Next: Computational Techniques
While the drying shrinkage of concrete has been studied extensively, it is only recently that the need to relate microstructure to basic mechanisms has been emphasized [1,2,3]. From the authors' perspective, this step is seen as a necessity to aid in the validation of proposed mechanisms [4,5] and the development of material parameter-based models to predict the shrinkage behavior of structures. A major obstacle in elucidating these relationships is the wide range of scales existing between the observed shrinkage behavior of 1 cubic meter samples of concrete and the controlling physical processes (capillary condensation, etc.) occurring at or below the nanometer level in the "gel" phase of the cement paste. For many of the size levels in between these two extremes, the material exhibits a heterogeneous structure which may need to be accounted for either explicitly or statistically in models for shrinkage behavior. Examples of this heterogeneity include: the cement paste microstructure at the micrometer level which consists of unhydrated cement particles, gel, crystalline hydration products such as calcium hydroxide, and porosity, and the concrete itself at the scale of millimeters, consisting of cement paste, aggregates, and air voids.
Currently, computational capabilities do not exist which would allow one to consider directly the heterogeneity present at these different scales in a single model. Thus, the use of a multi-scale approach [2,6] is necessitated. Here, a number of structural models are developed, each at a different scale. The property information computed at one scale is used as input into the next higher scale. For example, properties computed from a model of the nanostructure of the calcium silicate hydrate (C-S-H) gel can be used as input for the gel phase of a micrometer-level cement paste model. Likewise, the properties computed here can be input into a millimeter-level model of mortar or concrete. Because a complete set of models has not yet been developed and validated, an unanswered question remains as to what extent properties computed for a phase at one level can be homogenized at a higher level. For example, can the properties of the C-S-H gel be considered homogeneous at the micrometer level or are there differences between the inner and outer products that must be taken into account ? One example where inhomogeneity must be explicitly considered is the cement paste near an aggregate (the interfacial zone) in conventional concrete which has a different microstructure and properties than the bulk cement paste in concrete . Here, the paste heterogeneity can be explicitly accounted for in performance models , as the concrete must be considered as a three-phase material , even when air voids are ignored.
At each scale of interest, different techniques for probing the structure of a material are available. At the micrometer level, pore structure can be measured indirectly using mercury intrusion porosimetry and the microstructure can also be directly observed using scanning electron microscopy (SEM)  or X-ray microtomography . At the nanometer level, the structure of the C-S-H gel can be inferred from sorption experiments . At this level, small angle neutron scattering (SANS) is a useful nondestructive evaluation technique, providing a scattering profile representing a Fourier transform of the sample nanostructure [12,13] which can be analyzed to directly obtain pore surface area. Still, structural interpretations of these measurements can only be partially confirmed by high-resolution transmission electron microscopy (TEM) , with a resolution limit on the order of tens of nanometers, whereas the actual structure exists at levels of nanometers and tenths of nanometers. Atomic force microscopy (AFM) may offer one means of observing the gel structure directly at the nanometer level.
Our goal in the present work is to develop a set of computational tools which allows the generation of structures at a variety of scales and the subsequent calculation of properties and production of computer images in order to validate the structural models against experimental measurements. Because structural models of cement paste at the micrometer level have been developed previously [2,6,15], in this paper, we will concentrate on the nanometer level structure of the C-S-H gel, with the ultimate goal of linking to the existing models for cement paste. We will consider agglomeration of nanometer scale spherical particles as the basic model for the structure of C-S-H at this level. Although not considered here, one might also be interested in the "crystalline" or layer structure of the C-S-H within each spherical particle. While no definitively proven structure has been determined at this level, it should be noted that progress is being made towards accurately identifying this "crystalline" structure [16,17]. This layer structure could be important for understanding certain aspects of drying shrinkage, such as the irreversible shrinkage observed during a first drying .
Once a reasonable set of structural models has been developed, one can proceed to investigate shrinkage mechanisms using finite element and other computational techniques . The remainder of this paper is organized as follows. Section 2 introduces the computational techniques employed to generate structures and compute properties. Section 3 presents results generated for one particular set of model structures in comparison to available experimental data. Section 4 provides a discussion of the overall approach and outlines the plans for future research in this area and section 5 summarizes with conclusions.