challenges in modeling cementitious...

International RILEM Conference on Material Science – MATSCI, Aachen 2010 – Vol. II, HetMat 33

CHALLENGES IN MODELING CEMENTITIOUS MATERIALS

K. Scrivener, Laboratory of Construction Materials, EPFL, Switzerland

ABSTRACT: In order to meet the demands of sustainable development the range of cementitious materials used will need to become more diverse. To master the use of this range of materials, modelling has an essential role to play in linking composition and processing to the final properties and performance. This paper describes some of the challenges such modelling presents and progress made at the Laboratory of Construction Materials at EPFL, based on the microstructural models µic [Bis09a, Bis09b] and AMIE [Dun10].

1 INTRODUCTION

Concrete is the most used material on the planet and is the only material which can be produced in sufficient quantities to meet the demands of the growing world population. Intrinsically concrete has a low environmental footprint compared to alternatives (Table 1.1), however the enormous volumes produced means that concrete accounts for some 5-8% of man-made CO2 emissions. Many routes exist to lower CO2 emissions, but there is no single “magic bullet” solution. Rather we must learn to use an increasingly diverse range of materials optimised according to the raw materials available locally and the intended application.

Table 1.1. Energy and CO2 emissions of common materials [ICE09].

Material MJ/kg kgCO2/kgCement 4.6 0.83

Concrete 0.95 0.13Masonry 3.0 0.22Wood 8.5 0.46Wood: multilayer 15 0.81Steel: Virgin 35 2.8Steel: Recycled 9.5 0.43Aluminium: virgin 218 11.46Aluminium recycled 28.8 1.69Glass fibre composites

100 8.1

Glass 15.7 0.85 The current use of concrete is based mainly on empirical knowledge from testing often at near full scale. This, and justifiable demands for safety, mean that progress is slow and incremental. To speed up the use of new and a more diverse range of materials, modelling has a clear role to play; as has been well demonstrated in other fields of Materials Science. For example it is now possible to make a virtual crash test of a new car with a model which even incorporates the microstructure details of the porosity in the engine block from a simulation of the solidification during casting!

34 SCRIVENER: Challenges in Modelling Cementitious Materials

In order to be reliable, models should be based on the real physical and chemical processes linking the composition and processing of a material to its nano / microstructure and so to its properties and performance – this is the paradigm of Materials Science as shown in Fig. 1.1.

Properties and

performanceMODEL

Nano/micro‐structureMODEL

Composition and

processing

Fig. 1.1. Role of Models in linking composition and processing to microstructure and then this to

properties and performance: the Materials Science paradigm.

Due to their complexity and range of relevant length scales, modelling cementitious materials poses particular challenges, which must be overcome if progress is to be made.

Fig. 1.2 shows a polished section of concrete imaged with backscattered electrons in the SEM. The general features of the complex concrete microstructure can be identified – Aggregates, unhydrated cement, hydration products (mainly calcium hydroxide and C-S-H). The complexity comes from the number of phases and their range of sizes. This originates from the particle size distribution of the starting materials, which goes from under a micron to tens of microns for the cement grains, through millimetres and centimetres for the aggregates. The pores go from the nanometre range in the C-S-H “gel” to voids which may be in the millimetre range. It is difficult to use classic multiscale approaches due to the continuous dispersion of sizes.

partially reactedcement grain

“inner” C-S-H

“outer” or“undifferentiated”C-S-H

sand (aggregate)

calcium hydroxide(CH)

pores

Fig. 1.2. Microstructure of concrete.


2 EXAMPLES OF MODELLING

2.1 Kinetics and Microstructure

The first step in Material Science modelling is to simulate the microstructure from information on the composition and processing of the material. The microstructure must be sufficiently well represented to allow the model to then predict the desired behaviour. At EPFL we work with a vectorial model for cement paste as this allows the wide range of particle sizes to be represented without a lower resolution limit. The first version of the model – Integrated Particle Kinetics Model of Navi and Pignat [Nav96] was computationally limited to the representation of a few thousand particles. The new implementation of the model µic can deal with the hydration of several millions of particles in a typical 100 µm box.

The first challenge addressed by µic [Bis09a,b] was a computationally efficient implementation of the vector approach, but it was also realised that flexibility and easy extensibility were essential features as to avoid regular development (even rewriting) due to the complexity of cement and the gaps in our understanding of its chemistry coupled with extensive research progress. This high level of flexibility also means that the model is ideally suited to model the microstructural development of new cementitious materials. Figure 2.1 shows the basic design of µic [Bis09a]. Any number of reacting phases may be represented with their correct particle size distributions. These phases react according to user defined laws to give products which are deposited in the microstructure in different ways. Simulations involving several million particles can be run in a matter of hours.

Fig. 2.1. Schematic of the µic programme [Bis09a].

µic was used first to study the hydration of alite based on the data generated in the thesis of Costoya [Cos08]. The approach was to synthesise alite (which unlike C3S has a grains similar in size to cement) and separate the powder into fractions with, narrow particle size distributions. This approach is important as it is very difficult to derive correct kinetic behaviour from the full PSD as the complete reaction of small grains at short times makes it impossible to differentiate between different kinetics at the particle scale. Bishnoi [Bis09b] showed that while the acceleration part of the main heat evolution peak could be well fitted with a boundary nucleation model (such as developed by Cahn [Cah56] and adapted by Thomas for cements[Tho07] ), such a model could not capture the deceleration part of the


curve (Fig. 2.2a). In order to capture the decelerating part a radical suggestion was put forward that the initial products grow quickly to fill the available space with a low density and subsequently densify over time. This mechanism enabled excellent fits to the experimental data to be obtained (Fig. 2.2b) across all the different particle size distributions, with the same parameters for product nucleation and densification rates. The only parameter which needed to be adjusted was that for the outward growth rate which was found to depend on the distance between particles. This hypothesis and the simulation results are presented in detail in [Bis09b].

Despite the radical nature of this hypothesis compared to conventional thinking, a loose, low-density C–S–H, be observed in many micrographs [eg Ric99]. Quasi-elastic neutron scattering and NMR relaxation measurements of pore-sizes, which do not entail sample-drying, indicate that a larger than expected fraction of the water at this stage is close to the surface of hydration products [Hal94][Fra02][McD07]

Fig. 2.2. a) left: failure of surface nucleation model to capture decelerating part of hydration

reaction: b) right: Good agreement between simulation and experiment for the case of growth of a product with low density which subsequently densifies [Bis09b].

Recently Kumar [Kum10], has a mechanism to simulate the dissolution and induction periods based on work by Juilland in our group [Jui10]. In Fig. 2.2 it can be seen that there is not a good fit of the simulation to the experimental data in the first few hours. Initially, on addition of water there is a high rate of reaction. The rate of reaction slows quickly to be followed by the period of low heat evolution (the induction period) before the onset of the main hydration peak. By analogy with recent findings and hypotheses in geochemistry this slow down in reaction arises from the build up of ions in solution. In very dilute solutions, the dissolution rate is fast as it is energetically possible to open up etch pits on the surface; as the concentration increases the mechanism of dissolution changes to slow step retreat and this may occur even when the solution is still many orders of magnitude below equilibrium concentration. The implementation of this process allows the first part of the curve to be well captured (Fig. 2.3) and it is found that the parameter related to the dissolution process are the same across the range of particle sizes; for alite alone and in the presence of other phases and even for alite in commercial cements. However these parameters are sensitive to temperature and mixing intensity.

Furthermore it has been found that the same reaction mechanisms can capture the kinetics of hydration of C3A with gypsum, mixtures of alite, C3A and gypsum and even commercial Portland cements (Fig. 2.4), including considerations of the thermodynamics of the solution phase. Remarkably it has been found that the fundamental kinetic parameters do not vary significantly between systems.


Most importantly the kinetic simulations produce microstructures which can then be used to compute behaviours. The microstructures have no lower resolution limit and are three dimensional, Fig. 2.5. However, the structure of C-S-H itself is not explicitly represented.

Fig. 2.3. Simulations of reaction kinetics of alite with µic [Kum10].

Fig. 2.4. Simulations of alite, C3A gypsum mixture and a commercial cement.

Fig. 2.5. Simulated microstructure: unhydrate cement dark grey, C-S-H grey and calcium

hydroxide, bright grey.


2.2 Mechanical Properties

The primary requirement for most concrete is to support load. Therefore the most important property is compressive strength. Despite the simplicity of the compressive strength tests, the actual process of compressive failure of a material is very complex and not yet possible to model explicitly. However it is generally accepted that strength is a function of the elastic modulus, which can be more easily modelled. Of course it is well accepted that the primary factor determining mechanical strength is the total amount of capillary porosity. Fig. 2.6 below shows a typical plot which can be found in the literature. Although the general trend to higher strength with decreasing porosity is clear, it is important to realise that this correlation is completely inadequate from a practical point of view. If we look at an average porosity of around 20% we see that the scatter of strength values varies by a factor of 3! At present the reasons for this large scatter are very unclear. Of course there are intrinsic errors in the measurement of both porosity and strength, but these are much less than the observed scatter. From a Materials Science perspective one expects that this must be related to the spatial arrangement of the porosity. To date most attempts to model elastic properties have not shed much light on the reasons for this dispersion. Bary et al [Bar08, Bar10] showed that the results from most analytical schemes converge for low porosities.

Fig. 2.6. Strength porosity relationship from [Jen91], typical of many to be found in the literature.

From a practical point of view the area of most interest is the early age strength development, which is the area most sensitive to the substitution of clinker by supplementary cementitious materials. The recently competed thesis by Chamrova [Cha10] explored the possibility of numerically modelling elastic properties from the µic model at low degrees of hydration, via the FEM method. As previously observed the critical phenomenon at this stage is the connectivity between the hydrating cement grains. Fig. 2.7 shows the huge impact of considering all particles, or just those connected. The percolation threshold is very sensitive to the resolution of the model and, even with the increasing power of computers it will never be possible to represent the finest features in the cement paste microstructure on the scale of the RVE (representative volume element. Nevertheless despite the numerical limitations, the model illustrated well the potential impact on elastic properties of microstructural features such as the clustering of the cement grains and the number of calcium hydroxide crystals (Figs. 2.8 & 2.9).


Fig. 2.7. Impact of connectivity of prediction of elastic modulus [Cha10].

Fig. 2.8. Impact of cement grain clustering on prediction of elastic modulus [Cha10].

Fig.e 2.9. Impact of number of calcium hydroxide crystals on prediction of elastic modulus

[Cha10].


The impact of the correct microstructural arrangement is also apparent in the work of Dunant on modelling the alkali silica reaction [Dun10]. This model, at the paste aggregate level using AMIE, considers ASR as occurring at reactive sites embedded in a non-reactive matrix, corresponding to the situation observed experimentally with the aggregate types of interest, Fig. 2.10. This model can correctly capture the dependence of expansion on the amount of reaction, unlike the case where ASR is considered to occur only at the aggregate paste interface.

Fig. 2.10. Model (left) and real microstructure (right) for concrete affected by ASR [Dun10].

These examples illustrate how appropriate models can illuminate different mechanical behaviours, despite the limitations of resolution. In order to delve further into the impact of microstructure of mechanical properties we are now limited as much be good quantitative descriptions of the microstructures of new cementitious materials as by the available models.

2.3 Durability

The term “Durability” encompasses a vast array of phenomena many of which are not fully understood. However, common thread linking many processes related to the degradation of concrete is the transport of fluid, gas or ions through the porous network of concrete. Here the main challenges are to represent the porous network of a RVE at sufficient resolution. As described above this is almost impossible when the smallest size of interest is an ion and the RVE is on the order of 100 µm or more.

However, recently Kumar [Kum10b] has shown that it is possible to simulate absorption desorption of water directly from the µic model, with no fitting parameters, by considering explicitly the addition of water molecules layer by layer to the solid surfaces produced by the hydration process. Fig. 2.11, shows some results from this work. The very good agreement between the model and the simulation is extremely encouraging to be able to simulate transport in partically saturated conditions (which is usually the case in the field). In the present case features such as the surface roughness of the C-S-H of the shrinkage of this phase were not considered suggesting that such effects has a comparatively minor effect of the isotherms.


Fig. 2.11. Simulations of absorption desorption isotherms form µic [Kum10b].

3 CONCLUSIONS

This paper presents several examples of modelling cementitious materials. Despite the challenge of capturing small features at the level of the RVE the progress is quite encouraging. Such modelling based on mechanism rather than the encapsulation of empirical data holds great promise to understand and predict the behaviour of the increasingly diverse range of cementitious materials which must be used in the future is the environmental footprint of concrete is to be reduced.

ACKNOWLEDGMENT

The authors thank the members of LMC, EPFL who contributed to the research reported here: Shashank Bishnoi, Aditya Kumar, Mercedes Costoya, Alexandra Quennoz, Cyrille Dunant, Patrick Juilland.

REFERENCES

[Bis09a] Bishnoi, B. & Scrivener, K.: µic: A new platform for modelling the hydration of cements. Cement and Concrete Research, 39 (2009) 266-274.

[Bis09b] Bishnoi, B. & Scrivener, K.: Studying nucleation and growth kinetics of alite hydration using μic. Cement and Concrete Research, 39 (2009), 849-860.

[Dun10] Dunant, C.F.; Scrivener, K.L.: Micro-mechanical modelling of alkali–silica-reaction-induced degradation using the AMIE framework. Cement and Concrete Research, 40(2010), 517-525.

[ICE09] Inventory of Carbon and Energy (ICE), U. Bath, UK, http://people.bath.ac.uk/cj219/. [Nav96] Navi, P. and Pignat, C. "Simulation of cement hydration and the connectivity of the

capillary pore space", Advances in Cement Based Materials, Vol. 4, 1996, pp.58-67. [Cos08] Costoya, M. Effect of particle size on the hydration kinetics and microstructural

development of tricalcium silicate, http://library.epfl.ch/theses. [Cah56] Cahn, J.W.: The kinetics of grain boundary nucleated reactions, Acta Metallurgica 4

(1956) 449–459.


[Tho07] Thomas, J.J.: A new approach to modeling the nucleation and growth kinetics of tricalcium silicate hydration, J. Am. Ceram. Soc. 90 (2007) 3282–3288.

[Ric99] Richardson, I.G.: The nature of C–S–H in hardened cements, Cement and Concrete Research 29 (1999) 1131–1147.

[Hal94] Halperin, W.P.; Jyh-Yuar Jehngb, Yi-Qiao Song, Application of spin–spin relaxation to measurement of surface area and pore size distributions in a hydrating cement paste, Magnetic Resonance Imaging 12 (1994) 169–173.

[Fra02] Fratini, E. Chen, S.-H. Baglioni, P. Bellissent-Funel, M.-C. Quasi-elastic neutron scattering study of translational dynamics of hydrationwater in tricalcium silicate, J. Phys. Chem. B 106 (2002) 158–166.

[McD07] McDonald, P.J. Mitchell, J. Mulheron, M. Monteilhet, L. Korb, J.-P. Two-dimensional correlation relaxation studies of cement pastes, Magnetic Resonance Imaging 25 (2007) 470–473.

[Kum10a] Kumar, A. & Scrivener, K.: Modeling early age hydration kinetics of alite-model systems, submitted to J.Am. Ceram. Soc 2010.

[Jui10] Juilland, P.; Gallucci, E.; Flatt, R. and Scrivener, K.: Dissolution theory applied to the induction period in alite hydration, Cement and Concrete Research 2010, corrected proof doi:10.1016/j.cemconres.2010.01.012.

[Bar09] Bary, B., Ben Haha, M., Adam, E. and Montarnal, P.: Numerical and analytical effective elastic properties of degraded cement pastes, Cement and Concrete Research, 39(2009) 902-912.

[Cha10] Chamrova, R.: Numerical Modelling of Elecstic properties of cement paste, Thesis EPFL 2010, http://library.epfl.ch/theses.

[Kum10b] Kumar, A.; Sant, G. & Scrivener, K.: Modeling absorption desorption isotherms of cement pastes, submitted to Cement and Concrete Research 2010.

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