Materials and Structures, 1993, 26, 191-195

Computational materials science of cement-based materials* E . J. G A R B O C Z I Building and Fire Research Laboratory, Buildings Materials Division, 226/B348, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA

This paper describes recent research and theoretical results obtained for cement-based materials using computational materials science techniques. Computer-generated microstructure models are used to simulate the microstructure development during hydration, and exact algorithms are applied to these models to compute experimentally verifiable physical properties. Good agreement is found between experimental and simulation results. 1. I N T R O D U C T I O N One of the fundamental tasks of materials science is to quantitatively relate microstructure and properties, using scientifically-based principles and not just empirical relationships. Empirical relationships are very useful, but they are not the ultimate goal of materials science. The focus of the work described here is to use computational materials science techniques to try to accomplish this goal for cement-based materials. Cement-based materials, whether we are talking about cement paste, mortar, concrete, or some new, high-tech cementitious material, are composite materials that exhibit complex randomness over a wide range of length scales. Concrete can be considered to be a mortar-rock composite, where the randomness in the structure is on the order of a few centimetres, the size of a typical coarse aggregate. Mortar itself can be considered to be a cement paste-sand composite, with random structure on the order of a few millimetres. Cement paste can also be considered to be a random composite material, made up of unreacted cement, C - S - H , CH, capillary pores, and other chemical phases (standard cement chemistry notation is C = CaO, S = SiO 2 and H = H 2 0 ). The randomness in the cement paste microstructure is on the order of a few micrometres. Finally, C - S - H is itself a complex material, with random structure, as seen by neutron scattering [1], of the order of a few nanometres. This range of random structure from a few nanometres ( C - S - H ) to a few centimetres (concrete) covers seven orders of magnitude in size. Therefore it is a large and difficult task to try to theoretically relate microstructure and properties for cement-based materials. In fact, it is such a large and difficult task that it is hard to imagine it being accomplished at all without the aid of a very large and fast computer. Over the last four years, we have made some progress in the area of the transport properties and microstructure of cement paste, using a novel microstructure model and finite-difference algorithms applied to the model. Section 2 describes this microstructure model, section 3 describes *This paper is a non-verbatim written account of the 1992 Robert L'Hermite Medal lecture presented at the 46th General Council of RILEM, in Madrid, Spain, 1 October 1992. 0025-5432/93 (~'.) RILEM

its application to interracial zone microstructure in mortar and concrete, section 4 describes computations of electrical conductivity/chloride diffusivity and their analysis using concepts from percolation theory, section 5 briefly describes simulations of CH leaching and its effect on transport properties, and section 6 concludes by discussing new research directions and the exciting possibilities for microstructural design of cement-based materials using this modelling approach. 2. M I C R O S T R U C T U R E M O D E L O F C E M E N T PASTE The microstructure model described here is for cement paste, where the fine nanometre structure of C - S - H has been ignored, and so C - S - H has been treated as a uniform continuum material. Therefore we are working on the third of the four length scales mentioned above, that of a few micrometres. The heart of our original microstructure model is using a digital image to represent an initial mixture of water and cement particles. The cement particles are considered to be a single phase, similar to C3 S. Having the cement particles made up of individual pixels allows random shapes to be represented, and allows for material redistribution to simulate microstructural development during hydration. Fig. 1 is a schematic illustration of how the model works. Colour pictures of how the model works are available elsewhere [2,3]. Each cycle of the model has three steps. Dissolution

Diffusion

Reaction Precipitates into solid CSH upon contacting a

solid C3S or CSH surface

1.7 diffusing

CSH species Dissolved

C3S p=xel >--=

Forms

Nucleates into solid CH or -~ 0.61 diffusing CH species

precipitates into solid CH upon contacting a solid CH surface

Fig. 1 Schematic diagram of the operation of the digital-image-based microstructure development model for the hydration of C3S cement.

192 In the first step, all cement pixels in contact with water are identified. Some of these are dissolved at random and are then placed into the capillary pore space. For a given cement type, there are fixed values of the ratios of product volume to volume of cement consumed, although the total volume of reaction products to volume of cement consumed is roughly invariant, and is equal to about 2.3 [4]. How this volume is divided between products that form on or near cement surfaces, like C - S - H , and products that form in the pore space, like CH, differs for each cement type, but not by much [4]. In this version of our model, we explicitly follow C3S chemistry and form 1.7 volume units of C - S - H and 0.61 volume units of CH for every volume unit of cement consumed, and place them in the capillary pore space. We believe that the capillary pore structure produced by the model, however, is more general than just that of a pure C3S paste, because of the good agreement between various computed properties of the model and experimental results on Portland cement pastes [5]. In the second step of the cycle, all those pixels dissolved in the pore space that are destined to become either C - S - H or CH undergo random walks through the pore space. Reaction and product formation occur in the third step. Dissolved pixels that are destined to become C - S - H react and turn into solid C - S - H when they run into either unreacted cement or previously formed solid C - S - H gel. Dissolved pixels that are destined to become CH, on the other hand, on every step of their random walk have a probability, which depends on their total number in solution, of spontaneously stopping and forming the nucleus of a crystal. If another wandering CH pixel runs into such a nucleus, it sticks on and causes the crystal to grow. When all dissolved species have been consumed, new cement surfaces in contact with water are identified, and a new cycle of dissolution, diffusion and reaction begins. The model will continue to a preset degree of hydration, or until either all cement is hydrated (a slow process), or until there are no more cement surfaces in contact with water. In real materials, hydration could continue via the diffusion of water throughthe layers of C - S - H that cover unreacted cement, which is not allowed for in our model. We can typically reach 85-90% of hydration for a given water/cement ratio with the present model rules. Recently we have tried to build more of the real, complex chemistry of Portland cement into the model, in order to be able to simulate and study the effect of chemical admixtures on early hydration, and study the microstructure at the set point more carefully [6,7]. For that version of the model, we use a combination of back-scattered scanning electron micrographs and pixel-by-pixel X-ray maps to uniquely identify each phase in a given Portland cement. We then use the resulting colour-coded image as a starting point for hydration simulation, where now a separate set of dissolution-diffusion-reaction rules is formulated for each chemically distinct phase, similar to the rules for C3S described earlier.

Garboczi 3. INTERFACIAL Z O N E M I C R O S T R U C T U R E An immediate application of the microstructure model can be found in studying the microstructure of the interfacial zone in mortar and concrete. The characteristic features seen in this region are (i) higher capillary porosity than in the bulk and generally bigger pores, and (ii) higher CH volume fractions than are seen in the bulk. These features are typically seen in the cement paste volume that is within 50 p.m of an aggregate surface. Using the microstructure model, two major causes of this interfacial microstructure can be identified, neither of which depends on bleeding. They are (i) the particle packing effect [8] and (ii) the one-sided growth effect [9]. The particle packing effect arises from the fact that particles cannot pack together as well near a flat edge as in free space. Since the typical aggregate is many times larger than the typical cement particle, locally the aggregate edge appears flat. This inefficient packing causes less cement and higher porosity to be present initially near the aggregate surface, and so even after hydration this condition persists. The width of the interfacial zone will then scale with median cement particle size [10]. This is the main contribution to the interfacial zone microstructure, but not the only one. The one-sided growth effect arises in the following way. Consider a small region of capillary pore space located out in the bulk paste part of a mortar or concrete. On the average, there is reactive growth coming into this small region from all directions, since the cement particles are originally located randomly and isotropically. Now consider a similar small region of capillary pore space, but located very near an aggregate surface. Reactive growth is coming into this region from the cement side, but not from the aggregate side [9]. Mineral admixtures like silica fume and fly ash can also be incorporated into the model, and their effect on interfacial zone properties simulated [11]. We have found that the two main variables of importance are particle size, and reactivity with calcium hydroxide. The size of the mineral admixture controls the width of its packing effect at the aggregate edge, with smaller admixtures allowing better packing nearer to the aggregate edge. The reactivity controls how much calcium hydroxide can be consumed, and converted to C - S - H . Assuming adequate dispersion, we have shown, using the model, that the effectiveness of a mineral admixture in improving t h e interfacial zone microstructure increases as its reactivity increases and its size decreases ]-11-]. Colour pictures of some of these simulations can be found in Bentz and Garboczi [2] and detailed comparisons with experimental measurements in Bentz et al. [12]. Properties of the aggregate can be studied as well, such as the effect of porous and/or reactive aggregates. Bentz et al. [10] present results of the model for the effect of these variables on the interfacial zone microstructure. We have found it possible to explain the influence of each of these material variables on the interfacial zone microstructure in terms of the particle packing effect and

Materials and Structures the one-sided growth effect. These ideas then serve as a useful theoretical framework to unify analysis of how material variables affect interracial zone microstructure [10]. 4. T R A N S P O R T P R O P E R T I E S AND PERCOLATION THEORY We have found the ideas of percolation theory to be very helpful in understanding the relationship between the random microstructure of cement-based materials and their transport properties. The main concept of percolation theory is connectivity. Picture some sort of structure being built up inside a box by randomly attaching small pieces to a central core. Percolation theory attempts to answer the question: at what point does the structure span the box? An alternate form of this question, for a random structure that already spans the box, is: if pieces of the structure are removed at random~ when will it fall apart? The percolation threshold is defined by the value of some parameter, say volume fraction, right at the point where the structure either achieves or loses continuity across the box. These ideas can be applied to cement paste, for example, where the random structure being considered is now a particular material phase, and the 'box' is a macroscopic sample. Immediately after mixing, the solid phases are discontinuous, and so the freshly mixed paste is a viscous liquid. The solid phase is then built up through random growth of reaction products, and at some point becomes continuous across the sample. This percolation threshold is then a rigorous theoretical definition of the set point, which will tend to occur earlier in hydration than measured by the Vicat needle test, for example, since the needle could break through a percolated but still weak mixture. A percolation threshold that is more important for transport processes is the point at which the capillary pore space loses continuity. At this point, 'fast' transport of water or ions through the relatively large capillary pore system would end, and transport would then be regulated by the much smaller C - S - H gel pores. Using the model, this threshold can be investigated. Fig. 2a shows the 'fraction connected' of the capillary pore space versus degree of hydration for several water/cement ratios. The quantity 'fraction connected' is defined as the volume fraction of capillary pores that make up a connected path through the sample, divided by the total volume fraction of capillary pores. Immediately after mixing, the cement particles are isolated, and so the connected fraction of the capillary pore space is unity. As hydration occurs, small pockets of pore space can be trapped between particle clusters, and thus the connected fraction decreases gradually. At some point, large clusters of pore space become isolated and the 'connected fraction' goes to zero as connectivity is lost. This process can be seen in the data for all the water/cement ratios plotted, except for 0.6 and 0.7. We have found in the model that water/cement ratios of 0.6

193 (a)

[

I

I

I

I

I

I

I

I

1.01 cl U.l 0.8 III Z Z O 0.6 O Z O 0.4 O < r u.. 0.2

0

O O A v I

0

0C t i

0.45 0.50 0.60 0.70

w/c w/c w/c w/c

I 0.2

I

I 0.4

I

I

0.6

0.8

1.0

DEGREE OF HYDRATION

I

(b)

I

I

I

I

1.0

0.8 LU Z Z OO 0 . 6

9

Z

_o

O O

i - 0.4 o .< n" IJ_

[] 0.35 O 0.45 <> 0.50 9" 0.60 v 0.70

<>

0.2

w/c w/c w/c w/c w/c

[]

I

0.2

I

0.4

I

I

0.6

CAPILLARY POROSITY

Fig. 2 (a) Connected fraction of capillary pore space plotted against the degree of hydration for several different water/cement ratio simulated cement pastes; (b) the same data for the connected fraction of the capillary pore space but now plotted against the capillary porosity for several different water/cement ratio simulated cement pastes.

and above always have a continuous (or percolated) capillary pore system. This prediction is in good agreement with the limited experimental results available [13]. It is clearly seen in Fig. 2a that as the water/cement ratio decreases below 0.6, less and less hydration is required to close off the capillary pore system. In order to try to unify the previous results, we have re-plotted all the data from Fig. 2a in Fig. 2b, but now against capillary porosity. All the connectivity data now fall on one curve, and it is clearly seen that there is a common percolation threshold at a critical value of capillary porosity of about 0.18. Even the 0.6 and 0.7 water/cement ratio data fall on this curve, and now it is clear why these pastes always have an open capillary pore space: there is not enough cement present originally to be able to bring the capillary porosity down to the critical value, even after full hydration. This common percolation threshold for cement paste, which of course will have some small sensitivity to cement particle size distribution and degree of dispersion, implies that there are now three regions of behaviour for the transport properties of cement paste.

194 The first region is early in hydration, where the capillary pore space is fully percolated. These pores are much larger than the C - S - H gel pores (which are also fully connected fairly early in hydration [4]) and so dominate the transport. As the capillary porosity decreases, the capillary pores also become smaller, and so the second region is an intermediate region, for porosities around the percolation threshold, where pure capillary pore paths have about the same influence on flow as hybrid paths that are made up of isolated capillary pockets linked by C - S - H gel pores. Below the critical capillary porosity, all flow must now go through C - S - H gel pores, but the flow is still dominated by the hybrid paths, not just pure C - S - H gel pore paths. If this were not true, then after a certain point, transport properties would begin going up with increasing hydration, since more C - S - H was being formed. This is not the case [4]. The microstructure model has been used to compute the diffusivity of cement paste by solving Laplace's equation in the simulated microstructure with a finite difference method [14-]. Computational results confirm the above microstructural picture, and compare reasonably well with experimental measurements [7,143. When considering how to take these results for cement paste and apply them to predicting the transport properties of concrete, it is necessary to again consider the interfacial zone pores and their connectivity. Since interfacial zones are known to contain large pores, they can offer 'fast' transport pathways for ions and water. Recent work has shown, using what is known as a 'hard core/soft shell' percolation model, that in a typical concrete or mortar, the interfacial zone pores are almost certainly connected across a given sample (percolated), so they may indeed have an important effect on transport properties [15-]. 5. CALCIUM HYDROXIDE L E A C H I N G Changes in transport properties over time are important for predictions of service life and durability under various environmental conditions. For example, it is thought that the chloride diffusivity and thickness of the concrete cover are the main determinants of the service life of a reinforced structure exposed to chloride in the environment [-16]. Simple service life models can be made, if the values of the chloride diffusivity of the concrete cover and the critical chloride content needed for initiation of corrosion are known. But what if the pore structure of the concrete and hence its transport properties are changing over time? We have examined one simple example of this possibility by simulating the leaching of calcium hydroxide, and computing its effect on chloride diffusivity. A cement paste microstructure is 'grown' in the computer, and then calcium hydroxide is progressively dissolved using an algorithm similar to that used to dissolve cement in the hydration simulation. As the calcium hydroxide dissolves, new capillary pore space is created. At each stage of dissolution, the diffusivity is computed and compared with the original, unleached

Garboczi value. Using the percolation concepts explained above, it is then clear that large changes in diffusivity can occur during leaching only when the capillary pore space of a paste is originally disconnected, but becomes reconnected as the critical threshold for capillary pore space percolation is again attained or exceeded [17]. This reference discusses this topic in greater detail, including the concept of a critical amount of silica fume replacement required to prevent the re-percolation of the capillary pore space. The point to b e emphasized here is that percolation concepts can give good insight into the microstructure-transport property relationships in complex porous materials like cement-based materials, even when the microstructure is changing with time. 6. NEW RESEARCH DIRECTIONS AND CONCLUSIONS An exciting area that we are just starting to consider is that of elastic simulations. Treating each pixel in our digitized microstructure as a finite element, and assigning each pixel elastic properties according to its phase identification, we can apply an arbitrary strain and then solve the elastic equations for the stress everywhere. Using these results, we have produced two-dimensional stress maps [7], showing how different parts of a cement paste microstructure carry a given load, and can predict the elastic moduli of cement paste as a function of degree of hydration and capillary porosity. We plan to combine this new elastic algorithm with our previous interfacial zone microstructure simulations, and study load transfer between matrix and aggregate. We can also treat cement paste as a uniform continuum, embed sand particles in it, and study the effective elastic moduli of mortar as a function of sand volume fraction and particle size distribution. Another really exciting possibility for this kind of computational materials science approach is in the area of microstructural design. W h a t this means is using computer simulation to decide if a certain kind of microstructure could give improved performance by actually building it in the computer and computing its properties. An example might be if someone has an idea how to modify the cement manufacturing process to produce elongated cement particles with an aspect ratio of 10:1. Cement paste made from such a particle could easily be simulated, and its properties predicted. If these looked favourable, it might then be worthwhile for the would-be inventor to work on his modified cement manufacturing process. Another example might be producing cement grains with certain phases tending to appear more on the surface, or a blended cement with a certain composition. Again, such cement pastes could be simulated, and properties computed. Possible areas of application are wide, and became wider still as we develop simulations of new properties and build more chemical and structural information into our simulations. We will continue to carefully check predicted properties against experimental results, and simulated microstructures

Materials and Structures against real microstructures, to be sure that our computations are giving accurate predictions of the properties of real materials.

ACKNOWLEDGEMENTS I would like to thank the R I L E M General Council and the Jury members for awarding me the 1992 Robert L'Hermite Medal. There are many others who have shared in this work, and I would like to acknowledge them as well. First of all, the original version of the digital-image-based cement paste microstructure model was developed at N I S T by my colleague Dale Bentz, and almost all the work described above was carried out in collaboration with him. Second, I would like to acknowledge Hamlin Jennings, who, while at NIST, developed the first real cement paste microstructure model incorporating a simulation of reactive growth via hydration, which was an inspiration for our later work. And third, I would like "to acknowledge Professor Wittman and his collaborators' work in 'numerical concrete'. Their idea of applying a finite-element algorithm to a microstructural image, a diagram of which graced the cover of Materials and Structures for several years, foreshadows the work I have described. In addition, I would like to acknowledge all my other collaborators: P. E. Stutzman, K. A. Snyder, N. S. Martys, R. T. Coverdale, B. R. Christensen, T. O. Mason, A. R. Day, M. F. Thorpe, D. N. Winslow and M. D. Cohen. I would also like to thank the National Science Foundation Center for Advanced Cement-Based Materials for partial funding of nearly all the work described above. Finally, I would like to thank J. R. Clifton and G. J. Frohnsdorff for much encouragement, and for their long-term commitment to, and support of, the modelling of cement-based materials.

REFERENCES 1. Allen, A. J., Oberthur, R. C., Pearsons, D., Schofield, P. and Wilding, C. R., 'Development of the fine porosity and gel structure of hydrating cement systems', Phil. Ma 9. B 56(3) (1987) 263-288. 2. Bentz, D. P. and Garboczi, E. J., 'Computer modelling of cement-based materials', Cray Channels 14 (1992) 12-16.

RESUME Etude de mat~riaux ~ matrice de ciment par les techniques de simulation appliqu~es/i la science des mat6riaux Cet article d&rit les r~sultats th~oriques dYtudes r~centes de matbriaux ~ matrice de ciment au moyen des techniques de modklisation appliqukes ~ la science des matkriaux. On a utilisb des modules de microstructure obtenus par ordinateur pour simuler le dkveloppement de la

195 3. Hall, C., 'Looking at cement hydration', Oilfield Rev. 3(2) (1991) 4-6. 4. Bentz, D. P. and Garboczi, E. J., 'Percolation of phases in a three-dimensional cement paste microstructure model', Cem. Contr. Res. 21 (1991) 325-344. 5. Garboczi, E. J. and Bentz, D. P., in 'Materials Science of Concrete II', edited by J. Skalny (American Ceramic Society, Westerville, 1991) pp. 249-277. 6. Bentz, D. P., Coveney, P. V., Garboczi, E. J., Kleyn, M. F. and Stutzman, P. E. 'Cellular automaton simulations of cement hydration and microstructure development, Modellin9 & Simulation in Mater. Sei. & Engn9, submitted. 7. Garboczi, E. J. and Bentz, D. P., 'Computational materials science of cement-based materials, Mater. Res. Soe. Bull. in press. 8. Scrivener, K. L. and Gartner, E. M. 'Microstructural gradients in cement paste around aggregate particles' in 'Bonding in Cementitious Composites', edited by S. Mindess and S. P. Shah (Materials Research Society, Pittsburgh, 1988) pp. 77-85. 9. Garboczi, E. J. and Bentz, D. P., J. Mater. Res. 6 (1991) 196-201. 10. Bentz, D. P., Garboczi, E. J. and Stutzman, P. E., 'Computer modelling of the interfacial zone in concrete', in Proceedings of RILEM conference on Interfaces in Cementitious Composites, Toulouse, France, October 1992. 11. Bentz, D. P. and Garboczi, E. J., 'Simulation studies of the effects of mineral admixtures on the cement pasteaggregate interfacial zone', Amer. Coner. Inst. Mater. J. 88(5) (1991) 518-529. 12. Bentz, D. P., Stutzman, P. E. and Garboczi, E. J., 'Experimental and simulation studies of the interfacial zone in concrete', Cem. Concr. Res. 22 (1992) 891-902. 13. Powers, T. C., Copeland, L. E. and Mann, H. M., PCA Bull. 10 (1959). 14. Garboczi, E. J. and Bentz, D. P., 'Computer simulation of the diffusivity of cement-based materials', J. Mater. Sci. 27 (1992) 2083-2092. 15. Snyder, K. A., Winslow, D. N., Cohen, M., Bentz, D. P. and Garboczi, E. J., 'Percolation and pore structure in mortars and concretes', Cem. Concr. Res. in press. 16. Clifton, J. R. and Knab, L. I., 'Service life of concrete', Internal Report NISTIR 89-4086 (National Institute of Standards and Technology, Gaithersburg, MD, 1989). 17. Bentz, D. P. and Garboczi, E. J., 'Modelling the leaching of calcium hydroxide from cement paste: effects on pore space percolation and diffusivity', Mater. Struct. 25 (1992) 523-533.

microstructure pendant l'hydratation, et on applique des algorithmes exacts fi ces modOles afin de calculer les propriktbs physiques vbrifiables exp&imentalement. On trouve une bonne concordance entre les r~sultats expkrimentaux et ceux obtenus par simulation. Cet article est une adaptation de la confOrence pr&ent& • l'occasion de la remise de la MOdaille Robert L'Hermite, lots de la 46dine ROunion du Conseil Gkn&al de la R I L E M ~t Madrid, le l er octobre 1992.