degree of hydration concept for early...

CONCRACK 3 – RILEM-JCI International Workshop on Crack Control of Mass Concrete and Related Issues Concerning Early-Age of Concrete Structures, 15-16 March 2012, Paris, France

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DEGREE OF HYDRATION CONCEPT FOR EARLY AGE CONCRETE – A SUMMARY

Geert De Schutter (1)

(1) Magnel Laboratory for Concrete Research, Department of Structural Engineering, Ghent University, Belgium

Abstract

Early age thermal cracking in hardening massive concrete elements is a complicated issue. A detailed study of this phenomenon needs to take into account the evolving nature of thermal and mechanical material properties. A fundamental approach is provided by the degree of hydration concept. Within this concept, material properties are related to the microstructural development during the hydration process. This also includes the time dependent creep and relaxation behaviour. The degree of hydration concept can be implemented in finite element codes, enabling the evaluation of crack risks, and the optimization of the casting process. An overview is given of the degree of hydration concept, and some illustrative example is given.

Résumé La fissuration thermique dans le béton jeune est un phénomène assez complexe. Pour une

étude détaillée du phénomène, il faut prendre en compte la nature évolutive des propriétés thermiques et mécaniques. Cet article présente une approche fondamentale, basée sur le degré d’hydratation. Suivant cette approche, les propriétés du matériau sont liées au développement de la microstructure en phase de durcissement. Ceci est également valable pour les propriétés différées telles que le fluage et la relaxation. L’approche basée sur le degré d’hydratation s’introduit également dans des codes d’éléments finis, ce qui permet à évaluer les risques de fissuration et à étudier une optimisation du processus de gâchage. L’article résume l’approche basée sur le degré d’hydratation, et donne un exemple.

1. INTRODUCTION In hardening massive concrete structures, early age thermal cracking can occur due to

thermal gradients caused by the heat of hydration. The exothermal reaction process causes a temperature rise in the concrete. Typically, the core of massive elements will be at higher temperature than the element surface. Due to this thermal gradient, mechanical stresses will be initiated. In a first phase, the surface area will be under tension, while the element core will be under compression. After a while, when the hydration process tends to slow down making the element to cool down, the stress image will be inverted, now having tensile stresses in the core, and compressive stresses near the surface. The stress levels are depending on many parameters, like mix design, thermal properties, mechanical properties, creep and relaxation


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behaviour, shrinkage, element geometry, thermal and mechanical boundary conditions. Most of the influencing parameters evolve during the hydration process, which makes the study of early age thermal cracking a very complicated matter.

Early age thermal cracking in massive concrete structures due to the heat of hydration is not a new issue. Already in 1928, the spectacular failure of the St. Francis dam in Southern California has been ascribed to thermal stresses. Nevertheless, a fundamental understanding and modeling of early age thermal stresses and cracking indeed is more recent. In this paper, it is supposed that the reader is familiar with the phenomenon of early age thermal cracking. A summary is given of the degree of hydration concept as a fundamental approach for modeling early age concrete behaviour. This concept can be implemented in finite element codes, enabling the evaluation of crack risks, and the optimization of the casting process [1].

2. THERMAL STUDY

2.1 Specific heat Considering the conversion of free water into chemically bound water during the hydration

process, a decrease of the specific heat during hardening of the concrete at isothermal conditions is to be expected. Most of the experimental results reported in literature indeed show a decrease of the specific heat during hardening. However, there seems to be no general agreement on the magnitude of the decrease. In this respect, it has to be commented that some researchers published data obtained on concrete specimens, while others tested cement paste or mortar. An indicative conversion of the published results to a conventional gravel concrete shows a decrease up to 20%, depending on the different test parameters, e.g. cement type, w/c ratio, aggregate type, humidity… A typical evolution of 1.1 to 1.2 kJ/kg.K for fresh concrete down to 1.0 to 1.1 kJ/kg.K can be mentioned. The specific heat can be modeled as a linear function of the degree of hydration [2].

On the other hand, the specific heat is also temperature dependent. In massive concrete elements, where the heat of hydration causes a temperature increase, an increase of the specific heat by about 10% due to the semi-adiabatic temperature rise can be obtained. This might partly compensate the decrease of the specific heat due to the evolving hydration process.

2.2 Thermal conductivity There is no consensus yet about the evolution of the thermal conductivity during hydration.

While for specific heat there is some fundamental agreement between the various researchers, literature data on the thermal conductivity are not coherent. Constant values during hardening are reported as well as increasing and decreasing tendencies. Depending on the concrete composition, values ranging from 6 to 9 kJ/m.h.K have been reported, with small fluctuations during hardening. It is often assumed that the variations are quite small, and that for practical simulations the thermal conductivity can be considered as a constant value throughout the hydration process. Nevertheless, for the concrete compositions considered in [2], a linear evolution of the thermal conductivity as a function of the degree of hydration was found.


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2.3 Heat of hydration A general hydration model has been developed valid for Portland cement as well as for

blast furnace slag cement, following the degree of hydration concept. This model enables the calculation of the heat production rate as a function of the actual temperature and the degree of hydration. As a practical approximation the degree of reaction can be used instead of the degree of hydration. For blended cements like blast furnace slag cement, the hydration model is based on the superposition of the heat production of the Portland reaction (P-reaction) and of the slag reaction (S-reaction):

SP qqq += (1)

)(.)(.20max,, θPPPPP grfqq = (2)

[ ] ).(exp.)(sin.)( PPa

PPPP rbrcrf P −= π (3)

)(.)(.20max,, θSSSSS grfqq = (4)

[ ] SaSSS rrf )(sin)( π= (5)

with qP the heat production rate of the P-reaction, qS the heat production rate of the S-reaction, qP,max,20 the maximum heat production rate of the P-reaction at 20°C, rP the degree of hydration of the P-reaction, aP, bP, cp constants, gP(θ) an Arrhenius function depending on the temperature θ, qS,max,20 the maximum heat production rate of the S-reaction at 20°C, rS the degree of hydration (reaction) of the S-reaction, aS constant, gS(θ) an Arrhenius function depending on the temperature θ.

The degrees of hydration rP and rS can be estimated as the fraction of the heat of hydration already released by the corresponding reactions. Further parameters in the hydration model are the initial degrees of reaction of both reactions, and the temperature dependent value of the degree of hydration of the P-reaction from which value on the S-reaction initiates due to the Portland activation. The hydration model is presented in more detail in [3].

3. MECHANICAL STUDY

3.1 Coefficient of thermal expansion The coefficient of thermal expansion (CTE) is very high at early ages (15 to 20.10-6/K), but

decreases drastically as the concrete hardens (Fig. 1), reaching a value of 8 to 12.10-6/K for hardened concrete, depending on the concrete composition. In somewhat more detail, the CTE is reported to decrease strongly during the first day, followed by a slight increase gradually over time. A degree of hydration based formulation can be adopted. For high-early-strength cement concrete, a less pronounced time dependency is reported, due to faster hardening.


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Figure 1: Coefficient of thermal expansion

3.2 Strength properties The strength properties of the hardening concrete can be modelled by means of a degree of

hydration based formulation. As a typical formulation, the compressive strength evolution during the hydration process can be modelled by following equation:

a

C

C

rrr

rfrf

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

== 0

0

1)1()(

(6)

with fC the compressive strength, r the degree of hydration, r0 the percolation threshold, and a constant. Similar equations can be given for the other mechanical properties like tensile strength, Young’s modulus, etc. [4].

3.3 Fracture energy The evolution of the fracture energy while hardening can also be described by a degree of

hydration based formulation [5]: d

f

f

rrr

rGrG

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

== 0

0

1)1()(

(7)

with Gf the specific fracture energy, r the degree of hydration, r0 the percolation threshold, and d constant.

This degree of hydration based specific fracture energy model can be implemented in code provided softening functions. It can be combined with a non-linear softening function [6].

3.4 Basic creep and relaxation Based on fundamental physical observations, a degree of hydration based Kelvin chain has

been defined for early age concrete, including instantaneous deformation and basic creep (Figure 2). The Kelvin chain model was experimentally validated for constant and varying stress conditions, and a good accuracy was reported [7].


149

Figure 2: Degree of hydration based Kelvin chain for early age concrete

Even more fundamentally, the effect of ongoing hydration and microcracking on the basic

creep of early age concrete has been studied by fully linking it to the degree of hydration. Time is no longer an explicit parameter in the resulting model, its role being taken over by the degree of hydration. Besides a fundamental non-linear model for the basic creep under constant stresses, as given in equations (8) and (9), a new method for the situation of varying stresses was developed, called the fictitious degree of hydration method [8].

),(.),(),,( 0 bcbbcbbcc rrrrr ϕαεαε = (8)

)(

1

2

1)(),(

brc

b

bbbc r

rrrcrr ⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=ϕ (9)

In the equations, εcc is the basic creep strain, εc0 the instantaneous deformation due to the stress level αb at loading, r the degree of hydration, rb the degree of hydration at loading, ϕc the creep coefficient, c1 and c2 constants depending on rb. For details on the fictitious degree of hydration method for varying stress levels, reference is made to [8].

In equation (8), the non-linearity of the basic creep strain is perfectly correlated with the non-linearity of the instantaneous deformation at loading, which is pointing to the crucial role of microcracking for the time dependent mechanical behaviour of early age concrete.

4. NUMERICAL SIMULATION The degree of hydration based material laws can be implemented in finite element codes,

as illustrated in [6, 9, 10]. The simulation of early age thermal stresses and cracking typically consists of a staggered analysis. In a first step, the thermal fields are calculated following the well-know non-stationary Fourier equation with source term:

'qyyxxt

c TTT +⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

=∂∂ θλθλθ

(10)

with θ the temperature [K], t the time [s], x and y the co-ordinates [m], cT the heat capacity of the concrete [kJ/m³K], λT the heat conduction coefficient of the concrete [W/mK], and q’ the heat production [W/m³]. The Fourier equation has to be combined with the appropriate initial and boundary conditions.


150

In a second step, after the thermal calculations, the stresses and possibly crack formation have to be simulated by considering the evolving mechanical material behaviour. The visco-elastic behaviour (basic creep and relaxation) can be implemented by means of the degree of hydration based Maxwell chain shown in Figure 2. It is more complicated or even impossible to implement the fictitious degree of hydration model into commercially available software programs. Nevertheless, in own software or by considering user defined routines, this can also be achieved. The cracking behaviour of the hardening concrete can be implemented by means of a variety of available softening models, in which the degree of hydration based evolution of the fracture energy can be incorporated.

5. EXAMPLE For the storage of high level nuclear waste, a concept of concrete supercontainers has been

developed in Belgium. These supercontainers, containing the nuclear waste, will be stored in thick clay layers, 200 meter under ground level. As the supercontainer is rather massive, and as cracks have to be avoided for obvious reasons, the early age thermal behaviour has been studied in detail. In order to validate simulation results, a large scale test has been performed at the Magnel Laboratory for Concrete Research, Ghent, Belgium, on a so-called half-scale container (Figure 3).

Two construction steps have been evaluated: - The fabrication of the buffer in a steel envelope (Phase 1) and the evaluation of the construction feasibility of the buffer of the Supercontainer. These tests started 6th of June 2009; - The insertion of a heater element into the created opening of the buffer and the closure of the container by casting the filler and the lid material under thermal load (Phase 2). Phase 2 consists of a heating phase (672 hours) and a cooling phase (672 hours). These tests started 5th of October 2009.

Figure 3: 3D-sketch of the concrete supercontainer, and studied finite element mesh.


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Note that the term ‘Half-Scale’ originates from the original plans of casting a container,

identical to the Supercontainer in thickness and in diameter, but with a height that is 50 % of the height of the Supercontainer. Nevertheless, the height was increased, due to the additional tests that were planned and performed on the container: insertion of a heat-emitting overpack, filling of the gap, closure of the lid and quality determination of the interface between the filler, the buffer and the cylindrical metal overpack.

Figure 4 shows a vertical cross section of the tested half-scale supercontainer (left), and the instrumented container during the tests, just after casting the filler material of phase 2 inside the container (right). A detailed positioning of the thermocouples, LVDTs and strain gauges is shown in Figure 5. The sensors were placed at 5 different horizontal levels, as also indicated in Figure 4 (levels A, B, C, D and E).

A finite element modelling was performed, based on the degree of hydration concept as much as possible, within the possibilities of the commercially available software code HEAT. Details of the simulations and of the obtained results can be found in papers [10] and [11].

Figure 6 shows some thermal results, comparing the simulated and measured temperature in point 1 of levels B and D. Similar graphs have been obtained for the other points where thermocouples have been installed during testing. Figure 7 shows some mechanical results, comparing the vertical displacement of the top surface of the half-scale container. LVDT measurements started after 68 h, and all obtained results are plotted relative to this timing. Positive values refer to shrinkage (contraction) of the container. Although in general, the agreement between simulation and experiment is better for the thermal results, the displacements can also be simulated in a satisfying way.

Figure 4: dimensions of the half-scale test setup (left), and instrumented half-scale container (right)


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Figure 5: Instrumentation (Thermocouples, LVDTs and strain gauges)


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20

25

30

35

40

45

50

55

60

65

0 24 48 72 96 120 144 168

Time (hours)

Tem

pera

ture

(°C

)

B 1

D 1

TCB 1

TCD 1

Figure 6: Temperature evolution in point 1 of levels B and D (simulation and measurements)

-0.5

-0.3

-0.1

0.1

0.3

0.5

0 24 48 72 96 120 144 168

Time (hours)

Uy (

mm

)

E 1-2

LVE 1-2

Figure 7: Vertical displacement of top surface (simulation and measurements)


154

6. CONCLUSIONS This paper presents a short summary of the degree of hydration concept for the study of

early age thermal stresses and cracking in hardening massive concrete elements. Thermal and mechanical properties can be modelled as a function of the degree of hydration. The degree of hydration based models can be implemented in finite element software, enabling a fundamental study of the early age behaviour. The concept is illustrated with the example of concrete supercontainers for the storage of high level nuclear waste in Belgium.

ACKNOWLEDGEMENTS This paper presents an invited summary of the research performed by the author.

Consequently, reference is made to own work. Within the cited papers however, due reference is made to the inspiring work of many colleagues.

REFERENCES

[1] De Schutter, G., ‘Fundamental and practical study of early age thermal stresses in hardening massive concrete elements’(in Dutch), doctoral thesis, Magnel Laboratory for Concrete Research, Ghent University, Belgium, 1996.

[2] De Schutter, G., Taerwe, L., ‘Specific heat and thermal diffusivity of hardening concrete.’, Magazine of Concrete Research 47 (172) (1995) 203-208.

[3] De Schutter, G., Taerwe, L. ‘General hydration model for Portland cement and blast furnace slag cement’, Cem.Conc.Res. 3 (1995) 593-604.

[4] De Schutter, G. and Taerwe, L., ‘Degree of hydration-based description of mechanical properties of early age concrete’, Materials and Structures 29 (1996) 335-344.

[5] De Schutter, G. and Taerwe, L., ‘Fracture energy of concrete at early ages’, Materials and Structures 30 (1997) 67-71.

[6] De Schutter, G., 'Finite element simulation of thermal cracking in massive hardening concrete elements using degree of hydration based material laws', Computers and Structures 80 (27-30) (2002) 2035-2042.

[7] De Schutter, G.,’Degree of hydration based Kelvin model for the basic creep of early age concrete’, Materials and Structures 32 (1999) 260-265.

[8] De Schutter, G. and Taerwe, L.,‘Fictitious degee of hydration method for the basic creep of early age concrete’, Materials and Structures 33 (2000) 370-380.

[9] De Schutter, G., Vuylsteke, M., ‘Minimisation of early age thermal cracking in a J-shaped non-reinforced massive concrete quay wall’, Engineering Structures 26 (2004) 801-808.

[10] Craeye, B., De Schutter, G., Van Humbeeck, H., Van Cotthem, A., ‘Early age behaviour of concrete supercontainers for radioactive waste disposal’, Nuclear Engineering and Design 239 (2009) 23-35.

[11] Craeye, B., De Schutter, G., Wacquier, W., Van Humbeeck, H., Van Cotthem, A., Areias, L., ‘Closure of the concrete supercontainer in hot cell under thermal load’, Nuclear Engineering and Design 241 (2011) 1352-1359.

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