While cementitious materials are often viewed as simple "low-tech" materials, they are in fact inherently complex over many length scales. The starting material, cement powder, is obtained by grinding cement clinker. The cement clinker is manufactured by firing mixtures of limestone (providing Ca) and clay (providing Si, A1 and Fe). Gypsum (calcium sulphate dihydrate) is then added to moderate the hydration process. After grinding the clinker and gypsum, the cement powder then consists of multi-size, multi-phase, irregularly shaped particles generally ranging in size from less than 1 µm to slightly more than 100 µm. When this starting material is mixed with water, hydration reactions occur which ultimately convert the water-cement suspension into a rigid porous material, which serves as the matrix phase for concrete, a cement paste-sand-rock composite. The nominal point of hydration at which this conversion to a solid framework occurs is called the set point.
The various chemical phases within the cement powder hydrate at different rates and interact with one another to form various reaction products. Some products deposit on the remaining cement particle surfaces (surface products) while others form as crystals in the water-filled pore space between cement particles (pore products). Moreover, some of the hydration products contain nanometre-sized pores so that the size range of interest for these materials is from nanometres to hundreds of micrometres, or even centimetres if one includes the aggregates (rocks) used in concrete. Due to these complexities, many unanswered questions remain in the science of cementitious materials. For cementitious materials, in common with most materials of industrial interest, the key relationships between processing, microstructure, and properties must be understood in order to have better control over the material in use. The approach described in this paper is aimed at elucidating these relationships.
The initial chemical composition of cement is complex as is the dynamic behaviour of the hydration process. Both aspects are not well understood at a fundamental level. A better understanding of the early age behaviour is needed in speciality applications of cements such as those arising within the petroleum industry. Cement is used to line oil wells by pumping a cement slurry between the wellbore and the steel casing inserted in the well. The cement slurry sets, forming a low permeability annulus that isolates the productive zone of the well from the rest of the formation. A slurry which either sets too quickly (while being pumped) or too slowly is a costly ,failure. Thus, control and prediction of the time at which the cement slurry can no longer be pumped, its thickening time (American Petroleum Institute 1982), is needed. The thickening time is clearly related to the set point, as the viscosity diverges as a solid framework becomes establishes. The thickening time is controlled by an induction period during which very little hydration occurs. The induction period separates a short initial stage of fast but limited hydration from a somewhat slower but more complete hydration in which the cement is transformed into solid form. Additives which are known to influence the length of the induction period have been discovered empirically. For example, carbohydrates such as sucrose are very effective retarders; their addition can significantly extend the thickening time, or even prevent setting completely. It is the inherent complexity of the cement hydration process that has prevented the development of a well understood theory which would allow better control of the thickening time.
Another major problem in trying to characterize the thickening time or set point in terms of microstructure is how to describe the three-dimensional microstructure of cementitious materials, since electron microscopy and similar techniques provide only two-dimensional images. For example, the capillary pore system (generally consisting of pores larger than about 100nm) may appear discontinuous in a two-dimensional image while still being highly percolated in three dimensions (Bentz and Garboczi 1991b). Computer models offer a promising solution to this dilemma by allowing three-dimensional microstructures to be represented in a detailed fashion.
This paper outlines the application of a specific class of computerbased simulation models, called cellular automata, to modelling the complex process of microstructure development within hydrating cement slurries. The underlying cubic lattice for this cellular automaton (CA) is based on a two- or three-dimensional digital image representing the initial conditions. The physico−chemical process of hydration is modelled by the iterative application of a series of generally probabilistic rules for updating the microstructure at any given instant of discretized time based on its current state. The underlying lattice structure of the model microstructure allows for rapid quantification of clinker phase fractions and phase connectivity (Bentz and Garboczi 1991b) and the computation of physical properties such as elastic moduli and diffusivity (Day et al 1992, Garboczi and Bentz 1992) which can then be compared to experimental measurements to improve the model or provide new insights into relationships between microstructure and properties. The time evolution of the model can also be monitored by quantifying the phase fractions and the chemical species at each time step in the simulation. These can be compared to measurements made by attenuated total reflectance Fourier transform infrared spectroscopy (ATR/FTIR). This technique can be used to conveniently monitor the evolution of the infrared spectrum of a cement sample as it hydrates (Jones 1992), hence giving information on the chemical composition of the system.
A number of these issues are addressed in the present paper, which is structured as follows. Section 2 describes the CA approach to simulation, reviews the physico−chemical process of cement hydration, and shows how CA transition rules can be used to model various aspects of the process. Section 3 describes the methods we have used for creating starting images of cement slurries. Section 4 compares percolation results from our model simulations to experimental measurements on real cement slurries, and the paper concludes with a discussion in Section 5.