As with any material, understanding the links between the microstructure of cement-based materials and their properties is needed to allow the design of systems with improved performance. Unfortunately, three-dimensional quantitative characterization of microstructure is extremely tedious and difficult. While two-dimensional scanning electron microscope images of hydrated cement paste are straightforward to obtain, it is the three-dimensional microstructure that often has a critical influence on properties. Unlike phase volume fractions which are statistically the same in two and three dimensions for isotropic systems, the connectivity or percolation of phases is vastly different in two and three dimensions. Because percolation aspects are critical to the mechanical and transport properties of cementitious materials [1, 2] a three-dimensional representation of microstructure is required. Difficult to obtain experimentally at the necessary resolution, such representations can be simulated using computer models.
Using computer models to represent the microstructure of cement-based materials has evolved significantly over the past ten years or so. Wittmann et al. [3, 4] were perhaps the first to consider such an application with the development of their "numerical concrete". A concrete microstructure consisting of aggregates in a cement paste matrix was generated and mapped onto a finite element grid, allowing for the computation of thermal, hygral, and mechanical stress distributions. At the level of cement paste, pioneering work in directly representing the cement paste microstructure within the computer was performed by Jennings and Johnson [5], who developed a continuum representation based on spherical cement particles enveloped by hydration shells whose thickness increases over time. In addition, calcium hydroxide crystals were allowed to nucleate and grow in the continuum pore space. A somewhat similar approach was formulated by van Breugel [6], who, by accounting for the volumes of embedded cement particles and other morphological aspects of the hydrating cement paste system, was able to predict the hydration behavior, explicitly considering the cement particle size distribution, its chemical composition, water-to-cement (w/c) ratio, and temperature. In both of these latter two models, one finds it to difficult to directly compute mechanical and transport properties, in the former case because of the continuum representation of microstructure, and in the latter because no direct representation of microstructure is produced.
An alternate approach to continuum-based models has been the development of so called "digital-image-based models" [2, 7]. In these models, each cement particle is represented as a collection of elements (pixels). Hydration can then be simulated by operating on the entire collection of pixels using a set of cellular-automata-like rules [8]. This allows for the direct representation of multi-size, multi-phase, non-spherical cement particles. The model has evolved from one based simply on the hydration of tricalcium silicate (C3S) [9] (Fortran and C versions of which are available via anonymous ftp at 129.6.13.25 in the pub/bfrl/bentz/CMML/hydra3d subdirectory) to one that considers all of the major phases present in cement [10] (versions of which are available via anonymous ftp at 129.6.13.25 in the pub/bfrl/bentz/CEMHYD3D subdirectory). In addition, due to the underlying pixel representation of the microstructure, mapping the microstructure onto a finite difference or finite element grid becomes trivial. Thus, properties such as percolation [7], diffusivity [11], complex impedance [12], and setting behavior [2], are easily computable. The remainder of this chapter is organized as follows. Section 2 presents the experimental techinques used in obtaining representative 2-D images of cement particles in which all of the major phases are identified. Section 3 presents the numerical techniques used in converting a 2-D segmented image into a 3-D representation of the cement of interest. The rules and techniques employed in simulating hydration and microstructure development are detailed in Section 4. Section 5 presents the experimental techniques useful in validating data produced by the computer model. Section 6 presents a sample of the results obtained to date using the model, while future research is addressed in Section 7.
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