LICENTIATE T H E S I S
Department of Civil, Environmental and Natural Resources Engineering Division of Structural and Construction Engineering
Measurement and Modelling of Young Concrete Properties
Peter Fjellström
ISSN: 1402-1757 ISBN 978-91-7439-643-0 (print)
ISBN 978-91-7439-644-7 (pdf) Luleå University of Technology 2013
Peter Fjellström Measurement and Modelling of Young Concrete Properties
ISSN: 1402-1757 ISBN 978-91-7439-XXX-X Se i listan och fyll i siffror där kryssen är
Measurement and Modelling of Young Concrete Properties
Peter Fjellström
Luleå University of Technology
Department of Civil, Environmental and Natural Resources Engineering Division of Structural and Construction Engineering
Printed by Universitetstryckeriet, Luleå 2013 ISSN: 1402-1757
ISBN 978-91-7439-643-0 (print) ISBN 978-91-7439-644-7 (pdf) Luleå 2013
PREFACE
The work in this thesis has been carried out between 2010 and 2013 at the Division of Structural Engineering at Luleå University of Technology. The work contributes to a Nordic research project, Crack-Free Concrete, with partners in Sweden and Norway.
The research program has been financially supported by The Swedish Research Council Formas, Cementa AB, Betongindusti AB and the Elsa and Sven Thysell foundation. Therefore, they are here acknowledged.
The laboratory tests have been performed in cooperation with personnel from Complab at Luleå University of Technology. Therefore, I would like to give my appreciation to them. A special thanks to Mr. Hans-Olov Johansson, who patiently spent countless of hours with me in the laboratory, your lessons have been much appreciated.
I would like to give my gratitude to my supervisors, Professors Jan-Erik Jonasson and Mats Emborg. Thank you both for the care and guidance you have given me throughout these years.
Additionally, I would like to thank all colleagues at the Division of Structural Engineering for their friendly support. A special thanks to Professors Hans Hedlund, Lennart Elfgren, Martin Nilsson, Ulf Ohlsson and Vladimir Ronin;
Drs. Jonas Carlswärd and Peter Simonsson; Misters Johan Larsson and Jonny Nilimaa; Mss. Carina Hannu and Katalin Orosz.
Finally, I want to thank my wife Nurnihal Fjellström and son Atlas Fjellström.
Your existence, love and support have given me the motivation to finalize this work.
Luleå in May 2013 Peter Fjellström
ABSTRACT
The main aim of this thesis is to refine models for strength and heat development of the young concrete, and evaluate if developed models at Luleå University of Technology (LTU) for creep, autogenous shrinkage and thermal dilation needs refinement. These are of importance in hardening control and in crack control of a concrete structure.
Strength development is one of the most important properties in concrete to consider when analysing concrete structures. The need of actions on site is different at various stages of hardening, from the fresh concrete to the hardened concrete. This thesis defines a model analysing maturity and associated strength growth within three important time periods. The model can be applied separately within each of these periods depending on test data available. Known is that the temperature plays an important role on the strength development of concrete structures. Not so well known is that, if the concrete temperature remains high, strength reduction at later ages often occurs compared to hardening at lower temperature. Both these phenomena have been implemented in the model for strength growth and the functionality of the model is demonstrated by evaluation of laboratory tests for five concrete mixes and two types of cement.
As heat of hydration affects the temperature levels and several other properties of concrete structures it is important to document the parameters accurately. In the traditional semi-adiabat (TSA) the measured heat energy originates from the reaction between cement and water. This energy warms up the concrete sample and all the ambient materials of the equipment. In order to model these energies, the TSA setup is transformed into an associated sphere. A refined model using a correction factor is introduced, which accounts for energies lost to the TSA setup materials. Results show that the effect of this factor cannot be disregarded. An increased insulation amount gives a decreased cooling factor but an increased need for correction.
Creep at constant temperature, both for moist sealed specimens and drying out conditions, are evaluated. The Linear Logarithmic creep Model (LLM) is shown to work well for basic creep, i.e. creep at moist sealed conditions. But, for creep during simultaneous moist drying, there is a need to adjust the current model or develop a new model to account for the increase of creep due to ongoing drying.
Autogenous shrinkage and thermal dilation (free deformation) are evaluated from tests. For the free deformation of young concrete at variable temperature the existing models are satisfactory in modelling the thermal dilation, but in some cases the autogenous shrinkage cannot be adequately described. A new or refined model is needed that works for autogeneous shrinkage even at more complex temperature variations.
Key words: concrete, strength development, heat of hydration, calorimethric methods, adiabat, semi-adiabat, basic creep, drying creep, thermal dilation, autogenous shrinkage, free movement.
CONTENTS
PREFACE ... I ABSTRACT ... III
1 INTRODUCTION ... 1
1.1 Background ... 1
1.2 Research questions ... 4
1.3 Method ... 5
1.4 Limitations ... 5
1.5 Aims, scope and original features ... 6
1.6 Thesis disposition ... 6
1.7 Appended papers ... 7
2 STRENGTH DEVELOPMENT ... 9
2.1 Introduction... 9
2.1.1 Historical observations and modelling ... 9
2.1.2 Theoretical background... 12
Degree of hydration ... 12
Hydration rate ... 13
Equivalent time of maturity ... 14
Maturity function ... 18
2.1.3 Aims and purposes ... 23
2.2 New evaluation method ... 23
2.2.1 Description of reference strength development ... 23
Choice of time periods ... 23
Strength development during the fresh concrete period ... 25
Strength development during the surface finishing period ... 25
Tendency curve during the concrete hardening period ... 26
2.2.2 Modelling strength reduction ... 27
2.2.3 Total evaluation procedure ... 30
Determination processes for ET, Trefand N3 ... 30
Reference strength ... 33
Strength reduction ... 34
2.3 Example for hardening period III ... 35
2.3.1 Test preparation and procedure ... 35
2.3.2 Evaluated test data in hardening period III ... 36
2.4 Summary and conclusions ... 40
2.5 Future research ... 40
3 HEAT OF HYDRATION ... 41
3.1 Introduction... 41
3.1.1 Background to adiabatic calorimetric methods ... 41
3.1.2 Theoretical background... 42
Modelling of heat of hydration ... 42
Evaluating results from true-adiabatic measurement ... 44
Evaluating results from semi-adiabatic measurement ... 45
Empirical determination of the cooling factor... 46
3.1.3 Aims and purposes ... 48
3.2 New evaluation method ... 48
3.2.1 Refined heat of hydration evaluation for TSAs ... 48
3.2.2 Developed model for the correction factor ... 49
Laboratory setup and test preparation and procedure ... 49
General observations for the model ... 50
Prerequisites for the model concerning the correction factor ... 51
1D - heat transfer for a thermal tube ... 53
2D - heat transfer for a thermal long cylinder ... 57
3D - heat transfer for a thermal sphere ... 62
Determination of stationary heat transfer coefficient ... 66
3.2.3 Steps to determine the correction factor ... 66
3.2.4 Total evaluation procedure when using TSAs ... 68
3.3 Evaluated effect of the correction factor ... 69
3.3.1 Tested concrete recipes ... 69
3.3.2 Calculated values of the correction factor ... 69
3.3.3 Evaluated heat of hydration ... 70
3.3.4 Simulation of temperature development within walls ... 72
3.3.5 Pre-calculated correction factors for our TSAs ... 74
3.4 Summary and conclusions ... 75
3.5 Future research ... 76
4 BASIC AND DRYING CREEP ... 77
4.1 Introduction... 77
4.1.1 Background ... 77
4.1.2 Aims and purposes ... 78
4.2 Evaluation method ... 78
4.2.1 Determination and fitting of creep from laboratory tests ... 78
4.2.2 Prediction of creep and elastic modulus ... 81
4.3 Test preparation and procedure ... 82
4.3.1 Laboratory setup... 82
4.3.2 Test outline ... 84
4.4 Results ... 85
4.5 Concluding remarks ... 89
4.6 Future research ... 89
5 AUTOGENOUS SHRINKAGE AND THERMAL DILATION ... 91
5.1 Introduction... 91
5.2 Evaluation method ... 92
5.2.1 Description of what is measured ... 92
5.2.2 Evaluation Method I ... 94
5.2.3 Evaluation Method II ... 95
5.3 Test outline ... 96
5.3.1 Laboratory setup... 96
5.3.2 Tested concretes ... 97
5.4 Results ... 97
5.4.1 Model I ... 97
5.4.2 Model II ... 101
5.5 Concluding remarks ... 105
5.6 Future research ... 105
6 SUMMARY AND CONCLUSIONS ... 107
6.1 Short introduction ... 107
6.2 Answers to research questions ... 108
6.3 Contribution to the research community ... 111
6.4 Future research ... 111
7 REFERENCES... 113
1 INTRODUCTION
1.1 Background
Concrete is as known an integral part of the built society and knowledge of its material properties is essential in all stages of concreting; at planning, at construction as well as in follow-up situations. One important characteristic is the strength growth which affects a lot of actions at construction like assessment of form striking time, time for post-tensioning or any other situation affecting the strength/stiffness of the concrete of interest. This area is commonly called hardening control, and includes both choice of materials and measures to be taken on site to fulfil required conditions. When planning is to be done, often there is a need to simulate the temperature development and associated strength growth in a structure. By this, different possibilities can be analysed in order to make relevant pre-choices. An often used way is to estimate the strength growth by measuring the temperature development and by means of the maturity concept to transform the registered temperatures into concrete strength. To be able to follow the whole chain of hardening control, knowledge in maturity function (i.e. strength growth at variable temperatures) and heat of hydration is needed.
Additionally, in many situations, cracking of concrete at early ages cannot be tolerated due to the negative impact on durability and functionality. Avoiding cracks implies an evident reduction of repair, maintenance and strengthening.
Thermal cracking in concrete structures caused by heat of hydration occurs in the early ages of hydration i.e. for young concrete. Note that the definition of young concrete varies in the literature and in this thesis young concrete is defined as the time between mixing of concrete constituents to the age of 28 days, depending on sought properties in question.
Stress analysis of the young concrete, where thermal and mechanical properties are of major importance, is a valuable tool for crack avoidance, and the influencing factors on stress analysis can be shown in Figure 1.1. This have for a long period been of research interest at Luleå University of Technology (LTU), where the following material related properties of hardening concrete have been tested and modelled: maturity function, strength growth at variable temperature, heat of hydration, creep function, thermal deformations, stresses at full restraint and shrinkage.
Figure 1.1 – Schematic presentation of influencing factors in planning of crack- free concrete structures (freely from Emborg and Bernander, 1994). PI-PIV indicates areas in thesis and its appended papers.
This thesis focuses on four material property problem areas that concern both hardening control and stress analysis, i.e. PI-PIV in Figure 1.1. The background and identification of important lack of knowledge in these areas are
x Strength development of concrete has been of interest since long ago, e.g.
McDaniel (1915). Both temperature and moisture state heavily affects the strength growth. Whereas temperature is easy to measure and calculate and moisture is not. Therefore, temperature alone have commonly been used for estimating strength levels, e.g. McIntosh (1949), Nurse (1949),
ENVIRONMENT (Air temp, humidity etc)
STRUCTURE
(Geometry, dimension etc)) CONCRETING
(Sequence, joints etc)
MECHANICAL BEHAVIOUR
THERMAL PROPERTIES (Hydration heat etc)
Elasticity Creep Strength
Thermal expansion contraction Shrinkage/swelling Fracture mechanics Plasticity
MATURITY
MEASURES AGAINST CRACKING MOISTURE PROPERTIES
(Diffusion coefficients etc)
TEMPERATURE &
MOISTURE DEVELOPMENT
RESTRAINT
MATHEMATICAL MODELS
TEMPERATURE &
MOISTURE STRESSES
CRACKING RISKS
CRACK?
T S PIII
PIV PI PII
strength (Nurse, 1949; Saul, 1951; Klieger, 1958; Verbeck, 1968) and in Kjellsen et al (1990, 1991) it was shown that increased curing temperature resulted into increased porosity and coarser pore structure, which could explain the drop in strength at later ages. The maturity function, generally evaluated according to Freiesleben Hansen and Pedersen (1977), could be used to describe the strength development.
However, general models for strength development of today do not take into account the strength reduction and different applications that is needed at the construction site, e.g. EU Code (EN 1992-1-1:2004).
Therefore, there is a need for refined models.
x Heat of hydration in concrete is of major importance to both stress analysis and strength development. This heat is commonly estimated by various adiabatic calorimetric methods, e.g. (Rastrup, 1954; NT BUILD, 1992 and 1997; RILEM, 1998). The traditional semi-adiabat (TSA) is one of these methods, see Rastrup (1954), and it has the advantage that it is easy to use and has a relatively few and inexpensive parts. However, current models used to evaluate the heat of hydration with a TSA do not take into account heat lost to the measurement equipment. Therefore there is a need for refined models within this area.
x Creep deformations occurring when a hydrating concrete structure is under load. Both elastic modulus and deformations over time is of interest and is estimated in an evaluation process from laboratory tests. Suggested model for this purpose (Larson and Jonasson, 2003 I, II) have previously only been used to model the behaviour of creep at moist sealed conditions. Thus, there is a need to evaluate if this model works for drying out conditions.
x When no external load is applied on a hydrating concrete structure the deformations are considered to be derived from autogenous shrinkage and thermal deformation. To be able to describe this behaviour for a structure, measurements and modelling need to be done for a non-stationary temperature development. Suggested models from LTU (Emborg, 1989 and Hedlund, 1996 and 2000) have only been used to describe these deformations separately for concretes with relatively low w/C ratios around 0,40 using a “moderate heat” cement. Therefore, there is a need to evaluate these models for a broader range of w/C ratios and using more types of cement.
1.2 Research questions
From a production point of view it is essential to know when necessary strength has been reached on site for different applications, e.g. time period for trowelling or time for form stripping. For these purposes the maturity concept can be used as an assessment method. However, general models for strength development do not usually take this into account, see e.g. EN 1992-1-1:2004 (Euro Code 2). With respect to strength growth in structures the following research questions are formulated as
1. Is it possible to define and motivate separate time periods concerning strength growth in concrete with respect to rational information on site reflecting production behavior?
2. Is it possible to develop a refined model for strength development in concrete including early age behavior as well as strength reduction at elevated temperatures?
Heat lost to the TSA setup has not been taken into account in the traditional evaluation method. Therefore, the research questions with respect to evaluation of heat of hydration are formulated as
3. Is it possible to demonstrate the existence and need of taking into account the energy that is heating up the equipment using a semi-adiabatic test setup?
4. Is it possible to develop a reasonable simple model for evaluation of the heat of hydration in concrete, which accounts for energy stored within the different parts of a semi-adiabatic setup?
5. Is it possible to investigate how the different components of a semi- adiabatic setup affect the amount of energy to be compensated for?
The creep model LLM (Linear Logarithmic Model) have previously only been used to model the behaviour of concrete recipes under moist sealed conditions, and the research question is formulated as
6. Can the used creep model LLM (Linear Logarithmic Model) describe the moist sealed creep (basic creep) and creep in drying out conditions (drying creep) behavior for the tests performed in this thesis?
Free deformations for concretes with w/C ratios around 0,40 have using a moderate heat cement been successfully described by models developed at LTU. However, there is a lack of knowledge concerning a broader variety of w/C ratio using more types of cement. Therefore is the research question formulated as
7. Is it possible with existing models to split free deformation into thermal dilation and autogenous shrinkage adequately for tested concretes with w/C ratios for a broader range than only around 0,4 for two types of cement?
1.3 Method
In order to address these questions the following research methods have been chosen
x To lay a ground of knowledge within each concerned area mentioned above, a literature survey was performed.
x The young concrete laboratory at LTU was updated. This includes new cabling, calibration of the measurement devices, computers and a new control software
x A plan for laboratory tests was performed and executed in each of the mentioned stations used in stress analysis and hardening control, which provided material related properties needed in the research.
x The developed model was then evaluated by fitting against data received from the laboratory measurements.
1.4 Limitations
The following limitations are present in this thesis
x No full scale tests have been performed as well as no full scale analyses.
x Of all the parameters mentioned in Figure 1.1 it is only PI-PIV that are considered.
1.5 Aims, scope and original features
Main aim of this thesis is to refine models for strength and heat development of the young concrete. In addition, regarding creep and autogenous shrinkage, the aim is to evaluate if the currently used models at LTU works sufficiently well.
The refined models regarding strength development and heat of hydration are presented along with previously models developed at LTU. Several laboratory tests regarding compressive strength, heat of hydration, creep and free movements have been carried out for different concrete mixtures in order to provide material related properties in question. The resulting parameters have been used to evaluate both the developed models and the previously developed models functionality.
The following features are to the authors knowledge original:
x The presented model concerning strength development opens up the possibility to use different maturity functions at different periods in time, which can affect the production behaviour at the construction site. These periods are in the model defined as the fresh concrete period (I), surface finishing period (II) and the hardening period (III). In addition, the model is able to describe strength reduction occurring in the hardening period (III).
x The presented model for evaluation of heat of hydration in concrete is designed to account for energy stored within the different parts of any semi-adiabatic setup.
1.6 Thesis disposition
x Chapter 1 introduces the reader to the area of research.
x Chapter 2 is devoted to strength development. A deeper introduction is presented including literature review and aims and purposes connected to strength development. The theory of the developed model is described, motivated and connected to evaluation procedures. Defined time periods and corresponding strength development can be connected to the production behaviour on site.
x Chapter 3 deals with heat of hydration and a deeper introduction is given
including a literature review and aims and purposes regarding heat of hydration. It is shown how the traditional semi-adiabatic evaluation methodology can be improved by accounting for heat energy stored in the traditional semi-adiabatic equipment. The developed model theory is described, motivated and connected to evaluation procedures.
x Chapter 4 introduces the reader to creep deformation where aims and purposes of present research are given. The chapter describes the evaluation procedure used for measurements of sealed and drying creep of eight concrete mixtures and two types of cements. Measured results are used to evaluate the Linear Logarithmic Model.
x Chapter 5 is devoted to free deformation where a deeper introduction including aims and purposes are presented. A description is given on the evaluation procedure used for measurements of thermal dilation and autogenous shrinkage deformations. Laboratory measurements are used to evaluate if two LTU developed models work sufficiently well to describe the concrete behaviour.
x Chapter 6 gives a summary of the thesis x Chapter 7: references
1.7 Appended papers
The author contributed in all of these papers by performing a literature review, renovating the laboratory, setting up a schedule for laboratory tests and writing of the papers. Additional contributions are mentioned under each paper below.
Paper I: Fjellström, P., Jonasson, J-E., Emborg, M., and Hedlund, H., “Model for Concrete Strength Development Including Strength Reduction at Elevated Temperatures,” Nordic Concrete Research, Vol. 45, No. 1, July 2012, pp. 25- 44.
The author contributed by taking part in evaluation and analyse of the results with the developed model.
Paper II: Fjellström, P., Jonasson, J-E., Emborg, M., and Hedlund, H., “Heat Loss Compensation for Semi-Adiabatic Calorimetric Tests,” Submitted to:
Nordic Concrete Research, Vol. 47, No. 1, July 2013, pp. 22.
In this paper the author contributed by taking part in developing the presented model, and evaluated and analysed the results with both the traditional and refined evaluation method.
Paper III: Fjellström, P., Orosz, K., Jonasson, J-E., Emborg, M., and Hedlund, H., “Evaluation of the Linear Logarithmic Creep Model,” Intended for: XXIIth Symposium on Nordic Concrete Research & Development, June 2014, Reykjavik, Iceland, pp. 4.
The author took part in the evaluation process and analysed the results as contribution.
Paper IV: Fjellström, P., Orosz, K,. Jonasson, J-E., Emborg, M., and Hedlund, H., “Evaluation of LTU Models Describing Free Deformations,” Intended for:
XXIIth Symposium on Nordic Concrete Research & Development, June 2014, Reykjavik, Iceland, pp. 4.
In addition, the author contributed in the evaluation process as well as in analysis of the results.
2 STRENGTH DEVELOPMENT
2.1 Introduction
2.1.1 Historical observations and modelling
It has been generally known since long that the temperature and moisture state in concrete plays an important role for the hardening process, and therefore also for the strength growth. A rational way to take into account variable temperature effects on strength growth is presented by diagrams for practical use in McDaniel (1915), although no models where established. During the planning stage of the Hoover dam (Davis et al, 1933) a more complex role of temperature on concrete hardening was observed. Higher strength growth at higher temperatures was confirmed at early ages, but for long-term strength a strength reduction at higher temperatures was observed in some of the tests.
The latter phenomenon is today known as a cross over effect.
The temperature is fairly easy to measure and calculate, while moisture is difficult to measure and calculate. A consequence is that at use in practice only temperature is preferred as base for strength prediction. The first model analysing the single influence of the concrete temperature was presented in McIntosh (1949). The author used a basic age index, defined as the cumulative area below the temperature-time curve down to a datum temperature as the fundamental parameter related to the strength growth. This opened a door for an inviting way of taking temperature and time into consideration analysing strength development at variable temperature. Tests on strength rate using steam curing (Nurse, 1949) showed that initially steam cured cement paste showed accelerated strength growth for early ages, but also a drop in 28 day strength compared with air cured specimens. These observations confirmed the findings in Davis et al (1933). In Saul (1951) it was stated that for early age concrete a datum temperature of -10°C worked sufficiently enough for curing at normal temperature variations, and this was established as the well-known Nurse-Saul maturity function.
The Nurse-Saul maturity function was quickly adopted in the Scandinavian countries as a technique to estimate the concrete maturity and associated strength especially when casting in cold climate conditions (Bergström, 1953;
Rastrup, 1954; Nykänen, 1956; Jonasson, 1985). In Saul (1951) it was shown that a strength reduction occurred if the steam curing temperature of 95°C was reached before seven hours after casting, i.e. the rate of hardening at very early
ages seems to play an important role for the final strength. The findings in McIntosh (1956) were of importance for concrete casting in cold climate conditions, where the test results for curing temperatures about 6°C showed a compressive strength as high as or higher for equivalent age larger than 7 days compared with curing at room temperature. Shortly thereafter cross over effects for curing temperatures between -4°C to 49°C were demonstrated (Klieger, 1958), which again verifies the findings in Davis et al (1933), Saul (1951) and McIntosh (1956). So, the twofold effects of the curing temperature on strength: that higher curing temperatures accelerate the hardening at early ages but might result in lower final strength, has been known at least since the 1950s. In Klieger (1958) and Verbeck (1968) possible causes of the cross over effects are discussed, and the structure of the hydration products is assumed to be dependent on the curing temperature. This might explain the low final strength at high curing temperatures, and vice versa for low curing temperatures.
The importance of using the maturity concept at cold weather concreting was pinpointed by two collapses of concrete structure in U.S. with fatal consequences in the 1970s. These disasters started a number of investigations (Levendecker and Fattal, 1977; Lew et al, 1977), which resulted in the first versions of the standard ASTM C1074, updated to the current version in ASTM Standard C1074-11.
With the help of mercury intrusion and backscattered electron image analysis it was shown in Kjellsen et al (1990) that the porosity increased with increased curing temperature at the same degree of hydration. It was also found in Kjellsen et al (1991) that low curing temperatures gave a uniform distribution of hydration products, and elevated temperatures resulted in a coarser pore structure. Additionally, tests on one mortar mix showed that the maturity concept directly could be applied up to about 50% degree of hydration (Kjellsen et al, 1992). Above 50% degree of hydration, the tests indicate that the apparent activation energy also changes with the degree of hydration. This latter finding means that the hydration rate is decreased at higher degree of hydration, which might be designated a hydration retarding effect due to densification of the hydration products.
The “first model generation” completing the maturity concept with the cross over effect was established by separate adjustments of the strength growth by functions only dependent on the temperature without taking the retarding effect into account (Emborg, 1989; Tank and Carino, 1991; Jonasson, 1994; Carino
Kim et al, 2002; Yi et al, 2005; Kim and Rens, 2008 I and II) have used different techniques adding the retarding effect, either by adjusting the apparent activation energy by time or introducing separate retarding functions decreasing by time.
Another effect that retards the rate of hydration is drying, both external drying to the environment and self-desiccation at sealed conditions. The moisture effect is well known from laboratory tests (Powers, 1948) and observed in field tests (Radlinski, 2008), and this is taken care of by rules concerning moisture hardening in standards and specifications all over the world. Considering the drying effect separately is to difficult for most applications in practice, as the moisture state in a structure is rather complex to measure or calculate. The combined effect on hydration of temperature, moisture and retarding due to densification is possible to take into account for special applications, where the moisture plays a significant role, see for instance (Norling Mjörnell, 1997;
Jonasson et al, 2008). The maturity models only based on temperature might theoretically be denoted “temperature maturity models”, but this refined notation is usually not considered.
It is interesting to conclude that the maturity concept also is applicable for the stiffening during the time between initial and final set, see Pinto and Hover (1999), Schindler (2004 I), and Garcia et al (2008). This means that a comprehensive maturity model also should include this very early stage of concrete hardening.
Most results from the literature concerning maturity and evaluation of apparent activation energy is demonstrated for separate concrete mixes, but some attempts are presented where the activation energy is estimated based on information concerning chemical and physical properties of the binder (Schindler, 2004 II; and Riding, 2011).
As understood from above, the maturity concept has been used for up to 50 years in several countries to follow up the strength growth in concrete structures. When the concrete maturity properties are well known, the general conclusion is that the maturity concept is a good quality control tool for assessments of in-situ strength in concrete structures during hardening (Myers, 2000; Bagheri-Zadeh et al, 2007). One consequence in Sweden is that field object cubes have been replaced by temperature measurements on site since the beginning of the 1990s. In contrast to this, some countries in Europe still use field object cubes and compression tests when estimating strength on site, probably due to “traditional” use of existing local standards and since long established practical procedures.
2.1.2 Theoretical background
Degree of hydration
The degree of hydration, D, is an estimation of how reactions between cement and water have developed. when no reaction have occurred D 0, and at complete hydration D 1. All the mechanical properties of concrete are to some degree dependent on the degree of hydration and the kind and amount of products (gel) produced by the different clinker minerals. For instance, Bouge (1947) presented strength growth for a variety of clinker components, and Taplin (1959) could see an approximate linear relationship between the degree of hydration and compressive strength, see Figure 2.1. Note that the water-to- cement ratio affects both the rate of the load/strength growth and the degree of hydration at start of the strength growth significantly. For both of these observations it is reasonable to assume that the capillary porosity at any time is related to the strength growth.
Figure 2.1 Relationship between applied load and degree of hydration for different w0/C ratios (Taplin, 1959).
Byfors (1980) listed five commonly definitions used to determine the degree of hydration
Quantity of cement gel formed
Quantity of cement gel formed at complete hydration
D (2.1.1)
Quantity of hydrated cement Original quantity of cement
D (2.1.2)
Quantity of unhydrated cement 1 Original quantity of cement
D (2.1.3)
Quantity of heat developed
Quantity of heat developed at complete hydration
D (2.1.4)
Powers and Brownyard (1948) found, based on empirical data, that when cement hydrates completely, the gel products formed contain about 25 % chemically bound water (wn), which gives an additional formulation of the degree of hydration by
0, 25 wn
D C
(2.1.5)
The most important factors affecting the degree of hydration is according to Jonasson (1994) the type of cement, mixing procedure, mechanical activation, chemical activation, time after mixing, curing temperature and access of water.
Here, as in Jonasson (1994), the use of a certain cement with additives, admixtures and mix procedure is regarded as one type of cement.
Hydration rate
It has since long been known that temperature is one of many factors that affect the hydration process (McDaniel, 1915). Nurse (1949) could show that temperature affected the rate of reactions in the well-known way; higher concrete curing temperatures could result in accelerated strength growth compared to lower curing temperatures. Verbeck and Helmut (1968) got similar results, and showed an increased rate of reaction for higher curing temperatures, see Figure 2.2. The increased rate of reaction naturally corresponded to a higher 1 day compressive strength, but also important to mention, a decrease in 28 day strength. About 20 years later (Kjellsen et al, 1990) it was proved that for the same degree of hydration higher curing temperature resulted in higher paste porosity, which in turn affect the compressive strength.
Figure 2.2 To the left is shown that increased curing temperature increases the initial rate of hydration. To the right is shown that the initial increased rate of hydration results in higher strength at 1 day and lower strength at 28 days.
(Verbeck and Helmut, 1968).
Equivalent time of maturity
Since the first concept of maturity and equivalent time was established by McIntosh (1949) several different maturity functions have been presented in the literature. Today, the most frequently used maturity formulation comes from Freiesleben Hansen and Pedersen (1977), and their mathematical layout of the maturity age is therefore presented here. The formulation is based on
d g f T t
dt
D D (2.1.6)
where the hydration rate dD/dt in a paste, at a given degree of hydration, D , is considered only as a function f T t
of the temperature T t in question. The
prerequisites are that g
D and f T t
are mathematically separable functions. For variable temperature with time, an integration gives
t
d G f T t dt
D D
D
³ ³
(2.1.7)Curing temperature [qC]
Initial hydration rate [cal/gr/day]
Curing temperature [qC]
Compressive strength [MPa]
20 40 60 y 80
0
25 50 75 100 10 20 30 40 50
0 10 p 20 30
[ 40 At 28 days
At 1 day
If a general constant temperature, Ti, is compared with a isothermal curing process at the reference temperature, Tref, for the same degree of hydration, then G
D is the same in both cases described by
0 0
ref
i ref
ti t
f T dt f T dt
³ ³
(2.1.8)which gives
i i
ref ref
f T t f T t (2.1.9)
and
i
e ref i T i i
ref
t t f T t T t
f T E
{ (2.1.10)
or
ref i
T i
ref i
t T f T
f T t
E (2.1.11)
where te = the maturity age for curing at temperature Ti, and ET
Ti =
hydration rate factor depending on the temperature Ti.
As can be seen in Eq. 2.1.10 that E = 1 for T Ti Tref. For a curing process with variable temperature, te is expressed by
0 t
e T
t
³
E T t dt (2.1.12)where ET
T usually is called the temperature dependent maturity function or just simply maturity function, see also Freiesleben Hansen and Pedersen (1977).
Since there is an approximate linear relationship between the degree of hydration and compressive strength, see Figure 2.1, the relationship between
strength and degree of hydration can be formulated, see also Concrete Handbook (1994), as
cc 0
f for D D 0 (2.1.13)
0
fcc k D D for D Dt 0 (2.1.14) where D [-] = degree of hydration where 0 fcc 0; fcc[Pa] = compressive strength; k[Pa] = the inclination for strength growth with respect to degree of hydration.
The derivative of Eq. 2.1.14 with respect to time gives dfcc d
dt k dt
D (2.1.15)
From the Eqs. 2.1.14-2.1.15 it is clear that the compressive strength growth is here regarded as linear related to the degree of hydration, and that the strength rate is linear related to the degree of hydration rate. As a consequence of these linear relationships, Eq. 2.1.6 can be formulated as
0
cc
cc
df g k f f T t
dt D (2.1.16)
From Eq. 2.1.16 it is evident that the procedure described by Eqs. 2.1.7-2.1.12 is valid also for strength level and strength growth. So, in practice testing of strength development for variable temperature can be used to establish the maturity function ET
T . An example of possible strength developments from testing is shown in Figure 2.3.
Figure 2.3 Typical hypothetic behavior of strength development (fcc) in linear scale as a function of real time in logarithmic scale for different constant curing temperatures, Ti. The circles represent fabricated test results, and the solid lines represent ideal strength growth without strength reduction at later ages.
The strength developments for a reference strength curve (T Tref) and an ideal strength curve for curing at a higher temperature (T Ti !Tref) is shown schematically in Figure 2.4. For an arbitrary strength level (
cci
f ) the logarithm of time associated with the strength level is expressed by
ln tref ln ti ln xi (2.1.17)
or
ref i i
t t x (2.1.18)
A comparison with Eq. 2.1.11 gives
ref
T i i
i
T x t
E t (2.1.19)
Real time, logarithmic scale
Figure 2.4 Illustrations of two ideal compressive strength curves displaced solely dependent on difference in curing temperature. Note that, Ti !Tref. (freely from Ekerfors, 1995).
This means that the rate factor E can directly be obtained from relations in T time for ideal strength developments, which is easy to establish from strength tests.
It must be noted here that the first step in the evaluation of E is to determine T the reference strength curve, i.e. the blue curve (T20) in Figure 2.3. Then the ideal strength curves are determined, see the curves corresponding to T5, T35, and T50 in Figure 2.3. As shown, the ideal strength curves do not take strength reduction into account, and as a consequence, the measured results (circles) in Figure 2.3, may not fit the ideal curves when reduction is present.
Maturity function
Freiesleben Hansen and Pedersen (1977) found that the temperature function, defined in Eq. 2.1.6, could best be described by the Arrhenius function of thermally activated rate processes
exp E
f T k
R T
§ ·
¨© ¸¹ (2.1.20)
where k= proportionality constant; E[J/mol] = activation energy; R[J/mol K]
= the universal gas constant; T[K] = absolute temperature.
1 1
293 273
T
c
E
R T t
E ª« §¨ ·¸º»
« © ¹»
¬ ¼
(2.1.21)
where E = the temperature dependent maturity function based on the T Arrhenius function.
The activation energy is not always constant, and therefore Eq. 2.1.21 is not used in a strict way. However, it has a theoretical meaning of thermal activation of chemical reactions, and is therefore inviting to use. Jonasson (1984) introduced the following empirical expression for activation energy
30 3
10
c
ref c
E T t
R T t
N
T T ¨§ ·¸
© ¹
for T tc
! 10DC (2.1.22) and
T f for T tc
d 10DC (2.1.23) where Tref[K] and N [-] are fitting parameters, determined from test results. 3 However, ideal strength curves must exist before these parameters can be decided.
Using Eqs. 2.1.22 and 2.1.23, Eq. 2.1.21 can be reformulated as
T 0
E { for T tc
d 10DC (2.1.24)
30 3 1 1
exp 10 293 273
T ref
c c
T t T t
N
E T
ª § · § ·º
« ¨ ¸ ¨ ¸»
« © ¹ © ¹»
¬ ¼
for T tc
! 10DC (2.1.25) After evaluating the compressive strength results for different temperatures conditions (Figure 2.3 and Eq. 2.1.19), a maturity function can be drawn using Eq. 2.1.25, see Figure 2.5.
Figure 2.5 Maturity function fitted to test data considered to represent the ideal values of compressive strength (Figure 2.3). Here the reference temperature is chosen to be 20qC.
Many test results, see for instance Saul (1951), have shown that the concrete hydration process stops at a temperature about -10°C. This is reflected in Eq.
2.1.22 as 4(T) = f for T = -10°C. A similar behavior is formulated in Freiesleben Hansen and Pedersen (1977) by
E T A for T t20DC (2.1.26)
and
20
E T AB T for 10DCdT d20DC (2.1.27) where A[J/mol] and B[J/mol °C] are constants from fitting of test results.
In Freiesleben Hansen and Pedersen (1977) the following parameters were used 33500 J/mol C and 1470 J/mol C
A D B D (2.1.28)
Based on Eq. 2.1.28 and fitting to Eq. 2.1.22 using the method of least square deviation within the temperature span -10°C to 50°C gives the following values
The temperature rate factor, E , and the activation energy/general gas constant, T
/
E R, with the parameters in Eqs. 2.1.28-2.1.29 are presented in Figure 2.6.
The deviations in the E R/ values are visually rather big in Figure 2.6, but the agreement for the corresponding E values are acceptable in the left part of T Figure 2.6. So, within the temperature span -10°C to 50°C it is possible to use either Eq. 2.1.22 or Eqs. 2.1.26 and 2.1.27.
Figure 2.6 To the left ET
T [-] and to the right E R T [K] are shown as a /
function of temperature.
If we use a constant activation energy for the whole temperature span, either A
= 33500 J/mol and B = 0 according to Eqs. 2.1.26 and 2.1.27 or Tref = 4029 K and N = 0 in Eq. 2.1.22, we get the curves denoted “3 E= constant = 33500 J/mol” in Figure 2.6. From the calculated curves it is apparent that for temperatures below 20°C, the use of a constant activation energy gives higher temperature rate factors than expected. It is also seen that E significantly > 0 T for T= -10°C, which also is valid using Eq. 2.1.22 although the requirement E T
{ 0 for T = -10°C is mathematically fulfilled. If we have test results at curing temperatures below T = 20°C, it always results in B > 0 (Eq. 2.1.27) and N > 3 0 (Eq. 2.1.22). In situations where we only have tests results for T t 20°C, we have to state the condition
0, say larger than about 1000 J/mol C
B! B D (2.1.30)
using Eqs. 2.1.26 and 2.1.27, and
3 0, say 3 larger than about 0,25
N ! N (2.1.31)
0 1 2 3 4
-10 0 10 20 30 40 50
Beta_T [-]
Temperature qqC E = konstant = 33500 J/mol Freieslen Hansen and Pedersen (1977) using Eq. 2.1.28 Eq. 2.1.25 using Eq. 2.1.29
0 5000 10000 15000 20000
-10 0 10 20 30 40 50
E / R [K]
Temperature qqC E = konstant = 33500 J/mol Freieslen Hansen and Pedersen (1977) using Eq. 2.1.28 Eq. 2.1.22 using Eq. 2.1.29
using Eq. 2.1.22.
However, one must keep in mind that modelling maturity as dependent on temperature alone is a simplified modelling, and it can be enhanced by adding more details to the function. For example, in Jonasson (1984, 1994) and Concrete Handbook (1994), it is shown that the equivalent time of maturity also can be expressed as a function of temperature
ET , moisture (E ), effect of RH admixtures (E'), a densifying factor (E ) and when the equivalent time of D maturity should be considered as started, 'te0.
0 0
t
e T RH e
t
³
E E E ED 'dt 't (2.1.32)where te[s or h] = equivalent time of maturity; 'te0[s or h] = equivalent time of maturity at t 0; E [-] = rate factor depending on temperature; T E [-] = rate RH factor depending on relative humidity; E'[-] = adjustment parameter depending on admixtures; E [-] = densifying factor. D
For young concrete ED |1, and at high humidities ERH |1. At moist sealed conditions the humidity is also high for young concrete, which means that Eq.
2.1.32 (Jonasson, 1984) can be approximated to
0 0
t
e T e
t E'
³
E dt 't (2.1.33)Introducing the parameter'te0 gives the possibilities to
x Choose'te0 z0 as a time after mixing, when t 0 from time of casting.
x Model effects of different admixtures in cases where the observed shift approximately is constant in linear time scale.
x Simulate different casting times at different locations.
By introducing E' effects of different admixtures can be modelled in cases where the observed shift approximately is constant in logarithmic time scale.
When comparing one concrete mix without admixtures using 'te0 = 0 and E'
=1 with a similar mix with admixtures, we might observe a retarding effect
all parameters from the first mix and only introduce changes for the second mix with 'te0 < 0 and E' t 1.
2.1.3 Aims and purposes
As already mentioned, that from a production point of view it is essential to know when necessary strength for different applications has been reached on site, e.g. time period for trowelling or time for form stripping. For these purposes the maturity concept can be used as a method of assessment.
However, general models for strength development do not usually take this into account, see e.g. EN 1992-1-1:2004 (Euro Code 2). Therefore, with respect to strength growth in structures, the aims and purposes are
x To define and motivate separate time periods concerning strength growth in concrete with respect to rational information on site affecting production behaviour.
x To analyse and develop a refined model for strength development in concrete including early age behaviour as well as strength reduction at elevated curing temperatures.
2.2 New evaluation method
2.2.1 Description of reference strength development
Choice of time periods
It is important that different time periods are defined with respect to the behaviour on site, and that the periods can be defined from properties of concrete. Starting from casting, see Figure 2.7, three periods connected to the treatment of concrete are here defined as
I. Fresh concrete period II. Surface finishing period III. Hardening period
These three time periods are in line with what is used by Pinto and Hover (1999), Schindler (2004) and Garcia et al (2008), see Figure 2.7 where the
denotation fcc ref, means the strength growth at reference conditions – here for
ref 20 C
T T D . Some preliminary tests have shown that the influence of the temperature might be different within these time periods, and the modelling presented below is structured to take this into account.
Here the first period is denoted “fresh” concrete as the contractor is able to place and vibrate the concrete without damaging the structure of the cement paste.
Figure 2.7 Reference strength ( fcc ref, ) as a function of equivalent time (te).
Note that te may be calculated differently within each period, see further Eqs.
2.2.4, 2.2.6 and 2.2.9.
The second period in Figure 2.7 may approximately be regarded as the time between initial and final setting, which in practice means that the contractor is able to process the surface finishing within this period. The limits for the surface finishing period are usually defined by penetration resistance in cement paste (Garcia et al, 2008) or mortar. Here, concrete strength is used to describe the surface finishing period by
fresh 0MPa
f (2.2.1)
0,5MPa
surface
f (2.2.2)
where ffresh= 0MPa from casting to the equivalent time at the end of the fresh
the equivalent time, te surface, , at the end of the surface finishing period. The notation strength is here used for compression tests performed on 100mm or 150mm cubes.
Strength development during the fresh concrete period
The parameter te fresh, may be taken as the time when the concrete surface is walkable with a permanent imprint of about 5-10mm (Concrete Handbook, 1992). The strength growth and the equivalent time during the fresh concrete period are described by
: cc ref, 0
I f for 0d dt tI (2.2.3)
and
0 0
: e T e
t
I t E'³E dt 't for 0d dt tI (2.2.4)
where fcc ref, [MPa] = strength growth at reference conditions as a function of equivalent time, te [h]; t [h] is real time; tI [h] is the time when te te fresh, using Eq. 2.2.4 with Tref Tref I, and N3 N3, I for calculation of E ; and T
E' E', I . The parameters te fresh, [h], Tref I, [K], N3, I[-], E', I[-] and 'te0 [h] are evaluated from fitting of test data.
Strength development during the surface finishing period
The strength fsurface is here proposed to be 0,5MPa. In practice it has been shown that the actual surface finishing normally can be performed between the strength of about 0,1MPa to 0,4MPa (Petersson and Johansson, 1991) which is within the limits defined by Eqs. 2.2.1-2.2.2. Exact limits for different kinds of surface finishing treatments must be tested separately for each mix. The strength growth and the equivalent time during the surface finishing period are described by
, ,
, ,
:
surface e e fresh
cc ref surface
e surface e fresh
t t n
II f f
t t
§ ·
¨¨© ¸¸¹
for tI dt tII (2.2.5) with
: e e fresh, T
I
t
II t t dt
t E' E
³ for tI dt tII (2.2.6)
where fcc ref, [MPa] = strength growth at reference conditions as a function of equivalent time, te[h]; tII[h] is the time when te te surface, using Eq. 2.2.6 with
, ref ref II
T T and N3 N3, II for calculation of E ; and T E' E', II. The parameters
surface
n [-],te surface, [h], Tref II, [K], N3, II[-] and E', II[-] are evaluated from fitting of test data.
Tendency curve during the concrete hardening period
The strength growth according to EN 1992-1-1:2004 (Euro Code 2) is expressed by
, ,28
1 / 2 exp 1 672
cc ref cc d
f f s
t
ª º½
° « § · »°
® ¨ ¸ ¾
« © ¹ »
° ¬ ¼°
¯ ¿
(2.2.7)
where fcc,28d[MPa] = 28 days compressive strength for reference conditions; s [-] is a coefficient which depends on the type of cement; and t[h] is the time for mean temperature of 20°C and moist curing.
From the basic formulation in Eq. 2.2.7, the strength growth during the hardening period (III) is modified as
,28
, ,28
672 *
: exp 1
*
cc d
cc ref cc d
e
n
III f f s t
t t
ª § · º½
° « ¨ ¸ »°
®°¯ ««¬ ¨© ¸¹ »»¼¾°¿
for t!tII (2.2.8)
with : ,
II
e e surface T
t
III t t dt
t E' E
³ for t!tII (2.2.9)
where fcc ref, [MPa] = strength growth at reference conditions as a function of
Application of Eq. 2.2.8 means that Eq. 2.2.9 shall be used with Tref Tref III, and N3 N3, III for calculation of E , and T E' E', III. The parameters fcc,28d [MPa], s[-], ncc,28d[-], Tref III, [K], N3, III[-] and E', III[-] are evaluated from fitting of test data. t*[h] is introduced to fit the data point (te surface, , fsurface), which means that the compressive strength at end point of time period II has to be the same as at the start point of time period III, see Figure 2.7. The numerical value of t* has no physical meaning and is calculated by
, ,
,28
,28
,
let
1 1 / calculate using Eq.2.2.8 1 ln
* 672 and finally
1
surface cc ref e surface
cc d surface
c
cc d
c e surface
c
f f t
f n
f s
t t G
G G
§ ·
¨ ¸
¨ ¸
© ¹
(2.2.10)
When evaluating a specific recipe for the first time the parameters E', j[-] {j=I, II, III} are usually set = 1, and parameter 'te0 is usually set = 0. Then, if only the type of admixture is changed, it might be possible only to introduce E',j z1 and/or 'te0 z0 as additional parameters to existing model data for a basic recipe, see also Chapter 2.1.2.
2.2.2 Modelling strength reduction
The typical behaviour, when cross over effects occur, is shown in Figure 2.8.
The notation cross over originates from plotting linear strength as a function of real time, see left part of Figure 2.8. When time is transformed to equivalent time it is possible to use the term strength reduction for temperatures above a chosen reference temperature, here 20°C, see right part of Figure 2.8. The strength for temperatures below reference temperature also shows a cross over effect (or strength gain), but this part is here ignored and might be regarded as an extra margin.
Figure 2.8 Typically strength results for specimens cured between 5°C and 50°C, at left plotted in real time and to the right in equivalent time. Note that when plotted in equivalent time the lines are crossing, and hence, the background to the term “cross-over effect”.
The strength reduction due to elevated hardening temperatures is only calculated for the hardening period (III) by
max
, ,28 ,28
cc cc ref drop drop d cc d
f f J ' f for t!tII (2.2.11)
where 'maxdrop,28d[-] = maximum strength reduction at te= 672h; Jdrop{0,1} is the factor taking into account the temperature effect on strength reduction.
The technique to describe the reduction in strength according to Eq. 2.2.11 is here characterized by the following observations
1) The drop in strength starts at some minimum temperature, reflected by JTemp(Eq. 2.2.15).
2) Elevated temperatures influence the strength drop after a certain time, reflected by Jtime (Eq. 2.2.16).
3) The retarding effect at later ages (Kjellsen et al, 1992) is here modelled by the “relative” rate of reaction (dD* /dte, see Eqs. 2.2.17 and 2.2.18).
These three phenomena can be described by the following material related empirical model
drop drop
J G
G (2.2.12)
