generally much easier to

determine the oxide composition using wet-chemical analysis methods than it is to directly determine the

composition using microscopy or XRD. However, these calculations are not totally accurate, since

different calculation methods can yield different results, and since the cement minerals are typically

reported to the nearest 1%. The Bogue composition can be calculated using the following set of equations

(ASTM C150-05):

22

23323223 188.5852.2430.1718.6600.7071.4 COSOOFeOAlSiOCaOSC −−−−−=

Equation 2-5

SCSiOSC 322 754.0867.2 −= Equation 2-6

32323 692.1650.2 OFeOAlAC −= Equation 2-7

324 043.3 OFeAFC = Equation 2-8

These equations are only valid for neat Portland cements, so problems may arise should one try to use

these equations to determine the Bogue composition for a blended cement. In some cases there are other

solutions that will yield approximate Bogue compositions. For example, when dealing with silica fume

blended cement it may be possible to subtract the replacement level of the silica fume (typically 90%

SiO2) from the total silica content before performing the calculation.

2.2 Determining the Rate of Hydration

Most practical applications require knowledge of the rate of hydration of the cement being examined. The

simplest way to determine the rate of hydration is to measure it using calorimetry methods. Unfortunately,

this typically requires specialized equipment, and often more importantly, this testing requires a length of

time to perform. In situations where testing of the materials involved is not possible, a numerical hydration

model must instead be used to determine the rate of reaction.

However, this rate cannot be calculated in the same way as the total heat of hydration, because each of

the compounds reacts at a different rate, and all are affected by the mix temperature. Figure 2-8 shows

the differing rates at which the various compounds hydrate; note that the C3A and C4AF achieve in excess

of 80% hydration during the first 24 hours of curing. Cement fineness, the presence of supplementary

cementing materials, the amount of gypsum (Schindler, 2002) and proportion of C3A and C3S in the

cement can also affect the rate of hydration, particularly at early ages.

23

Figure 2-8: Rate of hydration of the various cement components (Neville, 1995)

In order to determine the rate of hydration, it is first important to develop a method for determining the

degree of hydration of various cements as they mature. This is important, since time alone is not sufficient

for comparison, as different mixes will hydrate at different rates based on the curing conditions. The most

commonly used approach for dealing with these different curing regimes is the equivalent age maturity

method, which is discussed later in this section.

2.2.1 Quantifying the Degree of Hydration

The degree of hydration, α, is defined as the ratio between the quantity of hydration products and the

original quantity of cementitious material present in the mix. It is a function of time, varying between 0%

(at the start of hydration) and 100% (when all cementitious materials have reacted). The importance of

this parameter on any heat of hydration model was stressed by van Breugel, who stated that “a reliable

prediction of temperatures without a simultaneous calculation of the progress of hydration process is

impossible.” (1998)

The degree of hydration can be determined in several ways, with the most common method being an

indirect method based on heat development of the cement (Schindler and Folliard, 2005; Kada-Benameur

et. al., 2000). This concept is mathematically expressed as follows:

( ) ( )uHtHt =α Equation 2-9

24

Figure 2-9: Influence of water-cement ratio on the ultimate degree of hydration (Schindler, 2002)

It has been noted by several authors that hydration typically stops before a degree of hydration of 100% is

reached. Mills (1966) noted that the ultimate degree of hydration what can be achieved by a concrete is

determined by its water cement ratio, as shown in Figure 2-9. He presented an equation to determine the

ultimate degree of hydration, as shown in Equation 2-10. This concept was later expanded by Schindler

and Folliard (2005) to account for the effects of supplementary cementing materials on the ultimate

degree of hydration, as shown in Equation 2-11. It should be noted that the ultimate degree of hydration is

not a function of the curing temperature.

cw

cwu /194.0

/031.1+⋅

=α Equation 2-10

0.130.050.0/194.0

/031.1≤⋅+⋅+

+⋅

= GGBSFlyAshu ppcw

cwα Equation 2-11

Finally, Equation 2-12 presents an exponential formulation that can be used in conjunction with

experimental data to predict the degree of hydration. This s-shaped function has been shown to

accurately represent the hydration development of various Portland cement systems (Schindler and

25

Folliard, 2005; Pane and Hansen, 2005). This formulation is dependent on two parameters: a hydration

slope parameter, β, and a time parameter τ.

( )⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅=

βτααe

ue tt exp Equation 2-12

It should be noted that given the nature of the hydration equation, only a single hydration peak will be

modelled for a given cementitious system. While this is an accurate assumption for neat Portland

cements, other researchers have suggested that a better approach for predicting the degree of hydration

for systems involving ground granulated blast-furnace slag or fly ashes would be to use the superposition

of two different hydration functions, to represent the two peaks that generally occur in these blended

systems (de Schutter, 1999; de Schutter and Taerwe, 1995).

In their 2005 paper, titled “Heat of Hydration Models for Cementitious Materials”, Schindler and Folliard

presented a model to determine the values of the two hydration parameters. This model is based on data

from their own semi-adiabatic tests, as well as data from past research projects by other independent

researchers, including an analysis of the Lerch and Ford hydration data set from 1948 (Schindler and

Folliard, 2005). Their model is based on a non-linear multivariate regression analysis, which yielded the

following two equations:

( )FlyAshCaOFlyAshGGBSSOSCAC ppppBlainepp ⋅⋅+⋅⋅⋅⋅⋅⋅= −−−− 50.9187.2exp78.66 758.0804.0401.0154.0333

τ

Equation 2-13

( )GGBSSOSCAC ppBlainepp ⋅−⋅⋅⋅⋅⋅= − 647.0exp4.181 558.0535.0227.0146.0333

β

Equation 2-14

The formulation of this hydration model requires the hydration time parameter, τ, to correspond to the time

at which a degree of hydration of 37% is reached (Schindler, 2002). The smaller this parameter is, the

26

more rapid the hydration. Figure 2-10 illustrates the effect of changes in this parameter, which produce a

time shift in the hydration curve.

The second hydration parameter, β, affects the slope of the hydration curve, as shown in Figure 2-11. This

parameter will also have an impact on the hydration time parameter, since the time to 37% hydration will

be affected, and this is accommodated in Schindler’s proposed model.

Figure 2-10: Effect of change in hydration time parameter on the degree of hydration development (Schindler, 2002)

Figure 2-11: Effect of change in hydration slope parameter on the degree of hydration development (Schindler, 2002)

27

Figure 2-12: Effect of change in hydration slope parameter on the degree of hydration development (Schindler, 2002)

Finally, the ultimate degree of hydration term, αu, is used to scale the magnitude of the heat of hydration

curve. This effect is shown in Figure 2-12, which shows that increasing the αu term causes the degree of

hydration curve to increase. Schindler (2002) notes that this term doesn’t exactly simulate the effects of

different water-cement ratios on the hydration process, when compared to experimental results. He

speculates that this is due to the fact that the effect of the water-cement ratio only emerges after ten to

twenty hours of hydration. However, he ultimately concludes based on his research that the use of this

term is sufficiently accurate for the modelling of the degree of hydration of cementitious systems.

Of course, it is important to understand what the limitations on such a model are, since the model is only

going to be valid for materials that fall within the range of materials that were included in the statistical

analysis. These limitations are given in Table 2-1 and Table 2-2. It should also be noted that this model

does not take into account the effects of chemical admixtures, and that the interactions for the SCMs and

Portland cements tested are valid for all combinations, including those which were not tested. (Schindler,

2002)

28

Table 2-1: Range of cement properties used for calibration of the hydration model (Schindler, 2002)

C3S (%) C2S (%) C3A (%) C4AF

(%) SO3 (%) Free

CaO (%) MgO

(%) Alkalies

(%) Blaine

(m2/kg) Average 52.5 20.8 8.4 9.3 2.6 1.4 1.8 0.6 373.7 Min 20.0 9.3 3.5 5.5 1.2 0.1 0.6 0.2 289.1 Max 64.5 55.0 13.2 16.6 4.4 2.9 4.0 1.1 579.5

Table 2-2: Range of mixture proportions and SCM properties used for the calibration of the hydration model (Schindler, 2002)

w/cm Fly Ash CaO

(%) Fly Ash SiO2

(%) Fly Ash

Alkalies (%) Fly Ash

Dosage (%) GGBS Dosage

(%) Average 0.42 - - - - - Min 0.36 10.8 35.8 0.3 0.0 0.0 Max 0.54 24.3 54.1 1.4 45.0 50.0

2.2.2 Equivalent Age Maturity Method

Maturity is a concept that accounts for the combined effects of temperature and time on the development

of concrete, both for its mechanical properties and the released hydration energy (Schindler, 2002;

Neville, 1995). The maturity method presented in ASTM C 1074 includes two different maturity functions,

namely the Nurse-Saul function and the Arrhenius formulation. These two maturity functions work in

slightly different manners: the Nurse-Saul function is used to calculate a time-temperature factor, while

the Arrhenius formulation is used to calculate an equivalent age based on the curing history and a

reference temperature. One drawback of these maturity methods is the fact that they assume proper

curing is performed during the hydration process (Schindler, 2002; Neville, 1995). There are alternate

maturity models available that consider the availability of moisture (Schindler, 2002), but these methods

are beyond the scope of this thesis project.

This thesis project will use the Arrhenius formula to determine maturity using the equivalent age method.

This formula is widely accepted as being the most applicable formula for determining the maturity of

cementitious systems (D’Aloia, 2003; Schindler, 2002; Kada-Benameur et. al., 2000; de Schutter and

Taerwe, 1995). The Arrhenius law is formulated as follows:

⎟⎠⎞

⎜⎝⎛−=

RTE

ATK aexp)( Equation 2-15

Freiesleben Hansen and Pedersen are credited with the initial use of the equivalent age Arrhenius

formulation for concrete applications (Schindler, 2002). Their implementation is shown in Equation 2-16:

29

( ) ∑ Δ⋅⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+

−+

=t

cr

are t

TTRE

Tt0 273

1273

1exp Equation 2-16

In this formula, te(Tr) is the equivalent age at the reference curing temperature (hours), Tc is the average

concrete temperature during the interval Δt (°C), Tr is the reference temperature (°C), Ea is the apparent

activation energy (J/mol) and R is the universal gas constant (8.3144 J/mol/K). This concept is sometimes

presented as an age conversion factor that is used to scale each curing interval based on the average

concrete temperature, as compared to concrete cured at the reference temperature. This conversion

factor is shown in Equation 2-17:

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+

−+

=cr

ac TTR

ETf

2731

2731exp Equation 2-17

For this thesis project, a reference temperature of 23°C was used. This value is very similar to the

reference value of 22.8°C specified by the ASTM, and is similar to the reference temperature of 20°C

commonly used in European studies.

2.2.3 Determination of the Apparent Activation Energy

In order to make use of the Arrhenius formulation in the determination of a concrete’s maturity, it is

necessary to determine a value that represents the apparent activation energy of the cementitious

materials in use. For concretes, this activation energy is considered as apparent because it is

characterizing several simultaneous and coupled chemical reactions as opposed to a single reaction

(Kada-Benameur et. al., 2000).

Historically, this value has been determined using both mechanical and calorimetric methods (Kada-

Benameur et. al., 2000). Although the determination of an apparent activation energy through mechanical

methods has certain advantages, the mechanical strength of a concrete does not rely solely on chemical

mechanisms, and as such it cannot fully abide by the Arrhenius concept. As such, Schindler (2002)

suggests that activation energy values derived from mechanical testing should not be used for the

determination of the progress of hydration at different temperatures. It should be noted that the

determination of activation energy is typically performed at an early age, generally from the setting time

30

until 24 or 48 hours (D’Aloia, 2003). This determination can be made somewhat more complicated by

concretes with a long dormant stage (D’Aloia, 2003).

In most cases, the apparent activation energy is assumed to be a constant, though this is not strictly true.

In fact, there is a significant decrease in the apparent activation energy at later ages; this can be

explained by the fact that at early ages the rate of reaction is controlled by a chemical process, whereas at

later ages this process is controlled by diffusion (D’Aloia, 2003). In reality, this assumption that Ea is a

constant is only applicable at early ages; for use at later ages, an appropriate model for the determination

of the apparent activation energy should be used (D’Aloia, 2003).

Schindler (2002) presents a detailed summary of the various activation energy values that have been

published by various authors for cementitious systems. These values range from 26,700 J/mol to 67,000

J/mol, with the most common values ranging from 30,000 – 45,000 J/mol. These values from literature

seem to vary according to the materials used, and sometimes even according to the water-cement ratio of

the concrete, and in all cases, the values given are independent of the reaction temperature. This

temperature independence is in agreement with the Arrhenius formulation (Schindler, 2002). He

concludes that it is best to determine an apparent activation energy based on cement composition and

fineness, and that this value should be taken as independent of temperature when predicting the progress

of hydration.

Schindler’s own model for the activation energy takes into account the fineness of cement, as well as the

presence of supplementary cementing materials. This model, based on results from calorimeter testing, is

shown in Equations 2-18 and 2-19:

35.025.030.043

100,22 BlaineppfE AFCACea ⋅⋅⋅⋅= Equation 2-18

GGBSFlyAshCaO

FlyAshe pp

pf ⋅+⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅⋅−= 40.0

40.0105.11 Equation 2-19

In this formula, Blaine refers to the specific surface area (m2/kg), and pi represents the weight ratio of the

i-th component.

31

Perhaps the best method for determining the apparent activation energy is to calculate it based on the

results from isothermal calorimetry tests on the cement in question (D’Aloia, 2003; Kada-Benameur et. al.,

2000). The method presented below is sometimes referred to as the “Speed Method.” This procedure is

only useful for the analysis of calorimetry data, since there are typically too few data points available from

mechanical testing to allow for a suitable degree of accuracy using this method (D’Aloia, 2003).

For two different curing temperatures, T1 and T2, the rate of hydration can be expressed as follows:

( ) ( )αα fTKdt

d

T

⋅=⎟⎠⎞

⎜⎝⎛

11

1

Equation 2-20a

( ) ( )αα

fTKdt

d

T

⋅=⎟⎠⎞

⎜⎝⎛

22

2

Equation 2-20b

For the same degree of hydration α = α1(T1) = α2(T2) and by introducing the Arrhenius law, one obtains:

( )( ) ⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−=⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛

122

121 11exp21

TTRE

TKTK

dtd

dtd a

TT

αα Equation 2-21

The knowledge of this ratio for two curing temperatures allows for the determination of the apparent

activation energy associated with the concrete as follows:

( )⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−⋅

=

dtddt

d

TTTTREa

2

1

21

21 lnα

α

α Equation 2-22

2.3 Calorimetry Methods

Whenever possible, the best method for determining the total heat of hydration and the rate of hydration

for a given set of cementitious materials is to measure it using calorimetry methods. This can be done

directly using isothermal heat-conduction calorimetry, or indirectly using one of the various adiabatic or

semi-adiabatic methods that have been developed.

32

The following sections will outline the various forms of calorimetry that have been used to quantify the

hydration of cementitious systems in order to produce inputs for the thermal simulation. The discussion

will focus on isothermal heat-conduction calorimetry, since this method was the method used for testing in

this thesis project, though adiabatic and semi-adiabatic methods are also included in the discussion.

2.3.1 Isothermal Heat-Conduction Calorimetry

This study has chosen to use isothermal heat conduction calorimetry to quantify the total heat and rate of

hydration of the various cements and binary cementitious systems. In isothermal calorimetry, the

reactions occur at a single constant temperature, with all of the heat produced being transferred to the

environment. This form of calorimetry relies on the heat flow principle, which states that heat created by

any physical or chemical reaction will flow to its surroundings at a rate proportional to the difference in

temperature (Thermometric AB, 2004). This means that the sample conditions will never be truly

isothermal, since some small temperature change is necessary to generate the heat flow to the

calorimeter itself, so the goal in isothermal calorimetry is to maintain the surroundings at a constant

temperature while providing enough thermal mass to minimize this temperature change within the sample

itself as much as possible.

Isothermal calorimetry has been shown to be a useful technique to study the hydration of cementitious

systems by several different authors (Evju, 2003; Wadsö, 2003), particularly during the first 72 hours of

hydration. Typically, isothermal calorimetry is used to investigate the major thermal peak that occurs

during the acceleration phase of the hydration process. The initial reactions are typically not included in

the analysis, because the mixing is done external to the calorimeter unit, though some studies have

examined the potential for in vessel mixing (Evju, 2003). This form of calorimetry is useful for examining

the influence of admixtures and partial SCM replacement on the hydration process.

Isothermal calorimetry is so known because samples are tested at a constant temperature. The heat flux

between the sample and a reference ampoule is measured, in order to determine the heat produced. This

method has the advantage of being able to test a material at a specific temperature, therefore removing

one of the testing variables (Evju, 2003). This form of calorimetry is also of interest because it directly

33

measures the hydration heat and rate of hydration, rather than relying on a calculation based on heat

transfer principles, as is the case with other calorimetry methods (see Section 2.5.2).

2.3.1.1 Layout of the TAM Air Isothermal Calorimeter

The TAM Air is a commercially available eight-channel calorimeter unit that operates in the milliwatt

range, with an operating range of 5 to 60°C (Thermometric AB, 2004). The calorimeter consists of eight

channels that are mounted together in a single aluminum heat-sink block that is housed inside an

insulated housing. A Peltier temperature control module controls the air temperature within the insulated

housing, maintaining an air temperature within ±0.02°C (Thermometric AB, 2004). The general layout of

the unit is shown in Figure 2-13, which gives a cutaway view of the calorimeter.

Figure 2-13: Cutaway diagram of the TAM Air calorimeter (Thermometric AB. 2004)

34

Figure 2-14: Cutaway diagram of one channel in the TAM Air calorimeter (Thermometric AB, 2004)

Each calorimetric channel is arranged in a twin configuration, as shown in Figure 2-14. In this

configuration, one chamber contains an ampoule that contains the material being tested while the other

chamber contains a reference ampoule that holds an inert material with a thermal capacity similar to that

of the sample. The size of the sample chambers allows for ampoules of up to 24 mL, though the reactivity

of the system will limit the actual useable sample size. This twin configuration helps when introducing

samples to the calorimeter as the sample and reference ampoule will equilibrate to the temperature of the

calorimeter at the same time, which will minimize the amount of unusable data at the start of testing. This

configuration also helps to reduce any amplifier noise that is generated by the system (Thermometric AB,

2004).

At the bottom of both the sample and reference cells lies a Seebeck heat flow sensor that measures the

flow of heat across the sensor, creating a voltage signal proportional to the heat flow. This signal is

passed through an amplifier unit within the calorimeter, and then processed to a digital signal that is

passed to a PC for collection. The software chosen to collect the data from the TAM Air unit was the

35

IsoCal Data Logger 5 software by Solidus Integration. This software was chosen over the native

PicoLogger software that is included with the TAM Air unit itself because of its improved user interface

and advanced features, including an automated calibration routine.

2.3.1.2 Limitations of the TAM Air Calorimeter

There are a couple of key limitations of this calorimeter unit that must be recognized in order to minimize

their impact on testing. Firstly, when measuring samples in the 600 mW range, there may be some

deviation in the temperature of the sample, particularly when the continuous rate of heat production is in

excess of 550 mW (Thermometric AB, 2004). This is a direct result of the efficiency of the heat sink unit at

dissipating the heat to the constant temperature air that is contained within the insulated housing of the

unit itself. Thermometric AB (2004) quotes a potential change in the sample temperature of nearly 3°C in

their product manual for these large exothermic (or endothermic) processes. Because of this limitation, it

is necessary to scale the size of the sample when testing cementitious systems so that this effect is

minimized. Thermometric recommends a sample size of roughly 7 g for cementitious systems (Hesse,

2005), which equates to a heat generation peak of approximately 20-40 mW for a typical neat Portland

cement paste with a water-cement ratio of 0.4. If larger samples are used, inaccuracies due to thermal

gradients in the samples can influence the results, since the conditions will deviate significantly from

isothermal (Evju, 2003), particularly when the samples are tested at elevated temperatures.

The second limitation is the fact that there is a significant amount of lag in the temperature stabilization of

the heat-sink block when changing temperatures for subsequent tests. The heat-sink block within the

calorimeter has a large thermal mass so that it is able to absorb and dissipate large amounts of heat from

the sample cells while maintaining a roughly constant temperature. As a result, it is quite slow to respond

to changes in the set temperature of the system which is controlled by air that is heated or cooled by the

Peltier heating unit. Large changes in temperature may take from 24 to 36 hours, depending on the

temperature change, and the direction of change (i.e. the Peltier unit takes longer to cool the heat-sink

than to heat it). This limits the usefulness of testing one material at subsequent temperatures for the

evaluation of the apparent activation energy, as it adds downtime between runs. This can be mitigated

somewhat by testing a larger number of samples at the same time, thereby limiting the number of

temperature changes required for the testing.

36

2.3.1.3 Advantages of Isothermal Calorimetry

There are a number of significant advantages to isothermal calorimetry that make it an ideal method for

examining the hydration of cementitious materials. Perhaps the most important advantage of an

isothermal calorimeter is the fact that it is able to directly measure the heat production rate (Wadsö,

2003). Other key advantages over adiabatic or semi-adiabatic calorimetry are as follows (Wadsö, 2003):

- There is no need to know the heat capacity or conductivity of the sample.

- The activation energy of hydration can be calculated directly from the test results performed at

different temperatures; by contrast, semi-adiabatic methods require the activation energy to

perform the conversion calculations.

- The modern isothermal calorimeters are typically more sensitive than the typical semi-adiabatic

apparatus, and require very infrequent calibrations (typically on the order of twice per year).

- There is no potential for unrealistic temperature increases, as can sometimes happen with an

adiabatic test.

However, this method does have a few disadvantages compared to other types of calorimetry. Firstly, the

apparatus is quite complex, though not as complex as a true adiabatic calorimeter. Also, as mentioned

previously, calorimeters of this type limit the size of the sample that can be tested, and they limit the

testing to mainly paste samples. Typically small paste samples in the range of 5 – 7 g are tested, and

while these samples can provide a good indication of what will occur when concrete is hydrated, it does

not provide a complete picture, since the buffering effect of the aggregates must be accounted for in the

heat calculations (Springenschmid, 1998). Secondly, this method typically does not allow for

quantification of the initial hydration stages. This is because of two factors; first, the mixing is typically

performed externally to the test ampoule, and this imparts a mixing offset to the test process. Second, and

perhaps more importantly, there is a certain amount of uncertainty that is introduced initially due to the

difference in temperature between the sample and the inside of the calorimeter unit; this difference in

temperature is measured by the calorimeter unit as heat flux, and this can cause significant errors to the

initial measurements.

37

2.3.2 Other Calorimetry Methods

Another form of calorimetry that has been widely used to characterize cement hydration is adiabatic

calorimetry. These methods can further be broken into two sub-categories: true adiabatic methods where

the heat loss from the sample vessel is zero, and semi-adiabatic methods, where a small known heat loss

is permitted.

2.3.2.1 Adiabatic Calorimetry

Adiabatic calorimetry relies on the assumption that zero heat is transferred to or from the test sample

during the measuring process; the term “adiabatic” literally means an absence of heat transfer. These

tests are performed by measuring the core temperature of the sample, which will increase during the test

period due to the heat produced by hydration.

With adiabatic calorimetry, since the sample is not allowed to lose any heat, all of the heat of hydration is

converted to temperature. As a result, the hydration will occur at an ever increasing temperature, which

will have a significant impact on the hydration rate. Due to the high temperatures produced by the

concrete sample, complete hydration can typically be achieved in as little as seven days (Schindler,

2002). Also, this method can more easily accommodate large samples than can isothermal calorimetry,

allowing for the testing of an actual concrete mixture. However, when testing concrete, the samples are

still typically mixed externally to the test vessel, which precludes the analysis of the early reactions.

The key disadvantage to adiabatic calorimetry is that the degree of hydration must be calculated using

heat transfer principles, which can introduce error as a result of inaccurate assumptions of the

conductivity, specific heat, etc. (Schindler, 2002). In a sensitivity analysis performed by Wadsö (2003) it

was determined that the conversion calculations are quite sensitive regarding the activation energy value

that is used, and he cautioned against using the total heat values calculated using this method where high

levels of accuracy are required.

2.3.2.2 Semi-Adiabatic Calorimetry

The semi-adiabatic is quite similar to the adiabatic method, but it allows for a known amount of heat

release, and therefore the temperatures produced by the sample will be somewhat lower than the

adiabatic method. A typical semi-adiabatic calorimeter is nothing more than a well insulated vessel that

38

contains a sample of concrete as it hydrates. Though this results in some heat loss as compared to a true

adiabatic test, it also removes much of the complexity, resulting in a very simple experimental apparatus.

The heat loss is quantified through a calibration process – typically this requires heating a sample with a

known amount of energy, while measuring the resulting temperature – and an adiabatic curve is produced

from the test results by correcting for this heat loss (Springenschmid, 1995). This form of calorimetry can

be something of an advantage, as there is less of a temperature correction required to perform the

conversion to an isothermal curing temperature (Schindler, 2002).

2.3.2.3 Advantages of Adiabatic and Semi-Adiabatic Methods

Both of these forms of calorimetry are popular because the temperatures developed by the sample closely

mirror those that occur in real world construction projects. The semi-adiabatic test results are typically

very similar to those that occur in concrete pavements and smaller elements, with a typical maximum

temperature of approximately 45°C (Schindler, 2002). Larger mass concrete elements such as bridge

piers and foundations are better represented by adiabatic calorimetry, since the internal temperatures

generated in these structures is generally higher, typically on the order of 60 – 65°C. This similarity in

temperature ranges may make these two test methods somewhat more useful than isothermal calorimetry

for predicting the effectiveness of a particular concrete mixture for a given application, but given the error

that is introduced during the conversion to an isothermal data curve these methods are less useful for

examining cement hydration behaviour in a lab environment (Wadsö, 2003). Also, one must consider that

in a real world construction project, there will be a good deal of temperature variation within the element

that does not follow the same temperature profile as the semi-adiabatic or adiabatic testing.

Another reason for the popularity of semi-adiabatic calorimetry in particular is the simple nature of the

testing apparatus. Typically, this consists of some sort of highly insulated container that can hold one or

two large cylinders, with a single thermocouple used to measure the internal heat rise of each concrete

sample. There are a few commercially available units for performing semi-adiabatic tests, including the

Solidus Thermocal system, and Q-Drums, which are simply insulated steel drums with a single

thermocouple that reads the sample temperature.

39

2.3.3 Relations between the Calorimetry Methods

Lars Wadsö (2003) explored the relationship between the various calorimetry methods, in order to

examine whether or not it was possible to calculate the result of semi-adiabatic or solution calorimetry

using the results of isothermal calorimetry performed at different temperatures. He reasoned that one

could accurately calculate the temperature increase in a hydrating concrete using only isothermal data;

this is generally the opposite of what is done, as typically results from a semi-adiabatic test are converted

to an isothermal (or sometimes, completely adiabatic) curing conditions for use in maturity calculations.

Figure 2-15 illustrates the relationships between the various calorimetry methods, as well as the

information that can be gleaned from each.

Figure 2-15: Relationship between the various calorimetry methods (Wadso, 2003)

Wadsö’s method for performing this comparison relied upon isothermal calorimetry measurements

performed at 20, 30, 40 and 50°C. The semi-adiabatic result simulations were performed using a forward

difference calculation using a time step of two minutes. His simulation model calculated the heat balance

for the theoretical semi-adiabatic calorimeter, assuming that the sample conditions were isothermal

(when, in reality there is likely some temperature variation within the sample itself), and assuming that the

heat flow to the surroundings can be accurately described with a thermal conductance term. At each step

of the calculation, the data from the four isothermal temperatures was used to calculate the specific

40

thermal power and hydration state of the simulated semi-adiabatic that corresponding to the reached

state.

Based on the results of his simulations, Wadsö concluded that his procedures were suitable for simulating

the results of semi-adiabatic tests, though he had somewhat less success calculating the results of

solution calorimetry. He also noted that despite advances in isothermal calorimetry instruments, there was

still potential for improvement, as he noticed that there was a spread in the isothermal measurements

from different laboratories. He suggested that these variations could be due to different mixing or testing

procedures, or due to slightly different mix proportions due to the small sample sizes used.

2.4 Modeling Concepts

This section will outline the theory that will be used to perform the heat generation and internal

temperature rise of concrete elements. The internal temperature development results from the interaction

between the concrete’s own internal heat generation and the various heat transfer mechanisms between

the element and its surroundings. The hydration of concrete under real world field conditions introduces a

host of other variables that can influence the temperature development. These variables may include the

following factors:

- Ambient air temperature

- Wind speed / evaporation of surface moisture

- Relative humidity

- Solar radiation / cloud cover

- Base or sub-grade temperature

- Curing methods

- Member thickness

The overall development of temperatures in a two-dimensional plane can be determined using Fourier’s

Law (Jonasson et. al., 1995), as shown in Equation 2-23:

dtdTcQ

dydTk

dyd

dxdTk

dtd

pH ⋅⋅=+⎟⎟⎠

⎞⎜⎜⎝

⎛⋅+⎟

⎠⎞

⎜⎝⎛ ⋅ ρ Equation 2-23

41

This equation gives the transient heat balance with respect to distance (x, y) and time (t), where T

represents the temperature (°C), k the thermal conductivity (W/m/°C), QH is the rate of heat generation

(W/m3), ρ is the concrete density (kg/m3), and cp is the specific heat capacity (J/kg/°C). The various

environmental influences are used to define the boundary conditions for the problem domain under

consideration.

The following sub-sections will expand on this transient heat balance (Equation 2-23), including the

various thermal characteristics of concrete that are required for the model. An outline of the various

methods for dealing with the environmental factors will also be presented.

2.4.1 Modeling the Heat Generation and Associated Internal Temperatures

From Equation 2-23 the temperature development of hydrating concrete can be written as follows

(Schindler, 2002):

⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅=

⋅=

pp

H

cdtdH

cQ

dtdT

ρρ1

Equation 2-24

The rate of heat generation, QH, is dependent on the degree of hydration, as outlined in Section 2.2.1.

This is shown in Equation 2-25:

dtdHQH = Equation 2-25

In this equation, H is defined as the total heat of hydration, which can be calculated as the product of the

ultimate heat of hydration, Hu, multiplied by the degree of hydration, α, and the total cementitious content

of the mix design, Cc (kg/m3). As outlined in Section 2.2.1, the rate of hydration is a function of time and

the temperature history of the specimen. When Equation 2-25 is calculated in terms of the current age of

the concrete, the age conversion factor given in Equation 2-17 can be applied, yielding the following

equation for QH (Schindler and Folliard, 2005):

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+

−+

⋅⋅⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅⋅=

cre

eecuH TTR

Ettt

CHtQ273

1273

1αβτβ

Equation 2-26

42

Alternatively, the rate of heat generation can be determined by finding the slope of the total energy curve,

which can be calculated from the degree of hydration versus time curves produced by Equation 2-12. This

alternate method yields results that are similar to Equation 2-26, and its simplicity makes it ideal for a

numerical modelling approach. Chapter 3 provides details as to its application and use using a finite

difference method.

2.4.2 Specific Heat and Thermal Conductivity of Hardening Concrete

There are two thermal properties of interest that must be known in order to perform the simulation of

temperature rise in concrete elements, namely the specific heat (cp) and the thermal conductivity (k). Both

of these values are variable dependent on the age of the concrete, due to internal changes in the physical

structure, as well as changes in the moisture content. This section will outline methods for dealing with

these two vital parameters, though a complete discussion of the models presented is beyond the scope of

this thesis project.

The specific heat, which represents the heat capacity of concrete, is dependent on the moisture content

and current temperature of the concrete, and is little affected by the aggregate used (Neville, 1995). The

specific heat varies proportionally to the temperature, and is inversely proportional to the density of the

concrete. The common range of values published for this variable are between 840 and 1170 J/kg/°C;

these are values that have been determined in various studies using elementary methods of physics

(Neville, 1995).

The following model for the specific heat of concrete at early ages was developed by von Breugel and

presented in his Ph.D. thesis in 1997 (De Schutter, 2003; Schindler, 2002). His model was chosen as it

accounts for the effect of temperature, mix proportions, and it decreases during curing:

( )wwaacccefcp cWcWcWcWc ⋅+⋅+⋅−⋅+⋅⋅⋅= )1(1 ααρ

Equation 2-27

In this formula, Wc, Wa and Ww represent the amount by weight of cement, aggregate and water

respectively (kg/m3), cc, ca, cw are the specific heats of cement, aggregate and water (J/kg/°C), ccef is a

43

fictitious specific heat of the hydrated cement (ccef = 8.4*Tc + 339; J/g/°C), and Tc is the current

temperature of the concrete.

The thermal conductivity is a measure of a material’s ability to conduct heat. It is defined as the ratio of the

flux to the temperature gradient, and is measured in Watts per square metre of area when the

temperature difference is 1°C per metre thickness of the body (W/m/°C) (Neville, 1995). This conductivity

is highly dependent on its composition, and in particular on the type of aggregate used, with published

values ranging from 1.4 to 3.6 W/m/°C (Neville, 1995). Table 2-3 gives a summary of the values for

thermal conductivity that can be expected when different aggregates are used. The thermal conductivity of

concrete varies little with temperature in the region of room temperature, up to about 60°C (Neville, 1995).

Table 2-3: Typical values of concrete wet density and thermal conductivity as a function of aggregate type (Neville, 1995) Type of aggregate Wet density of concrete (kg/m3) Thermal conductivity (W/m/°C) Quartzite 2440 3.5 Dolomite 2500 3.3 Limestone 2450 3.2 Sandstone 2400 2.9 Granite 2420 2.6 Basalt 2520 2.0 Barytes 3040 2.0 Expanded shale 1590 0.85

The thermal conductivity of concrete also varies depending on its maturity, with an early-age conductivity

value 33% higher than that of hardened concrete (Schindler, 2002; de Shutter and Taerwe, 1995).

Assuming that the decline of this parameter can be represented as a linear decline with the degree of

hydration, the following relationship can be written, with ku being the ultimate thermal conductivity of

mature concrete (Schindler, 2002):

( ) ( )αα ⋅−= 33.033.1ukk Equation 2-28

2.4.3 Coefficient of Thermal Expansion of Concrete

Another thermal property that varies according to the aggregate used is the coefficient of thermal

expansion. This variable relates the change in temperature to the change in a material's linear dimensions

as a fractional change in length per degree of temperature change. Like most engineering materials,

concrete has a positive coefficient of thermal expansion, which ranges between 11x10-6 and 20x10-6 per

44

°C (Neville, 1995). However, unlike other materials, the value of this coefficient depends on the mix

design and the hygral state at the time of the temperature change (Neville, 1995).

In general terms, the thermal expansion coefficient is a function of the aggregate used (Neville, 1995), as

shown in Figure 2-16. The moisture content will also have an impact on this thermal expansion coefficient,

due to the fact that the coefficient is made up of two parts, namely the true kinetic coefficient, and an

additional amount due to swelling pressure, which results from a decrease in the capillary tension of water

held within the hydrated cement paste (Neville, 1995). However, the effects of moisture will not be

considered for this thesis project, and the resulting thermal coefficient will be determined solely by the

type of aggregate used.

Figure 2-16: Influence of aggregate type on the linear coefficient of thermal expansion of concrete (Neville, 1995)

2.4.4 Boundary Conditions and Environment

There is a continuous heat flow to and from a concrete structure cast in the field under real-world

conditions. The internal temperature development of the concrete element is a result of the balance

between the internal heat generated due to hydration as well as the heat flow between the element and its

environment. As a result, it is important to accurately represent the boundary conditions that are involved

in this transient heat balance.

45

There are a variety of different conditions that can exist at the boundary of a concrete element. A

boundary can be defined by a constant temperature (i.e. adjacent soil or rock temperature when governed

by the deep ground temperature), or as a heat flux. In addition, there are many situations where there may

be several different heat flows acting on a given surface of the structure (i.e. both convection and solar

absorption on the top surface of an element cast outside). These various boundary conditions are

illustrated in Figure 2-17.

Figure 2-17: Heat transfer mechanisms between a concrete element and its environment (Guyer, 1999)

The following three sections will focus on the most critical boundary conditions that act upon a typical

concrete element; namely conduction to the supporting layers, convection, and solar absorption. For the

purposes of this idealized thermal simulation, the effects of evaporation and irradiation will be ignored.

2.4.4.1 Conduction to Supporting Layers (for Elements on Grade)

Depending on the environmental conditions at the time of casting, the supporting layers beneath concrete

cast on grade can act either as a heat sink or as a heat source. In hot weather, the sun can heat the forms

and sub-grade material, causing them to add heat to the concrete as it is poured. In the winter the

opposite can occur, and a significant amount of heat from the fresh concrete can be drawn away by the

forms and sub-grade. Neither of these conditions are desirable, and as a result measures are often taken

to minimize these effects (by heating the forms and sub-grade in the winter, or shading them in the

summer, for example).

46

Table 2-4: Material properties for supporting layers and formwork involved in conductive heat flow (Schindler, 2002; Janna, 2000; Guyer, 1999)

Material Density, kg/m3 Thermal conductivity,

W/m/°C Specific heat, J/kg/°C Asphalt 2302 1.38 1047 Cohesive sub-grade 2066 1.59 1214 Concrete 2350 – 2500 2.00 - 3.50 840 – 1170 Gravel, dry 1703 0.52 838 Gravel, moist 1898 2.42 1047 Rock, granite 2750 2.60 840 Rock, limestone 2450 3.20 920 Rock, sandstone 2400 2.90 795 Soil1 1100 – 1800 0.20 – 2.001 800 – 1500

Stabilised base 2339 3.32 1005 1 The physical and thermal properties of soil varies greatly depending on the soil type, the moisture content, the presence of organic material, and compaction of the soil in question

Heat transfer via conduction is a function of the thermal conductivity, specific heat, and density of the

materials in question (Schindler, 2002; Guyer, 1999). Table 2-4 summarizes these properties for a few of

the more common materials that concrete elements may be cast upon. The quality of contact between

layers will also influence the efficiency at which heat is able to flow from one material to another via

conduction; however, for this simulation, these effects are ignored due to the fact that the fluid concrete

will form itself to the supporting layers or form-work. The simulation relies on the assumption that the

concrete is properly consolidated (i.e. there are no air voids remaining between the concrete and the

adjacent surfaces that might restrict heat flow from the concrete).

2.4.4.2 Convection from the Concrete Surface and Form-Work

Convection is the term used to describe the heat that is transferred from the surface of the concrete – or

the formwork or surface covering - to the surrounding environment. The amount of heat that is transferred

to the environment through convection is a function of the temperatures of the surface and fluid, the fluid

properties (in this case, air), the inclination of the surface, the direction of heat transfer, and the wind

velocity across the surface (Hutcheon and Handegord, 1995). The resulting convective heat transfer with

the environment, qc (W/m2), can be expressed as follows:

)( asc TThq −⋅= Equation 2-29

Here, hc represents the surface convection coefficient (W/m2/°C), Ts is the surface temperature (°C) and

Ta is the ambient air temperature (°C).

47

Determining a suitable value for the convection coefficient can be a challenging task if one turns to the

literature available on the topic. The reported value for this coefficient varies greatly from source to

source, in the range of 5 – 15 W/m2/°C, with a typical value in the range of 5 – 5.5 W/m2/°C (Hagen, 1995,

Neville, 1995; Hutcheon and Handegord, 1995). However, these values are only applicable under the

conditions for which they were determined, and typically this does not include the effects of wind on the

rate of transfer (i.e. these coefficients assume a state of natural convection).

A better approach is to calculate the value of the convection coefficient using a formula that accounts for

these varying conditions. There are a variety of different formulae for calculating the convection

coefficient, depending on which parameters involved are considered most important. For the purposes of

this simulation, a comprehensive model that deals with both forced and free convection is most

appropriate, in order to cover the widest range of environmental conditions. The following formula,

recommended by ASHRAE (1993) is suitable for determining the surface convection coefficient, hc

(W/m2/°C), for both free and forced cases (Schindler, 2002):

wTTTTCh asasc ⋅+⋅−⋅++⋅⋅⋅= − 857.21)()32)(9.0(727.3 266.0181.0 Equation 2-30

In this formula, the surface convection coefficient is a function of the surface temperature, Ts (°C) and

ambient temperature, Ta (°C), the wind speed measured in metres per second (w), and a constant, C, that

accounts for the heat flow condition. This constant C has a value of 1.79 when the surface is warmer than

the air (i.e. when the surface is transferring heat to the environment) and a value of 0.89 when the surface

is cooler than the air.

For vertical cases, convection is aided somewhat by the fact that the air will move across the surface of

the material as it is heated or cooled; this mechanism tends to increase the rate at which convection

occurs from a vertical surface (Hutcheon and Handegord, 1995). The following two formulas are suitable

for the calculation of this vertical convection coefficient, hc (kJ/m2/h/°C) (Schindler, 2002):

whc ⋅+= 1420 w < 5 m/s Equation 2-31a

48

78.06.25 whc ⋅= w > 5 m/s Equation 2-31b

In cases where a surface covering is used, or where there is convection from the concrete formwork, it is

important to take into account both conduction to these covering layers and convection from the surface

simultaneously. This can be accomplished by calculating the overall heat transfer coefficient which results

from the combination of these two mechanisms. This overall heat transfer with the surface coverings (and

ultimately the surrounding environment) can be written as shown in Equation 2-32:

)(0 as TThq −⋅= Equation 2-32

In this equation, q is the heat flux between the concrete element and the environment, h0 is the overall

heat transfer coefficient (W/m2/°C), and Ts and Ta are the surface and ambient temperatures (°C). The

value of h0 is calculated using Equation 4-5, which requires the appropriate convection coefficient for the

surface orientation, hc, as well as the thermal conductivities (k1, k2, … kn; W/m/°C) and thicknesses (d1, d2,

… dn) in metres of the various surface coverings present on the surface of the concrete. Table 2-5 lists the

thermal conductivities for commonly used surface coverings and form materials, for use in this equation.

1

2

2

1

10

1−

⎟⎟⎠

⎞⎜⎜⎝

⎛++++=

n

n

c kd

kd

kd

hh K Equation 2-33

Table 2-5: Thermal conductivities and conductance values for common surface coverings and form materials (Schindler, 2002; Guyer, 1999; Hutcheon and Handegord, 1995)

Material Density, kg/m3 Thermal conductivity,

W/m/°C Surface Coverings Blanket, glass fibres 16 – 32 0.055 Blanket, mineral fibre 6.5 – 32 0.039 Blanket, organic fibre 12 – 24 0.043 24 – 48 0.033 Plastic sheet N.A. 0.043 Form Materials Engineered formwork system N.A. 0.115 Plywood, standard 545 0.115 Plywood, marine 680 0.130 Insulating Boards Glass fibre, organic bonded 65 – 145 0.036 Extruded polystyrene, cut cell surface 29 0.029 Extruded polystyrene, smooth skin surface 35 0.029 Extruded polystyrene, smooth skin surface 56 0.027 Polyurethane, R11 expanded 24 0.023

49

2.4.4.3 Solar Absorption

Energy from the sun in the form of solar radiation can also contribute heat to the fresh concrete element,

particularly at the surface layers of the element. This heat gain is referred to as the solar absorption heat

flux, qs (W/m2), which can be calculated based on the incident radiation for a given location, qsolar (W/m2),

as well as an intensity factor, If, that accounts for the angle of the sun throughout the day (taken as 0

during the night-time), and the solar absorptivity of the concrete, βs (generally taken to be in the range of

0.5 – 0.6). This relationship is shown in Equation 2-34 (Schindler, 2002):

solarfssol qIq ⋅⋅−= β Equation 2-34

The value for the instantaneous incident radiation, qsolar, should be obtained based on historical solar

radiation values for the location where the concrete element is being cast, as the intensity of this solar

radiation can vary greatly based on location and time (Schindler, 2002; Hutcheon and Handegord, 1995).

2.5 Determining the Cracking Potential

This section will present a brief discussion of the thermal cracking mechanism, as well as a simplified

method that can be used to consider the cracking potential of a concrete element. Of course, to get an

accurate prediction of the cracking potential due to thermally induced stresses (or any induced stresses

for that matter) one needs to not only consider the internal temperature development, but also the rate of

strength gain of the concrete, the effects of stress relaxation due to creep, and the effects of restraint on

the element (from both external and internal sources). However, a full discussion of these effects is

beyond the scope of this thesis project, and the prediction of the thermal cracking potential based on the

simulated thermal gradients will not be performed as a part of this thesis project.

2.5.1 Description of the Thermal Cracking Mechanism

The potential for thermal cracking is a direct result of the early-age behaviour of the concrete. An initial

temperature rise, resulting from the hydration of cementitious materials, occurs very early in the elements

life cycle - usually within the first day or so for HPC mixtures. This rise in temperature causes the concrete

to expand against its surroundings, but since the Young’s modulus of the concrete at this time is still low

very, little of this restrained expansion is transformed into compressive stresses. However, during the

subsequent cooling the concrete’s modulus and creep reaction have increased, and therefore the

50

resulting differential contraction can cause relatively high tensile stresses (Springenschmid and

Breitenbücher, 1998).

Figure 2-18: Development of early-age concrete thermal stresses and strength (Schindler, 2002)

Figure 2-18 illustrates the relationship between the external and internal concrete temperatures, and the

associated stresses that are generated as a result. Thermal stresses do not develop during the time

before the final set, which occurs at time tfs, since the concrete is plastic up to this point. After the final set,

internal compressive stresses are caused by the increasing internal temperature, which is restrained

against expansion by the now rigid paste. The internal temperature continues to increase to a maximum

of Tmax, which occurs at time ta. After this point the concrete begins to cool, until a state of zero stress is

reached at time tzs and temperature Tzs. The zero stress temperature is generally higher than the

temperature at final set due to stress relaxation that occurs in the developing paste (Schindler, 2002). As

the temperature continues to decrease, the internal tensile stresses will increase until they exceed the

tensile strength of the concrete, causing failure at time tc. The effective temperature change that caused

cracking is the difference between the zero-stress temperature and the temperature at cracking

(Schindler, 2002).

51

The restraint that the concrete is subjected to is the primary factor in the amount of stress that will be

developed within the concrete. This restraint can come from external structures, such as mechanical

connections to other parts of the structure, or from friction on grade, or it can come from the internal

structure of the concrete (Bush et al., 1995). A complete discussion of the different mechanisms that

induce tensile stresses within the concrete is beyond the scope of this literature review, but generally the

external restraints are influenced by the size and shape of the concrete specimen, the strength, and the

difference in the modulus of elasticity for the concrete and the neighbouring material (Bush et al., 1995).

Internal restraint, on the other hand, occurs in members with non-uniform volume change on a cross

section (Bush et al., 1995). This non-uniform volume change can be caused by temperature gradients

within the concrete (or uneven drying or autogenous shrinkage of the concrete, or even as a result of

chemical shrinkage). Internal restraint adds to the induced exterior restraint, with the exception that their

summation will never exceed the effect of 100% external restraint (Bush et al., 1995). It is interesting to

note that this form of restraint is very similar in effect to continuous edge restraint; the main difference

between the two is the fact that for internal restraint the boundary stresses are equal to zero (Bush et al.,

1995).

The resulting thermal stresses can be calculated using the following formula (Schindler, 2002):

rccT KET ⋅⋅⋅Δ= ασ Equation 2-1

In this formula, the thermal stresses (σt) are calculated as the product of the temperature change (ΔT; °C),

the concrete coefficient of thermal expansion (αc; 1/°C), the creep adjusted modulus of elasticity (Ec; Pa)

and the degree of restraint factor (Kr).

There are two types of cracking that can occur as a result of these thermal stresses. The first type of

cracking occurs very early in the heating (or expansion) of the structure, generally within the first few days

to a week after placing. These cracks are typically quite small, and they are usually – but not always –

surface cracks (Bernander, 1998). Because these cracks form in the heating stage, they will typically

close as the structure cools; this tends to mitigate their effect on the structure, though they may still impact

long-term durability (Bernander, 1998).

52

The second type of cracking that can occur is related to mean negative volume change as a result of axial

tension or flexure upon cooling of the structure (Bernander, 1998). These cracks are most commonly

through cracks and they can occur weeks, months or even years after casting, depending on the

dimensions and other prevailing conditions (Bernanber, 1998). Cracks that form in the cooling phase tend

to remain open permanently, and as such they are far more detrimental to the long term durability of the

structure.

2.6 Summary

This section has presented a brief discussion on the hydration of Portland cement based systems,

including a mechanistic-empirical hydration model that was developed by Schindler and Folliard in order

to characterize the hydration process for a variety of different cements. This model uses an exponential

formula to predict the degree of hydration at a given equivalent time, based on the cement’s chemistry

and fineness, the water-to-cementitious material ratio, and the presence of SCMs such as slag cement

and fly ash. This hydration model forms the basis for a prediction of a concrete element’s internal

temperature rise, which will be developed in Chapter 3.

Also presented in this chapter was a summary of the various calorimetry methods that are commonly

used to characterize the hydration of cementitious systems, with a focus on heat-conduction isothermal

calorimetry. These concepts will be applied in the experimental program of the project, which is discussed

in Chapters 4 and 5, with the intent of producing hydration data that can be used as an input for the

desired thermal simulations.

53

Chapter 3: Development of the Thermal Simulation

This section will outline the development of the thermal simulation, which will be used to determine the

internal heat rise in concrete elements associated with hydration at early ages. The discussion will focus

on the structure and implementation of the thermal simulation using a finite difference method, including

the various assumptions that were made to simplify the problem. A discussion of the boundary conditions

that will be applied to the simulation is also presented. Finally, the chapter will present a summary of the

procedures and logic behind the numerical simulation as implemented in Microsoft Excel using VBA.

3.1 Problem Outline

The purpose of this thermal simulation program will be to perform the heat flow calculations that are

required to determine the internal temperature development within concrete elements at early ages. This

temperature development is a function of several different factors, including the rate of hydration of the

cementitious materials present in the concrete element, as well as the rate at which this hydration heat is

transferred to the surrounding environment. Figure 3-1 illustrates the various factors that are required for

this in-place temperature prediction, as well as how they are combined to form the thermal simulation.

The first of these key factors is a characterization of the rate of hydration of the cementitious materials

present. This can be done using calorimetry data obtained by testing the materials in question, or it can be

determined using a hydration model, such as the one presented in Chapter 2. Of these two methods, it is

preferable to obtain the data from isothermal heat-conduction calorimetry; however, due to scheduling or

budgetary constraints, this may not always be possible.

The second part required for the solution of the problem at hand is an understanding of the various

environmental influences, such as the ambient temperature, wind, and the effects of solar radiation.

Though some of these factors do require a prediction of sorts (i.e. a determination of the probable weather

conditions at the time of construction), in general this part is well defined by the problem itself. These

various environmental influences will define the boundary conditions for the problem domain, as

discussed in Section 2.4.4.

54

Figure 3-1: Decision tree for the thermal simulation program (adapted from Schindler, 2002)

In-Place Temperature Prediction

Isothermal Calorimetry Results - From previous testing, stored in

database - Custom testing

Problem: Predict in-place temperature development of a concrete element

Characterize Hydration of Cementitious Materials Are isothermal calorimetry results available?

Use Hydration Model

- Chemistries stored in material database

Hydration Characterization

Time

Deg

ree

of

Yes No

Environmental Conditions

- Ambient temperature - Wind - Solar radiation - Conduction to supporting layers

Time

Cor

e T

empe

ratu

re

55

Once these two parts have been sufficiently defined, the governing heat flow equation (Equation 2-23)

can be used to calculate the heat flow between the element and the environment, and the associated

temperature rise.

It should be noted at this point that given the above information, there are a variety of different methods

that can be used to obtain a solution to the problem. Firstly, a general purpose application such as

ANSYS (a finite-element structural analysis program that can also perform linear and non-linear heat

conduction problems) or SINDA (a finite-difference heat transfer analysis program) could be used to solve

the problem (Guyer, 1999). However, using either of these programs to perform the thermal simulation

requires a reasonable degree of familiarity with the solution methods, as well as a detailed understanding

of the various thermal inputs.

A second approach to the solution of this problem would be a specific-purpose computer simulation,

tailored to the hydration of cementitious systems. This approach has several key advantages compared to

the general purpose applications. Firstly, a specific-purpose program allows many of the decisions

regarding problem discretization and the numerical solution methods to be made by the designer, rather

than the end-user, thus simplifying the use of the program. This approach also allows for the development

of a customized input database, based on material testing performed using calorimetry methods. Because

of these inherent advantages, this approach will be the one adopted for this thesis project, prompting the

development of the thermal simulator program.

3.1.1 Design Goals

The task of designing and developing a computer program to perform a heat transfer analysis requires an

intimate knowledge of the numerical techniques, and a commitment to balance the needs of the end user

with the various features of a good program (Guyer, 1999). Figure 3-2 illustrates the balance that must

occur between the key features, which include the program’s flexibility, robustness, portability and

usability among other things.

56

Figure 3-2: Software development considerations (Guyer, 1999)

As mentioned in Chapter 1, the first step in the development of the thermal simulation was the creation of

a set of design goals that would be used to guide the development, while establishing a criteria for

determining the successfulness of the simulation. To recap, these design goals were as follows:










analyzed.

Based on these design goals, the factors illustrated in Figure 3-2 can be prioritized for this particular

project. The most important factors would have to be the program’s usability and robustness, followed by

its flexibility, and finally the ease at which it can be maintained (this is particularly important for the

material database, which will be used as inputs for the simulation). The portability of the program is also

important; the choice to develop the program as a spreadsheet application in Microsoft Excel using VBA

will, however, ensure that a majority of users will be able to run it, assuming that their computers are up-

to-date. Of course, the total development time available must also be taken into account, so far as a

57

working simulation must be developed during the course of this thesis project. This leaves the minimum

run cost (i.e. computational efficiency) as the lowest priority, and while attempts to optimize and

streamline the simulation program will be made wherever possible, the main emphasis will be on

developing a working program in the time allotted.

The identification of the target end-users will also influence the development of this program. In this case,

two categories of end-users were identified:

1. Consulting engineers, who would use the project to perform a rough check of the

suitability of a particular mix design with regards to thermal cracking issues for a given

element.

2. Ready-mixed concrete and cement company technical service representatives, who

would use the simulation to demonstrate the effectiveness of mixes incorporating

supplementary cementing materials for mitigating thermal cracking issues.

These two categories are however really quite broad, and as such they will encompass a range of users

with varying backgrounds. For one thing, there may be a varying demand for the different inputs that are

available to the simulation; for example, a consulting engineer may prefer to use inputs based on

isothermal calorimetry, which the technical service representative is more likely to use the material

database, or their own current cement chemistry information. The two end-user groups may also have

different needs regarding the formatting of the resultant data, and the degree to which the simulation

program interprets the final results. As a result of these varying needs, care will be taken to provide input

and output overrides for more advanced users, wherever it is feasible, while keeping the default layout as

simple as possible.

3.2 Calculating the Associated Internal Heat Rise

There are a variety of methods that can be employed to perform the heat flow calculations required for the

solution of this problem. In some cases, a solution may be reached using applied mathematical methods.

However, for a more complex problem such as the one being considered with this program it is far more

common to resort to a numerical analysis based on the discretization of the problem, due to the inherent

flexibility of such methods (Guyer, 1999).

58

There are three broad classes of discretization methods, namely finite-difference, finite-element, and

control-volume methods, though the former two methods are the more commonly used methods when

solving heat flow problems (Guyer, 1999). The methods differ from one another mainly with respect to the

method of obtaining discretized equations, and the method by which these equations are solved. The

discretization method is of interest because it affects the accuracy and stability of the numerical model,

and the solution method is similarly of interest because it affects the stability and speed (i.e.

computational efficiency) of the end solution (Guyer, 1999). For this thesis project, an explicit finite-

difference method will be used to solve the heat production and temperature development at early ages.

3.2.1 Finite-Difference Methods

In this method, the continuous problem is discretized so that the dependent variables are considered only

at the defined grid points (Anderson et. al., 1984). The discretized equations are generated from a Taylor

series expansion of Fourier Law (Equation 2-23) using a central difference approximation around each

grid point, which results in an algebraic representation of the partial differential equation (PDE).

For any given partial differential equation, there are many different finite-difference representations

available, and as such it’s usually impossible to establish a “best” form on an absolute basis (Anderson et.

al., 1984). In general, the selection of a “best” scheme must be influenced by the accuracy of the given

scheme, as well as considerations regarding the accuracy, computational requirements, and the

programming simplicity.

There are two main considerations to consider when evaluating different-finite difference schemes. The

first consideration is the truncation error of the scheme, which results from using only the first few terms of

the Taylor series expansion as an approximation for the partial differential equation being solved. As an

example of this error, consider the heat equation, as shown in Equation 3-1,

2

2

xT

tT

D ∂∂

=∂∂ α Equation 3-1

59

Using a forward-difference representation for the second derivative, the heat equation can be

approximated as shown in Equation 3-2, where T is temperature, t is time, x is the location within the

element, and αD is the thermal diffusivity of the material in question:

( )nj

nj

nj

Dnj

nj TTT

xtTT

112

1

2)( −+

+

+−Δ

=Δ

− α Equation 3-2

This equation can be rearranged in order to put zero on the right side of the equation. If we also consider

the terms that were omitted from the difference representation of the derivatives, we obtain the following

(Anderson et. al., 1984):

( )

( ) ( )

4444444 34444444 21

L

4444444 34444444 214434421

ErrorTruncation

jnjn

FDE

nj

nj

nj

Dnj

nj

PDE

Dx

xTt

tTTTT

xtTT

xT

tT

⎥⎥⎦

⎤

⎢⎢⎣

⎡+

Δ⎟⎟⎠

⎞∂∂

+Δ

⎟⎟⎠

⎞∂∂

−++−Δ

−Δ

−=

∂∂

−∂∂

−+

+

1222

2

,4

4

,2

2

112

1

2

2 αα

Equation 3-3

Here, the quantity in square brackets is the truncation error for this finite difference representation, since

these terms are ignored in the finite difference representation of the original PDE. In the case of this

representation, the order of the truncation error, O, is a function of the time difference, and the square of

the difference along x; this is commonly represented as follows:

( )[ ]2, xtO ΔΔ Equation 3-4

The difference representation presented in Equation 3-2 is often referred to as the 1D simple explicit

scheme for the heat equation (Anderson et. al., 1984), which means that there is only one unknown in

each difference equation. Because of this, the simple explicit scheme allows the problem to be solved in a

time marching manner, since all of the temperature values at the grid points are known from the previous

time step. This method is perhaps the simplest difference method to implement, though care is required to

ensure that the system remains numerically stable (that is, that the system will converge to the PDE) due

to the fact that this scheme is only conditionally stable.

60

This numerical stability is ensured by limiting the maximum value of the time step parameter, in order to

ensure that errors from any source (including truncation errors, round-off, etc.) are not permitted to grow

in the sequence of calculations and the solution proceeds from one time step to the next (Anderson et. al.,

1984). Specifically, this stability criteria requires a positive contribution from the un j term. The stability

requirement for the simple explicit scheme presented in Equation 3-2 is as follows:

( )

5.02 ≤Δ

Δ⋅=

xt

r Dα Equation 3-5

As before, the αD represents the thermal diffusivity of the concrete, which is defined as follows:

ρ

α⋅

=p

D ck

Equation 3-6

Other errors that must be considered for any numerical method, including finite-difference methods, are

errors that result from numerical round-off by the computer performing the calculations. These round-off

errors can be minimized by assigning values used in the numerical simulation to appropriately sized

variables (i.e. single or double data types in VBA), though some round-off error will always exist due to the

nature of the underlying application (Walkenbach, 2004).

Of course, there are other representation schemes for the heat equation. Many of these alternate

schemes are implicit schemes; that is, there are more than one unknown variables in each equation.

These schemes, which include the Crank-Nicolson, ADI and ADE, and Keller Box methods, typically

require the simulation to solve a series of simultaneous equations involving the unknowns (Anderson et.

al., 1984). Another more advanced algorithm for solving a two-dimensional heat transfer problem is the

hopscotch method, which is an explicit procedure that is unconditionally stable method which performs

the calculations using two sweeps through the problem domain. The main advantages to these methods

are typically smaller truncation errors than the simple explicit method, and since they are unconditionally

stable, there is no limit on the time step that can be used in the solution method. Because of these

advantages, these implicit methods are often considered more suitable than explicit methods, though that

is not to imply that a properly implemented explicit method is unable to produce accurate results.

61

In the case of this thermal simulation program, the decision was made to employ the simple explicit

scheme over a two-dimensional section of the concrete element (similar to the one-dimensional example,

outlined above). The decision to use this scheme rather than a more advanced implicit scheme was made

because in this case the interest is in obtaining and storing the solution at a variety of times so that

thermal gradients within the structure can be identified and examined as hydration progresses. Because

of this, it is relatively simple to obtain a time step that satisfies both this requirement as well as the stability

requirements of the method. The use of this method also simplifies the code required to perform the

analysis substantially, allowing for easy modification. Finally, this scheme also reduces the computational

time required, since an iterative technique is not required to solve for the temperatures at each time step.

3.2.2 Finite-Element Methods

More complex thermal analyses will often employ a finite-element procedure. The greatest advantage of a

finite-element method is an improved ability to model complex shapes (Guyer, 1999), though these

methods can also be used to deal with changes in material (i.e. heterogeneous materials), or complex,

irregular boundary conditions (Chapra and Canale, 1998). A finite-element procedure can also be used to

perform the thermal analysis and stress-strain analysis simultaneously, if a more complex element is

chosen for the analysis. However, this more detailed procedure requires a more advanced discretization

procedure to divide up the area of interest, particularly if the area of interest is being examined in three

dimensions. However, for the purpose of this simulation program, these schemes introduce a level of

complexity that is undesirable, considering that they do not offer a significant advantage over a finite-

difference method for the types of problems being considered.

3.3 Design and Implementation of the Thermal Simulation Program

The following section outlines and documents the assembly of all the models necessary into a single

comprehensive thermal simulation for predicting the concrete temperature development. The section

starts with a discussion of the various assumptions that were made to simplify the problem. Next, a

discussion of the problem setup, including the relevant boundary conditions acting on the element is

presented, followed by a description of how the finite-difference methods were used to perform the heat

flow analysis. The section concludes with a brief discussion of how the problem was implemented in

Microsoft Excel using Visual Basic for Applications.

62

3.3.1 Assumptions and Limitations

Several assumptions were made in the development of the thermal simulation in order to simplify the

scope of the program. The following sections will outline these assumptions while providing an

explanation of any limitations that may arise as a direct consequence.

3.3.1.1 Problem Geometry

For this simulation, the problem will be simulated by calculating the temperature rise for a two-

dimensional section through the element under examination. This simplification assumes that all of the

heat is lost along these two dimensions, and that no heat transfer is occurring in the third dimension; as

such, this assumption is suitable for elements that have one dimension that is significantly larger than at

least one of the other two dimensions, such as slabs and concrete pavements, columns, beams, and

rectangular footings. In reality, heat is constantly being transferred in all three dimensions in the vast

majority of cases. However, for many problems of interest, this simplification will provide good results,

provided that the section contains the least dimension of the concrete element; for example, in the case of

a column or beam, a section would be taken perpendicular to its longitudinal axis, as it is assumed that

the majority of heat will be lost through its sides, rather than the ends of the element.

3.3.1.2 Member Types

Due to the limitations of the finite difference model that will be employed in the analysis, the thermal

simulation program will only have limited ability to deal with irregular shaped member boundaries. The

finite difference scheme best lends itself to elements with rectangular cross-sections, such as beams or

columns. These methods can also accommodate sections made up of several rectangular segments,

such as an irregularly shaped footing.

In order to further simplify the discretization scheme, the thermal simulator program will be developed to

work with a set of predefined member shapes, which will aid in the development while not significantly

limiting the usefulness of the program. These predetermined templates will be created to address the

sections that are commonly of interest in these sorts of problems, including: a slab or beam on grade; a

suspended slab or beam; a column or wall section; or a mass-concrete footing.

The initial development of this thermal simulation program will include four different geometric

arrangements. Case 1 is a special case, developed to aid in the simulation concrete elements hydrating

63

under isothermal conditions. This element is modelled with four convective boundaries, and a constant

ambient temperature. The remaining three cases deal with real world situations; they include a suspended

rectangular prism with four conduction-convection boundaries; a rectangular prism on grade with three

conduction-convection boundaries and one conduction boundary; and a rectangular prism that is partially

below grade, with three conduction-convection boundaries and three conduction boundaries. These four

cases are sketched in Figure 3-3.

Figure 3-3: Sketches of the four different cases available within the thermal simulation program; all cases are discretized using a body-centred grid

64

3.3.1.3 Boundary Conditions

There are a host of different boundary conditions that may define the heat flow between a concrete

element and its environment. These external influences typically include conduction to the supporting

layers, form-work and surface coverings; convection from the surface of the concrete and from the surface

of the formwork and other coverings; solar absorption; heat loss due to the effects of evaporation of water

on the surface (either from bleeding, or water added for curing purposes); and radiation from the

concrete’s surface.

Of these boundary conditions, only conduction, convection and solar absorption will be addressed by the

thermal simulator. These three boundary conditions are being included since they are the three most

significant boundary conditions that typically act upon concrete elements case under field conditions.

Evaporation from the concrete surface is being ignored under the assumption that the concrete’s surface

is adequately protected against evaporation by surface coverings.

A few additional assumptions regarding the environmental conditions will be made in order to further

simplify the boundary conditions for modelling purposes. The ambient temperature, Ta (°C), will be

simulated by a sinusoidal distribution, according to the following formula:

( ) ( ) ( )

22/2/

2,,,, lowahigha

slowahigha

a

TTtSIN

TTT

−⋅−⋅+

+= ππ Equation 3-7

In this formula, Ta, high is the maximum daily temperature, and Ta, low is the nightly minimum (both in °C),

and ts is the current time in the form of a serial decimal.

The solar intensity factor, If, required by the solar radiation boundary equation formula (Equation 2-34)

shall also be determined using a sinusoidal distribution between sunrise and sunset, with a value of 0

otherwise. Equation 3-8 can be used to determine the value of this intensity factor.

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

−−

= πriseset

risesf tt

ttSINI trise < ts < tset Equation 3-8a

0=fI Otherwise Equation 3-8b

65

In this equation, trise is the time of sunrise, tset is the time of sunset, and ts is the current time (all as serial

decimal numbers).

The temperature of the supporting layers will be governed by two temperatures, namely the surface

temperature, TSLs, and the temperature at depth, TSLd, both in degrees Celsius. For the purposes of this

simulation, the temperature of the supporting layer will be assumed to vary linearly with depth to a depth

of 4 m, at which point the temperature will be taken as equal to TSLd.

Finally, the wind speed at the surface of the concrete will be assumed to be constant, with a value equal

to the average expected wind speed.

3.3.1.4 Limitations of the Hydration Model

As mentioned in Chapter 2, there are several fundamental limitations in the hydration model itself that

must be taken into account in the development of the hydration model. The development of the model will

be conducted in such a way as to minimise these limitations, wherever possible.

The first limitation of the hydration model is the fact that the model is only valid within the range for which

it was calibrated (2002). As such, the model is appropriate only for extrapolating within the given ranges of

cement properties, but it should not be used to extrapolate beyond these limits. Table 3-1 summarizes the

limits on the range of cement properties that have been tested and included in the model, and Table 3-2

summarizes the range of tested mixture proportions and SCM properties (these tables were first

presented in Chapter 2). The hydration model will be programmed so that it does not accept input values

that fall outside of these ranges, in order to prevent extrapolation of values. The one exception to this is

that the simulation will allow the user to extrapolate when the w/c ratio is below a value of 0.36, in order to

make allowances for HPC mixes. Though preliminary testing has indicated that this allowance is

warranted, further testing is recommended in this area.

The second limitation that stems from the use of this hydration model is the fact that the effects of

chemical admixtures cannot be accounted for. This particular limitation can be overcome through the

manual adjustment of the rate of hydration curve by the user, though this adjustment will require additional

calorimeter testing. However, due to the nature of the exponential hydration equation, this model is not

66

able to gracefully deal with an initial retardation of the hydration process – as a result of an interaction with

a chemical or mineral admixture – nor is it able to accurately model hydration curves that feature multiple

rate peaks, which are common in cementitious systems with SCMs.

Table 3-1: Range of cement properties used for calibration of the hydration model (Schindler, 2002)

C3S (%) C2S (%) C3A (%) C4AF

(%) SO3 (%) Free

CaO (%) MgO

(%) Alkalies

(%) Blaine

(m2/kg) Average 52.5 20.8 8.4 9.3 2.6 1.4 1.8 0.6 373.7 Min 20.0 9.3 3.5 5.5 1.2 0.1 0.6 0.2 289.1 Max 64.5 55.0 13.2 16.6 4.4 2.9 4.0 1.1 579.5

Table 3-2: Range of mixture proportions and SCM properties used for the calibration of the hydration model (Schindler, 2002)

w/cm Fly Ash CaO

(%) Fly Ash SiO2

(%) Fly Ash

Alkalies (%) Fly Ash

Dosage (%) GGBS Dosage

(%) Average 0.42 - - - - - Min 0.36 10.8 35.8 0.3 0.0 0.0 Max 0.54 24.3 54.1 1.4 45.0 50.0

3.3.2 Solution Method

This section will outline the solution method for the thermal simulation program, from the initial gathering

of input data and problem setup, through the finite-difference heat flow calculations and the collection and

organization of the final solution. The discussion is divided up into a series of nine steps, much in the

same way that they are divided up logically within the thermal simulation program. While no actual code

will be presented here, the steps can be viewed as a rough summary of the analysis methods and logic

utilized by the simulation program.

The coding of the thermal simulation program was initially performed using C++, though that was quickly

abandoned in favour of Microsoft’s Visual Basic for Applications, in order to minimise the amount of work

that was required in terms of the development of the user interface. This choice to use program the

application within Excel using VBA means that the program is a spreadsheet application, with various

macro functions performing the actual heat flow calculations in the background. This also meant that the

development of the program could take full advantage of the existing tools and frameworks that are

present within VBA, which greatly simplified the design process and coding of the simulation.

67

Step 1: Gather Problem Information

The first step in the thermal simulation is to gather the input data required to render a solution. The user

must first select a member type from the four available templates, and then provide the necessary input

values for the problem geometry based on the template’s requirements. The user will also be prompted

for information regarding the concrete mix design, including the materials that will be used. Other inputs

that are collected at this stage include the various environmental conditions, information about the

boundary conditions; the current date, and the projected time of casting; and finally, the time duration that

should be simulated.

At this point, the user must indicate how the cement hydration rate should be determined. By default, the

thermal simulation program will prompt the user regarding custom input data based on isothermal heat-

conduction testing. If such information is unavailable, the user will be able to decide between using input

data generated from the material database (if available) and input data generated by the theoretical

hydration model based on the cement’s chemistry. If the latter option is chosen, the user will have the

option of using the default chemistries based on the materials selected, or they can input custom values

(i.e. based on more current testing than what is available in the database).

Step 2: Perform Initial Problem Setup

The next step in the simulation involves processing and storing the input data, and then using this data to

calculate all of the other input values required for the thermal simulation. Note that several of these

variables, including the concrete’s heat capacity and thermal conductivity, are dependent on the concrete

temperature or degree of hydration, and as such these parameters and all dependent parameters must be

calculated at each time step as the simulation progresses. However, initial values for these parameters

are calculated at this point so they can be used to evaluate the stability criteria.

Finally, a value for the time step must be determined. This is done by maximizing the length of time step,

while ensuring that the various stability criteria are satisfied. In practice, this typically results in a time step

of 10 or 12 minutes, though time steps as short as one minute and as long as one hour are supported by

the simulation.

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Step 3: Initialize Problem Domain

The next step is to initialize the three arrays that will contain the temperature results throughout the

calculation. One, a two-dimensional array called daTempOld, will contain the temperature data from the

previous time step, while a second, a two-dimensional array called daTempCur, will contain the

temperature values calculated during the current time step. The third, a three dimensional array called

daTemperatureResults, will be used to record the results of the thermal simulation. During this step, these

three arrays are dynamically allotted based on the size of the problem domain in order to minimize

memory usage, and the daTempCur array is initialized with values equal to the placing temperature of the

concrete. A fourth array, called daProblemInfo, will be used to contain various time dependent values

which will be calculated as the simulation progresses, such as the average concrete temperature, the

degree of hydration, and the rate of hydration.

Step 4: Start of Iteration

At this point, the value for the current time is incremented based on the chosen time interval (the default

time interval is 10 minutes), and the current elapsed time and serial time are recorded in the

daProblemInfo array. The values from daTempCur are copied to daTempOld in preparation for the next

set of heat flow calculations. A series of loops is performed to examine the daTempOld array, in order to

find the minimum and maximum temperatures at that time step, and to calculate the average core and top

surface temperatures of the concrete. These temperatures are stored in the daProblemInfo array.

Step 5: Calculate Current Degree of Hydration and Dependent Values

The current degree of hydration is calculated based on the current equivalent time, which is calculated

using the equivalent age maturity method. This equivalent age takes into account the current average

concrete temperature, which was calculated in Step 4 based on the data from the previous time step.

Once the degree of hydration is calculated, all of the dependent values can also be determined, including

the total heat evolved, the heat capacity, and the thermal conductivity of the concrete. The rate of

hydration is calculated based on the heat evolved for the current and the previous time steps, using a

backward difference method.

At this point, the simulation calculates the current ambient temperature, as well as the value of the solar

radiation intensity factor, based on the two equations presented in Section 3.3.1.3 (Equations 3-6 and 3-

69

7). The current convection coefficient is also calculated at this point based on the average concrete

surface temperature and current ambient temperature.

Finally, the simulation calculates the dimensionless terms required for the thermal simulation (the Biot and

Fourier numbers) as well as the thermal diffusivity of the concrete.

Step 6: Calculate Temperatures at Next Time Step

During this step, the current temperatures are calculated using the finite-difference method, as outlined in

Section 3.2.1. As previously mentioned, the two-dimensional heat flow problem is solved using an explicit

finite-difference scheme. A series of looping constructs are used to calculate the current temperature at

each point in the problem domain, based on the temperatures from the previous time step, and taking into

account the appropriate boundary conditions. The temperatures in the base material are also calculated to

a depth of equivalent to ten blocks (this depth is variable, depending on the difference length chosen), in

order to model the conduction of heat from the element. The current temperature values are recorded in

the daTempCur array.

Step 7: Record Calculated Temperatures to Solution Array

Next, the calculated temperatures are recorded to the daTemperatureData array for storage. Rather than

recording all of the temperature results, the results are only recorded after each hour of elapsed time in

the simulation, in order to minimize the amount of storage space required in memory. This is

accomplished through the use of a variable that compares the current time to a target value that is

equivalent to the next even hour. If these two values match, the current results are recorded to the

daTemperatureData array; otherwise, the simulation proceeds to the next time step.

Step 8: Repeat Iterative Solution Method

The simulation steps through time by repeating Steps 4 through 7 until the time value is equal to the

desired problem duration, as indicated by the user.

Step 9: Analyze and Summarize Results

Once the simulation has completed calculating the temperature results for the duration of interest, the

simulation program plots the rate of hydration and degree of hydration curves (either as input, or as

calculated, depending on the input source). A summary of the key thermal properties, and the idealized

70

environmental conditions are also plotted for the user. The maximum internal and surface temperatures,

as well as the time of the temperature peak are also reported.

At this point, the user can select certain locations within the element that are of interest; these typically

include a point near the centre of the element, as well as a point along each of the edges, and a corner

point. The temperature vs. time curves for these select locations are then plotted for the user. These

temperature values are also recorded in one of the program worksheets, so that further analysis can be

performed by the user.

The user can also use the program to display the temperature data for the entire cross-section for a

selected temperature as a graphical representation of the structure; this data is colour coded by

temperature range. The maximum, minimum and average temperatures are also reported for this cross-

section, as well as the value of the maximum thermal gradient.

3.4 Summary

This method has outlined the methods and logic that went into the development of the thermal simulation

program. However, before any such simulation can be used in a predictive manner, it must undergo

verification through a series of field trials. The results of two of these field tests will be presented as

verification in Chapter 5.

71

Chapter 4: Test Methods

This chapter will outline the test methods used in this thesis project. All of the isothermal heat-conduction

calorimetry tests were performed using a TAM Air 2002ab unit produced by Thermometric AB.

4.1 Purpose of the Testing Program

The main purpose of this testing program is to provide independent hydration data that can be used to

verify the hydration model that was presented at length in Chapter 2. This hydration model was calibrated

using data from a series of semi-adiabatic tests performed on a variety of cements and supplementary

cementing materials (Schindler, 2002). This testing program is meant to add an additional data set which

will be used to further verify the hydration model, while at the same time expanding the range of materials

tested.

Of particular interest in this testing program are pastes with partial replacement of SCMs, due to the

variability of these supplementary materials, as well as the fact that there was a limited number of tests

performed on these mixes in the data set used to calibrate the hydration model (Schindler, 2002). Another

area of interest that will be addressed is an independent verification of the temperature sensitivities of the

different cementitious systems being tested. This can be done by calculating the apparent activation

energy, Ea, based on the results of calorimeter tests performed at different temperatures.

4.2 Method Development

Prior to the experimental program, a series of tests were performed in order to develop a consistent and

repeatable testing procedure, and to become familiar with the TAM Air unit. These initial tests focused on

developing the mixing procedures and mix proportioning.

The initial training for the TAM Air isothermal calorimeter was provided by Thermometric representative

Dr. Nathan Hesse (2005). Dr. Hesse demonstrated an in-ampoule mixing procedure that involved

measuring the mass of cement and any supplementary cementing materials in the ampoule itself. Once

the dry materials were in place and weighed, the water and any admixtures were added using a syringe,

and the mixing was performed with a long stiff plastic rod. After mixing for two minutes, the end of the inert

stir rod was cut off, to prevent any loss of material from the ampoule. However, it was discovered that this

72

method was unsuitable for mixtures with a low water-cement ratio, as the decreased workability made it

extremely difficult to ensure a consistent dispersion of the cement within the paste. Also, this method

didn’t lend itself to the use of chemical admixtures, as the resulting dosages were extremely small and

therefore extremely difficult and time consuming to measure accurately. As a result, the required

admixtures had to be diluted in the mix water ahead of time so that an accurate dosage could be ensured.

Because of these difficulties with the in-ampoule mixing method, it was decided that all samples would be

mixed externally, before placing them into the test ampoules. The external mixing procedure adopted for

this project is very similar to the method demonstrated by Paul Sandberg and Gary Knight during the

calorimetry workshop held at the University of Toronto in June 2005. A series of trials were performed to

compare differences between hand mixing (for one, two and five minutes) and mixing with an electric

hand-mixer (for one, two and five minutes). The combined results from both the hand mixing and the

electric hand-mixer showed a standard deviation of only 4.99 J/gmat, or approximately 1.7% of the average

total energy value of 291.68 J/gmat, indicating that the mixing method does not significantly influence the

final results. One possible explanation for this is that even if one mixing method imparts somewhat more

heat to the sample, this heat will be removed shortly after the sample is placed in the calorimeter, thereby

reducing any effect that the choice of mixing method would have produced.

A second set of trials was performed to examine whether or not glass ampoules should be adopted for the

testing instead of the plastic ampoules that were supplied with the TAM Air unit by Thermometric AB.

Aside from the material difference, it was discovered that the tolerances on the plastic ampoules were not

as strict as those of the glass ampoules. The plastic ampoules supplied by Thermometric were found to

have a mass of approximately 4.8 g, though this varied by as much as 10% from one ampoule to the next;

by contrast, the glass ampoules used in this study had an average mass of 13.05 g, with a standard

deviation of 0.006 g. However, when these two different types of ampoules were used to test the same

sample material, the results yielded an average total energy of 271.7 J/gmat, with a standard deviation of

only 3.43 J/gmat for all of the samples tested (four samples in plastic ampoules and two in glass). A close

examination of the hydration peak is presented in Figure 4-1.

73

3.50

3.60

3.70

3.80

3.90

4.00

4.10

4.20

6 7 8 9 10 11 12

Time [hours]

Po

wer

[mW

/gM

at]

#01-T05 LAF Bath GU 040 Glass Ampoule#02-T05 LAF Bath GU 040 Glass Ampoule#05-T12 LAF Bath GU 040 Plastic Ampoule#06-T12 LAF Bath GU 040 Plastic Ampoule#07-T12 LAF Bath GU 040 Plastic Ampoule#08-T12 LAF Bath GU 040 Plastic Ampoule

Figure 4-1: Influence of ampoule type on the TAM Air results

In this figure, it’s evident that there is slightly more variation in the results of the samples contained in the

plastic ampoules, and that these values tend to bracket the samples that were contained in glass

ampoules, though these differences are very minor. In the end, glass ampoules were chosen for this trial

because of the simple fact that they were clear, as opposed to the translucent plastic ampoules. This

allowed for easy visual inspection of the samples after charging them into the ampoules (i.e. to look for

voids on the bottom surface of the ampoule which may influence the heat conduction from the sample), as

well as inspection after the calorimetry testing was completed.

4.3 Final Mixing Procedure

Based on the results of the early test trials, it was decided that the mixing would be performed using an

electric hand-held mixer for a duration of two minutes. This decision was made to keep the procedure

roughly similar to that of ASTM C186 (which requires five minutes of external, mechanical mixing), while

fixing the mixing offset at a total of five minutes. This decision was also made because the hand-held

74

mixer would be able to produce more consistent results from day to day and for different operators,

compared to hand mixing. The final mixing procedures adopted for this thesis project were in compliance

with the draft ASTM standard test method for measurement of heat of hydration of cement with heat

conduction calorimetry (Appendix C).

4.4 Materials

The materials for this thesis project were chosen based on their availability and common usage in the

Ontario market. A total of six CSA type GU cements from four companies were tested. In addition, ten

supplementary cementing materials (six slag cements and four fly ashes), were also included in the

experimental program at replacement levels of 10, 20% and 50% (for select combinations only). In order

to limit the number of material combinations, it was decided that only cements and supplementary

cementing materials from the same supplier would be tested together. In practice, there may be instances

where materials from different suppliers are used together, but these cases tend to be special cases.

Tables 4-1 through 4-4 outline the various combinations that were tested for this project. Note that all

materials were stored in airtight containers in the laboratory at a constant temperature of 23 ± 2°C in order

to pre-condition them prior to testing.

Table 4-1: Testing program summary, materials supplied by Essroc Italcementi Group

Material Neat Cement1 w. Essroc GGBS w. Essroc

Fly Ash Picton GU 10 and 20% 10 and 20%

Table 4-2: Testing program summary, materials supplied by Lafarge North America

Material Neat Cement1 w. Stoney Creek

GGBS w. Atikokan

Fly Ash w. Hatfield

Fly Ash Bath GU 10, 20 and 50% 10 and 20% 10 and 20%

Woodstock GU 10, 20 and 50% 10, 20 and 50% 10 and 20%

Table 4-3: Testing program summary, materials supplied by St. Lawrence Cement Inc.

Material Neat Cement1 w. Sault Ste. Marie

GGBS Mississauga GU 10, 20 and 50%

Table 4-4: Testing program summary, materials supplied by St. Marys Cement Group

Material Neat Cement1 w. Cemplus GGBS w. St. Marys Fly

Ash Bowmanville GU 10 and 20% 10 and 20% St. Marys GU 10 and 20% 10 and 20% 1 Note that a single check-mark indicates that the cement was tested for a duration of seven days at 23°C, while a pair of check-marks indicates that the material was additionally tested at 10 and 35°C. All of the blended systems were tested for a duration of three days.

75

The required chemistry information for the thermal simulation was provided by the cement suppliers. This

chemistry data is the result of regular production testing, and as such it is based on samples taken during

a particular production window. It’s important to note that the results from these tests may result in

chemistries that are slightly different from the samples themselves due to the nature of the sampling that

is typically performed, but for this project it was assumed that the provided chemistries are accurate. Also,

it should be noted that the chemical composition of the different cements have some variability and plant

targets may change over time; this means that while the results from this testing program are being used

in a predictive manner, one should not assume that current materials will perform exactly as indicated by

these trials, due to variations in the chemistry, fineness, etc. The chemistry information provided is

summarized in Appendix A.

4.5 Paste Mix Parameters

The paste for the mixes was produced in large batches of approximately 210 g in order to minimize any

errors that may be introduced when weighing out smaller amounts of materials, and to mimic the batch

requirements set out in ASTM C186. These batches were comprised of 150.0 g of cementitious material

and 60.0 g of water, for a resulting water-cement ratio of 0.4.

Once mixed, the samples were placed into glass ampoules, and the masses recorded. A target sample

mass of 7 g was used, based on a recommendation from Dr. Hesse of Thermometric AB (2005). This

recommendation is based on the limits of the heat sink and temperature control units within the

instrument, in order to ensure that the test conditions remain as close to isothermal as possible. A plastic

10 mL syringe with the end cut off was used to dispense the paste; approximately 4 mL of paste was

required to deliver a sample size close to 7 g; in practice, the samples ranged from 6.5 – 7.5 g using this

method. The syringe was found to be the best method of placing the sample into the ampoule because it

was able to consistently place the entire sample at the bottom of the ampoule, without having parts of the

sample on the side walls and lip of the vessels.

4.6 Isothermal Calorimetry Method

Once the samples were placed in the ampoules, they were transferred to the TAM Air unit and placed

within one of the testing chambers. All of the pastes tests were performed in duplicate, in order to

minimize non-repeatable errors.

76

For simplicity, all of the reference channels were pre-filled with samples consisting of 20 g of silica sand,

which has approximately the same heat capacity as the paste mixtures. During the mixing trials it was

observed that differences in the heat capacities of the reference and test samples did not produce a

significant error in the final results. This procedure of using a constant reference sample has the

advantage of speeding up the test procedure, though it negates the potential advantage of having the test

and reference sample equilibrate simultaneously, which can serve to reduce the noise at early ages

(Thermometric AB, 2004). As a result, the first thirty minutes of test data is ignored in the analysis of the

calorimeter data. Once in the calorimeter, samples were tested for a period of either 72 or 168 hours (3 or

7 days). At the end of testing, results were collected from the logger and stored for later analysis, which is

presented in the next chapter.

4.7 Summary

This chapter has outlined the various methods that were followed in this experimental program. The

following chapter will discuss the results of this experimental program, including the results of using these

TAM Air results as inputs for the thermal simulation program, which was developed in Chapter 3.

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Chapter 5: Experimental Results and Case Studies

This chapter will present the results of the experimental trials performed as a part of this thesis project.

This chapter will be divided into two parts; Section 5.1 will focus on the results from the isothermal heat-

conduction calorimetry, while Section 5.2 will focus on the results of two different field trials that were

documented during the course of this thesis project.

5.1 Isothermal Calorimetry Results

This section will present the results from the isothermal heat-conduction calorimetry tests, which were

performed during the second half of 2005 and the early part of 2006. All of the tests were performed

according to the methods outlined in Chapter 4.

The results will be presented in groups, based on the cement type and the inclusion of supplementary

cementing materials. First, the results from the testing of the neat GU cements will be presented in

Section 5.1.1, followed by the cement-slag and cement-fly ash combinations in Sections 5.1.2 and 5.1.3

respectively.

It is important to note that while these calorimetry results are being used as input values for the thermal

simulation, they are in reality a snapshot of the material’s performance at a specific point in time. This is

due to the fact that the chemistries and finenesses of the various materials do vary to a certain extent, due

in part to the demands of the manufacturing process, which requires constant adjustment based on the

variability of the input materials. As such, these results may not be fully representative of the relative

performance levels of these materials at the time of writing.

5.1.1 Neat Portland Cements (Type GU)

The first results that will be presented are those of the six neat Type GU Portland cements that were

included in the testing program. These six materials included one cement manufactured by Essroc

Italcementi, two from Lafarge North America, one from St. Lawrence Cement, and two from St. Marys

Cement. As mentioned previously, each of these neat Portland cements were tested for seven days at a

temperature of 23°C using the TAM Air calorimeter. Additionally, a minimum of two samples were tested

for each cement in order to ensure that the results obtained were repeatable and representative of the

cement’s actual performance.

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Essroc (Picton)Lafarge (Bath)Lafarge (Woodstock)St. Lawrence (Mississauga)St. Marys (Bowmanville)St. Marys (St. Marys)

Figure 5-1: Plot of the rate of hydration (power) vs. time curves for the six neat GU cements; measured at 23°C

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Figure 5-2: Detail of the main hydration peak of the neat GU cements, power vs. time; measured at 23°C

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Figure 5-1 shows a plot of the power versus time results that were obtained from this testing. The first

thing that is apparent in this plot is that the repeatability of the testing is quite good. Each of the different

cements was tested a minimum of two times, and when plotted the results from the two different runs are

virtually superimposed. The one exception to this was the Lafarge Woodstock GU, for which two

additional calorimeter tests were performed; this was required because the difference between the

calculated total heat results from the first two runs performed was found to be approximately 3.2%. Figure

5-2 shows that despite these additional tests, there is still some difference in the two results obtained for

the Lafarge Woodstock GU cement, which manifests itself as a slight time shift in the power versus time

curve. The precise reason for this difference is not known, though it could result from a slight non-

uniformity of the cement sample itself, though blending of the cement sample was performed before

batching. An error in the execution of the test method itself may also be responsible for this error, though

considering the good results obtained for all the other materials this is considered unlikely.

A second observation based on Figures 5-1 and 5-2 is that the rates of hydration for all of the six neat GU

cements are roughly similar. The main hydration peak for these six cements occurs at approximately 6 to

8 hours after the addition of water, and has a value ranging from 3.6 to 4.3 mW/gmat. A closer examination

of these various rate curves shows that they can be roughly divided into two different groups; this detail of

the hydration rate curves is shown in Figure 5-2. The first group, with a hydration peak of between 4 and

4.3 mW/gmat includes the Essroc (Picton), Lafarge (Bath), St. Lawrence (Mississauga) and St. Marys (St.

Marys) cements. The second group, comprised of the Lafarge (Woodstock) and the St. Marys

(Bowmanville) cements has a somewhat lower hydration peak of 3.5 – 3.6 mW/gmat. These peak values,

hydration rates, and peak times are summarized in Table 5-1.

Table 5-1: Summary of the peak hydration rates and peak times for the six GU cements, based on isothermal calorimetry at 23°C Cement Qpeak, mW/gmat tpeak, h Essroc (Picton) 4.32 7.22 Lafarge (Bath) 4.01 7.67 Lafarge (Woodstock) 3.56 8.99 St. Lawrence (Mississauga) 4.18 6.79 St. Marys (Bowmanville) 3.62 7.81 St. Marys (St. Marys) 4.32 6.48

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Table 5-2: Summary of isothermal calorimetry results for the six neat GU cements, measured at 23°C Cement H72, J/gmat H168, J/gmat Hcem, J/gmat Essroc (Picton) 294.7 323.8 460.5 Lafarge (Bath) 267.8 293.3 464.9 Lafarge (Woodstock) 289.0 322.2 486.4 St. Lawrence (Mississauga) 296.2 324.8 488.6 St. Marys (Bowmanville) 297.5 337.7 475.3 St. Marys (St. Marys) 269.5 307.6 475.0

Next, the values for the total heat evolved after 72 and 168 hours (H72 and H168 respectively; J/gmat) were

calculated from the calorimetry data. These values are summarized in Table 5-2, along with the total heat

of hydration values (Hcem, J/g) that were calculated using Equation 2-3. These total heat calculations were

performed using the Solidus IsoCal report generator, which integrated the power versus time curve from

an offset of thirty minutes after mixing to the end time of the test; this calculation method is in agreement

with the draft ASTM standard for a standard test method for heat conduction calorimetry. Note that these

calculated values are somewhat different than the energy values calculated by the TAM Air software; this

is because the values output directly by the calorimeter software do not include this time offset (i.e. they

include all of the data from the moment the sample is charged in the calorimeter). The total heat at 72

hours (H72) shown in Table 5-2 is an average of the two 72-hour calorimeter runs as well as the total heat

at 72 hours as calculated from the 168-hour test.

These results are interesting, because they tell us that the H72 or H168 values alone can not be used to

extrapolate the total heat (Hcem) value for a given cement. This is evident from the fact that the cement

with the highest calculated total heat release is the St. Lawrence (Mississauga) cement (Hcem = 488.6

J/gmat), though the H72 and H168 values rank this cement second in terms of heat evolution behind the St.

Marys (Bowmanville) GU at both ages. Similarly, the Essroc (Picton) GU had the lowest calculated value

for Hcem at 460.5 J/gmat, while the calorimetry results showed that this cement was in the top half in terms

of its H72 and H168 values.

There are two potential explanations for this result. Firstly, the calculated values for the total heat of

hydration, Hcem, may not be entirely accurate. This inaccuracy would stem from the fact that the total heat

of hydration calculation requires the cement’s Bogue composition as an input, despite the fact that Bogue

estimates are known not to be accurate. This is due to the fact that direct component determination by x-

81

ray diffraction (XRD) or microscopy methods are not commonly available for the materials of interest.

Instead, this Bogue composition is calculated using a set of equations, based on the cement’s oxide

composition, as shown in Section 2.1.3. This however can be a source of error, because the Bogue

equations typically underestimate the C3S and overestimate C2S present in the cement, due to the fact

that pure C3S does not exist in cements (Neville, 1995).

A second explanation would be that a prediction of Hcem based solely on the H72 or H168 value would have

to include an assumption regarding the degree of hydration at 72 or 168 hours respectively. In reality, the

samples are hydrating at differing rates at early ages, due to the fact that the rate of hydration is a function

of both the curing temperature (i.e. the equivalent curing time) and the cement chemical composition and

fineness; for example, a sample that hydrates particularly quickly during the first 72 hours may be

eventually surpassed by another sample that hydrates at a more consistent rate throughout the first 168

hours. This fact makes it difficult to extrapolate the hydration information for different cements and

cementitious systems, because each system hydrates differently from the rest. Of course, it’s probable

that the dissimilarity between the H72, H168 and the Hcem values for a given cement is due to the

combination of these two explanations.

Figure 5-3 shows the energy versus time plots for the six neat GU cements. The degree of hydration

versus time was calculated next, using the energy versus time results output from the TAM Air unit. This

calculation was performed under the assumption that the value for Hcem calculated using Equation 2-3 was

reasonably accurate for all of the cements; ideally, the value for Hcem should be determined using

experimental methods. Based on this assumption, the degree of hydration at any moment is simply the

heat evolved to that point divided by the total heat of hydration, as outlined in Equation 2-9. The results of

this calculation are plotted in Figure 5-4. The shapes of these curves are identical to the plots of the

energy versus time, but because of the different values for Hcem, the ordering of the cements has changed

in this figure.

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St. Marys (St. Marys)

Figure 5-3: Plot of the heat evolved (energy) vs. time for the six neat GU cements; measured at 23°C

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Figure 5-4: Plot of the degree of hydration vs. time for the six neat GU cements; measured at 23°C

83

Table 5-3: Degree of hydration at 72 and 168 hours for the six neat GU cements, based on isothermal calorimetry at 23°C Cement α72 α168 αu Essroc (Picton) 0.640 0.703 0.694 Lafarge (Bath) 0.576 0.631 0.694 Lafarge (Woodstock) 0.594 0.662 0.694 St. Lawrence (Mississauga) 0.606 0.665 0.694 St. Marys (Bowmanville) 0.626 0.710 0.694 St. Marys (St. Marys) 0.567 0.648 0.694

Table 5-3 provides a summary of the degree of hydration for the neat GU cements at 72 and 168 hours.

Note that in some cases, the measured degree of hydration at 168 hours is greater than the theoretical

maximum, which was determined using Equation 2-10 (Section 2.2.1). There are two potential

explanations: firstly, Mills’ formula for the ultimate degree of hydration was developed using materials

from the 1960s, which means that the model may not hold for currently available cements that are

significantly higher in C3S, and secondly, these degree of hydration values were determined based on the

assumption that the values for Hcem were accurate, when in reality these values are probably slightly in

error for the reasons outlined above.

In addition to this testing at 23°C, four of these cements – namely the Essroc (Picton), Lafarge

(Woodstock), St. Lawrence (Mississauga) and the St. Marys (St. Marys) – were also tested at 10 and 35°C

for a period of seven days. This additional testing was done so that the values for the apparent activation

energy (Ea, J/mol) could be calculated as outlined in Section 2.2.3.

The calorimetry results for the Essroc (Picton) GU are presented as a plot of power versus time in Figure

5-5. The results for all three temperatures are presented on the same plot so that comparisons can be

made. Also shown in this figure are the results of three isothermal simulations, which were performed

using the thermal simulation program developed in Chapter 3; there will be more discussion about these

three simulated curves, which are plotted in grey alongside the calorimeter results. Note that remainder of

the discussion that follows will focus on the calorimetry results for the Essroc (Picton) GU cement.

However, many of these comments are also applicable to the results for the other three cements tested at

10, 23 and 35°C; the results for these three series of tests are presented in Appendix B.

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Figure 5-5: Plot of the power vs. time for the Essroc GU (Picton) cement; measured at 10, 23 and 35°C

As mentioned, there are a series of simulated isothermal curves shown in Figure 5-5. These curves,

corresponding to temperatures of 10, 23 and 35°C were produced using the thermal simulation program.

This simulation was performed on a very small concrete element (50 mm x 50 mm) with a high convection

coefficient applied to the boundaries in order to roughly approximate the conditions inside the isothermal

calorimeter. Because of the size of the element, a short time step of six minutes was required to satisfy

stability criteria. After the simulation was performed, the temperature versus time plots were examined to

ensure that the simulated temperature did not deviate more than 2°C from the isothermal curing

temperature being simulated (in reality, this only applied for the 35°C run, as the other two simulations

had only a very slight temperature rise). For these simulations, the hydration time and slope parameters,

and the ultimate degree of hydration were all calculated using the methods outlined in Chapter 2, based

on the cement’s chemistry.

85

The first observation that one can make when looking at Figure 5-5 is that testing samples at an increased

temperature will produce a greater hydration peak than samples tested at a lower temperature. The 35°C

test produced a peak hydration rate approximately double that of the test performed at 23°C. This peak

also occurs earlier at higher temperatures, and later at lower temperatures. Of course, these results are

precisely what one would expect, based on the understanding that the rate of hydration is temperature

dependent.

A second observation regarding Figure 5-5 is that the simulated isothermal curves (plotted in grey) are

similar to the measured results. These curves are not perfect, in that both the magnitude and the timing of

the hydration rate peak are slightly off, but they are at least similar enough to be recognizable. However,

these simulated curves demonstrate that there is room for improvement regarding the hydration

parameters for the Essroc (Picton) GU cement. This result holds for all of the other cements, though in the

case of the Lafarge (Woodstock) and St. Marys (St. Marys) cements, the simulation does a much better

job at predicting the magnitude of the rate peak, as well as the time at which it occurs.

The curves for the degree of hydration versus time measured at the three temperatures are shown in

Figure 5-6. Again, these curves are plotted alongside the simulated isothermal curves, which are shown in

grey. This plot shows that the sample tested at 35°C has reached the maximum degree of hydration that

is measurable by the calorimeter, and that it reaches this degree of hydration somewhere between 120

and 132 hours after the start of testing. In reality, this sample is likely still hydrating, but at a rate so small

that the power from the reaction cannot be separated from the baseline noise of the unit. Note also that

the sample tested at 23°C is rapidly approaching this maximum degree of hydration value. A second

observation based on this figure is that the thermal simulation model is underestimating the degree of

hydration achieved at later ages. In addition, this underestimation of the degree of hydration seems to be

somewhat worse for the isothermal simulations performed at lower temperatures. These observations

hold true for all four of the cements included in this testing at a range of temperatures.

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Figure 5-6: Plot of the degree of hydration vs. time for the Essroc GU (Picton) cement; measured at 10, 23 and 35°C

One of the main purposes for performing the isothermal tests at multiple temperatures was to enable the

calculation of the apparent activation energy, Ea, as outlined in Section 2.2.3. This apparent activation

energy was determined at two different points, corresponding to a degree of hydration of 0.250 and 0.370.

The results of these calculations for all four of the cements tested at multiple temperatures are presented

in Table 5-4. Note that, for these results, the assumption regarding the accuracy of Hcem is irrelevant,

since this term cancels out during the calculation; this means that these values are accurate as-is, without

any need for additional information or testing.

Table 5-4: Calculated versus theoretical values for the apparent activation energy, calculated from isothermal calorimetry results at three temperatures Cement Ea, model, J/mol Ea, α = 0.250, J/mol Ea, α = 0.370, J/mol Essroc (Picton) 49110 44790 48700 Lafarge (Woodstock) 46580 49970 46200 St. Lawrence (Mississauga) 47948 47900 49740 St. Marys (St. Marys) 43875 46810 52570

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In general, these calculated activation energies corresponding to a degree of hydration of 0.370 are in

very close agreement with all of the theoretical values, with the exception of the value calculated for the

St. Marys (St. Marys) GU cement, which differed by 20%. By contrast, the values calculated at a degree of

hydration of 0.250 tend to vary quite a bit from the calculated values, by as much as ±10%. Based on

these results, and D’Aloia’s recommendation (2003) that the apparent activation energy be calculated

after a period of at least 24 hours, this project will use the apparent activation energy calculated at a

degree of hydration of 0.370 for all future calculations.

Ideally, the testing program would have included calorimetry testing at multiple temperatures for all of the

materials and material combinations included. However, changes made to the set temperature of the

calorimeter required a lengthy stabilization period of approximately 8-12 hours when increasing the

temperature, and of up to 48 hours when decreasing the set temperature. Ultimately, due to demand for

the TAM Air apparatus, and the fact that other researchers were only running tests at 23°C, there was

only a limited period during which tests at additional temperatures could be performed.

The next plot, Figure 5-7, shows the degree of hydration of the Essroc (Picton) GU plotted versus the

effective time, which was calculated using the maturity function given in Equation 2-16, and the newly

calculated apparent activation energy values. Though the three plots at the different temperatures do not

line up perfectly, this plot does show that the extent of the hydration process itself is not temperature

dependent within the measured range; rather, it is the rate of the reaction that is temperature dependent.

This result seems to confirm the modelling approach of predicting the degree of hydration based on the

effective time.

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Figure 5-7: Plot of the degree of hydration vs. effective time for the Essroc GU (Picton) cement; effective time

calculated using the experimental value for Ea; measured at 10, 23 and 35°C

5.1.2 GU Cements with Ground-Granulated Blast-furnace Slag

This experimental program included a series of pastes where the cement had been partially replaced by

ground granulated blast-furnace slag. A total of four CSA class S slags were including in the program;

these materials included one slag each from Essroc (Nanticoke, ON), Lafarge (Stoney Creek, ON; sold as

Newcem slag), St. Lawrence (Grancem), and St. Marys’ (Cemplus). These four materials resulted in six

material pairs, as only materials from the same company were tested together.

To focus the discussion, the results for the Lafarge (Bath) GU cement with partial replacement by Stoney

Creek GGBS will be presented in this section; this pair was tested at replacement levels of 10, 20 and

50%. However, many of the comments made here are also applicable to the other cement-slag systems;

as previously mentioned all of the calorimetry results are presented in Appendix B.

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Figure 5-8: Plot of power vs. time for the Lafarge GU (Bath) cement with varying levels of partial replacement with

Stoney Creek GGBS (class S); measured at 23°C

Figure 5-8 is a plot of the power versus time for this material pair at the three different replacement levels.

The key observation from this Figure is that replacement with GGBS causes a reduction in the main

hydration peak that occurs during the acceleration phase of the hydration process, and that this reduction

is roughly proportional to the replacement level used. This reduction is roughly equal to 90% of the

replacement level for this blended system; in general it ranged from 70 – 90% of the replacement level for

the material combinations tested. This result indicates that the slag cement is indeed contributing to the

reaction at this stage, albeit in a minor capacity, which is understandable considering that many slag

cements are latently hydraulic in nature.

The shape of the hydration curve and the time to the second hydration peak are more or less unchanged

compared to the neat cement at the lower replacement levels (10 and 20%); that is, there is no retardation

of the reaction caused by the slag. Even at a replacement level of 50% there is no significant delay of the

hydration peak, though the hydration peak is significantly reduced and flattened (i.e. is spread over a

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greater amount of time) at this level of replacement; this particular result is unique among the cement-slag

pairings tested, as in general there is some slight delay of the main hydration peak at slag replacement

levels of 50%. Table 5-5 summarizes the power level for the second hydration peak (Ppeak, mW/gmat) and

the time at which this occurs (tpeak) for this material pair, as well as for the other cement and slag pairings.

The two columns labelled “difference” list the relative change of the slag-cement combination as

compared to the neat GU cement.

Table 5-5: Effect of partial GGBS replacement on the peak hydration rate and peak time at various levels of replacement; tested at 23°C

Cement GGBS pGGBS Ppeak,

mW/gmat Difference tpeak, h Difference Essroc (Picton) Nanticoke 10% 4.03 -6.8% 7.14 4.1% Essroc (Picton) Nanticoke 20% 3.67 -15.0% 7.46 4.5% Lafarge (Bath) Stoney Creek 10% 3.65 -9.1% 7.58 -1.2% Lafarge (Bath) Stoney Creek 20% 3.32 -17.2% 7.52 -2.0% Lafarge (Bath) Stoney Creek 50% 2.12 -47.1% 7.74 0.9% Lafarge (Woodstock) Stoney Creek 10% 3.29 -8.1% 8.79 1.5% Lafarge (Woodstock) Stoney Creek 20% 2.98 -16.8% 8.79 1.5% Lafarge (Woodstock) Stoney Creek 50% 1.90 -46.9% 9.28 7.2% St. Lawrence (Mississauga) Grancem 10% 3.86 -7.6% 6.75 -0.2% St. Lawrence (Mississauga) Grancem 20% 3.53 -15.5% 6.78 0.3% St. Lawrence (Mississauga) Grancem 50% 2.11 -49.5% 7.48 10.5% St. Marys (Bowmanville) Cemplus 10% 3.36 -7.3% 7.77 -1.0% St. Marys (Bowmanville) Cemplus 20% 3.11 -14.2% 7.79 -0.8% St. Marys (St. Marys) Cemplus 10% 3.96 -8.3% 6.53 1.2% St. Marys (St. Marys) Cemplus 20% 3.60 -16.7% 6.47 0.2%

Figure 5-9 shows the plot of the total heat evolved versus time for the Lafarge GU cement with three

different levels of slag replacement, and Figure 5-10 shows the plot of the degree of hydration versus time

for this slag-cement system. These results were based on the calculated values for the total heat of

hydration (Hu, J/gmat), as outlined in Section 2.1.3. Once again it should be noted that the assumption that

this calculated total heat is correct is a potential source of error, particularly since there are very few

published values for the total heat of hydration of slag cements (HGGBS; J/g).

The plots of energy versus time and the degree of hydration versus time show that there is a slight

reduction in the amount of heat evolved and the degree of hydration achieved after 72 hours for this

material combination. At lower replacement levels, this reduction is very minor, though it does increase

somewhat as the slag replacement level is increased. At very low replacement levels of 10%, there is no

significant reduction in the degree of hydration at 72 hours.

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Figure 5-9: Plot of the total heat evolved vs. time for the Lafarge GU (Bath) cement with varying levels of partial

replacement with Stoney Creek GGBS; measured at 23°C

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Figure 5-10: Plot of the degree of hydration vs. time for the Lafarge GU (Bath) cement with varying levels of partial

replacement with Stoney Creek GGBS (class S); measured at 23°C

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Table 5-6 summarizes the values for the heat evolved at 72 hours (H72) as well as the corresponding

degree of hydration, both for this material combination and the others tested in this experimental program.

Once again, the two columns labelled “difference” are listing the relative change of the slag-cement

combination as compared to the H72 and α72 results for the neat GU cement. These results show that in

general there is only a minor reduction in the total heat evolved at 72 hours for the lower replacement

levels; this typically ranges from 0 to 6% for replacement levels up to 20%.


Cement GGBS pGGBS Hu, J/gmat H72,

J/gmat Difference α72 Difference Essroc (Picton) Nanticoke 10% 460.6 288.4 -2.1% 0.626 -2.2% Essroc (Picton) Nanticoke 20% 460.6 276.9 -6.0% 0.601 -6.1% Lafarge (Bath) Stoney Creek 10% 464.5 260.1 -2.9% 0.560 -2.8% Lafarge (Bath) Stoney Creek 20% 464.1 253.5 -5.3% 0.546 -5.2% Lafarge (Bath) Stoney Creek 50% 463.0 192.4 -28.2% 0.416 -27.9% Lafarge (Woodstock) Stoney Creek 10% 483.9 288.5 -0.2% 0.596 0.4% Lafarge (Woodstock) Stoney Creek 20% 481.3 271.0 -6.2% 0.563 -5.2% Lafarge (Woodstock) Stoney Creek 50% 473.7 196.2 -32.1% 0.414 -30.3% St. Lawrence (Mississauga) Grancem 10% 485.8 288.5 -2.6% 0.594 -2.0% St. Lawrence (Mississauga) Grancem 20% 483.1 282.0 -4.6% 0.584 -3.7% St. Lawrence (Mississauga) Grancem 50% 474.8 211.5 -28.6% 0.446 -26.5% St. Marys (Bowmanville) Cemplus 10% 473.9 288.4 -3.1% 0.609 -2.8% St. Marys (Bowmanville) Cemplus 20% 472.4 282.9 -4.9% 0.599 -4.3% St. Marys (St. Marys) Cemplus 10% 473.6 265.3 -1.6% 0.560 -1.3% St. Marys (St. Marys) Cemplus 20% 472.2 251.6 -6.6% 0.533 -6.1%

5.1.3 GU Cements with Fly Ash

This experimental program also included a series of pastes featuring partial replacement of the Portland

cement by fly ash. A total of four different fly ashes from four different suppliers were tested. These

materials included a class CH fly ash independently supplied by both Essroc and St. Marys (Baldwin, IL),

a class CI ash from Lafarge (Atikokan GS, ON) and finally a class F fly ash from Lafarge (Hatfield Station,

Masontown, PA). These four materials resulted in seven pairings, as only materials from the same

company were tested together.

To focus the discussion, the results for three of the parings will be presented in this section. These

pairings will include the St. Marys (St. Marys) GU plus Baldwin fly ash (CH); the Lafarge (Woodstock) GU

plus Atikokan fly ash (CI); and finally the Lafarge (Woodstock) GU plus Hatfield fly ash (F). The remaining

calorimetry data are presented in Appendix B.

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The power versus time plot for the three cement and fly ash pairs are presented in Figures 5-11 to 5-13.

These plots show that partial replacement by fly ash gives the same sort of reduction in the peak

hydration rate as partial replacement with GGBS at low replacement levels. However, unlike partial

replacement with slag cement, the reduction in the hydration rate is typically equal to 90-100% of the

replacement level, indicating that the fly ash is not reacting at this point in time. In some cases, such as

that of the St. Marys (St. Marys) GU plus Baldwin fly ash, this reduction in the peak hydration rate can

exceed the replacement level, indicating that for some combinations the fly ash is impeding the cement’s

hydration slightly.

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Figure 5-11: Plot of power vs. time for the St. Marys GU (St. Marys) with varying levels of partial replacement with

Baldwin fly ash (class CH); measured at 23°C

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Figure 5-12: Plot of power vs. time for the Lafarge GU (Woodstock) cement with varying levels of partial replacement

with Atikokan fly ash (class CI); measured at 23°C

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Figure 5-13: Plot of power vs. time for the Lafarge GU (Woodstock) cement with varying levels of partial replacement

with Hatfield fly ash (class F); measured at 23°C

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Another difference between the fly ash and slag replacement is the fact that partial replacement with fly

ash causes a retardation in the time to the peak hydration rate for almost all of the samples tested, even

at low replacement levels. Further, this time delay seems to be directly proportional to the replacement

level for levels up to about 20%, though it increases sharply at higher replacement levels. Like the partial

slag replacement, the addition of fly ash does not alter the shape of the hydration curve at lower

replacement levels.

The peak hydration rates and the times at which these peaks occur are summarized in Table 5-7 for all of

the material combinations involving fly ash that were tested in this experimental program. Once again, the

“difference” columns are comparing the results of fly ash replacement to that of the neat GU cement.

Table 5-7: Effect of partial fly ash replacement on the peak hydration rate and peak time at various levels of replacement; tested at 23°C

Cement GGBS (Class) pGGBS

Ppeak, mW/gmat Difference tpeak, h Difference

Essroc (Picton) Baldwin (CH) 10% 3.89 -10.1% 8.20 14.8% Essroc (Picton) Baldwin (CH) 20% 3.46 -19.9% 9.38 31.4% Lafarge (Bath) Atikokan (CI) 10% 3.67 -8.6% 7.94 3.4% Lafarge (Bath) Atikokan (CI) 20% 3.31 -17.6% 8.16 6.4% Lafarge (Bath) Hatfield (F) 10% 3.63 -9.5% 7.65 -0.3% Lafarge (Bath) Hatfield (F) 20% 3.23 -19.6% 7.83 2.0% Lafarge (Woodstock) Atikokan (CI) 10% 3.26 -9.1% 9.22 6.5% Lafarge (Woodstock) Atikokan (CI) 20% 2.98 -16.9% 9.80 13.1% Lafarge (Woodstock) Atikokan (CI) 50% 2.08 -41.9% 15.05 73.7% Lafarge (Bath) Hatfield (F) 10% 3.24 -9.5% 8.99 3.8% Lafarge (Bath) Hatfield (F) 20% 2.91 -18.7% 9.37 8.1% St. Marys (Bowmanville) Baldwin (CH) 10% 3.29 -9.1% 8.94 13.9% St. Marys (Bowmanville) Baldwin (CH) 20% 2.96 -18.2% 10.27 30.8% St. Marys (St. Marys) Baldwin (CH) 10% 3.83 -11.5% 7.17 11.2% St. Marys (St. Marys) Baldwin (CH) 20% 3.39 -21.6% 8.03 24.5%

The plots of the total heat evolved for the three cement plus fly ash systems are presented in Figures 5-14

through 5-16. These figures all show that there is a corresponding reduction in the total heat evolved that

remains fairly consistent throughout the 72 hours of testing. However, like the slag cement, this reduction

in the total heat at 72 hours is significantly less than the replacement level; for the materials tested, it is

typically in the range of 1 to 2% for replacement levels of 10%, and 5 to 10% for replacement levels of

20%. Also, these results show that there was slightly less heat released by the material pairings involving

class CI and class F fly ashes. These results are consistent with the test results that have been observed

by other researchers (Schindler and Folliard, 2003; Langan et. al, 2002).

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Figure 5-14: Plot of the total heat evolved vs. time for the St. Marys GU (St. Marys) with varying levels of partial

replacement with Baldwin fly ash (class CH); measured at 23°C

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Figure 5-15: Plot of the total heat evolved vs. time for the Lafarge GU (Woodstock) cement with varying levels of

partial replacement with Atikokan fly ash (class CI); measured at 23°C

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Figure 5-16: Plot of the total heat evolved vs. time for the Lafarge GU (Woodstock) cement with varying levels of

partial replacement with Hatfield fly ash (class F); measured at 23°C

The only combination tested at 50% replacement was the Lafarge (Woodstock) GU with Atikokan fly ash

(CI), and this pairing showed a 33.4% reduction in the H72 value. Table 5-8 summarizes all of the H72

values for the materials tested in this experimental program; once again, the difference values are relative

to the results for the neat Portland cements.

Figures 5-17 through 5-19 are plots of the degree of hydration versus time for the three combinations

under consideration. These curves were produced based on the total energy curves, and the

determination of the paste’s Hu value, based on Equations 2-3 and 2-4, as well Schindler and Folliard’s

recommendation to use a value for HFA equivalent to CaOFAp⋅1800 (2003); the degree of hydration was

then calculated using Equation 2-9.

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Figure 5-17: Plot of the degree of hydration vs. time for the St. Marys GU (St. Marys) cement with varying levels of

partial replacement with Baldwin fly ash (class CH); measured at 23°C

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Figure 5-18: Plot of the degree of hydration vs. time for the Lafarge GU (Woodstock) cement with varying levels of

partial replacement with Atikokan fly ash (class CI); measured at 23°C

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Figure 5-19: Plot of the degree of hydration vs. time for the Lafarge GU (Woodstock) cement with varying levels of

partial replacement with Hatfield fly ash (class F); measured at 23°C

Table 5-8 summarizes the values for Hu (J/g), H72 (J/g) and α72 for all of the cement and fly ash

combinations tested. As before, the columns marked “difference” are highlighting the results of the

cement-fly ash combination relative to the neat GU cement.


Cement GGBS pGGBS Hu, J/gmat H72,

J/gmat Difference α72 Difference Essroc (Picton) Baldwin (CH) 10% 485.2 290.5 -1.4% 0.599 -6.4% Essroc (Picton) Baldwin (CH) 20% 509.9 284.0 -3.6% 0.557 -13.0% Lafarge (Bath) Atikokan (CI) 10% 445.4 262.2 -2.1% 0.589 2.2% Lafarge (Bath) Atikokan (CI) 20% 425.9 246.6 -8.0% 0.579 0.5% Lafarge (Bath) Hatfield (F) 10% 432.8 262.7 -1.9% 0.607 5.4% Lafarge (Bath) Hatfield (F) 20% 400.7 246.6 -7.9% 0.615 6.8% Lafarge (Woodstock) Atikokan (CI) 10% 464.8 283.1 -2.0% 0.609 2.5% Lafarge (Woodstock) Atikokan (CI) 20% 443.1 261.0 -9.7% 0.589 -0.9% Lafarge (Woodstock) Atikokan (CI) 50% 378.2 192.6 -33.4% 0.509 -14.3% Lafarge (Woodstock) Hatfield (F) 10% 452.2 283.1 -2.0% 0.626 5.4% Lafarge (Woodstock) Hatfield (F) 20% 417.9 261.0 -9.7% 0.625 5.1% St. Marys (Bowmanville) Baldwin (CH) 10% 498.5 292.7 -1.6% 0.587 -6.2% St. Marys (Bowmanville) Baldwin (CH) 20% 521.7 281.5 -5.4% 0.540 -13.8% St. Marys (St. Marys) Baldwin (CH) 10% 498.2 264.8 -1.8% 0.531 -6.3% St. Marys (St. Marys) Baldwin (CH) 20% 521.5 255.2 -5.3% 0.498 -13.8%

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There is a marked difference between the degree of hydration curves for the three material pairs under

consideration. At early ages, the three plots show that there is a decrease in the degree of hydration that

corresponds to the level of fly ash replacement. However, as time progresses, the degree of hydration

curves with fly ash replacement start to converge with the curve for the neat Portland cement. The curves

for the CH fly ash, shown in Figure 5-17, continue to run parallel to each other up to the end of the test

duration (72 hours) though the results of other researchers have indicated that for a type C fly ash, the

time of surpassing may be 100+ hours depending on the fly ash CaO content (Schindler and Folliard,

2003; Langan et. al, 2002). Figure 5-18, which shows the results for the Lafarge (Woodstock) plus

Atikokan fly ash (type CI) system, shows that the curve representing 10% fly ash replacement is just

crossing the curve for the neat Portland cement at a time roughly equal to 70 hours, and that the 20%

curve is also very close to crossing the Portland cement curve. If one extrapolates these curves, it looks

as though all three replacement levels will surpass the Portland cement curve for this system by 100

hours. Finally, the curves for the Lafarge (Woodstock) GU with partial replacement of the Hatfield fly ash

(type F) are initially incident, and by a time of approximately 40 hours, both the 10% and 20% fly ash

curves surpassed that of the neat Portland cement. These results are consistent with the findings of other

researchers (Schindler and Folliard, 2003; Langan et. al, 2002).

These results seem to imply that the fly ashes being tested are contributing to the hydration process

within the first 72 hours. However, it’s commonly accepted that most fly ashes – particularly those that are

class CI and class F - do not begin to hydrate for a period of time of up to a week (Sakai et. al., 2005;

Langen et. al., 2002; Neville, 1995).

The cross-over observed in the degree of hydration curves can be explained by the fact that at early ages

only the cement is hydrating. When the H72 values from Table 5-8 are compared for the same GU cement,

it’s evident that the type of fly ash used is not as important as the replacement level, which reinforces the

notion that the fly ash itself is not hydrating at early ages. For example, the H72 value for the Lafarge

(Bath) GU plus Atikokan ash (type CI) at a replacement level of 10% is 262.2 J/g, which is very similar to

the 262.7 J/g that is observed for the Lafarge (Bath) GU plus Hatfield ash (type F) at the same 10%

replacement level. Similarly, at 20% replacement, these two systems result in H72 values of 246.6 J/g and

246.6 J/g respectively and the Lafarge (Woodstock) GU tests show a similar trend. This fact coupled with

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the lower Hu values that are calculated as a result of the fly ash replacement produces the crossing of the

curves that is seen in Figures 5-18 and 5-19.

5.1.4 Using the TAM Air Results as Thermal Simulation Inputs

A potential use for the isothermal hydration curves is as an input for the thermal simulation program,

which was developed in Chapter 3. At the core of this thermal simulation is a mechanistic-empirical model

that predicts the degree of hydration as a function of the effective time, based on a set of hydration

parameters and the ultimate degree of hydration. Equations for the various hydration parameters were

based on a statistical analysis of the semi-adiabatic testing of concrete samples.

The proposed method for using the TAM Air calorimetry results as input for this hydration model is to use

the isothermal data to determine values for the hydration parameters, so that the predicted degree of

hydration curve matches the curve that was experimentally determined. To do this, both the data from the

calorimeter and a reliable means of determining either the degree of hydration at a specific effective time,

or an accurate measure of the total heat evolved by the material (i.e. ∞H ; J/g) is needed. However, since

neither of these values were available for this thesis project, the calculated values for the total heat (Hcem

or Hu) were used in these calculations.

The hydration curve parameters – αu, τ and β – were determined by fitting Equation 2-12 to the isothermal

calorimetry data using a least-squares technique. Since the temperature was a constant 23°C in the

isothermal testing, the effective time was equal to the elapsed time during testing. The resulting hydration

parameters which were calculated for the six neat GU cements from the isothermal testing data are

summarized in Table 5-9. The hydration parameters for the six GU cements as calculated by the

hydration model are presented in Table 5-10 for comparative purposes. Note that in general, the

calculated values for αu and β are increased, while the value for τ is fairly similar to the values determined

using Schindler and Folliard’s hydration model.

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Table 5-9: Hydration curve parameters calculated from isothermal heat-conduction calorimetry data; tests performed for 7 days at 23°C Cement αu β τ Essroc (Picton) 0.744 1.060 11.97 Lafarge (Bath) 0.651 1.209 12.02 Lafarge (Woodstock) 0.703 1.173 15.31 St. Lawrence (Mississauga) 0.690 1.132 11.36 St. Marys (Bowmanville) 0.754 1.072 13.73 St. Marys (St. Marys) 0.706 0.881 11.97

Table 5-10: Hydration curve parameters calculated using Schindler and Folliard’s hydration model, based on the cement chemistries Cement αu β τ Essroc (Picton) 0.694 0.741 9.84 Lafarge (Bath) 0.694 0.656 15.20 Lafarge (Woodstock) 0.694 0.642 13.37 St. Lawrence (Mississauga) 0.694 0.784 10.38 St. Marys (Bowmanville) 0.694 0.743 10.93 St. Marys (St. Marys) 0.694 0.708 12.75

These hydration parameters were then used to perform the isothermal simulations, as described in

Section 5.1.1. Figure 5-20 shows the power versus time plot for the Essroc (Picton) GU, while Figure 5-21

shows the curve for the degree of hydration versus time; both of these figures have the curves for

isothermal temperatures of 10, 23 and 35°C. It is immediately apparent that the new hydration parameters

are better able to predict the shape of the degree of hydration and the rate of hydration curves at all three

temperatures, as compared to the values calculated by Schindler and Folliard’s hydration model (refer to

Figures 5-5 and 5-6 for the simulated curves based on the hydration model). In particular, these new

hydration parameters are able to more accurately represent both the magnitude of the main hydration

peak and the time at which it occurs. However, additional validation in the form of a field study is needed

before these values can be used as inputs in the thermal simulation program with any degree of

confidence.

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Figure 5-20: Plot of the power vs. time for the Essroc GU (Picton) cement; simulated curves produced using hydration

parameters based on isothermal calorimetry data; measured and simulated at 10, 23 and 35°C

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Figure 5-21: Plot of the degree of hydration vs. time for the Essroc GU (Picton) cement; simulated curves produced

using hydration parameters based on isothermal calorimetry data; measured and simulated at 10, 23 and 35°C

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5.2 Field Testing and Verification

The following sections will briefly examine two case studies as a means of performing some initial

validation for the thermal simulation program, and to test the accuracy of using the TAM Air hydration

parameters as inputs for the model. These case studies will focus on the determination of the internal

temperatures, based on the ambient conditions and the concrete used for the element under

consideration.

5.2.1 Innocon 1 m3 Test Cubes

The Innocon 1 m3 test cubes were cast as a part of another study. These cubes were cast on two dates in

June 2005 at the Innocon Commissioner St. Plant in order to compare the relative performance of three

different concrete mixes under field conditions. These three concrete mixes included a control mix

containing type GU cement, a fly-ash concrete comprised of the type GU cement with 50% class F fly ash,

and a slag concrete comprised of the type GU cement and 50% class S blast-furnace slag. For the

purposes of this case study, only the neat GU and the slag concrete cubes will be considered, since there

is no isothermal data available for the 50% class F fly ash concrete.

5.2.1.1 Element Layout

The concrete elements in this case study consisted of cubes measuring one metre on each side. They

were cast on grade; the supporting layers consisted of a concrete pavement that was used as a parking

area at the Commissioner Street plant. No reinforcing steel was used, though a series of wires were

strung through the element to provide supports for the thermocouples. Figure 5-22 shows a section

through the centre of the element and the accompanying form-work, with thermocouple locations marked.

This 1 m2 section was discretized using 100 mm blocks, resulting in a grid of ten blocks high by ten wide;

a time step of 600 seconds was chosen to satisfy the various stability criteria.

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Figure 5-22: Section through the centre of the Innocon 1 m3 field test setup, including thermocouple locations and

formwork details (typical); all dimensions in millimetres

5.2.1.2 Environmental and Boundary Conditions

The three Innocon 1 m3 cubes were cast on two dates; cubes 1 (neat GU cement) and 2 (GU plus slag

cement) were cast on June 14, 2005, with cube 3 (GU plus fly ash) cast approximately a week later on

June 22, 2005. The test cubes were located in an area of the plant that was subjected to direct sunlight

and wind throughout the day.

The formwork for the cubes consisted of ½ inch plywood sheeting that was braced at the bottom, midpoint

and top with 2 x 4 inch boards. These forms were placed directly onto the concrete pavement surface of

the parking area where the cubes were to be cast. The insides of the forms were lined with 50 mm thick

foam boards in order to insulate the concrete; the reason for this was to simulate the conditions of a large

foundation slab for the original study. Finally, a layer of polyethylene sheeting was used to line the forms.

Using the thermal simulation program, R-values were calculated for the side surfaces and the bottom of

the 1 m3 cubes. This resulted in an R-value of 1.984 m2-°C/W for the sides of the cube and 1.875 m2-°C/W

106

for the cube’s bottom; for this simulation, it was assumed that the concrete pavement would absorb any

heat transferred to it through the bottom insulation.

The ambient temperature for the two cubes under consideration at the time of casting was approximately

28°C for cube 1, and 32°C for cube 2, with a high temperature that afternoon of 36°C. For the remainder

of the week, the temperatures ranged from an overall high of 37°C to a night time low of just 13°C. In

order to approximate these conditions, the temperature was modelled using a sinusoidal function that

ranged between a high temperature of 27°C and a low of 18°C; this resulted in a temperature-time factor

of approximately 5500°C-h, which is comparable to the temperature-time factor of 5200°C-h that was

measured during the field testing. The wind speeds were taken as an average constant wind speed of 4.5

m/s (approximately 16 km/h), based on the average wind speeds recorded for Toronto over the time

period in question (NCDIA, 2002) and the relatively unprotected location of the elements.

5.2.1.3 Materials and Concrete Mix Designs

The two cubes under consideration were made from two different concrete mixes, in order to examine

their relative performance in reducing the total internal heat rise. The first cube was cast from a reference

concrete made from Type GU cement with heat characteristics of Type MH, with no fly ash or slag added.

The second cube was cast from a slag concrete, made from a Type GU cement (again with Type MH

characteristics) and blast-furnace slag. In both cases, the specified compressive strength at 120 days was

35 MPa. The mix design details for both concretes used in the field testing program are summarized in

Table 5-11. For the purposes of the simulation, the cement was assumed to be the Lafarge (Bath) GU and

the slag was assumed to be Lafarge’s Stoney Creek GGBS.

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Table 5-11: Mix designs and hydration parameters for the two concretes under consideration from the Innocon 1 m3 field tests Mix Parameters Mix 1 (Reference) Mix 2 (Slag-concrete) Cement type Type I/II (GU/MH) Type I/II (GU/MH) Water to cementitious material ratio (w/cm) 0.36 0.43 Cement content, kg/m3 383.4 130.8 Slag cement content, kg/m3 0 131.4 Water content, kg/m3 137.9 114.7 Coarse aggregate (limestone) content, kg/m3 1180.1 1056.6 Fine aggregate (limestone) content, kg/m3 699.5 400.1 Air content, % 5.6 6.6 Placing temperature, °C 27.2 26.0 Hydration parameters, from model Mix 1 (Reference) Mix 2 (Slag-concrete) Total heat of hydration, Hu, J/g 464.9 463.0 Ultimate degree of hydration, αu 0.670 0.862 Hydration slope parameter, β 0.656 0.475 Hydration time parameter, τ, hours 15.20 45.14 Apparent activation energy, Ea, kJ/mol 43610 52300 Hydration parameters, from TAM Air testing Mix 1 (Reference) Mix 2 (Slag-concrete) Ultimate degree of hydration, αu 0.651 1.0941

Hydration slope parameter, β 1.209 0.421 Hydration time parameter, τ, hours 12.02 64.12 1 See discussion

Pastes based on these two concrete mix designs were produced and tested on the TAM Air isothermal

calorimeter, following the procedures and guidelines set out in Chapter 4. The results of these trials are

presented in Figures 5-23 and 5-24, which show plots for the power versus time and the degree of

hydration versus time respectively for these two mixes.

These results were then used to determine hydration parameters as described in Section 5.1.4. It’s

interesting to note that the ultimate degree of hydration parameter calculated from the isothermal

calorimeter data is in excess of 1.0, which of course is an impossible result. This reason for this result is

most likely an underestimation of the total heat of hydration, Hu, of the cementitious system, due to the

fact that a reliable figure for the heat of hydration for the slag is not available. Note that this result should

not lead to any errors in the determination of the total heat released by the hydration model, since that

heat is calculated using both the degree of hydration value and the total heat (Hu) value, therefore

cancelling out any potential for error.

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Figure 5-23: Plot of power vs. time for the Innocon 1 m3 reference and slag-cement pastes, based on the concrete mix

designs used in the field trials; measured at 23°C

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Mix 2 (Slag-concrete)

Figure 5-24: Plot of the degree of hydration vs. time for the Innocon 1 m3 reference and slag-cement pastes, based on

the concrete mix designs used in the field trials; measured at 23°C

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5.2.1.4 Results of the Thermal Simulation

The results of the temperature prediction as performed by the thermal simulation program are presented

in Figures 5-25 and 5-26. These figures show the calculated and measured temperature profiles for two

different locations within the sample, as well as the simulated and recorded ambient temperatures. The

first location of interest was the thermocouple TC2, which was located on the centreline of the element at

a distance of 750 mm from the top surface, since this was the location where the highest measured

temperatures were observed. The second location of interest was on the top surface of the concrete,

directly adjacent to the insulated form-work, corresponding with thermocouple TC6 in the field study

(these locations are also marked in Figure 5-22). This location was the point at which the lowest

measured temperatures were recorded during the field trials.

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Figure 5-25: Comparison of the measured and predicted temperatures for Cube 1, made with Mix 1 (Reference concrete)

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Figure 5-26: Comparison of the measured and predicted temperatures for Cube 2, made with Mix 2 (Slag-concrete)

These results show that there is a very good agreement between the measured temperatures and the

temperatures predicted using the TAM Air hydration parameters for both locations of interest. The

maximum temperature within the core of the cubes were predicted within a single degree Celsius for both

Cube 1 and within two degrees for Cube 2, though there is a slight difference in the time at which these

peaks occurred between the modelled and measured temperature profiles. The shapes of the

temperature peaks are also somewhat different when compared to the in-situ measurements; the most

notable difference can be seen in the modelled results for location TC2 in Cube 1, which shows a far

sharper peak when compared to the more gradual curve of the measured results.

The modelled surface temperature is also quite close to the measured temperature, given the differences

between the modelled and actual ambient temperatures. For both cubes, the modelled temperatures are

slightly higher at a time of 168 hours at all locations, indicating that the rate of heat loss from the element

being used by the model is slightly conservative. However, this also indicates that the surface conduction-

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convection coefficients are fairly successful in representing the amount of heat that is being transferred to

and from the environment through these composite forms.

For the modelled temperatures that were generated using Schindler and Folliard’s hydration parameters

there is more of a difference observed between the measured and predicted temperatures, particularly for

the TC2 location, where there was as much as an eight degree Celsius difference between the two

curves. These results indicate that the hydration model is underestimating the degree of hydration at a

given equivalent time for these two materials, though it is impossible to pinpoint the cause of this

underestimation based on these results alone.

It should be noted that these results could be improved by using the daily high and low temperatures to

improve the simulated ambient temperature, particularly for the TC6 location. However, considering the

assumptions made in the analysis, the results are more than satisfactory, and they indicate that the

thermal simulation program is performing as intended. These results also indicate that the assumptions

and simplifications made in the development of the thermal simulation program do not significantly affect

the resulting temperature profiles for this very simple case study. However, a case with more widely

varying environmental conditions could prove to be problematic for the simplified thermal simulation

program; the next case study will seek to explore these limits further.

5.2.2 St. Lawrence Cement VRM Foundation Mass Concrete Pour

The second case study that will be presented is the foundation for a vertical roller mill (VRM), which was a

part of the Slag Mill Foundation (VRM) Project at the St. Lawrence Cement plant in Mississauga. This

project was undertaken to examine the suitability of high levels of slag replacement in reducing the heat

produced during hydration as a means of reducing the potential for cracking. Initially, there were to be two

large pours of 800 m3 with different mix parameters, but the final project only used a single mix for both

pours, which consisted of a slag concrete with 50% ground granulated blast-furnace slag. The VRM

foundation was cast on June 7, 2006, starting at approximately 05:00 h and finishing at 13:00 h. All testing

including the placing of the thermocouples for the collection of the temperature data was performed by

personnel from Davroc Testing Laboratories, Inc.

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5.2.2.1 Element Layout

The vertical roller mill foundation was a massive concrete element measuring approximately 14 m by 14

m in plan and 5 m in thickness. There was a smaller projection on the north side of the foundation,

measuring roughly 3.5 m by 3.7 m in plan. The supporting layers for the VRM foundation consisted of lean

concrete fill placed over solid bedrock. Figures 5-27 and 5-28 show plan and section views of the VRM

foundation, including the location of the thermocouples that were used to measure the temperature rise

within the element. For this brief case study, only location L1 at the centre of the VRM foundation will be

examined.

Figure 5-27: Plan view of the St. Lawrence VRM foundation, including thermocouple locations; all dimensions in

millimetres

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Figure 5-28: Section through the centre of the St. Lawrence VRM foundation, from west to east along line A, including thermocouple locations; all dimensions in millimetres

The section to be analyzed is located in along the centre line of the element, running from east to west.

The section measures 13.4 m by 4.8 m high, with the top 1.2 m of the element being located above grade

with the remaining concrete located below grade; this was initially to have been constructed in two stages,

but due to scheduling considerations, it was decided to cast the foundation in a single pour. The pit for the

foundation was prepared by removing the shale bedrock, and then lining the sides and bottom with a lean

fill concrete, in order to square up the sides for the VRM foundation itself. The section to be analyzed was

discretized using 200 mm blocks, with a time step of 1800 seconds (30 minutes) being chosen to satisfy

the stability criteria.

The VRM foundation contained a significant amount of steel reinforcement, including a series of rock

anchors that would be used to secure the foundation to the underlying bedrock. The reinforcement was

particularly dense underneath the three locations that would support the VRM itself. Because of the close

spacing of reinforcing steel required, a coarse aggregate with a nominal diameter of 20 mm was used for

this project.

5.2.2.2 Environmental and Boundary Conditions

The ambient temperature during the VRM pour ranged from a low of approximately 14°C at the start of the

day (05:00 h) to a high of 25°C at the completion of the pour (13:00 h). For the remainder of the week, the

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temperatures ranged from an overall high of 26°C to a night time low of just 9°C. In order to approximate

these conditions, the temperature was modelled using a sinusoidal function that ranged between a high

temperature of 20°C and a low of 13°C; this resulted in a temperature-time factor of approximately

4460°C-h, which is comparable to the temperature-time factor of 4550°C-h that was measured during the

field testing. The conditions for the remainder of the week were mainly sunny with some clouds, with only

trace precipitation (NCDIA, 2002). The wind speed was approximated as a constant 4.0 m/s

(approximately 14.5 km/h) based on the available data for Lester B. Pearson airport over the period in

question (NCDIA, 2002).

Compared to the Innocon 1 m3 field study, the boundary conditions for this problem were relatively

complex. The top surface of the concrete was protected by a layer of moist filter paper for curing purposes

(R-value of 0.06 m2-°C/W), which prevented evaporation from the surface of the concrete, thus satisfying

the assumption that proper curing practices were followed during the pour. The top 1.2 metres of the

element were enclosed by an engineered formwork solution, which was made up of heavy plywood

panels (assumed to be approximately 19 mm thick for this analysis) with steel frames and braces. A

corresponding R-value of 0.22 m2-°C/W was determined for this form-work based on the thermal

conductivity of the form material, but excluding the steel frames.

The remainder of the element - approximately 700 m3 of concrete – was located below the surface of the

prepared area. The walls of the pit were made up of a relatively smooth layer of lean fill concrete that was

cast over the weathered shale stone that existed below the site. These walls were prepared in advance to

act as forms for the VRM foundation. The main heat transfer mechanism between the concrete element

and these walls is via conduction; it was assumed that there were no significant transfer losses at the

interface between the lean concrete walls and the newly cast VRM foundation. Due to the large amount of

steel located in the element – and the rock anchors in particular – it was predicted that a large portion of

the internal heat produced in the element would be transferred out the bottom of the element. This

prediction was later confirmed by the results of the field testing.

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5.2.2.3 Materials and Concrete Mix Design

The concrete used for the St. Lawrence VRM foundation was designed to meet the CSA A23.1-04

standard for a concrete exposure classification of F1 with a specified minimum compressive strength of 30

MPa at 56 days and a minimum 310-330 kg/m3 of cementitious materials. The mix design called for a

HVSM-1 50/50 blend of Portland Type GU cement and slag cement with a slump of 80 ± 30 mm and a

plastic air content of 5-8%. The concrete was supplied at an average rate of 100 m3 per hour from two

different ready-mix plants over the eight hour duration of the pour.

The remainder of the mix design parameters are summarized in Table 5-12, along with the calculated

hydration parameters. This table also contains the hydration parameters that were calculated based on

the results of a TAM Air test performed on a representative paste consisting of 50% St. Lawrence

(Mississauga) GU cement and 50% Grancem slag cement, with a w/cm ratio of 0.45; this paste was

tested for 14 days at 23 and 35°C. As with the 50% slag-cement paste tested for the Innocon 1 m3 field

trial, the ultimate degree of hydration value calculated from the isothermal calorimetry data is greater than

1.0. This is most likely caused by the fact that the value for the total heat of hydration (Hu, J/gmat) is

conservative.

Table 5-12: Mix design information and hydration parameters for the St. Lawrence VRM Foundation pour Mix Parameters VRM Foundation Mix Cement type Type GU Water to cementitious material ratio (w/cm) 0.45 Cement content, kg/m3 175 Slag cement content, kg/m3 175 Water content, kg/m3 159 Coarse aggregate (limestone) content, kg/m3 1080 Fine aggregate (limestone) content, kg/m3 800 Air content, % 6.5 Placing temperature, °C 20.0 Hydration parameters, from model VRM Foundation Mix Total heat of hydration, Hu, J/g 474.8 Ultimate degree of hydration, αu 0.872 Hydration slope parameter, β 0.567 Hydration time parameter, τ, hours 30.97 Apparent activation energy, Ea, kJ/mol 57540 Hydration parameters, from TAM Air testing VRM Foundation Mix Ultimate degree of hydration, αu 1.0821

Hydration slope parameter, β 0.440 Hydration time parameter, τ, hours 52.98 Apparent activation energy, Ea, kJ/mol 60300 1 See discussion

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The apparent activation energy for the slag-concrete was also calculated based on the isothermal testing

results obtained at 23 and 35°C. The calculation was performed at a value of α = 0.370, in accordance

with the procedures outlined in Section 2.2.3 and to remain consistent with the apparent activation energy

results obtained in Section 5.1.1. This resulted in a calculated apparent activation energy of 60300 kJ/mol,

which is approximately 4.6% greater than the value calculated from the provided chemistry information

using Equation 2-18.

The results of the isothermal testing are presented in Figures 5-29 and 5-30, which present the power

versus time and the degree of hydration versus time respectively for the representative slag-cement paste

as well as an accompanying reference paste made from 100% Portland cement. It is clear from these

results that the 50% slag replacement is responsible for a corresponding reduction of the power

generation at early ages of approximately 50%. These results also indicate that this reduction in the rate

of heat generation is consistent at 35°C.

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Figure 5-29: Plot of the power vs. time for the St. Lawrence VRM foundation reference and slag-cement pastes, based on the concrete mix design used in the field trial; measured at 23 and 35°C

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Reference Mix, 23°CReference Mix, 35°CVRM Foundation Mix (Slag-concrete), 23°CVRM Foundation Mix (Slag-concrete), 35°C

Figure 5-30: Plot of the degree of hydration vs. time for the St. Lawrence VRM foundation reference and slag-cement

pastes, based on the concrete mix design used in the field trial; measured at 23 and 35°C

5.2.2.4 Results of the Thermal Simulation

The results of the thermal simulation program are plotted in Figure 5-31 alongside the measured

temperatures that were collected by Davroc personnel. These results show that the simulation results

were generally good, though this time both of the modelled results overestimated the maximum measured

temperature rise of 62°C, which occurred at the 50% depth at location T1, along the centre line of the

element.

The modelled results that were produced using hydration parameters based on the TAM Air isothermal

calorimetry show a peak temperature that is some 4°C higher than the measured peak temperature. In

addition, this peak occurs much later in the case of the modelled results; in general, the shape of the

temperature profile for the 50% depth is not a particularly good match for the measured profile. The

results for a depth of 25% were no better; at 48 hours, the temperature profiles began to diverge, with the

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temperature differential between the modelled and measured profiles increasing as time progressed.

However, the temperature results for the surface of the concrete and the bottom surface of the element

are both much closer to the measured values.

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Figure 5-31: Comparison of the measured and predicted temperatures for the St. Lawrence VRM foundation for

location T1 (centre of the element)

The results for the simulation using the parameters from Schindler and Folliard’s hydration model were

somewhat better than the simulation results based on the TAM Air parameters. At the 50% depth, the

peak temperature was predicted within 1°C, and while the predicted and measured profiles are not

identical, the predicted profile is within a few degrees of the actual temperature for the duration of the

simulation. Similarly, the 25% depth prediction is also a much better match for the measured results,

particularly during the initial 72 hours of the simulation. The predicted temperature profiles for the top

layer of concrete and the bottom surface are both very good for this simulation.

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A potential explanation for the fact that both of the simulations overestimated the internal temperatures

may stem from the fact that there was a large amount of reinforcing steel used in this foundation. This

included a number of rock anchors that were embedded some five plus metres into the underlying

bedrock. This could have led to a significant amount of the internal heat being transferred downwards

through the steel to the bedrock. In order to partially account for this, the thermal conductivity and the heat

capacity of the concrete was increased based on an estimate of the percentage of steel reinforcement

used in the foundation, which was assumed to be 4%; however, this increase in the thermal conductivity

would not take into account the direction of this increased heat flow, which would likely occur along the

length of the reinforcement.

A second potentially significant source of error was the fact that the thermal properties and the initial

temperature of the pit walls were not precisely known, which meant that approximate values and

estimates were used for the thermal simulation’s boundary conditions on the bottom half of the element.

For the purposes of the simulation, the pit walls were simulated as being 100% concrete, though in reality

there is only a layer of fill concrete of unknown thickness cast on top of the weathered shale that was

exposed by the excavation for the VRM foundation. Furthermore, the temperature at the bottom of the

foundation excavation was not known prior to the start of the pour, and as such the initial temperature

values used in the simulation may not be fully representative of the conditions present in the field. These

two factors, combined with the fact that more than 60% of the foundation was located below grade, are

the likely causes for the differences seen between the field measurements and the predictions made by

the thermal simulation program.

5.3 Summary

This chapter has presented the results from the experimental program that accompanied this thesis

project, as well as two case studies that were performed based on this information, with the hydration

model outlined in Chapter 2 as a basis for the analysis. The final chapter in this thesis project will use

these results to draw conclusions regarding the usefulness of this testing data as an input for the thermal

simulation program, as well as an evaluation of the simulation program itself. Chapter 6 will also make

some recommendations for future tests as well as some improvements to the test methods based on the

results presented here.

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Chapter 6: Conclusions and Recommendation

This chapter will use the results presented in Chapter 5 to draw some conclusions regarding this thesis

project. Section 6.1 will summarize the results of the isothermal calorimetry testing, followed by a brief

discussion of the suitability of using the TAM AIR data as an input for the thermal simulation program in

Section 6.2. Next, the success of the thermal simulation program will be examined in Section 6.3, based

on the four performance criteria that were set forth in Chapter 1. Finally, some recommendations for

additional testing, as well as potential refinements to the testing program will be presented in Section 6.4;

in particular, this section will outline some additional testing that would have been of use in refining the

results of the isothermal calorimetry testing program.

6.1 TAM Air Isothermal Calorimetry Results

The results of the TAM Air testing confirm that isothermal heat conduction calorimetry is a very useful

means of examining the hydration of various cementitious systems. These tests demonstrated that this

method was able to accurately measure the hydration rate versus time for the cementitious systems being

examined. These rate measurements are particularly useful in examining the effects of chemical or

mineral admixtures on cement hydration.

The resulting energy measurements suggest that there may not be a direct correlation between the

measured total heat values at 72 or 168 hours (H72 & H168; J/gmat) and the total heats of hydrations of the

various cements (Hcem). This suggests that it may not be possible to extrapolate from the H72 values alone

in order to obtain accurate values for Hcem, due to the fact that the cements hydrate at different rates at

early ages. Such a prediction would likely require knowledge of the degree of hydration at 72 or 168

hours, though it may be possible to determine this value by extrapolating from the rate of hydration curve

itself; it is recommended that this issue be examined further in future testing.

The results of the test program also demonstrated that testing at multiple temperatures provides a simple

and accurate method for determining the apparent activation energy of the cementitious system under

examination. The experimental values for the apparent activation energy of the neat GU cements were

generally very similar to the values calculated using Schindler and Folliard’s numerical model (Equations

2-18 and 2-19); typically, less than a 5% difference was observed between the real and calculated values,

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with the exception being for the St. Marys (St. Marys) GU, which was some 20% higher than the theoritical

value. This indicates that the Ea values for neat GU cements calculated from the numerical model are

generally good enough for most applications.

The resulting degree of hydration versus time curves highlighted the importance of an accurate value for

the total heat of hydration (Hu; J/g) of the cementitious systems, particularly when supplementary

cementing materials are included. This is due to the fact that this total heat value is required in order to

determine the degree of hydration from the results of the TAM Air testing. For the purposes of this thesis

project, it was assumed that the calculated total heat of hydration (Hu; J/g) was the most accurate of the

theoretically calculated values. However, when these values were used in the determination of the degree

of hydration versus time curves, it was found that the resulting curves showed a degree of hydration that

was higher than expected. For example, after 72 hours of testing at 23°C, both the Essroc (Picton) and St.

Marys (Bowmanville) GU cements were approaching the theoretical maximum degree of hydration

calculated using Mills’ formulation (Equation 2-11); by 168 hours, both of these cements had exceeded

the theoretical value of 0.695.

Similarly, when the TAM Air isothermal calorimetry results were fitted to the exponential hydration formula

(Equation 2-12), the resulting values for αu were again higher than the theoretical values calculated using

Mills’ formula. This occurred for four of the six neat cements tested, including the Essroc (Picton), Lafarge

(Woodstock), St. Marys (Bowmanville) and St. Marys (St. Marys) GU cements. When the hydration

parameters for the two slag-cements were determined for the case studies, the resulting values for αu

exceeded a value of 1.0, which is clearly not a meaningful result. These results clearly indicate that the

values for Hu are conservative as calculated – probably due to the inaccuracy in the Hcem, HGGBS and HFA

values - and that an improvement in the accuracy of this value would increase the accuracy of the degree

of hydration versus time curves that are produced from the experimental results. This is even more

important in the case of cements with partial SCM replacement, since there is only limited data regarding

the values for HFA and HGGBS, and these existing estimations are likely not representative of all SCMs

currently in use. This result may also indicate that Mills’ formulation itself is conservative for modern

cements.

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Finally, the TAM Air isothermal calorimeter proved to be a useful instrument for examining the effects of

partial replacement with SCMs such as slag or fly ash. This testing allowed for a simple means of

determining the relative decrease in early age heat that would be released by a blended system in

comparison to the neat GU cement. Of course, an accurate determination of the degree of hydration of the

cementitious system is once again dependent on the accuracy of the total heat value (Hu, J/gmat).

6.2 Using TAM Air Results as Hydration Model Inputs

The results of the two case studies presented in Section 5.2 show that the results of the TAM Air

isothermal testing are potentially very useful as inputs for the thermal simulation. In both cases, the use of

the TAM Air inputs to define the degree of hydration versus time curve produced results that were similar

to the measured temperatures; these values were also similar to the results predicted by the hydration

model, though the results using the TAM Air hydration parameters consistently predicted a slightly higher

internal temperature rise than the hydration model.

The great advantage of using the TAM Air isothermal calorimetry results as an input for the thermal

simulation is the ability to deal with cementitious combinations that are not contained within the range for

which the model was calibrated. This might include concretes made with Type GUb cements, concretes

containing certain SCMs, or concretes containing a wide range of chemical admixtures. By using these

curves as inputs, the user is able to deal with a much wider range of material inputs than would otherwise

be possible, at the expense of a small amount of additional testing.

However, even using the TAM Air to generate additional input parameters will not result in the best

solution possible. This is due to the current implementation of the hydration model itself; more specifically,

this is caused by the exponential formulation for the degree of hydration prediction. This exponential

model (see Section 2.2.1) is simple to implement, and it provides good results for neat GU cements and

for cementitious systems with low levels of replacement with SCMs, though it is somewhat worse for

concretes containing high levels of slag or fly ash. This is because the exponential function by nature is

only able to produce a single power peak at early ages, while most of the cementitious systems involving

high levels of SCM replacement have either a double peak, or a single extended plateau in the power

versus time curve. Improved results could be possibly be obtained by superimposing two separate

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hydration equations to deal with the Portland cement and slag reactions (P- and S-reactions,

respectively), as suggested by De Schutter (1999). This might result in a better approximation for the rate

of hydration versus time curves, as well as the predicted degree of hydration progression, for cementitious

systems with high levels (>20%) of SCM replacement.

6.3 Success of the Thermal Simulation Program

The effectiveness of the thermal simulation developed in Chapter 3 will be evaluated using the four

performance criteria presented in Section 1.2. To recap, these performance criteria are:










analyzed.

The results of the two case studies presented in Section 5.2 suggest that the thermal simulation is

successful in meeting the first performance criteria for the two cases present, though the accuracy of the

thermal simulator is highly dependent on the accuracy of the simplified boundary conditions. These

results suggest that the simulation program is best suited to solving relatively simple cases, such as a

beam or slab on grade, as opposed to a highly reinforced foundation element, due to the simplifications

that have been adopted in the development process.

Performance criteria #2 and #3 are also satisfied by the current thermal simulation program. This was

accomplished by adding a material database that is able to store the various cement chemistries which

are used as program inputs. To use this database, the end-user is only required to identify the materials

that are being used in the concrete mix design, as well as the design parameters; however, it should be

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noted that this database is dependent on regular updates in order to ensure that the results of the thermal

simulation program are as accurate as possible.

In addition to this, the user is presented with the option to use data from the TAM Air isothermal

calorimeter as a means of calibrating the hydration model. This is done by providing the program with the

output file from the TAM Air unit, which is then used to determine updated hydration parameters. A series

of user overrides also allows the user to replace the default values with better information, where

available.

At the time of writing, the fourth performance criterion is the only one that has not been sufficiently dealt

with in terms of the original development goals. Currently, the program is able to perform some formatting

of the final results based on the user’s requirements, but at the moment it does not help the end-user with

analysis, nor the determination of thermal gradients within the element. Further development in this area

is required in order for it to meet this development goal, in terms of providing for the needs of certain end-

users.

It should also be noted that while the thermal simulation program is currently a functional and useful tool

there is still a good deal of development that is required in order to produce a user interface for the

program that is able to gracefully deal with errors and improper inputs. A thorough debugging process is

strongly recommended before the thermal simulation program is considered for a wider release.

6.4 Recommendations for Future Testing

Based on the results of the testing program, it is recommended that future TAM Air tests be performed at

a minimum of two temperatures when the rate of hydration is of interest, in order to facilitate the

calculation of the apparent activation energy for the cement or cementitious system. The speed method

(Section 2.2.3) provides a simple means of calculating the apparent activation energy based on the

results of the testing at two temperatures; this calculated activation energy is particularly valuable for

cementitious systems with high levels of slag or fly ash replacement.

In addition, it is recommended that future TAM Air testing is accompanied by an analysis of the chemical

composition of the sample. If possible, this information could be supplemented by an XRD test in order to

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determine the component composition of the sample directly. This information would supplement the

chemistry information supplied by the manufacturers, and would allow for a greater degree of confidence

when determining input values for the thermal simulation.

A third area of testing that would greatly benefit any future testing program would be an accurate

determination of the total heat of hydration of the various materials to be tested (Hcem, HFA or HGGBS) so

that accurate degree of hydration curves can be produced using the TAM Air calorimeter results. These

determinations could potentially be performed using differential scanning calorimetry (DSC) or the

somewhat more common TGA/DTA instruments.

In addition to these additional tests, there is still a need for further testing with various supplementary

cementing materials, particularly at very high levels of replacement (50-70%). This thesis project did not

test material combinations from competing suppliers; however, in practice, it is not uncommon for

suppliers to purchase materials from one another to meet the needs of their customers in a given region.

If the goal of developing a material database of TAM Air results for the Ontario (or Canadian) market is to

be realized, testing is required on an ongoing basis in order to keep pace with the normal variations and

changing target values that occur in the production of cements and SCMs. However, this undertaking

represents a large commitment of resources which would require the cooperation of a number of different

organizations and individuals in order to succeed. Indeed, it may be more practical to use this

commitment of resources to continue development of improved modelling techniques in order to deal with

the issue of early age cracking due to thermally induced stresses.

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Bazant, Z.P. and M.F. Kaplan. 1996. Concrete at High Temperatures – Material Properties and

Mathematical Models. Essex: Longman Group Limited.

Bentur, A. (ed.) 2003. Early Age Cracking in Cementitious Systems – Report of RILEM Technical

Committee 181-EAS. Bagneux: RILEM Publications S.A.R.I.

Bernander, S. 1998. “Practical Measures to Avoiding early Age Thermal Cracking in Concrete Structures,”

Prevention of Thermal Cracking in Concrete at Early Ages – State-of-the-Art Report prepared by

RILEM Technical Committee 119, edited by R. Springenschmid. New York: E and FN Spon.

Bogue, R.H. 1955. Chemistry of Portland Cement. New York: Reinhold.

Bush, E.G.W., R.W. Cannon, G.R. Mass, and S.B. Tatro. 1995. “Effect of Restraint, Volume Change, and

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130

Appendix A: Material Information

131

Table A-1: Summary of cement chemistry data Manufacturer Essroc Lafarge Lafarge St. Lawrence St. Marys St. Marys Type GU GU GU GU GU GU Location Picton Bath Woodstock Mississauga Bowmanville St. Marys Date 2006-02-22 2005-06-15 2005-11-28 2005-12-08 2005-05-12 2005-05-26 SiO2, % 20.79 20.98 19.70 19.61 19.63 20.19 Al2O3, % 5.30 4.60 5.07 5.53 4.98 4.53 Fe2O3, % 2.51 2.90 2.45 2.31 2.54 2.85 CaO, % 63.29 62.60 62.79 62.61 61.38 62.08 MgO, % 1.88 2.60 3.22 2.51 2.56 3.22 SO3, % 4.56 3.20 2.99 4.32 4.21 3.76 LOI, % N.A. 1.41 N.A. 2.00 2.69 1.95 Na2O, % 0.16 0.20 0.36 N.A. 0.31 0.32 K2O, % 1.19 0.77 0.42 N.A. 1.13 0.53 Alkalis, % 0.94 0.97 0.64 1.00 1.44 0.67 Insoluble, % N.A. N.A. N.A. 0.41 N.A. N.A. CO2, % N.A. N.A. N.A. N.A. N.A. N.A. C3S, % 47.45 51.22 59.81 53.07 51.60 54.05 C2S, % 23.81 21.51 11.36 16.18 17.43 17.11 C3A, % 9.80 7.28 9.29 10.75 8.90 7.18 C4AF, % 7.64 8.82 7.46 7.03 7.73 8.67 Air content, vol % N.A. N.A. N.A. 7.84 N.A. N.A. Blaine fineness m2/kg

450 373 412 412 416 389

Residue, 45 μm % N.A. 3.70 N.A. 7.62 1.97 6.41

Table A-2: Summary of ground-granulated blast-furnace slag data Manufacturer Essroc Lafarge St. Lawrence St. Marys Type S S S S Location Nanticoke Stoney Creek Grancem Cemplus Date 2006-02-221 2005-05-11 2005-12-08 2005-06-061

Activity Index N.A. N.A. 102.6 N.A. Blaine fineness m2/kg

616 N.A. 419 N.A.

Heat of slag hydration, Hslag, J/g

4612 4612 4612 4612

1 Approximate date, based on delivery of sample 2 Assumed value, based on Schindler & Folliard’s recommendation (2003)

Table A-3: Summary of fly ash data Manufacturer Essroc Lafarge Lafarge St. Marys Type CH CI F CH Location Baldwin, IL Atikokan Hatfield Baldwin, IL Date 2006-02-221 2005-04-15 2005-06-27 2005-06-061 CaO,% 39.30 15.002 8.002 39.30 Blaine fineness m2/kg

504 N.A. N.A. N.A.

Heat of fly ash hydration, HFA, J/g

707 270 144 707

1 Approximate date, based on delivery of sample 2 Assumed value, based on fly ash class

132

Appendix B: Isothermal Calorimetry Results

133

Neat GU Cements: Comparative results; w/c 0.40, sample size 7.000 ± 0.500 g; measured at 23°C:

0.00

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2.00

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Pow

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]


3.00

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Lafarge (Bath)

Lafarge (Woodstock)




134

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Essroc GU (Picton) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 10, 23 and 35°C:

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23°C

35°C

10°C Simulated

23°C Simulated

35°C Simulated

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35°C

10°C Simulated

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35°C Simulated

136

0.0

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35°C

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23°C Simulated

35°C Simulated

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35°C

137

Lafarge GU (Woodstock) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 10, 23 and 35°C:

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35°C

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23°C Simulated

35°C Simulated

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23°C

35°C

10°C Simulated

23°C Simulated

35°C Simulated

138

0.0

0.1

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0.3

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0.6

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0 12 24 36 48 60 72 84 96 108 120 132 144 156 168

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[1]

10°C

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35°C

10°C Simulated

23°C Simulated

35°C Simulated

0.0

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[1]

10°C

23°C

35°C

139

St. Lawrence GU (Mississauga) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 10, 23 and 35°C:

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2.00

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8.00

9.00

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10°C Simulated

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35°C Simulated

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35°C

10°C Simulated

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35°C Simulated

140

0.0

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0 12 24 36 48 60 72 84 96 108 120 132 144 156 168

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[1]

10°C

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35°C

10°C Simulated

23°C Simulated

35°C Simulated

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[1]

10°C

23°C

35°C

141

St. Marys GU (St. Marys) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 10, 23 and 35°C:

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2.00

3.00

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5.00

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7.00

8.00

9.00

10.00

0 12 24 36 48 60 72

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10°C

23°C

35°C

10°C Simulated

23°C Simulated

35°C Simulated

0

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0 12 24 36 48 60 72 84 96 108 120 132 144 156 168

Time [h]

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23°C

35°C

10°C Simulated

23°C Simulated

35°C Simulated

142

0.0

0.1

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0.3

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0 12 24 36 48 60 72 84 96 108 120 132 144 156 168

Time [h]

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[1]

10°C

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35°C

10°C Simulated

23°C Simulated

35°C Simulated

0.0

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0.2

0.3

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0 12 24 36 48 60 72 84 96 108 120 132 144 156 168

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23°C

35°C

143

GU Cement + Fly Ash: Essroc GU (Picton) + Baldwin fly ash (CH) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 23°C:

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2.00

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5.00

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Essroc GU (Picton)

Essroc GU (Picton) + 10% Baldwin Fly Ash (CH)


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144

Lafarge GU (Bath) + Atikokan fly ash (CI) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 23°C:

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2.00

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Lafarge GU (Bath)

Lafarge GU (Bath) + 10% Atikokan Fly Ash (CI)


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Lafarge GU (Bath)



145

Lafarge GU (Bath) + Hatfield fly ash (F) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 23°C:

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Lafarge GU (Bath)

Lafarge GU (Bath) + 10% Hatfield Fly Ash (F)


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Lafarge GU (Bath)



146

Lafarge GU (Woodstock) + Atikokan fly ash (CI) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 23°C:

0.00

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2.00

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0 12 24 36 48 60 72Time [h]

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147

Lafarge GU (Woodstock) + Hatfield fly ash (F) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 23°C:

0.00

1.00

2.00

3.00

4.00

5.00

0 12 24 36 48 60 72Time [h]

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148

St. Marys GU (Bowmanville) + Baldwin fly ash (CH) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 23°C:

0.00

1.00

2.00

3.00

4.00

5.00

0 12 24 36 48 60 72Time [h]

Pow

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mat

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St. Marys GU (Bowmanville)

St. Marys GU (Bowmanville) + 10% Baldwin Fly Ash (CH)


0

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149

St. Marys GU (St. Marys) + Baldwin fly ash (CH) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 23°C:

0.00

1.00

2.00

3.00

4.00

5.00

0 12 24 36 48 60 72Time [h]

Pow

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mat

]




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150

GU Cement + Ground Granulated Blast-furnace Slag Essroc GU (Picton) + Nanticoke slag (S) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 23°C:

0.00

1.00

2.00

3.00

4.00

5.00

0 12 24 36 48 60 72Time [h]

Pow

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mat

]

Essroc GU (Picton)

Essroc GU (Picton) + 10% Nanticoke GGBS (S)


0

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350

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Essroc GU (Picton)



151

Lafarge GU (Bath) + Stoney Creek slag (S) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 23°C:

0.00

1.00

2.00

3.00

4.00

5.00

0 12 24 36 48 60 72Time [h]

Pow

er [m

W/g

mat

]

Lafarge GU (Bath)




0

50

100

150

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250

300

350

0 12 24 36 48 60 72Time [h]

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Lafarge GU (Bath)




152

Lafarge GU (Woodstock) + Stoney Creek slag (S) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 23°C:

0.00

1.00

2.00

3.00

4.00

5.00

0 12 24 36 48 60 72Time [h]

Pow

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mat

]


Lafarge GU (Woodstock) + 10% Stoney Creek GGBS (S)



0

50

100

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350

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153

St. Lawrence GU (Mississauga) + Grancem slag (S) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 23°C:

0.00

1.00

2.00

3.00

4.00

5.00

0 12 24 36 48 60 72Time [h]

Pow

er [m

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mat

]





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350

0 12 24 36 48 60 72Time [h]

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154

St. Marys GU (Bowmanville) + Cemplus slag (S) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 23°C:

0.00

1.00

2.00

3.00

4.00

5.00

0 12 24 36 48 60 72Time [h]

Pow

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mat

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St. Marys GU (Bowmanville) + 10% Cemplus GGBS (S)


0

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155

St. Marys GU (St. Marys) + Cemplus slag (S) results; w/c 0.40, sample size 7.000 ± 0.500 g; tested at 23°C:

0.00

1.00

2.00

3.00

4.00

5.00

0 12 24 36 48 60 72Time [h]

Pow

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156

Appendix C: ASTM Draft Test Method for Measurement of Heat of Hydration of Cement with Heat Conduction Calorimetry

177

Appendix D: Excerpt from “Factors Influencing the Early-Age Cracking of High Performance Concrete,” a Literature Review Project by M.E. Robbins

178

2.4.0 Thermally Induced Stresses Thermally induced stress is perhaps the most dominant mechanism that causes cracking in young

concrete. These stresses are developed due to differential expansion caused by the varying heat profile

within the concrete, which in turn is caused by hydration.

2.4.1 Definition and Mechanism “Thermal cracking on site is determined by thermal and other early-age deformations of the concrete on

the one hand and by the restrain[t] of the deformations on the other hand [Springenschmid &

Breitenbücher, 1998].” In order to understand whether or not the thermal conditions of a concrete can

potentially cause cracking, it is important to understand something about the cracking sensitivity of the

concrete mix, as well as the physical and boundary conditions of the concrete member [Springenschmid &

Breitenbücher, 1998]. One of the main contributing factors to thermal cracking is due to the early-age

behaviour of the concrete. The initial temperature rise occurs very early, usually within the first day or so

for HPC mixtures without large amounts of SCMs [Springenschmid & Breitenbücher, 1998]. This rise in

temperature causes the concrete to expand against its surroundings, but since the Young’s modulus of

the concrete is low at this time, very little of this induced compression is transformed into compressive

stresses, as illustrated in figure 11 [Springenschmid & Breitenbücher, 1998].

Figure 11: Illustration of how the early-age changes in modulus affect the amount of thermally induced stresses in restrained concrete [Springschmid, 1998].

179

However, during the subsequent cooling, the concrete’s modulus and creep reaction have increased, and

therefore the resulting shrinkage causes relatively high tensile stresses [Springenschmid & Breitenbücher,

1998].

The restraint that the concrete is subjected to is the primary factor in the amount of stress that will be

developed within the concrete. This restraint can come from external structures, such as mechanical

connections to other parts of the structure, or from friction on grade, or it can come from the internal

structure of the concrete [Bush et al., 1995]. A complete discussion of the different mechanisms that

induce tensile stresses within the concrete is beyond the scope of this literature review, but suffice it to

say that the external restraints are influenced by the size and shape of the concrete specimen, the

strength, and the difference in the modulus of elasticity for the concrete and the neighbouring material

[Bush et al., 1995].

Internal restraint, on the other hand, occurs in members with non-uniform volume change on a cross

section [Bush et al., 1995]. This non-uniform volume change can be caused by temperature gradients

within the concrete (or uneven drying or autogenous shrinkage of the concrete, or even as a result of

chemical shrinkage). Internal restraint adds to the induced exterior restraint, with the exception that their

summation will never exceed the effect of 100% external restraint [Bush et al., 1995]. It is perhaps

interesting to note that this form of restraint is very similar in effect to continuous edge restraint, with the

main difference between the two being that for internal restraint the boundary stresses are equal to zero

[Bush et al., 1995].

Mixes that are particularly sensitive to early-age cracking due to thermally induced stresses include the

majority of HPCs made from silica fume, though any concrete made with a high cement paste content and

those made in extremely hot or cool weather are also at risk [Bush et al., 1995; Springenschmid &

Breitenbücher, 1998]. Mass concretes are also particularly sensitive to thermal stresses, since their high

volume to surface area ratio causes a high internal temperature rise, which leads to high differential

cooling.

180

2.4.2 Influencing Factors & Prevention Many factors influence the stresses induced by thermal effects, including the amount and fineness of

cement used, the use of supplementary cementing materials, the placing temperature, the size of the

member and the degree of restraint of the member [Bush et al., 1995; Springenschmid & Breitenbücher,

1998]. The first four of these factors influence the amount of hydration temperature rise within the

concrete, while the last influences the amount of stress induced in the concrete.

The amount of cement impacts the amount of temperature rise due to hydration by increasing the amount

of paste that the concrete will contain. This increases the amount of hydration that can occur, which in

turn produces more heat [Bush et al., 1995]. The cement composition also plays an important role in the

temperature rise of the concrete, since different cements produce differing amounts of heat when they

hydrate [Neville, 1995; Bush et al., 1995]. This fact is shown in figure 12, which illustrates the effect of

changing the type of cement on the total temperature rise of a concrete element. Increasing the fineness

of the cement (or the SCM for that matter) also causes a higher temperature rise, since an increased

fineness tends to increase the rate of hydration within the cement, which causes heat to be generated

more quickly, with less heat loss to the surrounding environment due to the increased rate of heat

production [Bush et al., 1995]. Therefore, from the literature it can be concluded that in order to reduce

the heat of hydration it is best to use a coarsely ground Type 20 cement, as this will produce the least

heat of hydration possible without using SCMs. Of course, this cannot be done if the early-age strength of

the concrete is important, since a Type 20 cement is slower to hydrate than a Type 30 or even a Type 10,

and since the reduced fineness will further retard the rate of hydration [Neville, 1995].

181

Figure 12: Influence of cement type on the total (adiabatic) temperature rise of a concrete element [Bush et al., 1982].

The use of supplementary cementing materials can be greatly effective in producing concretes that have

low hydration heats [Bush et al., 1995; Douglas et al., 1990]. Research done by Douglas et al. [1990] has

shown that replacing some of the Portland cement with slag or fly ash can have a marked reduction in the

heat a cement produces during hydration (usually referred to as the heat of hydration). This decrease in

the heat of hydration is not strictly linear with replacement; instead, it tends to increase somewhat as

higher replacement levels are used [Douglas et al., 1990]. The use of SCMs doesn’t simply reduce the

amount of heat produced, it also generally delays the time to maximum temperature rise, resulting in a

temperature rise within the concrete that is less severe than in a normal Portland cement blend, but that

lasts longer [Douglas et al., 1990]. Figures 13 and 14 illustrate this fact, as they show not only a reduced

peak in heat evolution, but also a longer flatter curve when there was some replacement of Portland

cement with SCMs. Douglas et al. concluded from their research that while a slag replacement of 50%

provides the most acceptable compromise in terms of lowering the heat of hydration of the concrete while

retaining most of the compressive strength, fly ash is better overall at lowering the amount of heat

generated, and as such is better suited to use where the ultimate strength is not of as much concern

[1990].

182

Figure 13/14: Effect of 25% (top) and 50% (bottom) replacement of SCM on the heat evolution of a cement blend

[Douglas et al., 1990].

The placing temperature is a very important factor that determines how quickly the hydration will initially

occur, and it provides a base temperature on top of which the heat rise from hydration will be added

[Neville, 1995; Bush et al., 1995]. This temperature must be maintained within a range that allows the

concrete to be cool enough to be resistant to the increase in temperature from hydration, while at the

same time being warm enough to prevent frost damage [Neville, 1995; Ghosh & Mustard, 1982]. With

regards to the upper limit of the placing temperature, which is a constraint on hot weather concreting, it is

important to minimize the concrete temperature in order to minimize the overall temperature rise. Neville

[1995] gives a possible maximum placing temperature, used as standard by European countries, to be

183

30°C in order to prevent severe thermal cracking problems. A common preventative measure is to chill

the concrete before placing through the use of either chilled aggregate, the addition of ice shavings in the

mix water or through the use of liquid nitrogen [Neville, 1995]. An equation that determines the amount of

chilled material needed for a certain concrete placing temperature is given in Neville [1995] as:

wca

wwccaa

WWWWTWTWT

T++++

=)(22.0)(22.0

In this equation T represents the temperature in °C, W denotes the mass of ingredient per unit volume on

concrete, and the suffixes a, c, w refer to aggregate, cement and water respectively.

Cold weather concreting, on the other hand, poses another problem altogether. When concreting in cold

weather it is important to protect the concrete against freezing, as this can have a detrimental effect on the

ultimate strength of the concrete [Neville, 1995]. However, with regards to the early-age cracking of the

concrete, the more important factor is protecting the concrete from thermal shock when the forms are

eventually removed [Ghosh & Mustard, 1982]. Thermal shock occurs when forms are removed quickly,

and before the internal temperature of the concrete has had a chance to drop to a safe level. The result is

that the surface cools very rapidly while the interior is still quite warm, causing differential shrinkage, and

in many cases, severe cracking [Ghosh & Mustard, 1982]. The Canadian standard for winter concreting

limits the maximum temperature difference between the centre and surface of the concrete element to a

value of 20°C for high strength concretes, in order to minimize the chance of cracking due to this

differential cooling [CSA-A23.1-00 Clause 21.2.3.5]. Oftentimes insulation is used as a preventative

measure to protect the concrete from rapid cooling in cold weather applications, and generally the forms

are left on for a longer period of time, partly to protect against thermal shock and partly to compensate for

the longer time needed for the concrete to develop strength [Ghosh & Mustard, 1982; Neville, 1995].

Finally, the size and geometry of the element plays a role in the maximum temperature reached within the

element due to the surface area to volume ratio being higher for larger elements. Effectively, this means

that a larger element will produce more heat internally, with less surface area from which to dissipate this

heat [Neville, 1995]. The geometry will also play a role in the amount of external restraint exerted on the

184

concrete, which will influence how much of the expansion is transformed into tensile stresses [Bush et al.,

1995].

References: Springenschmid, R., Breitenbücher, R. 1998. “Influence of Constituents, Mix Proportions and

Temperature on Cracking Sensitivity of Concrete.” Prevention of Thermal Cracking in Concrete at Early Ages, 1998, R. Springenschmid, ed.

Bush, E.G.W., Cannon, R.W., Mass, G.R., Tatro, S.B. 1995. “Effect of Restraint, Volume Change, and Reinforcement on Cracking of Mass Concrete.” ACI Committee 207 Report ACI 207.2R-95.

Douglas, E., Elola, A., Malhotra, V.M. 1990. “Characterization of Ground Granulated Blast Furnace Slags and Fly Ashes and Their Hydration in Portland Cements.”

Ghosh, R.S., Mustard, J.N. 1982. “Winter Concreting In Canada.” Canadian Journal of Civil Engineering. Volume 10: 510-526.

Neville, A.M. 1995. Properties of Concrete, 4th Ed. Essex: Pearson Education, Limited.

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