The cellular automaton based approach provides a simple and powerful means of simulating the diverse physical and chemical processes that are involved in the hydration of cement slurries. The CA approach is justified by the fact that any tractable model of the process of cement hydration will be a simplification of the real activity. The approach allows a useful model to be developed despite the fact that much of the complex detail of cement hydration is not fully understood. It can also serve as a guide to suggest experimental work which may help to elucidate the key factors controlling cement hydration, such as the ultrasonic shear wave measurements which pinpoint the percolation point (D'Angelo et al 1992). The lattice−based structure associated with a cellular automaton provides several opportunities for defining the initial state of the system, and for computing time−dependent properties of the model. A combination of 3D white-noise-based images and 2D micrograph starting images may be able to produce a realistic 3D starting image. Other effects, such as varying temperature, could be simulated by varying reaction probabilities in accordance with the Arrhenius law.
An additional advantage of cellular−automata−based microstructure models is the visualization capabilities which they afford. When the models are executed on a graphics workstation, the hydration can be viewed as it occurs. In addition to being a great aid in modifying code, the visualization provides further insight into how cement microstructure develops. In fact, personal computer versions of this CA cement model are now being utilized at a number of universities for undergraduate-and-graduate-level classes in order to visually demonstrate the principles of cement hydration to students.
We are hoping to parallelize the present CA model so that much larger 3D lattices can be used. Some work has already been done on a parallel implementation of the original 2D algorithm onto a large parallel SIMD machine, the Connection Machine 2 (CM2), and onto a small four-processor MIMD machine (a Silicon Graphics Iris) (Kleyn et al 1990). The CM2 appears to be ideally suited for running CA computations: it has achieved 108 site updates s−1 for a microcode implementation of a lattice gas CA − this would allow a cube of about 500 x 500 x 500 sites to be updated every second (Boghosian et al 1988). Implementing the collision reactions for the cement CA model on a SIMD architecture was found to require sequential steps which reduced effective processor usage and a rate of only 105 site updates s−1 was attained. Implementation on a more massively parallel MIMD machine would allow a larger model incorporating finer detail and faster simulation runs. A cement hydration model of size 500 x 500 x 500 updated every second would be desirable in order to represent the microstructure at an adequate level of detail and to permit a reasonable picture of the time evolution of the model to emerge.
Should such a model eventually be used to predict setting and/or thickening times for a given cement, it would, of course, be desirable that the execution of the model be faster than the real time taken by the cement to set. A concept of relevance to the present simulation work is algorithmic compressibility (Chaitin 1989). This notion is concerned with the extent to which physical processes may be simplified mathematically or, equivalently, compressed into algorithms from which the phenomena in question can be computed rapidly. A process which is algorithmically incompressible is one for which there is no predictability: the most efficient simulation of the process is the physical process itself. While it has been clearly demonstrated that the long-term properties of cement paste can be predicted accurately in just a few hours of computer time, there may still be some question as to whether the algorithmic compression obtainable using these models is sufficient for short-term properties such as set point. If even the fastest simulation takes as long as the real process, then we have gained limited genuine predictability, even if our understanding of what is occurring has been enhanced. There is, however, a range of evidence now available which suggests that at least some aspects of the behaviour of these systems is 'universal' (Sayers and Grenfell 1993) and that therefore there is hope that it is possible to compress the behaviour in more elaborate simulations of the kind described in the present paper.
To make detailed comparisons with the time scales for dynamical evolution in real cements, it will be necessary to scale the time steps within the CA model appropriately. It may even prove possible to make comparisons with experimental heat evolution curves, determined by calorimetry, if an algorithm is included which computes the number of reactions which occur (i.e. the number of changes of species equals the number of sites at which a particular rule is applied), and assigns a specified heat release to each. This in turn could be fed back into temperaturedependent reaction probabilities (mentioned above) and a lattice−based algorithm that can be used for computing heat conduction (Garboczi and Bentz 1992), hence allowing for the effects of self−heating on the overall rate of hydration.
In conclusion, there are many additions, extensions and elaborations that could be made to the CA−type models discussed here without much difficulty. Such developments would serve to enhance the realism of an approach and models which we believe to be of considerable value in helping to unravel the complexity of cementitious materials.