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Model description

The microstructure model used to investigate ITZ microstructure was developed by Bentz and Garboczi [7]. The model has been described in detail by these authors [8,9] and is outlined briefly here. In the model, two-dimensional (2D) areas or three dimensional (3D) volumes are represented by a set of pixels each identified as a particular phase of concrete. For this paper, relevant phases are anhydrous cement (assumed to be pure C₃S), calcium hydroxide (CH), calcium silicate hydrate (CSH), porosity, aggregate, and mineral admixtures. Thus a cement particle is represented as a collection of contiguous pixels assigned to be C₃S. In this manner, real cement particle shapes may be used, as well as circles and spheres, in generating simulated cement microstructures. Figure 1 is an image of real cement particles in 2D, obtained using a scanning electron microscope and image analysis, placed randomly around an idealized square aggregate (left), and the same system (right) after 77% of the cement has been hydrated using the model. In the hydrated system, cement particles are red, CH is blue, CSH is yellow, and porosity is black.

Figure 1: Cement particles placed around a square aggregate (w/c = 0.47), before hydration (left),
after 77% hydration (right).

Hydration is simulated by operating on all the pixels present in the cement paste volume or area. The two reactions considered are the hydration of C₃S to form CH and CSH, and the pozzolanic reaction between CH and silica (found in silica fume or fly ash) to form secondary or pozzolanic CSH. The assumed reaction stoichiometry, based on the work of Young and Hansen [10], is as follows:

CaS + 5.3H ← C1.7SH4.0 + 1.3CH	(1)
S + 1.7CH + 2.3H ← C1.7SH4.0	(2)

In terms of volumes or areas, each unit of dissolved C₃S produces 1.7 units of CSH and 0.61 units of CH. Regarding the pozzolanic reaction, each unit volume of silica is capable of reacting with 2.08 units of CH to produce 4.6 units of pozzolanic CSH.

Hydration is executed in discrete cycles consisting of dissolution, diffusion, and reaction phases. During dissolution, all C₃S pixels in contact with water-filled porosity are given a chance to dissolve and produce diffusing CH and CSH species. The dissolution probability is based on the amount of C₃S surface in contact with water. During diffusion, the CSH and CH diffusing species execute random walks within the available pore space until reaction occurs. CSH forms on the surfaces of the original cement particles or on previously formed solid CSH. CH forms crystals by a nucleation and growth mechanism within the pore space. Additionally, if amorphous silica is present, the CH diffusing species react at silica surfaces to form pozzolanic CSH. When all diffusing species generated from one dissolution have reacted, a cycle is complete and a new dissolution is begun. By monitoring how much cement remains after any number of hydration cycles, the degree of hydration, α, of the system can be determined. As in real systems, the hydration is ultimately self-limiting as the surfaces of the remaining cement become totally surrounded by hydration product, preventing further dissolution. However, typically 80-90% of the cement can be hydrated before this situation occurs.

To simulate an ITZ in concrete, a single aggregate is first placed in the hydration volume (area) and then the cement particles are randomly placed such that no particles overlap. To simulate a lightweight absorptive aggregate, this original distribution of particles is modified by moving all particles toward the aggregate surface to simulate water absorption by the (dry) aggregate. This results in the aggregate acting somewhat as a filter, drawing in water and pulling cement particles towards its surface, as suggested by Fagerlund [11]. Additionally, the use of cement clinker as aggregate may be simulated by assigning the aggregate to be C₃S. Due to its small surface-to-volume ratio, only a thin layer on the outer surface of the clinker aggregate will undergo significant hydration. Except where indicated otherwise, all simulations described below were performed using the 2D version of the microstructure model. All 2D results are the average of 5 to 10 separate configurations of a given system.